Showing papers on "Brillouin zone published in 1982"
TL;DR: In this paper, the authors provide numerical and graphical information about many physical and electronic properties of GaAs that are useful to those engaged in experimental research and development on this material, including properties of the material itself, and the host of effects associated with the presence of specific impurities and defects is excluded from coverage.
Abstract: This review provides numerical and graphical information about many (but by no means all) of the physical and electronic properties of GaAs that are useful to those engaged in experimental research and development on this material. The emphasis is on properties of GaAs itself, and the host of effects associated with the presence of specific impurities and defects is excluded from coverage. The geometry of the sphalerite lattice and of the first Brillouin zone of reciprocal space are used to pave the way for material concerning elastic moduli, speeds of sound, and phonon dispersion curves. A section on thermal properties includes material on the phase diagram and liquidus curve, thermal expansion coefficient as a function of temperature, specific heat and equivalent Debye temperature behavior, and thermal conduction. The discussion of optical properties focusses on dispersion of the dielectric constant from low frequencies [κ0(300)=12.85] through the reststrahlen range to the intrinsic edge, and on the ass...
2,115 citations
TL;DR: In this article, the energy band structure of black phosphorus was calculated by using self-consistent pseudopotential method and the resulting band structure has the direct minimum gap at the point Z in the Brillouin zone in agreement with the result of the tight-binding approach.
Abstract: The energy band structure of black phosphorus is calculated by using self-consistent pseudopotential method. The resulting band structure has the direct minimum gap at the point Z in the Brillouin zone in agreement with the result of the tight-binding approach. Effective electron and hole masses and the level shift of the band edge by pressure are calculated from the bands obtained. The pressure dependence of the energy gap is in good agreement with experiment, but the anisotropy of the effective masses contradicts that of the electrical conductivity measured for the single crystal. The nature of the optical absorption edge is discussed in terms of the calculated band structure.
127 citations
TL;DR: In this article, the authors derived the correlation functions of mass, momentum, and energy densities for a fluid subject to a large temperature gradient, and the deviations of the intensity of each Brillouin line from its equilibrium value as a function of the temperature gradient were obtained for the optimal scattering geometry.
Abstract: The equations derived in the first paper of this series for the correlation functions of mass, momentum, and energy densities are solved for a fluid subject to a large temperature gradient. The shape and intensity of the Rayleigh line show deviations from equilibrium that are proportional to the square of the temperature gradient. The deviations of the intensity of each Brillouin line from its equilibrium value as a function of the temperature gradient is obtained for the optimal scattering geometry. The intensity of one of these two Brillouin lines shows a maximum or minimum as a function of the temperature gradient, depending on the sign of the temperature derivatives of the coefficient of sound attenuation and thermal conductivity and on the orientation of the momentum transfer between fluid and light with respect to the temperature gradient. Further, the difference in intensity of the two Brillouin lines is found to be about three times smaller than predicted by the linear theory, consistent with the experiments of Beysens et al. Since all these results are due to mode-coupling effects, an experimental verification would constitute the first observation of mode-coupling effects away from criticality. The connection between (a) the mode-coupling effects responsible for the changes in the intensities of the Rayleigh and Brillouin lines, (b) the long-time tail contributions to the transport coefficients, and (c) the nonexistence of a virial expansion of the transport coefficients is discussed.
119 citations
TL;DR: In this article, the surface energy-band structure of the As-stable GaAs(001)-(2\ifmmode\times\else\texttimes\fi{}4) reconstruction was investigated.
