Estimation of atomic displacement in a unit cell by means of convergent-beam elctron diffraction

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Large angle convergent-beam electron diffraction (LACBED) has been applied to determine structure factors, and following results have been obtained for alpha Al_2O_3.1. The extinction distance xi_<kappa> for g=0 0 6l for l*5 was found to be much larger than specimen thickness of 150-200 nm suggesting that the kinematical theory of electron diffraction can be applied.2. When convergent angle of the incident beam is so large that several reflections with l's from 5 to 9 may satisfy Bragg conditions simultaneously and the beam is illuminated onto a small area of specimen, intensities of the Braggreflections can be analyzed with the kinematical approximation.3. The position of Al ion in alumina was found to be displaced by 0.02435 nm along a C-axis from the ideal position. The static displacement thus evaluated is in good agreement with the one derived by using the dynamical theory of electron diffraction and those obtained by X-ray diffraction, demonstrating the adequateness of the present kinematical treatment.4. If the temperature factor is ignored in the analysis, the displacements of Al ion is over estimated by about 10%. An accuracy in measurements is improved when a specimen is cooled, since intensities of 0 0 6l reflections change more sensitively with the displacement of Al ion at lower temperature.5. In the present experiment neighboring reflections were compared to reduce errors originated from background intensities and from non-lineality of darkness of films. The accuracy will be improved and experiments will be easy provided imaging plates or a slow scan CCD camera will be used in place of films.