Avrami exponent determination

Table 2 shows the results for the effect of sample cooling rate for refined palm oil at 293 K. The cooling rates investigated are in the range normally used for most DSC analysis of oils and fats. From the results, it can be deduced that DSC cooling rates in the range of 5 to 20°C per minutes do not have any effect on the Avrami exponent determined. 

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

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. 

Effect of Differential Scanning Calorimetry Cooling Rate on the Determination of the Avrami Exponent ... 

The Avrami exponent, n, is related to the type of crystal nucleation, growth, and the dimensionality and nature of the crystals. Often the half-time of crystallization (f ) is used as an indication of the rate of overall crystal growth. OM is particularly useful in determining the... 

Where X t) is the normalized crystallinity given as the ratio of degree of crystallinity at time t and the final degree of crystallinity, is the induction period which is determined experimentally and defined as the time where deviations from baseline can be monitored (min), is the overall rate constant of crystallization (min ), and n the Avrami exponent. 

Differential scanning calorimetry was used to study the non-isothermal crystallization behavior of blends of poly(phenylene sulfide) (PPS) with the thermotropic liquid-crystalline copoly(ester amide) Vectra-B950 (VB) [126], The PPS crystallization temperature and the crystallization rate coefficient increased significantly when 2-50% VB was added. The Ozawa equation was shown to be valid for neat PPS as well as for the blends. The values of the Avrami exponents matched well against those determined previously using isothermal analysis, and they are independent of the concentration of VB. 

Plots of ln[-ln(l-x)] against In f are shown in Fig. 20. Values of Avrami exponent n and the reaction rate constants k were determined by least square fits of the experimental data. The average value of n is 2.62. Since n takes only integer values from 1 to 4, the n (close to 3) value observed in the present study indicates the near three-dimensional growth of LiNbOs (see Table 1). The values of In k are determined for all the temperatures from the plots of ln[-In(l-x)] against In f (Fig. 20). 

Thermochimica Acta, 355, pp. 239-253,0040-6031 Marotta, A., Saiello, S. Buri, A. (1983). Remarks on determination of the Avrami exponent by non-isothermal analysis. Journal of Non-Crystalline Solids, 57, pp. 473-475, 0022-3093... 

Table 2. Avrami exponent (n) and activation energy of crystallization (Ext) in terms of incubation time during isothermal annealing and the activation energy of crystallization (Eiso) determined from a Kissinger plot for the ball-milled amorphous Ti5oCui8Ni22Al4Sn6 alloy and its composite containing 10 vol.% TiC Reprinted from (Zhang, et al., 2006a), with permission from American Institute of Physics.

For fast heterogeneous nucleation, the Avrami coefficient becomes 3. The quantity of the Avrami exponent can be determined as the slope in a plot of (Eq. 1-8). 

Pas, S.J., Dargusch, M.S. and MacFarlane, D.R., Crystallisation kinetics of some archetypal ionic liquids Isothermal and non-isothermal determination of the Avrami exponent, Phys. Chem. Chem. Phys. 13 (25), 12033-12040 (2011). 

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 ... 

Harnisch and Muschick [193] used the Avrami equation to determine the Avrami exponents for PE, low density PE and iPP. However, the values they found (n = 2.9 for PE, n= 1.3 for low density PE, and n = 2.2 for iPP) are not in good agreement with those reported for isothermal crystallization. 

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. 

The crystallization curves were fitted to the Avrami equation by nonlinear regression (Marangoni, 1998) in order to quantify the crystallization kinetics and to gain insight into the nature of the crystal growth process. The Avrami exponent was then determined and plotted as a function of crystallization temperature (Fig. 8). Statistically, two different regions were determined from this graph (P <... 

On the other hand, a strong correlation was found between the Avrami exponent and the fractal dimension (P < 0.001). Distinctly different regions above and below 20°C were determined by both n and D. Also, the microstructures of these two regions observed by PLM were very different. The Avrami... 

Graydon, JW, SJ Thorpe, DW Kirk. (1994). Determination of the Avrami exponent for solid state transformations from non-isothermal differential scanning calorimetry. J Non-Cryst Solids 175 31—43. 

Chapter 2 The susceptibility of MAX phases to thermal dissociation at 1300-1550 °C in high vacuum is explored in this chapter. Above 1400 °C, MAX phases decomposed to binary carbide (e.g., TiC ) or binary nitride (e.g., TiN ), primarily through the sublimation of A-elements such as A1 or Si, which results in a porous surface layer of MX being formed. Positive activation energies were determined for decomposed MAX phases with coarse pores but a negative activation energy when the pore size was less than 1.0 pm. The kinetics of isothermal phase decomposition at 1550 C was modelled using a modified Avrami equation. An Avrami exponent... 

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