Abstract: We have carried out an experimental and theoretical study of the surface-energy-band structure of the As-stable GaAs(001)-(2\ifmmode\times\else\texttimes\fi{}4) reconstruction. Angle-resolved photoemission measurements with the use of synchrotron radiation at LURE, Orsay, have been performed on surfaces which were grown in situ by molecular beam epitaxy. Measurements made at high-symmetry points and along symmetry lines of the surface Brillouin zone show weakly dispersing dangling-bond-like surface states in the energy range between - 1.6 eV and the top of the valence band, and a nearly dispersionless state near - 3 eV. To clarify the origin of these states, we have applied the scattering theoretical method on the basis of an empirical tight-binding description of the GaAs bulk crystal to the ideal (1\ifmmode\times\else\texttimes\fi{}1) As-terminated surface and to a (2\ifmmode\times\else\texttimes\fi{}1) asymmetric As-As dimer model. The principal effect of the reconstruction is the introduction of a new dimer-related state at - 3.5 eV. In addition in the energy range near the top of the projected bulk bands, dangling-bond states with a significant in-plane component are found. Although we do not observe a direct one-to-one correspondence between experiment and theory, the essential features of an asymmetric As-As dimer are established.
108 citations
TL;DR: In this paper, the authors derived a qualitative molecular orbital model of NiPS3 in which the trigonal crystal field splits the P and S 3pxpy-3pa states, and strong covalent hybridization between p and S pxpy orbitals leads to covalents electronic bonding.
101 citations
TL;DR: In this paper, the relationship between structure, vibrational dispersion relations, and band structure for chalcopyrite and related compounds is discussed in a detailed and concentrated manner.
Abstract: Publisher Summary The chapter presents a study on the relationship between structure, vibrational dispersion relations, and band structure for chalcopyrite and related compounds. The essential step in this procedure is the “folding” of the dispersion relations [ ω (k) or E (k)] for the simplest structure into the smaller Brillouin zone of the more complicated one. In one-dimensional models, such folding is trivial enough and is discussed in relation to the nearly free electron approximation, Peierls instability, and so on. In three dimensions, it is more complex and therefore merits the detailed and concentrated description that is presented in this chapter. In addition to the chalcopyrites, the chapter includes certain quaternary and “defect” or “vacancy” compounds, such as HgIn 2 Te 4 . The vacancy compounds may be considered to have tetrahedral structures with a sublattice of unfilled sites. In this case, it is questionable whether the compound is to be regarded as derived from its parent structure by a small perturbation, as is often assumed for chalcopyrites. Compounds that have tetrahedrally coordinated structures generally have an average number of four valance electrons per atom. This is the Grimm–Sommerfeld rule.
95 citations
TL;DR: In this paper, a scheme for the semiclassical quantisation of the solitons of the 1-D continuum Heisenberg ferromagnet is examined, and a parameter that can be interpreted as the intrinsic wavenumber Q of a classical soliton is identified.
Abstract: The scheme for the semiclassical quantisation of the solitons of the 1-D continuum Heisenberg ferromagnet is examined. A parameter that can be interpreted as the intrinsic wavenumber Q of a classical soliton is identified. The cut-off restriction that Q lies within the first Brillouin zone has to be added to the continuum model if its results are to be consistently interpreted in terms of an underlying spin S lattice model.
88 citations
TL;DR: In this paper, a measurement of surface Brillouin scattering from a 2250-AA{} film of silica grown on (001) silicon is presented, and the spectrum shows many structures related to Rayleigh, Sezawa, and Lamb waves.
Abstract: A measurement of surface Brillouin scattering from a 2250-\AA{} film of silica grown on (001) silicon is presented. The spectrum shows many structures related to Rayleigh, Sezawa, and Lamb waves. We calculate the Brillouin cross section taking the ripple and the elasto-optic coupling mechanisms into account in the two media. Both the mechanisms are found to be important and there is evidence of strong interference effects between the ripple and the elasto-optic contributions to the scattering amplitude.
47 citations
TL;DR: Optic observation of phase conjugation by stimulated Brillouin scattering using KrF-laser radiation (248 nm) is reported.
Abstract: We report observation of phase conjugation by stimulated Brillouin scattering using KrF-laser radiation (248 nm). The backscattered signal consists of both phase-conjugate and non-phase-conjugate components, which have different temporal behavior. This phase-conjugate Brillouin mirror has been used in a double-pass KrF laser-amplifier system, and as an element in a KrF-laser resonator, to compensate for aberrations and to produce a diffraction-limited output beam.
