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

Song, Shaojie; Liu, F.; Jiang, Yihui

doi:10.1007/s10853-012-6504-1

Cited by 9 publications

(5 citation statements)

References 39 publications

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“…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%

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

Starink

2014

Thermochimica Acta

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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...

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Section: Scope and Overview Of Model Verificationmentioning

confidence: 99%

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

Starink

2014

Thermochimica Acta

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“…This model was applied to simulate the diffusion-controlled growth kinetics of Si grains. The results showed that the deviation from exact solution was effectively decreased [23]. By adopting the same approach, Tomellini [20] got the exact expression of the weighting function based on JMAK model during continuous heating.…”

Section: Introductionmentioning

confidence: 98%

“…The condition is that non-isothermal transformation rate can be represented as a state function of temperature and transformed fraction. This condition has been widely used in classical or modificatory Johnson-Mehl-Avrami-Kolmogorov (JMAK) model (from isothermal frame) [20][21][22] and the physically-based internal state variable model to predict kinetics [23,24]. However, some research found that a certain deviation existed in predictions from the exact solutions in diffusional transformations for these models.…”

Section: Introductionmentioning

confidence: 99%

“…actual temperature history effect) [25,26], because the transformation rate in the above condition is independent of temperature-time path. In view of this problem, Song et al [19,23] introduced a weighting function related to temperature-time path into the classical additive rule based on the condition described above and the model by Réti and Felde [27]. The weighting function was given by comparing the growth rate equation (i.e.…”

Section: Introductionmentioning

confidence: 99%

“…By adopting the same approach, Tomellini [20] got the exact expression of the weighting function based on JMAK model during continuous heating. With the use of the model of Song et al [23], Meng et al [28] predicted the volume fraction evolution of the primary α phase of TA15 alloy during cooling. However, the predicted results of the volume fraction evolution of primary α still showed a small difference from experimental data.…”

Section: Introductionmentioning

confidence: 99%

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Modeling of the precipitation kinetics and morphology evolution of lamellar α in Ti-alloys during non-isothermal treatments

Liu¹,

Li²,

Zhan³

2022

Modelling Simul. Mater. Sci. Eng.

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The non-isothermal diffusional phase transformation plays an important role in adjusting materials microstructure. In the modelling of non-isothermal transformation, actual temperature history has a remarkable effect on the precipitation kinetics of new phase. When morphology anisotropy effect is considered, taking actual temperature history effect into account is very difficult for guaranteeing the accuracy of kinetics prediction. In order to solve this problem, a new non-isothermal transformation model in combination with cellular automaton (CA) method with mixed-controlled mode was proposed. In this new model, actual temperature history effect was characterized by the effects of cooling path and additive isothermal path on the nucleation and growth of new phase. Firstly, the cooling path with the consideration of supercooling effect was introduced into the created isothermal transformation theory model. Secondly, the temperature-time path (i.e., additive isothermal path) in CA model was calibrated by using the solute concentration model from experiments. With the use of this new model, the precipitation kinetics and morphology evolution of the lamellar α for IMI834 titanium alloy during continuous cooling from single-phase region was predicted. The predicted results were in good agreement with experiments. It was also revealed that the dominant role of mixed-controlled mode for lamellar α precipitation was gradually changed from the diffusion control to the interface control with the increase of cooling rate.

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Soft impingement in diffusion-controlled growth of binary alloys: moving boundary effect in one-dimensional system

Tomellini

2013

J Mater Sci

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

Cited by 9 publications

References 39 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 the precipitation kinetics and morphology evolution of lamellar α in Ti-alloys during non-isothermal treatments

Soft impingement in diffusion-controlled growth of binary alloys: moving boundary effect in one-dimensional system

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