Showing papers on "Brillouin zone published in 1974"
TL;DR: In this article, a self-consistent calculation of energy bands in ferromagnetic nickel using the tight-binding method has been extended to include spin-orbit coupling, and the energy levels were obtained at 1357 points in 1/16th of the Brillouin zone.
Abstract: A previous self-consistent calculation of energy bands in ferromagnetic nickel using the tight-binding method has been extended to include spin-orbit coupling. Exchange was incorporated using the $X\ensuremath{\alpha}$ method with $\ensuremath{\alpha}=\frac{2}{3}$. Energy levels were obtained at 1357 points in 1/16th of the Brillouin zone. The direction of spin alignment was taken to be [001]. The density of states was computed by a hybrid method. Cross sections of the Fermi surface were determined, and effective masses were obtained. The interband contribution to the conductivity tensor was calculated using matrix elements computed from wave functions including spin-orbit coupling. Results were obtained for both the diagonal and the off-diagonal elements of the conductivity tensor.
296 citations
TL;DR: In this article, for each of the two-dimensional lattice types, the mean value point, the set of generating wave vectors, and the sets of special points in the Brillouin zone are presented.
Abstract: Using the method of Chadi and Cohen, we present, for each of the two-dimensional lattice types, the mean-value point, the set of generating wave vectors, and the sets of special points in the two-dimensional Brillouin zone which are the most efficient in finding accurate averages of a periodic function over the Brillouin zone.
294 citations
TL;DR: In this paper, the phase transition at 130°C is caused by condensation of the M 3 mode at the M point of the cubic Brillouin zone, while the one at 88°C results from condensing of the doubly degenerate R 25 -like mode (Z 9 mode) at the Z point of a tetragonal Brilloupin zone.
Abstract: Structural phase transitions in perovskite-type CsPbBr 3 have been investigated by neutron diffraction method. Phase transitions occur at 88°C and 130°C, which are respectively second and first order. The phase transition at 130°C is caused by condensation of the M 3 mode at the M point of the cubic Brillouin zone, while the one at 88°C results from condensation of the doubly degenerate R 25 -like mode ( Z 9 mode) at the Z point of the tetragonal Brillouin zone. Group theoretical considerations based on these results reveal that the crystal trans-forms from cubic perovskite structure (O h 1 - P m 3 m ) to tetragonal D 4h 5 - P 4/ m b m at 130°C and further to orthorhombic D 2h 16 - P m b n at 88°C. Possible atomic displacements induced at the phase transitions are obtained from the eigenvectors of the condensing modes.
204 citations
TL;DR: In this paper, a simple bond-charge model was proposed to simulate the density of valence states of germanium and zinc-blende-type semiconductors, and the valence bands at any point of the Brillouin zone were obtained in this model as the solution of a 4\ifmmode\times\else\texttimes\fi{}4 secular equation.
Abstract: The densities of valence states (DOVS) of the amorphous and crystalline forms of GaP, GaAs, GaSb, InP, InAs, InSb, AlSb, ZnTe, and CdTe have been determined from the energy-distribution spectra of photoelectrons emitted by high-energy photons (16.9, 21.2, 40.8, and 1486.6 eV). In general the DOVS of the amorphous forms can be represented by a broadened version of those of the corresponding crystalline forms. Fine structure which appears in the upper valence bands of the crystalline materials, due to critical points at $L$, $X$, and $W$, is completely washed out in the amorphous phase. The core-level spectra have nearly the same positions and widths in the amorphous as in the crystalline modifications. This fact indicates that the fluctuations in the Coulombic environment about each type of atom are small, suggesting that the structure is homogeneous and contains an insignificant number of odd-membered rings. The plasma frequencies, determined from the plasma-loss spectra associated with core levels, are the same in the amorphous as in the crystalline phases to within 3%. This fact enables us to conclude that the densities of both modification differ by less than 6%. We present a simple bond-charge model which can simulate realistically the density of valence states of germanium and zinc-blende-type semiconductors. The valence bands at any point of the Brillouin zone are obtained in this model as the solution of a 4\ifmmode\times\else\texttimes\fi{}4 secular equation. Within this model, the structure of the top $p$-like valence bands depends primarily on overlap between second-neighbor bonds. Thus fluctuations in the position of second neighbors can be invoked to explain the smearing of the fine structure of these bands in the amorphous modifications. A simple model which relates the chemical shifts of the compounds to their ionicity is also discussed.
