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The elastic properties of a flat graphene layer calculated using the classical empirical Tersoff, Brenner, AIREBO, PPBE-G, and LCBOP potentials have been compared. It is shown that, although the popular Brenner and AIREBO potentials have been developed formally taking into account the elastic properties of graphene, they give significant discrepancies in the values of Young’s modulus and Poisson’s ratio. Among the potentials under consideration, the LCBOP potential yields the values of these parameters that are closest to experimental data and results of ab initio calculations in the limit of zero elongation. For the quantitative simulation of mechanical phenomena in graphene-based systems, the potential parameters should be fitted to reproduce elastic properties of graphene completely taking into account system deformations and dependences of these constants on the elongation.

Novel logarithmic time algorithm is proposed for determining the order of chemical bonds from known valences of the atoms. The algorithm has the order of complexity N · log(N) and is applicable to polycyclic compounds containing a combination of the cycles of any size and the atoms with the valences ≤4 in cycle nodes. The algorithm is applicable to structures containing triple and cumulene bonds in the cycles. It was tested for graphene, C[12,12] nanotubes, graphyne-GY1, graphyne-GY7, graphyne-like nanotube, fullerenes C20, C60, C70, C80, C82 and their aza-analogs, polypentadienes, as well as for porphine. Determining the order of bonds in graphene, graphynes or nanotubes, containing >107 atoms, took less than 2 min on a personal computer. For the compounds containing aromatic cycles with an odd number of atoms, this algorithm becomes probabilistic and successful determination of bond orders is not guaranteed. However, the probability of successful determination of bond order is significant, and Kekule structures, if they existed, were generated for all studied fullerenes and their aza-analogs.

Molecular dynamics simulations show that a graphene nanoribbon with alternating regions which are one and three hexagons wide can transform into a hybrid 1D nanoobject with alternating double chains and polycyclic regions under electron irradiation in HRTEM. A scheme of synthesis of such a nanoribbon using Ullmann coupling and dehydrogenation reactions is proposed. The reactive REBO-1990EVC potential is adapted for simulations of carbon–hydrogen systems and is used in combination with the CompuTEM algorithm for modeling of electron irradiation effects. The atomistic mechanism of formation of the new hybrid 1D nanoobject is found to be the following. Firstly hydrogen is removed by electron impacts. Then spontaneous breaking of bonds between carbon atoms leads to the decomposition of narrow regions of the graphene nanoribbon into double chains. Simultaneously, thermally activated growth of polycyclic regions occurs. Density functional theory calculations give barriers along the growth path of polycyclic regions consistent with this mechanism. The electronic properties of the new 1D nanoobject are shown to be strongly affected by the edge magnetism and make this nanostructure promising for nanoelectronic and spintronic applications. The synthesis of the 1D nanoobject proposed here can be considered as an example of the general three-stage strategy of production of nanoobjects and macromolecules: (1) precursors are synthesized using a traditional chemical method, (2) precursors are placed in HRTEM with the electron energy that is sufficient only to remove hydrogen atoms, and (3) as a result of hydrogen removal, the precursors become unstable or metastable and transform into new nanoobjects or macromolecules., A. S. S., A. M. P. and A. A. K. acknowledge the Russian Foundation of Basic Research (Grants 18-02-00985 and 20-52-00035). S. V. R. and N. A. P. acknowledge the Belarusian Republican Foundation for Fundamental Research (Grant No. F20R-301) and Belarusian National Research Program ‘‘Convergence-2020’’. This work has been carried out using the computing resources of the federal collective usage center Complex for Simulation and Data Processing for Mega-science Facilities at NRC ‘‘Kurchatov Institute’’, http://ckp.nrcki.ru/ and was supported by the Research Center ‘‘Kurchatov Institute (order No. 1569 of July 16, 2019). D. G. O. has received funding from the Spanish Agencia Estatal de Investigacion (Grant No. PID2019-107338RB-C63).

