Filled band model

In a previous work we showed that we could reproduce qualitativlely the LMTO-CPA results for the Fe-Co system within a simple spin polarized canonical band model. The structural properties of the Fe-Co alloy can thus be explained from the filling of the d-band. In that work we presented the results in canonical units and we could of course not do any quantitative comparisons. To proceed that work we have here done calculations based on the virtual crystal approximation (VGA). In this approximation each atom in the alloy has the same surrounding neighbours, it is thus not possible to distinguish between random and ordered alloys, but one may analyze the energy difference between different crystal structures. 

Equation (43) assumes a specific value for Sq- A more general result follows from the fact that the Fourier transforms in (41) will be small, except for small values of o)p so that, as expected, to obtain high probabilities of charge transfer, Eq should either be in the solid band or, at least, not lie very far from the band. An interesting result, showing the dependence of P, on Eq, can be obtained for the one-dimensional model of section 3.3 with a half-filled band, V(t) of exponential form, P — co) = 0 and V% XB. This is... 

This simple band model predicts that an alloying metal with 10 - - z valence electrons outside a filled p shell (rare gas configuration) is expected to decrease the magnetization of nickel by approximately z Bohr magnetons per solute atom pb)- As illustrated in... 

On the terminology of the band model c- bonds form the completely filled low band, and rc-bonds make the partially filled band, which defines the electronic properties of the polyacetylene. 

In columnar stacked one-dimensional complexes, such as the tetracyanoplatinates, with relatively short intrachain Pt—Pt separations, it is possible to postulate a simple band model by considering overlap of the filled 5dzi orbitals on individual atoms in the chain to produce a full 5dp band, and overlap of the empty 6pz orbitals to produce an empty 6pz band (Figure 1). 

To cover the gap between them the Hubbard model Hamiltonian was quite generally accepted. This Hamiltonian apparently has the ability of mimicking the whole spectrum, from the free quasi-particle domain, at U=0, to the strongly correlated one, at U —> oo, where, for half-filled band systems, it renormalizes to the Heisenberg Hamiltonian, via Degenerate Perturbation Theory. Thence, the Heisenberg Hamiltonian was assumed to be acceptable only for rather small t/U values. 

Fig. 3.15 Band model for an intrinsic semiconductor. The valence band is totally filled and the conduction band empty. Conduction occurs via promotion of electrons from Ey to Ecy the conductivity increasing with increase in temperature, (a) Definition of energy levels (b) Variation of density of available states with...

In order to discuss the valence electronic state and chemical bonding of lithium vanadium oxide we made calculations using cluster models. The density of states (DOS) and the partial density of states (PDOS) of Li1.1V0.9O2 are obtained by this study as shown in Figure 3.4. The filled band located from —8 to —3 eV is mainly composed of O 2p orbital. The partially filled band located around —2 to 4 eV is mainly composed of V 3d orbital. Unoccupied band located above 5 eV is... 

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