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First Principles Thermoelasticity of Minerals: Insights into the Earth’s LM. Renata M. Wentzcovitch U. of Minnesota (USA) and SISSA (Italy). • Problems related with seismic observations T and composition in the lower mantle Origin of lateral heterogeneities

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## First Principles Thermoelasticity of Minerals: Insights into the Earth’s LM

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**First Principles Thermoelasticity of Minerals:Insights into**the Earth’s LM Renata M. Wentzcovitch U. of Minnesota (USA) and SISSA (Italy) • Problems related with seismic observations T and composition in the lower mantle Origin of lateral heterogeneities Origin of anisotropies • How and what we calculate MgSiO3-perovskite MgO • Geophysical inferences • Future directions**The Contribution from Seismology**Longitudinal (P) waves Transverse (S) wave from free oscillations**PREM(Preliminary Reference Earth Model)(Dziewonski &**Anderson, 1981) P(GPa) 0 24 135 329 364**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 (Mg1--x,Fex)O 0 20 40 60 80 100 V %**(Masters et al, 2000)**3D Maps of Vs and Vp Vs V Vp**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)**Lateral variations in V and VP**(MLDB-Masters et al., 2000) (SD-Su & Dziewonski, 1997) (Karato & Karki, 2001)**Relations**0.42 ≤ A ≤ 0.37 with (Karato & Karki, 2001)****Anisotropy isotropic azimuthal VP VS1= VS2 VP (,) VS1 (,) VS2 (,) transverse VP () VS1 () VS2 ()**Anisotropy in the Earth**(Karato, 1998)**Mantle Anisotropy**SH>SV SV>SH**Slip systems and LPO**Zinc wire Slip system F**Anisotropic Structures**(SPO) (LPO) Shape Preferred Orientation Lattice Preferred Orientation Mantle flow geometry LPO Seismic anisotropy slip system Cij**Upper Mantle**Mineral sequence II Transition Zone 410 km (Spinel) (520 km (?)) (Mgx,Fe(1-x))2SiO4(Olivine) Lower Mantle 670 km + (Mgx,Fe(1-x))O (Mgx,Fe(1-x))SiO3**Method**• Structural optimizations • First principles variable cell shape MDfor structural optimizations xxxxxxxxxxxxxxxxxx(Wentzcovitch, Martins,& Price, 1993) • Self-consistent calculation of forces and stresses (LDA-CA) • Phonon thermodynamics • Density Functional Perturbation Theory xxxxxxxxxxxxxxxxxx(Gianozzi, Baroni, and de Gironcoli, 1991) (http://www.pwscf.com) • Soft & separable pseudopotentials (Troullier-Martins)**Typical Computational Experiment**Damped dynamics (Wentzcovitch, 1991) P = 150 GPa**abcxP**(a,b,c)th < (a,b,c)exp ~ 1% Tilt angles th - exp < 1deg Kth = 259 GPa K’th=3.9 Kexp = 261 GPa K’exp=4.0 ( Wentzcovitch, Martins, & Price, 1993) ( Ross and Hazen, 1989)**Elastic constant tensor **ij cijkl kl kl equilibrium structure (i,j) m re-optimize • Crystal (Pbnm)**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.: with is the propagation direction**Anisotropy**P-azimuthal: S-azimuthal: S-polarization:**• Poly-Crystalline aggregate**•Voigt-Reuss averages: •Voigt: uniform strain •Reuss: uniform stress**Polarization anisotropy in transversely isotropic medium**(Karki et al. 1997; Wentzcovitch et al1998) Seismic anisotropy Isotropic inbulk LM 2% VSH > VSVin - - SH/SV Anisotropy (%) High P, slip systems MgO:{100} ? (c44 < c11-c12) MgSiO3 pv:{010} ? (soft c55) -**Acoustic Velocities of Potential LM Phases**(Karki, Stixrude, Wentzcovitch,2001)**Effect of Fe alloying**(Kiefer, Stixrude,Wentzcovitch,2002) (Mg0.75Fe0.25)SiO3 K (P=0 GPa) = + 2% K (P=135 GPa) = + 1% G (P = 0 GPa) = - 6% G (P = 135 GPa) = - 8%**TM of mantle phases**CaSiO3 (Mg,Fe)SiO3 5000 Mw Core T 4000 HA solidus T (K) 3000 Mantle adiabat 2000 peridotite 0 20 40 60 80 100 120 P(GPa) (Zerr, Diegler, Boehler, 1998)**High Temperature calculations**• MgO and MgSiO3perovskite • Phonon dispersions from density functional perturbation theory (DFPT). • Quasiharmonic approximation (QHA) and thermal properties (e.g., , CP, S, KS,T, Cij’s).**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, Gironcoli, Baroni PRB 62, 14750, 2000 Exp:Raman [Durben and Wolf 1992] Infrared [Lu et al. 1994] 100 GPa**Quasiharmonic approximation**MgO - static zero-point - F (Ry) - thermal - 4th order finite strain equation of state Static300KExp (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 Volume (Å3)**Thermal expansivity of MgO and MgSiO3**(Karki, Wentzcovitch, de Gironcoli and Baroni, Science 286, 1705, 1999) (10-5 K-1)**Elastic moduli of MgO**(Karki, Wentzcovitch, de Gironcoli and Baroni, Science 286, 1705, 1999) EoS: K = (c11 + 2c12 )/3 Tetragonal strain: cs = c11 - c12 Shear strain: c44**Elastic moduli of MgO at high P and T**(Karki et al., Science 1999)**Elastic anisotropy of MgO**(Karki et al., 1997, 1999) Velocity anisotropy -**Adiabatic bulk modulus at LM P-T**(Karki, Wentzcovitch, de Gironcoli and Baroni, GRL, 2001)**Adiabatic Moduli**where**Summary**• Building a consistent body of knowledge obout LM phases • QHA is suitable for studying thermal properties of minerals at LM conditions • A homogeneous and adiabatic LM model appears to be incompatible with PREM. • LPO in aggregates of MgO and MgSiO3 can exhibit strong anisotropy at LM conditions. • We have all ingredients now to re-examine what has been said about lateral variations.**Future directions**• Properties of solid solutions, e.g., Fe, Al, bearing perovskites and oxides • Rheology (deformations, slip systems, diffusion, anelasticity) of materials • Computationally intensive, e.g, large-scale MD simulations!!**Acknowledgements**Bijaya B. Karki (U. Of MN) Lars Stixrude (Ann Arbor) Shun-ichiro Karato (U. of MN) Stefano de Gironcoli (SISSA) Stefano Baroni (SISSA) Funding: NSF/EAR

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