SIAM Journal on Applied Mathematics, Volume 80, Issue 6, Page 2496-2517, January 2020.
High entropy alloys (HEAs) are single phase crystals that consist of random solid solutions of multiple elements in approximately equal proportions. This class of novel materials have exhibited superb mechanical properties, such as high strength combined with other desired features. The strength of crystalline materials is associated with the motion of dislocations. In this paper, we derive a stochastic continuum model based on the Peierls--Nabarro framework for interlayer dislocations in a bilayer HEA from an atomistic model that incorporates the atomic level randomness. We use asymptotic analysis and limit theorem in the convergence from the atomistic model to the continuum model. The total energy in the continuum model consists of a stochastic elastic energy in the two layers, and a stochastic misfit energy that accounts for the interlayer nonlinear interaction. The obtained continuum model can be considered as a stochastic generalization of the classical, deterministic Peierls--Nabarro model for the dislocation core and related properties. This derivation also validates the stochastic model adopted by Zhang et al. [Acta Mater., 166 (2019), pp. 424--434].

中文翻译：

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高熵合金中位错的随机Peierls-Nabarro模型

SIAM应用数学杂志，第80卷，第6期，第2496-2517页，2020年1月。
高熵合金（HEA）是单相晶体，由大约相等比例的多种元素的无规固溶体组成。这类新型材料表现出极好的机械性能，例如高强度以及其他所需的功能。晶体材料的强度与位错的运动有关。在本文中，我们从Peierls-Nabarro框架的基础上，从结合原子级随机性的原子模型推导了双层HEA层间位错的随机连续模型。我们使用渐近分析并限制了从原子模型到连续模型收敛的定理。连续模型中的总能量由两层中的随机弹性能组成，和随机失配能量，解释了层间非线性相互作用。获得的连续体模型可以看作是位错核心和相关属性的经典确定性Peierls-Nabarro模型的随机概括。这种推论也验证了Zhang等人采用的随机模型。[Acta Mater。，166（2019），第424--434页]。