npj: 原子级晶格形变—消除与连续弹性的鸿沟

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晶格形变可用明确的原子位置来微观地描述或通过连续弹性来宏观地描述。应变和缺陷引起的形变对单晶和多晶材料的宏观性质具有极大的影响。一个多世纪以来，这些影响从描述固体位错产生的弹性场开始，已有大量的研究。但如何用计算模型来描述晶体形变，尚未见报道。

来自德国德累斯顿工业大学的Marco Salvalaglio教授等，证明了可通过复振幅扩展（APFC）来描述晶格形变。APFC模型除了可直接获得振幅并可描述应变或旋转晶体之外，还可以轻松地作大规模模拟、接近连续理论的典型模拟，且仍能保留必要的微观特征。振幅和位移或应变之间的联系，使人们有可能详细研究由连续形变场表示的任何形变所带来的影响，例如由于单个位错或由于外部载荷引起的位移或应变/应力。提取出振幅函数，即可从晶体的原子表示很容易地计算出变形场，而无需任何特别的后处理过程，不必考虑系统的维度和晶格的对称性。他们的研究证明，将局域取向作为连续场直接提取，可对微观结构作直接的分析。

该文近期发表于npj Computational Materials 5: 48 (2019)，英文标题与摘要如下，点击左下角“阅读原文”可以自由获取论文PDF。

Closing the gap between atomic-scale lattice deformations and continuum elasticity

Marco Salvalaglio, Axel Voigt & Ken R. Elder 

Crystal lattice deformations can be described microscopically by explicitly accounting for the position of atoms or macroscopically by continuum elasticity. In this work, we report on the description of continuous elastic fields derived from an atomistic representation of crystalline structures that also include features typical of the microscopic scale. Analytic expressions for strain components are obtained from the complex amplitudes of the Fourier modes representing periodic lattice positions, which can be generally provided by atomistic modeling or experiments. The magnitude and phase of these amplitudes, together with the continuous description of strains, are able to characterize crystal rotations, lattice deformations, and dislocations. Moreover, combined with the so-called amplitude expansion of the phase-field crystal model, they provide a suitable tool for bridging microscopic to macroscopic scales. This study enables the in-depth analysis of elasticity effects for macroscale and mesoscale systems taking microscopic details into account.

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