A perfect lattice approach to nonstoichiometry

Although nonstoichiometry implies the presence of defects in a structure and hence a departure from perfect crystallinity, it is sometimes found that the defects are ordered or, at least, show a tendency to order. In these cases, it becomes possible to model the nonstoichiometry by considering a supercell and using perfect lattice techniques. We illustrate the viability of this approach with two examples. Firstly, we show how factors controlling the long-range ordering of extended defects in transition-metal oxides may be elucidated; indeed, we find that an adequate treatment of this phenomenon requires calculations on supercells. Secondly, we discuss how perfect lattice calculations may be used, in conjunction with diffraction data, to examine possible vacancy ordering schemes in the oxidation of magnetite, Fe₃O₄, to maghemite, the defect spinel structured γ-Fe₂O₃.