Auxeticity from nonlinear vibrational modes

Korznikova, Elena A.; Bokij, D. I.; Zhou, Kun

doi:10.1002/pssb.201600086

Cited by 20 publications

(10 citation statements)

References 58 publications

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“…One application of our results can be found in papers [24,25], where discrete breathers are constructed by imposition of certain bell-shaped functions on the displacement patterns of one-dimensional bushes in graphene. …”

Section: Resultsmentioning

confidence: 99%

Large-amplitude in-plane atomic vibrations in strained graphene monolayer: bushes of nonlinear normal modes

Chechin¹,

Ryabov²,

Shcherbinin³

2017

LoM

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Conventional normal modes are independent of each other in the framework of harmonic approximation. When small anharmonic terms in the Hamiltonian are taken into account, these dynamical objects are only approximate and one can speak about their interactions. In our previous works, the theory of bushes of nonlinear normal modes has been developed for dynamical systems with discrete symmetry groups. With the aid of this theory it is possible to find some exact solutions beyond the harmonic approximation. Each bush is an invariant manifold corresponding to a collection of m nonlinear normal modes, where m is the bush dimension. During the evolution of a given bush, this collection conserves, but amplitudes of the modes, entering the bush, change in time. Previously, we proved with the aid of group-theoretical methods, that in graphene under uniform strain (space symmetry group P6mm) there can exist 4 bushes with m = 1, 14 bushes with m = 2, 1 bush with m = 3, 6 bushes with m = 4, and etc. In this paper, we study some low-dimensional bushes in graphene using ab initio calculations based on the density functional theory. The amplitude-frequency dependencies of one-dimensional bushes are found. The excitation transfer between nonlinear vibrational modes of different symmetry that belong to the same bush is investigated.

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Section: Resultsmentioning

confidence: 99%

Large-amplitude in-plane atomic vibrations in strained graphene monolayer: bushes of nonlinear normal modes

Chechin¹,

Ryabov²,

Shcherbinin³

2017

LoM

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“…This fact allows an attempt of excitation of a DB based on the latter mode. One should mention that realization of those modes in the crystal can result in elastic properties modification [22] and modulation instability being a reason for excitation of random DBs [23].…”

Section: Simulation Detailsmentioning

confidence: 99%

Hard-type anharmonicity gap discrete breather in 2D biatomic crystal

Семенов¹,

Fomin²,

Soboleva³

et al. 2017

LoM

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Spatially localized nonlinear oscillations in the form of a discrete breather (DB) is a recently discovered phenomenon widely investigated in different physical systems due to its potential impact on the structure and dynamics of those systems. Our molecular dynamics research is focused on the variety of DB in crystals. Depending on the type of the crystal and corresponding phonon spectrum one can get a gap DB or a DB with the frequency above the phonon spectrum. Most of gap DBs previously addressed in the literature were characterized by a soft nonlinearity type with frequencies splitting off from the upper edge of the phonon spectrum gap. In this work we managed to excite a hard nonlinearity type DB with a frequency within the band gap. In order to achieve this goal we have excited four types of delocalized vibrational modes in biatomic crystal with atomic mass difference m 1 / m 2 = 10 providing the existence of sufficiently wide phonon band gap. Analysis of amplitude-frequency dependences of two of those modes obtained in molecular dynamics simulations revealed the hard nonlinearity type with the frequency within the spectrum. The fourth mode with moving heavy atoms had the frequency within the band gap growing with the amplitude. Application of localization function with radial symmetry to this delocalized vibrational mode allowed us to obtain a DB with hard nonlinearity type in the band gap within the considered model of the crystal. Properties of the DB were analyzed.Keywords: nonlinear dynamics, 2D lattice, phonon band, discrete breather. Пространственно локализованные нелинейные колебания в форме дискретных бризеров были открыты около трех десятилетий назад и в настоящее время являются объектом для интенсивного изучения в различных физических системах ввиду возможности их значительного влияния на структуру и динамику этих систем. Наша работа по-священа молекулярно-динамическому исследованию возможного многообразия конфигураций и типов дискретных бризеров в кристаллах. В зависимости от типа кристалла и его фононного спектра могут быть реализованы дискрет-ные бризеры с частотой выше фононного спектра либо в его щели. Большинство описанных в литературе бризеров с частотой в щели фононного спектра характеризовались мягким типом нелинейности амплитудно-частотная зави-симость которых отщеплялась от верхней границы щели. В данной работе нам удалось возбудить бризер с жестким типом нелинейности частота которого отщепляется от нижней границы спектра и сконцентрирована на тяжелых 328 Semenov et al. / Letters on materials 7 (3), 2017 pp. 327-331 атомах биатомной решетки. Для этого в двумерном модельном кристалле стехиометрии A3B с разницей масс тяже-лых и легких атомов m 1 / m 2 = 10 были возбуждены несколько коротковолновых фононных мод с волновым вектором на границе первой зоны Бриллюэна. Анализ полученной посредством моделирования амплитудно-частотной зави-симости мод локализованных на легких атомах решетки выявил жесткий тип нелинейности и частоту в пределах фононного спектра. Для случая локализации моды на тя...

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“…По ряду причин исследование ДНКМ представляет интерес в физике конденсированного состояния. Например, было показано, что возбуждение однокомпонентных ДНКМ в гексагональной решетке с кубической нелинейностью изменяет их константы упругости [6]. Некоторые из двумерных ДНКМ могут породить в графене отрицательное давление и привести к генерации второй гармоники с частотами заметно выше верхнего края спектра малоамплитудных фононных колебаний [7].…”

Section: Introductionunclassified

Динамика Трехкомпонентной Делокализованной Нелинейной Колебательной Моды В Графене

Щербинин¹,

Семенова²,

Семенов³

et al. 2019

Физика Твердого Тела

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The dynamics of a three-component nonlinear delocalized vibrational mode in graphene is studied with molecular dynamics. This mode, being a superposition of a root and two one-component modes, is an exact and symmetrically determined solution of nonlinear equations of motion of carbon atoms. The dependences of a frequency, energy per atom, and average stresses over a period that appeared in graphene are calculated as a function of amplitude of a root mode. We showed that the vibrations become periodic with certain amplitudes of three component modes, and the vibrations of one-component modes are close to periodic one and have a frequency twice the frequency of a root mode, which is noticeably higher than the upper boundary of a spectrum of low-amplitude vibrations of a graphene lattice. The data obtained expand our understanding of nonlinear vibrations of graphene lattice.

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Auxeticity from nonlinear vibrational modes

Cited by 20 publications

References 58 publications

Large-amplitude in-plane atomic vibrations in strained graphene monolayer: bushes of nonlinear normal modes

Large-amplitude in-plane atomic vibrations in strained graphene monolayer: bushes of nonlinear normal modes

Hard-type anharmonicity gap discrete breather in 2D biatomic crystal

Динамика Трехкомпонентной Делокализованной Нелинейной Колебательной Моды В Графене

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