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Renata M. Wentzcovitch Dept. of Chemical Engineering and Materials Science , Minnesota Supercomputing Institute UNIVERS

Phase transitions in silica (SiO 2 ). Phase transitions in silica-(SiO 2 ) . Renata M. Wentzcovitch Dept. of Chemical Engineering and Materials Science , Minnesota Supercomputing Institute UNIVERSITY OF MINNESOTA. Outline. Objective: motivate a study of the performance of

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Renata M. Wentzcovitch Dept. of Chemical Engineering and Materials Science , Minnesota Supercomputing Institute UNIVERS

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  1. Phase transitions in silica (SiO2) Phase transitions in silica-(SiO2) Renata M. Wentzcovitch Dept. of Chemical Engineering and Materials Science , Minnesota Supercomputing Institute UNIVERSITY OF MINNESOTA

  2. Outline • Objective: motivate a study of the performance of several DFT–based functionals • Why is silica under pressure important? archetypical problem for understanding coordination of silicon at high PTs in the Earth • Phase diagram of silica • My previous experience with DFT (LDA x GGA(PBE)) Equation of state parameters Thermodynamic phase boundaries

  3. quartz (~298 K) (~2,000 K) (~4,000 K) (~6,000 K) (~6,500 K) 1 atm ~ 1bar 1 GPa = 10 kbar 1 Mbar = 100 GPa

  4. Thickness of Earth’s crust (km) granite MORB Mid Ocean Ridge Basalt

  5. Silica is found on Earth surface as quartz in sand, in granite (continental crust), and basalt (oceanic crust). Sometimes other forms of silica, glass or stishovite, are found and that signals to meteorite impacts. Sahara desert sand California sand Fused silica also used in the production of window glass, drinking glass and bottles, bulbs, porcelain, cement, etc Technological applications include optical fibers, micro-electronics (SiO2 layer on silicon), etc

  6. Phase diagram of silica

  7. Phase diagram of silica amorphization

  8. PW91-GGA

  9. PBE-GGA

  10. PREM(Preliminary Reference Earth Model)(Dziewonski & Anderson, 1981) P(GPa) 0 13 23 135 329 360 0 410 660 2890 5150 6370 Depth (km)

  11. Mantle Mineralogy MgSiO3 Oxides (% weight) (Mg,Fe,Ca)SiO3 (Mg,Fe)SiO3 SiO245.0 MgO37.8 FeO 8.1 Al2O3 4.5 CaO3.6 Cr2O3 0.4 Na2O 0.4 NiO 0.2 TiO2 0.2 MnO 0.1 McDonough & Sun Chem. Geol. 120, 223-253 (1995) opx cpx Olivine- a phase ( (Mg1-x,Fex)2SiO4 ) Majorite Garnet (Mg,Al,Si)O3 b Phase(…) g Phase(…) CaSiO3 MW Perovskite (Mg1-x,Fex)O (Mg,Fe)SiO3 Bulk silicate Earth (“Pyrolite model”) after Ito & Takahashi (1987)

  12. Phase transitions in Mg2SiO4 MgSiO3 MgSiO3 MgSiO3 opx cpx forsterite- a phase (Mg2SiO4 ) Majorite Garnet (Mg,Al,Si)O3 b Phase(…) g Phase(…) CaSiO3 MW Perovskite MgO MgSiO3

  13. α-Mg2SiO4 410-km β-Mg2SiO4 410 660 γ-Mg2SiO4 520-km 520 + 660-km MgSiO3 MgO

  14. b c a Perovskite to Post-perovskite Transition P~125 GPa T~2500K Murakami at al, Science 2004 Tsuchiya et al, EPSL 2004 Ogonav and Ono, 2004

  15. Quasiharmonic Approximation (QHA) • VDoS and F(T,V) within the QHA N-th (N=3,4,5…) order isothermal (eulerian or logarithm) finite strain EoS IMPORTANT: crystal structure and phonon frequencies are uniquely related with volume !!….

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

  17. Equation of State Parameters Equation of State Parameters

  18. Zero Point Motion Effect Karki et al, PRB 2000 MgO ZP 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 LDA

  19. 300 K Mg2SiO4 Mg2SiO4 Mg2SiO4 MgSiO3 Wentzcovitch et al., Rev. Mineral. Geochem. 71, 59 (2010)

  20. Wentzcovitch et al., Rev. Mineral. Geochem. 71 (2010) MgSiO3 SiO2 MgSiO3 MgSiO3 MgSiO3 MgSiO3

  21. Thermodynamic Phase Boundaries Thermodynamic Phase Boundaries

  22. GI(T,P)= GII(T,P)↔phase boundary contributes to 520 km discontinuity 410 km discontinuity Mg2SiO4→ Mg2SiO4 Mg2SiO4→ Mg2SiO4 Yu, Wu, Wentzcovitch, EPSL 273, 115 (2008)

  23. (660 km discontinuity) Yu et al, GRL 34, L01306 (2007) Mg2SiO4→ MgO + MgSiO3

  24. LP-HP enstatite (MgSiO3) phase boundary Low pressure High pressure 3 MPa/K a β 5 GPa

  25. b c a Perovskite to Post-perovskite Transition P~125 GPa T~2500K Murakami at al, Science 2004 Tsuchiya et al, EPSL 224, 241 (2004) Ogonav and Ono, 2004

  26. LDA GGA 7.5 MPa/K Mantle adiabat Perovskite Post- perovskite ΔPT~10 GPa Valley bottom Hill top ~8 GPa ~250 km High-PT phase diagram Tsuchiya et al, 2004 (LDA & GGA) D” Tsuchiya, Tsuchiya, Umemoto, Wentzcovitch, EPSL 224, 241 (2004) 1000 K

  27. Clapeyron slopes (Wentzcovitch et al., Rev. Mineral. Geochem. 71, 59 (2010))

  28. LDA vs. PBE-GGA 410 km discontinuity Y. Yu et al. GRL 34, L10306 (2006)

  29. Summary Silica is an archetypical material that has been widely studied There is great urgency in determining phase boundaries accurately since it is very difficult to determine experimentally Which functional could give good structural properties and good atomization energies? Let’s try several functionals for silica

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