Transition metals energy bands

IV Transition between energy bands Metals, pure and doped semiconductors... 

Figure 2.16. Calculated dissociative nitrogen ( ), carbon monoxide ( ), and oxygen ( ) chemisorption energies over different 3d transition metals plotted as a function of the center of the transition metal rf-bands. A more negative adsorption energy indicates a stronger adsorbate-metal bond. Reproduced from [32].

Let us note some qualitative aspects of electron dynamics. If the bands are narrow in energy, electron velocities will be small and electrons will behave like heavy particles. These qualities arc observed in insulator valence bands and in transition-metal d bands. In simple metals and semiconductors the bands tend to be broader and the electrons arc more mobile in metals the electrons typically behave as free particles with masses near the true electron mass. 

A second key observation associated with the trends presented in fig. 7.15 is the variation in the vacancy formation energy as a function of band filling (i.e. the filling up of the transition metal d-band in passing from the left to right of each figure). In particular, there is the same trend in the vacancy formation energy... 

Simple metals like alkalis, or ones with only s and p valence electrons, can often be described by a free electron gas model, whereas transition metals and rare earth metals which have d and f valence electrons camiot. Transition metal and rare earth metals do not have energy band structures which resemble free electron models. The fonned bonds from d and f states often have some strong covalent character. This character strongly modulates the free-electron-like bands. 

Massidda S, Continenza A, Posternak M and Baldereschi A 1997 Quasiparticle energy bands of transition-metal oxides within a model GW scheme Phys. Rev. B 55 13 494-502... 

Fig. 5. Energy bands of a metallic CNT in the presence of a magnetic flux and allowed optical transitions for the x and y polarisations.

In the optical absorption, two different polarisations of light should be considered the electric field is along (parallel or y polarisation) and perpendicular (perpendicular or x) to the axis. Figure 5 shows the energy band of a metallic CNT for flux < )/< )o =0, 1/4 and 1/2 and the process of optical transitions for the parallel and perpendicular polarisations. Some examples of calculated absorption... 

We will limit ourselves to the surface segregation energy of an impurity of atomic number Z + 1 in a BCC matrix of atomic number Z and study the variation of this energy as a function of the number Nj of d electrons per atom in the d band of e transition metal Z. 

Figure 2. Segregation energy in layer Sp (p = 0 surface layer...) of a transition metal impurity of atomic number Z + 1 (d band-filling (Nj + l.l)e /atom, full curves (Nj + l)e /atom, dashed curve) in a BCC transition metal matrix of atomic number Z (d band-filling Nje" /atom) for various crystallographic orientations of the surface...

The mechanism of the poisoning effect of nickel or palladium (and other metal) hydrides may be explained, generally, in terms of the electronic theory of catalysis on transition metals. Hydrogen when forming a hydride phase fills the empty energy levels in the nickel or palladium (or alloys) d band with its Is electron. In consequence the initially d transition metal transforms into an s-p metal and loses its great ability to chemisorb and properly activate catalytically the reactants involved. 

Figure 6.14a shows the sp and d bands of a transition metal (e.g. Pt), i.e. the density of states (DOS) as a function of electron energy E. It also shows the outer orbital energy levels of a gaseous CO molecule. Orbitals 4a, l7t and 5cr are occupied, as indicated by the arrows, orbital 27c is empty. The geometry of these molecular orbitals is shown in Figure 6.14b. 

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