Transport across boundary layers in ionic crystals .1. General formalism and conception

In a sequence of papers we will systematically address the problem of mass and charge transport through boundaries from the standpoint of irreversible thermodynamics and kinetics. Special emphasis is put on the transport through space charge regions. As a model material we consider a binary crystal (MX(1 + delta)) exhibiting ionic and/or electronic conduction and thus allowing for changes in the nonstoichiometry as well. A typical situation is a mixed conductor sandwiched between two partially reversible electrodes. The boundaries are assumed to be morphologically stable. Driving forces considered are differences in chemical and/or electrical potential. They are assumed to be sufficiently small to allow for a linear response treatment. No reference to ad hoc assumptions such as the local electroneutrality condition is made. We also allow for compositional changes in the material. The continuum approach will be presented in the framework of linear irreversible thermodynamics. The introduction of virtual electric fields significantly facilitates the formalism with respect to electrochemical relationships, boundary conditions and analytical treatment. The instationary state will be formally tackled in Fourier space. A conceptual discretisation is generally of advantage - in particular in cases in which the continuum problem can only be solved numerically - since it takes account of the atomistic situation in a kinetic framework. This paper sets out the fundamental equations which will be applied to specific examples. One application already reveals quantitatively the important result that space charge regions necessarily appear in weakly disordered materials during a chemical diffusion even if one starts from a space - charge free initial situation. The steady state concentration profiles are derived.