Predictive model for the composition dependence of glassy dynamics

Guo, Xuan; Mauro, John C.; Allan, Douglas C.; Smedskjær, Morten Mattrup

doi:10.1111/jace.15272

Cited by 17 publications

(16 citation statements)

References 37 publications

(110 reference statements)

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“…The missing model required to understand structural relaxation is the bulk viscosity curve 15 . All previous relaxation (structural or stress) models 9,42 have relied on approximations that use a constant exponent β and on a constant (temperature‐independent) modulus value, whereas here, every parameter of Equation () may be modeled as a function of temperature. Furthermore, in combination with the relaxation models described by Guo et al, 42 in which multiple fictive temperatures are described using a Prony series and a temperature‐dependent modulus, one can construct a relaxation curve accounting for the temperature dependence and thermal history dependence of all relevant parameters:

\exp (‐ {()(, \frac{G (T) t}{η (T, T_{normalf})})}^{β (T_{f})}) \approx {false\sum}_{i = 1}^{N} w_{i} ()(, T_{normalf}) \exp ()(, ‐ \frac{G (T) k_{i} ()(, T_{normalf}) t}{η false(T, T_{f} false)}) .

…”

Section: Discussionmentioning

confidence: 99%

“…The composition‐dependent part of Equation () is

S_{\infty}

since we approximate A to be independent of composition. The fragility dependence of

S_{\infty}

was proposed by Guo et al, 42

S_{\infty} false(x false) = S_{\infty} false(x_{ref} false) \exp [\frac{m (x) ‐ m (x_{ref})}{m_{0}}],

where x is composition and x ref is a reference composition in the same glass family. Seeking the simplest possible expression to approximate the unknown ζ , we take the natural logarithm of Equation () and of Equation () and combine them to get

\ln ζ = \frac{m}{m_{0}} + \ln ζ^{'},

with the additional definition

\ln ζ^{'} = \ln (\frac{π S_{\infty} ()(, x_{ref})}{\sqrt{6} ()(, \ln 10) A^{1 false/ 2}}) ‐ \frac{m (x_{ref})}{m_{0}} .

…”

Section: Modelmentioning

confidence: 99%

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

et al. 2021

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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.

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\exp (‐ {()(, \frac{G (T) t}{η (T, T_{normalf})})}^{β (T_{f})}) \approx {false\sum}_{i = 1}^{N} w_{i} ()(, T_{normalf}) \exp ()(, ‐ \frac{G (T) k_{i} ()(, T_{normalf}) t}{η false(T, T_{f} false)}) .

…”

Section: Discussionmentioning

confidence: 99%

“…The composition‐dependent part of Equation () is

S_{\infty}

since we approximate A to be independent of composition. The fragility dependence of

S_{\infty}

was proposed by Guo et al, 42

S_{\infty} false(x false) = S_{\infty} false(x_{ref} false) \exp [\frac{m (x) ‐ m (x_{ref})}{m_{0}}],

\ln ζ = \frac{m}{m_{0}} + \ln ζ^{'},

with the additional definition

\ln ζ^{'} = \ln (\frac{π S_{\infty} ()(, x_{ref})}{\sqrt{6} ()(, \ln 10) A^{1 false/ 2}}) ‐ \frac{m (x_{ref})}{m_{0}} .

…”

Section: Modelmentioning

confidence: 99%

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

et al. 2021

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“…[66]. The MAP model is also able to predict the composition dependence of (T,Tf) based on the underlying topology of the glass network in terms of temperature-dependent constraint theory [67]- [70]. The detailed form of the MAP model is provided in Ref.…”

Section: Modeling Of Glass Relaxationmentioning

confidence: 99%

“…The detailed form of the MAP model is provided in Ref. [70]. However, please note that the analysis of the Prony series presented in the current paper does not depend upon the particular choice of model for (T,Tf).…”

Section: Modeling Of Glass Relaxationmentioning

confidence: 99%

On the Prony series representation of stretched exponential relaxation

Mauro

2018

Physica A: Statistical Mechanics and its Applications

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Stretched exponential relaxation is a ubiquitous feature of homogeneous glasses. The stretched exponential decay function can be derived from the diffusion-trap model, which predicts certain critical values of the fractional stretching exponent, . In practical implementations of glass relaxation models, it is computationally convenient to represent the stretched exponential function as a Prony series of simple exponentials. Here, we perform a comprehensive mathematical analysis of the Prony series approximation of the stretched exponential relaxation, including optimized coefficients for certain critical values of . The fitting quality of the Prony series is analyzed as a function of the number of terms in the series.With a sufficient number of terms, the Prony series can accurately capture the time evolution of the stretched exponential function, including its "fat tail" at long times. However, it is unable to capture the divergence of the first-derivative of the stretched exponential function in the limit of zero time. We also present a frequency-domain analysis of the Prony series representation of the stretched exponential function and discuss its physical implications for the modeling of glass relaxation behavior.

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“…Sub-T g glass relaxation -also called aging -has been extensively studied over the years [22][23][24][25][26][27][28][29][30][31][32][33][34] and it has been shown that the relaxation process depends on multiple factors including the nonexponentiality β, the non-linearity x, the fictive temperature T f and the fragility index m. The fragility is of particular interest as it affects the relaxation process in multiple ways that may appear contradictory. For example glasses located within the "reversibility window" are generally found to correspond to compositions exhibiting lower fragility index 35 so that prior suggestions that these glasses do not age, may appear to indicate that low fragility is associated with a resistance to relaxation.…”

Section: Introductionmentioning

confidence: 99%

Extended aging of Ge–Se glasses below the glass transition temperature

King

Sen

Takeda

et al. 2021

The Journal of Chemical Physics

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Germanium selenide glasses of compositions spanning the whole glass-formation range are aged at room temperature for up to twenty years. A prominent enthalpy relaxation process is observed in all glasses and its structural origin is analyzed by Raman spectroscopy. The structural relaxation is manifested in the Raman spectra as a decrease in the ratio of edge to corner-sharing GeSe 4/2 tetrahedral units. This structural evolution can be explained in terms of configurational entropy and density changes. Changes in Raman features and enthalpy follow an identical stretched exponential relaxation function characteristic of ageing in glasses. The compositional dependence of enthalpy relaxation after twenty years is in agreement with kinetic considerations based on the glass transition temperature of each glass. The relaxation behavior and heat-capacity curves are consistent with standard glass relaxation models for all compositions. These results indicate that the non-reversing enthalpy obtained by modulated differential scanning calorimetry (MDSC) which suggests the existence of non-aging glasses is not a reliable measure of the ability of a glass to relax. Instead, it is suggested that an interpretation of MDSC data in terms of complex heat capacity provides a more complete and reliable assessment of the relaxation properties of glasses. I.

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Predictive model for the composition dependence of glassy dynamics

Cited by 17 publications

References 37 publications

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

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

On the Prony series representation of stretched exponential relaxation

Extended aging of Ge–Se glasses below the glass transition temperature

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