Avrami exponent growth mechanisms

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... 

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

Sporadic nucleation is assumed to be a first-order mechanism, and if we consider that a two-dimensional disk is formed, then n = 2 -i- 1=3. Rapid nucleation is a zeroth-order process in which the growth centers are formed at the same time, and for each growth imit listed in Table 11.3, the corresponding values of the exponent would be (n — 1). Thus, the Avrami exponent is the sum of the order of the rate process and the number of dimensions the morphological unit possesses. 

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

Determine the Avrami exponent, n. [Data from A. J. Ryan et al., macromolecules, 28, 3860 (1995).] What mechanism of crystal growth is this consistent with ... 

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 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,... 

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