Nonchiral BN Haeckelite nanotubes

A new class of boron-nitrogen (BN) nanotubes composed of tetragons, pentagons, hexagons, heptagons, and octagons is considered. By analogy with carbon nanotubes of the same topological structure, these nanotubes were called Haeckelites. The geometry, energetics, and electronic properties were studied in detail for two regular mutual arrangements of the polygons. It was found that Haeckelite nanotubes are dielectrics with the energy gap E_g = 3.24–4.09 eV. As the nanotube diameter increases, the energy gap E_g decreases, approaching the value for the corresponding planar Haeckelite layer. The ground-state energy of the Haeckelite BN nanotubes is 0.3 eV/atom higher than that of well-known hexagonal BN nanotubes.     

Geometric structure and electronic properties of planar and nanotubular BN structures of the Haeckelite type

Planar and nanotubular structures that are based on boron and nitrogen and consist of tetragons, hexagons, and octagons are considered. By analogy with carbon nanoobjects of the same topology, these structures are referred to as Haeckelites. The geometric, electronic, and energy properties are thoroughly investigated for two variants of the regular mutual arrangement of the polygons. It is established that planar and nanotubular BN structures of the Haeckelite type are dielectrics with a band gap E _g ∼ 3.2–4.2 eV, which is less than the band gap E _g for BN nanotubes consisting only of hexagons. The cohesive energy of the BN nanotubes under investigation exceeds the cohesive energy of BN hexagonal nanotubes by 0.3 eV/atom.     

Quantum-chemical calculations of the piezoelectric characteristics of boron nitride and carbon nanotubes

The piezoelectric characteristics of boron-nitride and carbon nanotubes were calculated. The electronic structure of nanotubes was studied using the quantum-chemical semiempirical MNDO method within a molecular-cluster model. The piezoelectric constants e _zzz, e _xzz, and e _xxx of boron nitride nanotubes of two structural modifications (n, n) (n = 5, 6, ..., 9) and (n, 0) (n = 6, 7, ..., 12) were calculated. The values of the piezoelectric constants e _zzz of tubular boron nitride are found to be close in order of magnitude to the respective values obtained using nonempirical calculation methods. The piezoelectric constant e _xzz of a (6, 6) carbon nanotube doped with substitutional point defects was calculated.     

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.     

超长(n,n)型碳纳米管的密度泛函理论研究

用密度泛函B3LYP/3-21G(d)方法,并利用周期边界条件,研究了n=2—20不同管径的超长(n, n)型单壁碳纳米管的结构、能量、能带结构和能隙.结果表明,管径和能量(或生成焓)都随n有很好的变化规律,并可拟合成很好的解析函数.当n为2和3时,碳纳米管的能隙分别为1.836eV和0.228eV,呈半导体特征,且具有间接带隙;当n=4—20时,能隙介于0.027 eV和0.079 eV之间,呈较强的金属性,且具有直接带 关键词： 扶手椅型碳纳米管 周期边界条件(PBC) 超长模型 能带     

C在不同位置掺杂(n,n)型BN纳米管的密度泛函研究

用密度泛函B3LYP/3-21G(d)方法,并利用周期边界条件,研究了C原子在不同位置掺杂的(n,n)型BN纳米管的结构与性质.揭示了几何结构特征、能量、稳定性和能带结构的变化规律.研究了C原子在B位或N位置分别掺杂的BN纳米管的模型(掺杂浓度x=1/(4n),n=3—9),部分B位掺杂管发生了变形,而所有N位掺杂管则几乎不变形,而且N位比B位的掺杂能更低(管更稳定),B位掺杂管的能隙为1.054—2.411 eV,N掺杂管的能隙为0.252—1.207 eV,所有掺杂管都是半导体,所有掺杂管都具有直接带隙.     

Electronic structures of deformed B2C nanotubes under tensile strain

The vibrational properties and the band gaps of new B₂C nanotubes have been studied by the first principles calculations. It is found that (1) there is a typical Raman-active radial-breathing vibrational mode (RBM), which is similar to that of carbon nanotubes. The RBM frequency decreases in a linear proportion to the inverse diameter, whose variation slope depends on the types of B₂C nanotubes. (2) Under an applied tensile strain, the band gap of B₂C tubes is found to change greatly. For example, their band gaps can decrease to zero with increasing tensile strain for the (n, 0) B₂C tubes with odd n, showing clearly a metal–insulator transition, which cannot happen for the (n, 0) B₂C tubes with even n and the (0, n) B₂C tubes.     

