Fragility and temperature dependence of stretched exponential relaxation in glass‐forming systems

Abstract

Relaxation behavior is critically important for nearly all high‐tech applications of glass. It is also known as one of the most difficult unsolved problems in condensed matter physics. The relaxation behavior of glass can be described using the stretched exponential decay function exp‐)(tfalse/τβ, the shape of which is governed by the dimensionless stretching exponent β. Here, a temperature‐dependent model for β(T) is proposed. The model is derived based on the Adam‐Gibbs relationship and insights from the energy landscape description of glass‐forming systems. The model captures previously known limiting values of β(T) while also providing a continuous transition between these limits. Additionally, the model captures the effects of fragility and thermal history. The model is validated with experimental data for commercial silicate glasses and a borate glass.

Impact of a temperature‐dependent stretching exponent on glass relaxation

“…25 ζ is compositionally dependent on S ∞ , as shown by Guo et al, 27 and by taking the natural logarithm of ζ, an additional variable ζ ' is shown to vary linearly with m and the intercept of ζ ' is compositionally independent, or only depends on one reference composition. 25 Thus, a physically based model for the temperature dependent β can be described with only one free parameter. The goal of this paper is to understand how best to model relaxation for industrial processing applications.…”

“…This bifurcation needs to be explored in greater detail for other oxide glasses and non-oxide systems, and the fundamental atomic mechanisms must also be elucidated. Additionally, more relaxation modeling using temperature-dependent values is needed; this work starts to address the viability of using a temperaturedependent β, and work from Wilkinson et al 25 suggests a model where all values used to calculate the relaxation are a function of temperature. An additional avenue of research is to expand the RelaxPy software to reliably model non-oxide glasses and organic glasses with low T g values and high fragilities.…”

“…𝑤 𝑖 𝑇 𝑓𝑖 , and the weighting coefficients, 𝑤 𝑖 , are defined by the Prony series approximation of the stretched exponential function described below. 24 Recently, work has been done by Wilkinson et al 25 to create a physically motivated model describing the temperature dependence of β. Starting with the result from Richert and Richert, 26 where β can be related to an underlying structural relaxation time distribution, an expression for the temperature dependence of β is derived,…”

“…In the above equation, T f is the fictive temperature (equal to the physical temperature, T, for a liquid or super-cooled liquid), T g is the glass transition temperature, m is the fragility index, and m 0 is the lower limit of fragility for a strong liquid. 25 β (T f ) is a function of thermal history, glass transition, and fragility index with only one unknown, ζ,…”

Modeling the relaxation and crystallization kinetics of glass without fictive temperature: Toy landscape approach

“…This allows for a unified method to predict the structural relaxation time based on only and . In Figure 1, the relaxation times predicted for lead metasilicate ( 50 ) and Corning Jade ( 51 ) are shown and compared to experimental values. The stretching exponent values are also predicted through this method; however, due to the variable time step technique implemented here, some of the shorter relaxation times may not be overserved, which shifts the stretching exponent value higher.…”