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Shock compression of liquid nitrogenThermodynamic analysis of new experimental data in megabar range
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Igor
IosilevskiyJoint Institute for High Temperature (Russian Academy of Science)Moscow Institute of Physics and Technology (State University)
Victor GryaznovInstitute of Problem of Chemical Physics (Russian Academy of Science)
Sarov 2011 Chernogolovka 2010EMMI_GSI 2011
Mochalov
M Zhernokletov
M Ilʹkaev
R Mikhailov
A Mezhevov
A Kovalev
A Kirshanov
S Grigorieva
Yu Novikov
M Shuikin
А
Fortov V Gryaznov V Iosilevskiy I
JETP 137 77 (2010)Density temperature
and electroconductivity
measurements in shock compressed
condensed nitrogen
at megabar
pressure
CollaborationEugene amp
Lidia Yakyb
(Odessa University Ukraine)
Trunin
R Boriskov
G Bykov
A Medvedev
A Simakov
G Shuikin
AJETP Letters
88
(3) 189 (2008)
Shock compression
of condensed nitrogen
at megabar
pressure
1
2
Shock compression of liquid nitrogen(new experimental data in megabar pressure range)
Shock Hugoniot
of liquid nitrogen(primary experimental data in kinematic variables)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 182
4
6
8
10
12
14
16
18
20
22
24
3
2
1
Жидкий азот
D км
с
U кмс
D
and
U
ndash shock and mass velocitiesArrows
ndash
hypothetical transitions between molecular (1) polymeric (2) and plasma
(3) states
Trunin
et al
(2008)
Mochalov
et al
2010
Mochalov
et al
2010
(spherical)
Approximations (Mochalov
et al2010)1
D
= 1365U +
1572 2
D
=
3375U ndash
0337U 2
+ 0015U 3
ndash
20083
D
= 1407U
ndash
1174
‐
Mochalov
M Zhernokletov
M et alJETF
137 77
(2010)
‐
Trunin
R Boriskov
G Bykov
A Medvedev
AJETF Letters
88 220 (2008)
Mochalov
et al2010
(flat
geometry)
U kms
D -
U
D U
1203 plusmn
025 911
1460 plusmn
026 1129
1619 plusmn
036 1224
1728 plusmn
040 1314
2090 plusmn
068 1571
229 plusmn
04 174
Initial stateρ0
= 081(T0
= 77 K)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
)(01 UDD DUpp 001
2)(
2
22
01UDDhh
Shock Hugoniot
of liquid nitrogen(experimental data in thermodynamic variables)
‐
Mochalov
M Zhernokletov
M et al
JETP
137 77
(2010)
‐
Trunin
R Boriskov
G Bykov
A Medvedev
A
JETP Letters
88 220 (2008)
P GPa ρ
gcm3
884 plusmn
2 3325 plusmn
02
1333 plusmn
3 356 plusmn
015
1600 plusmn
3 331 plusmn
025
1830 plusmn
3 337 plusmn
035
2650 plusmn
5 325 plusmn
025
323 337 plusmn
020
ρρ0412
441410
418
403
416
()
(ρρ0
)ideal gas
= 40
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
E(PT)
reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal energy is close to be linear function of pressure
Internal Energy Pressure of sock compressed nitrogen
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
The region of approximate constancy for Gruneizen parameter
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Hugoniot
~ ρ
asymp
const
(33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Approximately linear function E ~ E0
+ constmiddotP
ρ
asymp
33
plusmn01
gcc 90
lt
P
lt 330
GPa
)(1121
0110
01 ppEE
NB
() Gridgas
= 23
asymp
067What does it mean
Temperature of shock compressed nitrogenmeasurements of thermal equation of state
2
ndash
linear approximation of experimental data
(Р
asymp
90 ndash 300 ГПа)
‐
Experiment
(Mochalov
M Zhernokletov
M et al
JETF
137 77
(2010)
0 100 200 3000
10
20
30
40
50
60
70
80
nN2
P ГПа
T kK
2
T kK
P GPa T
kK
884 plusmn
2 162 plusmn
09
1333 plusmn
3 246 plusmn
05
1600 plusmn
3 284 plusmn
22
1830 plusmn
3 -
2650 plusmn
5 560 plusmn
152
323 -
JETF
137 77
(2010)
‐
Mochalov
et al
JETP (2010)
0 100 200 3000
10
20
30
40
50
60
70
80
P GPa
T kK 4
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
Compressibility factor
(PVRT)
is almost
constant
on nitrogen isochore
What does it mean
ρ
asymp
33 plusmn01
gcc
(90
lt
P lt 330
GPa)
PVRTIdeal gas N2 Z= 05Ideal gas N
Z= 10
Id gas N+ + e Z= 20
Temperature is close to be linear function of pressure+
isochoric behavior of nitrogen Hugoniot
NB
Initial stateρ0
= 081
0 100 200 3000
10
20
30
40
50
60
70
80
P GPa
T kK 4
Сv
equiv
(partEpartT)v
asymp
const
asymp
20 (JgK)
ρ
asymp33 plusmn01
gcc
(90
lt
P lt 330
GPa)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
Internal energy ~ linear function on temperature at isochoreHigh-temperature part of nitrogen Hugoniot
Isochoric heat capacity
(CV
)
is almost constant
on nitrogen isochore
What does it mean
СV RN
asymp
35 NB
HugoniotHugoniot
0 100 200 3000
10
20
30
40
50
60
70
80
P GPa
T kK 4
γv
equiv
(vkB
)
(partppartT)v
asymp
const
asymp
ρ
asymp
33 plusmn01
gcc (90
lt
P lt 330
GPa)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
Constancy of Gruumlneizen parameter and Heat capacity at isochore
Gr
asymp
const
+
CV
asymp
const
thermal pressure coefficient γv
asymp
const
(partppartT)v
asymp
454 GPaK NB
HugoniotHugoniot
Thermodynamics of shock compressed nitrogen
ρ
asymp
33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
Mochalov
M Zhernokletov
M et alJETF
137 77
(2010) Trunin
R Boriskov
G Bykov
A Medvedev
AJETF Letters
88 220 (2008)
Expected behavior of nitrogen HugoniotМRoss amp FRogers
ACTEX(Rogers)
Interpolation(σmax
asymp
53)Experiments
New experiments vs
expected behavior of
nitrogen HugoniotМRoss amp FRogers
ACTEX(Rogers)
Interpolation(σmax
asymp
53)N‐polimer
N2Experiments
New experiments(σmax
asymp
41)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
New experiments are
in strong contradiction with expected behavior of
nitrogen Hugoniot
NB
Nitrogen Hugoniot
problem in plasma state ndash what do we need
In last experimentson deuterium
compression Pmax
asymp
50
Mbar(see Mochalov
et al NPP‐2011)(Mochalov
et al JETP Lett 2010)
NB
TheoryAb
initio
RPIMC DPIMCDFTMD WPMDChemical models
SAHA‐SSAHA‐N
(Gryaznov et al)WZ‐cell modelsTF TFC MHFShellip
Wide‐range EOS‐s
IPCP RASJIHT RASCCM (Sarov)
New experiments(σmax
asymp
41)
New experiments
‐Shock waves
-
Isentropic Compression‐
Heavy Ion Beams‐
Laser Heating etc etc
Interpolation(σmax
asymp
53)
ACTEX(Rogers)
Experiments
Nitrogen Hugoniot(comes trough polymeric phase )
ACTEX(Rogers)
Polymeric stateis expected between
molecular and plasma
regions (see below)
NB
N‐polymerN2
Experiments
THEORYAb
initio
RPIMC DPIMCDFTMD WPMDChem modelsSAHA‐SSAHA‐N
WZ‐cell modelsTFC MHFS
Wide‐range EOS
CCM (Sarov)
New experiments(σmax
asymp
41)
New experiments
‐
Shock waves
‐
Heavy Ion Beams‐
Laser Heating etc etc
N‐plasma
figure fromB Boates S Bonev Phys Rev Lett
102
(2009)
Ab initio calculations
‐
DFTMD
MolecularPolymeric
Critical point
CrossoverCrossover
11stst
order PTorder PT
MeltingMelting
Molecularfluid
Dissociated fluid
Fluidndashfluid
phase transitionin hydrogen [] ()
DFTMD
Scandolo
S PNAS
100 (2003)
Bonev S Militzer B Galli G PRB
69 (2004) WPMD
Jakob
B et al PRE
(2007) DFTMD Morales M et al PNAS
107 (2010)
DFTMD Lorenzen
W et al PRB
(2010)
Figure from
Giulia Galli SCCS-2005
Moscow= = = =
with additionsMorales et al 2010
andLorensen et al 2010
Morales et al
2010
Lorenzen
et al
2010
Ab initio calculations
‐
DFTMD
Experiment ndash single shock
compression ndash
reflected shock
compressionRadousky Nellis amp Ross et al Phys Rev Lett 57
(1986)Nellis Radousky
amp Hamilton et alJ Chem Phys 94
(1991)
0 50 100 150 200 250 3000
10
Tr Tr
CP
P GPa
T 103 K
Nitrogen phase diagram in the region of polymerizationPressure ndash temperature
melting (extrapolation)
HugoniotPlasma Model (SAHA‐code)
Yakubliquid
solidN2 N‐polimer
Theoretical models
estimation of polymer‐molecule
boundary in liquid nitrogen
(ЕYakub
ndash
1993) estimation of polymer‐molecule
boundary in solid nitrogen
(LYakub
ndash
1993)CP
ndash
critical point of 1st
order phase
transition polymer‐molecule
(ЕYakub
ndash
1993) ndash
triple point of 1st
order phase transition
polymer‐molecule
(Е amp L Yakub
ndash
1993)ЕS Yakub Low Temp Phys
20
579 (1994)LN Yakub Low Temp Phys
19 531 (1993)
estimation of polymer‐molecule bounda‐
ry
in liquid nitrogen (Ross amp Rogers
ndash
2006)MRoss
amp
FRogers Phys Rev
B 74 (2006)Ab
initio calculations DFTMD
ndash
calculation of of
polymer‐‐
molecule boundary in liquid nitrogen
(SBonev
et al ndash
2009)
the same as ldquosmoothedrdquo
phase transitionB Boates
amp
S Bonev Phys Rev Lett
102
(2009)
Gr
gt 0
Gr
lt 0 ndash domains of positive and negative sign of Gruumlneisen
coefficient
Gr
equiv
V(partPpartE)V
hypothetical boundary between polymeric and non‐ideal plasma states
(1st‐order phase transition or continuous )
melting
N2
N‐polimer
Gr
gt 0
Gr
lt 0
N‐plasma
Gr
gt 0
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
‐
Mochalov
M Zhernokletov
M et al
JETP
137 77
(2010) ‐
Trunin
R Boriskov
G Bykov
A Medvedev
A
JETP Letters
88 220 (2008)
Phase Diagram of Dense Nitrogen(summary)
N2
Npolimer
boundaryYakub Ross amp
Rogers etc
HypotheticalPressure Ionizationfrom N‐polymer
to N‐plasma
1st‐order phase transition
Critical point(s)
Domain
Gr
lt 0
Topology of theboundary
Gr
= 0
Pre‐compressed gaseous N2
Iso‐S
N2
N‐polimer
N‐plasma
Gr
gt 0
Gr
gt 0
Gr
lt 0
New experiments
‐
Shock waves‐ Iso‐S
Compression‐ Heavy Ion Beams‐
Laser Heating etc etc
THEORY Ab
initioRPIMC DPIMC
DFTMDChem modelsSAHA‐N
WZ‐cell modelsTFC MHFS
Wide‐range EOSEOS (IPCP
RAS)EOS (JIHT
RAS)CCM (Sarov)
Commentsmicrophysics
Simple molecules H2
N2
L = 074 A L = 11 A
D = 29 A D = 37 A
Triple covalent bond De
= 98 eV
(49 eVatom)
Single covalent bond De
= 30 eV
(45 eVatom)
L = 14 A
Figures after
Eugene Yakub ldquoNon‐simple
problems for simple moleculesrdquoFAIR‐Russia School laquoPhysics of high energy density in matterraquo
December
2009 Moscow
FZaharievAHuJHooperFZhangampTWoo PhysRev B 72214108 (2005 )
Polymeric nitrogen - structure
Eugene and Lidia Yakub Low Temp Phys 19 (1993)
Simple molecular modelsFirst estimations of molecular-polymeric transition
1 - Hugoniot2 - Phase equilibrium line
Experiment (Nellis ea 2001)3 - Single shock4 - Double shock
NN22
NN‐‐polimerpolimer
NN22
NN‐‐polimerpolimer
1st‐orderPhase transition
Critical point
Plasma model for nitrogen thermodynamics(code SAHA-N)
Shock compression of nitrogen(chemical picture)
SAHA-codeGryaznov Iosilevskiy (1970-2010)
Short range repulsionldquoSoft Spheresrdquo
approximation (DYoung)
modified for mixture
of soft spheres with different radii
ndash
shift of dissociation level
N
N+ + endash Ze
e
rcA
iA+
A+
i
Coulomb interactionModified pseudopotential
model
for partially ionized plasma(I
Iosilevskiy 1980-2010)
Equilibrium
compositionN2
N N+ e N2+ Nndash
Key parameter
ndash
ratio of intrinsic volumes molecule atom ion
R(N)
R(N2
)
= 063-
in accordance with recommendations of
ldquoAtom-atomic
approximationrdquo
of EYakub LT 1993
Basic points-
All assumption are provided at micro-level-
Input Choice of Фie
Фii
and Фее
pseudopotentials - Input Approximations for binary correlation functions - Strong correlation of the pseudopotentials
for ldquofreerdquocharges and upper energy level for partition functionsfor bound states
- Priority for general equalities (normalizing conditions)valid independently on degree of non-ideality
- Non-ideality corrections through the correlationfunctions and general equalities valid for Coulombinteraction
NN22
harrharr 2N2N NN22
++
harrharr NN ++
NN++ NNndashharrharr NN ++
eendash
[ ( ) ( )] 1n F r F r d r
Coulomb Corrections for Free Charge Subsystem
Modified Pseudopotential Approximation ()
Bound and free states of electron‐ionic pair
Effective electro-ionic potential (in Glaubermanrsquos form (1955))
2i
ie ( ) 1 e rZ err
( )
()
Iosilevskiy I High Temp 18
(1980) in ldquoEncyclopedia
of Low‐T Plasmardquo
(Suppl) Moscow FIZMATLIT 2004 pp 349
The form of i-i i-e e-e binary correlation functions-
laquoringraquo
(Debye) approximation with potential
Фie
(r)guarantee correct properties in the limit
of weak non-ideality
(Г
ltlt 1)
Binary i‐i i‐e e‐e
correlation functions
ldquoZero and second momentrdquo conditions (Stillinger amp Lovett)2
2[ ( ) ( )] 3D
rn F r F r dr
r
0e e sh ( ) 1 1 e
pr qrr
abrF r A
r r
Thermodynamic condition for the depth of i-e pseudopotentialand amplitude of electron-ionic correlation function
0 ln [ (0) ]ie ei e iF
Positive sign of all correlation functions Fab
(r) gt 0
F r Ae e
re
sh rrab
pr qrr( )
1 1 0
Pseudopotentials
U
= UKin
+ UPot
3PV
= 2UKin + UPot
Homogeneity of Coulomb potential
U Vn F F dpot coul ( ) r
U Vn F F dei ii 2 ( ) r
)2()2(3 potkinpot UUUUPV
2 2i i
ie ie1 e( ) (1 e (0) ~
rrZ e Z er
r r
( ))
Correlation Functions
Total Energy correction
Potential Energy Correction
-
UPot
Pressure Correction
-
P
i e i eN N U ( ) 1
Approximate relation between Coulomb corrections for chemical potential and energy
(
UN)
NB
Thermodynamic contributions inmodified pseudopotential model for Coulomb corrections
Positive shift in average kinetic energy due to non-ideality of free charges subsystem Ukin = 3PV ndash
U
Well-known relation between pressure and energy corrections for free charges subsystemU = 3PV
which is valid at weak non-ideality (Г
ltlt 1) is no longer valid in strong non-ideality conditions (Г
~ 1)
It is equivalent to additional effective electron-ion repulsion(in comparison with ordinary one-parametric Coulomb corrections depending on non-ideality parameter only
FNkT = f(Г)
Experimental data Theoretical models
(comparison)
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
Quasi‐isochoric behavior of nitrogen Hugoniot
‐
Mochalov
M Zhernokletov
M et al
JETP
137
(2010) ‐
Trunin
R Boriskov
G et alJETP Letters
88
(2008)
15 20 25 30 35 400
100
200
300
ExperimentsTrunin et al 2008Mochalov et al 2010
P GPa
gcm3
lim
Check of theoretical models
SAHA
CCM
Ross ampRogers
CCM ndash
Compressible Covolume
Model(A Medvedev
amp
VKopyshev)
SAHA‐code (V Gryaznov amp IIosilevskiy)
ρHug
asymp
33 plusmn
01
gcm390
lt
PHug
lt 330
GPa
NN
22 NN‐‐polymerpolymer
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
equiv
V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost
linear function of pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
Reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal Energy
Pressure (Hugonoit)
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
Blue curve
ndash
internal energy calculated via plasma model(code SAHA
Gryaznov Iosilevskiy)
SAHA
Hugoniot
~ ρ
asymp
const (33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
ρ
asymp33 plusmn01
gcc90
lt
P lt 330
GPa
NB
Quasi‐linear behavior of
E(p)
at ρ
=
constThermodynamics of shock compressed nitrogen
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
00
01
02
03
04
05
06
07
08
09
10 Mochalov et al PHug (Trunin et al) + T (EOSCCM) PHug (Trunin et al) + T (EOSSAHA)
xN+
xi
xN2
P GPa
T k
K
Tr
Tr
Plasma
Temperature of shock compressed nitrogen
CP()
General P‐T
diagram
Quasi‐linear behavior of
T(p)
at ρ
=
const
SAHA
‐
Experiment Mochalov
M et al
JETF
137
(2010)Nellis
W Radovsky
H et al J Chem Phys 94
(1991)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
Electroconductivity
of shock compressed nitrogen
20 25 30 351E-3
001
01
1
10
100
1000
C E B E 28061 B 29062
Con
duct
ivity
1
cm
Density gcc
Electroconductivity
of shock compressed nitrogen
Ternovoi
V et al (email ‐
30052010)
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1
P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
‐
Experiment Mochalov
M et al
JETF
137
(2010)
Quasi‐isentropic Plane Compression of Matter at Megabar
Pressures by Using of a Layered
System to Diminish First Shock Wave IntensityTernovoi
V Pyalling
A Filimonovet
A (052010) Summary and conclusion
Explosive driven quasi‐isentropic compression generators were proposed for matter investigation in
the megabar
pressure region Results of the first experiments on quasi‐isentropic compression of
liquid nitrogen are presented It was shown that pressure ionization
of nitrogen proceeds at
densities
from 315 to 34 gcc
at a temperature
of about 3000
K
Diminishing of temperature growth
was measured during onset of nitrogen electrical conductivity
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
Mochalov
M Zhernokletov
M Ilʹkaev
R Mikhailov
A Mezhevov
A Kovalev
A Kirshanov
S Grigorieva
Yu Novikov
M Shuikin
А
Fortov V Gryaznov V Iosilevskiy I
JETP 137 77 (2010)Density temperature
and electroconductivity
measurements in shock compressed
condensed nitrogen
at megabar
pressure
CollaborationEugene amp
Lidia Yakyb
(Odessa University Ukraine)
Trunin
R Boriskov
G Bykov
A Medvedev
A Simakov
G Shuikin
AJETP Letters
88
(3) 189 (2008)
Shock compression
of condensed nitrogen
at megabar
pressure
1
2
Shock compression of liquid nitrogen(new experimental data in megabar pressure range)
Shock Hugoniot
of liquid nitrogen(primary experimental data in kinematic variables)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 182
4
6
8
10
12
14
16
18
20
22
24
3
2
1
Жидкий азот
D км
с
U кмс
D
and
U
ndash shock and mass velocitiesArrows
ndash
hypothetical transitions between molecular (1) polymeric (2) and plasma
(3) states
Trunin
et al
(2008)
Mochalov
et al
2010
Mochalov
et al
2010
(spherical)
Approximations (Mochalov
et al2010)1
D
= 1365U +
1572 2
D
=
3375U ndash
0337U 2
+ 0015U 3
ndash
20083
D
= 1407U
ndash
1174
‐
Mochalov
M Zhernokletov
M et alJETF
137 77
(2010)
‐
Trunin
R Boriskov
G Bykov
A Medvedev
AJETF Letters
88 220 (2008)
Mochalov
et al2010
(flat
geometry)
U kms
D -
U
D U
1203 plusmn
025 911
1460 plusmn
026 1129
1619 plusmn
036 1224
1728 plusmn
040 1314
2090 plusmn
068 1571
229 plusmn
04 174
Initial stateρ0
= 081(T0
= 77 K)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
)(01 UDD DUpp 001
2)(
2
22
01UDDhh
Shock Hugoniot
of liquid nitrogen(experimental data in thermodynamic variables)
‐
Mochalov
M Zhernokletov
M et al
JETP
137 77
(2010)
‐
Trunin
R Boriskov
G Bykov
A Medvedev
A
JETP Letters
88 220 (2008)
P GPa ρ
gcm3
884 plusmn
2 3325 plusmn
02
1333 plusmn
3 356 plusmn
015
1600 plusmn
3 331 plusmn
025
1830 plusmn
3 337 plusmn
035
2650 plusmn
5 325 plusmn
025
323 337 plusmn
020
ρρ0412
441410
418
403
416
()
(ρρ0
)ideal gas
= 40
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
E(PT)
reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal energy is close to be linear function of pressure
Internal Energy Pressure of sock compressed nitrogen
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
The region of approximate constancy for Gruneizen parameter
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Hugoniot
~ ρ
asymp
const
(33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Approximately linear function E ~ E0
+ constmiddotP
ρ
asymp
33
plusmn01
gcc 90
lt
P
lt 330
GPa
)(1121
0110
01 ppEE
NB
() Gridgas
= 23
asymp
067What does it mean
Temperature of shock compressed nitrogenmeasurements of thermal equation of state
2
ndash
linear approximation of experimental data
(Р
asymp
90 ndash 300 ГПа)
‐
Experiment
(Mochalov
M Zhernokletov
M et al
JETF
137 77
(2010)
0 100 200 3000
10
20
30
40
50
60
70
80
nN2
P ГПа
T kK
2
T kK
P GPa T
kK
884 plusmn
2 162 plusmn
09
1333 plusmn
3 246 plusmn
05
1600 plusmn
3 284 plusmn
22
1830 plusmn
3 -
2650 plusmn
5 560 plusmn
152
323 -
JETF
137 77
(2010)
‐
Mochalov
et al
JETP (2010)
0 100 200 3000
10
20
30
40
50
60
70
80
P GPa
T kK 4
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
Compressibility factor
(PVRT)
is almost
constant
on nitrogen isochore
What does it mean
ρ
asymp
33 plusmn01
gcc
(90
lt
P lt 330
GPa)
PVRTIdeal gas N2 Z= 05Ideal gas N
Z= 10
Id gas N+ + e Z= 20
Temperature is close to be linear function of pressure+
isochoric behavior of nitrogen Hugoniot
NB
Initial stateρ0
= 081
0 100 200 3000
10
20
30
40
50
60
70
80
P GPa
T kK 4
Сv
equiv
(partEpartT)v
asymp
const
asymp
20 (JgK)
ρ
asymp33 plusmn01
gcc
(90
lt
P lt 330
GPa)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
Internal energy ~ linear function on temperature at isochoreHigh-temperature part of nitrogen Hugoniot
Isochoric heat capacity
(CV
)
is almost constant
on nitrogen isochore
What does it mean
СV RN
asymp
35 NB
HugoniotHugoniot
0 100 200 3000
10
20
30
40
50
60
70
80
P GPa
T kK 4
γv
equiv
(vkB
)
(partppartT)v
asymp
const
asymp
ρ
asymp
33 plusmn01
gcc (90
lt
P lt 330
GPa)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
Constancy of Gruumlneizen parameter and Heat capacity at isochore
Gr
asymp
const
+
CV
asymp
const
thermal pressure coefficient γv
asymp
const
(partppartT)v
asymp
454 GPaK NB
HugoniotHugoniot
Thermodynamics of shock compressed nitrogen
ρ
asymp
33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
Mochalov
M Zhernokletov
M et alJETF
137 77
(2010) Trunin
R Boriskov
G Bykov
A Medvedev
AJETF Letters
88 220 (2008)
Expected behavior of nitrogen HugoniotМRoss amp FRogers
ACTEX(Rogers)
Interpolation(σmax
asymp
53)Experiments
New experiments vs
expected behavior of
nitrogen HugoniotМRoss amp FRogers
ACTEX(Rogers)
Interpolation(σmax
asymp
53)N‐polimer
N2Experiments
New experiments(σmax
asymp
41)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
New experiments are
in strong contradiction with expected behavior of
nitrogen Hugoniot
NB
Nitrogen Hugoniot
problem in plasma state ndash what do we need
In last experimentson deuterium
compression Pmax
asymp
50
Mbar(see Mochalov
et al NPP‐2011)(Mochalov
et al JETP Lett 2010)
NB
TheoryAb
initio
RPIMC DPIMCDFTMD WPMDChemical models
SAHA‐SSAHA‐N
(Gryaznov et al)WZ‐cell modelsTF TFC MHFShellip
Wide‐range EOS‐s
IPCP RASJIHT RASCCM (Sarov)
New experiments(σmax
asymp
41)
New experiments
‐Shock waves
-
Isentropic Compression‐
Heavy Ion Beams‐
Laser Heating etc etc
Interpolation(σmax
asymp
53)
ACTEX(Rogers)
Experiments
Nitrogen Hugoniot(comes trough polymeric phase )
ACTEX(Rogers)
Polymeric stateis expected between
molecular and plasma
regions (see below)
NB
N‐polymerN2
Experiments
THEORYAb
initio
RPIMC DPIMCDFTMD WPMDChem modelsSAHA‐SSAHA‐N
WZ‐cell modelsTFC MHFS
Wide‐range EOS
CCM (Sarov)
New experiments(σmax
asymp
41)
New experiments
‐
Shock waves
‐
Heavy Ion Beams‐
Laser Heating etc etc
N‐plasma
figure fromB Boates S Bonev Phys Rev Lett
102
(2009)
Ab initio calculations
‐
DFTMD
MolecularPolymeric
Critical point
CrossoverCrossover
11stst
order PTorder PT
MeltingMelting
Molecularfluid
Dissociated fluid
Fluidndashfluid
phase transitionin hydrogen [] ()
DFTMD
Scandolo
S PNAS
100 (2003)
Bonev S Militzer B Galli G PRB
69 (2004) WPMD
Jakob
B et al PRE
(2007) DFTMD Morales M et al PNAS
107 (2010)
DFTMD Lorenzen
W et al PRB
(2010)
Figure from
Giulia Galli SCCS-2005
Moscow= = = =
with additionsMorales et al 2010
andLorensen et al 2010
Morales et al
2010
Lorenzen
et al
2010
Ab initio calculations
‐
DFTMD
Experiment ndash single shock
compression ndash
reflected shock
compressionRadousky Nellis amp Ross et al Phys Rev Lett 57
(1986)Nellis Radousky
amp Hamilton et alJ Chem Phys 94
(1991)
0 50 100 150 200 250 3000
10
Tr Tr
CP
P GPa
T 103 K
Nitrogen phase diagram in the region of polymerizationPressure ndash temperature
melting (extrapolation)
HugoniotPlasma Model (SAHA‐code)
Yakubliquid
solidN2 N‐polimer
Theoretical models
estimation of polymer‐molecule
boundary in liquid nitrogen
(ЕYakub
ndash
1993) estimation of polymer‐molecule
boundary in solid nitrogen
(LYakub
ndash
1993)CP
ndash
critical point of 1st
order phase
transition polymer‐molecule
(ЕYakub
ndash
1993) ndash
triple point of 1st
order phase transition
polymer‐molecule
(Е amp L Yakub
ndash
1993)ЕS Yakub Low Temp Phys
20
579 (1994)LN Yakub Low Temp Phys
19 531 (1993)
estimation of polymer‐molecule bounda‐
ry
in liquid nitrogen (Ross amp Rogers
ndash
2006)MRoss
amp
FRogers Phys Rev
B 74 (2006)Ab
initio calculations DFTMD
ndash
calculation of of
polymer‐‐
molecule boundary in liquid nitrogen
(SBonev
et al ndash
2009)
the same as ldquosmoothedrdquo
phase transitionB Boates
amp
S Bonev Phys Rev Lett
102
(2009)
Gr
gt 0
Gr
lt 0 ndash domains of positive and negative sign of Gruumlneisen
coefficient
Gr
equiv
V(partPpartE)V
hypothetical boundary between polymeric and non‐ideal plasma states
(1st‐order phase transition or continuous )
melting
N2
N‐polimer
Gr
gt 0
Gr
lt 0
N‐plasma
Gr
gt 0
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
‐
Mochalov
M Zhernokletov
M et al
JETP
137 77
(2010) ‐
Trunin
R Boriskov
G Bykov
A Medvedev
A
JETP Letters
88 220 (2008)
Phase Diagram of Dense Nitrogen(summary)
N2
Npolimer
boundaryYakub Ross amp
Rogers etc
HypotheticalPressure Ionizationfrom N‐polymer
to N‐plasma
1st‐order phase transition
Critical point(s)
Domain
Gr
lt 0
Topology of theboundary
Gr
= 0
Pre‐compressed gaseous N2
Iso‐S
N2
N‐polimer
N‐plasma
Gr
gt 0
Gr
gt 0
Gr
lt 0
New experiments
‐
Shock waves‐ Iso‐S
Compression‐ Heavy Ion Beams‐
Laser Heating etc etc
THEORY Ab
initioRPIMC DPIMC
DFTMDChem modelsSAHA‐N
WZ‐cell modelsTFC MHFS
Wide‐range EOSEOS (IPCP
RAS)EOS (JIHT
RAS)CCM (Sarov)
Commentsmicrophysics
Simple molecules H2
N2
L = 074 A L = 11 A
D = 29 A D = 37 A
Triple covalent bond De
= 98 eV
(49 eVatom)
Single covalent bond De
= 30 eV
(45 eVatom)
L = 14 A
Figures after
Eugene Yakub ldquoNon‐simple
problems for simple moleculesrdquoFAIR‐Russia School laquoPhysics of high energy density in matterraquo
December
2009 Moscow
FZaharievAHuJHooperFZhangampTWoo PhysRev B 72214108 (2005 )
Polymeric nitrogen - structure
Eugene and Lidia Yakub Low Temp Phys 19 (1993)
Simple molecular modelsFirst estimations of molecular-polymeric transition
1 - Hugoniot2 - Phase equilibrium line
Experiment (Nellis ea 2001)3 - Single shock4 - Double shock
NN22
NN‐‐polimerpolimer
NN22
NN‐‐polimerpolimer
1st‐orderPhase transition
Critical point
Plasma model for nitrogen thermodynamics(code SAHA-N)
Shock compression of nitrogen(chemical picture)
SAHA-codeGryaznov Iosilevskiy (1970-2010)
Short range repulsionldquoSoft Spheresrdquo
approximation (DYoung)
modified for mixture
of soft spheres with different radii
ndash
shift of dissociation level
N
N+ + endash Ze
e
rcA
iA+
A+
i
Coulomb interactionModified pseudopotential
model
for partially ionized plasma(I
Iosilevskiy 1980-2010)
Equilibrium
compositionN2
N N+ e N2+ Nndash
Key parameter
ndash
ratio of intrinsic volumes molecule atom ion
R(N)
R(N2
)
= 063-
in accordance with recommendations of
ldquoAtom-atomic
approximationrdquo
of EYakub LT 1993
Basic points-
All assumption are provided at micro-level-
Input Choice of Фie
Фii
and Фее
pseudopotentials - Input Approximations for binary correlation functions - Strong correlation of the pseudopotentials
for ldquofreerdquocharges and upper energy level for partition functionsfor bound states
- Priority for general equalities (normalizing conditions)valid independently on degree of non-ideality
- Non-ideality corrections through the correlationfunctions and general equalities valid for Coulombinteraction
NN22
harrharr 2N2N NN22
++
harrharr NN ++
NN++ NNndashharrharr NN ++
eendash
[ ( ) ( )] 1n F r F r d r
Coulomb Corrections for Free Charge Subsystem
Modified Pseudopotential Approximation ()
Bound and free states of electron‐ionic pair
Effective electro-ionic potential (in Glaubermanrsquos form (1955))
2i
ie ( ) 1 e rZ err
( )
()
Iosilevskiy I High Temp 18
(1980) in ldquoEncyclopedia
of Low‐T Plasmardquo
(Suppl) Moscow FIZMATLIT 2004 pp 349
The form of i-i i-e e-e binary correlation functions-
laquoringraquo
(Debye) approximation with potential
Фie
(r)guarantee correct properties in the limit
of weak non-ideality
(Г
ltlt 1)
Binary i‐i i‐e e‐e
correlation functions
ldquoZero and second momentrdquo conditions (Stillinger amp Lovett)2
2[ ( ) ( )] 3D
rn F r F r dr
r
0e e sh ( ) 1 1 e
pr qrr
abrF r A
r r
Thermodynamic condition for the depth of i-e pseudopotentialand amplitude of electron-ionic correlation function
0 ln [ (0) ]ie ei e iF
Positive sign of all correlation functions Fab
(r) gt 0
F r Ae e
re
sh rrab
pr qrr( )
1 1 0
Pseudopotentials
U
= UKin
+ UPot
3PV
= 2UKin + UPot
Homogeneity of Coulomb potential
U Vn F F dpot coul ( ) r
U Vn F F dei ii 2 ( ) r
)2()2(3 potkinpot UUUUPV
2 2i i
ie ie1 e( ) (1 e (0) ~
rrZ e Z er
r r
( ))
Correlation Functions
Total Energy correction
Potential Energy Correction
-
UPot
Pressure Correction
-
P
i e i eN N U ( ) 1
Approximate relation between Coulomb corrections for chemical potential and energy
(
UN)
NB
Thermodynamic contributions inmodified pseudopotential model for Coulomb corrections
Positive shift in average kinetic energy due to non-ideality of free charges subsystem Ukin = 3PV ndash
U
Well-known relation between pressure and energy corrections for free charges subsystemU = 3PV
which is valid at weak non-ideality (Г
ltlt 1) is no longer valid in strong non-ideality conditions (Г
~ 1)
It is equivalent to additional effective electron-ion repulsion(in comparison with ordinary one-parametric Coulomb corrections depending on non-ideality parameter only
FNkT = f(Г)
Experimental data Theoretical models
(comparison)
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
Quasi‐isochoric behavior of nitrogen Hugoniot
‐
Mochalov
M Zhernokletov
M et al
JETP
137
(2010) ‐
Trunin
R Boriskov
G et alJETP Letters
88
(2008)
15 20 25 30 35 400
100
200
300
ExperimentsTrunin et al 2008Mochalov et al 2010
P GPa
gcm3
lim
Check of theoretical models
SAHA
CCM
Ross ampRogers
CCM ndash
Compressible Covolume
Model(A Medvedev
amp
VKopyshev)
SAHA‐code (V Gryaznov amp IIosilevskiy)
ρHug
asymp
33 plusmn
01
gcm390
lt
PHug
lt 330
GPa
NN
22 NN‐‐polymerpolymer
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
equiv
V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost
linear function of pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
Reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal Energy
Pressure (Hugonoit)
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
Blue curve
ndash
internal energy calculated via plasma model(code SAHA
Gryaznov Iosilevskiy)
SAHA
Hugoniot
~ ρ
asymp
const (33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
ρ
asymp33 plusmn01
gcc90
lt
P lt 330
GPa
NB
Quasi‐linear behavior of
E(p)
at ρ
=
constThermodynamics of shock compressed nitrogen
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
00
01
02
03
04
05
06
07
08
09
10 Mochalov et al PHug (Trunin et al) + T (EOSCCM) PHug (Trunin et al) + T (EOSSAHA)
xN+
xi
xN2
P GPa
T k
K
Tr
Tr
Plasma
Temperature of shock compressed nitrogen
CP()
General P‐T
diagram
Quasi‐linear behavior of
T(p)
at ρ
=
const
SAHA
‐
Experiment Mochalov
M et al
JETF
137
(2010)Nellis
W Radovsky
H et al J Chem Phys 94
(1991)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
Electroconductivity
of shock compressed nitrogen
20 25 30 351E-3
001
01
1
10
100
1000
C E B E 28061 B 29062
Con
duct
ivity
1
cm
Density gcc
Electroconductivity
of shock compressed nitrogen
Ternovoi
V et al (email ‐
30052010)
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1
P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
‐
Experiment Mochalov
M et al
JETF
137
(2010)
Quasi‐isentropic Plane Compression of Matter at Megabar
Pressures by Using of a Layered
System to Diminish First Shock Wave IntensityTernovoi
V Pyalling
A Filimonovet
A (052010) Summary and conclusion
Explosive driven quasi‐isentropic compression generators were proposed for matter investigation in
the megabar
pressure region Results of the first experiments on quasi‐isentropic compression of
liquid nitrogen are presented It was shown that pressure ionization
of nitrogen proceeds at
densities
from 315 to 34 gcc
at a temperature
of about 3000
K
Diminishing of temperature growth
was measured during onset of nitrogen electrical conductivity
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
Shock Hugoniot
of liquid nitrogen(primary experimental data in kinematic variables)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 182
4
6
8
10
12
14
16
18
20
22
24
3
2
1
Жидкий азот
D км
с
U кмс
D
and
U
ndash shock and mass velocitiesArrows
ndash
hypothetical transitions between molecular (1) polymeric (2) and plasma
(3) states
Trunin
et al
(2008)
Mochalov
et al
2010
Mochalov
et al
2010
(spherical)
Approximations (Mochalov
et al2010)1
D
= 1365U +
1572 2
D
=
3375U ndash
0337U 2
+ 0015U 3
ndash
20083
D
= 1407U
ndash
1174
‐
Mochalov
M Zhernokletov
M et alJETF
137 77
(2010)
‐
Trunin
R Boriskov
G Bykov
A Medvedev
AJETF Letters
88 220 (2008)
Mochalov
et al2010
(flat
geometry)
U kms
D -
U
D U
1203 plusmn
025 911
1460 plusmn
026 1129
1619 plusmn
036 1224
1728 plusmn
040 1314
2090 plusmn
068 1571
229 plusmn
04 174
Initial stateρ0
= 081(T0
= 77 K)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
)(01 UDD DUpp 001
2)(
2
22
01UDDhh
Shock Hugoniot
of liquid nitrogen(experimental data in thermodynamic variables)
‐
Mochalov
M Zhernokletov
M et al
JETP
137 77
(2010)
‐
Trunin
R Boriskov
G Bykov
A Medvedev
A
JETP Letters
88 220 (2008)
P GPa ρ
gcm3
884 plusmn
2 3325 plusmn
02
1333 plusmn
3 356 plusmn
015
1600 plusmn
3 331 plusmn
025
1830 plusmn
3 337 plusmn
035
2650 plusmn
5 325 plusmn
025
323 337 plusmn
020
ρρ0412
441410
418
403
416
()
(ρρ0
)ideal gas
= 40
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
E(PT)
reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal energy is close to be linear function of pressure
Internal Energy Pressure of sock compressed nitrogen
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
The region of approximate constancy for Gruneizen parameter
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Hugoniot
~ ρ
asymp
const
(33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Approximately linear function E ~ E0
+ constmiddotP
ρ
asymp
33
plusmn01
gcc 90
lt
P
lt 330
GPa
)(1121
0110
01 ppEE
NB
() Gridgas
= 23
asymp
067What does it mean
Temperature of shock compressed nitrogenmeasurements of thermal equation of state
2
ndash
linear approximation of experimental data
(Р
asymp
90 ndash 300 ГПа)
‐
Experiment
(Mochalov
M Zhernokletov
M et al
JETF
137 77
(2010)
0 100 200 3000
10
20
30
40
50
60
70
80
nN2
P ГПа
T kK
2
T kK
P GPa T
kK
884 plusmn
2 162 plusmn
09
1333 plusmn
3 246 plusmn
05
1600 plusmn
3 284 plusmn
22
1830 plusmn
3 -
2650 plusmn
5 560 plusmn
152
323 -
JETF
137 77
(2010)
‐
Mochalov
et al
JETP (2010)
0 100 200 3000
10
20
30
40
50
60
70
80
P GPa
T kK 4
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
Compressibility factor
(PVRT)
is almost
constant
on nitrogen isochore
What does it mean
ρ
asymp
33 plusmn01
gcc
(90
lt
P lt 330
GPa)
PVRTIdeal gas N2 Z= 05Ideal gas N
Z= 10
Id gas N+ + e Z= 20
Temperature is close to be linear function of pressure+
isochoric behavior of nitrogen Hugoniot
NB
Initial stateρ0
= 081
0 100 200 3000
10
20
30
40
50
60
70
80
P GPa
T kK 4
Сv
equiv
(partEpartT)v
asymp
const
asymp
20 (JgK)
ρ
asymp33 plusmn01
gcc
(90
lt
P lt 330
GPa)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
Internal energy ~ linear function on temperature at isochoreHigh-temperature part of nitrogen Hugoniot
Isochoric heat capacity
(CV
)
is almost constant
on nitrogen isochore
What does it mean
СV RN
asymp
35 NB
HugoniotHugoniot
0 100 200 3000
10
20
30
40
50
60
70
80
P GPa
T kK 4
γv
equiv
(vkB
)
(partppartT)v
asymp
const
asymp
ρ
asymp
33 plusmn01
gcc (90
