Theoretical Investigation of the Anisotropy of Beryllium by Polarized K‐Emission, APS, and Compton Profiles

on the occasion of his 75th birthday Compton scattering of 10 keV X-rays by single crystals of beryllium is performed using the synchrotron radiation beam provided by the LURE-DCI storage ring of Orsay. By means of a three-axes spectrometer the scattering of the monochromatized beam, the spectral analysis by a focusing Des monocristaux de beryllium ont kt6 ktudi6s par diffusion Compton du rayonnement synchrotron X produit dans l'anneau de stockage LURE-DCI d'0rsay. Un spectromktre B trois axes rCalise la monochromatisation du rayonnement (10 keV), I'analyse spectrale par un cristal courbk focalisant; la detection du rayonnement diffuse est effectuee par un dbtecteur B localisation spatiale. La resolution obtenue est de 0.15 unit6 atomique de moment. Sept profils ont ktk mesurks pour diffkrentes directions du vecteur de diffusion; lo6 coups ont 6tB accumulks dans chaque profil.Les anisotropies des profils et de leurs transformkes de Fourier sont comparkes aux resultats fournis par les th6ories existantes. Aucune d'elle n'est en bon accord avec les profils en particulier dans la region du moment de Fermi. Le calcul "pseudo potentiel" fournit cependant une description qualitativement satisfaieante de l'anisotropie de la distribution de moment.

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“…The second one is a pseudopotential calculation [29] of the valence profile from the band structure of metallic Be obtained by Taut [30].…”

mentioning

confidence: 99%

X‐Ray Compton Scattering Study of Electronic Distribution in Beryllium

Loupias

Petiau

Issolah

et al. 1980

Physica Status Solidi (b)

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“…The calculations for beryllium are a continuation and improvement of earlier results [17]. The calculation of the K-spectra of magnesium and zinc is more complicated, because the orthogonalization corrections contribute to the spectra.…”

Section: (17)mentioning

confidence: 80%

Calculation of Polarized K and L X‐Ray Emission Spectra and of Partial Densities of States of the H.C.P. Metals Be, Mg, and Zn

Rennert¹,

Schelle²,

Gläser³

1984

Physica Status Solidi (b)

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Intensities for polarized X-ray emission spectra are given by the elements of the density matrix expanded with respect to lattice harmonics. These intensities and densities of states for special values of the angular momentum and special representations of the point group are presented for Be, Mg, and Zn starting from a pseudopotential calculation. The energy dependence and the anisotropy of the radial integration is investigated. It is shown that the anisotropic spectra can be described excellently by located densities of states. Non-diagonal elements of the density matrix give the main contribution to the anisotropy of the LII, 111-spectrum of magnesium. The spectra are broadened and compared with experimental K-spectra. A good agreement is achieved, some discrepancy remains concerning the size of the anisotropy.Die Intensitaten polarisierter Rontgenemissionwpektren werden durch die Elemente der beziiglich der Gitterharmonischen entwickelten Dichtematrix dargestellt. Diese Intensitiiten und partielle Zustandsdichten zu speziellen Darstellungen der Punktgruppe des atomaren Platzes werden fiir Be, Mg und Zn aus einer Pseudopotentialrechnung gewonnen. Die Energieabhiingigkeit und die Anisotropy der radialen Integration werden untersucht. Es wird gezeigt, &I3 die anisotropen Spektren sehr gut durch lokalisierte Zustandsdichten beschrieben werden konnen. Die Anisotropie des LII, 111-Spektrums von Magnesium wird durch die Nichtdirtponalelemente der Dichtematrix bestimmt. Nach einer Faltung werden die Spektren mit experimentell gewonnenen K-Spektren verglichen. Es besteht eine gute Obereinstimmung, beziiglich der GroBe der Anisotropy treten noch Unterschiede auf.

