The Thermodynamic Factors for the Cation Diffusion in a P-Type Oxide AO Doped with a Monovalent Impurity

Summary

The thermodynamic factors for the cation diffusion in a p-type semiconducting oxide of a divalent metal containing a monovalent impurity are evaluated by means of thermodynamic considerations, assuming that the defect structure of the base oxide is known. It is shown that these parameters are not only functions of the oxygen activity and of the dopant concentration, but depend also strongly on the ratio between the gradients of these two variables. Limiting expressions corresponding to the presence of only one gradient are obtained and evaluated approximately for very small or large impurity concentrations. It is found in particular that under constant oxygen activity the two thermodynamic factors are always close to one but change in opposite directions with the impurity concentration. On the contrary, under constant impurity concentration the thermodynamic factors are both very large and decrease as the oxygen activity increases. A general relationship between the two thermodynamic factors is obtained by means of the Gibbs-Duhem equation applied to the relevant ternary system. Finally, the theoretical equations are used to calculate the thermodynamic factors in NiO doped with a monovalent impurity at 1000°C, using a detailed model to represent its defect structure.