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

Novelty in materials discovery is conventionally assessed against databases of ordered crystal structures, yet a predicted ordered structure may simply be a particular ordering of a known disordered phase, rendering its apparent novelty misleading. We refer to such cases as ordered children of disordered parents. To address this limitation, 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 evaluated at the family level. Using a high-throughput family-matching procedure, we identify candidate disordered parents and symmetry-related ordered relatives for a given ordered structure. We test our framework using A-Lab results, where several targeted ordered structures are correctly identified as ordered children of known disordered parents. Extending the benchmark across experimental databases (ICSD), simulation datasets (MP-20, Alex-MP-20, GNoME), and crystal generative models reveals that many seemingly novel ordered structures are, in fact, better understood as members of experimentally known order-(dis)order family trees, establishing family trees as a key requirement for achieving genuine novelty in data-driven materials discovery.