The potential energy surface (PES) of interlayer interaction of twisted bilayer graphene with vacancies in one of the layers is investigated via density functional theory (DFT) calculations with van der Waals corrections. These calculations give a non-negligible magnitude of PES corrugation of 28 meV per vacancy and barriers for relative sliding of the layers of 7 - 8 meV per vacancy for the moir\'e pattern with coprime indices (2,1) (twist angle 21.8$^\circ$). At the same time, using the semiempirical potential fitted to the DFT results, we confirm that twisted bilayer graphene without defects exhibits superlubricity for the same moir\'e pattern and the magnitude of PES corrugation for the infinite bilayer is below the calculation accuracy. Our results imply that atomic-scale defects restrict the superlubricity of 2D layers and can determine static and dynamic tribological properties of these layers in a superlubric state. We also analyze computationally cheap approaches that can be used for modeling of tribological behavior of large-scale systems with defects. The adequacy of using state-of-the-art semiempirical potentials for interlayer interaction and approximations based on the first spatial Fourier harmonics for the description of interaction between graphene layers with defects is discussed., Comment: 11 pages, 4 figures

We propose a hypothesis that the potential energy surface (PES) of interlayer interaction in diverse 2D materials can be universally described by the first spatial Fourier harmonics. This statement (checked previously for the interactions between graphene and hexagonal boron nitride layers in different combinations) is verified in the present paper for the case of hydrofluorinated graphene (HFG) bilayer with hydrogen bonding between fluorine and hydrogen at the interlayer interface. The PES for HFG bilayer is obtained through density functional theory calculations with van der Waals corrections. An analytical expression based on the first Fourier harmonics describing the PES which corresponds to the symmetry of HFG layers is derived. It is found that the calculated PES can be described by the first Fourier harmonics with the accuracy of 3\% relative to the PES corrugation. The shear mode frequency, shear modulus and barrier for relative rotation of the layers to incommensurate states of HFG bilayer are estimated. Additionally it is shown that HFG bilayer is stable relative to the formation of HF molecules as a result of chemical reactions between the layers., Comment: 12 pages, 3 figures

Despite the high potential of endohedral metallofullerenes (EMFs) for application in biology, medicine and molecular electronics, and recent efforts in EMF synthesis, the variety of EMFs accessible by conventional synthetic methods remains limited and does not include, for example, EMFs of late transition metals. We propose a method in which EMF formation is initiated by electron irradiation in aberration-corrected high-resolution transmission electron spectroscopy (AC-HRTEM) of a metal cluster surrounded by amorphous carbon inside a carbon nanotube serving as a nanoreactor and apply this method for synthesis of nickel EMFs. The use of AC-HRTEM makes it possible not only to synthesize new, previously unattainable nanoobjects but also to study in situ the mechanism of structural transformations. Molecular dynamics simulations using the state-of-the-art approach for modeling the effect of electron irradiation are performed to rationalize the experimental observations and to link the observed processes with conditions of bulk EMF synthesis., A.S.S., I.V.L., A.A.K., and A.M.P. acknowledge the Russian Foundation of Basic Research (14-02-00739-a). I.V.L. acknowledges the financial support from Grupos Consolidados UPV/EHU del Gobierno Vasco (IT578-13) and EU-H2020 project “MOSTOPHOS” (no. 646259). A.N.K., T.W.C., and R.L.M. acknowledge the ERC and EPSRC for financial support, and the Nanoscale & Microscale Research Centre (nmRC). T.Z., J.B., and U.K. gratefully acknowledge the funding by the DFG (German Research Foundation) and the Ministry of Science, Research and the Arts (MWK) of Baden Wuerttemberg in the framework of the SALVE (Sub Angstrom Low-Voltage Electron Microscopy) project.

