Dimensional crossover of thermal conductance in graphene nanoribbons: a first-principles approach

First-principles density-functional calculations are performed to investigate the thermal transport properties in graphene nanoribbons (GNRs). The dimensional crossover of thermal conductance from one to two dimensions (2D) is clearly demonstrated with increasing ribbon width. The thermal conductance of GNRs of a few nanometers width already exhibits an approximate low-temperature dependence of T(1.5), like that of 2D graphene sheets which is attributed to the quadratic nature of the dispersion relation for the out-of-plane acoustic phonon modes. Using a zone-folding method, we heuristically derive the dimensional crossover of thermal conductance with the increase of ribbon width. Combining our calculations with the experimental phonon mean-free path, some typical values of thermal conductivity at room temperature are estimated for GNRs and for 2D graphene sheet. Our findings clarify the issue of the low-temperature dependence of thermal transport in GNRs and suggest a calibration range of thermal conductivity for experimental measurements in graphene-based materials.     

三氨基三硝基苯基高聚物粘结炸药热力学性质的理论计算研究

高聚物粘结炸药(PBX)的热力学性质是用于炸药结构响应、安全性评估、数值模拟分析等的重要参数.由于PBX结构的多尺度特性,完全采取实验方法精细表征这些参数存在巨大的挑战.本文运用第一性原理和分子动力学计算的方法,系统研究了三氨基三硝基苯(TATB)基高聚物粘结炸药的热力学参数和界面热传导性质.利用散射失配模型研究了TATB与聚偏二氟乙烯(PVDF)界面的热传导过程,发现热导率随温度升高而上升,并且在高温情况下接近于定值.基于分子动力学获得的TATB热导率并结合界面热导率,分析了PBX炸药的热导与颗粒尺寸的关系,当颗粒尺寸大于100 nm时,界面热阻对于PBX热导率的影响有限.     

Two-dimensional phonon transport in graphene

Properties of phonons-quanta of the crystal lattice vibrations-in graphene have recently attracted significant attention from the physics and engineering communities. Acoustic phonons are the main heat carriers in graphene near room temperature, while optical phonons are used for counting the number of atomic planes in Raman experiments with few-layer graphene. It was shown both theoretically and experimentally that transport properties of phonons, i.e. energy dispersion and scattering rates, are substantially different in a quasi-two-dimensional system such as graphene compared to the basal planes in graphite or three-dimensional bulk crystals. The unique nature of two-dimensional phonon transport translates into unusual heat conduction in graphene and related materials. In this review, we outline different theoretical approaches developed for phonon transport in graphene, discuss contributions of the in-plane and cross-plane phonon modes, and provide comparison with available experimental thermal conductivity data. Particular attention is given to analysis of recent results for the phonon thermal conductivity of single-layer graphene and few-layer graphene, and the effects of the strain, defects, and isotopes on phonon transport in these systems.     

A structural mechanics approach for the phonon dispersion analysis of graphene

A molecular structural mechanics model for the numerical simulation of phonon dispersion relations of graphene is developed by relating the C-C bond molecular potential energy to the strain energy of the equivalent beam-truss space frame. With the stiffness matrix known and further based on the periodic structure characteristics, the Bloch theorem is introduced to develop the dispersion relation of graphene sheet. Being different from the existing structural mechanics model, interactions between the fourth-nearest neighbor atoms are further simulated with beam elements to compensate the reduced stretching stiffness, where as a result not only the dispersion relations in the low frequency field are accurately achieved, but results in the high frequency field are also reasonably obtained. This work is expected to provide new opportunities for the dynamic properties analysis of graphene and future application in the engineering sector.     

Phonons in carbon nanotubes

A broad review of the unusual one-dimensional properties of phonons in carbon nanotubes is presented, including phonons in isolated nanotubes and in crystalline arrays of nanotubes in nanotube bundles. The main technique for probing the phonon spectra has been Raman spectroscopy and the many unique and unusual features of the Raman spectra of carbon nanotubes are reviewed. Also included is a brief review of the thermal properties of carbon nanotubes in relation to their unusual phonon dispersion relations and density of states.     

