First Principles Thermoelasticity of Mantle Minerals
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Transcript First Principles Thermoelasticity of Mantle Minerals
First Principles Thermoelasticity of
Mantle Minerals
Renata M. M. Wentzcovitch
Department of Chemical Engineering and Materials Science
U. of Minnesota, Minneapolis
&
SISSA/INFM, Trieste
• Research in the early 90’s (first principles MD)
• Current research (NSF/EAR funded)
Geophysical motivation
Thermoelasticity
• Research tomorrow
•
First Principles Thermoelasticity of
Mantle Minerals
Renata M. M. Wentzcovitch
Department of Chemical Engineering and Materials Science
U. of Minnesota, Minneapolis
&
SISSA/INFM, Trieste
• Research in the early 90’s (first principles MD)
• Current research (NSF/EAR funded)
Geophysical motivation
Thermoelasticity
• Research tomorrow
•
Research in the early nineties
• Development of a variable cell shape (VCS) molecular
dynamics (MD) method (Wentzcovitch, PRB,1991)
• Development of first principles MD
I. Self-consistent method with iterative diagonalization
used in MD simulations (Wentzcovitch and Martins, SSC,1991)
II. Implementation of finite temperature DFT
(Wentzcovitch, Martins, and Allen, PRB ,1992)
• Some original applications of combined methodologies
Collaborators: J. L. Martins (INESC, Lisbon) and
P. B. Allen (SUNY-Stony Brook, CHiPR)
First Principles VCS-MD
(Wentzcovitch, Martins, Price, PRL 1993)
Damped dynamics
~ ( PI )
r ~ f int f (r, )
MgSiO3
P = 150 GPa
Lattice
(a,b,c)th < (a,b,c)exp ~ 1%
Tilt angles
th - exp < 1deg
dP
K Vo
dV
Kth = 259 GPa K’th=3.9
Kexp = 261 GPa K’exp=4.0
(• Wentzcovitch, Martins, & Price, 1993)
( Ross and Hazen, 1989)
Acknowledgements
• David Price (UCL-London)
• Lars Stixrude (U. of Michigan, Ann Arbor)
• Shun-ichiro Karato (U. of Minnesota/Yale)
• Bijaya B. Karki (Louisiana S. U.)
• Boris Kiefer (Princeton U.)
The Contribution from Seismology
Longitudinal (P) waves
VP
4
K G
3
Transverse (S) wave
VS
G
from free oscillations
PREM
(Preliminary Reference Earth Model)
(Dziewonski & Anderson, 1981)
P(GPa)
0
24
135
329
364
Mantle Mineralogy
MgSiO3
Pyrolite model (% weight)
Olivine
cpx
(Mg1--x,Fex)2SiO4
300
8
(Mg,Ca)SiO3
12
garnets
500
-phase
spinel
700
(Mg1--x,Fex) O
(McDonough and Sun, 1995)
4
0
(‘’)
(Mg,Al,Si)O3
20
(‘’)
perovskite
MW(Mg,Fe) (Si,Al)O3
20
40
16
60
V%
CaSiO3
80
100
P (Kbar)
45.0
37.8
8.1
4.5
3.6
0.4
0.4
0.2
0.2
0.1
Depth (km)
SiO2
MgO
FeO
Al2O3
CaO
Cr2O3
Na2O
NiO
TiO2
MnO
opx
100
Mantle convection
Intermediate Model of Mantle Convection
(Kellogg, Hager, van der Hilst, Science, 1999)
3D Maps of Vs and Vp (Masters et al, 2000)
Vs
V
Vp
Lateral variations in VS and VP
RS / P
ln Vs
lnVP P
(Karato & Karki, JGR 2001)
(MLDB-Masters et al., 2000)
(KWH-Kennett et al., 1998)
(SD-Su & Dziewonski, 1997)
(RW-Robertson & Woodhouse,1996)
Anisotropy
isotropic
azimuthal
VP
VS1= VS2
VP (,)
VS1 (,) VS2 (,)
transverse
VP ()
VS1 () VS2 ()
Anisotropy in the Earth
(VSH VSV)%
VS
(Karato, 1998)
Mantle Anisotropy
SH>SV
SV>SH
Zinc wire
Slip systems and LPO
Slip system
F
Anisotropic Structures
Lattice Preferred Orientation (LPO) Shape Preferred Orientation (SPO)
Mantle flow
geometry
LPO
slip
system
Seismic anisotropy
Cij
Mineral sequence II
Lower Mantle
+
+
(Mgx,Fe(1-x))SiO3
(Mgx,Fe(1-x))O
CaSiO3
Mineral sequence II
Lower Mantle
+
+
(Mg(1-x),Fex)(Si(1-y),Aly)O3
(Mgx,Fe(1-x))O
CaSiO3
Elastic Waves
P-wave
(longitudinal)
S-waves
(shear)
n propagation
direction
Yegani-Haeri, 1994
Wentzcovitch et al, 1995
Karki et al, 1997
within 5%
Wave velocities in perovskite (Pbnm)
Cristoffel’s eq.:
VI iI ik kI
2
n
with
ik cij kln j nl
is the propagation direction
(Wentzcovitch, Karki, Karato, EPSL 1998)
Anisotropy
P-azimuthal:
VP
VP
max
VP
VP
min
av
S-azimuthal:
VS
VS
max
VSmin
VS
av
S-polarization:
VS
VS 1 VS 2
VS
max
av
(Karki, Stixrude, Wentzcovitch, Rev. Geophys. 2002)
•Voigt-Reuss averages:
• Poly-Crystalline aggregate
MN
CMNRS
MN
ij
ij
•Voigt: uniform strain
MN CMNRS RS
CMNRS agg ni nj nk nl cijkl f(n)
M
N
R
S
•Reuss: uniform stress
MN SMNRS RS
SMNRS agg niMnjNnkRnl S sijkl f(n)
CMNRS SMNRS
2
1
C44 G
C12 C11 2C44
C11 2C12
K
3
C11
C12
C12
*
*
*
C 12
C12
*
*
C11
C12
*
*
C 12
C11
*
*
*
*
C 44
*
*
*
*
C 44
*
*
*
*
*
*
*
*
*
C 44
Polarization anisotropy in transversely isotropic medium
(SH-SV)/S Anisotropy (%)
(Karki et al., JGR 1997; Wentzcovitch et al EPSL1998)
-
-
Seismic anisotropy
Isotropic in bulk LM
2% VSH > VSV in D’’
High P, slip systems
MgO: {100}
?
