The phonon spectra of trigonal selenium at 77 and 298°K

Phonon dispersion curves in the principal symmetry directions of trigonal selenium single crystals have been measured by neutron inelastic scattering, using a three-axis spectrometer. The acoustic modes and the three lowest-lying optical modes (q = 0 energy transfers of 13·5 and 18·5 meV) have been measured at 77°K. The acoustic modes have also been measured at 298°K. There are small frequency shifts between the two temperatures, but the general agreement between the acoustic mode frequencies measured at the two temperatures is excellent. The data have been fit by a force constant model which assumes completely general harmonic forces between the first two neighbors in the same covalently bonded chain and axially symmetric forces derived from a potential of the form V = ? Ar^?m + Br^?n between all other atoms out to an interatomic distance of 6·5 . Fits were carried out with (m; n) = (3; 5) and (6; 12). For the former, the best values of A and B correspond to a Van der Waals equilibrium distance of 3·9and a minimum energy at this distance of 1·5 × 10^?13 ergs (about 2 kcal/mol). There are, however, significant discrepancies between the calculated and observed dispersion curves which indicate that a more sophisticated force model is needed.     

Lattice dynamics of a disordered Ni1−xPtx system in the pseudo unit cell model

The phonon dispersion relations for a disordered Ni_1?xPt_x system have been derived using the pseudo unit cell model proposed by Varshney et al. The results are presented for a few values of x along the [00ζ] direction and compared with recent measurements of Kunitomi et al. Reasonable agreement is found between the calculated and measured dispersion curves at all concentrations. In particular the localised impurity mode for low Ni concentrations does not split off from the main phonon band, in agreement with experiment and in contrast with the mass defect CPA prediction.     

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.     

Some dynamical properties of a two-dimensional Wigner crystal

Results for the static part of the ground state energy of the square and hexagonal two-dimensional Wigner lattices are given. The hexagonal lattice has the lower energy. Phonon dispersion curves and the vibrational zeropoint energy are calculated for the hexagonal lattice. The dielectric susceptibility tensor of a two-dimensional Wigner crystal χ_αβ(q) has been determined in the long wavelength limit in the presence of a static magnetic field perpendicular to the crystal, and explicit expressions have been obtained for the hexagonal lattice. Applying the analysis developed by Chiu and Quinn, the results for the susceptibility have been used to obtain the dispersion relation for the plasma oscillations in the electron crystal on the assumption that the crystal is embedded in a dielectric medium. The dispersion curves have been calculated for differing magnitudes of the applied magnetic field.     

Experimental and theoretical study of the angular resolved auger emission L23 of a single crystal target of aluminium excited by ion impact

The measured angular distribution N(?) of the L₂₃ Auger electrons of aluminium excited by Ar⁺ ion impact on (110) and (111) single crystals have been obtained for several polar angles. Two theoretical models based on a LEED formalism which can be used to calculate these angular distributions were briefly described and compared. There is a fair agreement between the line shape of the experimental and calculated curves. However, the calculated angular distributions have more structures and the calculated anisotropy rates are much larger than the measured ones.     

Thin prism refraction. A new direct method of polariton spectroscopy

Refraction of light by thin prisms has been used for the first time to obtain dispersion curves of excitonic polaritons. This most direct method demonstrated here for the A- and B-exciton in thin prismatic CdS crystals is shown to be extremely precise in spite of its simplicity. Improved values of polariton parameters are reported. In the mixed mode orientation we observed birefringence due to spatial dispersion. This opens a way to study the problem of additional boundary conditions.     

Interionic potentials and force constant models for rocksalt structure crystals—II

A lattice dynamical model for rocksalt structure crystals is presented in which the interionic force constants are taken to be central and the departure from the Cauchy relations is accounted for by isotropic and anisotropic deformations of the anions. The model is applied to NaBr, NaI and KBr for which C₁₂ > C₄₄ and it is appropriate to consider only the anisotropic deformations. The model parameters are determined entirely from macroscopic data. By assuming an exponential form for the repulsive part of the interionic potential the cohesive energy of the crystals may be determined from the interionic force constants. The cohesive energies are in surprisingly good agreement with experiment although the potential parameters differ considerably from those of other workers. While the dispersion curves obtained from the model are in markedly worse agreement with experiment than those from the standard breathing shell model it is shown that the potentials(in addition to giving good cohesive energies) result in a reasonably consistent dynamical model.     

