Quantitative Comparison of Ternary Eutectic Phase-Field Simulations with Analytical 3D Jackson–Hunt Approaches

Steinmetz, Philipp; Kellner, Michael; Hötzer, Johannes; Nestler, Britta

doi:10.1007/s11663-017-1142-2

Cited by 14 publications

(6 citation statements)

References 42 publications

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“…The phase-field approach, based on the grand-potential formalism, has been employed extensively to model solidification [81][82][83][84] and solid-state transformation [85,86], including multicomponent systems [87,88]. Furthermore, this technique is also combined with an elastic model, in order to analyze chemoelastic transformations [89,90].…”

Section: A Grand-potential Modelmentioning

confidence: 99%

Multiphase-field model for surface diffusion and attachment kinetics in the grand-potential framework

et al. 2021

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Grand-potential based multiphase-field model is extended to include surface diffusion. Diffusion is elevated in the interface through a scalar degenerate term. In contrast to the classical Cahn-Hilliard-based formulations, the present model circumvents the related difficulties in restricting diffusion solely to the interface by combining two second-order equations, an Allen-Cahn-type equation for the phase field supplemented with an obstacletype potential and a conservative diffusion equation for the chemical potential or composition evolution. The sharp interface limiting behavior of the model is deduced by means of asymptotic analysis. A combination of surface diffusion and finite attachment kinetics is retrieved as the governing law. Infinite attachment kinetics can be achieved through a minor modification of the model, and with a slight change in the interpretation, the same model handles the cases of pure substances and alloys. Relations between model parameters and physical properties are obtained which allow one to quantitatively interpret simulation results. An extensive study of thermal grooving is conducted to validate the model based on existing theories. The results show good agreement with the theoretical sharp-interface solutions. The obviation of fourth-order derivatives and the usage of the obstacle potential make the model computationally cost-effective.

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Section: A Grand-potential Modelmentioning

confidence: 99%

Multiphase-field model for surface diffusion and attachment kinetics in the grand-potential framework

et al. 2021

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“…Because engineering materials are often both polycrystalline and multi-component, phase-field models are required that are capable of tracking an arbitrary number of chemical components, phases, and grains of each phase. Several phase-field models capable of simulating multi-phase, multi-grain materials have been developed in recent years [1][2][3][4][5][6][7][8], and others have also been developed that add the capability to simulate multiple chemical components [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. Each of these models has various advantages and disadvantages relative to desirable model characteristics.…”

Section: Introductionmentioning

confidence: 99%

“…[32] also showed that KKS-type models can be derived starting from the grand-potential functional. The grand-potential approach has been extended to multi-phase field models [16,[18][19][20][21][22][23][24][25]. (We refer to multi-phase field models as models that enforce the constraint that all phase field variables φ i sum to 1 at each point, and refer to multi-order parameter models as models where this requirement is not enforced.)…”

Section: Introductionmentioning

confidence: 99%

“…The multi-phase field, grand-potential based models in Refs. [16,[18][19][20][21][22][23][24] use the multi-phase free energy functional including double obstacle potential of Ref. [2], whereas Ref.…”

Section: Introductionmentioning

confidence: 99%

“…Refs. [16,[18][19][20][21][22][23][24], the authors mitigated spurious third-phase formation by adding penalty terms of the form W ijk φ i φ j φ k , where W ijk is a constant. Such terms can cause the contact angles at triple junctions to deviate from their equilibrium values; a procedure to calibrate W ijk to obtain improved accuracy in triple junction angles is given in Ref.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Grand-potential-based phase-field model for multiple phases, grains, and chemical components

Aagesen¹,

Gao²,

Schwen³

et al. 2018

Phys. Rev. E

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Grand-potential-based phase-field model for multiple phases, grains, and chemical components is derived from a grand-potential functional. Due to the grand-potential formulation, the chemical energy does not contribute to the interfacial energy between phases, simplifying parametrization and decoupling interface thickness from interfacial energy, which can potentially allow increased interface thicknesses and therefore improved computational efficiency. Two-phase interfaces are stable with respect to the formation of additional phases, simplifying implementation and allowing the variational form of the evolution equations to be used. Additionally, we show that grand-potential-based phase-field models are capable of simulating phase separation, and we derive conditions under which this is possible.

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Three-Phase Eutectic Microstructures: Influence of Interfacial Energy Anisotropy and Solute Diffusivities

Khanna

Choudhury

2021

Metall Mater Trans A

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Quantitative Comparison of Ternary Eutectic Phase-Field Simulations with Analytical 3D Jackson–Hunt Approaches

Cited by 14 publications

References 42 publications

Multiphase-field model for surface diffusion and attachment kinetics in the grand-potential framework

Multiphase-field model for surface diffusion and attachment kinetics in the grand-potential framework

Grand-potential-based phase-field model for multiple phases, grains, and chemical components

Three-Phase Eutectic Microstructures: Influence of Interfacial Energy Anisotropy and Solute Diffusivities

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