Showing papers on "Brillouin zone published in 1979"
TL;DR: In this paper, the Debye theory of lattice vibrations has been examined in terms of the lattice vibrational spectra, and it is demonstrated that heat capacities of silicates show large deviations from the behavior expected from Debye theories, and that the observed thermodynamic deviations in minerals probably arise from four effects not included in Debye model: anisotropy of elastic parameters, dispersion of acoustic waves toward Brillouin zone boundaries, optic vibrations in excess of Debye spectrum at low frequencies, and optic vibrations at frequencies much greater than the debye cutoff frequency predicted
Abstract: This is the first of a series of five papers in which the thermodynamic properties of minerals are interpreted in terms of lattice vibrational spectra. In this paper, measured heat capacities for minerals are examined in terms of the Debye theory of lattice vibrations, and it is demonstrated that heat capacities of silicates show large deviations from the behavior expected from Debye theory. The underlying assumptions of Debye theory are critically reviewed, and it is shown that the observed thermodynamic deviations in minerals probably arise from four effects not included in the Debye model: anisotropy of elastic parameters, dispersion of acoustic waves toward Brillouin zone boundaries, optic vibrations in excess of the Debye spectrum at low frequencies, and optic vibrations at frequencies much greater than the Debye cutoff frequency predicted by acoustic measurements. Each of the four effects influences the heat capacity in a particular temperature range: anisotropy, dispersion and low-frequency optic vibrations are important at low temperatures (0°K to ∼100°K); high-frequency vibrations are important at higher temperatures. It is necessary to include all four effects in a generalized lattice vibrational model for minerals; such a model is developed in papers 2-5 of this series. The minerals included in this study are halite, periclase, brucite, corundum, spinel, quartz, cristobalite, silica glass, coesite, stishovite, rutile, albite, microcline, jadeite, diopside, enstatite, tremolite, talc, muscovite, forsterite, zircon, kyanite, andalusite, sillimanite, pyrope, grossular, andradite, spessartine, almandine and calcite.
249 citations
TL;DR: In this paper, the authors determined the energy vs. k∥ dispersion of intrinsic surface states on Si(100) (2×1) by means of angle-resolved photoemission with synchrotron radiation.
Abstract: We have determined the energy vs. k∥ dispersion of intrinsic surface states on Si(100) (2×1) by means of angle‐resolved photoemission with synchrotron radiation. For k∥=0, there is a very pronounced surface state 0.7 eV below EF(i.e.,∠0.4 eV below the top of the valence band) which disperses downwards with increasing k∥. At J′ on the boundary of the surface Brillouin zone, we find two states with binding energies of 0.7 and 1.2 eV with respect to EF. A number of geometrical models and their corresponding theoretical surface state bands have recently been published for Si(100) (2×1). Our results disagree qualitatively with all surface state dispersions calculated up to date, i.e., the ideal surface, the vacancy model, the pairing model, and the zig‐zag‐chain model. Namely, we observed semiconducting surface state bands with a low state density at EF while all models calculated to date yield metallic surface states with a large state density at EF.
172 citations
TL;DR: In this paper, a model for the band structure of CuGaTe2 near the point Γ of the Brillouin zone was proposed and three transverse optical mode frequencies were obtained from an analysis of the optical transmission spectra in the photon energy range from 1 to about 3 eV.
129 citations
TL;DR: In this article, the acoustic normal modes were derived and numerically evaluated for a cylindrical step-index fiber with both an infinite and a finite cladding, and it was found that the phonon population which contributes to the Brillouin backscattering spectrum is both narrower in range and shifted in frequency when compared to the corresponding case in the bulk medium.
