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arXiv 2302.01965cond-mat.mtrl-sciphysics.comp-ph
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一种计算固体材料四阶弹性常数的第一性原理方法

A first-principles method to calculate fourth-order elastic constants of solid materials

Abhiyan Pandit, Angelo Bongiorno

AI总结:

本研究提出一种基于密度泛函理论的第一性原理方法,可计算立方、六方对称晶体的四阶以内弹性常数,经多种材料验证,结果与实验及现有计算结果吻合良好,还可用于预测零温压力区间内的体积和体积模量。

摘要:

本文提出了一种第一性原理方法,用于计算立方和六方对称晶体的最高至四阶的弹性常数。该方法依赖于第二Piola-Kirchhoff应力张量的数值微分,结合密度泛函理论方法,计算参考态的最少数量应变构型的柯西应力张量。计算二阶、三阶和四阶独立弹性常数所需的应变构型数量,立方对称晶体为24个,六方对称晶体为37个。本文将该方法应用于5种立方对称晶体材料(金刚石、硅、铝、银、金)和2种六方密堆积结构金属(铍、镁),并将所得结果与现有实验数据及此前的计算研究进行了对比。计算得到的线性和非线性弹性常数还被用于材料的非线性弹性处理中,以预测零温下一定压力区间内的体积和体积模量值。为进一步验证该方法,我们将这些预测结果与显式密度泛函理论计算得到的结果进行了对比。

英文摘要:

A first-principles method is presented to calculate elastic constants up to the fourth order of crystals with the cubic and hexagonal symmetries. The method relies on the numerical differentiation of the second Piola-Kirchhoff stress tensor and a density functional theory approach to compute the Cauchy stress tensors for a minimal list of strained configurations of a reference state. The number of strained configurations required to calculate the independent elastic constants of the second, third, and fourth order is 24 and 37 for crystals with the cubic and hexagonal symmetries, respectively. Here, this method is applied to five crystalline materials with the cubic symmetry (diamond, silicon, aluminum, silver, and gold) and two metals with the hexagonal close packing structure (beryllium and magnesium). Our results are compared to available experimental data and previous computational studies. Calculated linear and nonlinear elastic constants are also used, within a nonlinear elasticity treatment of a material, to predict values of volume and bulk modulus at zero temperature over an interval of pressures. To further validate our method, these predictions are compared to results obtained from explicit density functional theory calculations.

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