45 citations
TL;DR: In this paper, the authors investigated the Raman spectra of three polytypes of lead iodide (2H, 4H and 6H) as a function of temperature at ambient pressure.
Abstract: Raman spectra of three polytypes of lead iodide (2H, 4H and 6H) have been investigated as a function of temperature at ambient pressure. The band assignments have been carried out on the basis of folding of 2HPbI2 phonon dispersion curves in the Brillouin zone. The temperature induced changes in the Raman spectra are interpreted in terms of an interpolytypic phase transformation (at 415 K) and photodecomposition at 470 K.
42 citations
TL;DR: In this paper, the polar-angle dependence of the photoelectron emission was recorded along the two symmetry lines of the surface Brillouin zone, and six structures were identified in the spectra.
Abstract: Mg(0001) has been studied with angle-resolved photoemission spectroscopy for photon energies in the range 7.0-26.8 eV. The polar-angle dependence of the photoelectron emission was recorded along the two symmetry lines $\overline{\ensuremath{\Gamma}}\overline{M}$ and $\overline{\ensuremath{\Gamma}}\overline{K}$ of the surface Brillouin zone. Six structures are identified in the spectra. Two sharp peaks are assigned to emission from surface states. One is located in a band gap around $\overline{\ensuremath{\Gamma}}$, the other in a band gap near $\overline{M}$. Three peaks are interpreted as indirect transitions from different electron pockets in the Brillouin zone. These regions with high densities of occupied states are located close to $\ensuremath{\Gamma}$, $L$, and $K$ in the bulk Brillouin zone. Our experiments confirm earlier magnetoacoustic attenuation and de Haas---van Alphen experiments with respect to these electron pockets. Finally one broad structure is interpreted as a direct optical transition between bulk bands.
TL;DR: In this article, the phonon branches of graphite-alkali intercalation compounds are characterized by one-dimensional lattice-dynamical models: the alkali-graphite interplanar interaction is mediated by an electronic shell, while the interior graphite graphite interaction is represented by Born \char22{} von K\'arm\'an force constants.
Abstract: Neutron spectroscopic studies of the [001] $L$-phonon branches in graphite-alkali intercalation compounds ${\mathrm{C}}_{x}M$ ($x=8,24,36$; $M$ denotes K, Rb, Cs) have been undertaken. In all cases zone-folding effects as well as frequency gaps at the center and boundary of the Brillouin zone have been observed. The phonon branches of all stages and compounds measured are well described by one-dimensional lattice-dynamical models: The alkali-graphite interplanar interaction is mediated by an electronic shell, while the interior graphite-graphite interaction is represented by Born \char22{} von K\'arm\'an force constants. Sound velocities and elastic constants of the intercalation compounds are derived from the acoustical-phonon branches.
TL;DR: In this article, a relativistic first-principle band structure calculation on iridium is presented, based on the Hedin-Lundqvist form of the exchange-correlation potential and carried to self-consistency including 525 k points in the irreducible wedge of the Brillouin zone.
Abstract: A fully relativistic first-principles band structure calculation on iridium is presented. The energy range covers both the occupied electron bands which originate in the free atomic 5d and 6s levels, and the excited bands up to 30 eV above the Fermi level EF. The calculation is based on the Hedin-Lundqvist form of the exchange-correlation potential and was carried to self-consistency including 525 k points in the irreducible wedge of the Brillouin zone. Complete relaxation of all core states was allowed for. The results are compared with a recent angle-resolved photoemission study by van der Veen et al. (1980). The experimental values for critical points in the band structure of both valence and final states agree with the respective special points of the authors' bands within experimental error. In addition, most of the rich structure seen in the photoemission spectra can be quantitatively interpreted in terms of the energy bands.
TL;DR: In this paper, a scheme for deriving atomic force constants that is fairly accurate, yet simple enough to allow determination of the dynamical matrix of bulk solids, relaxed and reconstructed surfaces, defects, etc.
