Application of the thermodynamic extremal principle to the diffusional phase transformations

Svoboda, Jiřı́; Gamsjäger, Ernst; Fischer, Franz Dieter; Fratzl, Peter

doi:10.1016/j.actamat.2003.10.030

Cited by 67 publications

(55 citation statements)

References 12 publications

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“…In particular the model developed here conclusively explains recent experimental results in [29], see also [30], on the ferrite transformation at high temperature in low-carbon steels where a jump of the chemical potential across the interface is observed. This observation is not in agreement with wellestablished mathematical and physical models for interface dynamics like the Allen-Cahn or phase field equations, [5], the Cahn-Hilliard system, [12], the Stefan problem, [20], or other recent models for phase transitions in solids, see for instance [14,2], and [3].…”

Section: Introductionsupporting

confidence: 83%

“…In [29] also some numerical simulations are done. They are based on the representation f l = M i=1 X li µ li (X l1 , .…”

Section: Introductionmentioning

confidence: 99%

“…Explicit formulas for µ as a function of X li are provided by huge data bases in CALPHAD or SGTE, see [17,15], and http://www.calphad.org, http://www.sgte.org. In this way, the jump of the chemical potential is captured in the numerical computations in [29], but no further explanation for the jump of µ is given. This is the objective of the present article.…”

Section: Introductionmentioning

confidence: 99%

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On reconstitutive phase transitions and the jump of the chemical potential

Blesgen¹

2008

Analysis

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Summary:This article studies diffusion in solids in the case of two phases under isothermal conditions where due to plastic effects the number of vacancies changes when crossing a transition layer, i.e. a reconstitutive phase transition. A segregation model is derived and the equations are studied in the limit of a sharp interface. A Gibbs-Thomson law is derived and it is shown that the vacancy component of the chemical potential jumps across the transition layer thereby explaining recent experimental observations. The thermodynamic correctness of the model is shown as well as the existence of weak solutions with logarithmic free energies.

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Section: Introductionsupporting

confidence: 83%

“…In [29] also some numerical simulations are done. They are based on the representation f l = M i=1 X li µ li (X l1 , .…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On reconstitutive phase transitions and the jump of the chemical potential

Blesgen¹

2008

Analysis

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“…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%

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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“…During the last 15 years the TEP has been applied to the development of models in materials science [19][20][21][22][23][24][25][26][27][28]. The authors have demonstrated that the TEP seems to be a handy tool for the solution of practical problems of thermodynamics of irreversible processes, which are often unsolvable or solvable only with great complications in the conventional way.…”

Section: Introductionmentioning

confidence: 99%