Wyckoff letter

Group-subgroup relations from hexagonal closest-packing of spheres to some MX3 and M2X3 structures. The boxes represent octahedral voids, with the coordinates as given at the top left. The positions of the octahedron centers are labeled by their Wyckoff letters. Gray boxes refer to occupied voids. The dots indicate how the atoms Ru, P and N are shifted from the octahedron centers parallel to c... 

Atomic Positions Using Cartesian Coordinates and Corresponding Wyckoff Letters... 

In the International Tables of Crystallography, for each of the 230 space groups the list of all the Wyckoff positions is reported. For each of the positions (the general and the special ones) the coordinate triplets of the equivalent points are also given. The different positions are coded by means of the Wyckoff letter, a, b, c, etc., starting with a for the position with the lowest multiplicity and continuing in alphabetical order up to the general position. 

Multiplicity, Wyckoff letter, Site symmetry Coordinates ... 

This list is reproduced exactly as it appears in the International Tables. It tells us all the different kinds of locations that exist within one unit cell. In each instance we are given the multiplicity of the type of point, namely, how many of them there are that are equivalent and obtainable from each other by application of symmetry operations. There is also an italic letter, called the Wyckoff letter. This is simply an arbitrary code letter that some crystallographers sometimes find useful these letters need not concern us further. Next there is the symbol for the point symmetry that prevails at the site. Finally, there is a list of the fractional coordinates for each point in the set. 

Atomic positions indicate hie Wyckoff letter in parentheses. 

Both the multiplicity and Wyckoff letter combined together, are often used as the name of the equivalent position. Sometimes when... 

Using the International Tables for Crystallography describe every atom in terms of the multiplicities and Wyckoff letters of their site positions and establish the content of the unit cell, the simplest chemical formula and the number of formula units (Z) per unit cell. 

Multiplicity Wyckoff letter Site symmetry Coordinates of equivalent positions... 

From the forgoing, it is seen that in order to specify a two-dimensional crystal structure, all that needs to be specified are (i), the lattice parameters, (ii), the plane group symbol, (iii), a list of atom types together with the Wyckoff letter and the atomic coordinates. For complex crystals, it simplifies the amount of information to be recorded enormously. 

Wyckoff letters, as described in Chapter 3 for the plane groups, label the different site symmetries that can be occupied by an atom in a unit cell. When the position chosen for the atom,... 

Atom Multiplicity and Wyckoff letter Coordinates of atoms x y z ... 

If an atom is placed in the unit cell of a crystal at a position, or site, (jc, y, z), identical copies of the atom must, by operation of the symmetry elements present, lie at other sites, (jq, yu zi), (x2, y2, z2) and so on. A Wyckoff letter is a site label, and each different type of site in the unit cell is given a different Wyckoff letter. 

Niggli (1919) recognised the importance of lattice complexes for the description of structure types 1935 Hermann listed the lattice complexes in the Internationale Tabellen zur Bestimmung von Kristallstrukturen giving for eadi point position the space group and Wyckoff letter for the standard setting of the complex. 

In SICS, therefore, only the best determination of any phase has been selected - as defined by the chemical composition, the space group and the sites occupied in the unit cell (given by the Wyckoff letters and combined in the so-called Wyckoff sequence). These data are given in a standardized form. SICS is available as a supplement to ICSD. Aware of the problem of finding the best determination, there is a reference to the relevant entries in ICSD. Another advantage of SICS is described in Section 11.1.2. 

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