Void nucleation with embryo injection and destruction

Full text: Fifty years ago the liquid metal fast breeder reactor was under development in Germany, France, the United Kingdom, the USSR, and the USA. The plutonium breeding reactor was designed to operate at higher temperatures and much higher fast neutron fluxes than existing light water reactors. The developers were shocked to find that the intense irradiation produced large numbers of gas containing cavities (commonly termed voids), which caused loss of dimensional stability and embrittlement in the cladding and duct materials. An intense development program began to understand and at least control the level of void swelling. Theories for the rate of void nucleation in the presence of super saturations of vacancies and self interstitials were developed early on, then expanded to account for the effect of mobile helium atoms. The direct effects of displacement cascades in either destroying developing embryos or providing the nuclei for void nucleation remained a mystery until recently. This paper presents the theory for void nucleation in the presence of void embryo destruction and injection. Void nucleation is described by a linear, first degree, second order ordinary differential equation with constant coefficients. This equation is solved analytically, but is evaluated separately for embryo destruction or injection. To do both simultaneously would be inelegant and tend to obscure the physics of the various processes. Gaussian and Dirac source functions, which would serve to inject a monodisperse system of embryos, are found to be non-integrable. Trigonometric functions are found to be reasonable substitutes. Conditions are delineated under which embryo injection is likely to give a perceptible increase in the void nucleation rate. Our calculations suggest that embryos from displacement cascades may significantly promote void nucleation under fast reactor and fusion reactor irradiation conditions. Embryo destruction is found to be important if the destruction rate of embryos is the order of or greater than the rate of single vacancy capture. Embryo destruction has the greatest retarding effect for large critical nuclei and low activation barriers for nucleation. The reasons for these results are explainable in terms of incubation times for nucleus formation