Exchange-correlation functionals with corrections for van der Waals interactions (PBE-D2, PBE-D3, PBE-D3(BJ), PBE-TS, optPBE-vdW and vdW-DF2) are tested for graphene and hexagonal boron nitride, both inthe form of bulk and bilayer. The characteristics of the potential energy surface, such as the barrier to rel-ative sliding of the layers and magnitude of corrugation, and physically measurable properties associatedwith relative in-plane and out-of-plane motion of the layers including the shear modulus and modulusfor axial compression, shear mode frequency and frequency of out-of-plane vibrations are considered.The PBE-D3(BJ) functional gives the best results for the stackings of hexagonal boron nitride and graphitethat are known to be ground-state from the experimental studies. However, it fails to describe the orderof metastable states of boron nitride in energy. The PBE-D3 and vdW-DF2 functionals, which reproducethis order correctly, are identified as the optimal choice for general studies. The vdW-DF2 functional ispreferred for evaluation of the modulus for axial compression and frequency of out-of-plane vibrations,while the PBE-D3 functional is somewhat more accurate in calculations of the shear modulus and shearmode frequency. The best description of the latter properties, however, is achieved also using the vdW-DF2 functional combined with consideration of the experimental interlayer distance. In the specific caseof graphene, the PBE-D2 functional works very well and can be further improved by adjustment of theparameters., L and APacknowledge the Russian Foundation for Basic Research (Grant16-52-00181). IL acknowledges the financial support from GruposConsolidados UPV/EHU del Gobierno Vasco (IT578-13) and EU-H2020 project ‘‘MOSTOPHOS” (n. 646259).

The capacity of popular classical interatomic potentials to describe elastic properties of graphene is tested. The Tersoff potential, Brenner reactive bond-order potentials REBO-1990, REBO-2000, REBO-2002 and AIREBO as well as LCBOP, PPBE-G, ReaxFF-CHO and ReaxFF-C2013 are considered. Linear and non-linear elastic response of graphene under uniaxial stretching is investigated by static energy calculations. The Young's modulus, Poisson's ratio and high-order elastic moduli are verified against the reference data available from experimental measurements and ab initio studies. The density functional theory calculations are performed to complement the reference data on the effective Young's modulus and Poisson's ratio at small but finite elongations. It is observed that for all the potentials considered, the elastic energy deviates remarkably from the simple quadratic dependence already at elongations of several percent. Nevertheless, LCBOP provides the results consistent with the reference data and thus realistically describes in-plane deformations of graphene. Reasonable agreement is also observed for the computationally cheap PPBE-G potential. REBO-2000, AIREBO and REBO-2002 give a strongly non-linear elastic response with a wrong sign of the third-order elastic modulus and the corresponding results are very far from the reference data. The ReaxFF potentials drastically overestimate the Poisson's ratio. Furthermore, ReaxFF-C2013 shows a number of numerical artefacts at finite elongations. The bending rigidity of graphene is also obtained by static energy calculations for large-diameter carbon nanotubes. The best agreement with the experimental and ab initio data in this case is achieved using the REBO-2000, REBO-2002 and ReaxFF potentials. Therefore, none of the considered potentials adequately describes both in-plane and out-of-plane deformations of graphene., AMP and AAK acknowledge the Russian Foundation for Basic Research, Russia (Grant 18-02-00985). IVL acknowledges Grupos Consolidados del Gobierno Vasco (IT-578-13).

Single-layer and bilayer carbon and hexagonal boron nitride nanoscrolls as well as nanoscrolls made of bilayer graphene/hexagonal boron nitride heterostructure are considered. Structures of stable states of the corresponding nanoscrolls prepared by rolling single-layer and bilayer rectangular nanoribbons are obtained based on the analytical model and numerical calculations. The lengths of nanoribbons for which stable and energetically favorable nanoscrolls are possible are determined. Barriers to rolling of single-layer and bilayer nanoribbons into nanoscrolls and barriers to nanoscroll unrolling are calculated. Based on the calculated barriers nanoscroll lifetimes in the stable state are estimated. Elastic constants for bending of graphene and hexagonal boron nitride layers used in the model are found by density functional theory calculations., AL, AP, and YL acknowledge the Russian Foundation of Basic Research (16-52-00181). IL acknowledges the financial support from Grupos Consolidados UPV/EHU del Gobierno Vasco (IT578-13) and EU-H2020 project “MOSTOPHOS” (n. 646259). AS, NP, and SV acknowledge the Belarusian Republican Foundation for Fundamental Research (grant No. F16R107) and Belarusian National Research Program “Convergence”.

