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Quasiharmonic Thermodynamic Properties of Minerals Renata M. M. Wentzcovitch Department of Chemical Engineering and Materials Science Minnesota Supercomputer.

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Presentation on theme: "Quasiharmonic Thermodynamic Properties of Minerals Renata M. M. Wentzcovitch Department of Chemical Engineering and Materials Science Minnesota Supercomputer."— Presentation transcript:

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

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

7 Zero Point Motion Effect Volume (Å 3 ) F (Ry) MgO Static 300K Exp (Fei 1999) V (Å 3 ) 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 MgSiO 3 -Akimotoite to perovskite transition From Fukao et al., Rev. Geophys. (2001) Clapeyron equation: P T TcTc PcPc Ak Pv T<T c P>P c Akimotoite bearing slab Transformation inhibited in cold regions!! 23 GPa 1980 K

10 MgSiO 3 -ilmenite (Akimotoite) Si 2 O 3 layer Mg 2 O 3 layer 1.77 A < Si-O < 1.83 A 1.99 A < Mg-O < 2.16 A oo o o corundum ilmenite LiNbO 3 MgSi Al SiMg R3

11 MgSiO 3 -perovskite (Pbnm) SiO 3 octahedra 1.78 A < Si-O < 1.80 A 2.01 A < Mg-O < 3.12 A oo oo

12 Phonon dispersion of MgSiO 3 -ilmenite and perovskite Calc Exp Pv: Raman [Durben and Wolf 1992] Infrared [Lu et al. 1994] 0 GPa Calc Exp Aaaaa Aaaaaaa Ak: Raman [Reynard and Rubie, 1996] Infrared [Madon and Price, 1989] Octahedral deformation Octahedral deformation Mg displacement Mg displacement Octahedral rotation NEW !

13 Pressure (GPa) Temperature (K) MgSiO 3 akimotoite perovskite Static Experiment Theory Thermodynamic phase boundary Issue I: Change in P T after inclusion of zero point motion energy (E zp ) Issue II: discrepancy between theory and experiments Exp:Ito & Takahashi (1996) G il (P,T) X G pv (P,T)

14 “…Useful rule…” I s s u e I P c decreases F(V,T) V pv ak  E zp shifts PcPc

15 Pressure (GPa) Temperature (K) MgSiO 3 akimotoite perovskite Static Experiment Theory Thermodynamic phase boundary Issue I: Change in P T after inclusion of zero point motion energy (E zp ) Issue II: discrepancy between theory and experiments Exp:Ito & Takahashi (1996) G il (P,T) X G pv (P,T)

16 …a posteriori criterion for the validity of the QHA  (10 -5 K -1 ) MgSiO 3    Karki et al, GRL (2001) Issue II…

17 Pressure (GPa) Temperature (K) MgSiO 3 akimotoite Static Experiment Theory Exp:Ito & Takahashi (1996) perovskite Not OK!! QHA OK

18 Properties of MgSiO 3 -perovskite and -ilmenite 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] Ak 1.88 1.67 | 2.44 -0.025 ~ -0.042 4.8 4.7 201 212 176.8 175.2 3.908 3.943 Pv (256)

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 C = 1.9 GPaExp.: Reynard et al., 1996 Calc.: Karki & Wentzcovitch, 2002.

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

26 cijcij (Wentzcovitch, Karki, Cococciono, de Gioroncoli, 2003) 300 K 1000K 2000K 3000 K 4000 K ( Oganov et al,2001) C ij (P,T)

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) 77 K < T < 400K 0 GPa < P < 12 GPa o o o Calc.

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

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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