Phonon trigonal warping effect in graphite and carbon nanotubes

The one-dimensional structure of carbon nanotubes leads to quantum confinement of the wave vectors for the electronic states, thus making the double resonance Raman process selective, not only of the magnitude, but also of the direction of the phonon wave vectors. This additional selectivity allows us to reconstruct the phonon dispersion relations of 2D graphite, by probing individual single wall carbon nanotubes of different chiralities by resonance Raman spectroscopy, and using different laser excitation energies. In particular, we are able to measure the anisotropy, or the trigonal warping effect, in the phonon dispersion relations around the hexagonal corner of the Brillouin zone of graphite.     

Ab initio simulations on the atomic and electronic structure of single-walled BN nanotubes and nanoarches

To simulate the perfect single-walled boron nitride nanotubes and nanoarches with armchair- and zigzag-type chiralities and uniform diameter of ∼5 nm, we have constructed their one-dimensional (1D) periodic models. In this study, we have compared the calculated properties of nanotubes with those for both hexagonal and cubic phases of bulk: bond lengths, binding energies per B-N bond, effective atomic charges as well as parameters of total and projected one-electron densities of states. For both phases of BN bulk, we have additionally verified their lattice constants. In the density functional theory (DFT), calculations performed using formalism of the localized Gaussian-type atomic functions as implemented in the CRYSTAL-06 code we have applied Hamiltonians containing either PWGGA or hybrid (DFT+HF) B3PW exchange-correlation functionals. After calculation of Hessian matrix for the optimized structures of BN bulk (both phases) and nanotubes (both chiralities) using the CRYSTAL code we have estimated their normal phonon modes within the harmonic approximation. Applying both atomistic and continuum models we have calculated the elastic energies and moduli for SW BN nanoarches. Our calculations clearly show a reproducibility of the atomic structure, effective charges and total energy, as well as phonon and elastic properties when using either PWGGA or hybrid B3PW Hamiltonians. On other hand, there is a high sensitivity of the discrete energy spectra parameters (including band gap) to the choice of the first principles approach (the hybrid method reproduce them noticeably better).     

Ab initio lattice dynamics and elastic constants of ZrC

Ab initio calculations and a direct method are applied to derive the phonon dispersion relations and phonon density of states for the ZrC crystal. The results are in good agreement with neutron scattering data. The force constants are determined from the Hellmann-Feynman forces induced by atomic displacements in a 222 supercell. The elastic constants are found using the deformation method and successfully compare with experimental data. Received 2 July 1999 and Received in final form 26 November 1999     

单壁碳纳米扶手椅、锯齿管声子色散关系的计算

引用石墨经验力常数计算碳纳米管声子色散关系时，必须处理由二维平面卷曲形成三维实体纳米管所引入的问题. 报道对一系列扶手椅和锯齿单壁碳纳米管计及卷曲效应的声子色散关系的计算结果. 基于实际的数值计算结果，以及对单壁碳纳米扶手椅、锯齿管结构的对称性分析，讨论了Brillouin区中心Γ点晶格振动模的分类. 关键词： 碳纳米管 声子色散关系     

Vibrational properties of single-wall BC3 nanotubes

The phonon dispersions of single-wall BC₃ nanotubes with any chirality are calculated within a symmetry-based force constant model of the lattice dynamics. Based on the non-symmorphic symmetry group of the BC₃ tubes, the symmetries and number of the Raman- and infrared-active modes at Γ point of the one-dimensional Brillouin zone are given. The neighbor atom-atomic interaction force constants are recalculated by fitting them to the experimental phonon energy-dispersion curves of honeycomb BC₃ sheet. The frequencies of the optically active modes are presented as the function of diameters and chiralities for BC₃ tubes. The obtained phonon density-of-states spectra, phonon dispersion relations, and vibrational patterns of the zone-center phonons are presented and discussed in detail. The calculated frequencies of infrared-active modes are compared with the experimental values reported in the literature. The results provide comprehensive information about the vibrational properties of the BC₃ tubes and shed light on the interpretation of Raman scattering and infrared spectroscopies.     

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.     

