On the theory of void formation during irradiation

A simple theory of the swelling of materials subjected to high energy particle irradiation is developed. Chemical reaction rate equations are used as a basis. Point defects, interstitials and vacancies, are assumed to be produced randomly throughout the solid. They move by random walk through the material until they cease to exist either by recombination with the opposite type of defect or by incorporation into the crystal at sinks such as dislocations, grain boundaries and voids. The rate equations for interstitials and for vacancies, which are coupled via the recombination term, are solved for steady state conditions under irradiation. Defect concentrations, supersaturations, recombination and total sink annihilation rates are obtained in terms of the production rate, sink annihilation probabilities, jump frequencies and thermal equilibrium concentrations of defects. The swelling rate is derived using sink annihilation probabilities at three principally different types of sinks, i.e. voids, sinks which have a bias with regard to the annihilation of interstitials and vacancies (such as dislocations), and sinks with no bias. The defect annihilation probabilities at void, precipitate, dislocation and grain boundary sinks are estimated by using a cellular model and solving the diffusion equation for geometries approximating that of the cells, e.g. a concentric sphere around a void. The relative effects of different types of sinks, i.e. the microstructure, on the swelling rate is discussed. The swelling rate is integrated to give swelling-time or swelling-dose relations, making some simplifying assumptions about the changes in the sink structure as the irradiation proceeds. It is shown that the relation obtained is rather sensitive to the type of assumptions made.