  The lattice fluid model of the system with short range and long range Coulomb
interactions is suggested. In the framework of the collective variables method,
the screening of the Coulomb interactions in the bulk is considered. It is
shown that the Debye length includes additional concentration dependence
inversely proportional to the square root of the mean concentration of vacant
sites like what is known at the plane boundary. The Coulomb interaction
contribution to the free energy of the system is calculated in the approach
close to the mean spherical approximation and is given in an analytical form.
The influence of the variation of the crystal field near the system boundary on
the structure and characteristics of the electric double layer is investigated.
As compared to the system with equal crystal potentials at the lattice sites
throughout the system the pronounced difference for the electric capacitance
appears at low absolute values of the surface potential and it is more
pronounced for negative electric potentials. The capacitance diverges as the
potential values at which the electric field tends to zero and attains negative
values in regions of the surface potentials depending on their polarity and
values of the surface crystal potential. Negative values of the capacitance may
indicate the thermodynamic instability of the system that can result from
neglecting the short range interaction contribution.