Phonon dispersions in graphene sheet and single-walled carbon nanotubes

In the present research paper, phonons in graphene sheet have been calculated by constructing a dynamical matrix using the force constants derived from the second-generation reactive empirical bond order potential by Brenner and co-workers. Our results are comparable to inelastic X-ray scattering as well as first principle calculations. At Γ point, for graphene, the optical modes (degenerate) lie near 1685 cm^???1. The frequency regimes are easily distinguishable. The low-frequency (ω→ 0) modes are derived from acoustic branches of the sheet. The radial modes can be identified with ω→ 584 cm^???1. High-frequency regime is above 1200 cm^???1 (i.e. ZO mode) and consists of TO and LO modes. The phonons in a nanotube can be derived from zone folding method using phonons of a single layer of the hexagonal sheet. The present work aims to explore the agreement between theory and experiment. A better knowledge of the phonon dispersion of graphene is highly desirable to model and understand the properties of carbon nanotubes. The development and production of carbon nanotubes (CNTs) for possible applications need reliable and quick analytical characterization. Our results may serve as an accurate tool for the spectroscopic determination of the tube radii and chiralities.     

Lattice dynamics of black phosphorus

Phonon dispersion curves of black phosphorus are calculated using the force constant model, in which the valence force model is assumed for intralayer interatomic interactions and the axially symmetric force model for interlayer ones. Ten force constants in all are determined by “least-squares” fitting to optical Г-phonons and the symmetry relations between sound velocities. The phonon dispersion curves calculated are applied successfully to interpretation of experiments on the first and second order Raman spectra, effective Debye temperature, and inelastic neutron scattering. Large discrepancy between the calculated and observed linear compressibilities exists.     

一种计算半导体力常数的简单途径——对GaAs(111)-2×2表面声子研究的应用

本文利用成键轨道近似简化电子能带结构能量的计算,导出了任意杂化下半导体力常数的解析表达式。通过对一些材料声子色散曲线的计算和实验结果的比较,表明该方法是简单有效的。作者将其应用于GaAs(111)-2×2表面声子的研究,得到了该表面的强局域声子模的色散曲线。 关键词：     

A symmetry-adapted force-constant lattice-dynamical model for single-walled carbon nanotubes

We develop a lattice-dynamical model based on the screw symmetry of single-walled carbon nanotubes that allows for reducing the size of the dynamical matrix to six, for all tube chiralities. The model uses force constants derived from fitting to the phonon dispersion of 2D graphite. We present the calculation procedure in a clear and transparent way, making the model easier to follow. We calculate the phonon dispersions of a number of nanotubes of different chiralities. The splitting of two highest Raman active modes and the radial breathing mode frequency are studied by changing the tube diameter and chirality.     

Phonon dispersion relations and soft modes of 4? carbon nanotubes

The phonon dispersion relations of three kinds of 4~? carbon nanotubes are calculated by using the density functional perturbation theory. It is found that the frequencies of some phonon modes are very sensitive to the smearing width used in the calculations, and eventually become negative at low electronic temperature. Moreover, two kinds of soft modes are identified for the (5,0) tube which are quite different from those reported previously. Our results suggest that the (5,0) tube remains metallic at very low temperature, instead of the metallic-semiconducting transition claimed before.     

TiC lattice dynamics from ab initio calculations

Ab initio calculations and a direct method have been applied to derive the phonon dispersion curves and phonon density of states for the TiC crystal. The results are compared and found to be in a good agreement with the experimental neutron scattering data. The force constants have been determined from the Hellmann-Feynman forces induced by atomic displacements in a supercell. The calculated phonon density of states suggests that vibrations of Ti atoms form acoustic branches, whereas the motion of C atoms is confined to optic branches. The elastic constants have been found using the deformation method and compared with the results obtained from acoustic phonon slopes. Received 23 February 1998     

Mg2Sn电子结构及热力学性质的第一性原理计算

采用基于第一性原理的赝势平面波方法系统地计算了Mg₂Sn基态的电子结构、弹性常数和热力学性质.计算结果表明Mg₂Sn的禁带宽度为0.1198eV.运用线性响应方法确定了声子色散关系和态密度,得出Mg₂Sn的热力学性质如等容比热和德拜温度.计算Mg₂Sn的热导率并与实验数据相比较. 关键词： 第一性原理 电子结构 弹性常数 热力学性质     

毛刺状竹节结构氮化硼纳米管的合成与生长机理

以非晶硼和氧化镍纳米颗粒为原料,在氨气中1100 oC下合成了毛刺状竹节结构的氮化硼纳米管. 利用X射线衍射和透射电镜研究了氮化硼纳米管的结构和形貌. 竹节结构纳米管表面的毛刺是六方氮化硼的纳米薄片. 提出了一种基于固态硼和气态二氧化硼扩散的毛刺形貌生长机理.     

