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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.
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 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.
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Phase-Field Model for binary alloys.
Physical Review E, 1999Co-Authors: Seong Gyoon Kim, Won Tae Kim, Toshio SuzukiAbstract:We present a phase-Field Model (PFM) for solidification in binary alloys, which is found from the phase-Field Model for a pure material by direct comparison of the variables for a pure material solidification and alloy solidification. The Model appears to be equivalent with the Wheeler-Boettinger-McFadden (WBM) Model [A.A. Wheeler, W. J. Boettinger, and G. B. McFadden, Phys. Rev. A 45, 7424 (1992)], but has a different definition of the free energy density for interfacial region. An extra potential originated from the free energy density definition in the WBM Model disappears in this Model. At a dilute solution limit, the Model is reduced to the Tiaden et al. Model [Physica D 115, 73 (1998)] for a binary alloy. A relationship between the phase-Field mobility and the interface kinetics coefficient is derived at a thin-interface limit condition under an assumption of negligible diffusivity in the solid phase. For a dilute alloy, a steady-state solution of the concentration profile across the diffuse interface is obtained as a function of the interface velocity and the resultant partition coefficient is compared with the previous solute trapping Model. For one dimensional steady-state solidification, where the classical sharp-interface Model is exactly soluble, we perform numerical simulations of the phase-Field Model: At low interface velocity, the simulated results from the thin-interface PFM are in excellent agreement with the exact solutions. As the partition coefficient becomes close to unit at high interface velocities, whereas, the sharp-interface PFM yields the correct answer.
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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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 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
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Towards a Phase Field Model for Phase Transitions in Binary Alloys
On the Evolution of Phase Boundaries, 1992Co-Authors: A. A. Wheeler, W. J. BoettingerAbstract:To date phase Field Models have only been used to Model non-isothermal phase transitions in a pure material. Here we describe recent steps which aim to extend phase Field Models to deal with binary alloys; a situation of metallurgical and industrial importance. To this end we present a new phase Field Model for isothermal phase transitions in a binary alloy and discuss the results of an asymptotic analysis. Finally we suggest ways in which these Models may be further developed to achieve our aim of a non-isothermal phase Field Model of a binary alloy.
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phase Field Model for isothermal phase transitions in binary alloys
Physical Review A, 1991Co-Authors: A. A. Wheeler, W. J. Boettinger, G B McfaddenAbstract:In this paper we present a phase-Field Model to describe isothermal phase transitions between ideal binary-alloy liquid and solid phases. Governing equations are developed for the temporal and spatial variation of the phase Field, which identifies the local state or phase, and for the composition. An asymptotic analysis as the gradient energy coefficient of the phase Field becomes small shows that our Model recovers classical sharp-interface Models of alloy solidification when the interfacial layers are thin, and we relate the parameters appearing in the phase-Field Model to material and growth parameters in real systems. We identify three stages of temporal evolution for the governing equations: the first corresponds to interfacial genesis, which occurs very rapidly; the second to interfacial motion controlled by diffusion and the local energy difference across the interface; the last takes place on a long time scale in which curvature effects are important, and corresponds to Ostwald ripening. We also present results of numerical calculations.
Jun Chen - One of the best experts on this subject based on the ideXlab platform.
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Random Field Model of sequential ground motions
Bulletin of Earthquake Engineering, 2020Co-Authors: Jiaxu Shen, Jun Chen, Guo DingAbstract:This paper proposes a random Field Model of sequential ground motions, which considers the spatial correlation between the mainshock and aftershock from a stochastic view. First, the correlation between the mainshock and aftershock under the physical “source–path–local site” mechanism is explained. Based on the mechanism, the point-source Model, and uniform-isotropic-medium Model, a random single-point Model for sequential ground motion with eight basic parameters is presented. Second, the random Field Model is developed from the random single-point Model. More than 1000 pairs of sequential ground motions are used to identify and analyze statistically the basic parameters in the Model. Moreover, the probability distribution of each parameter is presented based on copula functions. The results show that the spatial correlations of sequential ground motions can be effectively simulated based on the proposed random Field Model. Furthermore, it is possible to realistically reproduce the attenuation and time lag of ground motions at a local site.
