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## Numerical simulation of solute trapping phenomena using phase-field solidification model for dilute binary alloys

Fonte: ABM, ABC, ABPol Publicador: ABM, ABC, ABPol
Tipo: Artigo de Revista Científica Formato: text/html
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Numerical simulation of solute trapping during solidification, using two phase-field model for dilute binary alloys developed by Kim et al. [Phys. Rev. E, 60, 7186 (1999)] and Ramirez et al. [Phys. Rev. E, 69, 05167 (2004)] is presented here. The simulations on dilute Cu-Ni alloy are in good agreement with one dimensional analytic solution of sharp interface model. Simulation conducted under small solidification velocity using solid-liquid interface thickness (2λ) of 8 nanometers reproduced the solute (Cu) equilibrium partition coefficient. The spurious numerical solute trapping in solid phase, due to the interface thickness was negligible. A parameter used in analytical solute trapping model was determined by isothermal phase-field simulation of Ni-Cu alloy. Its application to Si-As and Si-Bi alloys reproduced results that agree reasonably well with experimental data. A comparison between the three models of solute trapping (Aziz, Sobolev and Galenko [Phys. Rev. E, 76, 031606 (2007)]) was performed. It resulted in large differences in predicting the solidification velocity for partition-less solidification, indicating the necessity for new and more acute experimental data.

## Random-Walk Model of Diffusion in Three Dimensions in Brain Extracellular Space: Comparison with Microfiberoptic Photobleaching Measurements

Jin, Songwan; Zador, Zsolt; Verkman, A. S.
Fonte: The Biophysical Society Publicador: The Biophysical Society
Tipo: Artigo de Revista Científica
Português
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Diffusion through the extracellular space (ECS) in brain is important in drug delivery, intercellular communication, and extracellular ionic buffering. The ECS comprises ∼20% of brain parenchymal volume and contains cell-cell gaps ∼50 nm. We developed a random-walk model to simulate macromolecule diffusion in brain ECS in three dimensions using realistic ECS dimensions. Model inputs included ECS volume fraction (α), cell size, cell-cell gap geometry, intercellular lake (expanded regions of brain ECS) dimensions, and molecular size of the diffusing solute. Model output was relative solute diffusion in water versus brain ECS (Do/D). Experimental Do/D for comparison with model predictions was measured using a microfiberoptic fluorescence photobleaching method involving stereotaxic insertion of a micron-size optical fiber into mouse brain. Do/D for the small solute calcein in different regions of brain was in the range 3.0–4.1, and increased with brain cell swelling after water intoxication. Do/D also increased with increasing size of the diffusing solute, particularly in deep brain nuclei. Simulations of measured Do/D using realistic α, cell size and cell-cell gap required the presence of intercellular lakes at multicell contact points...

## Aperiodic Stepwise Growth Model for the Velocity and Orientation Dependence of Solute Trapping

Goldman, L.M.; Aziz, Michael
Fonte: Materials Research Society Publicador: Materials Research Society
Português
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An atomistic model for the dependence on interface orientation and velocity v of the solute partition coefficient k during rapid solidification is developed in detail. Starting with a simple stepwise growth model, the simple continuous growth model result is obtained for k(v) when the growth steps are assumed to pass at random intervals rather than periodically. The model is applied to rapid solidification of silicon. Crystal growth at all orientations is assumed to occur by the rapid lateral passage of (111) steps at speeds determined by the interface velocity and orientation. Solute escape is parametrized by a diffusion coefficient at the edge of the moving step and a diffusion coefficient at the terrace, far from the step edge. The model results in an excellent fit to data for the velocity and orientation dependence of k of Bi in Si.; Physics

## Solute Trapping of Group III, IV, and V Elements in Silicon by an Aperiodic Stepwise Growth Mechanism

Reitano, Riccardo; Aziz, Michael; Smith, Patrick M.
Fonte: American Institute of Physics Publicador: American Institute of Physics
Português
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513.27668%
With rapid solidification following pulsed laser melting, we have measured the dependence on interface orientation of the amount of solute trapping of several group III, IV, and V elements (As, Ga, Ge, In, Sb, Sn) in Si. The aperiodic stepwise growth model of Goldman and Aziz accurately fits both the velocity and orientation dependence of solute trapping of all of these solutes except Ge. The success of the model implies a ledge structure for the crystal/melt interface and a step-flow mechanism for growth from the melt. In addition, we have observed an empirical inverse correlation between the two free parameters (-“diffusive speeds”) in this model and the equilibrium solute partition coefficient of a system. This correlation may be used to estimate values of these free parameters for other systems in which solute trapping has not or cannot be measured. The possible microscopic origin of such a correlation is discussed.; Engineering and Applied Sciences

