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), whereQis the activation energy for the process andT(r,t), is the spike temperature at positionrand timet.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.