ISSN:
1600-5724
Source:
Crystallography Journals Online : IUCR Backfile Archive 1948-2001
Topics:
Chemistry and Pharmacology
,
Geosciences
,
Physics
Notes:
A modulated structure can be depicted as a section through a four-dimensional periodic structure. In the latter, each atom is represented by a string continuing endlessly in the overall direction (e4) of the normal to R3, R3 being the hyperplane of the section. The strings have periodic bends or densifications for displacive and substitutional modulation respectively. Formulae for structure factors can be derived from this picture with little effort. The pseudo-symmetry of modulated structures can be described conveniently in this picture. Each four-dimensional space group to which the four-dimensional structure can belong is a possible MS3 (modulated three-dimensional structure) group of pseudo-symmetry, and is called an MS3 space group. It is shown that MS3 point groups are reducible in the form Q⊕ε. 1, where 1 is the unit 2 × 2 matrix, and ε = ± 1. A list is presented of these 31 groups written as black-and-white or colourless groups of three-dimensional symmetry. The MS3 space groups are discussed briefly. As an example of the peculiar differentiations caused by e4 being a unique direction, the 23 MS2 space groups are listed explicitly. Finally, it is shown that MS groups are essential for the description of MS symmetry, because very often the latter cannot be represented completely and unambiguously by the normal space group of an approximate superstructure.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1107/S0567739474010710
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