Low-temperature powder X-ray diffraction measurements in vacuum: analysis of the thermal displacement of copper

Accurate charge densities from powder X-ray diffraction - a new version of the Aarhus vacuum imaging-plate diffractometer

In recent years powder X-ray diffraction has proven to be a valuable alternative to single-crystal X-ray diffraction for determining electron-density distributions in high-symmetry inorganic materials, including subtle deformation in the core electron density. This was made possible by performing diffraction measurements in vacuum using high-energy X-rays at a synchrotron-radiation facility. Here we present a new version of our custom-built in-vacuum powder diffractometer with the sample-to-detector distance increased by a factor of four. In practice this is found to give a reduction in instrumental peak broadening by approximately a factor of three and a large improvement in signal-to-background ratio compared to the previous instrument. Structure factors of silicon at room temperature are extracted using a combined multipole-Rietveld procedure and compared with ab initio calculations and the results from the previous diffractometer. Despite some remaining issues regarding peak asymmetry, the new diffractometer yields structure factors of comparable accuracy to the previous diffractometer at low angles and improved accuracy at high angles. The high quality of the structure factors is further assessed by modelling of core electron deformation with results in good agreement with previous investigations.

Spatial distribution of electrons near the Fermi level in the metallic LaB6 through accurate X-ray charge density study

Charge densities of iso-structural metal hexaborides, a transparent metal LaB₆ and a semiconductor BaB₆, have been determined using the d > 0.22 Å ultra-high resolution synchrotron radiation X-ray diffraction data by a multipole refinement and a maximum entropy method (MEM). The quality of the experimental charge densities was evaluated by comparison with theoretical charge densities. The strong inter-octahedral and relatively weak intra-octahedral boron-boron bonds were observed in the charge densities. A difference of valence charge densities between LaB₆ and BaB₆ was calculated to reveal a small difference between isostructural metal and semiconductor. The weak electron lobes distributed around the inter B₆ octahedral bond were observed in the difference density. We found the electron lobes are the conductive π-electrons in LaB₆ from the comparison with the theoretical valence charge density. We successfully observed a spatial distribution of electrons near the Fermi level from the X-ray charge density study of the series of iso-structural solids.