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Two-component localized vibrational modes in fcc metals

  • Regular Article - Statistical and Nonlinear Physics
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Abstract

Discrete breathers (DB) are spatially localized vibrational modes of large amplitude in a defect-free crystal lattice. In this work, for the first time, two-dimensional DBs based on a two-component delocalized nonlinear vibrational mode (DNVM) are excited in a single (111) close-packed atomic plane in fcc metals (Al, Cu, and Ni). DNVM provides a pattern according to which the initial displacements of atoms from their equilibrium lattice positions are set. Classical molecular dynamics simulations have demonstrated the possibility to excite a long-lived two-dimensional DB with the energy of the order of 0.5–1.0 eV per oscillating atom. The two-dimensional DBs have a hard-type of nonlinearity and a lifetime of 12–24 ps, after which they decay into one-dimensional DBs, which, in turn, decay into zero-dimensional DBs, which also have a sufficiently long lifetime. A new class of two-dimensional DBs expands our understanding of the variety of spatially localized vibrational modes in nonlinear fcc lattices.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: The raw/processed data required to reproduce these findings cannot be shared at this time as the data also form part of an ongoing study.]

References

  1. A.S. Dolgov, On localization of oscillations in nonlinear crystal structure. Sov. Phys. Solid State 28, 907 (1986)

    Google Scholar 

  2. A.J. Sievers, S. Takeno, Intrinsic localized modes in anharmonic crystals. Phys. Rev. Lett. 61(8), 970–973 (1988)

    Article  ADS  Google Scholar 

  3. J.B. Page, Asymptotic solutions for localized vibrational modes in strongly anharmonic periodic systems. Phys. Rev. B 41(11), 7835–7838 (1990)

    Article  ADS  Google Scholar 

  4. S. Flach, A.V. Gorbach, Discrete breathers - Advances in theory and applications. Phys. Rep. 467(1–3), 1–116 (2008)

    Article  ADS  Google Scholar 

  5. S. Flach, C.R. Willis, Discrete breathers. Phys. Rep. 295(5), 181–264 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  6. S.V. Dmitriev, E.A. Korznikova, Y.A. Baimova, M.G. Velarde, Discrete breathers in crystals. Phys. - Uspekhi 59(5), 446–461 (2016)

    Article  ADS  Google Scholar 

  7. R.I. Babicheva, A.S. Semenov, E.G. Soboleva, A.A. Kudreyko, K. Zhou, S.V. Dmitriev, Discrete breathers in a triangular \(\beta \)-Fermi-Pasta-Ulam-Tsingou lattice. Phys. Rev. E 103(5), 052202 (2021)

    Article  ADS  MathSciNet  Google Scholar 

  8. L. Kavitha, A. Muniyappan, A. Prabhu, S. Zdravkovic, S. Jayanthi, D. Gopi, Nano breathers and molecular dynamics simulations in hydrogen-bonded chains. J. Biol. Phys. 39(1), 15–35 (2013)

    Article  Google Scholar 

  9. S.V. Dmitriev, A.P. Chetverikov, M.G. Velarde, Discrete breathers in 2D and 3D crystals. Phys. Status Solidi B 252(7), 1682–1686 (2015)

    Article  ADS  Google Scholar 

  10. A. Fraile, E.N. Koukaras, K. Papagelis, N. Lazarides, G.P. Tsironis, Long-lived discrete breathers in free-standing graphene. Chaos Solit. Fractals 87, 262–267 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  11. G.M. Chechin, S.V. Dmitriev, I.P. Lobzenko, D.S. Ryabov, Properties of discrete breathers in graphane from ab initio simulations. Phys. Rev. B 90(4), 045432 (2014)

    Article  ADS  Google Scholar 

  12. L.Z. Khadeeva, S.V. Dmitriev, Discrete breathers in crystals with NaCl structure. Phys. Rev. B 81(21), 214306 (2010)

    Article  ADS  Google Scholar 

  13. R.T. Murzaev, D.V. Bachurin, E.A. Korznikova, S.V. Dmitriev, Localized vibrational modes in diamond. Phys. Lett. A 381(11), 1003–1008 (2017)

    Article  ADS  Google Scholar 

  14. O.V. Bachurina, R.T. Murzaev, A.S. Semenov, E.A. Korznikova, S.V. Dmitriev, Properties of moving discrete breathers in beryllium. Phys. Solid State 60(5), 989–994 (2018)

    Article  ADS  Google Scholar 

  15. R.T. Murzaev, A.A. Kistanov, V.I. Dubinko, D.A. Terentyev, S.V. Dmitriev, Moving discrete breathers in bcc metals V, Fe and W. Comp. Mater. Sci. 98, 88–92 (2015)

    Article  Google Scholar 

  16. K.A. Krylova, I.P. Lobzenko, A.S. Semenov, A.A. Kudreyko, S.V. Dmitriev, Spherically localized discrete breathers in bcc metals V and Nb. Comput. Mater. Sci. 180, 109695 (2020)

    Article  Google Scholar 

  17. R.T. Murzaev, R.I. Babicheva, K. Zhou, E.A. Korznikova, S.Y. Fomin, V.I. Dubinko, S.V. Dmitriev, Discrete breathers in alpha-uranium. Eur. Phys. J. B 89(7), 168 (2016)

