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Kinetics and elementary mechanisms in solid-gas reactions

  • Pijolat, Michèle
Publication Date
Aug 04, 2013
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Most of the kinetic studies in the gas-solid reactions field aim to extract the model of transformation (f(α)) and the kinetic constants (A, E<sub>a</sub>) from the analysis of the experimental data according to: d<i>α</i>/d<i>t</i> = A exp(-E<sub>a</sub>/RT) f(<i>α</i>) Many articles have already been devoted to the discussion of mathematical methods and these will not be discussed here. It is rather a different way of describing the kinetics and the associated mechanisms which will be presented and decomposed in both parts: the elementary mechanism describing the variations of the speed with the thermodynamic variables; the kinetic model which describes the variations of the speed with time. For that purpose, the rate equation will be written: d<i>α</i>/dt = Φ(T, Pi, ai, ...) S<sub>m</sub>(t, Φ, ...) where Φ(T, Pi, ai, ...) is called the areic reactivity of growth and is expressed in mol m<sup>-2</sup> s<sup>-1</sup>and S<sub>m</sub> (t, Φ, ...) is called the space function and is expressed in m<sup>2</sup> mol<sup>-1</sup>. Great efforts devoted in the past aimed to understand the reactions between metallic materials and gases. Even if still progresses are needed, especially for improving their resistance in complex atmospheres and/or at very high temperatures, it must be recognized that the mechanisms are rather well known. Using Kroger's formalism, it is possible to write the mechanism as a succession of elementary steps and, assuming one is the rate-determining step (rds), the rate law may be calculated as a function of the thermodynamic variables leading to the knowledge of the Φ function. From such a basis, it is possible to make the transposition to any kind of gas-solid reaction, including decomposition reactions and the mechanism of growth will involve adsorption/desorption steps, diffusion steps and interfacial steps, as in the oxidation of metallic materials. The function is independent of the symmetry of the solid. Using the rds assumption and considering a single solid particle, the variations of the kinetic rate with time may be predicted since the calculation resumes to that of the function S<sub>m</sub> which is: - in the case of adsorption/desorption or interfacial step, the extent of surface where the rds takes place, - in the case of diffusion through the product layer, the product of a surface by a term which comes from the flux expression. In all cases the S<sub>m</sub> function depends of the reacting particle symmetry. When a collection of solid particles is considered, the calculation of the S<sub>m</sub> function requires more assumptions as regards to the nucleation process: - if it can be considered as instantaneous, the reaction kinetics involves only the areic reactivity of growth Φ and the function S<sub>m</sub> is the same than for a single solid particle, - if the nucleation process is not instantaneous compared to the growth, it must be involved in the calculations of the S<sub>m</sub> function due the areic nucleation frequency γ (number of nuclei m<sup>-2</sup>s<sup>-1</sup>). Various examples will illustrate the kinetic modeling, especially the elementary mechanisms of growth of the product phase and the variations of the Φ function with the thermodynamic variables.

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