The method for production of atomic chains by heating of graphene nanoribbons (GNRs) is proposed and studied by molecular dynamics simulations. The Brenner potential is revised to adequately describe formation of atomic chains, edges and vacancy migration in graphene. A fundamentally different behaviour is observed for zigzag-edge GNRs with 3 and 4 atomic rows (3 and 4-ZGNRs) at 2500 K: formation of triple, double and single carbon chains with the length of hundreds of atoms in 3-ZGNRs and edge reconstruction with only short chains and GNR width reduction in 4-ZGNRs. The chain formation mechanism in 3-ZGNRs is revealed by analysis of bond reorganization reactions and is based on the interplay of two processes. The first one is breaking of bonds between 3 zigzag atomic rows leading to triple chain formation. The second one is bond breaking within the same zigzag atomic row, which occurs predominantly through generation of pentagons with subsequent bond breaking in pentagons and results in single or double chain formation. The DFT calculations of the barriers for relevant reactions are consistent with the mechanism proposed. The possibility of chain-based nanoelectronic devices with a controllable number of chains is discussed., ASS, AMP and AAK acknowledge the Russian Foundation for Basic Research, Russia (Grant 18-02-00985). IVL acknowledges Grupos Consolidados del Gobierno Vasco, Spain (IT-578-13) and EU-H2020 project "MOSTOPHOS" (n. 646259).

The telescopic contact between graphene layers with a dielectric spacer is considered as a new type of graphene-based nanoelectronic devices. The tunneling current through the contacts with and without an argon spacer is calculated as a function of the overlap length, stacking of the graphene layers and voltage applied using non-equilibrium Green function formalism. A negative differential resistance (similar to semiconductor tunnel diode) is found with the peak to valley ratio up to 10 and up to 2 for the contacts without any spacer and with the argon spacer, respectively. The capacitance of the contacts between the graphene layers with the argon spacer is calculated as a function of temperature taking into account the quantum contribution. The related RC time constant is estimated to be about 3 ps, which allows elaboration of fast-response nanoelectronic devices. The possibility of application of the contacts as memory cells is discussed.

Incomplete stacking dislocations are predicted to form at edges of the shorter upper layer in two-dimensional hexagonal bilayers upon stretching the longer bottom layer. A concept of the edge Burgers vector is introduced to describe such dislocations by analogy with the Burgers vector of standard bulk dislocations. Analytical solutions for the structure and energy of edge stacking dislocations in bilayer graphene are obtained depending on the magnitude of elongation and angles between the edge Burgers vector, direction of elongation and edge. The barrier for penetration of stacking dislocations inside the bilayer is estimated. The possibilities to measure the barrier to relative motion of graphene layers and strain of graphene on a substrate by observation of edge stacking dislocations are discussed., The authors acknowledge the Russian Foundation of Basic Research (14-02-00739-a). IL acknowledges the financial support from Grupos Consolidados UPV/EHU del Gobierno Vasco (IT578-13) and H2020-NMP-2014 project “MOSTOPHOS” (n. 646259).

Exchange-correlation functionals with corrections for van der Waals interactions (PBE-D2, PBE-D3, PBE-D3(BJ), PBE-TS, optPBE-vdW and vdW-DF2) are tested for graphene and hexagonal boron nitride, both in the form of bulk and bilayer. The characteristics of the potential energy surface, such as the barrier to relative sliding of the layers and magnitude of corrugation, and physically measurable properties associated with relative in-plane and out-of-plane motion of the layers including the shear modulus and modulus for axial compression, shear mode frequency and frequency of out-of-plane vibrations are considered. The PBE-D3(BJ) functional gives the best results for the stackings of hexagonal boron nitride and graphite that are known to be ground-state from the experimental studies. However, it fails to describe the order of metastable states of boron nitride in energy. The PBE-D3 and vdW-DF2 functionals, which reproduce this order correctly, are identified as the optimal choice for general studies. The vdW-DF2 functional is preferred for evaluation of the modulus for axial compression and frequency of out-of-plane vibrations, while the PBE-D3 functional is somewhat more accurate in calculations of the shear modulus and shear mode frequency. The best description of the latter properties, however, is achieved also using the vdW-DF2 functional combined with consideration of the experimental interlayer distance. In the specific case of graphene, the PBE-D2 functional works very well and can be further improved by adjustment of the parameters., AL and AP acknowledge the Russian Foundation for Basic Research (Grant 16-52-00181). IL acknowledges the financial support from Grupos Consolidados UPV/EHU del Gobierno Vasco (IT578-13) and EU-H2020 project “MOSTOPHOS” (n. 646259).

