Atomic ordering recognized by convergence characteristics of the radial distribution function

Convergence characteristics of the radial distribution function (RDF) in a condensed phase have been studied theoretically. Using a canonical ensemble, the reversible work theorem for the RDF is deduced in a new way, which interprets the reversible work in a fresh aspect. The radius of convergence of the RDF is defined. For periodic structures such as crystals, convergence of the RDF is strongly correlated with atomic ordering therein. This correlation is demonstrated by comparing the structural properties of SiO2 crystal, with the RDF of Al doped SiO2 structure and amorphous SiO2.