The free energy of hard dimer solids revisited

Free energies of a few crystalline structures of hard, homonuclear dimers have been calculated using the Einstein-crystal method for various sample sizes and extrapolated to the thermodynamic limit. In contrast to the two-dimensional case, large free energy differences between some structures have been found. This can explain the large difference in free energy between a typical aperiodic solid structure representing the dimers' thermodynamically stable solid phase, known as the degenerate crystal (DC), and some crystalline structures of the dimers studied earlier. The obtained results indicate that structures with orthogonally directed neighboring dimers have much higher free energy than those with parallel neighboring dimers. It is also shown that, in the thermodynamic limit, the free energy difference per particle between structures built of hexagonal layers of parallel dimers differing only in arrangement of atoms at close packing in the fcc and hcp lattice is the same as that between hard sphere fcc and hcp crystals (within experimental error).