Statistical mechanical model for the formation of octahedral silicon in phosphosilicate glasses

Unlike ambient pressure silicate glasses, some phosphosilicate glasses contain sixfold-coordinated silicon (Si⁶) units even when prepared at ambient pressure. The variation in the fraction of Si⁶ with composition remains a topic of interest, both for technological applications of phosphosilicate glasses and for fundamental understanding of the glass structure. In this work, we use statistical mechanical modeling to predict the composition–structure relationships in Na₂O–P₂O₅–SiO₂ and CaO–P₂O₅–SiO₂ glasses. This is achieved by accounting for the enthalpic and entropic contributions to the interactions between each pairwise modifier ion and structural unit. The initial enthalpy parameters are obtained based on experimental structural data for binary Na₂O–SiO₂, CaO–SiO₂, Na₂O–P₂O₅, and CaO–P₂O₅ glasses, which can then be transferred to predict the structure of mixed former glasses. This approach has previously been used to predict the short-range structure of borosilicate and aluminoborate glass systems. However, here we show that the formation of Si⁶ must be specifically included to make accurate predictions of the composition–structure relationships in phosphosilicate glasses. After incorporating the formation mechanism of Si⁶ in the statistical mechanics model, we find an excellent agreement between model predictions and experimental structure data for Na₂O–P₂O₅–SiO₂ and CaO–P₂O₅–SiO₂ glasses.