Читать книгу Solid State Chemistry and its Applications - Anthony R. West - Страница 58

The reason why structural distortions occur in many perovskites is that the A and/or B atoms are not exactly the right size to fit the sites generated by the remainder of the structure. In an oxide with the ideal, cubic perovskite structure, the bond lengths are related to the unit cell dimension, a, by

(1.6)

Since bond lengths for each element, oxidation state and coordination number usually fall within closely defined ranges (Appendix F), it is possible to use equation (1.6) to see how well the sizes of a particular A, B combination meet the requirements for an undistorted, ideal perovskite. The degree to which the sizes depart from equation (1.6) is given by a tolerance factor, t:

Table 1.18 Some compounds with the perovskite structure

Compound	a/Å	Compound	a/Å	Compound	a/Å
KNbO3	4.007	LaFeO3	3.920
KTaO3	3.9885	LaGaO3	3.875	CsCaF3	4.522
KIO3	4.410	LaVO3	3.99	CsCdBr3	5.33
NaNbO3	3.915	SrTiO3	3.9051	CsCdCl3	5.20
NaWO3	3.8622	SrZrO3	4.101	CsHgBr3	5.77
LaCoO3	3.824	SrHfO3	4.069	CsHgCl3	5.44
LaCrO3	3.874	SrSnO3	4.0334

(1.7)

In practice, there is some flexibility over bond lengths and usually, a cubic perovskite forms with t in the range 0.9 < t < 1.0.

For t > 1, the B site is larger than required. If t is only slightly greater than 1.0, the structure distorts but is still basically a perovskite as in BaTiO₃, t = 1.06. There may also be a change in the stacking sequence of the AX₃ close packed layers from ccp to hcp to give the family of hexagonal perovskites typified by BaNiO₃. For larger departures from t = 1.0, however, the B ion demands a smaller site, of lower coordination number, and the structure changes completely, as in BaSiO₃ which has tetrahedral Si.

For smaller tolerance factors, 0.85 < t < 0.90, several different kinds of structural distortion occur because now, as in GdFeO₃, the A cation is too small for its site. These distortions generally involve tilting and rotation of the BO₆ octahedra as shown in Fig. 1.41(g). Consequently some, or all, of the B–O–B linkages are no longer linear but are zig‐zag, which has the effect of reducing the size of the A cation site.