Abstract: Brillouin scattering in single-mode optical fibers has been investigated both theoretically and experimentally for a 180\ifmmode^\circ\else\textdegree\fi{} scattering geometry and experimentally for a 90\ifmmode^\circ\else\textdegree\fi{} scattering angle. The acoustic normal modes were derived and numerically evaluated for a cylindrical step-index fiber with both an infinite and a finite cladding. It was found that the phonon population which contributes to the Brillouin back-scattering spectrum is both narrower in range and shifted in frequency when compared to the corresponding case in the bulk medium. Back-scattering experiments were performed which yielded the intrinsic phonon lifetime for the longitudinally polarized excitations which are responsible for stimulated Brillouin scattering in the core of a 1.5-\ensuremath{\mu}m (radius) fiber. Brillouin spectra were also observed at a scattering angle of 90\ifmmode^\circ\else\textdegree\fi{}, and the widths of the spectral components were interpreted in terms of nonconservation of wave vector along the radial direction in the acousto-optic interaction. The consequences of these results to stimulated Brillouin scattering in optical fibers are discussed.
104 citations
TL;DR: In this article, the vibrational properties of six different polytypes of Pb${\mathrm{I}}_{2}$ crystals have been studied experimentally by means of Raman spectroscopy and x-ray diffraction.
Abstract: The vibrational properties of six different polytypes of Pb${\mathrm{I}}_{2}$ crystals have been studied experimentally by means of Raman spectroscopy and x-ray diffraction. The crystals were prepared either by gel growth or by thermal annealing. The Raman spectra are used to determine features of the phonon dispersion curves, in the crystallographic $c$ direction, which are common to all of the polytypes. The results are correlated with existing information obtained from measurements of Brillouin spectra and inelastic scattering of neutrons and then analyzed within the framework of a six-parameter force-constant model. Thermodynamic data, including new measurements of lattice parameters in the range $100lTl295$ K, are used to discuss anharmonic and two-dimensional contributions to the vibrational properties.
103 citations
TL;DR: In this article, the surface states at the top of the bulk $d$ bands of Cu(100) and Cu(111) single crystals have been observed using angle-resolved photoemission spectroscopy.
Abstract: Surface states at the top of the bulk $d$ bands of Cu(100) and Cu(111) single crystals have been observed using angle-resolved photoemission spectroscopy. The measured dispersion of the surface-state bands falls in absolute energy gaps of the projected bulk band structure near the symmetry point $\overline{M}$ of the two-dimensional Brillouin zone, for both faces. Since the parent energy gaps are not caused by the hybridization of crossed energy bands, the observed states are of the Tamm rather than the Shockley type; surface states of the latter type have been observed before in $\mathrm{sp}$ gaps of several noble metals. Tamm states require a sufficiently strong surface "perturbation." Only the self-consistent calculations of Gay, Smith, and Arlinghaus recently reported for Cu(100) contain surface states in the energy-wave-vector region studied here. The observed peaks are very narrow, due to their energy location above the bulk $d$-band continuum as well as the good angle and energy resolution of our spectrometer.
96 citations
TL;DR: In this article, a generalized Green's function is found that describes the impulse response for stimulated scattering by electron and ion modes in a coherent electromagnetic plane wave propagating in a uniform plasma.
Abstract: Stimulated Brillouin scattering, filamentation, and induced Thomson scattering are studied for a coherent electromagnetic plane wave propagating in a uniform plasma. A generalized Green’s function is found that describes the impulse response for stimulated scattering by electron and ion modes. Explicit asymptotic Green’s functions are calculated for those parametric instabilities involving ion modes or quasi‐modes. Special attention is given to whether the instabilities are convective or absolute. For a traveling wave pump in a uniform plasma, Brillouin and induced Thomson backscatter can be absolute, but sidescatter is convective; filamentation of traveling waves is always convective. Spatial growth rates are calculated for convectively unstable modes. Finally, the competition of filamentation and stimulated Brillouin scattering is considered for parameters typical of real laser‐fusion experiments.
79 citations
TL;DR: In this article, self-consistent APW calculations of the electronic energy bandstructure of the calcium hexaboride, CaB6, are reported, in the muffin-tin approximation and in the warped muffintin approximation.
Abstract: The calcium hexaboride, CaB6, is a typical semiconducting metal hexaboride. Here two self-consistent APW calculations of its electronic energy bandstructure are reported, in the muffin-tin approximation and in the warped muffin-tin approximation. In both calculations, the local-spin-density approximation is used and the relativistic effects are taken into account. The bandstructure of the muffin-tin approximation is semimetallic. The non-muffin-tin corrections in the warped muffin-tin approximation tends to cause a small, direct energy gap between the valence and conduction bands at the X points in the simple cubic Brillouin zone. The magnitude of the energy gap to 0.3 eV, in reasonable agreement with the experimental value, 0.4 eV, suggested by the temperature dependence of the electrical resistivity. The calculated result for the density of states agrees reasonably well with an experimental result for the XPS spectrum.
