Avrami

Thus the slope of a plot of ln[ln(l - 6) ] versus In t will have a slope equal to the Avrami exponent. 

If this result is substituted into the previous expressions containing f, the effect is to replace f with (20) " and to multiply those t s which accompany f by t This rather complex array of possibilities is summarized in Table 4.3. Table 4.3 lists the predicted values for the Avrami exponent for the following cases ... 

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... 

Table 4.3 Summary of Exponents in the Avrami Equation for Different Crystallization Mechanisms...

Avrami exponent Crystal geometry Nucleation mode Rate determination Equation ... 

While there are several instances of redundancy among the Avrami exponents arising from different pictures of the crystallization process, there is also enough variety to make the experimental value of this exponent a valuable way of characterizing the crystallization process. In the next section we shall examine the experimental side of crystallization kinetics. 

The decrease in amorphous content follows an S-shaped curve. The corresponding curve for the growth of crystallinity would show a complementary but increasing plot. This aspect of the Avrami equation was noted in connection with the discussion of Eq. (4.24). 

Next let us examine an experimental test of the Avrami equation and the assortment of predictions from its various forms as summarized in Table 4.3. Figure 4.9 is a plot of ln[ln(l - 0)" ] versus In t for poly (ethylene terephtha-late) at three different temperatures. According to Eq. (4.35), this type of... 

The testing of the Avrami equation reveals several additional considerations of note ... 

Deviations from the Avrami equation are frequently encountered in the long time limit of the data. This is generally attributed to secondary nucleation occurring at irregularities on the surface of crystals formed earlier. 

These unpredicted Avrami exponents may be indications that multiple mechanisms are operative and/or that f and/or N is itself a function of d. 

Experimental results are in general conformity with the Avrami equation, but the interpretation of various observations is still complicated in many instances. One intriguing observation is that the induction period for nucleation is inversely proportional to the length of time the liquid is held in the liquid state after previous melting. This dependence on prior history may be qualitatively understood... 

The crystallization of poly(ethylene terephthalate) at different temperatures after prior fusion at 294 C has been observed to follow the Avrami equation with the following parameters applying at the indicated temperatures ... 

Using density as the property measured to determine crystallinity, evaluate 0 as a function of time for these data. By an appropriate graphical analysis, determine the Avrami exponent (in doing this, ignore values of 6 < 0.15, since errors get out of hand in this region). Calculate (rather than graphically evaluate) the value of K consistent with your analysis. 

In an amorphous material, the aUoy, when heated to a constant isothermal temperature and maintained there, shows a dsc trace as in Figure 10 (74). This trace is not a characteristic of microcrystalline growth, but rather can be well described by an isothermal nucleation and growth process based on the Johnson-Mehl-Avrami (JMA) transformation theory (75). The transformed volume fraction at time /can be written as... 

Decompositions may be exothermic or endothermic. Solids that decompose without melting upon heating are mostly such that can give rise to gaseous products. When a gas is made, the rate can be affected by the diffusional resistance of the product zone. Particle size is a factor. Aging of a solid can result in crystallization of the surface that has been found to affect the rate of reaction. Annealing reduces strains and slows any decomposition rates. The decompositions of some fine powders follow a first-order law. In other cases, the decomposed fraction x is in accordance with the Avrami-Erofeyev equation (cited by Galwey, Chemistry of Solids, Chapman Hall, 1967)... 

Dehydration of CUSO4 pentahydrate at 53 to 63°C (127 to 145°F) and of the trihydrate at 70 to 86°C (158 to 187°F) obey the Avrami-Erofeyev equation. The rate of water loss from Mg(OH)9 at lower temperatures is sensitive to partial pressure of water. Its decomposition above 297°C (567°F) yields appreciable amounts of hydrogen and is not reversible. 

V. I. Avramis, in A Clinician s Guide to Chemotherapy, Pharmacokinetics and Pharmacodynamics,... 

L. E. Levine, K. Lakshmi Narayan, K. F. Kelton. Finite size corrections for the Johnson-Mehl-Avrami-Kolmogorov equation. J Mater Res 72 124, 1997. 

The work of Avrami et al on the impact sensy of Lead Azide-water (LA-w) mixts contg various expls and drying agents, conducted with the standard PicArsn impact test app, is of interest. 

A.R. Garabrant, J.F. Coburn L. Avrami, Moderation of the Sensitivity of Certain Lead Azide/RDX Mixtures , Third International Conference on Rocket Projectile Guidance/... 

AIAA, Solid Propulsion Conf, PicArsn Contract DAAA 21 -67-C-1108 (1968) 40) L. Avrami... 

Avrami W.E. Voreck, A Determination of Reactor-Radiation-Resistant Explosives, Propellants, and Related Materials , PATR 3782 (Nov 1959), 126, AD-506895 22) E.R. Ward... 

The effect of nuclear reactor irradiation on PETN was studied by Avrami and Voreck (Ref 71a). Weight losses ranged from 3.65% for an... 

Avrami et al (Ref 96a) made an extensive study of-the effects of 50Co irradiation on both powdered and pelletized expls. For PETN they found significant changes even at their lowest radiation exposure of 1 x 107 R [1 R (of dry air) =... 

Picryl Fluoride. See Fluoro-2,4,6-Trinitrobenzene in Vol 6, F137-L. This compd has been evaluated at PicArsn as an expl. The parameters are presented in the following limited distribution Refs 1) H J. Jackson et al, A Comparative Evaluation of Selected Fluoroexplosives , PATR 3941 (1970) 2) L. Avrami et al, Effects of... 

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