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Toshio Suzuki - One of the best experts on this subject based on the ideXlab platform.
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Phase-Field Model with a reduced interface diffuseness
Journal of Crystal Growth, 2004Co-Authors: Seong Gyoon Kim, Won Tae Kim, Toshio SuzukiAbstract:We reduce the interface diffuseness in Phase-Field Modeling of solidification by localizing the solute redistribution (or latent heat release) into a narrow region within the Phase-Field interface. The numerical computations on the dendritic solidification in a symmetric case and in an one-sided system yield quantitatively the same results with the standard Phase Field Model and the anti-trapping Model [Phys. Rev. Lett. 87 (2001) 115701], respectively, indicating the anomalous interfacial effects in thin interface Phase Field Model can be effectively suppressed. The adoption of the parabolic potential instead of the fourth-order potential makes this Model effective in suppressing a spurious attractive interaction between two closely spaced interfaces due to a clear cut of interface region.
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Phase-Field Model for solidification of ternary alloys coupled with thermodynamic database
Scripta Materialia, 2003Co-Authors: Hiroki Kobayashi, Won Tae Kim, Seong Gyoon Kim, Machiko Ode, Toshio SuzukiAbstract:Abstract A Phase-Field Model coupled to real thermodynamic data in which the vanishing kinetic coefficient condition is proposed. The validity of the Model is examined by comparing the calculated result of the equilibrium state with theoretical predictions for both one and two-dimensional simulations. Numerical simulations of micro-segregation and isothermal dendrite growth is presented to demonstrate the effectiveness of the Model.
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Phase-Field Model of dendritic growth
Journal of Crystal Growth, 2001Co-Authors: Toshio Suzuki, Seong Gyoon Kim, Machiko Ode, Won Tae KimAbstract:Abstract The Phase-Field Models for binary and ternary alloys are introduced, and the governing equations and Phase-Field parameters for dilute alloys are derived at a thin interface limit. The Phase-Field simulations on isothermal dendrite growth for Fe-C, Fe-P and Fe-C–P alloys are carried out and the effect of the ternary alloying element on dendrite growth is examined. The secondary arm spacing for Fe-C, Fe-P and Al–Cu alloys is numerically predicted using the Phase-Field Model and compared to the experimental data. The change in the arm spacing, and the exponent of local solidification time depending on alloy is systematically examined by imposing artificial set of physical properties. The Phase-Field simulation for the microstructure evolution during rapid solidification is also successfully carried out. Through the numerical examples, the wide potentiality of the Phase-Field Model to the applications on solidification has been demonstrated.
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Recent advances in the Phase-Field Model for solidification
ISIJ International, 2001Co-Authors: Machiko Ode, Seong Gyoon Kim, Toshio SuzukiAbstract:The recent development of the Phase-Field Models for solidification and their application examples are briefly reviewed. The Phase-Field Model is firstly proposed for pure material systems and then extended to binary alloy, multi-Phase and multi-component systems theoretically. Though the calculation conditions are limited due to the sharp interface limit parameters in the early stage, it is widened in the thin interface limit Model. The development of the Phase-Field Model is summarized from a viewpoint of the formulation of Phase-Field equation and parameters. The important studies and the latest results such as application examples of free dendrite growth, directional solidification, Ostwald ripening, interface-particle interaction and multi-Phase simulation are mentioned. Finally future works of the Phase-Field Model are prospected.
