The relationship between measured activation enthalpy and pre-exponential factor: Rate processes in ionic crystals in the intrinsic-extrinsic region

In measurement of activated processes, such as diffusion, ionic conduction, creep and sintering, it is common to use Arrhenius plots of the measured quantity, A(T), to give the logarithm of the pre-exponential factor, logA₀, and the experimental activation enthalpy, h. It is shown that, in the cases of conduction and diffusion in ionic crystals, well-defined relationships can exist between the values of logA₀, logA and h, measured on similar samples with differing doping or impurity levels. These relationships are derived for ionic crystals showing either Frenkel, Schottky, or interstitial disorder. In the resulting plots of logA₀ versus h, approximately linear regions are shown to exist, similar to those described by the compensation law for glasses and by the Meyer-Neldel rule for semiconductors.