Structure-Property Relations of Tellurium from High Photon Energy Single Crystal X-ray Diffraction and DFT Calculations

Temperature dependent diffraction measurements of small (≈60 μm) single crystals of tellurium were carried out between 26 K and 300 K using the recently upgraded high photon energy (101.5 keV) beamline P21.1 at PETRA III (DESY). Small crystals can be efficiently investigated at that beamline as 2D aluminum X-ray lenses for focusing of the X-ray beam were integrated into the beam. A helium open-flow cryostreamer provides low temperatures. The diffractometer setup was calibrated using standard ruby spheres from NIST (SRM 1990). The data confirmed results of earlier dilatometer-based thermal expansion measurements for Te, and in addition allows to derive the structural changes during cooling. The large number of reflection intensities collected (≈10.000 for Al2O3, ≈40.000 for Te) allows to benchmark a recent very efficient implementation of structure-factor calculations based on widely used pseudopotential/plane wave DFT calculations. The DFT calculations reproduce the experimentally determined structure factors and atomic displacement parameters very well, and also numerous other physical properties, such as the elastic stiffness tensor, and, to a lesser extent, the SHG tensor. The combination of high photon energy diffraction and DFT model calculations therefore provides a comprehensive summary of structure-property relations of tellurium.