    Article  ADS  Google Scholar 

  18. N.N. Medvedev, M.D. Starostenkov, M.E. Manley, Energy localization on the Al sublattice of Pt\(_{3}\)Al with L1(2) order. J. Appl. Phys. 114(21), 213506 (2013)

    Article  ADS  Google Scholar 

  19. P.V. Zakharov, E.A. Korznikova, S.V. Dmitriev, E.G. Ekomasov, K. Zhou, Surface discrete breathers in Pt\(_{3}\)Al intermetallic alloy. Surf. Sci. 679, 1–5 (2019)

    Article  ADS  Google Scholar 

  20. O.V. Bachurina, Linear discrete breather in FCC metals. Comput. Mater. Sci. 160, 217–221 (2019)

    Article  Google Scholar 

  21. O.V. Bachurina, R.T. Murzaev, D.V. Bachurin, Molecular dynamics study of two-dimensional discrete breather in nickel. J. Micromech. Mol. Phys. 3(4), 1950001 (2019)

    Article  Google Scholar 

  22. O.V. Bachurina, Plane and plane-radial discrete breathers in FCC metals. Model. Simul. Mater. Sci. 27(5), 055001 (2019)

    Article  ADS  Google Scholar 

  23. O.V. Bachurina, A.A. Kudreyko, Two-dimensional discrete breathers in FCC metals. Comput. Mater. Sci. 182, 109737 (2020)

    Article  Google Scholar 

  24. G.M. Chechin, Computers and group-theoretical methods for studying structural phase transitions. Comput. Math. Appl. 17(1–3), 255–278 (1989)

    Article  MathSciNet  Google Scholar 

  25. G.M. Chechin, V.P. Sakhnenko, Interactions between normal modes in nonlinear dynamical systems with discrete symmetry. Exact results. Physica D 117(1–4), 43–76 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  26. V.M. Burlakov, S.A. Kiselev, V.I. Rupasov, Localized excitations of uniform anharmonic lattices. JETP Lett. 51, 544–547 (1990)

    ADS  Google Scholar 

  27. T. Cretegny, T. Dauxois, S. Ruffo, A. Torcini, Localization and equipartition of energy in the \(\beta \)-FPU chain: chaotic breathers. Physica D 121, 109–126 (1998)

    Article  ADS  Google Scholar 

  28. Y.S. Kivshar, M. Peyrard, Modulational instabilities in discrete lattices. Phys. Rev. A 46(6), 3198–3205 (1992)

    Article  ADS  Google Scholar 

  29. E.A. Korznikova, D.V. Bachurin, S.Y. Fomin, A.P. Chetverikov, S.V. Dmitriev, Instability of vibrational modes in hexagonal lattice. Eur. Phys. J. B 90(2), 23 (2017)

    Article  ADS  Google Scholar 

  30. E.A. Korznikova, S.Y. Fomin, E.G. Soboleva, S.V. Dmitriev, Highly symmetric discrete breather in a two-dimensional Morse crystal. JETP Lett. 103(4), 277–281 (2016)

    Article  ADS  Google Scholar 

  31. S.A. Shcherbinin, M.N. Semenova, A.S. Semenov, E.A. Korznikova, G.M. Chechin, S.V. Dmitriev, Dynamics of a three-component delocalized nonlinear vibrational mode in graphene. Phys. Solid State 61(11), 2139–2144 (2019)

    Article  ADS  Google Scholar 

  32. G.M. Chechin, D.S. Ryabov, S.A. Shcherbinin, Nonlinear vibrational modes in graphene: group-theoretical results. Lett. Mater. 6(1), 9–15 (2016)

    Article  Google Scholar 

  33. D.S. Ryabov, G.M. Chechin, A. Upadhyaya, E.A. Korznikova, V.I. Dubinko, S.V. Dmitriev, Delocalized nonlinear vibrational modes of triangular lattices. Nonlinear Dyn. 102, 2793–2810 (2020)

    Article  Google Scholar 

  34. S. Plimpton, Fast Parallel Algorithms for Short-Range Molecular-Dynamics. J. Comput. Phys. 117(1), 1–19 (1995)

    Article  ADS  Google Scholar 

  35. LAMMPS: https://www.lammps.org/

  36. S.M. Foiles, M.I. Baskes, M.S. Daw, Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. Phys. Rev. B 33(12), 7983–7991 (1986)

    Article  ADS  Google Scholar 

  37. X.W. Zhou, H.N.G. Wadley, R.A. Johnson, D.J. Larson, N. Tabat, A. Cerezo, A.K. Petford-Long, G.D.W. Smith, P.H. Clifton, R.L. Martens, T.F. Kelly, Atomic scale structure of sputtered metal multilayers. Acta Mater. 49(19), 4005–4015 (2001)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work was supported by the Russian Science Foundation, Grant No. 21-12-00229.

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Authors and Affiliations

  1. Ufa State Petroleum Technological University, Kosmonavtov str. 1, 450062, Ufa, Russia

    O. V. Bachurina

  2. Bashkir State Medical University, Lenin str. 3, 450008, Ufa, Russia

    A. A. Kudreyko

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Correspondence to O. V. Bachurina.

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Bachurina, O.V., Kudreyko, A.A. Two-component localized vibrational modes in fcc metals. Eur. Phys. J. B 94, 218 (2021). https://doi.org/10.1140/epjb/s10051-021-00227-3

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