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Phase–Field Model for solidification of Fe–C alloys
Science and Technology of Advanced Materials, 2000Co-Authors: Machiko Ode, Toshio Suzuki, Seong Gyoon Kim, W.t KimAbstract:The Phase-Field Model for binary alloys by Kim et al. is briefly introduced and the main difference in the definition of free energy density in interface region between the Models by Kim et al. and by Wheeler et al. is discussed. The governing equations for a dilute binary alloy are derived and the Phase-Field parameters are obtained at a thin interface limit. The examples of the Phase-Field simulation on Ostwald ripening, isothermal dendrite growth and particle/interface interaction for Fe–C alloys are demonstrated. In Ostwald ripening, it is shown that small solid particles preferably melt out and then large particles agglomerate. In isothermal dendrite growth, the kinetic coefficient dependence on growth rate is examined for both the Phase-Field Model and the dendrite growth Model by Lipton et al. The growth rate by the dendrite Model shows strong kinetic coefficient dependence, though that by the Phase-Field Model is not sensitive to it. The particle pushing and engulfment by interface are successfully reproduced and the critical velocity for the pushing/engulfment transition is estimated. Through the simulation, it is shown that the Phase-Field Model correctly reproduces the local equilibrium condition and has the wide potentiality to the applications on solidification.
A. A. Wheeler - One of the best experts on this subject based on the ideXlab platform.
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Computation of Dendrites Using a Phase Field Model
2017Co-Authors: A. A. Wheeler, Bruce T. Murray, R. J. SchaeferAbstract:A Phase Field Model is used to numerically simulate the solidification of a pure material. We employ it to compute growth into an undercooled liquid for a one-dimensional spherically symmetric geometry and a planar two-dimensional rectangular region. The Phase Field Model equation are solved using finite difference techniques on a uniform mesh. For the growth of a sphere, the solutions from the Phase Field equations for sufficiently small interface widths are in good agreement with a numerical solution to the classical sharp interface Model obtained using a Green's function approach. In two dimensions, we simulate dendritic growth of nickel with four-fold anisotropy and investigate the effect of the level of anisotropy on the growth of a dendrite. The quantitative behavior of the Phase Field Model is evaluated for varying interface thickness and spatial and temporal resolution. We find quantitatively that the results depend on the interface thickness and with the simple numerical scheme employed it is not practical to do computations with an interface that is sufficiently thin for the numerical solution to accurately represent a sharp interface Model. However, even with a relatively thick interface the results from the Phase Field Model show many of the features of dendritic growth and they are in surprisingly good quantitative agreement with the Ivantsov solution and microscopic solvability theory.
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A Phase-Field Model of Convection With Solidification
40th AIAA Aerospace Sciences Meeting & Exhibit, 2002Co-Authors: Daniel M. Anderson, Geoffrey B. Mcfadden, A. A. WheelerAbstract:A Phase-Field Model for the solidification of a pure material that incorporates convection has recently been developed [Anderson, McFadden and Wheeler, Physica D, 135 (2000) pp. 175-194]. This Model is a two-fluid Model in which the solid Phase is Modeled as a sufficiently viscous fluid. The Model allows for the solid and liquid Phases to have different densities and hence allows for expansion or contraction flows upon solidification. In this paper we investigate numerically a simplified version of this Model by considering solidification occurring between the two closelyspaced parallel plates of a Hele-Shaw cell. We assess two key aspects of the Model: (1) the effect of density differences between the solid and liquid Phases during dendritic growth and (2) the role played by the viscosity ratio between the solid and liquid Phases.
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Anisotropic multi-Phase-Field Model: Interfaces and junctions
Physical Review E, 1998Co-Authors: Britta Nestler, A. A. WheelerAbstract:n this paper we bring together and extend two recent developments in Phase-Field Models, namely, a Phase-Field Model of a multiPhase system [I. Steinbach et al., Physica D 94, 135 (1996)] and the extension of the Cahn-Hoffman ?-vector theory of anisotropic sharp interfaces to Phase-Field Models [A. A. Wheeler and G. B. McFadden, Eur. J. Appl. Math. 7, 369 (1996); Proc. R. Soc. London, Ser. A 453, 1611 (1997)]. We develop the Phase-Field Model of a multiPhase system proposed by Steinbach et al. to include both surface energy and interfacial kinetic anisotropy. We show that this Model may be compactly expressed in terms of generalized Cahn-Hoffman ? vectors. This generalized Cahn-Hoffman ?-vector formalism is subsequently developed to include the notion of a stress tensor, which is used to succinctly derive the leading-order conditions at both moving interfaces and stationary multijunctions in the sharp interface limit.
