Title: On the kinetics of phase transformation of small particles in Kolmogorov's model
Author(s):

N.V. Alekseechkin (Akhiezer Institute for Theoretical Physics, National Science Centre "Kharkov Institute of Physics and Technology", Akademicheskaya Str. 1, Kharkov 61108, Ukraine)

The classical Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory is generalized to the case of a finite-size system. The problem of calculating the new-phase volume fraction in a spherical domain is solved within the framework of geometrical-probabilistic approach. The solutions are obtained for both homogeneous and heterogeneous nucleations. It is shown that the finiteness property results in a qualitative distinction of the volume-fraction time dependence from that in infinite space: the Avrami exponent in the process of homogeneous nucleation decreases with time from 4 to 1, i.e. a slowing down of the transformation process takes place. The obtained results can be used, in particular, for controlling the crystallization kinetics in amorphous powders.

Key words: KJMA theory, volume fraction, nucleation, Avrami exponent
PACS: 05.70.Fh, 68.55.Ac, 81.15.Aa

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