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Elastic constants of the hard-sphere glass: a density functional approach

The free energy and the static elastic constants of a hard-sphere glass are calculated using density functional theory. More specifically, Bennett's glass model is used where the packing fraction of random closed packing, eta RCP, is taken as an adjustable parameter. As regards the density functional, the modified weighted density approximation (MWDA) is employed. The results are compared with the FCC hard-sphere crystal. It is found that the free energy of the glass is always higher than the crystal free energy; however, for high densities and high eta RCP, it is lower than the free energy of a fluid resulting in a first-order liquid-to-glass phase transition. For the same temperature and densities, the bulk modulus in the glass is higher than that in the FCC crystal. For high eta RCP and high densities, the shear modulus is smaller than that of a polycrystalline sample.