A thick-interface model for diffusive and massive phase transformation in substitutional alloys

Svoboda, Jiřı́; Vála, Jiří; Gamsjäger, Ernst; Fischer, Franz Dieter

doi:10.1016/j.actamat.2006.04.027

Cited by 32 publications

(19 citation statements)

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“…However the formula for calculating the solute drag for a migrating phase boundary into a multi-component system in steady-state conditions has been a subject of debates over the years and it was only recently that a valid expression has been found with a remarkable amount of empirical insight [11]. The general expression has also been derived in a deductive and completely independent way by applying the principle of maximum dissipation in [12].Even if in the recent years more complex situations than the one treated in the initial works of Cahn [2] and …”

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confidence: 99%

“…Even if in the recent years more complex situations than the one treated in the initial works of Cahn [2] and Lücke and Stüwe [10] could be tackled, as two different types of solute [13][14], curved interfaces [15], solute drag occurring in a regular solid solution [16], during massive phase transformations [12,[17][18][19][20] or in non-steady state condition [21][22], they rely on the same framework: the composition profile of the solute atoms around the migrating phase boundary is calculated by solving Fick's law for diffusion and then the solute drag stems from the solute profile by applying the appropriate equation. In this paper, however we will limit our discussion to the initial case treated by Cahn [2] and Lücke and Stüwe [10]: a moving grain boundary in a binary solid solution which is supposed ideal.…”

Section: Introductionmentioning

confidence: 99%

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The Effect of Solute Atoms on Grain Boundary Migration: A Solute Pinning Approach

Hersent

Marthinsen

Nes

2013

Metall Mater Trans A

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The effect of solute atoms on grain boundary migration has been modelled on the basis of the idea that solute atoms will locally perturb the collective re-arrangements of solvent atoms associated with boundary migration. The consequence of such perturbations is cusping of the boundary and corresponding stress concentrations on the solute atoms which will promote thermal activation of these atoms out of the boundary. This thermal activation is considered to be the rate-controlling mechanism in boundary migration. It is demonstrated that the present statistical approach is capable of explaining, in phenomenological terms, the known effects of solute atoms on boundary migration. The experimental results on the effect of copper on boundary migration in aluminium, due to Gordon and Vandermeer, have been well accounted for. INTRODUCTIONIt has been known for a long time that impurity solid solution atoms have a tendency of segregation to grain boundaries, an effect which may strongly retard the grain boundary mobility and thus the kinetics of recrystallization and grain growth in pure metals, even when present in the ppm range. (commonly referred as the dissipation approach). Typical application examples for the force and dissipation approach are respectively [4][5] and [6]. In the force approach the solute drag is estimated by summing the forces that the solute atoms exert on the boundary and in the dissipation approach by evaluating the amount of free energy dissipated due to diffusion when the boundary goes through a volume containing one mole of material. Over the last decades, a lot of efforts have been made to generalize these approaches to a migrating phase boundary into a multi-component system [3,[7][8][9].Indeed in the initial treatment of the solute drag effect by Cahn and by Lücke and Stüwe [10] the equation used for evaluating the solute drag does not apply to phase transformations. It only applies to the migration of grain boundaries, i.e. to one phase materials.The force approach and the dissipation approach have both a sound physical basis and should therefore be equivalent. However the formula for calculating the solute drag for a migrating phase boundary into a multi-component system in steady-state conditions has been a subject of debates over the years and it was only recently that a valid expression has been found with a remarkable amount of empirical insight [11]. The general expression has also been derived in a deductive and completely independent way by applying the principle of maximum dissipation in [12].Even if in the recent years more complex situations than the one treated in the initial works of Cahn [2] and BACKGROUND THEORIESThe where m is the intrinsic boundary mobility (i.e. that corresponding to c = 0). The treatments by Cahn[2] and Lücke and Stüwe [10,23] are derived on the basis of the assumption that the effects on boundary mobility due to the cusp-formation resulting from the solute-boundary interaction can be neglected, the validity of this assumption is discussed belo...

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confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Effect of Solute Atoms on Grain Boundary Migration: A Solute Pinning Approach

Hersent

Marthinsen

Nes

2013

Metall Mater Trans A

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“…. Lu¨cke and Stu¨we [16], Svoboda et al [8,17], and Odqvist et al [18] demonstrated that transformation kinetics with diffusion processes in the interface (solute drag) playing a role can also be simulated within the framework of linear nonequilibrium thermodynamics by assigning a finite thickness to the interfacial region. The dissipation due to diffusion in the interface depends on the interface velocity, and different interface velocities are obtained by assigning different thicknesses to the interfacial region.…”

Section: Total Dissipation and Rate Of Gibbs Energy For The Sharp Intmentioning

confidence: 99%

A concise derivation of the contact conditions at a migrating sharp interface

Gamsjäger

2008

Philosophical Magazine Letters

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A sharp interface model can be used to simulate the kinetics of diffusional phase transformations provided the transformation process is controlled by migration of the interface and by diffusion of components in the bulk phases only. The contact conditions at the migrating sharp interface can be derived by applying the principles of mass balance and maximum dissipation. A concise derivation of the contact conditions on this basis is presented in this work.

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“…As temperature and pressure are assumed to be constant in the system at least for a limited period of time, the search for the maximum in entropy production can be shifted to that for maximum Gibbs energy dissipation Q. In linear non-equilibrium thermodynamics, the dissipation Q in a system with n degrees of freedom is given by a quadratic form of the rates q ؒ i (7) with B ik being a positive, definite coefficient matrix.…”

Section: Maximum Entropy Productionmentioning

confidence: 99%

“…Models that take into account all the above-mentioned dissipative processes are presented in the literature [6,7]. However, most of these thick interface-finite mobility (TI-FM) models are confined to steady-state conditions.…”

Section: Introductionmentioning

confidence: 99%

Kinetics of diffusive phase transformations: From local equilibrium to mobility-driven migration of thick interfaces

Gamsjäger

2011

Pure and Applied Chemistry

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It is a prerequisite for the occurrence of diffusive phase transformations that the system is in an off-equilibrium condition. The time-dependent development of the variables until equilibrium or steady-state conditions are reached can be calculated by solving the evolution equations that can be derived from the principle of maximum entropy production. These equations provide the theoretical framework for the kinetics of diffusive phase transformations. In this work, the development from sharp interface-local equilibrium (SI-LE) models to thick interface-finite mobility (TI-FM) models is reviewed and presented in the light of the above-mentioned principle. Experimental results indicate that the kinetics of diffusive solid-state phase transformations can, at least in certain ranges of composition and temperature, be modeled in a satisfactory manner by the TI-FM approach only.

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A thick-interface model for diffusive and massive phase transformation in substitutional alloys

Cited by 32 publications

References 11 publications

The Effect of Solute Atoms on Grain Boundary Migration: A Solute Pinning Approach

The Effect of Solute Atoms on Grain Boundary Migration: A Solute Pinning Approach

A concise derivation of the contact conditions at a migrating sharp interface

Kinetics of diffusive phase transformations: From local equilibrium to mobility-driven migration of thick interfaces

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