1. Renata M. Wentzcovitch Dept. of Chemical Engineering and Materials Science, Minnesota Supercomputing Institute UNIVERSITY OF MINNESOTA Phase transitions in silica (SiO 2 ) Phase transitions in silica-(SiO 2 )

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

4. Thickness of Earth’s crust (km) MORB granite 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. 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 (SiO 2 layer on silicon), etc California sand Sahara desert sand

6. Phase diagram of silica

7. amorphization

8. PW91-GGA

10. PBE-GGA

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

12. MgSiO 3 Olivine-  phase ( (Mg 1-x,Fe x ) 2 SiO 4 )  Phase  (…) (Mg 1-x,Fe x )O MWPerovskite (Mg,Fe)SiO 3 cpx opx Majorite Garnet (Mg,Al,Si)O 3 CaSiO 3 (Mg,Fe,Ca)SiO 3 (Mg,Fe)SiO 3 Bulk silicate Earth (“Pyrolite model”) after Ito & Takahashi (1987) Mantle Mineralogy  Phase  (…) SiO 2 45.0 MgO 37.8 FeO 8.1 Al 2 O 3 4.5 CaO 3.6 Cr 2 O 3 0.4 Na 2 O 0.4 NiO 0.2 TiO 2 0.2 MnO 0.1 McDonough & Sun Chem. Geol. 120, 223- 253 (1995) Oxides (% weight)

13. MgSiO 3 forsterite-  phase (Mg 2 SiO 4 )  Phase  (…)  Phase  (…) MgO MWPerovskite MgSiO 3 cpx opx Majorite Garnet (Mg,Al,Si)O 3 CaSiO 3 MgSiO 3 Phase transitions in Mg 2 SiO 4

14. + α-Mg 2 SiO 4 β-Mg 2 SiO 4 γ-Mg 2 SiO 4 MgO MgSiO 3 660-km 520-km 410-km 410660 520

15. 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

16. 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 !!….

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

18. Equation of State Parameters

19. 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 ZP LDA Karki et al, PRB 2000

20. 300 K Mg 2 SiO 4 MgSiO 3 Wentzcovitch et al., Rev. Mineral. Geochem. 71, 59 (2010)

21. MgSiO 3 SiO 2 Wentzcovitch et al., Rev. Mineral. Geochem. 71 (2010)

22. Thermodynamic Phase Boundaries

23. 410 km discontinuity contributes to 520 km discontinuity Mg 2 SiO 4 → Mg 2 SiO 4 Yu, Wu, Wentzcovitch, EPSL 273, 115 (2008) G I (T,P)= G II (T,P) ↔ phase boundary

24. Mg 2 SiO 4 → MgO + MgSiO 3 (660 km discontinuity) Yu et al, GRL 34, L01306 (2007)

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

26. 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

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

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

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

30. 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