Thermal expansion of silicate glass-forming systems at high temperatures from topological pruning of ring structures

The thermal expansion of a silicate glass system containing four types of modifiers at temperatures above the glass transition can be correlated with changes in medium range order (viz., the ring size distribution) without significant modifications in short range order such as Si coordination and Q-speciation. An empirical linear relation between the network densities of the two groups of silicate glass-forming systems and their characteristic ring size has been found using the topological pruning picture proposed by Stixrude and Bukowinski (Am Mineral, 1990, 75:1159-69). Although variation in thermal expansion among different samples exists, for individual composition of the glass-forming liquids, a strong linear correlation exists between the ring size distribution and the thermal expansion contributed by both configurational change and thermal vibration. The ring evolution of the glass-forming liquid driven by temperature has been modeled by assuming an Arrhenius-like activation picture for small member rings and treated as constant numbers for large rings. The compositional dependence of the ring structure can be reflected in the mixed-alkali or alkaline-earth effect on the small ring activation energy.