lt
P lt 330
GPa)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
Constancy of Gruumlneizen parameter and Heat capacity at isochore
Gr
asymp
const
+
CV
asymp
const
thermal pressure coefficient γv
asymp
const
(partppartT)v
asymp
454 GPaK NB
HugoniotHugoniot
Thermodynamics of shock compressed nitrogen
ρ
asymp
33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
Mochalov
M Zhernokletov
M et alJETF
137 77
(2010) Trunin
R Boriskov
G Bykov
A Medvedev
AJETF Letters
88 220 (2008)
Expected behavior of nitrogen HugoniotМRoss amp FRogers
ACTEX(Rogers)
Interpolation(σmax
asymp
53)Experiments
New experiments vs
expected behavior of
nitrogen HugoniotМRoss amp FRogers
ACTEX(Rogers)
Interpolation(σmax
asymp
53)N‐polimer
N2Experiments
New experiments(σmax
asymp
41)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
New experiments are
in strong contradiction with expected behavior of
nitrogen Hugoniot
NB
Nitrogen Hugoniot
problem in plasma state ndash what do we need
In last experimentson deuterium
compression Pmax
asymp
50
Mbar(see Mochalov
et al NPP‐2011)(Mochalov
et al JETP Lett 2010)
NB
TheoryAb
initio
RPIMC DPIMCDFTMD WPMDChemical models
SAHA‐SSAHA‐N
(Gryaznov et al)WZ‐cell modelsTF TFC MHFShellip
Wide‐range EOS‐s
IPCP RASJIHT RASCCM (Sarov)
New experiments(σmax
asymp
41)
New experiments
‐Shock waves
-
Isentropic Compression‐
Heavy Ion Beams‐
Laser Heating etc etc
Interpolation(σmax
asymp
53)
ACTEX(Rogers)
Experiments
Nitrogen Hugoniot(comes trough polymeric phase )
ACTEX(Rogers)
Polymeric stateis expected between
molecular and plasma
regions (see below)
NB
N‐polymerN2
Experiments
THEORYAb
initio
RPIMC DPIMCDFTMD WPMDChem modelsSAHA‐SSAHA‐N
WZ‐cell modelsTFC MHFS
Wide‐range EOS
CCM (Sarov)
New experiments(σmax
asymp
41)
New experiments
‐
Shock waves
‐
Heavy Ion Beams‐
Laser Heating etc etc
N‐plasma
figure fromB Boates S Bonev Phys Rev Lett
102
(2009)
Ab initio calculations
‐
DFTMD
MolecularPolymeric
Critical point
CrossoverCrossover
11stst
order PTorder PT
MeltingMelting
Molecularfluid
Dissociated fluid
Fluidndashfluid
phase transitionin hydrogen [] ()
DFTMD
Scandolo
S PNAS
100 (2003)
Bonev S Militzer B Galli G PRB
69 (2004) WPMD
Jakob
B et al PRE
(2007) DFTMD Morales M et al PNAS
107 (2010)
DFTMD Lorenzen
W et al PRB
(2010)
Figure from
Giulia Galli SCCS-2005
Moscow= = = =
with additionsMorales et al 2010
andLorensen et al 2010
Morales et al
2010
Lorenzen
et al
2010
Ab initio calculations
‐
DFTMD
Experiment ndash single shock
compression ndash
reflected shock
compressionRadousky Nellis amp Ross et al Phys Rev Lett 57
(1986)Nellis Radousky
amp Hamilton et alJ Chem Phys 94
(1991)
0 50 100 150 200 250 3000
10
Tr Tr
CP
P GPa
T 103 K
Nitrogen phase diagram in the region of polymerizationPressure ndash temperature
melting (extrapolation)
HugoniotPlasma Model (SAHA‐code)
Yakubliquid
solidN2 N‐polimer
Theoretical models
estimation of polymer‐molecule
boundary in liquid nitrogen
(ЕYakub
ndash
1993) estimation of polymer‐molecule
boundary in solid nitrogen
(LYakub
ndash
1993)CP
ndash
critical point of 1st
order phase
transition polymer‐molecule
(ЕYakub
ndash
1993) ndash
triple point of 1st
order phase transition
polymer‐molecule
(Е amp L Yakub
ndash
1993)ЕS Yakub Low Temp Phys
20
579 (1994)LN Yakub Low Temp Phys
19 531 (1993)
estimation of polymer‐molecule bounda‐
ry
in liquid nitrogen (Ross amp Rogers
ndash
2006)MRoss
amp
FRogers Phys Rev
B 74 (2006)Ab
initio calculations DFTMD
ndash
calculation of of
polymer‐‐
molecule boundary in liquid nitrogen
(SBonev
et al ndash
2009)
the same as ldquosmoothedrdquo
phase transitionB Boates
amp
S Bonev Phys Rev Lett
102
(2009)
Gr
gt 0
Gr
lt 0 ndash domains of positive and negative sign of Gruumlneisen
coefficient
Gr
equiv
V(partPpartE)V
hypothetical boundary between polymeric and non‐ideal plasma states
(1st‐order phase transition or continuous )
melting
N2
N‐polimer
Gr
gt 0
Gr
lt 0
N‐plasma
Gr
gt 0
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
‐
Mochalov
M Zhernokletov
M et al
JETP
137 77
(2010) ‐
Trunin
R Boriskov
G Bykov
A Medvedev
A
JETP Letters
88 220 (2008)
Phase Diagram of Dense Nitrogen(summary)
N2
Npolimer
boundaryYakub Ross amp
Rogers etc
HypotheticalPressure Ionizationfrom N‐polymer
to N‐plasma
1st‐order phase transition
Critical point(s)
Domain
Gr
lt 0
Topology of theboundary
Gr
= 0
Pre‐compressed gaseous N2
Iso‐S
N2
N‐polimer
N‐plasma
Gr
gt 0
Gr
gt 0
Gr
lt 0
New experiments
‐
Shock waves‐ Iso‐S
Compression‐ Heavy Ion Beams‐
Laser Heating etc etc
THEORY Ab
initioRPIMC DPIMC
DFTMDChem modelsSAHA‐N
WZ‐cell modelsTFC MHFS
Wide‐range EOSEOS (IPCP
RAS)EOS (JIHT
RAS)CCM (Sarov)
Commentsmicrophysics
Simple molecules H2
N2
L = 074 A L = 11 A
D = 29 A D = 37 A
Triple covalent bond De
= 98 eV
(49 eVatom)
Single covalent bond De
= 30 eV
(45 eVatom)
L = 14 A
Figures after
Eugene Yakub ldquoNon‐simple
problems for simple moleculesrdquoFAIR‐Russia School laquoPhysics of high energy density in matterraquo
December
2009 Moscow
FZaharievAHuJHooperFZhangampTWoo PhysRev B 72214108 (2005 )
Polymeric nitrogen - structure
Eugene and Lidia Yakub Low Temp Phys 19 (1993)
Simple molecular modelsFirst estimations of molecular-polymeric transition
1 - Hugoniot2 - Phase equilibrium line
Experiment (Nellis ea 2001)3 - Single shock4 - Double shock
NN22
NN‐‐polimerpolimer
NN22
NN‐‐polimerpolimer
1st‐orderPhase transition
Critical point
Plasma model for nitrogen thermodynamics(code SAHA-N)
Shock compression of nitrogen(chemical picture)
SAHA-codeGryaznov Iosilevskiy (1970-2010)
Short range repulsionldquoSoft Spheresrdquo
approximation (DYoung)
modified for mixture
of soft spheres with different radii
ndash
shift of dissociation level
N
N+ + endash Ze
e
rcA
iA+
A+
i
Coulomb interactionModified pseudopotential
model
for partially ionized plasma(I
Iosilevskiy 1980-2010)
Equilibrium
compositionN2
N N+ e N2+ Nndash
Key parameter
ndash
ratio of intrinsic volumes molecule atom ion
R(N)
R(N2
)
= 063-
in accordance with recommendations of
ldquoAtom-atomic
approximationrdquo
of EYakub LT 1993
Basic points-
All assumption are provided at micro-level-
Input Choice of Фie
Фii
and Фее
pseudopotentials - Input Approximations for binary correlation functions - Strong correlation of the pseudopotentials
for ldquofreerdquocharges and upper energy level for partition functionsfor bound states
- Priority for general equalities (normalizing conditions)valid independently on degree of non-ideality
- Non-ideality corrections through the correlationfunctions and general equalities valid for Coulombinteraction
NN22
harrharr 2N2N NN22
++
harrharr NN ++
NN++ NNndashharrharr NN ++
eendash
[ ( ) ( )] 1n F r F r d r
Coulomb Corrections for Free Charge Subsystem
Modified Pseudopotential Approximation ()
Bound and free states of electron‐ionic pair
Effective electro-ionic potential (in Glaubermanrsquos form (1955))
2i
ie ( ) 1 e rZ err
( )
()
Iosilevskiy I High Temp 18
(1980) in ldquoEncyclopedia
of Low‐T Plasmardquo
(Suppl) Moscow FIZMATLIT 2004 pp 349
The form of i-i i-e e-e binary correlation functions-
laquoringraquo
(Debye) approximation with potential
Фie
(r)guarantee correct properties in the limit
of weak non-ideality
(Г
ltlt 1)
Binary i‐i i‐e e‐e
correlation functions
ldquoZero and second momentrdquo conditions (Stillinger amp Lovett)2
2[ ( ) ( )] 3D
rn F r F r dr
r
0e e sh ( ) 1 1 e
pr qrr
abrF r A
r r
Thermodynamic condition for the depth of i-e pseudopotentialand amplitude of electron-ionic correlation function
0 ln [ (0) ]ie ei e iF
Positive sign of all correlation functions Fab
(r) gt 0
F r Ae e
re
sh rrab
pr qrr( )
1 1 0
Pseudopotentials
U
= UKin
+ UPot
3PV
= 2UKin + UPot
Homogeneity of Coulomb potential
U Vn F F dpot coul ( ) r
U Vn F F dei ii 2 ( ) r
)2()2(3 potkinpot UUUUPV
2 2i i
ie ie1 e( ) (1 e (0) ~
rrZ e Z er
r r
( ))
Correlation Functions
Total Energy correction
Potential Energy Correction
-
UPot
Pressure Correction
-
P
i e i eN N U ( ) 1
Approximate relation between Coulomb corrections for chemical potential and energy
(
UN)
NB
Thermodynamic contributions inmodified pseudopotential model for Coulomb corrections
Positive shift in average kinetic energy due to non-ideality of free charges subsystem Ukin = 3PV ndash
U
Well-known relation between pressure and energy corrections for free charges subsystemU = 3PV
which is valid at weak non-ideality (Г
ltlt 1) is no longer valid in strong non-ideality conditions (Г
~ 1)
It is equivalent to additional effective electron-ion repulsion(in comparison with ordinary one-parametric Coulomb corrections depending on non-ideality parameter only
FNkT = f(Г)
Experimental data Theoretical models
(comparison)
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
Quasi‐isochoric behavior of nitrogen Hugoniot
‐
Mochalov
M Zhernokletov
M et al
JETP
137
(2010) ‐
Trunin
R Boriskov
G et alJETP Letters
88
(2008)
15 20 25 30 35 400
100
200
300
ExperimentsTrunin et al 2008Mochalov et al 2010
P GPa
gcm3
lim
Check of theoretical models
SAHA
CCM
Ross ampRogers
CCM ndash
Compressible Covolume
Model(A Medvedev
amp
VKopyshev)
SAHA‐code (V Gryaznov amp IIosilevskiy)
ρHug
asymp
33 plusmn
01
gcm390
lt
PHug
lt 330
GPa
NN
22 NN‐‐polymerpolymer
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
equiv
V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost
linear function of pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
Reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal Energy
Pressure (Hugonoit)
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
Blue curve
ndash
internal energy calculated via plasma model(code SAHA
Gryaznov Iosilevskiy)
SAHA
Hugoniot
~ ρ
asymp
const (33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
ρ
asymp33 plusmn01
gcc90
lt
P lt 330
GPa
NB
Quasi‐linear behavior of
E(p)
at ρ
=
constThermodynamics of shock compressed nitrogen
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
00
01
02
03
04
05
06
07
08
09
10 Mochalov et al PHug (Trunin et al) + T (EOSCCM) PHug (Trunin et al) + T (EOSSAHA)
xN+
xi
xN2
P GPa
T k
K
Tr
Tr
Plasma
Temperature of shock compressed nitrogen
CP()
General P‐T
diagram
Quasi‐linear behavior of
T(p)
at ρ
=
const
SAHA
‐
Experiment Mochalov
M et al
JETF
137
(2010)Nellis
W Radovsky
H et al J Chem Phys 94
(1991)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
Electroconductivity
of shock compressed nitrogen
20 25 30 351E-3
001
01
1
10
100
1000
C E B E 28061 B 29062
Con
duct
ivity
1
cm
Density gcc
Electroconductivity
of shock compressed nitrogen
Ternovoi
V et al (email ‐
30052010)
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1
P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
‐
Experiment Mochalov
M et al
JETF
137
(2010)
Quasi‐isentropic Plane Compression of Matter at Megabar
Pressures by Using of a Layered
System to Diminish First Shock Wave IntensityTernovoi
V Pyalling
A Filimonovet
A (052010) Summary and conclusion
Explosive driven quasi‐isentropic compression generators were proposed for matter investigation in
the megabar
pressure region Results of the first experiments on quasi‐isentropic compression of
liquid nitrogen are presented It was shown that pressure ionization
of nitrogen proceeds at
densities
from 315 to 34 gcc
at a temperature
of about 3000
K
Diminishing of temperature growth
was measured during onset of nitrogen electrical conductivity
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
)(01 UDD DUpp 001
2)(
2
22
01UDDhh
Shock Hugoniot
of liquid nitrogen(experimental data in thermodynamic variables)
‐
Mochalov
M Zhernokletov
M et al
JETP
137 77
(2010)
‐
Trunin
R Boriskov
G Bykov
A Medvedev
A
JETP Letters
88 220 (2008)
P GPa ρ
gcm3
884 plusmn
2 3325 plusmn
02
1333 plusmn
3 356 plusmn
015
1600 plusmn
3 331 plusmn
025
1830 plusmn
3 337 plusmn
035
2650 plusmn
5 325 plusmn
025
323 337 plusmn
020
ρρ0412
441410
418
403
416
()
(ρρ0
)ideal gas
= 40
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
E(PT)
reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal energy is close to be linear function of pressure
Internal Energy Pressure of sock compressed nitrogen
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
The region of approximate constancy for Gruneizen parameter
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Hugoniot
~ ρ
asymp
const
(33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Approximately linear function E ~ E0
+ constmiddotP
ρ
asymp
33
plusmn01
gcc 90
lt
P
lt 330
GPa
)(1121
0110
01 ppEE
NB
() Gridgas
= 23
asymp
067What does it mean
Temperature of shock compressed nitrogenmeasurements of thermal equation of state
2
ndash
linear approximation of experimental data
(Р
asymp
90 ndash 300 ГПа)
‐
Experiment
(Mochalov
M Zhernokletov
M et al
JETF
137 77
(2010)
0 100 200 3000
10
20
30
40
50
60
70
80
nN2
P ГПа
T kK
2
T kK
P GPa T
kK
884 plusmn
2 162 plusmn
09
1333 plusmn
3 246 plusmn
05
1600 plusmn
3 284 plusmn
22
1830 plusmn
3 -
2650 plusmn
5 560 plusmn
152
323 -
JETF
137 77
(2010)
‐
Mochalov
et al
JETP (2010)
0 100 200 3000
10
20
30
40
50
60
70
80
P GPa
T kK 4
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
Compressibility factor
(PVRT)
is almost
constant
on nitrogen isochore
What does it mean
ρ
asymp
33 plusmn01
gcc
(90
lt
P lt 330
GPa)
PVRTIdeal gas N2 Z= 05Ideal gas N
Z= 10
Id gas N+ + e Z= 20
Temperature is close to be linear function of pressure+
isochoric behavior of nitrogen Hugoniot
NB
Initial stateρ0
= 081
0 100 200 3000
10
20
30
40
50
60
70
80
P GPa
T kK 4
Сv
equiv
(partEpartT)v
asymp
const
asymp
20 (JgK)
ρ
asymp33 plusmn01
gcc
(90
lt
P lt 330
GPa)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
Internal energy ~ linear function on temperature at isochoreHigh-temperature part of nitrogen Hugoniot
Isochoric heat capacity
(CV
)
is almost constant
on nitrogen isochore
What does it mean
СV RN
asymp
35 NB
HugoniotHugoniot
0 100 200 3000
10
20
30
40
50
60
70
80
P GPa
T kK 4
γv
equiv
(vkB
)
(partppartT)v
asymp
const
asymp
ρ
asymp
33 plusmn01
gcc (90
lt
P lt 330
GPa)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
Constancy of Gruumlneizen parameter and Heat capacity at isochore
Gr
asymp
const
+
CV
asymp
const
thermal pressure coefficient γv
asymp
const
(partppartT)v
asymp
454 GPaK NB
HugoniotHugoniot
Thermodynamics of shock compressed nitrogen
ρ
asymp
33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
Mochalov
M Zhernokletov
M et alJETF
137 77
(2010) Trunin
R Boriskov
G Bykov
A Medvedev
AJETF Letters
88 220 (2008)
Expected behavior of nitrogen HugoniotМRoss amp FRogers
ACTEX(Rogers)
Interpolation(σmax
asymp
53)Experiments
New experiments vs
expected behavior of
nitrogen HugoniotМRoss amp FRogers
ACTEX(Rogers)
Interpolation(σmax
asymp
53)N‐polimer
N2Experiments
New experiments(σmax
asymp
41)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
New experiments are
in strong contradiction with expected behavior of
nitrogen Hugoniot
NB
Nitrogen Hugoniot
problem in plasma state ndash what do we need
In last experimentson deuterium
compression Pmax
asymp
50
Mbar(see Mochalov
et al NPP‐2011)(Mochalov
et al JETP Lett 2010)
NB
TheoryAb
initio
RPIMC DPIMCDFTMD WPMDChemical models
SAHA‐SSAHA‐N
(Gryaznov et al)WZ‐cell modelsTF TFC MHFShellip
Wide‐range EOS‐s
IPCP RASJIHT RASCCM (Sarov)
New experiments(σmax
asymp
41)
New experiments
‐Shock waves
-
Isentropic Compression‐
Heavy Ion Beams‐
Laser Heating etc etc
Interpolation(σmax
asymp
53)
ACTEX(Rogers)
Experiments
Nitrogen Hugoniot(comes trough polymeric phase )
ACTEX(Rogers)
Polymeric stateis expected between
molecular and plasma
regions (see below)
NB
N‐polymerN2
Experiments
THEORYAb
initio
RPIMC DPIMCDFTMD WPMDChem modelsSAHA‐SSAHA‐N
WZ‐cell modelsTFC MHFS
Wide‐range EOS
CCM (Sarov)
New experiments(σmax
asymp
41)
New experiments
‐
Shock waves
‐
Heavy Ion Beams‐
Laser Heating etc etc
N‐plasma
figure fromB Boates S Bonev Phys Rev Lett
102
(2009)
Ab initio calculations
‐
DFTMD
MolecularPolymeric
Critical point
CrossoverCrossover
11stst
order PTorder PT
MeltingMelting
Molecularfluid
Dissociated fluid
Fluidndashfluid
phase transitionin hydrogen [] ()
DFTMD
Scandolo
S PNAS
100 (2003)
Bonev S Militzer B Galli G PRB
69 (2004) WPMD
Jakob
B et al PRE
(2007) DFTMD Morales M et al PNAS
107 (2010)
DFTMD Lorenzen
W et al PRB
(2010)
Figure from
Giulia Galli SCCS-2005
Moscow= = = =
with additionsMorales et al 2010
andLorensen et al 2010
Morales et al
2010
Lorenzen
et al
2010
Ab initio calculations
‐
DFTMD
Experiment ndash single shock
compression ndash
reflected shock
compressionRadousky Nellis amp Ross et al Phys Rev Lett 57
(1986)Nellis Radousky
amp Hamilton et alJ Chem Phys 94
(1991)
0 50 100 150 200 250 3000
10
Tr Tr
CP
P GPa
T 103 K
Nitrogen phase diagram in the region of polymerizationPressure ndash temperature
melting (extrapolation)
HugoniotPlasma Model (SAHA‐code)
Yakubliquid
solidN2 N‐polimer
Theoretical models
estimation of polymer‐molecule
boundary in liquid nitrogen
(ЕYakub
ndash
1993) estimation of polymer‐molecule
boundary in solid nitrogen
(LYakub
ndash
1993)CP
ndash
critical point of 1st
order phase
transition polymer‐molecule
(ЕYakub
ndash
1993) ndash
triple point of 1st
order phase transition
polymer‐molecule
(Е amp L Yakub
ndash
1993)ЕS Yakub Low Temp Phys
20
579 (1994)LN Yakub Low Temp Phys
19 531 (1993)
estimation of polymer‐molecule bounda‐
ry
in liquid nitrogen (Ross amp Rogers
ndash
2006)MRoss
amp
FRogers Phys Rev
B 74 (2006)Ab
initio calculations DFTMD
ndash
calculation of of
polymer‐‐
molecule boundary in liquid nitrogen
(SBonev
et al ndash
2009)
the same as ldquosmoothedrdquo
phase transitionB Boates
amp
S Bonev Phys Rev Lett
102
(2009)
Gr
gt 0
Gr
lt 0 ndash domains of positive and negative sign of Gruumlneisen
coefficient
Gr
equiv
V(partPpartE)V
hypothetical boundary between polymeric and non‐ideal plasma states
(1st‐order phase transition or continuous )
melting
N2
N‐polimer
Gr
gt 0
Gr
lt 0
N‐plasma
Gr
gt 0
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
‐
Mochalov
M Zhernokletov
M et al
JETP
137 77
(2010) ‐
Trunin
R Boriskov
G Bykov
A Medvedev
A
JETP Letters
88 220 (2008)
Phase Diagram of Dense Nitrogen(summary)
N2
Npolimer
boundaryYakub Ross amp
Rogers etc
HypotheticalPressure Ionizationfrom N‐polymer
to N‐plasma
1st‐order phase transition
Critical point(s)
Domain
Gr
lt 0
Topology of theboundary
Gr
= 0
Pre‐compressed gaseous N2
Iso‐S
N2
N‐polimer
N‐plasma
Gr
gt 0
Gr
gt 0
Gr
lt 0
New experiments
‐
Shock waves‐ Iso‐S
Compression‐ Heavy Ion Beams‐
Laser Heating etc etc
THEORY Ab
initioRPIMC DPIMC
DFTMDChem modelsSAHA‐N
WZ‐cell modelsTFC MHFS
Wide‐range EOSEOS (IPCP
RAS)EOS (JIHT
RAS)CCM (Sarov)
Commentsmicrophysics
Simple molecules H2
N2
L = 074 A L = 11 A
D = 29 A D = 37 A
Triple covalent bond De
= 98 eV
(49 eVatom)
Single covalent bond De
= 30 eV
(45 eVatom)
L = 14 A
Figures after
Eugene Yakub ldquoNon‐simple
problems for simple moleculesrdquoFAIR‐Russia School laquoPhysics of high energy density in matterraquo
December
2009 Moscow
FZaharievAHuJHooperFZhangampTWoo PhysRev B 72214108 (2005 )
Polymeric nitrogen - structure
Eugene and Lidia Yakub Low Temp Phys 19 (1993)
Simple molecular modelsFirst estimations of molecular-polymeric transition
1 - Hugoniot2 - Phase equilibrium line
Experiment (Nellis ea 2001)3 - Single shock4 - Double shock
NN22
NN‐‐polimerpolimer
NN22
NN‐‐polimerpolimer
1st‐orderPhase transition
Critical point
Plasma model for nitrogen thermodynamics(code SAHA-N)
Shock compression of nitrogen(chemical picture)
SAHA-codeGryaznov Iosilevskiy (1970-2010)
Short range repulsionldquoSoft Spheresrdquo
approximation (DYoung)
modified for mixture
of soft spheres with different radii
ndash
shift of dissociation level
N
N+ + endash Ze
e
rcA
iA+
A+
i
Coulomb interactionModified pseudopotential
model
for partially ionized plasma(I
Iosilevskiy 1980-2010)
Equilibrium
compositionN2
N N+ e N2+ Nndash
Key parameter
ndash
ratio of intrinsic volumes molecule atom ion
R(N)
R(N2
)
= 063-
in accordance with recommendations of
ldquoAtom-atomic
approximationrdquo
of EYakub LT 1993
Basic points-
All assumption are provided at micro-level-
Input Choice of Фie
Фii
and Фее
pseudopotentials - Input Approximations for binary correlation functions - Strong correlation of the pseudopotentials
for ldquofreerdquocharges and upper energy level for partition functionsfor bound states
- Priority for general equalities (normalizing conditions)valid independently on degree of non-ideality
- Non-ideality corrections through the correlationfunctions and general equalities valid for Coulombinteraction
NN22
harrharr 2N2N NN22
++
harrharr NN ++
NN++ NNndashharrharr NN ++
eendash
[ ( ) ( )] 1n F r F r d r
Coulomb Corrections for Free Charge Subsystem
Modified Pseudopotential Approximation ()
Bound and free states of electron‐ionic pair
Effective electro-ionic potential (in Glaubermanrsquos form (1955))
2i
ie ( ) 1 e rZ err
( )
()
Iosilevskiy I High Temp 18
(1980) in ldquoEncyclopedia
of Low‐T Plasmardquo
(Suppl) Moscow FIZMATLIT 2004 pp 349
The form of i-i i-e e-e binary correlation functions-
laquoringraquo
(Debye) approximation with potential
Фie
(r)guarantee correct properties in the limit
of weak non-ideality
(Г
ltlt 1)
Binary i‐i i‐e e‐e
correlation functions
ldquoZero and second momentrdquo conditions (Stillinger amp Lovett)2
2[ ( ) ( )] 3D
rn F r F r dr
r
0e e sh ( ) 1 1 e
pr qrr
abrF r A
r r
Thermodynamic condition for the depth of i-e pseudopotentialand amplitude of electron-ionic correlation function
0 ln [ (0) ]ie ei e iF
Positive sign of all correlation functions Fab
(r) gt 0
F r Ae e
re
sh rrab
pr qrr( )
1 1 0
Pseudopotentials
U
= UKin
+ UPot
3PV
= 2UKin + UPot
Homogeneity of Coulomb potential
U Vn F F dpot coul ( ) r
U Vn F F dei ii 2 ( ) r
)2()2(3 potkinpot UUUUPV
2 2i i
ie ie1 e( ) (1 e (0) ~
rrZ e Z er
r r
( ))
Correlation Functions
Total Energy correction
Potential Energy Correction
-
UPot
Pressure Correction
-
P
i e i eN N U ( ) 1
Approximate relation between Coulomb corrections for chemical potential and energy
(
UN)
NB
Thermodynamic contributions inmodified pseudopotential model for Coulomb corrections
Positive shift in average kinetic energy due to non-ideality of free charges subsystem Ukin = 3PV ndash
U
Well-known relation between pressure and energy corrections for free charges subsystemU = 3PV
which is valid at weak non-ideality (Г
ltlt 1) is no longer valid in strong non-ideality conditions (Г
~ 1)
It is equivalent to additional effective electron-ion repulsion(in comparison with ordinary one-parametric Coulomb corrections depending on non-ideality parameter only
FNkT = f(Г)
Experimental data Theoretical models
(comparison)
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
Quasi‐isochoric behavior of nitrogen Hugoniot
‐
Mochalov
M Zhernokletov
M et al
JETP
137
(2010) ‐
Trunin
R Boriskov
G et alJETP Letters
88
(2008)
15 20 25 30 35 400
100
200
300
ExperimentsTrunin et al 2008Mochalov et al 2010
P GPa
gcm3
lim
Check of theoretical models
SAHA
CCM
Ross ampRogers
CCM ndash
Compressible Covolume
Model(A Medvedev
amp
VKopyshev)
SAHA‐code (V Gryaznov amp IIosilevskiy)
ρHug
asymp
33 plusmn
01
gcm390
lt
PHug
lt 330
GPa
NN
22 NN‐‐polymerpolymer
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
equiv
V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost
linear function of pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
Reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal Energy
Pressure (Hugonoit)
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
Blue curve
ndash
internal energy calculated via plasma model(code SAHA
Gryaznov Iosilevskiy)
SAHA
Hugoniot
~ ρ
asymp
const (33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
ρ
asymp33 plusmn01
gcc90
lt
P lt 330
GPa
NB
Quasi‐linear behavior of
E(p)
at ρ
=
constThermodynamics of shock compressed nitrogen
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
00
01
02
03
04
05
06
07
08
09
10 Mochalov et al PHug (Trunin et al) + T (EOSCCM) PHug (Trunin et al) + T (EOSSAHA)
xN+
xi
xN2
P GPa
T k
K
Tr
Tr
Plasma
Temperature of shock compressed nitrogen
CP()
General P‐T
diagram
Quasi‐linear behavior of
T(p)
at ρ
=
const
SAHA
‐
Experiment Mochalov
M et al
JETF
137
(2010)Nellis
W Radovsky
H et al J Chem Phys 94
(1991)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
Electroconductivity
of shock compressed nitrogen
20 25 30 351E-3
001
01
1
10
100
1000
C E B E 28061 B 29062
Con
duct
ivity
1
cm
Density gcc
Electroconductivity
of shock compressed nitrogen
Ternovoi
V et al (email ‐
30052010)
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1
P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
‐
Experiment Mochalov
M et al
JETF
137
(2010)
Quasi‐isentropic Plane Compression of Matter at Megabar
Pressures by Using of a Layered
System to Diminish First Shock Wave IntensityTernovoi
V Pyalling
A Filimonovet
A (052010) Summary and conclusion
Explosive driven quasi‐isentropic compression generators were proposed for matter investigation in
the megabar
pressure region Results of the first experiments on quasi‐isentropic compression of
liquid nitrogen are presented It was shown that pressure ionization
of nitrogen proceeds at
densities
from 315 to 34 gcc
at a temperature
of about 3000
K
Diminishing of temperature growth
was measured during onset of nitrogen electrical conductivity
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
E(PT)
reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal energy is close to be linear function of pressure
Internal Energy Pressure of sock compressed nitrogen
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
The region of approximate constancy for Gruneizen parameter
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Hugoniot
~ ρ
asymp
const
(33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Approximately linear function E ~ E0
+ constmiddotP
ρ
asymp
33
plusmn01
gcc 90
lt
P
lt 330
GPa
)(1121
0110
01 ppEE
NB
() Gridgas
= 23
asymp
067What does it mean
Temperature of shock compressed nitrogenmeasurements of thermal equation of state
2
ndash
linear approximation of experimental data
(Р
asymp
90 ndash 300 ГПа)
‐
Experiment
(Mochalov
M Zhernokletov
M et al
JETF
137 77
(2010)
0 100 200 3000
10
20
30
40
50
60
70
80
nN2
P ГПа
T kK
2
T kK
P GPa T
kK
884 plusmn
2 162 plusmn
09
1333 plusmn
3 246 plusmn
05
1600 plusmn
3 284 plusmn
22
1830 plusmn
3 -
2650 plusmn
5 560 plusmn
152
323 -
JETF
137 77
(2010)
‐
Mochalov
et al
JETP (2010)
0 100 200 3000
10
20
30
40
50
60
70
80
P GPa
T kK 4
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
Compressibility factor
(PVRT)
is almost
constant
on nitrogen isochore
What does it mean
ρ
asymp
33 plusmn01
gcc
(90
lt
P lt 330
GPa)
PVRTIdeal gas N2 Z= 05Ideal gas N
Z= 10
Id gas N+ + e Z= 20
Temperature is close to be linear function of pressure+
isochoric behavior of nitrogen Hugoniot
NB
Initial stateρ0
= 081
0 100 200 3000
10
20
30
40
50
60
70
80
P GPa
T kK 4
Сv
equiv
(partEpartT)v
asymp
const
asymp
20 (JgK)
ρ
asymp33 plusmn01
gcc
(90
lt
P lt 330
GPa)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
Internal energy ~ linear function on temperature at isochoreHigh-temperature part of nitrogen Hugoniot
Isochoric heat capacity
(CV
)
is almost constant
on nitrogen isochore
What does it mean
СV RN
asymp
35 NB
HugoniotHugoniot
0 100 200 3000
10
20
30
40
50
60
70
80
P GPa
T kK 4
γv
equiv
(vkB
)
(partppartT)v
asymp
const
asymp
ρ
asymp
33 plusmn01
gcc (90
lt
P lt 330
GPa)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
Constancy of Gruumlneizen parameter and Heat capacity at isochore
Gr
asymp
const
+
CV
asymp
const
thermal pressure coefficient γv
asymp
const
(partppartT)v
asymp
454 GPaK NB
HugoniotHugoniot
Thermodynamics of shock compressed nitrogen
ρ
asymp
33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
Mochalov
M Zhernokletov
M et alJETF
137 77
(2010) Trunin
R Boriskov
G Bykov
A Medvedev
AJETF Letters
88 220 (2008)
Expected behavior of nitrogen HugoniotМRoss amp FRogers
ACTEX(Rogers)
Interpolation(σmax
asymp
53)Experiments
New experiments vs
expected behavior of
nitrogen HugoniotМRoss amp FRogers
ACTEX(Rogers)
Interpolation(σmax
asymp
53)N‐polimer
N2Experiments
New experiments(σmax
asymp
41)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
New experiments are
in strong contradiction with expected behavior of
nitrogen Hugoniot
NB
Nitrogen Hugoniot
problem in plasma state ndash what do we need
In last experimentson deuterium
compression Pmax
asymp
50
Mbar(see Mochalov
et al NPP‐2011)(Mochalov
et al JETP Lett 2010)
NB
TheoryAb
initio
RPIMC DPIMCDFTMD WPMDChemical models
SAHA‐SSAHA‐N
(Gryaznov et al)WZ‐cell modelsTF TFC MHFShellip
Wide‐range EOS‐s
IPCP RASJIHT RASCCM (Sarov)
New experiments(σmax
asymp
41)
New experiments
‐Shock waves
-
Isentropic Compression‐
Heavy Ion Beams‐
Laser Heating etc etc
Interpolation(σmax
asymp
53)
ACTEX(Rogers)
Experiments
Nitrogen Hugoniot(comes trough polymeric phase )
ACTEX(Rogers)
Polymeric stateis expected between
molecular and plasma
regions (see below)
NB
N‐polymerN2
Experiments
THEORYAb
initio
RPIMC DPIMCDFTMD WPMDChem modelsSAHA‐SSAHA‐N
WZ‐cell modelsTFC MHFS
Wide‐range EOS
CCM (Sarov)
New experiments(σmax
asymp
41)
New experiments
‐
Shock waves
‐
Heavy Ion Beams‐
Laser Heating etc etc
N‐plasma
figure fromB Boates S Bonev Phys Rev Lett
102
(2009)
Ab initio calculations
‐
DFTMD
MolecularPolymeric
Critical point
CrossoverCrossover
11stst
order PTorder PT
MeltingMelting
Molecularfluid
Dissociated fluid
Fluidndashfluid
phase transitionin hydrogen [] ()
DFTMD
Scandolo
S PNAS
100 (2003)
Bonev S Militzer B Galli G PRB
69 (2004) WPMD
Jakob
B et al PRE
(2007) DFTMD Morales M et al PNAS
107 (2010)
DFTMD Lorenzen
W et al PRB
(2010)
Figure from
Giulia Galli SCCS-2005
Moscow= = = =
with additionsMorales et al 2010
andLorensen et al 2010
Morales et al
2010
Lorenzen
et al
2010
Ab initio calculations
‐
DFTMD
Experiment ndash single shock
compression ndash
reflected shock
compressionRadousky Nellis amp Ross et al Phys Rev Lett 57
(1986)Nellis Radousky
amp Hamilton et alJ Chem Phys 94
(1991)
0 50 100 150 200 250 3000
10
Tr Tr
CP
P GPa
T 103 K
Nitrogen phase diagram in the region of polymerizationPressure ndash temperature
melting (extrapolation)
HugoniotPlasma Model (SAHA‐code)
Yakubliquid
solidN2 N‐polimer
Theoretical models
estimation of polymer‐molecule
boundary in liquid nitrogen
(ЕYakub
ndash
1993) estimation of polymer‐molecule
boundary in solid nitrogen
(LYakub
ndash
1993)CP
ndash
critical point of 1st
order phase
transition polymer‐molecule
(ЕYakub
ndash
1993) ndash
triple point of 1st
order phase transition
polymer‐molecule
(Е amp L Yakub
ndash
1993)ЕS Yakub Low Temp Phys
20
579 (1994)LN Yakub Low Temp Phys
19 531 (1993)
estimation of polymer‐molecule bounda‐
ry
in liquid nitrogen (Ross amp Rogers
ndash
2006)MRoss
amp
FRogers Phys Rev
B 74 (2006)Ab
initio calculations DFTMD
ndash
calculation of of
polymer‐‐
molecule boundary in liquid nitrogen
(SBonev
et al ndash
2009)
the same as ldquosmoothedrdquo
phase transitionB Boates
amp
S Bonev Phys Rev Lett
102
(2009)
Gr
gt 0
Gr
lt 0 ndash domains of positive and negative sign of Gruumlneisen
coefficient
Gr
equiv
V(partPpartE)V
hypothetical boundary between polymeric and non‐ideal plasma states
(1st‐order phase transition or continuous )
melting
N2
N‐polimer
Gr
gt 0
Gr
lt 0
N‐plasma
Gr
gt 0
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
‐
Mochalov
M Zhernokletov
M et al
JETP
137 77
(2010) ‐
Trunin
R Boriskov
G Bykov
A Medvedev
A
JETP Letters
88 220 (2008)
Phase Diagram of Dense Nitrogen(summary)
N2
Npolimer
boundaryYakub Ross amp
Rogers etc
HypotheticalPressure Ionizationfrom N‐polymer
to N‐plasma
1st‐order phase transition
Critical point(s)
Domain
Gr
lt 0
Topology of theboundary
Gr
= 0
Pre‐compressed gaseous N2
Iso‐S
N2
N‐polimer
N‐plasma
Gr
gt 0
Gr
gt 0
Gr
lt 0
New experiments
‐
Shock waves‐ Iso‐S
Compression‐ Heavy Ion Beams‐
Laser Heating etc etc
THEORY Ab
initioRPIMC DPIMC
DFTMDChem modelsSAHA‐N
WZ‐cell modelsTFC MHFS
Wide‐range EOSEOS (IPCP
RAS)EOS (JIHT
RAS)CCM (Sarov)
Commentsmicrophysics
Simple molecules H2
N2
L = 074 A L = 11 A
D = 29 A D = 37 A
Triple covalent bond De
= 98 eV
(49 eVatom)
Single covalent bond De
= 30 eV
(45 eVatom)
L = 14 A
Figures after
Eugene Yakub ldquoNon‐simple
problems for simple moleculesrdquoFAIR‐Russia School laquoPhysics of high energy density in matterraquo
December
2009 Moscow
FZaharievAHuJHooperFZhangampTWoo PhysRev B 72214108 (2005 )
Polymeric nitrogen - structure
Eugene and Lidia Yakub Low Temp Phys 19 (1993)
Simple molecular modelsFirst estimations of molecular-polymeric transition
1 - Hugoniot2 - Phase equilibrium line
Experiment (Nellis ea 2001)3 - Single shock4 - Double shock
NN22
NN‐‐polimerpolimer
NN22
NN‐‐polimerpolimer
1st‐orderPhase transition
Critical point
Plasma model for nitrogen thermodynamics(code SAHA-N)
Shock compression of nitrogen(chemical picture)
SAHA-codeGryaznov Iosilevskiy (1970-2010)
Short range repulsionldquoSoft Spheresrdquo
approximation (DYoung)
modified for mixture
of soft spheres with different radii
ndash
shift of dissociation level
N
N+ + endash Ze
e
rcA
iA+
A+
i
Coulomb interactionModified pseudopotential
model
for partially ionized plasma(I
Iosilevskiy 1980-2010)
Equilibrium
compositionN2
N N+ e N2+ Nndash
Key parameter
ndash
ratio of intrinsic volumes molecule atom ion
R(N)
R(N2
)
= 063-
in accordance with recommendations of
ldquoAtom-atomic
approximationrdquo
of EYakub LT 1993
Basic points-
All assumption are provided at micro-level-
Input Choice of Фie
Фii
and Фее
pseudopotentials - Input Approximations for binary correlation functions - Strong correlation of the pseudopotentials
for ldquofreerdquocharges and upper energy level for partition functionsfor bound states
- Priority for general equalities (normalizing conditions)valid independently on degree of non-ideality
- Non-ideality corrections through the correlationfunctions and general equalities valid for Coulombinteraction
NN22
harrharr 2N2N NN22
++
harrharr NN ++
NN++ NNndashharrharr NN ++
eendash
[ ( ) ( )] 1n F r F r d r
Coulomb Corrections for Free Charge Subsystem
Modified Pseudopotential Approximation ()
Bound and free states of electron‐ionic pair
Effective electro-ionic potential (in Glaubermanrsquos form (1955))
2i
ie ( ) 1 e rZ err
( )
()
Iosilevskiy I High Temp 18
(1980) in ldquoEncyclopedia
of Low‐T Plasmardquo
(Suppl) Moscow FIZMATLIT 2004 pp 349
The form of i-i i-e e-e binary correlation functions-
laquoringraquo
(Debye) approximation with potential
Фie
(r)guarantee correct properties in the limit
of weak non-ideality
(Г
ltlt 1)
Binary i‐i i‐e e‐e
correlation functions
ldquoZero and second momentrdquo conditions (Stillinger amp Lovett)2
2[ ( ) ( )] 3D
rn F r F r dr
r
0e e sh ( ) 1 1 e
pr qrr
abrF r A
r r
Thermodynamic condition for the depth of i-e pseudopotentialand amplitude of electron-ionic correlation function
