A General Fourier Synthesis Program for the London University Atlas Computer

1. Relationships between structure factors The symmetry of each spacegroup leads to relationships between the geometric structure factors A(hkl), BQikl) for various triplets h, k, I. Various positions x', y', z' which are equivalent to the position x, y, z produce the relationships listed in Fig. 1. The symmetry of the point groups leads to the relationships shown in Table 1, where the c-axis is unique and the numbers are those given in the fourth column of Fig. 1. The symmetry of each spacegroup in the range 1-74 consists of one of the above point-group symmetries with translations of \n. (cell edge) (where n is an integer) in the appropriate lattice. Such translations added to a position x', y', z' cause the indices to fall into pairs of sets as shown in Table 2. The first set has the relationships due to the point group symmetry and the second has the same relationships with the signs reversed for the relationships corresponding to the equivalent position x', y', z' to which the translation is applied. The presence of a further translation of this type may cause the indices to fall into four sets, each of which has different relationships between the structure factors. Each triplet h, k, I belongs to an index parity group g, (/ = 0 — 7) as shown in Table 3, where e and o represent even and odd. The sets of indices obtained by adding translations to the point symmetry may be described by listing the g-t present. The spacegroups 43 and 70 contain translations of i • (cell edge) and cannot be so listed.