Nucleation of Voids in Materials Supersaturated with Vacancies and Interstitials

Abstract

High‐energy radiation simultaneously produces vacancies and interstitials in crystalline materials and, therefore, both types of defects are supersaturated during irradiation. The nucleation of defect precipitates under this circumstance is fundamentally different from the usual nucleation problem because of the competing effects of interstitials and vacancies on the size distribution of precipitate embryos. The rate of homogeneous nucleation of voids in such a material in which interstitials as well as vacancies are supersaturated is derived in this paper. It is shown that the thermodynamically derivable void embryo size distribution $n^0\mathrm{(x)}$ (that is, the distribution which is in equilibrium with a given vacancy supersaturation) is in equilibrium with interstitials only when the latter are in equilibrium with the vacancies, i.e., when the interstitials are undersaturated to the same extent as the vacancies are supersaturated. The constrained distribution of voids $\mathrm{n(x)}$ (that is, when the interstitials are also supersaturated) is determined by the kinetics of incorporation of vacancies and interstitials into the embryos. Explicit expressions are given for $\mathrm{n(x)}$ in terms of kinetic parameters and $n^0\mathrm{(x)}$ . The rate of nucleation is then derived from $\mathrm{n(x)}$ along the lines of classical nucleation theory. The procedure developed here can readily be applied to the nucleation of other types of defect precipitates such as dislocation loops. A useful parameter to characterize the effect of excess interstitials on the nucleation of voids is the ratio of the rates at which interstitials and vacancies arrive at and are incorporated into void embryos. At a constant vacancy supersaturation, as this arrival rate ratio increases from essentially zero (i.e., interstitials in equilibrium with vacancies) the nucleation rate decreases and the size of the critical nucleus increases. Thus, to obtain a given rate of nucleation, increasingly larger supersaturations are required as the arrival rate ratio increases. The calculated changes are gradual at lower values of this ratio but become so drastic as the ratio approaches one that no nucleation of voids is then possible. As in classical nucleation theory, the rate of nucleation increases very rapidly with increases in supersaturation. This rapid increase of rate is obtained for all arrival rate ratios. We find that the supersaturations of defects which occur during irradiation in a high flux of energetic neutrons or ions are sufficient for readily observable nucleation rates for voids at intermediate temperatures but insufficient at high temperatures.