## Parameter-Free Test of Alloy Dendrite Growth Theory

Arnold, Craig B.; Herlach, Dieter M.; Aziz, Michael; Schwarz, Matthias
Fonte: The American Physical Society Publicador: The American Physical Society
Português
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289.7422%
In rapid alloy solidification the dendrite-growth velocity depends sensitively on the deviations from local interfacial equilibrium manifested by kinetic effects such as solute trapping. The dendrite tip velocity undercooling function was measured in dilute Ni~Zr! over the range 1–25 m/s and 50–255 K using electromagnetic levitation techniques and compared to theoretical predictions of the model of Trivedi and colleagues for dendritic growth with deviations from local interfacial equilibrium. The input parameter to which the model predictions are most sensitive, the diffusive speed VD characterizing solute trapping, was not used as a free parameter but was measured independently by pulsed laser melting techniques, as was another input parameter, the liquid diffusivity DL. Best-fit values from the pulsed laser melting experiment are VD526 m/s and DL 52.731029 m2/s. Inserting these values into the dendrite growth model results in excellent agreement with experiment with no adjustable parameters.; Engineering and Applied Sciences

## Solute Trapping of Ge in Al

West, Jeffrey A.; Smith, Patrick M.; Aziz, Michael
Fonte: Materials Research Society Publicador: Materials Research Society
Português
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500.68805%
Partitioning during rapid solidification of dilute Al-Ge alloys has been investigated. Implanted thin films of Al have been pulsed-laser melted to obtain solidification at velocities in the range of 0.01 m/s to 3.3 m/s, as measured by the transient conductance technique. Previous and subsequent Rutherford Backscattering depth profiling of the Ge solute in the Al alloys has been used to determine the nonequilibrium partition coefficient k. A significant degree of lateral film growth during solidification confines determination of k to the placing of an upper bound of 0.22 on k for solidification velocities in this range. We place a lower limit of 10 m/s on the "diffusive velocity," which locates the transition from solute paritioning to solute trapping in the Continuous Growth Model.; Engineering and Applied Sciences

## Crystal Growth and Solute Trapping

Aziz, Michael J.
Fonte: Materials Research Society Publicador: Materials Research Society
Tipo: Artigo de Revista Científica
Português
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506.7324%
A simple model for solute trapping during rapid solidification is presented in terms of a single unknown parameters, the interfacial diffusivity Di. A transition from equilibrium segregation to complete solute trapping occurs over roughly an order of magnitude in growth speed, as the interface speed surpasses the maximum speed with which solute atoms can diffuse across the interface to remain ahead of the growing crystal. This diffusive speed is given by Di/Lambda, where Lambda is the interatomic spacing, and is typically of the order 10 meters per second. Comparison is made with experiment. The steady-state speed of a planar interface is predicted by calculating the free energy dissipated by irreversible processes at the interface and equating it to the available driving free energy. Steady-state solutions are presented for Bi-doped Si during pulsed laser annealing.; Engineering and Applied Sciences

## Dissipation-Theory Treatment of the Transition from Diffusion-Controlled to Diffusionless Solidification

Aziz, Michael J.
Fonte: American Institute of Physics Publicador: American Institute of Physics
Tipo: Artigo de Revista Científica
Português
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The steady-state velocity of a planar liquid-solid interface is predicted by calculating the free energy dissipated by irreversible processes at the interface and equating it to the available driving free energy. A solute drag term and an intrinsic interfacial mobility term are included in the dissipation calculations for a binary alloy. The solute drag calculation employs a solute trapping model, which has been extended to concentrated alloys. The result is presented in terms of a single unknown parameter, the interfacial diffusivity Di. A transition from diffusion controlled to diffusionless solidification occurs over approximately an order of magnitude in growth velocity, as the interface speed surpasses the maximum speed with which solute atoms can diffuse across the interface to remain ahead of the growing crystal.; Engineering and Applied Sciences

## Dendritic Growth Velocity and Diffusive Speed in Solidification of Undercooled Dilute Ni-Zr Melts

Schwarz, Mikael; Aziz, Michael; Arnold, Craig B.; Herlach, Dieter M.
Português
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506.2821%
During rapid solidification of undercooled melts deviations from local equilibrium occur at the solid-liquid interface. With increasing interface velocity v, the interfacial undercooling DeltaT-i increases and solute trapping becomes important. These phenomena are well characterized for planar interfaces, but for dendritic growth they must be incorporated into dendrite growth theory and the combination tested. The predictions of dendrite growth theory are very sensitive to the diffusive speed-the interface speed at which the solute trapping function is in mid transition between local equilibrium and complete trapping. Dendrite growth velocities have been measured as a function of undercooling in levitated droplets of Ni99Zr1 alloys. The results are described within current theory of dendrite growth taking into account deviations from local equilibrium. The diffusive speed is independently determined by preliminary pulsed laser melting experiments on thin film specimens for the same alloy system. Best fit values of the diffusive speed inferred from both sets of measurements are similar in magnitude. Given the preliminary nature of the pulsed laser melting measurements, this result is encouraging for the prospects of a parameter-free test of modern dendrite growth theory.; Engineering and Applied Sciences

