Systematic Evaluation of Mixture-Design for Multi-Oxide Magnesium Aluminosilicate Glass Development: Model Comparison, Modifier Interactions, and Predictive Limitations

A constrained ternary mixture design (Design of Experiments, DoE) was applied to four magnesium aluminosilicate (MAS) glass series to evaluate the predictive capability of Scheffé mixture polynomials for the specific Young’s modulus (spE = E/ρ), the key figure of merit for lightweight glass-fibre reinforcements. Two base compositions (V, Al2O3-rich; T, MgO-rich) were each modified with a 14 wt.% Y2O3–ZnO–CeO2 or La2O3–ZnO–CeO2 block. Linear, quadratic and special-cubic models were fitted to ten design points per series and ranked by R2, R2(adj) and the leave-one-out coefficient R2(pred). Three distinct regimes emerge: the V-series requires a special-cubic model with a dominant ternary Y2O3·ZnO·CeO2 term (β = −47.2, p = 0.001; R2(pred) = 97 %); the T-series is strictly linear (R2(pred) = 55 %), higher orders overfitting; and both La-series show a significant La2O3·CeO2 interaction absent in their Y-analogues. Three additive property models (Makishima–Mackenzie, an extended variant, and Yamane–Sakaino) deviate systematically from measured spE (absolute errors 6.9–12.2 × 106 N·m·kg-1, negative R2), most strongly where DoE detects interactions. The study delineates where additive approaches suffice, where binary synergy dominates, and where genuinely ternary cooperative effects must be resolved.