Lattice dynamics and inelastic neutron scattering experiments on andalusite,Al2SiO5

We report coherent inelastic neutron scattering measurements of the phonon dispersion relations and lattice dynamics shell model calculations of several microscopic and macroscopic properties of andalusite, Al₂SiO₅. Andalusite has an orthorhombic structure with 32 atoms/unit cell. The inelastic neutron scattering measurements (up to energy transfers of 45 meV) were carried out using the triple axis spectrometer at Dhruva reactor, India using a single crystal of andalusite and the phonon dispersion relations along the [100] direction have been measured. The shell model calculations have been used to compute the crystal structure, elastic constants, phonon frequencies, dispersion relations, density of states and the specific heat. The calculated results are in good agreement with available experimental data. The computed one-phonon neutron scattering structure factors based on the shell model have been very useful in the planning and analysis of the inelastic neutron scattering experiments.     

铬银氧共掺n型，p型特性氮化硼纳米管第一性原理研究

基于第一性原理的平面波超软赝势法对(6, 0)单壁氮化硼纳米管、Cr掺杂、Ag掺杂、以及Cr-O共掺纳米管进行电子结构和光学性质的计算。结果表明：Cr掺杂和Cr-O共掺体系相比于本征体系的带隙值均减小,掺杂体系的导带底穿过费米能级从而实现了氮化硼纳米管的n型掺杂。Ag掺杂实现了纳米管的p型掺杂。本征氮化硼纳米管、Ag掺杂、Cr掺杂、以及Cr-O共掺纳米管的静态介电常数分别为1.17、1.61、1.32和1.48,相对于本征体系静介电性能有所提高。     

Phonon density of states in nanocrystalline<Superscript>57</Superscript>Fe

The Born-von Karman model is used to calculate phonon density of states (DOS) of nanocrystalline bcc Fe. It is found that there is an anisotropic stiffening in the interatomic force constants and hence there is shrinking in the nearest-neighbour distances in the nanophase. This leads to additional vibrational modes above the bulk phonons near the bottom of the phonon band. It is found that the high energy phonon modes of nanophase Fe are the surface modes. The calculated phonon DOS closely agree with the experimental data except a peak at 37 meV. The calculated phonon dispersion relations are also compared with those of the bulk phonons and anomalous behaviour is discussed in detail. The specific heat in nanophase enhances as compared to bulk phase at low temperatures and the calculated Debye temperature Θ_D agrees with the experimental results. It is predicted that the nanocrystalline Fe may consist of about 14 GPa pressure     

Three-body interaction and phonon dispersion relations in aluminium

Based on an ab initio cohesive energy calculation and a model of three-body interaction, the pair potential can be calculated using the Möbius inversion theorem in the theory of numbers. Then the atomic force constants and the phonon dispersion for A1 are evaluated both with and without three-body interaction. Compared with experiments, the results show that taking the three-body interaction into account considerably improves the dispersions. Contrary to previous work, the method for calculating the atomic force constants and phonon dispersions presented here is simple, with only two adjustable parameters.     

Structural and phonon dynamical properties of perovskite manganites: (Tb, Dy, Ho)MnO3

A shell model has been used to study the structure, phonon dynamics and phase coexistence of perovskite manganites RMnO₃ (R=Tb, Dy, Ho). The calculated crystal structure, Raman and IR frequencies and specific heats are found to be in good agreement with the available experimental data. The phonon density of states, elastic constants, elastic stiffness, shear constants and phonon dispersion curves have been computed for these manganites. A zone center imaginary A_u mode is revealed in these phonon dispersion curves, which indicates the occurrence of the metastability of the perovskite phase. The Gibbs free energy values calculated as a function of temperature and pressure for RMnO₃ in the orthorhombic phase, when compared with those of the hexagonal phase, reveal the possibility of coexistence of these two phases in the present multiferroic manganites under ambient conditions.