Abstract
A simple statistical model of the diffusion of impurity atoms in the crystal lattice of metals has been developed. The relationship between the diffusion flux of atoms and the gradient of their chemical potential is obtained from the basic principles of statistical thermodynamics. For an ideal solid solution of a substance atoms in a metal, an expression is found for the zero diffusion coefficient, which depends on the square of the temperature. The calculated diffusion coefficients of hydrogen and carbon atoms in iron are in a fairly good agreement with the known experimental data.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Ya. S. Umansky and Yu. A. Skakov, Physics of Metals (Atomizdat, Moscow, 1978) [in Russian].
H. Ascroft and H. Mermin, Solid State Physics (Saunders College, Philadelphia, 1981).
J. S. Blakemore, Solid State Physics (Cambridge Univ. Press, New York, 1985).
G. Grosso and P. G. Pastori, Solid State Physics (Academic, London, 2003).
J. R. Hook and H. E. Hall, Solid State physics. Introduction to the Theory (Springer, Berlin, 2007).
M. V. Belous and M. P. Brown, Physics of Metals (Vi-shcha Schkola, Kiev, 1985) [in Russian].
Ya. I. Frenkel’, Introduction to the Theory of Metals (Fizmatgiz, Moscow, 1948) [in Russian].
S. D. Gerzriken and I. Ya. Dehtyar, Diffusion in Metals and Alloys in Solid Phase (Fizmatgiz, Moscow, 1960) [in Russian].
M. A. Cristal, The Diffusion Mechanism in Iron Alloys (Metallurgiya, Moscow, 1972) [in Russian].
K. P. Gurov and M. G. Chudinov, in Diffusion Processes in Metals (Naukova Dumka, Kiev, 1966) [in Russian].
V. A. Kozheurov, Statistical Thermodynamics (Metallurgiya, Moscow, 1975) [in Russian].
E. M. Lifshitz and L. P. Pitaevskiy, Course of Theoretical Physics, Vol. 9: Statistical Physics, Part 2: Theory of Condensed Matter (Fizmatlit, Moscow, 2000; Pergamon, New York, 1980).
B. S. Bokshtein, Diffusion in Metals (Metallurgiya, Moscow, 1978) [in Russian].
S. V. Bobyr, in Proceedings of the International Conference on Diffusion Fundamentals VIII, Erlangen, Germany, September, 2019.
K. J. Haman, in Diffusion in Body-Centered Cubic Metals, Ed. by J. A. Wheeler, Jr. and F. R. Winslow (Am. Soc. Metals, Metals Park, Ohio, 1965), p. 83.
L. N. Larikov and V. I. Isaychev, Diffusion in Metals and Alloys. Catalogue (Naukova Dumka, Kiev, 1987) [in Russian].
D. Graham, in Diffusion in Body-Centered Cubic Metals, Ed. by J. A. Wheeler, Jr. and F. R. Winslow (Am. Soc. Metals, Metals Park, Ohio, 1965), Chap. 2.
ACKNOWLEDGMENTS
I would like to express my sincere gratitude to my son Bobyr Vladislav and Dr. Michael Rauch from the Friedrich-Alexander-University Erlangen, thanks to whose participation it became possible to complete and present some parts of this work at the conference “Diffusion Fundamentals VIII” in September 2019. This article takes into account the critical remarks gratefully accepted by the author at this conference.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The authors declare that they have no conflicts of interest.
Rights and permissions
About this article
Cite this article
Bobyr, S.V. Statistical Model of Impurity Atoms Diffusion in the Crystal Lattice of Metals and Its Application for Calculating the Diffusion Coefficients of Hydrogen and Carbon Atoms in Iron. Phys. Solid State 63, 420–424 (2021). https://doi.org/10.1134/S1063783421030033
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063783421030033