# Generating derivative superstructures for systems with high configurational freedom

## TL;DR

This paper introduces an extended algorithm that efficiently generates all unique atomic configurations and displacements in alloy systems, overcoming combinatorial challenges in modeling complex materials.

## Contribution

The authors extend an existing enumeration algorithm to include atomic displacements, enabling the exploration of systems with high configurational freedom.

## Key findings

- Successfully enumerates configurations with atomic displacements
- Avoids combinatorial explosion in large supercells
- Enables modeling of previously inaccessible alloy systems

## Abstract

Modeling potential alloys requires the exploration of all possible configurations of atoms. Additionally, modeling the thermal properties of materials requires knowledge of the possible ways of displacing the atoms. One solution to finding all symmetrically unique configurations and displacements is to generate the complete list of possible configurations and remove those that are symmetrically equivalent. This approach, however, suffers from the combinatorial explosion that happens when the supercell size is large, when there are more than two atom types, or when there are multiple displaced atoms. This problem persists even when there are only a relatively small number of unique arrangements that survive the elimination process. Here, we extend an existing algorithm\cite{enum1,enum2,enum3} to include the extra configurational degree of freedom from the inclusion of displacement directions. The algorithm uses group theory to eliminate large classes of configurations, avoiding the combinatoric explosion. With this approach we can now enumerate previously inaccessible systems, including atomic displacements.