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“…In the case of the orthorhom bic structure of single crystalline YBa2Cu30 7 the crystallographic axes of the specimen under investiga tion are chosen as a principal coordinate system [5]. Then the emitted intensity I (v, e) can be decomposed into three components: Ix = I(v,e\\x), Iy = I (v,e\\y) and Iz = / (v, e || z), with the polarization unit vector e of the electrical field aligned along the x-, y-and z-di rection, respectively.…”

Section: X-ray Emission and Density Of Statesmentioning

confidence: 99%

Polarized Oxygen K_α and Copper L_α X-Ray Emission Spectroscopy of YBa₂Cu₃O₇

Kottmann

Siebinger

Steeb

1995

Zeitschrift Für Naturforschung A

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The high temperature superconductor YBa2Cu30 7 is characterized by a very anisotropic struc ture. The electronic structure of this compound is studied using high resolution valence band spectroscopy within an electron probe microanalyzer. From single crystals and melt-textured spec imens, orientation dependent Cu-La spectra are obtained using a beryl crystal. The Cu-La spectra with polarization parallel to the z-direction show a larger energetic breadth compared to those obtained with polarization perpendicular to z. This is caused by occupied Cu3d3z2_r2 like states, as could be shown by other workers using cluster calculations.With a chlinochlore crystal, the polarized O-K, spectra can be used to investigate the orientation of single crystal areas. The spectra map the bandlike 02p states. In contrast to the Cu-La spectra, the partial 0 -K a spectra agree with band structure calculations in the local density approximation done by other workers. IntroductionFor the microscopic comprehension of material properties, knowledge of the electronic structure is essential. X-ray emission spectroscopy (XES) exam ines the occupied electronic states. With 0 -K a and C u-La spectra the 02p and Cu3d valence band state of copper-oxide superconductors can be probed sepa rately.Electron probe microanalysis (EPMA) [1, 2] focuses an electron beam on very small regions and, according to the large information depth of X-rays, probes the bulk properties.The specimen spots from which the spectra are recorded, can be investigated directly concerning their oxygen content and stoichiometry.By studying the orientation dependence of the emis sion bands from untwinned regions of single crystal or textured materials, additional information is obtained concerning the symmetry of Op2 or Cu3d states, which are determined by the magnetic quantum num ber m.Thus, in the case of the 0 -K a-emission line, the Opx-, Opy-, and Op.,-state can be measured. With the C u-La-emission line the single d-orbitals contribute according to their weight to the intensity components Ix, Iy or Iz, which leads to a rather complicated corre lation with the density of states.Reprint requests to S. Steeb.Presently the calculation of band structures has reached a high accuracy and it is possible to calculate partial densities of states. The comparison of such calculated results with the experimental data yields hints on how far the corresponding model describes the real facts and which states contribute to the differ ent structural features of the observed spectra. Theoretical Fundamentals X-ray Emission and Density of StatesIn the electron microprobe the specimen is excited by electron impact, causing the formation of vacancies in core levels which are filled up by electronic transi tions from the valence band following the electric dipole selection rules. This may lead to the emission of X-rays with the quantum energy h v. The total inten sity of this radiation is given in the one electron-and dipole-approximation [3,4] by

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Theoretical Investigation of the Anisotropy of Beryllium by Polarized K‐Emission, APS, and Compton Profiles

Cited by 28 publications

References 10 publications

X‐Ray Compton Scattering Study of Electronic Distribution in Beryllium

X‐Ray Compton Scattering Study of Electronic Distribution in Beryllium

Calculation of Polarized K and L X‐Ray Emission Spectra and of Partial Densities of States of the H.C.P. Metals Be, Mg, and Zn

Polarized Oxygen K_α and Copper L_α X-Ray Emission Spectroscopy of YBa₂Cu₃O₇

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Theoretical Investigation of the Anisotropy of Beryllium by Polarized K‐Emission, APS, and Compton Profiles

Cited by 28 publications

References 10 publications

X‐Ray Compton Scattering Study of Electronic Distribution in Beryllium

X‐Ray Compton Scattering Study of Electronic Distribution in Beryllium

Calculation of Polarized K and L X‐Ray Emission Spectra and of Partial Densities of States of the H.C.P. Metals Be, Mg, and Zn

Polarized Oxygen Kα and Copper Lα X-Ray Emission Spectroscopy of YBa2Cu3O7

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Polarized Oxygen K_α and Copper L_α X-Ray Emission Spectroscopy of YBa₂Cu₃O₇