The nearest neighbours approximation and the analysis of the melting point of 2D- and 3D-Yukawa systems

We present the numerical and theoretical analysis of melting conditions of crystal lattices in two- and three-dimensional Yukawa systems of charged grains. The values of the coupling parameter of the systems under study on the melting line are presented depending on the screening parameter of the grains. The calculations of the characteristic frequencies and the energies of the lattices were done with the help of the nearest neighbours approximation, and oscillation amplitudes of the grains in the lattice nodes were normalized by the theoretical values of the Lindemann parameters on the melting lines of the structures under study^1-3. We considered the classical approach of harmonic oscillations, as well as the nonlinear (anharmonic) effects of the pair interaction forces and the concentration of the interacting grains on the positions of the equilibrium phase boundary curves. Unlike the existing empirical and half-empirical approximations for the boundary curves, the model proposed in the present work has a simple theoretical explanation and allows to correctly predict the melting conditions for the systems of particles with various isotropic interaction potentials. The obtained results were compared to the existing theoretical and numerical data.