On the density-wave theory of classical Wigner crystallisation

Abstract

The density-wave theory of freezing developed by Ramakrishnan and Yussouff (1979) for classical liquids, is analysed in detail in relation to the crystallisation of a classical plasma on a neutralising background into a body-centered cubic lattice. It is first pointed out that the equilibrium between solid and liquid at coexistence is maintained in this model system by interfacial dipole layers. The microscopic theory is then re-examined in order to establish full contact with the thermodynamic treatment of the phase transition. Microscopic calculations of the coexistence point as a function of the Coulomb coupling strength and alternative theories of structure require a knowledge of the liquid structure are examined comparatively in the present context against computer simulation data. Calculations are presented for the phase transition at constant density; these demonstrate the quantitatively important role of couplings between some of the order parameters of the transition. A lower limit is obtained for the magnitude of the Coulomb coupling strength at coexistence; this is not far from the best available estimate from computer simulation data on the Helmholtz free energies of the two phases.