Band filling

In the quantum level stmctures illustrated in Figure lb, electrons in each band fill up the energy levels, up to the available chemical potential. From Figure lb two critical optoelectronic devices can be explained. 

We observe that for the Fe-Co system a sim le spin polarized canonical model is able to reproduce qualitatively the results obtained by LMTO-CPA calculations. Despite the simplicity of this model the structural properties of the Fe-Co alloy are explained from simple band-filling arguments. 

In Figure 1(b) we have plotted the negative of anti-phase boundary energy e = — ( as a function of band filling for Pd Vi- with x = 0.25, 0.5 and 0.75. The number of zeros is in agreement with the arguments based on moments (there has to be at least four zeros). ... 

The surface have been assumed, unrelaxed and unreconstructed. The d band filling has been varied in the range (3 - 4.6)e per atom which includes the BCC transition metals and, in particular, the case of Ta and W. The results are displayed in Fig. 2. As often assumed, we have taken Nd(Z + 1) - Nd(Z) = 1.1. However, as shown in Fig. 2, changing this difference to 1 modifies only slightly the numerical results. 

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...

Here, we address the more general question of the relative stability of monomers, dimers and triangular trimers on the (111) surface of FCC transition metals of the same chemical species as a function of the d band filling Nd. All possible atomic configurations of the systems are considered monomers and dimers at sites N and F, triangles with A and B borders at sites N and F (Fig. 4). The d band-filling includes the range of stability of the FCC phase (Nd > 7.5e /atom). The densities of states are obtained from... 

It is well known that in bulk crystals there are inversions of relative stability between the HCP and the FCC structure as a fxmction of the d band filling which follow from the equality of the first four moments (po - ps) of the total density of states in both structures. A similar behaviour is also expected in the present problem since the total densities of states of two adislands with the same shape and number of atoms, but adsorbed in different geometries, have again the same po, pi, P2/ P3 when the renormalization of atomic levels and the relaxation are neglected. This behaviour is still found when the latter effects are taken into account as shown in Fig. 5 where our results are summarized. 

Figure 5. Diagram giving the relative stability of the various atomic configurations shown in Fig. 4 as a function of the d band-filling Nj- From the second to the fifth line relative stability of the F and N sites for the monomer, dimer, A trimer and B trimer. On the sixth and seventh lines relative stability of A and B triangles at N and F sites. The relative stability of HCP and FCC bulk phases is given for comparison in the first line.

It is seen that there exists a domain of d band-fillings Nchemical species. This domain narrows very rapidly when the cluster size increases. Consequently, outside this domain and in the range of stability of bulk FCC, i.e., when N 8.2e /atom, we predict that cluster adatoms sit always at normal sites irrespective of the size of the... 

Why do many catalytic reactions exhibit volcano behavior as a function of d-band filling of the metal catalyst ... 

Alloys of Pd-Au-Fe (2 at%) Mossbauer effect in Fe and Au, study of band filling, hyperfine fields, isomer shifts... 

Routes to Molecular Metals with Widely Variable Counterions and Band-Filling... 

Evidence is presented for continuous tuning of the band-filling between y - 0.00 and 0.50. In comparison, electrochemical oxidation of monoclinic /)-Ni(Pc) under the same conditions is also accompanied by a significant overpotential in forming tetragonal Ni(Pc)-(BF4)0.48- However, electrochemical undoping produces the monoclinic 7-Ni(Pc) phase with far less band structure tunability than in the silicon polymer. Experiments with tosylate as the anion indicate that tetragonal [Si(Pc)0](tosylate)y n can be tuned continuously between y = 0.00 and 0.67. For the anions PFg,... 

The charge transport and optical properties of the [Si(Pc)0]-(tos)y)n materials as y=0 -+ 0.67 are reminiscent of the [Si(Pc)0]-(BF4)y)n system, but with some noteworthy differences. Again there is an insulator-to-metal transition in the thermoelectric power near y 0.15-0.20. Beyond this doping stoichiometry, the tosylates also show a continuous evolution through a metallic phase with decreasing band-filling. However, the transition seems somewhat smoother than in the BF4 system for y)>0.40, possibly a consequence of a more disordered tosylate crystal structure. Both [Si(Pc)0]-(tos)y)n optical reflectance spectra and four-probe conductivities are also consistent with a transition to a metal at y 0.15-0.20. Repeated electrochemical cycling leads to considerably more decomposition than in the tetrafluoroborate system. 

There is currently great commercial interest in plastic alternatives to conventional silicon-based components in electronic devices. Polymeric architectures offer flexible, low-cost, processable materials for this lucrative global market, and can be designed with more emphasis on device performance. The principal goals of improved band filling, dimensionality and new conductance mechanisms remain the same, and provide a subtly different challenge to the materials chemist. 

Our discussion of electronic structure has been in terms of band filling only. Of course, there is a lot more to know about band structures. The density of states represents only a highly simplified representation of the actual electronic structure, which ignores the three-dimensional structure of electron states in the crystal lattice. Angle-dependent photoemission gives information on this property of the electrons. The interested reader is referred to standard books on solid state physics [9,10] and photoemission [16,17]. The interpretation of photoemission and X-ray absorption spectra of catalysis-oriented questions, however, is usually done in terms of the electron density of states only. 

Fig. 7.15 Band filling in an intercalation model according to Friedel s (1954) notion of screening. The upper panel shows the position of the bands at various degrees of filling the lower panel shows the corresponding values of the electron chemical potential (Fermi energy).

Figure 1.34. E a < Epi, = 0 (a) 3D band structure and (b) contour plot. E a < Epb < 0 (c) 3D band structure and (d) contour plot. E a = E t < 0 (e) 3D band structure and (f) contour plot. FSs of half-tilled systems are represented by black lines while FSs of lower and higher band fillings by short dashed and continuous grey lines, respectively.

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