Towards understanding the local structure of liquids

In this article we discuss the problem of well-defined crystalline patterns of local atomic arrangements in equilibrium liquids, and their statistical mechanics modelling. We present arguments in favor of the existence of local crystalline structures in liquids (local crystal order hypothesis) and discuss a generalized energy landscape picture in the theory of the liquid state. This picture allows a quantification of the hypothesis of local order and offers basic concepts for the statistical mechanics modelling of the melting phase transition. We review recent results of probabilistic-based searches for local structures in various two-and three-dimensional computer-simulated liquids. Next, some statistical-mechanics models of melting and amorphization in terms of structural states of small clusters are proposed. The models, which have only two characteristic energies, that of the orientationally disordered locally crystalline state, and that of completely amorphous state, are studied in a mean-probability approximation. If the amorphization energy is high, the material retains local crystallinity even in the melt; at higher temperatures a crossover to the locally amorphous state occurs. A material that has a low energy non-crystalline local packing exhibits an amorphization melting; the phase transition is from orientationally ordered crystal state to a locally amorphous melt.