Bulk and surface thermodynamics of stoichiometric ionic crystals consisting of three ionic species

Abstract

The bulk and surface thermodynamics of stoichiometric ionic crystals consisting of three ionic species are developed. In contrast with the case of crystals having variable stoichiometry, chemical potentials of two electrically neutral components, λ₁ and λ₃, cannot be defined in the usual way as derivatives of the Gibbs free energy per ion with respect to composition because the composition is invariant. They may, however, be taken as equal to λ₁ and λ₃ in the bulk solution at equilibrium with the crystal. If a given crystal separates two bulk solutions for which λ₁ and λ₃ differ, the system is not at equilibrium with respect to diffusion and the methods of non-equilibrium thermodynamics can be applied. Such an analysis demonstrates the existence of a diffusion potential in the crystal. It also shows that the chemical potentials are functions of T, p and λ₁, and that only at constant λ₁ does the inner potential conform to the classical Nernst equation. Expressions are derived which enable reduced transport numbers in the crystal phase to be found from suitable e.m.f. measurements. Application of the Gibbs adsorption equation shows that the solution/crystal interfacial tension will exhibit a maximum when the adsorptions of both potential-determining species are zero and also that for a given λ₁, σ has its maximum value at the corresponding zero point of charge. When the crystal is an insulator and can support an applied field without any measurable transport effects taking place, it appears that a similar analysis to the case of a conducting crystal can apply only if the adsorptions of all non-potential-determining species are independent of the field strength in the bulk crystal.