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4He, 3He, and 3He-4He dilution refrigerator
Physics 590 B, Spring 2014
4He, 3He, and 3He-4He dilution refrigerator
LN2 Dewar
LHe Dewar
Vacuum pump
Turbo pump
Rotary pump
Instrument
LN2 trap
Gas handling system
Pump room3He pumping
Computer-data acquisition
Oxford 14 T cryostat
Dil fridge
Still pumping line
Typical dil-fridge room
Magnet power supply Dump (mixture storage)
4He, 3He, and 3He-4He dilution refrigerator
LN2 Dewar
LHe Dewar
Vacuum pump
Turbo pump
Rotary pump
Instrument
LN2 trap
Gas handling system
Pump room3He pumping
Computer data acquisition
Oxford 14 T cryostat
Dil fridge
Still pumping line
Typical dil-fridge room
Magnet powersupply Dump (mixture storage)
DON’T
4He, 3He, and 3He-4He dilution refrigerator
LN2 Dewar
LHe Dewar
Vacuum pump
Turbo pump
Rotary pump
Instrument
LN2 trap
Gas handling system
Pump room3He pumping
Computer data acquisition
Oxford 14 T cryostat
Dil fridge
Still pumping line
Magnet powersupply Dump (mixture storage)
March 3-7
Kaminski
cryogens
March 10-14measurements
March 3-7
Kaminski
cryogens
How to cool below 4 K
4He, 3He, and 3He-4He dilution refrigerator
4HePhase diagram
Cryostat
Cooling power
Pressure, thermometer
3HeIsotopes of Helium
Phase diagram
Cooling power
Refrigerator- closed system with charcoal, measurements in liquid
Thermometer
3He-4He MixturePhase diagram of mixture
Properties of mixture
Cooling power of mixture
Operation
Cryogen free system
Thermometer
Very nice reference book: Matter and Methods at Low Temperatures, 2nd Edition, F.Pobell
Cryogenic systems
4He Phase Diagram
Critical point 5.19 K
(0.22746 MPa)Triple point ~ 2.17 K at 1 atm Boiling point 4.222 K
• Helium-4 : triple point involving two different fluid phase. The λ(lamda)-point is the
temperature below which normal fluid helium transition to superfluid helium.
• 4He has no spin, Boson
• No solid phase (1 atm) due to weak van der Waals inter-atomic interactions, large
quantum mechanical-zero-point energy due to small mass (high kinetic energy and
low Potential energy), Bose-Einstein condensate instead of a solid
4He Cryostat
Base temperature 4.2 K at 1 atm
Cool below 4.2 K
Reduce pressure – pumping cryostat down to ~ 1K
Reality! 1.5 ~ 2 K
4He pumping
Sample
space
Sample
space
LN2
Vacuum sapce
LHe
Sample holder
Cooling power is proportional to vapor pressure.
Cryostat design magnetic field – March 10-14
Sample
space
1K pot pumping
Needle valve
1K
pot
Sample
space
Cool down sample stage by 1 K pot or use VTI
4He Cryostat with 1 K pot
Save Helium! Save money! Efficient!
Difficult to cool down below 1.5 K
should be called 2 K pot?
