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

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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  1. 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

  2. The Contribution from Seismology Longitudinal (P) waves Transverse (S) wave from free oscillations

  3. PREM(Preliminary Reference Earth Model)(Dziewonski & Anderson, 1981) P(GPa) 0 24 135 329 364

  4. 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 %

  5. Mantle convection

  6. Temperature and Composition of LM

  7. Lateral Heterogeneities

  8. (Masters et al, 2000) 3D Maps of Vs and Vp Vs V Vp

  9. 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)

  10. Lateral variations in V and VP (MLDB-Masters et al., 2000) (SD-Su & Dziewonski, 1997) (Karato & Karki, 2001)

  11. Relations 0.42 ≤ A ≤ 0.37 with (Karato & Karki, 2001)

  12. Anisotropy  isotropic azimuthal VP VS1= VS2 VP (,) VS1 (,) VS2 (,) transverse VP () VS1 () VS2 ()

  13. Anisotropy in the Earth (Karato, 1998)

  14. Mantle Anisotropy SH>SV SV>SH

  15. Slip systems and LPO Zinc wire Slip system F

  16. Anisotropic Structures (SPO) (LPO) Shape Preferred Orientation Lattice Preferred Orientation Mantle flow geometry LPO Seismic anisotropy slip system Cij

  17. 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

  18. 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)

  19. Typical Computational Experiment Damped dynamics (Wentzcovitch, 1991) P = 150 GPa

  20. 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)

  21. Elastic constant tensor  ij cijkl kl kl equilibrium structure (i,j) m re-optimize • Crystal (Pbnm)

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

  23. Wave velocities in perovskite (Pbnm) Cristoffel’s eq.: with is the propagation direction

  24. Anisotropy P-azimuthal: S-azimuthal: S-polarization:

  25. • Poly-Crystalline aggregate •Voigt-Reuss averages: •Voigt: uniform strain •Reuss: uniform stress

  26. 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) -

  27. Theory x PREM

  28. Acoustic Velocities of Potential LM Phases (Karki, Stixrude, Wentzcovitch,2001)

  29. 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%

  30. 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)

  31. 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).

  32. Phonon dispersions in MgO (Karki, Wentzcovitch, de Gironcoli and Baroni, PRB 61, 8793, 2000) - Exp: Sangster et al. 1970

  33. 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

  34. 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)

  35. Thermal expansivity of MgO and MgSiO3 (Karki, Wentzcovitch, de Gironcoli and Baroni, Science 286, 1705, 1999) (10-5 K-1)

  36. 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

  37. Elastic moduli of MgO at high P and T (Karki et al., Science 1999)

  38. Elastic anisotropy of MgO (Karki et al., 1997, 1999) Velocity anisotropy -

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

  40. LM geotherms

  41. Elasticity of MgSiO3 at LM Conditions

  42. Adiabatic Moduli where

  43. Seismic Velocities

  44. 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.

  45. 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!!

  46. 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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