Читать книгу Solid State Chemistry and its Applications - Anthony R. West - Страница 93

We see in Chapter 5 how the presence of lattice centring or elements of space symmetry lead to systematically absent reflections from X‐ray (but also electron and neutron) diffraction patterns. For example, in space group C2, the C‐centring imposes the condition that only those reflections that satisfy the rule: for (hkl: h + k = 2n) are allowed. The 2₁ screw axes parallel to b impose the condition for reflection: for (0k0: k = 2n). However, this is also a consequence of the C‐centring condition, for the special case that h = l = 0, and so does not lead to any extra systematic absences. Information on the conditions limiting possible reflections is given for every space group in International Tables for X‐ray Crystallography. In the above case, since the 2₁ screw axes do not impose an extra set of conditions, they are often written in parentheses.

The presence of glide planes in a crystal may sometimes by detected by the absence of a set of X‐ray reflections. For an a glide perpendicular to b, the condition limiting the h0l reflections is that h = 2n (i.e. only even h values may be observed). In the space group C2/m, this condition is part of the more general condition for C‐centring, namely: for hkl, h + k = 2n. Independent evidence for the existence of the glide plane is therefore not immediately available from the X‐ray patterns.

Two further examples: in space group P222₁, the only symmetry element which causes systematic absences is the 2₁ axis parallel to z, i.e. for 00l reflections, only those for which l = 2n may be observed; there are no general conditions on hkl reflections since the space group is primitive. For space group I4₁, two conditions are imposed on the possible reflections: for the body centring, only the reflections hkl: h + k + l = 2n may be observed; the 4₁ screw axis places the additional condition that: for 00l reflections, l = 4n.