Magnetism of single-walled silicon carbide nanotubes doped by boron,nitrogen and oxygen

We calculated, using spin polarized density functional theory, the electronic properties of zigzag (10,0) and armchair (6,6) semiconductor silicon carbide nanotubes (SiCNTs) doped once at the time with boron, nitrogen, and oxygen. We have looked at the two possible scenarios where the guest atom X (B, N, O), replaces the silicon X_Si, or the carbon atom X_C, in the unit cell. We found that in the case of one atom B @ SiCNT replacing a carbon atom position annotated by B_C exhibits a magnetic moment of 1 μ_B/cell in both zigzag and armchair nanotubes. Also, B replacing Si, (B_Si), induce a magnetic moment of 0.46 μ_B/cell in the zigzag (10,0) but no magnetic moment in armchair (6,6). For N substitution; (N_C) and (N_Si) each case induce a magnetic moment of 1 μ_B/cell in armchair (6,6), while N_Si give rise to 0.75 μ_B/cell in zigzag (10,0) and no magnetic moment for N_C. In contrast the case of O_C and O_Si did not produce any net magnetic moment in both zigzag and armchair geometries.     

Size-dependent electronic structures of boron carbonitride (BC2N) nanotubes. A DFT approach

The electronic structures and physical properties of zigzag BC₂N (n,0; n = 4–10) and armchair BC₂N (n,m; n = m = 4–10) nanotubes (type III) are studied by using density functional theory with the generalized gradient approximation. From a comparison of the binding energies, it is inferred that in the large diameter BC₂N nanotubes, the zigzag form is thermally more stable than the armchair form. BC₂N nanotubes (with the exception of (4,0) which is conductor) are gapless semiconductors. Depend on the chirality index, the zigzag forms of BC₂N nanotubes have narrower band gap than the armchair form. Semiconductor character in the studied BC₂N nanotubes is due to contribution of p electrons in the Fermi level. Mulliken population analyses show that significant amounts of electron charge are transferred between atoms; which suggests the existence of polar covalent bonds in the BC₂N nanotubes.     

石墨带的晶格动力学研究

基于晶格动力学理论,采用力常数模型,计算了石墨带的声子色散关系、振动模式密度和比热.计算结果表明,石墨带的声子谱特征介于一维碳纳米管和二维石墨片之间.扶手椅型和锯齿型石墨带的中、高频声子支分别与锯齿型和扶手椅型碳纳米管的类似.由于声子限域效应,低频声子支随着石墨带带宽的改变出现明显的频移现象.振动模式密度在高频区几乎不敏感于带宽,而低频区的峰位随着带宽的增加而逐渐向低频移动.此外,无论是在低温还是高温,比热都随着带宽的增加而逐渐降低,呈现量子尺寸效应.在300K时,比热可以拟合成C_V=C_Vg+A/n,其中C_Vg为石墨片的热容,而A/n项反映了石墨带中边缘效应对比热的影响. 关键词： 石墨带 声子色散关系 比热     

Encapsulation of small fullerenes into nitrogenated holey nanotubes: a density functional theory study

Encapsulation of fullerene into nanotubes based on a C₂N sheet, known as nitrogenated holey graphene, was investigated using density functional theory. The structural and electronic properties of these carbon hybrid materials, consisting of nitrogenated holey nanotubes and a small C₂₀ fullerene, were studied. The formation energies showed that encapsulation of the fullerene into the nitrogenated holey nanotube is an exothermic process. To characterise the electronic properties, the electronic band structure and density of states of armchair and zigzag nitrogenated holey nanotubes were calculated. Filling these nanotubes with the C₂₀ fullerene resulted in a p-type semiconducting character. The energy band gap of the nitrogenated holey nanotubes decreased with fullerene encapsulation. The results are indicative of the possibility of band gap engineering by encapsulation of small fullerenes into nitrogenated holey nanotubes.     

First-principles study of single-walled armchair Cx(BN)y nanotubes

The structural and electronic properties of the armchair C_x(BN)_y nanotubes are studied using the density functional theory with a generalized gradient approximation. The results show that the properties of the C_x(BN)_y nanotubes are intermediate between those of carbon nanotubes and BN nanotubes, and also adjustable by their radius, ratio of carbon component, and configurations.     

