THE "COMBINATION METHOD" OF QUANTITATIVE CBED AND X-RAY DIFFRACTION APPLIED TO CORUNDUM.

Philip N.H. Nakashima,^a Victor A. Streltsov,^b and Andrew W.S. Johnson^c

^aSchool of Physics and Materials Engineering, Monash University, Clayton Vic 3800, Australia; ^bStructural Biology, CSIRO Division of Health Sciences and Nutrition, Parkville Vic 3052, Australia; ^cCentre for Microscopy and Microanalysis, University of Western Australia, Crawley WA 6009, Australia (philip.nakashima@spme.monash.edu.au)

Corundum, or a-Al₂O₃, has a great tendency to form perfect crystals. A lot of theoretical and experimental charge density research has been conducted with corundum as a benchmark compound because experimental results should, in principle, be very reproducible from this highly ideal material. However, very high crystal perfection often leads to significant extinction in the integrated intensity measurements of strong, lower order reflections (those most sensitive to the bonding charge density distribution) by conventional single crystal X-ray diffraction due to the increased likelihood of multiple scattering. In addition, the data lacks an absolute scale, the relativity of the structure factor measurements resulting from the application of kinematic scattering theory. The conventional least squares methods of refining extinction and scale simultaneously are heavily compromised in the presence of significant extinction due to the strong correlation between the two quantities. Different approaches to applying extinction and scale corrections can result in great variability in the experimentally determined charge densities [1, 2]. Such variability eliminates the possibility of making a reliable comparison of experimentally measured charge density with that computed by theoretical models.

The "combination method" overcomes the problems discussed above by using quantitative convergent beam electron diffraction (QCBED) to measure the lower order structure factors to high precision (uncertainty of order 0.1%) on an absolute scale. The technique fully accounts for multiple scattering and measures the structure factors from the angular distribution of intensity within the corresponding reflections on or near the Laue circle. This negates the issues of scale and extinction. QCBED is less accurate in measuring higher order structure factors and therefore, a combination of the low order QCBED data with the higher order X-ray data is required to optimise charge density measurements. An overlap of the QCBED data set with the valid, extinction free portion of the X-ray data allows the latter to be scaled to the QCBED data. A similar approach was used successfully by Zuo et al [3] to measure charge density in Cu₂O.

We will present comparisons of our experimental results with DFT (GGA/FPLAPW) and PHF calculations.

References

1 Streltsov, V.A. and Maslen, E.N. (1992) Acta Cryst. A48, 651.

2 Streltsov, V.A., Nakashima, P.N.H. and Johnson, A.W.S. (2001) J. Phys. chem. Solids 62, 2109.

3 Zuo, J.M., Kim, M., O'Keeffe, M. and Spence, J.C.H. (1999) Nature 401, 49.