Kolmogoroff-Avrami model

Under the aforementioned hypotheses, as two different crystalline phases are formed (a and mesomorphic), at least two kinetic processes take place simultaneously. The simplest model is a parallel of two kinetic processes non-interacting and competing for the available molten material. The kinetic equation adopted here for both processes is the non-isothermal formulation by Nakamura et al. (Nakamura et al., 1973, Nakamura et al., 1972) of the Kolmogoroff Avrami and Evans model (Avrami, 1939,1940,1941, Evans, 1945). 

The kinetics of crystallization is described the Avrami-Kolmogoroff-Evans model,... 

The Kolmogoroff-Avrami formalism can be used without restrictions in the case of 3D, 2D and ID crystallization in three-, two- and onedimensional space, respectively [5.19]. However, the method cannot be applied directly to the nucleation, growth and coalescence of 3D clusters on a plane substrate. The reason is that such clusters caimot grow in the direction perpendicular to the substrate and therefore the spread of the 3D deposit is not random in space [5.53]. Since the formulation of a rigorous theoretical model encounters principle difficulties, here we do not consider this complex case of mass electrocrystaUization. However, theoretical treatment of the nucleation, growth and overlap of circular cones, hemispheres and three-dimensional clusters with more complex geometrical forms can be found in [5.29, 5.53-5.61],... 

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