Virtual bound states

Room temperature deposition of silver on Pd(lOO) produces a rather sharp Ag/Pd interface [62]. The interaction with a palladium surface induces a shift of Ag 3d core levels to lower binding energies (up to 0.7 eV) while the Pd 3d level BE, is virtually unchanged. In the same time silver deposition alters the palladium valence band already at small silver coverage. Annealing of the Ag/Pd system at 520 K induces inter-diffusion of Ag and Pd atoms at all silver coverage. In the case when silver multilayer was deposited on the palladium surface, the layered silver transforms into a clustered structure slightly enriched with Pd atoms. A hybridization of the localized Pd 4d level and the silver sp-band produces virtual bound state at 2eV below the Fermi level. 

If the localized electron tunnels out through the barrier (state 1 in Fig. 12 b) a certain amount of f-f overlapping is present. States like 1 in Fig. 12 b are called sometimes resonant states or "virtually bound" states. In contrast with case 2 in Fig. 12b, which we may call of full localization , the wave function of a resonant state does not die out rapidly, but keeps a finite amplitude in the crystal, even far away from the core. For this reason, overlapping may take place with adjacent atoms and a band may be built as in ii. (If the band formed is a very narrow band, sometimes the names of localized state or of resonance band are employed, too. Attention is drawn, however, that in this case one refers to a many-electron, many-atoms wave function of itinerant character in the sense of band theory whereas in the case of resonant states one refers to a one-electron state, bound to the central potential of the core (see Chap. F)). 

The field round an impurity screening and virtual bound states... 

As regards the magnitude of the moment on each atom, the analysis is similar to that of Section 7 for the moment on a single atom for a virtual bound state. However, we cannot now assume that the Fermi energy is not shifted when our equations are expanded to third order irt U. Unless N (E )=0, it is, and the moment becomes... 

If the active metal becomes highly diluted the minimum polarity model leads to the virtual bound-state model (127, 128, 129). This model has also been applied to highly diluted Ni-Cu alloys (121a). The nickel d-states are then found to form not a common band with the copper d-states but narrow virtual levels between the copper d-states and the Fermi level. The levels are in resonance with the s,p-band of the metal. 

Additionally and equally significant, the spectral features assigned to the antibonding state of Hf 5f electrons display seven features indicating a completely removal of the Hf 4fs/2 and Hf 4f7/2 degeneracies of three and four, respectively. This is consistent with the local field induced symmetries of Hf 4f orbitals that are mixed with O 2p, and possibly O 2s states as well. This is the same mechanism that activated the Ti 3p and O 2s virtual bound state resonance absorptions in Fig. 12. The spectral widths of the Hf 5d" features (4 states) and Hf 4f features (7 states)... 

Lastly, a localized model with a large/-rf hybridization has been proposed by Jullien et al (42). In this model, two virtual bound states are present they are hybridized 6d and 5/ states, and their characteristics can explain the magnetic properties of actinides. 

Fig. 7. Resistivity data of YbAls and YbAl2. The solid lines give the experimentally obtained Ap p vs. T curves corrected for residual and electron-phonon scattering contributions. The dotted lines show the estimated contributions due to spin-disorder scattering by the Yb magnetic moments described by the second term of eq. (16). The dashed lines show the estimated contribution connected with scattering processes on Yb virtual bound states which is described by the first term of eq. (16) (Havinga et al., 1973).

The Mossbauer spectra of alloys of 0.1 and 1 at.% Fe in Cu with 5 at.% Pt have been obtained by [1971 Win]. Analysis shows electric field gradients and changes in the isomer shift with Pt neighbors that can be explained by the increased density of states due to the virtual bound state on the Pt impurity. 

Conway and Phillips (1974) measured the heat capacities of mixed-phase samples, from which they extrapolated to the pure phases, using the magnetic ordering anomaly in the /3-phase as a measure of the composition. Small concentration independent peaks near 0.15, 0.9 and 6 K were neglected as being impurity related. They found y. = 22 mJ/mole-K and 0d.o(O) 125 K, results which can be explained as above in terms of a shift in the 4f band or virtual bound state relative to the conduction band (Coqblin and Blandin 1%8). 

Meadon and Sze (1969), on the other hand, found anomalies in the thermopower and resistivity of 99.9% pure Eu at around 22.5 K and 21 K, respectively. Cold-working raised the thermopower anomaly to 25 K, whereas annealing weakened it and depressed it to 18 K. They suggested an electronic transformation based on 4f virtual bound states close to the Fermi level, but this is doubtful in view of energy band calculations (Andersen and Loucks 1968) and... 

Baberschke and Davidov (1975) discussed the size of the 64 parameters obtained for YSb, YBi, LaSb and LaBi in terms of a virtual-bound state model. In this model the conduction electrons of 5d character, originating from the Gd atoms, are supposed to act as screening charges and to over-compensate the influence of the ligands. In this way they offer a plausible explanation for the discrepancy of expected 64 values and lattice parameter uq- According to a simple point charge model, 64 should be proportional to in contrast to the experimental observations. 

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