The structure hierarchy hypothesis states that structures may be ordered hierarchically according to the polymerization of coordination polyhedra of higher bond valence. A mathematical hierarchy is an ordered set of elements where the ordering reflects a natural hierarchical relation between (or arrangement of) the elements. Here, I review the structure hierarchies for the borate, uranyl oxide, phosphate, sulfate, beryllate and oxide-centred Cu, Pb and Hg minerals (plus synthetics where appropriate). Structure hierarchies have two functions: (1) they serve to organize our knowledge of minerals (crystal structures) in a coherent manner; (2) if the basis of the classification involves factors that are related to the mechanistic details of the stability and behaviour of minerals, then the physical, chemical and paragenetic characteristics of minerals should arise as natural consequences of their crystal structures and the interaction of those structures with the environment in which they occur. We may justify the structure hierarchy hypothesis by considering a hypothetical structure-building process whereby higher bond-valence polyhedra polymerize to form the structural unit. The clusters constituting the FBBs (fundamental building blocks) may polymerize to form the following types of structural unit: (1) isolated polyhedra; (2) clusters; (3) chains and ribbons; (4) sheets; and (5) frameworks. The major advantage of this approach to structure hierarchy is the fact that the hypothetical structure-building process outlined above resembles (our ideas of) crystallization from an aqueous solution, whereby complexes in aqueous and hydrothermal solutions condense to form crystal structures, or fragments of linked polyhedra in a magma condense to form a crystal. Although our knowledge of these processes is rather vague from a mechanistic perspective, the foundations of the structure hypothesis give us a framework within which to think about the processes of crystallization and dissolution.

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