International
Tables for
Crystallography
Volume G
Definition and exchange of crystallographic data
Edited by S. R. Hall and B. McMahon

International Tables for Crystallography (2006). Vol. G, ch. 3.8, pp. 207-208

Section 3.8.3. Arrangement of the dictionary

I. D. Browna*

aBrockhouse Institute for Materials Research, McMaster University, Hamilton, Ontario, Canada L8S 4M1
Correspondence e-mail: idbrown@mcmaster.ca

3.8.3. Arrangement of the dictionary

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The three categories in version 1.0 of the symmetry CIF dictionary all lie within the SPACE_GROUP category group and are classified among the category groups defining the structural model listed in Section 3.1.10[link] . (For convenience, in Chapters 3.2[link] and 3.4[link] the _space_group_* items introduced from the symmetry dictionary to the core and modulated structures dictionaries are discussed within an informal DDL1 SYMMETRY category group.)

The categories in the symmetry CIF dictionary are:

SPACE_GROUP
SPACE_GROUP_SYMOP
SPACE_GROUP_WYCKOFF

The first describes the properties of the space group as a whole, the second describes the properties of the symmetry operations and the third describes the properties of the special positions. The three categories are linked by a space-group identifier which allows items looped in the last two categories to be related back to one of the space groups defined in the first.

Data items in these categories are as follows:

(a) SPACE_GROUP [Scheme scheme1]

(b) SPACE_GROUP_SYMOP [Scheme scheme2]

(c) SPACE_GROUP_WYCKOFF [Scheme scheme3]

The bullet • indicates a category key. The arrow [(\rightarrow)] is a reference to a parent data item. Items in italics are also found in the core CIF dictionary.

The information contained in the SPACE_GROUP category relates to the properties of the space group as a whole. Three different kinds of properties are defined here.

Firstly, the names (or symbols) used to describe the space group are defined. As mentioned above, these divide themselves into ones that identify the space group without specifying any particular setting, and ones that can be used to generate the symmetry operations and therefore also specify the setting. Because of the ambiguities involved in the Hermann–Mauguin symbol, three different versions are defined with different degrees of rigour. _space_group.name_H-M_ref may only include the Hermann–Mauguin symbol of the reference setting. _space_group.name_H-M_alt and _space_group.name_H-M_full give the user the freedom to give the symbol in any setting, but cannot be reliably interpreted by a computer.

Secondly, the SPACE_GROUP category contains information about the symmetry properties of the space group, such as its Laue class, Bravais type and point group.

Thirdly, the SPACE_GROUP category contains information which specifies the setting. Although this is implicit in the Hall symbol or in the list of symmetry operations that are given in the SPACE_GROUP_SYMOP category, it can be made explicit by including the transformation needed to generate the setting used in the CIF from the reference setting specified in the dictionary. The reference setting is defined in two ways: firstly, in the list of allowed values of _space_group.name_H-M_ref; and secondly in a concordance correlating the International Tables number and the Schoenflies symbol of the space group with the Hermann–Mauguin symbol of the reference setting and the Hall symbol. Either of the latter two can be used to generate the symmetry operations in the reference setting.

Information on several space groups may be looped. In this case, each space group is identified by the item _space_group.id, which is a parent to various *.sg_id items in the other categories. This allows a number of different space groups, or different settings of the same space group, to be defined within the same CIF.

Although the most elegant way of specifying the symmetry operations of the space group is to use the Hermann–Mauguin symbol of the reference setting or the Hall symbol (depending on the setting), it is common practice to list all the symmetry operations explicitly in a CIF. For each space group these must appear in a loop and so require their own category, SPACE_GROUP_SYMOP. The symmetry operations may be specified in one of two ways, either through a full list of all the operations of the group or through a restricted list of generators which, when multiplied by each other, generate the full list.

The list of symmetry operations may contain the operations of several space groups, the particular space group being identified by _space_group_symop.sg_id.

Special positions are looped in the SPACE_GROUP_WYCKOFF category, which permits a description of the properties of each special position of one or more space groups. In the current structure of CIF it is not possible to give all the equivalent positions associated with a particular special position, but these can easily be generated by applying the symmetry operations of the space group to the representative special position whose coordinates are included. Although the multiplicity and site symmetry of a given special position can be calculated if the symmetry operations are known, the Wyckoff letter cannot be calculated since it is assigned arbitrarily and is setting-independent.

As with the symmetry operations, it is possible to include the special positions of more than one space group, each space group being identified by _space_group_Wyckoff.sg_id.








































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