A Crystallographic Metric for Continuous Quantification of Unit Cell Deformation

TL;DR

This paper introduces a cubic deviation metric that provides a continuous measure of unit cell deformation, aiding in the analysis of phase transitions and structural comparisons across diverse material systems.

Contribution

The paper presents a new simple metric for quantifying unit cell distortion relative to a cube, facilitating continuous comparison of structures with different geometries.

Findings

Effective in analyzing phase transitions in pseudobrookites

Useful for classifying structures homologically

Assists in correlating structure with piezoelectricity and superconductivity

Abstract

Describing the deviation of a real structure from a hypothetical higher-symmetry ideal can be a powerful tool to understand and interpret phase transitions. Here we introduce a simple yet effective metric that quantifies the degree of unit cell distortion relative to a cube, called the cubic deviation metric. This enables continuous comparisons between unit cells of different geometries. We demonstrate the potential of this tool with four separate case study applications to real material systems: 1) discontinuous structural phase transitions in pseudobrookites; 2) homological structure classification; 3) structure-correlated piezoelectricity in hexagonal materials; and 4) superconducting materials design in the cuprate family. Although this metric does not replace detailed structural or group theory analysis, it enables comparison across different compositional and structural compound variants, even in the presence of disorder or absence of group-subgroup correlation.