Dispersion of Flexural Modes in Graphene Ipatov, A. N.; Parshin, D. A.; Conyuh, D. A.
Journal of experimental and theoretical physics,
10/2021, Volume:
133, Issue:
4
Journal Article
Peer reviewed
Using the Born–von Karman model, we have constructed a simple analytic theory of dispersion of flexural vibrations in graphene, which makes it possible to take into account any number of ...configuration spheres. In the framework of this theory, the quadratic dispersion of flexural acoustic phonons in graphene has been analyzed. It is shown that such a dispersion of flexural vibrations in graphene is the interaction of each atom with not only nearest neighbors, but also with more distant atoms. The signs of effective force constants corresponding to different coordination spheres must be various, preserving the system stability. We have obtained analytic relations between elastic constants, for which flexural vibrations can propagate in the plane of graphene. In the “critical” relation derived in this study, negative elastic constants of the second and third coordination sphere compensate the positive contribution from the first coordination sphere almost completely. As a result, the propagation of low-frequency flexural acoustic waves with conventional linear dispersion in a narrow interval of wavevector values near
k
= 0 turns out to be impossible. We have determined the conditions in which the dispersion relation of flexural modes in graphene becomes quadratic, which is typical of flexural vibrations in thin macroscopic membranes.
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DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, SIK, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
The paper describes the experimental technique and presents data obtained when measuring the flux of monochromatic neutrons in the sample position at installations located on the horizontal ...experimental channels of the IR-8 reactor (NRC Kurchatov Institute) and used in research in the field of condensed matter physics and materials science.
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We have constructed a consistent theory of flexural phonon mode spectra of simple 2D crystal lattice. Analytic expressions have been obtained for the dispersion relations of 2D lattices with ...different configurations. It is shown that the propagation of flexural modes with a quadratic dispersion relation becomes possible during the interaction of each atom with not only nearest neighbors, but also with more distant atoms. It turns out that the signs of the effective force constants must be different to provide mechanical stability of the system. Moreover, there exists a relation between force constants of the lattice, which depends on its geometrical configuration and for which the account for the influence of more distant coordination spheres reproduces the square of the dispersion relation of the first sphere, preserving its angular isotropy in a wide range of wavevectors.
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We present the results of simulations and experimental studies of a W-band surface-wave oscillator powered by a ribbon high-current relativistic electron beam produced by SINUKI accelerator (IAP RAS, ...Nizhny Novgorod, 1 kA / 650 keV / 17 ns). Planar geometry of the interaction space facilitates efficient mode selection over wide transverse coordinate by using open waveguide at fairly large oversize factor (the width of the waveguide is ~ 8 wavelengths). Stable oscillation regime is obtained at frequency of 75 GHz with a pulse duration of about 5 ns. The output power measured by the calorimetric method reaches 25 MW.
In the classical representation theory of locally compact groups, there are well-known constructions of a unitary dual space of irreducible representations, the Fourier transform, and the Plancherel ...theorem. In this paper, we present analogs of these constructions for the discrete Heisenberg group and its irreducible infinite-dimensional representations in a vector space without topology.
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The effect of disorder in the distribution of force constants on optical and acoustic phonons in the scalar model of crystalline graphene is studied for both oscillations lying in the sheet plane and ...for flexural modes. It was shown that in the model of stable random matrices with translational symmetry, an additional to Debye vibrational density of states arises at a sufficient degree of disorder, i.e., the boson peak. The boson peak shifts to lower frequencies with increasing relative fluctuations of force constants and decreasing Young’s modulus of the system. At a weak disorder (or with no disorder), there are two peaks in the density of states
g
(ω), which correspond to logarithmic van-Hove singularity for acoustic and optical phonons of crystalline graphene. These peaks broaden and merge into a single boson peak with increasing disorder. Optical phonons are first destroyed due to disorder, while acoustic phonons gradually transform to the boson peak. For flexural modes there is a slightly different situation. Van-Hove singularities still spread disorder, but lead to the appearance of phonons in the system, which form the boson peak and move with it to low frequencies with increasing disorder.
A theory of flexural modes in graphene Raikov, I. O.; Conyuh, D. A.; Ipatov, A. N. ...
Journal of physics. Conference series,
12/2020, Volume:
1695, Issue:
1
Journal Article
Peer reviewed
Open access
We present a theory of flexural modes in graphene. The theory is based on the idea of negative springs in the second coordination circle between next nearest neighbours. As a result these negative ...springs change the dispersion law of vibrational modes in graphene from phonon-like linear dispersion ω ∝ q to a flexural kind dispersion ω ∝ q2, when the elastic modulus of the lattice goes to zero. At this point positive springs of the first shell are completely compensated by the negative springs which are 1/6 of the positive springs. Phonons cannot propagate through such a soft lattice with zero Young modulus and sound velocities, but flexural modes can.
