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

Bruno Poletto Rodrigues,Lothar Wondraczek,Joachim Deubener

doi:10.3389/fmats.2016.00025

Bruno Poletto Rodrigues, Lothar Wondraczek + Show 1 more

Open Access

https://doi.org/10.3389/fmats.2016.00025

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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 or stiffen with decreasing or 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 re-accommodate 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 re-accommodate deformation.

Highlights

The bond constraint theory (BCT), as originally formulated by Phillips (1979) and Phillips and Thorpe (1985), rationalizes the glass structure in terms of a simple “ball-and-stick” network
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 Modifier Interaction in Ternary Alkali Metaphosphate Glasses reasonable guess about the relative strength of the constraints considered are required for relatively accurate property prediction
The interactions between the non-bridging oxygens and the network modifiers have a strongly ionic character. This requires adaptations to the “ball-and-stick” model due to the lower directionality and longer ranges characteristic of the Coulombic interactions. This adaptation was achieved by the introduction of the characteristic “constraint strengths” to the model, for which there are two ways of implementation: in our previous work (Rodrigues and Wondraczek, 2014; Rodrigues et al, 2014), we argue that the “constraint strength” defined as the ratio between the number of constraints each modifier R adds to the system (KR) and its coordination number (CNR) represents the number of constraints each modifier/non-bridging oxygen bond adds to the system, with the caveat that the numbers are relative to the absolute strength of all other constraints which are assumed to be equal to unity

Summary

Introduction

The bond constraint theory (BCT), as originally formulated by Phillips (1979) and Phillips and Thorpe (1985), rationalizes the glass structure in terms of a simple “ball-and-stick” network. 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 Modifier Interaction in Ternary Alkali Metaphosphate Glasses reasonable guess about the relative strength of the constraints considered are required for relatively accurate property prediction.

Results

Conclusion