Charge itinerant electrons

The mixed-valence iron oxides provide an experimental test-bed for studying the evolution of charge-transfer processes from the localized-electron to the itinerant-electron regimes. Moreover, it is possible to monitor the influence of the charge transfer on the interatomic magnetic coupling since the iron ions in oxides carry localized magnetic moments. 

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. 

It is found that for metals, low temperature field evaporation almost always produces surfaces with the (1 x 1) structure, or the structure corresponding to the truncation of a solid. A few such surfaces have already been shown in Fig. 2.32. That this should be so can be easily understood. For metals, field penetration depth is usually less than 0.5 A,1 or much smaller than both the atomic size and the step height of the closely packed planes. Low temperature field evaporation proceeds from plane edges of these closely packed planes where the step height is largest and atoms are also much more exposed to the applied field. Atoms in the middle of the planes are well shielded from the applied field by the itinerant electronic charges which will form a smooth surface to lower the surface free energy, and these atoms will not be field evaporated. Therefore the surfaces produced by low temperature field evaporation should have the same structures as the bulk, or the (lxl) structures, and indeed with a few exceptions most of the surfaces produced by low temperature field evaporation exhibit the (1 x 1) structures. 

Many perovskites in the insulating state are, in fact, semiconductors. There are several models for the mechanism of charge transport, which can generally be differentiated by considering the temperature variation of the conductivity or resistivity of the sample. If the conductivity can be considered to be due to itinerant electrons promoted to an empty conduction band by thermal energy and holes left... 

Ideally, the specific heat of conduction electrons (or holes) in a metal is a linear function of temperature C = yT, where y, known as the Sommerfeld constant, is in the range 0.001 to 0.01 J/(molK ) for normal materials. In HF compounds, y reaches values up to 10 times larger (see tables 9, 10 and 11). In the basic theory of the specific heat of itinerant electrons (free Fermi gas), y is proportional to the effective mass m of the charge carriers, and so the name heavy fermions has come to be attached to these high-y materials (see Stewart 1984). The linear relation between C and T is strictly fulfilled only in the limit of a free degenerate electron gas. In real materials, weak non-linearities show up that can be encompassed by, for example, allowing y to be temperature dependent, y T). The Sommerfeld constant of interest is then the extrapolation of y for... 

One of the most striking properties of lanthanide metals and compounds is the relative insensitivity of electrons in the unfilled 4f shell to the local environment, compared to non-f electron shells with similar atomic binding energies. Whereas the 5d and 6s electrons form itinerant electron bands in the metallic solids, the 4f electrons remain localised with negligible overlap with neighbouring ions. For the maximum in the 4f radial charge distribution lies within those of the closed 5s and 5p shells, so the 4f shell is well shielded from external perturbations on the atomic potential, such as the crystal field. 

The resistivity of a polycrystalline sample of CaVOs showed a typical metallic temperature dependence, p(T) T, but it became higher above room temperature than is calculated on the basis of itinerant-electron scattering with a mean-free-path as short as one V—0—V distance, which makes CaVOs a bad metal. The resistivity also showed an unusually strong decrease with pressure as might be expected if pressure transfers charge carriers from a lower Hubbard band to the Fermi surface of a Fermi liquid. Pressure would increase not only Wb, but also coq, of Eq. (3), thereby broadening W. However, resistivity data on a polycrystalline sample may not be considered definitive, and they do not provide a measure of m. ... 

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