Melting in two dimensions: Determination of phase transition boundaries

Abstract

Molecular dynamics computations are reported for systems of soft repulsive discs of the inverse twelfth-power potential and for Lennard-Jones atoms in two dimensions. In the case of soft discs the melting transition is obtained by assuming a first-order transition and subsequent application of Ross’s melting rule. The assumption is vindicated by additional computations for the 2-D L-J model in which the melting and freezing parameters are determined by direct MD computation along the isotherm T=0.8 ε/k and the isochore ρr20=1.0079. The results reaffirm the presence of first-order phase boundaries and refute the postulated existence of a ’’hexatic mesophase’’ bounded by second-order transitions. These two-dimensional models are seen to have much smaller discontinuities in density and entropy than their three-dimensional counterparts and to exhibit more pronounced premelting increases in the heat capacity. This is interpreted to be a consequence of the proximity of the mechanical instability points to the first-order thermodynamic melting transition for these two-dimensional systems. Previously reported lambdalike behavior of the heat capacity through the melting transition of the 2-D one-component plasma is consistent with this interpretation for an irreversible isochoric traversal of a two-phase region and hence suggests an ordinary, albeit weaker, first-order melting transition in this system also.