Extended defects, shear structures

Non-stoichiometric oxides with high levels of disorder may adopt two modes of stabilization aggregation or elimination of point defects. Point defect aggregates forming clusters are examples of the former and extended defect structures like crystallographic shear-plane structures are examples of the latter. 

Chapter 2 describes non-stoichiometric compounds derived from extended defects . Research in this field showed significant growth towards the end of the 1960s (although important papers by Professor A. Magneli and Professor A. D, Wadsley were published in the 1950s), initiated by the proposition of the shear structure model by Professor J. S. Anderson and... 

The extended defect structures that occur in certain non-stoicheiometric compounds have in recent years provided some of the most intriguing problems in solid-state chemistry. The most intensively studied phase showing this class of disorder is Ti02-x> which planar defects known as shear planes have been detected and characterized by electron microscopy. Examples of other simple inorganic compounds containing shear planes are provided by V02 x and The range of... 

Until recently very little was understood as to the factors which determine whether point or extended defects are formed in a non-stoicheiometric phase, although interesting empirical correlations between shear-plane formation and both dielectric and lattice dynamical properties of the defective solid had been noted. Theoretical techniques have, however, provided valuable insight into this problem and into the related one of the relative stabilities of extended and point defect structures. The role of these techniques is emphasized in this article. 

Thus to summarize, the extent of cation relaxation around a shear plane has emerged from our analysis as the most decisive factor in stabilizing shear planes with respect to point defect structures. Our discussion now continues with an account of the behaviour of the crystals at low deviations from stoicheiometry where an equilibrium may exist between point and extended defect structures. 

Shear Plane-Point Defect Equilibria.—The question of the existence of point defects in compounds where extended defects are known to occur has been controversial. Indeed, it has occasionally been claimed that point defects cannot form in such phases and that they will always be eliminated with the formation of extended structures. We reject these latter arguments as thermodynamically unsound. From a thermodynamic standpoint, the formation of extended defects can be viewed as a special mode of point defect aggregation as such, shear planes will be in equilibrium with point defects, with the position of the equilibrium depending on both temperature and the extent of the deviation from stoicheiometry. Thus, if we assume, as is suggested by our calculations, that anion vacancies are the predominant point defects in reduced rutile (a further point of controversy as mentioned above) then there will exist an equilibrium of the type... 

Long-range periodicity based on extended defects is not, however, confined to shear-plane structures. Indeed the occurrence of extended defect super-lattices is widespread. The adaptive structures discussed by Anderson have already been referred to in the Introduction. A further illustration of the phenomenon, which strikingly illustrates its generality, is provided by the void lattice observed in certain irradiated metals, e.g., Mo, where voids, typically of diameters 50 A, formed by the aggregation of irradiation induced vacancies, order to give a stable f.c.c. lattice in which the voids are separated by 300 A. 

Tilley s article complements that of Catlow, but it also extends it in that he has brought up to date, in an organized fashion, the wealth of information that continues to emerge from high-resolution electron microscopic studies of various kinds of solids. Moreover, other defective solids, besides those that are encompassed by the term shear structures, are discussed by Tilley. 

It is already dear that the equilibrium behavior of materials having gross defects is not predicted by theories which are a simple extension of the classical point defect models. This is because strong interactions between defects in parent structures yield extended defects that become regular structural features of textured intermediate phases, which when ordered leave very low concentrations of point defects. The most studied of these structural features is the Wadsley defect resulting from crystallographic shear in typical... 

The determination of how nonstoichiometry is accommodated (i.e., by what type and amount of defect) is an active research area. Nonstoichiometry can also be accommodated by subtle changes in structure known as extended defects or crystallographic shear. Crystallinity, impurity levels, point-defect structure, and nonstoichiometry are each controlled by or influenced by the preparation method therefore, it is discussed further in Section III. 

The influence of defect clusters or extended defects in the sense of this section on the mobility of structure elements of a crystal or, more generally, on the reactivity of solids has not yet been explored and is certainly an important field of future research. It is understood, however, that beside shear planes, defect superstructures, or defect clusters, there are also free point defects present in the crystal lattice of compounds with extended ranges of homogeneity. 

Besides, crystals often contain extended defects. Among these are dislocations, which are classified as linear or one-dimensional defects. Grain bonndaries, chemical twinning, stacking faults, crystallographic shear planes, intergrowth structures, and snrfaces are two-dimensional... 

In recent years it has been shown that in many defect compounds, particularly oxides, the predominant defects are not random point defects, but rather the defect structure may consist of complexes, microdomains, block structures, or crystallographic shear planes. These extended defects will be described in more detail by Eyring and Tai in Chapter 4 of Volume 3. 

Schematic illustration of shear-plane formation. Structure (a) with aligned oxygen vacancies shears to eliminate these vacancies in favour of an extended planar defect in the cation lattice as in (b). % cations oxygen ions are at the mesh intersections...

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