Statistical mechanics of pentagonal and icosahedral order in dense liquids

Abstract

A Ginzburg-Landau model of short-range icosahedral order in bulk liquids, and of pentagonal order in two-dimensional fluids, is used to calculate density correlation functions in these systems. The theory predicts peaks in the structure factor, at positions determined by symmetries of ideal curved-space ‘‘crystals.’’ The peaks are broadened in a way which reflects the inability of icosahedra and pentagons to form a close-packed lattice in flat space. The results in three dimensions provide a good fit to experiments on vapor-deposited metal films and to computer simulations.