ABSTRACT

A family of equilibria corresponding to a dislocation–dipole, with variable separation between the two dislocations of opposite sign, is constructed in a one-dimensional lattice model. A continuous path is constructed, in the space of lattice configurations, connecting certain members of this family; eventually leading to an energy landscape, using the concept of order-parameter. The energy landscape is found to exhibit the familiar Peierls relief for the variation of energy associated with certain sequential transitions between these equilibria. The results allow an interpretation in terms of quasi-statically separating pair of dislocations of opposite sign from the viewpoint of the original Frenkel–Kontorova model albeit a piecewise-quadratic onsite potential is employed in the paper. The closed form expressions are provided after an application of detailed analytical means wherein an analysis of the effect of an intermediate spinodal region is included.

摘要

在一维晶格模型中构建了与位错-偶极子相对应的平衡族，在两个相反符号的位错之间具有可变间隔。在晶格配置的空间中构建了一条连续的路径，连接该家族的某些成员；最终导致使用顺序参数的概念的能源景观。发现能量景观表现出熟悉的 Peierls 浮雕，用于与这些平衡之间的某些顺序转换相关的能量变化。从原始 Frenkel-Kontorova 模型的角度来看，结果允许在准静态分离相反符号的位错对方面进行解释，尽管在论文中使用了分段二次现场势。