Analysis of crystallization kinetics (original) (raw)
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Physical Review B, 2007
A simple numerical model which calculates the kinetics of crystallization involving randomly distributed nucleation and isotropic growth is presented. The model can be applied to different thermal histories and no restrictions are imposed on the time and the temperature dependencies of the nucleation and growth rates. We also develop an algorithm which evaluates the corresponding emerging grain size distribution. The algorithm is easy to implement and particularly flexible making it possible to simulate several experimental conditions. Its simplicity and minimal computer requirements allow high accuracy for two-and three-dimensional growth simulations. The algorithm is applied to explore the grain morphology development during isothermal treatments for several nucleation regimes. In particular, thermal nucleation, pre-existing nuclei and the combination of both nucleation mechanisms are analyzed. For the first two cases, the universal grain size distribution is obtained. The high accuracy of the model is stated from its comparison to analytical predictions. Finally, the validity of the Kolmogorov-Johnson-Mehl-Avrami model is verified for all the cases studied.
Lattice model for kinetics and grain-size distribution in crystallization
Physical Review B, 2000
We propose a simple, versatile and fast computational model to understand the deviations from the well-known Kolmogorov-Johnson-Mehl-Avrami kinetic theory found in metal recrystallization and amorphous semiconductor crystallization. Our model describes in detail the kinetics of the transformation and the grain size distribution of the product material, and is in good agreement with the available experimental data. Other morphological and kinetic features amenable of experimental observation are outlined, suggesting new directions for further validation of the model.
Crystallisation kinetics and microstructure development in metallic systems
Progress in Materials Science, 2002
The primary crystallisation of a highly undercooled/supersaturated liquid is considered, and the application to nanocrystallisation by heat treatment of metallic glasses is studied from the thermodynamic, kinetic and microstructural point of view. The thermodynamic evolution is modelled assuming transformation rates low enough to ensure thermal equilibrium to be almost achieved. A mean field approximation is used, which allows us to determine the time evolution of the kinetic variables governing the transformation. The interplay between interface and diffusion controlled growth rate is studied, and both nucleation and crystal growth changes within the transformation are considered as soft mechanisms. The kinetics of the transformation is described in the framework of the Kolmogorov, Johnson and Mehl and Avrami (KJMA) model, which is adequately generalized for primary transformations. The microstructural evolution is described by a populational model, also based on KJMA. The predicted kinetic evolution results are compared to the experimental data on the primary nanocrystallisation of a FINEMET alloy. #
Model for crystallization kinetics: Deviations from Kolmogorov–Johnson–Mehl–Avrami kinetics
Applied physics letters, 1999
We propose a simple and versatile model to understand the deviations from the well-known Kolmogorov-Johnson-Mehl-Avrami kinetics theory found in metal recrystallization and amorphous semiconductor crystallization. We analyze the kinetics of the transformation and the grain size distribution of the product material, finding a good overall agreement between our model and available experimental data. The information so obtained could help to relate the mentioned experimental deviations due to preexisting anisotropy along some regions, to certain degree of crystallinity of the amorphous phases during deposition, or more generally to impurities or roughness of the substrate.
Analytical Model for Heterogeneous Crystallization Kinetics of Spherical Glass Particles
Journal of the American Ceramic Society, 2009
An analytical model developed to describe the crystallization kinetics of spherical glass particles has been derived in this work. A continuous phase transition from three-dimensional (3D)-like to 1D-like crystal growth has been considered and a procedure for the quantitative evaluation of the critical time for this 3D-1D transition is proposed. This model also allows straightforward determination of the density of surface nucleation sites on glass powders using differential scanning calorimetry data obtained under different thermal conditions.
Journal of Non-Crystalline Solids, 2006
The aim of this article is to propose a simple analytical model that can describe the isothermal crystallization process in materials when the formation of a stable crystalline phase is preceded by the formation of a metastable phase. This model explains deviations from the well-known Johnson-Mehl-Avrami-Kolmogorov kinetics theory and predicts the three slopes in AvramiÕs plot. The model predictions were compared with experimental results obtained from X-ray measurements in the chalcogenide glasses with composition of Ge 2 Sb 2 Te 5 (thin films) and in aqueous solutions of methylhydrazine monohydrate during isothermal phase transformations. In order to validate the proposed model to represent experimental results, a computer program was developed. This program uses experimental data from measurements of the total volume fraction at different times during isothermal transformations and fits the model parameters that best represent the kinetic behavior of the system.
