Читать книгу Solid State Chemistry and its Applications - Anthony R. West - Страница 21

A centre of symmetry, , exists when any part of a structure can be reflected through this centre of symmetry, which is a point and an identical arrangement found on the other side. An AlO₆ octahedron has a centre of symmetry, Fig. 1.7(b), located on the Al atom. If a line is drawn from any oxygen, e.g. 1, through the centre and extended an equal distance on the other side, it terminates at another oxygen, 2. A tetrahedron, e.g. SiO₄, does not have a centre of symmetry (a).

The inversion axis, , is a combined symmetry operation involving rotation (according to n) and inversion through the centre. A (fourfold inversion) axis is shown in (c). The first stage involves rotation by 360/4 = 90° and takes, for example, oxygen 2 to position 2′. This is followed by inversion through the centre, at Si, and leads to position 3. Oxygens 2 and 3 are therefore related by a axis. Possible inversion axes in crystals are limited to and for the same reason that only certain pure rotation axes are allowed. The onefold inversion axis is not a separate symmetry element, but is simply equivalent to the centre of symmetry; also, the twofold inversion axis is the same as a mirror plane perpendicular to that axis.

Figure 1.7 Symmetry elements: (a) mirror plane; (b) centre of symmetry; (c) fourfold inversion axis. (d) The British comedian Harry Worth creating a mirror image of half of his body by reflection in a shop window.