Shear modulus of fluids and solids

The shear modulus tensor, whose components are Voigt elastic moduli, is expressed as an N-particle average. The Born-Green and the fluctuation contributions are identified and, where possible, also expressed in terms of integrals over the pair-correlation function. Symmetry considerations are invoked for systems of spherical particles in both isotropic and cubic states. Results from molecular dynamics simulations are presented for particles with a purely repulsive Lennard-Jones interaction. Shear and bulk moduli are displayed graphically as functions of the density for fluid and cubic crystalline states. The shear modulus proves to be a good indicator for the fluid-solid phase transition.