Structure and properties of BeO nanotubes

The structure of a new non-carbon (beryllium oxide BeO) nanotube consisting of a rolled-up graphene sheet is proposed, and its physical properties are described. Ab initio calculations of the binding energy, the electronic band structure, the density of states, the dependence of the strain energy of the nanotube on the nanotube diameter D, and the Young’s modulus Y for BeO nanotubes of different diameters are performed in the framework of the density functional theory (DFT). From a comparison of the binding energies calculated for BeO nanotubes and crystalline BeO with a wurtzite structure, it is inferred that BeO nanotubes can be synthesized by a plasma-chemical reaction or through chemical vapor deposition. It is established that BeO nanotubes are polar dielectrics with a band gap of ～5.0 eV and a stiffness comparable to that of the carbon nanotubes (the Young’s modulus of the BeO nanotubes Y _BeO is approximately equal to 0.7Y _C, where Y _C is the Young’s modulus of the carbon nanotubes). It is shown that, for a nanotube diameter D > 1 nm, the (n, n) armchair nanotubes are energetically more favorable than the (n, 0) zigzag nanotubes.     

单壁碳纳米管弹性性质的羟基接枝效应

用分子动力学方法研究了端口接枝不同数量羟基对扶手椅型和锯齿型单壁碳纳米管弹性模量的影响.结果表明,未接枝的扶手椅型(5, 5),(10,10)管和锯齿型(9, 0),(18, 0)管杨氏模量分别为948,901和804,860GPa.在接枝2—8个羟基情况下,锯齿型单壁碳纳米管拉伸杨氏模量基本不随接枝数量增加发生变化,而扶手椅单壁碳纳米管则不同,接枝状态下的弹性模量比未接枝状态小很多,但接枝一定数量后,其杨氏模量又略增到某一稳定值.分别从接枝后碳纳米管变形电子密度等值线结构、C—C键长和系统结合能变化规律等方面,对单壁碳纳米管弹性模量的接枝效应进行了分析. 关键词： 碳纳米管 羟基 接枝效应 杨氏模量     

Ab initio study of dielectric function of C-substituted single walled boron nanotubes

We report dielectric function related optical properties namely dielectric constant, static dielectric constant, and absorption coefficients of C-substituted hexagonal boron nanotubes. The optical properties were computed for parallel and perpendicular polarized light in the framework of density functional theory. In this regard, three models of BNTs namely armchair (3,3), zigzag (5,0), and chiral (4,2) have been undertaken for probing the effect of carbon impurity. Our calculations show high dielectric constant of armchair and chiral BNTs for parallel polarized light and magnitude becomes smaller for higher impurity concentration, while zigzag BNT exhibits reverse trend for high impurity concentration. For perpendicular polarized light, the magnitude of dielectric constant ε ₁(ω) is decreased and shifts at higher frequencies. The absorption is revealed highest for armchair followed by zigzag and chiral BNTs independent of impurity concentration. The intensity of absorption gets weaken for higher concentration. The chiral BNTs show smaller but uniform absorption in smaller frequency range results in uniform field emission. These findings are also compared with available experimental and theoretical results. These metallic nanotubes are promising candidate as interconnects for nanodevices as well as field emission devices.     

Derivation of a universal estimate for the stiffness of carbon nanotubes

An algorithm has been developed based on numerical simulation to relate physical geometry to the Young’s modulus of symmetric and asymmetric single-walled carbon nanotubes (SWCNTs). A large number of finite element results for the stiffness of SWCNTs has been categorized into three main classes (i.e., armchair, zigzag and chiral) and the best curve fitting function has been obtained to describe the relation between the geometry of SWCNTs and their stiffness. For two standard configurations of carbon nanotubes (i.e., armchair and zigzag), four equations referring to geometry parameters (n, m) and diameter (d) have been introduced. To find the size dependence of asymmetric nanotubes, three-dimensional surfaces of stiffness (E(n, m)) have been used. However, since the stiffness of asymmetric nanotubes depends upon n and m, it was impossible to define any diameter dependency. To account for the hidden mechanical behavior of asymmetric SWCNTs, a new physical factor (CF) was introduced as the major novelty in this work. The proposed CF converts any asymmetric geometry (n, m) into a value between 0 and 1. The CF for a chiral nanotube can imply the percentage of similarity in its mechanical properties to the two standard symmetric configurations. Based on the CF concept, a new equation is derived to predict the Young’s modulus of asymmetric carbon nanotubes based on the symmetric prediction of standard models. The new physical factor (CF) which is developed in this study can be useful for the characterization of SWCNTs and the selection of all configurations.     

The interaction of Cr(CO)3 on the (n, 0) nanotube side-walls: a density functional study through a cluster model approach

Density functional calculations have been performed to investigate the functionalization of single-wall carbon nanotubes (SWNTs) with the Cr(CO)₃ metal fragment, employing extended molecular models. A circumcoronene molecule (C₅₄H₁₈), made by the fusion of 19 hexagonal carbon rings, can be regarded as a fragment of a graphene sheet. To reproduce the curvature of the SWNT surface, suitable geometric constraints have been imposed on the C₅₄H₁₈ model, freezing the positions of the outer hydrogens along the directions of the nanotube C-C bonds. Geometry optimizations have then been performed under this constraint on the Cr(CO)₃-C₅₄H₁₈ complexes, pointing out the most favourable coordination sites on the hexagonal rings of the carbon atom surface and the electronic properties of the resulting system. The effect of the curvature on the metal coordination to nanotubes has been analysed by investigating the interaction of the Cr(CO)₃ metal complex with the C₅₄H₁₈ molecules, modelling (n, 0) nanotubes with different degrees of curvature, i.e. with various values of the chiral vector (n, 0).     

