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
Research in the early 90s (first principles
MD) Current research (NSF/EAR funded)
Geophysical motivation
Thermoelasticity Some inferences
about the lower mantle Research tomorrow
2
First Principles Thermoelasticity of Mantle
Minerals
Renata M. M. Wentzcovitch
Department of Chemical Engineering and Materials
Science U. of Minnesota,
Minneapolis
Research in the early 90s (first principles
MD) Current research (NSF/EAR funded)
Geophysical motivation
Thermoelasticity Some Inferences
about the Lower Mantle 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)
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First Principles VCS-MD (Wentzcovitch, Martins,
Price, PRL 1993)
Damped dynamics
MgSiO3
P 150 GPa
5
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.)
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The Contribution from Seismology
Longitudinal (P) waves
Transverse (S) wave
from free oscillations
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PREM (Preliminary Reference Earth
Model)(Dziewonski Anderson, 1981)
P(GPa)
0
24
135
329
364
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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
9
Mantle convection
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Intermediate Model of Mantle Convection
(Kellogg, Hager, van der Hilst, Science, 1999)
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3D Maps of Vs and Vp
(Masters et al, 2000)
Vs
V?
Vp
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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)
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Anisotropy
?

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



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



(Mgx,Fe(1-x))O
(Mg(1-x),Fex)(Si(1-y),Aly)O3
CaSiO3
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Elastic constant tensor ?
?ij
cijkl
?kl
?kl
equilibrium structure
(i,j) m
re-optimize
Crystal (Pbnm)
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Elastic Waves
P-wave (longitudinal)
S-waves (shear)
n propagation direction
Yegani-Haeri, 1994 Wentzcovitch et al, 1995 Karki
et al, 1997
within 5
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Wave velocities in perovskite (Pbnm)
Cristoffels eq.
with
is the propagation direction
(Wentzcovitch, Karki, Karato, EPSL 1998)
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Anisotropy
P-azimuthal S-azimuthal
S-polarization
(Karki, Stixrude, Wentzcovitch, Rev. Geophys.
2002)
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Poly-Crystalline aggregate
Voigt-Reuss averages

Voigt uniform strain
Reuss uniform stress
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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 ?
-
(Karki, Stixrude, Wentzcovitch, Rev. Geophys.
2002)
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Acoustic Velocities of Potential LM Phases
(Karki, Stixrude, Wentzcovitch, Rev. Geophys.
2002)
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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)
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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)

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(Thermo) Elastic constant tensor ?
?kl
equilibrium structure
re-optimize
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Phonon dispersions in MgO
(Karki, Wentzcovitch, de Gironcoli and Baroni,
PRB 61, 8793, 2000)
-
Exp Sangster et al. 1970
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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
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Zero Point Motion Effect
MgO
F (Ry)
-
-
Volume (Å3)
Static 300K Exp (Fei
1999) V (Å3) 18.5 18.8
18.7 K (GPa) 169 159 160 K
4.18 4.30
4.15 K(GPa-1) -0.025 -0.030
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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
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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)
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Elasticity of MgO
(Karki et al., Science 1999)
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Adiabatic bulk modulus at LM P-T
(Karki, Wentzcovitch, de Gironcoli and Baroni,
GRL, 2001)
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LM geotherms
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Elastic constant tensor
(Wentzcovitch, Karki, Coccociono, 2002)
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Velocities
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Effect of Fe alloying

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

4
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Comparison with PREM
perovskite
pyrolite
Along BS-geotherm
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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

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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
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Acknowledgements

• Bijaya B. Karki (LSU)
• Stefano de Gironcoli, Matteo Coccocioni (SISSA,
  Italy)