Developing New Theoretical Models of the Formation of Atomic Collision Cascades and Subcascades in Irradiated Solids

摘要

A new theoretical model is developed for the investigation of atomic collision cascades and subcascades in irradiated solids consisting of atoms of a single type. The model is based on an analytical description of the elastic collisions between moving atoms knocked out of the crystal lattice sites and the immobile atoms of the lattice. The description is based on the linear kinetic Boltzmann equation describing the retardation of primary recoil atoms (PRAs) in irradiated solids. The laws of conservation for the total number and the kinetic energy of moving atoms, which follow from the kinetic Boltzmann equation, are analyzed using the proposed model. An analytical solution is obtained for the stationary kinetic Boltzmann equation, which describes the retardation of PRAs for a given source responsible for their production. A kinetic equation for the moving atoms and the corresponding laws of conservation are also analyzed with allowance for the binding energy of atoms at the crystal lattice sites. A criterion for determining the threshold energy of subcascade formation in irradiated solids is formulated. Based on this criterion, the threshold energy of subcascade formation is calculated using the Thomas-Fermi potential. Formulas are presented for determining the mean size and number of subcascades formed in a solid as functions of the PRA energy.