Energy distributions of recoil atoms in collision cascades in composite media are studied analytically. The pertinent integral transport equations are reduced to a computationally much simpler system of differential equations. This is possible for arbitrary particle interaction potentials. The accuracy of this transformation is demonstrated by comparison with Monte Carlo computer simulation. As a case study, energy partitioning among the target species in a collision cascade in the (hypothetical) binary compound HfxCl-x is investigated. We find that the number of recoils produced is understoichiometric for both species. On the other hand, the particle flux of the lighter species is overstoichiometric, while the flux of the heavy species shows only small deviations from stoichiometry. The energy is deposited preferentially in low-energy recoil motion of the lighter species. Reference is made to earlier theoretical treatments of the problem for less-general-interaction cross sections. The differences found are mainly quantitative, and their origin is traced back partly to the differences in the physical input, and partly to the restricted validity of the previous methods. Energy spectra of particles sputtered from a compound are studied, concentrating on an experiment on HfC sputtering. We find, in agreement with the experiment, that Hf and C species show similar slopes. We predict that energy spectra from diluted compounds will show larger differences in their slopes.
