Model for vacancy-loop nucleation in displacement cascades

A model is proposed for the nucleation of collapsed vacancy clusters in irradiated metals, based on the principle that a vacancy loop may be nucleated in a cascade which has melted and recrystallized. The equation of thermal conduction is solved using the discretization method and initial temperature and vacancy distributions given by the m a r l o w e code. The model simulates the processes of heat propagation, local melting, absorption and release of latent heat, and the redistribution of the density within the melt. Under the influence of the temperature gradient, the concentration of vacancies in the depleted zone increases. Simulation of hundreds of cascades gives the distribution of zones as a function of vacancy concentration and number of vacancies in them, and it is assumed that critical values ${\mathit{C}}^{\mathrm{cr}}$ and ${\mathit{N}}_{\mathit{v}}^{\mathrm{cr}}$ have to be achieved to produce a visible vacancy loop. However, if the concentration exceeds a value ${\mathit{C}}_{\mathit{v}}^{\mathrm{am}}$ under sufficiently fast cooling, for example under strong electron-phonon coupling (EPC), the melted zone cannot crystallize completely and solidifies instead to a semiamorphous core. This prevents collapse to a vacancy loop. The model has been used to calculate the yield and mean size of vacancy loops in ion-irradiated Cu, Ni, and Cu-Ge and Cu-Ni alloys. Physically reasonable values of ${\mathit{C}}^{\mathrm{cr}}$, ${\mathit{N}}^{\mathrm{cr}}$, and ${\mathit{C}}_{\mathit{v}}^{\mathrm{am}}$ have been obtained to give good agreement with experimental values of yield and size. Furthermore, the trends with alloy content can be explained, and it is found that EPC can have a strong influence on loop yield.