tting the coordinate systems of diffusion equation in the diffusion problems is essentially necessary for understanding of the diffusion phenomena.

2) An element in the interdiffusion region has only one diffusivity value. The so-called interdiffusion coefficient means the unsolved one in the partial differential equation. On the other hand, the intrinsic diffusion coefficient corresponds to the solved one using the given initial and boundary values for the general solutions. Therefore, such an especial intrinsic diffusion coefficient conceived in the diffusion history is essentially nonexistent in accordance with the mathematical theory.

In view of the influence of misunderstanding problems pointed out here on the younger, we hope that the conclusions are universally known in the concerned research field as soon as possible, just because of the fundamental matters themselves.

Appendix

Even if the diffusion couple satisfies in the diffusion system shown in Figure 2, the generality of diffusion system holds still. In that case, the particles of element I diffuse from the interface at into the diffusion region between. On the other hand, the particles of element II diffuse from the interface at into the diffusion region between. The diffusion junction depths and are estimated as

and, (A-1)

where is a parameter and is tentatively adopted in the present work.

Using (A-1) and the concentration difference of boundary values

and, the actual diffusion fluxes of elements I and II are expressed as

(A-2)

Equation (A-2) yields

(A-3)

The diffusion flux of (A-3) caused by the coordinate transformation corresponds to the flux of diffusion region space given by

(A-4)

since the flux of diffusion region space moves in the opposite direction to the diffusion flux of (A-3). Substituting (A-4) into (29) yields

(30)

Submit or recommend next manuscript to SCIRP and we will provide best service for you:

Accepting pre-submission inquiries through Email, Facebook, LinkedIn, Twitter, etc.

A wide selection of journals (inclusive of 9 subjects, more than 200 journals)

Providing 24-hour high-quality service

User-friendly online submission system

Fair and swift peer-review system

Efficient typesetting and proofreading procedure

Display of the result of downloads and visits, as well as the number of cited articles

Maximum dissemination of your research work

Submit your manuscript at: http://papersubmission.scirp.org/

Or contact jmp@scirp.org

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] Fourier, J.B.J. (1822) Analytique de la Chaleur. Didot, Paris, 499-508.
[2] Fick, A. (1855) Philosophical Magazine, 10, 31-39.
[3] Gauss, C.F. (1840) Resultateaus den Beobachtungen des Magnetishen Vereins, 4, 1.
[4] Okino, T. (2015) Journal of Modern Physics, 6, 2109-2144.
https://doi.org/10.4236/jmp.2015.614217
[5] Okino, T. (2013) Journal of Modern Physics, 4, 1495-1498.
https://doi.org/10.4236/jmp.2013.411180
[6] Haug, K., Keiser, D. and Sohn, Y. (2013) Metallurgical and Materials Transactions A, 44, 738-746.
https://doi.org/10.1007/s11661-012-1425-9
[7] Kuhn, P., Horbach, J., Kargl, F. and Meyer, A.Th. (2014) Physical Review B, 90, Article ID: 023409.
https://doi.org/10.1103/PhysRevA.90.023409
[8] Paul, T.R., Belova, I.V., Levchenko, E.V., Evteev, A.V. and Murch, G.E. (2015) Diffusion Foundations, 4, 25-54.
https://doi.org/10.4028/www.scientific.net/DF.4.25
[9] Boltzmann, L. (1894) Annual Review of Physical Chemistry, 53, 959-964.
https://doi.org/10.1002/andp.18942891315
[10] Matano, C. (1933) Japanese Journal of Applied Physics, 8, 109-113.
[11] Okino, T. (2011) Materials Transactions, 52, 2220-2227.
https://doi.org/10.2320/matertrans.M2011137
[12] Smigelskas, A.D. and Kirkendall, E.O. (1947) Transactions of the Metallurgical Society of AIME, 171, 130-142.
[13] Okino, T. (2012) Journal of Modern Physics, 3, 1388-1393.
https://doi.org/10.4236/jmp.2012.310175
[14] Okino, T. (2012) Journal of Modern Physics, 3, 255-259.
https://doi.org/10.4236/jmp.2012.33034
[15] Darken, L.S. (1948) Transactions of the Metallurgical Society of AIME, 175, 184-201.
[16] Okino, T. (2014) Applied Physics Research, 6, 1-7.
https://doi.org/10.5539/apr.v6n2p1

  
comments powered by Disqus
JMP Subscription
E-Mail Alert
JMP Most popular papers
Publication Ethics & OA Statement
JMP News
Frequently Asked Questions
Recommend to Peers
Recommend to Library
Contact Us

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.