Capillary flow
(impedances)
Sample
space
1K pot pumping
Needle valve
1K
pot
sample
charcoal
High vacuum
Small He bath/VTI
pumping < 2K
He gas
Liquid He
Sample space
pumping below 1 K
Sample inside
liquid
Small volume with low impedance: easy to reach low pressure
4He Cryostat with 1 K pot
reach ~0.9 K and sample in liquid
Cooling power of evaporative cooling
Latent heat L ~ independent of temperature
Cooling power: proportional to vapor pressure and
exponentially small with temperature
2~
RT
LP
TV
L
VV
SS
dT
dP
gasliqgas
liqgas=
−
−
=
Assuming Vgas >> Vliq and using L ~ TdS
2T
dT
R
L
P
dP=
)exp(RT
LP −∝
latent heat of 3He and 4He
Late
nt
heat L
(J/m
ol)
Temperature (K)
3He
4He
Pressure
Pressure ranges of vacuum -details March 3-7 low pressure, vacuum generation and gauge (Kaminski)
Torr Vacuum gauge pump
Atmospheric 760
Low vacuum 25 ~ 1 X 10-3 Pirani gauge (0.5 ~ 10-4 Torr) Rotary pump
High vacuum 1 X 10-3 ~ 1 X 10-9 Ionization gauge (10-3 ~ 10-10 Torr)
Penning gauge (10-3 ~ 10-13 Torr)
Inverted magnetrons (~ 1 X 10-12)
Turbo pump, diffusion pump,
cryopump (charcoal)Ultra high vacuum 1 X 10-9 ~ 1 X 10-12
Outer space 1 X 10-6 < 3 X 10-17
Perfect vacuum 0
10-13
10-11
10-9
10-7
10-5
10-3
10-1
101
103
Pirani gauge
Bourdon Tube
U-Tube Manometer
Capacitance Manometer
Themocouple
McLeod
Schulz-Phelps IG
Bayert-Alpert IG
Cold Cathode IG
Pressure in Torr
Mass Spectrometer (RGA)
Penning gauge
1 atm
= 1.01325 X 105 Pascal (Pa)
= 1.01325 Bar (bar)
= 760 Torr (mmHg)
= 14.69595 Pound per square inch (psi)
4He thermometer
CX-1050-SD/BC X00000
Cernox™ sensors can be used from 100 mK to 420 K with good sensitivity over the whole range. They have a low
magnetoresistance, and are the best choice for applications with magnetic fields up to 30 T (for temperatures greater than 2 K).
Cernox™ are resistant to ionizing radiation, and are available in robust mounting packages and probes. Because of their versatility,
they are used in a wide variety of cryogenic applications, such as particle accelerators, space satellites, MRI systems, cryogenic
systems, and research science. From Lakeshore.com
: good sensitivity and stability
Response time 1.5ms
Response time 15ms
CX-1050 for 4He CX-1030 for 3He
Consider response time
BC: 1.5 ms at 4.2 K, 50 ms at 77 K, 135 ms at 273 K
SD: 15 ms at 4.2 K, 0.25 s at 77 K, 0.8 s at 273 K
AA: 0.4 s at 4.2 K, 2 s at 77 K, 1.0 s at 273 K Low current or voltage (~2mV): Joule heating I2R
Time related measurements such as AC heat capacity
January 22-24 measuring temperature (Prozorov)
Isotopes of Helium
3He 4He
Parent isotopes 3H (beta decay of tritium)
Neutron 1 2
proton 2 2
Isotope (atomic) mass (ma/u) 3.016 4.002
Nuclear spin (I) 1/2 0
Magnetic Moment (µ/µN) -2.127 0
Half life Stable stable
Natural abundance (atom %) on Earth 0.000137 99.99986
Boiling point at 1atm 3.19 K 4.23 K
Critical point 3.35 K 5.19 K (0.22746 MPa)
Triple point 2.177 K (5.043 kPa)
Density of liquid at boiling point 0.059 g/mol 0.12473 g/mol
Latent heat of vaporization 0.26 kJ/mol 0.0829 kJ/mol
Molar heat capacity 5/2 R = 20.768 J/mol
Other isotopes, He-5, He-6 He-7 … extremely short half-life
The shortest-lived heavy helium isotope is He-5 with a half-life of 7.6×10−22 s. He-6 decays by emitting a beta
particle and has a half-life of 0.8 second. He-7 also emits a beta particle as well as a gamma ray. He-7 and He-8
are created in certain nuclear reactions. He-6 and He-8 are known to exhibit a nuclear halo. C. A. Hampel (1968). The
Encyclopedia of the Chemical Elements. pp. 256–268.
3He Phase Diagram
Critical point 3.35 K
Boiling point 3.19 K
Triple point 3.05
• 3He: Nuclear spin I = ½, Fermion, Pauli principle.
• Superfluid phases: Bose-Einstein condensate of pairs, spins in the liquid state are
indistinguishable.
• Diamagnetic: levitation under high magnetic field
PS) Supersolid state of 3He or 4He? A supersolid is a spatially ordered material with superfluid properties.
Superfluidity; a special quantum state of matter, substance is flowing without viscosity.
Quantum magnet in triangular angular lattice; breaking translational and rotational symmetry.