MgSiO3 pv: {010} ?
Acoustic Velocities of Potential LM Phases
(Karki, Stixrude, Wentzcovitch, Rev. Geophys. 2002)
Effect of Fe alloying
(Kiefer, Stixrude,Wentzcovitch, GRL 2002)
(Mg0.75Fe0.25)SiO3
||
+
+
4
+
TM of mantle phases
CaSiO3
(Mg,Fe)SiO3
5000
T (K)
Mw
4000
HA
Core T
solidus
3000
Mantle adiabat
2000
peridotite
0
20
40
60
P(GPa)
80
100
120
(Zerr, Diegler, Boehler, Science1998)
Method
• Thermodynamic method:
VDoS and F(T,V) within the QHA
F (V , T ) U (V )
qj
qj (V )
2
qj (V )
k BT ln1 exp
k BT
qj
N-th order finite strain EoS (N=3,4,5…)
F
P
V T
F
S
T V
G F TS PV
• Density Functional Perturbation Theory for phonons
xxxxxxxxxxxxxxxxxx(Gianozzi, Baroni, and de Gironcoli, 1991)
(www.pwscf.com)
Collaborators: Stefano de Gironcoli and Stefano Baroni
(Thermo) Elastic constant tensor
2
G
T
cij (T , P )
i j
kl
cij (T , P) cij (T , P)
S
equilibrium
structure
re-optimize
T
S
i
i
T
i jVT
CV
Phonon dispersions in MgO
-
(Karki, Wentzcovitch, de Gironcoli and Baroni, PRB 61, 8793, 2000)
Exp: Sangster et al. 1970
Phonon dispersion of MgSiO3 perovskite
Calc Exp
-
Calc Exp
0 GPa
-
Calc: Karki, Wentzcovitch, de Gironcoli, Baroni
PRB 62, 14750, 2000
Exp: Raman [Durben and Wolf 1992]
Infrared [Lu et al. 1994]
100 GPa
MgSiO3-perovskite and MgO
(gr/cm-3)
V
(A3)
KT
(GPa)
d KT/dP
d KT2/dP2
(GPa-1)
d KT/dT
(Gpa K-1)
10-5 K-1
3.580
18.80
159
4.30
-0.030
-0.014
3.12
Calc.
MW
3.601
18.69
160
4.15
-0.0145
3.13
Exp.
MW
4.210
164.1
247
4.0
-0.016
-0.031
2.1
Calc.
Pv
3.7
|
4.0
~
162.3
246
|
266
-0.02
|
-0.07
1.7
|
2.2
Exp.
Pv
4.247
~
Exp.: [Ross & Hazen, 1989; Mao et al., 1991; Wang et al., 1994; Funamori et al., 1996;
Chopelas, 1996; Gillet et al., 2000; Fiquet et al., 2000]
(10-5 K-1)
Thermal expansivity of MgO and MgSiO3
(Karki, Wentzcovitch, de Gironcoli and Baroni, Science 1999)
(Karki, Wentzcovitch, de Gironcoli and Baroni, GRL 2001)
Elasticity of MgO
(Karki et al., Science 1999)
Elasticity of MgSiO3 at LM Conditions
(Wentzcovitch, Coccocioni, and Karki 2002)
Cijtable
##
#
477
536
468
198
172
151
132
135
149
**
455
509
446
185
164
145
125
126
140
## Wentzcovitch et al, 1998 (static)
* Karki et al., 1997 (static)
+ Wetzcovitch et al., 1995 (static)
Expt.: Yegani-Haeri, 1994
# Wentzcovitch et al, 2002 (static)
**
“
(300 K)
Adiabatic bulk modulus at LM P-T
(Karki, Wentzcovitch, de Gironcoli and Baroni, GRL, 2001)
LM Geotherms
6000
LM geotherms
5000
T (K)
Pv
Tc
4000
Solidus
Pyrolite
3000
2000
1000
500
Isentropes
1000
1500
2000
De pth (k m )
2500
CMB
|
3000
Summary
• Building a consistent body of knowledge obout LM phases
• We have adequate methods (DFT, QHA) to examine elasticity
of major mantle phases
• The objective is to interpret seismic observations (1D, 3D,
anisotropy) in terms of composition, temperature, ``flow’’…
Summary
• Building a consistent body of knowledge obout LM phases
• We have adequate methods (DFT, QHA) to examine elasticity
of major mantle phases
• The objective is to interpret seismic observations (1D, 3D,
anisotropy) in term of composition, temperature, ``flow’’…
Mineral
Physics
Geodynamics
Seismology