  A solid ionic conductor with cation conductivity in the interelectrode region
is studied. Due to their large size, the anions are considered fixed and form a
homogeneous neutralizing electric background. The model can be used to describe
properties of ceramic conductors. For a statistical mechanical description of
such systems, which are characterized by short-range Van der Waals interactions
and long-range Coulomb interactions, an approach combining the collective
variables method and the method of mean cell potentials is used. This formalism
was applied in our previous work [Bokun G., Kravtsiv I., Holovko M., Vikhrenko
V., Di Caprio D., Condens. Matter Phys., 2019, 29, 3351] to a homogeneous state
and in the present work is extended to an inhomogeneous case induced by an
external electric field. As a result, mean cell potentials become functionals
of the density field and can be described by a closed system of integral
equations. We investigate the solution of this problem in the lattice
approximation and study charge and electric field distributions in the
interelectrode region as functions of plate electrode charges. The differential
electric capacitance is subsequently calculated and discussed.