3He cooling power
Cooling Power proportional to Vapour Pressure
Cooling power: exponentially small at low temperature
Pumping on 4He T~1 K (normally down to 1.8 K)
Pumping on 3He T~0.26 K (down to 0.3 K)
)exp(RT
LP −∝
Latent heat 4He ~90 J/mol
Latent heat 3He ~40 J/mol
3He Refrigerator
• Sample in vacuum configuration, only few places operate sample in liquid 3He
• Operation
one-shot mode: keep base temperature 10-60 hours
continuous mode: forever? ~very long time
• 3He is stored in a sealed space (closed system) to avoid loss, keep low pressure
(<1atm)
• 3He pump: sealed (tight, casted) pump or charcoal pump
Pumping
(gas)
1 K
Pumping
(gas)
One-shot mode Continuous mode
3He Refrigerator operation
Reach 0.3 K base temp: Clean gas => Make liquid 3He => Reduce pressure
3He operation
1) Cleaning gas through LN2
trap or use cryopump
2) Condense by heat
exchange with 1 K pot
3) Cool condensate to 1.5 K
(below 2 K)
4) Start pumping to reach
base temperature
Sample
space
1K pot pumping
3He Storage LN2 trap
cleaning gas
condensing
pumping
Needle valve
3He
pot
1K
pot
1
2
3
4
Charcoal
Charcoal is a light black residue consisting of carbon and any
remaining ash, obtained by removing water and other volatile
constituents from animal and vegetation substances.
Cryopumps are often combined with sorption pumps by coating the
cold head with highly adsorbing materials such as activated charcoal
or a zeolite. As the sorbent saturates, the effectiveness of a sorption
pump decreases, but can be recharged by heating the zeolite
material (preferably under conditions of low pressure) to outgas it.
The breakdown temperature of the zeolite material’s porous structure
may limit the maximum temperature that it may be heated to for
regeneration. from Wikipedia
Activate ~ 40 K, control with heater and thermometer
3He Refrigerator operation: closed system
3He Refrigerator operation: closed system
Sample
space
1K pot pumpingNeedle valve
3He
pot
1K
pot
Charcoal
Sorption pump
3He gas storage3He operation
1)Cleaning gas cryopump (charcoal) – at 4 K
all gases inside charcoal sorption pump
2)Release gas by heating up to 40 K
3)Condense by heat exchange with 1 K pot
4)Cool condensate to 1.5 K (below 2 K) in
He-3 pot
5)Start pumping to reach base temperature
using sorption pump-set 4 K
3He pot
1K pot
Charcoal
Sorption pump
3He storage vessel
3He Refrigerator operation: closed system
4 K 40 K 4 K
1 2 3
Top loading: measurements inside 3He liquid )
Knife gate valve (KF)
O-ring seal
Vacuum line
3He 4He
vacuum
Sample holder
3He Refrigerator operation: sample in liquid
3He gas handling system
Rotator
Electrical transport
Resistivity
300 kHz
50 µA, 500 µA ?
3He thermometer
1 10 100
0.1
1
10
0.4 0.6 0.8 1.0
2
4
6
8
10
R (
kΩ
)
T (K)
H = 0
1 T
3 T
5 T
7 T
9 T
14 T
R (
kΩ
)
T (K)
Cernox CX-1030 - negative magnetoresistance (MR) < 10 K
MR effect can be ignored T > 30 K
at 14 Tesla: 0.14 K shift
How cool below 0.2 K?
How can exponentially small vapor pressure be overcome?
Below 0.3 K ?
Cooling Power proportional to Vapour Pressure
)exp(RT
LP −∝
Oxford dil
3He and 4He Mixture
Phase separation
Fermi liquid 3He
in superfluid 4He
3He concentration x
Tem
pera
ture
(K
)
Phase separation starts
T = 800 mK
x = 0.675
The working fluid mixture of the dilution refrigerator: phase separation into 3He
rich (concentrated) and 3He poor (dilute) phase below 800 mK (NOT PURE 3He
and 4He).
3He and 4He mixtures as Fermi Liquid• 4He: Nuclear spin I = 0, Bose static. At low temp Bose liquid under Bose condensation in
momentum space (correspond to transition to super-liquid for 4He).
• At T < 0.5 K 4He condensed into quantum mechanical ground state, no excitation (phonon)
• In mixture: 4He acts as inert superfluid background contributes to the volume and to the
dissolved isotope 3He.
• 3He: Nuclear spin I = ½ , Fermion, Pauli principle.
