Читать книгу Solid State Chemistry and its Applications - Anthony R. West - Страница 91

The basic information that we need to know is the following:

Unit cell: cubic, a = 3.905 Å

Space group: Pm3m (number 221)

Atomic coordinates: Ti in 1(a) at 0, 0, 0; Sr in 1(b) at ½, ½, ½; O in 3(d) at 0, 0, ½

This is, in fact, a very simple example since although the space group Рm3m is complicated, as are all cubic space groups, all the atoms in perovskite lie on special positions. There are 48 general equivalent positions in this space group, but a large number of special positions arise when atoms lie on symmetry elements. Ti occupies a 1‐fold special position at the origin of the unit cell; the symbol 1(a) indicates that there is only one position in this set and (a) the Wyckoff label, for this (set of) position(s). Sr also occupies a 1‐fold special position, 1(b), at the body centre of the cell. Oxygen occupies a 3‐fold special position 3(d); the coordinates of one of these positions, 0, 0, ½ are given and the only remaining information that is needed from the space group are the coordinates of the other two oxygen positions. From International Tables, these are 0, ½, 0 and ½, 0, 0.

From this information, the unit cell and atomic positions may be drawn, first as a projection down one of the cubic cell axes, Fig. 1.41(a) and then as an oblique projection to show the atomic positions more clearly, Fig. 1.41(c). [Note: Fig. 1.41(b) shows an alternative unit cell with Sr at the origin, as discussed in Section 1.17.7.] The coordination environment of each atom may be seen in (c) and interatomic distances calculated by simple geometry, as detailed in Section 1.17.7, together with a more extended discussion of perovskites, structural distortions in some cases and structure–property relations.