A brute-force code searching for cell of non-identical displacement for CSL grain boundaries and interfaces

Atomic simulation of coincidence-site lattice (CSL) grain boundaries (GBs) and interfaces is of importance for understanding GBs in polycrystalline materials and for making functional films. A common process of high-throughput simulation for CSL GBs and interfaces is to explore rigid body translation (RBT) of one crystal respect to the other. Cell of non-identical displacement (CNID) is the minimum cell including all non-identical RBTs in the GB or interface plane and is important for effective sampling. This work proposes an algorithm to compute the CNID of any two-dimensional CSL GB or interface based on a reciprocity relation between the displacement shift complete (DSC) and CSL.重合位置点阵(Coincidence-site Lattice, CSL)晶界(grain boundaries, GBs)与界面的原子模拟，对于理解多晶材料中的晶界、制备功能薄膜具有重要意义。针对重合位置点阵晶界与界面的高通量模拟，通常采用的常规流程是探究一块晶体相对于另一块晶体的刚体平移(rigid body translation, RBT)。非同位移胞(Cell of Non-identical Displacement, CNID)是晶界或界面平面内包含全部非同刚体平移的最小晶胞，对高效采样具有关键价值。本研究提出了一种基于位移完全点阵(Displacement Shift Complete, DSC)与重合位置点阵间互易关系的算法，可用于计算任意二维重合位置点阵晶界或界面的非同位移胞。