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Phase-Field Model for solidification of a eutectic alloy
Proceedings of the Royal Society of London. Series A: Mathematical Physical and Engineering Sciences, 1996Co-Authors: A. A. Wheeler, Geoffrey B. Mcfadden, W. J. BoettingerAbstract:In this paper we discuss two Phase-Field Models for solidification of a eutectic alloy, a situation in which a liquid may transform into two distinct solid Phases. The first is based on a regular solution Model for the solid with a chemical miscibility gap. This Model suffers from the deficiency that, in the sharp interface limit, it approximates a free-boundary problem in which the surface energy of the solid-solid interface is zero and consequently mechanical equilibrium at a trijunction requires that the solid-solid interface has zero dihedral angle (locally planar). We propose a second Model which uses two order parameters to distinguish the liquid Phase and the two solid Phases. We provide a thermodynamically consistent derivation of this Phase-Field Model which ensures that the local entropy production is positive. We conduct a sharp interface asymptotic analysis of the liquid-solid Phase transition and show it is governed by a free-boundary problem in which both surface energy and interface kinetics are present. Finally, we consider a sharp interface asymptotic analysis of a stationary trijunction between the two solid Phases and the liquid Phase, from which we recover the condition that the interfacial surface tensions are in mechanical equilibrium (Young's equation). This sharp interface analysis compares favourably with numerical solutions of the Phase-Field Model appropriate to a trijunction.
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Phase Field Model of solute trapping during solidification
Physical Review A, 1993Co-Authors: A. A. Wheeler, W. J. Boettinger, G B McfaddenAbstract:A Phase-Field Model for isothermal solidification of a binary alloy is developed that includes gradient energy contributions for the Phase Field and for the composition Field. When the gradient energy coefficient for the Phase Field is smaller than that for the solute Field, planar steady-state solutions exhibit a reduction in the segregation predicted in the liquid Phase ahead of an advancing front (solute trapping), and, in the limit of high solidification speeds, predict alloy solidification with no redistribution of composition. Such situations are commonly observed experimentally
P W Voorhees - One of the best experts on this subject based on the ideXlab platform.
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Phase-Field Model of oxidation: Kinetics.
Physical Review E, 2020Co-Authors: Kyoungdoc Kim, Quentin Sherman, Larry K. Aagesen, P W VoorheesAbstract:The kinetics of oxidation is examined using a Phase-Field Model of electrochemistry when the oxide film is smaller than the Debye length. As a test of the Model, the Phase-Field approach recovers the results of classical Wagner diffusion-controlled oxide growth when the interfacial mobility of the oxide-metal interface is large and the films are much thicker than the Debye length. However, for small interfacial mobilities, where the growth is reaction controlled, we find that the film increases in thickness linearly in time, and that the Phase-Field Model naturally leads to an electrostatic overpotential at the interface that affects the prefactor of the linear growth law. Since the interface velocity decreases with the distance from the oxide vapor, for a fixed interfacial mobility, the film will transition from reaction- to diffusion-controlled growth at a characteristic thickness. For thin films, we find that in the limit of high interfacial mobility we recover a Wagner-type parabolic growth law in the limit of a composition-independent mobility. A composition-dependent mobility leads to a nonparabolic kinetics at small thickness, but for the materials parameters chosen, the deviation from parabolic kinetics is small. Unlike classical oxidation Models, we show that the Phase-Field Model can be used to examine the dynamics of nonplanar oxide interfaces that are routinely observed in experiment. As an illustration, we examine the evolution of nonplanar interfaces when the oxide is growing only by anion diffusion and find that it is morphologically stable.
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Phase-Field Model of oxidation: Equilibrium.