The interlayer interaction in graphene/boron-nitride heterostructures is studied using density functional theory calculations with the correction for van der Waals interactions. It is shown that the use of the experimental interlayer distance allows one to describe the potential energy surface at the level of more accurate but expensive computational methods. On the other hand, it is also demonstrated that the dependence of the interlayer interaction energy on the relative in-plane position of the layers can be fitted with high accuracy by a simple expression determined by the system symmetry. The use of only two independent parameters in such an approximation suggests that various physical properties of flat graphene/boron-nitride systems are interrelated and can be expressed through these two parameters. Here we estimate some of the corresponding physical properties that can be accessed experimentally, including the correction to the period of the moiré superstructure for the highly incommensurate ground state of the graphene/boron-nitride bilayer coming from the interlayer interaction, the width of stacking dislocations in slightly incommensurate systems of boron nitride on stretched graphene, and shear mode frequencies for commensurate graphene/boron-nitride systems, such as a flake on a layer. We propose that the commensurate-incommensurate phase transition can be observed in boron nitride on stretched graphene and that experimental measurements of the corresponding critical strain can be also used to gain insight into graphene/boron-nitride interactions., A.V.L. and A.M.P. acknowledge the Russian Foundation of Basic Research (Grant No. 16-52-00181) and computational time on the Multipurpose Computing Complex NRC “Kurchatov Institute”. I.V.L. acknowledges financial support from Grupos Consolidados UPV/EHU del Gobierno Vasco (Grant No. IT578-13) and H2020-NMP-2014 Project “MOSTOPHOS” (No. 646259).

The possibility to control the commensurability and distance between graphene layers separated by a dielectric spacer is considered by the example of a heterostructure consisting of double-layer graphene separated by atomic layers of argon. Van der Waals-corrected density functional theory (DFT-D) is applied to study structural, energetic, and tribological characteristics of this heterostructure. It is found that, in the ground state, monolayer and bilayer argon spacers are incommensurate with the graphene layers, whereas sub-monolayer argon spacers which are commensurate with the graphene layers can exist only as metastable states. The calculations show that this incommensurability provides negligibly small static friction for relative motion of argon-separated graphene layers; therefore, such a heterostructure holds great promise for use in nanoelectromechanical systems. A scheme and operational principles of the nanorelay based on the revealed tribological properties of the heterostructure are proposed.

The possibility of designing nanoelectromechanical systems (NEMS) based on relative motion or vibrations of graphene layers is analyzed. Ab initio and empirical calculations of the potential relief of interlayer interaction energy in bilayer graphene are performed. A new potential based on the density functional theory calculations with the dispersion correction is developed to reliably reproduce the potential relief of interlayer interaction energy in bilayer graphene. Telescopic oscillations and small relative vibrations of graphene layers are investigated using molecular dynamics simulations. It is shown that these vibrations are characterized with small Q-factor values. The perspectives of nanoelectromechanical systems based on relative motion or vibrations of graphene layers are discussed., Comment: 19 pages, 4 figures

A new type of ultrahigh frequency resonator based on the relative vibrations of carbon nanotubes walls is proposed. Microcanonical molecular dynamics simulations performed for a model resonator based on the (9,0)@(18,0) double-walled carbon nanotube with the movable outer wall give the value of frequency equal to 130 GHz and the quality factor up to 500. Possible applications of the resonator are discussed. The estimated mass sensitivity of the mass sensor based on the proposed resonator reaches the atomic mass limit at liquid helium temperature. The possibility of resonator based on relative vibrations of graphene layers is also considered.

