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Quasiharmonic Thermodynamic Properties of Minerals

Quasiharmonic Thermodynamic Properties of Minerals. Renata M. M. Wentzcovitch. Department of Chemical Engineering and Materials Science Minnesota Supercomputer Institute U. of Minnesota. • Motivation • First Principles Thermodynamic Method

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Quasiharmonic Thermodynamic Properties of Minerals

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  1. Quasiharmonic Thermodynamic Properties of Minerals Renata M. M. Wentzcovitch Department of Chemical Engineering and Materials Science Minnesota Supercomputer Institute U. of Minnesota • Motivation • First Principles Thermodynamic Method How reliable is it? • Examples MgSiO3- Ilmenite to perovskite phase transition Thermoelasticity of perovskite Crystal structures at high (P,T) • Summary •

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

  3. Seismic Discontinuities and Phase Transitions PREM Dziewonski and Anderson, 1981 “660 km” topography J. M. Kendall, 2000

  4. Methods •Local Density Approximation •Soft norm-conserving pseudopotentials • Born-Oppenheimer variable cell shape molecular dynamics • Density functional perturbation theory for phonons

  5. Thermodynamic Method • VDoS and F(T,V) within the QHA N-th (N=3,4,5…) order isothermal (eulerian or logarithm) finite strain EoS IMPORTANT: structural parameters and phonon frequencies depend on volume alone!!….

  6. (Thermo) Elastic constant tensor  i equilibrium structure re-optimize

  7. Zero Point Motion Effect MgO F (Ry) - - Volume (Å3) 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

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

  9. MgSiO3-Akimotoite to perovskite transition Akimotoite bearing slab Clapeyron equation: 23 GPa 1980 K Tc Pv Ak T T<Tc From Fukao et al., Rev. Geophys. (2001) Pc P>Pc P Transformation inhibited in cold regions!!

  10. MgSiO3-ilmenite (Akimotoite) corundum Si2O3 layer ilmenite Al o o 1.77 A < Si-O < 1.83 A LiNbO3 Mg2O3 layer Mg Si R3 Mg Si o o 1.99 A < Mg-O < 2.16 A

  11. MgSiO3-perovskite (Pbnm) SiO3 octahedra o o 2.01 A < Mg-O < 3.12 A o o 1.78 A < Si-O < 1.80 A

  12. Pv:Raman [Durben and Wolf 1992] Infrared [Lu et al. 1994] Phonon dispersion of MgSiO3-ilmenite and perovskite Ak:Raman [Reynard and Rubie, 1996] Infrared [Madon and Price, 1989] Calc Exp Octahedral deformation Calc Exp Calc Exp Mg displacement Octahedral rotation NEW! 0 GPa Aaaaaaa Octahedral deformation Aaaaa Mg displacement

  13. Thermodynamic phase boundary Exp:Ito & Takahashi (1996) Issue I: Change in PTafter inclusion of zero point motion energy (Ezp) Issue II: discrepancy between theory and experiments perovskite Static Experiment Pressure (GPa) Theory Gil(P,T) X Gpv(P,T) akimotoite MgSiO3 Temperature (K)

  14. Issue I “…Useful rule…” pv F(V,T) Pc Ezp shifts ak V  Pcdecreases

  15. Thermodynamic phase boundary Exp:Ito & Takahashi (1996) Issue I: Change in PTafter inclusion of zero point motion energy (Ezp) Issue II: discrepancy between theory and experiments perovskite Static Experiment Pressure (GPa) Theory Gil(P,T) X Gpv(P,T) akimotoite MgSiO3 Temperature (K)

  16. Issue II… …a posteriori criterion for the validity of the QHA (10-5 K-1)    MgSiO3 Karki et al, GRL (2001)

  17. Static perovskite Experiment Not OK!! Pressure (GPa) Theory QHA OK akimotoite MgSiO3 Temperature (K) Exp:Ito & Takahashi (1996)

  18. Properties of MgSiO3-perovskite and -ilmenite 1.88 Ak 4.7 3.908 176.8 201 -0.042 -0.025 1.67 | 2.44 ~ Ak 3.943 175.2 212 4.8 Pv Pv (256) 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;Weidner & Ito, 1985; Reynard & Rubie, 1996; Hofmeister and Ito, 1992; Chopelas, 1999]

  19. Ad hoc correction to DFT results… (perovskite)

  20. Ad hoc correction to DFT results… (perovskite) !!!... but…

  21. Ad hoc correction to DFT results… (perovskite) !!!... but… ?!

  22. Ad hoc correction to DFT results… (perovskite) !!!... but… ?!

  23. EoS for Perovskite C = 2.5 GPa

  24. EoS for Ilmenite Calc.: Karki & Wentzcovitch, 2002. C = 1.9 GPa Exp.: Reynard et al., 1996

  25. Ad hoc correction to Pc… (ilmenite to perovskite) Pc at 300K should increase (not really conclusive…!!)

  26. 300 K 1000K 2000K 3000 K 4000 K Cij(P,T) cij (Oganov et al,2001) (Wentzcovitch, Karki, Cococciono, de Gioroncoli, 2003)

  27. …IMPORTANT: structural parameters and phonon frequencies depend on volume alone!! • Structures at high P are determined at T= 0 P(V,0) • P’(V,T’) within the QHA • At T 0… V(P’,T’)=V(P,0)  structure(P’,T’) = structure(P,0) Corresponding States

  28. Comparison with Experiments (Ross & Hazen, 1989) o Calc. 77 K < T < 400K 0 GPa < P < 12 GPa o o

  29. Comparison with Experiments (Ross & Hazen, 1989) o Calc. 77 K < T < 400K 0 GPa < P < 12 GPa o o LDA +ZP Exp. LDA

  30. (Funamori et al., 1996) 300 K < T < 2000 K 21 GPa < P < 29 GPa

  31. (Fiquet et al., 1998) 300 K < T < 2000 K 26 GPa < P < 58 GPa

  32. Predictions a,b,c(P,T) 4000 K 3000 K 2000 K 1000 K 300 K

  33. Summary • LDA + QHA is a good and useful FP method for high P,T thermodynamics (..lots of insights) •  The validity criterion based on  suggests avoidance of • phase boundaries •  Prediction of high P,T crystal structures through corresponding • states

  34. Acknowledgements Bijaya B. Karki (LSU) Stefano de Gironcoli, Stefano Baroni, Matteo Coccocioni (SISSA, Italy) NSF-EAR and NSF-COMPRES, SISSA and INFM (Italy)

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