Theoretical investigations on vibrational properties and thermal conductivities of ternary antimonides TiXSb,ZrXSb and HfXSb (X = Si,Ge)

We have performed density functional calculations of the vibrational and thermodynamic properties of the ternary antimonides TiXSb, ZrXSb and HfXSb (X = Si, Ge). The direct method is used to calculate the phonon dispersion relation and phonon density of states for these compounds as well as their infrared and Raman active mode frequencies for the first time. Their dynamical stability is confirmed by phonon spectra. The lattice thermal conductivities of these compounds have been calculated from third-order force constants and plotted as a function of temperature. We have also evaluated the high temperature thermal conductivity by means of the Clarke’s model and Cahill’s model. Some selected thermodynamical properties, e.g. Gibbs free energy, entropy and heat capacity at constant volume are predicted theoretically and discussed. We have showed the relationships between thermodynamical properties and temperature.     

势能模型对石墨烯导热性质分子动力学模拟的影响

针对常用的Tersoff势、Rebo势和Airebo势,系统性地分析势能模型对分子动力学模拟计算石墨烯色散关系、声子态密度、群速度和热导率的影响. 结果表明：Rebo势和Airebo势描述的声子色散关系接近实验值,Airebo势对应的声子态密度与第一性原理计算的结果较为符合,Rebo势和Airebo势计算的Γ点处声子群速度高于Tersoff势. 采用Airebo势得到石墨烯热导率约为1 150 W·（m·K）^-1,与实验值相近. 综合各种影响,相比于Tersoff势和Rebo势,Airebo势能模型更适合计算石墨烯的导热性质.     

Phonon scattering and thermal conductance properties in two coupled graphene nanoribbons modulated with bridge atoms

The phonon scattering and thermal conductance properties have been studied in two coupled graphene nanoribbons connected by different bridge atoms by using density functional theory in combination with non-equilibrium Green's function approach. The results show that a wide range of thermal conductance tuning can be realized by changing the chemical bond strength and atom mass of the bridge atoms. It is found that the chemical bond strength (bridge atom mass) plays the main role in phonon scattering at low (high) temperature. A simple equation is presented to describe the relationship among the thermal conductance, bridge atom, and temperature.     

Multiphonon Raman spectroscopy properties and Raman mapping of 2D van der Waals solids: graphene and beyond

Strong in‐plane bonding (covalent) and weak van der Waals (vdW) interplanar interactions characterize a number of layered solids, as epitomized by graphite. The advent of graphene (Gr), individual atomic two‐dimensional (2D) layers, isolated from mineral graphite via micromechanical exfoliation enabled the ability to pick, place and stack of arbitrary compositions. Moreover, this discovery implicated an access to other 2D vdW solids beyond graphene and artificially stacking atomic layers forming heterostructures/superlattices. Raman spectroscopy (RS) is a fast reliable non‐destructive analytical tool and an integral part for lattice dynamical structural characterization of crystalline solids at nanoscale, revealing not only the collective atomic/molecular motions but also localized vibrations/modes and specifically used to determine the number of graphene layers and of other 2D vdW solids. We present Raman spectroscopy in first‐, second‐ and higher‐order vibrational modes involving 3 and 4 phonons (overtones and combination) and mapping of graphene (mono‐, bi‐, tri‐ and few‐) layers, semiconducting transition metal dichalcogenides (TMDs) [molybdenum disulfide (MoS₂) and tungsten disulfide (WS₂)] and wide bandgap hexagonal boron nitride (h‐BN) dispersed monolayers, revealing various molecular vibrations and structural quality/disorder. First‐ and higher‐order phonon modes are observed and analyzed in terms of Raman intensity (spatial inhomogeneity or thickness variation), band position (intrinsic mechanical strain) and intensity ratio (structural disorder) as a function of graphene layer (n). An empirical relation for G band position with n is corroborated. All of the higher order modes are observed to upshift almost linearly with n, betraying the underlying interlayer vdW interactions. These findings exemplify the evolution of structural parameters in layered materials in changing from 3‐ to 2‐ or low‐dimensional regime. The results are presented in view of applications of graphene by itself and in combination that help better understanding of physical and electronic properties for nano‐/optoelectronics. Copyright © 2015 John Wiley & Sons, Ltd.     