Symmetry and models of single-walled TiO<Subscript>2</Subscript> nanotubes with rectangular morphology

The formalism of line symmetry groups for one-periodic (1D) nanostructures with rotohelical symmetry has been applied for symmetry analysis of single-walled titania nanotubes (SW TiO₂ NTs) formed by rolling up the stoichiometric two-periodic (2D) slabs of anatase structure. Either six- or twelve-layer (101) slabs have been cut from TiO₂ crystal in a stable anatase phase. After structural optimization, the latter keeps the centered rectangular symmetry of initial slab slightly compressed along a direction coincided with large sides of elemental rectangles. We have considered two sets of SW TiO₂ NTs with optimized six- and twelve-layer structures, which possess chiralities (−n, n) and (n, n) of anatase nanotubes. To analyze the structural and electronic properties of titania slabs and nanotubes, we have performed their ab initio LCAO calculations, using the hybrid Hartree-Fock/Kohn-Sham exchange-correlation functional PBE0. The band gaps (Δɛ _gap ) and strain energies (E _strain ) of six-layer nanotubes have been computed and analyzed as functions of NT diameter (D _NT). As to models of 12-layer SW TiO₂ NTs of both chiralities, their optimization results in structural exfoliation, i.e., the multi-walled structure should be rather formed in nanotubes with such a number of atomic layers.     

Modified cascade model of resonant Raman scattering: a case study of UV Raman scattering in Zn1−xMnxO thin films

The cascade model of inelastic resonant Raman scattering considers real electronic states in the conduction band (CB) as intermediaries to explain multiple longitudinal optical (LO) Stokes‐shifted lines in the emission spectra. In this study, we report modification in the cascade model under conditions where the scattered photons after multiple transitions have energy lower than the bandgap (E_g) and give rise to higher order n‐LO lines. The higher order n‐LO lines involve electron transition between the trap levels, which are created by impurities or defects in the forbidden energy gap, and are analogous to the real electronic states in CB, depending on the density of defects or impurities in the lattice. The presence of traps in the forbidden gap (1) acts as virtual intermediate states giving rise to higher order n‐LO modes and (2) tends to decrease the radiative recombination probability leading to quenching of the luminescence emission and line width (full‐width at half‐maximum) broadening. Ultraviolet Raman scattering in Mn‐doped ZnO (Zn_1−xMn_xO) thin films were investigated and the experimental observations analyzed in the domain of the modified cascade model. Copyright © 2011 John Wiley & Sons, Ltd.     

On the existence and stability of double-walled armchair silicon carbide nanotubes

A systematic study of type 1 armchair double-walled SiC nanotubes (DWNTs) (n,n)@(m,m) (3≤n≤6;7≤m≤12) using the finite cluster approximation is presented. The geometries of the tubes have been spin optimized using the hybrid functional B3LYP (Becke’s three-parameter exchange functional and the Lee-Yang-Parr correlation functional) and the all-electron 3-21G* basis set. The study indicates that the stabilities of the double-walled SiC nanotubes are of the same order as those of single-walled SiC nanotubes suggesting the possibilities of experimental synthesis of both single-walled and double-walled SiC nanotubes. The binding energy per atom or the cohesive energy of the double-walled nanotubes depends not only on the number of atoms but also on the coupling of the constituent single-walled nanotubes. The formation energy of the DWNTs is found to be maximum when the interlayer separation is about 3.5 Å. The DWNTs (n,n)@(n+4,n+4) are found to have large formation energies. In particular, (5,5)@(9,9) DWNT is the most stable tube in our study with a binding energy per atom of 5.07 eV, the largest formation energy of 12.39 eV, an interlayer separation of 3.58 Å and a “band gap” of 1.97 eV. All double-walled SiC nanotubes are found to be semiconductors, with the band gaps decreasing from single-walled nanotubes to double-walled nanotubes.     

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.     

