ISSN:
1600-5724
Source:
Crystallography Journals Online : IUCR Backfile Archive 1948-2001
Topics:
Chemistry and Pharmacology
,
Geosciences
,
Physics
Notes:
This paper is the continuation of another paper devoted to the systematic derivation of space subgroups and changes in standard setting of space groups. In the present paper, the correspondence of the sets of equivalent positions in such transitions is examined. Any set WG of general positions of the space group G splits up into ig/G sets Wg of general positions of the space subgroup g (ig/G is the index of subgroup g): there is a one-to-one correspondence between the Wg sets and the complexes of g in the partition of G; the coordinates of each Wg are obtained, as a function of coordinates of WG, from generating the symmetry operation of the corresponding complex. Miscellaneous examples of splitting of the WG set are investigated in the transitions: I422-P222, Fddd-Bb, P{\bar 1}-P{\bar 1}, I23-F23, P6222-P222. Any set WGP of special positions of G is the result of the superposition of general positions on particular points of point symmetry P. Such superpositions arise in the connected sets of g; there are three ways of grouping the positions in these sets: superposition in one set which turns into one special set WgP, superposition of several general sets which become one general set Wg, and mixed inner-outer superposition which leads to one special set of positions Wgp, their point groups being any subgroup p of P. These properties are illustrated by example of the transition P6222-P222 (10 types of special sets WgP). In the changes in standard setting in a given space group, each general or special set is connected with only one set; if the change of setting is associated with any symmetry operation of the space group, each set of positions is applied to itself.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1107/S0567739478001631
