Delocalized Nonlinear Vibrational Modes of BCC Lattice

УДК 538.9

  • Denis S. Ryabov Southern Federal University, Rostov-on-Don, Russia Email: dryabov@yandex.ru
  • Igor V. Kosarev Institute of Molecule and Crystal Physics UFRC RAS; Ufa University of Science and Technology, Ufa, Russia Email: igor.v.kosarev@gmail.com
  • Dina U. Abdullina Institute of Molecule and Crystal Physics UFRC RAS, Ufa, Russia Email: dina.abdullina25@gmail.com
  • Sergey V. Dmitriev Institute of Molecule and Crystal Physics UFRC RAS; Institute for Metals Superplasticity Problems, Ufa, Russia Email: dmitriev.sergey.v@gmail.com
DOI_disc_logo https://doi.org/10.14258/izvasu(2025)1-07
Keywords: bcc lattice, long-range interactions, dispersion relation, nonlinear dynamics, delocalized nonlinear vibrational mode, exact solution

Abstract

The article presents several exact solutions of the equations of motion of atoms in a BCC crystal, called delocalized nonlinear vibrational modes (DNVMs). The exact solutions are obtained by analyzing the BCC lattice point symmetry group only, therefore, they exist for any type of interatomic interactions and for any amplitudes. All studied DNVMs are vibrational modes with one degree of freedom. The dependence between frequency and amplitude of DNVMs is calculated using the Fermi-Pasta-Ulam potential with hard type nonlinearity when considering interatomic interactions up to the fourth neighbor. There are seven groups among the 34 studied DNVMs with the same frequency of vibrational modes in the small amplitude limit within each group. This fact is explained by some DNVMs being superpositions of others after applying point symmetry transformations. The obtained results can be to test the interatomic potentials of BCC crystals.

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Author Biographies

Denis S. Ryabov, Southern Federal University, Rostov-on-Don, Russia

Candidate of Sciences in Physics and Mathematics, Associate Professor of the Department of Theoretical and Computational Physics

Igor V. Kosarev, Institute of Molecule and Crystal Physics UFRC RAS; Ufa University of Science and Technology, Ufa, Russia

Postgraduate Student, Research Engineer; Research Engineer at the Research Laboratory of "Metals and Alloys under Extreme Effects"

Dina U. Abdullina, Institute of Molecule and Crystal Physics UFRC RAS, Ufa, Russia

Postgraduate Student, Junior Researcher

Sergey V. Dmitriev, Institute of Molecule and Crystal Physics UFRC RAS; Institute for Metals Superplasticity Problems, Ufa, Russia

Doctor of Sciences in Physics and Mathematics, Professor, Head of the Laboratory Nonlinear Dynamics of Molecules and Crystals; Chief Researcher

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Published
2025-04-02
How to Cite
Ryabov D. S., Kosarev I. V., Abdullina D. U., Dmitriev S. V. Delocalized Nonlinear Vibrational Modes of BCC Lattice // Izvestiya of Altai State University, 2025, № 1(141). P. 58-66 DOI: 10.14258/izvasu(2025)1-07. URL: https://izvestiya.asu.ru/article/view/%282025%291-07.
Issue
No 1(141) (2025): Известия Алтайского государственного университета
Section
Физика

Copyright (c) 2025 Денис Сергеевич Рябов, Игорь Витальевич Косарев, Дина Ураловна Абдуллина, Сергей Владимирович Дмитриев

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