Theory of Displacement Cascades in Compounds

The theory undertakes the determination, for a simple model, of functions $N_{\mathrm{ik}}\mathrm{}\left(T\right)\mathrm{}$ which represent the numbers of atoms of various kinds displaced when a primary atom receives an energy $T$. Assuming isotropic collisions involving pairs of free atoms, differential equations are formulated which contain concentrations, collision cross sections and mass ratios as parameters. Binding of the atoms is introduced through initial conditions which define threshold energies for displacement. Assuming a single threshold, linear equations for Laplace transforms are obtained and used to study the high-energy behavior of the functions. The effect of separate thresholds for the various kinds of atoms is examined for the case of equal masses.