Structural diversity in condensed matter: A general characterization of crystals, amorphous solids, and the structures between

A definition of structural diversity, adapted from the biodiversity literature, is introduced to provide a general characterization of structures of condensed matter. Using the favored local structure lattice model as a testbed, the diversity measure is found to effectively filter extrinsic noise and provide a useful differentiation between crystal and amorphous structures. We identify an interesting class of structures intermediate between crystals and glasses that are characterized by a complex combination of short-range ordering and long-range disorder. We demonstrate how the diversity can be used as an order parameter to organize various scenarios by structure change in response to increasing diversity.