Shear Plane-Point Defect Equilibria

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 

Now the configurational entropy associated with the shear planes will be small as the total number of these species is small compared with the total number of point defects. The activity of the shear planes is therefore roughly constant, and we can write the following mass-action equation  

A difficulty, however, arises in that detailed analysis of the data of Baumard et al. in the near-stoicheiometric regions suggests that the predominant point defects are metal interstitials rather than the oxygen vacancies assumed so far in 

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. 

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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. 

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