AI 中文总结
利用密度泛函理论计算系统研究了四种GeO2多晶型物在高达120 GPa下的弹性质，结合朗道理论揭示金红石型到CaCl2型转变的弹性软化机制，并发现转变附近弹性波各向异性显著增强。
AI 中文摘要
我们基于密度泛函理论的理论计算，系统研究了四种GeO2多晶型物——金红石型、CaCl2型、alpha-PbO2型和黄铁矿型——的相稳定性及弹性质对压力的依赖关系。在由静态焓计算确定的四个相的各自稳定范围内，以5 GPa的间隔计算了弹性常数。我们进一步采用经典的应变耦合朗道自由能展开来描述与金红石型到CaCl2型转变相关的弹性响应的压力演化，并阐明转变附近弹性软化的起源。金红石型到CaCl2型的相变与朗道型二级相变一致，基于应变分析得到的临界压力为14.6 GPa。随着转变压力的接近，金红石型相中发展出弹性软化，导致体积模量和剪切模量出现异常的压力依赖性。计算得到的弹性波各向异性在转变附近显著增加，主要归因于剪切波速度的快速降低，在22.5 GPa时达到约122%的最大值。转变后，CaCl2型相的各向异性急剧下降，并在CaCl2型/alpha-PbO2型相界处出现不连续性。较高压力的alpha-PbO2型和黄铁矿型相表现出相对较弱的各向异性压力依赖性，在其各自的相变边界处存在小的不连续性。黄铁矿型相具有最低的各向异性，在高压下仅达到约4-5%，这与其高对称性立方结构和近乎各向同性的弹性波传播一致。
英文摘要
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.
