Wyckoff positions
Encyclopedia
In crystallography
, a Wyckoff position is a point belonging to a set of points for which site symmetry group
s are conjugate subgroup
s of the space group
. 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.
Crystallography
Crystallography is the experimental science of the arrangement of atoms in solids. The word "crystallography" derives from the Greek words crystallon = cold drop / frozen drop, with its meaning extending to all solids with some degree of transparency, and grapho = write.Before the development of...
, a Wyckoff position is a point belonging to a set of points for which site symmetry group
Symmetry group
The symmetry group of an object is the group of all isometries under which it is invariant with composition as the operation...
s are conjugate subgroup
Subgroup
In group theory, given a group G under a binary operation *, a subset H of G is called a subgroup of G if H also forms a group under the operation *. More precisely, H is a subgroup of G if the restriction of * to H x H is a group operation on H...
s of the space group
Space group
In mathematics and geometry, a space group is a symmetry group, usually for three dimensions, that divides space into discrete repeatable domains.In three dimensions, there are 219 unique types, or counted as 230 if chiral copies are considered distinct...
. Crystallography tables give the Wyckoff positions for different space groups.
Wyckoff positions are used in calculations of crystal
Crystal
A crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. The scientific study of crystals and crystal formation is known as crystallography...
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.