148 citations
TL;DR: In this paper, the shear and longitudinal Brillouin shifts, longitudinal linewidth, Pockel's coefficient, and the Landau-Placzek ratio were measured in fused silica from room temperature, through the glass transition temperature (1200°C), and up to near the melting temperature of quartz (∼1700°C).
Abstract: Thermal Brillouin scattering has been studied in fused silica from room temperature, through the glass transition temperature (1200°C), and up to near the melting temperature of quartz (∼1700°C). The shear and longitudinal Brillouin shifts, the longitudinal linewidth, Pockel's coefficient, and the Landau‐Placzek ratio are measured. From these the behavior of the elastic moduli and absorption coefficient with temperature are obtained. A significant change in the temperature dependence of the moduli and Pockel's coefficient is found to occur above 500°C. In addition, by using the Landau‐Placzek ratio the first measurement in fused quartz of the equilibrium static compressibility above the glass transition has been obtained. Surprisingly little temperature dependence is observed.
126 citations
TL;DR: In this paper, the absorptivity or reflectivity of crystals of V, Ta, and Mo was measured from 0.1 to 35 eV. The data were Kramers-Kronig analyzed to determine the dielectric functions.
Abstract: The absorptivity or reflectivity of crystals of V, Ta, and Mo was measured from 0.1 to 35 eV. The data were Kramers-Kronig analyzed to determine the dielectric functions. The inadequacy of a simple Drude model to describe absorption at low energy is discussed. Structure in the dielectric functions is discussed in terms of direct interband transitions which extend to about 18 eV. Features below 6 eV are attributed to transitions near $\ensuremath{\Sigma}$, $G$, and perhaps along $P(D)N$ for V, Ta, and Mo, with additional transitions in Mo from the $\ensuremath{\Delta}$ portion of the Brillouin zone. High-lying energy bands are identified as giving rise to high-energy structure in the dielectric functions. Results obtained previously for Nb are reviewed and compared. The electron-energy-loss functions were calculated and are discussed in terms of volume and surface plasmons. These metals all exhibit two volume and two surface plasmons.
117 citations
TL;DR: In this paper, the energy distribution of photoelectrons emitted normal to three single-crystal faces of tungsten has been measured for photon energies between 7.7 and 21.2 eV, and the results are interpreted in terms of one-dimensional electronic properties along the symmetry lines in $k$ space that correspond to the emitting crystal faces.
Abstract: Energy-distribution spectra of photoelectrons emitted normal to three single-crystal faces of tungsten have been measured for photon energies between 7.7 and 21.2 eV. The results are interpreted in terms of one-dimensional electronic properties along the symmetry lines in $k$ space that correspond to the emitting crystal faces. The emitted spectra may be considered to consist of three types of contributions. One part is due to electrons that, after excitation by direct interband transitions in the bulk, have left the crystal unscattered. This contribution may be described by the energy density of a one-dimensional joint density of states along a symmetry line in the Brillouin zone. Another part, evident for photon energies above 12 eV, is due to electrons that have suffered inelastic scattering processes after optical excitation. This part carries information on the density of conduction states along the symmetry line under observation. Finally, a third contribution to the emitted spectrum is assigned to surface emission. This part reflects the surface density of states and bears evidence of a narrowing of the $d$ bands near the surface. A theoretical surface density of states, derived from a simple model that scales the width of the $d$ bands by the square root of an effective number of neighbor atoms, is found to describe the energy distribution of the electrons emitted by the surface effect satisfactorily.
93 citations
TL;DR: In this paper, Bismuth selenide crystals were grown from melts with liquid concentrations within 0·2 per cent of stoichiometry, and the resulting crystals were examined structurally showing that single crystal samples could be cut for electronic property measurements.
67 citations
TL;DR: In this paper, a broad-band laser showed more effective heating of the plasmas than a narrowband laser and the decrease of the reflectivity appeared when the laser intensity increased up to 1 order of magnitude larger than the threshold of parametric instability.
