Structure factor algebra (Bertaut, 1956) provides a general method of incorporating space group symmetry into crystallographic programs. We shall consider some elementary applications, along the lines described by S.R. Hall at the 1970 Advanced Study Institute on Direct and Patterson Methods at Parma.

Structure Factor Algebra: Structure Invariants and Seminvariants

This paper describes a proposal for a standardized presentation of inorganic crystal-structure data with the aim to recognize identical or nearly identical structures from the similarity of the numerical values of the atom coordinates

The standardization of inorganic crystal-structure data

Structure invariants and seminvariants for noncentrosymmetric space groups

References BEARDEI~, J. A. & Stu~w, C. H. (1935). Phys. Rev. 48, 18. HOYT, A. (1932). Phys. Rev. 40, 477. LADELL, J., PARRISH, W. & TAYLOR, J. (1957). Am. Cryst. Assn. Pittsburgh Meeting, Paper No. 46, Nov. 8. LADELL, J. , PA_RRISH, W. & TAYLOR, J. (1959a). Acta Cryst. 12, 253. LADELL, J., PARRISH, W. & TAYLOR, J . (1959b). Acta Cryst. 12, 561. LANO, A. R. (1956). J. Appl. Phys. 27, 485. P~_RRATT, L. G. (1936). Phys. Rev. 50, 1. P~A~RISE, W. & WILSON, A. J. C. (1954). Acta Cryst. 7, 622. Pn_ams~, W. & WILSON, A. J. C. (1959). International Tables for X-ray Crystallography, vol. 2, 216. PIKE, E. ]:~. (1957). J. Sci. Instrum. 34, 355. PIKE, E. R. (1959). Acta Cryst. 12. 87. PIKE, E. 1:~. & WILSON, A. J. C. (1959). Brit. J. Appl. Phys. 10, 57. WILSON, A. J. C. (1950). J. Sci. Instrum. 27, 321.

V. Algèbre des facteurs de structure

Errors in the tables of seminvariants given by Karle & Hauptman [Acta Cryst. (1961). 14, 217-223] are corrected.

Structure Factor Algebra: Structure Invariants and Seminvariants

References

The standardization of inorganic crystal-structure data

Structure invariants and seminvariants for noncentrosymmetric space groups

V. Algèbre des facteurs de structure

Seminvariants for space groupsI\overline{4}2mandI\overline{4}2d

Seminvariants for space groups I2m and I2d

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