Avrami equation athermal nucleation

From the slope on the right graph of Fig. 99 an Avrami exponent of 3.2 results, close to the value expected for athermal nucleation followed by sphemlitic growth, but because of the many assumptions that went into the derivation of the Avrami equation still not proven without a detailed structural analysis. 

The plots at the bottom of Fig. 2.12 illustrate the Avrami expressions for the experimental data for the UPO3 case of Figs. 2.10 and 2.11. Equation (19), finally, gives the general form of the Avrami equation. The constant K collects all crystal-geometry- and nucleation-dependent terms that arise from crystal growth. Crystal growths other than athermally nucleated spherical... 

To illustrate the general Avrami equation, a particularly simple case is selected athermal nucleation followed by a spherical free growth in three dimensions. All nuclei are formed and start to grow at time t = 0. The spherical crystals grow at a constant rate f. It is an established fact that crystallization from a relatively pure melt occurs at a constant linear growth rate. All nuclei within the radius rt from... 

The experimental data were analyzed with the Ozawa and Ziabicki theories. The Ozawa equation was satisfactorily used to describe the dynamic solidification of PBl. The value of the Avrami exponent, calculated with the Ozawa method, was close to 3, as shown in Table 5, in quite good agreement with the value obtained in isothermal conditions (see Section II.C.4). Conversely, the use of Ziabicki theory was not in good agreement with the experimental results it was found that the zero-order approximation did not describe the nonisothermal crystallization process of PBl, probably indicating that athermal nucleation is not negligible. 

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