Theory of regular arrays of defects: The void lattice
Defects in crystals may form a regular array, rather than a random distribution. The lattice of voids produced in irradiated molybdenum is a remarkable example of this. We give a general method of calculating the energy per defect in the array which exploits the periodicity of the defect lattice. The existence of the void lattice depends on the elastic interaction between voids. The present approach can treat both arbitrarily anisotropic elastic continua and discrete lattices, and is readily extended to discuss the stability of the defect lattice. The results predict that a void lattice should occur in molybdenum, and compare a number of models for the void. Stability against shear of the void lattice is not discussed in the present paper. The ratio of the void lattice spacing to void radius predicted is 2.2 to 4.5 and is smaller than the value of about 10 observed. The results are in general agreement with the more approximate Malen-Bullough treatment.
Elastic Green's Function for Anisotropic Cubic Crystals
The Green's function describing the elastic displacement due to a unit force in an infinite cubic material is investigated in detail. Only for special cases can an exact solution be given, i.e., for ${c}_{11}\ensuremath{-}{c}_{12}\ensuremath{-}2{c}_{44}=0$ (isotropy), for ${c}_{12}+{c}_{44}=0$, and for 100g directions. Perturbation theory is applied to the cases where these conditions are only approximately fulfilled. Divergencies or strong maxima of the Greens' function, occurring in nearly unstable materials for ${c}_{11}\ensuremath{-}{c}_{12}\ensuremath{\rightarrow}0$ or ${c}_{44}\ensuremath{\rightarrow}0$, are examined. Analytical approximations for the Green's function are given by fitting the exact known Fourier transform with a suitably chosen ansatz in certain directions. Other simple approximations are derived by variational techniques and give good results for crystals with small and medium anisotropy.
The elastic interaction of point defects
Abstract In an isotropic material it is known that two point defects regarded as centres of dilatation interact with one another only indirectly through the modification of their elastic fields by the surface of the body. In a cubic material there is an additional direct interaction energy equal to the product of the inverse cube of their separation and a function of direction whose average over all angles is zero. This function is evaluated approximately. If in a more refined elastic model we replace each defect by a centre of dilatation plus a small region where the elastic constants differ from those of the matrix there is an additional interaction proportional to the inverse sixth power of the distance between them.