Valence pnictides

The electrostatically favored cation (Li) and anion (RE) arrangement implies the presence of two different E-, Si- and Li sorts, which has been established by solution and solid-state NMR spectroscopy. The electronic structures of the mixed-valent pnictides 10 and 11 have been simply described as electron-deficient clusters with delocalized framework electrons. Formally the latter consist of two low-valent anediyl moieties RE and eight andiides (RE)2- (E = P, As). The relatively large E-E distances of >4 A exclude the occurrence of localized E-E bonds. However, delocalization of the cluster valence electrons is achieved without Li-Li bonds via Li-mediated multiple bonding. Evidence for this has been seen in the NMR spectra (31P, 7Li, 29Si), which are in accordance with the electron delocalization model (see later discussion). 

Though all TiP-type representatives are metallic their structure indicates a striving towards bond saturation. Only Ti-group pnictides are known with this structure, hence the cations carry one excess valence electron. As is needed to bind this excess d electron, the structure indeed shows cation pairs (Fig. 48d), but obviously the actual M—M distances are too long to represent single bonds (2.91 A in TiP, 3.23 A in TiAs and 3.13 A in ZrP). 

The jumps in the lattice constants in Figure 1, seen for the elemental Eu and Yb, as well as at the chalcogenides of Sm, Eu, Tm, and Yb, are due to the change in valence from trivalent to divalent. If a transition to the trivalent state were to occur, the lattice constant would also follow the monotonous behaviour of the other lanthanides, as seen in Figure 2, where the ionic radii of trivalent lanthanide ions are displayed. For the pnictides, only CeN shows an anomaly, indicating a tetravalent state, whereas all the other compounds show a smooth, decreasing behaviour as a function of the lanthanide atomic number. 

Pnictide R " ", Chalcogenide R, and valence imbalanced compounds such as... 

At ambient conditions, the Yb monopnictides and monochalcogenides crystallize in the B1 structure. As outlined, the Yb pnictides are all foimd to be well described by the nominally trivalent scenario, where the effective valence varies from 2.88 in YbN to 2.69, 2.63, and 2.53 in YbP, YbAs, and YbSb, respectively. Experimentally, the position of the/ band is found 0.2 eV above the Fermi level in YbN, YbP, and YbAs (Degiorgi et al., 1990,1993). Other experiments have revealed heavy-electron behaviour in Yb pnictides (Ott et al., 1985 Sakon et al., 1992 Takeda et al., 1993), but this can be a reflection of sample non-stoichiometry (Degiorgi et al., 1990,1993). The discrepancy between the present electronic structure and the pictme provided by Degiorgi et al. (1990,1993) can be due to the LSD approximation, since the position of the narrow band in the theory is solely determined by the LSD potential (no correlation correction). LDA - - U calculations on YbN (Larson et al., 2007) include a positive correlation shift of the unoccupied f-states that leads to an ideal trivalent Yb ion in accordance with Degiorgi et al. (1990,1993). 

In contrast to the pnictides, the equilibrium volumes of the Yb chalcogenides are accurately described assuming the divalent/ configuration for Yb. As pressme is applied to the Yb chalcogenides, the configuration becomes more and more favourable, and eventually a transition to an intermediate valence state occurs. Valence transitions in lanthanide systems will be discussed in the next section. 

Fig. 9.13. Lattice parameter vs atomic number plot for R.E. pnictides. The deviation of a of CeN is due to the higher valence state of Ce. The right fig. is the P-V relationship for CeP and the anomaly is due to a valence change in Ce towards the 4 state. The data point for LaP is shown for comparison (from Jayaraman et al., 1976).

In fig. 19 results for the valence PES spectra of the Ce pnictides are shown (Gunnarsson and Schonhammer 1985b). The off-resonance spectra of the pnictides show spectra with a peak at — 2eV. For simplicity we have therefore used a simple triangular shape for V eY as shown in the insert. The figure shows results for both U = CO and for a finite U. In this case the finite U effects have a small influence on the spectra. The weight of the Kondo peak is also negligible. In these cases the hybridization effects dominate. The same conclusion was reached by Sakai et al. (1984). 

The first experimental evidence of a double-peaked structure due to f-emission in the valence band photoemission spectrum of a lanthanide was reported by MSrtensson et al. (1982) and Wieliczka et al. (1982) for Ce, by Franciosi et al. (1981) and Gudat et al. (1982) for the cerium pnictides. (The spectrum had been seen by other groups before, but was not realized as such.) The spectra of Ce exhibit a double-peak structure associated with the 4f-electrons, with a peak near p and another 2eV below p. The data for cerium pnictides indicated a peak about 3eV below Ep and one about O.SeV below p. Moreover, the intensity ratio between the two peaks changed as one worked down the series (CeP, Ce As, CeSb, CeBi) with... 

Selected band results for the cerium pnictides. The angular momentum decomposition is a single-site decomposition of the wave function within the mufiln tins, not the LCAO decomposition. The radial charge density of the 4f-orbital at the muffine tin boundary and the valence band width (Ep - [,) are tabulated here as they enter into the discussion of relative peak heights (section 3.7). Units are atomic units except the band width which is given in electron... 

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