The term Wyckoff position takes its origin from the first English collection of equivalent positions in space groups, which appeared in The analytical expression of the results of the theory of space groups by Ralph W.

But MMs at the first group of sites are antiparallel to those at the second group of sites, if a small noncollinearity with the. Concerning magnetic order (occurring below TN ), MMs at Fe1 and Fe3 sites are parallel, as well as those at Fe2 and Fe4. Like in space groups, in point groups, too, each Wyckoff position is labelled by a Wyckoff letter. We note that these Fe positions are all crystallographically equivalent (Wyckoff position 4c). This is no longer true when one makes use of Wyckoff sets.īy analogy to the Wyckoff positions of space groups, Wyckoff positions of point groups have been defined too: here the term 'position' indicates the position of face poles (for face forms) or of points (for point forms) in the stereographic projection. The transfer of Wyckoff positions from individual space groups to space-group types is not unique because Wyckoff positions with the same type of site-symmetry group may be exchanged in different space groups of the same type. There is a total of 72 Wyckoff positions in plane groups and 1731 Wyckoff positions in space groups. The number of different Wyckoff positions of each space group is finite, the maximal numbers being 9 for plane groups (realized in p2 mm) and 27 for space groups (realized in Pmmm). A Wyckoff position of a space group G consists of all points X for which the site-symmetry groups are conjugate subgroups of G.Įach Wyckoff positon of a space group is labelled by a letter which is called the Wyckoff letter.

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