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

Abstract

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.

K-emission spectra of Zn, ZnS, and ZnSe within dipole and quadrupole approximations

“…The dipole spectrum of pure Zn has been calculated earlier. 14 In the present work, we discuss the Zn K-emission spectra of Zn, ZnS, and ZnSe in terms of the dipole and quadrupole approximations and use the obtained theoretical spectra to analyze the experimental K␤ 2,5 spectra of the investigated materials.…”

Polarized X‐Ray Emission Spectra of Single Crystals

“…The peak intensity ratio Q of the x and CI bands, however, could be determined not exactly and only with additional assumptions, &Be = 1.07 can be estimated from experiment. Spectrum calculations reproduced the shape anisotropy qualit,atively [12], but after recent accomplished improvements of the calculations now the agreement between theory and experiment is very good [44].…”

“…These follow from the small intensity of the MoLP, core line which was used for the normalization of the polarized M o L P~,~~ and are caused furthermore by the SK absorption edge appearing between the MoLP, and MoLPZ,~~ emissions. Moreover, a possible influence of self-absorption effects will still be studied, and in our estimation we neglected the contribution of the "mixed terms" of the partial DOS to the intensity of polarized I, emission spectra [44]. Nevertheless, this example offers the PXES as a useful tool for the interpretation and the proof of more complicated band structure models of transition metal compounds.…”

“…The analytic relations between the LB, principal intensities and the reflected m-resolved d-like DOS, however, are more complicated than that for the K emission given in (13). They depend on the structure and symmetry of the emitting crystal and can be deduced advantageously by using the appropriate lattice harmonics [44].…”

Polarized x-ray emission and absorption spectra ofMgB2

“…14 In the future, this provides an opportunity to measure the polarized K-emission and absorption spectra giving much more detailed and accurate knowledge concerning the electronic structure of this compound. 15 Due to the anisotropic character of the hexagonal crystal structure, 16,17 one would expect that the spectra should be dependent on the polarization vector e of the radiation whether it is parallel (e ʈ c) or perpendicular (eЌc) to the c axis reflecting the p zor p x,y -like states, respectively. In the present study we calculate the corresponding polarized K-emission spectra in the ground state and the absorption spectra also in the excited state, when the 1s electron has been moved to the empty conduction band.…”