Phonon spectra of <Emphasis Type="Italic">L</Emphasis>1<Subscript>2</Subscript> Ni<Subscript>3</Subscript>Al and <Emphasis Type="Italic">B</Emphasis>2 NiAl: Ab initio calculations

Phonon spectra and phonon density of states of intermetallic compounds Ni₃Al and NiAl are studied using the ab initio linear-response method. The calculated phonon dispersion curves agree well with the inelastic neutron scattering data available for the crystals under study.     

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.     

The Second Moments of the Line Shapes of Multiple Quantum NMR Coherences in One-Dimensional Systems

The second moments of the line shapes of the zeroth- and second-order multiple quantum NMR coherences determined by the dipole–dipole interactions of nuclear spins in crystals have been calculated. The second moments determined by the zz part of the dipole–dipole interaction have been derived both by a direct calculation and based on the exact solution (in terms of the zz model) for the decay of the multiple quantum coherence intensities on the evolution period of a multi-quantum NMR experiment. The decay of the multiple quantum NMR coherence intensities in a single crystal of calcium fluorapatite is well described by the Gaussian curves with the calculated second moments.     

Observation of magnetoplasma type surface polaritons on n-InSb

Surface polariton dispersion curves have been obtained for an n-InSb—air interface in a magnetic field using the ATR method and are found to be in qualitative agreement with theory. In particular the curves show the predicted non-reciprocal nature of the surface polariton propagation, and the appearance of virtual excitation type branches of the dispersion curves. On the basis of data obtained in zero magnetic field on etched surfaces, the quantitative differences between experimental and theoretical dispersion curves are attributed to surface damage.     

极化子在正弦色散声子场中的性质

本文计及纵光学声子的色散,在正弦近似下,用微扰法了多原子晶体中极化子的基态能量,有效质量和自能。     

A pseudopotential calculation of the phonon spectrum of aluminium

The phonon dispersion curves for Al are calculated from a theory based on Coulomb interactions among the ions and a local pseudopotential interaction between ions and conduction electrons. Conduction electron correlations are taken into account according to a theory of Singwiet al. ^1,2. A dielectric constant is constructed which satisfies the compressibility sum rule. This is especially important for longitudinal phonons. The agreement of the computed frequencies with the experimental dispersion curves of Stedman and Nilsson³ is good. Sites, sizes and widths of Kohn anomalies in the dispersion curves are also calculated. As expected the theoretical curves show larger anomalies than the experimental data. Finally a comparison is made with the recent calculations of Wallace⁴.     

Band structure of collective modes and effective properties of binary magnonic crystals

In this paper a theoretical study of the band structure of collective modes of binary ferromagnetic systems formed by a submicrometric periodic array of cylindrical cobalt nanodots partially or completely embedded into a permalloy ferromagnetic film is performed. The binary ferromagnetic systems studied are two-dimensional periodic, but they can be regarded as three-dimensional, since the magnetization is non uniform also along the z direction due to the contrast between the saturation magnetizations of the two ferromagnetic materials along the thickness. The dynamical matrix method, a finite-difference micromagnetic approach, formulated for studying the dynamics in one-component periodic ferromagnetic systems is generalized to ferromagnetic systems composed by F ferromagnetic materials. It is then applied to investigate the spin dynamics in four periodic binary ferromagnetic systems differing each other for the volume of cobalt dots and for the relative position of cobalt dots within the primitive cell. The dispersion curves of the most representative frequency modes are calculated for each system for an in-plane applied magnetic field perpendicular to the Bloch wave vector. The dependence of the dispersion curves on the cobalt quantity and position is discussed in terms of distribution of effective “surface magnetic charges” at the interface between the two ferromagnetic materials. The metamaterial properties in the propagative regime are also studied (1) by introducing an effective magnetization and effective “surface magnetic charges” (2) by describing the metamaterial wave dispersion of the most representative mode in each system within an effective medium approximation and in the dipole-exchange regime. It is also shown that the interchange between cobalt and permalloy does not necessarily lead to an interchange of the corresponding mode dispersion. Analogously to the case of electromagnetic waves in two-dimensional photonic crystals, the degree of localization of the localized collective modes is expressed in terms of an energy concentration factor.     