0 ln [ (0) ]ie ei e iF
Positive sign of all correlation functions Fab
(r) gt 0
F r Ae e
re
sh rrab
pr qrr( )
1 1 0
Pseudopotentials
U
= UKin
+ UPot
3PV
= 2UKin + UPot
Homogeneity of Coulomb potential
U Vn F F dpot coul ( ) r
U Vn F F dei ii 2 ( ) r
)2()2(3 potkinpot UUUUPV
2 2i i
ie ie1 e( ) (1 e (0) ~
rrZ e Z er
r r
( ))
Correlation Functions
Total Energy correction
Potential Energy Correction
-
UPot
Pressure Correction
-
P
i e i eN N U ( ) 1
Approximate relation between Coulomb corrections for chemical potential and energy
(
UN)
NB
Thermodynamic contributions inmodified pseudopotential model for Coulomb corrections
Positive shift in average kinetic energy due to non-ideality of free charges subsystem Ukin = 3PV ndash
U
Well-known relation between pressure and energy corrections for free charges subsystemU = 3PV
which is valid at weak non-ideality (Г
ltlt 1) is no longer valid in strong non-ideality conditions (Г
~ 1)
It is equivalent to additional effective electron-ion repulsion(in comparison with ordinary one-parametric Coulomb corrections depending on non-ideality parameter only
FNkT = f(Г)
Experimental data Theoretical models
(comparison)
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
Quasi‐isochoric behavior of nitrogen Hugoniot
‐
Mochalov
M Zhernokletov
M et al
JETP
137
(2010) ‐
Trunin
R Boriskov
G et alJETP Letters
88
(2008)
15 20 25 30 35 400
100
200
300
ExperimentsTrunin et al 2008Mochalov et al 2010
P GPa
gcm3
lim
Check of theoretical models
SAHA
CCM
Ross ampRogers
CCM ndash
Compressible Covolume
Model(A Medvedev
amp
VKopyshev)
SAHA‐code (V Gryaznov amp IIosilevskiy)
ρHug
asymp
33 plusmn
01
gcm390
lt
PHug
lt 330
GPa
NN
22 NN‐‐polymerpolymer
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
equiv
V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost
linear function of pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
Reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal Energy
Pressure (Hugonoit)
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
Blue curve
ndash
internal energy calculated via plasma model(code SAHA
Gryaznov Iosilevskiy)
SAHA
Hugoniot
~ ρ
asymp
const (33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
ρ
asymp33 plusmn01
gcc90
lt
P lt 330
GPa
NB
Quasi‐linear behavior of
E(p)
at ρ
=
constThermodynamics of shock compressed nitrogen
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
00
01
02
03
04
05
06
07
08
09
10 Mochalov et al PHug (Trunin et al) + T (EOSCCM) PHug (Trunin et al) + T (EOSSAHA)
xN+
xi
xN2
P GPa
T k
K
Tr
Tr
Plasma
Temperature of shock compressed nitrogen
CP()
General P‐T
diagram
Quasi‐linear behavior of
T(p)
at ρ
=
const
SAHA
‐
Experiment Mochalov
M et al
JETF
137
(2010)Nellis
W Radovsky
H et al J Chem Phys 94
(1991)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
Electroconductivity
of shock compressed nitrogen
20 25 30 351E-3
001
01
1
10
100
1000
C E B E 28061 B 29062
Con
duct
ivity
1
cm
Density gcc
Electroconductivity
of shock compressed nitrogen
Ternovoi
V et al (email ‐
30052010)
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1
P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
‐
Experiment Mochalov
M et al
JETF
137
(2010)
Quasi‐isentropic Plane Compression of Matter at Megabar
Pressures by Using of a Layered
System to Diminish First Shock Wave IntensityTernovoi
V Pyalling
A Filimonovet
A (052010) Summary and conclusion
Explosive driven quasi‐isentropic compression generators were proposed for matter investigation in
the megabar
pressure region Results of the first experiments on quasi‐isentropic compression of
liquid nitrogen are presented It was shown that pressure ionization
of nitrogen proceeds at
densities
from 315 to 34 gcc
at a temperature
of about 3000
K
Diminishing of temperature growth
was measured during onset of nitrogen electrical conductivity
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
Temperature of shock compressed nitrogenmeasurements of thermal equation of state
2
ndash
linear approximation of experimental data
(Р
asymp
90 ndash 300 ГПа)
‐
Experiment
(Mochalov
M Zhernokletov
M et al
JETF
137 77
(2010)
0 100 200 3000
10
20
30
40
50
60
70
80
nN2
P ГПа
T kK
2
T kK
P GPa T
kK
884 plusmn
2 162 plusmn
09
1333 plusmn
3 246 plusmn
05
1600 plusmn
3 284 plusmn
22
1830 plusmn
3 -
2650 plusmn
5 560 plusmn
152
323 -
JETF
137 77
(2010)
‐
Mochalov
et al
JETP (2010)
0 100 200 3000
10
20
30
40
50
60
70
80
P GPa
T kK 4
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
Compressibility factor
(PVRT)
is almost
constant
on nitrogen isochore
What does it mean
ρ
asymp
33 plusmn01
gcc
(90
lt
P lt 330
GPa)
PVRTIdeal gas N2 Z= 05Ideal gas N
Z= 10
Id gas N+ + e Z= 20
Temperature is close to be linear function of pressure+
isochoric behavior of nitrogen Hugoniot
NB
Initial stateρ0
= 081
0 100 200 3000
10
20
30
40
50
60
70
80
P GPa
T kK 4
Сv
equiv
(partEpartT)v
asymp
const
asymp
20 (JgK)
ρ
asymp33 plusmn01
gcc
(90
lt
P lt 330
GPa)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
Internal energy ~ linear function on temperature at isochoreHigh-temperature part of nitrogen Hugoniot
Isochoric heat capacity
(CV
)
is almost constant
on nitrogen isochore
What does it mean
СV RN
asymp
35 NB
HugoniotHugoniot
0 100 200 3000
10
20
30
40
50
60
70
80
P GPa
T kK 4
γv
equiv
(vkB
)
(partppartT)v
asymp
const
asymp
ρ
asymp
33 plusmn01
gcc (90
lt
P lt 330
GPa)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
Constancy of Gruumlneizen parameter and Heat capacity at isochore
Gr
asymp
const
+
CV
asymp
const
thermal pressure coefficient γv
asymp
const
(partppartT)v
asymp
454 GPaK NB
HugoniotHugoniot
Thermodynamics of shock compressed nitrogen
ρ
asymp
33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
Mochalov
M Zhernokletov
M et alJETF
137 77
(2010) Trunin
R Boriskov
G Bykov
A Medvedev
AJETF Letters
88 220 (2008)
Expected behavior of nitrogen HugoniotМRoss amp FRogers
ACTEX(Rogers)
Interpolation(σmax
asymp
53)Experiments
New experiments vs
expected behavior of
nitrogen HugoniotМRoss amp FRogers
ACTEX(Rogers)
Interpolation(σmax
asymp
53)N‐polimer
N2Experiments
New experiments(σmax
asymp
41)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
New experiments are
in strong contradiction with expected behavior of
nitrogen Hugoniot
NB
Nitrogen Hugoniot
problem in plasma state ndash what do we need
In last experimentson deuterium
compression Pmax
asymp
50
Mbar(see Mochalov
et al NPP‐2011)(Mochalov
et al JETP Lett 2010)
NB
TheoryAb
initio
RPIMC DPIMCDFTMD WPMDChemical models
SAHA‐SSAHA‐N
(Gryaznov et al)WZ‐cell modelsTF TFC MHFShellip
Wide‐range EOS‐s
IPCP RASJIHT RASCCM (Sarov)
New experiments(σmax
asymp
41)
New experiments
‐Shock waves
-
Isentropic Compression‐
Heavy Ion Beams‐
Laser Heating etc etc
Interpolation(σmax
asymp
53)
ACTEX(Rogers)
Experiments
Nitrogen Hugoniot(comes trough polymeric phase )
ACTEX(Rogers)
Polymeric stateis expected between
molecular and plasma
regions (see below)
NB
N‐polymerN2
Experiments
THEORYAb
initio
RPIMC DPIMCDFTMD WPMDChem modelsSAHA‐SSAHA‐N
WZ‐cell modelsTFC MHFS
Wide‐range EOS
CCM (Sarov)
New experiments(σmax
asymp
41)
New experiments
‐
Shock waves
‐
Heavy Ion Beams‐
Laser Heating etc etc
N‐plasma
figure fromB Boates S Bonev Phys Rev Lett
102
(2009)
Ab initio calculations
‐
DFTMD
MolecularPolymeric
Critical point
CrossoverCrossover
11stst
order PTorder PT
MeltingMelting
Molecularfluid
Dissociated fluid
Fluidndashfluid
phase transitionin hydrogen [] ()
DFTMD
Scandolo
S PNAS
100 (2003)
Bonev S Militzer B Galli G PRB
69 (2004) WPMD
Jakob
B et al PRE
(2007) DFTMD Morales M et al PNAS
107 (2010)
DFTMD Lorenzen
W et al PRB
(2010)
Figure from
Giulia Galli SCCS-2005
Moscow= = = =
with additionsMorales et al 2010
andLorensen et al 2010
Morales et al
2010
Lorenzen
et al
2010
Ab initio calculations
‐
DFTMD
Experiment ndash single shock
compression ndash
reflected shock
compressionRadousky Nellis amp Ross et al Phys Rev Lett 57
(1986)Nellis Radousky
amp Hamilton et alJ Chem Phys 94
(1991)
0 50 100 150 200 250 3000
10
Tr Tr
CP
P GPa
T 103 K
Nitrogen phase diagram in the region of polymerizationPressure ndash temperature
melting (extrapolation)
HugoniotPlasma Model (SAHA‐code)
Yakubliquid
solidN2 N‐polimer
Theoretical models
estimation of polymer‐molecule
boundary in liquid nitrogen
(ЕYakub
ndash
1993) estimation of polymer‐molecule
boundary in solid nitrogen
(LYakub
ndash
1993)CP
ndash
critical point of 1st
order phase
transition polymer‐molecule
(ЕYakub
ndash
1993) ndash
triple point of 1st
order phase transition
polymer‐molecule
(Е amp L Yakub
ndash
1993)ЕS Yakub Low Temp Phys
20
579 (1994)LN Yakub Low Temp Phys
19 531 (1993)
estimation of polymer‐molecule bounda‐
ry
in liquid nitrogen (Ross amp Rogers
ndash
2006)MRoss
amp
FRogers Phys Rev
B 74 (2006)Ab
initio calculations DFTMD
ndash
calculation of of
polymer‐‐
molecule boundary in liquid nitrogen
(SBonev
et al ndash
2009)
the same as ldquosmoothedrdquo
phase transitionB Boates
amp
S Bonev Phys Rev Lett
102
(2009)
Gr
gt 0
Gr
lt 0 ndash domains of positive and negative sign of Gruumlneisen
coefficient
Gr
equiv
V(partPpartE)V
hypothetical boundary between polymeric and non‐ideal plasma states
(1st‐order phase transition or continuous )
melting
N2
N‐polimer
Gr
gt 0
Gr
lt 0
N‐plasma
Gr
gt 0
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
‐
Mochalov
M Zhernokletov
M et al
JETP
137 77
(2010) ‐
Trunin
R Boriskov
G Bykov
A Medvedev
A
JETP Letters
88 220 (2008)
Phase Diagram of Dense Nitrogen(summary)
N2
Npolimer
boundaryYakub Ross amp
Rogers etc
HypotheticalPressure Ionizationfrom N‐polymer
to N‐plasma
1st‐order phase transition
Critical point(s)
Domain
Gr
lt 0
Topology of theboundary
Gr
= 0
Pre‐compressed gaseous N2
Iso‐S
N2
N‐polimer
N‐plasma
Gr
gt 0
Gr
gt 0
Gr
lt 0
New experiments
‐
Shock waves‐ Iso‐S
Compression‐ Heavy Ion Beams‐
Laser Heating etc etc
THEORY Ab
initioRPIMC DPIMC
DFTMDChem modelsSAHA‐N
WZ‐cell modelsTFC MHFS
Wide‐range EOSEOS (IPCP
RAS)EOS (JIHT
RAS)CCM (Sarov)
Commentsmicrophysics
Simple molecules H2
N2
L = 074 A L = 11 A
D = 29 A D = 37 A
Triple covalent bond De
= 98 eV
(49 eVatom)
Single covalent bond De
= 30 eV
(45 eVatom)
L = 14 A
Figures after
Eugene Yakub ldquoNon‐simple
problems for simple moleculesrdquoFAIR‐Russia School laquoPhysics of high energy density in matterraquo
December
2009 Moscow
FZaharievAHuJHooperFZhangampTWoo PhysRev B 72214108 (2005 )
Polymeric nitrogen - structure
Eugene and Lidia Yakub Low Temp Phys 19 (1993)
Simple molecular modelsFirst estimations of molecular-polymeric transition
1 - Hugoniot2 - Phase equilibrium line
Experiment (Nellis ea 2001)3 - Single shock4 - Double shock
NN22
NN‐‐polimerpolimer
NN22
NN‐‐polimerpolimer
1st‐orderPhase transition
Critical point
Plasma model for nitrogen thermodynamics(code SAHA-N)
Shock compression of nitrogen(chemical picture)
SAHA-codeGryaznov Iosilevskiy (1970-2010)
Short range repulsionldquoSoft Spheresrdquo
approximation (DYoung)
modified for mixture
of soft spheres with different radii
ndash
shift of dissociation level
N
N+ + endash Ze
e
rcA
iA+
A+
i
Coulomb interactionModified pseudopotential
model
for partially ionized plasma(I
Iosilevskiy 1980-2010)
Equilibrium
compositionN2
N N+ e N2+ Nndash
Key parameter
ndash
ratio of intrinsic volumes molecule atom ion
R(N)
R(N2
)
= 063-
in accordance with recommendations of
ldquoAtom-atomic
approximationrdquo
of EYakub LT 1993
Basic points-
All assumption are provided at micro-level-
Input Choice of Фie
Фii
and Фее
pseudopotentials - Input Approximations for binary correlation functions - Strong correlation of the pseudopotentials
for ldquofreerdquocharges and upper energy level for partition functionsfor bound states
- Priority for general equalities (normalizing conditions)valid independently on degree of non-ideality
- Non-ideality corrections through the correlationfunctions and general equalities valid for Coulombinteraction
NN22
harrharr 2N2N NN22
++
harrharr NN ++
NN++ NNndashharrharr NN ++
eendash
[ ( ) ( )] 1n F r F r d r
Coulomb Corrections for Free Charge Subsystem
Modified Pseudopotential Approximation ()
Bound and free states of electron‐ionic pair
Effective electro-ionic potential (in Glaubermanrsquos form (1955))
2i
ie ( ) 1 e rZ err
( )
()
Iosilevskiy I High Temp 18
(1980) in ldquoEncyclopedia
of Low‐T Plasmardquo
(Suppl) Moscow FIZMATLIT 2004 pp 349
The form of i-i i-e e-e binary correlation functions-
laquoringraquo
(Debye) approximation with potential
Фie
(r)guarantee correct properties in the limit
of weak non-ideality
(Г
ltlt 1)
Binary i‐i i‐e e‐e
correlation functions
ldquoZero and second momentrdquo conditions (Stillinger amp Lovett)2
2[ ( ) ( )] 3D
rn F r F r dr
r
0e e sh ( ) 1 1 e
pr qrr
abrF r A
r r
Thermodynamic condition for the depth of i-e pseudopotentialand amplitude of electron-ionic correlation function
0 ln [ (0) ]ie ei e iF
Positive sign of all correlation functions Fab
(r) gt 0
F r Ae e
re
sh rrab
pr qrr( )
1 1 0
Pseudopotentials
U
= UKin
+ UPot
3PV
= 2UKin + UPot
Homogeneity of Coulomb potential
U Vn F F dpot coul ( ) r
U Vn F F dei ii 2 ( ) r
)2()2(3 potkinpot UUUUPV
2 2i i
ie ie1 e( ) (1 e (0) ~
rrZ e Z er
r r
( ))
Correlation Functions
Total Energy correction
Potential Energy Correction
-
UPot
Pressure Correction
-
P
i e i eN N U ( ) 1
Approximate relation between Coulomb corrections for chemical potential and energy
(
UN)
NB
Thermodynamic contributions inmodified pseudopotential model for Coulomb corrections
Positive shift in average kinetic energy due to non-ideality of free charges subsystem Ukin = 3PV ndash
U
Well-known relation between pressure and energy corrections for free charges subsystemU = 3PV
which is valid at weak non-ideality (Г
ltlt 1) is no longer valid in strong non-ideality conditions (Г
~ 1)
It is equivalent to additional effective electron-ion repulsion(in comparison with ordinary one-parametric Coulomb corrections depending on non-ideality parameter only
FNkT = f(Г)
Experimental data Theoretical models
(comparison)
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
Quasi‐isochoric behavior of nitrogen Hugoniot
‐
Mochalov
M Zhernokletov
M et al
JETP
137
(2010) ‐
Trunin
R Boriskov
G et alJETP Letters
88
(2008)
15 20 25 30 35 400
100
200
300
ExperimentsTrunin et al 2008Mochalov et al 2010
P GPa
gcm3
lim
Check of theoretical models
SAHA
CCM
Ross ampRogers
CCM ndash
Compressible Covolume
Model(A Medvedev
amp
VKopyshev)
SAHA‐code (V Gryaznov amp IIosilevskiy)
ρHug
asymp
33 plusmn
01
gcm390
lt
PHug
lt 330
GPa
NN
22 NN‐‐polymerpolymer
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
equiv
V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost
linear function of pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
Reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal Energy
Pressure (Hugonoit)
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
Blue curve
ndash
internal energy calculated via plasma model(code SAHA
Gryaznov Iosilevskiy)
SAHA
Hugoniot
~ ρ
asymp
const (33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
ρ
asymp33 plusmn01
gcc90
lt
P lt 330
GPa
NB
Quasi‐linear behavior of
E(p)
at ρ
=
constThermodynamics of shock compressed nitrogen
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
00
01
02
03
04
05
06
07
08
09
10 Mochalov et al PHug (Trunin et al) + T (EOSCCM) PHug (Trunin et al) + T (EOSSAHA)
xN+
xi
xN2
P GPa
T k
K
Tr
Tr
Plasma
Temperature of shock compressed nitrogen
CP()
General P‐T
diagram
Quasi‐linear behavior of
T(p)
at ρ
=
const
SAHA
‐
Experiment Mochalov
M et al
JETF
137
(2010)Nellis
W Radovsky
H et al J Chem Phys 94
(1991)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
Electroconductivity
of shock compressed nitrogen
20 25 30 351E-3
001
01
1
10
100
1000
C E B E 28061 B 29062
Con
duct
ivity
1
cm
Density gcc
Electroconductivity
of shock compressed nitrogen
Ternovoi
V et al (email ‐
30052010)
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1
P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
‐
Experiment Mochalov
M et al
JETF
137
(2010)
Quasi‐isentropic Plane Compression of Matter at Megabar
Pressures by Using of a Layered
System to Diminish First Shock Wave IntensityTernovoi
V Pyalling
A Filimonovet
A (052010) Summary and conclusion
Explosive driven quasi‐isentropic compression generators were proposed for matter investigation in
the megabar
pressure region Results of the first experiments on quasi‐isentropic compression of
liquid nitrogen are presented It was shown that pressure ionization
of nitrogen proceeds at
densities
from 315 to 34 gcc
at a temperature
of about 3000
K
Diminishing of temperature growth
was measured during onset of nitrogen electrical conductivity
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
‐
Mochalov
et al
JETP (2010)
0 100 200 3000
10
20
30
40
50
60
70
80
P GPa
T kK 4
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
Compressibility factor
(PVRT)
is almost
constant
on nitrogen isochore
What does it mean
ρ
asymp
33 plusmn01
gcc
(90
lt
P lt 330
GPa)
PVRTIdeal gas N2 Z= 05Ideal gas N
Z= 10
Id gas N+ + e Z= 20
Temperature is close to be linear function of pressure+
isochoric behavior of nitrogen Hugoniot
NB
Initial stateρ0
= 081
0 100 200 3000
10
20
30
40
50
60
70
80
P GPa
T kK 4
Сv
equiv
(partEpartT)v
asymp
const
asymp
20 (JgK)
ρ
asymp33 plusmn01
gcc
(90
lt
P lt 330
GPa)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
Internal energy ~ linear function on temperature at isochoreHigh-temperature part of nitrogen Hugoniot
Isochoric heat capacity
(CV
)
is almost constant
on nitrogen isochore
What does it mean
СV RN
asymp
35 NB
HugoniotHugoniot
0 100 200 3000
10
20
30
40
50
60
70
80
P GPa
T kK 4
γv
equiv
(vkB
)
(partppartT)v
asymp
const
asymp
ρ
asymp
33 plusmn01
gcc (90
lt
P lt 330
GPa)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
Constancy of Gruumlneizen parameter and Heat capacity at isochore
Gr
asymp
const
+
CV
asymp
const
thermal pressure coefficient γv
asymp
const
(partppartT)v
asymp
454 GPaK NB
HugoniotHugoniot
Thermodynamics of shock compressed nitrogen
ρ
asymp
33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
Mochalov
M Zhernokletov
M et alJETF
137 77
(2010) Trunin
R Boriskov
G Bykov
A Medvedev
AJETF Letters
88 220 (2008)
Expected behavior of nitrogen HugoniotМRoss amp FRogers
ACTEX(Rogers)
Interpolation(σmax
asymp
53)Experiments
New experiments vs
expected behavior of
nitrogen HugoniotМRoss amp FRogers
ACTEX(Rogers)
Interpolation(σmax
asymp
53)N‐polimer
N2Experiments
New experiments(σmax
asymp
41)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
New experiments are
in strong contradiction with expected behavior of
nitrogen Hugoniot
NB
Nitrogen Hugoniot
problem in plasma state ndash what do we need
In last experimentson deuterium
compression Pmax
asymp
50
Mbar(see Mochalov
et al NPP‐2011)(Mochalov
et al JETP Lett 2010)
NB
TheoryAb
initio
RPIMC DPIMCDFTMD WPMDChemical models
SAHA‐SSAHA‐N
(Gryaznov et al)WZ‐cell modelsTF TFC MHFShellip
Wide‐range EOS‐s
IPCP RASJIHT RASCCM (Sarov)
New experiments(σmax
asymp
41)
New experiments
‐Shock waves
-
Isentropic Compression‐
Heavy Ion Beams‐
Laser Heating etc etc
Interpolation(σmax
asymp
53)
ACTEX(Rogers)
Experiments
Nitrogen Hugoniot(comes trough polymeric phase )
ACTEX(Rogers)
Polymeric stateis expected between
molecular and plasma
regions (see below)
NB
N‐polymerN2
Experiments
THEORYAb
initio
RPIMC DPIMCDFTMD WPMDChem modelsSAHA‐SSAHA‐N
WZ‐cell modelsTFC MHFS
Wide‐range EOS
CCM (Sarov)
New experiments(σmax
asymp
41)
New experiments
‐
Shock waves
‐
Heavy Ion Beams‐
Laser Heating etc etc
N‐plasma
figure fromB Boates S Bonev Phys Rev Lett
102
(2009)
Ab initio calculations
‐
DFTMD
MolecularPolymeric
Critical point
CrossoverCrossover
11stst
order PTorder PT
MeltingMelting
Molecularfluid
Dissociated fluid
Fluidndashfluid
phase transitionin hydrogen [] ()
DFTMD
Scandolo
S PNAS
100 (2003)
Bonev S Militzer B Galli G PRB
69 (2004) WPMD
Jakob
B et al PRE
(2007) DFTMD Morales M et al PNAS
107 (2010)
DFTMD Lorenzen
W et al PRB
(2010)
Figure from
Giulia Galli SCCS-2005
Moscow= = = =
with additionsMorales et al 2010
andLorensen et al 2010
Morales et al
2010
Lorenzen
et al
2010
Ab initio calculations
‐
DFTMD
Experiment ndash single shock
compression ndash
reflected shock
compressionRadousky Nellis amp Ross et al Phys Rev Lett 57
(1986)Nellis Radousky
amp Hamilton et alJ Chem Phys 94
(1991)
0 50 100 150 200 250 3000
10
Tr Tr
CP
P GPa
T 103 K
Nitrogen phase diagram in the region of polymerizationPressure ndash temperature
melting (extrapolation)
HugoniotPlasma Model (SAHA‐code)
Yakubliquid
solidN2 N‐polimer
Theoretical models
estimation of polymer‐molecule
boundary in liquid nitrogen
(ЕYakub
ndash
1993) estimation of polymer‐molecule
boundary in solid nitrogen
(LYakub
ndash
1993)CP
ndash
critical point of 1st
order phase
transition polymer‐molecule
(ЕYakub
ndash
1993) ndash
triple point of 1st
order phase transition
polymer‐molecule
(Е amp L Yakub
ndash
1993)ЕS Yakub Low Temp Phys
20
579 (1994)LN Yakub Low Temp Phys
19 531 (1993)
estimation of polymer‐molecule bounda‐
ry
in liquid nitrogen (Ross amp Rogers
ndash
2006)MRoss
amp
FRogers Phys Rev
B 74 (2006)Ab
initio calculations DFTMD
ndash
calculation of of
polymer‐‐
molecule boundary in liquid nitrogen
(SBonev
et al ndash
2009)
the same as ldquosmoothedrdquo
phase transitionB Boates
amp
S Bonev Phys Rev Lett
102
(2009)
Gr
gt 0
Gr
lt 0 ndash domains of positive and negative sign of Gruumlneisen
coefficient
Gr
equiv
V(partPpartE)V
hypothetical boundary between polymeric and non‐ideal plasma states
(1st‐order phase transition or continuous )
melting
N2
N‐polimer
Gr
gt 0
Gr
lt 0
N‐plasma
Gr
gt 0
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
‐
Mochalov
M Zhernokletov
M et al
JETP
137 77
(2010) ‐
Trunin
R Boriskov
G Bykov
A Medvedev
A
JETP Letters
88 220 (2008)
Phase Diagram of Dense Nitrogen(summary)
N2
Npolimer
boundaryYakub Ross amp
Rogers etc
HypotheticalPressure Ionizationfrom N‐polymer
to N‐plasma
1st‐order phase transition
Critical point(s)
Domain
Gr
lt 0
Topology of theboundary
Gr
= 0
Pre‐compressed gaseous N2
Iso‐S
N2
N‐polimer
N‐plasma
Gr
gt 0
Gr
gt 0
Gr
lt 0
New experiments
‐
Shock waves‐ Iso‐S
Compression‐ Heavy Ion Beams‐
Laser Heating etc etc
THEORY Ab
initioRPIMC DPIMC
DFTMDChem modelsSAHA‐N
WZ‐cell modelsTFC MHFS
Wide‐range EOSEOS (IPCP
RAS)EOS (JIHT
RAS)CCM (Sarov)
Commentsmicrophysics
Simple molecules H2
N2
L = 074 A L = 11 A
D = 29 A D = 37 A
Triple covalent bond De
= 98 eV
(49 eVatom)
Single covalent bond De
= 30 eV
(45 eVatom)
L = 14 A
Figures after
Eugene Yakub ldquoNon‐simple
problems for simple moleculesrdquoFAIR‐Russia School laquoPhysics of high energy density in matterraquo
December
2009 Moscow
FZaharievAHuJHooperFZhangampTWoo PhysRev B 72214108 (2005 )
Polymeric nitrogen - structure
Eugene and Lidia Yakub Low Temp Phys 19 (1993)
Simple molecular modelsFirst estimations of molecular-polymeric transition
1 - Hugoniot2 - Phase equilibrium line
Experiment (Nellis ea 2001)3 - Single shock4 - Double shock
NN22
NN‐‐polimerpolimer
NN22
NN‐‐polimerpolimer
1st‐orderPhase transition
Critical point
Plasma model for nitrogen thermodynamics(code SAHA-N)
Shock compression of nitrogen(chemical picture)
SAHA-codeGryaznov Iosilevskiy (1970-2010)
Short range repulsionldquoSoft Spheresrdquo
approximation (DYoung)
modified for mixture
of soft spheres with different radii
ndash
shift of dissociation level
N
N+ + endash Ze
e
rcA
iA+
A+
i
Coulomb interactionModified pseudopotential
model
for partially ionized plasma(I
Iosilevskiy 1980-2010)
Equilibrium
compositionN2
N N+ e N2+ Nndash
Key parameter
ndash
ratio of intrinsic volumes molecule atom ion
R(N)
R(N2
)
= 063-
in accordance with recommendations of
ldquoAtom-atomic
approximationrdquo
of EYakub LT 1993
Basic points-
All assumption are provided at micro-level-
Input Choice of Фie
Фii
and Фее
pseudopotentials - Input Approximations for binary correlation functions - Strong correlation of the pseudopotentials
for ldquofreerdquocharges and upper energy level for partition functionsfor bound states
- Priority for general equalities (normalizing conditions)valid independently on degree of non-ideality
- Non-ideality corrections through the correlationfunctions and general equalities valid for Coulombinteraction
NN22
harrharr 2N2N NN22
++
harrharr NN ++
NN++ NNndashharrharr NN ++
eendash
[ ( ) ( )] 1n F r F r d r
Coulomb Corrections for Free Charge Subsystem
Modified Pseudopotential Approximation ()
Bound and free states of electron‐ionic pair
Effective electro-ionic potential (in Glaubermanrsquos form (1955))
2i
ie ( ) 1 e rZ err
( )
()
Iosilevskiy I High Temp 18
(1980) in ldquoEncyclopedia
of Low‐T Plasmardquo
(Suppl) Moscow FIZMATLIT 2004 pp 349
The form of i-i i-e e-e binary correlation functions-
laquoringraquo
(Debye) approximation with potential
Фie
(r)guarantee correct properties in the limit
of weak non-ideality
(Г
ltlt 1)
Binary i‐i i‐e e‐e
correlation functions
ldquoZero and second momentrdquo conditions (Stillinger amp Lovett)2
2[ ( ) ( )] 3D
rn F r F r dr
r
0e e sh ( ) 1 1 e
pr qrr
abrF r A
r r
Thermodynamic condition for the depth of i-e pseudopotentialand amplitude of electron-ionic correlation function
0 ln [ (0) ]ie ei e iF
Positive sign of all correlation functions Fab
(r) gt 0
F r Ae e
re
sh rrab
pr qrr( )
1 1 0
Pseudopotentials
U
= UKin
+ UPot
3PV
= 2UKin + UPot
Homogeneity of Coulomb potential
U Vn F F dpot coul ( ) r
U Vn F F dei ii 2 ( ) r
)2()2(3 potkinpot UUUUPV
2 2i i
ie ie1 e( ) (1 e (0) ~
rrZ e Z er
r r
( ))
Correlation Functions
Total Energy correction
Potential Energy Correction
-
UPot
Pressure Correction
-
P
i e i eN N U ( ) 1
Approximate relation between Coulomb corrections for chemical potential and energy
(
UN)
NB
Thermodynamic contributions inmodified pseudopotential model for Coulomb corrections
Positive shift in average kinetic energy due to non-ideality of free charges subsystem Ukin = 3PV ndash
U
Well-known relation between pressure and energy corrections for free charges subsystemU = 3PV
which is valid at weak non-ideality (Г
ltlt 1) is no longer valid in strong non-ideality conditions (Г
~ 1)
It is equivalent to additional effective electron-ion repulsion(in comparison with ordinary one-parametric Coulomb corrections depending on non-ideality parameter only
FNkT = f(Г)
Experimental data Theoretical models
(comparison)
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
Quasi‐isochoric behavior of nitrogen Hugoniot
‐
Mochalov
M Zhernokletov
M et al
JETP
137
(2010) ‐
Trunin
R Boriskov
G et alJETP Letters
88
(2008)
15 20 25 30 35 400
100
200
300
ExperimentsTrunin et al 2008Mochalov et al 2010
P GPa
gcm3
lim
Check of theoretical models
SAHA
CCM
Ross ampRogers
CCM ndash
Compressible Covolume
Model(A Medvedev
amp
VKopyshev)
SAHA‐code (V Gryaznov amp IIosilevskiy)
ρHug
asymp
33 plusmn
01
gcm390
lt
PHug
lt 330
GPa
NN
22 NN‐‐polymerpolymer
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
equiv
V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost
linear function of pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
Reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal Energy
Pressure (Hugonoit)
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
Blue curve
ndash
internal energy calculated via plasma model(code SAHA
Gryaznov Iosilevskiy)
SAHA
Hugoniot
~ ρ
asymp
const (33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
ρ
asymp33 plusmn01
gcc90
lt
P lt 330
GPa
NB
Quasi‐linear behavior of
E(p)
at ρ
=
constThermodynamics of shock compressed nitrogen
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
00
01
02
03
04
05
06
07
08
09
10 Mochalov et al PHug (Trunin et al) + T (EOSCCM) PHug (Trunin et al) + T (EOSSAHA)
xN+
xi
xN2
P GPa
T k
K
Tr
Tr
Plasma
Temperature of shock compressed nitrogen
CP()
General P‐T
diagram
Quasi‐linear behavior of
T(p)
at ρ
=
const
SAHA
‐
Experiment Mochalov
M et al
JETF
137
(2010)Nellis
W Radovsky
H et al J Chem Phys 94
(1991)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
Electroconductivity
of shock compressed nitrogen
20 25 30 351E-3
001
01
1
10
100
1000
C E B E 28061 B 29062
Con
duct
ivity
1
cm
Density gcc
Electroconductivity
of shock compressed nitrogen
Ternovoi
V et al (email ‐
30052010)
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1
P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
‐
Experiment Mochalov
M et al
JETF
137
(2010)
Quasi‐isentropic Plane Compression of Matter at Megabar
Pressures by Using of a Layered
System to Diminish First Shock Wave IntensityTernovoi
V Pyalling
A Filimonovet
A (052010) Summary and conclusion
Explosive driven quasi‐isentropic compression generators were proposed for matter investigation in
the megabar
pressure region Results of the first experiments on quasi‐isentropic compression of
liquid nitrogen are presented It was shown that pressure ionization
of nitrogen proceeds at
densities
from 315 to 34 gcc
at a temperature
of about 3000
K
Diminishing of temperature growth
was measured during onset of nitrogen electrical conductivity
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
0 100 200 3000
10
20
30
40
50
60
70
80
P GPa
T kK 4
Сv
equiv
(partEpartT)v
asymp
const
asymp
20 (JgK)
ρ
asymp33 plusmn01
gcc
(90
lt
P lt 330
GPa)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
Internal energy ~ linear function on temperature at isochoreHigh-temperature part of nitrogen Hugoniot
Isochoric heat capacity
(CV
)
is almost constant
on nitrogen isochore
What does it mean
СV RN
asymp
35 NB
HugoniotHugoniot
0 100 200 3000
10
20
30
40
50
60
70
80
P GPa
T kK 4
γv
equiv
(vkB
)
(partppartT)v
asymp
const
asymp
ρ
asymp
33 plusmn01
gcc (90
lt
P lt 330
GPa)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
Constancy of Gruumlneizen parameter and Heat capacity at isochore
Gr
asymp
const
+
CV
asymp
const
thermal pressure coefficient γv
asymp
const
(partppartT)v
asymp
454 GPaK NB
HugoniotHugoniot
Thermodynamics of shock compressed nitrogen
ρ
asymp
33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
Mochalov
M Zhernokletov
M et alJETF
137 77
(2010) Trunin
R Boriskov
G Bykov
A Medvedev
AJETF Letters
88 220 (2008)
Expected behavior of nitrogen HugoniotМRoss amp FRogers
ACTEX(Rogers)
Interpolation(σmax
asymp
53)Experiments
New experiments vs
expected behavior of
nitrogen HugoniotМRoss amp FRogers
ACTEX(Rogers)
Interpolation(σmax
asymp
53)N‐polimer
N2Experiments
New experiments(σmax
asymp
41)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
New experiments are
in strong contradiction with expected behavior of
nitrogen Hugoniot
NB
Nitrogen Hugoniot
problem in plasma state ndash what do we need
In last experimentson deuterium
compression Pmax
asymp
50
Mbar(see Mochalov
et al NPP‐2011)(Mochalov
et al JETP Lett 2010)
NB
TheoryAb
initio
RPIMC DPIMCDFTMD WPMDChemical models
SAHA‐SSAHA‐N
(Gryaznov et al)WZ‐cell modelsTF TFC MHFShellip
Wide‐range EOS‐s
IPCP RASJIHT RASCCM (Sarov)
New experiments(σmax
asymp
41)
New experiments
‐Shock waves
-
Isentropic Compression‐
Heavy Ion Beams‐
Laser Heating etc etc
Interpolation(σmax
asymp
53)
ACTEX(Rogers)
Experiments
Nitrogen Hugoniot(comes trough polymeric phase )
ACTEX(Rogers)
Polymeric stateis expected between
molecular and plasma
regions (see below)
NB
N‐polymerN2
Experiments
THEORYAb
initio
RPIMC DPIMCDFTMD WPMDChem modelsSAHA‐SSAHA‐N
WZ‐cell modelsTFC MHFS
Wide‐range EOS
CCM (Sarov)
New experiments(σmax
asymp
41)
New experiments
‐
Shock waves
‐
Heavy Ion Beams‐
Laser Heating etc etc
N‐plasma
figure fromB Boates S Bonev Phys Rev Lett
102
(2009)
Ab initio calculations
‐
DFTMD
MolecularPolymeric
Critical point
CrossoverCrossover
11stst
order PTorder PT
MeltingMelting
Molecularfluid
Dissociated fluid
Fluidndashfluid
phase transitionin hydrogen [] ()
DFTMD
Scandolo
S PNAS
100 (2003)
Bonev S Militzer B Galli G PRB
69 (2004) WPMD
Jakob
B et al PRE
(2007) DFTMD Morales M et al PNAS
107 (2010)
DFTMD Lorenzen
W et al PRB
(2010)
Figure from
Giulia Galli SCCS-2005
Moscow= = = =
with additionsMorales et al 2010
andLorensen et al 2010
Morales et al
2010
Lorenzen
et al
2010
Ab initio calculations
‐
DFTMD
Experiment ndash single shock
compression ndash
reflected shock
compressionRadousky Nellis amp Ross et al Phys Rev Lett 57
(1986)Nellis Radousky
amp Hamilton et alJ Chem Phys 94
(1991)
0 50 100 150 200 250 3000
10
Tr Tr
CP
P GPa
T 103 K
Nitrogen phase diagram in the region of polymerizationPressure ndash temperature
melting (extrapolation)
HugoniotPlasma Model (SAHA‐code)
Yakubliquid
solidN2 N‐polimer
Theoretical models
estimation of polymer‐molecule
boundary in liquid nitrogen
(ЕYakub
ndash
1993) estimation of polymer‐molecule
boundary in solid nitrogen
(LYakub
ndash
1993)CP
ndash
critical point of 1st
order phase
transition polymer‐molecule
(ЕYakub
ndash
1993) ndash
triple point of 1st
order phase transition
polymer‐molecule
(Е amp L Yakub
ndash
1993)ЕS Yakub Low Temp Phys
20
579 (1994)LN Yakub Low Temp Phys
19 531 (1993)
estimation of polymer‐molecule bounda‐
ry
in liquid nitrogen (Ross amp Rogers
ndash
2006)MRoss
amp
FRogers Phys Rev
B 74 (2006)Ab
initio calculations DFTMD
ndash
calculation of of
polymer‐‐
molecule boundary in liquid nitrogen
(SBonev
et al ndash
2009)
the same as ldquosmoothedrdquo
phase transitionB Boates
amp
S Bonev Phys Rev Lett
102
(2009)
Gr
gt 0
Gr
lt 0 ndash domains of positive and negative sign of Gruumlneisen
coefficient
Gr
equiv
V(partPpartE)V
hypothetical boundary between polymeric and non‐ideal plasma states
(1st‐order phase transition or continuous )
melting
N2
N‐polimer
Gr
gt 0
Gr
lt 0
N‐plasma
Gr
gt 0
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
‐
Mochalov
M Zhernokletov
M et al
JETP
137 77
(2010) ‐
Trunin
R Boriskov
G Bykov
A Medvedev
A
JETP Letters
88 220 (2008)
Phase Diagram of Dense Nitrogen(summary)
N2
Npolimer
boundaryYakub Ross amp
Rogers etc
HypotheticalPressure Ionizationfrom N‐polymer
to N‐plasma
1st‐order phase transition
Critical point(s)
Domain
Gr
lt 0
Topology of theboundary
Gr
= 0
Pre‐compressed gaseous N2
Iso‐S
N2
N‐polimer
N‐plasma
Gr
gt 0
Gr
gt 0
Gr
lt 0
New experiments
‐
Shock waves‐ Iso‐S
Compression‐ Heavy Ion Beams‐
Laser Heating etc etc
THEORY Ab
initioRPIMC DPIMC
DFTMDChem modelsSAHA‐N
WZ‐cell modelsTFC MHFS
Wide‐range EOSEOS (IPCP
RAS)EOS (JIHT
RAS)CCM (Sarov)
Commentsmicrophysics
Simple molecules H2
N2
L = 074 A L = 11 A
D = 29 A D = 37 A
Triple covalent bond De
= 98 eV
(49 eVatom)
Single covalent bond De
= 30 eV
(45 eVatom)
L = 14 A
Figures after
Eugene Yakub ldquoNon‐simple
problems for simple moleculesrdquoFAIR‐Russia School laquoPhysics of high energy density in matterraquo
December
2009 Moscow
FZaharievAHuJHooperFZhangampTWoo PhysRev B 72214108 (2005 )
Polymeric nitrogen - structure
Eugene and Lidia Yakub Low Temp Phys 19 (1993)