Abstract: Brillouin backscattering from laser-produced plasmas of hydrogen and deuterium has shown an isotope effect in the red-side region of the generated second-harmonic light. This isotope shift is explained by the parametric instability at the cutoff region using the phase-matching condition of the waves. The decrease of the reflectivity appeared when the laser intensity increased up to 1 order of magnitude larger than the threshold of the parametric instability. A broad-band laser showed more effective heating of the plasma than a narrow-band laser.
65 citations
TL;DR: In this paper, the two-phonon Raman spectrum of silicon has been measured in backscattering configuration at room temperature using Argon ion laser and critical point analysis has been done on the twophonons overtone and combination spectra, and phonon frequencies of points of high symmetry in the Brillouin zone.
65 citations
TL;DR: In this article, the effect of the actual dipole-dipole Hamiltonian is shown to give a priori a very good account of the lifting of the degeneracy of spin waves near the Brillouin zone center.
TL;DR: In this article, a two-dimensional ferromagnet K 2 CuF 4 was used for a parallel pumping experiment and a magnon relaxation time was measured at a pumping frequency of 8.9 GHz.
Abstract: There is a very flat branch in the spin-wave spectrum of two-dimensional ferromagnets. Since the energy of the lowest Brillouin-zone-boundary magnon is very small in this case, those magnons can be excited by a conventional parallel pumping experiment. Instability of the zone-boundary magnons in a two-dimensional ferromagnet K 2 CuF 4 is observed and a magnon relaxation time is measured at a pumping frequency of 8.9 GHz. Another feature of this case is the existence of measurable steady state absorption below the instability threshold (subthreshold absorption), because the magnon density of states of the lowest branch is very large. It is usually difficult to observe this absorption in three-dimensional ferromagnets. From the shape of the subthreshold absorption observed at pumping frequencies of 8.9, 35 and 73 GHz, the interlayer exchange field in K 2 CuF 4 is determined to be 126 Oe (or equivalent to 0.017 K). The ratio of the interlayer to the intralayer exchange fields is estimated to be 0.00042.
TL;DR: In this paper, a self-consistent Hartree-fock band-structure calculation for LiF was performed and the energy bands were evaluated directly by the linear-combination-of-local-basis functions method along with the crystal wave functions for 89 points in the irreducible wedge of the first Brillouin zone.
Abstract: In this paper, we examine the optical properties of LiF. The fundamental calculations performed are a self-consistent Hartree-Fock band-structure calculation. As has been found previously, such a calculation has substantial errors when compared with experiment. Correlation corrections are needed and are included by means of the electronic-polaron method. The usual electronic polaron is extended to include short-range polarization corrections which the usual model neglects but which are peculiarly large for LiF. The energy bands are evaluated directly by the linear-combination-of-local-basis-functions method along with the crystal wave functions for 89 points in the irreducible wedge of the first Brillouin zone. Using these results and the Lemann-Taut interpolation scheme the density of states, the joint density of states, and the imaginary part of the dielectric function are computed. These results which neglect the formation of excitons and "plasmons" are in poor agreement with experiment. The effect of the exciton formation is included by a Koster-Slater one-band---one-site calculation. We find that the inclusion of exciton effects substantially improves the level of agreement with experiment. This is in direct contrast with recent work of Menzel et al. in which energy-band theory alone is found to account for the optical properties of LiF. This disagreement is discussed in detail.
TL;DR: In this paper, it was shown that BaMnF4 has a second-order phase transition and a soft phonon at the Brillouin zone boundary of the orthorhombic C122V phase.
TL;DR: In this paper, photoelectron energy spectra have been measured on the layer compounds 1 T − TaSe 2 and 1T − TaS 2 at various polar angles of emission and the azimuthal angle was set to select only those photoelectrons propagating in a plane containing the points of the Brillouin zone.
TL;DR: In this paper, small (18-32 atoms) periodic clusters of two-dimensional hexagonal graphite and boron nitride are shown to represent high-symmetry points in the Brillouin zone of the infinite crystal.