First-principles study on the mechanics,optical, and phonon properties of carbon chains

Besides graphite, diamond, graphene, carbon nanotubes, and fullerenes, there is another allotrope of carbon, carbyne,existing in the form of a one-dimensional chain of carbon atoms. It has been theoretically predicted that carbyne would be stronger, stiffer, and more exotic than other materials that have been synthesized before. In this article, two kinds of carbyne, i.e., cumulene and polyyne are investigated by the first principles, where the mechanical properties, electronic structure, optical and phonon properties of the carbynes are calculated. The results on the crystal binding energy and the formation energy show that though both are difficult to be synthesized from diamond or graphite, polyyne is more stable and harder than cummulene. The tensile stiffness, bond stiffness, and Young's modulus of cumulene are 94.669 eV/?A,90.334 GPa, and 60.62 GPa, respectively, while the corresponding values of polyyne are 94.939 eV/?A, 101.42 GPa, and60.06 GPa. The supercell calculation shows that carbyne is most stable at N = 5, where N is the supercell number, which indicates that the carbon chain with 10 atoms is most stable. The calculation on the electronic band structure shows that cumulene is a conductor and polyyne is a semiconductor with a band gap of 0.37 eV. The dielectric function of carbynes varies along different directions, consistent with the one-dimensional nature of the carbon chains. In the phonon dispersion of cumulene, there are imaginary frequencies with the lowest value down to-3.817 THz, which indicates that cumulene could be unstable at room temperature and normal pressure.     

硅功能化石墨烯热导率的分子动力学模拟

采用Tersoff势函数与Lennard-Jones势函数,结合速度形式的Verlet算法和Fourier定律,对单层和两层硅功能化石墨烯沿长度方向的导热性能进行了正向非平衡态分子动力学模拟.通过模拟发现,硅原子的加入改变了石墨烯声子的模式、平均自由程和移动速度,使得单层硅功能化石墨烯模型的热导率随着硅原子数目的增加而急剧地减小.在300 K至1000 K温度变化范围内,单层硅功能化石墨烯的热导率呈下降趋势,具有明显的温度效应.对双层硅功能化石墨烯而言,少量的硅原子嵌入,起到了提高热导率的作用,但当硅原子数目达到一定数量后,材料的导热性能下降.     

Analytical model of transverse oscillations of graphene

A simple analytical model of transverse oscillations of graphene is constructed. The model is applicable to both free and stretched graphene monolayers. The dispersion relation for transverse oscillations of graphene and the corresponding phonon state density are determined.     

极化子在正弦色散声子场中的性质

本文计及纵光学声子的色散,在正弦近似下,用微扰法了多原子晶体中极化子的基态能量,有效质量和自能。     

Electronic structures and coronene on Ru（0001）： vibrational properties of first-principles study

We calculate the configurations,electronic structures,vibrational properties at the coronene/Ru(0001) interface,and adsorption of a single Pt atom on coronene/Ru(0001) based on density functional theory calculations.The geometric structures and electronic structures of the coronene on Ru(0001) are compared with those of the graphene/Ru(0001).The results show that the coronene/Ru(0001) can be a simplified model system used to describe the interaction between graphene and ruthenium.Further calculations of the vibrational properties of coronene molecule adsorbed on Ru(0001) suggest that the phonon properties of differently corrugated regions of graphene on Ru(0001) are different.This model system is also used to investigate the selective adsorption of Pt atoms on graphene/Ru(0001).The configurations of Pt on coronene/Ru(0001) with the lowest binding energy give clues to explain the experimental observation that a Pt cluster selectively adsorbs on the second highest regions of graphene/Ru(0001).This work provides a simple model for understanding the adsorption properties and vibrational properties of graphene on Ru(0001) substrate.     

Electronic structures and vibrational properties of coronene on Ru(0001): first-principles study

We calculate the configurations, electronic structures, vibrational properties at the coronene/Ru(0001) interface, and adsorption of a single Pt atom on coronene/Ru(0001) based on density functional theory calculations. The geometric structures and electronic structures of the coronene on Ru(0001) are compared with those of the graphene/Ru(0001). The results show that the coronene/Ru(0001) can be a simplified model system used to describe the interaction between graphene and ruthenium. Further calculations of the vibrational properties of coronene molecule adsorbed on Ru(0001) suggest that the phonon properties of differently corrugated regions of graphene on Ru(0001) are different. This model system is also used to investigate the selective adsorption of Pt atoms on graphene/Ru(0001). The configurations of Pt on coronene/Ru(0001) with the lowest binding energy give clues to explain the experimental observation that a Pt cluster selectively adsorbs on the second highest regions of graphene/Ru(0001). This work provides a simple model for understanding the adsorption properties and vibrational properties of graphene on Ru(0001) substrate.     

