Extended 4f states

In order to gain such insight into the CeOz valence problem in relation with the study of localized and extended 4f states, Miv-v XAS measurements have been performed (Kamatak et al. 1985,1987a,b) on Pr and Tb homologues with related fluorite structure. 

The concept of an extended 4f state is better understood by invoking a quasi-atomic model based on the principles described in sect. 2 of this chapter. The general idea is that a barrier is formed, owing to the combined effects of the Coulomb interaction in a many-electron atom and the centrifugal repulsion for a 4f electron. This gives rise to a double-well potential in which the outer well is shallow and extended. We discuss this idea in more detail below, in connection with the XAS of higher oxides of Ce, Pr and Tb. 

The challenge is to develop a description taking account of both atomic and solid state effects. Difficulties surrounding the theoretical description of extended 4f states within the prevailing Anderson localization models show that a fully consistent theory as yet does not yet exist. 

Two models exist vdiich are in a sense complementary and allow valence transitions to be discussed. The Anderson localization model is mostly applied in a parametric scheme, and allows many phenomena to be considered together as resulting fi om hybridisation effects in the conduction band. However, atomic effects are not so well accounted for in this picture essentially, they are added in by hand. Another proach is the quasi-atomic double-well model. This scheme is not parametric, since it is based on ab initio Hartree-Fock calculations. It accounts for atomic aspects, such as the general region of the Periodic Table vriiere such phenomena are encountered. Also, it provides a mechanism for localization (orbital collapse). Finally, it allows one to understand and explain the properties of rather special states (the extended 4f states) which are delocalized, but retain certain atomic features. However, this model is unable to incorporate solid state efifects in a simple way. 

It is generally accepted nowadays that the sequentially increasing occupation of 5f states dominates the electronic properties in the series of actinide elements (see table 2.1). The analogy with lanthanides, in which the 4f states are gradually filled, is not complete. The 4f electronic states are confined deeply in the core of the lanthanide ion and can be treated in most cases as localized. On the other hand, a non-negligi-ble overlap of the more extended 5f wave functions belonging to neighbouring actinide atoms in a solid leads to the delocalization of the 5f states which resembles the formation of the d band in transition metals. The question about the localized versus itinerant 5f electron behaviour has become one of the most central ones within electronic structure considerations. This controversial behaviour is quite well... 

An LDA band structure calculation is expected to yield a good description of the ground state properties of rather extended 4f-band Ce metal, provided it is carried out to self-consistency. Kmetko and Hill (1976) performed the first self-consistent APW band structure calculation for y- and a-Ce and pointed out the increase in hybridization of the 4f-states with the conduction band with reduction of the atomic volume. Glotzel (1978) reported the cohesive and magnetic properties of fee Ce obtained with the self-consistent relativistic LMTO method (Andersen 1975) and... 

The unoccupied states in the lanthanides can be reached by transitions from deep or shallow core levels. Following Wendin (1983), deep core levels are states in completely filled main shells, i.e. in the K, L and M levels. Levels in the incompletely filled main shells (N, O) are labelled as shallow core levels (except 5d, which is a valence electron level). The impact of this classification becomes clear by inspection of the strongly different types of absorption spectra, observed upon excitation of M and N core levels (fig. 6c). N,y yand M,y y spectra turn out to be completely different, although the d electrons from the shallow Nw.v levels (4d nf,n >4) reach 4f states as the photoelectrons from deep core Miy y levels (3d - nf,n > 4). Each of the M y y spectra exhibits a set of discrete narrow lines. The N,y y spectra on the other hand are dominated by a broad giant resonance above threshold (cf the strong line in fig. 6c). It exhibits only a weak and extended discrete line spectrum at threshold. 

---