Deuteron on deuteron 2H(d,nd)p break-up in the AGS formalism

Differential cross sections for the kinematically complete break-up experiment ²H(d, nd)p have been calculated using the four-body theory of Alt, Grassberger and Sandhas (AGS). The four-body rearrangement amplitudes involved were computed in first order K-matrix approximation, while the subamplitudes occurring in the (3 + 1) and (2 + 2) channels have been expanded using the generalized unitary pole expansion (GUPE). At low energies the shapes of the cross sections are in good agreement with experiment but the magnitudes are too high. It is shown that the quintet channel is dominant at these energies. With increasing energy the agreement of the magnitude with experiment improves, but there is some discrepancy concerning the shapes.     

Semiempirical tight-binding calculation of the Schottky barrier heights

Barrier heights of the interfaces between metal monolayers and the (110) surfaces of GaAs, GaP, ZnSe and ZnS were calculated in the tight-binding approach. The slopes of the calculated dependences of barrier height vs work function agree very well with experiment in all cases. In accordance with recent empirical conclusions the calculation indicates that covalent crystals have stronger chemical bonds with metal overlayers than do ionic crystals.     

Messungen der anomalen Durchlässigkeit und der Reflexion von Röntgenstrahlung an guten Germanium-Einkristallen im Bragg-Fall der Interferenz Vergleich mit der dynamischen Theorie der Röntgeninterferenzen

Curves of anomalous transmission, rocking curves, and integral reflection of very good germanium crystals (some of them were free from dislocations) were measured in the Bragg-case of x-ray diffraction and compared with curves resp. values calculated from dynamical theory. CuK _α radiation was used. According to the measurements the quotient ¦χ_ih¦/¦χ_io¦ of imaginary parts of the fourier coefficients of electron density function is found to be 0.61 for (333)- and 0.73 for (444)-reflection. Though qualitative conformity of measurement with theory is very good there exists systematic differences especially with (444)-reflection: the measured maximum of rocking curves comes out about 11% too low, the measured minimum of transmission curves about 20% too high. At the same time integral reflection is too small. It is discussed whether the discrepancy may be caused by lattice defects.     

KTP和7.5mol%Nb:KTP晶体在Nd:YAG激光中的倍频和和频

本文在获得精确的7.5mol%Nb:KTP晶体的Sellmeier主折射率色散方程的基础上,计算7.5mol%Nb:KTP晶体对1.0642μm和1.3188μmNd:YAG激光的倍频和和频的型相位匹配曲线.通过研究KTP和7.5mol%Nb:KTP晶体的主折射率,双折射率和相位匹配,可以看出Nb掺入KTP晶体后产生的折射率和双折射率的色散和各向异型的变化是引起KTP晶体相位变化的根本原因.     

The group velocity variation of Lamb wave in fiber reinforced composite plate

Experimentally measured Lamb wave group velocities in composite materials with anisotropic characteristics are not the same as the theoretical group velocities which is calculated with the Lamb wave dispersion equation. This discrepancy arises from the fact that the angle between the group velocity direction and the phase velocity direction in anisotropic materials exists. Wave propagation in a composite material with anisotropic characteristics should be considered with respect to magnitude correction in addition to direction correction. In this study, S0 mode phase velocity dispersion curves are depicted with the variation of degree with respect to the fiber direction using a Lamb wave dispersion relation in the unidirectional, bidirectional, and quasi-isotropic composite plates. Slowness surface is sketched by the reciprocal value of the phase velocity curves. The magnitude and direction of the group velocity could be calculated from the slowness surface. The recalculated group velocities with consideration of the magnitude and direction from the slowness surface are compared with experimentally measured group velocities. The proposed method shows good agreements with theoretical and experimental results.     

Electronic structure of LiGaS2

X-ray photoelectron spectroscopy (XPS) measurement has been performed to determine the valence band structure of LiGaS₂ crystals. The experimental measurement is compared with the electronic structure obtained from the density functional calculations. It is found that the Ga 3d states in the XPS spectrum are much higher than the calculated results. In order to eliminate this discrepancy, the LDA+U method is employed and reasonable agreement is achieved. Further calculations show that the difference of the linear and nonlinear optical coefficients between LDA and LDA+U calculations is negligibly small, indicating that the Ga 3d states are actually independent of the excited properties of LiGaS₂ crystals since they are located at a very deep position in the valence bands.