Ni原子链填充碳纳米管的能量、电子结构和磁性的第一性原理计算

在广义梯度近似(GGA)下,利用密度泛函理论(DFT)框架下的第一性原理投影缀加波(PAW)赝势方法,研究了单根Ni原子链填充扶手椅型(n,n)(5≤n≤9)单壁碳纳米管的能量、电子结构和磁性.结果表明(5,5)碳纳米管直径过小排斥Ni原子链的插入,(6,6)碳纳米管是容纳Ni原子链的最小碳纳米管,特别是Ni原子链位于其中心轴线上时的形成能最低.以Ni@(6,6)和Ni@(7,7)系统为例,计算并分析了其自旋极化能带结构,电子总态密度,分波态密度和磁性,发现Ni原子的3d态电子 关键词： Ni原子链 碳纳米管 电子结构 磁性能     

The lie algebra of invariant group of the KdV,MKdV, or Burgers equation

Let (E): u _t=H(u) denote the KdV, MKdV or Burgers equation, and U(s)=(D^j _s)/u _j, where D=d/dx, u _i=Dⁱ _u, s=s(u, u ₁, ..., u _n) is a polynomial of u _i with constant coefficients, be the generator of invariant group of equation (E). We prove in this paper that all such generators form a commutative Lie algebra, from which it follows that for any symmetry s(u, ..., u _n) of (E), the evolution equation u _t=s(u, ..., u _n) possesses an infinite number of symmetries (or conservation laws in the case of KdV and MKdV equations).     

Sonochemical growth of antimony sulfoiodide in multiwalled carbon nanotube

This paper presents for the first time the nanocrystalline, semiconducting ferroelectrics antimony sulfoiodide (SbSI) grown in multiwalled carbon nanotubes (CNTs). It was prepared sonochemically using elemental Sb, S and I in the presence of methanol under ultrasonic irradiation (35 kHz, 2.6 W/cm²) at 323 K for 3 h. The CNTs filled with SbSI were characterized by using techniques such as powder X-ray diffraction, scanning electron microscopy, energy dispersive X-ray analysis, high-resolution transmission electron microscopy, selected area electron diffraction, and optical diffuse reflection spectroscopy. These investigations exhibit that the SbSI filling the CNTs is single crystalline in nature and in the form of nanowires. It has indirect forbidden energy band gap E_gIf = 1.871(1) eV.     

Existence and stability of co-axial and meshed double-walled armchair silicon nanotubes

A systematic study of armchair double-walled Si nanotubes (DWNT) (n, n)@(m, m) (3≤n≤6; 7≤m≤12) using the finite cluster approximation is presented. The geometries of the tubes have been spin optimized with an all electron 3–21 G^⁎ basis set and the B3LYP functional. Analysis of the electronic structure properties of these tubes has also been performed with a larger basis set. The study indicates that the stabilities of the Si nanotubes are of the same order as those of single-walled Si nanotubes. It should be possible to experimentally synthesis both single-walled and double-walled Si nanotubes. The binding energy per atom or the cohesive energy of the nanotubes depends not only on the number of atoms but also on the coupling of the constituent single-walled nanotubes. Nanotubes with small interlayer separations, called meshed tubes, do not hold the coaxial cylindrical structure after optimization. The SiNTs (n, n)@(n+3, n+3) are found to have large formation energies and binding energies per atom. For example, (3, 3)@(6, 6), (4, 4)@(7, 7), (5, 5)@(8, 8), and (6, 6)@(9, 9) all have large binding energies per atom, around 3.7 eV/atom. All Si nanotubes are found to be semiconductors. However, the band gap, in general, is observed to decrease from single walled nanotubes to double walled nanotubes.     

Canonical realizations of the lie algebrasp(2n,R)

The generators of the Lie algebra of the symplectic groupsp(2n, R) are, recurrently, realized by means of polynomials in the quantum canonical variablesp _i andq _i. These realizations are skew-Hermitian, the Casimir operators are realized by constant multiples of identity elements, and, depending on the number of the canonical pairs used, they depend ond, d=1, 2, ...,n free real parameters.     

Effect of the degree of ordering of structural vacancies on the fine structure of the valence-band top in cubic boron nitride

The electronic energy structure of the defect system of c-BN_x with ZnS-type structure is calculated in the multiple-scattering theory by the local coherent potential method. The cluster version of the MT approximation is used to calculate the crystal potential. The effect of the relaxation of the crystal lattice on the electronic structure of nonstoichiometric boron nitride c-BN_0.75 is studied and a comparison is made with the electronic energy structure of c-BN in the same approximation. Fiz. Tverd. Tela (St. Petersburg) 39, 1064–1065 (June 1997)     

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.     

