Equation of state of MgGeO₃ perovskite to 65 GPa: Comparison with the post-perovskite phase

The equation of state of MgGeO₃ perovskite was determined between 25 and 66 GPa using synchrotron X-ray diffraction with the laser-heated diamond anvil cell. The data were fit to a third-order Birch-Murnaghan equation of state and yielded a zero-pressure volume (V₀) of 182.2 ± 0.3 ų and bulk modulus (K₀) of 229 ± 3 GPa, with the pressure derivative (K′₀ = ∂K₀/ ∂)_T) fixed at 3.7. Differential stresses were evaluated using lattice strain theory and found to be typically less than about 1.5 GPa. Theoretical calculations were also carried out using density functional theory from 0 to 205 GPa. The equation of state parameters from theory (V₀ = 180.2 ų, K₀ = 221.3 GPa, and K′₀ = 3.90) are in agreement with experiment, although theoretically calculated volumes are systematically lower than experiment. The properties of the perovskite phase were compared to MgGeO₃ post-perovskite phase near the observed phase transition pressure (∼65 GPa). Across the transition, the density increased by 2.0(0.7)%. This is in excellent agreement with the theoretically determined density change of 1.9%; however both values are larger than those for the (Mg,Fe)SiO₃ phase transition. The bulk sound velocity change across the transition is small and is likely to be negative [-0.5(1.6)% from experiment and -1.2% from theory]. These results are similar to previous findings for the (Mg,Fe)SiO₃ system. A linearized Birch-Murnaghan equation of state fit to each axis yielded zero-pressure compressibilities of 0.0022, 0.0009, and 0.0016 GPa^-1 for the a, b, and c axis, respectively. Magnesium germanate appears to be a good analog system for studying the properties of the perovskite and post-perovskite phases in silicates.