hello, everyone.
How to estimate or calculate the crystallinity of an arbitrary heating progress based on the Avrami equation? thank you.
Dear Chao,
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
Avrami (JMAK) equation:
ln (- ln [1-Y(t)]) = ln K + n ln (t)
which allows the determination of the constants n and k from a plot of lnln(1/(1-Y)) vs ln(t). If the transformation follows the Avrami equation this yields a straight line with gradient n and intercept ln K.
Interpretation of Avrami constants
There is no clear physical interpretation of the Avrami constants k and n. Originally, n was held to have an integer value between 1 and 4 which reflected the nature of the transformation in question. In the derivation above, for example, the value of 4 can be said to have contributions from three dimensions of growth and one representing a constant nucleation rate. Alternative derivations exist where n has a different value. If the nuclei are preformed, and so all present from the beginning, the transformation is only due to the 3-dimensional growth of the nuclei and n has a value of 3. An interesting condition occurs when nucleation occurs on specific sites (such as grain boundaries or impurities) which rapidly saturate soon after the transformation begins. Initially, nucleation may be random and growth unhindered leading to high values for n (3,4). Once the nucleation sites are consumed the formation of new particles will cease. Furthermore, if the distribution of nucleation sites is non-random then the growth may be restricted to 1 or 2-dimensions. Site saturation may lead to n values of 1, 2 or 3 for surface, edge and point sites, respectively.
Avramov, I (2007). "Kinetics of distribution of infections in networks". Physica A. 379: 615–620.
AK Jena, MC Chaturvedi (1992). Phase Transformations in Materials. Prentice Hall. p. 247. ISBN 0-13-663055-3.
JW Cahn (1956). "Transformation kinetics during continuous cooling". Acta Metallurgica. 4 (6): 572–575.
https://en.wikipedia.org/wiki/Avrami_equation
Examples of studies utilized Avrami equation:
http://www.sciencedirect.com/science/article/pii/S0142941806001917
http://www.personal.psu.edu/irh1/PDF/Kinetics.pdf
https://core.ac.uk/download/files/375/11603655.pdf
Hoping this will be helpful,
Rafik
Hi, Rafik:
thank you for your answer. But your method is based on constant temperature history, do you have any experience on varying temperature history?
Dear Chao,
Please see pages 246-251 of the publication contained in the following link:
http://cdn.intechopen.com/pdfs-wm/14381.pdf
Rafik
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