Size-Dependent Properties of a Two-Dimensional Solid near Melting

Abstract

The behavior of a two-dimensional solid near melting is analyzed by the molecular-dynamics technique. Two size-dependent properties are determined: the mean amplitude of vibration ($\theta$) from the lattice positions and the elasticity (shear modulus $\mu$), which vary logarithmically with system size. When the size is increased to give $\theta \approx 0.18$ the particles begin to diffuse and the elasticity is close to its predicted melting value. The result demonstrates that previous computer models have been too small to simulate bulk solid near melting.