Extending the limits of powder diffraction analysis: Diffraction parameter space, occupancy defects, and atomic form factors

Although the determination of site occupancies is often a major goal in Rietveld refinement studies, the accurate refinement of site occupancies is exceptionally challenging due to many correlations and systematic errors that have a hidden impact on the final refined occupancy parameters. Through the comparison of results independently obtained from neutron and synchrotron powder diffraction, improved approaches capable of detecting occupancy defects with an exceptional sensitivity of 0.1% (absolute) in the class of layered NMC (Li[Ni_xMn_yCo_z]O₂) Li-ion battery cathode materials have been developed. A new method of visualizing the diffraction parameter space associated with crystallographic site scattering power through the use of f∗ diagrams is described, and this method is broadly applicable to ternary compounds. The f∗ diagrams allow the global minimum fit to be easily identified and also permit a robust determination of the number and types of occupancy defects within a structure. Through a comparison of neutron and X-ray diffraction results, a systematic error in the synchrotron results was identified using f∗ diagrams for a series of NMC compounds. Using neutron diffraction data as a reference, this error was shown to specifically result from problems associated with the neutral oxygen X-ray atomic form factor and could be eliminated by using the ionic O^2- form factor for this anion while retaining the neutral form factors for cationic species. The f∗ diagram method offers a new opportunity to experimentally assess the quality of atomic form factors through powder diffraction studies on chemically related multi-component compounds.