论文标题
从头开始计算三阶弹性系数
Ab initio calculations of third-order elastic coefficients
论文作者
论文摘要
三阶弹性（脚趾）理论可预测应变诱导的二阶弹性系数变化（SOEC），并且可以在压力培养基中建模弹性波传播。尽管已经基于先前研究的第一原理确定了三阶弹性张量，但它们的当前定义是基于热力学能量在自然压力附近或零压力（零压力）参考状态的Lagrangian菌株方面的扩展。在重大初始应力下对SOEC的预测是不方便的。因此，当脚趾理论研究弹性的应变依赖性所必需时，地震界已诉诸于该理论的经验版本。 这项研究回顾了三阶弹性张量的热力学定义，并提出使用“有效”的三阶弹性张量。给出并验证有效的三阶弹性张量的显式表达。我们扩展了在有限压力下计算三阶弹性张量的AB启动方法，并将其应用于两个立方系统，即NACL和MGO。作为应用和验证，我们根据从头算的计算评估了（a）SOEC的应变诱导的SOEC变化和（b）SOEC的压力衍生物。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 is predictive of 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 the ab initio approach 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 on ab initio calculations. Good agreement between third-order elasticity-based predictions and numerically calculated values confirms the validity of our theory.
