Effect of intrinsic defects on the electronic structure of BN nanotubes

The effect of intrinsic defects on the electronic structure of boron-nitrogen nanotubes (5, 5) and (9, 0) is investigated by the method of linearized associated cylindrical waves. Nanotubes with extended defects of substitution N _B of a boron atom by a nitrogen atom and, vice versa, nitrogen by boron BN with an impurity concentration of 1.5 to 5% are considered. It is shown that the presence of such defects significantly affects the band structure of boron-nitrogen nanotubes. A defect band D^π(B, N) is formed in the bandgap, which sharply reduces the width of the gap. The presence of impurities also affects the valence band: the widths of s, sp, and p_π bands change and the gap between s and sp bands is partially filled. These effects may be detected experimentally by, e.g., optical and photoelectron spectroscopy.     

Electronic energy structure and x-ray spectra of wide-gap AlN and BN crystals and B<Subscript>x</Subscript>Al<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>N solid solutions

The electronic energy structure of 2H and 3C AlN and BN crystals and B_xAl_1?xN solid solutions is calculated on the basis of the local coherent potential method using the cluster version of the MT approximation and the theory of multiple scattering. The features of the electronic structure of 2H-AlN crystals are compared with x-ray K and L absorption and emission spectra of aluminum and nitrogen. An interpretation of these features is given. The concentration dependences of the width of the upper subband of the valence band and the band gap in B_xAl_1?xN solid solutions (x = 0.25, 0.5, 0.75) are investigated. Charge transfer from aluminum to nitrogen atoms is shown to occur and increase with boron doping in both crystallographic modifications.     

Effect of doping by boron,carbon, and nitrogen atoms on the magnetic and photocatalytic properties of anatase

The effect of doping of titanium dioxide with the anatase structure by boron, carbon, and nitrogen atoms on the magnetic and optical properties and the electronic spectrum of this compound has been investigated using the ab initio tight-binding linear muffin-tin orbital (TB-LMTO) band-structure method in the local spin density approximation explicitly including Coulomb correlations (LSDA + U) in combination with the semiempirical extended Hückel theory (EHT) method. The LSDA + U calculations of the electronic structure, the imaginary part of the dielectric function, the total magnetic moments, and the magnetic moments at the impurity atoms have been carried out. The diagrams of the molecular orbitals of the clusters Ti₃ X (X = B, C, N) have been calculated and the pseudo-space images of the molecular orbitals of the clusters have been constructed. The effect of doping on the nature and origin of photocatalytic activity in the visible spectral range and the specific features of the generation of ferromagnetic interactions in doped anatase have been discussed based on the analysis of the obtained data. It has been shown that, in the sequence TiO_{2 ? y} N _y → TiO_{2 ? y} C _y → TiO_{2 ? y} B _y (y = 1/16), the photocatalytic activity can increase with the generation of electronic excitations with the participation of impurity bands. The calculated magnetic moments for boron and nitrogen atoms are equal to 1 μ_B, whereas the impurity carbon atoms are nonmagnetic.     

A nonradiative intersystem crossing <Emphasis Type="Italic">S</Emphasis>(ππ*) ↝ <Emphasis Type="Italic">T</Emphasis>(ππ*) transition in dibenzo-<Emphasis Type="Italic">p</Emphasis>-dioxin

The probability of the nonradiative S-T intersystem crossing in dibenzo-p-dioxin is theoretically studied using a model for the vibronically induced spin-orbit coupling between electronic states and taking into account all out-of-plane vibrational modes. Several symmetry variants for the lowest S ₁(ππ*) singlet state are considered. In the case of g symmetry of this state, a provision is made for the possibility of its vibronic coupling with the nearest dipole-active singlet ¹ B _2u ππ* state. The rate constants K _ST of the S ₁ ? T(ππ*) transitions to the T ₁(³ B _3g ) state are estimated taking into account several intermediate triplet T _m (ππ*) states of g and u symmetry. For different symmetry types of the S ₁ state, the effect of K _ST on the fluorescence quantum yield ?_fl is discussed. The ¹ B _3g symmetry state is found to be the lowest S ₁ state. It is found that the main contribution to K _ST is made by the S ₁(¹ B _3g ) ? T ₄(³ A _g ) transition.     

