Multicomponent diffusion in a sublattice of an ionic crystal

We report a phenomenological description of multicomponent diffusion in ionic crystals with no restriction on the number and electric charge of species. The diffusion of ions is assumed to occur via a vacancy mechanism in one sublattice while the species of the other sublattices are immobile. Non-equilibrium thermodynamics is used to derive the entropy production and flux expressions during diffusion. Two relations on the fluxes, the zero net ion flux and the zero net electric current, are derived from the conservation of sites and electric charge. It is assumed that the internal electric field and chemical potential gradient of vacancies that rise from the movement of the species are such that they ensure the fulfillment of these two relations. General and simplified generalized Fick's laws are derived in the two cases of isovalent and non-isovalent diffusing ions. It is shown that neglecting the chemical potential gradient of vacancies implies a relation between the phenomenological coefficients when the ions are not isovalent. The consequence is that the off-diagonal phenomenological coefficients cannot be generally set to zero and particularly that the use of Nernst-Planck equation is not appropriate for describing the diffusion of non-isovalent ions in a sublattice of an ionic crystal.