Navigating Order-(Dis)Order Family Trees via Group-Subgroup Transitions

TL;DR

This paper introduces a symmetry-based framework called order-(dis)order family trees to organize and evaluate the novelty of crystal structures by relating ordered and disordered phases through group-subgroup relations.

Contribution

It develops a high-throughput method to identify disordered parents and ordered relatives, improving the understanding of structure novelty in materials discovery.

Findings

Correctly recovers known disordered parents in case studies.

Many seemingly novel structures are part of known order-(dis)order families.

Symmetry-constrained models produce fewer structures derived from known disordered parents.

Abstract

As closed-loop materials discovery systems scale to produce millions of candidate compounds, the credibility of the novelty they reward becomes a critical concern. Novelty is commonly assessed against databases of ordered crystal structures, in which atomic sites are fully occupied. Yet, a predicted ordered structure may simply correspond to a particular ordering of a known disordered phase, whose sites are occupied by multiple species in the statistical average structure; we refer to such a structure as an ordered child of a disordered parent. Here, we introduce order-(dis)order family trees, a symmetry-based framework that organizes ordered and disordered structures through group-subgroup relations and enables novelty to be explicitly evaluated. We develop a high-throughput family matching procedure, to identify possible disordered parents and symmetry-related ordered relatives for a given ordered structure. As validation, we test our framework on synthesis-facing case studies (A-Lab), where it correctly recovers existing disordered parents for the targeted ordered structures. Extending this family-tree-based benchmark to experimental structure databases (ICSD), computational datasets (MP-20, Alex-MP-20, and GNoME), and crystal generative models further reveals that many ordered structures that appear novel as individual entries are, in fact, better understood as members of experimentally known order-(dis)order family trees. We also show that this is particularly evident in symmetry-agnostic all-atom generative models, which more frequently produce ordered structures derived from known disordered parents, whereas symmetry-constrained models are 2-4x less prone to this behavior. Our results establish order-(dis)order family trees as a key requirement for achieving genuine novelty in data-driven materials discovery.