ON THE AVERAGE COULOMB POTENTIAL (PHI(0)) AND CONSTRAINTS ON THE ELECTRON-DENSITY IN CRYSTALS

The role of the average Coulomb potential (mean inner potential), PHI0, in electron diffraction and methods for its calculation are reviewed. From an examination of model and real crystals, it is shown that a prescription of Becker & Coppens [Acta Cryst. (1990), A46, 254-258] for calculating the average potential from X-ray data may lead to incorrect results because of an artificial surface-dipole term that is independent of crystal size. It is suggested that measurements of PHI0 for crystals with adsorbed monolayers could be used to measure the density and sign of a real surface dipole moment. Published data for MgO, silicon and aluminium show that PHI0 is very sensitive to bonding effects when atoms combine to form crystals. The often-reported expansion of the silicon valence shell deduced from pseudo-atom refinements of X-ray diffraction data is shown to be an artifact of the refinement method, as recent accurate measurements of PHI0 for silicon instead require a contraction of the outer part of the valence shell. It is concluded that X-ray diffraction data alone do not allow a determination of PHI0. However, PHI0 provides information about valence-electron distributions that is not available in practice from X-ray data and places powerful constraints on pseudo-atom refinements.