Abstract: Small (18-32 atoms) periodic clusters of two-dimensional hexagonal graphite and boron nitride are shown to represent some high-symmetry points in the Brillouin zone of the infinite crystal Semi-empirical all-valence electron calculations are performed on these clusters and the binding energy, work function, bandwidth, band-to-band transition energy, band gap, charges and equilibrium distances are computed and compared with values obtained by tight binding and truncated crystal calculations Favourable agreement with experimental data is obtained with selfconsistent calculations on these clusters
TL;DR: In this article, the Brillouin doublet was observed in liquid CS2 and the half-widths increased from 11 to 19 GHz, yielding orientational relaxation times of 14×10−12 to 8× 10−12 sec.
Abstract: The depolarized doublet found in the Brillouin spectra of many molecular liquids has been observed in liquid CS2. This doublet is best resolved at 162°K (near the freezing point); it broadens rapidly with increasing temperature and is unresolved at temperatures higher than 192°K. In this temperture range, the half‐widths increase from 11 to 19 GHz, yielding orientational relaxation times of 14×10−12 to 8×10−12 sec, respectively. The observed spectra are in good agreement with the predictions of hydrodynamic (Rytov) and microscopic (Keyes and Kivelson) theories.
TL;DR: In this paper, a truncated crystal approach is applied to the hexagonal boron nitride structure and electronic properties such as work function, different band widths, energy of band-to-band transition and cohesion energy are studied and compared with tight binding, OPW methods and experimental optical and thermochemical data.
Abstract: A truncated crystal approach is applied to the hexagonal boron nitride structure and electronic properties such as work function, different band widths, energy of band-to-band transition and cohesion energy are studied and compared with tight binding, OPW methods and experimental optical and thermochemical data. It is demonstrated that whenever the relation between one-electron energy levels of a finite molecular cluster and energy states at the Brillouin zone of the crystal are established, good results can be obtained. Properties that are not amenable to calculation by simple band theories, like energy of Frenkel pair formation, point defect states and dependence on interatomic distance of various energy states, are computed by the same method and discussed with reference to experiment.
TL;DR: In this article, the reflectivity spectra of the chalcopyrite ternary compound ZnGe${\mathrm{P}}_{2}$ are studied experimentally and theoretically.
Abstract: Reflectivity spectra of the chalcopyrite ternary compound ZnGe${\mathrm{P}}_{2}$ are studied experimentally and theoretically. The measurements of the reflectivity in both the complete parallel and perpendicular polarizations are made at 5\ifmmode^\circ\else\textdegree\fi{}K. A full zone energy-band structure, the reflectivity and imaginary part of the frequency-dependent dielectric function are calculated using the empirical pseudopotential method. Comparison is made with the measured reflectivity and modulated reflectivity and prominent features in the experimental spectra are identified and associated with interband transitions. In addition, spin-orbit interactions are included at a few points of the Brillouin zone.
TL;DR: In this article, the elastic constants of diamond are determined from the shifts of the Brillouin components, and the discrepancy between the intensities observed experimentally and those expected on the basis of the elasto-optic constants given in the literature is investigated.
TL;DR: In this article, a group theoretical analysis of the lattice vibrations of the e and γ polytypes of GaSe for different directions of the wave vector in the Brillouin zone is presented.
Abstract: We present here a group theoretical analysis of the lattice vibrations of the e and γ polytypes of GaSe for different directions of the wave vector in the Brillouin zone. The effect of the interlay...
TL;DR: In this paper, the ferromagnetic anisotropy energy of H. P. Co metal is calculated by the use of the energy bands of ferromagnetagnetic Co metal given by Ishida.
Abstract: The ferromagnetic anisotropy energy of H. C. P. Co metal is calculated by the use of the energy bands of ferromagnetic Co metal given by Ishida. The doubly degenerate energy levels along [0001] axis on the Brillouin zone produce the contributions to make c -axis to be the easy axis. The other doubly degenerate energy levels and the approaching energy levels produce the contributions to make c -plane to be the easy direction. It is shown that at 0 K, c -axis is the easy axis, and when the temperature is raised and the exchange splitting decreases, c -plane becomes the easy direction. The anisotropy energies of Co alloys including 1 at% of Fe and Ni metal are also calculated. The obtained results are in agreement with the experimental results.
TL;DR: The hypersonic attenuation coefficient over one wavelength (α λs) is insensitive to temperature variation below Tg; above Tg, α λ s increases rapidly with increasing temperature as mentioned in this paper.
