Phase transitions in silica
(SiO22)
silica-(SiO
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
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
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
Thickness of Earth’s crust (km)
granite
MORB
Mid
Ocean
Ridge
Basalt
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.
California sand
Sahara desert 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
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)
Mantle Mineralogy
MgSiO3
Oxides (% weight)
SiO2
MgO
FeO
Al2O3
CaO
Cr2O3
Na2O
NiO
TiO2
MnO
45.0
37.8
8.1
4.5
3.6
0.4
0.4
0.2
0.2
0.1
McDonough & Sun
Chem. Geol. 120, 223253 (1995)
(Mg,Fe,Ca)SiO3 (Mg,Fe)SiO3
cpx
opx
Olivine- a phase
( (Mg1-x,Fex)2SiO4 )
b Phase (…)
g Phase (…)
MW
(Mg1-x,Fex)O
Majorite
Garnet
(Mg,Al,Si)O3
CaSiO3
Perovskite
(Mg,Fe)SiO3
Bulk silicate Earth (“Pyrolite model”)
after Ito & Takahashi (1987)
Phase transitions in Mg2SiOMgSiO
4
MgSiO3
cpx
MgSiO3
opx
forsterite- a phase
(Mg2SiO4 )
b Phase (…)
g Phase (…)
MW
MgO
Majorite
Garnet
(Mg,Al,Si)O3
CaSiO3
Perovskite
MgSiO3
3
α-Mg2SiO4
+
MgSiO3
660-km
MgO
520-km
γ-Mg2SiO4
410 660
520
410-km
β-Mg2SiO4
Perovskite to Post-perovskite Transition
P~125 GPa
T~2500K
b
c
a
Murakami at al, Science 2004
Tsuchiya et al, EPSL 2004
Ogonav and Ono, 2004
Quasiharmonic Approximation (QHA)
• VDoS and F(T,V) within the QHA
F (V , T )  U (V ) 

qj
  qj (V )
2
 k BT 
qj

   qj (V )  


ln 1  exp  


k B T  


N-th (N=3,4,5…) order isothermal (eulerian or logarithm) finite strain EoS
P  
 F 
 V 

T
S  
 F 
 T 

V
G  F  TS  PV
IMPORTANT: crystal structure and phonon frequencies
are uniquely related with volume !!….
Phonon dispersions in MgO
-
(Karki, Wentzcovitch, de Gironcoli and Baroni, PRB 61, 8793, 2000)
Exp: Sangster et al. 1970
Equation of State Parameters
Zero Point Motion Effect
Karki et al, PRB 2000
MgO
F (Ry)
ZP
F U 
1
2
 i  k BT 
i
i
Volume (Å3)
V (Å3)
K (GPa)
K´
K´´(GPa-1)
Static 300K
18.5 18.8
169
159
4.18 4.30
-0.025 -0.030
Exp (Fei 1999)
18.7
160
4.15
LDA
i


k T
ln  1  e B






300 K
Mg2SiO4
Mg2SiO4
Mg2SiO4
MgSiO3
Wentzcovitch et al., Rev. Mineral. Geochem. 71, 59 (2010)
Wentzcovitch et al., Rev. Mineral. Geochem. 71 (2010)
MgSiO3
SiO2
MgSiO3
MgSiO3
MgSiO3
MgSiO3
Thermodynamic Phase Boundaries
GI(T,P)= GII(T,P) ↔ phase boundary
410 km discontinuity
contributes to
520 km discontinuity
Mg2SiO4→ Mg2SiO4
Mg2SiO4→ Mg2SiO4
Yu, Wu, Wentzcovitch, EPSL 273, 115 (2008)
(660 km discontinuity)
Yu et al, GRL 34, L01306 (2007)
Mg2SiO4→ MgO + MgSiO3
LP-HP enstatite (MgSiO3) phase boundary
Low
pressure
High
pressure
3 MPa/K
5 GPa
β
a
Perovskite to Post-perovskite Transition
P~125 GPa
T~2500K
b
c
a
Murakami at al, Science 2004
Tsuchiya et al, EPSL 224, 241 (2004)
Ogonav and Ono, 2004
High-PT phase diagram
Tsuchiya et al, 2004
LDA GGA
D”
(LDA & GGA)
CM B
4500
4000
Tsuchiya, Tsuchiya, Umemoto,
Wentzcovitch, EPSL 224, 241 (2004)
T em p eratu re (K )
3500
1000 K
7.5 MPa/K
3000
2500
2000
1500
1000
500
0
70
OrthorhombicPerovskite
Postperovskite
Perovskite
Postperovskite
ΔPT~10 GPa
80
90
100
110
120
130
140
150
Pressure (GPa)
Hill top
Valley
~8 GPa bottom
~250 km
Clapeyron slopes
(Wentzcovitch et al., Rev. Mineral. Geochem. 71, 59 (2010))
LDA vs. PBE-GGA
410 km discontinuity
Y. 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