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Failure of Kissinger(-like) methods for determination of the activation energy of phase transformations in the vicinity of the equilibrium phase-transformation temperature

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Abstract

The activation energies of heterogeneous equilibrium phase transformations have been frequently determined by Kissinger(-like) analysis. This work demonstrates that the applicability of Kissinger(-like) method(s) to determine activation energies of heterogeneous phase transformations is justified if the phase transformation occurs far away from the equilibrium phase-transformation temperature but not if the phase transformation is investigated in the vicinity of the equilibrium phase-transformation temperature. Experimental results on the kinetics of the order–disorder transformation in Ni3Sn2, obtained both near the equilibrium phase-transformation temperature and considerably below it (using quenched samples), expose the non-validity and confirm the validity, respectively, of activation-energy values obtained by Kissinger(-like) analyses applied in the corresponding temperature ranges. Application of the Kissinger(-like) analysis in a temperature range close to the equilibrium phase-transformation temperature leads to erroneous, abnormally high values for the activation energy.

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Notes

  1. Here the phase transformation α → β is focus of the attention. However, the considerations of “Kissinger-like method” section also pertain to other transformations, e.g. of the type α → β + γ, as long as start state and end state are identical for the range of temperatures for which the Arrhenius-type temperature dependence of the reaction rate (cf. Eq. 2) is adopted.

  2. Note that without recourse to a specific rate law in practice explicit values for k are not determinable because g/A together with kA, with A being a f- and T-independent constant, gives the same transformation rate.

  3. The XRPD analyses pertain to isothermal treatments of the alloys at various temperatures.

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Acknowledgements

This work was funded by the Max Planck Society within the inter-institutional research initiative “The Nature of Laves Phases”. The authors thank Prof. Dr F. Sommer for valuable discussion.

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Authors and Affiliations

  1. Max Planck Institute for Metals Research, Heisenbergstrasse 3, 70569, Stuttgart, Germany

    Wolfgang Baumann, Andreas Leineweber & Eric Jan Mittemeijer

  2. Institute for Materials Science, University of Stuttgart, Heisenbergstrasse 3, 70569, Stuttgart, Germany

    Eric Jan Mittemeijer

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  1. Wolfgang Baumann
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  2. Andreas Leineweber
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  3. Eric Jan Mittemeijer
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Correspondence to Andreas Leineweber.

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Baumann, W., Leineweber, A. & Mittemeijer, E.J. Failure of Kissinger(-like) methods for determination of the activation energy of phase transformations in the vicinity of the equilibrium phase-transformation temperature. J Mater Sci 45, 6075–6082 (2010). https://doi.org/10.1007/s10853-010-4693-z

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