PyLRO: A Python calculator for analyzing long-range structural order

Abstract

We present PyLRO, an open-source Python calculator designed to detect, quantify, and display long-range order in periodic structures. The program’s design methodology, workflow, and approach to order quantification are described and demonstrated using a simple toy model. Additionally, we apply PyLRO to a series of metastable AlPO4 structural intermediates from a prior high-pressure study, demonstrating how to compute and visualize structural order in all directions on a Miller sphere. We further highlight the program’s capabilities through a high-throughput analysis of structural patterns in the pressure-induced amorphization of AlPO4, revealing atomistic insights into specific energy regions of massive amorphous structures. These results suggest that PyLRO can be a valuable tool for investigating crystal–amorphous transition in materials research.