Spinel octahedral, compared

Normal spinel would have tetrahedral with two octahedral Mn inverse spinel would have tetrahedral Mn, octahedral Mn + and octahedral compare LFSE values ... 

The successful rationalization of these transition-metal inverse spinel structures in terms of the relative LFSE s of tetrahedral and octahedral sites is another attractive vindication of ligand-field theory as applied to structure and thermodynamic properties. Once again, however, we must be very careful not to extrapolate this success. Thus, we have a clear prediction that LSFE contributions favour tetrahedral over octahedral coordination, except for d" with n = 0, 5 or 10. We do not expect to rationalize the relative paucity of tetrahedral nickel(ii) species relative to octahedral ones on this basis, however. Many factors contribute to this, the most obvious and important one being the greater stabilization engendered by the formation of six bonds in octahedral species relative to only four bonds in tetrahedral ones. Compared with that, the differences in LSFE s is small beer. Why , one asks, was our rationalization of spinel structures so successful when we neglected to include consideration of the bond count The answer is that cancellations within the extended lattice of the spinels tend to diminish the importance of this term. 

The value of A, and hence the calculated CFSE, for Ni2+ ions in the olivine Ml sites appears to be anomalously high compared to values acquired in other octahedral sites in oxide structures, including bunsenite and MgO (table 5.1), Ni2Si04 spinel ( 5.4.3), and other phases listed later (table 5.19). The dis-crepency results from incorrect assignments of bands i and j listed in table 5.4... 

It is only in structures in which small proportions of the two types of hole are occupied that the nearest neighbours of an atom in a tetrahedral (octahedral) hole are only the nearest 4 (6) c.p. atoms. This is true, for example, in the spinel and olivine structures (Table 4.8). The CogSg structure is closely related to the spinel structure, which has 32 c.p. 0 atoms in the cubic unit cell. In CogSg there are 32 c.p. S atoms with 4 Co in octahedral and 32 Co in tetrahedral holes compare C03S4 with a slightly distorted spinel structure, also with 32 S in the cubic unit cell, but 16 Co in octahedral and 8 Co in tetrahedral holes. The spinel structure is discussed in detail on p.490 for the olivine structure see p. 811. An expanded version of part of Table 4.8 will be found on p. 619, where the structures of a number... 

In the normal ABjO spinel structure, the A ions (Fe in this example) occupy tetrahedral sites and the ions (Cr in this example) occupy octahedral sites. The fact that FeCf204 exhibits the normal spinel structure can be understood by comparing the ligand-field stabilization energy of high-spin octahedral Fe and octahedral Cr. With six d electrons, LFSE = -0.4Ao for high-spin Fe. With only three d electrons, LFSE = -1.2Ao for Cr. Since the Cr ions experience more stabilization in octahedral sites than do the Fe ions, the normal spinel structure is more stable than the inverse spinel structure, which would exchange the positions of the Fe ions with half of the ions. 

Just as the edges of cation-centred polyhedra represent anion diffusion paths in a crystal, the edges of anion centred polyhedra represent cation diffusion paths. The polyhedra shown in Figures 7.18 reveal that cation diffusion in cubic close-packed structures will take place via alternative octahedral and tetrahedral sites. Direct pathways, across the faces of the polyhedron, are unlikely, as these mean that a cation would have to squeeze directly between two anions. There is no preferred direction of diffusion. For ions that avoid either octahedral or tetrahedral sites, for bonding or size reasons, diffusion will be slow compared to ions which are able to occupy either site. In solids in which only a fraction of the available metal atom sites are filled, such as the spinel structure, clear and obstructed diffusion pathways can easily be delineated. 

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