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Non-integer temporal exponents in trans-interface diffusion-controlled coarsening

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Abstract

The kinetics of γ′-type (Ni3X) precipitate growth and solute depletion in Ni–Al, Ni–Ga, Ni–Ge, Ni–Si, Ni–Ti and Ni–Al–Cr alloys is successfully predicted by the trans-interface diffusion-controlled theory of coarsening using non-integer temporal exponents, n, satisfying 2 ≤ n ≤ 3, which are obtained from analyses of particle size distributions (PSDs). The origin of non-integer n is concentration-dependent diffusion through the γ/γ′ interface. The literature on diffusion of Al and Ni in Ni3Al is specifically examined. It is shown unequivocally that the concentration-dependent diffusion of Al can account semi-quantitatively for the value of n that successfully describes the PSDs and kinetics of coarsening of the γ′ precipitates. There is no need to invoke a particle size-dependent γ/γ′ interface width, as was done in prior work. It is argued that existing theory and computational modeling of coarsening in systems with highly disparate diffusion mobilities in both phases do not correctly represent the mobilities in the matrix, precipitate, and interface in Ni–Al alloys. These theories predict temporal exponents satisfying 3 ≤ n ≤ 4, for which there is no experimental support.

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Notes

  1. The factor of 3 in the exponential term in Eq. (4) was mistakenly omitted in [35–37], but was included in all fitting of experimental PSDs.

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Acknowledgements

Professor Vidvuds Ozolins, University of California, Los Angeles, provided particularly valuable insights into the thermodynamics and kinetics of transport through diffuse interfaces, as well as the limitations and nuances of phase field modeling. The author is truly grateful to the said professor for his help. Professor Jeffrey J. Hoyt, McMaster University, also provided helpful comments on coarsening and diffusion.

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  1. Department of Materials Science and Engineering, Henry Samueli School of Engineering and Applied Science, University of California, Los Angeles, CA, 90095-1595, USA

    Alan J. Ardell

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Ardell, A.J. Non-integer temporal exponents in trans-interface diffusion-controlled coarsening. J Mater Sci 51, 6133–6148 (2016). https://doi.org/10.1007/s10853-016-9953-0

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