Mixed modifier effect in Na₂O·K₂O·CaO aluminosilicate glasses: Pairwise and ternary interactions

The mixed modifier effect (MME) is one of the most challenging puzzles in the field of oxide glasses, as there exists no universal quantitative theoretical model for accurately describing and predicting the nonlinear deviation of property values. In this paper, pairwise and ternary interactions are examined experimentally to understand the MME in a series of aluminosilicate glasses. By keeping the glass network former concentration constant and adjusting the molar ratios of three network modifiers (Na₂O, K₂O, and CaO), the MMEs in glass transition temperature (T_g), Vickers hardness (H_v), and activation energy (E_a) for aqueous dissolution for each modifier cation are investigated. We examine whether a pairwise interaction model is sufficient, or if ternary interactions also need to be included to predict the MME in these aluminosilicate glass systems. This work reveals that the pairwise model can be used to predict the MME for T_g in complex multiple-modifier glass systems using only two-body interaction factors. However, ternary mixed-modifier interactions are present in other properties such as H_v and E_a.