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Structural Vacancy Model of Grain Boundaries

  • STRUCTURE, PHASE TRANSFORMATIONS, AND DIFFUSION
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Abstract

A structural vacancy model of tilt grain boundaries in metals has been developed. For construction of the stable structure of the boundary, the initial pattern was chosen according to the CSL model. The introduction of additional atoms and vacancies into the boundary region and shifting of atoms by the interatomic forces stabilize its structure. The criterion of a stable structure is the grain-boundary energy. The comparison of two main approaches to the stabilization of the grain structure demonstrated that changing the number of atoms at the boundary is more energetically advantageous than the relative shift of grains. The stability of the structure obtained has been studied under the shear stress. In the model developed, atomic structures obtained with pair and many-body potentials have been compared. The comparative analysis has shown that the grain-boundary structure does not depend on the choice of potential; atomic positions differ by less than 0.1 Å, which is 2.5% of the lattice parameter. The atomic structure is in agreement with experimental images of grain boundaries.

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REFERENCES

  1. M. L. Kronberg and F. N. Wilson, “Structure of high angle grain boundaries,” Trans. AIME 185, 506–508 (1949).

    Google Scholar 

  2. V. V. Gorbunov and B. M. Darinskii, “Emission of vacancies by an intercrystallite boundary,” Fiz. Tverd. Tela 34, 1059–1063 (1992).

    Google Scholar 

  3. M. D. Starostenkov, B. F. Dem’yanov, S. L. Kustov, and E. L. Grakhov, “Symmetric Σ = 5 tilt boundaries in the Ni3Fe alloy,” Phys. Met. Metallogr. 85, 530–535 (1998).

    Google Scholar 

  4. A. S. Dragunov, B. F. Dem’yanov, and A. V. Weckman, “Computer simulation of internal interfaces in metals and alloys,” Izv. Vyssh. Uchebn. Zaved., Fiz. 53, 82–87 (2010).

    Google Scholar 

  5. M. A. Tschopp and D. L. McDowell, “Asymmetric tilt grain boundary structure and energy in copper and aluminium,” Philos. Mag. 87, 3871–3892 (2007).

    Article  Google Scholar 

  6. A. N. Orlov, V. N. Perevezentsev, and V. V. Rybin, “Analysis of defects in the crystal structure of a symmetric tilt boundary,” Fiz. Tverd. Tela 17, 1662–1670 (1975).

    Google Scholar 

  7. V. V. Rybin and V. N. Perevezentsev, “General theory of grain boundary shifts,” Fiz. Tverd. Tela 17, 3188–3193 (1975).

    Google Scholar 

  8. W. Bollmann, Crystal Defects and Crystalline Interfaces (Springer Verlag, Berlin, 1970).

    Book  Google Scholar 

  9. G. H. Bishop and B. Chalmers, “A coincidence-ledge-dislocation description of grain boundaries,” Scr. Metall. 2, 133–139 (1968).

    Article  Google Scholar 

  10. L. K. Fionova, “Ordinary grain boundaries,” Phys. Met. Metallogr., 73, 333–336 (1992).

    Google Scholar 

  11. G. Hasson, J. Y. Boos, J. Herbeuval, M. Biscondi, and E. C. Goux, “Theoretical and experimental determination of grain boundary structures and energies: Correlation with various experimental results,” Surf. Sci. 31, 115–137 (1972).

    Article  Google Scholar 

  12. M. F. Ashby, F. Spaepen, and S. Williams, “The structure of grain boundaries described as a packing of polyhedra,” Acta Metall. 26, 1647–1664 (1978).

    Article  Google Scholar 

  13. R. C. Pond, D. A. Smith, and V. Vitek, “Computer simulation of 〈110〉 tilt boundaries: Structure and symmetry,” Acta Metall. 27, 235–241 (1979).

    Article  Google Scholar 

  14. J. D. Bernal, “The Bakerian Lecture, 1962. The Structure of Liquids,” Proc. R. Soc. London, Ser. A 280 (1382), 299–322 (1964).

