Simultaneous statistical description of a crystal and fluid

In previous publications by the author the crystalline state was studied with the help of statistical methods based upon utilization of distribution functions. The approximation used for a crystal was not, however, fully adequate for fluids, which did not permit one, in particular, to construct a phase diagram with a triple and critical point. The present paper begins with analysis of the pair correlation function in crystals in order to find an approximation adequate for a crystal as well as fluid. The relevant thermodynamics is developed. It is shown that the fluid can be described, for example, by the hypernetted-chain equation or by the van der Waals or Dieterici equations of state, and such a description will be compatible with the proposed description of the crystal. A phase diagram is constructed which exhibits the region of the crystalline state together with the triple and critical points.