Abstract: A scheme is presented for deriving atomic force constants that is fairly accurate, yet simple enough to allow determination of the dynamical matrix of bulk solids, relaxed and reconstructed surfaces, defects, etc. For illustrative purposes, the method is applied to bulk SiC to predict the phonon dispersion curves throughout the entire Brillouin zone, and to a carbon vacancy in SiC to study the change of atomic force constants due to atomic relaxations.
TL;DR: In this paper, the vibrational spectra of V2+ and Cr3+ impurities in MgO phonons were used to determine the pressure dependences of the energies of phonons at several critical points of the Brillouin zone.
Abstract: Vibronic spectra of V2+ and Cr3+ impurities in MgO have been used to determine the pressure dependences of the energies of MgO phonons at several critical points of the Brillouin zone to more than 100 kbar at 90 and 295 K. From these data, approximate densities of states for MgO at 100 and 500 kbar and vibrational partition functions were constructed, and contributions to the constant-volume heat capacity, entropy, internal and free energies, and the Debye temperature were calculated. Argon was successfully used as a nearly hydrostatic pressure medium for the measurements at 90 K to 102 kbar.
TL;DR: In this article, the elastic stiffness constants have been determined at room temperature using Brillouin spectroscopy, and the spectral width of the corresponding spectral width has been shown to show important variations around the transition temperature (Ti = -143°C) between prototypic and incommensurate phases.
Abstract: All elastic stiffness constants have been determined at room temperature using Brillouin spectroscopy. Some of them and the spectral width of the corresponding Brillouin peaks show important variations around the transition temperature (Ti = -143°C) between prototypic and incommensurate phases. Below Ti, the anomalies associated with the acoustic phonons propagating in the (001) direction are explained assuming a linear coupling between deformations and an overdamped mode. This mode is equivalent to a Debye relaxation process characterized by a relaxation time τ0 = 2.6 10-12 s.K.
TL;DR: The second-order spectrum originates largely from pairs of phonons with wave vectors near the Brillouin zone boundary as discussed by the authors, where the presence of impurities raised the cubic to tetragonal phase transition temperature to 120 K, where a new impurity-related band was observed at 793 cm−1.
Abstract: At room-temperature the Raman spectrum was second-order, in agreement with, the selection rules for the cubic perovskite structure. The second-order spectrum originates largely from pairs of phonons with wave vectors near the Brillouin zone boundary. First-order Raman-active modes predicted in the tetragonal phase of SrTiO3 are observed on cooling to 120 K, where a new impurity-related band is observed at 793 cm−1. The presence of impurities raised the cubic to tetragonal phase transition temperature to 120 K.
TL;DR: In this article, the theoretical problem of wave propagation and the definition of the signal velocity in a medium exhibiting resonant, absorptive, anomalous dispersion is investigated, and the special case of a dilute medium is considered, such as the upper atmosphere with dispersion due to resonant line structure, as opposed to plasma dispersion, which is not resonant.
Abstract: The theoretical problem of wave propagation and the definition of the signal velocity in a medium exhibiting resonant, absorptive, anomalous dispersion is investigated. The special case of a dilute medium is considered, such as the upper atmosphere with dispersion due to resonant line structure (e.g., the water vapor or oxygen lines in the microwave region), as opposed to plasma dispersion, which is not resonant. Signal velocity definitions analogous to those first made by Brillouin were derived in another work and are called to question as a result of an exact solution of the problem derived here, using a Bessel function series, which allows exact wave forms to be calculated and displayed. When one represents the signal development by using the simulations, it is found that one cannot realistically separate signal from precursor. The pulse envelopes do have some interesting ringing characteristics which are shown to depend upon the density of absorbers and the resonance linewidth. Qualitative experimental results are presented that verify the simulations. The measurement of this ringing appears to be a more sensitive technique than does differential absorption for determining constituent number densities.
TL;DR: In this article, the Brillouin spectra of single crystals of the solid electrolyte Li2SO4 were obtained for various crystal orientations in the temperature range 899-1120 K.
