Specific features of the electronic band structure and x-ray spectra of boron nitride in sphalerite and wurtzite modifications

The electronic band structure of boron nitride compounds with crystal lattices of the sphalerite (c-BN) and wurtzite (w-BN) types is calculated by the local coherent potential method in the cluster muffin-tin approximation within the framework of the multiple scattering theory. The local partial densities of 2p states for boron and nitrogen in c-BN and w-BN modifications are compared with the experimental boron and nitrogen K x-ray emission spectra and band-structure calculations. A comparison of the total densities of states in c-BN and w-BN with the x-ray photoelectron spectra and the band calculations has revealed both similarities and differences in the electronic structures of these modifications. The fine structure in the vicinity of the valence band top of boron nitride in different crystal modifications is theoretically calculated for the first time. The specific features of the electronic structure and the x-ray spectra of boron nitride in different modifications are discussed.     

Analytical optimization of the lattice parameter using the binding energy calculated in the quasi-classical approximation

The dependence of the static binding energy of a crystal on the crystal structure as calculated in the initial quasi-classical approximation is shown to allow the equilibrium lattice parameter to be found analytically. The application of this method to boron nitride modifications leads to lattice parameters that coincide with experimental values to within several percent. This method gives lattice parameters of 2.66, 3.49, and 2.44 Å for the BN hexagonal layer and the cubic c-BN and “ideal” wurtzite-like w-BN crystals, respectively. The corresponding binding energies are estimated to be 23.2, 14.1, and 13.6 eV/mol, respectively.     

Electronic band structure and x-ray spectra of boron nitride polytypes

The electronic band structures of boron nitride crystal modifications of the graphite (h-BN), wurtzite (w-BN), and sphalerite (c-BN) types are calculated using the local coherent potential method in the cluster muffin-tin approximation within the framework of the multiple scattering theory. The specific features of the electronic band structure of 2H, 4H, and 3C boron nitride polytypes are compared with those of experimental x-ray photoelectron, x-ray emission, and K x-ray absorption spectra of boron and nitrogen. The features of the experimental x-ray spectra of boron nitride in different crystal modifications are interpreted. It is demonstrated that the short-wavelength peak revealed in the total densities of states (TDOS) in the boron nitride polytypes under consideration can be assigned to the so-called outer collective band formed by 2p electrons of boron and nitrogen atoms. The inference is made that the decrease observed in the band gap when changing over from wurtzite and sphalerite to hexagonal boron nitride is associated with the change in the coordination number of the components, which, in turn, leads to a change in the energy location of the conduction band bottom in the crystal.     

Photo- and cathodoluminescence of cubic boron nitride micropowders activated by Tm,Tb, and Eu rare-earth ions

This work is devoted to the production of cubic boron nitride (c-BN) micropowders that are activated by ions of rare-earth elements, such as europium (Eu), terbium (Tb), and thulium (Tm), as well as to the study of the structural properties and photo- and cathodoluminescence of these micropowders. The micropowders have been synthesized from a hexagonal boron nitride powder in the presence of a catalyst under pressures of 4–6 GPa at temperatures of 1800–1900 K. The activation of the micropowders by the rareearth elements (REEs) has been carried out by introducing the corresponding REE compounds into synthesis precursor. The efficiency of the introduction of an impurity into the c-BN lattice is ~5%. The composition and structure of the samples have been examined using X-ray diffraction analysis, scanning electron microscopy, and energy-dispersive spectrometry. The results obtained during studying c-BN, c-BN:Tm, c-BN:Tb, and c-BN:Eu micropowders using color cathodoluminescence clearly demonstrate their ability to emit light in the wide spectral range, which is of interest for developing new light-emitting devices that are intended for operation in corrosive ambient. An analysis of the photoluminescence spectra of c-BN:REE micropowders has made it possible to find that the observed spectral bands belong to the corresponding transitions between the energy levels of the REEs, as well as to determine the probable positions of Tb³⁺ and Eu³⁺ ions in the cubic boron nitride lattice.     