Study of the compressibility of FeSi,MnSi, and CoS<Subscript>2</Subscript> transition-metal compounds at high pressures

Silicides and sulfides of transition metals attract great attention of researchers because of a wide spectrum of interesting magnetic, electronic, and optical properties. The crystal structure of FeSi, MnSi, and CoSi silicides is P2₁3(B20), whereas FeS₂, CoS₂, and MnS₂ sulfides have a structure of pyrite Pa3. Despite the great interest in these systems and the cubic symmetry of crystals, the structure and compressibility of these compounds at high pressures are still insufficiently studied. There is a significant spread (more than a factor of two!) in the bulk modulus and its pressure derivative for a single compound. Most studies were performed under nonhydrostatic conditions. In this work, the compressibility of FeSi and MnSi silicides (at pressures up to 35 GPa) and CoS₂ sulfide (up to 22 GPa) has been studied by the X-ray diffraction method in a diamond anvil cell with the use of helium as the softest pressure-transmitting medium. The values obtained for the bulk modulus and its derivative—B = 178 ±3 GPa and B_p = 5.6 ± 0.5 for FeSi, B = 167 ± 3 GPa and B_p^' = 4.6 ± 0.5 for MnSi, and B = 94 ± 2 GPa and B_p^' = 6.9 ± 0.5 for CoS₂—can be considered as the most reliable and can be used to test numerous theoretical models. The results for the compressibility of FeSi are important for the verification of models of the Earth’s core.     

Simulation of the structural,electronic, and magnetic properties of Fe<Subscript>3</Subscript>C<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>B<Subscript>x</Subscript> borocementites

The structural, electronic, and magnetic properties and the enthalpy of formation of iron borocementites Fe₃C_1?x B_x (x= 0, 0.25, 0.50, 0.75, 1.00) are analyzed using ab initio calculations in the framework of the electron density functional theory. It is found that the unit cell parameter a of the orthorhombic lattice increases linearly and the parameters b and c decrease as the boron concentration increases. The density of states at the Fermi level changes only slightly, and the main variations in the band structure occur in the region of the bottom of the valence bands. The magnetic moment of the iron atoms and the total magnetization and stability of the Fe₃C_1?x B_x phases increase linearly with an increase in the boron concentration.     

Extended <Emphasis Type="Italic">E</Emphasis>(5) and <Emphasis Type="Italic">X</Emphasis>(5) symmetries: Series of models providing parameter-independent predictions

The E(5) symmetry describes nuclei related to the U(5)-SO(6) phase transition, while the X(5) symmetry is related to the U(5)-SU(3) phase transition. First, a chain of potentials interpolating between the U(5) symmetry of the five-dimensional harmonic oscillator and the E(5) symmetry is considered. Parameter-independent predictions for the spectra and B(E2) values of nuclei with R₄ = E(4)/E(2) ratios of 2.093, 2.135, and 2.157 (compared to the ratio of 2.000 of the U(5) case and the ratio of 2.199 of the E(5) case) are derived numerically and compared to existing experimental data, suggesting several new experiments. TheX(5) symmetry describes nuclei characterized byR₄=2.904.Using the same separation of variables of the original Bohr Hamiltonian as in X(5), an exactly soluble model with R₄=2.646 is constructed and its parameter-independent predictions are compared to existing spectra and B(E2) values. In addition, a chain of potentials interpolating between this new model and the X(5) symmetry is considered. Parameter-independent predictions for the spectra and B(E2) values of nuclei with R₄ ratios of 2.769, 2.824, and 2.852 are derived numerically and compared to existing experimental data, suggesting several new experiments.     