75 citations
TL;DR: In this paper, two distinct approaches to the calculation of first-order properties with a limited CI wave function are discussed, one based on the Hellmann-Feynman theorem and the other based on direct evaluation of the total energy derivative at zero perturbation.
Abstract: Two distinct approaches to the calculation of first-order properties with a limited CI wave function are discussed. One is based on the Hellmann–Feynman theorem and the other on the direct evaluation of the total energy derivative at zero perturbation. Corrections to the Hellmann–Feynman expectation value are given for the CI wave function consisting of a single determinant reference state and all single and double replacements of this. These corrections are the extended Brillouin matrix elements and involve interactions between the zeroth-order wave function and triply substituted configurations. The usefulness of these matrix elements for the generation of MC SCF orbitals and for the calculation of cluster corrections to the wave function is briefly discussed. The formulas for the Brillouin matrix elements expressed in terms of one- and two-electron integrals have been automatically generated using the syntax of the algebraic program SCHOONSCHIP.
67 citations
TL;DR: In this paper, a study was made of wavefront reversal, accompanying stimulated Brillouin scattering in various media, and of the way it was affected by the geometrical, temporal, and polarization characteristics of the exciting radiation.
Abstract: A study was made of wavefront reversal, accompanying stimulated Brillouin scattering in various media, and of the way it was affected by the geometrical, temporal, and polarization characteristics of the exciting radiation. In an oscillator-amplifier system, practically complete compensation was achieved for phase distortions of the oscillator signal introduced by the amplifier components. The output energy of the light beam was then 3 J, its diameter was 4 mm, and its divergence (diffraction limited) was 0.3 mrad. The results of the experiments indicated a practical possibility of applying the wavefront reversal phenomenon in high-power multichannel lasers.
65 citations
TL;DR: In this paper, a simple cubic Ising-system with nearest neighbor exchangeJ and dipolar interaction of strengthµcffff3/a3 was considered and the ordering at nonzero temperature was studied by means of mean-field approximations (MFA) and Monte Carlo (MC) calculations.
Abstract: As a simple model of order-disorder ferroelectrics or dipolar magnets we consider a simple cubic Ising-system with nearest neighbor exchangeJ and dipolar interaction of strengthµ
2/a
3. ForJa
3/µ
2<−1.3384 the ground-state is antiferromagnetic, while for −1.33840.16429 the ferromagnetic phase becomes stable (with domain arrangements depending on the shape of the sample). For all critical values ofJa
3/µ
2 where the bulk energies of two phases become equal also the interface energy between these phases is found to be zero. The ordering at nonzero temperature is studied by means of mean-field approximations (MFA) and Monte Carlo (MC) calculations. It turns out that forJa
3/µ
2 of order unity the MFA overestimates ordering temperatures by about a factor of two, and predicts multicritical points (between the disordered and two ordered phases) at nonzero temperature, including two biaxial Lifshitz points which the MC work suggests to occur atT=0. In contrast to MFA the layered antiferromagnetic structure is found to be stable only at extremely lowT, because a metastable spin-glass phase (with random arrangement of ferromagnetic rows in the spin direction) has only slightly higher energy. The MFA also yields two regimes of helical phases which are “locked in” to the antiferromagnetic phases at uniaxial Lifshitz points occurring at the Brillouin zone boundary. In the MC-work various methods of treating the long-range interaction are investigated. While all kinds of truncations as well as compensating field methods are rather unsatisfactory in our case, Ewald summation techniques yield satisfactory results. Nevertheless strong fluctuations as well as strong finite size effects prevent us from making accurate exponent estimates, but arguments are given that there is no regime of broad visibility of Landaulike critical behavior. Finally the extension of our results to other lattices as well as experimental applications are briefly discussed.