Optically nonlinear phonon-polariton modes in a three-layered structure

A theory is presented for the propagation of phonon-polariton modes arising when phonons are coupled to electromagnetic waves in multilayered structures. A multi-layered structure consists of a thin film surrounded symmetrically by a bounding media. Numerical calculations are given for s-polarized phonon-polariton modes in the case where the bounding media are assumed to be semi-infinite layers with nonlinear dielectric functions of ionic crystal type supporting optical phonon modes and the thin film is characterized by a Kerr-type nonlinear dielectric function. The phonon-polaritons were found to have distinct branches characteristic of optical phonons and showing features that are different from those of plasmon-polaritons [S. Baher, M.G. Cottam, Surf. Rev. Lett. 10 (2003) 13]. The parameters that modify the modes are the in-plane wave vector, the thickness of the film, the phonon frequency and the nonlinearity of each layer. It was found that by increasing the film thickness and nonlinearity coefficient, the curves move to the left and the number of the branches increases without changing the pattern of the curves.     

Temperature dependent polariton measurements in BaTiO3

Polariton techniques are used to determine the temperature dependence of all three A₁ modes between room temperature and T_c = 134°C in the ferroelectric phase of BaTiO₃. The results shows that there is a large difference between the clamped dielectric constant, ?(0), determined from these results and ?(0) determined from microwave capacitance techniques. It is argued that, while soft modes in displacive ferroelectrics are the driving force for the transition, other oscillators play an important role in low frequency dielectric behavior.     

Temperature and pressure dependences of the properties and phase transition in paratellurite (TeO2: Ultrasonic,dielectric and Raman and Brillouin scattering results

The effects of temperature and pressure on the ultrasonic propagation properties, dielectric constants and the Raman and Brillouin spectra in paratellurite (TeO₂) were investigated with emphasis on the behavior in the vicinity of the newly-discovered, pressure-induced phase transition. The transition is found to be second-order and purely strain-induced, driven by a soft shear acoustic mode propagating along a <110〉 and polarized along a (110) crystal direction. Such pure-strain transitions were previously discussed by Anderson and Blount and the transition in paratellurite is the first observation of this kind of transition. No evidence was found for any coupling of the soft mode to any other acoustic or optic mode, although small anomalies associated with lattice strains accompanying the transition were observed in some of the elastic and dielectric constants. Analysis of the effective elastic constant C, governing the soft mode velocity indicates that, within experimental uncertainty, the transition can be described by mean-field theory. Although the apparent attenuation of the soft mode increased significantly near the transition, it is concluded that this effect is probably due to the fact that the phase and group velocities are not parallel rather than to intrinsic dissipative processes in the crystal. With the exception of C₄₄, the remaining elastic constants and Raman-active phonon frequencies displayed normal increases with pressure. No soft Raman-active modes were observed in either phase. The static dielectric constants ?₁ are large, due to the large electronic polarizability of TeO₂, and the anisotropy in ? results almost entirely from the anisotropy in the optical dielectric constants ?_∞. In the low pressure tetragonal phase both ?_a and ?_c exhibit normal temperature dependences and ?_c decreases with pressure; however, ?_a exhibits an anomalous increase with pressure. Temperature, pressure and uniaxial stress measurements are combined to evaluate the various contributions to the temperature and pressure dependences of ?. Combining the ? data with available i.r. measurements demonstrated that the generalized Lyddane-Sachs-Teller relation is well obeyed for TeO₂. Finally, the Szigetti effective charge ratios were determined for the lowest frequency IR-active modes. These ratios were found to be quite low, being 0.27 and 0.18 for the a-axis responses, respectively, indicating that the bonding is highly covalent.     

