What lies between crystal and randomly packed structures? A general characterization of non-periodic order

In this paper, we address the characterization of the structure of condensed materials, periodic and non-periodic. Carrying out an extensive study of over 7000 different ground-state structures of a 2D lattice model of binary packing, we find a predominance of non-periodic structures (over 96%) that extend across the entire range of possible diversities. These non-periodic structures are resolved by establishing whether a structure will accommodate or reject additional local structures. This property, structural selectivity, is treated as a signature of an underlying ordering principle. The major result of this paper is the determination that roughly 35% of the non-periodic structures are selective and, hence, ordered in some way. This selectivity extends up to a diversity of ∼9, well beyond the upper threshold for diversity in periodically ordered states.