Eine scheinbare Abschwächung der Lokalitätsbedingung. II

If for a relativistic field theory the expectation values of the commutator (Ω|[A (x),A(y)]|Ω) vanish in space-like direction like exp {? const|(x-y ²|^α/2#x007D; with α>1 for sufficiently many vectors Ω, it follows thatA(x) is a local field. Or more precisely: For a hermitean, scalar, tempered fieldA(x) the locality axiom can be replaced by the following conditions 1. For any natural numbern there exist a) a configurationX(n): $$X_1 ,...,X_{n - 1} X_1^i = \cdot \cdot \cdot = X_{n - 1}^i = 0i = 0,3$$ with \(\left[ {\sum\limits_{i = 1}^{n - 2} {\lambda _i } (X_i^1 - X_{i + 1}^1 )} \right]^2 + \left[ {\sum\limits_{i = 1}^{n - 2} {\lambda _i } (X_i^2 - X_{i + 1}^2 )} \right]^2 > 0\) for all λ _i ≧0i=1,...,n?2, \(\sum\limits_{i = 1}^{n - 2} {\lambda _i > 0} \) , b) neighbourhoods of theX _i 's:U _i (X _i )?R ⁴ i=1,...,n?1 (in the euclidean topology ofR ⁴) and c) a real number α>1 such that for all points (x):x ₁, ...,x _n?1:x _i ∈U _i (X _r ) there are positive constantsC ⁽ⁿ⁾{(x)},h ⁽ⁿ⁾{(x)} with: $$\left| {\left\langle {\left[ {A(x_1 )...A(x_{n - 1} ),A(x_n )} \right]} \right\rangle } \right|< C^{(n)} \left\{ {(x)} \right\}\exp \left\{ { - h^{(n)} \left\{ {(x)} \right\}r^\alpha } \right\}forx_n = \left( {\begin{array}{*{20}c} 0 \\ 0 \\ 0 \\ r \\ \end{array} } \right),r > 1.$$ 2. For any natural numbern there exist a) a configurationY(n): $$Y_2 ,Y_3 ,...,Y_n Y_3^i = \cdot \cdot \cdot = Y_n^i = 0i = 0,3$$ with \(\left[ {\sum\limits_{i = 3}^{n - 1} {\mu _i (Y_i^1 - Y_{i{\text{ + 1}}}^{\text{1}} } )} \right]^2 + \left[ {\sum\limits_{i = 3}^{n - 1} {\mu _i (Y_i^2 - Y_{i{\text{ + 1}}}^{\text{2}} } )} \right]^2 > 0\) for all μ _i ≧0,i=3, ...,n?1, \(\sum\limits_{i = 3}^{n - 1} {\mu _i > 0} \) , b) neighbourhoods of theY _i 's:V _i(Y _i )?R ⁴ i=2, ...,n (in the euclidean topology ofR ⁴) and c) a real number β>1 such that for all points (y):y ₂, ...,y _n y _i ∈V _i (Y _i there are positive constantsC _(n){(y)},h _(n){(y)} and a real number γ_(n){(y)∈a closed subset ofR?{0}?{1} with: γ_(n){(y)}\y ₂,y ₃, ...,y _n totally space-like in the order 2, 3, ...,n and $$\left| {\left\langle {\left[ {A(x_1 ),A(x_2 )} \right]A(y_3 )...A(y_n )} \right\rangle } \right|< C_{(n)} \left\{ {(y)} \right\}\exp \left\{ { - h_{(n)} \left\{ {(y)} \right\}r^\beta } \right\}$$ for \(x_1 = \gamma _{(n)} \left\{ {(y)} \right\}r\left( {\begin{array}{*{20}c} 0 \\ 0 \\ 0 \\ 1 \\ \end{array} } \right),x_2 = y_2 - [1 - \gamma _{(n)} \{ (y)\} ]r\left( {\begin{array}{*{20}c} 0 \\ 0 \\ 0 \\ 1 \\ \end{array} } \right)\) and for sufficiently large values ofr.     

Effects of cation order on the energy bands of GaAs-AlAs heterostructures

Pseudopotential band structure calculations of (GaAs)_n ? (A$\text{l}$As)_n with n = 1, 2, 3 and of Ga_0.5A$\text{l}$_0.5As show that the effects of cation order are small due to the weakness of the Ga-A$\text{l}$ potential difference. The energy bands of the n = 1 heterostructure can be obtained by folding those of the alloy except for small energy shifts and splittings which can be handled in perturbation theory. The superlattice energy gap decreases with increasing n, the shrinkage being 4 meV for n = 2 and 10 meV for n = 3.