Starting from the known average structure (Dubbeldam & de Wolff, Acta Cryst. (1969), B25, 2665-2667) and four-dimensional space group, the actual modulated structure has been determined by taking into account 758 newly measured main reflexions and 1152 first-order satellites. The analysis is based on a harmonic displacive modulation model, with 14 modulation parameters as well as 9 positional and 26 thermal parameters (individual anisotropic, in Debye-Waller factors of the usual type).The final value of YA/Y~Fo is 0.108 excluding, and 0.238 including non-observed reflexions. The main features of the modulation are (a) an overall modulation with an amplitude of close to 0.33 A, for all atoms except oxygen; (b) an orientational modulation of the COa ion which is out of phase with the overall modulation. Calculation of the interatomic distances yields the result that the Dab symmetry of the CO3 ions is hardly distorted by the modulation. Certain second-order effects point to anharmonic components in the modulation, with amplitudes up to 0"03 A,. The structure turns out to consist of chains of NaO6 octahedra sharing faces and with Na-O bond lengths under 2"45 /~, showing little variation. The chains run in the direction of c and are mutually coupled in other directions by CO3 ions. The remaining Na atoms occupy the remaining spacious voids; their distances (averages > 2.60/~) to eight out of the nine surrounding oxygen atoms vary strongly, and for each with a different phase.

147others may be allowed to vibrate independently. The T and e~ tensors of the several rigid units are refined directly, as in Pawley's method, along with the usual coordinates, occupancy factors, etc. Experience suggests that this onestage procedure may be highly advantageous, especially in rate of convergence, provided the molecules are sufficiently rigid and the f curves used (for X-ray data) represent the stationary-atom electron densities to the required accuracy. When these conditions are not met, the two-stage procedure, or a comparison of the two, may help to reveal inadequacies of the model, due to internal vibrations, charge polarization, altered hybridization, etc., more readily than extensive difference syntheses.The tensor formulation is also useful for evaluation of the libration corrections to the atomic coordinates. Assuming for simplicity that our refinement procedure has located the centroids of the atomic peaks rather than their maxima (either assumption is an approximation requiring justification in particular circumstances), we may, for the present argument, disregard the factor D(a(o) in Cruickshank's (1961) equation (6) and obtain from his equations (10) Acta Cryst. (1966). 20, 147The anisotropie temperature factor of atoms in special positions. In this paper a table of symmetry restrictions on anisotropic temperature factor parameters for all special positions of the 230 space groups is presented. The text explains the table and describes the computer program which was used to derive it. The relationships between the various restricted forms are displayed diagrammatically. No recommendations for the method of programming these restrictions in least-squares refinement are included. M3M ]aM 432