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Analytical methods for the calculation of the elastic interaction of point defects with dislocation loops in hexagonal crystals

  • Mechanical Properties, Physics of Strength, and Plasticity
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Abstract

The Green’s function method for hexagonal crystals within the Lifshitz–Rosenzweig (1947) and Kröner (1953) approaches has been used to obtain analytical expressions for the energy of elastic interaction of radiation-induced point defects with dislocation loops of three types: the basal edge dislocation loop (cloop), the basal shear dislocation loop, and the edge a-loop (bedding plane {11 20}, Burgers vector b D = 1/3〈11 20〉). In the case of the basal edge dislocation loop, a similar expression has been obtained independently by solving the equilibrium equations using the Elliott method. A numerical comparison of the derived expressions for zirconium has demonstrated a complete identity of the results obtained within the approaches considered in this study.

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References

  1. Progress in Solid State Physics, Ed. by F. Seitz and D. Turnbull, Vol. 3: J. D. Eshelby, The Continuum Theory of Lattice Defects (Academic, New York, 1956, Nauka, Moscow, 1963).

  2. Ian. N. Sneddon, Fourier Transforms (McGraw-Hill, New York, 1951).

    MATH  Google Scholar 

  3. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 7: Theory of Elasticity (Nauka, Moscow, 1987, Butterworth–Heinemann, Oxford, 1995).

    Google Scholar 

  4. J. P. Hirth and J. Lothe, Theory of Dislocations (McGraw-Hill, New York, 1968, Atomizdat, Moscow, 1972).

    MATH  Google Scholar 

  5. I. M. Lifshitz and L. N. Rosenzweig, Zh. Eksp. Teor. Fiz. 17, 783 (1947).

    Google Scholar 

  6. E. Kröner, Z. Phys. 136, 402 (1953).

    Article  ADS  MathSciNet  Google Scholar 

  7. J. R. Willis, Quart. J. Mech. Appl. Math. 18, 419 (1965).

    Article  MathSciNet  Google Scholar 

  8. P. N. Ostapchuk, Phys. Solid State 54 (1), 98 (2012).

    Article  ADS  Google Scholar 

  9. P. N. Ostapchuk, Phys. Solid State 55 (1), 109 (2013).

    Article  ADS  Google Scholar 

  10. S. M. Ohr, J. Appl. Phys. 43, 1361 (1973).

    Article  ADS  Google Scholar 

  11. S. M. Ohr, Phys. Status Solidi B 58, 613 (1973).

    Article  ADS  Google Scholar 

  12. H. A. Elliott, Proc. Cambridge Philos. Soc. 44, 522 (1948)

    Article  ADS  MathSciNet  Google Scholar 

  13. H. A. Elliott, Proc. Cambridge Philos. Soc. 45, 621 (1949).

    Article  ADS  MathSciNet  Google Scholar 

  14. F. Kroupa, Czech. J. Phys. B 10, 284 (1960).

    Article  ADS  MathSciNet  Google Scholar 

  15. P. N. Ostapchuk and O. G. Trotsenko, Phys. Solid State 58 (9), 1810 (2016).

    Article  ADS  Google Scholar 

  16. M. H. Yoo, Phys. Status Solidi B 61, 411 (1974).

    Article  ADS  Google Scholar 

  17. L. Fast, J. M. Wills, B. Johansson, and O. Eriksson, Phys. Rev. B: Condens. Matter 51 (24), 17431 (1995).

    Article  ADS  Google Scholar 

  18. C. H. Woo, J. Nucl. Mater. 276, 90 (2000).

    Article  ADS  Google Scholar 

  19. S. A. Kukushkin, A. V. Osipov, and R. S. Telyatnik, Phys. Solid State 58 (5), 971 (2016).

    Article  ADS  Google Scholar 

  20. V. I. Dubinko, A. S. Abyzov, and A. A. Turkin, J. Nucl. Mater. 336, 11 (2005).

    Article  ADS  Google Scholar 

  21. T. Jourdan, J. Nucl. Mater. 467, 286 (2015).

    Article  ADS  Google Scholar 

  22. V. F. Zelenskii, I. M. Neklyudov, and T. P. Chernyaeva, Radiation-Induced Defects and Swelling of Metals (Naukova Dumka, Kiev, 1988) [in Russian].

    Google Scholar 

  23. P. T. Heald and M. V. Speight, Philos. Mag. 29, 1075 (1974).

    Article  ADS  Google Scholar 

  24. L. K. Mansur, Philos. Mag. A 39, 497 (1979).

    Article  ADS  Google Scholar 

  25. V. I. Dubinko, S. A. Kotrechko, and V. F. Klepikov, Rad. Eff. Defects Solids 164, 647 (2009).

    Article  ADS  Google Scholar 

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Correspondence to P. N. Ostapchuk.

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Original Russian Text © P.N. Ostapchuk, O.G. Trotsenko, 2017, published in Fizika Tverdogo Tela, 2017, Vol. 59, No. 5, pp. 912–919.

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Ostapchuk, P.N., Trotsenko, O.G. Analytical methods for the calculation of the elastic interaction of point defects with dislocation loops in hexagonal crystals. Phys. Solid State 59, 934–943 (2017). https://doi.org/10.1134/S1063783417050237

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  • DOI: https://doi.org/10.1134/S1063783417050237

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