Low-angle atomic scattering factors and the charge density of beryllium

Abstract

The X-ray structure factors for the 27 lowest-angle Bragg reflections of beryllium measured by Brown (1972) have been placed on an absolute scale using the very accurate 1011 and 0002 low-angle structure factors determined by high-energy electron diffraction. A set of atomic scattering (form) factors calculated from these results appear to be much more accurate than those deduced from these original X-ray measurements. At low angles these new structure factors show excellent agreement with recent values obtained by gamma-and X-ray diffractometry, except for the 0002 reflection where the recent X-ray result is somewhat high. At higher angles (sin θ/λ ≥ 0.7.Å⁻¹) the experimental atomic scattering factors agree quite closely with the best theoretical free-atom values, but the low-angle form factors deviate considerably from the free-atom results. These deviations can be explained as corresponding to (sp²) ^a −(sp) ^b hybridization of the Be atoms with b > a, although other workers have suggested that sp³-like hybrids can also explain the structure-factor data.