Hard discs with embedded three dimensional quadrupoles

Abstract

A survey of the structural and thermodynamic behaviour of hard discs with embedded three dimensional quadrupoles of linear symmetry has been made using Monte Carlo methods. The results for dilute samples at high temperatures (small quadrupole moments) are consistent with thermodynamic perturbation theory. Those for higher density or lower temperatures (larger quadrupole moments) indicate the existence of two solid phases, one a high density hexagonal solid and the other a lower density square structure. No convincing evidence was found for the existence of a distinct liquid phase, but the data are not sufficiently detailed to provide a reliable determination of the phase diagram. Structural evidence has been found for the coexistence of the two solids, and the interface between the two structures seems to lead to relatively little disruption in either phase, at least for small ‘domain’ sizes. The stability of the square structure is easily understood in terms of the large quadrupole energy it achieves, in spite of being about 15 per cent less dense than the hexagonal solid, which has approximately the same energy.