4f-Electron Density Distribution in Crystals of CeB₆ at 165 K and its Analysis Based on the Crystal Field Theory

Abstract

Abstract4f-Electron density in single crystals of CeB 6, cerium hexaboride, was measured at 165 K by X-ray diffractometry. Significant peaks 2.0eA -3 high were found along the (100) directions at 0.41A from Ce on the deformation density map. Analysis based on the crystal field theory removed the peaks, confirming that they were due to the Ce 4f-electrons on the tlu-orbital. The deformation density in the B 6 octahedron was also markedly improved by the analysis and coincides qualitatively with a theoretical molecular orbital (MO) calculation. It also coincides with the model deformation density map of CaB 6 composed of only light atoms. These facts guarantee the accuracy of the intensity measurement for the present study. Since Ce 3+ has only one 4f-electron, a highly accurate intensity measurement is necessary to detect its 4f-electron density distribution. A ~-scan technique was therefore employed to avoid multiple diffraction (MD) and to measure the intensities at w and X angles with minimum fluctuation of temperature at the sample position. Relativistic radial functions for orbitals of Ce 3+ and the corresponding scattering factors, which take the aspherical electron density distribution of 4f-electrons into account, were used for the analysis. CeB 6 is a typical dense Kondo material. The Kondo effect occurs in CeB 6 from low temperature to above room temperature. X-ray analysis of the f-electron density based on atomic orbitals (AO) revealed that 1.5(2) electrons are donated from B 6 to Ce and a total of 2.5 (2) electrons localize on the 4f-orbital. x values are consistent with the 4f-orbitals being highly contracted and thus stabilized. These may be related to the Kondo effect.

Resonant inelastic x-ray scattering of CeB6 at the Ce L1- and L3-edges

“…Furthermore, from an x-ray diffraction experiment on CeB 6 , Tanaka et al suggested that at 165 K, B 6 donates 1.5 electrons to the Ce, more consistent with a covalent picture than the ionic one. 11 Recent research from their group also shows that the crystal field in CeB 6 varies with temperature because of charge transfer from B 2p to Ce 5d. 12 In this paper, we report measurements of the L 3 -and L 1edge XANES and the corresponding 2p3d (L α1,2 ) and 2s(5p + valence p) (L γ 4 ) RIXS for CeB 6 .…”

“…7 The electronic structure of CeB 6 has been subjected to many experimental investigations. Various spectroscopic [8][9][10] as well as diffraction techniques 11,12 have been applied. These previous experimental works, however, did not lead to the same conclusions, showing wide discrepancies.…”

Integrated X-ray L Absorption Spectra. Counting Holes in Ni Complexes

“…19,20 There are surprisingly few methods for directly measuring electron density distributions, and most techniques that purport to do so are based on empirical correlations. In some cases, electron density distributions can be measured with very high accuracy diffraction data; X-ray studies of 4f electron density in CeB 6 21 and 3d density in Ni(ND 3 ) 4 (NO 2 ) 2 22 are recent examples. Spin density distributions are also recoverable from magnetic resonance measurements.…”

How do specimen preparation and crystal perfection affect structure factor measurements by quantitative convergent-beam electron diffraction?

“…Cerium hexaboride is the material of choice because it is a strongly correlated electron material whose bonding electron density has previously presented significant challenges in terms of both theoretical modelling and experimental measurement by X-ray diffraction (Tanaka et al, 1997;Tanaka & Onuki, 2002;Makita et al, 2007Makita et al, , 2008. QCBED has the potential to cast new light on this material in terms of its bonding structure.…”