A model for phosphate glass topology considering the modifying ion sub-network

Abstract

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.

Modifier Interaction and Mixed-Alkali Effect in Bond Constraint Theory Applied to Ternary Alkali Metaphosphate Glasses

“…One can see that according to these equations, even at the metaphosphate composition (x = 0.5), there would still be a finite number of modifiers that should be surrounded by double-bonded oxygens since 2 × R(x crit ) > 0, but from 31 P NMR measurements, it is known that at the metaphosphate composition there are no (or almost no) Q 3 groups and, therefore, double-bonded oxygens (Brow, 2000) and also NMR from the modifiers does not show evidence for more than one site (Schneider et al, 2013). On the other hand, for this study, the values of constraints per modifier (K R ) as they are listed in were recalculated, as the previous calculation used an inconsistent counting of the phosphate network constraints (Hermansen et al, 2014a). The final values of K R are shown in Table 1.…”

“…More recently, Gupta and Mauro (2009) and Mauro et al (2009) introduced the concept of temperature-dependent constraints, based on previous work by Naumis (2005,2006), taking into account the temperature dependence of configurational entropy and, hence, the number of bond constraints. This allowed for applying constraint counting to calculate the compositional trends of properties, such as the glass transition temperature Mauro et al, 2009;Smedskjaer et al, 2010bSmedskjaer et al, , 2011Fu and Mauro, 2013;Jiang et al, 2013;Wondraczek, 2013, 2014;Hermansen et al, 2014a;, fragility Mauro et al, 2009;Hermansen et al, 2014a), and surface hardness (Smedskjaer et al, 2010a(Smedskjaer et al, ,c, 2011Wondraczek et al, 2011;Smedskjaer, 2014). While useful applications of the BCT need detailed structural information, the strength of this approach lies in its simplicity, as only the knowledge of the components' first shell coordination number and a reasonable guess about the relative strength of the constraints considered are required for relatively accurate property prediction.…”

“…In glass science, one such example is the so-called "mixed-alkali effect" (MAE), where the mixture of two alkali species results in a non-linear variation of several properties, such as ionic conductivity, glass transition temperature, internal friction, and volumetric relaxation (Bunde et al, 2004;Changstrom and Sidebottom, 2008). Here, we, therefore, aim to expand the current understanding of the BCT toward incorporation of such non-linear interaction terms, choosing the example of mixed-alkali phosphate glasses (Fu and Mauro, 2013;Hermansen et al, 2014a;. We demonstrate how appropriate interaction terms can be used to incorporate the MAE into BCT so as to enable accurate calculation of the glass transition temperature.…”

Relaxation and physical aging in network glasses: a review

“…Typical applications for the prediction of the glass transition temperature concern simple chalcogenides [35], borates [280], borosilicates [284] phosphates [283], or borophosphate glasses [281] (Figure 24, right). Equation (49) usually leads to a good reproduction of fragility data with composition, but requires a certain number of onset temperatures T α that can be estimated from basic assumptions, or which act as parameters for the theory.…”

“…A certain number of thermal and relaxation properties of network glass-forming liquids can now be determined, and a simple steplike function (thick black line in Fig. 24) with an onset temperature T α for various constraints allows obtaining analytical expressions for fragility and glass transition temperature [35,280,281,282,283], heat capacity [284], and glass hardness [283,285]. Two central ingredients are necessary.…”