Shear planes formation

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...

Crystallographic shear plane. Series of discrete shear phases are observed among the oxides of several transition metals. By progressive reduction, series of Ti 02 i, V 02 i phases are obtained from the dioxides, as Me 03 i phases may be related to trioxides such as M0O3 or WO3. An example of a crystallographic shear plane formation is schematically shown in Fig. 7.54. 

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. 

Figure 1 Schematic representation of shear-plane formation, (a) Aligned vacancies in cross-section of hypothetical structure (b) Shear plane formed by vacancy elimination arrows indicate direction of relaxations of cations adjacent to shear plane)...

Shear-plane structures in real systems are invariably more complex. Figure 2 gives a still partially simplified illustration of the shear plane in Ti02-x- However, the essential features of the schematic plane discussed above apply to real systems that is, shear-plane formation eliminates point defects by a change in the mode of linking of MOe octahedra. 

These alternative descriptions of shear-plane formation will be valuable in our discussion of mechanism in Section 4. In the account now presented of the relative stabilities of shear plane and point defect structures we will assume that vacancies are the predominant point defects. However, the arguments we present could be adapted for metal interstitial defect structures. 

Support for our proposal is obtained from an observation made by Tilley that shear-plane formation may be correlated with the dielectric properties of the solid. Compounds in which extended defects are formed are found to have very high values of the static dielectric constant, Sq. Thus Ti02 and WO3, both of which form shear planes on reduction, have values of Cq of 150 and 300 respectively. Typical values for oxides are 10—20. Sn02 provides a significant example of the latter Eq is measured as 15, and reduction of the compound does not apparently result in shear-plane formation although the oxide is isostructural with Ti02 and has a similar lattice parameter. 

A further set of problems which obviously follows from the above discussion concerns the mechanism of shear-plane formation, although we should emphasize that the considerations involved here are quite separate from the thermodynamic ones discussed above. We discuss these mechanistic problems in Section 4 after considering a second structural feature in shear-plane systems, viz. the remarkable long-range ordering that commonly occurs in oxides containing these defects. 

It seems therefore that little or no stability is to be expected for the point defect aggregates which provide the necessary shear-plane precursors in the homogeneous shear-plane formation mechanisms. These homogeneous nucleation mechanisms are therefore unlikely to operate, and we turn our attention now to a heterogeneous mechanism, in which point defects aggregate at pre-existing planar-defect sites. 

The most obvious heterogeneous mechanism follows from our discussion in Section 2 where we showed that shear planes could be related to metal interstitial defects, but that a pre-existing anti-phase boundary (APB) is required. Thus shear-plane formation may occur by metal interstitial capture at pre-exist ng APBs (Bursill et More particularly, it is proposed that metal interstitial ions produced by... 

Fig. 1. Shear plane formation in the W 03n, (above) and Wn03n 2 (below) systems14 ...

Fig. 21. (a) The nature of the glide shear plane defects in three-dimensional projection and (b) in one layer of idealized structure, showing the novel glide shear process and the formation of glide shear plane defects. Filled circles are anion vacancies, (c) Schematic of glide shear. Glide defects accommodate the misfit at the interface between catalyst surface layers with anion vacancies (filled circles) and the underlying bulk (85,89). 

VOPO4 is reduced through the formation of crystallographic shear planes. 

Fig. 5—Schematic representation of a shear plane (CS) formation (a) idealized W03 structure showing anion vacancies aligned on a plane and (b) sheared structure after vacancies are eliminated (following ref. 43).

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