Crystallographic Shear and Non-stoicheiometry

1 Introduction

When the previous Report in this series was written, detailed experimental evidence about the microstructure of crystallographic shear structures (CS phases) was just becoming available. Two themes were therefore emphasized. The first was the relation between the concept of crystallographic shear and existing views of defects and non-stoicheiometry in inorganic compounds. Most CS phases do not appear to contain point defects in significant concentrations — i.e. in sufficient number to contribute materially to the apparent composition ranges of CS compounds. In a heuristic sense, at least, the collapse of the parent crystal structure which produces a CS plane eliminates point defects; it is not implied that the presence of point defects in high concentration is a necessary precursor stage in the formation of a CS plane. The mechanism of this transformation process is still not clear, and the role of point defects in certain structural types, notably the 'block' structure oxides, has continued to excite interest.

A second topic, which has also been actively pursued in the review period, was the importance of coherent intergrowth between structures that are topologically compatible, but of different composition, exhibited particularly by the CS phases. It was shown that in many macroscopically homogeneous CS phases there may be a considerable measure of internal disorder, associated with irregularities in the spacing between parallel CS planes. Even though this state may not represent a true equilibrium structure, it may be experimentally inescapable and it provides a basis for apparent non-stoicheiometric properties at the macroscopic level. The usual methods of characterization and structure analysis may fail to reveal and analyse such microscopic heterogeneity; to do so needs methods for determining the local microstructure, at the unit-cell level, as distinct from the averaged structure derived from diffraction methods and from postulated models for defect structures. Such methods were beginning to emerge from the application of electron microscopy.

In the intervening two years, the power of lattice-imaging methods in electron microscopy has developed markedly. Considerable attention has been devoted to coherent intergrowth (Wadsley defects) and other forms of faulting, as observed at or below the unit-cell level, and the topological constraints and relationships that determine the possibilities of intergrowth or structural relaxation in CS phases have been analysed. This advance in our knowledge of structure has not been matched by advances in knowledge of transport and reaction processes, and the physical properties associated with CS structures have received little study. In this review, we consider particularly the increasingly important role of electron microscopy, and the way in which structure adjusts itself to composition, both in materials that simulate non-stoicheiometric behaviour and those that are genuinely variable in composition. Crystallographic shear — the term has a very specific meaning, which should not be loosely used — is not the only transformation whereby inorganic structures can accommodate changes in the atomic ratio of metal : non-metal so as to maintain some high degree of order. Recent work has drawn attention to the formation of ordered structures, with large repeating units, where randomized solid solutions might be expected. Without venturing an answer to the difficult questions of how a solid compound should now be defined, or how complex ordering is established, we summarize also some recent developments in this wider field.

2 The Direct Observation of Structure in Crystals: Lattice Imaging

The newer experimental findings about CS phases have come largely from transmission electron microscopy and electron diffraction, rather than from X-ray diffraction, which has limitations imposed by the large unit cells, by the small differences in structure between one member and another in a homologous series, and, above all, by disorder in the crystals. The first results accruing from electron microscopy 1 indicated that complete order in crystals of CS phases was rarely attained; it may, indeed, be impossible even by the most careful preparative methods to obtain perfectly ordered crystals of many CS compounds for structure determination by single-crystal methods.

Transmission electron microscopy can present the essentials of the structure of CS phases and other suitable classes of compound very directly, although detailed metrical information — e.g. interatomic distances — cannot be extracted. For this, there is no alternative to precise structure determination by X-ray or, increasingly and for some purposes advantageously, neutron-diffraction methods. Lattice images can now be obtained, however, which show the projected structure at the level of the individual co-ordination polyhedron in oxide structures. Development of the technique has been largely pragmatic, based on the experimental finding that, provided that the crystals under examination were extremely thin, the contrast in micrographs made at 'optimum under-focus' approximated closely to a projection of the potential distribution in the crystal. Thus, for CS phases, in which the density of heavy cations, of high charge, is considerably higher in the CS planes than in the relatively open matrix of parent structure, the CS planes appear as fringes which collapse into dark lines of contrast when the crystal is so oriented as to bring the CS planes parallel to the incident beam. At the highest lattice resolution, individual corner-sharing (MO6) octahedral groups appear darker than the empty voids between them.

Interpretation of these lattice images is, however, not as straightforward as might appear at first sight. Ideally, an electron micrograph should be compared, point for point, with the intensity of the transmitted electron beam, as calculated from dynamical scattering theory. In practice, the theory of an electron-microscope image formed by the operation of many diffracted beams has been developed only in parallel with the experimental applications. Most results on CS and other structures have relied upon a less rigorous comparison with electron optic theory; much of the interpretation has, indeed, come from chemical intuition regarding the structural geometry that might be expected in the system concerned.

The correspondence between...