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, …)
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