TL;DR: In this paper, two semi-empirical crystal orbital schemes for the calculation of the properties of perfect and defective solids are presented. Butler et al. use periodic boundary conditions with a large unit cell (LUC) to map special points of the Brillouin zone onto the point k = 0.
Abstract: Two semiempirical crystal orbital schemes are outlined for the calculation of the properties of perfect and defective solids. Both use periodic boundary conditions with a large unit cell (LUC) to map special points of the Brillouin zone onto the point k=0. One method involves the complete neglect of differential overlap (LUC-CNDO), the other uses intermediate neglect of differential overlap (LUC-INDO). The determination of parameter sets for the elements is discussed.
TL;DR: In this article, the authors report a theroetical prediction of a new feature in the spectrum of light scattered from a fluid in a nonequilibrium stationary state with a temperature gradient.
Abstract: We report a theroetical prediction of a new feature in the spectrum of light scattered from a fluid in a nonequilibrium stationary state with a temperature gradient. The spectrum is not symmetric in the frequency shift and the Brillouin components have different intensities. The phenomenon is linked to the breaking of time-reversal symmetry and to the appearance of a static correlation function between momentum and number densities which is zero in equilibrium, but has a $\frac{1}{{k}^{2}}$ dependence in the stationary state. We suggest a light scattering experiment by means of which these predictions can be verified.
TL;DR: From angle-resolved photoelectron energy distribution curves, this paper identified an occupied surface state band at the symmetry point of the two-dimensional Brillouin zone of Cu(110), which has been predicted theoretically by Dempsey and Kleinman.
TL;DR: In this paper, the linear response theory using a complete set of dynamic variables involving density, velocity, and energy fluctuations is used to analyze the Rayleigh-Brillouin spectrum of a viscoelastic liquid.
Abstract: The linear response theory using a complete set of dynamic variables involving density, velocity, and energy fluctuations is used to analyze the Rayleigh–Brillouin spectrum of a viscoelastic liquid. The result is discussed in the fast and slow relaxation limits. In the former case, the Rayleigh–Brillouin spectrum is identical to that predicted by the classical hydrodynamic equations; whereas in the latter case a new structural central peak is found, in addition to the anomalous dispersion and relaxation effects present in the frequency and linewidth data associated with the Brillouin peak. The evolution of structural relaxation and its effect on the entire Rayleigh–Brillouin spectrum is described. The structural central peak is most pronounced when the frequency dispersion and the linewidth maximum are present. The theoretical result has been used to calculate the Rayleigh–Brillouin spectra of polypropylene glycol at various temperatures. The results of the frequency shift, the spectral linewidth, and the Landau–Placzek ratio are in good agreement with the experiment.
TL;DR: In this paper, the variational form of the Schrodinger equation is shown to be equivalent to a set of generalized Brillouin conditions in terms of arbitrary antihermitean operators R.
TL;DR: A narrow peak (full width at half maximum about 60 meV) just above the top of the bulk $d$ bands has been observed in angle-resolved energy distribution curves of Cu(100) as discussed by the authors.
Abstract: A narrow peak (full width at half maximum about 60 meV) just above the top of the bulk $d$ bands has been observed in angle-resolved energy distribution curves of Cu(100). The peak is attributed to a $d$-like surface state in an energy gap of the projected bulk band structure near the symmetry point $\overline{M}$ of the two-dimensional Brillouin zone. A surface state near $\overline{M}$ was predicted in recent self-consistent calculations.
TL;DR: In this paper, a device which uses an induced Raman or Brillouin scattering process to amplify laser pulses is described and a technique is presented to analyze the amplification of ultrashort laser pulses with effects such as pump depletion included.
Abstract: A device which uses an induced Raman or Brillouin scattering process to amplify laser pulses is described A technique is presented to analyze the amplification of ultrashort laser pulses with effects such as pump depletion included The results of the examples considered indicate that such a device can be realized with current technology
TL;DR: In this article, the authors used the Brillouin spectra from thermally excited surface acoustic phonons in GaAs and Si surfaces coated with a thin Al film and gave a theoretical explanation of the experimental results in terms of the coupling between the normal modes of the film and the substrate.
