Polar multipoles in wurtzite-like crystals (ZnO, GaN)

A theoretical analysis and simulation of resonance-enhanced x-ray Bragg diffraction by wurtzite-like crystals is presented for parity-even and polar (parity-odd) atomic resonant processes. Compounds with this crystal structure are of great interest for a range of technologies. The electronic properties of a crystal are represented as ground-state expectation values of atomic multipoles, and the analysis respects all selection rules imposed on diffraction by atomic and crystal symmetry. Our main focus is directed at weak, space-group forbidden reflections that are a result of angular anisotropy in the cation electron distribution. Expected variations of the diffracted intensity with orientation of the crystal due to angular anisotropy of the electron distribution are simulated. The crystal symmetry allows the intensity to be coupled to circular polarization in the primary beam and illustrative examples for the creation of circular polarization in diffraction are provided. These polarization effects are unique probes of electronic structure. Moreover, we prove that recent diffraction experiments on ZnO reveal the pyroelectric (dipole) and polar octupole moment of the cation. (fast track communication)