Numerical Data for Some Commonly Used Solid State Reaction Equations
01 Jul 1966-Journal of the American Ceramic Society (Blackwell Publishing Ltd)-Vol. 49, Iss: 7, pp 379-382
TL;DR: In this paper, the authors give numerical tables of F(α) in relation to α, and to (t/t0.5) where t 0.5 is the time for 50% reaction and A is a calculable constant depending on the form of F (α).
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.
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TL;DR: In this paper, the importance of the correct selection for the assessment of the progress of the reaction and the acquisition of representative experimental data, as well as the effect of non-isothermal conditions and possible change of the equilibrium on the kinetic equation are stressed.
1,249 citations
TL;DR: In this article, a method of comparing the kinetics of isothermal solid-state reactions based on the classical equation for analysis of nucleation-and growth processes is described, where plots of In In (1-α) vs In (time), where α is the fraction reacted, are used to distinguish reaction mechanisms.
Abstract: A method of comparing the kinetics of isothermal solid-state reactions based on the classical equation for analysis of nucleation-and-growth processes is described. In this method, plots of In In (1-α) vs In (time), where α is the fraction reacted, are used to distinguish reaction mechanisms. Even nonintegral slopes obtained for values of the fraction reacted from 0.15 to 0.50 may indicate whether the reaction rate is diffusion- or phase-boundary-controlled. The problems of ascertaining zero time and self-cooling (or heating) of the reacting sample can be observed in the analysis but do not cause severe difficulties in interpretation, as they can for analyses based on reduced-time plots. The analysis is applied to the dehydroxylation of kaolinite and of brucite and the decomposition of BaCO3.
636 citations
TL;DR: In this paper, the concept of generalized time, introduced by Ozawa, has been used to define master plots for the analysis of solid-state reactions, regardless of the type of temperature program used for recording the experimental data.
Abstract: Master plot methods based on the integral and/or the differential forms of the kinetic equation describing solid-state reactions have been redefined by using the concept of the generalized time, θ, introduced by Ozawa. This redefinition permits the application of these master plots to the kinetic analysis of solid-state reactions, whatever the type of temperature program used for recording the experimental data. In isothermal conditions, a single curve is enough to construct the experimental master plots. In nonisothermal conditions, the knowledge of both α as a function of temperature and activation energy is required for calculating the master plot curves from the experimental data. Practical usefulness of the present master plot methods is examined, and exemplified by being applied to the thermal decomposition of ZnCO3 under isothermal, linear nonisothermal, and nonlinear nonisothermal conditions.
506 citations
TL;DR: A submitted manuscript is the version of the article upon submission and before peer-review as discussed by the authors, while a published version is the final layout of the paper including the volume, issue and page numbers.
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TL;DR: There is general agreement in the literature that chalcopyrite leaching is significantly affected by solution redox potential with an optimum E(h) range suggesting the participation of leach steps that involve both oxidation and reduction.
338 citations
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TL;DR: In this paper, the theory of phase change is developed with the experimentally supported assumptions that the new phase is nucleated by germ nuclei which already exist in the old phase, and whose number can be altered by previous treatment.
Abstract: The theory of the kinetics of phase change is developed with the experimentally supported assumptions that the new phase is nucleated by germ nuclei which already exist in the old phase, and whose number can be altered by previous treatment. The density of germ nuclei diminishes through activation of some of them to become growth nuclei for grains of the new phase, and ingestion of others by these growing grains. The quantitative relations between the density of germ nuclei, growth nuclei, and transformed volume are derived and expressed in terms of a characteristic time scale for any given substance and process. The geometry and kinetics of a crystal aggregate are studied from this point of view, and it is shown that there is strong evidence of the existence, for any given substance, of an isokinetic range of temperatures and concentrations in which the characteristic kinetics of phase change remains the same. The determination of phase reaction kinetics is shown to depend upon the solution of a functional equation of a certain type. Some of the general properties of temperature‐time and transformation‐time curves, respectively, are described and explained.
9,458 citations
TL;DR: In this paper, a model for solid-solid or solid-gas reactions between spherical particles and a fine powder or gas has been developed, and the oxidation of uniformly sized nickel spheres has been shown to fit this model to 100% reaction.
Abstract: A model for solid‐solid or solid‐gas reactions between spherical particles and a fine powder or gas has been developed. The oxidation of uniformly sized nickel spheres has been shown to fit this model to 100% reaction. Previously reported models are inadequate because they do not meet the boundary conditions set down and because the volume of the product was assumed to equal that of one of the reactants. The inadequacy of earlier experimental results has been explained by the failure to experimentally meet the boundary conditions imposed.
401 citations
TL;DR: In this paper, the deformation of kaolinite was carried out in a vacuum to evaluate the kinetics without the marked effect of water vapor, and the reaction was found to be diffusion-controlled, with an activation energy of 43.5 kcal.
Abstract: The dehydration of kaolinite was carried out in a vacuum to evaluate the kinetics without the marked effect of water vapor. Samples of carefully fractionated particles were used and the effect of surface area was determined. At pressures in the order of 1μ of Hg the reaction was found to be diffusion-controlled, with an activation energy of 43.5 kcal. The rate of dehydration was found to decrease linearly with increasing water vapor at moderate pressures. A change from parabolic to first-order kinetics was observed with increasing pressures.
87 citations
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