X-ray spectra and electronic band structure of nitrogen in Al<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Ga<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>N solid solid solutions

The electronic energy structure of the valence band and the x-ray absorption near edge structure (XANES) region of nitrogen in Al _x Ga_1?x N solid solutions and binary crystals of gallium nitride GaN and aluminum nitride AlN are calculated using the local coherent potential method and the cluster version of the muffin-tin approximation within the framework of the multiple scattering theory. It is demonstrated that the calculated electron densities of states correlate with the nitrogen K x-ray emission and nitrogen K x-ray absorption spectra. The electronic energy structure of the top of the valence band and the XANES region in Al _x Ga_1?x N solid solutions are compared with those in the binary crystals of the GaN and AlN nitrides, and an interpretation of their specific features is proposed. An analogy is drawn between the evolution of the electronic energy structure of the valence band and the XANES region in the alloys under investigation and the evolution of the electronic band structure in the Al _x B_1?x N and B _x Ga_1?x N alloys. General trends in the transformation of the structure and variations in properties of these alloys are discussed.     

Energy and optical absorption spectra of endohedral metallofullerenes with Gd or Ho as strongly correlated π-electron systems

Isomerically pure endohedral metallofullerenes Gd@C82(C2v), Ho@C₈₂(C_2v), and their monoanions have been synthesized and separated. The optical absorption spectra of solutions of obtained compounds in o-dichlorobenzene have been studied. Within the Hubbard model, the energy spectrum of isomer of C_2v symmetry (no. 9) of fullerene С₈₂ has been calculated. Based on the obtained spectrum, optical absorption spectra of endohedral metallofullerenes Gd@C₈₂ and Ho@C₈₂ and their monoanions have been simulated. The calculated optical absorption spectra have been compared with experimental ones; it has been found that qualitative agreement between them is observed.     

Intensity of singlet-triplet transitions in C<Subscript>60</Subscript> fullerene calculated on the basis of the time-dependent density functional theory and taking into account the quadratic response

The singlet-singlet and triplet-triplet absorption spectra of C₆₀ fullerene are calculated using the density functional method and taking into account the theory of linear and quadratic responses. The B3LYP density functional and the 6–31G and 3–21G atomic basis sets are used. The calculations are performed using the D_2h and D_5d symmetry groups, although the real symmetry of the ground state is described by the I _h symmetry group. The matrix elements of the operator of the spin-orbit coupling are calculated and the probabilities of some singlet-triplet transitions are estimated. Taking into account the data in the literature on vibronic interactions of vibrations of the t_1u, t_2u, g _u , and h _u symmetry species, the radiative lifetime of the 1³T_2g → 1¹A _g phosphorescence was estimated to be 45 s. The fact that this time proved to be considerably greater than the experimentally observed total lifetime of the triplet testifies to a fast nonradiative deactivation of the lowest triplet state of C₆₀ fullerene and agrees with a low phosphorescence intensity. The zero-field splitting of some triplets and the intensities of magnetic dipole transitions are discussed.     

Untersuchungen von (d,p)- und (d, α)-Reaktionen an B10 und B11

Investigating reaction mechanisms, angular distributions and cross sections of the reaction B¹⁰(d, p) B¹¹ have been measured in the energy interval from 1,4 to 3,3 MeV of deuteron energy. More detailed measurements than until known have shown, that besides the well known stripping mechanism withl _n =1 contributions of compound nucleus formation are not neglectable. Especially atE _d =2,3 MeV,E _X (C¹²)=27,1 MeV, the effect of a single resonance contributes a great deal to the cross section of the groupsp ₁ andp ₃ . Further angular distributions and yield curves between 1,4 and 3,3 MeV have been measured in the (d, α)-reactions on B¹⁰ and B¹¹, showing quite different behaviour for both target nuclei.     

Spin-orbit interactions in heterocyclic analogues of fluorene

For carbazole, dibenzofuran, and dibenzothiophene—heterocyclic analogues of fluorene containing N-H, O, and S groups, respectively—the transition dipole moments P ₀₀ ⁱ for the transitions ³ B ₂→S ₀ and ³ A ₁→S ₀ from the sublevels i=z, y, x of the triplet electronic ππ* states, which are caused by intramolecular spin-orbit (SO) interactions, are calculated. The effect that the SO coupling between the S ₀ state and highest triplet states has on the calculation results is considered. The effects exerted on the value of P ₀₀ ⁱ by such specific features of the molecular structure as the position of a heteroatom on the symmetry axis, its valence, and different constants of SO coupling in heteroatoms are discussed. The reason for the weak influence of the quantity ?_HA on the rate constant of radiative deactivation of the lowest T state is ascertained.     

