Ab-initio primitive cell parameters from single convergent-beam electron diffraction patterns: a converse route to the identification of microcrystals with electrons.

A new method for the ab initio derivation of Buerger-reduced primitive cell parameters from coordinate measurements of spots on single convergent-beam electron diffraction (CBED) patterns is described, which does not involve trial-and-error. The pattern can be taken along any zone axis, and misorientations of the crystallite by as much as a few degrees are taken into account without loss of accuracy. This derivation of cell parameters by least-squares analysis of the measurements has been automated in a program called NRCBED. Present accuracy is about 1% on lengths and 2 degrees on angles, but could be significantly improved by modelling projector lens aberrations, or by using a microscope without a projector lens. With present technology, it is possible to obtain a CBED pattern and a semi-quantitative energy-dispersive X-ray (EDX) analysis simultaneously from a single microcrystal a few hundred Angstr?ms across. It becomes therefore possible to identify the material of the crystal on a single CBED pattern: a cell parameter database for known compounds is searched with the primitive cell parameters obtained in the above way, and with a mask describing the EDX results qualitatively. Feasibility is demonstrated on a crystallite of CeO2 500 Angstr?ms across. With this new approach, trial-and-error should disappear from the solution of other long-standing problems: interpretation of X-ray powder patterns for new compounds in the presence of impurity lines, or in the case of multiple phases should become straight-forward.