Physical properties of Ima2-BN under pressure: First principles calculations

A fully orthorhombic boron nitride (BN) polymorph with an orthorhombic symmetry (Ima2-BN, space group: Ima2) was investigated by first-principles calculations. The Ima2-BN under 30 GPa is both mechanically and dynamically stable via elastic constants and phonon spectra. The anisotropic and electronic properties of Ima2-BN under different pressure are investigated in this work. The anisotropic properties calculations show that the Young's modulus of Ima2-BN in (001) plane exhibits the greatest anisotropy under ambient pressure, while in (111) plane it is the greatest when P > 20 GPa, while the (010) plane has always exhibited the minimal anisotropy whether under ambient pressure or high pressure. Ima2-BN is an indirect wider band gap semiconductor material under ambient pressure, and the band gap of Ima2-BN decreases with the increasing pressure. The minimum thermal conductivities κ_min of Ima2-BN is 1.85 W/(cmK), it is slightly higher than of B₄N₄-I and c-BN.     

Two dimensional cubic boron nitride nanosheets converted from hexagonal boron nitride bilayers: electrical conductivity,magnetism and visible absorption properties

The development of novel structure, fabrication methods, formation mechanisms, and versatile applicability of boron nitride (BN) nanomaterials is still one of the research hotspots. In this report, we developed a novel two dimensional cubic boron nitride nanosheets (2D c-BNNSs) based on the first principles calculations. This structure is converted from hexagonal BN (h-BN) bilayers induced by hydroxyl (OH) radical and fluoride (F) atom codoping. The geometrical, electronic, and optical properties of the novel 2D OH radical and F atom codoped c-BNNSs (OH-F-c-BNNSs) have been systematically investigated. The results reveal that the unpaired electrons appear due to the electronegativity difference between OH radical and F atoms, resulting in the excellent electrical and magnetic properties of OH-F-c-BNNSs. In addition, OH-F-c-BNNSs also exhibit a strong response to the visible light with an absorption range covering the whole visible light region. More importantly, when the doping positions of OH radical and F atom are exchanged (F-OH-c-BNNSs), the F-OH-c-BNNS will have only electrical conductivity, which will make us to regulate the intrinsic properties of c-BNNSs for different applications only by adjusting the element doping positions. This work can provide a theoretical and experimental basis/support for designing and fabricating new types of 2D c-BN nanomaterials for different applications.     

Hyper-Raman scattering spectra in the low frequency range in cubic BaTiO3 and the mechanism of the phase transition

The hyper-Raman spectra in the cubic phase of BaTiO₃ are studied with special emphasis on the lowest-freauency phonon mode. The spectral structure is found to change as the temperature T is raised from T_c (130 °C) to 400 °C. It is shown that the overall experimental results can be well accounted for in terms of the critical dynamical theory based on pseudospin-phonon coupled system developed by Y. Yamada et al. As the consequence, it is found that the coupling between TO phonons and pseudospins presumably constituted by flipping motion of Ti ions causes the cubic-tetragonal phase transition, and plays an important role in understanding the dynamical aspects including the anomalous increase in dielectric constant as T approaches T_c from above.     

Absolute photonic band gaps in a two-dimensional photonic crystal with hollow anisotropic rods

The plane-wave expansion method is used to calculate photonic band gaps for two structures with hollow anisotropic tellurium (Te) rods. Both structures are found to have absolute band gaps at the low- and high-frequency regions. Compared with the photonic crystal with solid Te rods, the photonic crystal with hollow Te rods has a large absolute band gap at the high-frequency region: for the triangular lattice of oval hollow Te rods, there is an absolute band gap of 0.058w_e (w_e=2πc/a), and for the square lattice of square hollow Te rods, there is an absolute band gap of 0.056w_e.     