Abstract: Brillouin spectra of single crystals of the solid electrolyte Li2SO4 were obtained for various crystal orientations in the temperature range 899–1120 K. The spectra contained one longitudinal component and at least one and sometimes both transverse components. The frequency shifts varied between 14.5 and 17.4 GHz for the longitudinal and between 4.1 and 9.0 GHz for the transverse component, the shift being strongly dependent on crystal orientation. The observed frequency shifts correspond to values of the elastic constants typical for plastic materials.
TL;DR: In this article, an extensive investigation of the room temperature elastic constants is presented yielding a complete evaluation of their anistropy, and it is found that scattering intensity and correlation time are caused by the modulation and driving of defects by an external periodic applied stress pulse.
Abstract: Brillouin and Rayleigh scattering techniques have been employed to study the elastic behavior of single crystals of urea over the temperature range 15–300 K. An extensive investigation of the room temperature elastic constants is presented yielding a complete evaluation of their anistropy. The temperature dependence of these elastic modes along the [001] and near the [110] directions is followed to 15 K; no evidence of a structural phase transition has been found. Rayleigh scattering experiments reveal a correlation time in the ms range and an intensity behavior that are temperature dependent but show no anomalies as a function of temperature for a number of directions in the crystal. It is found that scattering intensity and correlation time are caused by the modulation and driving of defects by an external periodic applied stress pulse. Neither the correlation time nor the intensity behavior supports the conclusion that urea undergoes a structural second order phase transition in the temperature range 1...
TL;DR: In this paper, angle-resolved UV photoemission was used to measure impurity-stabilized Si(111) 1 × 1 and clean Si( 111) 7 × 7 surfaces.
TL;DR: In this paper, temperature dependence of elastic stiffness is measured in the range -100 to +70 degrees C. The results are discussed in terms of coupling between strain and soft modes which are allowed by symmetry.
Abstract: Temperature dependence of elastic stiffness is measured in the range -100 to +70 degrees C. At the lock-in transition near -81 degrees C, only slight slope changes appear for some stiffnesses. Weak anomalies are observed near the incommensurate-commensurate transition at 29 degrees C for c22, c33, c44, c55 and c66. No broadening of Brillouin lines is detected. The results are discussed in terms of coupling between strain and soft modes which are allowed by symmetry. The value of 0.6+or-0.1 for the exponent 2 beta of the order parameter squared is determined from the temperature dependence of c44. The evolution of c33 in the incommensurate phase below the 29 degrees C transition agrees with a relaxational behaviour of the susceptibility associated with the ampliton mode normal coordinate, characterised by a critical slowing down of the relaxation time. This result is compatible with the overdamped ampliton mode observed by Raman scattering.
IBM1
TL;DR: A 5f-like photoemission feature in normal emission from UN(100) appears for T N e el = 53 K as mentioned in this paper, which arises from band states that are modified due to a halving of the Brillouin zone in the antiferromagnetic phase.
TL;DR: In this article, two essentially different semi-empirical methods (Mulliken-Ruedenberg and INDO) were used to calculate the electronic structure of the (001) surface for some alkali halides (LiF, LiCl, NaF, NaCl) within the framework of different surface models (slab infinite in two dimensions, molecular cluster and the slab placed over the point-ion support).
Abstract: Two essentially different semiempirical methods (Mulliken-Ruedenberg and INDO) have been used to calculate the electronic structure of the (001) surface for some alkali halides (LiF, LiCl, NaF, NaCl) within the framework of different surface models (slab infinite in two dimensions, molecular cluster and the slab placed over the point-ion support). The computational procedure has taken into account both the bond breaking of surface atoms and the electrostatic potential difference between the surface atoms and the bulk together with the charge density redistribution obtained self-consistently. The problem of the optimum choice of the set of points in the two-dimensional Brillouin zone necessary for the calculation of the self-consistent crystal potential is discussed. The results for the electronic structure of the surfaces of alkali halides are compared with those obtained by means of surface Green functions methods.
TL;DR: In this article, angle-resolved ultraviolet photoelectron spectra from the valence bands of NiTe2, PdTe2 and PtTe2 are presented and their empirical band structures along high-symmetry directions of the Brillouin zone are determined.
