Showing papers on "Brillouin zone published in 1975"

Statistical mechanics of dense ionized matter. IV. Density and charge fluctuations in a simple molten salt

Abstract: The results of a molecular-dynamics study of a simple model of a molten salt are reported. The interionic pair potential which is used consists of the Coulombic term an an inverse-power repulsion which is assumed to be the same for all ions. The structure of the liquid is found to be dominated by charge-ordering effects and the calculated equilibrium properties are in good agreement with the predictions of the hypernetted-chain approximation. The relation between the self-diffusion coefficient and the electrical conductivity is discussed, and the observed deviations from the Nernst-Einstein relation in real molten salts are shown to have a natural explanation in terms of short-lived cross correlations. Data on the spectra of charge and particle density fluctuations are presented. At small wave numbers there is a propagating optic-type mode which shows a strong negative dispersion, but no Brillouin peak is seen even at the lowest wave number which is accessible. The data are analyzed in terms of a single-relaxation-time model incorporating the low-order spectral moments, for which we give explicit formulas. The fit achieved is fair, but the low-frequency behavior of the charge fluctuations at small wave numbers is incorrectly reproduced, and there is evidence for the necessity of introducing a second relaxation time. Comparison is made with results previously obtained for the classical one-component plasma.

Magnetic behaviour of cobalt, iron and manganese dissolved in palladium

Abstract: This paper is meant to be a report on the experimental work on dilute Pd-based alloys with Co, Fe and Mn. These alloys exhibit the phenomenon of giant moments. The importance of measurements on paramagnetic alloys is emphasized. From these measurements the conclusion can be drawn that Co and Fe dissolved in Pd does not behave like a normal paramagnet, i.e. according to a Brillouin function. This result makes it possible to explain the existing discrepancy in the interpretations of magnetic measurements on one hand and of specific-heat experiments on the other. The main conclusions of this paper are: The giant moment should be accounted for by ‘normal’ values of the magnetic quantum number (3/2 for Co, 2 for Fe and 5/2 for Mn) and a large value of geff. Paramagnetic alloys of Mn in Pd behave according to Brillouin functions, but alloys of Co or Fe in Pd do not. Hence, a number of interpretations of magnetic measurements should be considered as incorrect. The localized model for ferromagnetism can ...

Relativistic Brillouin flow in the high ν/γ diode

Abstract: Relativistic Brillouin solutions have been derived for electron flow in crossed electric and magnetic fields. The application of these solutions to the high ν/γ diode is discussed and an approximate analytical expression for the anode current is derived. Measurements of diode current are compared to the theoretical and empirical expressions for diode current which have been developed.

Splitting of the interband absorption edge in Au

Abstract: Very accurate ellipsometric measurements were made on very pure bulk samples of Au at room temperature in the 1.0-3.5-eV energy region. A model calculation has been developed for $d$ bands to Fermi-surface transitions occuring near the $X$ point in the Brillouin zone and it is shown that for topological reasons the line shape of the imaginary part of the dielectric constant ${\ensuremath{\epsilon}}_{2}$ is considerably different from what has been calculated for $L$ transitions. Using this model to fit our experimental data it has been possible to show that the absorption edge in Au is "split" into two separate contributions. The onset of $X$ transitions has been located at 1.94 eV while the onset of the $L$ transitions has been confirmed at 2.45 eV in excellent agreement with previous determinations.

Model calculation of the electronic structure of a (111) surface in a diamond-structure solid?

Abstract: The authors present exact results for a model calculation of the surface electronic structure of a (111) face of a diamond-type solid The model contains only one s-state per atom, but allows for surface rearrangement both at the outer layer and at the outer bounds Two kinds of surface states are found The first kind are localized at the outer bounds and split off the bulk bands as the bond potential increases beyond a critical value The second kind are intrinsic surface states and exist independently of the surface rearrangement but only in a restricted domain in the Brillouin zone where structure factors are smaller than 1 These intrinsic states have not been discussed before; they exist also in more realistic hybrid models of diamond-structure solids

Magnetooptik und elektronische Struktur der magnetisch ordnenden Europiumchalkogenide

