Metal-oxygen bands

It is to be expected that tire conduction data for ceramic oxides would follow the same trends as those found in semiconductors, i.e. the more ionic the metal-oxygen bond, the more the oxides behave like insulators or solid elee-trolytes having a large band gap between the valence electrons and holes, and... 

The internal vibrations of the MnOi ion seem to be influenced less by the cations than other metal-oxygen vibrations [see(705)]. For example, the isotypical potassium-, rubidium-, cesium-, and ammonium permanganates have practically the same vi and vz frequencies. The difference observed in the case of AgMn04 is explained in Ref. 83). By the large cations, such as tetraphenylarsonium and tetraphenylphosphonium, the vz band is very sharp and well defined. Since these vz bands are not spht as expected it can be concluded that the anion... 

Spodumen is a monoclinic pyroxene, space group C C2 c), with two not equivalent metal cation sites Ml and M2. The aluminum occupies the smaller Ml site, which is approximately octahedral (actual symmetry C2) with an average metal-oxygen distance of 1.92 A. The M2 site, occupied by Li, is also six-fold coordinated with an average metal-oxygen distance of 2.23 A. Both A1 and Li sites may be substitutionally replaced by ions of the transitional metals in various proportions. Both Mn " " and Cr " centers have been identified in luminescence spectra by steady-state spectroscopy (Tarashchan 1978 Walker et al. 1997). At room and lower temperatures only one emission band of Mn + occurs and the excitation spectra taken for the different wavelengths of the luminescence bands are always the same. So it is very probable that Mn + ions in the spodumen matrix present only in one site. The calculated values of 10D,j and B are consistent with the occupation of larger M2(Li) weak-field site. Mn + is mainly in Li-sites rather than Al-sites. 

The band gap between the oxygen 2p band and the metal 4s band is sufficiently wide that the pure oxides would be considered insulators. However, they are almost invariably found to be non-stoichiometric, that is their formulae are not exactly MO, and this leads to semiconducting properties which will be discussed in Chapter 5. 

Electron correlation plays an important role in determining the electronic structures of many solids. Hubbard (1963) treated the correlation problem in terms of the parameter, U. Figure 6.2 shows how U varies with the band-width W, resulting in the overlap of the upper and lower Hubbard states (or in the disappearance of the band gap). In NiO, there is a splitting between the upper and lower Hubbard bands since IV relative values of U and W determine the electronic structure of transition-metal compounds. Unfortunately, it is difficult to obtain reliable values of U. The Hubbard model takes into account only the d orbitals of the transition metal (single band model). One has to include the mixing of the oxygen p and metal d orbitals in a more realistic treatment. It would also be necessary to take into account the presence of mixed-valence of a metal (e.g. Cu ", Cu ). 

Figure 2.16. Calculated dissociative nitrogen ( ), carbon monoxide ( ), and oxygen ( ) chemisorption energies over different 3d transition metals plotted as a function of the center of the transition metal rf-bands. A more negative adsorption energy indicates a stronger adsorbate-metal bond. Reproduced from [32].

In the case discussed here a Mott transition is unlikely the Hubbard U deduced from the Neel temperature is not relevant if the carriers are in the s-p oxygen band, but if the carriers have their mass enhanced by spin-polaron formation then the condition B U for a Mott transition seems improbable. In those materials no compensation is expected. We suppose, then, that the metallic behaviour does not occur until the impurity band has merged with the valence band. The transition will then be of Anderson type, occurring when the random potential resulting from the dopants is no longer sufficient to produce localization at the Fermi energy. 

Intermediate between these two extremes are minerals classified as Class II compounds in which the two sites are similar but distinguishable that is, both are octahedral sites, but with slightly different metal-oxygen distances, ligand orientation or bond-type. Examples include the amphibole Ml, M2 and M3 sites (figs 4.14 and 5.18), the mica trans-Ml and c -M2 sites (fig. 5.21) and babingtonite (Bums and Dyar, 1991). Such materials still exhibit properties of cations with discrete valences, but they have low energy IVCT bands and may be semiconductors. 

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