Bond orientational order in liquids and amorphous solids

Abstract

Abstract Recent theoretical work1) on the Kosterlitz-Thouless2) model of dislocation-mediated melting in two dimensions suggests the existence of a new “hexatic” phase of matter, intermediate between a solid and a liquid. Hexatic liquids display persistent correlations in the “bonds” joining near neighbor atoms. Although these unusual materials have some properties in common with a liquid crystal, there need not be an anisotropy in the constituent particles. Although computer simulations have produced conflicting evidence for an equilibrium hexatic phase3), the discovery of a “stacked hexatic” phase in bulk smectic liquid crystals has been reported recently4). It is interesting to consider bond orientational order in other contexts. Translational and orientational order can be studied, for example, in randomly packed planar array of hard spheres with two different sizes5). For an appropriate size ratio, and a dilute concentration of large spheres, one finds a phase without translational order, but with very long range correlations in the orientations of local hexagonal axes. The phase appears to be quenched analogue of the equilibrium hexatic phase. 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. Bond orientational order can assume a variety of forms in bulk materials. Crystals disordered by an equilibrium concentration of unbound dislocation loops display bond orientational order with a cubic symmetry6). Another possibility is orientational order with an “icosahedral” symmetry. It is well known that an icosahedral clustering of twelve atoms about a central sphere is energetically preferable to crystalline packings for most simple pair potentials7). These questions have been studied recently via computer simulations of 864 particles interacting through a Lennard-Jones pair potential8). Long-range orientational fluctuations appear upon supercooling about ten percent below the equilibrium melting temperature. The fluctuations suggest a broken icosahedral symmetry with extended correlations in the orientations of local icosahedral packing units. More a detailed review of the material sketched above may be found in ref. 9 below.