Abstract: The absorption coefficient and the interband Faraday rotation of EuS, EuSe and EuTe thin films have been measured as function of the photon energy (1–6 eV), the temperature (2.7–300 K) and the applied magnetic field (0–11.5 kOe). In addition a magnetic field modulation technique has been developed, with a resolution of 2 ⋅ 10−4 deg. This allows the measurement of the Faraday rotation in fields of only 100 Oe, which is important for metamagnetic samples with low critical fields. A Kramers-Kronig transformation of the Faraday rotation leads to the circular dichroism and from these two quantities and the optical constants the off-diagonal elements of the conductivity tensor have been computed. From a comparison of this experimental result with values obtained from a modified atomic model, we deduce the character of the involved transitions and the spin polarization of the occupied ground states (4f 7,p(anion)). In addition the ratio of exchange splitting to band width of the empty 5d final state can be evaluated. The fine structure of the first main peak is discussed in terms of Kasuya's coupling scheme between the 4f 6 multiplett and the excited 5d electron. In the antiferromagnetic EuTe the temperature dependence of the Faraday rotation does not follow the net magnetization of the sample for all photon energies, but some transitions show a “ferromagnetic” behavior. This is interpreted in Slater's model of the magnetic Brillouin zone.

Low-energy interband absorption in Pd

Abstract: The optical absorptivity of crystalline Pd was measured at 4.2 K between 0.15 and 4.4 eV. The data were Kramers-Kronig analyzed to determine the dielectric functions and the optical conductivity, $\ensuremath{\sigma}$. A strong maximum was observed in $\ensuremath{\sigma}$ at 0.46 eV followed by a broad shoulder near 1.25 eV. These are interpreted in terms of transitions involving the bands near $L$ in the Brillouin zone.

Perturbation theory and three body forces in hcp metals

Abstract: An analysis is presented of the role of the non pair forces in the lattice dynamics of sp bonded hcp metals: Be, Mg and Li. By expanding the total energy up to third order in the electron-ion pseudopotential, a dynamical matrix is derived which contains terms arising from central pairwise interactions between the ions as well as contributions due to sums of three body forces. The phonon dispersion relations are calculated using a local form of the model potential, which allows for a realistic evaluation of the third order contributions. The results show that the three body forces are very important in Be and are responsible for the peculiarities of the spectrum, as is most clearly seen from the analysis of the frequencies at the K point of the Brillouin zone.

Helical Spin Structure of Mn 3 Si

Abstract: The magnetic structure of Mn 3 Si (bcc Fe 3 Al type crystal structure) at low temperatures has been determined by neutron diffraction using single crystal samples. It is found that Mn 3 Si has a helical spin structure (Neel temperature 25.8 K) with a wave vector q parallel to one of directions and of magnitude 0.85·1/2·2π K 111 , which is near the boundary of the Brillouin zone. The magnetic structure is either a proper screw or a transversal sinusoidal structure and the magnetic moments at the two Mn sites are µ Mn I =1.72 µ B and µ Mn II =0.19 µ B . The temperature dependence of the magnitude of the wave vector q is similar to that of Cr. From these data the possibility of an itinerant electron antiferromagnetism of Mn 3 Si is suggested in comparison with the SDW in Cr.

Band structure, crystal conformation, and hydrogen bond potentials for solid HF

Abstract: The electronic structure of hydrogen fluoride chains is calculated using the small‐periodic‐cluster approach by representing some high‐symmetry points in the Brillouin zone of the infinite solid by the one‐electron energies of a finite periodic structure. The LCAO representation is used for the crystal orbitals, and a self‐consistent calculation is performed. Problems regarding the convergence of the band structure as a function of the number of K‐grid points used to construct the Hartree–Fock elements, the number of interacting neighbors, and the approach to self‐consistency in the iteration cycle are examined. Band energies, ionization potential, cohesive energy, charge, and electrostatic potential distribution are computed. The adequacy of other methods currently used to investigate electronic and structural problems in hydrogen‐bonded solids is discussed in view of the results obtained. The crystal structure is optimized, and the stability of the crystal against unit cell deformations and atom displacements is examined. Potentials for either collective or single proton movements are computed and discussed in view of the experimental vibrational force constants.

