CORRELATION-FUNCTIONS IN CLASSICAL SOLIDS

By invoking thermodynamic potentials as generating functions for hiera rchies of correlation functions, we develop a description of solids wr itten in the same statistical language used to describe inhomogeneous fluids. Important constraints then follow from consideration of the sy mmetries of the crystalline solid. Considerable insight into the two-p article density is obtained by appealing to the harmonic model of the solid, which motivates the idea of parametrizing the correlation funct ions using parameters unique tb each lattice site. By paralleling the derivation of the Ornstein-Zernike equation we are led to an equivalen t relation for the solid between the parameters of the direct correlat ion function and the parameters of the two-particle density. By simila rly paralleling the derivation of Percus identity, we develop an equat ion for the parametrization of correlation functions of a solid analog ous to the hypernetted-chain equation of inhomogeneous fluids. The har monic model of the solid thus emerges from the appropriate limit of th e hypernetted-chain equation for an extremely inhomogeneous fluid.