Fig. 8: Two types of photoelectron diffraction for Rhenium (0001) in the hard X-ray range.

a As-measured valence-band (VB) (k_x, k_y) momentum pattern at the final-state energy E_final = 3.4 keV; crosses mark signatures of Kikuchi diffraction. b Re 4f_7/2 core-level X-ray photoelectron diffraction (XPD) pattern taken at the same final-state energy and identical settings of the microscope. Crosses and ellipses mark the same features as in (a), the circled cross marks the centre of symmetry ([0001]-direction) and the double arrow marks the principal Kikuchi band (width 2|G_11–20|). c Ratio image of the valence-band pattern (VB) and the core-level diffractogram (4f_7/2 XPD) showing the valence-band structure with eliminated diffraction modulation. Pluses mark the centres of the Brillouin zones. d–f Binding energy E_B vs. momentum k_y, k_x sections of valence-band and 4f core-level signals. Dashed ellipses in (d, e) mark signatures of Laue-type diffraction. g, h Time-of-flight spectra for the Re 4f core level and valence band, respectively. The bars denote the energy regions integrated for momentum patterns (a) and (b). i Real-space model illustrating the origin of the principal Kikuchi band marked in (b) as double arrow. j Brillouin zone of the hexagonal-close-packed Re lattice. k–m Same as (a–c) but for 6.0 keV; crosses and dashed ellipses mark intensity-modulations by Kikuchi diffraction. Sections (c) and (m) run through different planes of the Brillouin zone (dashed and dotted lines in (j)). The lateral shifts of the valence-band pattern with respect to the [0001]-direction (difference between circled plusses and circled crosses in (c) and (m)) reflect the transfer of photon momentum k_hν to the valence-band photoelectrons.