Relationships between chemical and tracer diffusion coefficients in strongly ionic crystals

In this paper, we make extensive use of various sum-rules relating the phenomenological transport coefficients in randomly mixed systems in order to address cation chemical interdiffusion and tracer diffusion in strongly ionic crystals such as alkali and silver halides and alkaline earth fluorides, oxides and silicates showing Schottky disorder. We derive general expressions for the intrinsic and inter-diffusivities for the case of unbound vacancies. Next, we derive a general expression relating the chemical interdiffusivity and the cation and anion tracer diffusivities. This expression reduces to the well-known Darken-Manning and Nernst-Planck equations according to the relative magnitude of the anion mobility. This analysis is repeated for the vacancy-pair mechanism. It is shown that the resulting expressions have exactly the same formal structure as for the unbound vacancies case, but the internal structure of the transport quantities differs because of the different correlation behaviour of the vacancy-pair mechanism compared with that of unbound vacancies.