title: An extended topological model for binary phosphate glasses.
abstract: 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 Tg(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 non-bridging oxygens, 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, qγ, the Tg(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.
authors.affiliation: Section of Chemistry, Aalborg University, 9220 Aalborg, Denmark.
authors.forename: Christian
authors.initials: C
authors.lastname: Hermansen
authors.affiliation: Otto Schott Institute of Materials Research, University of Jena, 07743 Jena, Germany.
authors.forename: Bruno P
authors.initials: BP
authors.lastname: Rodrigues
authors.affiliation: Otto Schott Institute of Materials Research, University of Jena, 07743 Jena, Germany.
authors.forename: Lothar
authors.initials: L
authors.lastname: Wondraczek
authors.affiliation: Section of Chemistry, Aalborg University, 9220 Aalborg, Denmark.
authors.forename: Yuanzheng
authors.initials: Y
authors.lastname: Yue