标题： 关于有限温度下的柯西-玻恩近似 显示英文标题

标题： On the Cauchy-Born Approximation at Finite Temperature

摘要： 我们讨论了有限温度下柯西-伯恩近似应力推导和实现中的几个问题。 特别是，采用渐近展开来推导第一皮奥拉-基尔霍夫应力的闭合形式表达式。 对于处于周期性边界条件下的系统，给出了一个推导过程，该过程考虑了平移不变性并阐明了零声子模的去除。 此外，渐近方法还揭示了原子间势的光滑性的作用。 提供了几个数值例子来验证此方法。 显示英文摘要

摘要： We address several issues regarding the derivation and implementation of the Cauchy-Born approximation of the stress at finite temperature. In particular, an asymptotic expansion is employed to derive a closed form expression for the first Piola-Kirchhoff stress. For systems under periodic boundary conditions, a derivation is presented, which takes into account the translational invariance and clarifies the removal of the zero phonon modes. Also revealed by the asymptotic approach is the role of the smoothness of the interatomic potential. Several numerical examples are provided to validate this approach.