Towards the Quantification of 5f Delocalization

Abstract

By using M4,5 X-ray Emission Spectroscopy (XES) in the tender X-ray regime, it is possible to quantify 5f delocalization in the actinides. Previous analyses, utilizing the Branching Ratio (BR) in the N4,5 X-ray Absorption Spectroscopy (XAS), could not discriminate between the cases of localized n = 2 and delocalized n = 3, in uranium materials, where n is the number of 5f electrons on the U entity. Here, it is shown that, by employing the ubiquitous 6p → 3d XES as a point of normalization, the localized n = 2 and delocalized n = 3 cases can be easily distinguished and quantified.

The Limitations of 5f Delocalization and Dispersion

“…There is a remarkable level of agreement between the earlier measurements of Baer and Lang [14,15] and the theory from Kutepov et al [8,16,17]. The X-ray Photoelectron Spectroscopy (XPS) and Bremsstrahlung Isochromat Spectroscopy (BIS, a type of high energy inverse photoelectron spectroscopy) provide a good measure of the occupied (ODOS) and unoccupied (UDOS) density of states, respectively.…”

“…The X-ray emission and absorption spectroscopy (XES and XAS) measurements were carried out at the Stanford Synchrotron Radiation Lightsource (SSRL), the particulars of which are described elsewhere [17,26,27]. The details of the other experiments and calculations can be found in the source articles, quoted in the text and cited as references below.…”

“…However, before considering the extant ARPES results for U, it is useful to define some of the experimental conditions and review some cases of successful analyses with ARPES. Thus, the sections that follow are: Section 2-experiment; Section 3-digression on ARPES; Section [14] from the Naegele review [15] Lower panel: Theory results from Kutepov [8,16,17]. E F is the Fermi energy (0 eV), shown as a blue vertical line.…”

“…It has also recently been shown that while the XAS branching ratio depends upon the 5f 5/2 /5f 7/2 mixing of the unoccupied 5f states, the XES cross sectional variation is driven by the 5f 5/2 /5f 7/2 mixing of the occupied 5f states [17]. It can be shown that for UF 4 and UO 2 , where n = 2, and U metal, where n = 3, the 5f 5/2 /5f 7/2 mixing of the unoccupied 5f states is the same but the 5f 5/2 /5f 7/2 mixing of the occupied 5f states is distinctly different (see Reference [17] for the full derivation and other details). Using the model developed in Reference [17], it can be shown that the M 4 XES of UF 4 and U metal should be significantly different, as illustrated below in Figure 13.…”

“…It can be shown that for UF 4 and UO 2 , where n = 2, and U metal, where n = 3, the 5f 5/2 /5f 7/2 mixing of the unoccupied 5f states is the same but the 5f 5/2 /5f 7/2 mixing of the occupied 5f states is distinctly different (see Reference [17] for the full derivation and other details). Using the model developed in Reference [17], it can be shown that the M 4 XES of UF 4 and U metal should be significantly different, as illustrated below in Figure 13.…”