Molecular-Statistical Description of Nonuniformly Deformed Specimens. 2. Calculation of the Distribution Functions of Molecules and Vacancies in a One-Dimensional Uniformly Deformed Statistical Extension–Compression Model

Within the framework of a two-level molecular-statistical study of the thermodynamic and mechanical properties of condensed systems, a one-dimensional statistical model of uniform extension and compression of a crystal with vacancies has been developed. The micro- and macrostructures of the model are described using correlative distribution functions of real molecules (particles of the r (real) type) and vacancies, account of which is carried out using a subsystem of fictitious particles (quasiparticles of the f (fictitious) type) that do not interact with the molecules and with each other. A nonlinear integral equation for the average-force potentials which determine the single- and two-particle correlative functions of the two-component statistical system of real and fictitious particles has been obtained. The analytical solution of the integral equation has been found within the framework of a modified approach due to the vacancies of the Gauss approximation.