Influence of Mass Ratio on Displacement Cascades in Diatomic Solids

The influence of mass ratio on the displacement cascade initiated when an atom of a solid of type AB receives considerable energy is investigated for a simple model. Isotropic scattering, equal probabilities for collisions of various pairs of atoms, and a single threshold energy for displacement are assumed. The formulation of the problem is like that of Harris, but threshold energy is introduced in the manner of Kinchin and Pease. Comparatively simple equations are obtained and solutions which are always approximately correct have been found by the Laplace transform method.The total number of displacements does not vary greatly with mass ratio. When the mass of the heavy atom is more than about ten times that of the light, the difference between the numbers of A atoms and B atoms displaced by a primary A atom increases as a fractional power of the primary energy. For smaller mass ratios, the difference approaches a constant. To illustrate some implications of the results, the relative numbers of A and B atoms displaced by incident monoenergetic protons are considered.