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Simulation of characteristics determining pressure effects on the concentration and diffusivity of vacancies in BCC metals: A new approach

  • Theory of Metals
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Abstract

This work is devoted to the development of a new model (based on the molecular-statics method) for studying the diffusion properties of point defects in metals. In the model, a new algorithm is realized, which makes it possible in a self-consistent manner to calculate the atomic structure in the vicinity of a defect and the constants which determine atomic displacements in the elastic medium surrounding the computational cell. We also took into account the fact that the energy of the system depends on pressure. This dependence is different in the case of an ideal system and a system with a defect, which gives an additional contribution to the volumes of formation and migration. Furthermore, we took into consideration that the time required for an atom to jump into a vacancy is about that required for an atom to execute only a few vibrations in a lattice site. In this period, only atoms that are located in the immediate proximity to the center of dilation have time to respond for the disturbances arising in the system; therefore, when calculating the volume for the vacancy migration we carried out only a partial relaxation of the system. Within the framework of this model, we calculated the energies and volumes of vacancy formation and migration in different bcc metals.

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References

  1. F. J. Kedves and G. Erdelyi, “Diffusion under High Pressure,” Defects Diffus. Forum 66–69, 175–188 (1989).

    Google Scholar 

  2. R. A. Johnson, “Interstitials and Vacancies in α Iron,” Phys. Rev. A 134(5A), 1329–1336 (1964).

    Article  CAS  Google Scholar 

  3. R. A. Johnson and E. Brown, “Point Defects in Copper,” Phys. Rev. 127(2), 446–454 (1962).

    Article  CAS  Google Scholar 

  4. H. R. Schober and K. W. Ingle, “Calculation of Relaxation Volumes, Dipole Tensors and Kanzaki Forces for Point Defects,” J. Phys. F: Metal Phys. 10(4), 575–582 (1980).

    Article  CAS  Google Scholar 

  5. P. H. Dederichs, C. Lehmann, H. R. Schober, et al., “Lattice Theory of Point Defects,” J. Nucl. Mater. 69–70, 176–199 (1978).

    Article  Google Scholar 

  6. G. J. Ackland, D. J. Bacon, A. F. Calder, and T. Harry, “Computer Simulation of Point Defect Properties in Dilute Fe-Cu Alloy Using a Many-Body Potential,” Philos. Mag. A 75(3), 713–732 (1997).

    Article  CAS  Google Scholar 

  7. C. Domain and C. S. Becquart, “Ab Initio Calculations of Defects in Fe and Dilute Fe-Cu Alloys,” Phys. Rev. B: Condens. Matter Mater. Phys. 65, 024103 (2001).

    Google Scholar 

  8. G. Simonelli, R. Pasianot, and G. Savino, “Point-Defect Computer Simulation Including Angular Forces in BCC Iron,” Phys. Rev. B: Condens. Matter 50(2), 727–738 (1994).

    CAS  Google Scholar 

  9. D. Lazarus, “Diffusion under High Pressures,” in DIMETA-82: Diffusion in Metals and Alloys (Solid State Phenomena), Ed. by F. J. Kedves and P. L. Beke (Trans. Tech., Aedermannsdorf, 1983), pp. 134–139.

    Google Scholar 

  10. I. V. Valikova, A. V. Nazarov, and A. A. Mikheev, “Calculation of Atom Configuration and Characteristic of Vacancy in BCC Lattice of α-Fe,” Defect Diffus. Forum 249, 55–60 (2006).

    CAS  Google Scholar 

  11. I. V. Valikova and A. V. Nazarov, “Simulation of Diffusion under Pressure in BCC Metals,” Diffusion Fundamentals (Online Journal) 3, 11.1–11.15 (2005); http://www.unileipzig.de/diffusion/journal/pdf/volume3/diff_fund_3(2005) 11.pdf.

    Google Scholar 

  12. I. V. Valikova, “Simulation of Atom Configuration and Characteristic of Vacancy in BCC Lattice of α-Fe,” in Proc. Conf. Lomonosov-2005, Vol. 2, pp. 190–192.

  13. L. Girifalko, Statistical Physics of Materials (Wiley, New York, 1973; Mir, Moscow, 1975).

    Google Scholar 

  14. A. V. Nazarov and A. A. Mikheev, “Effect of Elastic Stress Field on Diffusion,” Defect Diffus. Forum 143–147, 177–184 (1997).

