Avrami equation

Summary

The Avrami equation describes how solids transform from one phase to another at constant temperature. It can specifically describe the kinetics of crystallisation, can be applied generally to other changes of phase in materials, like chemical reaction rates, and can even be meaningful in analyses of ecological systems. The equation is also known as the Johnson–Mehl–Avrami–Kolmogorov (JMAK) equation. The equation was first derived by Johnson, Mehl, Avrami and Kolmogorov (in Russian) in a series of articles published in the Journal of Chemical Physics between 1939 and 1941. Moreover, Kolmogorov treated statistically the crystallization of a solid in 1937 (in Russian, Kolmogorov, A. N., Izv. Akad. Nauk. SSSR., 1937, 3, 355). Transformation kinetics Transformations are often seen to follow a characteristic s-shaped, or sigmoidal, profile where the transformation rates are low at the beginning and the end of the transformation but rapid in between. The initial slow rate c

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https://en.wikipedia.org/wiki/Avrami_equation

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Ce cours est une introduction aux transformations de phases liquide-solide et solide-solide. Il aborde les aspects thermodynamiques et cristallographiques. Il traite principalement des matériaux métalliques, et établira des ponts vers les céramiques et la minéralogie.

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Studying nucleation and growth kinetics of alite hydration using μic

Shashank Bishnoi, Karen Scrivener

This paper investigates the applicability of nucleation and growth mechanisms to the hydration of alite. Various possible mechanisms of nucleation and growth were simulated using the recently-developed microstructural modelling platform mu ic. Comparison with the Avrami equation and the boundary nucleation model demonstrate the limitations of these equations. Experimental measurements of the rates of hydration of alite powders with different particle size distributions were then simulated with a boundary nucleation and growth model in mu ic. The results show that while the nucleation and growth of C-S-H having bulk densities in the currently accepted range can explain the acceleration during the first few hours of hydration, it cannot explain the later deceleration. It was also found that the resistance to flow of ions offered by the layer of hydrates forming over the surface of the alite particles (diffusion control) cannot explain the deceleration. The deceleration could be reproduced when C-S-H was assumed to be loosely packed in the beginning with its density of packing increasing with hydration. It is proposed that during the early hours of hydration a loosely-packed C-S-H fills a large fraction of the microstructure and the further development of its microstructure occurs due to an increase in its packing. (C) 2009 Elsevier Ltd. All rights reserved.

2009

Reduction of nickel oxide particles by hydrogen studied in an environmental TEM

Cécile Hébert, Aïcha Hessler-Wyser, Quentin Thomas Jeangros, Jan Van Herle

In situ reduction of nickel oxide (NiO) particles is performed under 1.3 mbar of hydrogen gas (H-2) in an environmental transmission electron microscope (ETEM). Images, diffraction patterns and electron energy-loss spectra (EELS) are acquired to monitor the structural and chemical evolution of the system during reduction, whilst increasing the temperature. Ni nucleation on NiO is either observed to be epitaxial or to involve the formation of randomly oriented grains. The growth of Ni crystallites and the movement of interfaces result in the formation of pores within the NiO grains to accommodate the volume shrinkage associated with the reduction. Densification is then observed when the sample is nearly fully reduced. The reaction kinetics is obtained using EELS by monitoring changes in the shapes of the Ni L-2,L-3 white lines. The activation energy for NiO reduction is calculated from the EELS data using both a physical model-fitting technique and a model-independent method. The results of the model-fitting procedure suggest that the reaction is described by Avrami models (whereby the growth and impingement of Ni domains control the reaction), in agreement with the ETEM observations.

Springer US2013