Thermal spikes and activated processes

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Abstract
In the thermal spike model of the interaction of energetic radiation with matter, it is assumed that energy is deposited instantaneously in a very small region, producing a localized increase of temperature which spreads and dissipates according to the laws of classical heat conduction in a continuum. If an activated process (e.g. the migration of atoms, evaporation of atoms from a surface, etc.) is energized by the spike, the number of elementary steps caused by one spike can be expressed as an integral over space and time of the exponential of − Q/T(r, t), where Q is the activation energy for the process and T(r, t), is the spike temperature at position r and time t. In the past quantitative results have been obtained from this model only with the aid of further approximations and the assumption that thermal conductivity and heat capacity are independent of temperature. In this paper it is shown that, with zero starting temperature, the model can be evaluated rigorously for two kinds of spikes, spherical and cylindrical, and while allowing the material to have heat capacity C and thermal conductivity k which are either constant or temperature-dependent according to the forms C = CoTn −1 and K = KoTn −1, where C0 and K0 are constants and n is any positive number. The desorption coefficient of a surface is discussed as an application.

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