Application of the Arrhenius equation to solid state kinetics: can this be justified?

Application of the Arrhenius equation to the kinetics of solid state reactions has been criticised on several grounds. One of the main theoretical objections has been that the energy distribution amongst the immobilised constituents of a crystalline reactant is not represented by the Maxwell–Boltzmann equation. The detailed band structure of a solid may, however, include interface energy levels (analogous to impurity levels in semiconductors) that participate in the crucial bond redistribution step. Occupancy of such levels would be determined by energy distribution functions based on Fermi–Dirac statistics for electrons, and Bose–Einstein statistics for phonons. For the highest energies, necessary for reaction, both distributions approximate to an exponential energy term, thereby countering the above objection to the application of the Arrhenius equation to reactions of solids. The existence of such interface levels, with a limited range of energies, would also allow for the variation of apparent activation energy with extent of reaction, and also with temperature, reported for many complex solid state reactions.