Mean-square displacements of metal and boron atoms in crystal lattices of rare-earth hexaborides

The intensities of the I₄₁₀ and I₄₁₁ reflections of nine rare-earth hexaborides MB₆ (M=La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy) are experimentally studied in the temperature range 4.2–300 K. The mean-square displacements of metal and boron atoms are calculated from the temperature dependences of the intensities I₄₁₀(T) and I₄₁₁(T). The characteristic temperatures of the metal (θ_M) and boron (θ_B) sublattices of rare-earth hexaborides are determined in the Debye approximation. It is found that the characteristic temperatures decrease with an increase in the atomic number of the metal.     

Ab initio calculations of B<Subscript>2</Subscript> type RHg (R = Ce,Pr, Eu and Gd) intermetallic compounds

Spin polarized ab initio calculations have been carried out to study the structural, electronic, elastic and thermal properties of RHg (R = Ce, Pr, Eu and Gd) intermetallic compounds in B₂ structure. The calculations have been performed by using both generalized gradient approximation (GGA) and local spin density approximation (LSDA). The calculated value of lattice constant (a ₀) for these compounds with GGA is in better agreement with the experimental data than those with LSDA. Bulk modulus (B), first-order pressure derivative of bulk modulus and magnetic moment (μ _B ) are also presented. The energy band structure and electron density of states show the occupancy of 4f states for light as well as heavy rare earth atom. The elastic constants are predicted from which all the related mechanical properties like Poisson’s ratio (σ), Young’s modulus (E), shear modulus (G _H ) and anisotropy factor (A) are calculated. The ductility or brittleness of these compounds is predicted from Pugh’s rule (B/G _H ) and Cauchy pressure (C ₁₂ ? C ₄₄). The Debye temperature (θ _D ) is estimated from the average sound velocity, which have not been calculated and measured yet.     

Withdrawal of Electrodynamical Forbiddance and Peculiarities of the SERS Spectra in Fullerene C<Subscript>70</Subscript>

It is demonstrated that in fullerene C₇₀, which can be considered as a deformed fullerene C₆₀ in some mean sense there is a withdrawal of an Electrodynamical forbiddance of a strong quadrupole light-molecule interaction, which is realized in the fullerene C₆₀. This situation occurs because of the reduction of symmetry of C₆₀ from the icosahedral symmetry group Y_h to the group D_5h. The withdrawal results in appearance of the lines in the SERS spectra of C₆₀, which are forbidden in usual Raman scattering and are active in the infrared absorption spectra. The experimentally measured SERS spectra of C₇₀ demonstrates existence of such lines that strongly confirms our ideas about the dipole-quadrupole SERS mechanism.     

Effect of the orbital structure and symmetry of electronic states on nonradiative <Emphasis Type="Italic">S-T</Emphasis> intersystem crossing: Dibenzofuran

The nonradiative S-T intersystem crossing S ₁(ππ*) ? T ₁(ππ*) in dibenzofuran (DB(O)) molecules has been theoretically investigated within the model of vibronically induced spin-orbit (VISO) coupling of electronic states, where the vibronic perturbation takes into account all out-of-plane vibrational modes of a molecule. It is established that the S-T intersystem crossing S ₁(¹ A ₁) ? T ₁(³ B ₂) involves also the intermediate (T _m )T ₂(³ A ₁) and T ₃(³ B ₂) triplet states. The calculated rate constant K _ST = (4.5–4.7) × 10⁷s^?1 of the nonradiative transition is in agreement with the known experimental data. The manifestation of approximate (belonging to the D _2h group) symmetry of singlet and triplet molecular states in VISO couplings has been studied. An effect of the heavy (oxygen) atom of a DB(O) molecule on K _ST is established.     

