Theoretical Study of Short-Range Order in Supercooled Liquids and Amorphous Solids.

The measurable properties of supercooled liquids and amorphous solids reflect the short-range packing geometry of the constituent particles. This paper is devoted to the description of that short-range order by the Born-Green-Yvon (BGY) local stress equation which relates pair and triplet distribution functions to the pair potential. Since metastable (but long- lived) phases are at issue, it has been necessary to identify an appropriate class of ensembles for which the BGY relation can be justified. In particular low-temperature amorphous solids have preparation- method-dependent properties, and we propose to classify their representative ensembles by the choice of a triplet superposition correction function K. As background for such choice, we have re-examined and extended Alder's lattice enumeration method for K in regular structures. The Kirkwood superposition approximation K == 1 has disastrous consequences for the BGY equation at low temperature; numerical pair correlation functions for the cases of hard spheres and of repelling Gaussian particles display long-range ordering that is impossible for the amorphous solid state. This failure is partially relieved by choosing a K that enhances the concentration of compact pentagonal particle groupings. Study of the inverse problem of determining K from physically reasonable pair correlation functions suggests that K must possess relatively long-ranged fluctuations about unity. These considerations highlight the desirability of accurate simulation studies of K for amorphous deposits at absolute zero.