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We established a new approach to hard-X-ray photoelectron spectroscopy (HAXPES). The instrumental key feature is an increase of the dimensionality of the recording scheme from 2D to 3D. A high-energy momentum microscope can detect electrons with initial kinetic energies more than 6 keV with high angular resolution < 0.1{\deg}. The large k-space acceptance of the special objective lens allows for simultaneous full-field imaging of many Brillouin zones. Combined with time-of-flight parallel energy recording, this method yields maximum parallelization of data acquisition. In a pilot experiment at the new beamline P22 at PETRA III, Hamburg, count rates of more than $10^{6}$ counts per second in the d-band complex of transition metals established an unprecedented HAXPES recording speed. It was found that the concept of tomographic k-space mapping previously demonstrated in the soft X-ray regime works equally well in the hard X-ray range. Sharp valence band k-patterns of Re collected at an excitation energy of 6 keV correspond to direct transitions to the 28th repeated Brillouin zone. Given the high X-ray brilliance (1.1x$10^{13}$ hv/s in a spot of less than 20x15 $mu^{2}$), the 3D bulk Brillouin zone can be mapped in a few hours. X-ray photoelectron diffraction (XPD) patterns with < 0.1{\deg} resolution are recorded within minutes. Previously unobserved fine details in the diffractograms reflect the large number of scatterers, several $10^{4}$ to $10^{6}$, depending on energy. The short photoelectron wavelength (an order of magnitude smaller than the interatomic distance) amplifies phase differences and makes hard X-ray XPD with high resolution a very sensitive structural tool. The high count rates pave the way towards spin-resolved HAXPES using an imaging spin filter.

Owing to strongly enhanced bulk sensitivity, angle- or momentum-resolved photoemission using X-rays is an emergent powerful tool for electronic structure mapping. A novel full-field k-imaging method with time-of-flight energy detection allowed rapid recording of 4D (EB,k) data arrays (EB binding energy; k final-state electron momentum) in the photon-energy range of 400-1700eV. Arrays for the d-band complex of several transition metals (Mo, W, Re, Ir) reveal numerous spots of strong local intensity enhancement up to a factor of 5. The enhancement is confined to small (EB,k)-regions (dk down to 0.01 A-1; dEB down to 200 meV) and is a fingerprint of valence-band photoelectron diffraction. Regions of constructive interference in the (EB,k)-scheme can be predicted in a manner resembling the Ewald construction. A key factor is the transfer of photon momentum to the electron, which breaks the symmetry and causes a rigid shift of the final-state energy isosphere. Working rigorously in k-space, our model does not need to assume a localization in real space, but works for itinerant band states without any assumptions or restrictions. The role of momentum conservation in Fermi's Golden Rule at X-ray energies is revealed in a graphical, intuitive way. The results are relevant for the emerging field of time-resolved photoelectron diffraction and can be combined with standing-wave excitation to gain element sensitivity., Comment: 24 pages, 7 figures