    Google Scholar 

  15. A. V. Nazarov, M. G. Ganchenkova, and A. A. Mikheev, “Theory of Diffusion under Pressure,” Defect Diffus. Forum 194–199, 49–55 (2001).

    Google Scholar 

  16. A. V. Nazarov and A. A. Mikheev, “Diffusion under High Pressures. Microscopic Theory and Calculations of Activation Volume for Migration,” Metallofizika 12(3), 125–128 (1990).

    CAS  Google Scholar 

  17. J. D. Eshelby, The Continuum Theory of Lattice Defects, in Solid State Physics, Vol. 3 (Academic, New York, 1956; Inostrannaya Literatura, Moscow, 1963).

    Google Scholar 

  18. M. W. Finnis and J. E. Sinclair, “A Simple Empirical NBody-Potential for Transition Metals,” Philos. Mag. A 50, 45–55 (1984).

    Article  CAS  Google Scholar 

  19. M. I. Mendelev, S. Han, D. J. Srolovitz, G. J. Ackland, et al., “Development of New Interatomic Potentials Appropriate for Crystalline and Liquid Iron,” Philos. Mag. A 83(35), 3977–3994 (2003).

    Article  CAS  Google Scholar 

  20. R. Johnson and W. D. Wilson, Defect Calculations for FCC and BCC Metals. Interatomic Potentials and Simulation Lattice Defects (Battelle Inst., Seatle, Wash-Harrison Hot Springs, 1971), pp. 301–317.

    Google Scholar 

  21. W. Lojkowski, “Evidence for Pressure Effect on Impurity Segregation in Grain Boundaries and Interstitial Grain Boundary Diffusion Mechanism,” Defect Diffus. Forum 129–130, 269–278 (1996).

    Google Scholar 

  22. A. N. Orlov and Yu. V. Trushin, Energies of Point Defects in Metals (Energoatomizdat, Moscow, 1983) [in Russian].

    Google Scholar 

  23. N. Osetsky and A. Serra, “Study of Cu Precipitates in Iron by Computer Simulation,” Philos. Mag. A 72, 361–381 (1995).

    Article  CAS  Google Scholar 

  24. M. Ludwig, D. Farkas, D. Pedraza, and S. Schmauder, “Embedded Atom Potential for Fe-Cu Interactions and Simulations of Precipitate-Matrix Interfaces,” Modell. Simul. Mater. Sci. Eng. 6, 19–28 (1998).

    Article  CAS  Google Scholar 

  25. H. E. Schaefer, K. Maier, M. Weller, et al., “Vacancy Formation in Iron Investigated by Positron Annihilation in Thermal Equilibrium,” Scr. Metall. 11, 803–815 (1977).

    Google Scholar 

  26. K. Fürderer, K.-P. Døring, M. Gladisch, et al., “Vacancy Formation in Thermal Equilibrium in Ferromagnetic Iron and Cobalt Studied by the Spin Rotation of Positive Muons,” Mater. Sci. Forum 15–18, 125–130 (1987).

    Article  Google Scholar 

  27. H. R. Schober, W. Petry, and J. Trampenau, “Migration Enthalpies in FCC and BCC Metals,” J. Phys.: Condens. Matter 4, 9321–9338 (1992).

    Article  CAS  Google Scholar 

  28. P. Ehrhart, K. H. Robrock, and H. R. Schober, Physics of Radiation Effects in Crystals, Ed. by R. A. Johnson and A. N. Orlov (Elsevier, Amsterdam, 1986), p. 63.

    Google Scholar 

  29. A. Vehanen, P. Hautojarvi, J. Johansson, et al., “Vacancies and Carbon Impurities in α-Iron: Electron Irradiation,” Phys. Rev. B: Condens. Matter 25, 762–780 (1982).

    CAS  Google Scholar 

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Original Russian Text © I.V. Valikova, A. V. Nazarov, 2008, published in Fizika Metallov i Metallovedenie, 2008, Vol. 105, No. 6, pp. 578–586.

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Valikova, I.V., Nazarov, A.V. Simulation of characteristics determining pressure effects on the concentration and diffusivity of vacancies in BCC metals: A new approach. Phys. Metals Metallogr. 105, 544–552 (2008). https://doi.org/10.1134/S0031918X08060033

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  • DOI: https://doi.org/10.1134/S0031918X08060033

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