Microscopic Model of Intergrain Boundary Junction

The statistical mechanics differential-difference equations for the ions concentration distribution that account for the diffusion, electrical conductivity and Poisson contributions are derived. They represent differential-difference analogues of the phenomenological continuity equations for the ions. Spatial inhomogeneities (grain interiors, grain boundaries, intergrain regions, etc.) can easily be taken into account by proper adjusting the system material parameters (diffusion coefficients or particle transition rates, electric conductivities, thermodynamic factors or chemical capacitances). The solution of the equations allows investigating impedance spectra of inhomogeneous systems, e. g. electro-conducting ceramics. The results can be used for interpretation of experimental impedance spectra and evaluation of the medium transport characteristics. A simple example of the intergrain boundary junction is considered.