Solid-phase crystallization under continuous heating: Kinetic and microstructure scaling laws
Journal of Materials Research, 2008
The kinetics and microstructure of solid-phase crystallization under continuous heating conditions and random distribution of nuclei are analyzed. An Arrhenius temperature dependence is assumed for both nucleation and growth rates. Under these circumstances, the system has a scaling law such that the behavior of the scaled system is independent of the heating rate. Hence, the kinetics and microstructure obtained at different heating rates differ only in time and length scaling factors. Concerning the kinetics, it is shown that the extended volume evolves with time according to αex = [exp(κCt′)]m+1, where t′ is the dimensionless time. This scaled solution not only represents a significant simplification of the system description, it also provides new tools for its analysis. For instance, it has been possible to find an analytical dependence of the final average grain size on kinetic parameters. Concerning the microstructure, the existence of a length scaling factor has allowed the gr...
Phase-field modelling of microstructural evolution in primary crystallization
Journal of Alloys and Compounds, 2009
One of the main routes to obtain nanostructured materials is through the primary crystallization of metallic glasses. In such transformations, crystallites with a different composition than the amorphous precursor grow with a diffusion-controlled regime. Particle growth is slowed and eventually halted by the impingement between the concentration gradients of surrounding particles. Primary crystallization kinetics is not well described by the KJMA equation, and this fact was generally ascribed to both the soft-impingement effect and the non-random nucleation. However, recent phase-field simulations showed that the underlying physical reason is the change in the local diffusion properties of the amorphous precursor due to the variation of the composition during the transformation. The kinetics of primary crystallization is thus well described by considering a diffusion coefficient of the slowest diffusing species dependent on the local concentration. The nanostructure developed in such transformations is a key point to explain the macroscopic properties of these materials. In this work the grain size distributions obtained in realistic phase-field simulations of transformations with continuous nucleation and both constant and variable diffusion coefficient are presented.
The Chemical Engineering Journal and the Biochemical Engineering Journal, 1994
A comparison of methods proposed for the determination of crystallization kinetics from the crystal size distribution in continuous mixed-suspension, mixed-product-removal (MSMPR) crystallizers is presented for several systems exhibiting size-dependent crystal growth rates reported in the literature. Wide variations in inferred kinetic parameters are obtained depending on the analytical method adopted, leading to uncertainty in their utility. Direct fitting of differential population density data using exponential sizedependent growth models, however, gives an improved estimation of growth rates over the whole size range and leads to higher zero-size crystal growth and nucleation rates in comparison with other models tested.
Time-evolution of grain size distributions in random nucleation and growth crystallization processes
Physical Review B, 2010
We study the time dependence of the grain size distribution N (r, t) during crystallization of a d−dimensional solid. A partial differential equation including a source term for nuclei and a growth law for grains is solved analytically for any dimension d. We discuss solutions obtained for processes described by the Kolmogorov-Avrami-Mehl-Johnson model for random nucleation and growth (RNG). Nucleation and growth are set on the same footing, which leads to a time-dependent decay of both effective rates. We analyze in detail how model parameters, the dimensionality of the crystallization process, and time influence the shape of the distribution. The calculations show that the dynamics of the effective nucleation and effective growth rates play an essential role in determining the final form of the distribution obtained at full crystallization. We demonstrate that for one class of nucleation and growth rates the distribution evolves in time into the logarithmicnormal (lognormal) form discussed earlier by Bergmann and Bill [J. Cryst. Growth 310, 3135 (2008)]. We also obtain an analytical expression for the finite maximal grain size at all times. The theory allows for the description of a variety of RNG crystallization processes in thin films and bulk materials. Expressions useful for experimental data analysis are presented for the grain size distribution and the moments in terms of fundamental and measurable parameters of the model.