Elastic properties of the degenerate crystalline phase of two-dimensional hard dimers

Abstract

Hard homonuclear dimers, each consisting of two identical and tangent hard disks, exhibit a thermodynamically stable, aperiodic solid phase, known as a degenerate crystal. The elastic properties of this phase are determined by the box fluctuation Monte Carlo method in the NpT ensemble. The computed elastic constants are well described by the free volume approximation and the coefficients of the leading singularities are estimated in the close packing limit. Three mechanisms decreasing Poisson’s ratio are indicated: one is based on increasing the pressure to temperature ratio, another comes from the constrains imposed on the disks forming a dimer, yet another, working in the close packing limit, arises from molecular motions. It is also shown that Poisson’s ratio increases with increasing concentration of vacancies.