Wyckoff positions

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In crystallography, a Wyckoff position is a point belonging to a set of points for which site symmetry groups are conjugate subgroups of the space group.[1] Crystallography tables give the Wyckoff positions for different space groups.

Wyckoff positions are used in calculations of crystal properties. There are two types of positions: general and special.

  • General positions are left invariant only for the identity operation (E). Each space group has only one general position.
  • Special positions are left invariant by the identity operation and at least one other operation of the space group.

The Wyckoff positions are named after Ralph Walter Graystone Wyckoff, an American X-ray crystallographer who authored several books in the field. His 1922 book, The Analytical Expression of the Results of the Theory of Space Groups, contained tables with the positional coordinates, both general and special, permitted by the symmetry elements. This book was the forerunner of International Tables for X-ray Crystallography, which first appeared in 1935.

External links[edit]


  1. ^ Lev. Kantorovich (2004). Quantum Theory of the Solid State: An Introduction. Springer. p. 28.