Cuboctahedral coordination

When Li metal is cold-worked it transforms from body-centred cubic to cubic close-packed in which each atom is surrounded by 12 others in twinned cuboctahedral coordination below 78 K the stable crystalline modification is hexagonal dose-packed in which each lithium atom has 12 nearest neighbours in the form of a cuboctahedron. This very high coordination... 

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). 

Figure 2.6 Arrangements of ligands about a transition metal ion in (a) tetrahedral and cubic coordinations, and (b) dodecahedral or cuboctahedral coordination. In tetrahedral coordination, the ligands may be regarded as lying at alternate vertices of a cube. In cubic coordination the ligands are situated on all eight vertices.

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. 

Most dense ceramic membranes are made from perovskite oxides with general formula ABO3, where the A-site cation is coordinated to 12 oxygen ions forming a cuboctahedral coordination environment while the B-site cation is coordinated to six oxygen ions with... 

Fig. 5. The MES f-factors versus site coordination numbers calculated for cub-octahedral Auj3 and AUjs as well as several larger magic-number and non-magic-number cuboctahedral cluster sizes. The symbols are defined as follows ...

Figure 9.3 The perovskite crystal structure, (a) Ideal cubic phase showing comer-shared octahedra surrounding the twelve-coordinated cuboctahedral site (b) projection of the orthorhombic perovskite MgSi03 structure at 6.7 GPa along the c axis (from Kudoh etal., 1987). Rotation and tilting of [Si06] octahedra relative to the cubic structure are shown. The eight shorter bonds (Mg-0 distances = 199 to 244 pm) are indicated by solid lines and the four longer bonds (Mg-0 = 277 to 315 pm) by dashed lines.

FIGURE 12 Average coordination number as a function of platinum cluster diameter for cuboctahedral clusters. 

We may eliminate the first two structures immediately since X is obviously in contact with 4 X in the coordination shell around an A atom (cuboctahedron), but we can go further than this and show that all the structures to the left of the vertical line are impossible. In cubic close packing the coordination polyhedron of an atom is a cuboctahedral group, and in the above structures the coordination group of X is made up of certain numbers of A and X atoms. Since A is to be surrounded entirely by X atoms we cannot permit A atoms to occupy adjacent vertices of the cuboctahedral group around an X atom. The problem is therefore to fiiid the maximum number of vertices of a cuboctahedron that may be occupied by... 

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