In Brief

Crystallography can tell us what structure a crystal has — its symmetry, its lattice, its unit cell, its polymorphs. But there is another question hiding underneath all of that: when matter reorganizes itself into different ordered forms, how close does it come to the boundary where ordered structure stops being comfortably realizable?

We evaluated eight crystallographic material families — ferroic phase chains, polymorph oxide systems, a metallic pair, and a single-phase control — under the admissibility inequality. Every tested phase chain and polymorph family remained admissible. But they did not sit equally deep inside the safe interior. The law held throughout. And in doing so, it revealed a geometry.