SWORD: Symmetry and Wyckoff-sequence of Ordered and Disordered crystals

TL;DR

SWORD is a symmetry-aware, Wyckoff-based string representation for ordered and disordered crystals that improves structure comparison, deduplication, and novelty assessment in large crystallographic databases.

Contribution

It introduces a novel, symmetry-aware representation that explicitly encodes disorder and co-occupancy, enabling more reliable structure analysis and database curation.

Findings

SWORD remains invariant under symmetry transformations.

It effectively identifies duplicates in large databases.

It correlates unrelaxed structures with relaxed states.

Abstract

Novelty in materials discovery requires candidates to be distinct, non-redundant, and thermodynamically plausible. While crystallographic databases continue to expand in both size and complexity, making efficient and reliable novelty assessment has become increasingly difficult. This becomes particularly acute when crystallographic disorder is involved, as partial occupancies greatly enlarge the structure-composition space and obscure the identification of genuinely distinct structures. Here, we introduce SWORD, a symmetry-aware, Wyckoff-based string representation compatible with both ordered and disordered crystals. SWORD provides (i) standardization of symmetry-equivalent structural descriptions into a consistent label, (ii) explicitly represents co-occupying species on partially occupied sites, and (iii) quantifies complex disorder through a degree of mixing descriptor that captures continuous variation in site stoichiometry. These features enable efficient structure grouping, duplicate identification, and finer refinement of disordered structures. Benchmarking against existing fingerprint and structure-matching methods shows that SWORD remains invariant under identity-preserving transformations while retaining interpretable sensitivity to structural perturbations. In addition, SWORD shows competitive performance in associating unrelaxed and intermediate configurations with their final relaxed states along relaxation trajectories. This feature could enable more reliable novelty assessment directly from partially relaxed or even unrelaxed generated structures. Finally, SWORD was used to showcase its capability of disorder-aware database-scale deduplication and curation for the Inorganic Crystal Structure Database (ICSD). The curated ICSD would serve as the basis for the materials informatics and data-driven materials design in the era of artificial intelligence.