Simple molecular modelsFirst estimations of molecular-polymeric transition
1 - Hugoniot2 - Phase equilibrium line
Experiment (Nellis ea 2001)3 - Single shock4 - Double shock
NN22
NN‐‐polimerpolimer
NN22
NN‐‐polimerpolimer
1st‐orderPhase transition
Critical point
Plasma model for nitrogen thermodynamics(code SAHA-N)
Shock compression of nitrogen(chemical picture)
SAHA-codeGryaznov Iosilevskiy (1970-2010)
Short range repulsionldquoSoft Spheresrdquo
approximation (DYoung)
modified for mixture
of soft spheres with different radii
ndash
shift of dissociation level
N
N+ + endash Ze
e
rcA
iA+
A+
i
Coulomb interactionModified pseudopotential
model
for partially ionized plasma(I
Iosilevskiy 1980-2010)
Equilibrium
compositionN2
N N+ e N2+ Nndash
Key parameter
ndash
ratio of intrinsic volumes molecule atom ion
R(N)
R(N2
)
= 063-
in accordance with recommendations of
ldquoAtom-atomic
approximationrdquo
of EYakub LT 1993
Basic points-
All assumption are provided at micro-level-
Input Choice of Фie
Фii
and Фее
pseudopotentials - Input Approximations for binary correlation functions - Strong correlation of the pseudopotentials
for ldquofreerdquocharges and upper energy level for partition functionsfor bound states
- Priority for general equalities (normalizing conditions)valid independently on degree of non-ideality
- Non-ideality corrections through the correlationfunctions and general equalities valid for Coulombinteraction
NN22
harrharr 2N2N NN22
++
harrharr NN ++
NN++ NNndashharrharr NN ++
eendash
[ ( ) ( )] 1n F r F r d r
Coulomb Corrections for Free Charge Subsystem
Modified Pseudopotential Approximation ()
Bound and free states of electron‐ionic pair
Effective electro-ionic potential (in Glaubermanrsquos form (1955))
2i
ie ( ) 1 e rZ err
( )
()
Iosilevskiy I High Temp 18
(1980) in ldquoEncyclopedia
of Low‐T Plasmardquo
(Suppl) Moscow FIZMATLIT 2004 pp 349
The form of i-i i-e e-e binary correlation functions-
laquoringraquo
(Debye) approximation with potential
Фie
(r)guarantee correct properties in the limit
of weak non-ideality
(Г
ltlt 1)
Binary i‐i i‐e e‐e
correlation functions
ldquoZero and second momentrdquo conditions (Stillinger amp Lovett)2
2[ ( ) ( )] 3D
rn F r F r dr
r
0e e sh ( ) 1 1 e
pr qrr
abrF r A
r r
Thermodynamic condition for the depth of i-e pseudopotentialand amplitude of electron-ionic correlation function
0 ln [ (0) ]ie ei e iF
Positive sign of all correlation functions Fab
(r) gt 0
F r Ae e
re
sh rrab
pr qrr( )
1 1 0
Pseudopotentials
U
= UKin
+ UPot
3PV
= 2UKin + UPot
Homogeneity of Coulomb potential
U Vn F F dpot coul ( ) r
U Vn F F dei ii 2 ( ) r
)2()2(3 potkinpot UUUUPV
2 2i i
ie ie1 e( ) (1 e (0) ~
rrZ e Z er
r r
( ))
Correlation Functions
Total Energy correction
Potential Energy Correction
-
UPot
Pressure Correction
-
P
i e i eN N U ( ) 1
Approximate relation between Coulomb corrections for chemical potential and energy
(
UN)
NB
Thermodynamic contributions inmodified pseudopotential model for Coulomb corrections
Positive shift in average kinetic energy due to non-ideality of free charges subsystem Ukin = 3PV ndash
U
Well-known relation between pressure and energy corrections for free charges subsystemU = 3PV
which is valid at weak non-ideality (Г
ltlt 1) is no longer valid in strong non-ideality conditions (Г
~ 1)
It is equivalent to additional effective electron-ion repulsion(in comparison with ordinary one-parametric Coulomb corrections depending on non-ideality parameter only
FNkT = f(Г)
Experimental data Theoretical models
(comparison)
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
Quasi‐isochoric behavior of nitrogen Hugoniot
‐
Mochalov
M Zhernokletov
M et al
JETP
137
(2010) ‐
Trunin
R Boriskov
G et alJETP Letters
88
(2008)
15 20 25 30 35 400
100
200
300
ExperimentsTrunin et al 2008Mochalov et al 2010
P GPa
gcm3
lim
Check of theoretical models
SAHA
CCM
Ross ampRogers
CCM ndash
Compressible Covolume
Model(A Medvedev
amp
VKopyshev)
SAHA‐code (V Gryaznov amp IIosilevskiy)
ρHug
asymp
33 plusmn
01
gcm390
lt
PHug
lt 330
GPa
NN
22 NN‐‐polymerpolymer
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
equiv
V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost
linear function of pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
Reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal Energy
Pressure (Hugonoit)
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
Blue curve
ndash
internal energy calculated via plasma model(code SAHA
Gryaznov Iosilevskiy)
SAHA
Hugoniot
~ ρ
asymp
const (33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
ρ
asymp33 plusmn01
gcc90
lt
P lt 330
GPa
NB
Quasi‐linear behavior of
E(p)
at ρ
=
constThermodynamics of shock compressed nitrogen
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
00
01
02
03
04
05
06
07
08
09
10 Mochalov et al PHug (Trunin et al) + T (EOSCCM) PHug (Trunin et al) + T (EOSSAHA)
xN+
xi
xN2
P GPa
T k
K
Tr
Tr
Plasma
Temperature of shock compressed nitrogen
CP()
General P‐T
diagram
Quasi‐linear behavior of
T(p)
at ρ
=
const
SAHA
‐
Experiment Mochalov
M et al
JETF
137
(2010)Nellis
W Radovsky
H et al J Chem Phys 94
(1991)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
Electroconductivity
of shock compressed nitrogen
20 25 30 351E-3
001
01
1
10
100
1000
C E B E 28061 B 29062
Con
duct
ivity
1
cm
Density gcc
Electroconductivity
of shock compressed nitrogen
Ternovoi
V et al (email ‐
30052010)
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1
P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
‐
Experiment Mochalov
M et al
JETF
137
(2010)
Quasi‐isentropic Plane Compression of Matter at Megabar
Pressures by Using of a Layered
System to Diminish First Shock Wave IntensityTernovoi
V Pyalling
A Filimonovet
A (052010) Summary and conclusion
Explosive driven quasi‐isentropic compression generators were proposed for matter investigation in
the megabar
pressure region Results of the first experiments on quasi‐isentropic compression of
liquid nitrogen are presented It was shown that pressure ionization
of nitrogen proceeds at
densities
from 315 to 34 gcc
at a temperature
of about 3000
K
Diminishing of temperature growth
was measured during onset of nitrogen electrical conductivity
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
0 100 200 3000
10
20
30
40
50
60
70
80
P GPa
T kK 4
γv
equiv
(vkB
)
(partppartT)v
asymp
const
asymp
ρ
asymp
33 plusmn01
gcc (90
lt
P lt 330
GPa)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
Constancy of Gruumlneizen parameter and Heat capacity at isochore
Gr
asymp
const
+
CV
asymp
const
thermal pressure coefficient γv
asymp
const
(partppartT)v
asymp
454 GPaK NB
HugoniotHugoniot
Thermodynamics of shock compressed nitrogen
ρ
asymp
33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
Mochalov
M Zhernokletov
M et alJETF
137 77
(2010) Trunin
R Boriskov
G Bykov
A Medvedev
AJETF Letters
88 220 (2008)
Expected behavior of nitrogen HugoniotМRoss amp FRogers
ACTEX(Rogers)
Interpolation(σmax
asymp
53)Experiments
New experiments vs
expected behavior of
nitrogen HugoniotМRoss amp FRogers
ACTEX(Rogers)
Interpolation(σmax
asymp
53)N‐polimer
N2Experiments
New experiments(σmax
asymp
41)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
New experiments are
in strong contradiction with expected behavior of
nitrogen Hugoniot
NB
Nitrogen Hugoniot
problem in plasma state ndash what do we need
In last experimentson deuterium
compression Pmax
asymp
50
Mbar(see Mochalov
et al NPP‐2011)(Mochalov
et al JETP Lett 2010)
NB
TheoryAb
initio
RPIMC DPIMCDFTMD WPMDChemical models
SAHA‐SSAHA‐N
(Gryaznov et al)WZ‐cell modelsTF TFC MHFShellip
Wide‐range EOS‐s
IPCP RASJIHT RASCCM (Sarov)
New experiments(σmax
asymp
41)
New experiments
‐Shock waves
-
Isentropic Compression‐
Heavy Ion Beams‐
Laser Heating etc etc
Interpolation(σmax
asymp
53)
ACTEX(Rogers)
Experiments
Nitrogen Hugoniot(comes trough polymeric phase )
ACTEX(Rogers)
Polymeric stateis expected between
molecular and plasma
regions (see below)
NB
N‐polymerN2
Experiments
THEORYAb
initio
RPIMC DPIMCDFTMD WPMDChem modelsSAHA‐SSAHA‐N
WZ‐cell modelsTFC MHFS
Wide‐range EOS
CCM (Sarov)
New experiments(σmax
asymp
41)
New experiments
‐
Shock waves
‐
Heavy Ion Beams‐
Laser Heating etc etc
N‐plasma
figure fromB Boates S Bonev Phys Rev Lett
102
(2009)
Ab initio calculations
‐
DFTMD
MolecularPolymeric
Critical point
CrossoverCrossover
11stst
order PTorder PT
MeltingMelting
Molecularfluid
Dissociated fluid
Fluidndashfluid
phase transitionin hydrogen [] ()
DFTMD
Scandolo
S PNAS
100 (2003)
Bonev S Militzer B Galli G PRB
69 (2004) WPMD
Jakob
B et al PRE
(2007) DFTMD Morales M et al PNAS
107 (2010)
DFTMD Lorenzen
W et al PRB
(2010)
Figure from
Giulia Galli SCCS-2005
Moscow= = = =
with additionsMorales et al 2010
andLorensen et al 2010
Morales et al
2010
Lorenzen
et al
2010
Ab initio calculations
‐
DFTMD
Experiment ndash single shock
compression ndash
reflected shock
compressionRadousky Nellis amp Ross et al Phys Rev Lett 57
(1986)Nellis Radousky
amp Hamilton et alJ Chem Phys 94
(1991)
0 50 100 150 200 250 3000
10
Tr Tr
CP
P GPa
T 103 K
Nitrogen phase diagram in the region of polymerizationPressure ndash temperature
melting (extrapolation)
HugoniotPlasma Model (SAHA‐code)
Yakubliquid
solidN2 N‐polimer
Theoretical models
estimation of polymer‐molecule
boundary in liquid nitrogen
(ЕYakub
ndash
1993) estimation of polymer‐molecule
boundary in solid nitrogen
(LYakub
ndash
1993)CP
ndash
critical point of 1st
order phase
transition polymer‐molecule
(ЕYakub
ndash
1993) ndash
triple point of 1st
order phase transition
polymer‐molecule
(Е amp L Yakub
ndash
1993)ЕS Yakub Low Temp Phys
20
579 (1994)LN Yakub Low Temp Phys
19 531 (1993)
estimation of polymer‐molecule bounda‐
ry
in liquid nitrogen (Ross amp Rogers
ndash
2006)MRoss
amp
FRogers Phys Rev
B 74 (2006)Ab
initio calculations DFTMD
ndash
calculation of of
polymer‐‐
molecule boundary in liquid nitrogen
(SBonev
et al ndash
2009)
the same as ldquosmoothedrdquo
phase transitionB Boates
amp
S Bonev Phys Rev Lett
102
(2009)
Gr
gt 0
Gr
lt 0 ndash domains of positive and negative sign of Gruumlneisen
coefficient
Gr
equiv
V(partPpartE)V
hypothetical boundary between polymeric and non‐ideal plasma states
(1st‐order phase transition or continuous )
melting
N2
N‐polimer
Gr
gt 0
Gr
lt 0
N‐plasma
Gr
gt 0
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
‐
Mochalov
M Zhernokletov
M et al
JETP
137 77
(2010) ‐
Trunin
R Boriskov
G Bykov
A Medvedev
A
JETP Letters
88 220 (2008)
Phase Diagram of Dense Nitrogen(summary)
N2
Npolimer
boundaryYakub Ross amp
Rogers etc
HypotheticalPressure Ionizationfrom N‐polymer
to N‐plasma
1st‐order phase transition
Critical point(s)
Domain
Gr
lt 0
Topology of theboundary
Gr
= 0
Pre‐compressed gaseous N2
Iso‐S
N2
N‐polimer
N‐plasma
Gr
gt 0
Gr
gt 0
Gr
lt 0
New experiments
‐
Shock waves‐ Iso‐S
Compression‐ Heavy Ion Beams‐
Laser Heating etc etc
THEORY Ab
initioRPIMC DPIMC
DFTMDChem modelsSAHA‐N
WZ‐cell modelsTFC MHFS
Wide‐range EOSEOS (IPCP
RAS)EOS (JIHT
RAS)CCM (Sarov)
Commentsmicrophysics
Simple molecules H2
N2
L = 074 A L = 11 A
D = 29 A D = 37 A
Triple covalent bond De
= 98 eV
(49 eVatom)
Single covalent bond De
= 30 eV
(45 eVatom)
L = 14 A
Figures after
Eugene Yakub ldquoNon‐simple
problems for simple moleculesrdquoFAIR‐Russia School laquoPhysics of high energy density in matterraquo
December
2009 Moscow
FZaharievAHuJHooperFZhangampTWoo PhysRev B 72214108 (2005 )
Polymeric nitrogen - structure
Eugene and Lidia Yakub Low Temp Phys 19 (1993)
Simple molecular modelsFirst estimations of molecular-polymeric transition
1 - Hugoniot2 - Phase equilibrium line
Experiment (Nellis ea 2001)3 - Single shock4 - Double shock
NN22
NN‐‐polimerpolimer
NN22
NN‐‐polimerpolimer
1st‐orderPhase transition
Critical point
Plasma model for nitrogen thermodynamics(code SAHA-N)
Shock compression of nitrogen(chemical picture)
SAHA-codeGryaznov Iosilevskiy (1970-2010)
Short range repulsionldquoSoft Spheresrdquo
approximation (DYoung)
modified for mixture
of soft spheres with different radii
ndash
shift of dissociation level
N
N+ + endash Ze
e
rcA
iA+
A+
i
Coulomb interactionModified pseudopotential
model
for partially ionized plasma(I
Iosilevskiy 1980-2010)
Equilibrium
compositionN2
N N+ e N2+ Nndash
Key parameter
ndash
ratio of intrinsic volumes molecule atom ion
R(N)
R(N2
)
= 063-
in accordance with recommendations of
ldquoAtom-atomic
approximationrdquo
of EYakub LT 1993
Basic points-
All assumption are provided at micro-level-
Input Choice of Фie
Фii
and Фее
pseudopotentials - Input Approximations for binary correlation functions - Strong correlation of the pseudopotentials
for ldquofreerdquocharges and upper energy level for partition functionsfor bound states
- Priority for general equalities (normalizing conditions)valid independently on degree of non-ideality
- Non-ideality corrections through the correlationfunctions and general equalities valid for Coulombinteraction
NN22
harrharr 2N2N NN22
++
harrharr NN ++
NN++ NNndashharrharr NN ++
eendash
[ ( ) ( )] 1n F r F r d r
Coulomb Corrections for Free Charge Subsystem
Modified Pseudopotential Approximation ()
Bound and free states of electron‐ionic pair
Effective electro-ionic potential (in Glaubermanrsquos form (1955))
2i
ie ( ) 1 e rZ err
( )
()
Iosilevskiy I High Temp 18
(1980) in ldquoEncyclopedia
of Low‐T Plasmardquo
(Suppl) Moscow FIZMATLIT 2004 pp 349
The form of i-i i-e e-e binary correlation functions-
laquoringraquo
(Debye) approximation with potential
Фie
(r)guarantee correct properties in the limit
of weak non-ideality
(Г
ltlt 1)
Binary i‐i i‐e e‐e
correlation functions
ldquoZero and second momentrdquo conditions (Stillinger amp Lovett)2
2[ ( ) ( )] 3D
rn F r F r dr
r
0e e sh ( ) 1 1 e
pr qrr
abrF r A
r r
Thermodynamic condition for the depth of i-e pseudopotentialand amplitude of electron-ionic correlation function
0 ln [ (0) ]ie ei e iF
Positive sign of all correlation functions Fab
(r) gt 0
F r Ae e
re
sh rrab
pr qrr( )
1 1 0
Pseudopotentials
U
= UKin
+ UPot
3PV
= 2UKin + UPot
Homogeneity of Coulomb potential
U Vn F F dpot coul ( ) r
U Vn F F dei ii 2 ( ) r
)2()2(3 potkinpot UUUUPV
2 2i i
ie ie1 e( ) (1 e (0) ~
rrZ e Z er
r r
( ))
Correlation Functions
Total Energy correction
Potential Energy Correction
-
UPot
Pressure Correction
-
P
i e i eN N U ( ) 1
Approximate relation between Coulomb corrections for chemical potential and energy
(
UN)
NB
Thermodynamic contributions inmodified pseudopotential model for Coulomb corrections
Positive shift in average kinetic energy due to non-ideality of free charges subsystem Ukin = 3PV ndash
U
Well-known relation between pressure and energy corrections for free charges subsystemU = 3PV
which is valid at weak non-ideality (Г
ltlt 1) is no longer valid in strong non-ideality conditions (Г
~ 1)
It is equivalent to additional effective electron-ion repulsion(in comparison with ordinary one-parametric Coulomb corrections depending on non-ideality parameter only
FNkT = f(Г)
Experimental data Theoretical models
(comparison)
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
Quasi‐isochoric behavior of nitrogen Hugoniot
‐
Mochalov
M Zhernokletov
M et al
JETP
137
(2010) ‐
Trunin
R Boriskov
G et alJETP Letters
88
(2008)
15 20 25 30 35 400
100
200
300
ExperimentsTrunin et al 2008Mochalov et al 2010
P GPa
gcm3
lim
Check of theoretical models
SAHA
CCM
Ross ampRogers
CCM ndash
Compressible Covolume
Model(A Medvedev
amp
VKopyshev)
SAHA‐code (V Gryaznov amp IIosilevskiy)
ρHug
asymp
33 plusmn
01
gcm390
lt
PHug
lt 330
GPa
NN
22 NN‐‐polymerpolymer
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
equiv
V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost
linear function of pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
Reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal Energy
Pressure (Hugonoit)
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
Blue curve
ndash
internal energy calculated via plasma model(code SAHA
Gryaznov Iosilevskiy)
SAHA
Hugoniot
~ ρ
asymp
const (33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
ρ
asymp33 plusmn01
gcc90
lt
P lt 330
GPa
NB
Quasi‐linear behavior of
E(p)
at ρ
=
constThermodynamics of shock compressed nitrogen
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
00
01
02
03
04
05
06
07
08
09
10 Mochalov et al PHug (Trunin et al) + T (EOSCCM) PHug (Trunin et al) + T (EOSSAHA)
xN+
xi
xN2
P GPa
T k
K
Tr
Tr
Plasma
Temperature of shock compressed nitrogen
CP()
General P‐T
diagram
Quasi‐linear behavior of
T(p)
at ρ
=
const
SAHA
‐
Experiment Mochalov
M et al
JETF
137
(2010)Nellis
W Radovsky
H et al J Chem Phys 94
(1991)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
Electroconductivity
of shock compressed nitrogen
20 25 30 351E-3
001
01
1
10
100
1000
C E B E 28061 B 29062
Con
duct
ivity
1
cm
Density gcc
Electroconductivity
of shock compressed nitrogen
Ternovoi
V et al (email ‐
30052010)
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1
P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
‐
Experiment Mochalov
M et al
JETF
137
(2010)
Quasi‐isentropic Plane Compression of Matter at Megabar
Pressures by Using of a Layered
System to Diminish First Shock Wave IntensityTernovoi
V Pyalling
A Filimonovet
A (052010) Summary and conclusion
Explosive driven quasi‐isentropic compression generators were proposed for matter investigation in
the megabar
pressure region Results of the first experiments on quasi‐isentropic compression of
liquid nitrogen are presented It was shown that pressure ionization
of nitrogen proceeds at
densities
from 315 to 34 gcc
at a temperature
of about 3000
K
Diminishing of temperature growth
was measured during onset of nitrogen electrical conductivity
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
Thermodynamics of shock compressed nitrogen
ρ
asymp
33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
Mochalov
M Zhernokletov
M et alJETF
137 77
(2010) Trunin
R Boriskov
G Bykov
A Medvedev
AJETF Letters
88 220 (2008)
Expected behavior of nitrogen HugoniotМRoss amp FRogers
ACTEX(Rogers)
Interpolation(σmax
asymp
53)Experiments
New experiments vs
expected behavior of
nitrogen HugoniotМRoss amp FRogers
ACTEX(Rogers)
Interpolation(σmax
asymp
53)N‐polimer
N2Experiments
New experiments(σmax
asymp
41)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
New experiments are
in strong contradiction with expected behavior of
nitrogen Hugoniot
NB
Nitrogen Hugoniot
problem in plasma state ndash what do we need
In last experimentson deuterium
compression Pmax
asymp
50
Mbar(see Mochalov
et al NPP‐2011)(Mochalov
et al JETP Lett 2010)
NB
TheoryAb
initio
RPIMC DPIMCDFTMD WPMDChemical models
SAHA‐SSAHA‐N
(Gryaznov et al)WZ‐cell modelsTF TFC MHFShellip
Wide‐range EOS‐s
IPCP RASJIHT RASCCM (Sarov)
New experiments(σmax
asymp
41)
New experiments
‐Shock waves
-
Isentropic Compression‐
Heavy Ion Beams‐
Laser Heating etc etc
Interpolation(σmax
asymp
53)
ACTEX(Rogers)
Experiments
Nitrogen Hugoniot(comes trough polymeric phase )
ACTEX(Rogers)
Polymeric stateis expected between
molecular and plasma
regions (see below)
NB
N‐polymerN2
Experiments
THEORYAb
initio
RPIMC DPIMCDFTMD WPMDChem modelsSAHA‐SSAHA‐N
WZ‐cell modelsTFC MHFS
Wide‐range EOS
CCM (Sarov)
New experiments(σmax
asymp
41)
New experiments
‐
Shock waves
‐
Heavy Ion Beams‐
Laser Heating etc etc
N‐plasma
figure fromB Boates S Bonev Phys Rev Lett
102
(2009)
Ab initio calculations
‐
DFTMD
MolecularPolymeric
Critical point
CrossoverCrossover
11stst
order PTorder PT
MeltingMelting
Molecularfluid
Dissociated fluid
Fluidndashfluid
phase transitionin hydrogen [] ()
DFTMD
Scandolo
S PNAS
100 (2003)
Bonev S Militzer B Galli G PRB
69 (2004) WPMD
Jakob
B et al PRE
(2007) DFTMD Morales M et al PNAS
107 (2010)
DFTMD Lorenzen
W et al PRB
(2010)
Figure from
Giulia Galli SCCS-2005
Moscow= = = =
with additionsMorales et al 2010
andLorensen et al 2010
Morales et al
2010
Lorenzen
et al
2010
Ab initio calculations
‐
DFTMD
Experiment ndash single shock
compression ndash
reflected shock
compressionRadousky Nellis amp Ross et al Phys Rev Lett 57
(1986)Nellis Radousky
amp Hamilton et alJ Chem Phys 94
(1991)
0 50 100 150 200 250 3000
10
Tr Tr
CP
P GPa
T 103 K
Nitrogen phase diagram in the region of polymerizationPressure ndash temperature
melting (extrapolation)
HugoniotPlasma Model (SAHA‐code)
Yakubliquid
solidN2 N‐polimer
Theoretical models
estimation of polymer‐molecule
boundary in liquid nitrogen
(ЕYakub
ndash
1993) estimation of polymer‐molecule
boundary in solid nitrogen
(LYakub
ndash
1993)CP
ndash
critical point of 1st
order phase
transition polymer‐molecule
(ЕYakub
ndash
1993) ndash
triple point of 1st
order phase transition
polymer‐molecule
(Е amp L Yakub
ndash
1993)ЕS Yakub Low Temp Phys
20
579 (1994)LN Yakub Low Temp Phys
19 531 (1993)
estimation of polymer‐molecule bounda‐
ry
in liquid nitrogen (Ross amp Rogers
ndash
2006)MRoss
amp
FRogers Phys Rev
B 74 (2006)Ab
initio calculations DFTMD
ndash
calculation of of
polymer‐‐
molecule boundary in liquid nitrogen
(SBonev
et al ndash
2009)
the same as ldquosmoothedrdquo
phase transitionB Boates
amp
S Bonev Phys Rev Lett
102
(2009)
Gr
gt 0
Gr
lt 0 ndash domains of positive and negative sign of Gruumlneisen
coefficient
Gr
equiv
V(partPpartE)V
hypothetical boundary between polymeric and non‐ideal plasma states
(1st‐order phase transition or continuous )
melting
N2
N‐polimer
Gr
gt 0
Gr
lt 0
N‐plasma
Gr
gt 0
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
‐
Mochalov
M Zhernokletov
M et al
JETP
137 77
(2010) ‐
Trunin
R Boriskov
G Bykov
A Medvedev
A
JETP Letters
88 220 (2008)
Phase Diagram of Dense Nitrogen(summary)
N2
Npolimer
boundaryYakub Ross amp
Rogers etc
HypotheticalPressure Ionizationfrom N‐polymer
to N‐plasma
1st‐order phase transition
Critical point(s)
Domain
Gr
lt 0
Topology of theboundary
Gr
= 0
Pre‐compressed gaseous N2
Iso‐S
N2
N‐polimer
N‐plasma
Gr
gt 0
Gr
gt 0
Gr
lt 0
New experiments
‐
Shock waves‐ Iso‐S
Compression‐ Heavy Ion Beams‐
Laser Heating etc etc
THEORY Ab
initioRPIMC DPIMC
DFTMDChem modelsSAHA‐N
WZ‐cell modelsTFC MHFS
Wide‐range EOSEOS (IPCP
RAS)EOS (JIHT
RAS)CCM (Sarov)
Commentsmicrophysics
Simple molecules H2
N2
L = 074 A L = 11 A
D = 29 A D = 37 A
Triple covalent bond De
= 98 eV
(49 eVatom)
Single covalent bond De
= 30 eV
(45 eVatom)
L = 14 A
Figures after
Eugene Yakub ldquoNon‐simple
problems for simple moleculesrdquoFAIR‐Russia School laquoPhysics of high energy density in matterraquo
December
2009 Moscow
FZaharievAHuJHooperFZhangampTWoo PhysRev B 72214108 (2005 )
Polymeric nitrogen - structure
Eugene and Lidia Yakub Low Temp Phys 19 (1993)
Simple molecular modelsFirst estimations of molecular-polymeric transition
1 - Hugoniot2 - Phase equilibrium line
Experiment (Nellis ea 2001)3 - Single shock4 - Double shock
NN22
NN‐‐polimerpolimer
NN22
NN‐‐polimerpolimer
1st‐orderPhase transition
Critical point
Plasma model for nitrogen thermodynamics(code SAHA-N)
Shock compression of nitrogen(chemical picture)
SAHA-codeGryaznov Iosilevskiy (1970-2010)
Short range repulsionldquoSoft Spheresrdquo
approximation (DYoung)
modified for mixture
of soft spheres with different radii
ndash
shift of dissociation level
N
N+ + endash Ze
e
rcA
iA+
A+
i
Coulomb interactionModified pseudopotential
model
for partially ionized plasma(I
Iosilevskiy 1980-2010)
Equilibrium
compositionN2
N N+ e N2+ Nndash
Key parameter
ndash
ratio of intrinsic volumes molecule atom ion
R(N)
R(N2
)
= 063-
in accordance with recommendations of
ldquoAtom-atomic
approximationrdquo
of EYakub LT 1993
Basic points-
All assumption are provided at micro-level-
Input Choice of Фie
Фii
and Фее
pseudopotentials - Input Approximations for binary correlation functions - Strong correlation of the pseudopotentials
for ldquofreerdquocharges and upper energy level for partition functionsfor bound states
- Priority for general equalities (normalizing conditions)valid independently on degree of non-ideality
- Non-ideality corrections through the correlationfunctions and general equalities valid for Coulombinteraction
NN22
harrharr 2N2N NN22
++
harrharr NN ++
NN++ NNndashharrharr NN ++
eendash
[ ( ) ( )] 1n F r F r d r
Coulomb Corrections for Free Charge Subsystem
Modified Pseudopotential Approximation ()
Bound and free states of electron‐ionic pair
Effective electro-ionic potential (in Glaubermanrsquos form (1955))
2i
ie ( ) 1 e rZ err
( )
()
Iosilevskiy I High Temp 18
(1980) in ldquoEncyclopedia
of Low‐T Plasmardquo
(Suppl) Moscow FIZMATLIT 2004 pp 349
The form of i-i i-e e-e binary correlation functions-
laquoringraquo
(Debye) approximation with potential
Фie
(r)guarantee correct properties in the limit
of weak non-ideality
(Г
ltlt 1)
Binary i‐i i‐e e‐e
correlation functions
ldquoZero and second momentrdquo conditions (Stillinger amp Lovett)2
2[ ( ) ( )] 3D
rn F r F r dr
r
0e e sh ( ) 1 1 e
pr qrr
abrF r A
r r
Thermodynamic condition for the depth of i-e pseudopotentialand amplitude of electron-ionic correlation function
0 ln [ (0) ]ie ei e iF
Positive sign of all correlation functions Fab
(r) gt 0
F r Ae e
re
sh rrab
pr qrr( )
1 1 0
Pseudopotentials
U
= UKin
+ UPot
3PV
= 2UKin + UPot
Homogeneity of Coulomb potential
U Vn F F dpot coul ( ) r
U Vn F F dei ii 2 ( ) r
)2()2(3 potkinpot UUUUPV
2 2i i
ie ie1 e( ) (1 e (0) ~
rrZ e Z er
r r
( ))
Correlation Functions
Total Energy correction
Potential Energy Correction
-
UPot
Pressure Correction
-
P
i e i eN N U ( ) 1
Approximate relation between Coulomb corrections for chemical potential and energy
(
UN)
NB
Thermodynamic contributions inmodified pseudopotential model for Coulomb corrections
Positive shift in average kinetic energy due to non-ideality of free charges subsystem Ukin = 3PV ndash
U
Well-known relation between pressure and energy corrections for free charges subsystemU = 3PV
which is valid at weak non-ideality (Г
ltlt 1) is no longer valid in strong non-ideality conditions (Г
~ 1)
It is equivalent to additional effective electron-ion repulsion(in comparison with ordinary one-parametric Coulomb corrections depending on non-ideality parameter only
FNkT = f(Г)
Experimental data Theoretical models
(comparison)
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
Quasi‐isochoric behavior of nitrogen Hugoniot
‐
Mochalov
M Zhernokletov
M et al
JETP
137
(2010) ‐
Trunin
R Boriskov
G et alJETP Letters
88
(2008)
15 20 25 30 35 400
100
200
300
ExperimentsTrunin et al 2008Mochalov et al 2010
P GPa
gcm3
lim
Check of theoretical models
SAHA
CCM
Ross ampRogers
CCM ndash
Compressible Covolume
Model(A Medvedev
amp
VKopyshev)
SAHA‐code (V Gryaznov amp IIosilevskiy)
ρHug
asymp
33 plusmn
01
gcm390
lt
PHug
lt 330
GPa
NN
22 NN‐‐polymerpolymer
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
equiv
V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost
linear function of pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
Reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal Energy
Pressure (Hugonoit)
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
Blue curve
ndash
internal energy calculated via plasma model(code SAHA
Gryaznov Iosilevskiy)
SAHA
Hugoniot
~ ρ
asymp
const (33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
ρ
asymp33 plusmn01
gcc90
lt
P lt 330
GPa
NB
Quasi‐linear behavior of
E(p)
at ρ
=
constThermodynamics of shock compressed nitrogen
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
00
01
02
03
04
05
06
07
08
09
10 Mochalov et al PHug (Trunin et al) + T (EOSCCM) PHug (Trunin et al) + T (EOSSAHA)
xN+
xi
xN2
P GPa
T k
K
Tr
Tr
Plasma
Temperature of shock compressed nitrogen
CP()
General P‐T
diagram
Quasi‐linear behavior of
T(p)
at ρ
=
const
SAHA
‐
Experiment Mochalov
M et al
JETF
137
(2010)Nellis
W Radovsky
H et al J Chem Phys 94
(1991)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
Electroconductivity
of shock compressed nitrogen
20 25 30 351E-3
001
01
1
10
100
1000
C E B E 28061 B 29062
Con
duct
ivity
1
cm
Density gcc
Electroconductivity
of shock compressed nitrogen
Ternovoi
V et al (email ‐
30052010)
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1
P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
‐
Experiment Mochalov
M et al
JETF
137
(2010)
Quasi‐isentropic Plane Compression of Matter at Megabar
Pressures by Using of a Layered
System to Diminish First Shock Wave IntensityTernovoi
V Pyalling
A Filimonovet
A (052010) Summary and conclusion
Explosive driven quasi‐isentropic compression generators were proposed for matter investigation in
the megabar
pressure region Results of the first experiments on quasi‐isentropic compression of
liquid nitrogen are presented It was shown that pressure ionization
of nitrogen proceeds at
densities
from 315 to 34 gcc
at a temperature
of about 3000
K
Diminishing of temperature growth
was measured during onset of nitrogen electrical conductivity
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
Expected behavior of nitrogen HugoniotМRoss amp FRogers
ACTEX(Rogers)
Interpolation(σmax
asymp
53)Experiments
New experiments vs
expected behavior of
nitrogen HugoniotМRoss amp FRogers
ACTEX(Rogers)
Interpolation(σmax
asymp
53)N‐polimer
N2Experiments
New experiments(σmax
asymp
41)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
New experiments are
in strong contradiction with expected behavior of
nitrogen Hugoniot
NB
Nitrogen Hugoniot
problem in plasma state ndash what do we need
In last experimentson deuterium
compression Pmax
asymp
50
Mbar(see Mochalov
et al NPP‐2011)(Mochalov
et al JETP Lett 2010)
NB
TheoryAb
initio
RPIMC DPIMCDFTMD WPMDChemical models
SAHA‐SSAHA‐N
(Gryaznov et al)WZ‐cell modelsTF TFC MHFShellip
Wide‐range EOS‐s
IPCP RASJIHT RASCCM (Sarov)
New experiments(σmax
asymp
41)
New experiments
‐Shock waves
-
Isentropic Compression‐
Heavy Ion Beams‐
Laser Heating etc etc
Interpolation(σmax
asymp
53)
ACTEX(Rogers)
Experiments
Nitrogen Hugoniot(comes trough polymeric phase )
ACTEX(Rogers)
Polymeric stateis expected between
molecular and plasma
regions (see below)
NB
N‐polymerN2
Experiments
THEORYAb
initio
RPIMC DPIMCDFTMD WPMDChem modelsSAHA‐SSAHA‐N
WZ‐cell modelsTFC MHFS
Wide‐range EOS
CCM (Sarov)
New experiments(σmax
asymp
41)
New experiments
‐
Shock waves
‐
Heavy Ion Beams‐
Laser Heating etc etc
N‐plasma
figure fromB Boates S Bonev Phys Rev Lett
102
(2009)
Ab initio calculations
‐
DFTMD
MolecularPolymeric
Critical point
CrossoverCrossover
11stst
order PTorder PT
MeltingMelting
Molecularfluid
Dissociated fluid
Fluidndashfluid
phase transitionin hydrogen [] ()
DFTMD
Scandolo
S PNAS
100 (2003)
Bonev S Militzer B Galli G PRB
69 (2004) WPMD
Jakob
B et al PRE
(2007) DFTMD Morales M et al PNAS
107 (2010)
DFTMD Lorenzen
W et al PRB
(2010)
Figure from
Giulia Galli SCCS-2005
Moscow= = = =
with additionsMorales et al 2010
andLorensen et al 2010
Morales et al
2010
Lorenzen
et al
2010
Ab initio calculations
‐
DFTMD
Experiment ndash single shock
compression ndash
reflected shock
compressionRadousky Nellis amp Ross et al Phys Rev Lett 57
(1986)Nellis Radousky
amp Hamilton et alJ Chem Phys 94
(1991)
0 50 100 150 200 250 3000
10
Tr Tr
CP
P GPa
T 103 K
Nitrogen phase diagram in the region of polymerizationPressure ndash temperature
melting (extrapolation)
HugoniotPlasma Model (SAHA‐code)
Yakubliquid
solidN2 N‐polimer
Theoretical models
estimation of polymer‐molecule
boundary in liquid nitrogen
(ЕYakub
ndash
1993) estimation of polymer‐molecule
boundary in solid nitrogen
(LYakub
ndash
1993)CP
ndash
critical point of 1st
order phase
transition polymer‐molecule
(ЕYakub
ndash
1993) ndash
triple point of 1st
order phase transition
polymer‐molecule
(Е amp L Yakub
ndash
1993)ЕS Yakub Low Temp Phys
20
579 (1994)LN Yakub Low Temp Phys
19 531 (1993)
estimation of polymer‐molecule bounda‐
ry
in liquid nitrogen (Ross amp Rogers
ndash
2006)MRoss
amp
FRogers Phys Rev
B 74 (2006)Ab
initio calculations DFTMD
ndash
calculation of of
polymer‐‐
molecule boundary in liquid nitrogen
(SBonev
et al ndash
2009)
the same as ldquosmoothedrdquo
phase transitionB Boates
amp
S Bonev Phys Rev Lett
102
(2009)
Gr
gt 0
Gr
lt 0 ndash domains of positive and negative sign of Gruumlneisen
coefficient
Gr
equiv
V(partPpartE)V
hypothetical boundary between polymeric and non‐ideal plasma states
(1st‐order phase transition or continuous )
melting
N2
N‐polimer
Gr
gt 0
Gr
lt 0
N‐plasma
Gr
gt 0
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
‐
Mochalov
M Zhernokletov
M et al
JETP
137 77
(2010) ‐
Trunin
R Boriskov
G Bykov
A Medvedev
A
JETP Letters
88 220 (2008)
Phase Diagram of Dense Nitrogen(summary)
N2
Npolimer
boundaryYakub Ross amp
Rogers etc
HypotheticalPressure Ionizationfrom N‐polymer
to N‐plasma
1st‐order phase transition
Critical point(s)
Domain
Gr
lt 0
Topology of theboundary
Gr
= 0
Pre‐compressed gaseous N2
Iso‐S
N2
N‐polimer
N‐plasma
Gr
gt 0
Gr
gt 0
Gr
lt 0
New experiments
‐
Shock waves‐ Iso‐S
Compression‐ Heavy Ion Beams‐
Laser Heating etc etc
THEORY Ab
initioRPIMC DPIMC
DFTMDChem modelsSAHA‐N
WZ‐cell modelsTFC MHFS
Wide‐range EOSEOS (IPCP
RAS)EOS (JIHT
RAS)CCM (Sarov)
Commentsmicrophysics
Simple molecules H2
N2
L = 074 A L = 11 A
D = 29 A D = 37 A
Triple covalent bond De
= 98 eV
(49 eVatom)
Single covalent bond De
= 30 eV
(45 eVatom)
L = 14 A
Figures after
Eugene Yakub ldquoNon‐simple
problems for simple moleculesrdquoFAIR‐Russia School laquoPhysics of high energy density in matterraquo
December
2009 Moscow
FZaharievAHuJHooperFZhangampTWoo PhysRev B 72214108 (2005 )
Polymeric nitrogen - structure
Eugene and Lidia Yakub Low Temp Phys 19 (1993)
Simple molecular modelsFirst estimations of molecular-polymeric transition
1 - Hugoniot2 - Phase equilibrium line
Experiment (Nellis ea 2001)3 - Single shock4 - Double shock
NN22
NN‐‐polimerpolimer
NN22
NN‐‐polimerpolimer
1st‐orderPhase transition
Critical point
Plasma model for nitrogen thermodynamics(code SAHA-N)
Shock compression of nitrogen(chemical picture)
SAHA-codeGryaznov Iosilevskiy (1970-2010)
Short range repulsionldquoSoft Spheresrdquo
approximation (DYoung)
modified for mixture
of soft spheres with different radii
ndash
shift of dissociation level
N
N+ + endash Ze
e
rcA
iA+
A+
i
Coulomb interactionModified pseudopotential
model
for partially ionized plasma(I
Iosilevskiy 1980-2010)
Equilibrium
compositionN2
N N+ e N2+ Nndash
Key parameter
ndash
ratio of intrinsic volumes molecule atom ion
R(N)
R(N2
)
= 063-
in accordance with recommendations of
ldquoAtom-atomic
approximationrdquo
of EYakub LT 1993
Basic points-
All assumption are provided at micro-level-
Input Choice of Фie
Фii
and Фее
pseudopotentials - Input Approximations for binary correlation functions - Strong correlation of the pseudopotentials
for ldquofreerdquocharges and upper energy level for partition functionsfor bound states
- Priority for general equalities (normalizing conditions)valid independently on degree of non-ideality
