The properties of crystals consisting of several components can be widely tuned. Often solid solutions are produced, where substitutional or interstitional disorder determines the crystal thermodynamic and mechanical properties. The chemical and structural disorder impedes the study of the elasticity of such solid solutions, since standard procedures like potential expansions cannot be applied. We present a generalization of a density functional–based approach recently developed for one-component crystals to multi-component crystals. It yields expressions for the elastic constants valid in solid solutions with arbitrary amounts of point defects and up to the melting temperature. Further, both acoustic and optical phonon eigenfrequencies can be computed in linear response from the equilibrium particle densities and established classical density functionals. As a proof of principle, dispersion relations are computed for two different binary crystals: A random fcc crystal as an example for a substitutional, and a disordered sodium chloride structure as an example of an interstitial solid solution. In cases where one of the components couples only weakly to the others, the dispersion relations develop characteristic signatures. The acoustic branches become flat in much of the first Brillouin zone, and a crossover between acoustic and optic branches takes place at a wavelength which can far exceed the lattice spacing.

中文翻译：

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无序二元晶体的弹性

由多种成分组成的晶体的特性可以广泛调整。通常会产生固溶体，其中置换或间隙无序决定了晶体的热力学和机械性能。化学和结构无序阻碍了对此类固溶体弹性的研究，因为无法应用标准程序，如潜在的膨胀。我们介绍了最近为单组分晶体开发的基于密度泛函的方法到多组分晶体的推广。它产生了在具有任意数量点缺陷和高达熔化温度的固溶体中有效的弹性常数表达式。更多，声学和光学声子本征频率都可以从平衡粒子密度和已建立的经典密度泛函的线性响应中计算出来。作为原理证明，计算了两种不同二元晶体的色散关系：随机 fcc 晶体作为置换的示例，无序氯化钠结构作为间隙固溶体的示例。在其中一个组件与其他组件仅微弱耦合的情况下，色散关系会产生特征签名。在第一布里渊区的大部分区域，声分支变得平坦，并且声分支和光学分支之间的交叉发生在远超过晶格间距的波长处。无规 fcc 晶体作为置换的例子，无序的氯化钠结构作为间隙固溶体的例子。在其中一个组件与其他组件仅微弱耦合的情况下，色散关系会产生特征签名。在第一布里渊区的大部分区域，声分支变得平坦，并且声分支和光学分支之间的交叉发生在远超过晶格间距的波长处。无规 fcc 晶体作为置换的例子，无序的氯化钠结构作为间隙固溶体的例子。在其中一个组件与其他组件仅微弱耦合的情况下，色散关系会产生特征签名。在第一布里渊区的大部分区域，声分支变得平坦，并且声分支和光学分支之间的交叉发生在远超过晶格间距的波长处。