By M. Woolfson

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**Extra resources for An Introduction to X-Ray Crystallography**

**Sample text**

It is useful first of all to consider diffraction from a single row of n atoms, each atom separated from its neighbour by a vector distance a. 33), it was found that the scattering amplitude from a centrosymmetric arrangement of scatterers is real if the centre of symmetry is used as origin. The analysis of the present case is simplified if we assume that n is odd and if we take the centre atom, which is at the centre of symmetry, as the coordinate origin. =/. 1) where/a is the atomic scattering factor.

4(a). The amplitude of the disturbance at P due to scattering at Ox is represented by the vector AB and that due to scattering at O2 by the vector BC. Both these vectors have the same magnitude, rt(29,D), and the angle between them equals the difference of phase of the radiation scattered from O1 and O2, 27irs. The resultant AC has magnitude rj2(29,D) and differs in phase from the radiation scattered at Ox by the angle 0. However in this description we have given a special role to one of the scatterers, Ol9 with respect to which as origin all phases are quoted.

26 in the form given in the International Tables. The twofold axis is at the origin of the cell and it will reproduce one of the structural units, represented by an open circle, in the way shown. The right-hand diagram shows the symmetry elements; the twofold axis manifests itself in two dimensions as a centre of symmetry. It will be seen that three other centres of symmetry are generated - at the points (x, y) = (\, 0), (0,^) and ({,\). The four centres of symmetry are all different in that the structural arrangement is different as seen from each of them.