On the sensitivity of electron and X-ray scattering factors to valence charge distributions

The sensitivity of atomic scattering factors to valence charge distributions has been compared quantitatively for X-ray and electron diffraction. It is found that below a critical scattering vector, s (|s| = sinθ/λ), ranging typically from 0.2 to 0.6 Å⁻¹ depending on the atomic number, electron diffraction is more sensitive to valence charge densities than X-ray diffraction. Thus, electron diffraction provides crucial electronic structure information via the low-order structure factors, which are relatively insensitive to thermal vibrations, but sensitive to the charge distribution that characterizes the chemical bonding properties of the materials. On the other hand, the high-order structure factors, which are mainly influenced by atomic position and core charge, in many cases can be replaced by structure factors of a procrystal (superposition of neutral atoms), or by calculated structure factors from modern density functional theory (DFT), without losing significant accuracy. This is demonstrated by detailed analyses of an MgB₂ superconductor. The work reveals the importance of accurate determination of a very few low-order structure factors in valence electron density studies, and suggests the merit of the combined use of electron diffraction and DFT calculations for solids, especially those with large unit cells and nanocrystalline grains, unsuitable for X-ray studies.