Kinetic analysis of solid-state processes
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kefumi Mitsuhashi National Institute for Research in Inorganic Materials, Science and Technology Agency of Japan, Namiki 1-1, Tsukuba, Ibaraki 305, Japan
Jose´ Manuel Criado Instituto de Ciencia de Materiales de Sevilla, Centro Mixto Universidad de Sevilla-C.S.I.C., c/ Ame´rico Vespucio s/n, 41092 Sevilla, Spain (Received 16 October 2000; accepted 4 April 2001)
A simple method for kinetic analysis of solid-state processes has been developed. A criteria capable of classifying different processes is explored here with a view toward visualizing the complexity of solid-state kinetics. They provide a useful tool for the determination of the most suitable kinetic model. The method has been applied to the analysis of crystallization processes in amorphous ZrO2 and RuO2. It is found that the crystallization kinetics of as-prepared sample exhibits a complex behavior under nonisothermal conditions. This is probably due to an overlapping of the nucleation- and crystal-growth processes at the beginning of crystallization. As a consequence, the Johnson–Mehl–Avrami nucleation-growth model cannot be applied. A two-parameter autocatalytic model provides a good description of the crystallization process under isothermal and nonisothermal conditions. I. INTRODUCTION
The kinetics of solid-state processes has been discussed extensively.1–5 It is generally considered to be a rather controversial topic.6–10 Most interpretations concerning kinetic data are based on the assumption that the kinetic parameters are intrinsic constants that uniquely characterize a given solid-state process. Such an approach, however, inevitably leads to misunderstandings, because solid-state processes usually exhibit rather complex kinetics.11 One reason for studying kinetics is the practical importance of the ability to predict how quickly a system approaches equilibrium. Another reason is related to an understanding of the mechanism of the process. It should be stated clearly that, in the first case, we can actually get suitable mathematical descriptions for most solid-state processes (even complicated ones) and, therefore, we may be able to optimize the rate by an appropriate change of variables under certain controls (temperature, pressure, etc.). Nevertheless, it is usually extremely difficult to explore the real mechanism of the solid-state process unless a careful and meticulous study has been made, including complementary experimental techniques and
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J. Mater. Res., Vol. 16, No. 6, Jun 2001 Downloaded: 12 Mar 2015
morphological observations. As pointed out recently by Scho¨llhorn,12 there is a considerable lack of such studies at the moment. It is often found that the rate of a chemical reaction is proportional to the concentration of reactants, raised to a power. In the case of solid-state processes, the concentration is replaced by the fractional conversion ␣. Table I summarizes the rate laws for some simple processes in gaseous and liqu
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