Dielectric photonic crystal as medium with negative electric permittivity and magnetic permeability

We show that the two-dimensional photonic crystal (PC) made from a non-magnetic dielectric is a left-handed material in the sense defined by Veselago. Namely, it has negative values for both the electric permittivity ? and the magnetic permeability μ in some frequency range. This follows from a recently proven general theorem. The negative values of ? and μ are found by a numerical simulation. Using values |?| and |μ| for the medium surrounding the PC slab we simulate the Veselago lens, a unique optical device predicted by Veselago. An approximate analytical theory is proposed to calculate the values of ? and μ from the PC band structure. It gives the results that are close to those obtained by the numerical simulation. The theory explains how a non-zero magnetization arises in a non-magnetic PC.     

Inter-relationship between optical dielectric constant and interatomic separation of mixed crystals in ionic and covalent binary compound families

An ion dependent dielectric model is developed for mixed binary crystals. The interatomic separation (R) and optical dielectric constant (ε_∞) of the mixed crystals are computed from the measured values of R and ε_∞ of pure crystals. An empirical relation between ε_∞ and R is therefore found for mixed crystals by using the computed values. It is found that the dielectric behaviour of ionic mixed crystals is cation dependent while that of covalent mixed crystals is anion dependent. The prescribed theory can therefore be used to form different mixed crystals with particular values of ε_∞ required in any specific opto-electronic devices.     

Excitation of ultrasonic Lamb waves using a phased array system with two array probes: Phantom and in vitro bone studies

Long bones are good waveguides to support the propagation of ultrasonic guided waves. The low-order guided waves have been consistently observed in quantitative ultrasound bone studies. Selective excitation of these low-order guided modes requires oblique incidence of the ultrasound beam using a transducer-wedge system. It is generally assumed that an angle of incidence, θ_i, generates a specific phase velocity of interest, c_o, via Snell’s law, θ_i = sin⁻¹(v_w/c_o) where v_w is the velocity of the coupling medium. In this study, we investigated the excitation of guided waves within a 6.3-mm thick brass plate and a 6.5-mm thick bovine bone plate using an ultrasound phased array system with two 0.75-mm-pitch array probes. Arranging five elements as a group, the first group of a 16-element probe was used as a transmitter and a 64-element probe was a receiver array. The beam was steered for six angles (0°, 20°, 30°, 40°, 50°, and 60°) with a 1.6-MHz source signal. An adjoint Radon transform algorithm mapped the time-offset matrix into the frequency-phase velocity dispersion panels. The imaged Lamb plate modes were identified by the theoretical dispersion curves. The results show that the 0° excitation generated many modes with no modal discrimination and the oblique beam excited a spectrum of phase velocities spread asymmetrically about c_o. The width of the excitation region decreased as the steering angle increased, rendering modal selectivity at large angles. The phenomena were well predicted by the excitation function of the source influence theory. The low-order modes were better imaged at steering angle ?30° for both plates. The study has also demonstrated the feasibility of using the two-probe phased array system for future in vivo study.     

Formation of a monolayer <Emphasis Type="Italic">h</Emphasis>-BN nanomesh on Rh (111) studied using <Emphasis Type="Italic">in-situ</Emphasis> STM

As a member of the 2D family of materials, h-BN is an intrinsic insulator and could be employed as a dielectric or insulating inter-layer in ultra-thin devices. Monolayer h-BN can be synthesized on Rh (111) surfaces using borazine as a precursor. Using in-situ variable-temperature scanning tunneling microscopy (STM), we directly observed the formation of h in real-time. By analyzing the deposition under variable substrate temperatures and the filling rate of the h-BN overlayer vacant hollows during growth, we studied the growth kinetics of how the borazine molecules construct the h-BN overlayer grown on the Rh surface.     

