Condensed Matter Physics, 2008, vol. 11, No. 4(56), p. 597-613
On the kinetics of phase transformation of small particles in Kolmogorov's model
(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.
KJMA theory, volume fraction, nucleation, Avrami exponent
05.70.Fh, 68.55.Ac, 81.15.Aa