A thermodynamically self-consistent statistical theory of the crystalline state

The approach in equilibrium statistical mechanics proposed by the author in a previous publication is extended to studies of the crystalline state. In the classical case considered in this paper, the approach leads to the equilibrium BBGKY hierarchy. The distinctive feature of the approach in this case lies in construction of thermodynamics, which is made consistently with solutions of the hierarchy relevant to crystals. A special form of the pair correlation function is assumed which greatly simplifies the matter. Two methods for solving the equations obtained are considered too. The first of these is based on expansion in powers of the temperature, and the second one uses bifurcation theory. Results given by the bifurcation method are compared with the Landau theory of phase transitions. In addition, the stability of a liquid with respect to formation of a periodic structure is considered from the viewpoint of a kinetic theory.