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The rise and fall of Weber indices
Author(s) -
Nespolo Massimo
Publication year - 2018
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s1600576718007033
Subject(s) - reciprocal lattice , hexagonal crystal system , reciprocal , lattice (music) , trigonal crystal system , integer (computer science) , hexagonal lattice , mathematics , theoretical physics , physics , computer science , condensed matter physics , crystal structure , crystallography , diffraction , quantum mechanics , chemistry , philosophy , antiferromagnetism , acoustics , programming language , linguistics
Weber indices were introduced to provide a unique expression of a lattice direction with respect to the four‐axis setting used for hexagonal and rhombohedral crystals. They are in general fractional indices, even in the case of a primitive hexagonal unit cell, but they are often carelessly reduced to integer values. This corresponds, on the one hand, to taking as direction indices the nodes of a lattice further from the origin and, on the other hand, to adopting a hybrid indexing between direct and reciprocal space. A critical analysis of the drawbacks of Weber indices is presented, which justifies the reluctance of crystallographers to adopt them, despite a more widespread use in fields like electron microscopy and metal science.