Raman spectroscopy at high pressureand temperature for the study of Earth's

mantle and planetary minerals

Bruno Reynard, Gilles Montagnac, and Hervé CardonLaboratoire de Géologie de Lyon

Coupling HP and HT to Raman

High temperatures

Daniel et al 1995

Sample

Ruby

100 µm

ruby fluorescence

5000 5050 5100 5150 5200

wavenumber (cm-1)

P=10 GPa

P=0

thermocouple

IR laser

wavelength

Intn

esity

Tspectrum of thermal emission

Gillet 1993 Gillet et al 1993

Pressure measurementsRuby fluorescence: up to 150 GPa

Other fluorescent sensors

Raman sensors

Diamond peak up to 400 GPa

How to choose?

Substance that has an incompressibility (or bulk modulus)close to the pressure range you are studying

Goncharov et al 1985

Goncharov et al 1985

Convenient because you do notneed to add another material inthe experimental chamber

b

c

High temperatures

Daniel et al 1995

High temperatures

High temperatures

Daniel et al 1995Anorthite liquid

High temperatures

Pulsed-laser gated-detector systemBN up to 2300 KExarhos and Schaaf 1991

High temperatures

Why do HP-HT Raman?

Follow structural transformations of materials

Probe the interaction potential of the crystal

Define P-T calibrants for DAC cell

Calculate thermodynamic properties

Relate it to geophysical issueshigh-pressure phases in Earthphase transformations in meteoritesfossil pressure

Upper mantle

Olivine : (Mg,Fe)2SiO4

Pyroxene : (Ca,Mg,Fe)SiO3

Garnet : (Ca,Mg,Fe)3(Al,Fe)2Si3O12

Transition zone β-(Mg,Fe)2SiO4

γ-(Mg,Fe)2SiO4

(Mg,Fe)SiO3-ilmenite Majoritic garnet

Lower mantle (Mg,Fe)SiO3-perovskite (Mg,Fe)O ferropericlase CaSiO3-perovskite

The high-pressure phases of the transitionzone and lower mantle are inferred fromexperiments, minerals observed in shock vein melts of chondritic meteorites andinclusions in diamonds

NWA2737 (Diderot)Dunite with homogeneous olivine Fo79

T= 1150-1070°C, fO2 ≈ FMQ

Raman spectroscopy

200 400 600 800 1000

Ram

an in

tens

ity (a

rbitr

ary

units

)

Wavenumber (cm-1)

clear stripe

dark zone

dark zone

Mg2SiO4 Durben et al. AM 1993 Mg2GeO4 Reynard et al. PCM 1994

(100)(010)

[001]

Van de Moortele et al. AM 2007ab

Paleostress

Izreali et al 1999

Raman shift of the diamond line because of residual pressure in the inclusions0.7 cm-1 = 1 GPa along <100>, 2.2 cm-1 along <111>Olivine 5-6 cm-1 = 1 GPa

Mineral inclusion

Diamond host

Lattice potentials and vibrational levels

!

En = (n +12) h"

crystal = harmonic oscillatork

Vibrational energy

!k

21!

="Reduced mass; E Δm/mm’Force constant

!

Pn =e"En / kBT

e"Ei / kBTi= 0

N

#

!

Uvib = Pi Eii"

Lattice potentials and vibrational levels

Anharmonicity

e.g. Morse potential

!

"e =12#

keµ

!

a =ke2De

!

En /hc ="e n +1/2( ) # "e2

4De

n +1/2( )2

Lattice potentials and vibrational levels

!

"e =12#

keµ

!

a =ke2De

!

En /hc ="e n +1/2( ) # "e2

4De

n +1/2( )2

!

( " s / s) # fanh =" u i exp $ " u i / 2+ " x i " u i / 4( ) / 1$ exp($ " u i )( ) 1$ 2 " x i " u i exp $ " u i( ) / 1$ exp($ " u i )( )2[ ]

ui exp $ui / 2+ xiui / 4( ) / 1$ exp($ui )( ) 1$ 2xiui exp $ui( ) / 1$ exp($ui )( )2[ ]i%

ui = hcωi/kBT, xi = ωi/4De

Bigeleisen and Mayer 1947; Urey 1947

Lattice potentials and vibrational levels

Varying P and T allows exploring the potential parametersand their variations with volume

A case studyMg2GeO4

Olivine analogue to forsterite

Modes soften with T andharden with P

Mode anharmonicity

Vibrational frequenciesνi(P,T0) and νi(P0,T)

Anharmonic parameters extrinsic (volume dependent)γiT = -(∂ lnνi/∂ lnV)Tamb = KT(∂ lnνi/∂P)Tamb

γiP = -(∂ lnνi/∂ lnV)Pamb = -1/α (∂ lnνi/∂T)Pamb

intrinsic (volume independent)ai = (∂ lnνi/∂T)V

mi = (∂ lnai/∂ lnV)T

!

ln("(P0,T ))qh = ln("(P0,T0)) - #/q( ) V (P0,T ) /V (P0,T0)( )( )q$1

%

& '

(

) *

+

, - .

