Growth mechanisms, Avrami

Values of the Avrami Exponent n for the Various Types of Nucleation and Growth Mechanisms ... 

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. 

More generally it can be shown that, whatever the precise nucleation and growth mechanisms, the following equation, called the Avrami equation, holds ... 

It should be noted that now the time is raised to the fourth power. In general it is found that crystallization based on diflferent nucleation and growth mechanisms can be described by the same general formula, the general Avrami equation ... 

Table 6.2 Avrami exponent n for different nucleation and growth mechanisms." ...

The two-dimensional condensation of bases proceeds by nucleation and growth mechanism, which can be analyzed by Avrami plot from the measurements of the capacitance-time curves [19, 28-32, 67]. 

The Avrami exponent, w, can be determined from the slope of a plot of log n[ ht - hoo)l ho - hoo)] against log t. Fig. 4.26 shows an Avrami plot for polypropylene crystallizing at different temperatures. It is often difficult to estimate n from such plots because its value can vary with time. Also, non-integral values can be obtained and care must be exercised in using the Avrami analysis, as interpretation of the value of n in terms of specific nucleation and growth mechanisms can sometimes be ambiguous. 

Avrami exponent. The Avrami constant A is a measure of the velocity of reaction and shows an Arrhenius-type dependence on the crystallization temperature (Christian, 1965 Graydon et al., 1994). The Avrami exponent n is sensitive to the mechanism of crystallization. This parameter is also sensitive to both the time dependence of nucleation and the dimensionality of growth. Nucleation can be either sporadic or instantaneous, and crystal growth may occur in one, two, or three dimensions to give rods, disks, or spherulites, respectively (Sharpies, 1966). The different combinations of nucleation and growth mechanisms for different values of the Avrami exponent are shown in Table 4 (Sharpies, 1966). A value of n can describe many types of nucleation and subsequent crystal growth as well as different combinations of these two processes. 

The Avrami exponent, n, sometimes referred to as an index of crystallization, indicates the crystal growth mechanism. This parameter is a combined function of the time dependence of nucleation and the number of dimensions in which growth takes place (Sharpies, 1966). Nucleation is either instantaneous, with nuclei appearing all at once early on in the process, or sporadic, with the number of nuclei increasing linearly with time (Sharpies, 1966). Growth occurs as rods, disks, or spherulites in one, two, or three dimensions, respectively (Kawamura,... 

Those exponents which we have discussed expUcitly are identified by equation number in Table 4.3. Other tabulated results are readily rationalized from these. For example, according to Eq. (4.24) for disk (two-dimensional) growth on contact from simultaneous nucleations, the Avrami exponent is 2. If the dimensionality of the growth is increased to spherical (three dimensional), the exponent becomes 3. If, on top of this, the mechanism is controlled by diffusion, the... 

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