Supplemental information for
High-pressure, high-temperature deformation of CaGeO3 (perovskite)±MgO aggregates:
implications for multi-phase rheology of the lower mantle
Yanbin Wang1, Nadege Hilairet1, †, Norimasa Nishiyama1,*, Naoya Yahata2, Taku Tsuchiya2,
Guillaume Morard3, and Guillaume Fiquet3
1
Center for Advanced Radiation Sources, The University of Chicago, 5640 S. Ellis Ave.,
Chicago, IL, 60637
2
Geodynamics Research Center, Ehime University, Japan
3
Institut de Minéralogie et de Physique des Milieux Condensés, Institut de Physique du Globe de
Paris, France
† Now at: UMET - Université Lille 1, France
*
Now at: PETRA-III, DESY, Hamburg, Germany
1. First-principles calculations on elastic constants for GePv
We used first-principles calculations based on the density function theory (DFT), within the
local density approximation (Perdew and Zunger 1981), to calculate elastic constants for GePv.
Fundamental techniques of the first principles calculations are the same as those in (Tsuchiya,
Tsuchiya et al. 2004; Tsuchiya, Tsuchiya et al. 2004). Ionic core potentials of Ca, Ge, and O
modeled based on the ultrasoft scheme (Vanderbilt 1990) were already well tested ((Tsuchiya
and Tsuchiya 2007; Tsuchiya and Tsuchiya 2007); (Usui, Tsuchiya et al. 2010); (Tsuchiya
2011)). We applied a kinetic energy cutoff of 50 Ry and k-point sampling (Monkhorst and Pack,
1976) on the 4×4×2 mesh of the irreducible edge of the Brillouin zone. These computational
conditions yielded sufficient convergences for total energy less than 1 mRy/atom and for stress
less than 0.02 GPa. To determine elastic constants, the stress-strain relation was applied with
sufficiently small strains of ±0.01 ensuring linear elasticity ((Tsuchiya, Tsuchiya et al. 2004)).
Table S1 lists computed elastic constants (Cij) for GePv at various pressures in orthorhombic
setting. Compliances (Sij) with their pressure derivatives are given in Table 2.
2. Shear-wave anisotropy based on SPO development
In this section we calculate potential SPO-induced seismic anisotropy in the lower mantle.
Here we consider a case where simple shear has produced an IWL-like fabric in the SiPv+Fp
mineral assemblage. We further assume that the fabric can be represented by a weak,
transversely anisotropic composite, in other words, the Fp “films” are sub-parallel to each other,
lying in the shear plane. Using the thermoelastic parameters of SiPv and Fp given in Table S2,
we calculate elastic properties of the two minerals at a depth of ~1,250 km (50 GPa, 2500 K).
The composite fabric is treated by the Thomsen model (Thomsen 1986). Seismic anisotropy is
then calculated based on the procedure described by ((Brittan and Warner 1995). The resultant
Thomsen parameters are plotted in Fig. S1 for various Fp contents and P- and S-wave anisotropy
for a lower mantle with 10 to30 vol% Fp is displayed in Fig. 11.
For the range of volume fraction of Fp examined, the ratio of VSV/VSH varies ~1.04 (Fp=10
vol%) to ~1.1 (Fp = 30 vol%) at the propagation angle of 90°, suggesting that effects of fabric on
lower mantle anisotropy may be significant.
References cited in Supplemental Information
Brittan, J. and M. P. Warner, G. (1995). "Anisotropic parameters of layered media in terms of composite
elastic properties." Geophysics 60: 1243-1248.
Cordier, P., T. Ungar, et al. (2004). "Dislocation creep in MgSiO3 perovskite at conditions of the Earth's
uppermost lower mantle." Nature 428(6985): 837-840.
Kung, J., B. Li, et al. (2002). "Elasticity of (Mg0.83,Fe0.17)O ferropericlase at high pressure: ultrasonic
measurements in conjunction with X-radiation techniques." Earth and Planetary Science Letters
203(1): 557-566.
Li, B. and J. Zhang (2005). "Pressure and temperature dependence of elastic wave velocity of MgSiO3
perovskite and the composition of the lower mantle." Physics of The Earth and Planetary Interiors
151(1-2): 143-154.
Perdew, J. P. and A. Zunger (1981). "Self-interaction correction to density-functional approximations for
many-electron systems." Physical Review B 23(10): 5048-5079.
Sasaki, S., C. T. Prewitt, et al. (1983). "The crystal structure of CaGeO3 perovskite and the crystal
chemistry of GdFeO30-type perovskites." The American Mineralogist 68: 1189-1198.
Thomsen, L. (1986). "Weak elastic anisotropy." Geophysics 51: 1954-1966.
Tsuchiya, T. (2011). "Elasticity of subducted basaltic crust at the lower mantle pressures: Insights on the
nature of deep mantle heterogeneity." Physics of The Earth and Planetary Interiors 188: 142-149.
Tsuchiya, T. and J. Tsuchiya (2007). "High-pressure–high-temperature phase relations of MgGeO_{3}:
First-principles calculations." Physical Review B 76(9): 092105.
Tsuchiya, T. and J. Tsuchiya (2007). "Structure and elasticity of Cmcm CaIrO_{3} and their pressure
dependences: Ab initio calculations." Physical Review B 76(14): 144119.
Tsuchiya, T., J. Tsuchiya, et al. (2004). "Elasticity o fpost-perovskite MgSiO3." Geophys. Res. Lett. 31:
L14603(4).
Tsuchiya, T., J. Tsuchiya, et al. (2004). "Phase transition in MgSiO3 perovskite in the earth's lower
mantle." Earth and Planetary Science Letters 224(3-4): 241-248.
Usui, Y., J. Tsuchiya, et al. (2010). "Elastic, vibrational, and thermodynamic properties of MgGeO3
postperovskite investigated by first principles simulation." J. Geophys. Res. 115(B3): B03201.
Vanderbilt, D. (1990). "Soft self-consistent pseudopotentials in a generalized eigenvalue formalism."
Physical Review B 41(11): 7892-7895.
Wang, Y., F. Guyot, et al. (1990). "Twinning in MgSiO3 perovskite." Science 248: 468-471.
Wang, Z. C., C. Dupas-Bruzek, et al. (1999). "High temperature creep of an orthorhombic perovskite-YAlO3." Physics of The Earth and Planetary Interiors 110(1-2): 51-69.
Figure Caption:
Figure S1. Thomsen parameters , and  (Thomsen 1986) as a function of volume fraction of Fp in
the SiPv+Fp assemblage. Here we assume that the Fp grains are preferentially aligned in the shear
plane, due to large shear strains due to convection currents in the lower mantle. We further assume
that the fabric can be approximated as weakly transversely isotropic.