Crystallographic analysis of the lattice metric (CALM) from single electron backscatter diffraction or transmission Kikuchi diffraction patterns

Ideas of lattice-basis reduction theory for error-stable Bravais lattice determination and abinitio indexing

In ab initio indexing, for a given diffraction/scattering pattern, the unit-cell parameters and the Miller indices assigned to reflections in the pattern are determined simultaneously. `Ab initio' means a process performed without any good prior information on the crystal lattice. Newly developed ab initio indexing software is frequently reported in crystallography. However, it is not widely recognized that use of a Bravais lattice determination method, which is tolerant of experimental errors, can simplify indexing algorithms and increase their success rates. One of the goals of this article is to collect information on the lattice-basis reduction theory and its applications. The main result is a Bravais lattice determination algorithm for 2D lattices, along with a mathematical proof that it works even for parameters containing large observational errors. It uses two lattice-basis reduction methods that seem to be optimal for different symmetries, similarly to the algorithm for 3D lattices implemented in the CONOGRAPH software. In indexing, a method for error-stable unit-cell identification is also required to exclude duplicate solutions. Several methods are introduced to measure the difference in unit cells known in crystallography and mathematics.

Identification of Kikuchi lines in electron diffraction patterns collected in small-angle geometry

It is demonstrated that Kikuchi features become clearly visible if reflection high-energy electron diffraction (RHEED) patterns are filtered using digital image processing software. The results of such pattern transformations are shown for SrTiO3 with mixed surface termination for data collected at different azimuths of the incident electron beam. A simplified analytical approach for the theoretical description of filtered Kikuchi patterns is proposed and discussed. Some examples of raw and filtered patterns for thin films are shown. RHEED patterns may be treated as a result of coherent and incoherent scattering of electron waves. The effects of coherent scattering may be considered as those occurring due to wave diffraction by an idealized crystal and, usually, only effects of this type are analysed to obtain structural information on samples investigated with the use of RHEED. However, some incoherent scattering effects mostly caused by thermal vibrations of atoms, known as Kikuchi effects, may also be a source of valuable information on the arrangements of atoms near the surface. Typically, for the case of RHEED, Kikuchi features are hidden in the intensity background and researchers cannot easily recognize them. In this paper, it is shown that the visibility of features of this type can be substantially enhanced using computer graphics methods.

A remark on ab initio indexing of electron backscatter diffraction patterns

There is a growing interest in ab initio indexing of electron backscatter diffraction (EBSD) patterns. The methods of solving the problem are presented as innovative. The purpose of this note is to point out that ab initio EBSD indexing belongs to the field of indexing single-crystal diffraction data, and it is solved on the same principles as indexing of patterns of other types. It is shown that reasonably accurate EBSD-based data can be indexed by programs designed for X-ray data.