Skip to main content
Top
Published in: Physics of Metals and Metallography 5/2022

01-05-2022 | THEORY OF METALS

On the Theory of Interdiffusion in Ternary Alloys

Author: A. V. Nazarov

Published in: Physics of Metals and Metallography | Issue 5/2022

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

A mathematical apparatus for studying interdiffusion in three-component systems, using a theoretical approach similar to that previously proposed for describing interdiffusion in binary alloys, has been developed. This approach takes into account the active role of vacancies without assuming their equilibrium distribution; therefore, the equations for component fluxes contain contributions due to the vacancy density gradient. Solutions of a linearized system of interrelated diffusion equations for three components and vacancies are obtained. It has been found that the time dependences of the component density distributions in the diffusion zone, up to terms having a higher order in the expansion in powers of the vacancy concentration, are determined by two coefficients of interdiffusion. These coefficients depend nonlinearly on the component concentrations and the self-diffusion coefficients.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference P. G. Shewmon, Diffusion in Solids (McGraw-Hill, Warrendale, 1989). P. G. Shewmon, Diffusion in Solids (McGraw-Hill, Warrendale, 1989).
2.
go back to reference J. R. Manning, Diffusion Kinetics for Atoms in Crystals (Van Nostrand Reinhold, Princeton, 1968).CrossRef J. R. Manning, Diffusion Kinetics for Atoms in Crystals (Van Nostrand Reinhold, Princeton, 1968).CrossRef
3.
go back to reference I. B. Borovskii, K. P. Gurov, I. D. Marchukova, and Yu. E. Ugaste, Processes of Mutual Diffusion in Alloys (Nauka, Moscow, 1973). I. B. Borovskii, K. P. Gurov, I. D. Marchukova, and Yu. E. Ugaste, Processes of Mutual Diffusion in Alloys (Nauka, Moscow, 1973).
4.
go back to reference K. P. Gurov, B. A. Kartashkin, and Yu. E. Ugaste, Mutual Diffusion in Multicomponent Metallic Systems (Nauka, Moscow, 1981) [in Russian]. K. P. Gurov, B. A. Kartashkin, and Yu. E. Ugaste, Mutual Diffusion in Multicomponent Metallic Systems (Nauka, Moscow, 1981) [in Russian].
5.
go back to reference H. Mehrer, Diffusion in Solids – Fundamentals, Methods, Materials, Diffusion-Controlled Processes. Textbook (Springer, Berlin, 2007), Vol. 155, p. 651. H. Mehrer, Diffusion in Solids – Fundamentals, Methods, Materials, Diffusion-Controlled Processes. Textbook (Springer, Berlin, 2007), Vol. 155, p. 651.
6.
go back to reference A. Paul, T. Laurila, V. Vuorinen, and S. V. Divinski, Thermodynamics, Diffusion and the Kirkendall Effect in Solids (Springer, Heidelberg, 2014).CrossRef A. Paul, T. Laurila, V. Vuorinen, and S. V. Divinski, Thermodynamics, Diffusion and the Kirkendall Effect in Solids (Springer, Heidelberg, 2014).CrossRef
7.
go back to reference A. van de Walle and M. Asta, “High-throughput calculations in the context of alloy design,” MRS Bull. 44, No. 4, 252–256 (2019).CrossRef A. van de Walle and M. Asta, “High-throughput calculations in the context of alloy design,” MRS Bull. 44, No. 4, 252–256 (2019).CrossRef
9.
go back to reference Y. N. Osetsky, L. K. Beland, A. V. Barashev, and Y. Zhang, “On the existence and origin of sluggish diffusion in chemically disordered concentrated alloys,” Curr. Opin. Solid State Mater. Sci. 22, No. 3, 65–74 (2018).CrossRef Y. N. Osetsky, L. K. Beland, A. V. Barashev, and Y. Zhang, “On the existence and origin of sluggish diffusion in chemically disordered concentrated alloys,” Curr. Opin. Solid State Mater. Sci. 22, No. 3, 65–74 (2018).CrossRef
10.
go back to reference A. V. Nazarov and K. P. Gurov, “Microscopic theory of mutual diffusion in a binary system with nonequilibrium vacancies,” Fiz. Met. Metalloved. 34, No. 5, 936–941 (1972). A. V. Nazarov and K. P. Gurov, “Microscopic theory of mutual diffusion in a binary system with nonequilibrium vacancies,” Fiz. Met. Metalloved. 34, No. 5, 936–941 (1972).
11.
go back to reference A. V. Nazarov, “Uncompensated vacancy flow and the Kirkendall effect,” Fiz. Met. Metalloved. 35, No. 3, 645–649 (1973). A. V. Nazarov, “Uncompensated vacancy flow and the Kirkendall effect,” Fiz. Met. Metalloved. 35, No. 3, 645–649 (1973).
12.
go back to reference A. V. Nazarov and K. P. Gurov, “Kinetic theory of mutual diffusion in a binary system. Concentration of vacancies during mutual diffusion,” Fiz. Met. Metalloved. 37, No. 3, 496–503 (1974). A. V. Nazarov and K. P. Gurov, “Kinetic theory of mutual diffusion in a binary system. Concentration of vacancies during mutual diffusion,” Fiz. Met. Metalloved. 37, No. 3, 496–503 (1974).
13.