- Non-ideality corrections through the correlationfunctions and general equalities valid for Coulombinteraction
NN22
harrharr 2N2N NN22
++
harrharr NN ++
NN++ NNndashharrharr NN ++
eendash
[ ( ) ( )] 1n F r F r d r
Coulomb Corrections for Free Charge Subsystem
Modified Pseudopotential Approximation ()
Bound and free states of electron‐ionic pair
Effective electro-ionic potential (in Glaubermanrsquos form (1955))
2i
ie ( ) 1 e rZ err
( )
()
Iosilevskiy I High Temp 18
(1980) in ldquoEncyclopedia
of Low‐T Plasmardquo
(Suppl) Moscow FIZMATLIT 2004 pp 349
The form of i-i i-e e-e binary correlation functions-
laquoringraquo
(Debye) approximation with potential
Фie
(r)guarantee correct properties in the limit
of weak non-ideality
(Г
ltlt 1)
Binary i‐i i‐e e‐e
correlation functions
ldquoZero and second momentrdquo conditions (Stillinger amp Lovett)2
2[ ( ) ( )] 3D
rn F r F r dr
r
0e e sh ( ) 1 1 e
pr qrr
abrF r A
r r
Thermodynamic condition for the depth of i-e pseudopotentialand amplitude of electron-ionic correlation function
0 ln [ (0) ]ie ei e iF
Positive sign of all correlation functions Fab
(r) gt 0
F r Ae e
re
sh rrab
pr qrr( )
1 1 0
Pseudopotentials
U
= UKin
+ UPot
3PV
= 2UKin + UPot
Homogeneity of Coulomb potential
U Vn F F dpot coul ( ) r
U Vn F F dei ii 2 ( ) r
)2()2(3 potkinpot UUUUPV
2 2i i
ie ie1 e( ) (1 e (0) ~
rrZ e Z er
r r
( ))
Correlation Functions
Total Energy correction
Potential Energy Correction
-
UPot
Pressure Correction
-
P
i e i eN N U ( ) 1
Approximate relation between Coulomb corrections for chemical potential and energy
(
UN)
NB
Thermodynamic contributions inmodified pseudopotential model for Coulomb corrections
Positive shift in average kinetic energy due to non-ideality of free charges subsystem Ukin = 3PV ndash
U
Well-known relation between pressure and energy corrections for free charges subsystemU = 3PV
which is valid at weak non-ideality (Г
ltlt 1) is no longer valid in strong non-ideality conditions (Г
~ 1)
It is equivalent to additional effective electron-ion repulsion(in comparison with ordinary one-parametric Coulomb corrections depending on non-ideality parameter only
FNkT = f(Г)
Experimental data Theoretical models
(comparison)
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
Quasi‐isochoric behavior of nitrogen Hugoniot
‐
Mochalov
M Zhernokletov
M et al
JETP
137
(2010) ‐
Trunin
R Boriskov
G et alJETP Letters
88
(2008)
15 20 25 30 35 400
100
200
300
ExperimentsTrunin et al 2008Mochalov et al 2010
P GPa
gcm3
lim
Check of theoretical models
SAHA
CCM
Ross ampRogers
CCM ndash
Compressible Covolume
Model(A Medvedev
amp
VKopyshev)
SAHA‐code (V Gryaznov amp IIosilevskiy)
ρHug
asymp
33 plusmn
01
gcm390
lt
PHug
lt 330
GPa
NN
22 NN‐‐polymerpolymer
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
equiv
V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost
linear function of pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
Reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal Energy
Pressure (Hugonoit)
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
Blue curve
ndash
internal energy calculated via plasma model(code SAHA
Gryaznov Iosilevskiy)
SAHA
Hugoniot
~ ρ
asymp
const (33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
ρ
asymp33 plusmn01
gcc90
lt
P lt 330
GPa
NB
Quasi‐linear behavior of
E(p)
at ρ
=
constThermodynamics of shock compressed nitrogen
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
00
01
02
03
04
05
06
07
08
09
10 Mochalov et al PHug (Trunin et al) + T (EOSCCM) PHug (Trunin et al) + T (EOSSAHA)
xN+
xi
xN2
P GPa
T k
K
Tr
Tr
Plasma
Temperature of shock compressed nitrogen
CP()
General P‐T
diagram
Quasi‐linear behavior of
T(p)
at ρ
=
const
SAHA
‐
Experiment Mochalov
M et al
JETF
137
(2010)Nellis
W Radovsky
H et al J Chem Phys 94
(1991)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
Electroconductivity
of shock compressed nitrogen
20 25 30 351E-3
001
01
1
10
100
1000
C E B E 28061 B 29062
Con
duct
ivity
1
cm
Density gcc
Electroconductivity
of shock compressed nitrogen
Ternovoi
V et al (email ‐
30052010)
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1
P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
‐
Experiment Mochalov
M et al
JETF
137
(2010)
Quasi‐isentropic Plane Compression of Matter at Megabar
Pressures by Using of a Layered
System to Diminish First Shock Wave IntensityTernovoi
V Pyalling
A Filimonovet
A (052010) Summary and conclusion
Explosive driven quasi‐isentropic compression generators were proposed for matter investigation in
the megabar
pressure region Results of the first experiments on quasi‐isentropic compression of
liquid nitrogen are presented It was shown that pressure ionization
of nitrogen proceeds at
densities
from 315 to 34 gcc
at a temperature
of about 3000
K
Diminishing of temperature growth
was measured during onset of nitrogen electrical conductivity
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
New experiments vs
expected behavior of
nitrogen HugoniotМRoss amp FRogers
ACTEX(Rogers)
Interpolation(σmax
asymp
53)N‐polimer
N2Experiments
New experiments(σmax
asymp
41)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
New experiments are
in strong contradiction with expected behavior of
nitrogen Hugoniot
NB
Nitrogen Hugoniot
problem in plasma state ndash what do we need
In last experimentson deuterium
compression Pmax
asymp
50
Mbar(see Mochalov
et al NPP‐2011)(Mochalov
et al JETP Lett 2010)
NB
TheoryAb
initio
RPIMC DPIMCDFTMD WPMDChemical models
SAHA‐SSAHA‐N
(Gryaznov et al)WZ‐cell modelsTF TFC MHFShellip
Wide‐range EOS‐s
IPCP RASJIHT RASCCM (Sarov)
New experiments(σmax
asymp
41)
New experiments
‐Shock waves
-
Isentropic Compression‐
Heavy Ion Beams‐
Laser Heating etc etc
Interpolation(σmax
asymp
53)
ACTEX(Rogers)
Experiments
Nitrogen Hugoniot(comes trough polymeric phase )
ACTEX(Rogers)
Polymeric stateis expected between
molecular and plasma
regions (see below)
NB
N‐polymerN2
Experiments
THEORYAb
initio
RPIMC DPIMCDFTMD WPMDChem modelsSAHA‐SSAHA‐N
WZ‐cell modelsTFC MHFS
Wide‐range EOS
CCM (Sarov)
New experiments(σmax
asymp
41)
New experiments
‐
Shock waves
‐
Heavy Ion Beams‐
Laser Heating etc etc
N‐plasma
figure fromB Boates S Bonev Phys Rev Lett
102
(2009)
Ab initio calculations
‐
DFTMD
MolecularPolymeric
Critical point
CrossoverCrossover
11stst
order PTorder PT
MeltingMelting
Molecularfluid
Dissociated fluid
Fluidndashfluid
phase transitionin hydrogen [] ()
DFTMD
Scandolo
S PNAS
100 (2003)
Bonev S Militzer B Galli G PRB
69 (2004) WPMD
Jakob
B et al PRE
(2007) DFTMD Morales M et al PNAS
107 (2010)
DFTMD Lorenzen
W et al PRB
(2010)
Figure from
Giulia Galli SCCS-2005
Moscow= = = =
with additionsMorales et al 2010
andLorensen et al 2010
Morales et al
2010
Lorenzen
et al
2010
Ab initio calculations
‐
DFTMD
Experiment ndash single shock
compression ndash
reflected shock
compressionRadousky Nellis amp Ross et al Phys Rev Lett 57
(1986)Nellis Radousky
amp Hamilton et alJ Chem Phys 94
(1991)
0 50 100 150 200 250 3000
10
Tr Tr
CP
P GPa
T 103 K
Nitrogen phase diagram in the region of polymerizationPressure ndash temperature
melting (extrapolation)
HugoniotPlasma Model (SAHA‐code)
Yakubliquid
solidN2 N‐polimer
Theoretical models
estimation of polymer‐molecule
boundary in liquid nitrogen
(ЕYakub
ndash
1993) estimation of polymer‐molecule
boundary in solid nitrogen
(LYakub
ndash
1993)CP
ndash
critical point of 1st
order phase
transition polymer‐molecule
(ЕYakub
ndash
1993) ndash
triple point of 1st
order phase transition
polymer‐molecule
(Е amp L Yakub
ndash
1993)ЕS Yakub Low Temp Phys
20
579 (1994)LN Yakub Low Temp Phys
19 531 (1993)
estimation of polymer‐molecule bounda‐
ry
in liquid nitrogen (Ross amp Rogers
ndash
2006)MRoss
amp
FRogers Phys Rev
B 74 (2006)Ab
initio calculations DFTMD
ndash
calculation of of
polymer‐‐
molecule boundary in liquid nitrogen
(SBonev
et al ndash
2009)
the same as ldquosmoothedrdquo
phase transitionB Boates
amp
S Bonev Phys Rev Lett
102
(2009)
Gr
gt 0
Gr
lt 0 ndash domains of positive and negative sign of Gruumlneisen
coefficient
Gr
equiv
V(partPpartE)V
hypothetical boundary between polymeric and non‐ideal plasma states
(1st‐order phase transition or continuous )
melting
N2
N‐polimer
Gr
gt 0
Gr
lt 0
N‐plasma
Gr
gt 0
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
‐
Mochalov
M Zhernokletov
M et al
JETP
137 77
(2010) ‐
Trunin
R Boriskov
G Bykov
A Medvedev
A
JETP Letters
88 220 (2008)
Phase Diagram of Dense Nitrogen(summary)
N2
Npolimer
boundaryYakub Ross amp
Rogers etc
HypotheticalPressure Ionizationfrom N‐polymer
to N‐plasma
1st‐order phase transition
Critical point(s)
Domain
Gr
lt 0
Topology of theboundary
Gr
= 0
Pre‐compressed gaseous N2
Iso‐S
N2
N‐polimer
N‐plasma
Gr
gt 0
Gr
gt 0
Gr
lt 0
New experiments
‐
Shock waves‐ Iso‐S
Compression‐ Heavy Ion Beams‐
Laser Heating etc etc
THEORY Ab
initioRPIMC DPIMC
DFTMDChem modelsSAHA‐N
WZ‐cell modelsTFC MHFS
Wide‐range EOSEOS (IPCP
RAS)EOS (JIHT
RAS)CCM (Sarov)
Commentsmicrophysics
Simple molecules H2
N2
L = 074 A L = 11 A
D = 29 A D = 37 A
Triple covalent bond De
= 98 eV
(49 eVatom)
Single covalent bond De
= 30 eV
(45 eVatom)
L = 14 A
Figures after
Eugene Yakub ldquoNon‐simple
problems for simple moleculesrdquoFAIR‐Russia School laquoPhysics of high energy density in matterraquo
December
2009 Moscow
FZaharievAHuJHooperFZhangampTWoo PhysRev B 72214108 (2005 )
Polymeric nitrogen - structure
Eugene and Lidia Yakub Low Temp Phys 19 (1993)
Simple molecular modelsFirst estimations of molecular-polymeric transition
1 - Hugoniot2 - Phase equilibrium line
Experiment (Nellis ea 2001)3 - Single shock4 - Double shock
NN22
NN‐‐polimerpolimer
NN22
NN‐‐polimerpolimer
1st‐orderPhase transition
Critical point
Plasma model for nitrogen thermodynamics(code SAHA-N)
Shock compression of nitrogen(chemical picture)
SAHA-codeGryaznov Iosilevskiy (1970-2010)
Short range repulsionldquoSoft Spheresrdquo
approximation (DYoung)
modified for mixture
of soft spheres with different radii
ndash
shift of dissociation level
N
N+ + endash Ze
e
rcA
iA+
A+
i
Coulomb interactionModified pseudopotential
model
for partially ionized plasma(I
Iosilevskiy 1980-2010)
Equilibrium
compositionN2
N N+ e N2+ Nndash
Key parameter
ndash
ratio of intrinsic volumes molecule atom ion
R(N)
R(N2
)
= 063-
in accordance with recommendations of
ldquoAtom-atomic
approximationrdquo
of EYakub LT 1993
Basic points-
All assumption are provided at micro-level-
Input Choice of Фie
Фii
and Фее
pseudopotentials - Input Approximations for binary correlation functions - Strong correlation of the pseudopotentials
for ldquofreerdquocharges and upper energy level for partition functionsfor bound states
- Priority for general equalities (normalizing conditions)valid independently on degree of non-ideality
- Non-ideality corrections through the correlationfunctions and general equalities valid for Coulombinteraction
NN22
harrharr 2N2N NN22
++
harrharr NN ++
NN++ NNndashharrharr NN ++
eendash
[ ( ) ( )] 1n F r F r d r
Coulomb Corrections for Free Charge Subsystem
Modified Pseudopotential Approximation ()
Bound and free states of electron‐ionic pair
Effective electro-ionic potential (in Glaubermanrsquos form (1955))
2i
ie ( ) 1 e rZ err
( )
()
Iosilevskiy I High Temp 18
(1980) in ldquoEncyclopedia
of Low‐T Plasmardquo
(Suppl) Moscow FIZMATLIT 2004 pp 349
The form of i-i i-e e-e binary correlation functions-
laquoringraquo
(Debye) approximation with potential
Фie
(r)guarantee correct properties in the limit
of weak non-ideality
(Г
ltlt 1)
Binary i‐i i‐e e‐e
correlation functions
ldquoZero and second momentrdquo conditions (Stillinger amp Lovett)2
2[ ( ) ( )] 3D
rn F r F r dr
r
0e e sh ( ) 1 1 e
pr qrr
abrF r A
r r
Thermodynamic condition for the depth of i-e pseudopotentialand amplitude of electron-ionic correlation function
0 ln [ (0) ]ie ei e iF
Positive sign of all correlation functions Fab
(r) gt 0
F r Ae e
re
sh rrab
pr qrr( )
1 1 0
Pseudopotentials
U
= UKin
+ UPot
3PV
= 2UKin + UPot
Homogeneity of Coulomb potential
U Vn F F dpot coul ( ) r
U Vn F F dei ii 2 ( ) r
)2()2(3 potkinpot UUUUPV
2 2i i
ie ie1 e( ) (1 e (0) ~
rrZ e Z er
r r
( ))
Correlation Functions
Total Energy correction
Potential Energy Correction
-
UPot
Pressure Correction
-
P
i e i eN N U ( ) 1
Approximate relation between Coulomb corrections for chemical potential and energy
(
UN)
NB
Thermodynamic contributions inmodified pseudopotential model for Coulomb corrections
Positive shift in average kinetic energy due to non-ideality of free charges subsystem Ukin = 3PV ndash
U
Well-known relation between pressure and energy corrections for free charges subsystemU = 3PV
which is valid at weak non-ideality (Г
ltlt 1) is no longer valid in strong non-ideality conditions (Г
~ 1)
It is equivalent to additional effective electron-ion repulsion(in comparison with ordinary one-parametric Coulomb corrections depending on non-ideality parameter only
FNkT = f(Г)
Experimental data Theoretical models
(comparison)
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
Quasi‐isochoric behavior of nitrogen Hugoniot
‐
Mochalov
M Zhernokletov
M et al
JETP
137
(2010) ‐
Trunin
R Boriskov
G et alJETP Letters
88
(2008)
15 20 25 30 35 400
100
200
300
ExperimentsTrunin et al 2008Mochalov et al 2010
P GPa
gcm3
lim
Check of theoretical models
SAHA
CCM
Ross ampRogers
CCM ndash
Compressible Covolume
Model(A Medvedev
amp
VKopyshev)
SAHA‐code (V Gryaznov amp IIosilevskiy)
ρHug
asymp
33 plusmn
01
gcm390
lt
PHug
lt 330
GPa
NN
22 NN‐‐polymerpolymer
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
equiv
V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost
linear function of pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
Reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal Energy
Pressure (Hugonoit)
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
Blue curve
ndash
internal energy calculated via plasma model(code SAHA
Gryaznov Iosilevskiy)
SAHA
Hugoniot
~ ρ
asymp
const (33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
ρ
asymp33 plusmn01
gcc90
lt
P lt 330
GPa
NB
Quasi‐linear behavior of
E(p)
at ρ
=
constThermodynamics of shock compressed nitrogen
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
00
01
02
03
04
05
06
07
08
09
10 Mochalov et al PHug (Trunin et al) + T (EOSCCM) PHug (Trunin et al) + T (EOSSAHA)
xN+
xi
xN2
P GPa
T k
K
Tr
Tr
Plasma
Temperature of shock compressed nitrogen
CP()
General P‐T
diagram
Quasi‐linear behavior of
T(p)
at ρ
=
const
SAHA
‐
Experiment Mochalov
M et al
JETF
137
(2010)Nellis
W Radovsky
H et al J Chem Phys 94
(1991)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
Electroconductivity
of shock compressed nitrogen
20 25 30 351E-3
001
01
1
10
100
1000
C E B E 28061 B 29062
Con
duct
ivity
1
cm
Density gcc
Electroconductivity
of shock compressed nitrogen
Ternovoi
V et al (email ‐
30052010)
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1
P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
‐
Experiment Mochalov
M et al
JETF
137
(2010)
Quasi‐isentropic Plane Compression of Matter at Megabar
Pressures by Using of a Layered
System to Diminish First Shock Wave IntensityTernovoi
V Pyalling
A Filimonovet
A (052010) Summary and conclusion
Explosive driven quasi‐isentropic compression generators were proposed for matter investigation in
the megabar
pressure region Results of the first experiments on quasi‐isentropic compression of
liquid nitrogen are presented It was shown that pressure ionization
of nitrogen proceeds at
densities
from 315 to 34 gcc
at a temperature
of about 3000
K
Diminishing of temperature growth
was measured during onset of nitrogen electrical conductivity
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
Nitrogen Hugoniot
problem in plasma state ndash what do we need
In last experimentson deuterium
compression Pmax
asymp
50
Mbar(see Mochalov
et al NPP‐2011)(Mochalov
et al JETP Lett 2010)
NB
TheoryAb
initio
RPIMC DPIMCDFTMD WPMDChemical models
SAHA‐SSAHA‐N
(Gryaznov et al)WZ‐cell modelsTF TFC MHFShellip
Wide‐range EOS‐s
IPCP RASJIHT RASCCM (Sarov)
New experiments(σmax
asymp
41)
New experiments
‐Shock waves
-
Isentropic Compression‐
Heavy Ion Beams‐
Laser Heating etc etc
Interpolation(σmax
asymp
53)
ACTEX(Rogers)
Experiments
Nitrogen Hugoniot(comes trough polymeric phase )
ACTEX(Rogers)
Polymeric stateis expected between
molecular and plasma
regions (see below)
NB
N‐polymerN2
Experiments
THEORYAb
initio
RPIMC DPIMCDFTMD WPMDChem modelsSAHA‐SSAHA‐N
WZ‐cell modelsTFC MHFS
Wide‐range EOS
CCM (Sarov)
New experiments(σmax
asymp
41)
New experiments
‐
Shock waves
‐
Heavy Ion Beams‐
Laser Heating etc etc
N‐plasma
figure fromB Boates S Bonev Phys Rev Lett
102
(2009)
Ab initio calculations
‐
DFTMD
MolecularPolymeric
Critical point
CrossoverCrossover
11stst
order PTorder PT
MeltingMelting
Molecularfluid
Dissociated fluid
Fluidndashfluid
phase transitionin hydrogen [] ()
DFTMD
Scandolo
S PNAS
100 (2003)
Bonev S Militzer B Galli G PRB
69 (2004) WPMD
Jakob
B et al PRE
(2007) DFTMD Morales M et al PNAS
107 (2010)
DFTMD Lorenzen
W et al PRB
(2010)
Figure from
Giulia Galli SCCS-2005
Moscow= = = =
with additionsMorales et al 2010
andLorensen et al 2010
Morales et al
2010
Lorenzen
et al
2010
Ab initio calculations
‐
DFTMD
Experiment ndash single shock
compression ndash
reflected shock
compressionRadousky Nellis amp Ross et al Phys Rev Lett 57
(1986)Nellis Radousky
amp Hamilton et alJ Chem Phys 94
(1991)
0 50 100 150 200 250 3000
10
Tr Tr
CP
P GPa
T 103 K
Nitrogen phase diagram in the region of polymerizationPressure ndash temperature
melting (extrapolation)
HugoniotPlasma Model (SAHA‐code)
Yakubliquid
solidN2 N‐polimer
Theoretical models
estimation of polymer‐molecule
boundary in liquid nitrogen
(ЕYakub
ndash
1993) estimation of polymer‐molecule
boundary in solid nitrogen
(LYakub
ndash
1993)CP
ndash
critical point of 1st
order phase
transition polymer‐molecule
(ЕYakub
ndash
1993) ndash
triple point of 1st
order phase transition
polymer‐molecule
(Е amp L Yakub
ndash
1993)ЕS Yakub Low Temp Phys
20
579 (1994)LN Yakub Low Temp Phys
19 531 (1993)
estimation of polymer‐molecule bounda‐
ry
in liquid nitrogen (Ross amp Rogers
ndash
2006)MRoss
amp
FRogers Phys Rev
B 74 (2006)Ab
initio calculations DFTMD
ndash
calculation of of
polymer‐‐
molecule boundary in liquid nitrogen
(SBonev
et al ndash
2009)
the same as ldquosmoothedrdquo
phase transitionB Boates
amp
S Bonev Phys Rev Lett
102
(2009)
Gr
gt 0
Gr
lt 0 ndash domains of positive and negative sign of Gruumlneisen
coefficient
Gr
equiv
V(partPpartE)V
hypothetical boundary between polymeric and non‐ideal plasma states
(1st‐order phase transition or continuous )
melting
N2
N‐polimer
Gr
gt 0
Gr
lt 0
N‐plasma
Gr
gt 0
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
‐
Mochalov
M Zhernokletov
M et al
JETP
137 77
(2010) ‐
Trunin
R Boriskov
G Bykov
A Medvedev
A
JETP Letters
88 220 (2008)
Phase Diagram of Dense Nitrogen(summary)
N2
Npolimer
boundaryYakub Ross amp
Rogers etc
HypotheticalPressure Ionizationfrom N‐polymer
to N‐plasma
1st‐order phase transition
Critical point(s)
Domain
Gr
lt 0
Topology of theboundary
Gr
= 0
Pre‐compressed gaseous N2
Iso‐S
N2
N‐polimer
N‐plasma
Gr
gt 0
Gr
gt 0
Gr
lt 0
New experiments
‐
Shock waves‐ Iso‐S
Compression‐ Heavy Ion Beams‐
Laser Heating etc etc
THEORY Ab
initioRPIMC DPIMC
DFTMDChem modelsSAHA‐N
WZ‐cell modelsTFC MHFS
Wide‐range EOSEOS (IPCP
RAS)EOS (JIHT
RAS)CCM (Sarov)
Commentsmicrophysics
Simple molecules H2
N2
L = 074 A L = 11 A
D = 29 A D = 37 A
Triple covalent bond De
= 98 eV
(49 eVatom)
Single covalent bond De
= 30 eV
(45 eVatom)
L = 14 A
Figures after
Eugene Yakub ldquoNon‐simple
problems for simple moleculesrdquoFAIR‐Russia School laquoPhysics of high energy density in matterraquo
December
2009 Moscow
FZaharievAHuJHooperFZhangampTWoo PhysRev B 72214108 (2005 )
Polymeric nitrogen - structure
Eugene and Lidia Yakub Low Temp Phys 19 (1993)
Simple molecular modelsFirst estimations of molecular-polymeric transition
1 - Hugoniot2 - Phase equilibrium line
Experiment (Nellis ea 2001)3 - Single shock4 - Double shock
NN22
NN‐‐polimerpolimer
NN22
NN‐‐polimerpolimer
1st‐orderPhase transition
Critical point
Plasma model for nitrogen thermodynamics(code SAHA-N)
Shock compression of nitrogen(chemical picture)
SAHA-codeGryaznov Iosilevskiy (1970-2010)
Short range repulsionldquoSoft Spheresrdquo
approximation (DYoung)
modified for mixture
of soft spheres with different radii
ndash
shift of dissociation level
N
N+ + endash Ze
e
rcA
iA+
A+
i
Coulomb interactionModified pseudopotential
model
for partially ionized plasma(I
Iosilevskiy 1980-2010)
Equilibrium
compositionN2
N N+ e N2+ Nndash
Key parameter
ndash
ratio of intrinsic volumes molecule atom ion
R(N)
R(N2
)
= 063-
in accordance with recommendations of
ldquoAtom-atomic
approximationrdquo
of EYakub LT 1993
Basic points-
All assumption are provided at micro-level-
Input Choice of Фie
Фii
and Фее
pseudopotentials - Input Approximations for binary correlation functions - Strong correlation of the pseudopotentials
for ldquofreerdquocharges and upper energy level for partition functionsfor bound states
- Priority for general equalities (normalizing conditions)valid independently on degree of non-ideality
- Non-ideality corrections through the correlationfunctions and general equalities valid for Coulombinteraction
NN22
harrharr 2N2N NN22
++
harrharr NN ++
NN++ NNndashharrharr NN ++
eendash
[ ( ) ( )] 1n F r F r d r
Coulomb Corrections for Free Charge Subsystem
Modified Pseudopotential Approximation ()
Bound and free states of electron‐ionic pair
Effective electro-ionic potential (in Glaubermanrsquos form (1955))
2i
ie ( ) 1 e rZ err
( )
()
Iosilevskiy I High Temp 18
(1980) in ldquoEncyclopedia
of Low‐T Plasmardquo
(Suppl) Moscow FIZMATLIT 2004 pp 349
The form of i-i i-e e-e binary correlation functions-
laquoringraquo
(Debye) approximation with potential
Фie
(r)guarantee correct properties in the limit
of weak non-ideality
(Г
ltlt 1)
Binary i‐i i‐e e‐e
correlation functions
ldquoZero and second momentrdquo conditions (Stillinger amp Lovett)2
2[ ( ) ( )] 3D
rn F r F r dr
r
0e e sh ( ) 1 1 e
pr qrr
abrF r A
r r
Thermodynamic condition for the depth of i-e pseudopotentialand amplitude of electron-ionic correlation function
0 ln [ (0) ]ie ei e iF
Positive sign of all correlation functions Fab
(r) gt 0
F r Ae e
re
sh rrab
pr qrr( )
1 1 0
Pseudopotentials
U
= UKin
+ UPot
3PV
= 2UKin + UPot
Homogeneity of Coulomb potential
U Vn F F dpot coul ( ) r
U Vn F F dei ii 2 ( ) r
)2()2(3 potkinpot UUUUPV
2 2i i
ie ie1 e( ) (1 e (0) ~
rrZ e Z er
r r
( ))
Correlation Functions
Total Energy correction
Potential Energy Correction
-
UPot
Pressure Correction
-
P
i e i eN N U ( ) 1
Approximate relation between Coulomb corrections for chemical potential and energy
(
UN)
NB
Thermodynamic contributions inmodified pseudopotential model for Coulomb corrections
Positive shift in average kinetic energy due to non-ideality of free charges subsystem Ukin = 3PV ndash
U
Well-known relation between pressure and energy corrections for free charges subsystemU = 3PV
which is valid at weak non-ideality (Г
ltlt 1) is no longer valid in strong non-ideality conditions (Г
~ 1)
It is equivalent to additional effective electron-ion repulsion(in comparison with ordinary one-parametric Coulomb corrections depending on non-ideality parameter only
FNkT = f(Г)
Experimental data Theoretical models
(comparison)
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
Quasi‐isochoric behavior of nitrogen Hugoniot
‐
Mochalov
M Zhernokletov
M et al
JETP
137
(2010) ‐
Trunin
R Boriskov
G et alJETP Letters
88
(2008)
15 20 25 30 35 400
100
200
300
ExperimentsTrunin et al 2008Mochalov et al 2010
P GPa
gcm3
lim
Check of theoretical models
SAHA
CCM
Ross ampRogers
CCM ndash
Compressible Covolume
Model(A Medvedev
amp
VKopyshev)
SAHA‐code (V Gryaznov amp IIosilevskiy)
ρHug
asymp
33 plusmn
01
gcm390
lt
PHug
lt 330
GPa
NN
22 NN‐‐polymerpolymer
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
equiv
V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost
linear function of pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
Reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal Energy
Pressure (Hugonoit)
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
Blue curve
ndash
internal energy calculated via plasma model(code SAHA
Gryaznov Iosilevskiy)
SAHA
Hugoniot
~ ρ
asymp
const (33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
ρ
asymp33 plusmn01
gcc90
lt
P lt 330
GPa
NB
Quasi‐linear behavior of
E(p)
at ρ
=
constThermodynamics of shock compressed nitrogen
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
00
01
02
03
04
05
06
07
08
09
10 Mochalov et al PHug (Trunin et al) + T (EOSCCM) PHug (Trunin et al) + T (EOSSAHA)
xN+
xi
xN2
P GPa
T k
K
Tr
Tr
Plasma
Temperature of shock compressed nitrogen
CP()
General P‐T
diagram
Quasi‐linear behavior of
T(p)
at ρ
=
const
SAHA
‐
Experiment Mochalov
M et al
JETF
137
(2010)Nellis
W Radovsky
H et al J Chem Phys 94
(1991)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
Electroconductivity
of shock compressed nitrogen
20 25 30 351E-3
001
01
1
10
100
1000
C E B E 28061 B 29062
Con
duct
ivity
1
cm
Density gcc
Electroconductivity
of shock compressed nitrogen
Ternovoi
V et al (email ‐
30052010)
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1
P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
‐
Experiment Mochalov
M et al
JETF
137
(2010)
Quasi‐isentropic Plane Compression of Matter at Megabar
Pressures by Using of a Layered
System to Diminish First Shock Wave IntensityTernovoi
V Pyalling
A Filimonovet
A (052010) Summary and conclusion
Explosive driven quasi‐isentropic compression generators were proposed for matter investigation in
the megabar
pressure region Results of the first experiments on quasi‐isentropic compression of
liquid nitrogen are presented It was shown that pressure ionization
of nitrogen proceeds at
densities
from 315 to 34 gcc
at a temperature
of about 3000
K
Diminishing of temperature growth
was measured during onset of nitrogen electrical conductivity
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
Nitrogen Hugoniot(comes trough polymeric phase )
ACTEX(Rogers)
Polymeric stateis expected between
molecular and plasma
regions (see below)
NB
N‐polymerN2
Experiments
THEORYAb
initio
RPIMC DPIMCDFTMD WPMDChem modelsSAHA‐SSAHA‐N
WZ‐cell modelsTFC MHFS
Wide‐range EOS
CCM (Sarov)
New experiments(σmax
asymp
41)
New experiments
‐
Shock waves
‐
Heavy Ion Beams‐
Laser Heating etc etc
N‐plasma
figure fromB Boates S Bonev Phys Rev Lett
102
(2009)
Ab initio calculations
‐
DFTMD
MolecularPolymeric
Critical point
CrossoverCrossover
11stst
order PTorder PT
MeltingMelting
Molecularfluid
Dissociated fluid
Fluidndashfluid
phase transitionin hydrogen [] ()
DFTMD
Scandolo
S PNAS
100 (2003)
Bonev S Militzer B Galli G PRB
69 (2004) WPMD
Jakob
B et al PRE
(2007) DFTMD Morales M et al PNAS
107 (2010)
DFTMD Lorenzen
W et al PRB
(2010)
Figure from
Giulia Galli SCCS-2005
Moscow= = = =
with additionsMorales et al 2010
andLorensen et al 2010
Morales et al
2010
Lorenzen
et al
2010
Ab initio calculations
‐
DFTMD
Experiment ndash single shock
compression ndash
reflected shock
compressionRadousky Nellis amp Ross et al Phys Rev Lett 57
(1986)Nellis Radousky
amp Hamilton et alJ Chem Phys 94
(1991)
0 50 100 150 200 250 3000
10
Tr Tr
CP
P GPa
T 103 K
Nitrogen phase diagram in the region of polymerizationPressure ndash temperature
melting (extrapolation)
HugoniotPlasma Model (SAHA‐code)
Yakubliquid
solidN2 N‐polimer
Theoretical models
estimation of polymer‐molecule
boundary in liquid nitrogen
(ЕYakub
ndash
1993) estimation of polymer‐molecule
boundary in solid nitrogen
(LYakub
ndash
1993)CP
ndash
critical point of 1st
order phase
transition polymer‐molecule
(ЕYakub
ndash
1993) ndash
triple point of 1st
order phase transition
polymer‐molecule
(Е amp L Yakub
ndash
1993)ЕS Yakub Low Temp Phys
20
579 (1994)LN Yakub Low Temp Phys
19 531 (1993)
estimation of polymer‐molecule bounda‐
ry
in liquid nitrogen (Ross amp Rogers
ndash
2006)MRoss
amp
FRogers Phys Rev
B 74 (2006)Ab
initio calculations DFTMD
ndash
calculation of of
polymer‐‐
molecule boundary in liquid nitrogen
(SBonev
et al ndash
2009)
the same as ldquosmoothedrdquo
phase transitionB Boates
amp
S Bonev Phys Rev Lett
102
(2009)
Gr
gt 0
Gr
lt 0 ndash domains of positive and negative sign of Gruumlneisen
coefficient
Gr
equiv
V(partPpartE)V
hypothetical boundary between polymeric and non‐ideal plasma states
(1st‐order phase transition or continuous )
melting
N2
N‐polimer
Gr
gt 0
Gr
lt 0
N‐plasma
Gr
gt 0
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
‐
Mochalov
M Zhernokletov
M et al
JETP
137 77
(2010) ‐
Trunin
R Boriskov
G Bykov
A Medvedev
A
JETP Letters
88 220 (2008)
Phase Diagram of Dense Nitrogen(summary)
N2
Npolimer
boundaryYakub Ross amp
Rogers etc
HypotheticalPressure Ionizationfrom N‐polymer
to N‐plasma
1st‐order phase transition
Critical point(s)
Domain
Gr
lt 0
Topology of theboundary
Gr
= 0
Pre‐compressed gaseous N2
Iso‐S
N2
N‐polimer
N‐plasma
Gr
gt 0
Gr
gt 0
Gr
lt 0
New experiments
‐
Shock waves‐ Iso‐S
Compression‐ Heavy Ion Beams‐
Laser Heating etc etc
THEORY Ab
initioRPIMC DPIMC
DFTMDChem modelsSAHA‐N
WZ‐cell modelsTFC MHFS
Wide‐range EOSEOS (IPCP
RAS)EOS (JIHT
RAS)CCM (Sarov)
Commentsmicrophysics
Simple molecules H2
N2
L = 074 A L = 11 A
D = 29 A D = 37 A
Triple covalent bond De
= 98 eV
(49 eVatom)
Single covalent bond De
= 30 eV
(45 eVatom)
L = 14 A
Figures after
Eugene Yakub ldquoNon‐simple
problems for simple moleculesrdquoFAIR‐Russia School laquoPhysics of high energy density in matterraquo
December
2009 Moscow
FZaharievAHuJHooperFZhangampTWoo PhysRev B 72214108 (2005 )
Polymeric nitrogen - structure
Eugene and Lidia Yakub Low Temp Phys 19 (1993)
Simple molecular modelsFirst estimations of molecular-polymeric transition
1 - Hugoniot2 - Phase equilibrium line
Experiment (Nellis ea 2001)3 - Single shock4 - Double shock
NN22
NN‐‐polimerpolimer
NN22
NN‐‐polimerpolimer
1st‐orderPhase transition
Critical point
Plasma model for nitrogen thermodynamics(code SAHA-N)
Shock compression of nitrogen(chemical picture)
SAHA-codeGryaznov Iosilevskiy (1970-2010)
Short range repulsionldquoSoft Spheresrdquo
approximation (DYoung)
modified for mixture
of soft spheres with different radii
ndash
shift of dissociation level
N
N+ + endash Ze
e
rcA
iA+
A+
i
Coulomb interactionModified pseudopotential
model
for partially ionized plasma(I
Iosilevskiy 1980-2010)
Equilibrium
compositionN2
N N+ e N2+ Nndash
Key parameter
ndash
ratio of intrinsic volumes molecule atom ion
R(N)
R(N2
)
= 063-
in accordance with recommendations of
ldquoAtom-atomic
approximationrdquo
of EYakub LT 1993
Basic points-
All assumption are provided at micro-level-
Input Choice of Фie
Фii
and Фее
pseudopotentials - Input Approximations for binary correlation functions - Strong correlation of the pseudopotentials
for ldquofreerdquocharges and upper energy level for partition functionsfor bound states
- Priority for general equalities (normalizing conditions)valid independently on degree of non-ideality
- Non-ideality corrections through the correlationfunctions and general equalities valid for Coulombinteraction
NN22
harrharr 2N2N NN22
++
harrharr NN ++
NN++ NNndashharrharr NN ++
eendash
[ ( ) ( )] 1n F r F r d r
Coulomb Corrections for Free Charge Subsystem
Modified Pseudopotential Approximation ()
Bound and free states of electron‐ionic pair
Effective electro-ionic potential (in Glaubermanrsquos form (1955))
2i
ie ( ) 1 e rZ err
( )
()
Iosilevskiy I High Temp 18
(1980) in ldquoEncyclopedia
of Low‐T Plasmardquo
(Suppl) Moscow FIZMATLIT 2004 pp 349
The form of i-i i-e e-e binary correlation functions-
laquoringraquo
(Debye) approximation with potential
Фie
(r)guarantee correct properties in the limit
of weak non-ideality
(Г
ltlt 1)
Binary i‐i i‐e e‐e
correlation functions
ldquoZero and second momentrdquo conditions (Stillinger amp Lovett)2
2[ ( ) ( )] 3D
rn F r F r dr
r
0e e sh ( ) 1 1 e
pr qrr
abrF r A
r r
Thermodynamic condition for the depth of i-e pseudopotentialand amplitude of electron-ionic correlation function
0 ln [ (0) ]ie ei e iF
Positive sign of all correlation functions Fab
(r) gt 0
F r Ae e
re
sh rrab
pr qrr( )
1 1 0
Pseudopotentials
U
= UKin
+ UPot
3PV
= 2UKin + UPot
Homogeneity of Coulomb potential
U Vn F F dpot coul ( ) r
U Vn F F dei ii 2 ( ) r
)2()2(3 potkinpot UUUUPV
2 2i i
ie ie1 e( ) (1 e (0) ~
rrZ e Z er
r r
( ))
Correlation Functions
Total Energy correction
Potential Energy Correction
-
UPot
Pressure Correction
-
P
i e i eN N U ( ) 1
Approximate relation between Coulomb corrections for chemical potential and energy
(
UN)
NB
Thermodynamic contributions inmodified pseudopotential model for Coulomb corrections
Positive shift in average kinetic energy due to non-ideality of free charges subsystem Ukin = 3PV ndash
U
Well-known relation between pressure and energy corrections for free charges subsystemU = 3PV
which is valid at weak non-ideality (Г
ltlt 1) is no longer valid in strong non-ideality conditions (Г
~ 1)
It is equivalent to additional effective electron-ion repulsion(in comparison with ordinary one-parametric Coulomb corrections depending on non-ideality parameter only
FNkT = f(Г)
Experimental data Theoretical models
(comparison)
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
Quasi‐isochoric behavior of nitrogen Hugoniot
‐
Mochalov
M Zhernokletov
M et al
JETP
137
(2010) ‐
Trunin
R Boriskov
G et alJETP Letters
88
(2008)
15 20 25 30 35 400
100
200
300
ExperimentsTrunin et al 2008Mochalov et al 2010
P GPa
gcm3
lim
Check of theoretical models
SAHA
CCM
Ross ampRogers
CCM ndash
Compressible Covolume
Model(A Medvedev
amp
VKopyshev)
SAHA‐code (V Gryaznov amp IIosilevskiy)
ρHug
asymp
33 plusmn
01
gcm390
lt
PHug
lt 330
GPa
NN
22 NN‐‐polymerpolymer
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
equiv
V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost
linear function of pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
Reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal Energy
Pressure (Hugonoit)
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
Blue curve
ndash
internal energy calculated via plasma model(code SAHA
Gryaznov Iosilevskiy)
SAHA
Hugoniot
~ ρ
asymp
const (33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
ρ
asymp33 plusmn01
gcc90
lt
P lt 330
GPa
NB
Quasi‐linear behavior of
E(p)
at ρ
=
constThermodynamics of shock compressed nitrogen
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
00
01
02
03
04
05
06
07
08
09
10 Mochalov et al PHug (Trunin et al) + T (EOSCCM) PHug (Trunin et al) + T (EOSSAHA)
xN+
xi
xN2
P GPa
T k
K
Tr
Tr
Plasma
Temperature of shock compressed nitrogen
CP()
General P‐T
diagram
