Kinetic Model for Solid‐State Reactions
01 Jun 1961-Journal of Chemical Physics (American Institute of Physics)-Vol. 34, Iss: 6, pp 2010-2015
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.
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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 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.
801 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
Book•
01 Jan 1974
TL;DR: In this article, the authors dealt with the reaction between two solids A and B to form one or more product phases (A m B n ), during which the reaction has to be attributed to a transport of the reactants across phase boundaries and through reaction product.
Abstract: This chapter deals essentially with the reaction between two solids A and B to form one or more product phases (A m B n ). During the course of this heterogeneous solid-solid reaction A m B n separates the reactants spatially. Therefore the progress of the reaction has to be attributed to a transport of the reactants across phase boundaries and through the reaction product.
519 citations
TL;DR: Self-propagating high-temperature synthesis (SHS) and processes based on SHS are currently being developed the world over for the production of powders and near-net shape components of advanced materials as discussed by the authors.
Abstract: Self-propagating high-temperature synthesis (SHS) and processes based on SHS are currently being developed the world over for the production of powders and near-net shape components of advanced materials. The research activities that have been and are being carried out in this field are reviewed here. Theoretical principles underlying SHS process, such as equlibrium computation and kinetics involving heat and mass transfer are described. General concepts about the SHS reaction mechanisms with a few illustrative examples are presented. Along with a detailed description of the processing techniques such as powder production,in situ consolidation and casting, a few of the novel techniques based on SHS are also elaborated.
357 citations
References
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31 Dec 1959
TL;DR: In this paper, a classic account describes the known exact solutions of problems of heat flow, with detailed discussion of all the most important boundary value problems, including boundary value maximization.
Abstract: This classic account describes the known exact solutions of problems of heat flow, with detailed discussion of all the most important boundary value problems.
21,807 citations
TL;DR: In this paper, the rate of oxidation of silicon carbide was measured in an atmosphere of dry oxygen between 900° and 1600°C. The rate was studied by using a thermogravimetric apparatus and was found to be diffusion controlled.
Abstract: The rate of oxidation of silicon carbide was measured in an atmosphere of dry oxygen between 900° and 1600°C. The rate was studied by using a thermogravimetric apparatus and was found to be diffusion controlled. The products of oxidation were amorphous silica and cristobalite, depending on the temperature. The effect of surface area was determined, and a correlation between the various sizes was made with the aid of an equation derived on the assumptions that (1) the reaction was diffusion controlled, (2) the particles were essentially spherical, and (3) the interfacial area was constantly changing. The presence of water vapor in the gaseous atmosphere was found to be extremely critical.
145 citations
TL;DR: In this paper, the effect of time, temperature, and surface pretreatment on rate of oxidation of high purity nickel was studied for the temperature range of 400°-750°C using a vacuum microbalance technique.
Abstract: The effect of time, temperature, and surface pretreatment on rate of oxidation of high purity nickel is studied for the temperature range of 400°–750°C using a vacuum microbalance technique. The data are compared to previous studies in the literature and with other metals. Oxidation data are interpreted in terms of the parabolic rate law and classical theory of diffusion.Large deviations from the parabolic rate law are found to occur during the initial stages of reaction and smaller deviations over long periods of time, especially at low temperatures. However, reasonable values of heat and entropy of activation for the over‐all reaction can be calculated; these are 41,200 cal/mole and −6.0 entropy units (eu), respectively. Parabolic rate law constants over the temperature range of 550°– 700°C are given by The negative value for entropy of activation for the over‐all reaction when corrected for entropy of formation of the vacancies leads to a value of 1.5 for entropy of activation for diffusion. Theoretical considerations suggest that the latter term should have a value of 1.7–3.3 eu. The good agreement between theoretical and experimental entropies of activation suggests that diffusion is occurring largely through the lattice of nickel oxide and not at grain boundaries, at least for the temperature and time region over which analyses were made.A comparison of present data with older studies in the literature shows a large variation in parabolic rate law constants. These variations are interpreted in terms of impurities increasing the concentration of nickel ion vacancies.
95 citations