High-resolution X-ray absorption spectroscopy as a probe of crystal-field and covalency effects in actinide compounds

Significance

This work is to our knowledge the first illustration of the ability of the high-energy resolution fluorescence-detection X-ray absorption spectroscopy (HERFD-XAS) technique to directly probe the crystal-field splitting in the 5f shell of actinides. This is a breakthrough for actinide science, allowing for the easy extraction of desired information from the spectroscopic method, which is easy to interpret and to calculate. Furthermore, the HERFD-XAS technique allows us to resolve the charge-transfer satellites in actinide spectra that were hidden before, thus enhancing the sensitivity to the covalent character of the chemical bonding. Using ThO₂ as an example, we show that other common techniques underestimate the crystal-field strength and that ThO₂ is not an anionic compound as previously believed.

Abstract

Applying the high-energy resolution fluorescence-detection (HERFD) mode of X-ray absorption spectroscopy (XAS), we were able to probe, for the first time to our knowledge, the crystalline electric field (CEF) splittings of the $5f$ shell directly in the HERFD-XAS spectra of actinides. Using ThO₂ as an example, data measured at the Th 3d edge were interpreted within the framework of the Anderson impurity model. Because the charge-transfer satellites were also resolved in the HERFD-XAS spectra, the analysis of these satellites revealed that ThO₂ is not an ionic compound as previously believed. The Th $6d$ occupancy in the ground state was estimated to be twice that of the Th $5f$ states. We demonstrate that HERFD-XAS allows for characterization of the CEF interaction and degree of covalency in the ground state of actinide compounds as it is extensively done for 3d transition metal systems.

For strongly electron-correlated systems, X-ray absorption spectroscopy (XAS) is viewed as a technique capable of providing information on the ground-state character despite the presence of the core hole in the final state of the spectroscopic process. In the 3d transition metal compounds, XAS at the metal 2p edge is routinely used to probe the magnitude of the crystalline electric field (CEF) splittings in the 3d shell and the degree of the 3d hybridization in the ground state (1).

However, for the $5f$ shell of actinides, such a use of XAS is difficult. At the U 3d and 4d edges, where the transitions to the 5f states are probed, core-hole lifetime broadenings [full width at half maximum (FWHM)] are about 3.2 eV and 4.2 eV, respectively (2), whereas at the 5d edge, the broadening can be as large as 6.0 eV. Therefore, the conventional XAS spectra of actinide materials at the 3d and 4d edges often appear as single lines where splittings of the 5f states (e.g., due to the CEF interaction) are completely smeared out (3–8).

The CEF effects for actinides are usually characterized with the help of optical absorption (reviewed in ref. 9) and electron paramagnetic resonance (EPR) (10, 11) spectroscopies but that is often done on doped systems when the actinide ions in question are introduced into the lattice of a compound without 5f electrons. Another high-resolution technique that can provide information about the CEF splittings is inelastic neutron scattering (INS) (12, 13) but the spectra usually cover a very limited energy range. In both optical absorption and INS spectroscopies, the CEF strength and parameters are evaluated by fitting the calculated energy levels of the CEF Hamiltonian to the energies of the measured lines of the 5f–5f transitions, whereas attempts to calculate spectral intensities are rare.

On the other hand, for XAS at the $3d$ threshold of actinides it is relatively straightforward to calculate both energy levels and spectral intensities due to dipole selection rules. The effects of the hybridization of the valence states of actinides with ligand states in compounds and the charge transfer between ligand and actinide sites are expected to result in the appearance of charge-transfer satellites in the XAS spectra. The interpretation of such satellites can provide information on the degree of the $5f$ hybridization, covalency of the compound, and the nature of the ground state.

An advanced technique, high-energy resolution fluorescence-detection X-ray absorption spectroscopy (HERFD-XAS), has been recently used for measurements at the 3d edge of U compounds (14, 15). This has led to a tremendous improvement in the experimental resolution and revealed additional structures in the XAS spectra, not measurable before. We demonstrate, using ThO₂, that the HERFD-XAS technique now allows us to directly probe the CEF splittings in the $5f$ shell with the results clearly shown in the spectra. An analysis of the newly resolved charge-transfer satellites indicates significant occupancy of Th valence states, which contradicts the common view of ThO₂ as an ionic system.

Materials and Methods

The measurements at the Th $3d$ edge were performed at beamline ID26 (16) of the European Synchrotron Radiation Facility in Grenoble, France. The XAS data were measured in the HERFD mode, using an X-ray emission spectrometer (17). The HERFD spectrum of ThO₂ at the Th $M_4$ ($3d_{3/2}\to 5f_{5/2},7p$ transitions) edge was obtained by recording the outgoing photons with an energy of ∼3,145.7 eV as a function of the incident energy. This emission energy corresponds to the maximum of the Th $M\beta$ ($4f_{5/2}\to 3d_{3/2}$ transitions) line. The directions of the incident and emitted photons were 45° to the surface of the sample. A total energy resolution of 0.4 eV was determined by measuring the FWHM of the elastic peak. The sample of reference bulk ThO₂ as characterized and used in refs. 18 and 19 was used for these experiments.

Experiments at the Ce $M_{\mathrm{4,5}}$ edges ($3d\to 4f,6p$ transitions) of CeO₂ were performed at beamline 7.0.1 of the Advanced Light Source, Lawrence Berkeley National Laboratory (20). The data were measured in the total electron yield (TEY) mode, using drain current from the sample. The incidence angle of the incoming photons was close to 90° with respect to the surface of the samples. The monochromator resolution was set to ∼500 meV at 890 eV. The CeO₂ sample was a pressed pellet from powder acquired from Alfa-Aesar.

