Simple solid transition-metal bands

The use of CO as a chemical probe of the nature of the molecular interactions with the surface sites of metallic catalysts [6] was the first clear experimental example of the transposition to surface science and in particular to chemisorption of the concepts of coordination chemistry [1, 2, 5], In fact the Chatt-Duncanson model [7] of coordination of CO, olefins, etc. to transition metals appeared to be valid also for the interactions of such probes on metal surfaces. It could not fit with the physical approach to the surface states based on solid state band gap theory [8], which was popular at the end of 1950, but at least it was a simple model for the evidence of a localized process of chemical adsorption of molecules such as olefins, CO, H, olefins, dienes, aromatics, and so on to single metal atoms on the surfaces of metals or metal oxides [5]. 

It is possible to characterize f-electron states in the actinides in quite a simple manner and to compare them with the states of other transition metal series. To this, we employ some simple concepts from energy band theory. Firstly, it is possible to express the real bandwidth in a simple elose-packed metal as the product of two parts . One factor depends only upon the angular momentum character of the band and the structure of the solid but not upon its scale. Therefore, since we shall use the fee structure throughout, the scaling factor X is known once and for all. 

The above simple picture of solids is not universally true because we have a class of crystalline solids, known as Mott insulators, whose electronic properties radically contradict the elementary band theory. Typical examples of Mott insulators are MnO, CoO and NiO, possessing the rocksalt structure. Here the only states in the vicinity of the Fermi level would be the 3d states. The cation d orbitals in the rocksalt structure would be split into t g and eg sets by the octahedral crystal field of the anions. In the transition-metal monoxides, TiO-NiO (3d -3d% the d levels would be partly filled and hence the simple band theory predicts them to be metallic. The prediction is true in TiO... 

Recent advances in the techniques of photoelectron spectroscopy (7) are making it possible to observe ionization from incompletely filled shells of valence elctrons, such as the 3d shell in compounds of first-transition-series elements (2—4) and the 4/ shell in lanthanides (5, 6). It is certain that the study of such ionisations will give much information of interest to chemists. Unfortunately, however, the interpretation of spectra from open-shell molecules is more difficult than for closed-shell species, since, even in the simple one-electron approach to photoelectron spectra, each orbital shell may give rise to several states on ionisation (7). This phenomenon has been particularly studied in the ionisation of core electrons, where for example a molecule (or complex ion in the solid state) with initial spin Si can generate two distinct states, with spin S2=Si — or Si + on ionisation from a non-degenerate core level (8). The analogous effect in valence-shell ionisation was seen by Wertheim et al. in the 4/ band of lanthanide tri-fluorides, LnF3 (9). More recent spectra of lanthanide elements and compounds (6, 9), show a partial resolution of different orbital states, in addition to spin-multiplicity effects. Different orbital states have also been resolved in gas-phase photoelectron spectra of transition-metal sandwich compounds, such as bis-(rr-cyclo-pentadienyl) complexes (3, 4). 

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... 

The problem may not be as severe for the/-shell metals particularly in the 4f series. The / electrons (in most cases n — 3 electrons in the Fn column for 4 < < 17) are so well localized that they may be treated as core electrons. The corresponding values were calculated from the ionization potentials of the atoms (see Problem 16-2,c), and are listed in the Solid State Table. Then the bonding properties of the /-shell metals can be treated exactly as the simple metals (or as beginning transition series if the effects of d states are sufficiently large to make that necessary) and effects of the /-shell electrons (such as the magnetic properties discussed in Section 20-F) can be treated separately. As an example, the equilibrium spacing of the rare earths is discussed in Problem 20-2, in which any d-state effects are ignored. This is a rather crude approximation, since with three non-/ electrons there is always some occupation of /-like bands. 

The rest of this section is devoted to a discussion of amorphous semiconductors, which play a special role within the field of the electronic structures of disordered materials for two reasons. First, as discussed below, the transport properties of amorphous semiconductors are dominated by carriers within kT of the transition energy where the states are uniquely characteristic of disordered materials. Secondly, the amorphous semiconductors are all covalent, and it is the electronic structures of the covalent materials which should be most sensitive to disorder. Simple metals, where the electrons interact weakly with the atoms via small pseudopotentials are free-electron-like near the Fermi surface both as solids and liquids. Insulating materials with large band gaps but narrow bands again have electronic structures relatively insensitive to order. The covalent semiconductors correspond to intermediate cases of maximal sensitivity of electronic structure to atomic structure and composition. 

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