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Voronoi Polyhedra: A Useful Tool to Determine the Symmetry and Bravais Class of Crystal Lattices
Author(s) -
Bohm J.,
Heimann R. B.,
Bohm M.
Publication year - 1996
Publication title -
crystal research and technology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.377
H-Index - 64
eISSN - 1521-4079
pISSN - 0232-1300
DOI - 10.1002/crat.2170310816
Subject(s) - bravais lattice , voronoi diagram , polyhedron , lattice plane , lattice (music) , primitive cell , mathematics , combinatorics , crystal structure , reciprocal lattice , physics , geometry , crystallography , chemistry , quantum mechanics , diffraction , acoustics
A handy PC‐supported method will be described to deduce the Bravais lattice (Bravais class) of a crystal lattice from an arbitrary set of lattice parameters. The method involves the construction of the related Voronoi polyhedron (Dirichlet domain, Wirkugsbereich , Fedorov parallelohedron, Wigner‐Seitz cell) whose metric relations between its edge lengths can be used to unequivocally identify the Bravais lattice. This is particularly useful if an unconventional setting of the unit cell, or inaccurately determined lattice parameters may result in misleading conclusions as to identify the correct Bravais lattice.