Electronic charge densities in PbSe and PbTe

Abstract: The electronic charge densities for PbSe and PbTe are derived from recent pseudopotential-band-structure calculations. The results are displayed as contour plots for individual bands and for the total valence charge. Fractional amounts of charge inside touching spheres around each atom are calculated for different $l$ values by an angular momentum projection method. Rough estimates of the charge transfers in PbSe and PbTe are made. The charge densities for the states forming the gap at the point $L$ of the Brillouin zone are presented and related to pressure and temperature coefficients of the fundamental gap.

Phonon Side Bands of UV Absorption in NaNO2

Abstract: Phonon side bands of u v absorption in NaNO 2 have been studied by the measurement of high resolution spectrum with light polarized along each crystallographic axis at low temperatures. Strong peaks in the side bands are assigned to the phonon branches in the first Brillouin zone by taking account of the selection rules for the optical transitions in which an exciton and a phonon are created simultaneously. The integrated intensities of the E // b and E // c absorptions have been found to increase with temperature obeying the coth ( h ν/2 k T ) law with ν b ≃220 cm -1 and ν c ≃130 cm -1 respectively. The relation between the temperature dependence of the E // b and E // c absorptions and the profiles of their phonon side bands is discussed in terms of the averaged phonon frequency \barν.

Use of representative points of the Brillouin zone for the self-consistent calculations of solids in the large unit cell approach

Abstract: For the self-consistent (SC) calculation of solids an approach is suggested combining the “large unit cell” method with the theory of representative (special) pointsin the Brillouin zone. In the framework of the approach suggested the SC calculation of a solid can be realized by the self-consistent methods developed for molecules. As an example cubic LiH, MgO, and KCl crystals are considered having face-centered Bravais lattice. The SCCC (self-consistent charge configuration) procedure used in molecular calculations is modified to be applicable for solids. Basing on the results obtained the character of the chemical bonding in the crystals considered is discussed. [Russian Text Ignored]

Ground-state wave function for shallow-donor electrons in silicon. I. Isotropic electron-nuclear-double-resonance hyperfine interactions

Abstract: In a new theoretical investigation of electrons bound to the shallow-donor impurities (P, As, Sb) in silicon we have calculated the Fermi-contact hyperfine-interaction constants for the ${\mathrm{Si}}^{29}$ lattice nuclei surrounding the impurity nucleus. We have used a model potential which represents the impurity potential, a wave-vector-dependent dielectric function which represents the screening of the impurity potential by the silicon lattice, and pseudopotential Bloch functions for the calculation of the wave-function density of the $1s({A}_{1})$ ground state at the nuclear sites. The restrictions of the effective-mass theory to a single band and to conduction-band-minima Bloch functions have been removed because we represent the wave function in terms of a Bloch-function expansion throughout the Brillouin zone for several bands. With the use of the Fermi-contact constants calculated from this wave function, we have been able to make definite matchings of ${\mathrm{Si}}^{29}$ lattice sites and the electron-nuclear-double-resonance (ENDOR) shells measured by Hale and Mieher. With these matchings we are able to explain the experimentally observed lack of inversion symmetry of the electronic wave function and to explain most of the donor dependence of the experimental ENDOR data. Tutorial type discussions of the comparison of this calculation with effective-mass calculations are presented. These results contain several features that are due to the complex values of the wave-function expansion coefficients and the complex values of the Bloch functions; these features cannot be obtained from any real-valued effective-mass Hamiltonian.

de Haas-van Alphen effect study of dislocations in copper

Abstract: The influence of lattice dislocations on conduction electrons has been studied both theoretically and experimentally in copper single crystals. A first-principles de Haas-van Alphen (dHvA) dephasing calculation was made, using the dislocation strain field with a realistic dislocation array. Both the Dingle temperature $X$, which characterizes the amplitude reduction, and the dHvA relative phase shift were measured using dHvA wave-shape analysis. Breaking the cubic symmetry by introducting a forest of edge dislocations allows a test of the sensitivity of previously equivalent neck orbits to the relative orientation with respect to the dislocation lines. Both magnitude and anisotropy agree with the theory. Orbits in contact with the Brillouin zone were found to have larger $X$. A slight field dependence predicted by the dephasing calculation was observed. The large discrepancy observed among different $\frac{1}{\ensuremath{\tau}}$ results obtained from dHvA, radio-frequency size effect, and resistivity measurements is due to the different sensitivity of each method to small-angle scattering by the long-range strain field around dislocations. It is shown how to separate dislocation effects from mosaic-structure effects also present in these strained crystals.

