Avrami equation thermal nucleation

Ziabicki proposed to analyze nonisothermal processes as a sequence of isothermal steps [170-172]. The proposed equation is a series expansion of the Avrami equation. In quasi-static conditions, provided that nucleation and growth of the crystals are governed by thermal mechanisms only, that their time dependence comes from a change in external conditions, and that the Avrami exponent is constant throughout the whole process, the nonisothermal crystallization kinetics can be expressed in terms of an observable half-time of crystallization, T]/2, a function of time, and of the external conditions applied. The following equation was derived for the dependence of the total volume of the growing crystal, E(t), with time ... 

The thermal dehyi-ation of Na2C03.H20 between 336 and 400 K fits the Avrami-Erofeev equation with = 2 (E, = 71.5 kJ mol and., 4 = 2.2 x 10 s [110]). The apparent reduction in rate resulting from an increase of /r(H20) is ascribed to competition from the rehydration reaction. Electron micrographs confirm the nucleation and growth mechanism indicated by the kinetic behaviour, nucleation develops from circular defects that may be occluded solution. 

Selcuk and Price [101] reported that the thermal decomposition of PbC204 in Nj between 611 and 707 K, studied by isothermal thermogravimetry, fitted the Avrami-Erofeev equation with n = 2, ascribed to random nucleation followed by two dimensional growth, , = 119 7 kJ mol. Incorporation of 1% Zn was found to increase E, to 137 5 kJ mol but did not change the kinetic fit. It is suggested that zinc oxalate within the host crystal restricts the formation of Smekal cracks along which decomposition is favoured. 

In constructing the ITT diagram (101), if it is assumed that the nucleation and growth rates are constant, which is applicable when the volume crystallized is small, the volume fraction of crystals produced by a given thermal history can be ealculated by Avrami s equation (102),... 

---