Optical absorption spectra of boron clusters B<Subscript>n</Subscript> (n = 2–5) for application in nano scintillator – a time dependent density functional theory study

Boron nano-clusters of various shapes and sizes have potential applications asscintillating detector and hydrogen storage material. Using time dependent densityfunctional theory (TDDFT) as implemented in CASIDA we have studied the linear opticalabsorption spectra for boron clusters B_n (n = 2–5) and compared withpreviously reported results using Hatree-Fock (H-F) based method where the spectrum islimited to 8 eV due to exclusion of excitation into very high energy unoccupied orbital.The optical spectra fall in the visible and near UV region and are very much dependent onthe shape of the isomer. We have obtained additional peaks for B₂ linear, B₃ triangular, B₄ rhombus and square shapedisomers beyond 8 eV which were missing in the previous H-F based study and hassignificance as they fall below the ionization potential. We correlate the opticalspectrum with the shape of the Kohn-Sham orbitals and HUMO-LUMO gap and assess comparativestability of various B_n (n = 2–5) clusters in termsof HUMO-LUMO gap, bond-length and relative energy. TDDFT computed optical spectroscopycorrelated with Kohn-Sham orbitals and HUMO-LUMO gap and its comparison with H-F basedmethod may give significant knowledge regarding geometry and optical properties ofB_n (n = 2–5) clusters enablingto distingush between various isomers of B_n clusters.     

Rotation of the inner shell in a C<Subscript>20</Subscript>@C<Subscript>80</Subscript> nanoparticle

The stability of a C₂₀@C₈₀ nanoparticle and the rotation of its inner shell are studied theoretically within the tight-binding approximation. It is found that the C₂₀ skeleton in the free state is described by space group D_3d; in the case where C₂₀ is placed into the C₈₀(I _h ) fullerene field, the space group of C₂₀ is raised to I _h due to isomerization. The total energy surface of the C₂₀@C₈₀ compound is scanned over two rotation angles. Based on an analysis of the surface relief and energy isoline map, orientational melting of the nanoparticle is predicted. A nanoparticle gyroscope—C₂₀ rotating in the field of C₈₀ at a certain relative orientation and energy supply—is also predicted to exist.     

Raman spectroscopy of crystalline,glassy, and molten states of lead diborate

Polarized Raman spectra of single crystals of lead diborate, PbB₄O₇ (PBO), are studied in detail at 300 K. The TO-, LO-, and IO-phonon lines of the A ₁, A ₂, B ₁, and B ₂ symmetries in the Raman spectra of this compound are assigned. Changes in the Raman spectra of the internal vibrations of boron–oxygen complexes upon transition from the crystalline to the glassy and the molten states of PBO are observed. On the basis of the obtained results, the regularities in the formation of boron–oxygen complexes in glasses, melts, and crystals of the PbO · 2B₂O₃, SrO · 2B₂O₃, and Li₂O · 2B₂O₃. diborate compositions are analyzed.     

QED with vector and axial vector types of interaction and dynamical generation of particle masses

We consider a model of electrodynamics with two types of interaction, the vector \((e\bar \psi (\gamma ^\mu A_\mu )\psi )\) and axial vector \((e_A \bar \psi (\gamma ^\mu \gamma ^5 B_\mu )\psi )\) interactions, i.e., with two types of vector gauge fields, which corresponds to the local nature of the complete massless-fermion symmetry group U(1) ? U _A (1). We present a phenomenological model with spontaneous symmetry breaking through which the fermion and the axial vector field B_μ acquire masses. Based on an approximate solution of the Dyson equation for the fermion mass operator, we demonstrate the phenomenon of dynamical chiral symmetry breaking when the field B_μ has mass. We show the possibility of eliminating the axial anomalies in the model under consideration when introducing other types of fermions (quarks) within the standard-model fermion generations. We consider the polarization operator for the field B_μ and the procedure for removing divergences when calculating it. We demonstrate the emergence of a mass pole in the propagator of the particles that correspond to the field B_03BC when chiral symmetry is broken and consider the problems of regularizing closed fermion loops with axial vector vertices in connection with chiral symmetry breaking.