Ab initio calculations of third-order elastic coefficients
Ab initio calculations of third-order elastic coefficients
复制标题
三阶弹性系数的从头算
DOI：
10.1103/physrevb.106.214104
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发表时间：
2022
影响因子：
3.7
通讯作者：
Wentzcovitch, Renata M.
中科院分区：
文献类型：
--
作者：
Luo, Chenxing;Tromp, Jeroen;Wentzcovitch, Renata M.
三阶弹性 (TOE) 理论可预测应变引起的二阶弹性系数 (SOEC) 变化，并可以模拟弹性波在应力介质中的传播。尽管三阶弹性张量是根据先前研究中的第一原理确定的，但它们当前的定义是基于热力学能量的扩展，以接近自然或零压力参考状态的拉格朗日应变表示。该定义不便于预测显着初始应力下的 SOEC。因此，当需要使用 TOE 理论来研究弹性的应变依赖性时，地震学界就求助于该理论的经验版本。本研究回顾了三阶弹性张量的热力学定义，并提出使用“有效”三阶弹性张量。给出并验证了有效三阶弹性张量的显式表达式。我们扩展了从头计算方法来计算有限压力下的三阶弹性张量，并将其应用于两个立方系统，即 NaCl 和 MgO。作为应用和验证，我们评估 (a) SOEC 中应变引起的变化和 (b) 基于初始计算的 SOEC 压力导数。基于三阶弹性的预测与数值计算值之间的良好一致性证实了我们理论的有效性。
Third-order elasticity (TOE) theory predicts strain-induced changes in second-order elastic coefficients (SOECs) and can model elastic wave propagation in stressed media. Although third-order elastic tensors have been determined based on first principles in previous studies, their current definition is based on an expansion of thermodynamic energy in terms of the Lagrangian strain near the natural, or zero pressure, reference state. This definition is inconvenient for predictions of SOECs under significant initial stresses. Therefore, when TOE theory is necessary to study the strain dependence of elasticity, the seismological community has resorted to an empirical version of the theory. This study reviews the thermodynamic definition of the third-order elastic tensor and proposes using an “effective” third-order elastic tensor. An explicit expression for the effective third-order elastic tensor is given and verified. We extend theab initioapproach to calculate third-order elastic tensors under finite pressure and apply it to two cubic systems, namely, NaCl and MgO. As applications and validations, we evaluate (a) strain-induced changes in SOECs and (b) pressure derivatives of SOECs based onab initiocalculations. Good agreement between third-order elasticity-based predictions and numerically calculated values confirms the validity of our theory.