Modeling of isothermal solid-state precipitation using an analytical treatment of soft impingement

Fan, Kai; Liu, F.; Liu, X.N.; Zhang, Y.X.; Gao, Yang; Zhou, Yaohe

doi:10.1016/j.actamat.2008.04.053

Cited by 32 publications

(53 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The JMAK and KW models do not possess such an exponential decay and are thus inconsistent with the analysis of impingement in a diffusion-controlled reaction by Ham [36] and by the present work, whilst the model by Fan et al [32] does possess an exponential decay. (It should be noted that the approach by Ham involves a regular array of particles, which is known [37] to substantially underestimate impingement.…”

contrasting

confidence: 47%

“…4 and Table 1 typically show an improvement by an order of magnitude with existing models referred to here (e.g. [4,24,20,5,5,29,30,32]). …”

Section: Scope and Overview Of Model Verificationmentioning

confidence: 95%

“…The survey includes all data of isothermal experiments on diffusion-controlled reactions that in the past has been used to support the various kinetic models in [4,23,30,32,38,39] and attempts to avoid any bias other than to exclude the following:…”

Section: Scope and Overview Of Model Verificationmentioning

confidence: 99%

“…Appropriate treatments of nucleation for various reactions can be found in [5,6,30]. The initial growth, before impingement becomes significant, is identical to the KW model [5], and also identical to the JMAK model and models in [4,20,24,32]. …”

mentioning

confidence: 99%

“…Through adjusting the impingement parameter this equation can encompass the JMAK model [18,19,21,24,25] Further, several authors [30,31,32] have applied approaches in which impingement of diffusion fields is approximated through approximating diffusion profiles (concentration as a function of the distance to the interface) as linear and subsequently assuming that the progress can be divided into two stages: one where no interaction occurs followed by a stage of interaction.…”

mentioning

confidence: 99%

See 4 more Smart Citations

A new model for diffusion-controlled precipitation reactions using the extended volume concept

Starink

2014

Thermochimica Acta

View full text Add to dashboard Cite

In this work a new model for diffusion-controlled precipitation reactions is derived, IntroductionDiffusion-controlled precipitation reactions are important in a wide variety of commercially important materials. It is important to have available an accurate model for the kinetics of the reaction as heat treatment can determine a range of properties.Preferably such a kinetic model should be accurate, transparent, avoid computationally expensive implementations, and lead to analysis methods that are widely applicable.The objective of this work is to derive and test a new model for diffusion-controlled precipitation reactions that meets these criteria.Diffusion-controlled precipitation reactions can be thought of as being the combination of 4 overlapping processes: nucleation, growth, soft impingement and coarsening.Several attempts at providing a computationally friendly suitable framework for predicting the progress of diffusion-controlled reactions incorporating a treatment of impingement have been published (see e.g. [1,2,3]), and some less computationally friendly attempts at models have been published more recently [4]. The present paper focuses primarily on the treatment of soft impingement.One group of existing modelling approaches is based on direct consideration of the diffusion flux at the interface. For instance, the numerical method formulated by Kampmann and Wagner [5], as applied by several authors (e.g. [6,7,8,9]), treats the growth of individual spherical particles following the equation:where R is the radius of a growing particle, D is the diffusion constant, c p is the solute concentration in the precipitate, c m is the solute concentration at the precipitate/matrix interface that is evaluated by the Gibbs-Thompson relationship [10,11], ) (t c is the mean concentration of the matrix. A characteristic of this approach is that the interaction of the diffusional growth of the various particles is drastically simplified: a spherical geometry of diffusion field is assumed and interaction is described through a single parameter, the mean concentration ) (t c . We can term this a mean field approach.Published as: Starink, M.J. (2014) Thermochimica Acta, 596, pp. 109-119 3 Some of the users of KW model have described this treatment of impingement as 'a simple response equation ' [12], i.e. it is an approximation for which the accuracy is as yet unproven and it has been suggested that the mean field approach underestimates impingement because it ignores a geometrical component to the impingement process [13]. The contribution of a geometrical component has been investigated in [13,14].Benefits of the KW approach are that basic capillarity effects can be included and that, in principle and at some computational costs, the numerical scheme can be implemented to model different groups of precipitates and (in principle 1 ) incorporate coarsening [7,8]. The models described by Svoboda, Fisher and co-workers [15,16] applying the thermodynamic extremal principle (first described by Onsager [17]) empl...

show abstract

contrasting

confidence: 47%

“…4 and Table 1 typically show an improvement by an order of magnitude with existing models referred to here (e.g. [4,24,20,5,5,29,30,32]). …”

Section: Scope and Overview Of Model Verificationmentioning

confidence: 95%

Section: Scope and Overview Of Model Verificationmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

A new model for diffusion-controlled precipitation reactions using the extended volume concept

Starink

2014

Thermochimica Acta

View full text Add to dashboard Cite

show abstract

Modeling of soft impingement effect during solid-state partitioning phase transformations in binary alloys

Chen

Zwaag

2010

J Mater Sci

View full text Add to dashboard Cite

The soft impingement effect at the later stage of partitioning phase transformations has been modeled both for the diffusion-controlled growth model and for the mixed-mode model. Instead of the linear and exponential approximations for the concentration gradient in front of the interface used in the past, a general polynomial method of dealing with the diffusion field is proposed. The linear and exponential diffusion field approximations are two specific cases of the polynomial diffusion field approximation. The effect of soft impingement on the overall partitioning phase transformation is only related to the degree of the super-saturation in case of the diffusioncontrolled growth model, while it is determined by both the growth mode and the degree of super-saturation in case of the mixed-mode model.

show abstract

An analytic approach to the effect of anisotropic growth on diffusion-controlled transformation kinetics

2012

View full text Add to dashboard Cite

Modeling of isothermal solid-state precipitation using an analytical treatment of soft impingement

Cited by 32 publications

References 29 publications

A new model for diffusion-controlled precipitation reactions using the extended volume concept

A new model for diffusion-controlled precipitation reactions using the extended volume concept

Modeling of soft impingement effect during solid-state partitioning phase transformations in binary alloys

An analytic approach to the effect of anisotropic growth on diffusion-controlled transformation kinetics

Contact Info

Product

Resources

About