Department of Chemistry, College of Staten Island, Staten Island, New York 10314, USA.
Advanced Science Research Center, City University of New York, 85 St. Nicholas Terrace, New York, New York 10031, USA.
Phys Rev Lett. 2018 Nov 23;121(21):216001. doi: 10.1103/PhysRevLett.121.216001.
A general method is presented to calculate from first principles the full set of third-order elastic constants of a material of arbitrary symmetry. The method here illustrated relies on a plane-wave density functional theory scheme to calculate the Cauchy stress and the numerical differentiation of the second Piola-Kirchhoff stress tensor to evaluate the elastic constants. It is shown that finite difference formulas lead to a cancellation of the finite basis set errors, whereas simple solutions are proposed to eliminate numerical errors arising from the use of Fourier interpolation techniques. Applications to diamond, silicon, aluminum, magnesium, graphene, and a graphane conformer give results in excellent agreement with both experiments and previous calculations based on fitting energy density curves, demonstrating both the accuracy and generality of our new methodology to investigate nonlinear elastic behaviors of materials.
本文提出了一种从第一性原理计算任意对称性材料的完整三阶弹性常数的通用方法。本文所阐述的方法依赖于平面波密度泛函理论方案来计算柯西应力和第二皮奥拉-基尔希霍夫应力张量的数值微分，以评估弹性常数。结果表明，有限差分公式导致有限基集误差的消除，而简单的解决方案则被提出以消除由于使用傅里叶插值技术而产生的数值误差。对金刚石、硅、铝、镁、石墨烯和一个石墨烷构象体的应用给出了与实验和基于拟合能量密度曲线的先前计算结果非常吻合的结果，证明了我们新的方法学在研究材料的非线性弹性行为方面的准确性和通用性。
