Analysis of transformation kinetics by nonisothermal dilatometry
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I.
INTRODUCTION
EVALUATION of kinetic reaction parameters, as activation energies, can be based on the analysis of measurements, taken as a function of time, t, and temperature, T, of a physical property (e.g., specific volume/length, electrical resistivity, magnetization), p, of the material subject to investigation. The fraction transformed, f, can be defined as f _ p - p0 pl - p0
[1]
where p0 and Pl refer to start and finish of the transformation, respectively. An obvious experimental approach implies the determination of f as a function of time for a series of fixed temperatures. Studying solid-state reactions the JohnsonMehl-Avrami (JMA) description, originally developed for the analysis of isothermal behavior off, can often be applied satisfactorily although the limitations of this theory are generally recognized, l However, experiments are frequently performed in a nonisothermal fashion. For example, application of a constant heating rate (isochronal annealing) may afford better experimental stability and reproducibility. It is tempting to adopt the JMA description also in the case of nonisothermal annealing, but its application is not straightforward (see Section II). 1,2,3 Isochronal annealing for the determination of kinetic parameters of transformations has mostly been performed in thermal analyses as differential scanning calorimetry (DSC). Then, the operating activation energy can be obtained according to the Kissinger analysis, 4 or variants thereof (e.g., Reference 5). To that end the temperature where the reaction rate is maximal, associated with the DSC peak signal, is investigated as a function of heating rate. The analysis of length changes, dilatometry, provides a sensitive method to describe many solid-state transformations. Dilatometry is usually performed applying a constant heating rate. According to the present authors' opinion, in nonisothermal dilatometry a development of methods for E.J. MITTEMEIJER, Professor, and P. J. VAN DER SCHAAF, Technical Assistant, are with the Laboratory of Metallurgy, Delft University of Technology, Rotterdamseweg 137, 2628 AL Delft, The Netherlands. A. VAN GENT is a former Graduate Student at the Laboratory of Metallurgy of the Delft University of Technology. Manuscript submitted September 26, 1985. METALLURGICALTRANSACTIONS A
kinetic analysis, analogous to those applied for constant heating-rate experiments in thermal analyses, has been neglected until now. It is the purpose of this paper to demonstrate that such methods are possible. In particular it will be shown that a powerful method for the determination of the activation energy can be based on tracing the temperature where an inflection point occurs in the dilatometric curve, as a function of heating rate. Relative length changes are proportional to relative volume changes if the system undergoing phase transformation can be conceived as (macroscopically) isotropic. In the case of anisotropy, that may occur in the case of specimens exhibiting preferred orientation for the constituent crystallites/
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