Читать книгу Solid State Chemistry and its Applications - Anthony R. West - Страница 88

The new feature of this space group is that it has a face centred lattice which, as can be seen from Fig. 1.65, leads to a considerable increase in the number of symmetry elements and equivalent positions. The basic symmetry elements are three intersecting 2‐fold axes, parallel to x, у and z and passing through the origin. Many other 2‐fold axes occur automatically, e.g. one intersecting the cell at a = , с = , parallel to b and another at a = , b = , parallel to c. Many 2₁ axes are also created, e.g. at a = 0, b = , parallel to с and at b = , c = 0, parallel to a.

Figure 1.64 Orthorhombic space group P2221 (No 17); Coordinates of equivalent positions 4(e): x, y, z; , y, ½ − z; x, ; . Special positions with point symmetry 2, 2(a): x, 0, 0; , 0, ½; 2(b): x, ½, 0; _, ½, ½; 2(c): 0, y, ; 0, , ; 2(d): ½, y, ; ½, _,

Figure 1.65 Orthorhombic space group F222 (No 22); coordinates of equivalent positions 16(k)

Special positions with point symmetry 222, 4(a): only one position is given as the other three are generated by the face centring; 0, 0, 0; 4(b): 0, 0, ½; 4(c): , , ; 4(d): , , ; special positions with point symmetry 2, 8(e): x, 0, 0; _, 0, 0; 8(f): 0, y, 0; 0, , 0; 8(g): 0, 0, z; 0, 0, ; 8(h): , , z; , , ½ − z; 8(i): , y, ; , ½ − y, ; 8(j): x, , ; ½ − x, , _.

There are sixteen general equivalent positions that fall into four groups related by the face‐centring condition. The four sets are related as (0, 0, 0); (½, ½, 0); (½, 0, ½) and (0, ½, ½). Thus, position l, (x, y, z), is related to positions 2–4: (x + ½, у + ½, z); (x + ½, y, z + ½) and (x, y + ½, z + ½). Generation of the remaining equivalent positions by the action of the 2‐fold axes should be straightforward.