Density-of-states curve

The XPS valence band as shown in Fig. 11, and especially the narrow and intense peak just below Ep (observed in all experiments) have been discussed following mainly hne I. Theoretical partial 5f density of states calculations agree in reproducing this feature, which can therefore be attributed to nearly pure 5 f states. But these density of states curves predict additional structmes which, although differing considerably in their position, are not observed experimentally. A maximum, observed only once at 1.8 eV might be qualitatively described by one calculation however, relatively poor statistics (only 100 c/s) may have artificially introduced this structure since it is difficult to understand why other XPS valence band spectra (of comparable or even higher resolutions) do not show it. 

From the comparison of the spectra with calculated one-electron density of states curves (lines I and II), therefore, the valence band spectra of U, from photoemission and BIS, are interpreted as due to a hybridized (d, f) continuous band, with a much large itinerant 5 f contribution than in Th for the occupied part . As for the broad structure at about 2.5 eV, qualitative agreements point to a 6d character. 

FIGURE 4.1 A density of states curve based on the free electron model. The levels occupied at 0 K are shaded. 

For conductors the valence band is completely filled and the conduction band is only partially filled (Fig. 2a). This means that there are many carriers. A semiconductor possesses a completely filled valence band and completely empty conduction band at 0° K (Fig. 2 b) but at higher temperatures the number of conduction electrons is controlled by the distribution of electrons between the valence and conduction band. This in turn is controlled by the width of the energy gap and the density of states curve, i. e. the number of allowed states for an energy lying within the range E + 6E (Fig. 2 c). 

Fig. 2. Density of states curves, a) metallic conductors, b) semiconductors at 0° K, c) semiconductors at temperatures above 0° K...

Fig. 80. Simplified density of states curve for metallic chromium. Energy scale is referred to bottom of s-p band. The Fermi level relative to the d bands is also shown for b.c.c. Ti, V, and Mn given the same relative positions of d and s-p bands. Ferromagnetic, simple-cubic sublattices are coupled antiferro-magnetically in b.c.c. Cr-Mn alloys.

Fig. 81. Simplified density of states curve for ferromagnetic a-Fe. Energy scale is referred to bottom of 8-p band. The [eg -f t2g (antibonding)] bands each contain 3.5 electrons per atom. Bonding t2g band held same as in Figure 80 and magnetic-electron band drawn to give 104yei = 12 cal/mole/deg2.

Fig. 84. Schematic density of states curve for f.c.c. nickel, where n(E) for 48 band is enlarged by a factor of ten. The Fermi level Ef is 5 eV above the bottom of the 48 band. Efb for Mn, Fe, and Co are also indicated.

Fig. 9. X-ray and UV photoelectron spectra of the conduction bands of Au and a theoretical density of states curve. For purposes of comparison the theoretical curve includes broadening with a 0.6 eV resolution function. Ref. (32)...

According to the results obtained already at 3 percent H spikes and dips occur in the density of states curve of the mixed system. At larger concentrations of impurities due to clustering effect of the impurity, a part of the gaps disappear (16). Finally, it should be mentioned that with the increase of the impurity concentration, as the calculations show, the density of states at the Fermi level increases and therefore we would expect an increase of the transition temperature between the superconducting and normal states. (This experiment, as far as we know, has not been performed yet). We can conclude from this CPA calculation that aperiodicity (disorder) has a rather serious effect on the band structure of polymers. 

A very clear distinction between the total DOS D s) and the LDOS D e,t) is shown by calculations on binary alloys [51]. Look, e.g., at the (partly hypothetical) series of isoelectronic 1 1 alloys TcTc, MoRu, NbRh, ZrPd, YAg, where the alloying partners have nominal valence differences between 0 (for pure Tc) and 8 (for YAg). As shown in Figure 5, the overall density of states curves look more or less alike for all five alloys, but the partial densities on the sites of the individual partners are very different. Such curves also show why the so-called collective electron model does not work for catalytic activity [52, p. 458], or even for alloy properties in general. 

Figure 6 and 7 show the density of states curves for all binary B32 type Zintl phases. The shapes of the curves are very similar. The main difference between the AB and the ab " compounds is the position of the Fermi energy. This is discussed in the next subsection. 

In Table 7 the Fermi energies Ep and the densities of states at the Fermi level N(Ef) are listed for all binary compounds covered. In order to study the defect structure of the AB" compounds, Ep and N(Ep) are given for two valence electron concentrations Cve = 2.0 and Cve 1.98. For the latter Cve Ep lies in the minimum of the density of states curve and the 5th band is not occupied. Values of N(Ef) obtained by the two different procedures (RAPW and ASA) are listed for LiAl, LiZn and LiCd. It seems that the differences in the N(Ep) values are caused by differences in the hybridization effect in both methods (cf. Sect. C.II above). 

In order to study the influence of electronic effects on the stability of binary and ternary Zintl phases within the rigid band model (Sect. C.VI) Fig. 16 shows AEba (j of LiTl and LiCd as a function of the valence electron concentration. The maxima of the density of states curves for the B2 and the B32 types of structures occur at different energy values (cf. Fig. 15), and therefore AEband as a function of cve is an oscillating curve. The reasons why the curve for LiTl changes its sign are discussed below. 

Fig. 9. Three density-of-states curves that fit the hypothetical field-effect data of Fig. 10. The density of states of Spear and LeComber (1976) (Fig. 4) is shown by the solid curve. (From Goodman and Fritzsche ( 980).]...

Fig. 27. Three density-of-states curves with different mobility gaps of1.44,1.54,and 1.64 eV corresponding to the values of a (see Eq. (13)] of 1.2 X 1(F (dotted), 2.0 X 10 (dotted-dashed), and 1.8 X 10 (dashed), as indicated. The original density of states of Spear and LeComber (1976) is shown by the solid curve. Each of these densities of states fits the hypothetical data of Fig. 28. [From Goodman and Fritzsche (1980).]...

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