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The Normalized Reduced Form and Cell Mathematical Tools for Lattice Analysis--Symmetry and Similarity



Alan D. Mighell


To intelligently and effectively use the crystallographic databases, dierse mathematical and computer tools are required that can delve into the nature of a given lattice or that can cut across a set of lattices to elucidate various types of interlatice relationships. One such tool is the normalized reduced cell and form. With respect to intralattice relationships, practical experience has revealed that this tool is valuable for analyzing the reduced form to dtermine symmetry and to deduce other significant relationships between the elements of reduced form. Likewise, with respect to interlattice relationships, experience has shouwn that this tool is ideal for the determining metrically similar lattices. Knowlege of similar latices has practical value in solving structures, in assignment of structure types, in materials design and in nanotechnology. It is recommended that routine lattice-matching strategies based on normalized reduced cell in additon to the reduced cell be routinely carried out in database searching, in data evaluation, and in experinental work.
Journal of Research (NIST JRES) -
108 No. 6


identification, lattice relationships, lattice similarity, lattice-matching strategies, metric lattice, normalized reduced cell and form, symmetry


Mighell, A. (2003), The Normalized Reduced Form and Cell Mathematical Tools for Lattice Analysis--Symmetry and Similarity, Journal of Research (NIST JRES), National Institute of Standards and Technology, Gaithersburg, MD (Accessed April 19, 2024)
Created November 1, 2003, Updated February 19, 2017