Mathematical modeling of elastic wave propagation in crystals: 3D-wave surfaces

Kochaev, A. I.; Brazhe, R. A.

doi:10.1007/s00707-011-0514-y

Cited by 13 publications

(12 citation statements)

References 3 publications

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“…l, Å Е, эВ Е b , эВ/атом (С) 6 1,42 -15,3 -7,8 (С) 44 1,35 -13,1 -3,0 (С) 63 (6) 2,20 -13,2 -3,6 (С) 63 121,71 -14,7 -4,6 (С) 664 1,56 -11,3 -1,2 (С) 634 1,10 -12,3 -2,2…”

Section: графенunclassified

“…4. Расположение координатных осей для двумерных кристаллов Методика отыскания направлений распространения и поляризации чистых мод упругих волн в 3D и 2D кристаллах была разработана нами и описана в работах [42][43][44][45][46][47]…”

Section: акустические свойстваunclassified

“…Интегралы перескока (C) 44 (C) 63 (12) обладают нулевой запрещенной зоной и принадлежат к полуметаллам, а (C) 664 является узкозонным полупроводником, причем ширина запрещенной зоны, полученная нами, составляет 0,33 эВ (ТВ метод) и 0,34 эВ (DFT метод), что сильно отличается от результата работы [6], в которой приводится значение 1,14 эВ. Как нам представляется, результат 0,33 эВ ближе к истинному, так как p z электрон слабо связан с атомом и для его перевода в зону проводимости не требуется много энергии.…”

Section: таблицаunclassified

“…Целью данной обзорной статьи является систематизация сведений по их физическим свойствам, главным образом, по акустическим и оптическим характеристикам. Объектами исследования являются классический графен (С) 6 , а также (С) 44 -октатетраграфен (октаграфен), (С) 63 (6) -гексатриграфен, (С) 63 (12) -додекатриграфен, (С) 664 -додекагексатетраграфен, (С) 634 -гексатетратриграфен. Использованы аналитические и численные методы расчетов, основанные на приближениях сильной связи и Хартри -Фока, с применением программных пакетов VASP и Abinit.…”

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Acoustic and optical properties of graphenes

Brazhe¹,

Kochaev²,

Meftahutdinov³

2016

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“…l, Å Е, эВ Е b , эВ/атом (С) 6 1,42 -15,3 -7,8 (С) 44 1,35 -13,1 -3,0 (С) 63 (6) 2,20 -13,2 -3,6 (С) 63 121,71 -14,7 -4,6 (С) 664 1,56 -11,3 -1,2 (С) 634 1,10 -12,3 -2,2…”

Section: графенunclassified

Section: акустические свойстваunclassified

Section: таблицаunclassified

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Acoustic and optical properties of graphenes

Brazhe¹,

Kochaev²,

Meftahutdinov³

2016

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“…Figure 2 shows, in the general case, the phase velocity surfaces for one quasi longitudinal and two quasi transverse elastic waves in the (C) CTO supracrys tal. The surfaces were constructed based on the model described in [13] based on solution of the GreenChristoffel equation [14].…”

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Elastic and acoustic characteristics of a three-dimensional carbon supracrystal (C)CTO

Brazhe

Kochaev

2012

Phys. Solid State

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Nanoallotropic forms of carbon, such as fullerenes, nanotubes, graphene, etc., attract attention of researchers in relation to their unusual mechanical, electrical, and thermal properties having their practi cal application [1]. In [2], a possibility was shown of the existence of a new class of 2D and 3D nanoallot ropes, namely, supracrystals in which the atoms in the crystal lattice sites are replaced with their symmetri cally organized complexes. In particular, the atoms can form an octahedron, a truncated octahedron, and a rhombocubooctahedron in sites of the cubic supra cell of a 3D supracrystal. Only one type of the 3D supracrystals, i.e., (C) CTO can be built from carbon atoms (Fig. 1). The first index "C" indicated behind the brackets determines the type of a supracell (cubic). The subsequent indices denote the type of polyhedron forming the site element (truncated octahedron). To form chemical bonds in other 3D supracrystals, atoms capable of taking the valences of five and six are needed.The elastic and acoustic characteristics of 2D supracrystals consisting of carbon atoms being in states with sp 2 and sp 3 hybridizations were studied in [3,4]. Here, we extend the proposed technique to 3D supracrystals. The groundwork of the technique was laid in [5-9], and its modified version was used in [3,4] for calculations of the elastic properties of 2D supracrystals.In a (C) CTO supracrystal, each of the carbon atoms has four nearest neighbors (sp 3 hybridization), and its covalent energy can be calculated by the relationship [7] (1)where ប is the reduced Planck constant; m 0 is the free electron mass; and l is the bond length. The metalliza tion energy [7] was found as (2) where E atom is the energy per atom calculated in [2] for the (C) CTO structure based on the density functional theory using the Abinit 5.8.4 program package. LATTICE DYNAMICSAbstract-The force constants of the central and noncentral interactions of carbon atoms in a three dimen sional supracrystal (C) CTO have been calculated using the ab initio and Harrison bond orbital methods. The components of the elastic rigidity tensor and the propagation velocity of elastic waves in the supracrystal have been calculated. The results are close in magnitude to corresponding characteristics of diamond. Fig. 1. Spatial structure of the (C) CTO supracrystal.

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