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Discussion of “On the Boltzmann–Matano Analysis of Diffusion in a Semi-infinite Medium”

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Abstract

Ernst et al. analyzed the concentration-dependent diffusion of carbon in austenitic steel in the semi-infinite geometry by the Boltzmann–Matano method. They assumed that the origin of the position coordinate be at the surface, and tried to justify it from the particular nature of interstitial diffusion. We point out that their ‘assumption’ is prerequisite to applying the method to the problem, irrespective of the mechanism.

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Notes

  1. Here we ignore the formal mathematical problem that the value of \(\eta \) for Eq. [1] is indefinite. That for Eq. [2] is evaluated to be \(+\infty \) by taking the limit \(t\rightarrow 0+\), since we consider only \(t \ge 0\).

  2. For example, Crank[4] states ‘It is only when the initial and boundary conditions are expressible in terms of \(\eta \) alone, and x and t are not involved separately, that the transformations ... can be used.’

References

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  4. J. Crank: The Mathematics of Diffusion, 2nd edn., Oxford University Press, Oxford, 1975, p. 106.

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  5. J. Philibert: Atom Movements—Diffusion and Mass Transport in Solids, Les Editions de Physique, Les Ulis, 1991

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Acknowledgments

We thank Professors Tabata M. (Osaka Prefecture University), Koiwa M. (Kyoto University Emeritus), and W. Sprengel (Graz University of Technology) for discussion.

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Authors and Affiliations

  1. Department of Materials Science, Graduate School of Engineering, Osaka Prefecture University, Gakuen-cho 1-1, Naka-ku, Sakai, 599-8531, Japan

    Masayuki Okugawa (Graduate student) & Hiroshi Numakura (Professor)

Authors
  1. Masayuki Okugawa
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  2. Hiroshi Numakura
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Correspondence to Hiroshi Numakura.

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Manuscript submitted May 14, 2015.

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Okugawa, M., Numakura, H. Discussion of “On the Boltzmann–Matano Analysis of Diffusion in a Semi-infinite Medium”. Metall Mater Trans A 46, 3813–3814 (2015). https://doi.org/10.1007/s11661-015-3022-1

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  • DOI: https://doi.org/10.1007/s11661-015-3022-1

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