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

Abstract

Introducing an interaction parameter γ, we implement modifier interaction and the mixed-alkali effect into bond constraint theory and apply this extension for simplistic property prediction on ternary phosphate glasses. The severity of the mixed-alkali effect results from the interplay of two simultaneous contributions: bond constraints on the modifier species soften and stiffen with decreasing and increasing γ, respectively. When the modifier size is not too dissimilar, the decrease in γ reflects that the alkali ions can easily migrate between different sites, forcing the network to continuously reaccommodate for any subsequent distortions. With increasing size difference, migration becomes increasingly difficult without considerable network deformation. This holds even for smaller ions, where the sluggish dynamics of the larger constituent result in blocking of the fast ion movement, leading to the subsequent increase in γ. Beyond a certain size difference in the modifier pair, a value of γ exceeding unity may indicate the presence of steric hindrance due to the large surrounding modifiers impeding the phosphate network to reaccommodate deformation.

Electrodiffusion of alkali ions in alkali niobophosphate glasses and glass‐forming melts

“…Coordination number of an alkali ion represents the number of constraints each alkali ion/nonbridging oxygen bond adds to the process of diffusion, K + has larger coordination number (equal to 6), in contrast to Li + and Na + coordination number (equal to 5). Ionic radius increases from Li + to K + and, likewise, the steric hindrance in the phosphate network becomes more considerable …”

Trends in Effective Diffusion Coefficients for Ion-Exchange Strengthening of Soda-Lime-Silicate Glasses

“…The model then rationalizes attractive reactions among cation species and their effect on the overall activation energy. Major additional factors which then affect the transport properties (Bunde et al, 1996) include site mismatch, site relaxation (frequently called structural relaxation), interionic interaction, and the mixedmodifier effect (Maass et al, 1992;Karlsson et al, 2015;Poletto Rodrigues et al, 2016;Griebenow et al, 2017).…”

Thermodiffusion of alkali ions in alkali niobophosphate glasses

“…For potassium, CN = 6.4, for sodium-5, and for lithium-4.7. [50][51][52] It should be noted that the ratio of the heats of transfer for glasses containing a different type of alkaline ion is very close to the ratio of the ionic radii of the corresponding ions, which is shown in Table 7. Data on the radii of the ions are retrieved from Ref.…”

“…This coordination number (CN) is directly proportional to the force that prevents the act of migration and shows how many ions oppose the movement of the alkaline ion. For potassium, CN = 6.4, for sodium—5, and for lithium—4.7 50–52 …”