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 90’s (first principles MD) Current research (NSF/EAR funded) Geophysical motivation Thermoelasticity Some inferences about the lower mantle Research tomorrow

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 90’s (first principles MD) Current research (NSF/EAR funded) Geophysical motivation Thermoelasticity Some Inferences about the Lower Mantle 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 P = 150 GPa MgSiO 3

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 Transverse (S) wave from free oscillations

PREM (Preliminary Reference Earth Model) (Dziewonski & Anderson, 1981) P(GPa)

Mantle Mineralogy SiO MgO 37.8 FeO 8.1 Al 2 O CaO 3.6 Cr 2 O Na 2 O 0.4 NiO 0.2 TiO MnO 0.1 (McDonough and Sun, 1995) Pyrolite model (% weight) Depth (km) P (Kbar) V % Olivine perovskite  -phase spinel MW garnets opx cpx (Mg 1--x,Fe x ) 2 SiO 4 (‘’) MgSiO 3 (Mg,Al,Si)O 3 (Mg,Fe) (Si,Al)O 3 (Mg 1--x,Fe x ) O (Mg,Ca)SiO 3 CaSiO 3

Mantle convection

Intermediate Model of Mantle Convection (Kellogg, Hager, van der Hilst, Science, 1999)

3D Maps of V s and V p V s V  V p ( Masters et al, 2000)

(MLDB-Masters et al., 2000) (KWH-Kennett et al., 1998) (SD-Su & Dziewonski, 1997) (RW-Robertson & Woodhouse,1996) Lateral variations in V S and V P (Karato & Karki, JGR 2001)

Anisotropy   isotropic transverse azimuthal V P V S1 = V S2 V P (  ) V S1 (  )  V S2 (  ) V P ( ,  ) V S1 ( ,  )  V S2 ( ,  )

Anisotropy in the Earth (Karato, 1998)

Mantle Anisotropy SH>SV SV>SH

Slip system Zinc wire F Slip systems and LPO

Lattice Preferred Orientation (LPO) Shape Preferred Orientation (SPO) Mantle flow geometry LPOSeismic anisotropy slip system C ij Anisotropic Structures

+ Mineral sequence II Lower Mantle (Mg x,Fe (1-x) )O(Mg x,Fe (1-x) )SiO 3 + CaSiO 3

+ Mineral sequence II Lower Mantle (Mg x,Fe (1-x) )O(Mg (1-x),Fe x )(Si (1-y),Al y )O 3 + CaSiO 3

Crystal ( Pbnm ) equilibrium structure  kl re-optimize  kl  ij c ijkl (i,j) m Elastic constant tensor 

Yegani-Haeri, 1994 Wentzcovitch et al, 1995 Karki et al, 1997 within 5% S-waves (shear) P-wave (longitudinal) n propagation direction Elastic Waves

Cristoffel’s eq.: with is the propagation direction Wave velocities in perovskite (Pbnm) (Wentzcovitch, Karki, Karato, EPSL 1998)

Anisotropy P-azimuthal: S-azimuthal: S-polarization: (Karki, Stixrude, Wentzcovitch, Rev. Geophys. 2002)

Voigt: uniform strain Reuss: uniform stress Voigt-Reuss averages: Poly-Crystalline aggregate

Polarization anisotropy in transversely isotropic medium High P, slip systems MgO: {100} ? MgSiO 3 pv: {010} ? Seismic anisotropy Isotropic in bulk LM 2% V SH > V SV in D’’ (SH-SV)/S Anisotropy (%) (Karki et al., JGR 1997; Wentzcovitch et al EPSL1998 ) (Karki, Stixrude, Wentzcovitch, Rev. Geophys. 2002)

Acoustic Velocities of Potential LM Phases (Karki, Stixrude, Wentzcovitch, Rev. Geophys. 2002)

T M of mantle phases Core T Mantle adiabat solidus HA Mw (Mg,Fe)SiO 3 CaSiO 3 peridotite P(GPa) T (K) (Zerr, Diegler, Boehler, Science1998)

Method Density Functional Perturbation Theory for phonons xxxxxxxxxxxxxxxxxx (Gianozzi, Baroni, and de Gironcoli, 1991) Thermodynamic method: VDoS and F(T,V) within the QHA N-th order finite strain EoS (N=3,4,5…)

equilibrium structure  kl re-optimize (Thermo) Elastic constant tensor 

Phonon dispersions in MgO Exp: Sangster et al (Karki, Wentzcovitch, de Gironcoli and Baroni, PRB 61, 8793, 2000) -

Phonon dispersion of MgSiO 3 perovskite Calc Exp Calc: Karki, Wentzcovitch, de Gironcoli, Baroni PRB 62, 14750, 2000 Exp: Raman [Durben and Wolf 1992] Infrared [Lu et al. 1994] 0 GPa 100 GPa - -

Zero Point Motion Effect Volume (Å 3 ) F (Ry) MgO Static 300K Exp (Fei 1999) V (Å 3 ) K (GPa) K´ K´´(GPa -1 )

MgSiO 3 -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]

Thermal expansivity of MgO and MgSiO 3 (Karki, Wentzcovitch, de Gironcoli and Baroni, Science 1999) (Karki, Wentzcovitch, de Gironcoli and Baroni, GRL 2001)  (10 -5 K -1 )

Elasticity of MgO (Karki et al., Science 1999)

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

LM geotherms

Elastic constant tensor (Wentzcovitch, Karki, & Coccociono, 2002)

Velocities

Effect of Fe alloying (Kiefer, Stixrude,Wentzcovitch, GRL 2002) (Mg 0.75 Fe 0.25 )SiO ||

Comparison with PREM Along B&S-geotherm perovskite pyrolite

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’’… Seismology Mineral Physics Geodynamics

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