Three-stage melting in two dimensions initiated by the formation of grain boundaries: A molecular-dynamics study.

Constant-pressure and constant-volume isothermal molecular dynamics are used to study the melting of two-dimensional piecewise linear-force-law lattices. Constant-pressure simulation shows that melting is first order and is initiated by the formation of grain-boundary clusters as predicted by Chui; however, most of the latent heat and free volume of transition is only released after dislocations and disclinations unbind. This implies that the unbinding transitions, predicted to be continuous by Kosterlitz and co-workers, become discontinuous by virtue of grain-boundary interactions with free dislocations and free disclinations. Constant-volume simulations are used to extract the dislocation-unbinding temperature ${T}_{0}$ from elasticity calculations. For low pressure the observed melting point is 3.5\ifmmode\pm\else\textpm\fi{}0.9 % lower than ${T}_{0}$ which corresponds to the large dislocation-core energy limit of the Chui theory. The constant-volume method is, however, subject to equilibrium-phase coexistence which mimics a single-phase continuous transition; where possible, therefore, constant-pressure methods should be used near phase transitions.