renata m. wentzcovitch dept. of chemical engineering and materials science, minnesota supercomputing...

Renata M. Wentzcovitch

Dept. of Chemical Engineering and Materials Science ,Minnesota Supercomputing InstituteUNIVERSITY OF MINNESOTA

Phase transitions in silica (SiO2)Phase transitions in silica-(SiO2)

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

(~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

Thickness of Earth’s crust (km)

MORB

granite

Mid OceanRidgeBasalt

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 (SiO2 layer on silicon), etc

California sand Sahara desert sand

Phase diagram of silica

Phase diagram of silica

amorphization

PW91-GGA

PBE-GGA

PREM (Preliminary Reference Earth Model)

(Dziewonski & Anderson, 1981)

P(GPa)0 13 23 135 329 360

0 410 660 2890 5150 6370

Depth (km)

MgSiO3

Olivine- phase( (Mg1-x,Fex)2SiO4 )

Phase(…)

(Mg1-x,Fex)O

MW Perovskite

(Mg,Fe)SiO3

cpx opx

MajoriteGarnet(Mg,Al,Si)O3

CaSiO3

(Mg,Fe,Ca)SiO3 (Mg,Fe)SiO3

Bulk silicate Earth (“Pyrolite model”) after Ito & Takahashi (1987)

Mantle Mineralogy

Phase(…)

SiO2 45.0MgO 37.8FeO 8.1Al2O3 4.5CaO 3.6Cr2O3 0.4Na2O 0.4NiO 0.2TiO2 0.2MnO 0.1

McDonough & SunChem. Geol. 120, 223-253 (1995)

Oxides (% weight)

MgSiO3

forsterite- phase(Mg2SiO4 )

Phase(…)

Phase(…)

MgO

MW Perovskite

MgSiO3

cpx opx

MajoriteGarnet(Mg,Al,Si)O3

CaSiO3

MgSiO3 MgSiO3

Phase transitions in Mg2SiO4

+

α-Mg2SiO4

β-Mg2SiO4

γ-Mg2SiO4

MgOMgSiO3

660-km

520-km410-km

410 660520

b

ca

Perovskite to Post-perovskite Transition

P~125 GPa

T~2500K

Murakami at al, Science 2004Tsuchiya et al, EPSL 2004Ogonav and Ono, 2004

Quasiharmonic Approximation (QHA)

qj B

qjB

qj

qj

Tk

VTk

VVUTVF

)(exp1ln

2

)()(),(

• VDoS and F(T,V) within the QHA

PVTSFG TV

FP

VT

FS

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 !!….

Phonon dispersions in MgO

Exp: Sangster et al. 1970

(Karki, Wentzcovitch, de Gironcoli and Baroni, PRB 61, 8793, 2000)

-

Equation of State ParametersEquation of State Parameters

Zero Point Motion Effect

Volume (Å3)

F (

Ry)

MgO

Static 300K Exp (Fei 1999)V (Å3) 18.5 18.8 18.7K (GPa) 169 159 160K´ 4.18 4.30 4.15K´´(GPa-1) -0.025 -0.030

1ln 1

2

i

Bk Ti B

i i

F U k T e

ZP

LDA

Karki et al, PRB 2000

300 K

Mg2SiO4

Mg2SiO4

Mg2SiO4

MgSiO3

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

MgSiO3

MgSiO3

MgSiO3

MgSiO3

MgSiO3

SiO2

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

Thermodynamic Phase BoundariesThermodynamic Phase Boundaries

410 km discontinuity contributes to520 km discontinuity

Mg2SiO4→ Mg2SiO4 Mg2SiO4→ Mg2SiO4

Yu, Wu, Wentzcovitch, EPSL 273, 115 (2008)

GI(T,P)= GII(T,P) ↔ phase boundary

Mg2SiO4→ MgO + MgSiO3

(660 km discontinuity)

Yu et al, GRL 34, L01306 (2007)

LP-HP enstatite (MgSiO3) phase boundary

5 GPa

Low pressure

Highpressure

β a

3 MPa/K

b

ca

Perovskite to Post-perovskite Transition

P~125 GPa

T~2500K

Murakami at al, Science 2004Tsuchiya et al, EPSL 224, 241 (2004)Ogonav and Ono, 2004

High-PT phase diagram

70 80 90 100 110 120 130 140 1500

500

1000

1500

2000

2500

3000

3500

4000

4500

Pressure (GPa)

Tem

per

atu

re (

K)

Orthorhombic-Perovskite

Post-perovskite

CM

B

Mantle adiabat

ΔPT~10 GPa

Hill top Valley bottom~8 GPa

~250 km

7.5 MPa/K

LDA GGA

Perovskite Post-perovskite

1000 K

D”(LDA & GGA)

Tsuchiya, Tsuchiya, Umemoto, Wentzcovitch, EPSL 224, 241 (2004)

Tsuchiya et al, 2004

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

Clapeyron slopes

LDA vs. PBE-GGA

410 km discontinuityY. Yu et al. GRL 34, L10306 (2006)

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