Cuboctahedral order

The plumbides R(Ag, Pb)3 with R = Y, Sm, Gd-Tm crystallize with a very simple structure type, i.e. Q13AU, an ordered version of the cubic close packing. The rare earth atoms fill Wyckoff position la (the origin of the unit cell, see Figure 19), while the silver and lead atoms show random distribution on the 3c site. The phase analytical investigations reveal that up to 78% lead can occupy that site. Both sites have cuboctahedral coordination (CN 12). 

Despite its simplicity, the tolerance factor has reasonable predictive power, especially for oxides, where ionic radii are known with greatest precision. Ideally t should be equal to 1.0 and it has been found empirically that if t lies in the approximate range 0.9-1.0 a cubic perovskite structure is a reasonable possibility. If t>l, that is, large A and small B, a hexagonal packing of the AXj layers is preferred and hexagonal phases of the BaNiOj type form (Chapter 3). In cases where t of the order of 0.71-0.9, the structure, particularly the octahedral framework, distorts to close down the cuboctahedral coordination polyhedron, which results in a crystal structure of lower symmetry than cubic. For even lower values of t, the A and B cations are of similar size and are associated with the ilmenite, FeTiOj, structure or the C-type rare earth Ln Oj stmcture. 

The perovskite stracture is illustrated in Figure 6.10(b). The ideal stoichiometry of a perovskite is ABX3, where X is an anion, B is a cation with octahedral coordination, and A is a large cation with cuboctahedral coordinatioa The two cation sites are cormnordy referred to as the B-site (coordination number = 6) and the A-site (coordination number = 12). In order for the ideal cubic stracture to be realized the size of the A- and B-site cations mnst be well matched. The size match or lack thereof between the two cations is given by the Goldschmidt tolerance factor, t ... 

The question of icosahedral versus crystalline order in clusters has also been studied for clusters of Al. There are two sizes, n = 13 and n = 55, corresponding to closed neighbor structural shells of both the icosahedral and the cuboctahedral... 

Practically all the structures of the ordered phases studied by now, in fluoride systems with RE elements, belong to the class of phases with ordered cuboctahedral clusters. The position in the centre of cuboctahedron can be occupied by an anion (8 12 1) or can be vacant (8 12 0). In oxyfluoride ordered phases, the position in the centre of cuboctahedron is usually vacant, as for instance in PbZr3Fe04 [60], PbgY6p320 [61], Ba2.iBio.9(0,F)6.g [59]. 

---