The Ordering of Extended Defects

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. 

Malen and R. Bullough, Brit. Nucl. Eng. Conf. (Reading 1971)(ed. S. F. Pugh), AEREHarwell, p. 109. 

Stoneham and Durham s theory thus appears to be as satisfactory as its generality allows. Two recent developments promise greater specificity. The first (Iguchi and Tilley follows directly from Stoneham and Durham s work. However, the calculations in these studies were based on the real 102 shear-plane structure in VO3 x rather than the hypothetical 100 plane used in Stoneham and Durham s work. Furthermore, information from microscopy studies was used to quantify the magnitude of the defect forces F. The approach is promising it has supported Stoneham and Durham s conclusion that elastic interactions are sufficient to lead to the observed ordering. As yet, however, details of the interaction function have not been worked out. 

An alternative approach to the problem is provided by the atomistic lattice-energy calculations discussed in Section 2, p. 108. In addition to the obvious advantages of atomistic theories, such calculations also require no assumptions as to the nature of the shear-plane interactions. Thus electrostatic terms, which may play an appreciable role in shear-plane systems are automatically included in such theories. Ordered shear-plane compounds, e.g. the Ti 02 -i, series can be described in terms of large unit cells. If the lattice energies of these structures are calculated as described in E. Iguchi and R. J. D. Tilley, Phil. Trans., 1977, 286, 55. 

Kittel s simple theory gives rise to the prediction of purely repulsive interaction curves. This is in marked contrast to the defect force theories which predict the existence of minima in the interaction function. Kittel argues that repulsive curves are required to explain infinite adaptability. For if minima were present in the interaction function, those solutions whose compositions corresponded to interplanar spacings considerably displaced from the minimum would be unstable with respect to separation into two phases, one of whose composition gave a separation nearer to the minimum. The argument cannot be faulted granted thermodynamic control of the ordering in these structures. It is, however, far from certain that kinetic factors do not play a decisive role in the structure of these compounds. 

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