/ 0

Mode anharmonicity

Vibrational frequenciesνi(P,T)

Anharmonic parametersextrinsic (volume dependent)γiT = -(∂ lnνi/∂ lnV)Tamb = KT(∂ lnνi/∂P)Tamb

γiP = -(∂ lnνi/∂ lnV)Pamb = -1/α (∂ lnνi/∂T)Pamb

intrinsic (volume independent)ai = (∂ lnνi/∂T)V

mi = (∂ lnai/∂ lnV)T

Small quantities difficult to measure

Intrinsic anharmonic parameters

!

ln("(P0,T ))measured - ln("(P0,T ))qh = aidT = #T0

Tm$ "th

THERMODYNAMIC MODELLING

Vibrational frequenciesνi(P,T)

Anharmonic parameters γiT = -(∂ lnνi/∂ lnV)Tamb = KT(∂ lnνi/∂P)Tamb γiP = -(∂ lnνi/∂ lnV)Pamb = -1/α (∂ lnνi/∂T)Pamb ai = (∂ lnνi/∂T)V

mi = (∂ lnai/∂ lnV)T

Fvib = h!2 +kBTln 1"exp

"h!kBT

#

$ %

&

' (

#

$

% %

&

'

( ( +akBT2

)

*

+ +

,

-

.

. / g(!)d!

Pth =! TV

h"2

+h"

exp h"kBT#

$ % &

' ( )1

#

$ % &

' (

#

$

% % %

&

'

( ( (

)makBT

2

V

*

+

, , ,

-

.

/ / /

0 g "( )d"

Computed thermodynamicproperties of magnesite MgCO3 at

low pressures

Carbonates stability at high P and T

THERMODYNAMIC MODELLING

Raman spectroscopy gives a very partial sample of the vibrational density ofstates, no account of the dispersion in the Brillouin zoneIt is necessary to couple Raman and first-principles calculations for prediction ofthermodynamics, phase diagrams, isotopic fractionation, …

Intrinsic anharmonic parameters

ai = constantmi = 0

Fvib = h!2 +kBTln 1"exp

"h!kBT

#

$ %

&

' (

#

$

% %

&

'

( ( +akBT2

)

*

+ +

,

-

.

. / g(!)d!

Pth =! TV

h"2

+h"

exp h"kBT#

$ % &

' ( )1

#

$ % &

' (

#

$

% % %

&

'

( ( (

)makBT

2

V

*

+

, , ,

-

.

/ / /

0 g "( )d"

!

ln("(P0,T ))measured - ln("(P0,T ))qh = aidT = #T0

Tm$ "th

Intrinsic anharmonicity No contribution to V(P,T)Contribution to free energy

Phase transitions

1st and 2nd order

100 200 300 400 500 600 700

T

U

V

W

X

Y

Z

AA

AC

AD

Intensity (a.u)

Wavenumbers (cm-1)

546 cs

525 qz

432 cs

273 cs

287 qz

222 cs

160 cs

Quartz

Coesite

quenched

300 K

~ 900 K

Quartz

Heating of quartz at 7 GPa

progressive heating

Raman Shift (cm-1)

SiO2

Stishovite

Kingma et al. Nature 1995

Second-order phase transition

Critical softening at high orderphase transition

Elastic softening of orthopyroxenes above 600°C

Low frequency Raman modes thatderive from acoustic modes

Critical softening at high orderphase transition

Softening of orthopyroxene Ramanmodes assigned to transition fromPnma to Cmcm

Metastable transformationsReynard et al 1994 Richet and Gillet 1997Mg2GeO4

Relevant to shock transformations in meteorites

Ge-O-Ge bonds

Densifiedsilica glassPIA

Mirror effects of P and T

Low P glass

Si2O7 dimersWadsleyite

SiO3 chains!

SiO4 monomersOlivine

MgSiO3 ilmenite

Heating of HP phase at room P

Should we keep doing Ramanspectroscopy on solids at HP and HT?

Murakami et al 2007

Should we keep doing Ramanspectroscopy on solids at HP and HT?

Murakami et al 2007

Why not…Easy to use technique

exploratory experiment before synchrotron runs or beforeusing a more cumbersome technique (Brillouin, …)

Coupling with first-principles calculation necessary

Raman data provide a benchmark for extending predictionsof elastic, thermodynamic and transport properties (thermalconductivity)

Complex systems (fluids, melts, …)