Mampel model

The fact of observing small islands of B on A suggests a phenomenon of slow nucleation and isotropic growth on spherical particles, which excludes the diffusion as the rate-determining step, and thus, we adopt a mode of growth limited by a step taking place at the internal interface, with inward development. We will thus use the Mampel model for spheres. 

Figure 18.22. Lines giving the experimental rate obtained by pressure switches versus the reactivity ofgrowth given by the Mampel model (a) from the higher value of coefficient A and (b) from the lower value of this coefficient...

Many mathematical models have bees advanced relating nucleation and nuclei growth rates to the overall kinetics of phase transformation, such as Johnson and Mehl [427], Avrami [428], Yerofyeyev [429], Kolmogorov [430] as well as Jacobs-Tompkins [431] or Mampel [432] and were agreeably suinmarized elsewhere [1,3,413,144, 421,422,423,426,43 I ]. 

Thus, Bouineau [BOU 98] retains the model of Mampel with spheres for the decomposition of calcium carbonate. Figure 13.13 shows conpatibility between an experimental curve obtained under 1,200 Pa and 700°C, with the one calculated in the model of Mampel, for two values, one low and the other high value of the Hg model parameter, leading to the same position of the maximum. If the agreement seems correct with the first examination for the two Hg values, an analysis of the sum of the squares of the differences between experimental and calculated curves shows that the value for the lowest value for Hg gives better results. This is confirmed by microscopic examinations, which show a small number of nuclei formed during a quite short time. 

From kinetic curves, it has been concluded a good agreement with Mampel s model. Parameter A and ratio Bit for a certain number of experiments have been calculated. 

---