COMPUTATION OF THE FREE-ENERGY FOR ALTERNATIVE CRYSTAL-STRUCTURES OF HARD-SPHERES

A single-occupancy cell (SO-cell) method has been applied to calculate the free energies of different crystal structures of hard spheres via molecular dynamics (MD). The objectives are (i) to examine the nature of the phase transition in the SO-cell model, (ii) to determine the t hermodynamic stability of the bcc crystal phase relative to the fee an d the free fluid, (iii) to establish the relative stability of the fee and hcp crystal structures, and (iv) to investigate hybrid structures of the unit stacking type '-ABCAB-'. MD computations are reported for the pressures of the SO-cell models of all these structures. The SO-c ell phase transition for fee and hcp is first-order, with ordered and disordered phases coexisting at the same p, V and T. The transition is much weaker for bcc. The metastable fluid-bce phase transition parame ters are determined; the bce phase is everywhere unstable compared wit h fcc. The bcc solid melts to the metastable fluid at a pressure of 14 .5 k(B) T/sigma(3), and has a melting volume of 0.95 N sigma(3), i.e., very close to that of the fee crystal. A more precise numerical estim ate for the fcc-hcp entropy difference is reported. At close packing t he fee phase is the more stable by 0.0026(1) Nk(B)T; the Gibbs and Hel moltz energy differences are the same at close packing. For expanded v olumes close to melting, the hcp crystal has a slightly higher pressur e than the fee; the enthalpy difference at melting is 0.0030(5) Nk(B)T . Consequently the Gibbs energy difference approaching melting becomes less than the uncertainty in the computations, i.e. < 0.001 Nk(B)T.