One and two component hard sphere models for the structure of metallic glasses an integral equation approach

Abstract

The pair correlation function g(r) and the structure factor S(k) for a one com ponent system of hard spheres at a high density near random close packing are calculated using the analytic solutions of the generalized mean spherical approxima tion and the Percus-Yevick (PY) equation. These integral equation methods have proven to be very accurate at lower densities in the stable fluid phase. Both approaches give a g(r) with many features in good agreement with that obtained by the methods of Bennett (1972) and others, including the peak positions and asymmetric shape of the second peak. However, the theory for the one com ponent system gives a shoulder rather than a split in the second peak. The partial pair correlation functions g_ij (r) and partial structure factors S _ij(k) are then computed using the analytic solution of the PY equation for the experi mentally more relevant case of a dense binary mixture of hard spheres of differing diameters. The second peak in the partial pair correlation functions is split for a wide range of the ratio of the diameters and the relative heights of the members of the split peak vary as a function of this ratio and the composition of the mixture. These ‘size-difference’ correlations can be easily understood from simple geometric considerations and should play an important role in determining the structure of real binary mixtures. Finally, the qualitative changes in the hard sphere g(r) and S(k) that occur when considering a more realistic ‘soft core’ potential are briefly discussed.