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

Abstract

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. Program summaryProgram title: cnidcalCPC Library link to program files:https://doi.org/10.17632/wzy67jd56d.1Code Ocean capsule:https://codeocean.com/capsule/1648641Licensing provisions: MIT licenseProgramming language: Python Nature of problemDetermination of atomic structure of crystalline interfaces and grain boundaries is a key issue for understanding the properties of polycrystalline materials, where atomic simulation has made notable contribution in this field. Simulation of crystalline interfaces often applies a bicrystal model of a coincidence-site lattice (CSL) [1, 2] interface comprising two slabs of crystals which coincides in the interface plane. To determine the most stable structure of this interface model, a main task is often to tailor the initial bicrystal model to obtain many non-identical and non-relaxed structures for subsequent relaxation to explore the energy landscape of the system to find the ‘global minimum’ at 0 K, where one of the most important operations to tailor the model is applying rigid body translation (RBT) [1] of one crystal respect to the other by a vector confined in the interface plane. Because of symmetry of the two crystals, there exist periodicity of this translation vector which is reflected by a special cell called ‘cell of non-identical displacement’ (CNID) [1] which is the minimum cell including all non-identical choices of this vector and is key for effective sampling. Although CNID has a straightforward definition that it is a lattice including both the two overlapping two-dimensional lattices, finding a method capable to determine a primitive basis of CNID in general cases can be non-trivial and there has not been a reported programme capable to do so. Solution methodCNID in nature is a displacement shift complete (DSC) lattice [2]. While there has not been effective reported programme to compute DSC, several programmes have been made to compute CSL [3, 4, 5]. Besides, Grimmer [6] has proposed a mathematical relationship between the DSC and the CSL. In this way, based on a previously reported programme computing the CSL by brute-force method [5] and the relationship between DSC and CSL proposed by Grimmer, we generated a python code to compute CNID. This code is available to compute the CNID of a CSL interface comprising any two lattices if only they coincide even including complex cases involving heterogeneous lattices with difference in both shape and size.