Thermodynamic pressures for hard spheres and closed-virial equation-of-state

Hard-sphere molecular dynamics (MD) simulation results, with six-figure accuracy in the thermodynamic equilibrium pressure, are reported and used to test a closed-virial equation-of-state. This latest equation, with no adjustable parameters except known virial coefficients, is comparable in accuracy both to Padé approximants, and to numerical parameterizations of MD data. There is no evidence of nonconvergence at stable fluid densities. The virial pressure begins to deviate significantly from the thermodynamic fluid pressure at or near the freezing density, suggesting that the passage from stable fluid to metastable fluid is associated with a higher-order phase transition; an observation consistent with some previous experimental results. Revised parameters for the crystal equation-of-state [R. J. Speedy, J. Phys.: Condens. Matter 10, 4387 (1998)] are also reported.