Order in two-dimensional binary random arrays

Abstract

Translational and orientational order in randomly packed planar arrays of hard spheres of two different sizes is investigated. For an appropriate size ratio, we find a dilute phase without translational order, but with very-long-range correlations in the orientations of local hexagonal axes. The phase appears to be a quenched analogue of the equilibrium hexatic phase, which appears in two-dimensional melting theories. The peculiar properties of this hexatic glass are attributed to the tendency of a dilute array of large spheres imbedded in a medium of smaller spheres to trap dislocations. Significant orientational correlations also appear in more concentrated mixtures, giving rise to a six-fold modulation of the structure function in large, but finite, samples.