Crystal growth general Avrami equation

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 ... 

This chapter presents first some fundamental aspects of nucleation, and second the general Avrami equation, which is frequently used to describe overall crystallization. The growth theories of Lauritzen and Hoffman and Sadler and Gilmer are discussed in sections 8.4.2 and 8.4.3. Molecular fractionation and orientation-induced crystallization are dealt with in sections 8.5 and 8.6. 

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... 

Avrami Analysis The Avrami equation, a general approach for description of isothermal phase transformation kinetics originally developed for polymers (46), is often used for describing nucleation and crystal growth in fats. The Avrami equation is given as... 

The Avrami equation [Eq. (2.15)], which was originally proposed in the general context of phase changes, has provided the starting point for many studies of polymer crystallization and spherulitic growth. It relates the fraction of a sample still molten, 9, to the time, t, which has elapsed since crystallization began. The temperature must be held constant. 

There are several methods for studying crystallization kinetics of polymers, which fall into two general categories bulk or volumetric analysis, and crystal growth analysis. The simplest experimental study is the bulk growth, but it is the most difficult to analyze in detail. However, it can be analyzed partially using the Avrami equation [1,2]. 

The overall crystallization rate is used to follow the course of solidification of iPP. Differential scanning calorimetry (DSC), dilatometry, dynamic X-ray diffraction and light depolarization microscopy are then the most useful methods. The overall crystallization rate depends on the nucleation rate, 1(0 and the growth rate of spherulites, G(0. The probabilistic approach to the description of spherulite patterns provides a convenient tool for the description of the conversion of melt to spherulites. The conversion of melt to spherulites in the most general case of nonisothermal crystallization is described by the Avrami equation ... 

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... 

As discussed above, these rate equations make no allowance for the restrictions on growth of the nuclei. It is necessary to relate the unrestricted fractional decomposition, nr, to the true value, nr. A general but complicated solution to the problem has been provided [1,8]. For the simpler case of three-dimensional growth of randomly-distributed nuclei on large crystals, Avrami [21] has shown that nr and... 

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