• In analogy to conduction electrons, the specific heat of liquid 3He behaves as: Fermi degenerate
or Classical;
• Behavior is classical-gas-like at : T > 1 K
• Behavior is Fermi-gas-like at : T << 0.1 K
• 3He-4He mixture can be described by the law of an interacting Fermi gas
tconstPTTatRC
TTatRT
TC
F
F
F
tan2
5 :Classical
2:degenerate Fermi
2
⋅=→>→→=
<→→=π
3He and 4He Mixture
Finite solubility of 3He in 4He• 3He in pure 3He: The chemical potential of pure liquid 3He is given by the latent heat of
evaporation, corresponding to the binding energy.
• One 3He atom in liquid 4He: Identical chemical structure of the He isotopes-van der Walls force.
The liquid phase 4He atoms occupy a smaller volume than 3He atoms. Its binding energy, due to
the smaller distance or larger density, is stronger if it is in 4He that it would be in 3He.
• Many 3He atoms in liquid 4He: attractive interaction between the 3He atoms and in liquid 4He,
due to i)magnetic interaction due to the nuclear magnetic moments of 3He as in pure 3He
ii)density effect
• Pauli principle: the energy states up to the Fermi energy are filled with two 3He atoms of
opposite nuclear spin EF
= kBTF.
• Result: The binding energy of the 3He atoms has to decrease, due to their Fermi character, if
their number is increased.
3He and 4He Mixture
Phase separation: purely quantum effect (classical liquids separate into pure
components), the Fermi statistics 3He and Bose statistics 4He
The cooling capacity is the heat mixing of the two isotopes.
The cooling power of an evaporating cryogenic liquid;
)()( TLTVPQ =
nLHnQ =∆=
Make use of the latent heat L of evaporation, pumping with a pump of constant volume
rate V on 3He and 4He bath with vapour pressure;
3He-4He dilution refrigeration: use the difference of the specific heats of the two phases
(the enthalpy of mixing);
∫ ∝∆∝=>∆∝∆2THxQCdTH
Dilution refrigerator
cooling power:~T 2
3He and 4He Mixture
3He-4He Dilution Refrigerator
Sample
space
1K pot pumping
Dump3He- 3He Storage
LN2 trap
cleaning gas
condensing
pumping
Needle valve
sorption
3He circulation
1K
still
Mixing chamber
dilute
concent
trubo pump vs
0.02 K cryopump
Reach base temp: Clean gas => Make liquid 3He-4He => pumping 3He (circulation)
3He-4He operation
1) Cleaning mixture through
LN2 and LHe trap
2) Condensing mixture
through 1 K pot
3) 3He circulation
Keep always low pressure P < 1 atm to avoid loss of mixture
3He-4He Dilution Refrigerator
Pumping
(gas)
Evaporation
Liquid
Vapour
1 K
3He
pump
Dilution
3He
1 K
3He-4He
Phase separation line
Still-evaporates 3He from mixture
Mixing Chamber
• Evaporation: depends on the classical heat of evaporation for cooling
• Dilution refrigeration: depends on the enthalpy of mixing of two quantum liquid, the different zero-
point motions of the two Heluim isotopes and the different statistics
From Makariy note
3He-4He Dilution Refrigerator
3He-4He Dilution Refrigerator: liquid operation
Knife gate valve (KF)
O-ring seal
Sample holder
Vacuum line
~3m long
Sample in liquid
1 K pot
still
Mixing
chamber
Cryogen free 3He-4He Dilution Refrigerator
Base temperature limit
• Radiation – shield
• Ground loop - !!!
• RF heating – proper shielding
• Vibration – rigid tail
Oxford triton
Pulse tube
cryocooler
Mixing chamber
With cryogen free magnet
CCR - Unltra low vibration - absolute
vibration amplitudes less than 100 nm
Still
High efficient
Heat exchange
NO 1 K POT: by driving condensation at higher pressures,
higher condensation temperatures are possible
Ruthenium Oxide (ROx) Thermometer
Ruthenium Oxide (ROx) Thermometer
0.1 12
4
6
8
10
12
14
161820
0.05 0.06 0.07 0.08 0.09 0.1012
14
16
18
20
R (
kΩ
)
T (K)
H=0T
H=1T
H=2T
H=3T
H=4T
H=5T
H=7T
H=9T
H=11T
H=13T
R (
kΩ
)T (K)
~10 mK shift at 13 T
(due to positive MR)