Thermal properties of transition-metal dichalcogenide

Beyond graphene, the layered transition metal dichalcogenides(TMDs) have gained considerable attention due to their unique properties. Herein, we review the lattice dynamic and thermal properties of monolayer TMDs, including their phonon dispersion, relaxation time, mean free path(MFP), and thermal conductivities. In particular, the experimental and theoretical studies reveal that the TMDs have relatively low thermal conductivities due to the short phonon group velocity and MFP, which poses a significant challenge for efficient thermal management of TMDs-based devices. Importantly,recent studies have shown that this issue could be largely addressed by connecting TMDs and other materials(such as metal electrode and graphene) with chemical bonds, and a relatively high interfacial thermal conductance(ITC) could be achieved at the covalent bonded interface. The ITC of MoS_2/Au interface with chemical edge contact is more than 10 times higher than that with physical side contact. In this article, we review recent advances in the study of TMD-related ITC.The effects of temperature, interfacial vacancy, contact orientation, and phonon modes on the edge-contacted interface are briefly discussed.     

Phonon dispersion for the bcc metals Mo and Cr

In this paper the phonon dispersion for the bcc metals Mo and Cr is calculated based on the pair potentials obtained from cohesive energies and the Slater-Kirkwood- type three body interaction. In the calculation of the pair potentials the Möbius transform in the number theory is used and the cohesive energy is evaluated by the LMTO method. The results show a good agreement with inelastic neutron scattering data and indicate that the three-body interaction is necessary to account for the phonon dispersion.     

Effects of surface charges on phonon properties and thermal conductivity in GaN nanofilms

Surface charges can modify the elastic modulus of nanostructure, leading to the change of the phonon and thermal properties in semiconductor nanostructure. In this work, the influence of surface charges on the phonon properties and phonon thermal conductivity of GaN nanofilm are quantitatively investigated. In the framework of continuum mechanics,the modified elastic modulus can be derived for the nanofilm with surface charges. The elastic model is presented to analyze the phonon properties such as the phonon dispersion relation, phonon group velocity, density of states of phonons in nanofilm with the surface charges. The phonon thermal conductivity of nanofilm can be obtained by considering surface charges. The simulation results demonstrate that surface charges can significantly change the phonon properties and thermal conductivity in a GaN nanofilm. Positive surface charges reduce the phonon energy and phonon group velocity but increase the density of states of phonons. The surface charges can change the size and temperature dependence of phonon thermal conductivity of GaN nanofilm. Based on these theoretical results, one can adjust the phonon properties and temperature/size dependent thermal conductivity in GaN nanofilm by changing the surface charges.     

Hole-interface optical phonon relaxation rates with valence band-mixing effects

We theoretically investigate the hole-interface optical phonon scattering rates for a InGaAs-AlGaAs quantum well structure, taking into account the valence-band mixing. The dispersion relation and the electrostatic potentials for interface optical phonon modes are obtained based on the macroscopic dielectric continuum model. For the hole dispersion relation, the Luttinger-Kohn Hamiltonian is used. The hole-interface optical phonon interaction is evaluated by the Fermi's golden rule taking into account the Bloch overlap factor.Our results show that the hole-interface phonon scattering rates within the parabolic band approximation are different from those including valence band mixing effects. Especially, in the low energy region, the hole-interface phonon scattering rates within the parabolic band approximation are overestimated very significantly.     

Molecular dynamics study on the thermal conductivity and mechanical properties of boron doped graphene

We investigated the effects of boron atoms substitution on the thermal conductivity and mechanical properties of single-layer graphene using the non-equilibrium molecular dynamics (NEMD) simulations. By performing the uniaxial tension simulations, we observed that substituted boron atoms slightly decrease the elastic modulus and tensile strength of graphene. On the other hand, it was observed that only 0.75% concentration of boron atoms in graphene reduces the thermal conductivity of graphene by more than 60% and leads to vanishing chirality effect.