Consideration of mechanical properties of single-walled carbon nanotubes under various loading conditions

In this article, mechanical properties of single-walled carbon nanotubes (SWCNTs) with various radiuses under tensile, compressive and lateral loads are considered. Stress–strain curve, elastic modulus, tensile, compressive and rotational stiffness, buckling behaviour, and critical axial compressive load and pressure of eight different zigzag and armchair SWCNTs are investigated to figure out the effect of radius and chirality on mechanical properties of nanotubes. Using molecular dynamic simulation (MDS) method, it can be explained that SWCNTs have higher Young’s modulus and tensile stiffness than compressive elastic modulus and compressive stiffness. Critical axial force of zigzag SWCNT is independent from the radius, but that of armchair type rises by increasing of radius, also these two types show different buckling modes.     

Structural and electronic properties of endohedral doped SWCNTs: A DFT study

The structural and electronic properties of semiconductors (Si and Ge) and metal (Au and Tl) atoms doped armchair (n, n) and zigzag (n, 0); n=4–6, single wall carbon nanotubes (SWCNTs) have been studied using an ab-initio method. We have considered a linear chain of dopant atoms inside CNTs of different diameters but of same length. We have studied variation of B.E./atom, ionization potential, electron affinity and HOMO–LUMO gap of doped armchair and zigzag CNTs with diameter and dopant type. For armchair undoped CNTs, the B.E./atom increases with the increase in diameter of the tubes. For Si, Ge and Tl doped CNTs, B.E./atom is maximum for (6, 6) CNT whereas for Au doped CNTs, it is maximum for (5, 5) CNTs. For pure CNTs, IP decreases slightly with increasing diameter whereas EA increases with diameter. The study of HOMO–LUMO gap shows that on doping metallic character of the armchair CNTs increases whereas for zigzag CNTs semiconducting character increases. In case of zigzag tubes only Si doped (5, 0), (6, 0) and Ge doped (6, 0) CNTs are stable. The IP and EA for doped zigzag CNTs remain almost independent of tube diameter and dopant type whereas for doped armchair CNTs, maximum IP and EA are observed for (5, 5) tube for all dopants.     

Effects of carbon nanotube structures on mechanical properties

This paper describes a structural mechanics approach to modelling the mechanical properties of carbon nanotubes (CNTs). Based on a model of truss structures linked by inter-atomic potentials, a closed-form elastic solution is obtained to predict the mechanical properties of single-walled carbon nanotubes (SWNTs). Moreover, the elastic modulus of multi-walled carbon nanotubes (MWNTs) is also predicted for a group of the above mentioned SWNTs with uniform interval spacing. Following the structural mechanics approach, the elastic modulus, Poissons ratio, and the deformation behaviors of SWNTs were investigated as a function of the nanotube size and structure. Poissons ratio of SWNTs shows a chirality dependence, while the elastic modulus is insensitive to the chirality. The disposition of the strain energy of bonds shows quite a difference between the zigzag and armchair tubes subjected to axial loading. A zigzag tube is predicted to have a lower elongation property than an armchair tube. PACS 62.20-x; 62.20.Dc; 62.25+g     

Cyclacenes and short zigzag nanotubes with alternanting Ge―C bonds: theoretical impacts of Ge on the ground state,strain, and band gap

[6]_n Cyclacenes and short zigzag [6]_n carbon nanotubes (n = 5–10) have unstable singlet open‐shell (S_os) ground states. We have boosted their stability by implementing altering Ge―C bonds that acquire S_cs ground states with larger band gap (ΔE_LUMO–HOMO) at B3LYP and BPW91 levels of theory. Fascinatingly, homodesmic calculations indicated release of almost two folds of strain energy upon substitution of germanium for carbon. This may turn the green lights for synthesis of germanium–carbon cyclacenes and short zigzag nanotubes. Copyright © 2014 John Wiley & Sons, Ltd.     

