Transition metal compounds band structure

The general understanding of the electronic structure and the bonding properties of transition-metal silicides is in terms of low-lying Si(3.s) and metal-d silicon-p hybridization. There are two dominant contributions to the bonding in transition-metal compounds, the decrease of the d band width and the covalent hybridization of atomic states. The former is caused by the increase in the distance between the transition-metal atoms due to the insertion of the silicon atoms, which decreases the d band broadening contribution to the stability of the lattice. 

First we consider the origin of band gaps and characters of the valence and conduction electron states in 3d transition-metal compounds [104]. Band structure calculations using effective one-particle potentials predict often either metallic behavior or gaps which are much too small. This is due to the fact that the electron-electron interactions are underestimated. In the Mott-Hubbard theory excited states which are essentially MMCT states are taken into account dfd -y The subscripts i and] label the transition-metal sites. These... 

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 ). 

The ZSA phase diagram and its variants provide a satisfactory description of the overall electronic structure of stoichiometric and ordered transition-metal compounds. Within the above description, the electronic properties of transition-metal oxides are primarily determined by the values of A, and t. There have been several electron spectroscopic (photoemission) investigations in order to estimate the interaction strengths. Valence-band as well as core-level spectra have been analysed for a large number of transition-metal and rare-earth compounds. Calculations of the spectra have been performed at different levels of complexity, but generally within an Anderson impurity Hamiltonian. In the case of metallic systems, the situation is complicated by the presence of a continuum of low-energy electron-hole excitations across the Fermi level. These play an important role in the case of the rare earths and their intermetallics. This effect is particularly important for the valence-band spectra. 

Analysis of the valence-band spectrum of NiO helped to understand the electronic structure of transition-metal compounds. It is to be noted that th.e crystal-field theory cannot explain the features over the entire valence-band region of NiO. It therefore becomes necessary to explicitly take into account the ligand(02p)-metal (Ni3d) hybridization and the intra-atomic Coulomb interaction, 11, in order to satisfactorily explain the spectral features. This has been done by approximating bulk NiO by a cluster (NiOg) ". The ground-state wave function Tg of this cluster is given by,... 

The crystal structures of transition metal compounds and minerals have either cubic or lower symmetries. The cations may occur in regular octahedral (or tetrahedral) sites or be present in distorted coordination polyhedra in the crystal structures. When cations are located in low-symmetry coordination environments in non-cubic minerals, different absorption spectrum profiles may result when linearly polarized light is transmitted through single crystals of the anisotropic phases. Such polarization dependence of absorption bands is illustrated by the spectra ofFe2+ in gillespite (fig. 3.3) and of Fe3+in yellow sapphire (fig. 3.16). 

X-Ray absorption data in combination with atomic theory and solid-state band-structure theory can yield detailed information about the ground-state electronic structure of solids on an energy scale on the order of meV. This holds particularly true for correlated narrow-band systems, such as the rare-earth and transition-metal compounds. In broad-band materials, such as the... 

Finally, lei us use the transition-metal pseudopotential theory to estimate matrix elements between d states and s and p states. These are not so useful in the transition metals themselves since the description of the electronic structure is better made in terms of d bands coupled to free-electron bands, ti k /(2m) d-<01 IT 10>, rather than in terms of d bands coupled to s and p bands. However, the matrix elements and so forth, directly enter the electronic structure of the transition-metal compounds, and it is desirable to obtain these matrix elements in terms of the d-state radius r. We do this by writing expressions for the bands in terms of pseudopotentials and equating them to the LCAO expressions obtained in Section 20-A. 

J. Zaanen, G. A. Sawatzky, and J. W. Allen, Band gaps and electronic structure of transition-metal compounds, Phys. Rev. Letters 55, 418 (1985). 

Calais, J.-L. (1977). Band structure of transition metal compounds. Adv. in Physics 26, 847-85. 

Hufner, S., and G. K. Wertheim (1973). X-ray photoelectron band structure of some transition metal compounds. Phys. Rev. B8, 4857-67. 

Simple metallic solids are elements or alloys with close-packed structures where the large number of interatomic overlaps gives rise to wide bands with no gaps between levels from different atomic orbitals. Metallic properties can arise, however, in other contexts. In transition metal compounds a partially occupied d shell can give rise to a partly filled band. Thus rhenium in Re03 has the formal... 

Comba, P. Modeling of structures and molecular properties of transition metal compounds - toward metalloprotein modeling. In Molecular Modeling and Dynamics of Bioinorganic Systems Band, L. Comba, P., Eds. Kluwer Academic Publishers Dordrecht, 1997, p. 21. 

Although for wide band metallic materials the valence band XPS spectra probably provide a fairly direct picture of the occupied band structure, where the valence electrons are localized the correlation with the final hole state must be considered. This is apparent for 4/compounds and also quite nicely for FeFa . The situation for other transition metal compounds with possibly wider d bands and greater covalent mixing is less clearcut, but a similar effect is observed in the exchange splitting of core levels in magnetic ions . 

Since some properties of each sublattice, ei ecially the anisotropy of the lanthanide sublattice, as experimentally established, govern the behavior of the whole crystal of the magnet, the magnetic properties of the lanthanide sublattice will affect the sublattice of the transition metals, i.e., interactions between sublattices exist. The 4f electrons, however, have almost no direct bonds with the 3d electrons of the transition-metal sublattice, so the anisotropy of the 4f electrons initially transfers to the outer orbitals of 6s, 5d and/or 6p electrons of the lanthanide atoms, and these in turn interact with 4s and/or 4d electrons of the transition-metal sublattice, which is composed of and/or spd bands with the transition metal s 3d electrons. The interactions between the 4f and 3d electrons, therefore, are indirect. Figure la schematically shows the band structure in the lanthanide-transition-metal compounds. 

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