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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)
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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
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(~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
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Thickness of Earth’s crust (km)
MORB
granite
Mid OceanRidgeBasalt
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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
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Phase diagram of silica
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Phase diagram of silica
amorphization
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PW91-GGA
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PBE-GGA
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PREM (Preliminary Reference Earth Model)
(Dziewonski & Anderson, 1981)
P(GPa)0 13 23 135 329 360
0 410 660 2890 5150 6370
Depth (km)
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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)
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MgSiO3
forsterite- phase(Mg2SiO4 )
Phase(…)
Phase(…)
MgO
MW Perovskite
MgSiO3
cpx opx
MajoriteGarnet(Mg,Al,Si)O3
CaSiO3
MgSiO3 MgSiO3
Phase transitions in Mg2SiO4
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+
α-Mg2SiO4
β-Mg2SiO4
γ-Mg2SiO4
MgOMgSiO3
660-km
520-km410-km
410 660520
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b
ca
Perovskite to Post-perovskite Transition
P~125 GPa
T~2500K
Murakami at al, Science 2004Tsuchiya et al, EPSL 2004Ogonav and Ono, 2004
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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 !!….
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Phonon dispersions in MgO
Exp: Sangster et al. 1970
(Karki, Wentzcovitch, de Gironcoli and Baroni, PRB 61, 8793, 2000)
-
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Equation of State ParametersEquation of State Parameters
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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
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300 K
Mg2SiO4
Mg2SiO4
Mg2SiO4
MgSiO3
Wentzcovitch et al., Rev. Mineral. Geochem. 71, 59 (2010)
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MgSiO3
MgSiO3
MgSiO3
MgSiO3
MgSiO3
SiO2
Wentzcovitch et al., Rev. Mineral. Geochem. 71 (2010)
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Thermodynamic Phase BoundariesThermodynamic Phase Boundaries
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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
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Mg2SiO4→ MgO + MgSiO3
(660 km discontinuity)
Yu et al, GRL 34, L01306 (2007)
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LP-HP enstatite (MgSiO3) phase boundary
5 GPa
Low pressure
Highpressure
β a
3 MPa/K
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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
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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
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(Wentzcovitch et al., Rev. Mineral. Geochem. 71, 59 (2010))
Clapeyron slopes
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LDA vs. PBE-GGA
410 km discontinuityY. Yu et al. GRL 34, L10306 (2006)
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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