Algorithm for generating irreducible site-occupancy configurations

TL;DR

This paper introduces a new, efficient algorithm for generating irreducible site-occupancy configurations in crystal structures, applicable to arbitrary cells and atom types, significantly improving speed over existing methods.

Contribution

The authors present a novel algorithm that efficiently generates irreducible configurations using symmetry and integer representation, applicable to any parent cell and atom stoichiometry.

Findings

Algorithm works for arbitrary parent cells and atom types.

Significantly faster than existing codes like supercell, enumlib, and SOD.

Code implementation in FORTRAN demonstrates superior performance.

Abstract

Generating irreducible site-occupancy configurations by taking advantage of crystal symmetry is a ubiquitous method for accelerating of disordered structure prediction, which plays an important role in condensed matter physics and material science. Here, we present a new algorithm for generating irreducible site-occupancy configurations, that works for arbitrary parent cell with any supercell expansion matrix, and for any number of atom types with arbitrary stoichiometry. The new algorithm identifies the symmetrically equivalent configurations by searching the space group operations of underlying lattice and building the equivalent atomic matrix based on it. Importantly, an integer representation of configurations can greatly accelerate the speed of elimination of duplicate configurations, resulting into a linear scale of run time with the number of irreducible configurations that finally found. Moreover, based on our new algorithm, we write the corresponding code named as disorder in FORTRAN programming language, and the performance test results show that the time efficiency of our disorder code is superior to that of other related codes (supercell, enumlib and SOD).