Mechanical properties of single- and double-walled carbon nanotubes under hydrostatic pressure

Based on a molecular mechanics coupled with atomistic-based continuum theory, a closed-form formula is presented to examine the elastic properties of single- and double-walled carbon nanotubes subjected to hydrostatic pressure. Following the present model, the effects of the armchair and zigzag CNT structures on the pressure behavior are theoretically investigated. The computational result indicates that the bulk modulus is less sensitive to the chiral structures except for very small tube diameters. Moreover, closed-end nanotubes under hydrostatic pressure exhibit a larger bulking modulus than open ended nanotubes. The cap of the zigzag tubes has a larger effect on the bulk modulus when compared to the armchair tubes, especially in small diameter nanotubes. The predicted strain and the bulk modulus are in good agreement with existing theoretical results. PACS 61.46.+w; 62.20.Dc; 62.20.-x; 62.25.+g     

The calculation of energy gaps in small single-walled carbon nanotubes within a symmetry-adapted tight-binding model

This paper studies in detail the electronic properties of the semimetallic single-walled carbon nanotubes by applying the symmetry-adapted tight-binding model.It is found that the hybridization of π-σ states caused by the curvature produces an energy gap at the vicinity of the Fermi level.Such effects are obvious for the small zigzag and chiral single-walled carbon nanotubes.The energy gaps decrease as the diameters and the chiral angles of the tubes increase,while the top of the valence band and the bottom of the conduction band of armchair tubes cross at the Fermi level.The numeral results agree well with the experimental results.     

Gallium doped in armchair and zigzag models of boron phosphide nanotubes (BPNTs): A NMR study

The electrical properties and NMR parameters of the pristine and Ga-doped structures of two representative (8, 0) zigzag and (4, 4) armchair of boron phosphide nanotubes (BPNTs) have been investigated. The structural geometries of above nanotubes have been allowed to relax by optimization and then the isotropic and anisotropic chemical shielding parameters (CSI and CSA) of ¹¹B and ³¹P have been calculated based on DFT theory. The results reveal that the influence of Ga-doping was more significant on the geometries of the zigzag model than the armchair one. The difference of band gap energies between the pristine and Ga-doped armchair BPNTs was larger than the zigzag model. Significant differences of NMR parameters of those nuclei directly contributed to the Ga-doping atoms have been observed.     

On the structural properties of B–C–N nanotubes

We apply a first-principles method, based on the density functional theory, to calculate the structural stability of B–C–N armchair nanotubes, comparing such results with the ones obtained for zigzag configuration. Analysis of the corresponding strain energies confirm that the stability of BC₂N nanotubes is independent of their chirality and demonstrate that such nanostructures have lower strain than BCN and carbon nanotubes. The results show that the formation energy decreases with the tube diameter and indicate that the most stable nanotubes have the maximum number of B–N and C–C bonds. Therefore, from the experimental point of view, larger diameter BC₂N model-I nanotubes should be more probable to be synthesized.     

Carbon nanoribbons and nanotubes based on δ-graphyne: A first-principles study

As a stable allotropy of two-dimensional (2D) carbon materials, δ-graphyne has been predicted to be superior to graphene in many aspects. Using first-principles calculations, we investigated the electronic properties of carbon nanoribbons (CNRs) and nanotubes (CNTs) formed by δ-graphyne. It is found that the electronic band structures of CNRs depend on the edge structure and the ribbon width. The CNRs with zigzag edges (Z-CNRs) have spin-polarized edge states with ferromagnetic (FM) ordering along each edge and anti-ferromagnetic (AFM) ordering between two edges. The CNRs with armchair edges (A-CNRs), however, are semiconductors with the band gap oscillating with the ribbon width. For the CNTs built by rolling up δ-graphyne with different chirality, the electronic properties are closely related to the chirality of the CNTs. Armchair (n, n) CNTs are metallic while zigzag (n, 0) CNTs are semiconducting or metallic. These interesting properties are quite crucial for applications in δ-graphyne-based nanoscale devices.     

Structure and electronic properties of native and defected gallium nitride nanotubes

Structure and electronic properties of GaN nanotubes (GaNNTs) are investigated by using ab initio density functional theory. By full optimization, the optimized structures (bond-lengths and angles between them) of zigzag GaNNTs (n,0) and armchair GaNNTs (n,n) (4<n<11) are calculated. The difference between nitrogen ring diameter and gallium ring diameter (buckling distance) and semiconducting energy gap in term of diameter for zigzag and armchair GaNNTs have also been calculated. We found that buckling distance decreases by increasing nanotube diameter. Furthermore, we have investigated the effects of nitrogen and gallium vacancies on structure and electronic properties of zigzag GaNNT (5,0) using spin dependent density functional theory. By calculating the formation energy, we found that N vacancy in GaNNT (5,0) is more favorable than Ga vacancy. The nitrogen vacancy in zigzag GaNNT induces a 1.0μB magnetization and makes a polarized structure. We have shown that in polarized GaNNT a flat band near the Fermi energy splits to occupied spin up and unoccupied spin down levels.