Stability of in-plane delocalized vibrational modes in triangular Morse lattice

Open School-Conference of NIS Countries Ultrafine Grained and Nanostructured Materials

Abdullina, D.U.^1,2 ; Semenova, M.N.^3 ; Semenov, A.S.^3 ; Ryabov, D.S.^4 ; Chechin, G.M.^4 ; Korznikova, E.A.^1 ; Baimova, J.A.^1,2 ; Dmitriev, S.V.^1,5

Institute for Metals Superplasticity Problems, 39 Khalturin st., Ufa

450001, Russia^1

Bashkir State University, 32 Validy St., Ufa

450076, Russia^2

North-Eastern Federal University N.a. M.K. Ammosov, Polytechnic Institute (Branch) in Mirny, 5/1 Tikhonova st., Mirny, Sakha, Yakutia

678170, Russia^3

Southern Federal University, 105 Bolshaya Sadovaya st., Rostov-on-Don

344006, Russia^4

National Research Tomsk State University, 36 Lenin Ave., Tomsk

634050, Russia^5

关键词: Critical exponent;    Exact solution;    Nonlinear lattices;    Threshold-value;    Triangular lattice;    Two Dimensional (2 D);    Vibrational modes;    Zero values;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/447/1/012060/pdf
DOI  :  10.1088/1757-899X/447/1/012060

来源: IOP

【 摘 要 】

Delocalized nonlinear vibrational modes (DNVMs) play a very important role in the study of the dynamics of a nonlinear lattice in solid state physics. Such modes are exact solutions to the equations of motion of atoms dictated by the lattice space symmetry. If the amplitude of DNVM is above the threshold value, it is modulationally unstable. In the present study, we consider the stability of DNVMs in a two-dimensional (2D) triangular lattice with atoms interacting via the Morse potential. Critical exponents are calculated numerically as functions of the DNVM amplitude. Extrapolation to the zero value of the critical exponent gives an estimation of the DNVM amplitude, below which it is stable.