The thermodynamic factors for cation diffusion in AO,p-type oxides doped with a trivalent impurity

The thermodynamic factors for cation diffusion in p-type semiconducting oxides of the formula AO doped with a trivalent impurity are evaluated, assuming a known structure of defects of the base oxide. It is shown that these parameters are not only functions of the oxygen activity and of the dopant concentration, but also strongly depend on the ratio between the gradients of these two variables. Limiting expressions corresponding to the presence of only one of these gradients are derived and evaluated by means of suitable approximations under conditions of very small or very large impurity concentrations. A general relationship between the two thermodynamic factors is obtained by means of the Gibbs-Duhem equation as applied to the relevant ternary system. Finally, the thermodynamic factors for cation diffusion are evaluated numerically for the case of NiO doped with a trivalent impurity at 1000°C, using a convenient detailed model to represent its defect structure.