Intraatomic Versus Interatomic Interactions

The condition for localized electrons with spontaneous atomic moments is U w that for itinerant electrons with no spontaneous moment is Un w. The intermediate case Un = w is of considerable theoretical interest. In the case of iron oxides, a U5 = 3 eV ensures a localized 3 d majority-spin configuration at both Fe and Fe ions since the cubic-field splitting Ag Ag, is small enough to leave the ions in the high-spin state. However, localization of the minority-spin electron, particularly in the mixed Fe / Fe state, does not necessarily follow. Similarly, a much smaller U4 will be seen to make U4 = w for Fe in the perovskites A Fe03. 

Two types of mixed-valence compounds must be distinguished at the outset those with mixed valency on energetically equivalent sites and those in which the different valences occupy inequivalent sites. Section 1.2.3 deals with the former case. Sect. 1.2.5 with the latter. 

3 Classification of Mobile Charge Carriers in Mixed-Valence Compounds 

With mixed-valence compounds, charge transfer does not require creation of a polar state, and a criterion for localized versus itinerant electrons depends not on the intraatomic energy defined by U , but on the ability of the structure to trap a mobile charge carrier with a local lattice deformation. The two limiting descriptions for mobile charge carriers in mixed-valence compounds are therefore small-polaron theory and itinerant-electron theory. We shall find below that we must also distinguish mobile charge carriers of intennediate character. 

Itinerant electrons occupy band states, which are molecular orbitals for an entire crystal they therefore belong equally to all like atoms on energetically equivalent sites and are described by band theory. 

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