International
Tables for Crystallography Volume G Definition and exchange of crystallographic data Edited by S. R. Hall and B. McMahon © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. G. ch. 3.4, pp. 134-136
Section 3.4.3.3. Atomicity, chemistry and structure^{a}Departamento de Física de la Materia Condensada, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apartado 644, 48080 Bilbao, Spain |
The categories relevant to the description of the structural model are as follows:
Categories marked with ¶ are already defined in the core CIF dictionary.
Most of the new categories introduced to the msCIF dictionary appear here, since their function is to describe in great detail the modulation of the atom-site properties. They fall naturally into families describing the modulation of atomic displacement, of site occupation or of thermal parameters.
New data items are added to several categories in the core CIF dictionary that describe molecular or packing geometry. There are also new data items to describe superspace-group symmetry.
Data items in these categories are as follows:
The bullet () indicates a category key. The arrow () is a reference to a parent data item.
The ATOM_SITEcategory is extended in the msCIF dictionary by the addition of a small number of items that may appear in the main looped list of atom-site information (see Section 3.2.4.1.1 ). The *_flag items indicate whether each individual atom site has been modelled through modulation of atomic displacement, site occupation or thermal parameters. In each case, the default value of the item is no, so that any or all of the flags may be omitted when that particular type of modulation has not been applied to the structural model.
_atom_site_subsystem_code identifies the cell subsystem to which the atom site must be assigned in the description of composite structures. Each value of _atom_site_subsystem_code must match one of the values of _cell_subsystem_code in the overall description of the subsystems defined for a composite.
The ATOM_SITE_PHASON category allow details of an atom-dependent phason correction, as implemented in JANA2000, to be given. The use of these phason corrections is discouraged.
Data items in these categories are as follows:
(a) ATOM_SITE_DISPLACE_FOURIER
(b) ATOM_SITE_DISPLACE_FOURIER_PARAM
(c) ATOM_SITE_FOURIER_WAVE_VECTOR
(e) ATOM_SITE_OCC_FOURIER_PARAM
(g) ATOM_SITE_ROT_FOURIER_PARAM
(j) ATOM_SITES_DISPLACE_FOURIER
The bullet () indicates a category key. The arrow () is a reference to a parent data item.
It is common to represent a modulated structure using a reference periodic structure on which are superimposed atomic modulation functions expanded as Fourier series. (A full discussion of this is given in Section 3.4.4.3.) The msCIF dictionary provides separate categories for listing the modulated parameters that apply to atom positions, site occupancies and thermal parameters. The structuring of the data items within each of these categories follows a similar pattern.
For example, consider the modulation of the atomic displacements. The ATOM_SITE_DISPLACE_FOURIER category allows a listing of the axis along which the displacement occurs (*_axis) and the wave vectors contributing to that displacement component (*_wave_vector_seq_id) for each relevant atom site (labelled by _atom_site_displace_Fourier_atom_site_label). *_wave_vector_seq_id is a pointer to the description of the separate modulation wave vectors and must match one of the identifiers _atom_site_Fourier_wave_vector_seq_id listed separately in the ATOM_SITE_FOURIER_WAVE_VECTOR category. Likewise, the *_atom_site_label data item must match a value of _atom_site_label in the main list of atom positions. This is how the modulation is linked to the atom list. The item _atom_site_displace_Fourier_id is the formal key for the ATOM_SITE_DISPLACE_FOURIER category. It is used to locate the matching Fourier coefficients in the ATOM_SITE_DISPLACE_FOURIER_PARAM category. The coefficients may be reported in a sine–cosine ( _atom_site_displace_Fourier_param_sin, *_cos) or modulus–argument (*_mod, *_phase) representation.
Where a group of atoms is treated as a rigid group, the categories above describe only the translational part of the positional distortion. ATOM_SITE_ROT_FOURIER and ATOM_SITE_ROT_FOURIER_PARAM are used to describe the rotational components.
ATOM_SITE_OCC_FOURIER and ATOM_SITE_U_FOURIER, and their associated *_PARAM categories, are the analogous categories for the modulation of site occupation and thermal parameters.
All the categories above describe the properties of individual atom sites. Larger-scale descriptions of the displacive modulation or of the rotational component of a rigid group are covered by the categories ATOM_SITES_DISPLACE_FOURIER and ATOM_SITES_ROT_FOURIER, each of which at present contains one descriptive data item.
The ATOM_SITES_MODULATION category contains data items describing the initial phases of the modulation waves, which are essential for determining the space group of the commensurate superstructure. More details are given in the dictionary.
Data items in these categories are as follows:
(a) ATOM_SITE_DISPLACE_SPECIAL_FUNC
(b) ATOM_SITE_OCC_SPECIAL_FUNC
The bullet () indicates a category key. The arrow () is a reference to a parent data item.
Several data items cover modulation functions that are not expressed as Fourier expansions. The examples in the current msCIF dictionary are restricted to the one-dimensional modulations (sawtooth displacive and occupational crenel functions) implemented in the program JANA2000 (see Section 3.4.2).
New data items in these categories are as follows:
For each of the geometry categories, there are two groups of extensions. One set covers maximum, minimum and average values of bonds, contact distances, angles and torsion angles. The other extends the symmetry-operation code used in geometry listings in the core CIF dictionary (see Section 3.2.4.3.2 ) to the higher-dimensional superspace form.
New data items in these categories are as follows:
At present, the msCIF dictionary extends the core CIF dictionary symmetry categories to describe superspace groups for one-dimensional modulated structures in four ways: as the superspace-group number in Janssen et al. (2004) ( _space_group_ssg_IT_number), as the International Tables superspace-group symbol (*_ssg_name_IT), as one of the notations from de Wolff et al. (1981) (*_ssg_name_WJJ, *_ssg_WJJ_code), or in some other formalism (*_ssg_name). At present, superspace-group names for higher dimensions can only be indicated using _space_group_ssg_name.
Symmetry operations in the superspace group are specified in the SPACE_GROUP_SYMOP category by an obvious extension to the method used in the core dictionary. These items must always be present in a CIF corresponding to a modulated or composite structure.
References
Janssen, T., Janner, A., Looijenga-Vos, A. & de Wolff, P. M. (2004). Incommensurate and commensurate modulated structures. International Tables for Crystallography, Volume C, Mathematical, chemical and physical tables, 3rd ed., edited by E. Prince, ch. 9.8. Dordrecht: Kluwer Academic Publishers.Google ScholarWolff, P. M. de, Janssen, T. & Janner, A. (1981). The superspace groups for incommensurate crystal structures with a one-dimensional modulation. Acta Cryst. A37, 625–636.Google Scholar