Hydrodynamic properties of the perfect hard-sphere crystal: Microscopic computations with Helfand moments

Abstract

Within the framework of the local-equilibrium approach, the equilibrium and nonequilibrium properties relevant to the hydrodynamics of the perfect hard-sphere crystal are obtained with molecular dynamics simulations using the Helfand moments associated with momentum and energy transports. Since this crystal is face-centered cubic, the hydrodynamic properties we consider are the hydrostatic pressure, the isothermal bulk modulus, the specific heat capacities and their ratio, the three isothermal elastic constants $(C_{11}^T,C_{12}^T,C_{44}^T)$, the heat conductivity, and the three viscosities $({\eta }_{11},{\eta }_{12},{\eta }_{44})$ (in Voigt's notations). These properties are computed as a function of the particle density. The pressure and the transport coefficients diverge near the close-packing density, as the collision frequency per particle does.