Phase field benchmark problems for nucleation

Wu, W.; Montiel, David; Guyer, Jonathan E.; Voorhees, Peter W.; Warren, James A.; Wheeler, Daniel; Gránásy, László; Pusztai, Tamás; Heinonen, Olle

doi:10.1016/j.commatsci.2021.110371

Cited by 20 publications

(14 citation statements)

References 27 publications

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“…We used a computationally-efficient (Julia-GPU) implementation of a simple phase-field nucleation benchmark [21] in order to (i) produce a statistically significant data (over hundreds of simulations and thousands of particles), (ii) analyze the kinetics of transformation, and (iii) compare the results to the classical, and widely used, JMAK theory.…”

Section: Discussionmentioning

confidence: 99%

“…One recently published benchmark problem, considered in this article, focuses on nucleation [21]. The problem considers an undercooled liquid undergoing a first-order phase transformation through nucleation and growth mechanisms.…”

Section: Phase-field Benchmark Problemsmentioning

confidence: 99%

“…The non-dimensional form of Eqs ( 12)-( 14) are numerically implemented. In the remainder of this article, for clarity (and in order to be consistent with the original paper [21]), we refer exclusively this dimensionless form of the equations, but drop the tilde notation on all symbols, e.g., writing simply ∆f , r0, and r * in place of ∆f , r0, and r * .…”

Section: Phase-field Modelmentioning

confidence: 99%

See 2 more Smart Citations

On the Effect of Nucleation Undercooling on Phase Transformation Kinetics

Mancias¹,

Attari²,

Arróyave³

et al. 2022

Preprint

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We carry out an extensive comparison between Johnson-Mehl-Avrami-Kolmogorov (JMAK) theory of firstorder phase transformation kinetics and phase-field (PF) results of a benchmark problem on nucleation. To address the stochasticity of the problem, several hundreds of simulations are performed to establish a comprehensive, statistically-significant analysis of the coincidences and discrepancies between PF and JMAK transformation kinetics. We find that PF predictions are in excellent agreement with both classical nucleation theory and JMAK theory, as long as the original assumptions of the latter are appropriately reproduced -in particular, the constant nucleation and growth rates in an infinite domain. When deviating from these assumptions, PF results are at odds with JMAK theory. In particular, we observe that the size of the initial particle radius r0 relative to the critical nucleation radius r * has a significant effect on the rate of transformation. While PF and JMAK agree when r0 is sufficiently higher than r * , the duration of initial transient growth stage of a particle, before it reaches a steady growth velocity, increases as r0/r * → 1. This incubation time has a significant effect on the overall kinetics, e.g., on the Avrami exponent of the multi-particle simulations. In contrast, for the considered conditions and parameters, the effect of interface curvature upon transformation kinetics -in particular negative curvature regions appearing during particle impingement, present in PF but absent in JMAK theory -appears to be minor compared to that of r0/r * . We argue that rigorous benchmarking of phase-field models of stochastic processes (e.g., nucleation) need sufficient statistical data in order to make rigorous comparisons against ground truth theories. In these problems, analysis of probability distributions is clearly preferable to a deterministic approach.

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Section: Discussionmentioning

confidence: 99%

Section: Phase-field Benchmark Problemsmentioning

confidence: 99%

Section: Phase-field Modelmentioning

confidence: 99%

See 1 more Smart Citation

On the Effect of Nucleation Undercooling on Phase Transformation Kinetics

Mancias¹,

Attari²,

Arróyave³

et al. 2022

Preprint

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“…Zhang et al [13] tested a class of linear numerical schemes for the functionalized CH equation using stabilized scalar auxiliary variable (SAV) method. Wu et al [14] presented two benchmark problems on homogeneous and heterogeneous nucleation. Li et al [15] suggested the numerical benchmark solution of the CH equation.…”

Section: Introductionmentioning

confidence: 99%

Benchmark Problems for the Numerical Schemes of the Phase‐Field Equations

Hwang

Lee

Kwak

et al. 2022

Discrete Dynamics in Nature and Society

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In this study, we present benchmark problems for the numerical methods of the phase-field equations. To find appropriate benchmark problems, we first perform a linear stability analysis and then take a growth mode solution as the benchmark problem, which is closely related to the dynamics of the original governing equations. As concrete examples, we perform convergence tests of the numerical methods of the Allen–Cahn (AC) and Cahn–Hilliard (CH) equations using the proposed benchmark problems. The one- and two-dimensional computational experiments confirm the accuracy and efficiency of the proposed scheme as the benchmark problems.

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“…22 The phase-field model is widely accepted in the materials science since the 1980s. 23,24 Recently, the phase-field model is applied to simulate numerically the electrodeposition processes based on the basic physico-chemical properties of the electrorefining system. 25,26 Phase-field model is also an important method for the study of nucleation mechanism especially the microstructure of electrodeposited cathode.…”

mentioning

confidence: 99%

Phase-Field Modelling and Morphological Classification of Uranium Dendrites for the Electrorefining of Used Nuclear Fuel

Zhao¹,

Yan²,

Jiang³

et al. 2023

J. Electrochem. Soc.

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Electrorefining is an important unit operation for the pyroprocessing of used nuclear fuel; however, the uncontrolled growth of uranium dendrites on the cathode is hindering its engineering application. In this study, the phase-field modelling is applied to the study of the growth of uranium dendrites using the finite element method, and the fractal dimension and the perimeter-to-area ratio are employed to classify quantitatively the morphologies of uranium dendrites. It is shown that uranium dendrites can form sprout-like, fishbone-like, and tree-like morphologies, and the effects of anisotropic strength, symmetry index, overpotential, and temperature to the morphologies of uranium dendrites are discussed. It is concluded that the diffusion of uranium cations (diffusion rate-controlling) in molten salt and the electrode kinetics (kinetic rate-controlling) are the two rate-controlling steps for the electrodeposition of uranium, and the diffusion rate-controlling mechanism is responsible for the growth of complicated dendritic morphologies.

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Phase field benchmark problems for nucleation

Cited by 20 publications

References 27 publications

On the Effect of Nucleation Undercooling on Phase Transformation Kinetics

On the Effect of Nucleation Undercooling on Phase Transformation Kinetics

Benchmark Problems for the Numerical Schemes of the Phase‐Field Equations

Phase-Field Modelling and Morphological Classification of Uranium Dendrites for the Electrorefining of Used Nuclear Fuel

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