The authors use a slave-boson technique in the mean-field approximation to obtain the temperature dependence of the valence, nf, the susceptibility, chi S, and the specific heat, CV, for a lattice of mixed-valence ions. They find that the mean-field solution is sufficient to extrapolate between the low- and high-temperature regimes giving for example an enhanced Pauli-like susceptibility for low T and a Curie-Weiss-like susceptibility at high T. They consider an extension to the Anderson model in which direct f-f- hopping is included and show that such a model exhibits a variety of interesting low-temperature behaviour.
The effects of Co addition on the chemical and electronic structure of PbTiO 3 were explored both by theory and through experiment. Cobalt was incorporated to PbTiO 3 during sol gel process. The XRD data of the compounds confirmed the perovskite structure for the pure samples. The XRD lines broadened and showed emerging cubiclike features as the Co incorporation increased. The changes in the XRD pattern were interpreted as double perovskite structure formation. 207 Pb NMR measurements revealed a growing isotropic component in the presence of Co. In line with the experiments, DFT calculated chemical-shift values corroborate isotropic coordination of Pb suggesting the formation of cubic Pb 2 CoTiO 6 domains in the prepared samples. The state-of-the-art hybrid functional first-principles calculations indicate formation of Pb 2 CoTiO 6 with cubic structure and confirms that Co addition can decrease oxygen binding energy significantly. Experimental UV-Vis spectroscopy results indicate that upon addition of Co, the band gap is shifted towards visible wavelengths which was confirmed by the energy bands and absorption spectra calculations. The oxygen binding energies were determined by temperature programmed reduction (TPR) measurements. Upon addition of Co, TPR lines shifted to lower temperatures and new features appeared in the TPR patterns. This shift was interpreted as weakening of oxygen cobalt bond strength. The change in the electronic structure by the alterations of oxygen vacancy formation energy and bond lengths upon Co insertion are determined by DFT calculations.
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