In the present paper we establish a temperature dependent constraint model of alkali phosphate glasses considering the structural and topological role of the modifying ion sub-network constituted by alkali ions and their non-bonding oxygen coordination spheres. The model is consistent with available structural data by NMR and molecular dynamics simulations and with dynamic data such glass transition temperature (T g ) and liquid fragility (m). Alkali phosphate glasses are exemplary systems for developing constraint model since the modifying cation network plays an important role besides the primary phosphate network. The proposed topological model predicts the changing trend of the T g and m with increasing alkali oxide content for alkali phosphate glasses, including an anomalous minimum at around 20 mol.% alkali oxide content. We find that the minimum in T g and m is caused by increased connectivity of the modifying ion sub-network, as the alkali ions must share non-bonding oxygen to satisfy their coordination requirements at higher alkali oxide contents. We argue that the systematically decreasing the T g values of alkali phosphate glasses from Li 2 O to Na 2 O to Cs 2 O could be caused by a weakening of the modifying ion sub-network and can be accounted for by lower constraint onset temperatures.

In this work, we investigate the correlations among structure, topology, and properties in a series of sodium phosphosilicate glasses with [SiO2]/[SiO2 + P2O5] ranging from 0 to 1. The network structure is characterized by (29)Si and (31)P magic-angle spinning nuclear magnetic resonance and Raman spectroscopy. The results show the formation of six-fold coordinated silicon species in phosphorous-rich glasses. Based on the structural data, we propose a formation mechanism of the six-fold coordinated silicon, which is used to develop a quantitative structural model for predicting the speciation of the network forming units as a function of chemical composition. The structural model is then used to establish a temperature-dependent constraint description of phosphosilicate glass topology that enables prediction of glass transition temperature, liquid fragility, and indentation hardness. The topological constraint model provides insight into structural origin of the mixed network former effect in phosphosilicate glasses.

To quantify and study the densification and plastic deformation under Vicker's indentation we prepared a series of simple soda-lime-silicate glasses with different modifying ion contents and four glasses with constant silica content but potassium and/or barium substituted for sodium and/or calcium. The densification and plastic deformation in these glasses were determined using atomic force microscopy (AFM) by measuring each sample twice, i.e., once immediately following indentation, and once after annealing to relax the densified volume. The results show that the densified volume of the glasses decreases approximately linearly with the bulk modulus, and the plastic deformation volume with silica mole fraction. These results have important implications in the prediction of hardness and crack resistance (i.e. load for crack initiation) from composition.

We establish a topological model of alkali borophosphate and calcium borophosphate glasses, which describes the effect of both the network formers and network modifiers on physical properties. We show that the glass transition temperature (Tg), Vickers hardness (HV), liquid fragility (m), and isobaric heat capacity jump at Tg (ΔCp) of these glasses are related to the network topology, which is determined by structure of the glass. Therefore, we also demonstrate that the temperature dependent constraint theory can quantitatively explain the mixed network former effect in borophosphate glasses. The origin of the effect of the type of network modifying oxide on Tg, HV, m, and ΔCp of calcium borophosphate glasses is revealed in terms of the modifying ion sub-network. The same topological principles quantitatively explain the significant differences in physical properties between the alkali and the calcium borophosphate glasses. This work has implications for quantifying structure-property relations in complex glass forming systems containing several types of network forming and modifying oxides.

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.