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Spatial transitions between local structures in condensed systems

Scattering data and radial distributions in amorphous matter can be represented accurately in terms of models based on a small set of structural elements which specify local atomic configurations, and on certain spatial random processes specifying the fraction of such elements and the decay of their correlations with distance. The local structural elements, expressed in terms of globally ordered structures, particularly in terms of lattices (L), are subject to radially evolving Markoffian-like processes of relative displacements and of transitions between Ls at different points in space. Including an empty lattice L 0 in the set (L) leads to a definition of random voids and their spatial correlations, depending on the size of the local domains considered. The models provide representation of a continuous range of amorphous structures from liquids and glasses via nanomaterials to crystalline powders.