Crystals of cubic symmetry in statistical theory

General results obtained earlier by the author for the crystalline state with the help of statistical methods based upon utilization of distribution functions are applied to investigate the properties of cubic-symmetry crystals. An approximation relevant to the potential of interaction between particles is used, which enables one to reduce an infinite set of equations for Fourier coefficients of the crystal density to one equation. The form of such an equation depends upon the crystal symmetry and for the purpose of establishing this form the symmetry of Fourier series for all 36 cubic space groups is analysed. The resulting equation and properties of a crystal that follow from it are investigated using four space groups O-h(9), O-8, O-h(5), O-h(7) as an example. In the case of space group O-h(9) the temperature-pressure phase diagram is constructed, its peculiarities are found out, the temperature dependence of diverse characteristics of the crystal is calculated. It is shown also how statistical theory can treat second-order phase transitions. Results given by statistical theory are in agreement with the Landau phenomenological theory of phase transitions. (C) 2004 Elsevier B.V. All rights reserved.