go back to reference A. V. Nazarov and K. P. Gurov, “Kinetic theory of mutual diffusion in a binary system. Influence of the concentration dependence of self-diffusion coefficients on the process of mutual diffusion,” Fiz. Met. Metalloved. 38, No. 3, 486–492 (1974). A. V. Nazarov and K. P. Gurov, “Kinetic theory of mutual diffusion in a binary system. Influence of the concentration dependence of self-diffusion coefficients on the process of mutual diffusion,” Fiz. Met. Metalloved. 38, No. 3, 486–492 (1974).
14.
go back to reference A. V. Nazarov and K. P. Gurov, “Kinetic theory of mutual diffusion in a binary system. Kirkendall effect,” Fiz. Met. Metalloved. 38, No. 4, 689–695 (1974). A. V. Nazarov and K. P. Gurov, “Kinetic theory of mutual diffusion in a binary system. Kirkendall effect,” Fiz. Met. Metalloved. 38, No. 4, 689–695 (1974).
15.
go back to reference A. V. Nazarov and K. P. Gurov, “Accounting for nonequilibrium vacancies in the phenomenological theory of mutual diffusion,” Fiz. Met. Metalloved. 45, No. 4, 885–887 (1978). A. V. Nazarov and K. P. Gurov, “Accounting for nonequilibrium vacancies in the phenomenological theory of mutual diffusion,” Fiz. Met. Metalloved. 45, No. 4, 885–887 (1978).
16.
go back to reference K. S. Musin, A. V. Nazarov, and K. P. Gurov, “Effect of ordering on interdiffusion in binary alloys,” Fiz. Met. Metalloved. 63, No. 2, 267–277 (1987). K. S. Musin, A. V. Nazarov, and K. P. Gurov, “Effect of ordering on interdiffusion in binary alloys,” Fiz. Met. Metalloved. 63, No. 2, 267–277 (1987).
17.
go back to reference K. P. Gurov and A. M. Gusak, “Mutual diffusion in an external electric field with allowance for nonequilibrium vacancies,” Fiz. Met. Metalloved. 52, No. 3, 603–611 (1981). K. P. Gurov and A. M. Gusak, “Mutual diffusion in an external electric field with allowance for nonequilibrium vacancies,” Fiz. Met. Metalloved. 52, No. 3, 603–611 (1981).
18.
go back to reference G. S. Zhdanov, K. P. Gurov, and T. V. Kryukova, “Description of the relaxation process for nonequilibrium vacancies created by irradiation,” Vestn. Mosk. Un-Ta, Ser. 3. Fiz. Astron. 27, No. 5, 83–85 (1986). G. S. Zhdanov, K. P. Gurov, and T. V. Kryukova, “Description of the relaxation process for nonequilibrium vacancies created by irradiation,” Vestn. Mosk. Un-Ta, Ser. 3. Fiz. Astron. 27, No. 5, 83–85 (1986).
19.
go back to reference A. V. Nazarov and A. A. Mikheev, “Effect of elastic stress field on diffusion,” Defect Diffus. Forum 143–147, 177–185 (1997). A. V. Nazarov and A. A. Mikheev, “Effect of elastic stress field on diffusion,” Defect Diffus. Forum 143–147, 177–185 (1997).
20.
go back to reference V. L. Gapontsev, A. G. Kesarev, and V. V. Kondrat’ev, “Theory of diffusional phase transformations in nanocrystalline alloys upon severe plastic deformation: I. The stage of the formation of concentration inhomogeneities near grain boundaries,” Phys. Met. Metallogr. 94, No. 3, 219–224 (2002). V. L. Gapontsev, A. G. Kesarev, and V. V. Kondrat’ev, “Theory of diffusional phase transformations in nanocrystalline alloys upon severe plastic deformation: I. The stage of the formation of concentration inhomogeneities near grain boundaries,” Phys. Met. Metallogr. 94, No. 3, 219–224 (2002).
21.
go back to reference A. M. Gusak, Yu. A. Lyashenko, S. Kornienko, M. Pasichnyy, A. Shirinyan, and T. V. Zaporozhets, Diffusion-Controlled Solid State Reactions: In Alloys, Thin-Films, and Nanosystems (Wiley, Weinheim, 2010). A. M. Gusak, Yu. A. Lyashenko, S. Kornienko, M. Pasichnyy, A. Shirinyan, and T. V. Zaporozhets, Diffusion-Controlled Solid State Reactions: In Alloys, Thin-Films, and Nanosystems (Wiley, Weinheim, 2010).
22.
go back to reference A. V. Nazarov, “K.P. Gurov’s hole gas method and an alternative theory of interdiffusion,” Fiz. Khim. Obr. Mater., No. 2, 48–62 (2018). A. V. Nazarov, “K.P. Gurov’s hole gas method and an alternative theory of interdiffusion,” Fiz. Khim. Obr. Mater., No. 2, 48–62 (2018).
23.
go back to reference A. N. Tikhonov and A. A. Samarskii, Equations of Mathematic Physics (Nauka, Moscow, 1972) [in Russian]. A. N. Tikhonov and A. A. Samarskii, Equations of Mathematic Physics (Nauka, Moscow, 1972) [in Russian].
24.
go back to reference G. Korn and T. Korn, Handbook on Mathematics (Nauka, Moscow, 1970). G. Korn and T. Korn, Handbook on Mathematics (Nauka, Moscow, 1970).
Metadata
Title
On the Theory of Interdiffusion in Ternary Alloys
Author
A. V. Nazarov
Publication date
01-05-2022
Publisher
Pleiades Publishing
Published in
Physics of Metals and Metallography / Issue 5/2022
Print ISSN: 0031-918X
Electronic ISSN: 1555-6190
DOI
https://doi.org/10.1134/S0031918X22050106

Other articles of this Issue 5/2022

Physics of Metals and Metallography 5/2022 Go to the issue