Study of the kinetics of the mechanism of solid-state reactions at increasing temperatures
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.
About: This article is published in Thermochimica Acta.The article was published on 1971-10-01. It has received 1249 citations till now. The article focuses on the topics: Nucleation & Differential equation.
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TL;DR: In this article, the authors have developed recommendations for reliable evaluation of kinetic parameters (the activation energy, the preexponential factor, and the reaction model) from the data obtained by means of thermal analysis methods such as TGA, differential scanning calorimetry (DSC), and differential thermal analysis (DTA).
4,112 citations
TL;DR: This work summarizes commonly employed models and presents their mathematical development as nucleation, geometrical contraction, diffusion, and reaction order.
Abstract: Many solid-state kinetic models have been developed in the past century. Some models were based on mechanistic grounds while others lacked theoretical justification and some were theoretically incorrect. Models currently used in solid-state kinetic studies are classified according to their mechanistic basis as nucleation, geometrical contraction, diffusion, and reaction order. This work summarizes commonly employed models and presents their mathematical development.
1,437 citations
TL;DR: A critical review of kinetic models and mathematical approximations currently employed in solid state thermal analysis is provided and analysis of thermal decomposition data obtained from two agricultural residues, nutshells and sugarcane bagasse reveals the inherent difficulty and risks involved in modeling heterogeneous reaction systems.
976 citations
TL;DR: The results of the ICTAC Kinetics Project as mentioned in this paper have been used to forecast the tendencies for the future development of solid state kinetics, as well as the findings of the participants are compared.
794 citations
TL;DR: A review of previously suggested methods for analysis of experimental data of non-isothermal crystallization kinetics based on the Johnson-Mehl-Avrami transformation rate equation is given in this paper.
Abstract: A brief review is given of previously suggested methods for analysis of experimental data of non-isothermal crystallization kinetics based on the Johnson-Mehl-Avrami transformation rate equation. Conditions for applicability are outlined and an estimate of error is made. A method of non-isothermal analysis is presented which facilitates rapid data evaluation over large temperature ranges and which justifies the previous applications in the literature of Kissinger's method to the analysis of crystallizations kinetics. An extension of these methods is made to the case of growth rates which obey a Vogel-Further temperature relation.
678 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 article, a relation between the actual transformed volume V and a related extended volume V1 ex is derived upon statistical considerations, and a rough approximation to this relation is shown to lead, under the proper conditions, to the empirical formula of Austin and Rickett.
Abstract: Following upon the general theory in Part I, a considerable simplification is here introduced in the treatment of the case where the grain centers of the new phase are randomly distributed. Also, the kinetics of the main types of crystalline growth, such as result in polyhedral, plate‐like and lineal grains, are studied. A relation between the actual transformed volume V and a related extended volume V1 ex is derived upon statistical considerations. A rough approximation to this relation is shown to lead, under the proper conditions, to the empirical formula of Austin and Rickett. The exact relation is used to reduce the entire problem to the determination of V1 ex, in terms of which all other quantities are expressed. The approximate treatment of the beginning of transformation in the isokinetic range is shown to lead to the empirical formula of Krainer and to account quantitatively for certain relations observed in recrystallization phenomena. It is shown that the predicted shapes for isothermal transfo...
7,448 citations
TL;DR: In this paper, a comprehensive description of the phenomena of phase change may be summarized in Phase Change, Grain Number and Microstructure Formulas or Diagrams, giving, respectively, the transformed volume, grain, and microstructure densities as a function of time, temperature, and other variables.
Abstract: The theory of the preceding papers is generalized and the notation simplified. A cluster of molecules in a stable phase surrounded by an unstable phase is itself unstable until a critical size is reached, though for statistical reasons a distribution of such clusters may exist. Beyond the critical size, the cluster tends to grow steadily. The designation ``nuclei'' or ``grains'' is used according as the clusters are below or above the critical size. It is shown that a comprehensive description of the phenomena of phase change may be summarized in Phase Change, Grain Number and Microstructure Formulas or Diagrams, giving, respectively, the transformed volume, grain, and microstructure densities as a function of time, temperature, and other variables. To facilitate the deduction of formulas for these densities the related densities of the ``extended'' grain population are introduced. The extended population is that system of interpenetrating volumes that would obtain if the grains granulated and grew through each other without mutual interference. The extended densities are much more readily derivable from an analysis of the fundamental processes of granulation and growth. It is shown that, under very general circumstances, the densities of the actual grain population may be expressed simply in terms of the extended population.
5,550 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
412 citations