Читать книгу Solid State Chemistry and its Applications - Anthony R. West - Страница 87

This primitive orthorhombic space group has 2‐fold rotation axes parallel to x and у and a 2₁ screw axis parallel to z. The feature of this space group, Fig. 1.64, which makes the generation of the equivalent positions a little difficult to visualise, is that the 2‐fold rotation axes parallel to у occur at а с height of . Consider first the axis parallel to у at a = 0 and c = . The starting position 1 has a small positive z coordinate of +z; the twofold axis is at z = . Therefore, position 1 is at ( − z) below the 2‐fold axis. The new position, 2′, formed by rotation about this axis is, therefore, at ( − z) above the 2‐fold axis, i.e. it has z coordinate + ( − z) = ½ − z. This is shortened to ½– in Fig. 1.64.

Consider now the 2‐fold axis parallel to x and at b = c = 0 (i.e. passing through the origin). This axis generates positions 3″ from 1 and 4‴ (its equivalent in the cell below) from 2′. With these two axes we have generated all four equivalent positions in this space group. The third axes, such as the 2₁ axis parallel to z, are automatically generated by the combined action of the other two axes and are not independent of them. This 2₁ axis relates, for example, positions 1 and 4‴, (i.e. translation of position 1 by c/2 followed by 180° rotation about с gives 4‴). Positions 2′ and 3″ are similarly related.