Phase measurement for accurate mapping of chemical bonds in acentric space groups

Although the electron density is fundamental to the study of chemical bonding and density-functional theory, it cannot be accurately mapped experimentally for the important class of crystals lacking inversion symmetry, since structure factor phase information is normally inaccessible. We report the combination of x-ray and electron diffraction experiments for the determination of the electron density in acentric AlN, using multiple-scattering effects in convergent-beam electron diffraction to obtain sensitivity to structure factor phases, and describe a new error metric and weighting scheme for multipole refinement using combined measurements of structure factor magnitudes and phases.