About Kolmogorov's statistical theory of phase transformation

Burbelko, A.; Fraś, E.; Kapturkiewicz, W.

doi:10.1016/j.msea.2005.08.161

Cited by 59 publications

(49 citation statements)

References 16 publications

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“…Indeed, available experimental data on precipitate density in a range of systems indicates that the density of precipitates is close to constant during many transformations for nearly all of the transformation (see [41] for ageing of a Nb-V micro-alloyed steel, Booth-Morrison et al [28] for ageing of Ni-6.5 at%Al-9.5 at% Cr at 873 K, [42] for precipitation in an Fe-Si-Ti alloy and Schober et al [43] for precipitation of intermetallic NiAl particles in Fe-6 at%Al-4 at%Ni). The existence of only two modes 4 suggests that the classical models for nucleation, which generally allow a continuous variation in nucleation rate, cannot fully capture the mechanism. Whilst a full discussion of nucleation models is beyond the scope of the present paper, there are few points that need to be considered with regards to the relation between the present findings and classical nucleation theories.…”

Section: The Relation Between Reaction Exponent N Nucleation Undercmentioning

confidence: 99%

“…As a result, a diffusion event causing growth of a precipitate in a nearby location does not 4 In some older literature the term 'site saturated' nucleation is used to describe processes with B=0, for instance 3 dimensional growth with n=1½. This 'site saturation' can occur for heterogeneous nucleation where the number of nucleation sites is limited, but this seems to not be the case for the reactions studied here: there is no indication in microstructural studies on these alloys that there is a limit on the number of sites.…”

Section: The Relation Between Reaction Exponent N Nucleation Undercmentioning

confidence: 99%

“…A key factor in the model is that it derives and employs an expanded form of the imaginary extended volume concept (see e.g. [2,3,4,5,6]), through applying an integration of impingement over various extended volumes defined by iso-composition surfaces [1]. Through this approach the new model avoids the over-simplification of soft impingement inherent in mean field approaches such as the Kampmann and Wagner (KW) model [7,8,9,10,11] and the model by Svoboda and co-workers [12,13,14].…”

Section: Introductionmentioning

confidence: 99%

“…1b and c by a set of graphs each reflecting one particle. 1 The basic concept of and terminology 'extended volume' derives from the JMAK model [2,3,4]. In this paragraph and Fig.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of nucleation and growth with the model for diffusion-controlled precipitation reactions based on the extended volume concept

Starink

2015

Journal of Alloys and Compounds

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Recently (M.J. Starink, Thermochim Acta 596, 2014, 109-119) a new model for diffusioncontrolled precipitation reactions based on the extended volume concept was derived.The model leads to an analytical equation describing the relation between the fraction transformed, α, the reaction time, t, and the reaction exponent, n, as:In the present work, new analysis methods are derived which allow determination of the reaction exponent n. The new methods are applied to analysis of nucleation and it is shown that generally during a reaction with growth in 3 dimensions there are only 2 modes: either the nucleation rate in the extended volume is constant or it is negligibly small. A new approach to the interaction of diffusion-controlled growth and nucleation is proposed to rationalise these findings. The exponential decay of the average solute content predicted by the new model is further analysed and compared with a range of

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Section: The Relation Between Reaction Exponent N Nucleation Undercmentioning

confidence: 99%

Section: The Relation Between Reaction Exponent N Nucleation Undercmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…1b and c by a set of graphs each reflecting one particle. 1 The basic concept of and terminology 'extended volume' derives from the JMAK model [2,3,4]. In this paragraph and Fig.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of nucleation and growth with the model for diffusion-controlled precipitation reactions based on the extended volume concept

Starink

2015

Journal of Alloys and Compounds

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“…This theory, developed for isothermal processes, describes the variation of the transformed fraction with the annealing time based on simple laws of nucleation and growth. In order to be described by JMAK theory, a transformation should fulfill the five postulates of Kolmogorov [14]:…”

Section: Introductionmentioning

confidence: 99%

On the use of classical JMAK crystallization kinetic theory to describe simultaneous processes leading to the formation of different phases in metals

Blázquez

Conde

2015

International Journal of Thermal Sciences

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The classical theory of Johnson-Mehl-Avrami-Kolmogorov (JMAK) is widely used to describe the kinetics of crystallization even when the premises required for its application are not strictly fulfilled. In this paper we propose a procedure to obtain the JMAK parameters of the independent transformations that simultaneously occur during a crystallization process (e.g. leading to the formation of several crystalline phases). The predictions of the analysis have been used to describe the crystallization process of two amorphous alloys with Fe 90 Zr 10 and (Fe 0.7 Co 0.3 )Zr 10 composition, respectively, which consists of two overlapped processes ascribed to the formation of -Fe(Co) phase and a Zr-rich intermetallic.

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A Review of Different Models Derived from Classical Kolmogorov, Johnson and Mehl, and Avrami (KJMA) Theory to Recover Physical Meaning in Solid‐State Transformations

Blázquez

Romero

Conde

et al. 2022

Physica Status Solidi (b)

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The classical theory of solid‐state transformation based on nucleation and growth processes, developed by Kolmogorov, Johnson and Mehl, and Avrami (KJMA theory), is widely used in many different fields of research. In KJMA theory, two parameters (the frequency factor and, particularly, the Avrami exponent) can supply information about the mechanisms involved in the transformation. Despite its apparent simplicity, on the one hand, the results derived from this theory can be strongly affected by the indetermination of experimental data (e.g., onset of the transformation). On the other hand, KJMA theory is developed for isothermal polymorphic transformations in which randomly distributed nuclei grow in convex shapes. However, several procedures have extended KJMA theory to nonisothermal regimes and to many different processes deviating from those premises. Herein, the requirements of KJMA theory and the expected deviations for these approximations are briefly discussed. In addition, some strategies are proposed for recovering physical meaning from the effective parameters deduced in several transformations including nanocrystallization and martensitic transformations for which results can be interpreted under the approximation of instantaneous growth.

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About Kolmogorov's statistical theory of phase transformation

Cited by 59 publications

References 16 publications

Analysis of nucleation and growth with the model for diffusion-controlled precipitation reactions based on the extended volume concept

Analysis of nucleation and growth with the model for diffusion-controlled precipitation reactions based on the extended volume concept

On the use of classical JMAK crystallization kinetic theory to describe simultaneous processes leading to the formation of different phases in metals

A Review of Different Models Derived from Classical Kolmogorov, Johnson and Mehl, and Avrami (KJMA) Theory to Recover Physical Meaning in Solid‐State Transformations

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