A system with a complex phase transition: Indium chains on Si(111)

Abstract: We examined in detail the geometric and electronic structure of thin In chains on vicinal Si(111) surfaces by means of low energy electron diffraction and ultrahigh-resolution photoemission as a function of temperature. Our data reveal a transition around T c = 115 K from a high temperature ( 4×1)- to a low temperature ( 8×2)-phase being reversible with a small hysteresis of the order 10 K. ARPES spectra exhibit clearly important concomitant changes in the electronic band structure near the Fermi surfaces and at the border of the surface Brillouin zones. We derive the dispersive behavior of the bands involved in the transition in detail and demonstrate that at least two surface state bands m2 and m3 show the opening of a pseudo energy gap on the Fermi surface leaving small but finite spectral weight in the low-temperature state. We conclude that this transition is probably driven by a similar but more complex mechanism than in a conventional Peierls transition.

Elastic constants of ZnSe

Abstract: Brillouin scattering experiments have been performed on single crystals of ZnSe at 295 °K. From the observed Brillouin frequency shifts the elastic constants of ZnSe have been evaluated. At 295 °K the following results have been obtained: C11 = 87.2 ± 0.8, C12 = 52.4 ± 0.8, and C44 = 39.2 ± 0.4 in units of 1010 dyn/cm2. The values have been compared to previous experimental results and satisfactory agreement obtained. A comparison with values calculated from a rigid ion lattice dynamics model has provided poor agreement however and the origin of this discrepancy has been reviewed. Brillouin-Lichtstreuung wurde an ZnSe-Einkristallen bei 295 °K gemessen. Aus der beobachteten Brillouin-Verschiebung wurden die elastischen Konstanten von ZnSe bei 295 °K zu C11 = 87,2 ± 0,8; C12 = 52,4 ± 0,8; und C44 = 39,2 ± 0,4 in Werten von 1010 dyn/cm2 bestimmt. Diese Werte werden mit fruheren Arbeiten verglichen und zeigen ausreichende Ubereinstimmung. Ein Vergleich mit errechneten Werten des gitterdynamischen Modells ergibt jedoch nur geringe Ubereinstimmung. Der Grund dieser Abweichung wird diskutiert.

Lattice dynamics of sapphire (corundum)

Abstract: Theoretical models of the lattice dynamics of sapphire (α — Al2O3), based on the assumption of rigid ions, have been fitted to measured phonons at theΓ-point of the Brillouin zone Short range interactions were taken into account by assuming 2-body interactions between touching ions Additional 3-body interactions could not improve the fit significantly Calculated dispersion curves are presented and compared with inelastic neutron scattering data A good agreement for branches along the trigonal axis can be stated

Structure independent properties of expanded crystalline mercury

Abstract: The band structure of expanded crystalline mercury has been calculated in the density range 14.6-5 g cm-3 for three different crystal structures, bcc, fcc, and rhombohedral structure. A simple local pseudopotential calculation scheme has been used in a few symmetry points of the Brillouin zone. The main results of our calculations, more or less independent of the chosen structure, are: a normal metallic region 14.6 g cm-3> rho >11 g cm-3, a real band gap starting at about 8.5 g cm-3 and a semiconducting region 8 g cm-3> rho >5 g cm-3. A comparison with experimental data for expanded liquid mercury has been made.

Electronic surface structure of a tetrahedrally coordinated covalent solid with a simple four-state Hamiltonian

Abstract: It is shown that for electronic surface problems in a tetrahedrally coordinated solid it is possible to reduce a four-orbital sp3 tight-binding model to an equivalent one-orbital s model. This is the surface analogue of the Weaire-Thorpe transformation (1971) for the bulk. One example of the transformation, which is a reasonably good representation of (111) surface of silicon, is carried out in detail. It exhibits four bands of surface states-two of them almost totally overlapping-in the valence-band region and one band of dangling-bond surface states in the optical gap. The calculation is for the whole two-dimensional Brillouin zone and compares satisfactorily with other calculations.