Abstract: Brillouin spectra from thermally excited surface acoustic phonons in GaAs and Si surfaces coated with a thin Al film are presented. The measurements show features different from the Al and the semiconductor surfaces. We are able to give a theoretical explanation of the experimental results in terms of the coupling between the normal modes of the film and of the substrate.
TL;DR: In this article, a simple expression is derived for the effect of LRO on the relaxation time tau to give an overall dependence of resistivity with LRO of the form rho (S,T)=(1-S2)/(1-AS2))+(T/Tc)(1/(1-As2)) where T is the measuring temperature, S the Bragg-Williams LRO Parameter, Tc the critical order-disorder temperature and A a parameter whose sign and magnitude depend upon the relative positions of the Fermi surface and superlattice
Abstract: Long range atomic ordering (LRO) is known to affect the effective number of conduction electrons neff as a result of new energy gaps forming in the Fermi surface at the superlattice Brillouin zone boundaries. A simple expression is derived for this behaviour and combined with the effects of LRO on the relaxation time tau to give an overall dependence of resistivity with LRO of the form rho (S,T)=(1-S2)/(1-AS2))+(T/Tc)(1/(1-AS2)) where T is the measuring temperature, S the Bragg-Williams LRO Parameter, Tc the critical order-disorder temperature and A a parameter whose sign and magnitude depend upon the relative positions of the Fermi surface and superlattice Brillouin zone boundaries. This is found to be in good agreement with experimental data for Cu3Au and Fe3Al.
TL;DR: In this article, the surface-sensitive peak at the Fermi energy was revealed near the surface Brillouin-zone edges in both the [10] and [11] directions.
Abstract: Angle-resolved photoelectron spectra, utilizing polarized synchrotron radiation, from Ni(100) reveal a narrow surface-sensitive peak at the Fermi energy. This structure exists near the surface-Brillouin-zone edges in both the [10] and [11] directions. The symmetry of this state is odd (even) with respect to the (100) [(110)] mirror plane. Projections of the bulk bands onto the surface Brillouin zone show that these surface-sensitive energy levels exist in regions of the surface Brillouin zone where there are gaps in only one spin band. The very narrow energy width of these states indicates that they are surface states and consequently magnetic.
TL;DR: In this paper, the vibrational dispersion over the Brillouin zone is small and all triply degenerate vibrations are split into their longitudinal and transverse components, and the vibrations were assigned within the factor group approximation.
Abstract: Absorption and magnetic circular dichroism spectroscopy have been used to study the cubic crystal Cs2NaTmCl6. Transitions between the Oh crystal field levels in 3 H 6 and 3 H 4, 3 F 3, 3 F 2, 1 G 4 and 1 D 2 have been observed and assigned. Rich vibrational structure was observed in all transitions and the vibrations were assigned within the factor group approximation. The vibrational dispersion over the Brillouin zone is small and all triply degenerate vibrations are split into their longitudinal and transverse components. Transition intensities for magnetic dipole and selected electric dipole (vibronic) transitions were calculated using the ligand polarization model. There was good agreement between the calculated and experimental intensities in a number of transitions. The model failed to predict absolute and relative vibronic intensities within any one crystal field transition. This is probably due to the restricted vibrational model used.
TL;DR: Saturation of stimulated Brillouin scattering has been observed in the interaction of long-pulse C${O}}_{2}$-laser radiation with underdense hydrogen plasma at intensities of \ensuremath{le}${10}^{13}$ W/${\mathrm{cm}}^{2} as discussed by the authors.
Abstract: Saturation of stimulated Brillouin scattering has been observed in the interaction of long-pulse C${\mathrm{O}}_{2}$-laser radiation with underdense hydrogen plasma at intensities of \ensuremath{\le}${10}^{13}$ W/${\mathrm{cm}}^{2}$. The stimulated Brillouin scattering is strongly modulated with average long-time reflectivity approximately half the peak value. The maximum reflectivity measured was 60% and wave breaking is postulated as the principal saturation mechanism.
TL;DR: In this article, a method for small-signal wavefront reversal during stimulated Brillouin scattering in an optical waveguide was proposed and implemented for nanosecond pulses, which may find applications in the wave-front reversal of nanoscond pulses.
