The symmetry-adapted configurational ensemble approach to the computer simulation of site-disordered solids

Site-occupancy disorder, defined as the non-periodic occupation of lattice sites in a crystal structure, is a ubiquitous phenomenon in solid-state physics and chemistry. Examples are mineral solid solutions, synthetic non-stoichiometric compounds and metal alloys. The experimental investigation of these materials using diffraction techniques only provides averaged information of their structure. However, many properties of interest in these solids are determined by the local geometry and degree of disorder, which escape an "average crystal" description, either from experiments or from theory. In this paper, we describe a methodology for the computer simulation of site-disordered solids, based on the consideration of configurational ensembles and statistical mechanics, where the number of occupancy configurations is reduced by taking advantage of the crystal symmetry of the lattice. Thermodynamics and non-thermodynamic properties are then defined from the statistics in the symmetry-adapted configurational ensemble. We will briefly summarize and discuss some recent applications of this methodology to problems in materials science.