1. Post-perovskite Transition in MgSiO3
Taku Tsuchiya, Jun Tsuchiya, Koichiro Umemoto,
and Renata M. Wentzcovitch
Dept. of Chemical Engineering and Materials Science ,
Minnesota Supercomputing Institute
UNIVERSITY OF MINNESOTA

2. MgSiO3 Perovskite
----- Most abundant constituent in the Earth’s lower mantle
----- Orthorhombic distorted perovskite structure (Pbnm, Z=4)
----- Its stability is important for understanding deep mantle (D” layer)

3. UNKNOWN PHASE Pbnm Perovskite
Drastic change in X-ray diffraction pattern around 125 GPa and 2500 K
UNKNOWN PHASE
Pbnm Perovskite
(M. Murakami and K. Hirose, private communication)

4. Method --- Density Functional Theory (Hohenberg and Kohn, 1964)
--- Local Density Approximation
(Ceperley and Alder, 1985)
--- Plane wave basis – pseudopotential
(Troullier and Martins, 1991)
--- Variable Cell Shape Molecular Dynamics
for structural search (Wentzcovitch, 1991)

5. Ab initio exploration of post-perovskite phase in MgSiO3
- Reasonable polyhedra type and connectivity under ultra high pressure -
SiO4 chain
SiO3 layer
Perovskite
SiO3 Mg
MgSiO3

6. Crystal structure of post-perovskiteb c a Pt
Lattice system: Bace-centered orthorhombic
Space group: Cmcm
Formula unit [Z]: 4 (4)
Lattice parameters [Å] a: (4.286)
[120 GPa] b: (4.575)
c: (6.286)
Volume [120 GPa] [Å3]: (123.3) ( )…perovskite

7. A structure has lower energy than Pbnm perovskite under high pressure!
Pt = 98 GPa

8. Deformation of perovskite under shear strain ε6
Structural relation between Pv and Post-pv θ
Post-perovskite c’ a’ b’
Si-O bonds break
Share-edges form
Perovskite a b c
Deformation of perovskite under shear strain ε6

9. Thermodynamics with QHA
--- VDoS and F(T,V)
--- Other thermodynamics quantities
--- Density Functional Perturbation Theory for calculating phonon frequencies
(Gianozzi et al., 1991)

10. Thermodynamic properties
( )…Pv
Bulk modulus [GPa]
[300 K, 0 GPa] B0
222 (248)
dB/dP
4.2 (3.9)
Ambient volume [cm3/mol] V0
(24.704)
Grüneisen parameter γ0
1.6 (1.5)
(∂lnγ/∂lnV)T
(V/V0)
( (V/V0))
Debye temperature [K] Θ0
1100 (1114)

11. High-PT phase diagram 7.5 MPa/K Core-mantle boundary D” layer Hill top
Mantle adiabat
error ~5 GPa
Core-mantle boundary
Hill top
Valley bottom
~8 GPa
~250 km
7.5 MPa/K
D” layer

12. Elasticity of MgSiO3 Post-perovskite

13. Post-perovskite : layered structure large compressibility along b axis
Large elastic anisotropy b c Si
Large anisotropy as well as large heterogeneity have been observed in D” region Mg a

14. Thermoelastic constant tensor CijS(T,P)
kl
equilibrium
structure
re-optimize

15. Elastic Constants a c c b b a b a c a

16. Aggregate Elastic Moduli
Bppv ≈ Bpv
Gppv > Gpv

17. Tsuchiya, Tsuchiya, Umemoto,
Single crystal azimuthal anisotropy
P-azimuthal:
S-azimuthal:
Wentzcovitch et al. (1998)
Tsuchiya, Tsuchiya, Umemoto,
Wentzcovitch, GRL (2004)

18. Shear wave splitting in transversely isotropic aggregates
[100]
[010]
[001]
Vertical direction//
The degree of polarization anisotropy of shear waves for three crystallographic direction can be determined
It is important from the point view of seismology to estimate the anisotropy of a transversely isotropic aggregate of minerals.
This figure shows polarization anisotropy as a function of pressure for a transversely isotropic composite of post-perovskite with the a, b, and c axis as a symmetric axis.
Post-pv shows very strong polarization anisotropy than pv.
Lattice preferred orientation of post-PV polycrystals can produce seismically detectable anisotropy in the bottom of lower mantle.
Vsh
Vsv
Horizontal plane

19. Seismic velocities <
Longitudinal
Shear
Bulk
Post-pv transition should produce larger anomaly in VS than in VP

20. Summary -10% < AST < 15%
Post-pv phase has almost the same B as pv but larger G
Across the transition at 125 GPa (2750 K)
Δρ ~ 1.5% ΔVS ~ 1.5% > ΔVP ~ 1% ΔVΦ ~ -0.7%
Post-pv has larger dV/dT’s
Lateral ΔT → ΔVppv> ΔVpv
Post-pv is very anisotropic at D” conditions
Perfect transversely isotropic aggregates
-10% < AST < 15%

21. Acknowledgements
Thanks to Murakami and Hirose for early communication of their X-ray diffraction
NSF COMPRES, NSF/EAR