Combined structure-factor phase measurement and theoretical calculations for mapping of chemical bonds in GaN

For non-centrosymmetric crystals, the refinement of charge-density maps requires highly accurate measurements of structure-factor phase, which can now be obtained using the extinction-free convergent-beam electron microdiffraction method. We report here accurate low-order structure-factor phases and amplitudes for gallium nitride (GaN) in the wurtzite structure. The measurement accuracy is up to 0.1% for amplitude and 0.2° for phases. By combining these with high-order structure factors from electronic structure calculation, charge-density maps were obtained. Fine bonding features suggest that the Ga-N bonds are polar and covalent, with charge transfer from Ga to N; however, the polarity effect is extremely small.