    Article  Google Scholar 

  15. V. Vitek, “Intrinsic stacking faults in body-centered cubic crystals,” Philos. Mag. 18 (154), 773–786 (1968).

    Article  Google Scholar 

  16. D. A. Smith, V. V. Vitek, and R. C. Pond, “Computer simulation of symmetrical high angle boundaries in aluminium,” Acta Metall. 25, 475–483 (1977).

    Article  Google Scholar 

  17. M. J. Weins, H. Gleiter, and B. Chalmers, “Computer calculations of the structure and energy of high-angle grain boundaries,” J. Appl. Phys. 42, 2636–2645 (1971).

    Article  Google Scholar 

  18. P. D. Bristowe and A. G. Crocker, “A computer simulation study of the structures of twin boundaries in body-centered cubic crystals,” Philos. Mag. 31, 503–517 (1975).

    Article  Google Scholar 

  19. E. Tarnow, P. D. Bristowe, J. P. Joannopoulos, and M. C. Payne, “Predicting the structure and energy of a grain boundary in germanium,” J. Phys.: Condens. Matter 1, 327–333 (1989).

    Google Scholar 

  20. P. Guyot and J. P. Simon, “Symmetrical high angle tilt boundary energy calculation in aluminium and lithium,” Phys. Status Solidi A 38, 207–216 (1976).

    Article  Google Scholar 

  21. H. Gleiter and B. Chalmers, High-Angle Grain Boundaries (Pergamon, Oxford, U. K. 1972; Mir, Moscow, 1975).

  22. A. N. Orlov, V. N. Perevezentsev, and V. V. Rybin, Grain Boundaries in Metals (Metallurgiya, Moscow, 1980) [in Russian].

    Google Scholar 

  23. O. A. Kaibyshev and R. Z. Valiev, Grain Boundaries and Properties of Metals (Metallurgiya, Moscow, 1987) [in Russian].

    Google Scholar 

  24. Ch. V. Kopetskii, A. N. Orlov, and L. K. Fionova, Grain Boundaries in Pure Metals (Nauka, Moscow, 1987) [in Russian].

    Google Scholar 

  25. D. Wolf, “Effect of interatomic potential on the calculated energy and structure of high-angle coincident site grain boundaries—I. (100) twist boundaries in aluminum,” Acta Metall. 32, 242–258 (1984).

    Google Scholar 

  26. D. Wolf, “Structure–energy correlation for grain boundaries in fcc metals—I. Boundaries on the (111) and (100) planes,” Acta Metall. 37, 1983–1993 (1989).

    Article  Google Scholar 

  27. D. Wolf, “Structure–energy correlation for grain boundaries in fcc metals—II. Boundaries on the (110) and (113) planes,” Acta Metall. 37, 2823–2833 (1989).

    Article  Google Scholar 

  28. J. D. Rittner and D. N. Seidman, “〈110〉 symmetric tilt grain-boundary structures in fcc metals with low stacking-fault energies,” Phys. Rev. B 54, 6999–7015 (1996).

    Article  Google Scholar 

  29. J. S. Braithwaite and P. Rez, “Grain boundary impurities in iron,” Acta Mater. 53, 2715–2726 (2005).

    Article  Google Scholar 

  30. A. G. Lipnitskii, A. V. Ivanov, and Yu. R. Kolobov, “Studying grain-boundary stresses in copper by the molecular-statistics method,” Phys. Met. Metallogr. 101, 303–309 (2006).

    Article  Google Scholar 

  31. M. A. Tschopp and D. L. McDowell, “Structures and energies of Σ3 asymmetric tilt grain boundaries in copper and aluminium,” Philos. Mag. 87, 3147–3173 (2007).

    Article  Google Scholar 

  32. R. Matsumoto, M. Riku, S. Taketomi, and N. Miyazaki, “Hydrogen–grain boundary interaction in Fe, Fe–C, and Fe–N systems,” Prog. Nucl. Sci. Technol. 2, 9–15 (2011).

    Article  Google Scholar 

  33. A. I. Tsaregorodtsev, N. V. Gorlov, B. F. Dem’yanov, and M. D. Starostenkov, “The atomic structure of the antiphase boundary and its effect on the lattice state near a dislocation in ordered alloys with L12 superstructure,” Fiz. Met. Metalloved. 58, 336–343 (1984).