Vibrational and dielectric properties of La2Hf2O7 : Experiment and theory

The physical origin of the static dielectric constant and its relationship with lattice dynamics of La₂Hf₂O₇are studied by combining infrared spectroscopy and density functional perturbation theory (DFPT). Both La and Hf show obvious effective charge anomaly which is attributed to the hybridization between 2p states of the oxygen and 5d states of the cations, indicating a mixed covalent-ionic bonding between the cations and the oxygen. The dielectric response is determined by seven infrared phonon modes and the static dielectric constant extracted from infrared reflection spectrum is in close agreement with DFPT calculation. Both experiment and theory reveal that most of the contributions to the static dielectric constant are dominated by three infrared phonon modes at 137, 172 and 297 cm⁻¹. Two of them (172 and 297 cm⁻¹) are from the displacements of oxygen atoms inside HfO₆ octahedra and the other one (137 cm⁻¹) is from the bending of La₂O′ chain. This result indicates that the origin of the static dielectric constant of La₂Hf₂O₇ is directly connected with the two interpenetrating sub-networks of pyrochlore structure (HfO₆ octahedra and La₂O′ chain).     

The theory of cylindrical photonic wires

The energy modes for a photonic nanowire have been studied and calculated. We model our photonic crystals after Noda et al. (1999) [18] where logs of semiconductor material are stacked to produce photonic band gaps in both the near and far infrared regions. A nominal dispersion relation was adopted in order to achieve qualitatively useful results. Photonic wires were modeled in two schemes, each with two specific geometries. In the first scheme, a pillar of one photonic crystal is embedded in a larger photonic crystal to produce a wire. This pillar was modeled as having either a square or a circular cross-section. The photonic crystals considered consisted of varying proportions of Ga_xAl_1−xAs, so that the wire could be adjusted. The second scheme investigated was a dielectric material for the central pillar, rather than a photonic crystal. Again, circular and square cross sections were considered. It was found that many more modes fit into the near infrared band gap than the far infrared band gap, and that a circular cross-section permits fewer modes. Finally, a dielectric pillar allows for a wire which is physically much smaller than a wire with a photonic crystal in the middle. As many photonic devices include such wires, these qualitative results could be useful in their design.     

Magnetic field effects in the onset of superconductivity

Using the time dependent Ginzburg-Landau theory the influence of a finite and even strong magnetic field on the fluctuations in superconductors aboveT _c is studied. We calculate the dynamical conductivity, the Hall angle, and the static magnetisation from the fluctuations of the charge current associated with the fluctuations of the order parameter. It is found that the magnetic field generally enhances the singular contributions of the fluctuations to the conductivity and the susceptibility. Associated with this enhancement is a reduction of the characteristic frequency scale close toT _c .     

Dielectric Properties of Fine-Grained BaTiO3 Ceramics under High Pressure

We investigate the temperature dependence of the dielectric constant of BaTiO3 ceramic with coarse to nanograin size under different hydrostatic high pressures up to 5000 bar in the range between room temperature and 200℃. The ferroelectric-to-paraelectric phase transition temperatures Tc are determined from the peak of dielectric constant versus temperature. The values of average grain-size are estimated from the SEM images. It is found that the magnitude of dTc/dp varies considerably from sample to sample depending on grain size. The Curie point Tc of the sample with small grain size decreases more sharply than that of samples with larger one.     

Renormalization of two-dimensional R2-gravity

Two-dimensional gravity with an R²-term is quantized around the R2-Liouville solution in the semiclassical way. Renormalization, regularization (infra-red, ultra-violet) and a topological term ∂ (ϕ∂ϕ)) ) are carefully treated. All (1-loop) divergences are renormalized by the cosmological constant (μ) and the R2-coupling-constant (β) for the case β > 0. The quantum meaning of the topological term is clarified. The renormalization group beta-functions of the couplings β and μ are obtained. It is found that the theory is conformal (i.e. the if beta-functions = 0) for w = (β/A) · (16π · 48π/(26 − c_m)) ⩾ 1 (where A is a fixed area) exactly when the coupling constant ξ of the topological term takes the value of 1. As for 0 < w < 1, β is asymptotically free for c_m < 26 and μ is asymptotically non-free.