arXiv.-- et al., A way to produce new metal-carbon nanoobjects by transformation of a graphene flake with an attached transition metal cluster under electron irradiation is proposed. The transformation process is investigated by molecular dynamics simulations by the example of a graphene flake with a nickel cluster. The parameters of the nickel-carbon potential (I. V. Lebedeva et al., J. Phys. Chem. C, 2012, 116, 6572) are modified to improve the description of the balance between the fullerene elastic energy and graphene edge energies in this process. The metal-carbon nanoobjects formed are found to range from heterofullerenes with a metal patch to particles consisting of closed fullerene and metal clusters linked by chemical bonds. The atomic-scale transformation mechanism is revealed by the local structure analysis. The average time of formation of nanoobjects and their lifetime under electron irradiation are estimated for the experimental conditions of high-resolution transmission electron microscopy (HRTEM). The sequence of images of nanostructure evolution with time during its observation by HRTEM is also modelled. Furthermore, the possibility of batch production of studied metal-carbon nanoobjects and solids based on these nanoobjects is discussed., AS, IL, AK and AP acknowledges Russian Foundation of Basic Research (14-02-00739-a). AP acknowledges Samsung Global Research Outreach Program. IL acknowledges support from the Marie Curie International Incoming Fellowship within the 7th European Community Framework Programme (Grant Agreement PIIF-GA-2012-326435 RespSpatDisp), Grupos Consolidados del Gobierno Vasco (IT-578-13) and the computational time on the Supercomputing Center of Lomonosov Moscow State University and the Multipurpose Computing Complex NRC “Kurchatov Institute.” EB acknowledges EPSRC Career Acceleration Fellowship, New Directions for EPSRC Research Leaders Award (EP/G005060), and ERC Starting Grant for financial support.

A new concept of an electromechanical nanodynamometer based on the relative displacement of layers of bilayer graphene is proposed. In this nanodynamometer, force acting on one of the graphene layers causes the relative displacement of this layer and related change of conductance between the layers. Such a force can be determined by measurements of the tunneling conductance between the layers. Dependences of the interlayer interaction energy and the conductance between the graphene layers on their relative position are calculated within the first-principles approach corrected for van der Waals interactions and the Bardeen method, respectively. The characteristics of the nanodynamometer are determined and its possible applications are discussed., 5 pages, 4 figures

Structural, energetic, and tribological characteristics of double-layer graphene with commensurate and incommensurate krypton spacers of nearly monolayer coverage are studied within the van der Waals-corrected density functional theory. It is shown that when the spacer is in the commensurate phase, the graphene layers have the AA stacking. For this phase, the barriers to relative in-plane translational and rotational motion and the shear mode frequency of the graphene layers are calculated. For the incommensurate phase, both of the barriers are found to be negligibly small. A considerable change of tunneling conductance between the graphene layers separated by the commensurate krypton spacer at their relative subangstrom displacement is revealed by the use of the Bardeen method. The possibility of nanoelectromechanical systems based on the studied tribological and electronic properties of the considered heterostructures is discussed.

Both van der Waals corrected density functional theory and classical calculations show that the potential relief of interaction energy between layers of graphite and few-layer graphene can be described by a simple expression containing only the first Fourier components. Thus a set of physical quantities and phenomena associated with in-plane relative vibration, translational motion and rotation of graphene layers are interrelated and are determined by a single parameter characterizing the roughness of the potential energy relief. This relationship is used to estimate the barriers to relative motion and rotation of graphene layers based on experimental measurements of shear mode frequencies., 16 pages, 1 figure

Transformation of graphene flakes to fullerenes assisted by Ni clusters is investigated using molecular dynamics simulations. The bond-order potential for Ni-C systems is developed. The potential reproduces the experimental and first-principles data on the physical properties of pure Ni as well as on relative energies of carbon species on Ni surfaces and in Ni bulk. The potential is applied for molecular dynamics simulations of the transformation of graphene flakes consisting of 50 - 400 atoms with and without Ni clusters attached. Free fullerenes, fullerenes with Ni clusters attached from outside and fullerenes encapsulating Ni clusters (Ni endofullerenes) are observed to form in the presence of Ni clusters consisting of 5 - 80 atoms. Moreover, a new type of heterofullerenes with a patch made of a Ni cluster is found to form as an intermediate structure during the transformation. The Ni clusters are shown to reduce the activation energy for the graphene-fullerene transformation from 4.0 eV to 1.5 - 1.9 eV, providing the decrease of the minimal temperature at which such a transformation can be observed experimentally from about 1400 K for free graphene flakes to about 700 - 800 K. While the transformation of free graphene flakes is found to occur through formation of chains of two-coordinated carbon atoms at the flake edges, the mechanism of the Ni-assisted graphene-fullerene transformation is revealed to be based on the transfer of carbon atoms from the graphene flake to the Ni cluster and back. The way of controlled synthesis of endofullerenes with a transition metal cluster inside and heterofullerenes with a transition metal patch is also proposed., Comment: 39 pages, 8 figures

