On the Consistency of QCBED Structure Factor Measurements for TiO ₂ (Rutile)

The same Bragg reflection in TiO₂ from 12 different (CBED) patterns (from different crystals, orientations, and thicknesses) are analyzed quantitatively to evaluate the consistency of the quantitative CBED method for bond-charge mapping. The standard deviation in the resulting distribution of derived X-ray structure factors is found to be an order of magnitude smaller than that in conventional X-ray work, and the standard error (0.026% for F _X(110)) is slightly better than obtained by the X-ray Pendellösung method applied to silicon. This is sufficiently accurate to distinguish between atomic, covalent, and ionic models of bonding. We describe the importance of extracting experimental parameters from CCD camera characterization, and of surface oxidation and crystal shape. The current experiments show that the QCBED method is now a robust and powerful tool for low-order structure factor measurement, which does not suffer from the large extinction (multiple scattering) errors that occur in inorganic X-ray crystallography, and may be applied to nanocrystals. Our results will be used to understand the role of d-electrons in the chemical bonding of TiO ₂.