High-pressure elastic properties of GeO2 polymorphs up to 120 GPa
We systematically investigated the phase stability and pressure dependence of the elastic properties of four GeO2 polymorphs: rutile-, CaCl2-, alpha-PbO2-, and pyrite-type phases using theoretical calculations based on density functional theory. The elastic constants were calculated at 5 GPa intervals within the respective stability ranges of the four phases, as determined from static enthalpy calculations. We further employed a classical strain-coupled Landau free-energy expansion to describe the pressure evolution of the elastic response associated with the rutile- to CaCl2-type transition and to elucidate the origin of the elastic softening near the transition. The rutile- to CaCl2-type phase transition is consistent with a Landau-type second-order transition, with a critical pressure of 14.6 GPa obtained from the strain-based analysis. As the transition pressure approaches, elastic softening develops in the rutile-type phase, resulting in anomalous pressure dependence of the bulk and shear modulus. The calculated elastic-wave anisotropy increases markedly near the transition, primarily due to the rapid reduction in shear-wave velocity, reaching a maximum of approximately 122% at 22.5 GPa. Following the transition, the anisotropy decreases sharply in the CaCl2-type phase and exhibits a discontinuity at the CaCl2-type/alpha-PbO2 -type phase boundary. The higher-pressure alpha-PbO2- and pyrite-type phases exhibit comparatively weak pressure dependence of anisotropy, with a small discontinuity at their respective phase transition boundaries. The pyrite-type phase has the lowest anisotropy, reaching only approximately 4-5% at high pressure, consistent with the high-symmetry cubic structure and nearly isotropic elastic-wave propagation.