Temperature-activated diffusion of a graphene flake on a graphene layer and a commensurate-incommensurate phase transition in bilayer graphene are investigated using the classical potential for graphene developed recently on the basis of first-principles calculations with the van der Waals correction. It is shown that rotation of graphene flakes to incommensurate states can significantly contribute to diffusion of the flakes consisting of several tens of atoms even at room temperature. Formation of incommensurability defects in bilayer graphene upon stretching of one of the layers is observed by molecular dynamics simulations.

The self-retracting motion of a graphene flake on a stack of graphene flakes is studied using molecular dynamics simulations. It is shown that in the case when the extended flake is initially rotated to an incommensurate state, there is no barrier to the self-retracting motion of the flake and the flake retracts as fast as possible. If the extended flake is initially commensurate with the other flakes, the self-retracting motion is hindered by potential energy barriers. However, in this case, the rotation of the flake to incommensurate states is often observed. Such a rotation is found to be induced by the torque acting on the flake on hills of the potential relief of the interaction energy between the flakes. Contrary to carbon nanotubes, telescopic oscillations of the graphene flake are suppressed because of the high dynamic friction related to the excitation of flexural vibrations of the flake. This makes graphene promising for the use in fast-responding electromechanical memory cells., Comment: 24 pages, 8 figures

A commensurate-incommensurate phase transition in bilayer graphene is investigated in the framework of the Frenkel-Kontorova model extended to the case of two interacting chains of particles. Analytic expressions are derived to estimate the critical unit elongation of one of the graphene layers at which the transition to the incommensurate phase takes place, the length and formation energy of incommensurability defects (IDs) and the threshold force required to start relative motion of the layers on the basis of dispersion-corrected density functional theory calculations of the interlayer interaction energy as a function of the relative position of the layers. These estimates are confirmed by atomistic calculations using the DFT-D based classical potential. The possibility to measure the barriers for relative motion of graphene layers by the study of formation of IDs in bilayer graphene is discussed., 22 pages, 4 figures

Diffusion and drift of a graphene flake on a graphite surface are analyzed. A potential energy relief of the graphene flake is computed using ab initio and empirical calculations. Based on the analysis of this relief, different mechanisms of diffusion and drift of the graphene flake on the graphite surface are considered. A new mechanism of diffusion and drift of the flake is proposed. According to the proposed mechanism, rotational transition of the flake from commensurate to incommensurate state takes place with subsequent simultaneous rotation and translational motion until a commensurate state is reached again, and so on. Analytic expressions for the diffusion coefficient and mobility of the flake corresponding to different mechanisms are derived in wide ranges of temperatures and sizes of the flake. The molecular dynamics simulations and estimates based on ab initio and empirical calculations demonstrate that the proposed mechanism can be dominant under certain conditions. The influence of structural defects on the diffusion of the flake is examined on the basis of calculations of the potential energy relief and molecular dynamics simulations. The methods of control over the diffusion and drift of graphene components in nanoelectromechanical systems are discussed. The possibility to experimentally determine the barriers to relative motion of graphene layers based on the study of diffusion of a graphene flake is considered. The results obtained can be also applied to polycyclic aromatic molecules on graphene and should be qualitatively valid for a set of commensurate adsorbate-adsorbent systems., Comment: 42 pages, 7 figures