## Solute Trapping in Silicon by Lateral Motion of {111} Ledges

White, C. Woody; Aziz, Michael
Fonte: American Physical Society Publicador: American Physical Society
Português
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489.7422%
The orientation dependence of the nonequilibrium partition coefficient of Bi in Si at constant solid-liquid interface velocity has been measured. The partition coefficient, measured with pulsed-laser melting techniques on a series of Si wafers cut at 5° increments from (110) through (111) to (001), is sharply peaked at (111) and decreases monotonically with increasing inclination from (111). The results suggest that crystal growth and solute trapping occur by the lateral motion of {111} ledges.; Engineering and Applied Sciences

## Model for Solute Redistribution During Rapid Solidification

Aziz, Michael
Fonte: American Institute of Physics Publicador: American Institute of Physics
Português
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403.51277%
A microscopic model for impurity uptake at a sharp crystal-liquid interface during alloy solidification is presented in terms of the bulk properties of the liquid and solid phases. The results for stepwise growth and continuous growth at the same interface velocity differ quantitatively but exhibit the same qualitative features. A transition from equilibrium segregation to complete solute trapping occurs as the velocity surpasses the diffusive speed of solute in the liquid. The location of the transition varies little with equilibrium segregation coefficient, and a kinetic limit to solute trapping is found to be quite unlikely. Comparison is made with other models; critical differences are pointed out. Coupled with a growth velocity equation and with macroscopic heat- and solute-diffusion equations, the model forms a complete description of one-dimensional crystal growth. The steady-state solution to this system is indicated for the case of a planar interface. The results are applied to describe regrowth from laser-induced melting. Preliminary comparison with experiment is made. The steady-state solution for thermal and impurity transport is suggested for use whenever detailed computer calculations are unavailable or are unnecessarily involved.; Engineering and Applied Sciences

## Experimental Constraints on Nonequilibrium Interface Kinetic Models

Aziz, Michael
Português
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Experimental results relevant to models for nonequilibrium interface kinetics during rapid solidification are reviewed. Models are examined critically in light of these experiments. The kinetic Ising model is shown to compare unfavorably with experiment. The Continuous Growth Model without solute drag and its extension to non-(001) interfaces, the Aperiodic Stepwise Growth Model, account well for all relevant experimental results.; Engineering and Applied Sciences

## Numerical simulation of solute trapping phenomena using phase-field solidification model for dilute binary alloys

Furtado, Henrique Silva; Bernardes, Am?rico Trist?o; Machado, Romuel Figueiredo; Silva, Carlos Ant?nio da
Português
Relevância na Pesquisa
723.7819%
Numerical simulation of solute trapping phenomena using phase-field solidification model for dilute binary alloys Numerical simulation of solute trapping during solidification, using two phase-field model for dilute binary alloys developed by Kim et al. [Phys. Rev. E, 60, 7186 (1999)] and Ramirez et al. [Phys. Rev. E, 69, 05167 (2004)] is presented here. The simulations on dilute Cu-Ni alloy are in good agreement with one dimensional analytic solution of sharp interface model. Simulation conducted under small solidification velocity using solid liquid interface thickness (2?) of 8 nanometers reproduced the solute (Cu) equilibrium partition coefficient. The spurious numerical solute trapping in solid phase, due to the interface thickness was negligible. A parameter used in analytical solute trapping model was determined by isothermal phase-field simulation of Ni-Cu alloy. Its application to Si-As and Si-Bi alloys reproduced results that agree reasonably well with experimental data. A comparison between the three models of solute trapping (Aziz, Sobolev and Galenko [Phys. Rev. E, 76, 031606 (2007)]) was performed. It resulted in large differences in predicting the solidification velocity for partition-less solidification...

## Solute trapping and diffusionless solidification in a binary system

Galenko, Peter
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
509.5571%
Numerous experimental data on the rapid solidification of binary systems exhibit the formation of metastable solid phases with the initial (nominal) chemical composition. This fact is explained by complete solute trapping leading to diffusionless (chemically partitionless) solidification at a finite growth velocity of crystals. Special attention is paid to developing a model of rapid solidification which describes a transition from chemically partitioned to diffusionless growth of crystals. Analytical treatments lead to the condition for complete solute trapping which directly follows from the analysis of the solute diffusion around the solid-liquid interface and atomic attachment and detachment at the interface. The resulting equations for the flux balance at the interface take into account two kinetic parameters: diffusion speed $V_{DI}$ on the interface and diffusion speed $V_D$ in bulk phases. The model describes experimental data on nonequilibrium solute partitioning in solidification of Si-As alloys [M.J. Aziz et al., J. Cryst. Growth {\bf 148}, 172 (1995); Acta Mater. {\bf 48}, 4797 (2000)] for the whole range of solidification velocity investigated.; Comment: Regular article in Physical Review E, Vol. 76 (2007)