    Google Scholar 

  34. W. Krakow, “Structural multiplicity observed at a Σ5/[001] 53.1° tilt boundary in gold,” Philos. Mag. A 63, 233–240 (1991).

    Article  Google Scholar 

  35. F. Cosandey, S.-W. Chan, and P. Stadelmann, “HREM studies of [001] tilt grain boundaries in gold,” Colloq. Phys. Colloq. Cl. 51, 109–113 (1990).

    Google Scholar 

  36. M. S. Daw and M. I. Baskes, “Embedded-atom method: Derivation and application to impurities, surfaces and other defects in metals,” Phys. Rev. B 29, 6443–6453 (1984).

    Article  Google Scholar 

  37. M. S. Daw, S. M. Foiles, and M. I. Baskes, “The embedded-atom method: a review of theory and applications,” Mater. Sci. Rep. 9, 251–310 (1993).

    Article  Google Scholar 

  38. F. Ercolessi, E. Tosatti, and M. Parrinello, “Au (100) surface reconstruction,” Phys. Rev. Lett. 57, 719–722 (1986).

    Article  Google Scholar 

  39. F. Ercolessi, M. Parrnello, and E. Tosatti, “Simulation of gold in the glue model,” Philos. Mag. 58, 213–226 (1988).

    Article  Google Scholar 

  40. M. W. Finnis and J. E. Sinclair, “A simple empirical N‑body potential for transition metals,” Philos. Mag. A 50, 45–55 (1984).

    Article  Google Scholar 

  41. A. P. Sutton and J. Chen, “Long-range Finnis–Sinclair potentials,” Philos. Mag. Lett. 61, 139–146 (1990).

    Article  Google Scholar 

  42. H. Rafii-Tabar and A. P. Sulton, “Long-range Finnis–Sinclair potentials for f.c.c. metallic alloys,” Philos. Mag. Lett. 63, 217–224 (1991).

    Article  Google Scholar 

  43. B. R. Eggen, R. L. Johnston, S. Li, and J. N. Murrell, “Potential energy functions for atomic solids. IV. Reproducing the properties of more than one solid phase,” Mol. Phys. 76, 619–633 (1992).

    Article  Google Scholar 

  44. H. Cox, R. L. Johnston, and J. N. Murrell, “Empirical potentials for modelling solid, surfaces and clusters,” J. Solid State Chem. 145, 517–540 (1999).

    Article  Google Scholar 

  45. D. Wolf, “Correlation between the energy and structure of grain boundaries in bcc metals. 1. Symmetrical boundaries on the (110) and (100) planes,” Philos. Mag. B 59, 667–680 (1989).

    Article  Google Scholar 

  46. J. Th. M. De Hosson and V. Vitek, “Atomic structure of (111) twist grain boundaries in f.c.c metals,” Philos. Mag. A 61, 305–327 (1990).

    Article  Google Scholar 

  47. N. Takata, K. Ikeda, H. Nakashima, and H. Abe, “Grain boundary energy and atomic structure of symmetric tilt boundaries in copper, Nippon Kinzoku Gakkaishi 68, 240–246 (2004).

    Google Scholar 

  48. F. Cleri and V. Rosato, “Tight-binding potentials for transition metals and alloys,” Phys. Rev. B 48, 22–33 (1993).

    Article  Google Scholar 

  49. J. P. Hirth and J. Lothe, Theory of Dislocations (McGraw-Hill, New York, 1967; Atomizdat, Moscow, 1972).

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Authors and Affiliations

  1. Altai State Technical University, 656038, Barnaul, Russia

    A. V. Weckman & B. F. Dem’yanov

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  1. A. V. Weckman
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  2. B. F. Dem’yanov
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Correspondence to A. V. Weckman.

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Translated by O. Golovnya

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Weckman, A.V., Dem’yanov, B.F. Structural Vacancy Model of Grain Boundaries. Phys. Metals Metallogr. 120, 50–59 (2019). https://doi.org/10.1134/S0031918X18110200

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