Orbitally anisotropic hybridization

For concentrated Kondo systems orbitally driven anisotropic hybridization of the f electrons with conduction electrons is crucial (Cooper et al. 1988, Levy and Zhang 1989). The anisotropic part of the mixing interaction causes a substructure within the rather narrow f band, which leads to crystal-field effects even in highly itinerant-electron systems. On account of this crystal-field dressing a localized 5f electron in NpSnj might develop. 

Combination of isotropy and anisotropy Since any orbital may be considered as a hybrid of suitable combinations of s, p or d orbitals, so also may a hyperfine coupling be divided into a contribution arising from p or d orbitals (anisotropic) and s orbitals (isotropic). In general both isotropic and anisotropic hyperfine couplings occur when one or more nuclei with 1 0 are present in the system. The whole interaction is therefore dependent on orientation and must be expressed by the second rank A tensor as given in Equation [13]. The A tensor may be split into an anisotropic and isotropic part as follows... 

Results for C02 and N02 are important in that they illustrate one of the major successes of the electron spin resonance method. This is that, provided the ratio of p- to s-character is smaller than about ten, the results from the isotropic coupling (giving the s-character) and the anisotropic coupling (giving the p-character) yield a good estimate of the 8+p hybridization of the molecular orbital on the atom concerned. As shown by the squares of the coefficients of the wave function (a2) given in Table 16, both C02- and N02 have appreciable 2s-character for the orbital of the impaired electron, showing that these radicals are bent. The structure of C02 has been discussed in detail by Ovenall and Whiffen (1961) and that of N02 by Atkins et al. (1962). 

In this chapter, the structures and textures of carbons at different scales are explained. The carbon materials are classified into four families, diamond, graphite, fullerene, and carbyne on the basis of hybridized sp3, flat sp2, curved sp2, and sp orbitals used, respectively. Each family has its own characteristic diversity in structure and also in the possibility of accepting foreign species. The formation of these carbon materials from organic precursors (carbonization) is shortly described by dividing the process into three phases (gas, solid, and liquid), based on the intermediate phases formed during carbonization. The importance of nanotexture, mainly due to the preferred orientation of the anisotropic BSU in the graphite family, i.e., planar, axial, point, and random orientation schemes, is particularly emphasized. 

Both the isotropic and anisotropic F hf splittings to the two fluorines at the C=C carbons of c-C3F4 are about two times larger than those to the four fluorines of C2p4 , see Table 5.1. This suggests that both anions have almost the same type of hybrid orbital for the unpaired electron, but that the degree of unpaired electron delocalization to the a -fluorine orbitals is inversely proportional to the number of F-atoms. 

The observation of a layer of amorphous carbon at the film surface, in combination with the observation of liquid crystal alignment on this surface, suggested the breakthrough idea to replace the polyimide polymer film with an amorphous carbon layer [34]. The essential requirement for liquid crystal alignment (as stated by our model), namely the presence of an anisotropic distribution of directional bonds, can be fulfilled by an ion beam irradiated amorphous carbon layer. This is demonstrated by the presence of the resonance associated with tt orbitals at 285 eV in the absorption spectrum of amorphous carbon (bottom of Fig, 6.12). Its presence indicates that amorphous carbon contains unsaturated sp2 and sp hybridized carbon atoms. While sps hybridization does not lead to any anisotropy, the directional nature of carbon double and triple bonds formed by sp2 and sp hybridized carbon atoms can lead to a breaking of the isotropy of the molecular distribution. It therefore mainly remains the question whether a statistically significant anisotropy in these carbon bonds can be achieved by ion beam irradiation of an amorphous carbon layer. 

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