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Article citations


Boltzmann, L. (1894) Annual Review of Physical Chemistry, 53, 959-964.

has been cited by the following article:

  • TITLE: Fundamental Concept of Interdiffusion Problems

    AUTHORS: Takahisa Okino, Hiroki Cho, Kazu-Masa Yamada

    KEYWORDS: Interdiffusion, Intrinsic Diffusion, Kirkendall Effect, Parabolic Law

    JOURNAL NAME: Journal of Modern Physics, Vol.8 No.6, May 26, 2017

    ABSTRACT: In accordance with the definition of diffusivity, the origin of coordinate system of the original diffusion equation is set at a point in the solvent material. Kirkendall revealed that Cu atoms, Zn atoms and vacancies move simultaneously in the interdiffusion region. This indicates that the original diffusion equation is a moving coordinate system for the experimentation system outside the diffusion region. The diffusion region space which means vacancies and interstices among atoms plays an important role in the diffusion phenomena. The theoretical equation of the Kirkendall effect is reasonably obtained as a shift between coordinate systems of the diffusion equation. The situation is similar to the well-known Doppler effect in the wave equation. Boltzmann transformed the original diffusion equation of a binary system into the nonlinear ordinary differential equation in accordance with the parabolic law. In the previous works, the solutions of the diffusion equation transformed by Boltzmann were analytically obtained and we found that the well-known Darken equation is mathematically wrong. In the present study, we found that the so-called intrinsic diffusivity corresponds in appearance to the physical solution obtained previously. However, the intrinsic diffusivity itself conceived in the diffusion research history is essentially nonexistent.