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Random Field Model for crowd jumping loads
Structural Safety, 2019Co-Authors: Jiecheng Xiong, Jun ChenAbstract:Abstract A reliable Model for crowd jumping loads is a prerequisite to an accurate prediction of a long-span structure’s response when subjected to crowd motion triggered by music and other mass appeal events. Because of the lack of crowd jumping experimental data, crowd jumping load Models are scarce with few data available on this type of synchronisation among people. Inspired by the random Field Model of earthquake excitations, this study attempts to develop a random Field Model for crowd jumping loads based on extensive records from unique crowd jumping load experiments. A framework for the random Field Model of crowd jumping is first proposed, in which auto-power spectral density (PSD) and cross-PSD functions of individual and group jumping loads are defined. The auto-PSD was obtained by updating a Model in a previous study. Experiments were conducted on a jumping group of 48 persons using a 3D motion capture technology. A cross-PSD Model for any two persons in a jumping group was then developed based on the experimental data. Having obtained a PSD matrix for crowd jumping, the structural response could then be predicted by the stochastic vibration theory. Finally, the feasibility of the Model was verified by comparing the measured responses of an existing floor with the prediction responses using the proposed Model.
Rongshan Qin - One of the best experts on this subject based on the ideXlab platform.
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A phase-Field Model for bainitic transformation
Computational Materials Science, 2013Co-Authors: Tansel T. Arif, Rongshan QinAbstract:A phase-Field Model for the computation of microstructure evolution for the bainite transformation has been developed. The Model has a classical phase-Field foundation, incorporates the phenomenological displacive transformation theory and the symmetric analysis of cubic crystals, and is able to reproduce realistic grain morphology and crystal orientation after adequate calibration. Using the free energy expression for the shape change of displacive transformations along with the free energy formula for the chemical free energy change of the two phases derived from established regular solution Models, the current Model is able to deal with autocatalysis.
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A phase-Field Model for the solidification of multicomponent and multiphase alloys
Journal of Crystal Growth, 2005Co-Authors: Rongshan Qin, E. R. Wallach, Rachel C. ThomsonAbstract:Abstract A phase-Field Model for the simulation of solidification of a multicomponent and multiphase systems has been developed, which is based on an earlier developed multiphase Field Model for binary alloys and a phase-Field multicomponent Model for single-solid-phase systems. After incorporation with alloy thermodynamics and commercial software for the calculation of phase equilibria, the Model has been implemented to study the microstructural evolution of an Al–11.5 mol% Si–0.9 mol% Cu–0.4 mol% Fe alloy. Numerical results for the morphological evolution of primary aluminium, silicon and AlFeSi intermetallic phases agree with experimental observations very well.
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A phase-Field Model coupled with a thermodynamic database
Acta Materialia, 2003Co-Authors: Rongshan Qin, E. R. WallachAbstract:Abstract A phase-Field Model for the solidification of multi-component alloys, capable of being integrated with thermodynamic databases, has been developed. The solid–liquid interface is Modelled as a mixture of solid and liquid phases. The solute concentration of the solid phase depends only on the local temperature while the solute concentration of the liquid phase is affected by solute rejection (or absorption) from the solid being formed together with the extent of any chemical diffusion in the liquid. The governing equations for the phase-Field Model have been derived in a thermodynamically consistent way such that the parameters in these equations are fully determined. By linking directly with the thermodynamic database MTDATA, the Model is capable of simulating the microstructural evolution of real alloys. Numerical calculations for aluminium–silicon alloys show that the phase-Field driving force changes in a similar manner to the thermodynamic driving force, although the phase-Field driving force changes more quickly than the thermodynamic driving force when the system approaches equilibrium. The phase-Field mobility is shown not to be a trivial function of constitutional undercooling. With the new phase-Field Model, the width of the liquid–solid interface region is allowed a much large value with the continuity of all parameters in the phase-Field Model and properties of interface maintained, and hence the Model is suitable for simulating large-scale systems.
