Abstract In this work, after formulating the weakly nonlocal micromorphic equations of motion for non-Bravais crystals with general anisotropy, specialization to diamond structures is made. A critical dilemma is the determination of the elastic moduli tensor appearing in the equations of motion. From the equivalency of these equations with the pertinent equations obtained in the context of lattice dynamics, the expressions of the components of the elastic moduli tensors in terms of the atomic force constants are derived analytically. Subsequently, the atomic force constants are calculated via ab initio density functional perturbation theory (DFPT) with high precision. As a benchmark for the accuracy and potency of the proposed theory, it is shown that the theory can capture not only all the acoustic branches but also all the optical branches of the dispersion curves for non-Bravais crystals like diamond and silicon over the entire first Brillouin zone. The accuracy of the results depends on the implemented order of the approximation of weakly nonlocal micromorphic theory. For illustration, the zeroth, tenth, and twentieth order approximations are employed to probe the dispersion curves pertinent to the crystallographic directions [100], [110], and [111] for diamond and silicon. For verification, the results are compared to those obtained independently from ab initio DFPT calculations.

中文翻译：

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金刚石结构相对于晶格动力学的弱非局部微晶弹性

摘要 在这项工作中，在制定了具有一般各向异性的非布拉维晶体的弱非局部微晶运动方程后，专门研究了金刚石结构。一个关键的难题是确定出现在运动方程中的弹性模量张量。从这些方程与在晶格动力学上下文中获得的相关方程的等价性，可以解析地推导出弹性模量张量分量在原子力常数方面的表达式。随后，通过从头算密度泛函微扰理论 (DFPT) 高精度计算原子力常数。作为所提出理论的准确性和效力的基准，结果表明，该理论不仅可以捕获所有声学分支，还可以捕获整个第一布里渊区上非布拉维晶体（如金刚石和硅）的色散曲线的所有光学分支。结果的准确性取决于弱非局部微晶理论逼近的实现顺序。为了说明，使用零阶、十阶和二十阶近似值来探测与金刚石和硅的结晶方向 [100]、[110] 和 [111] 相关的色散曲线。为了验证，将结果与从 ab initio DFPT 计算中独立获得的结果进行比较。结果的准确性取决于弱非局部微晶理论逼近的实现顺序。为了说明，使用零阶、十阶和二十阶近似值来探测与金刚石和硅的结晶方向 [100]、[110] 和 [111] 相关的色散曲线。为了验证，将结果与从 ab initio DFPT 计算中独立获得的结果进行比较。结果的准确性取决于弱非局部微晶理论逼近的实现顺序。为了说明，使用零阶、十阶和二十阶近似值来探测与金刚石和硅的结晶方向 [100]、[110] 和 [111] 相关的色散曲线。为了验证，将结果与从 ab initio DFPT 计算中独立获得的结果进行比较。