First Principles Thermoelasticity of Mantle Minerals

1
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 90s (first principles
MD) Current research (NSF/EAR funded)
Geophysical motivation
Thermoelasticity Research tomorrow
2
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 90s (first principles
MD) Current research (NSF/EAR funded)
Geophysical motivation
Thermoelasticity Research tomorrow
3
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)
4
First Principles VCS-MD (Wentzcovitch, Martins,
Price, PRL 1993)
Damped dynamics
MgSiO3
P 150 GPa
5
Lattice
(a,b,c)th lt (a,b,c)exp 1
Tilt angles ?th - ?exp lt 1deg
Kth 259 GPa Kth3.9
Kexp 261 GPa Kexp4.0
( Wentzcovitch, Martins, Price, 1993)
( Ross and Hazen, 1989)
6
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.)
7
The Contribution from Seismology
Longitudinal (P) waves
Transverse (S) wave
from free oscillations
8
PREM (Preliminary Reference Earth
Model)(Dziewonski Anderson, 1981)
P(GPa)
0
24
135
329
364
9
Mantle Mineralogy
MgSiO3
Pyrolite model ( weight)
opx
100
4
Olivine
SiO2 45.0 MgO 37.8 FeO
8.1 Al2O3 4.5 CaO 3.6 Cr2O3
0.4 Na2O 0.4 NiO 0.2 TiO2
0.2 MnO 0.1 (McDonough and
Sun, 1995)
8
cpx
(Mg1--x,Fex)2SiO4
300
(Mg,Ca)SiO3
12
P (Kbar)
Depth (km)
garnets
16
500
?-phase
()
(Mg,Al,Si)O3
20
spinel
()
700
perovskite
MW
(Mg,Fe) (Si,Al)O3
CaSiO3
60
20
40
80
100
0
(Mg1--x,Fex) O
V
10
Mantle convection
11
Intermediate Model of Mantle Convection
(Kellogg, Hager, van der Hilst, Science, 1999)
12
3D Maps of Vs and Vp
(Masters et al, 2000)
Vs
V?
Vp
13
Lateral variations in VS and VP
(Karato Karki, JGR 2001)
(MLDB-Masters et al., 2000) (KWH-Kennett et al.,
1998) (SD-Su Dziewonski, 1997) (RW-Robertson
Woodhouse,1996)
14
Anisotropy
?

?
isotropic
azimuthal
VP VS1 VS2
VP (?,?) VS1 (?,?) ? VS2 (?,?)
transverse
VP (?) VS1 (?) ? VS2 (?)
15
Anisotropy in the Earth
(Karato, 1998)
16
Mantle Anisotropy
SHgtSV
SVgtSH
17
Slip systems and LPO
Zinc wire
Slip system
F
18
Anisotropic Structures
(SPO)
(LPO)
Shape Preferred Orientation
Lattice Preferred Orientation
Mantle flow geometry
LPO
Seismic anisotropy
slip system
Cij
19
Mineral sequence II
Lower Mantle



(Mgx,Fe(1-x))O
(Mgx,Fe(1-x))SiO3
CaSiO3
20
Mineral sequence II
Lower Mantle



(Mgx,Fe(1-x))O
(Mg(1-x),Fex)(Si(1-y),Aly)O3
CaSiO3
21
Elastic Waves
P-wave (longitudinal)
S-waves (shear)
n propagation direction
Yegani-Haeri, 1994 Wentzcovitch et al, 1995 Karki
et al, 1997
within 5
22
Wave velocities in perovskite (Pbnm)
Cristoffels eq.
with
is the propagation direction
(Wentzcovitch, Karki, Karato, EPSL 1998)
23
Anisotropy
P-azimuthal S-azimuthal
S-polarization
(Karki, Stixrude, Wentzcovitch, Rev. Geophys.
2002)
24
Poly-Crystalline aggregate
Voigt-Reuss averages

Voigt uniform strain
Reuss uniform stress
25
Polarization anisotropy in transversely isotropic
medium
(Karki et al., JGR 1997 Wentzcovitch et al
EPSL1998)
Seismic anisotropy Isotropic in bulk LM 2 VSH gt
VSV in D
-
(SH-SV)/S Anisotropy ()
-
High P, slip systems MgO 100 ? MgSiO3
pv 010 ?
-
26
Acoustic Velocities of Potential LM Phases
(Karki, Stixrude, Wentzcovitch, Rev. Geophys.
2002)
27
Effect of Fe alloying

• (Kiefer, Stixrude,Wentzcovitch, GRL 2002)
• (Mg0.75Fe0.25)SiO3

4
28
TM of mantle phases
CaSiO3
(Mg,Fe)SiO3
5000
Mw
Core T
4000
HA
solidus
T (K)
3000
Mantle adiabat
2000
peridotite
0
40
20
60
80
100
120
P(GPa)
(Zerr, Diegler, Boehler, Science1998)
29
Method
Thermodynamic method VDoS and F(T,V) within
the QHA
N-th order finite strain EoS (N3,4,5)

• Density Functional Perturbation Theory for
  phonons
• xxxxxxxxxxxxxxxxxx(Gianozzi, Baroni, and de
  Gironcoli, 1991)
• (www.pwscf.com)
• Collaborators Stefano de Gironcoli
  and Stefano Baroni

30
(Thermo) Elastic constant tensor ?
?kl
equilibrium structure
re-optimize
31
Phonon dispersions in MgO
(Karki, Wentzcovitch, de Gironcoli and Baroni,
PRB 61, 8793, 2000)
-
Exp Sangster et al. 1970
32
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
33
MgSiO3-perovskite and MgO
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
34
Thermal expansivity of MgO and MgSiO3
(Karki, Wentzcovitch, de Gironcoli and Baroni,
Science 1999) (Karki, Wentzcovitch, de Gironcoli
and Baroni, GRL 2001)
? (10-5 K-1)
35
Elasticity of MgO
(Karki et al., Science 1999)
36
Elasticity of MgSiO3 at LM Conditions
(Wentzcovitch, Coccocioni, and Karki 2002)
37
Cij- table

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)
38
Adiabatic bulk modulus at LM P-T
(Karki, Wentzcovitch, de Gironcoli and Baroni,
GRL, 2001)
39
LM geotherms
40
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

41
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