Density of states alloys

ANG AO ATA BF CB CF CNDO CPA DBA DOS FL GF HFA LDOS LMTO MO NN TBA VB VCA WSL Anderson-Newns-Grimley atomic orbital average t-matrix approximation Bessel function conduction band continued fraction complete neglect of differential overlap coherent-potential approximation disordered binary alloy density of states Fermi level Green function Flartree-Fock approximation local density of states linear muffin-tin orbital molecular orbital nearest neighbour tight-binding approximation valence band virtual crystal approximation Wannier-Stark ladder... 

The heats of formation of equiatomic AB transition-metal alloys may be predicted by generalizing the rectangular d band model for the elements to the case of disordered binary systems, as illustrated in the lower panel of Fig. 7.13. Assuming that the A and transition elements are characterized by bands of width WA and WB, respectively, then they will mix together in the disordered AB alloy to create a common band with some new width, WAB. The alloy bandwidth, WAB may be related to the elemental bond integrals, hAA and , and the atomic energy level mismatch, AE — EB — EAt by evaluating the second moment of the total alloy density of states per atom ab( ), namely... 

Hence, within the rectangular d band model for the AB alloy density of states, from eqs (7.33) the bond energy becomes... 

Fig, 3.11. Alloy density of states (in arbitrary units) and properties related to localiza-tion, calculated by the CPA with x = 0.1, and 6 = (a) 0.7, (b) 0.8, (c) 0.95, and (d) 1.1. Regions of localized states have been shaded. The heavy line above each density of states indicates the localization function F(E) defined by Eq. (3.32b) the dotted line the A parentage n- (E) defined in the text (Economou 1970a). 

Figure. 3 (a) Partial pair correlation function.s gij(B.) in liquid K-Sb alloys, (b) Total, partial, and local electronic densities of states in liquid Ko.soSbo.so- Cf. text. 

This disorder decrease on alloying is in principle unexpected, because alloying introduces chemical disorder in addition to bond disorder. However, Silva et al. [14] reported results on the joint density of states as determined by EELS which showed a clear decrease in the density of tail states at 7-at.% N and showed a further increase for higher nitrogen content. 

Photoemission experiments with flat surfaces revealed that atoms of lower coordination may have a different population of d-orbitals and a different local density of states (138-140). These effects have been also predicted and analyzed theoretically (94-97, 136, 137), and should be always considered. The only question is whether they manifest themselves in the chemisorption and catalytic behavior. In any case, the impression is that by making metal particles small in size, one can cause the electronic structure of a certain fraction of the metal atoms to vary more than by making a bulk solution alloy. 

The charge transfer, - Qde, which accompanies a given atomic energy-level separation, AE, in the binary AB alloy may be obtained by filling the local densities of states up to the Fermi level as shown in Fig. 7.13. For the skew rectangular local densities of states this gives... 

A transition of this kind from metal to insulator will occur when some parameter, for instance the specific volume, the c/a ratio or the composition in an alloy, changes in such a way that two bands cease to overlap, producing a full valence band and an empty conduction band with an energy gap between them (see Fig. 4.1). A simple case is that due to the change in volume of a divalent metal. In any divalent metal, if the volume increases sufficiently, an s-like valence band will separate off from a p-like conduction band, the density of states going from the form of Fig. 1.13(b) to that of Fig. 1.13(c). The most favourable case is mercury,... 

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