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.
Kinetics of void-lattice formation in metals
Since the discovery1 that voids form in neutron-irradiated stainless steel and that these could form into a three-dimensional lattice2, void-lattices have been observed in some b.c.c. metals2,3 such as Mo, W, Nb, and Ta, and in f.c.c. metals4,5 such as Al and Ni. The irradiation conditions in which a void-lattice is formed are not understood6, but several explanations7–11 of the stability of the void-lattice have been given on the basis of void–void elastic interaction9–11. Our present approach regards the void-lattice formation as a phase transition associated with the bifurcation of the homogeneous steady state in the mean field theory12,13. The void-lattice is an interesting example of a class of phase transitions manifested by open, nonequilibrium, dis-sipative structures and have an inherent capability of self-organization. Although void-lattice formation has already been examined on this basis14,15, we show here that the transition is induced in certain microstructural conditions where vacancy loop dynamics has an important role. The theory generally agrees with experimental features and predicts that another spatially dependent state exists which can influence irradiation-induced phenomena that have important technological implications for the development of fast reactor materials.
GAS BUBBLES IN SOLIDS.
Abstract This note points out that, as a consequence of the distinction in solids between surface tension γ and surface energy [sgrave], a strain field generally exists around gas bubbles even in thermodynamic equilibrium. The existence of this strain field leads to a small attraction between bubbles but in typical practical situations this is only significant for bubble migration when they are close together compared to their radii.