Thermally activated nanocrystallization processes in metallic alloys consist of the formation of a partially crystalline material with 40-70 % in volume of nanocrystals embedded in a residual amorphous matrix. This implies the formation of an atypically huge number of crystalline nuclei. The observed constraining in the crystal growth has been explained by the so called soft impingement due to the slow diffusing atoms which pile up at the edge of the growing crystals. A very simplistic idea could describe an initial fast growth of the crystallites till the surface of the crystal is covered by the rejected atoms non soluble in the crystal. Afterwards, the growth is very slow. If this very slow growth is neglected, the time required by the growing crystal to achieve an almost constant size becomes very small in comparison with the time required by the nanocrystallization process to be completed. Under these premises, it is possible to establish an instantaneous growth approximation in which the crystallization kinetics is reduced to the nucleation of crystallites with a constant size (~5 nm). This approach strongly simplifies the kinetic analysis and allows us to obtain the nucleation rate from both isothermal and non-isothermal nanocrystallization processes. Moreover, as no constraining mechanism is considered but the absence of growth, the results could be discussed in the frame of Jhonson-Mehl-Avrami-Kolmogorov theory with a growth index equal to zero. Cellular automata simulations are in agreement with the observed kinetics and microstructure.

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