On infinitely adaptive structures

Abstract

A class of crystalline substances is recognized in which changes of chemical composition are accompanied neither by forming a step-wise succession of phases nor by forming nonstoicheiometric or solid solution phases with disordered, defect structures. Instead, every composition orders into a superlattice and the diffraction patterns invariably show only a single set of superstructure lines which is, however, different at every composition. The true superlattice multiplicity is that of a large unit cell, built up by the ordered repetition of a set of sub-units, which differ in compositions but are structurally closely related and readily interconvertible with a minimum of adjustment of atomic positions. Infinitesimal changes of total composition can then be accommodated in a fully ordered structure by a change in the relative numbers of these sub-units and a consequential change in total multiplicity. The consequences of this adaptive ordering are discussed in relation to phases derived from L-Ta₂O₅ and the crystallographic shear structures, and it is shown that the observed complexities in the chemistry of a wider range of solid-state systems can be interpreted consistently on the same basis.