High-resolution hard-x-ray photoelectron diffraction in a momentum microscope—the model case of graphite

Abstract

Hard x-ray photoelectron diffraction (hXPD) patterns recorded with a momentum microscope with high k-resolution (0.025 Å −1 equivalent to an angular resolution of 0.034°at 7 keV) reveal unprecedented rich fine structure. We have studied hXPD of the C 1s core level in the prototypical low-Z material Graphite at 20 photon energies between 2.8 and 7.3 keV. Sharp bright and dark lines shift with energy; regions of Kikuchi band crossings near zone axis exhibit a filigree structure which varies rapidly with energy. Calculations based on the Bloch wave approach to electron diffraction from lattice planes show excellent agreement with the experimental results throughout the entire energy range. The main Kikuchi bands in the [001] zone axis appear fixed on the momentum scale with a width of the corresponding reciprocal lattice vector, allowing to reconstruct the size of the projected Brillouin zone. The newly developed high-energy k-microscope allows full-field imaging of (k x , k y )-distributions in large k-fields (up to >22 Å −1 dia.) and time-of-flight energy recording.XPD cluster picture and dynamical electron scattering from lattice planes showed that the latter is more appropriate for very high energies. Hence, for the present study of hard x-ray photoelectron diffraction (hXPD) the dynamical scattering approach for bulk crystals is expected to be the more efficient theoretical description. By exploiting exchange scattering and multiplet splittings, even antiferromagnetic short-range order has been probed by XPD [17,18].Experimentally, XPD is studied using angular-resolved photoelectron spectroscopy. Large polar angular ranges of typically 0°-60°can be observed, mostly by rotating the sample about its surface normal (e.g. [8,10,11]). But also display-type electron analysers were developed [19][20][21] which give direct 2D full-field angular distributions in a wide angular range [22][23][24][25]. One main emphasis was to observe the pronounced forward scattering along atom rows in off-normal directions [4,8], hence the trend to observe a maximum polar angular range. Typical angular resolutions in both angular-scanning and display-type recording modes are ∼1°, but in some cases higher resolutions (<1°FWHM) have been reached [26][27][28].Here we present the first study of XPD using the new technique of momentum microscopy. In this type of photoelectron analyser, a cathode-lens (usually with an electrostatic extractor field) yields a reciprocal image in its backfocal plane (BFP), which is magnified on the image detector. This recording mode bears several essential differences in comparison with previous approaches: The diffractograms are observed in reciprocal space (i.e. on a momentum scale) instead of real-space polar coordinates. The k-field of view in the present study is up to ∼14 Å −1 at 7 keV, corresponding to a small polar angular range of 0°-9°. The k-resolution of ∼0.03 Å −1 corresponds to an angular resolution of 0.03°. For the small angular range, full-field imaging works without sample rotation, similar to...

Hard x-ray photoelectron spectroscopy: a snapshot of the state-of-the-art in 2020

“…The agreement of Figure 10(f-h) with experiment Figure 10(a-c) is excellent. Strikingly good agreement between measured hXPD diffractograms and Kikuchi patterns calculated by the Blochwave approach have also been found for graphite [204] and Si [205,226], i.e. for light elements with their relatively small scattering factors.…”

“…The increasing sharpness and sensitivity with increasing energy is clearly visible in the sequence of hXPD patterns for graphite between E final = 2.6 and 7 keV. [204] XPD differs in several respects from conventional diffraction. The most important practical aspect is the element specificity based on addressing a specific core level.…”

“…Publications since the pilot studies have continued to exploit the microscope to study the valence band structure or to acquire XPD information of a range of materials and some are discussed in detail below. [137,198,[201][202][203][204][205][206] Initial studies in the HAXPES regime were conducted by Medjanik et al and presented proof of principle of the instrument by successfully mapping the electronic structure of Re(0001) at hν = 3.83 keV in a similar manner to the soft X-ray measurements conducted on W(110) prior. [197] Space-charge effects stemming from the Coloumb interaction of the photoelectron cloud induced an energy shift and an anisotropic acceleration of the electrons, which led to a Lorentzian deformation of the spectra.…”

“…[202,203] Fedchenko et al presented the first instance of using the momentum microscope directly for its diffraction capability in the hard X-ray regime rather than its valence band mapping capability. [204] Core level XPD were conducted on single crystal graphite across a photon energy range of 2.5 -7.3 keV with a focus on the C 1s core level. Results were compared with dynamical calculations in an attempt to correlate diffraction with the experimentally observed inelastic scattering events, namely the well-known generation of Kikuchi band features.…”

Theory for High‐Angular‐Resolution Photoelectron Holograms Considering the Inelastic Mean Free Path and the Formation Mechanism of Quasi‐Kikuchi Band

“…In addition, high‐energy photoelectron diffraction (hologram) patterns of graphite with high kinetic energies (>2.4 keV) have been reported. [ 12 ] In this study, they assumed that the line‐shaped pattern in the hologram was formed by the normal Kikuchi band process. It has been found that the quasi‐Kikuchi band in the photoelectron hologram, with a kinetic energy of several hundreds of eV, has two different formation mechanisms.…”