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Diffraction pattern indexing in lithium niobate
Author(s) -
Twigg M. E.,
Nakahara S.,
Maher D. M.,
Sheng T. T.,
Homes R. J.
Publication year - 1986
Publication title -
journal of microscopy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.569
H-Index - 111
eISSN - 1365-2818
pISSN - 0022-2720
DOI - 10.1111/j.1365-2818.1986.tb04283.x
Subject(s) - diffraction , lithium niobate , crystal system , lattice (music) , crystallography , electron diffraction , crystal structure , materials science , reciprocal lattice , condensed matter physics , optics , physics , chemistry , acoustics
SUMMARY Crucial to the interpretation of diffraction contrast experiments conducted in the transmission electron microscope is the self consistent indexing of zone‐axis patterns for the crystal under study. Because indexing the diffraction patterns of a crystal as complicated as lithium niobate is not a trivial exercise, computer simulation of diffraction patterns, extinction distance calculations, and consideration of several unit cell representations are used in order to make diffraction pattern interpretation more tractable. It was found that the zone‐axes were most easily indexed by considering the pseudo‐cubic representation of rhombohedral perovskite crystals. The pseudo‐cubic system also facilitates the indexing of Bragg reflections and the visualization of the major features of the reciprocal lattice. Ultimately, however, hexagonal indices must be used to understand a particular lattice defect, since the symmetries associated with the hexagonal lattice are real symmetries, unlike the apparent symmetries that are implied by a pseudo‐cubic crystal. For this reason, we have tabulated the matrices for transforming from the hexagonal system to the pseudo cubic system. For the sake of completeness, transformation matrices relating all four relevant lattice systems (hexagonal, pseudo‐cubic, primitive rhombohedral, and orthohexagonal), as well as the atomic positions in each system, are tabulated.