Properties of discrete breathers in 2D and 3D Morse crystals

Kistanov, Andrey A.; Korznikova, Elena A.; Fomin, S Yu; Zhou, Kaihang; Дмитриев, С. В.

doi:10.22226/2410-3535-2014-4-315-318

Cited by 8 publications

(7 citation statements)

References 33 publications

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“…We considered the value α = 5, for which the equilibrium interatomic distance is a = 0.98813 at the potential cutoff radius of 5.5a. We note that the Morse potential was often used for the simulation of different properties of discrete breathers in crystals [23][24][25][26][27][28][29][40][41][42][43][44][45][46].…”

Section: Nonlinear Phenomenamentioning

confidence: 99%

“…The authors of [38] could excite only the discrete breathers with the soft type of nonlinearity, considering a diatomic chain with a gap in the phonon spectrum. It was shown later that discrete breathers with the hard type of nonlinearity can exist in two-and threedimensional crystals with Morse interaction [39][40][41][42][43][44][45][46]. The reason is that the effect of the increase in the average interatomic distances in the core of the discrete breathers can be suppressed to some extent in crystals of dimension higher than unity and, thus, the hard core of the interatomic potential makes a larger contribution to the dynamics of the system than the soft tail.…”

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Highly symmetric discrete breather in a two-dimensional Morse crystal

et al. 2016

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It has been shown recently that a moving discrete breathers localized in one close-packed atomic row can be excited in a two-dimensional monoatomic crystal with Morse interaction. In this work, a motionless discrete breathers having the threefold symmetry axis has been excited in the same crystal. The initial conditions for the excitation of such discrete breathers are set by the superposition of a bell-shaped function on a planar nonlinear phonon mode with the wave vector lying at the edge of the Brillouin zone. In addition, the displacement of the centers of atomic oscillations from the center of the discrete breathers owing to the asymmetry of the Morse potential is taken into account. The results obtained make it possible to approach the search for highly symmetric discrete breathers in three-dimensional crystals.

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Section: Nonlinear Phenomenamentioning

confidence: 99%

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confidence: 99%

Highly symmetric discrete breather in a two-dimensional Morse crystal

et al. 2016

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“…By now, a large volume of works has been performed to analyze properties of DB in various crystalline materials, particularly, the results of the molecular dynamics studies have been reported in . Several works have been devoted to the study of DB in model crystals with Morse interatomic potentials [4][5][6][7], while other works to the study of DB in graphene and related materials [8][9][10]. In the work [8], for the first time, DB in a crystalline body has been studied with the help of DFT theory, using graphane as an example.…”

Section: Introductionmentioning

confidence: 99%

Effect of the interatomic potential stiffness on the properties of gap discrete breathers in 2D biatomic Morse crystal

Korznikova¹,

Fomin²,

Ustiuzhanina³

et al. 2015

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Discrete breathers (DB) are spatially localized nonlinear vibrational modes in discrete lattices. The latest trend is the study of DB in various crystals. Many studies have been done recently for the two-dimensional (2D) model of crystal with Morse interatomic potentials. Two types of DB have been discussed for Morse crystals, the gap DB with soft type of nonlinearity and the hard-type anharmonicity DB with frequency above the phonon spectrum. Here we focus on the analysis of the effect of rigidity of the Morse potential on the properties of gap discrete breathers in the 2D biatomic crystal model of composition A3B. Atoms A are ten times heavier than atoms B and this is the reason of the presence of a wide gap in the phonon spectrum of the crystal. The same Morse potentials are used to describe the A-A, B-B, and A-B interactions. Two of the three Morse potential parameters are fixed to unity without the loss of generality. For the third parameter, which defines the stiffness of the interatomic bond, two different values are considered. In both cases two polarizations of DB are investigated. It was found that for a smaller stiffness of the interatomic bond DB have larger maximal amplitude, regardless the type of polarization. On the other hand, they demonstrate a higher rate of radiation of the small-amplitude waves and thus, they have smaller lifetime.

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“…/ Письма о материалах 5 (1), 2015 стр. [11][12][13][14] Semenov et al / Letters on materials 5 (1), 2015 pp. 11-14 дах физических систем, включая оптические, механиче-ские, электрические, атомные и др.…”

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“…В классических работах по изучению ДБ рассматри-вались модельные дискретные системы низкой размер-ности с простейшими видами ангармонизмов в меж-частичных взаимодействиях [1][2][3] и были развиты аналитические и полуаналитические методы построе-ния бризерных решений, изучены их основные свойства. В настоящее время растет число работ по исследованию ДБ в различных кристаллических материалах [4][5][6][7][8][9][10][11][12][13][14][15], что требует существенного уточнения рассматриваемых моделей.…”

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Discrete breathers with hard and soft type of nonlinearity in 1D Morse lattices with long-range interactions

Семенов¹,

Korznikova²,

Дмитриев³

2015

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1Мирнинский политехнический институт (филиал) Северо-Восточного федерального университета, ул. Тихонова 5/1, 678175, Мирный, Россия 2 Институт проблем сверхпластичности металлов РАН, ул. Степана Халтурина 39, 450001, Уфа, Россия † sash-alex@yandex.ru, ‡ elena.a.korznikova@gmail.com В последнее время в области изучения дискретных бризеров наблюдается переход от теоретических исследований, связанных с доказательством их существования в упрощенных нелинейных системах, к поиску долгоживущих бри-зеров в реальных объектах, например, в кристаллических решетках. Изучение дискретных бризеров в различных физических системах требует учета различных факторов. Атомы в кристалле обычно взаимодействуют не только с ближайшими соседями, ввиду чего важным представляется учет дальнодействующих межатомных взаимодей-ствий. При наличии последних, не представляется возможным использовать потенциалы в виде разложения в ряд Тейлора до третьей или четвертой степени, как это делалось в подавляющем большинстве теоретических работ. В данной работе обсуждаются различные виды дискретных бризеров (точнее квазибризеров), которые могут быть возбуждены в одномерных моно-и биатомных решетках с дальнодействующим морзевским взаимодействием и си-нусоидальным локальным потенциалом. Данная модель описывает на качественном уровне дискретные бризеры в чистых металлах и упорядоченных сплавах. Recently the focus of studies on discrete breathers has arguably shifted from the mathematical proof of their existence in simplified nonlinear lattices towards the search for the long-lived quasi-breathers in real systems, e.g., in crystal lattices. In each particular field, different factors should be taken into account. Atoms in crystals typically interact not only with the nearest neighbors and thus, the effect of long-range interatomic forces is an important issue. When the long-range forces are involved, the tails of the interatomic potentials contribute essentially to the dynamics of the system and in these circumstances one cannot use truncated Taylor expansions of the potentials such as cubic or quartic. In this work we discuss various discrete breathers (more precisely, quasi-breathers) that can be excited in 1D monatomic and diatomic Morse lattices with long-range interactions and sinusoidal on-site potential. This model describes at a qualitative level discrete breathers in pure metals and ordered alloys.

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Properties of discrete breathers in 2D and 3D Morse crystals

Cited by 8 publications

References 33 publications

Highly symmetric discrete breather in a two-dimensional Morse crystal

Highly symmetric discrete breather in a two-dimensional Morse crystal

Effect of the interatomic potential stiffness on the properties of gap discrete breathers in 2D biatomic Morse crystal

Discrete breathers with hard and soft type of nonlinearity in 1D Morse lattices with long-range interactions

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