Abstract: Light scattering studies of polybutadiene from 110 to 350°K reported herein include measurements of Brillouin shift, Brillouin linewidth, and Rayleigh depolarization ratios as functions of temperature. The hypersonic attenuation coefficient over one wavelength (α λs) is insensitive to temperature variation below Tg; above Tg, α λs increases rapidly with increasing temperature. The sound attenuation theory of Woodruff and Eihsenreich gives an adequate description of the measure α λs value below Tg; no quantitative theory describes the sound attenuation above Tg. The Krishnan effect, depolarization ratio ρn = Vh/Hn ≠ 1, was observed for polybutadiene below 250 °K. The frozen‐in density fluctuation mechanism proposed by Mueller fails to explain the effect; frozen‐in fluctuations of the dielectric anisotropy are a possible mechanism.
TL;DR: In this paper, the stress dependence of the amplitude and position of the magnetophonon extrema of n -Si was employed to distinguish the f - and g -type intervalley scattering series.
TL;DR: In this article, a model consisting of first, second and third-neighbor Lennard-Jones interactions together with harmonic angle bending interactions is employed to fit the equilibrium lattice spacing, the elastic constants, and certain phonon frequencies at high symmetry points in the Brillouin zone.
TL;DR: In this paper, the Brillouin scattering spectra in NaNO 2 have been studied using a Fabry-Perot interferometer using acoustic phonons in nine scattering geometries with particular emphasis in the region close to the Curie and the Neel points.
Abstract: The Brillouin scattering spectra in NaNO 2 have been studied using a Fabry-Perot interferometer. The observed Brillouin shifts for eighteen acoustic phonons in nine scattering geometries have been assigned to specific modes of vibration. The determined values of nine elastic constants in units of 10 10 dyn/cm 2 are C 11 =31.7, C 22 =58.2, C 33 =66.0, C 44 =12.4, C 55 =9.91, C 66 =4.79 ( C 66 D =4.98), C 12 =12.6, C 23 =17.4 and C 13 =19.7 at room temperature. The temperature dependence of C 22 D associated with the longitudinal phonon propagating along the ferroelectric b -axis has been studied with particular emphasis in the region close to the Curie and the Neel points. The elastic stiffness constant C 22 D showed anomalous decrease both at the Curie and the Neel temperatures. These results are compared with those obtained in the ultrasonic region.
TL;DR: In this article, the authors discussed how the orbital ambiguity in general SCF theory can be removed to obtain the orbital set which is stable to an excitation, and the definition of Huzinaga's potential to obtain meaningful virtual orbitals is generalized to include wave functions for open shells systems.
Abstract: We discussed how the orbital ambiguity in general SCF theory can be removed to obtain the orbital set which is stable to an excitation. The orbital ambiguity for the ground state wavefunction can be resolved while at the same time performing the configuration interaction calculation for the specific singly excited states. That is, the orbitals can be uniquely determined so that they have the physical significance that they satisfy particular types of the Brillouin conditions for the excited states considered in addition to the Brillouin theorem for the ground state. This implies that the definition of Huzinaga's potential to obtain meaningful virtual orbitals is generalized to include wavefunction for open‐shell systems.
TL;DR: In this paper, two distinct processes of electron energy relaxation are identified from the resonant structure: the first involves emission of a Gamma point LO phonon accompanied by the capture of the warm electron at an impurity site; the second corresponds to inter-Landau-level transitions by emission of TA phonons near the X point of the Brillouin zone.
Abstract: The magnetophonon effect has been observed in the longitudinal and transverse magnetoresistance and the Hall voltage of n-InP under warm-electron conditions. Two distinct processes of electron energy relaxation are identified from the resonant structure: the first involves emission of a Gamma point LO phonon accompanied by the capture of the warm electron at an impurity site; the second corresponds to inter-Landau-level transitions by emission of a pair of TA phonons near the X point of the Brillouin zone. Three other extrema in the magnetoresistance are tentatively ascribed to resonant impact ionization of neutral donors.
TL;DR: In this article, the force constants for interactions extending to eighth neighbours in lead were fitted to the frequencies of normal modes with wave vectors spread uniformly through the first Brillouin zone, and the frequency distribution function calculated from the model was in good agreement with results obtained by other methods.