Abstract: Angle-resolved ultraviolet photoelectron spectra from the valence bands of NiTe2, PdTe2 and PtTe2 are presented and their empirical band structures along high-symmetry directions of the Brillouin zone are determined. Photon polarisation-dependent data together with photoionisation cross section behaviour give the position and character of the metal d bands at the Gamma point. The positions of these filled metal d bands are found to shift progressively to higher binding energies from Ni to Pd to Pt. Spectral features are discussed in terms of the details of theoretical band structure calculations (especially for PdTe2), as are also implications for superconductivity in the compounds.
TL;DR: In this paper, the paramagnetic scattering of neutrons from a single crystal of spectrographically pure chromium was investigated and the scattering was found to be strongly peaked around (100).
Abstract: Polarised neutrons and polarisation analysis has been used to investigate the paramagnetic scattering of neutrons from a single crystal of spectrographically pure chromium. The scattering was found to be strongly peaked around (100). For the three temperatures at which measurements were made, 1.18, 1.53 and 2.23TN the peak intensity was found to decrease by 90% and the characteristic wavelength for short range magnetic order from 57. A to 36 A. The scattering was found to be isotropically disposed about 100 and to fall to a low background level for wavevectors greater than “2π/aA from 100. Integration of the observed scattering throughout the Brillouin zone indicated the average moment per chromium atom to be 0.1±0.05 μB independent of temperature.
TL;DR: In this paper, angle-resolved photoemission measurements using synchrotron radiation have been performed for the As-stable GaAs(001)-2 × 4 reconstruction, which was grown in situ by molecular beam epitaxy.
Abstract: Angle-resolved photoemission measurements using synchrotron radiation have been performed for the As-stable GaAs(001)-2 × 4 reconstruction, which was grown in situ by molecular beam epitaxy Measurements made at high symmetry points and along symmetry lines of the surface Brillouin zones show weakly dispersing dangling bond-like surface states in the energy range between -16 eV and the top of the valence band and a nearly dispersionless state near -3 eV
TL;DR: In this article, the relativistic Brillouin flow stability was extended to the case of nonzero anode resistivity, for wave propagation across the equilibrium magnetic field, and it was found that transverse magnetic (TM) waves are unstable at frequencies below the equilibrium cyclotron frequency, unlike the case for a perfectly conducting anode.
Abstract: Previous treatments of relativistic Brillouin flow stability are extended to the case of nonzero anode resistivity, for the case of wave propagation across the equilibrium magnetic field. It is found that transverse magnetic (TM) waves are unstable at frequencies below the equilibrium cyclotron frequency, unlike the case for a perfectly conducting anode. Transverse electric (TE) waves, always oscillatory in the case of a perfectly conducting anode, are damped; an explicit expression for the damping rate, valid for large conductivities, is given.
TL;DR: In this paper, the authors measured phonon dispersion for Au-40 at.% Ni above the miscibility gap (≈1023 K) and reported a structural softening which accounts quantitatively for the measured excess entropy, which appears to be due to shielding by electrons from the 3d band of Ni in the vicinity of the Fermi surface.
TL;DR: In this article, reflectivity and electrolyte electroreflectance measurements have been performed on ZnSe single crystals polished and etched like those used in electrochemical and photoelectrochemical studies, and a determination of the principal optical constants (absorption coefficient alpha, complex dielectric constant epsilon and complex refractive index n) has been possible by Kramers-Kronig analysis.
Abstract: Reflectivity and electrolyte electroreflectance measurements have been performed on ZnSe single crystals polished and etched like those used in electrochemical and photoelectrochemical studies. From the reflectivity measurements in the energy range 2-26 eV, a determination of the principal optical constants (absorption coefficient alpha , complex dielectric constant epsilon and complex refractive index n) has been possible by Kramers-Kronig analysis. The various features of the reflectivity spectrum between 2-10 eV may be correlated to the different band to band transitions in the Brillouin zone. Complementary information concerning the fundamental transition and its spin-orbit splitting are provided by electrolyte electroreflectance measurements. In particular, the existence of excitons at room temperature is demonstrated and an energy gap value Eg=2.72 eV is determined.