We present a systematic ab initio study of the temperature- and pressure-dependent thermoelastic properties of hcp beryllium within the quasiharmonic approximation (QHA). The accuracies of the zero static internal stress approximation (ZSISA) and of the volume-constrained ZSISA that are widely applied in ab initio thermodynamic calculations are quantified. Particularly, the effect of ZSISA on the calculation of $C_{11}$ and $C_{12}$ is compared with a numerical approach which minimizes the free energy with respect to the atomic positions at each strain. In beryllium, minor deviations are found within ZSISA, which gives elastic constants (ECs) in good agreement with the full free energy minimization. A substantial difference is found between the QHA and the quasistatic approximation (QSA), with the former closer to experiments. Within the QSA, we compare the ECs obtained by interpolating from a set of geometries along the “stress-pressure” isotherm at 0 K (within the constant-volume ZSISA) with a more general interpolation on a two-dimensional grid of crystal parameters, which allows the calculation of the ECs along the 0 kbar isobar. This paper provides a practical approach for the investigation of the thermoelastic properties of hcp metals at extreme conditions.

中文翻译：

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从头算准谐波自由能计算得出的 hcp 金属的高温高压热弹性：铍的情况


我们在准调和近似 (QHA) 内对 hcp 铍的温度和压力依赖性热弹性特性进行了系统的从头开始研究。对广泛应用于从头热力学计算中的零静态内应力近似 (ZSISA) 和体积约束 ZSISA 的精度进行了量化。特别是，ZSISA 对计算的影响 $C_{11}$ 和 $C_{12}$ 与数值方法进行比较，该方法最小化每个应变下原子位置的自由能。在铍中，ZSISA 中存在微小偏差，其给出的弹性常数 (EC) 与完全自由能最小化非常一致。 QHA 和准静态近似 (QSA) 之间存在显着差异，前者更接近实验。在 QSA 中，我们将通过沿着 0 K​​（在恒定体积 ZSISA 内）的“应力-压力”等温线从一组几何形状插值获得的 EC 与晶体参数二维网格上更一般的插值进行比较，它允许计算沿 0 kbar 等压线的 EC。本文为研究极端条件下 hcp 金属的热弹性性能提供了一种实用的方法。