D band occupation

The Liix and Ln edge white-line surface area of 5d metals is generally accepted to be a measure for the d-band occupancy, or better the d-band vacancy (28). Small reduced platinum and iridium clusters were reported to be electron deficient compared to the bulk metal (28). For a given particle size the whiteline surface area provides information on the relative degree of oxidation of the metal the higher the white-line surface area the higher the oxidation state of the metal. 

These model calculations have treated all the transition metals as equivalent except for the d-band occupancy. This is of cause a gross oversimplification and much more detailed calculations are needed for a detailed picture. The simple description does. 

The relative occupancy of the NFE and bands varies under compression. We see from Fig. 7.9 that the d band occupancy Nd increases dramatically for compressions about equilibrium for the early transition metals but that it holds steady for the later transition metals. For less than... 

Fig. 7.9 The d band occupancy Nd as a function of the Wigner-Seitz radius, / ws. The circles mark the equilibrium values.

The trivalent rare-earth crystal structure sequence from hep - Sm type -> La type -> fee, which is observed for both decreasing atomic number and increasing pressure, is also determined by the d-band occupancy. Figure 8.11(a) shows the self-consistent LDA energy bands of fee lanthanum as a function of the normalized atomic volume fi/Q0, where Q0 is the equilibrium atomic volume. We see that the bottom of the NFE sp band moves up rapidly in energy in the vicinity of the equilibrium atomic volume as the free electrons are compressed into the ion core region from where they are repelled by orthogonality constraints (cf eqn (7.29)). At the same time the d band widens, so that the number of d electrons increases under pressure... 

Fig. 8.11 (a) The energy bands of La about the equilibrium atomic volume Q0 and the corresponding d band occupancy, A/d. of La and Lu. d, t, and b label the centre of gravity, the top and bottom of the d band respectively is the bottom of the NFE sp band, and F is the Fermi energy, (b) The relative d bond energies in units of the d bandwidth, W, of hep (full curve). La structure type (dashed curve), and Sm structure type (dot-dashed curve) with respect to fee as a function of the d band occupancy /Vd. The resulting stable structures for the ideal and a non-ideal axial ratio are also shown. (From Duthie and Pettifor (1977).)... 

The activation barriers AE for dissociation and recombination belong to the same realm of relative energies as AQAB. For this reason, we shall not discuss here purely numerical calculations of AE. Remarkably, many authors tried to conceptualize their computational results in terms of simple analytic models, which have no direct relation to the computations. For example, the effective medium theory (EMT) is a band-structure model with a complex and elaborated formalism including many parameters (154). Nevertheless, while reviewing the numerical EMT applications to surface reactions, Norskov and Stoltze (155) discussed the calculated trends in the activation energies for AB dissociation in terms of a one-parameter model (unfortunately, no details were provided) projecting A b to vary as NJ, 10 - Nd), where Nd is the d band occupancy [cf. Eqs. (21a)—(21c) of the BOC-MP theory]. 

The use of XANES spectroscopy to determine the d-band occupancy (or more correctly the unfilled d-band) in pure metals and supported catalysts was discovered early on by Lytle et al. (1976,1979). 

It is clearly seen that 4d-4d, 4d-5d, 5d-4d and 5d-5d combinations exhibit similar patterns of "+" and signs. This is because the bonding in transition metals as well as in transition metal alloys is mainly determined by the valence d-electrons [29,31], which form quite localized bonds in contrast to the free-electron like bonding found in the simple metals. As a result the d-band occupation is the main parameter for the characterization of the bonding in this case. 

The concept of canonical bands [1.19] was used by Tettifor in a series of three papers [1.47-49] where he related the superconducting and cohesive properties of the 4d transition metals to the variation of ASA potential parameters as functions of volume and atomic number. By similar means Duthie and Petti for [1.50] established a correlation with the d-band occupation numbers which explained the particular sequence of crystal structures found in the series of rare-earth metals. 

It is unnecessary to provide details of the results of such calculations, or of their comparison with experimental determinations by for example soft X-ray spectroscopy band structures for Transition Metals can adopt quite complex forms, so we must content ourselves with a few qualitative observations. For the metals of catalytic interest, the nrf-electron band is narrow but has a high density of states (Figure 1.8), because these electrons are to some degree localised about each ion core, whereas the (n + l)s band is broad with a much lower density of states because s-electrons extend further and interact more. On progressing from iron through to copper, the d-band occupancy increases quickly, and the level density at the Fermi surface falls. The extent of vacancy of the d-band is provided by the saturation moment of magnetisation thus for example the electronic structure of metallic nickel is (Ar core) and is said to have 0.6 holes in the d-band . 

Luczak FJ (1976) Determination of d-band occupancy in pure metals and supported catalysts by measurement of the liii x-ray absorption threshold. J Catal 43 376-379... 

The resulting values plotted in fig. 6 are close to the values of Skriver (1983). The occupancy of the s- and p-bands increases linearly with atomic number and small discontinuities are found at Eu and Yb. In contrast to this behavior the d-band occupancy decreases with increasing atomic number (from 1.93 for La to 1.44 for Lu) and large dips are found at Eu and Yb due to their divalent configurations. The electron transfer from the sp- to the d-band with decreasing atomic number is... 

The relation between the observed structural sequence in the lanthanides and the d-band occupancy can be examined qualitatively using the above values of the number of occupied d-electrons. The study of the pressure-induced structural transition of Lu above (Min et al. 1986c) shows that the dependence of the d-band oecupaney on the structure is small at the given lattice constant the differences obtained between struetures are only 0.02 or 0.03 electrons. Hence it is possible to relate, within a small uneertainty, the observed structures in the lanthanide metals with the absolute values of the d-band occupancy obtained in the fee structure. From fig. 6, the resulting ranges of d-band occupancy (JV ) for the stable structures are < 1.7 for hep and 1.75 [Pg.178]

Furthermore, one can notice that not only the radius ratios r o for the regular lanthanides at ambient condition show an almost linear increase with Z, but also a linear decrease of the effective d-electron number, n, for the conduction bands of these lanthanides was derived from theory (Skriver 1985), and, therefore, one can consider the simple scaling with the radius ratio just as the purely experimental manifestation of simple scaling rules related to the d-band occupation, n, and to the related s->d transfer induced under pressure. 

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