Quasi‐linear behavior of
T(p)
at ρ
=
const
SAHA
‐
Experiment Mochalov
M et al
JETF
137
(2010)Nellis
W Radovsky
H et al J Chem Phys 94
(1991)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
Electroconductivity
of shock compressed nitrogen
20 25 30 351E-3
001
01
1
10
100
1000
C E B E 28061 B 29062
Con
duct
ivity
1
cm
Density gcc
Electroconductivity
of shock compressed nitrogen
Ternovoi
V et al (email ‐
30052010)
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1
P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
‐
Experiment Mochalov
M et al
JETF
137
(2010)
Quasi‐isentropic Plane Compression of Matter at Megabar
Pressures by Using of a Layered
System to Diminish First Shock Wave IntensityTernovoi
V Pyalling
A Filimonovet
A (052010) Summary and conclusion
Explosive driven quasi‐isentropic compression generators were proposed for matter investigation in
the megabar
pressure region Results of the first experiments on quasi‐isentropic compression of
liquid nitrogen are presented It was shown that pressure ionization
of nitrogen proceeds at
densities
from 315 to 34 gcc
at a temperature
of about 3000
K
Diminishing of temperature growth
was measured during onset of nitrogen electrical conductivity
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
figure fromB Boates S Bonev Phys Rev Lett
102
(2009)
Ab initio calculations
‐
DFTMD
MolecularPolymeric
Critical point
CrossoverCrossover
11stst
order PTorder PT
MeltingMelting
Molecularfluid
Dissociated fluid
Fluidndashfluid
phase transitionin hydrogen [] ()
DFTMD
Scandolo
S PNAS
100 (2003)
Bonev S Militzer B Galli G PRB
69 (2004) WPMD
Jakob
B et al PRE
(2007) DFTMD Morales M et al PNAS
107 (2010)
DFTMD Lorenzen
W et al PRB
(2010)
Figure from
Giulia Galli SCCS-2005
Moscow= = = =
with additionsMorales et al 2010
andLorensen et al 2010
Morales et al
2010
Lorenzen
et al
2010
Ab initio calculations
‐
DFTMD
Experiment ndash single shock
compression ndash
reflected shock
compressionRadousky Nellis amp Ross et al Phys Rev Lett 57
(1986)Nellis Radousky
amp Hamilton et alJ Chem Phys 94
(1991)
0 50 100 150 200 250 3000
10
Tr Tr
CP
P GPa
T 103 K
Nitrogen phase diagram in the region of polymerizationPressure ndash temperature
melting (extrapolation)
HugoniotPlasma Model (SAHA‐code)
Yakubliquid
solidN2 N‐polimer
Theoretical models
estimation of polymer‐molecule
boundary in liquid nitrogen
(ЕYakub
ndash
1993) estimation of polymer‐molecule
boundary in solid nitrogen
(LYakub
ndash
1993)CP
ndash
critical point of 1st
order phase
transition polymer‐molecule
(ЕYakub
ndash
1993) ndash
triple point of 1st
order phase transition
polymer‐molecule
(Е amp L Yakub
ndash
1993)ЕS Yakub Low Temp Phys
20
579 (1994)LN Yakub Low Temp Phys
19 531 (1993)
estimation of polymer‐molecule bounda‐
ry
in liquid nitrogen (Ross amp Rogers
ndash
2006)MRoss
amp
FRogers Phys Rev
B 74 (2006)Ab
initio calculations DFTMD
ndash
calculation of of
polymer‐‐
molecule boundary in liquid nitrogen
(SBonev
et al ndash
2009)
the same as ldquosmoothedrdquo
phase transitionB Boates
amp
S Bonev Phys Rev Lett
102
(2009)
Gr
gt 0
Gr
lt 0 ndash domains of positive and negative sign of Gruumlneisen
coefficient
Gr
equiv
V(partPpartE)V
hypothetical boundary between polymeric and non‐ideal plasma states
(1st‐order phase transition or continuous )
melting
N2
N‐polimer
Gr
gt 0
Gr
lt 0
N‐plasma
Gr
gt 0
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
‐
Mochalov
M Zhernokletov
M et al
JETP
137 77
(2010) ‐
Trunin
R Boriskov
G Bykov
A Medvedev
A
JETP Letters
88 220 (2008)
Phase Diagram of Dense Nitrogen(summary)
N2
Npolimer
boundaryYakub Ross amp
Rogers etc
HypotheticalPressure Ionizationfrom N‐polymer
to N‐plasma
1st‐order phase transition
Critical point(s)
Domain
Gr
lt 0
Topology of theboundary
Gr
= 0
Pre‐compressed gaseous N2
Iso‐S
N2
N‐polimer
N‐plasma
Gr
gt 0
Gr
gt 0
Gr
lt 0
New experiments
‐
Shock waves‐ Iso‐S
Compression‐ Heavy Ion Beams‐
Laser Heating etc etc
THEORY Ab
initioRPIMC DPIMC
DFTMDChem modelsSAHA‐N
WZ‐cell modelsTFC MHFS
Wide‐range EOSEOS (IPCP
RAS)EOS (JIHT
RAS)CCM (Sarov)
Commentsmicrophysics
Simple molecules H2
N2
L = 074 A L = 11 A
D = 29 A D = 37 A
Triple covalent bond De
= 98 eV
(49 eVatom)
Single covalent bond De
= 30 eV
(45 eVatom)
L = 14 A
Figures after
Eugene Yakub ldquoNon‐simple
problems for simple moleculesrdquoFAIR‐Russia School laquoPhysics of high energy density in matterraquo
December
2009 Moscow
FZaharievAHuJHooperFZhangampTWoo PhysRev B 72214108 (2005 )
Polymeric nitrogen - structure
Eugene and Lidia Yakub Low Temp Phys 19 (1993)
Simple molecular modelsFirst estimations of molecular-polymeric transition
1 - Hugoniot2 - Phase equilibrium line
Experiment (Nellis ea 2001)3 - Single shock4 - Double shock
NN22
NN‐‐polimerpolimer
NN22
NN‐‐polimerpolimer
1st‐orderPhase transition
Critical point
Plasma model for nitrogen thermodynamics(code SAHA-N)
Shock compression of nitrogen(chemical picture)
SAHA-codeGryaznov Iosilevskiy (1970-2010)
Short range repulsionldquoSoft Spheresrdquo
approximation (DYoung)
modified for mixture
of soft spheres with different radii
ndash
shift of dissociation level
N
N+ + endash Ze
e
rcA
iA+
A+
i
Coulomb interactionModified pseudopotential
model
for partially ionized plasma(I
Iosilevskiy 1980-2010)
Equilibrium
compositionN2
N N+ e N2+ Nndash
Key parameter
ndash
ratio of intrinsic volumes molecule atom ion
R(N)
R(N2
)
= 063-
in accordance with recommendations of
ldquoAtom-atomic
approximationrdquo
of EYakub LT 1993
Basic points-
All assumption are provided at micro-level-
Input Choice of Фie
Фii
and Фее
pseudopotentials - Input Approximations for binary correlation functions - Strong correlation of the pseudopotentials
for ldquofreerdquocharges and upper energy level for partition functionsfor bound states
- Priority for general equalities (normalizing conditions)valid independently on degree of non-ideality
- Non-ideality corrections through the correlationfunctions and general equalities valid for Coulombinteraction
NN22
harrharr 2N2N NN22
++
harrharr NN ++
NN++ NNndashharrharr NN ++
eendash
[ ( ) ( )] 1n F r F r d r
Coulomb Corrections for Free Charge Subsystem
Modified Pseudopotential Approximation ()
Bound and free states of electron‐ionic pair
Effective electro-ionic potential (in Glaubermanrsquos form (1955))
2i
ie ( ) 1 e rZ err
( )
()
Iosilevskiy I High Temp 18
(1980) in ldquoEncyclopedia
of Low‐T Plasmardquo
(Suppl) Moscow FIZMATLIT 2004 pp 349
The form of i-i i-e e-e binary correlation functions-
laquoringraquo
(Debye) approximation with potential
Фie
(r)guarantee correct properties in the limit
of weak non-ideality
(Г
ltlt 1)
Binary i‐i i‐e e‐e
correlation functions
ldquoZero and second momentrdquo conditions (Stillinger amp Lovett)2
2[ ( ) ( )] 3D
rn F r F r dr
r
0e e sh ( ) 1 1 e
pr qrr
abrF r A
r r
Thermodynamic condition for the depth of i-e pseudopotentialand amplitude of electron-ionic correlation function
0 ln [ (0) ]ie ei e iF
Positive sign of all correlation functions Fab
(r) gt 0
F r Ae e
re
sh rrab
pr qrr( )
1 1 0
Pseudopotentials
U
= UKin
+ UPot
3PV
= 2UKin + UPot
Homogeneity of Coulomb potential
U Vn F F dpot coul ( ) r
U Vn F F dei ii 2 ( ) r
)2()2(3 potkinpot UUUUPV
2 2i i
ie ie1 e( ) (1 e (0) ~
rrZ e Z er
r r
( ))
Correlation Functions
Total Energy correction
Potential Energy Correction
-
UPot
Pressure Correction
-
P
i e i eN N U ( ) 1
Approximate relation between Coulomb corrections for chemical potential and energy
(
UN)
NB
Thermodynamic contributions inmodified pseudopotential model for Coulomb corrections
Positive shift in average kinetic energy due to non-ideality of free charges subsystem Ukin = 3PV ndash
U
Well-known relation between pressure and energy corrections for free charges subsystemU = 3PV
which is valid at weak non-ideality (Г
ltlt 1) is no longer valid in strong non-ideality conditions (Г
~ 1)
It is equivalent to additional effective electron-ion repulsion(in comparison with ordinary one-parametric Coulomb corrections depending on non-ideality parameter only
FNkT = f(Г)
Experimental data Theoretical models
(comparison)
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
Quasi‐isochoric behavior of nitrogen Hugoniot
‐
Mochalov
M Zhernokletov
M et al
JETP
137
(2010) ‐
Trunin
R Boriskov
G et alJETP Letters
88
(2008)
15 20 25 30 35 400
100
200
300
ExperimentsTrunin et al 2008Mochalov et al 2010
P GPa
gcm3
lim
Check of theoretical models
SAHA
CCM
Ross ampRogers
CCM ndash
Compressible Covolume
Model(A Medvedev
amp
VKopyshev)
SAHA‐code (V Gryaznov amp IIosilevskiy)
ρHug
asymp
33 plusmn
01
gcm390
lt
PHug
lt 330
GPa
NN
22 NN‐‐polymerpolymer
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
equiv
V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost
linear function of pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
Reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal Energy
Pressure (Hugonoit)
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
Blue curve
ndash
internal energy calculated via plasma model(code SAHA
Gryaznov Iosilevskiy)
SAHA
Hugoniot
~ ρ
asymp
const (33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
ρ
asymp33 plusmn01
gcc90
lt
P lt 330
GPa
NB
Quasi‐linear behavior of
E(p)
at ρ
=
constThermodynamics of shock compressed nitrogen
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
00
01
02
03
04
05
06
07
08
09
10 Mochalov et al PHug (Trunin et al) + T (EOSCCM) PHug (Trunin et al) + T (EOSSAHA)
xN+
xi
xN2
P GPa
T k
K
Tr
Tr
Plasma
Temperature of shock compressed nitrogen
CP()
General P‐T
diagram
Quasi‐linear behavior of
T(p)
at ρ
=
const
SAHA
‐
Experiment Mochalov
M et al
JETF
137
(2010)Nellis
W Radovsky
H et al J Chem Phys 94
(1991)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
Electroconductivity
of shock compressed nitrogen
20 25 30 351E-3
001
01
1
10
100
1000
C E B E 28061 B 29062
Con
duct
ivity
1
cm
Density gcc
Electroconductivity
of shock compressed nitrogen
Ternovoi
V et al (email ‐
30052010)
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1
P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
‐
Experiment Mochalov
M et al
JETF
137
(2010)
Quasi‐isentropic Plane Compression of Matter at Megabar
Pressures by Using of a Layered
System to Diminish First Shock Wave IntensityTernovoi
V Pyalling
A Filimonovet
A (052010) Summary and conclusion
Explosive driven quasi‐isentropic compression generators were proposed for matter investigation in
the megabar
pressure region Results of the first experiments on quasi‐isentropic compression of
liquid nitrogen are presented It was shown that pressure ionization
of nitrogen proceeds at
densities
from 315 to 34 gcc
at a temperature
of about 3000
K
Diminishing of temperature growth
was measured during onset of nitrogen electrical conductivity
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
Molecularfluid
Dissociated fluid
Fluidndashfluid
phase transitionin hydrogen [] ()
DFTMD
Scandolo
S PNAS
100 (2003)
Bonev S Militzer B Galli G PRB
69 (2004) WPMD
Jakob
B et al PRE
(2007) DFTMD Morales M et al PNAS
107 (2010)
DFTMD Lorenzen
W et al PRB
(2010)
Figure from
Giulia Galli SCCS-2005
Moscow= = = =
with additionsMorales et al 2010
andLorensen et al 2010
Morales et al
2010
Lorenzen
et al
2010
Ab initio calculations
‐
DFTMD
Experiment ndash single shock
compression ndash
reflected shock
compressionRadousky Nellis amp Ross et al Phys Rev Lett 57
(1986)Nellis Radousky
amp Hamilton et alJ Chem Phys 94
(1991)
0 50 100 150 200 250 3000
10
Tr Tr
CP
P GPa
T 103 K
Nitrogen phase diagram in the region of polymerizationPressure ndash temperature
melting (extrapolation)
HugoniotPlasma Model (SAHA‐code)
Yakubliquid
solidN2 N‐polimer
Theoretical models
estimation of polymer‐molecule
boundary in liquid nitrogen
(ЕYakub
ndash
1993) estimation of polymer‐molecule
boundary in solid nitrogen
(LYakub
ndash
1993)CP
ndash
critical point of 1st
order phase
transition polymer‐molecule
(ЕYakub
ndash
1993) ndash
triple point of 1st
order phase transition
polymer‐molecule
(Е amp L Yakub
ndash
1993)ЕS Yakub Low Temp Phys
20
579 (1994)LN Yakub Low Temp Phys
19 531 (1993)
estimation of polymer‐molecule bounda‐
ry
in liquid nitrogen (Ross amp Rogers
ndash
2006)MRoss
amp
FRogers Phys Rev
B 74 (2006)Ab
initio calculations DFTMD
ndash
calculation of of
polymer‐‐
molecule boundary in liquid nitrogen
(SBonev
et al ndash
2009)
the same as ldquosmoothedrdquo
phase transitionB Boates
amp
S Bonev Phys Rev Lett
102
(2009)
Gr
gt 0
Gr
lt 0 ndash domains of positive and negative sign of Gruumlneisen
coefficient
Gr
equiv
V(partPpartE)V
hypothetical boundary between polymeric and non‐ideal plasma states
(1st‐order phase transition or continuous )
melting
N2
N‐polimer
Gr
gt 0
Gr
lt 0
N‐plasma
Gr
gt 0
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
‐
Mochalov
M Zhernokletov
M et al
JETP
137 77
(2010) ‐
Trunin
R Boriskov
G Bykov
A Medvedev
A
JETP Letters
88 220 (2008)
Phase Diagram of Dense Nitrogen(summary)
N2
Npolimer
boundaryYakub Ross amp
Rogers etc
HypotheticalPressure Ionizationfrom N‐polymer
to N‐plasma
1st‐order phase transition
Critical point(s)
Domain
Gr
lt 0
Topology of theboundary
Gr
= 0
Pre‐compressed gaseous N2
Iso‐S
N2
N‐polimer
N‐plasma
Gr
gt 0
Gr
gt 0
Gr
lt 0
New experiments
‐
Shock waves‐ Iso‐S
Compression‐ Heavy Ion Beams‐
Laser Heating etc etc
THEORY Ab
initioRPIMC DPIMC
DFTMDChem modelsSAHA‐N
WZ‐cell modelsTFC MHFS
Wide‐range EOSEOS (IPCP
RAS)EOS (JIHT
RAS)CCM (Sarov)
Commentsmicrophysics
Simple molecules H2
N2
L = 074 A L = 11 A
D = 29 A D = 37 A
Triple covalent bond De
= 98 eV
(49 eVatom)
Single covalent bond De
= 30 eV
(45 eVatom)
L = 14 A
Figures after
Eugene Yakub ldquoNon‐simple
problems for simple moleculesrdquoFAIR‐Russia School laquoPhysics of high energy density in matterraquo
December
2009 Moscow
FZaharievAHuJHooperFZhangampTWoo PhysRev B 72214108 (2005 )
Polymeric nitrogen - structure
Eugene and Lidia Yakub Low Temp Phys 19 (1993)
Simple molecular modelsFirst estimations of molecular-polymeric transition
1 - Hugoniot2 - Phase equilibrium line
Experiment (Nellis ea 2001)3 - Single shock4 - Double shock
NN22
NN‐‐polimerpolimer
NN22
NN‐‐polimerpolimer
1st‐orderPhase transition
Critical point
Plasma model for nitrogen thermodynamics(code SAHA-N)
Shock compression of nitrogen(chemical picture)
SAHA-codeGryaznov Iosilevskiy (1970-2010)
Short range repulsionldquoSoft Spheresrdquo
approximation (DYoung)
modified for mixture
of soft spheres with different radii
ndash
shift of dissociation level
N
N+ + endash Ze
e
rcA
iA+
A+
i
Coulomb interactionModified pseudopotential
model
for partially ionized plasma(I
Iosilevskiy 1980-2010)
Equilibrium
compositionN2
N N+ e N2+ Nndash
Key parameter
ndash
ratio of intrinsic volumes molecule atom ion
R(N)
R(N2
)
= 063-
in accordance with recommendations of
ldquoAtom-atomic
approximationrdquo
of EYakub LT 1993
Basic points-
All assumption are provided at micro-level-
Input Choice of Фie
Фii
and Фее
pseudopotentials - Input Approximations for binary correlation functions - Strong correlation of the pseudopotentials
for ldquofreerdquocharges and upper energy level for partition functionsfor bound states
- Priority for general equalities (normalizing conditions)valid independently on degree of non-ideality
- Non-ideality corrections through the correlationfunctions and general equalities valid for Coulombinteraction
NN22
harrharr 2N2N NN22
++
harrharr NN ++
NN++ NNndashharrharr NN ++
eendash
[ ( ) ( )] 1n F r F r d r
Coulomb Corrections for Free Charge Subsystem
Modified Pseudopotential Approximation ()
Bound and free states of electron‐ionic pair
Effective electro-ionic potential (in Glaubermanrsquos form (1955))
2i
ie ( ) 1 e rZ err
( )
()
Iosilevskiy I High Temp 18
(1980) in ldquoEncyclopedia
of Low‐T Plasmardquo
(Suppl) Moscow FIZMATLIT 2004 pp 349
The form of i-i i-e e-e binary correlation functions-
laquoringraquo
(Debye) approximation with potential
Фie
(r)guarantee correct properties in the limit
of weak non-ideality
(Г
ltlt 1)
Binary i‐i i‐e e‐e
correlation functions
ldquoZero and second momentrdquo conditions (Stillinger amp Lovett)2
2[ ( ) ( )] 3D
rn F r F r dr
r
0e e sh ( ) 1 1 e
pr qrr
abrF r A
r r
Thermodynamic condition for the depth of i-e pseudopotentialand amplitude of electron-ionic correlation function
0 ln [ (0) ]ie ei e iF
Positive sign of all correlation functions Fab
(r) gt 0
F r Ae e
re
sh rrab
pr qrr( )
1 1 0
Pseudopotentials
U
= UKin
+ UPot
3PV
= 2UKin + UPot
Homogeneity of Coulomb potential
U Vn F F dpot coul ( ) r
U Vn F F dei ii 2 ( ) r
)2()2(3 potkinpot UUUUPV
2 2i i
ie ie1 e( ) (1 e (0) ~
rrZ e Z er
r r
( ))
Correlation Functions
Total Energy correction
Potential Energy Correction
-
UPot
Pressure Correction
-
P
i e i eN N U ( ) 1
Approximate relation between Coulomb corrections for chemical potential and energy
(
UN)
NB
Thermodynamic contributions inmodified pseudopotential model for Coulomb corrections
Positive shift in average kinetic energy due to non-ideality of free charges subsystem Ukin = 3PV ndash
U
Well-known relation between pressure and energy corrections for free charges subsystemU = 3PV
which is valid at weak non-ideality (Г
ltlt 1) is no longer valid in strong non-ideality conditions (Г
~ 1)
It is equivalent to additional effective electron-ion repulsion(in comparison with ordinary one-parametric Coulomb corrections depending on non-ideality parameter only
FNkT = f(Г)
Experimental data Theoretical models
(comparison)
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
Quasi‐isochoric behavior of nitrogen Hugoniot
‐
Mochalov
M Zhernokletov
M et al
JETP
137
(2010) ‐
Trunin
R Boriskov
G et alJETP Letters
88
(2008)
15 20 25 30 35 400
100
200
300
ExperimentsTrunin et al 2008Mochalov et al 2010
P GPa
gcm3
lim
Check of theoretical models
SAHA
CCM
Ross ampRogers
CCM ndash
Compressible Covolume
Model(A Medvedev
amp
VKopyshev)
SAHA‐code (V Gryaznov amp IIosilevskiy)
ρHug
asymp
33 plusmn
01
gcm390
lt
PHug
lt 330
GPa
NN
22 NN‐‐polymerpolymer
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
equiv
V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost
linear function of pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
Reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal Energy
Pressure (Hugonoit)
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
Blue curve
ndash
internal energy calculated via plasma model(code SAHA
Gryaznov Iosilevskiy)
SAHA
Hugoniot
~ ρ
asymp
const (33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
ρ
asymp33 plusmn01
gcc90
lt
P lt 330
GPa
NB
Quasi‐linear behavior of
E(p)
at ρ
=
constThermodynamics of shock compressed nitrogen
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
00
01
02
03
04
05
06
07
08
09
10 Mochalov et al PHug (Trunin et al) + T (EOSCCM) PHug (Trunin et al) + T (EOSSAHA)
xN+
xi
xN2
P GPa
T k
K
Tr
Tr
Plasma
Temperature of shock compressed nitrogen
CP()
General P‐T
diagram
Quasi‐linear behavior of
T(p)
at ρ
=
const
SAHA
‐
Experiment Mochalov
M et al
JETF
137
(2010)Nellis
W Radovsky
H et al J Chem Phys 94
(1991)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
Electroconductivity
of shock compressed nitrogen
20 25 30 351E-3
001
01
1
10
100
1000
C E B E 28061 B 29062
Con
duct
ivity
1
cm
Density gcc
Electroconductivity
of shock compressed nitrogen
Ternovoi
V et al (email ‐
30052010)
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1
P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
‐
Experiment Mochalov
M et al
JETF
137
(2010)
Quasi‐isentropic Plane Compression of Matter at Megabar
Pressures by Using of a Layered
System to Diminish First Shock Wave IntensityTernovoi
V Pyalling
A Filimonovet
A (052010) Summary and conclusion
Explosive driven quasi‐isentropic compression generators were proposed for matter investigation in
the megabar
pressure region Results of the first experiments on quasi‐isentropic compression of
liquid nitrogen are presented It was shown that pressure ionization
of nitrogen proceeds at
densities
from 315 to 34 gcc
at a temperature
of about 3000
K
Diminishing of temperature growth
was measured during onset of nitrogen electrical conductivity
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
Experiment ndash single shock
compression ndash
reflected shock
compressionRadousky Nellis amp Ross et al Phys Rev Lett 57
(1986)Nellis Radousky
amp Hamilton et alJ Chem Phys 94
(1991)
0 50 100 150 200 250 3000
10
Tr Tr
CP
P GPa
T 103 K
Nitrogen phase diagram in the region of polymerizationPressure ndash temperature
melting (extrapolation)
HugoniotPlasma Model (SAHA‐code)
Yakubliquid
solidN2 N‐polimer
Theoretical models
estimation of polymer‐molecule
boundary in liquid nitrogen
(ЕYakub
ndash
1993) estimation of polymer‐molecule
boundary in solid nitrogen
(LYakub
ndash
1993)CP
ndash
critical point of 1st
order phase
transition polymer‐molecule
(ЕYakub
ndash
1993) ndash
triple point of 1st
order phase transition
polymer‐molecule
(Е amp L Yakub
ndash
1993)ЕS Yakub Low Temp Phys
20
579 (1994)LN Yakub Low Temp Phys
19 531 (1993)
estimation of polymer‐molecule bounda‐
ry
in liquid nitrogen (Ross amp Rogers
ndash
2006)MRoss
amp
FRogers Phys Rev
B 74 (2006)Ab
initio calculations DFTMD
ndash
calculation of of
polymer‐‐
molecule boundary in liquid nitrogen
(SBonev
et al ndash
2009)
the same as ldquosmoothedrdquo
phase transitionB Boates
amp
S Bonev Phys Rev Lett
102
(2009)
Gr
gt 0
Gr
lt 0 ndash domains of positive and negative sign of Gruumlneisen
coefficient
Gr
equiv
V(partPpartE)V
hypothetical boundary between polymeric and non‐ideal plasma states
(1st‐order phase transition or continuous )
melting
N2
N‐polimer
Gr
gt 0
Gr
lt 0
N‐plasma
Gr
gt 0
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
‐
Mochalov
M Zhernokletov
M et al
JETP
137 77
(2010) ‐
Trunin
R Boriskov
G Bykov
A Medvedev
A
JETP Letters
88 220 (2008)
Phase Diagram of Dense Nitrogen(summary)
N2
Npolimer
boundaryYakub Ross amp
Rogers etc
HypotheticalPressure Ionizationfrom N‐polymer
to N‐plasma
1st‐order phase transition
Critical point(s)
Domain
Gr
lt 0
Topology of theboundary
Gr
= 0
Pre‐compressed gaseous N2
Iso‐S
N2
N‐polimer
N‐plasma
Gr
gt 0
Gr
gt 0
Gr
lt 0
New experiments
‐
Shock waves‐ Iso‐S
Compression‐ Heavy Ion Beams‐
Laser Heating etc etc
THEORY Ab
initioRPIMC DPIMC
DFTMDChem modelsSAHA‐N
WZ‐cell modelsTFC MHFS
Wide‐range EOSEOS (IPCP
RAS)EOS (JIHT
RAS)CCM (Sarov)
Commentsmicrophysics
Simple molecules H2
N2
L = 074 A L = 11 A
D = 29 A D = 37 A
Triple covalent bond De
= 98 eV
(49 eVatom)
Single covalent bond De
= 30 eV
(45 eVatom)
L = 14 A
Figures after
Eugene Yakub ldquoNon‐simple
problems for simple moleculesrdquoFAIR‐Russia School laquoPhysics of high energy density in matterraquo
December
2009 Moscow
FZaharievAHuJHooperFZhangampTWoo PhysRev B 72214108 (2005 )
Polymeric nitrogen - structure
Eugene and Lidia Yakub Low Temp Phys 19 (1993)
Simple molecular modelsFirst estimations of molecular-polymeric transition
1 - Hugoniot2 - Phase equilibrium line
Experiment (Nellis ea 2001)3 - Single shock4 - Double shock
NN22
NN‐‐polimerpolimer
NN22
NN‐‐polimerpolimer
1st‐orderPhase transition
Critical point
Plasma model for nitrogen thermodynamics(code SAHA-N)
Shock compression of nitrogen(chemical picture)
SAHA-codeGryaznov Iosilevskiy (1970-2010)
Short range repulsionldquoSoft Spheresrdquo
approximation (DYoung)
modified for mixture
of soft spheres with different radii
ndash
shift of dissociation level
N
N+ + endash Ze
e
rcA
iA+
A+
i
Coulomb interactionModified pseudopotential
model
for partially ionized plasma(I
Iosilevskiy 1980-2010)
Equilibrium
compositionN2
N N+ e N2+ Nndash
Key parameter
ndash
ratio of intrinsic volumes molecule atom ion
R(N)
R(N2
)
= 063-
in accordance with recommendations of
ldquoAtom-atomic
approximationrdquo
of EYakub LT 1993
Basic points-
All assumption are provided at micro-level-
Input Choice of Фie
Фii
and Фее
pseudopotentials - Input Approximations for binary correlation functions - Strong correlation of the pseudopotentials
for ldquofreerdquocharges and upper energy level for partition functionsfor bound states
- Priority for general equalities (normalizing conditions)valid independently on degree of non-ideality
- Non-ideality corrections through the correlationfunctions and general equalities valid for Coulombinteraction
NN22
harrharr 2N2N NN22
++
harrharr NN ++
NN++ NNndashharrharr NN ++
eendash
[ ( ) ( )] 1n F r F r d r
Coulomb Corrections for Free Charge Subsystem
Modified Pseudopotential Approximation ()
Bound and free states of electron‐ionic pair
Effective electro-ionic potential (in Glaubermanrsquos form (1955))
2i
ie ( ) 1 e rZ err
( )
()
Iosilevskiy I High Temp 18
(1980) in ldquoEncyclopedia
of Low‐T Plasmardquo
(Suppl) Moscow FIZMATLIT 2004 pp 349
The form of i-i i-e e-e binary correlation functions-
laquoringraquo
(Debye) approximation with potential
Фie
(r)guarantee correct properties in the limit
of weak non-ideality
(Г
ltlt 1)
Binary i‐i i‐e e‐e
correlation functions
ldquoZero and second momentrdquo conditions (Stillinger amp Lovett)2
2[ ( ) ( )] 3D
rn F r F r dr
r
0e e sh ( ) 1 1 e
pr qrr
abrF r A
r r
Thermodynamic condition for the depth of i-e pseudopotentialand amplitude of electron-ionic correlation function
0 ln [ (0) ]ie ei e iF
Positive sign of all correlation functions Fab
(r) gt 0
F r Ae e
re
sh rrab
pr qrr( )
1 1 0
Pseudopotentials
U
= UKin
+ UPot
3PV
= 2UKin + UPot
Homogeneity of Coulomb potential
U Vn F F dpot coul ( ) r
U Vn F F dei ii 2 ( ) r
)2()2(3 potkinpot UUUUPV
2 2i i
ie ie1 e( ) (1 e (0) ~
rrZ e Z er
r r
( ))
Correlation Functions
Total Energy correction
Potential Energy Correction
-
UPot
Pressure Correction
-
P
i e i eN N U ( ) 1
Approximate relation between Coulomb corrections for chemical potential and energy
(
UN)
NB
Thermodynamic contributions inmodified pseudopotential model for Coulomb corrections
Positive shift in average kinetic energy due to non-ideality of free charges subsystem Ukin = 3PV ndash
U
Well-known relation between pressure and energy corrections for free charges subsystemU = 3PV
which is valid at weak non-ideality (Г
ltlt 1) is no longer valid in strong non-ideality conditions (Г
~ 1)
It is equivalent to additional effective electron-ion repulsion(in comparison with ordinary one-parametric Coulomb corrections depending on non-ideality parameter only
FNkT = f(Г)
Experimental data Theoretical models
(comparison)
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
Quasi‐isochoric behavior of nitrogen Hugoniot
‐
Mochalov
M Zhernokletov
M et al
JETP
137
(2010) ‐
Trunin
R Boriskov
G et alJETP Letters
88
(2008)
15 20 25 30 35 400
100
200
300
ExperimentsTrunin et al 2008Mochalov et al 2010
P GPa
gcm3
lim
Check of theoretical models
SAHA
CCM
Ross ampRogers
CCM ndash
Compressible Covolume
Model(A Medvedev
amp
VKopyshev)
SAHA‐code (V Gryaznov amp IIosilevskiy)
ρHug
asymp
33 plusmn
01
gcm390
lt
PHug
lt 330
GPa
NN
22 NN‐‐polymerpolymer
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
equiv
V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost
linear function of pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
Reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal Energy
Pressure (Hugonoit)
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
Blue curve
ndash
internal energy calculated via plasma model(code SAHA
Gryaznov Iosilevskiy)
SAHA
Hugoniot
~ ρ
asymp
const (33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
ρ
asymp33 plusmn01
gcc90
lt
P lt 330
GPa
NB
Quasi‐linear behavior of
E(p)
at ρ
=
constThermodynamics of shock compressed nitrogen
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
00
01
02
03
04
05
06
07
08
09
10 Mochalov et al PHug (Trunin et al) + T (EOSCCM) PHug (Trunin et al) + T (EOSSAHA)
xN+
xi
xN2
P GPa
T k
K
Tr
Tr
Plasma
Temperature of shock compressed nitrogen
CP()
General P‐T
diagram
Quasi‐linear behavior of
T(p)
at ρ
=
const
SAHA
‐
Experiment Mochalov
M et al
JETF
137
(2010)Nellis
W Radovsky
H et al J Chem Phys 94
(1991)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
Electroconductivity
of shock compressed nitrogen
20 25 30 351E-3
001
01
1
10
100
1000
C E B E 28061 B 29062
Con
duct
ivity
1
cm
Density gcc
Electroconductivity
of shock compressed nitrogen
Ternovoi
V et al (email ‐
30052010)
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1
P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
‐
Experiment Mochalov
M et al
JETF
137
(2010)
Quasi‐isentropic Plane Compression of Matter at Megabar
Pressures by Using of a Layered
System to Diminish First Shock Wave IntensityTernovoi
V Pyalling
A Filimonovet
A (052010) Summary and conclusion
Explosive driven quasi‐isentropic compression generators were proposed for matter investigation in
the megabar
pressure region Results of the first experiments on quasi‐isentropic compression of
liquid nitrogen are presented It was shown that pressure ionization
of nitrogen proceeds at
densities
from 315 to 34 gcc
at a temperature
of about 3000
K
Diminishing of temperature growth
was measured during onset of nitrogen electrical conductivity
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
‐
Mochalov
M Zhernokletov
M et al
JETP
137 77
(2010) ‐
Trunin
R Boriskov
G Bykov
A Medvedev
A
JETP Letters
88 220 (2008)
Phase Diagram of Dense Nitrogen(summary)
N2
Npolimer
boundaryYakub Ross amp
Rogers etc
HypotheticalPressure Ionizationfrom N‐polymer
to N‐plasma
1st‐order phase transition
Critical point(s)
Domain
Gr
lt 0
Topology of theboundary
Gr
= 0
Pre‐compressed gaseous N2
Iso‐S
N2
N‐polimer
N‐plasma
Gr
gt 0
Gr
gt 0
Gr
lt 0
New experiments
‐
Shock waves‐ Iso‐S
Compression‐ Heavy Ion Beams‐
Laser Heating etc etc
THEORY Ab
initioRPIMC DPIMC
DFTMDChem modelsSAHA‐N
WZ‐cell modelsTFC MHFS
Wide‐range EOSEOS (IPCP
RAS)EOS (JIHT
RAS)CCM (Sarov)
Commentsmicrophysics
Simple molecules H2
N2
L = 074 A L = 11 A
D = 29 A D = 37 A
Triple covalent bond De
= 98 eV
(49 eVatom)
Single covalent bond De
= 30 eV
(45 eVatom)
L = 14 A
Figures after
Eugene Yakub ldquoNon‐simple
problems for simple moleculesrdquoFAIR‐Russia School laquoPhysics of high energy density in matterraquo
December
2009 Moscow
FZaharievAHuJHooperFZhangampTWoo PhysRev B 72214108 (2005 )
Polymeric nitrogen - structure
Eugene and Lidia Yakub Low Temp Phys 19 (1993)
Simple molecular modelsFirst estimations of molecular-polymeric transition
1 - Hugoniot2 - Phase equilibrium line
Experiment (Nellis ea 2001)3 - Single shock4 - Double shock
NN22
NN‐‐polimerpolimer
NN22
NN‐‐polimerpolimer
1st‐orderPhase transition
Critical point
Plasma model for nitrogen thermodynamics(code SAHA-N)
Shock compression of nitrogen(chemical picture)
SAHA-codeGryaznov Iosilevskiy (1970-2010)
Short range repulsionldquoSoft Spheresrdquo
approximation (DYoung)
modified for mixture
of soft spheres with different radii
ndash
shift of dissociation level
N
N+ + endash Ze
e
rcA
iA+
A+
i
Coulomb interactionModified pseudopotential
model
for partially ionized plasma(I
Iosilevskiy 1980-2010)
Equilibrium
compositionN2
N N+ e N2+ Nndash
Key parameter
ndash
ratio of intrinsic volumes molecule atom ion
R(N)
R(N2
)
= 063-
in accordance with recommendations of
ldquoAtom-atomic
approximationrdquo
of EYakub LT 1993
Basic points-
All assumption are provided at micro-level-
Input Choice of Фie
Фii
and Фее
pseudopotentials - Input Approximations for binary correlation functions - Strong correlation of the pseudopotentials
for ldquofreerdquocharges and upper energy level for partition functionsfor bound states
- Priority for general equalities (normalizing conditions)valid independently on degree of non-ideality
- Non-ideality corrections through the correlationfunctions and general equalities valid for Coulombinteraction
NN22
harrharr 2N2N NN22
++
harrharr NN ++
NN++ NNndashharrharr NN ++
eendash
[ ( ) ( )] 1n F r F r d r
Coulomb Corrections for Free Charge Subsystem
Modified Pseudopotential Approximation ()
Bound and free states of electron‐ionic pair
Effective electro-ionic potential (in Glaubermanrsquos form (1955))
2i
ie ( ) 1 e rZ err
( )
()
Iosilevskiy I High Temp 18
(1980) in ldquoEncyclopedia
of Low‐T Plasmardquo
(Suppl) Moscow FIZMATLIT 2004 pp 349
The form of i-i i-e e-e binary correlation functions-
laquoringraquo
(Debye) approximation with potential
Фie
(r)guarantee correct properties in the limit
of weak non-ideality
(Г
ltlt 1)
Binary i‐i i‐e e‐e
correlation functions
ldquoZero and second momentrdquo conditions (Stillinger amp Lovett)2
2[ ( ) ( )] 3D
rn F r F r dr
r
0e e sh ( ) 1 1 e
pr qrr
abrF r A
r r
Thermodynamic condition for the depth of i-e pseudopotentialand amplitude of electron-ionic correlation function
0 ln [ (0) ]ie ei e iF
Positive sign of all correlation functions Fab
(r) gt 0
F r Ae e
re
sh rrab
pr qrr( )
1 1 0
Pseudopotentials
U
= UKin
+ UPot
3PV
= 2UKin + UPot
Homogeneity of Coulomb potential
U Vn F F dpot coul ( ) r
U Vn F F dei ii 2 ( ) r
)2()2(3 potkinpot UUUUPV
2 2i i
ie ie1 e( ) (1 e (0) ~
rrZ e Z er
r r
( ))
Correlation Functions
Total Energy correction
Potential Energy Correction
-
UPot
Pressure Correction
-
P
i e i eN N U ( ) 1
Approximate relation between Coulomb corrections for chemical potential and energy
(
UN)
NB
Thermodynamic contributions inmodified pseudopotential model for Coulomb corrections
Positive shift in average kinetic energy due to non-ideality of free charges subsystem Ukin = 3PV ndash
U
Well-known relation between pressure and energy corrections for free charges subsystemU = 3PV
which is valid at weak non-ideality (Г
ltlt 1) is no longer valid in strong non-ideality conditions (Г
~ 1)
It is equivalent to additional effective electron-ion repulsion(in comparison with ordinary one-parametric Coulomb corrections depending on non-ideality parameter only
FNkT = f(Г)
Experimental data Theoretical models
(comparison)
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
Quasi‐isochoric behavior of nitrogen Hugoniot
‐
Mochalov
M Zhernokletov
M et al
JETP
137
(2010) ‐
Trunin
R Boriskov
G et alJETP Letters
88
(2008)
15 20 25 30 35 400
100
200
300
ExperimentsTrunin et al 2008Mochalov et al 2010
P GPa
gcm3
lim
Check of theoretical models
SAHA
CCM
Ross ampRogers
CCM ndash
Compressible Covolume
Model(A Medvedev
amp
VKopyshev)
SAHA‐code (V Gryaznov amp IIosilevskiy)
ρHug
asymp
33 plusmn
01
gcm390
lt
PHug
lt 330
GPa
NN
22 NN‐‐polymerpolymer
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
equiv
V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost
linear function of pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
Reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal Energy
Pressure (Hugonoit)
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
Blue curve
ndash
internal energy calculated via plasma model(code SAHA
Gryaznov Iosilevskiy)
SAHA
Hugoniot
~ ρ
asymp
const (33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
