Determination of unit cell

UnitCell Tools, a package to determine unit-cell parameters from a single electron diffraction pattern

Electron diffraction techniques in transmission electron microscopy (TEM) have been successfully employed for determining the unit-cell parameters of crystal phases, albeit they exhibit a limited accuracy compared with X-ray or neutron diffraction, and they often involve a tedious measurement procedure. Here, a new package for determining unit-cell parameters from a single electron diffraction pattern has been developed. The essence of the package is to reconstruct a 3D reciprocal primitive cell from a single electron diffraction pattern containing both zero-order Laue zone and high-order Laue zone reflections. Subsequently, the primitive cell can be reduced to the Niggli cell which, in turn, can be converted into the unit cell. Using both simulated and experimental patterns, we detail the working procedure and address some effects of experimental conditions (diffraction distortions, misorientation of the zone axis and the use of high-index zone axis) on the robustness and accuracy of the software developed. The feasibility of unit-cell determination of the TiO₂ nanorod using this package is also demonstrated. Should the parallel-beam, nano-beam and convergent-beam modes of the TEM be used flexibly, the software can determine unit-cell parameters of unknown-structure crystallites (typically >50 nm).

Automated Reconstruction of Spherical Kikuchi Maps

An automated approach to fully reconstruct spherical Kikuchi maps from experimentally collected electron backscatter diffraction patterns and overlay each pattern onto its corresponding position on a simulated Kikuchi sphere is presented in this study. This work demonstrates the feasibility of warping any Kikuchi pattern onto its corresponding location of a simulated Kikuchi sphere and reconstructing a spherical Kikuchi map of a known phase based on any set of experimental patterns. This method consists of the following steps after pattern collection: (1) pattern selection based on multiple threshold values; (2) extraction of multiple scan parameters and phase information; (3) generation of a kinematically simulated Kikuchi sphere as the "skeleton" of the spherical Kikuchi map; and (4) overlaying the inverse gnomonic projection of multiple selected patterns after appropriate pattern center calibration and refinement. The proposed method is the first automated approach to reconstructing spherical Kikuchi maps from experimental Kikuchi patterns. It potentially enables more accurate orientation calculation, new pattern center refinement methods, improved dictionary-based pattern matching, and phase identification in the future.

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 Angströms 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 Angströms 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.