Fluctuating valence state

Many works have been devoted to the study of compounds with fluctuating valency states (ICF systems), especially for semimetallic compounds. An international Colloquium on the metal-non-metal transitions in rare earth compounds, was held in 1976 and the results have been published in the Journal de Physique (Colloque C4, supplement au No. 10, Tome 37, October 1976). Theory and experiments concerning intermetallic ICF systems have not so far received an analogous development. 

Rare earth systems in fluctuating valence state... 

The interatomic distances found are V—S = 2.186 0.040 A and Cu—S — 2.285 i 0.014 A. The Cu—S distance is somewhat smaller than the sum of the tetrahedral radii2) for sulfur and univalent copper, 2.39 A. As in the case of chalcopyrite, this probably indicates that the valence states are not well defined as CuIiVvSi, but fluctuate, the copper resonating between cuprous and cupric states and the vanadium between quinquivalent and lower states. 

The orbitals of the d states in clusters of the 3d, 4d, and 5d transition elements (or in the bulk metals) are fairly localized on the atoms as compared with the sp valence states of comparable energy. Consequently, the d states are not much perturbed by the cluster potential, and the d orbitals of one atom do not strongly overlap with the d orbitals of other atoms. Intraatomic d-d correlations tend to give a fixed integral number of d electrons in each atomic d-shell. However, the small interatomic d-d overlap terms and s-d hybridization induce intraatomic charge fluctuations in each d shell. In fact, a d orbital contribution to the conductivity of the metals and to the low temperature electronic specific heat is obtained only by starting with an extended description of the d electrons.7... 

To allow for fluctuation of atomic electronegativities in response to the environment it has been proposed [120] that valence-state, rather than ground-state energies be used in Mulliken s formula to define orbital electronegativities. Despite common terminology, the valence state invoked here, is not the same as that of section 5.4, and refers to the improbable condition of an atom promoted to some hypothetical hybridized state. In the case of the carbon... 

It has further been argued by Band and Fomichev [623] who have performed Dirac-Fock calculations of the transition from collapsed to decol-lapsed orbitals that a coexistence of states in the same atom, due to the formation of hybrid states, can occur One thus forms a picture in which it could also happen, in cases of fluctuating valence, that two different valence states would coexist on the same site [624]. 

To reconcile the diverging Raman and neutron scattering results the following point of view has been taken by Giintherodt et al. (1985b) similarly to the valence fluctuations between two integral valence states (4f"< 4f" -l- e ) in IV rare-earth compounds the systems CeAlj, TmSe and Smo Yp jjS show... 

Up to now, we have concentrated on the physics at zero kelvin. In this section, we extend the studies to finite temperatures and discuss finite temperature phase diagrams. The physics at finite temperatures is dominated by thermal fluctuations between low lying excited states of the system. These fluctuations can include spin fluctuations, fluctuations between different valence states, or fluctuations between different orbitally ordered states, if present. Such fluctuations can be addressed througih a so-called alloy analogy. If there is a timescale that is slow compared to the motion of the valence electrons, and on which the configurations persist between the system fluctuations, one can replace the temporal average over all fluctuations by an ensemble average over all possible (spatially... 

It was remarked earlier that there is a strong correlation between systems which exhibit a mixed or fluctuating valence and systems which show Kondo-like anomalies. This connection was particularly clear in the Ce systems considered previously. A wide variety of experimental measurements has shown that in SmB6 and collapsed SmS, the Sm ions have a mixed valence (Sm -Sm ). We consider these systems not because they are classic Kondo systems (they are not), but because they provide considerable insight into the nature of the mixed valence state. These systems are also interesting with respect to the study of metal-insulator transitions, but this aspect will be discussed in ch. 20 by Jayaraman. 

Independent of the conditions inducing the valence transition (pressure, temperature or chemical alloying) the valence numbers observed just after the first-order transition, converge to u = 2.6 0.05. The theoretical answer to why just the ratio 3/2 of the two valence state populations stabilizes SmS at low volumes might be obtained in the framework of the thermodynamics of valence fluctuations (see e.g. Wohlleben (1984a,b)). 

The lanthanide compounds are usually treated in magnetism by an f-localized model, but show various interesting phenomena such as valence fluctuations, gap states, Kondo lattice, and heavy electrons. These originate from the 4f electrons in the lantiianide compounds, which are either bound to the lanthanide atoms or delocalized, indicating... 

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