First-principles calculation of higher-order elastic constants from divided differences

IF 3.4 2区 物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Ruvini Attanayake , Umesh C. Roy , Abhiyan Pandit , Angelo Bongiorno
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引用次数: 0

Abstract

A method is presented to calculate from first principles the higher-order elastic constants of a solid material. The method relies on finite strain deformations, a density functional theory approach to calculate the Cauchy stress tensor, and a recursive numerical differentiation technique homologous to the divided differences polynomial interpolation algorithm. The method is applicable as is to any material, regardless its symmetry, to calculate elastic constants of, in principle, any order. Here, we introduce conceptual framework and technical details of our method, we discuss sources of errors, we assess convergence trends, and we present selected applications. In particular, our method is used to calculate elastic constants up to the 6th order of two crystalline materials with the cubic symmetry, silicon and gold. To demonstrate general applicability, our method is also used to calculate the elastic constants up to the 5th order of α-quartz, a crystalline material belonging to the trigonal crystal system, and the second- and third-order elastic constants of kevlar, a material with an anisotropic bonding network. Higher order elastic constants computed with our method are validated against density functional theory calculations by comparing stress responses to large deformations derived within the continuum approximation.
用分差法计算高阶弹性常数的第一性原理
提出了一种从第一性原理计算固体材料高阶弹性常数的方法。该方法基于有限应变变形,采用密度泛函理论计算柯西应力张量,并采用与差分多项式插值算法相对应的递推数值微分技术。该方法原则上适用于任何材料,不论其对称性如何,计算任何阶次的弹性常数。在这里,我们介绍了我们的方法的概念框架和技术细节,我们讨论了误差的来源,我们评估收敛趋势,我们提出了选择的应用。特别地,我们的方法被用于计算两种具有立方对称的晶体材料硅和金的六阶弹性常数。为了证明该方法的普遍适用性,我们还计算了属于三角晶体体系的α-石英晶体材料的5阶弹性常数,以及具有各向异性键合网络的凯夫拉尔材料的2阶和3阶弹性常数。用我们的方法计算的高阶弹性常数通过比较连续统近似下大变形的应力响应,与密度泛函理论计算进行了验证。
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来源期刊
Computer Physics Communications
Computer Physics Communications 物理-计算机:跨学科应用
CiteScore
12.10
自引率
3.20%
发文量
287
审稿时长
5.3 months
期刊介绍: The focus of CPC is on contemporary computational methods and techniques and their implementation, the effectiveness of which will normally be evidenced by the author(s) within the context of a substantive problem in physics. Within this setting CPC publishes two types of paper. Computer Programs in Physics (CPiP) These papers describe significant computer programs to be archived in the CPC Program Library which is held in the Mendeley Data repository. The submitted software must be covered by an approved open source licence. Papers and associated computer programs that address a problem of contemporary interest in physics that cannot be solved by current software are particularly encouraged. Computational Physics Papers (CP) These are research papers in, but are not limited to, the following themes across computational physics and related disciplines. mathematical and numerical methods and algorithms; computational models including those associated with the design, control and analysis of experiments; and algebraic computation. Each will normally include software implementation and performance details. The software implementation should, ideally, be available via GitHub, Zenodo or an institutional repository.In addition, research papers on the impact of advanced computer architecture and special purpose computers on computing in the physical sciences and software topics related to, and of importance in, the physical sciences may be considered.
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