A Relationship between Prefactor and Activation Energy for Diffusion

Very often a relationship is observed between activation energies, Q, of diffusion and the corresponding prefactors, D0. Contrary to the Zener-Wert relation, where activation energy and prefactor of different species migrating in the same matrix are compared, one species diffusing in a matrix with different defects or slightly varying composition is considered. It is shown that a linear relationship between In D0 and Q very often exists due to the special form of the Arrhenius equation. The slope of the corresponding graph is close to 1/kTa, where Ta is the average temperature of the range covered by the experiments. Experimental results are compiled and compared with this prediction.