A lattice-like construction to explain diffraction patterns of some non-stoichiometric phases

Abstract

ONE of the most significant advances in the understanding of non-stoichiometric compounds was Andersen's concept of infinitely adaptive structures¹. These materials exhibit a continuum of perfectly ordered structures as the stoichiometry is varied. X-ray crystallography has not yielded satisfactory structures for these phases, and high-resolution electron microscopy has also been unable to unravel the difficulties. To try to resolve these problems, we have focused our attention on the nature of the diffraction patterns that the compounds produce. We find that in many cases the diffraction patterns can be reproduced by the use of lattice-like constructions which we term shift lattices. Here we describe the method of construction of a one-dimensional shift lattice and mathematical representations of it and its Fourier transform. The method has wide applicability to complex structures, of which we have investigated several examples: the low-temperature tantalum pentoxide (L-Ta₂O₅) family of structures, Bi₂TeO₅-related phases in the Bi₂O₃–TeO₂ system and a number of non-stoichiometric heavy-metal oxyfluoride phases. For simplicity, we limit ourselves to a consideration of the one-dimensional case which we illustrate by reference to L-Ta₂O₅; nevertheless, all the examples that we have considered are explicable by such one-dimensional shift lattices.