Numerical Data for Some Commonly Used Solid State Reaction Equations

Abstract

Many solid state reactions can be represented by equations of the type F(α) =kt, where α is the fraction of material reacted in time, t. These equations can be expressed in the form F(α) =A(t/t0.5) where t0.5 is the time for 50% reaction and A is a calculable constant depending on the form of F(α). Numerical tables are given of F(α) in relation to α, and to (t/t0.5), for nine equations corresponding to reactions which are diffusion controlled, or are reaction‐rate controlled, or obey first order kinetics, or follow the equations of Avrami and Erofe'ev. The application of the tables to the analysis of experimental data is described.

Reducibility of Potassium-Promoted Iron Oxide under Hydrogen Conditions

“…25,42 The differential method applied to solid-state reactions requires a reaction order based on the particle geometry corresponding to the movement of the solid-gas interface through the particle. 26,43,45,46 The primary particle morphology for the iron oxide in the current study, which was found from SEM to be acicular with branching, could best be represented by either cylindrical or spherical particle geometry. Therefore, reaction orders of n ) 1 / 2 , corresponding to cylindrical morphology, and 2 / 3 , corresponding to spherical morphology, were both considered in the analysis.…”

Isothermal Reduction Kinetics of Powdered Hematite and Calcium Ferrite with CO–N₂ Gas Mixtures

“…16) According to the Avrami-Erofeev 5,17,18) equation, the reduction degree α can be expressed as the relationship of time t and rate constant k: The value of n is directly related to G(α), which means that G(α) can be determined by first attaining the value of n. Table 1 shows the corresponding relationship between G(α) and n. It worthy to say that functions A 2 and A 3 represent a 2D reaction with a plane-like mechanism and a 3D reaction with a spherulitic-type mechanism, respectively. Sharp analysis defines a non-dimensional parameter y(α) as The relationship between ln[ − ln(1 − α)] and lnt for hematite and CF was determined through ln-ln analysis and is presented in Fig.…”

Evaluation of Kinetic Parameters and Thermal Stability of Melt-Quenched BixSe100-xAlloys (x ≤7.5 at%) by Non-Isothermal Thermogravimetric Analysis

“…Improving resolution of non-isothermal TG measurements and separating possible thermal processes can be realized via long experimental runs at slow heating rates (2°C/min~30°C/ min), so the time at any T must be long enough to permit completeness of a kinetic reaction, by reducing sample's size (5~30 mg), hence minimizing temperature gradients and inhomogeneities across it, and by choosing a suitable purge gas during TG measurements. As regards to kinetic analysis of experimental thermoanalytical data, two main approaches are realized: the modelfree and model-based analysis methods, both demand a set of accurate isothermal or non-isothermal measurements at different conditions, such as the sample's temperature T and the heating rate β (Abdel- Rahim et al, 2008;Abu ElOyoun, 2000;Achar et al, 1966;Atmani, 1988;Brown, 2004;Coat & Redfern, 1964;Flynn & Wall, 1966;Jones et al, 1975;Keattch & Dollimore, 1975;Marini et al, 1979;Moharram & Abu El-Oyoun, 2000;Moukhina, 2012;Ozawa, 1965;Ptáček et al, 2010;Šesták, 1984;Sharp & Wentworth, 1969;Sharp et al, 1966). The model-based kinetic (discrimination) analysis solves an equation (Eq.)…”