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

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.

Determining the Bravais lattice using a single electron backscatter diffraction pattern

Theab initioderivation of the Bravais lattice from the Kikuchi bands detected from a single electron backscatter diffraction (EBSD) pattern is successfully performed. The as-measured band widths and azimuths always suffer from gnomonic distortions which need to be corrected. A primitive reciprocal cell is first reconstructed by means of the corrected data and the cell parameters are then refined by least-squares analysis of hugely over-determined equations. This allows one to further derive a Niggli reduced cell from the primitive cell. The algorithm presented is not related to any crystal symmetry information and is therefore applicable to all crystal systems. The feasibility of the determination of the Bravais lattice type and parameters from a single EBSD pattern is demonstrated using a mineral sample without anya prioriinformation about its crystal structure. The novel application developed in the present work opens the way to the determination of the Bravais lattice of crystalline materials using scanning electron microscopy combined with the EBSD technique.

EBSDL: a computer program for determining an unknown Bravais lattice using a single electron backscatter diffraction pattern

Electron backscatter diffraction (EBSD) patterns provide a wealth of crystallographic information but disappointingly low accuracy. Adopting a strategy of compensating the poor accuracy by the large amount of information, a computer program, EBSDL, has been successfully developed to determine the unknown Bravais lattice of bulk crystalline materials using a single EBSD pattern. Unlike programs that perform phase identification, the new application is completely independent of chemical information.

Accurate d-spacings from zero-order Laue zone patterns

Experimental d-spacing values are criteria towards the identification of crystallites by electron diffraction. Conclusive identifications often rely on accurate d-spacings. It is shown here that accurate orthogonal components (in mm) for the primitive unit vectors of a zero-level diffraction pattern can be obtained through least-squares processing of (x,y) coordinates for all spots on the film. Valid vectors from the origin spot to any spot in the plane of the film are integer linear combinations of the two selected unit vectors. Accurate lengths and standard deviations for such vectors therefore can be calculated from the least-squares results. Corresponding d-spacings can then be calculated from the vector lengths on the film and the camera constant. In order to obtain d-spacing values that are not only precise, but also accurate, an accurate value of the camera constant should be used. This requires calibration of the experimental setup with reference materials in the same experimental conditions, with careful control of the sample height. For the same quality of measurements, the improvement in the accuracy of the d-spacings obtained with the proposed method is approximately proportional to the square root of the number of measurements taken. Practically, typical improvement in accuracy is about threefold, and accuracies of a fraction of a percent in d-spacings are achievable in this way. The above approach has been programmed as an option in the NRCBED program.