Diffusion of a graphene flake on a graphene layer is analyzed and a new diffusion mechanism is proposed for the system under consideration. According to this mechanism, rotational transition of the flake from commensurate to incommensurate states takes place with subsequent simultaneous rotation and translational motion until the commensurate state is reached again, and so on. The molecular dynamics simulations and analytic estimates based on ab initio and semi-empirical calculations demonstrate that the proposed diffusion mechanism is dominant at temperatures T ~ Tcom, where Tcom corresponds to the barrier for transitions of the flake between adjacent energy minima in the commensurate states. For example, for the flake consisting of ~ 40, 200 and 700 atoms the contribution of the proposed diffusion mechanism through rotation of the flake to the incommensurate states exceeds that for diffusion of the flake in the commensurate states by one-two orders of magnitude at temperatures 50 - 150 K, 200 - 600 K and 800 - 2400 K, respectively. The possibility to experimentally measure the barriers to relative motion of graphene layers based on the study of diffusion of a graphene flake is considered. The results obtained are also relevant for understanding of dynamic behavior of polycyclic aromatic molecules on graphene and should be qualitatively valid for a set of commensurate adsorbate-adsorbent systems., 33 pages, 6 figures

The dispersion-corrected density functional theory (DFT-D) is applied for investigation of structure and electronic properties of a sulfur-terminated graphene nanoribbon (S-GNR) encapsulated in a carbon nanotube. Two mechanisms of accommodation of the GNR in the carbon nanotube, distortion of the nanotube cross-section into an elliptic shape accompanied by bending of the GNR and transformation of the GNR to a helical conformation, are analyzed. Three types of elastic distortions of the nanotube and encapsulated GNR are revealed depending on the ratio of the diameter of the nanotube cavity to the GNR width. Helical states of the GNR are shown to be stabilized by the van der Waals attraction of sulfur atoms at neighbouring edges of adjacent turns of the GNR. The results of calculations are correlated with the experimental observations for the S-GNR synthesized recently inside the carbon nanotube. The hybrid DFT calculations of band structures of zigzag GNRs terminated with different atoms demonstrate that as opposed to O- and H-GNRs, the S-GNR is metallic even when deformed inside carbon nanotubes. Possible applications of GNRs encapsulated in carbon nanotubes are discussed.

Current research on graphene, a 2D hexagonal structure of carbon atoms, is presented. The structural features of and basic methods for obtaining graphene are discussed. The phononic properties of graphene and their dependent graphene characteristics are examined. In particular, how to measure the thermal conductivity of graphene is discussed and recent experimental and theoretical advances on this subject are described. The stability problems of 2D crystal structures are addressed and the dimensional effects in the dependence of graphene characteristics on the lateral size are discussed. Simulation methods for determining the phononic characteristics and thermal conductivity of graphene are reviewed.

The van der Waals corrected first-principles approach (DFT-D) is for the first time applied for investigation of interlayer interaction and relative motion of graphene layers. A methodological study of the influence of parameters of calculations with the dispersion corrected and original PBE functionals on characteristics of the potential relief of the interlayer interaction energy is performed. Based on the DFT-D calculations, a new classical potential for interaction between graphene layers is developed. Molecular dynamics simulations of relative translational vibrations of graphene layers demonstrate that the choice of the classical potential considerably affects dynamic characteristics of graphene-based systems. The calculated low values of the Q-factor for these vibrations Q ≈ 10–100 show that graphene should be perfect for the use in fast-responding nanorelays and nanoelectromechanical memory cells.

We investigate how parameters of the model of semi-infinite graphene based on a graphene nanoribbon under periodic boundary conditions affect the accuracy of ab initio calculations of reactions at graphene edges by the example of the first stage of reconstruction of zigzag graphene edges, formation of a pentagon-heptagon pair. It is shown that to converge properly the results, the nanoribbon should consist of at least 6 zigzag rows and periodic images of the pair along the nanoribbon axis should be separated by at least 6 hexagons. The converged reaction energy and activation barrier for formation of an isolated pentagon-heptagon pair are found to be –0.15 eV and 1.61 eV, respectively. It is also revealed that such defects reduce the graphene edge magnetization only locally but ordering of spins at opposite nanoribbon edges switches from the antiparallel (antiferromagnetic) to parallel one (ferromagnetic) upon increasing the defect density., IVL acknowledges the European Union MaX Center of Excellence (EU-H2020 Grant No. 824143).