The self-organized criticality (SOC) phenomena for dynamical systems with spatial degrees of freedom is commonly observed in application to different aspects of natural sciences. In our study we also ...consider our sandpile model as such a system. Since the first mention in 1987, a sandpile model, which is a common example of spatiotemporal evolution, became widely applied for avalanche-like processes. With a simple computer simulation we show that an avalanche as a result of natural system evolution has a fractal border structure, and approves SOC phenomena of a sandpile model. We also demonstrate Gutenberg-Richter dependence for avalanche process in a sandpile model.
In this work we construct a harmonic analysis on free Abelian groups of rank , namely: we construct and investigate spaces of functions and distributions, Fourier transforms and actions of discrete ...and extended discrete Heisenberg groups. In the case of the rank- value group of a two-dimensional local field with finite last residue field we connect this harmonic analysis with harmonic analysis on the two-dimensional local field, where the latter harmonic analysis was constructed in earlier works by the authors. Bibliography: 15 titles.
Major types of mineralization distinguished at the Krasniy deposit: (a) dispersed idiomorphic pyrite crystals, (b) a veinlet with pyrite and pyrrhotite, (c) veinlets of milky-white quartz bearing ...fine cubic pyrite, (d) a vein of brownish quartz with pyrite pocket.
Morphological varieties of pyrite. a – banded cluster of thin impregnated aggregates of framboidal pyrite-I; b – fine idiomorphic crystals of pyrite–II; c – gold inclusions through fracture in pyrite-III; d – joint aggregates of pyrrhotite and chalcopyrite over pyrite–III rim; e – sphalerite inclusions in pyrite-III and over its edge; f – pyrite-IV crystal.
Scheme presenting formation of Sukhoi Log-type gold deposits (after (Nemerov et al., 2010) supplemented by the authors).
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•The Krasniy gold deposit localized in black-shist metasediments has been studied.•Au as nanoparticles in diagenetic pyrite and inclusions in later metamorphic pyrite.•S-Pb isotopes indicate redistribution of metals within host rocks without external fluid.•Metalliferous crude oils (up to 1 ppm Au in host-rock bitumens) as potential transporters of metals.•Ore formation involved diagenesis, catagenesis and greenschist metamorphism.
Orogenic gold deposits localized in carbonaceous sedimentary (black-shale) complexes are major contributors to worldwide balance of gold extracted from the crust, though there is a limited consensus about the role of host sedimentary rocks, involvement of external (i.e., magma-derived) fluids and brittle deformations into ore remobilization and transport. This paper presents the original results of mineralogical, petrographic and isotope-geochemical studies of rocks and ores from the large Krasniy gold deposit (Baikal-Patom plateau, southern Siberian craton) given in comparison with the thoroughly studied giant Sukhoi Log deposit, with both deposits hosted by the Neoproterozoic carbonaceous metasedimentary rocks. The multi-stage ore process occurred discretely at 200–400 °C (greenschist-facies metamorphism) and included (1) low-P-T diagenetic formation of globular pyrite, (2) catagenetic (<200 °C, 1–2 kbar) formation of small euhedral pyrite, (3) high-temperature and high-pressure (300–380 °C, 5–6 kbar) crystallization of arsenopyrite and pyrrhotite related to metamorphic transformation, and (4) formation of the major ore assemblage (arsenopyrite, pyrrhotite, pyrite meta-aggregates, native gold, galena, sphalerite, fahl ores) during almost isothermal decompression (270–320 °C, 0.5 kbar). Gold is detected as nanoparticles unevenly distributed at the surface of the early globular pyrite (up to 0.4 ppm) and occurs as inclusions in later metamorphic pyrite. Relatively narrow ranges of sulfur (δ34S within −4.7 – −6.9‰) and lead isotopic composition (206Pb/204Pb = 18.33–18.65, 207Pb/204Pb = 15.65–15.68 and 208Pb/204Pb = 38.13–38.82) in sulfides from the ores was continuously inherited from earlier generation of sulfides to the later (associate with native gold) and is similar to the values obtained for sulfides from the host Neoproterozoic metasedimentary rocks of the Aunakit formation. The compositional inheritance together with geochemical evidence of no additional contribution of К, Na, Mg and Si into the ores and no correlation between gold and organic carbon content highlight the absence of the external metasomatic overprint of metal-bearing fluids. Instead, both the above facts and high Au content (up to 1 ppm) in bitumens derived from the host metasediments indicate a key role of the host carbonaceous substrate in the supply of metals through release and local transport of internally derived diagenetic/catagenetic carbon-rich fluids. Overall, the obtained results for the Krasniy deposit led to distinguishing the three key stages of the gold deposit formation, including 1) sedimentation of gold-specialized sediments in the spreading of the back-arc basin, where gold was associated with the scattered diagenetic pyrite mineralization (610–590 Ma), 2) catagenetic redistribution of sedimentary pore fluids from preconditioned sedimentary rocks into the vaulted parts of gentle anticlines with the formation of abnormally high concentrations of gold (~570 Ma), and 3) metamorphic-metasomatic redistribution of gold as a result of decarbonization of catagenic fluid with the formation of economically significant ore bodies (450–420 Ma). The compilation of the available geochemical and isotopic data allows to suspect this model as a general for the other Bodaibo region deposits, so that it can be used further for prediction and exploration purposes.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
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