Читать книгу Solid State Chemistry and its Applications - Anthony R. West - Страница 41

In order to describe crystal structures, it is necessary to specify (a) the unit cell type, (b) its dimensions and (c) the fractional coordinates of the atoms in the unit cell. As described earlier, an fcc unit cell containing anions at corner and face centre positions has, effectively, four anions in the unit cell, one at a corner and three at face centres. The fractional coordinates of the four anions A–D in the unit cell, Fig. 1.24, are

Figure 1.25 (a, b) Tetrahedral sites T+, T– and their relation to a cube. (c) Bond length calculations and some symmetries of a tetrahedron.

Only one corner, at 000, is included since the other seven, e.g. at 100, 010, etc., are equivalent and can be regarded as the corner atoms of adjacent cells. The alternative would be to list all eight corner atoms, with the qualification that only 1/8 of each belonged to the unit cell in question. This would be equivalent to, but much more cumbersome than, regarding one corner only as specifically belonging, completely, to our unit cell. Likewise, for each pair of opposite faces, e.g. ½½0 and ½½1, it is most convenient to regard ½½0 as belonging completely to our unit cell; ½½1 then becomes the bottom face centre in the cell above.

The various cation positions in Fig. 1.24 have the following coordinates:

Note that there are four of each type of cation site, O, T₊, T_–, in the unit cell, together with four anions. When different sites are fully or partially occupied by the cations, different structures are generated, as indicated in Table 1.4 and discussed later.