ρ
asymp33 plusmn01
gcc90
lt
P lt 330
GPa
NB
Quasi‐linear behavior of
E(p)
at ρ
=
constThermodynamics of shock compressed nitrogen
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
00
01
02
03
04
05
06
07
08
09
10 Mochalov et al PHug (Trunin et al) + T (EOSCCM) PHug (Trunin et al) + T (EOSSAHA)
xN+
xi
xN2
P GPa
T k
K
Tr
Tr
Plasma
Temperature of shock compressed nitrogen
CP()
General P‐T
diagram
Quasi‐linear behavior of
T(p)
at ρ
=
const
SAHA
‐
Experiment Mochalov
M et al
JETF
137
(2010)Nellis
W Radovsky
H et al J Chem Phys 94
(1991)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
Electroconductivity
of shock compressed nitrogen
20 25 30 351E-3
001
01
1
10
100
1000
C E B E 28061 B 29062
Con
duct
ivity
1
cm
Density gcc
Electroconductivity
of shock compressed nitrogen
Ternovoi
V et al (email ‐
30052010)
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1
P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
‐
Experiment Mochalov
M et al
JETF
137
(2010)
Quasi‐isentropic Plane Compression of Matter at Megabar
Pressures by Using of a Layered
System to Diminish First Shock Wave IntensityTernovoi
V Pyalling
A Filimonovet
A (052010) Summary and conclusion
Explosive driven quasi‐isentropic compression generators were proposed for matter investigation in
the megabar
pressure region Results of the first experiments on quasi‐isentropic compression of
liquid nitrogen are presented It was shown that pressure ionization
of nitrogen proceeds at
densities
from 315 to 34 gcc
at a temperature
of about 3000
K
Diminishing of temperature growth
was measured during onset of nitrogen electrical conductivity
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
Commentsmicrophysics
Simple molecules H2
N2
L = 074 A L = 11 A
D = 29 A D = 37 A
Triple covalent bond De
= 98 eV
(49 eVatom)
Single covalent bond De
= 30 eV
(45 eVatom)
L = 14 A
Figures after
Eugene Yakub ldquoNon‐simple
problems for simple moleculesrdquoFAIR‐Russia School laquoPhysics of high energy density in matterraquo
December
2009 Moscow
FZaharievAHuJHooperFZhangampTWoo PhysRev B 72214108 (2005 )
Polymeric nitrogen - structure
Eugene and Lidia Yakub Low Temp Phys 19 (1993)
Simple molecular modelsFirst estimations of molecular-polymeric transition
1 - Hugoniot2 - Phase equilibrium line
Experiment (Nellis ea 2001)3 - Single shock4 - Double shock
NN22
NN‐‐polimerpolimer
NN22
NN‐‐polimerpolimer
1st‐orderPhase transition
Critical point
Plasma model for nitrogen thermodynamics(code SAHA-N)
Shock compression of nitrogen(chemical picture)
SAHA-codeGryaznov Iosilevskiy (1970-2010)
Short range repulsionldquoSoft Spheresrdquo
approximation (DYoung)
modified for mixture
of soft spheres with different radii
ndash
shift of dissociation level
N
N+ + endash Ze
e
rcA
iA+
A+
i
Coulomb interactionModified pseudopotential
model
for partially ionized plasma(I
Iosilevskiy 1980-2010)
Equilibrium
compositionN2
N N+ e N2+ Nndash
Key parameter
ndash
ratio of intrinsic volumes molecule atom ion
R(N)
R(N2
)
= 063-
in accordance with recommendations of
ldquoAtom-atomic
approximationrdquo
of EYakub LT 1993
Basic points-
All assumption are provided at micro-level-
Input Choice of Фie
Фii
and Фее
pseudopotentials - Input Approximations for binary correlation functions - Strong correlation of the pseudopotentials
for ldquofreerdquocharges and upper energy level for partition functionsfor bound states
- Priority for general equalities (normalizing conditions)valid independently on degree of non-ideality
- Non-ideality corrections through the correlationfunctions and general equalities valid for Coulombinteraction
NN22
harrharr 2N2N NN22
++
harrharr NN ++
NN++ NNndashharrharr NN ++
eendash
[ ( ) ( )] 1n F r F r d r
Coulomb Corrections for Free Charge Subsystem
Modified Pseudopotential Approximation ()
Bound and free states of electron‐ionic pair
Effective electro-ionic potential (in Glaubermanrsquos form (1955))
2i
ie ( ) 1 e rZ err
( )
()
Iosilevskiy I High Temp 18
(1980) in ldquoEncyclopedia
of Low‐T Plasmardquo
(Suppl) Moscow FIZMATLIT 2004 pp 349
The form of i-i i-e e-e binary correlation functions-
laquoringraquo
(Debye) approximation with potential
Фie
(r)guarantee correct properties in the limit
of weak non-ideality
(Г
ltlt 1)
Binary i‐i i‐e e‐e
correlation functions
ldquoZero and second momentrdquo conditions (Stillinger amp Lovett)2
2[ ( ) ( )] 3D
rn F r F r dr
r
0e e sh ( ) 1 1 e
pr qrr
abrF r A
r r
Thermodynamic condition for the depth of i-e pseudopotentialand amplitude of electron-ionic correlation function
0 ln [ (0) ]ie ei e iF
Positive sign of all correlation functions Fab
(r) gt 0
F r Ae e
re
sh rrab
pr qrr( )
1 1 0
Pseudopotentials
U
= UKin
+ UPot
3PV
= 2UKin + UPot
Homogeneity of Coulomb potential
U Vn F F dpot coul ( ) r
U Vn F F dei ii 2 ( ) r
)2()2(3 potkinpot UUUUPV
2 2i i
ie ie1 e( ) (1 e (0) ~
rrZ e Z er
r r
( ))
Correlation Functions
Total Energy correction
Potential Energy Correction
-
UPot
Pressure Correction
-
P
i e i eN N U ( ) 1
Approximate relation between Coulomb corrections for chemical potential and energy
(
UN)
NB
Thermodynamic contributions inmodified pseudopotential model for Coulomb corrections
Positive shift in average kinetic energy due to non-ideality of free charges subsystem Ukin = 3PV ndash
U
Well-known relation between pressure and energy corrections for free charges subsystemU = 3PV
which is valid at weak non-ideality (Г
ltlt 1) is no longer valid in strong non-ideality conditions (Г
~ 1)
It is equivalent to additional effective electron-ion repulsion(in comparison with ordinary one-parametric Coulomb corrections depending on non-ideality parameter only
FNkT = f(Г)
Experimental data Theoretical models
(comparison)
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
Quasi‐isochoric behavior of nitrogen Hugoniot
‐
Mochalov
M Zhernokletov
M et al
JETP
137
(2010) ‐
Trunin
R Boriskov
G et alJETP Letters
88
(2008)
15 20 25 30 35 400
100
200
300
ExperimentsTrunin et al 2008Mochalov et al 2010
P GPa
gcm3
lim
Check of theoretical models
SAHA
CCM
Ross ampRogers
CCM ndash
Compressible Covolume
Model(A Medvedev
amp
VKopyshev)
SAHA‐code (V Gryaznov amp IIosilevskiy)
ρHug
asymp
33 plusmn
01
gcm390
lt
PHug
lt 330
GPa
NN
22 NN‐‐polymerpolymer
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
equiv
V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost
linear function of pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
Reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal Energy
Pressure (Hugonoit)
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
Blue curve
ndash
internal energy calculated via plasma model(code SAHA
Gryaznov Iosilevskiy)
SAHA
Hugoniot
~ ρ
asymp
const (33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
ρ
asymp33 plusmn01
gcc90
lt
P lt 330
GPa
NB
Quasi‐linear behavior of
E(p)
at ρ
=
constThermodynamics of shock compressed nitrogen
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
00
01
02
03
04
05
06
07
08
09
10 Mochalov et al PHug (Trunin et al) + T (EOSCCM) PHug (Trunin et al) + T (EOSSAHA)
xN+
xi
xN2
P GPa
T k
K
Tr
Tr
Plasma
Temperature of shock compressed nitrogen
CP()
General P‐T
diagram
Quasi‐linear behavior of
T(p)
at ρ
=
const
SAHA
‐
Experiment Mochalov
M et al
JETF
137
(2010)Nellis
W Radovsky
H et al J Chem Phys 94
(1991)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
Electroconductivity
of shock compressed nitrogen
20 25 30 351E-3
001
01
1
10
100
1000
C E B E 28061 B 29062
Con
duct
ivity
1
cm
Density gcc
Electroconductivity
of shock compressed nitrogen
Ternovoi
V et al (email ‐
30052010)
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1
P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
‐
Experiment Mochalov
M et al
JETF
137
(2010)
Quasi‐isentropic Plane Compression of Matter at Megabar
Pressures by Using of a Layered
System to Diminish First Shock Wave IntensityTernovoi
V Pyalling
A Filimonovet
A (052010) Summary and conclusion
Explosive driven quasi‐isentropic compression generators were proposed for matter investigation in
the megabar
pressure region Results of the first experiments on quasi‐isentropic compression of
liquid nitrogen are presented It was shown that pressure ionization
of nitrogen proceeds at
densities
from 315 to 34 gcc
at a temperature
of about 3000
K
Diminishing of temperature growth
was measured during onset of nitrogen electrical conductivity
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
Simple molecules H2
N2
L = 074 A L = 11 A
D = 29 A D = 37 A
Triple covalent bond De
= 98 eV
(49 eVatom)
Single covalent bond De
= 30 eV
(45 eVatom)
L = 14 A
Figures after
Eugene Yakub ldquoNon‐simple
problems for simple moleculesrdquoFAIR‐Russia School laquoPhysics of high energy density in matterraquo
December
2009 Moscow
FZaharievAHuJHooperFZhangampTWoo PhysRev B 72214108 (2005 )
Polymeric nitrogen - structure
Eugene and Lidia Yakub Low Temp Phys 19 (1993)
Simple molecular modelsFirst estimations of molecular-polymeric transition
1 - Hugoniot2 - Phase equilibrium line
Experiment (Nellis ea 2001)3 - Single shock4 - Double shock
NN22
NN‐‐polimerpolimer
NN22
NN‐‐polimerpolimer
1st‐orderPhase transition
Critical point
Plasma model for nitrogen thermodynamics(code SAHA-N)
Shock compression of nitrogen(chemical picture)
SAHA-codeGryaznov Iosilevskiy (1970-2010)
Short range repulsionldquoSoft Spheresrdquo
approximation (DYoung)
modified for mixture
of soft spheres with different radii
ndash
shift of dissociation level
N
N+ + endash Ze
e
rcA
iA+
A+
i
Coulomb interactionModified pseudopotential
model
for partially ionized plasma(I
Iosilevskiy 1980-2010)
Equilibrium
compositionN2
N N+ e N2+ Nndash
Key parameter
ndash
ratio of intrinsic volumes molecule atom ion
R(N)
R(N2
)
= 063-
in accordance with recommendations of
ldquoAtom-atomic
approximationrdquo
of EYakub LT 1993
Basic points-
All assumption are provided at micro-level-
Input Choice of Фie
Фii
and Фее
pseudopotentials - Input Approximations for binary correlation functions - Strong correlation of the pseudopotentials
for ldquofreerdquocharges and upper energy level for partition functionsfor bound states
- Priority for general equalities (normalizing conditions)valid independently on degree of non-ideality
- Non-ideality corrections through the correlationfunctions and general equalities valid for Coulombinteraction
NN22
harrharr 2N2N NN22
++
harrharr NN ++
NN++ NNndashharrharr NN ++
eendash
[ ( ) ( )] 1n F r F r d r
Coulomb Corrections for Free Charge Subsystem
Modified Pseudopotential Approximation ()
Bound and free states of electron‐ionic pair
Effective electro-ionic potential (in Glaubermanrsquos form (1955))
2i
ie ( ) 1 e rZ err
( )
()
Iosilevskiy I High Temp 18
(1980) in ldquoEncyclopedia
of Low‐T Plasmardquo
(Suppl) Moscow FIZMATLIT 2004 pp 349
The form of i-i i-e e-e binary correlation functions-
laquoringraquo
(Debye) approximation with potential
Фie
(r)guarantee correct properties in the limit
of weak non-ideality
(Г
ltlt 1)
Binary i‐i i‐e e‐e
correlation functions
ldquoZero and second momentrdquo conditions (Stillinger amp Lovett)2
2[ ( ) ( )] 3D
rn F r F r dr
r
0e e sh ( ) 1 1 e
pr qrr
abrF r A
r r
Thermodynamic condition for the depth of i-e pseudopotentialand amplitude of electron-ionic correlation function
0 ln [ (0) ]ie ei e iF
Positive sign of all correlation functions Fab
(r) gt 0
F r Ae e
re
sh rrab
pr qrr( )
1 1 0
Pseudopotentials
U
= UKin
+ UPot
3PV
= 2UKin + UPot
Homogeneity of Coulomb potential
U Vn F F dpot coul ( ) r
U Vn F F dei ii 2 ( ) r
)2()2(3 potkinpot UUUUPV
2 2i i
ie ie1 e( ) (1 e (0) ~
rrZ e Z er
r r
( ))
Correlation Functions
Total Energy correction
Potential Energy Correction
-
UPot
Pressure Correction
-
P
i e i eN N U ( ) 1
Approximate relation between Coulomb corrections for chemical potential and energy
(
UN)
NB
Thermodynamic contributions inmodified pseudopotential model for Coulomb corrections
Positive shift in average kinetic energy due to non-ideality of free charges subsystem Ukin = 3PV ndash
U
Well-known relation between pressure and energy corrections for free charges subsystemU = 3PV
which is valid at weak non-ideality (Г
ltlt 1) is no longer valid in strong non-ideality conditions (Г
~ 1)
It is equivalent to additional effective electron-ion repulsion(in comparison with ordinary one-parametric Coulomb corrections depending on non-ideality parameter only
FNkT = f(Г)
Experimental data Theoretical models
(comparison)
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
Quasi‐isochoric behavior of nitrogen Hugoniot
‐
Mochalov
M Zhernokletov
M et al
JETP
137
(2010) ‐
Trunin
R Boriskov
G et alJETP Letters
88
(2008)
15 20 25 30 35 400
100
200
300
ExperimentsTrunin et al 2008Mochalov et al 2010
P GPa
gcm3
lim
Check of theoretical models
SAHA
CCM
Ross ampRogers
CCM ndash
Compressible Covolume
Model(A Medvedev
amp
VKopyshev)
SAHA‐code (V Gryaznov amp IIosilevskiy)
ρHug
asymp
33 plusmn
01
gcm390
lt
PHug
lt 330
GPa
NN
22 NN‐‐polymerpolymer
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
equiv
V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost
linear function of pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
Reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal Energy
Pressure (Hugonoit)
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
Blue curve
ndash
internal energy calculated via plasma model(code SAHA
Gryaznov Iosilevskiy)
SAHA
Hugoniot
~ ρ
asymp
const (33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
ρ
asymp33 plusmn01
gcc90
lt
P lt 330
GPa
NB
Quasi‐linear behavior of
E(p)
at ρ
=
constThermodynamics of shock compressed nitrogen
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
00
01
02
03
04
05
06
07
08
09
10 Mochalov et al PHug (Trunin et al) + T (EOSCCM) PHug (Trunin et al) + T (EOSSAHA)
xN+
xi
xN2
P GPa
T k
K
Tr
Tr
Plasma
Temperature of shock compressed nitrogen
CP()
General P‐T
diagram
Quasi‐linear behavior of
T(p)
at ρ
=
const
SAHA
‐
Experiment Mochalov
M et al
JETF
137
(2010)Nellis
W Radovsky
H et al J Chem Phys 94
(1991)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
Electroconductivity
of shock compressed nitrogen
20 25 30 351E-3
001
01
1
10
100
1000
C E B E 28061 B 29062
Con
duct
ivity
1
cm
Density gcc
Electroconductivity
of shock compressed nitrogen
Ternovoi
V et al (email ‐
30052010)
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1
P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
‐
Experiment Mochalov
M et al
JETF
137
(2010)
Quasi‐isentropic Plane Compression of Matter at Megabar
Pressures by Using of a Layered
System to Diminish First Shock Wave IntensityTernovoi
V Pyalling
A Filimonovet
A (052010) Summary and conclusion
Explosive driven quasi‐isentropic compression generators were proposed for matter investigation in
the megabar
pressure region Results of the first experiments on quasi‐isentropic compression of
liquid nitrogen are presented It was shown that pressure ionization
of nitrogen proceeds at
densities
from 315 to 34 gcc
at a temperature
of about 3000
K
Diminishing of temperature growth
was measured during onset of nitrogen electrical conductivity
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
FZaharievAHuJHooperFZhangampTWoo PhysRev B 72214108 (2005 )
Polymeric nitrogen - structure
Eugene and Lidia Yakub Low Temp Phys 19 (1993)
Simple molecular modelsFirst estimations of molecular-polymeric transition
1 - Hugoniot2 - Phase equilibrium line
Experiment (Nellis ea 2001)3 - Single shock4 - Double shock
NN22
NN‐‐polimerpolimer
NN22
NN‐‐polimerpolimer
1st‐orderPhase transition
Critical point
Plasma model for nitrogen thermodynamics(code SAHA-N)
Shock compression of nitrogen(chemical picture)
SAHA-codeGryaznov Iosilevskiy (1970-2010)
Short range repulsionldquoSoft Spheresrdquo
approximation (DYoung)
modified for mixture
of soft spheres with different radii
ndash
shift of dissociation level
N
N+ + endash Ze
e
rcA
iA+
A+
i
Coulomb interactionModified pseudopotential
model
for partially ionized plasma(I
Iosilevskiy 1980-2010)
Equilibrium
compositionN2
N N+ e N2+ Nndash
Key parameter
ndash
ratio of intrinsic volumes molecule atom ion
R(N)
R(N2
)
= 063-
in accordance with recommendations of
ldquoAtom-atomic
approximationrdquo
of EYakub LT 1993
Basic points-
All assumption are provided at micro-level-
Input Choice of Фie
Фii
and Фее
pseudopotentials - Input Approximations for binary correlation functions - Strong correlation of the pseudopotentials
for ldquofreerdquocharges and upper energy level for partition functionsfor bound states
- Priority for general equalities (normalizing conditions)valid independently on degree of non-ideality
- Non-ideality corrections through the correlationfunctions and general equalities valid for Coulombinteraction
NN22
harrharr 2N2N NN22
++
harrharr NN ++
NN++ NNndashharrharr NN ++
eendash
[ ( ) ( )] 1n F r F r d r
Coulomb Corrections for Free Charge Subsystem
Modified Pseudopotential Approximation ()
Bound and free states of electron‐ionic pair
Effective electro-ionic potential (in Glaubermanrsquos form (1955))
2i
ie ( ) 1 e rZ err
( )
()
Iosilevskiy I High Temp 18
(1980) in ldquoEncyclopedia
of Low‐T Plasmardquo
(Suppl) Moscow FIZMATLIT 2004 pp 349
The form of i-i i-e e-e binary correlation functions-
laquoringraquo
(Debye) approximation with potential
Фie
(r)guarantee correct properties in the limit
of weak non-ideality
(Г
ltlt 1)
Binary i‐i i‐e e‐e
correlation functions
ldquoZero and second momentrdquo conditions (Stillinger amp Lovett)2
2[ ( ) ( )] 3D
rn F r F r dr
r
0e e sh ( ) 1 1 e
pr qrr
abrF r A
r r
Thermodynamic condition for the depth of i-e pseudopotentialand amplitude of electron-ionic correlation function
0 ln [ (0) ]ie ei e iF
Positive sign of all correlation functions Fab
(r) gt 0
F r Ae e
re
sh rrab
pr qrr( )
1 1 0
Pseudopotentials
U
= UKin
+ UPot
3PV
= 2UKin + UPot
Homogeneity of Coulomb potential
U Vn F F dpot coul ( ) r
U Vn F F dei ii 2 ( ) r
)2()2(3 potkinpot UUUUPV
2 2i i
ie ie1 e( ) (1 e (0) ~
rrZ e Z er
r r
( ))
Correlation Functions
Total Energy correction
Potential Energy Correction
-
UPot
Pressure Correction
-
P
i e i eN N U ( ) 1
Approximate relation between Coulomb corrections for chemical potential and energy
(
UN)
NB
Thermodynamic contributions inmodified pseudopotential model for Coulomb corrections
Positive shift in average kinetic energy due to non-ideality of free charges subsystem Ukin = 3PV ndash
U
Well-known relation between pressure and energy corrections for free charges subsystemU = 3PV
which is valid at weak non-ideality (Г
ltlt 1) is no longer valid in strong non-ideality conditions (Г
~ 1)
It is equivalent to additional effective electron-ion repulsion(in comparison with ordinary one-parametric Coulomb corrections depending on non-ideality parameter only
FNkT = f(Г)
Experimental data Theoretical models
(comparison)
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
Quasi‐isochoric behavior of nitrogen Hugoniot
‐
Mochalov
M Zhernokletov
M et al
JETP
137
(2010) ‐
Trunin
R Boriskov
G et alJETP Letters
88
(2008)
15 20 25 30 35 400
100
200
300
ExperimentsTrunin et al 2008Mochalov et al 2010
P GPa
gcm3
lim
Check of theoretical models
SAHA
CCM
Ross ampRogers
CCM ndash
Compressible Covolume
Model(A Medvedev
amp
VKopyshev)
SAHA‐code (V Gryaznov amp IIosilevskiy)
ρHug
asymp
33 plusmn
01
gcm390
lt
PHug
lt 330
GPa
NN
22 NN‐‐polymerpolymer
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
equiv
V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost
linear function of pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
Reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal Energy
Pressure (Hugonoit)
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
Blue curve
ndash
internal energy calculated via plasma model(code SAHA
Gryaznov Iosilevskiy)
SAHA
Hugoniot
~ ρ
asymp
const (33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
ρ
asymp33 plusmn01
gcc90
lt
P lt 330
GPa
NB
Quasi‐linear behavior of
E(p)
at ρ
=
constThermodynamics of shock compressed nitrogen
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
00
01
02
03
04
05
06
07
08
09
10 Mochalov et al PHug (Trunin et al) + T (EOSCCM) PHug (Trunin et al) + T (EOSSAHA)
xN+
xi
xN2
P GPa
T k
K
Tr
Tr
Plasma
Temperature of shock compressed nitrogen
CP()
General P‐T
diagram
Quasi‐linear behavior of
T(p)
at ρ
=
const
SAHA
‐
Experiment Mochalov
M et al
JETF
137
(2010)Nellis
W Radovsky
H et al J Chem Phys 94
(1991)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
Electroconductivity
of shock compressed nitrogen
20 25 30 351E-3
001
01
1
10
100
1000
C E B E 28061 B 29062
Con
duct
ivity
1
cm
Density gcc
Electroconductivity
of shock compressed nitrogen
Ternovoi
V et al (email ‐
30052010)
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1
P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
‐
Experiment Mochalov
M et al
JETF
137
(2010)
Quasi‐isentropic Plane Compression of Matter at Megabar
Pressures by Using of a Layered
System to Diminish First Shock Wave IntensityTernovoi
V Pyalling
A Filimonovet
A (052010) Summary and conclusion
Explosive driven quasi‐isentropic compression generators were proposed for matter investigation in
the megabar
pressure region Results of the first experiments on quasi‐isentropic compression of
liquid nitrogen are presented It was shown that pressure ionization
of nitrogen proceeds at
densities
from 315 to 34 gcc
at a temperature
of about 3000
K
Diminishing of temperature growth
was measured during onset of nitrogen electrical conductivity
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
Eugene and Lidia Yakub Low Temp Phys 19 (1993)
Simple molecular modelsFirst estimations of molecular-polymeric transition
1 - Hugoniot2 - Phase equilibrium line
Experiment (Nellis ea 2001)3 - Single shock4 - Double shock
NN22
NN‐‐polimerpolimer
NN22
NN‐‐polimerpolimer
1st‐orderPhase transition
Critical point
Plasma model for nitrogen thermodynamics(code SAHA-N)
Shock compression of nitrogen(chemical picture)
SAHA-codeGryaznov Iosilevskiy (1970-2010)
Short range repulsionldquoSoft Spheresrdquo
approximation (DYoung)
modified for mixture
of soft spheres with different radii
ndash
shift of dissociation level
N
N+ + endash Ze
e
rcA
iA+
A+
i
Coulomb interactionModified pseudopotential
model
for partially ionized plasma(I
Iosilevskiy 1980-2010)
Equilibrium
compositionN2
N N+ e N2+ Nndash
Key parameter
ndash
ratio of intrinsic volumes molecule atom ion
R(N)
R(N2
)
= 063-
in accordance with recommendations of
ldquoAtom-atomic
approximationrdquo
of EYakub LT 1993
Basic points-
All assumption are provided at micro-level-
Input Choice of Фie
Фii
and Фее
pseudopotentials - Input Approximations for binary correlation functions - Strong correlation of the pseudopotentials
for ldquofreerdquocharges and upper energy level for partition functionsfor bound states
- Priority for general equalities (normalizing conditions)valid independently on degree of non-ideality
- Non-ideality corrections through the correlationfunctions and general equalities valid for Coulombinteraction
NN22
harrharr 2N2N NN22
++
harrharr NN ++
NN++ NNndashharrharr NN ++
eendash
[ ( ) ( )] 1n F r F r d r
Coulomb Corrections for Free Charge Subsystem
Modified Pseudopotential Approximation ()
Bound and free states of electron‐ionic pair
Effective electro-ionic potential (in Glaubermanrsquos form (1955))
2i
ie ( ) 1 e rZ err
( )
()
Iosilevskiy I High Temp 18
(1980) in ldquoEncyclopedia
of Low‐T Plasmardquo
(Suppl) Moscow FIZMATLIT 2004 pp 349
The form of i-i i-e e-e binary correlation functions-
laquoringraquo
(Debye) approximation with potential
Фie
(r)guarantee correct properties in the limit
of weak non-ideality
(Г
ltlt 1)
Binary i‐i i‐e e‐e
correlation functions
ldquoZero and second momentrdquo conditions (Stillinger amp Lovett)2
2[ ( ) ( )] 3D
rn F r F r dr
r
0e e sh ( ) 1 1 e
pr qrr
abrF r A
r r
Thermodynamic condition for the depth of i-e pseudopotentialand amplitude of electron-ionic correlation function
0 ln [ (0) ]ie ei e iF
Positive sign of all correlation functions Fab
(r) gt 0
F r Ae e
re
sh rrab
pr qrr( )
1 1 0
Pseudopotentials
U
= UKin
+ UPot
3PV
= 2UKin + UPot
Homogeneity of Coulomb potential
U Vn F F dpot coul ( ) r
U Vn F F dei ii 2 ( ) r
)2()2(3 potkinpot UUUUPV
2 2i i
ie ie1 e( ) (1 e (0) ~
rrZ e Z er
r r
( ))
Correlation Functions
Total Energy correction
Potential Energy Correction
-
UPot
Pressure Correction
-
P
i e i eN N U ( ) 1
Approximate relation between Coulomb corrections for chemical potential and energy
(
UN)
NB
Thermodynamic contributions inmodified pseudopotential model for Coulomb corrections
Positive shift in average kinetic energy due to non-ideality of free charges subsystem Ukin = 3PV ndash
U
Well-known relation between pressure and energy corrections for free charges subsystemU = 3PV
which is valid at weak non-ideality (Г
ltlt 1) is no longer valid in strong non-ideality conditions (Г
~ 1)
It is equivalent to additional effective electron-ion repulsion(in comparison with ordinary one-parametric Coulomb corrections depending on non-ideality parameter only
FNkT = f(Г)
Experimental data Theoretical models
(comparison)
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
Quasi‐isochoric behavior of nitrogen Hugoniot
‐
Mochalov
M Zhernokletov
M et al
JETP
137
(2010) ‐
Trunin
R Boriskov
G et alJETP Letters
88
(2008)
15 20 25 30 35 400
100
200
300
ExperimentsTrunin et al 2008Mochalov et al 2010
P GPa
gcm3
lim
Check of theoretical models
SAHA
CCM
Ross ampRogers
CCM ndash
Compressible Covolume
Model(A Medvedev
amp
VKopyshev)
SAHA‐code (V Gryaznov amp IIosilevskiy)
ρHug
asymp
33 plusmn
01
gcm390
lt
PHug
lt 330
GPa
NN
22 NN‐‐polymerpolymer
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
equiv
V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost
linear function of pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
Reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal Energy
Pressure (Hugonoit)
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
Blue curve
ndash
internal energy calculated via plasma model(code SAHA
Gryaznov Iosilevskiy)
SAHA
Hugoniot
~ ρ
asymp
const (33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
ρ
asymp33 plusmn01
gcc90
lt
P lt 330
GPa
NB
Quasi‐linear behavior of
E(p)
at ρ
=
constThermodynamics of shock compressed nitrogen
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
00
01
02
03
04
05
06
07
08
09
10 Mochalov et al PHug (Trunin et al) + T (EOSCCM) PHug (Trunin et al) + T (EOSSAHA)
xN+
xi
xN2
P GPa
T k
K
Tr
Tr
Plasma
Temperature of shock compressed nitrogen
CP()
General P‐T
diagram
Quasi‐linear behavior of
T(p)
at ρ
=
const
SAHA
‐
Experiment Mochalov
M et al
JETF
137
(2010)Nellis
W Radovsky
H et al J Chem Phys 94
(1991)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
Electroconductivity
of shock compressed nitrogen
20 25 30 351E-3
001
01
1
10
100
1000
C E B E 28061 B 29062
Con
duct
ivity
1
cm
Density gcc
Electroconductivity
of shock compressed nitrogen
Ternovoi
V et al (email ‐
30052010)
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1
P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
‐
Experiment Mochalov
M et al
JETF
137
(2010)
Quasi‐isentropic Plane Compression of Matter at Megabar
Pressures by Using of a Layered
System to Diminish First Shock Wave IntensityTernovoi
V Pyalling
A Filimonovet
A (052010) Summary and conclusion
Explosive driven quasi‐isentropic compression generators were proposed for matter investigation in
the megabar
pressure region Results of the first experiments on quasi‐isentropic compression of
liquid nitrogen are presented It was shown that pressure ionization
of nitrogen proceeds at
densities
from 315 to 34 gcc
at a temperature
of about 3000
K
Diminishing of temperature growth
was measured during onset of nitrogen electrical conductivity
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
Plasma model for nitrogen thermodynamics(code SAHA-N)
Shock compression of nitrogen(chemical picture)
SAHA-codeGryaznov Iosilevskiy (1970-2010)
Short range repulsionldquoSoft Spheresrdquo
approximation (DYoung)
modified for mixture
of soft spheres with different radii
ndash
shift of dissociation level
N
N+ + endash Ze
e
rcA
iA+
A+
i
Coulomb interactionModified pseudopotential
model
for partially ionized plasma(I
Iosilevskiy 1980-2010)
Equilibrium
compositionN2
N N+ e N2+ Nndash
Key parameter
ndash
ratio of intrinsic volumes molecule atom ion
R(N)
R(N2
)
= 063-
in accordance with recommendations of
ldquoAtom-atomic
approximationrdquo
of EYakub LT 1993
Basic points-
All assumption are provided at micro-level-
Input Choice of Фie
Фii
and Фее
pseudopotentials - Input Approximations for binary correlation functions - Strong correlation of the pseudopotentials
for ldquofreerdquocharges and upper energy level for partition functionsfor bound states
- Priority for general equalities (normalizing conditions)valid independently on degree of non-ideality
- Non-ideality corrections through the correlationfunctions and general equalities valid for Coulombinteraction
NN22
harrharr 2N2N NN22
++
harrharr NN ++
NN++ NNndashharrharr NN ++
eendash
[ ( ) ( )] 1n F r F r d r
Coulomb Corrections for Free Charge Subsystem
Modified Pseudopotential Approximation ()
Bound and free states of electron‐ionic pair
Effective electro-ionic potential (in Glaubermanrsquos form (1955))
2i
ie ( ) 1 e rZ err
( )
()
Iosilevskiy I High Temp 18
(1980) in ldquoEncyclopedia
of Low‐T Plasmardquo
(Suppl) Moscow FIZMATLIT 2004 pp 349
The form of i-i i-e e-e binary correlation functions-
laquoringraquo
(Debye) approximation with potential
Фie
(r)guarantee correct properties in the limit
of weak non-ideality
(Г
ltlt 1)
Binary i‐i i‐e e‐e
correlation functions
ldquoZero and second momentrdquo conditions (Stillinger amp Lovett)2
2[ ( ) ( )] 3D
rn F r F r dr
r
0e e sh ( ) 1 1 e
pr qrr
abrF r A
r r
Thermodynamic condition for the depth of i-e pseudopotentialand amplitude of electron-ionic correlation function
0 ln [ (0) ]ie ei e iF
Positive sign of all correlation functions Fab
(r) gt 0
F r Ae e
re
sh rrab
pr qrr( )
1 1 0
Pseudopotentials
U
= UKin
+ UPot
3PV
= 2UKin + UPot
Homogeneity of Coulomb potential
U Vn F F dpot coul ( ) r
U Vn F F dei ii 2 ( ) r
)2()2(3 potkinpot UUUUPV
2 2i i
ie ie1 e( ) (1 e (0) ~
rrZ e Z er
r r
( ))
Correlation Functions
Total Energy correction
Potential Energy Correction
-
UPot
Pressure Correction
-
P
i e i eN N U ( ) 1
Approximate relation between Coulomb corrections for chemical potential and energy
(
UN)
NB
Thermodynamic contributions inmodified pseudopotential model for Coulomb corrections
Positive shift in average kinetic energy due to non-ideality of free charges subsystem Ukin = 3PV ndash
U
Well-known relation between pressure and energy corrections for free charges subsystemU = 3PV
which is valid at weak non-ideality (Г
ltlt 1) is no longer valid in strong non-ideality conditions (Г
~ 1)
It is equivalent to additional effective electron-ion repulsion(in comparison with ordinary one-parametric Coulomb corrections depending on non-ideality parameter only
FNkT = f(Г)
Experimental data Theoretical models
(comparison)
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
Quasi‐isochoric behavior of nitrogen Hugoniot
‐
Mochalov
M Zhernokletov
M et al
JETP
137
(2010) ‐
Trunin
R Boriskov
G et alJETP Letters
88
(2008)
15 20 25 30 35 400
100
200
300
ExperimentsTrunin et al 2008Mochalov et al 2010
P GPa
gcm3
lim
Check of theoretical models
SAHA
CCM
Ross ampRogers
CCM ndash
Compressible Covolume
Model(A Medvedev
amp
VKopyshev)
SAHA‐code (V Gryaznov amp IIosilevskiy)
ρHug
asymp
33 plusmn
01
gcm390
lt
PHug
lt 330
GPa
NN
22 NN‐‐polymerpolymer
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
equiv
V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost
linear function of pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
Reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal Energy
Pressure (Hugonoit)
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
Blue curve
ndash
internal energy calculated via plasma model(code SAHA
Gryaznov Iosilevskiy)
SAHA
Hugoniot
~ ρ
asymp
const (33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
ρ
asymp33 plusmn01
gcc90
lt
P lt 330
GPa
NB
Quasi‐linear behavior of
E(p)
at ρ
=
constThermodynamics of shock compressed nitrogen
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
00
01
02
03
04
05
06
07
08
09
10 Mochalov et al PHug (Trunin et al) + T (EOSCCM) PHug (Trunin et al) + T (EOSSAHA)
xN+
xi
xN2
P GPa
T k
K
Tr
Tr
Plasma
Temperature of shock compressed nitrogen
CP()
General P‐T
diagram
Quasi‐linear behavior of
T(p)
at ρ
=
const
SAHA
‐
Experiment Mochalov
M et al
JETF
137
(2010)Nellis
W Radovsky
H et al J Chem Phys 94
(1991)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
Electroconductivity
of shock compressed nitrogen
20 25 30 351E-3
001
01
1
10
100
1000
C E B E 28061 B 29062
Con
duct
ivity
1
cm
Density gcc
Electroconductivity
of shock compressed nitrogen
Ternovoi
V et al (email ‐
30052010)
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1
P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
‐
Experiment Mochalov
M et al
JETF
137
(2010)
Quasi‐isentropic Plane Compression of Matter at Megabar
Pressures by Using of a Layered
System to Diminish First Shock Wave IntensityTernovoi
V Pyalling
A Filimonovet
A (052010) Summary and conclusion
Explosive driven quasi‐isentropic compression generators were proposed for matter investigation in
the megabar
pressure region Results of the first experiments on quasi‐isentropic compression of
liquid nitrogen are presented It was shown that pressure ionization
of nitrogen proceeds at
densities
from 315 to 34 gcc
at a temperature
of about 3000
K
Diminishing of temperature growth
was measured during onset of nitrogen electrical conductivity
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
Shock compression of nitrogen(chemical picture)
SAHA-codeGryaznov Iosilevskiy (1970-2010)
Short range repulsionldquoSoft Spheresrdquo
approximation (DYoung)
modified for mixture
of soft spheres with different radii
ndash
shift of dissociation level
N
N+ + endash Ze
e
rcA
iA+
A+
i
Coulomb interactionModified pseudopotential
model
for partially ionized plasma(I
Iosilevskiy 1980-2010)
Equilibrium
compositionN2
N N+ e N2+ Nndash
Key parameter
ndash
ratio of intrinsic volumes molecule atom ion
R(N)
R(N2
)
= 063-
in accordance with recommendations of
ldquoAtom-atomic
approximationrdquo
of EYakub LT 1993
Basic points-
All assumption are provided at micro-level-
Input Choice of Фie
Фii
and Фее
pseudopotentials - Input Approximations for binary correlation functions - Strong correlation of the pseudopotentials
for ldquofreerdquocharges and upper energy level for partition functionsfor bound states
