Concept

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). 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 can be attributed to the time required for a significant number of nuclei of the new phase to form and begin growing. During the intermediate period the transformation is rapid as the nuclei grow into particles and consume the old phase while nuclei continue to form in the remaining parent phase. Once the transformation approaches completion, there remains little untransformed material for further nucleation, and the production of new particles begins to slow. Additionally, the previously formed particles begin to touch one another, forming a boundary where growth stops. The simplest derivation of the Avrami equation makes a number of significant assumptions and simplifications: Nucleation occurs randomly and homogeneously over the entire untransformed portion of the material. The growth rate does not depend on the extent of transformation. Growth occurs at the same rate in all directions. Growth stops as a result of impingement of the growing grains. If these conditions are met, then a transformation of into will proceed by the nucleation of new particles at a rate per unit volume, which grow at a rate into spherical particles and only stop growing when they impinge upon each other.

Official source

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

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