Physical review. E, 2017Co-Authors: Q C Sherman, P W VoorheesAbstract:A Phase-Field Model of an oxide relevant to corrosion resistant alloys for film thicknesses below the Debye length L_{D}, where charge neutrality in the oxide does not occur, is formulated. The Phase-Field Model is validated in the Wagner limit using a sharp interface Gouy-Chapman Model for the electrostatic double layer. The Phase-Field simulations show that equilibrium oxide films below the Wagner limit are charged throughout due to their inability to electrostatically screen charge over the length of the film, L. The character of the defect and charge distribution profiles in the oxide vary depending on whether reduced oxygen adatoms are present on the gas-oxide interface. The Fermi level in the oxide increases for thinner films, approaching the Fermi level of the metal in the limit L/L_{D}→0, which increases the driving force for adsorbed oxygen reduction at the gas-oxide interface.
Seong Gyoon Kim - One of the best experts on this subject based on the ideXlab platform.
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Phase-Field Model with a reduced interface diffuseness
Journal of Crystal Growth, 2004Co-Authors: Seong Gyoon Kim, Won Tae Kim, Toshio SuzukiAbstract:We reduce the interface diffuseness in Phase-Field Modeling of solidification by localizing the solute redistribution (or latent heat release) into a narrow region within the Phase-Field interface. The numerical computations on the dendritic solidification in a symmetric case and in an one-sided system yield quantitatively the same results with the standard Phase Field Model and the anti-trapping Model [Phys. Rev. Lett. 87 (2001) 115701], respectively, indicating the anomalous interfacial effects in thin interface Phase Field Model can be effectively suppressed. The adoption of the parabolic potential instead of the fourth-order potential makes this Model effective in suppressing a spurious attractive interaction between two closely spaced interfaces due to a clear cut of interface region.
-
Phase-Field Model for solidification of ternary alloys coupled with thermodynamic database
Scripta Materialia, 2003Co-Authors: Hiroki Kobayashi, Won Tae Kim, Seong Gyoon Kim, Machiko Ode, Toshio SuzukiAbstract:Abstract A Phase-Field Model coupled to real thermodynamic data in which the vanishing kinetic coefficient condition is proposed. The validity of the Model is examined by comparing the calculated result of the equilibrium state with theoretical predictions for both one and two-dimensional simulations. Numerical simulations of micro-segregation and isothermal dendrite growth is presented to demonstrate the effectiveness of the Model.
-
Phase-Field Model of dendritic growth
Journal of Crystal Growth, 2001Co-Authors: Toshio Suzuki, Seong Gyoon Kim, Machiko Ode, Won Tae KimAbstract:Abstract The Phase-Field Models for binary and ternary alloys are introduced, and the governing equations and Phase-Field parameters for dilute alloys are derived at a thin interface limit. The Phase-Field simulations on isothermal dendrite growth for Fe-C, Fe-P and Fe-C–P alloys are carried out and the effect of the ternary alloying element on dendrite growth is examined. The secondary arm spacing for Fe-C, Fe-P and Al–Cu alloys is numerically predicted using the Phase-Field Model and compared to the experimental data. The change in the arm spacing, and the exponent of local solidification time depending on alloy is systematically examined by imposing artificial set of physical properties. The Phase-Field simulation for the microstructure evolution during rapid solidification is also successfully carried out. Through the numerical examples, the wide potentiality of the Phase-Field Model to the applications on solidification has been demonstrated.
-
Recent advances in the Phase-Field Model for solidification
ISIJ International, 2001Co-Authors: Machiko Ode, Seong Gyoon Kim, Toshio SuzukiAbstract:The recent development of the Phase-Field Models for solidification and their application examples are briefly reviewed. The Phase-Field Model is firstly proposed for pure material systems and then extended to binary alloy, multi-Phase and multi-component systems theoretically. Though the calculation conditions are limited due to the sharp interface limit parameters in the early stage, it is widened in the thin interface limit Model. The development of the Phase-Field Model is summarized from a viewpoint of the formulation of Phase-Field equation and parameters. The important studies and the latest results such as application examples of free dendrite growth, directional solidification, Ostwald ripening, interface-particle interaction and multi-Phase simulation are mentioned. Finally future works of the Phase-Field Model are prospected.
