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.
The interaction of finite gas bubbles in a solid
Abstract The accurate elastic interaction between two finite gas bubbles, each of arbitrary size and excess gas pressures, is obtained. It is found that two such bubbles always attract one another in an elastically isotropic medium and the magnitude of the attraction is very large when the bubble separation is small. The significance of this attraction is discussed in relation to the swelling in nuclear fuels.
The formation and behaviour of gas bubbles in a non-uniform temperature environment
Abstract Irradiation of uranium- and plutonium-based fuels results in the accumulation of fission products of which about 10% are the inert gases xenon and krypton. These gas atoms are insoluble and precipitate in the matrix to eventually form gas bubbles. This paper considers in detail the nucleation and subsequent behaviour of the gas bubbles in a non-uniform temperature environment. It is therefore particularly relevant to ceramic fuels in which steep temperature gradients are typically present during operation. A homogeneous nucleation model is used to describe the formation of the gas atom clusters during irradiation. It is shown that the scale of nucleation is a function of temperature, and thus in a temperature gradient the distribution of nuclei is non-uniform. The subsequent growth of the nuclei to form gas bubbles leads to the development of non-uniform swelling stresses. The gas bubbles are subjected to forces resulting from the temperature and stress gradients, which tend to drive them up the gradients. They are also subjected to restraining forces applied by structural heterogeneities. The present paper considers these forces, and in particular the stress gradient driving force, and the interaction between a bubble and a dislocation are treated in detail. Consideration is also given to the energies involved in the process of coalescence between bubbles that collide. It is concluded that during irradiation when a large supersaturation of vacancies is present, the energy gained by the matrix from the vacancies absorbed into the bubble provides the dominant driving force for growth. Finally, the theory developed in the paper has been applied to a uranium carbide pellet operating under a specific set of conditions typical of those existing in a fast reactor environment. Up to 10% burn-up the predicted swelling is consistent with the values estimated from experiments.