Crystallization Driving Force of Supercooled Oxide Liquids

Cassar, Daniel R.

doi:10.1111/ijag.12218

Cited by 15 publications

(11 citation statements)

References 40 publications

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“…where σ is the surface energy between the nucleus and the ambient phase, and ∆G V is the change in the Gibbs free energy (per unit of volume) when the ambient phase transforms into the phase of the nucleus [8,9]. Eqs.…”

Section: Classical Nucleation Theorymentioning

confidence: 99%

Solving the classical nucleation theory with respect to the surface energy

Cassar

2019

Journal of Non-Crystalline Solids

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An essential parameter of the Classical Nucleation Theory (CNT) is the surface energy between a critical-size nucleus and the ambient phase, σ. In condensed matter, this parameter cannot be experimentally determined independently of CNT. A common practice to obtain σ is to assume a model for its temperature-dependence and perform a regression of the CNT equation against experimental nucleation data. The drawback of this practice is that assuming the temperaturedependence of σ adds a bias to the analysis. Nonetheless, this practice is common because an analytical solution of the Classical Nucleation Theory with respect to σ is not possible considering common expressions of this theory. In this article, a general numerical solution to this problem using the Lambert W function is proposed, tested, and compared with typical regression methods. The major advantage of the proposed method is that there is no need to assume a model for the temperature-dependence of σ.

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Section: Classical Nucleation Theorymentioning

confidence: 99%

Solving the classical nucleation theory with respect to the surface energy

Cassar

2019

Journal of Non-Crystalline Solids

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“…In the above equations, U is the crystal growth rate, D U is the effective diffusion coefficient controlling crystal growth, d 0 is the jump distance that some (unknown) diffusing entities or “structural units” must travel through the liquid to attach onto a growing crystal, σ is the crystal‐liquid interfacial energy, R is the universal gas constant and V m is the molar volume. The driving force for crystallization, Δμ, for a closed system in an isobaric condition can be calculated using heat capacity data:

\begin{matrix} Δ μ (T) & = Δ H_{normalm} (1 - \frac{T}{T_{normalm}}) - \int_{T}^{T_{m}} false(C_{normalp, normall} (T) - C_{normalp, normalc} (T) false) \\ d T + T \int_{T}^{T_{m}} \frac{C_{p, l} false(T false) - C_{p, c} false(T false)}{T} d T \end{matrix}

where Δ H m is the enthalpy of melting, C p,l is the heat capacity of the supercooled liquid, C p,c is the heat capacity of the crystal and T is the absolute temperature.…”

Section: Literature Review and Governing Equationsmentioning

confidence: 99%

“…In the above equations, U is the crystal growth rate, D U is the effective diffusion coefficient controlling crystal growth, d 0 is the jump distance that some (unknown) diffusing entities or "structural units" must travel through the liquid to attach onto a growing crystal, r is the crystalliquid interfacial energy, R is the universal gas constant and V m is the molar volume. The driving force for crystallization, Dl, for a closed system in an isobaric condition can be calculated 19,20 using heat capacity data:…”

Section: Crystal Growth Kineticsmentioning

confidence: 99%

The diffusion coefficient controlling crystal growth in a silicate glass‐former

Cassar

Rodrigues

Nascimento

et al. 2017

Int J of Appl Glass Sci

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One of the most relevant open issues in glass science refers to our ignorance concerning the nature of the diffusing entities that control crystal nucleation and growth in non‐crystalline materials. This information is very relevant because all the existing nucleation and growth equations account for the diffusion coefficient (DU) of these unknown entities. In this article, we measured the shear viscosity (η) and the crystal growth rates of a supercooled diopside liquid (CaMgSi2O6) in a wide temperature range. The well‐known decoupling of viscosity and crystal growth rates at deep supercoolings was detected. We tested and analyzed 4 different approaches to compute DU, three existing and one proposed here. As expected, the classical approach (DU ~ η−1) and the fractional viscosity approach (DU ~ η−ε) were not able to describe the crystal growth rates near the glass transition temperature. However, our proposed expression to calculate DU—gradually changing from a viscosity‐controlled to an Arrhenian‐controlled process—was able to describe the available data in the whole temperature range and yielded the lowest uncertainty for the adjustable parameters. Our results suggest that viscous flow ceases to control the crystal growth process below the so‐called decoupling temperature, corroborating some previous studies.

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“…With respect to melt crystallization caused by temperature changes, such assumption (

{normalγ}_{T} ≅ 0

) is known to overestimate as a rule in the thermodynamic driving force, while the account of the two terms in Eqs. and is known to lead to a widely correct description …”

Section: Dependence Of the Thermodynamic Driving Force Of Crystallizamentioning

confidence: 91%

“…(12) and (13) is known to lead to a widely correct description. 11,22,23 Hence, following the approach similar to the one as employed for the determination of the thermodynamic driving force in dependence on undercooling as described in detail in Ref. [11,12,15] and already employed here as well, we included an additional term similarly to Eq.…”

Section: Approximationsmentioning

confidence: 99%

Thermodynamic Aspects of Pressure‐Induced Crystallization: Kauzmann Pressure

Schmelzer

Abyzov

Fokin

2016

Int J of Appl Glass Sci

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General equations for the dependence of the thermodynamic driving force and the specific interfacial energy melt‐crystal of critical clusters on temperature and pressure are derived. Analytical estimates of these and related thermodynamic quantities are advanced directly applicable in the analysis of experimental data of crystal nucleation. Similar to the well‐known notation of a Kauzmann temperature, the concept of a Kauzmann pressure is introduced. It is shown that the thermodynamic driving force of crystal nucleation has maxima not only at the Kauzmann temperature but also at the Kauzmann pressure. Estimates of the magnitude of the thermodynamic driving force of crystallization at these states are given and some consequences are discussed.

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Crystallization Driving Force of Supercooled Oxide Liquids

Cited by 15 publications

References 40 publications

Solving the classical nucleation theory with respect to the surface energy

Solving the classical nucleation theory with respect to the surface energy

The diffusion coefficient controlling crystal growth in a silicate glass‐former

Thermodynamic Aspects of Pressure‐Induced Crystallization: Kauzmann Pressure

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