Variation of the glass transition temperature with rigidity and chemical composition

TL;DR

This paper presents a theoretical approach based on Lindemann criteria to explain how glass transition temperature varies with chemical composition and rigidity, successfully aligning with experimental data in chalcogenide glasses.

Contribution

It introduces a simple method linking vibrational properties to the modified Gibbs-DiMarzio law for predicting glass transition temperature changes.

Findings

The modified Gibbs-DiMarzio law can be derived from vibrational frequency ratios.

The model accurately predicts the glass transition temperature for Se-Ge-As glasses.

The constant in the law depends on the ratio of characteristic vibrational frequencies.

Abstract

The effects of flexibility and chemical composition in the variation of the glass transition temperature are obtained by using the Lindemann criteria, that relates melting temperature with atomic vibrations. Using this criteria and that floppy modes at low frequencies enhance in a considerable way the average cuadratic displacement, we show that the consequence is a modified glass transition temperature. This approach allows to obtain in a simple way the empirically modified Gibbs-DiMarzio law, which has been widely used in chalcogenide glasses to fit the changes in the glass transition temperature with the chemical composition . The method predicts that the constant that appears in the law depends upon the ratio of two characteristic frequencies (or temperatures). Then, the constant for the Se-Ge-As glass is estimated by using the experimental density of vibrational states, and the result shows a very good agreement with the experimental fit from glass transition temperature variation.