Stability of delocalized nonlinear vibrational modes in graphene lattice

Abstract

Crystal lattices support delocalized nonlinear vibrational modes (DNVMs), which are determined solely by the lattice point symmetry, and are exact solutions of the equations of atomic motion for any interatomic potential. DNVMs are interesting for a number of reasons. In particular, DNVM instability can result in the formation of localized vibrational modes concentrating a significant part of the lattice energy. In some cases, localized vibrational modes can be obtained by imposing localizing functions upon DNVM. In this regard, stability of DNVMs is an important issue. In this paper, molecular dynamics is employed to address stability of all four delocalized modes in a graphene lattice in the presence of small perturbations both in the plane and normal to the plane of the lattice. When DNVM amplitude is above the stability threshold, atom trajectories deviate from the mode pattern exponentially in time. Critical exponents are calculated for the in-and out-of-plane displacements. Stability threshold amplitudes are established. Interestingly, in three of the studied DNVMs the in-plane displacements diverge faster, but in one of them the instability develops through the out-of-plane displacements. This result can be explained by the difference in atomic vibration patterns of DNVMs. Reported results refine our understanding of the nonlinear dynamics of graphene lattice and can be useful in the design of electro-mechanical resonators and sensors.

Elastic Damper Based on the Carbon Nanotube Bundle

“…where the first term in the right-hand side gives the kinetic energy of the carbon atoms, the second to the fourth terms stand for the energy of valence bonds, the energy of valence angles and the energy of van der Waals interactions between CNTs, respectively. The model parameters were calculated based on the Savin interatomic potential developed for sp 2 -carbon [66] and successfully used for solving various problems [66][67][68][69][70][71]. Compression up to ||=0.3 is analyzed for all three loading schemes, which is sufficient for the purpose of our study.…”

Evolution of the Carbon Nanotube Bundle Structure Under Biaxial and Shear Strains

“…Here the first term, K, gives the kinetic energy of the carbon atoms, UB stands for the energy of valence bonds, UA is the energy of valence angles, and UVdW is the energy of van der Waals interactions between CNTs. The model parameters were calculated based on the interatomic potential developed for sp 2 -carbon by Savin et al [56] and further applied for investigation of various phenomena [56][57][58][59][60][61]. The initially constructed CNT bundle is subjected to relaxation in order to obtain minimum energy configuration.…”

Effect of the stiffness of interparticle bonds on properties of delocalized nonlinear vibrational modes in an fcc lattice

“…By now, DNVMs have been studied in various materials, for example, in nonlinear chains [12,[16][17][18][19], carbyne [13], graphene [15,[20][21][22][23], diamond [14], and face-centered cubic (fcc) and body-centered cubic (bcc) metals [17,[24][25][26][27][28]. DNVMs with frequencies outside the phonon band of the lattice can be used for obtaining new types of DBs by superimposing a localizing function [20,25,[29][30][31][32].…”