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Thermoelasticity of (Mg,Fe)SiO 3 -perovskite at lower mantle conditions

Thermoelasticity of (Mg,Fe)SiO 3 -perovskite at lower mantle conditions. Renata M. M. Wentzcovitch. Department of Chemical Engineering and Materials Science U. of Minnesota, Minneapolis. • Research in the early 90’s (first principles MD)

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Thermoelasticity of (Mg,Fe)SiO 3 -perovskite at lower mantle conditions

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  1. Thermoelasticity of (Mg,Fe)SiO3-perovskite at lower mantle conditions 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 (thermo-chemical state of the LM) Thermoelasticity of (Mg,Fe)SiO3 and MgO Comparisons with PREM • Summary •

  2. 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)

  3. Methods • Density Functional Theory ( , ) •Local Density Approximation •First Principles Pseudopotentials • Plane-wave expansion ( ) • Self-consistent Forces and Stresses (molecular dynamics)

  4. First Principles VCS-MD(Wentzcovitch, Martins, Price, PRL 1993) Damped dynamics MgSiO3 P = 150 GPa

  5. Lattice (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)

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

  8. 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 %

  9. Mantle convection

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

  11. Lower Mantle Mineral sequence II + + (Mg(1-x-z),Fex Alz)(Si(1-y),Aly)O3 (Mgx,Fe(1-x))O CaSiO3

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

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

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

  15. Theory x PREM (Voigt-Reuss-Hill averages)

  16. 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, Science1998)

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

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

  19. 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

  20. 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]

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

  22. Thermal expansivity of MgSiO3 (Karki, Wentzcovitch, de Gironcoli and Baroni, GRL 2001) (10-5 K-1)

  23. The QHA Criterion: inflection point of (T) B&S geotherm

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

  25. LM geotherms

  26. Elastic constant tensor 300 K 1000K 2000K 3000 K 4000 K 1500 K 2500 K 3500 K Oganov et al 2001 (Wentzcovitch, Karki, & Coccociono, 2002)

  27. Velocities V (km/sec) &  (gr/cm3)

  28. Effect of Fe alloying (Kiefer, Stixrude,Wentzcovitch, GRL 2002) (Mg0.75Fe0.25)SiO3 || + + + 4

  29. Comparison with PREM Pyrolite Perovskite Brown & Shankland T(r)

  30. 38 GPa 88 GPa Moduli Pyrolite Perovskite Brown & Shankland T(r)

  31. 88 GPa 38 GPa 88 GPa 38 GPa Moduli Pyrolite Perovskite Brown & Shankland T(r)

  32. 38 GPa 88 GPa 38 GPa 100 GPa Moduli Pyrolite Perovskite Brown & Shankland T(r)

  33. Me “…At depths greater than 1400 km, the rate of rise of the bulk and shear moduli are too small and too large respectively for the lower mantle to consist of a homogeneous isotropic layer of pure perovskite or pyrolite composition. It seems that changes in chemical composition, or subtle phase changes, or anisotropy, or a combination of all, are required to account for the elastic moduli of the deeper part of the LM ,….” (2002)

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

  35. 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’’…

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

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