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. 131-132
Section 3.4.2. Dictionary design considerations^{a}Departamento de Física de la Materia Condensada, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apartado 644, 48080 Bilbao, Spain |
The CIF dictionary for modulated and composite structures (msCIF dictionary) is an extension of the core CIF dictionary (Chapter 4.1 ). This means that the dictionary defines items that are basically related to single-crystal data. The close relationship between the msCIF and core dictionaries has led to synergies between and benefits for both dictionaries.
The design of the msCIF dictionary had two objectives: (i) it should be as functional as possible, i.e. as little information in an msCIF as possible should be given as unstructured text; (ii) it should be possible to include even the oldest modulated and composite structures in an msCIF, even if the way they were reported did not follow the guidelines used now.
There were two major difficulties in implementing the msCIF dictionary. Firstly, the number of additional wave vectors used to index a diffraction diagram is theoretically not limited. Secondly, a CIF containing information about a modulated or composite structure should, in general, be composed of several (related) data blocks. As CIF definitions do not at present include vectors or matrices as distinct types of data values, an arbitrary upper limit of 11 was assigned to the dimension of superspace to limit the number of new data names. Linking between data blocks is handled by using recommended values for items in the AUDIT and AUDIT_LINK categories, like those used in the powder CIF (pdCIF) dictionary (Chapters 3.3 and 4.2 ).
An additional problem arises when special (ideal) modulation functions are considered. Although periodic modulations are normally parameterized by Fourier series, in certain cases it is convenient to use discontinuous functions which lead to a severe reduction in the number of structural parameters. The shape of these functions is not restricted and new materials could require new functions. Given that it is not possible at this moment to define logical or mathematical relations between data values within a CIF [although an initiative for including algorithms in the definitions of CIF dictionaries has been proposed by Spadaccini et al. (2000)], general functions cannot be defined and therefore the type of special functions included in the msCIF dictionary are those implemented in the most widely used program, JANA2000 (Petříček & Dušek, 2000). They only apply to one-dimensional modulations and are sawtooth displacive functions and occupational crenel functions. Both functions define discontinuous occupational atomic domains and are normally combined with (smoother) atomic modulation functions (involving atom positions and/or thermal parameters) that are expressed by Fourier series. Because of the discreteness of the atomic domains, members of the set of harmonic functions used to expand these series are no longer mutually orthogonal as they are only defined within each atomic domain and not in the (internal space) interval [0, 1]. As a consequence, severe correlation effects among the coefficients of the Fourier series are expected. A solution for this problem lies in the selection and orthogonalization of a set of basic functions (Petříček et al., 1995). The atomic modulation functions are then expressed as linear combinations of an orthogonal basis whose elements are specific combinations of harmonic functions. Discontinuous atomic domains are being increasingly used in composite materials, in some cases revealing that considering such materials as composites or modulated structures is a matter of convenience (Elcoro et al., 2003; Pérez-Mato et al., 2003).
CIFs that conform to the msCIF dictionary are highly itemized for the human reader, but have a strong relational structure even though the dictionary itself is written in DDL1.
The major drawbacks of the dictionary are:
(i) Items describing the superspace symmetry should be reconsidered and perhaps included within the symmetry CIF (symCIF) dictionary (Chapters 3.8 and 4.7 ).
(ii) There is still some information in an msCIF that cannot be interpreted by a computer [e.g. rigid rotations and translations around (along) noncrystallographic axes cannot be parsed, since the description of the axes is textual].
(iii) A full description of the modulation in terms of orthogonalized functions (used when the atomic domains are discrete) is not supported yet.
References
Elcoro, L., Pérez-Mato, J. M., Darriet, J. & El Abed, A. (2003). Superspace description of trigonal and orthorhombic A_{1+x}A′_{x}B_{1−x}O_{3} compounds as modulated layered structures; application to the refinement of trigonal Sr_{6}Rh_{5}O_{15}. Acta Cryst. B59, 217–233.Petříček, V. & Dušek, M. (2000). The Crystallographic Computing System JANA. Institute of Physics, Prague, Czech Republic.
Petříček, V., van der Lee, A. & Evain, M. (1995). On the use of crenel functions for occupationally modulated structures. Acta Cryst. A51, 529–535.
Pérez-Mato, J. M., Etrillard, J., Kiat, J. M., Liang, B. & Lin, C. T. (2003). Competition between composite and modulated configurations in Bi_{2}Sr_{2}CaCu_{2}O_{8 + δ} and its relation to oxygen stoichiometry. Phys. Rev. B, 67, 24504-1–24504-13.
Spadaccini, N., Hall, S. R. & Castleden, I. R. (2000). Relational expressions in STAR File dictionaries. J. Chem. Inf. Comput. Sci. 40, 1289–1301.