- Priority for general equalities (normalizing conditions)valid independently on degree of non-ideality
- Non-ideality corrections through the correlationfunctions and general equalities valid for Coulombinteraction
NN22
harrharr 2N2N NN22
++
harrharr NN ++
NN++ NNndashharrharr NN ++
eendash
[ ( ) ( )] 1n F r F r d r
Coulomb Corrections for Free Charge Subsystem
Modified Pseudopotential Approximation ()
Bound and free states of electron‐ionic pair
Effective electro-ionic potential (in Glaubermanrsquos form (1955))
2i
ie ( ) 1 e rZ err
( )
()
Iosilevskiy I High Temp 18
(1980) in ldquoEncyclopedia
of Low‐T Plasmardquo
(Suppl) Moscow FIZMATLIT 2004 pp 349
The form of i-i i-e e-e binary correlation functions-
laquoringraquo
(Debye) approximation with potential
Фie
(r)guarantee correct properties in the limit
of weak non-ideality
(Г
ltlt 1)
Binary i‐i i‐e e‐e
correlation functions
ldquoZero and second momentrdquo conditions (Stillinger amp Lovett)2
2[ ( ) ( )] 3D
rn F r F r dr
r
0e e sh ( ) 1 1 e
pr qrr
abrF r A
r r
Thermodynamic condition for the depth of i-e pseudopotentialand amplitude of electron-ionic correlation function
0 ln [ (0) ]ie ei e iF
Positive sign of all correlation functions Fab
(r) gt 0
F r Ae e
re
sh rrab
pr qrr( )
1 1 0
Pseudopotentials
U
= UKin
+ UPot
3PV
= 2UKin + UPot
Homogeneity of Coulomb potential
U Vn F F dpot coul ( ) r
U Vn F F dei ii 2 ( ) r
)2()2(3 potkinpot UUUUPV
2 2i i
ie ie1 e( ) (1 e (0) ~
rrZ e Z er
r r
( ))
Correlation Functions
Total Energy correction
Potential Energy Correction
-
UPot
Pressure Correction
-
P
i e i eN N U ( ) 1
Approximate relation between Coulomb corrections for chemical potential and energy
(
UN)
NB
Thermodynamic contributions inmodified pseudopotential model for Coulomb corrections
Positive shift in average kinetic energy due to non-ideality of free charges subsystem Ukin = 3PV ndash
U
Well-known relation between pressure and energy corrections for free charges subsystemU = 3PV
which is valid at weak non-ideality (Г
ltlt 1) is no longer valid in strong non-ideality conditions (Г
~ 1)
It is equivalent to additional effective electron-ion repulsion(in comparison with ordinary one-parametric Coulomb corrections depending on non-ideality parameter only
FNkT = f(Г)
Experimental data Theoretical models
(comparison)
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
Quasi‐isochoric behavior of nitrogen Hugoniot
‐
Mochalov
M Zhernokletov
M et al
JETP
137
(2010) ‐
Trunin
R Boriskov
G et alJETP Letters
88
(2008)
15 20 25 30 35 400
100
200
300
ExperimentsTrunin et al 2008Mochalov et al 2010
P GPa
gcm3
lim
Check of theoretical models
SAHA
CCM
Ross ampRogers
CCM ndash
Compressible Covolume
Model(A Medvedev
amp
VKopyshev)
SAHA‐code (V Gryaznov amp IIosilevskiy)
ρHug
asymp
33 plusmn
01
gcm390
lt
PHug
lt 330
GPa
NN
22 NN‐‐polymerpolymer
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
equiv
V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost
linear function of pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
Reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal Energy
Pressure (Hugonoit)
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
Blue curve
ndash
internal energy calculated via plasma model(code SAHA
Gryaznov Iosilevskiy)
SAHA
Hugoniot
~ ρ
asymp
const (33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
ρ
asymp33 plusmn01
gcc90
lt
P lt 330
GPa
NB
Quasi‐linear behavior of
E(p)
at ρ
=
constThermodynamics of shock compressed nitrogen
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
00
01
02
03
04
05
06
07
08
09
10 Mochalov et al PHug (Trunin et al) + T (EOSCCM) PHug (Trunin et al) + T (EOSSAHA)
xN+
xi
xN2
P GPa
T k
K
Tr
Tr
Plasma
Temperature of shock compressed nitrogen
CP()
General P‐T
diagram
Quasi‐linear behavior of
T(p)
at ρ
=
const
SAHA
‐
Experiment Mochalov
M et al
JETF
137
(2010)Nellis
W Radovsky
H et al J Chem Phys 94
(1991)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
Electroconductivity
of shock compressed nitrogen
20 25 30 351E-3
001
01
1
10
100
1000
C E B E 28061 B 29062
Con
duct
ivity
1
cm
Density gcc
Electroconductivity
of shock compressed nitrogen
Ternovoi
V et al (email ‐
30052010)
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1
P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
‐
Experiment Mochalov
M et al
JETF
137
(2010)
Quasi‐isentropic Plane Compression of Matter at Megabar
Pressures by Using of a Layered
System to Diminish First Shock Wave IntensityTernovoi
V Pyalling
A Filimonovet
A (052010) Summary and conclusion
Explosive driven quasi‐isentropic compression generators were proposed for matter investigation in
the megabar
pressure region Results of the first experiments on quasi‐isentropic compression of
liquid nitrogen are presented It was shown that pressure ionization
of nitrogen proceeds at
densities
from 315 to 34 gcc
at a temperature
of about 3000
K
Diminishing of temperature growth
was measured during onset of nitrogen electrical conductivity
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
[ ( ) ( )] 1n F r F r d r
Coulomb Corrections for Free Charge Subsystem
Modified Pseudopotential Approximation ()
Bound and free states of electron‐ionic pair
Effective electro-ionic potential (in Glaubermanrsquos form (1955))
2i
ie ( ) 1 e rZ err
( )
()
Iosilevskiy I High Temp 18
(1980) in ldquoEncyclopedia
of Low‐T Plasmardquo
(Suppl) Moscow FIZMATLIT 2004 pp 349
The form of i-i i-e e-e binary correlation functions-
laquoringraquo
(Debye) approximation with potential
Фie
(r)guarantee correct properties in the limit
of weak non-ideality
(Г
ltlt 1)
Binary i‐i i‐e e‐e
correlation functions
ldquoZero and second momentrdquo conditions (Stillinger amp Lovett)2
2[ ( ) ( )] 3D
rn F r F r dr
r
0e e sh ( ) 1 1 e
pr qrr
abrF r A
r r
Thermodynamic condition for the depth of i-e pseudopotentialand amplitude of electron-ionic correlation function
0 ln [ (0) ]ie ei e iF
Positive sign of all correlation functions Fab
(r) gt 0
F r Ae e
re
sh rrab
pr qrr( )
1 1 0
Pseudopotentials
U
= UKin
+ UPot
3PV
= 2UKin + UPot
Homogeneity of Coulomb potential
U Vn F F dpot coul ( ) r
U Vn F F dei ii 2 ( ) r
)2()2(3 potkinpot UUUUPV
2 2i i
ie ie1 e( ) (1 e (0) ~
rrZ e Z er
r r
( ))
Correlation Functions
Total Energy correction
Potential Energy Correction
-
UPot
Pressure Correction
-
P
i e i eN N U ( ) 1
Approximate relation between Coulomb corrections for chemical potential and energy
(
UN)
NB
Thermodynamic contributions inmodified pseudopotential model for Coulomb corrections
Positive shift in average kinetic energy due to non-ideality of free charges subsystem Ukin = 3PV ndash
U
Well-known relation between pressure and energy corrections for free charges subsystemU = 3PV
which is valid at weak non-ideality (Г
ltlt 1) is no longer valid in strong non-ideality conditions (Г
~ 1)
It is equivalent to additional effective electron-ion repulsion(in comparison with ordinary one-parametric Coulomb corrections depending on non-ideality parameter only
FNkT = f(Г)
Experimental data Theoretical models
(comparison)
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
Quasi‐isochoric behavior of nitrogen Hugoniot
‐
Mochalov
M Zhernokletov
M et al
JETP
137
(2010) ‐
Trunin
R Boriskov
G et alJETP Letters
88
(2008)
15 20 25 30 35 400
100
200
300
ExperimentsTrunin et al 2008Mochalov et al 2010
P GPa
gcm3
lim
Check of theoretical models
SAHA
CCM
Ross ampRogers
CCM ndash
Compressible Covolume
Model(A Medvedev
amp
VKopyshev)
SAHA‐code (V Gryaznov amp IIosilevskiy)
ρHug
asymp
33 plusmn
01
gcm390
lt
PHug
lt 330
GPa
NN
22 NN‐‐polymerpolymer
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
equiv
V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost
linear function of pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
Reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal Energy
Pressure (Hugonoit)
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
Blue curve
ndash
internal energy calculated via plasma model(code SAHA
Gryaznov Iosilevskiy)
SAHA
Hugoniot
~ ρ
asymp
const (33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
ρ
asymp33 plusmn01
gcc90
lt
P lt 330
GPa
NB
Quasi‐linear behavior of
E(p)
at ρ
=
constThermodynamics of shock compressed nitrogen
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
00
01
02
03
04
05
06
07
08
09
10 Mochalov et al PHug (Trunin et al) + T (EOSCCM) PHug (Trunin et al) + T (EOSSAHA)
xN+
xi
xN2
P GPa
T k
K
Tr
Tr
Plasma
Temperature of shock compressed nitrogen
CP()
General P‐T
diagram
Quasi‐linear behavior of
T(p)
at ρ
=
const
SAHA
‐
Experiment Mochalov
M et al
JETF
137
(2010)Nellis
W Radovsky
H et al J Chem Phys 94
(1991)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
Electroconductivity
of shock compressed nitrogen
20 25 30 351E-3
001
01
1
10
100
1000
C E B E 28061 B 29062
Con
duct
ivity
1
cm
Density gcc
Electroconductivity
of shock compressed nitrogen
Ternovoi
V et al (email ‐
30052010)
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1
P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
‐
Experiment Mochalov
M et al
JETF
137
(2010)
Quasi‐isentropic Plane Compression of Matter at Megabar
Pressures by Using of a Layered
System to Diminish First Shock Wave IntensityTernovoi
V Pyalling
A Filimonovet
A (052010) Summary and conclusion
Explosive driven quasi‐isentropic compression generators were proposed for matter investigation in
the megabar
pressure region Results of the first experiments on quasi‐isentropic compression of
liquid nitrogen are presented It was shown that pressure ionization
of nitrogen proceeds at
densities
from 315 to 34 gcc
at a temperature
of about 3000
K
Diminishing of temperature growth
was measured during onset of nitrogen electrical conductivity
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
F r Ae e
re
sh rrab
pr qrr( )
1 1 0
Pseudopotentials
U
= UKin
+ UPot
3PV
= 2UKin + UPot
Homogeneity of Coulomb potential
U Vn F F dpot coul ( ) r
U Vn F F dei ii 2 ( ) r
)2()2(3 potkinpot UUUUPV
2 2i i
ie ie1 e( ) (1 e (0) ~
rrZ e Z er
r r
( ))
Correlation Functions
Total Energy correction
Potential Energy Correction
-
UPot
Pressure Correction
-
P
i e i eN N U ( ) 1
Approximate relation between Coulomb corrections for chemical potential and energy
(
UN)
NB
Thermodynamic contributions inmodified pseudopotential model for Coulomb corrections
Positive shift in average kinetic energy due to non-ideality of free charges subsystem Ukin = 3PV ndash
U
Well-known relation between pressure and energy corrections for free charges subsystemU = 3PV
which is valid at weak non-ideality (Г
ltlt 1) is no longer valid in strong non-ideality conditions (Г
~ 1)
It is equivalent to additional effective electron-ion repulsion(in comparison with ordinary one-parametric Coulomb corrections depending on non-ideality parameter only
FNkT = f(Г)
Experimental data Theoretical models
(comparison)
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
Quasi‐isochoric behavior of nitrogen Hugoniot
‐
Mochalov
M Zhernokletov
M et al
JETP
137
(2010) ‐
Trunin
R Boriskov
G et alJETP Letters
88
(2008)
15 20 25 30 35 400
100
200
300
ExperimentsTrunin et al 2008Mochalov et al 2010
P GPa
gcm3
lim
Check of theoretical models
SAHA
CCM
Ross ampRogers
CCM ndash
Compressible Covolume
Model(A Medvedev
amp
VKopyshev)
SAHA‐code (V Gryaznov amp IIosilevskiy)
ρHug
asymp
33 plusmn
01
gcm390
lt
PHug
lt 330
GPa
NN
22 NN‐‐polymerpolymer
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
equiv
V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost
linear function of pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
Reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal Energy
Pressure (Hugonoit)
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
Blue curve
ndash
internal energy calculated via plasma model(code SAHA
Gryaznov Iosilevskiy)
SAHA
Hugoniot
~ ρ
asymp
const (33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
ρ
asymp33 plusmn01
gcc90
lt
P lt 330
GPa
NB
Quasi‐linear behavior of
E(p)
at ρ
=
constThermodynamics of shock compressed nitrogen
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
00
01
02
03
04
05
06
07
08
09
10 Mochalov et al PHug (Trunin et al) + T (EOSCCM) PHug (Trunin et al) + T (EOSSAHA)
xN+
xi
xN2
P GPa
T k
K
Tr
Tr
Plasma
Temperature of shock compressed nitrogen
CP()
General P‐T
diagram
Quasi‐linear behavior of
T(p)
at ρ
=
const
SAHA
‐
Experiment Mochalov
M et al
JETF
137
(2010)Nellis
W Radovsky
H et al J Chem Phys 94
(1991)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
Electroconductivity
of shock compressed nitrogen
20 25 30 351E-3
001
01
1
10
100
1000
C E B E 28061 B 29062
Con
duct
ivity
1
cm
Density gcc
Electroconductivity
of shock compressed nitrogen
Ternovoi
V et al (email ‐
30052010)
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1
P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
‐
Experiment Mochalov
M et al
JETF
137
(2010)
Quasi‐isentropic Plane Compression of Matter at Megabar
Pressures by Using of a Layered
System to Diminish First Shock Wave IntensityTernovoi
V Pyalling
A Filimonovet
A (052010) Summary and conclusion
Explosive driven quasi‐isentropic compression generators were proposed for matter investigation in
the megabar
pressure region Results of the first experiments on quasi‐isentropic compression of
liquid nitrogen are presented It was shown that pressure ionization
of nitrogen proceeds at
densities
from 315 to 34 gcc
at a temperature
of about 3000
K
Diminishing of temperature growth
was measured during onset of nitrogen electrical conductivity
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
Experimental data Theoretical models
(comparison)
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
Quasi‐isochoric behavior of nitrogen Hugoniot
‐
Mochalov
M Zhernokletov
M et al
JETP
137
(2010) ‐
Trunin
R Boriskov
G et alJETP Letters
88
(2008)
15 20 25 30 35 400
100
200
300
ExperimentsTrunin et al 2008Mochalov et al 2010
P GPa
gcm3
lim
Check of theoretical models
SAHA
CCM
Ross ampRogers
CCM ndash
Compressible Covolume
Model(A Medvedev
amp
VKopyshev)
SAHA‐code (V Gryaznov amp IIosilevskiy)
ρHug
asymp
33 plusmn
01
gcm390
lt
PHug
lt 330
GPa
NN
22 NN‐‐polymerpolymer
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
equiv
V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost
linear function of pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
Reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal Energy
Pressure (Hugonoit)
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
Blue curve
ndash
internal energy calculated via plasma model(code SAHA
Gryaznov Iosilevskiy)
SAHA
Hugoniot
~ ρ
asymp
const (33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
ρ
asymp33 plusmn01
gcc90
lt
P lt 330
GPa
NB
Quasi‐linear behavior of
E(p)
at ρ
=
constThermodynamics of shock compressed nitrogen
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
00
01
02
03
04
05
06
07
08
09
10 Mochalov et al PHug (Trunin et al) + T (EOSCCM) PHug (Trunin et al) + T (EOSSAHA)
xN+
xi
xN2
P GPa
T k
K
Tr
Tr
Plasma
Temperature of shock compressed nitrogen
CP()
General P‐T
diagram
Quasi‐linear behavior of
T(p)
at ρ
=
const
SAHA
‐
Experiment Mochalov
M et al
JETF
137
(2010)Nellis
W Radovsky
H et al J Chem Phys 94
(1991)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
Electroconductivity
of shock compressed nitrogen
20 25 30 351E-3
001
01
1
10
100
1000
C E B E 28061 B 29062
Con
duct
ivity
1
cm
Density gcc
Electroconductivity
of shock compressed nitrogen
Ternovoi
V et al (email ‐
30052010)
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1
P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
‐
Experiment Mochalov
M et al
JETF
137
(2010)
Quasi‐isentropic Plane Compression of Matter at Megabar
Pressures by Using of a Layered
System to Diminish First Shock Wave IntensityTernovoi
V Pyalling
A Filimonovet
A (052010) Summary and conclusion
Explosive driven quasi‐isentropic compression generators were proposed for matter investigation in
the megabar
pressure region Results of the first experiments on quasi‐isentropic compression of
liquid nitrogen are presented It was shown that pressure ionization
of nitrogen proceeds at
densities
from 315 to 34 gcc
at a temperature
of about 3000
K
Diminishing of temperature growth
was measured during onset of nitrogen electrical conductivity
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
Quasi‐isochoric behavior of nitrogen Hugoniot
‐
Mochalov
M Zhernokletov
M et al
JETP
137
(2010) ‐
Trunin
R Boriskov
G et alJETP Letters
88
(2008)
15 20 25 30 35 400
100
200
300
ExperimentsTrunin et al 2008Mochalov et al 2010
P GPa
gcm3
lim
Check of theoretical models
SAHA
CCM
Ross ampRogers
CCM ndash
Compressible Covolume
Model(A Medvedev
amp
VKopyshev)
SAHA‐code (V Gryaznov amp IIosilevskiy)
ρHug
asymp
33 plusmn
01
gcm390
lt
PHug
lt 330
GPa
NN
22 NN‐‐polymerpolymer
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
equiv
V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost
linear function of pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
Reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal Energy
Pressure (Hugonoit)
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
Blue curve
ndash
internal energy calculated via plasma model(code SAHA
Gryaznov Iosilevskiy)
SAHA
Hugoniot
~ ρ
asymp
const (33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
ρ
asymp33 plusmn01
gcc90
lt
P lt 330
GPa
NB
Quasi‐linear behavior of
E(p)
at ρ
=
constThermodynamics of shock compressed nitrogen
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
00
01
02
03
04
05
06
07
08
09
10 Mochalov et al PHug (Trunin et al) + T (EOSCCM) PHug (Trunin et al) + T (EOSSAHA)
xN+
xi
xN2
P GPa
T k
K
Tr
Tr
Plasma
Temperature of shock compressed nitrogen
CP()
General P‐T
diagram
Quasi‐linear behavior of
T(p)
at ρ
=
const
SAHA
‐
Experiment Mochalov
M et al
JETF
137
(2010)Nellis
W Radovsky
H et al J Chem Phys 94
(1991)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
Electroconductivity
of shock compressed nitrogen
20 25 30 351E-3
001
01
1
10
100
1000
C E B E 28061 B 29062
Con
duct
ivity
1
cm
Density gcc
Electroconductivity
of shock compressed nitrogen
Ternovoi
V et al (email ‐
30052010)
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1
P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
‐
Experiment Mochalov
M et al
JETF
137
(2010)
Quasi‐isentropic Plane Compression of Matter at Megabar
Pressures by Using of a Layered
System to Diminish First Shock Wave IntensityTernovoi
V Pyalling
A Filimonovet
A (052010) Summary and conclusion
Explosive driven quasi‐isentropic compression generators were proposed for matter investigation in
the megabar
pressure region Results of the first experiments on quasi‐isentropic compression of
liquid nitrogen are presented It was shown that pressure ionization
of nitrogen proceeds at
densities
from 315 to 34 gcc
at a temperature
of about 3000
K
Diminishing of temperature growth
was measured during onset of nitrogen electrical conductivity
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
Quasi‐isochoric behavior of nitrogen Hugoniot
‐
Mochalov
M Zhernokletov
M et al
JETP
137
(2010) ‐
Trunin
R Boriskov
G et alJETP Letters
88
(2008)
15 20 25 30 35 400
100
200
300
ExperimentsTrunin et al 2008Mochalov et al 2010
P GPa
gcm3
lim
Check of theoretical models
SAHA
CCM
Ross ampRogers
CCM ndash
Compressible Covolume
Model(A Medvedev
amp
VKopyshev)
SAHA‐code (V Gryaznov amp IIosilevskiy)
ρHug
asymp
33 plusmn
01
gcm390
lt
PHug
lt 330
GPa
NN
22 NN‐‐polymerpolymer
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
equiv
V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost
linear function of pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
Reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal Energy
Pressure (Hugonoit)
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
Blue curve
ndash
internal energy calculated via plasma model(code SAHA
Gryaznov Iosilevskiy)
SAHA
Hugoniot
~ ρ
asymp
const (33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
ρ
asymp33 plusmn01
gcc90
lt
P lt 330
GPa
NB
Quasi‐linear behavior of
E(p)
at ρ
=
constThermodynamics of shock compressed nitrogen
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
00
01
02
03
04
05
06
07
08
09
10 Mochalov et al PHug (Trunin et al) + T (EOSCCM) PHug (Trunin et al) + T (EOSSAHA)
xN+
xi
xN2
P GPa
T k
K
Tr
Tr
Plasma
Temperature of shock compressed nitrogen
CP()
General P‐T
diagram
Quasi‐linear behavior of
T(p)
at ρ
=
const
SAHA
‐
Experiment Mochalov
M et al
JETF
137
(2010)Nellis
W Radovsky
H et al J Chem Phys 94
(1991)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
Electroconductivity
of shock compressed nitrogen
20 25 30 351E-3
001
01
1
10
100
1000
C E B E 28061 B 29062
Con
duct
ivity
1
cm
Density gcc
Electroconductivity
of shock compressed nitrogen
Ternovoi
V et al (email ‐
30052010)
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1
P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
‐
Experiment Mochalov
M et al
JETF
137
(2010)
Quasi‐isentropic Plane Compression of Matter at Megabar
Pressures by Using of a Layered
System to Diminish First Shock Wave IntensityTernovoi
V Pyalling
A Filimonovet
A (052010) Summary and conclusion
Explosive driven quasi‐isentropic compression generators were proposed for matter investigation in
the megabar
pressure region Results of the first experiments on quasi‐isentropic compression of
liquid nitrogen are presented It was shown that pressure ionization
of nitrogen proceeds at
densities
from 315 to 34 gcc
at a temperature
of about 3000
K
Diminishing of temperature growth
was measured during onset of nitrogen electrical conductivity
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp
33 plusmn
01
gcc (90
lt
P
lt 330
GPa)
Gr
equiv
V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost
linear function of pressure at isochore
Summary
High-temperature part of
Hugoniot is close to isochore
(partppartT)V
asymp
const
asymp
454 (GPaK)
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
Reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal Energy
Pressure (Hugonoit)
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
Blue curve
ndash
internal energy calculated via plasma model(code SAHA
Gryaznov Iosilevskiy)
SAHA
Hugoniot
~ ρ
asymp
const (33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
ρ
asymp33 plusmn01
gcc90
lt
P lt 330
GPa
NB
Quasi‐linear behavior of
E(p)
at ρ
=
constThermodynamics of shock compressed nitrogen
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
00
01
02
03
04
05
06
07
08
09
10 Mochalov et al PHug (Trunin et al) + T (EOSCCM) PHug (Trunin et al) + T (EOSSAHA)
xN+
xi
xN2
P GPa
T k
K
Tr
Tr
Plasma
Temperature of shock compressed nitrogen
CP()
General P‐T
diagram
Quasi‐linear behavior of
T(p)
at ρ
=
const
SAHA
‐
Experiment Mochalov
M et al
JETF
137
(2010)Nellis
W Radovsky
H et al J Chem Phys 94
(1991)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
Electroconductivity
of shock compressed nitrogen
20 25 30 351E-3
001
01
1
10
100
1000
C E B E 28061 B 29062
Con
duct
ivity
1
cm
Density gcc
Electroconductivity
of shock compressed nitrogen
Ternovoi
V et al (email ‐
30052010)
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1
P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
‐
Experiment Mochalov
M et al
JETF
137
(2010)
Quasi‐isentropic Plane Compression of Matter at Megabar
Pressures by Using of a Layered
System to Diminish First Shock Wave IntensityTernovoi
V Pyalling
A Filimonovet
A (052010) Summary and conclusion
Explosive driven quasi‐isentropic compression generators were proposed for matter investigation in
the megabar
pressure region Results of the first experiments on quasi‐isentropic compression of
liquid nitrogen are presented It was shown that pressure ionization
of nitrogen proceeds at
densities
from 315 to 34 gcc
at a temperature
of about 3000
K
Diminishing of temperature growth
was measured during onset of nitrogen electrical conductivity
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
50 100 150 200 250 300 350
0
50
100
150
E k
Jg
P GPa
()
Reference point
ndash
energy of ideal atomic gas N at
Т
= 0 K
Internal Energy
Pressure (Hugonoit)
‐
Mochalov
М et al
(2010) ‐
Trunin
R et al (2008)
Blue curve
ndash
internal energy calculated via plasma model(code SAHA
Gryaznov Iosilevskiy)
SAHA
Hugoniot
~ ρ
asymp
const (33 plusmn
01
gcc)
Gr
= V(partPpartE)V
asymp
const
asymp
062
ρ
asymp33 plusmn01
gcc90
lt
P lt 330
GPa
NB
Quasi‐linear behavior of
E(p)
at ρ
=
constThermodynamics of shock compressed nitrogen
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
00
01
02
03
04
05
06
07
08
09
10 Mochalov et al PHug (Trunin et al) + T (EOSCCM) PHug (Trunin et al) + T (EOSSAHA)
xN+
xi
xN2
P GPa
T k
K
Tr
Tr
Plasma
Temperature of shock compressed nitrogen
CP()
General P‐T
diagram
Quasi‐linear behavior of
T(p)
at ρ
=
const
SAHA
‐
Experiment Mochalov
M et al
JETF
137
(2010)Nellis
W Radovsky
H et al J Chem Phys 94
(1991)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
Electroconductivity
of shock compressed nitrogen
20 25 30 351E-3
001
01
1
10
100
1000
C E B E 28061 B 29062
Con
duct
ivity
1
cm
Density gcc
Electroconductivity
of shock compressed nitrogen
Ternovoi
V et al (email ‐
30052010)
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1
P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
‐
Experiment Mochalov
M et al
JETF
137
(2010)
Quasi‐isentropic Plane Compression of Matter at Megabar
Pressures by Using of a Layered
System to Diminish First Shock Wave IntensityTernovoi
V Pyalling
A Filimonovet
A (052010) Summary and conclusion
Explosive driven quasi‐isentropic compression generators were proposed for matter investigation in
the megabar
pressure region Results of the first experiments on quasi‐isentropic compression of
liquid nitrogen are presented It was shown that pressure ionization
of nitrogen proceeds at
densities
from 315 to 34 gcc
at a temperature
of about 3000
K
Diminishing of temperature growth
was measured during onset of nitrogen electrical conductivity
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
Thermodynamics of shock compressed nitrogen(primary thermodynamic results of experiment)
ρ
asymp33 plusmn01
gcc
(90
lt
P
lt 330
GPa)
Gr
= V(partPpartE)V
asymp
const
asymp
062
Z
equiv
PVRT
equiv
PnN
kT
asymp
const
asymp
266 plusmn
020
СV
equiv
(partEpartT)V
asymp
const
asymp
206 (JgK)
Internal energy is almost linear on temperature at isochore
Temperature is almost linear on pressure at isochore
Internal energy is almost linear on pressure at isochore
Summary
High-temperature part nitrogen Hugoniot is close to be isochoric
(partppartT)V
asymp
const
asymp
454 (GPaK)
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
00
01
02
03
04
05
06
07
08
09
10 Mochalov et al PHug (Trunin et al) + T (EOSCCM) PHug (Trunin et al) + T (EOSSAHA)
xN+
xi
xN2
P GPa
T k
K
Tr
Tr
Plasma
Temperature of shock compressed nitrogen
CP()
General P‐T
diagram
Quasi‐linear behavior of
T(p)
at ρ
=
const
SAHA
‐
Experiment Mochalov
M et al
JETF
137
(2010)Nellis
W Radovsky
H et al J Chem Phys 94
(1991)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
Electroconductivity
of shock compressed nitrogen
20 25 30 351E-3
001
01
1
10
100
1000
C E B E 28061 B 29062
Con
duct
ivity
1
cm
Density gcc
Electroconductivity
of shock compressed nitrogen
Ternovoi
V et al (email ‐
30052010)
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1
P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
‐
Experiment Mochalov
M et al
JETF
137
(2010)
Quasi‐isentropic Plane Compression of Matter at Megabar
Pressures by Using of a Layered
System to Diminish First Shock Wave IntensityTernovoi
V Pyalling
A Filimonovet
A (052010) Summary and conclusion
Explosive driven quasi‐isentropic compression generators were proposed for matter investigation in
the megabar
pressure region Results of the first experiments on quasi‐isentropic compression of
liquid nitrogen are presented It was shown that pressure ionization
of nitrogen proceeds at
densities
from 315 to 34 gcc
at a temperature
of about 3000
K
Diminishing of temperature growth
was measured during onset of nitrogen electrical conductivity
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
00
01
02
03
04
05
06
07
08
09
10 Mochalov et al PHug (Trunin et al) + T (EOSCCM) PHug (Trunin et al) + T (EOSSAHA)
xN+
xi
xN2
P GPa
T k
K
Tr
Tr
Plasma
Temperature of shock compressed nitrogen
CP()
General P‐T
diagram
Quasi‐linear behavior of
T(p)
at ρ
=
const
SAHA
‐
Experiment Mochalov
M et al
JETF
137
(2010)Nellis
W Radovsky
H et al J Chem Phys 94
(1991)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
Electroconductivity
of shock compressed nitrogen
20 25 30 351E-3
001
01
1
10
100
1000
C E B E 28061 B 29062
Con
duct
ivity
1
cm
Density gcc
Electroconductivity
of shock compressed nitrogen
Ternovoi
V et al (email ‐
30052010)
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1
P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
‐
Experiment Mochalov
M et al
JETF
137
(2010)
Quasi‐isentropic Plane Compression of Matter at Megabar
Pressures by Using of a Layered
System to Diminish First Shock Wave IntensityTernovoi
V Pyalling
A Filimonovet
A (052010) Summary and conclusion
Explosive driven quasi‐isentropic compression generators were proposed for matter investigation in
the megabar
pressure region Results of the first experiments on quasi‐isentropic compression of
liquid nitrogen are presented It was shown that pressure ionization
of nitrogen proceeds at
densities
from 315 to 34 gcc
at a temperature
of about 3000
K
Diminishing of temperature growth
was measured during onset of nitrogen electrical conductivity
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
‐
Experiment Mochalov
M et al
JETF
137
(2010)Nellis
W Radovsky
H et al J Chem Phys 94
(1991)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
Electroconductivity
of shock compressed nitrogen
20 25 30 351E-3
001
01
1
10
100
1000
C E B E 28061 B 29062
Con
duct
ivity
1
cm
Density gcc
Electroconductivity
of shock compressed nitrogen
Ternovoi
V et al (email ‐
30052010)
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1
P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
‐
Experiment Mochalov
M et al
JETF
137
(2010)
Quasi‐isentropic Plane Compression of Matter at Megabar
Pressures by Using of a Layered
System to Diminish First Shock Wave IntensityTernovoi
V Pyalling
A Filimonovet
A (052010) Summary and conclusion
Explosive driven quasi‐isentropic compression generators were proposed for matter investigation in
the megabar
pressure region Results of the first experiments on quasi‐isentropic compression of
liquid nitrogen are presented It was shown that pressure ionization
of nitrogen proceeds at
densities
from 315 to 34 gcc
at a temperature
of about 3000
K
Diminishing of temperature growth
was measured during onset of nitrogen electrical conductivity
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
20 25 30 351E-3
001
01
1
10
100
1000
C E B E 28061 B 29062
Con
duct
ivity
1
cm
Density gcc
Electroconductivity
of shock compressed nitrogen
Ternovoi
V et al (email ‐
30052010)
20 40 601E-4
1E-3
001
01
1
10
100
1000
1
G О
м-1см
-1
P ГПа
Experiment- Mochalov et al(2010)- Nellis et al (1991)
‐
Experiment Mochalov
M et al
JETF
137
(2010)
Quasi‐isentropic Plane Compression of Matter at Megabar
Pressures by Using of a Layered
System to Diminish First Shock Wave IntensityTernovoi
V Pyalling
A Filimonovet
A (052010) Summary and conclusion
Explosive driven quasi‐isentropic compression generators were proposed for matter investigation in
the megabar
pressure region Results of the first experiments on quasi‐isentropic compression of
liquid nitrogen are presented It was shown that pressure ionization
of nitrogen proceeds at
densities
from 315 to 34 gcc
at a temperature
of about 3000
K
Diminishing of temperature growth
was measured during onset of nitrogen electrical conductivity
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
Improvement of Plasma model (SAHA-code)- From EOS of soft spheres to EOS of exp
- 6 potential system
Improvement of Polymeric models (Е amp L Yakub)- Calibration of both model on results of ab initio calculations
(DFTMD)Collaboration (Gryaznov Iosilevskiy Е amp L Yakub)
- Incorporation of polymeric state model into SAHA-code
New approaches are desirable (new calculations and comparisons)- Ab initio RPIMC DPIMC DFTMD WPMD TBM - Wigner-Zeits cell model TFC MHFS
- Semiempirical (wide-range) EOS-s
PerspectivesModelling
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
-
Strong shock compression of liquid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of solid nitrogen at high pressure (P gt 3 Mbar)
- Strong shock compression of pre-compressed gaseous nitrogen at high pressure (mesurement of series of Hugoniots with varying initial densities (like in VNIIEF experiments with deuterium )
- Strong isentropic compression of nitrogen by explosive at Mb pressuresearch of density discontinuity (hypothetical phase transition ) on nitrogen isentrope(s)
(like in VNIIEFrsquos
experiments with deuterium (MMochalov VFortov
et al PRL 2007)
Exotics - Heavy Ion Beam and
Laser heating of cryogenic nitrogen
(new experiments)Perspectives
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
Conclusions- New experimental data on shock compression of cryogenic liquid
nitrogen in megabar
pressure range ldquoopen new pagerdquo
in investigation of properties for warm dense matter of ldquosimplerdquo
molecular gases
- Simultaneous measurement of caloric and thermal equation of state (EOS) (pressure density temperature and internal energy) on the same Hugoniot
give
powerful
tool for checking theoretical models and ldquocalibrationrdquo
of wide-range EOS-s
- New experimental data in nitrogen may be considered as the thermodynamic manifestation of non-standard form of pressure ionization (from polymeric to plasma state )
-
This new form of pressure ionization (from polymeric to plasma state ) seems to be
general universal and interesting phenomenon
- It is promising to continue and extend experimental investigation of pressure ionization of polymeric state
- It is promising to study pressure ionization of polymeric state in directnumerical simulations (ldquonumerical experimentrdquo) DFT_MD PIMC WP_MD
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
Thank youThank you
Support ISTC 3755 CRDF MO-011-0and by RAS Scientific Programs ldquoPhysics and Chemistry of Extreme States of Matterrdquo
and by
MIPT Education Center ldquoPhysics of High Energy Density Matterrdquo
and by
Extreme Matter Institute (EMMI)
15 20 25 30 35 400
50
100
150
200
250
300
350
33
2
1
gcm3
Р GPa
Annual Moscow Workshop
Non‐ideal Plasma PhysicsRussian Academy of Science
November 23‐24
2011
Sarov 2011 Chernogolovka 2010EMMI GSI 2011
