Molecular-statistical description of the specific heat of thermal-vacancy crystals. 1. statistical model of allowance for the contribution of the vacancy subsystem to the lattice specific heat of crystals

Abstract

A simple statistical model of a condensed system with pair particle interaction, which is described by the Lennard-Jones potential, has been proposed. Under the assumption that the probability of filling a microcell pair is equal to the product of the probabilities of filling single cells, a variational problem on minimization of free energy by the model’s internal parameter has been formulated. An analytical expression for the addition to the vibrational specific heat of a molecular vacancy crystal has been obtained. A refined model in which the correlation in filling microcell pairs with pores is allowed for has been considered; a refined expression for the addition to the vibrational specific heat, which contains the corresponding small corrections, has been obtained.