A detailed analysis of generation and potential recrystallization of amorphous zones resulting from ion irradiation of solid materials is given. The criterion for generation of such spikes is considered to be that sufficient energy is deposited locally to induce melting. Subsequently the heated zone is considered to cool via unperturbed thermal diffusion from an initial temperature distribution of Gaussian form, although the expected ellipsoidal geometry is idealized to spherical symmetry for analytical convenience. Recrystallization is considered to occur via a thermally activated process during spike quenching and criteria for crystallization at both zone boundaries and centers are deduced. These criteria are shown to correspond well to earlier analyses, but other parameters such as substrate temperature and energy deposition density are found to be of considerable importance. Suggestions for more accurate modeling are also examined.