JMAK equation

The absorption curves in Fig. 2.4a were analyzed by a linear fitting to the JMAK equation from which the reaction rate constant, k, and the reaction order,p, can be determined. The values of the reaction order p are listed in Table 2.4. At the lowest absorption temperature of 250°C, the p parameter is close to 2, and then it decreases to about 1, remaining close to this value at all the other temperatures. The different values of the reaction order suggest that different mechanisms are controlling the rates at various temperature ranges of absorption. It can be seen from Table 2.3, that the value of 2 (1.83 in Table 2.4) suggests that the transformation of Mg to... 

Table Z4 The values of the reaction order p in the JMAK equation for the absorption experiments on the unmiUed, activated, and cycled ABCR powder presented ...

DSC tests show a substantial reduction of the hydrogen desorption onset (red circles) (T J and peak (T ) temperatures due to the catalytic effects of n-Ni as compared to the hydrogen desorption from pure MgH also milled for 15 min. (Fig. 2.57). It is interesting to note that there is no measurable difference between spherical (Fig. 2.57a) and fdamentary (Fig. 2.57b) n-Ni, although there seems to be some effect of SSA. We also conducted desorption tests in a Sieverts apparatus for each SSA and obtained kinetic curves (Fig. 2.58), from which the rate constant, k, in the JMAK equation was calculated. The enhancement of desorption rate by n-Ni is clearly seen. At the temperature of 275°C, which is close to the equilibrium at atmospheric pressure (0.1 MPa), all samples desorb from 4 to 5.5 wt.% within 2,000 s. 

Andreasen et al. [86] also found that ball milling increased the rate constant, k, in the JMAK equation (Sect. 1.4.1), of reaction (Rib) in solid state but virtually had no effect on the rate constant of reaction (R2). They also showed that the reaction constant, k, of reaction (Rib) in solid state increases with decreasing grain size of ball-milled LiAlH within the range 150-50 mn. Andreasen et al. concluded that the reaction (Rib) in solid state is limited by a mass transfer process, e.g., long range atomic diffusion of Al while the reaction (R2) is limited by the intrinsic kinetics (too low a temperature of decomposition). In conclusion, one must say that ball milling alone is not sufficient to improve the kinetics of reaction (R2). A solution to improvement of the kinetics of reaction (R2) could be a suitable catalytic additive. 

Fig. 3.36 (a) Desorption curves for the (MgHj + Xwt%Al) composites with the content of A1 additive equivalent to the content of free A1 formed after decomposition of Awt%LiAlH in (MgH + Xwt%LiAlH ) composites (300°C 0.1 MPa Hj). The (MgH + Xwt%Al) composites were baU milled for 20 h. (b) Dependence of an effective kinetic parameter, k, in the JMAK equation on the equivalent content of A1 metal additive... 

We have studied the phase transformation from nanometer-sized amorphous titania (Ti02) to nanocrystalline anatase at 300 - 400° C (unpublished). Amorphous titania samples were prepared by fast hydrolysis of titanium ethoxide in water at 0° C (Zhang et al. 2001). The extent of transformation was monitored using XRD determination of the phase mixture as a function of time. We also found that the transformation kinetics do not follow the widely employed JMAK equation. 

Phase transformations in nanomaterials have been studied in other systems. The phase transformation from nanocrystalline maghemite (y-Fe203) to hematite (a-Fe203) at 385° C obeyed the simple form of the JMAK equation withw 1.0 (Ennas et al. 1999). Schimanke and Martin (2000) examined the transition of nanocrystalline y-to-a-Fe203 and described it as first order, with an activation energy that increased with increasing crystal size. 

Weinberg MC, Bimie DP III, Shneidman VA (1997) Crystallization kinetics and the JMAK equation. J Non-crystal Solids 219 89-99... 

The rate of transformation of a metastable solid (parent) phase (A) to form a more stable solid (product) phase (B) is usually modeled using the Avrami equation (Avrami, 1939, 1940), which is also known as the Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation. This equation is based on a model that assmnes that the transformation involves the nucleation of the product phase followed by its growth imtil the parent phase is replaced by the... 

Wegiel LA, Mauer LJ, Edgeir KJ, Taylor LS (2012) Mid-infrared spectroscopy as a polymer selection tool for formulating amorphous solid dispersions. J Phtirm Phtirmacol. doi 10. Ill 1/jphp. 12079 Weinberg MC, Bimie I DP, Shneidman VA (1997) Crysttillization kinetics and the JMAK equation. J Non-Cryst Solids 219 89-99... 

Weinberg (1992a), Weinberg et al. (1997), and Zanotto (1997), reported in detail on transformation kinetics via nucleation and crystal growth. The standard theory of this type of phase transformation kinetics was developed by Johnson and Mehl and Avrami and Kolmogorov (see Weinberg et al., 1997). Therefore, this theory is called the JMAK theory. The JMAK equation (Eq. 1-6) is universal and applicable to glass-ceramics. 

The kinetics of mica crystallization in DICOR glass-ceramic was studied by Bapta et al. (1996). The formal kinetic parameters were established according to the JMAK equation (Eq. 1-6 in Section 1.4.3). The activation energy of crystallization was determined as 203 kj moT the formal reaction order n as 3.4 0.2 and the pre-exponential factor as 2.88 x 10 s ... 

---