An extended topological model for binary phosphate glasses

We present a topological model for binary phosphate glasses that builds on the previously introduced concepts of the modifying ion sub-network and the strength of modifier constraints. The validity of the model is confirmed by the correct prediction of T_g(x) for covalent polyphosphoric acids where the model reduces to classical constraint counting. The constraints on the modifying cations are linear constraints to first neighbor NBOs, and all angular constraints are broken as expected for ionic bonding. For small modifying cations, such as Li⁺, the linear constraints are almost fully intact, but for larger ions a significant fraction is broken. By accounting for the fraction of intact modifying ion related constraints, q_γ, the T_g(x) of alkali phosphate glasses is predicted. By examining alkali, alkaline earth and rare earth metaphosphate glasses we find that the effective number of intact constraints per modifying cation is linearly related to the charge-to-distance ratio of the modifying cation to oxygen.