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

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)

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)

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)

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

Crystal structure of post-perovskite b c a Pt Lattice system: Bace-centered orthorhombic Space group: Cmcm Formula unit [Z]: 4 (4) Lattice parameters [Å] a: 2.462 (4.286) [120 GPa] b: 8.053 (4.575) c: 6.108 (6.286) Volume [120 GPa] [Å3]: 121.1 (123.3) ( )…perovskite

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

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

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

Thermodynamic properties ( )…Pv Bulk modulus [GPa] [300 K, 0 GPa] B0 222 (248)   dB/dP 4.2 (3.9) Ambient volume [cm3/mol] V0 24.662 (24.704) Grüneisen parameter γ0 1.6 (1.5) (∂lnγ/∂lnV)T -0.25+2.13(V/V0) (-0.32+0.86(V/V0)) Debye temperature [K] Θ0 1100 (1114)

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

Elasticity of MgSiO3 Post-perovskite

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

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

Elastic Constants a c c b b a b a c a

Aggregate Elastic Moduli Bppv ≈ Bpv Gppv > Gpv

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

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

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

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%

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