-
Phase–Field Model for solidification of Fe–C alloys
Science and Technology of Advanced Materials, 2000Co-Authors: Machiko Ode, Toshio Suzuki, Seong Gyoon Kim, W.t KimAbstract:The Phase-Field Model for binary alloys by Kim et al. is briefly introduced and the main difference in the definition of free energy density in interface region between the Models by Kim et al. and by Wheeler et al. is discussed. The governing equations for a dilute binary alloy are derived and the Phase-Field parameters are obtained at a thin interface limit. The examples of the Phase-Field simulation on Ostwald ripening, isothermal dendrite growth and particle/interface interaction for Fe–C alloys are demonstrated. In Ostwald ripening, it is shown that small solid particles preferably melt out and then large particles agglomerate. In isothermal dendrite growth, the kinetic coefficient dependence on growth rate is examined for both the Phase-Field Model and the dendrite growth Model by Lipton et al. The growth rate by the dendrite Model shows strong kinetic coefficient dependence, though that by the Phase-Field Model is not sensitive to it. The particle pushing and engulfment by interface are successfully reproduced and the critical velocity for the pushing/engulfment transition is estimated. Through the simulation, it is shown that the Phase-Field Model correctly reproduces the local equilibrium condition and has the wide potentiality to the applications on solidification.
Britta Nestler - One of the best experts on this subject based on the ideXlab platform.
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Calibration of a multi-Phase Field Model with quantitative angle measurement
Journal of Materials Science, 2016Co-Authors: Johannes Hötzer, Oleg Tschukin, Marouen Ben Said, Marco Berghoff, Marcus Jainta, Georges Barthelemy, Nikolay Smorchkov, Daniel Schneider, Michael Selzer, Britta NestlerAbstract:Over the last years, the Phase-Field method has been established to Model capillarity-induced microstructural evolution in various material systems. Several Phase-Field Models were introduced and different studies proved that the microstructure evolution is crucially affected by the triple junction (TJ’s) mobilities as well as the evolution of the dihedral angles. In order to understand basic mechanisms in multi-Phase systems, we are interested in the time evolution of TJ’s, especially in the contact angles in these regions. Since the considered multi-Phase systems consist of a high number of grains, it is not feasible to measure the angles at all TJ’s by hand. In this work, we present a method enabling the localization of TJ’s and the measurement of dihedral contact angles in the diffuse interface inherent in the Phase-Field Model. Based on this contact angle measurement method, we show how to calibrate the Phase-Field Model in order to satisfy Young’s law for different contact angles.
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Anisotropic multi-Phase-Field Model: Interfaces and junctions
Physical Review E, 1998Co-Authors: Britta Nestler, A. A. WheelerAbstract:n this paper we bring together and extend two recent developments in Phase-Field Models, namely, a Phase-Field Model of a multiPhase system [I. Steinbach et al., Physica D 94, 135 (1996)] and the extension of the Cahn-Hoffman ?-vector theory of anisotropic sharp interfaces to Phase-Field Models [A. A. Wheeler and G. B. McFadden, Eur. J. Appl. Math. 7, 369 (1996); Proc. R. Soc. London, Ser. A 453, 1611 (1997)]. We develop the Phase-Field Model of a multiPhase system proposed by Steinbach et al. to include both surface energy and interfacial kinetic anisotropy. We show that this Model may be compactly expressed in terms of generalized Cahn-Hoffman ? vectors. This generalized Cahn-Hoffman ?-vector formalism is subsequently developed to include the notion of a stress tensor, which is used to succinctly derive the leading-order conditions at both moving interfaces and stationary multijunctions in the sharp interface limit.