Abstract: A method is proposed and implemented for small-signal wavefront reversal during stimulated Brillouin scattering in an optical waveguide. This method may find applications in the wavefront reversal of nanosecond pulses.
TL;DR: In this article, the lattice dynamics of incommensurate modulated crystals are discussed in the harmonic approximation, based on the symmetry group of such a crystal, i.e. a superspace group.
Abstract: The lattice dynamics of incommensurate modulated crystals is discussed in the harmonic approximation. The study is based on the symmetry group of such a crystal, i.e. a superspace group. The normal modes may be characterised by irreducible representations of the symmetry group. It is shown that the relevant representations may be labelled by wave-vectors in the Brillouin zone of the basic space group. The reduction of the equations of motion is treated. Finally selection rules for infrared absorption are derived.
TL;DR: The first absolute measurement of 35-GHz hypersound velocity with a 10(-4) relative uncertainty is reported, and previous errors due to imperfect calibration and nonlinearity of the Fabry-Perot interferometer are eliminated.
Abstract: A new method for the accurate measurement of Brillouin line shifts is presented. By modulating a reference beam at a microwave frequency corresponding exactly to the shift of the Brillouin line, the Brillouin scattering frequency is obtained by direct comparison. Previous errors due to imperfect calibration and nonlinearity of the Fabry-Perot interferometer are therefore eliminated. The first absolute measurement of 35-GHz hypersound velocitywith a 10-4 relative uncertainty is reported.
TL;DR: In this paper, the influence of hydrostatic pressure on the electronic structure and the optical spectra of trigonal Te is investigated using a selfconsistent pseudopotential formalism based on realistic pseudopotentials of the free ion and atom.
Abstract: Using a self-consistent pseudopotential formalism based on realistic pseudopotentials of the free ion and atom, the influence of hydrostatic pressure on the electronic structure and the optical spectra of trigonal Te is investigated. The pressure derivative of the fundamental gap is found to be in good agreement with experimental results. The joint density of states, ${\ensuremath{\epsilon}}_{1}$ and ${\ensuremath{\epsilon}}_{2}$, energy-loss function, reflectivity, and absorption coefficient are calculated from 0 to 13 eV. Very good agreement is obtained with experimental spectra. The very strong pressure-induced enhancement of the reflectivity can be reproduced. The anisotropy anomaly in the reflectivity at high energies is explained and traced to distinct transitions in the Brillouin zone. Predictions are made about the pressure dependence of the optical spectra above 4 eV. Finally, selfconsistent charge densities and the electronic density of states are also presented.
TL;DR: In this paper, the first experimental observation of heavy and light excitons by resonant Brillouin scattering of polaritons in ZnSe has been reported, based on a three-branch polariton dispersion curve.
Abstract: This Letter reports the first experimental observation of heavy and light excitons by resonant Brillouin scattering of polaritons in ZnSe. The number of the Brillouin peaks as well as their variations with the excitation light energy are well accounted for on the basis of a three-branch polariton dispersion curve in which the longitudinal-transverse splitting ${E}_{\mathrm{LT}}$ and the exchange energy $\ensuremath{\Delta}$ mix both kinds of excitons. The observation of the three branches allows us to determine ${E}_{\mathrm{LT}}$, $\ensuremath{\Delta}$, and the translational masses ${M}_{h}$ and ${M}_{1}$ of heavy and light excitons.
TL;DR: In this article, the performance of hyper-Raman spectra of CsI, CsBr, RbI, and SrTiO3 was compared with data due to other experimental techniques.
Abstract: Hyper-Raman spectra of CsI, CsBr, RbI, and SrTiO3 are measured at room temperature. All optical phonons at the I′-point of the Brillouin zone can be detected including the longitudinal modes and one silent mode. The results obtained for SrTiO3 are compared with data due to other experimental techniques. Superiority of hyper-Raman speetroscopy in determining frequencies and linewidths is demonstrated.
TL;DR: In this paper, the authors derived properties derived from lithium b.c. crystal Hartree-Fock (HF) calculations, using LCAO-type Bloch functions and including 2 s, 2 p and 3 d Slater-type basis orbitals, including total energies, lattice parameters, band gaps, widths of the occupied part of valence band, bulk modulus and Fermi surface geometry.