## Phase-field modelling of solute trapping during rapid solidification of a Si-As alloy

Danilov, Denis; Nestler, Britta
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
489.7422%
The effect of nonequilibrium solute trapping by a growing solid under rapid solidification conditions is studied using a phase-field model. Considering a continuous steady-state concentration profile across the diffuse solid-liquid interface, a new definition of the nonequilibrium partition coefficient in the phase-field context is introduced. This definition leads, in particular for high growth velocities, to a better description of the available experimental data in comparison with other diffuse interface and sharp-interface predictions.; Comment: revised version published in Acta Mater

## Nonequilibrium molecular dynamics simulation of rapid directional solidification

Celestini, F.; Debierre, J. M.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
296.5182%
We present the results of non-equilibrium molecular dynamics simulations for the growth of a solid binary alloy from its liquid phase. The regime of high pulling velocities, $V$, for which there is a progressive transition from solute segregation to solute trapping, is considered. In the segregation regime, we recover the exponential form of the concentration profile within the liquid phase. Solute trapping is shown to settle in progressively as $V$ is increased and our results are in good agreement with the theoretical predictions of Aziz [J. Appl. Phys. {\bf 53}, 1158 (1981)]. In addition, the fluid advection velocity is shown to remain directly proportional to $V$, even at the highest velocities considered here ($V\simeq10$ms$^{-1}$).; Comment: Submitted to Phys. Rev.B

## A Phase Field Crystal Study of Solute Trapping

Humadi, Harith; Hoyt, Jeffrey J.; Provatas, Nikolas
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
499.5061%
In this study we have incorporated two time scales into the phase field crystal model of a binary alloy to explore different solute trapping properties as a function of crystal-melt interface velocity. With only diffusive dynamics, we demonstrate that the segregation coefficient, K as a function of velocity for a binary alloy is consistent with the model of Kaplan and Aziz where K approaches unity in the limit of infinite velocity. However, with the introduction of wave like dynamics in both the density and concentration fields, the trapping follows the kinetics proposed by S. Sobolev[Phys. Rev. A. 199:383386, 1995.], where complete trapping occurs at a finite velocity.; Comment: 22 pages, 8 figures

## Quantitative Phase Field Model of Alloy Solidification

Echebarria, Blas; Folch, Roger; Karma, Alain; Plapp, Mathis
Tipo: Artigo de Revista Científica
Português
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278.20305%
We present a detailed derivation and thin interface analysis of a phase-field model that can accurately simulate microstructural pattern formation for low-speed directional solidification of a dilute binary alloy. This advance with respect to previous phase-field models is achieved by the addition of a phenomenological "antitrapping" solute current in the mass conservation relation [A. Karma, Phys. Rev. Lett 87, 115701 (2001)]. This antitrapping current counterbalances the physical, albeit artificially large, solute trapping effect generated when a mesoscopic interface thickness is used to simulate the interface evolution on experimental length and time scales. Furthermore, it provides additional freedom in the model to suppress other spurious effects that scale with this thickness when the diffusivity is unequal in solid and liquid [R. F. Almgren, SIAM J. Appl. Math 59, 2086 (1999)], which include surface diffusion and a curvature correction to the Stefan condition. This freedom can also be exploited to make the kinetic undercooling of the interface arbitrarily small even for mesoscopic values of both the interface thickness and the phase-field relaxation time, as for the solidification of pure melts [A. Karma and W.-J. Rappel, Phys. Rev. E 53...

## Microscopic Treatment of Solute Trapping and Drag

Humadi, Harith; Hoyt, J. J.; Provatas, Nikolas
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
389.1489%
The long wavelength limit of a recent microscopic phase field crystal (PFC) theory of a binary alloy mix- ture is used to derive an analytical approximation for the segregation coefficient as a function of the interface velocity, and relate it to the two-point correlation function of the liquid and the thermodynamic properties of solid and liquid phases. Our results offer the first analytic derivation of solute segregation and solute drag de- rived from a microscopic model, and analytically support recent molecular dynamics and fully numerical PFC simulations. Our analytical result also provides an independent framework, motivated from classical density functional theory, from which to elucidate the fundamental nature of solute drag, which is still highly contested in the literature.

## Electron Trapping by Polar Molecules in Alkane Liquids: Cluster Chemistry in Dilute Solution

Shkrob, Ilya A.; Sauer, Jr., Myran C.