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Description of the geometry of crystals with a hexagonal close-packed structure based on pair interaction potentials

  • Mechanical Properties, Physics of Strength, and Plasticity
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Abstract

The pair force interaction potential that allows one to describe a deviation from spherical symmetry, which is typical for hexagonal close-packed structures, is constructed using the “spherically symmetric” Mie potential that depends only on the interatomic distance. The parameters of the considered potential, which ensure the stability of hexagonal close-packed lattices, are obtained for a wide range of metals, namely, beryllium, gadolinium, hafnium, holmium, dysprosium, yttrium, cobalt, lutetium, magnesium, osmium, rhenium, ruthenium, scandium, thallium, terbium, technetium, titanium, thulium, cerium, zirconium, and erbium. It is shown that for this pair interaction potential the hexagonal close-packed structure is energetically more favorable than the face-centered cubic structure. The proposed potential can be used to perform computational experiments and analytical investigations.

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References

  1. A. M. Krivtsov, Phys. Solid State 46(6), 1055 (2004).

    Article  ADS  Google Scholar 

  2. A. M. Krivtsov, Deformation and Fracture of Solids with Microstructure (Fizmatlit, Moscow, 2007) [in Russian].

    Google Scholar 

  3. B. D. Annin, S. N. Korobeinikov, and A. V. Babichev, Sib. Zh. Ind. Mat. 11(1), 3 (2008).

    MathSciNet  MATH  Google Scholar 

  4. A. Yu. Kuksin, G. E. Norman, V. V. Stegailov, and A. V. Yanilkin, J. Eng. Thermophys. 18(3), 197 (2009).

    Article  Google Scholar 

  5. J. A. Zimmerman, R. E. Jones, and J. A. Templeton, J. Comput. Phys. 229, 2364 (2010).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. A. M. Krivtsov and N. F. Morozov, Phys. Solid State 44(12), 2260 (2002).

    Article  ADS  Google Scholar 

  7. R. V. Gol’dshtein and A. V. Chentsov, Izv. Akad. Nauk, Mech. Tverd. Tela, No. 4, 57 (2005).

  8. A. M. Krivtsov, Elastic Properties of Monoatomic and Diatomic Crystals (St. Petersburg State Polytechnical University, St. Petersburg, 2009) [in Russian].

    Google Scholar 

  9. I. E. Berinskii, N. G. Dvas, A. M. Krivtsov, et al., Theoretical Mechanics. Elastic Properties of Monoatomic and Diatomic Crystals, Ed. by A. M. Krivtsov (St. Petersburg State Polytechnical University, St. Petersburg, 2009) [in Russian].

    Google Scholar 

  10. I. E. Berinskiy, A. M. Krivtsov, and A. M. Kudarova, in Proceedings of the XXXVI Summer School “Advanced Problems in Mechanics,“ St. Petersburg, Russia, July 6–10, 2008, p. 122.

  11. E. A. Ivanova, A. M. Krivtsov, and N. F. Morozov, Prikl. Mat. Mekh. 71(4), 595 (2007).

    MathSciNet  MATH  Google Scholar 

  12. D. M. Vasil’ev, Physical Crystallography (Metallurgiya, Moscow, 1981) [in Russian].

    Google Scholar 

  13. M. S. Daw and M. I. Baskes, Phys. Rev. Lett. 50(17), 1285 (1983).

    Article  ADS  Google Scholar 

  14. R. Pasianot and E. J. Savino, Phys. Rev. B: Condens. Matter 45(22), 12704 (1992).

    Article  ADS  Google Scholar 

  15. M. I. Baskes and R. A. Johnson, Modell. Simul. Mater. Sci. Eng. 2, 147 (1994).

    Article  ADS  Google Scholar 

  16. W. Hu, B. Zhang, B. Huang, F. Gao, and D. J. Bacon J. Phys.: Condens. Matter 13(6), 1193 (2001).

    Article  ADS  Google Scholar 

  17. Y.-M. Kim, B.-J. Lee, and M. I. Baskes, Phys. Rev. B: Condens. Matter 74 (1), 014101 (2006).

    Article  ADS  Google Scholar 

  18. M. A. Baranov, E. A. Dubov, I. V. Dyatlova, and E. V. Chernykh, Phys. Solid State 46(2), 213 (2004).

    Article  ADS  Google Scholar 

  19. A. M. Krivtsov and E. A. Podolskaya, Izv. Akad. Nauk, Mekh. Tverd. Tela, No. 3, 77 (2010).

  20. V. A. Lagunov and A. B. Sinani, Phys. Solid State 40(10), 1742 (1998).

    Article  ADS  Google Scholar 

  21. N. J. Wagner, B. L. Holian, and A. F. Voter, Phys. Rev. A: At., Mol., Opt. Phys. 45(12), 8457 (1992).

    Article  ADS  Google Scholar 

  22. WebElements: the Periodic Table on the www (http://www.webelements.com/) (Copyright 1993–2010, Mark Winter, The University of Sheffield and WebElements, United Kingdom).

  23. Handbook of Physical Quantities, Ed. by I. S. Grigoriev and E. Z. Meilikhov (Energoatomizdat, Moscow, 1991; CRC Press, Boca Raton, Florida, United States, 1997).

    Google Scholar 

  24. A. I. Lurie, Nonlinear Theory of Elasticity (Nauka, Moscow, 1980; North-Holland, Amsterdam, 1990).

    Google Scholar 

  25. F. Milstein, Phys. Rev. B: Solid State 4(3), 1130 (1971).

    Article  ADS  Google Scholar 

  26. G. Simmons and H. F. Wang, Single Crystal Elastic Constants and Calculated Aggregate Properties: A Handbook (Massachusetts Institute of Technology, Cambridge, Massachusetts, United States, 1971).

    Google Scholar 

  27. E. A. Brandes and G. B. Brook, Smithells Metals Reference Book (Butterworth-Heinemann, Oxford, 1992).

    Google Scholar 

  28. N. G. Dvas, in Proceedings of the XXXIV Summer School “Advanced Problems in Mechanics,” St. Petersburg, Russia, June 25–July 1, 2006, p. 138.

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Authors and Affiliations

  1. Institute of Problems in Mechanical Engineering, Russian Academy of Sciences, Bolshoj pr. 61, St. Petersburg, 199178, Russia

    E. A. Podolskaya & A. M. Krivtsov

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  1. E. A. Podolskaya
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  2. A. M. Krivtsov
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Correspondence to A. M. Krivtsov.

Additional information

Original Russian Text © E.A. Podolskaya, A.M. Krivtsov, 2012, published in Fizika Tverdogo Tela, 2012, Vol. 54, No. 7, pp. 1327–1334.

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Podolskaya, E.A., Krivtsov, A.M. Description of the geometry of crystals with a hexagonal close-packed structure based on pair interaction potentials. Phys. Solid State 54, 1408–1416 (2012). https://doi.org/10.1134/S1063783412070311

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  • DOI: https://doi.org/10.1134/S1063783412070311

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