The calculations were performed in framework of the Anderson impurity model (21) (AIM) in a manner described in refs. 22 and 23. Besides the inclusion of the full multiplet due to actinide intraatomic interactions, the CEF acting on the $5f$ shell (24) was taken into account.

To simulate a spectrum obtained in the HERFD-XAS mode, the resonant inelastic X-ray scattering (RIXS) map around the actinide $M\beta$ line was calculated using the Kramers–Heisenberg formula

$$\begin{array}{c}{I}_{q_2,q_1}\left(\omega ,\omega \prime \right)={{\displaystyle \sum _j\left|{\displaystyle \sum _m\frac{\langle j\left|r{C}_{q_2}^{\left(1\right)}\right|m\rangle \langle m\left|r{C}_{q_1}^{\left(1\right)}\right|g\rangle }{E_g+\omega -E_m-i{\mathrm{\Gamma }}_m/2}}\right|}}^2\\ \times \frac{{\mathrm{\Gamma }}_j/\pi }{{\left(E_j+\omega \prime -E_g-\omega \right)}^2+{\mathrm{\Gamma }}_j^2},\end{array}$$ [1]

where $|g\rangle ,$ $|m\rangle ,$ and $|j\rangle$ are the ground, intermediate, and final states of the spectroscopic process with energies $E_g,$ $E_m,$ and $E_j,$ respectively. ω and $\omega \prime$ are the energies of the incident and scattered/emitted photons with polarizations $q_1$ and $q_2,$ respectively, and ${\mathrm{\Gamma }}_m$ and ${\mathrm{\Gamma }}_j$ are the lifetime broadenings of the intermediate and final states in terms of half width at half maximum (HWHM). Operators for optical dipole transitions (D) are expressed in terms of spherical tensor operators $C_q^{\left(1\right)}.$ The HERFD-XAS spectrum is represented by a linear cut of such a RIXS map (14) along the diagonal of the plane defined by the incident energy axis and energy transfer axis or parallel to the incident energy axis at a constant emitted energy (the energy of the line maximum in this case) in the plane of the emitted vs. incident energies. The required Slater integrals $F^k,$ $G^k,$ and $R^k$ (25); spin-orbit coupling constants ζ; and matrix elements were obtained with the modified TT-MULTIPLETS package (26–28).

Results and Discussion

The main reason for the improved resolution of the HERFD-XAS spectrum is a reduced core-hole lifetime broadening. For example, in HERFD-XAS measurements at U $M_{\mathrm{4,5}}$ edges, the $3d$ core hole is replaced by the $4f$ core hole in the final state of the spectroscopic process (Fig. 1). This results in approximately four times better resolution because the $4f$ core-hole lifetime broadening (FWHM) is estimated to be ∼0.8 eV (29) vs. ∼3.2 eV for the $3d$ core hole.

Fig. 1.

Schematic representation of HERFD process for actinides (An), using 3d-to-4f transitions.

A schematic representation of the HERFD spectroscopic process involving the $3d\to 5f$ electronic excitations with the consequent $4f\to 3d$ deexcitations at the actinide (An) atom is shown in Fig. 1, using a many-body approach. A couple of arbitrary transitions between the ground state of the system described by the $3d^{10}5f^n$ electronic configuration and core-excited states of the $3d^{9}5f^{n+1}$ configuration for varying incident photon energy ω are depicted. The core-excited states decay to the states of the $4f^{13}5f^{n+1}$ configurations with the emittance of a photon and only photons with an energy equal to $\omega \prime$ are detected.

Fig. 2A displays the RIXS map around the $M\beta$ line of the Th(IV) ion in the cubic (eightfold ligand coordination) CEF environment calculated with Eq. 1 for the route $3d^{10}5f^0\to 3d^{9}5f^1\to 4f^{13}5f^1$ with ${\mathrm{\Gamma }}_m$ and ${\mathrm{\Gamma }}_j$ set to 1.65 eV and 0.3 eV, respectively. The experimental X-ray polarization geometry was taken into account in calculations. Fig. 2B shows the calculated conventional XAS and HERFD-XAS spectra at the Th(IV) $M_4$ edge. The conventional XAS spectrum is represented by the transitions between the $3d^{10}5f^0$ (ground state) and $3d^{9}5f^1$ (excited state) configurations. The HERFD-XAS spectrum is represented by the corresponding cut in the RIXS map. The result of the cut is a one-dimensional spectrum of intensity vs. incident energy ω obtained for fixed $\omega \prime$ corresponding to the main maximum of the $4f_{5/2}\to 3d_{3/2}$ line. In both cases, the Hartree–Fock values of the Slater integrals were scaled down to 80% (the reasoning is in ref. 30) and Wybourne’s CEF parameters (24) for the $5f$ shell were set to $B_0^4=-1.3$ eV and $B_0^6=0.55$ eV. Although the effects of the hybridization of Th states with ligand states (which lead to an appearance of low-intensity high-energy satellites, described below) were not taken into account, we can conclude that the conventional XAS and HERFD-XAS spectra agree with each other quite well. To simplify the computational framework, we compare the experimental HERFD-XAS data to calculations from conventional XAS.

Fig. 2.

Calculated RIXS map around the $M\beta$ line of the Th(IV) ion in the cubic CEF environment (A) and HERFD-XAS and conventional XAS spectra at the Th(IV) $M_4$ edge (B).

CeO₂ is often used by researchers in the actinide science as a model compound and nonradioactive replacement of ThO₂ (UO₂) as an approximation for the physical and chemical properties and dynamic behavior of actinide materials in particular situations. However, there are significant differences between CeO₂ and ThO₂ from the electronic structure point of view. According to the local-density approximation with added Coulomb U interaction (LDA + U) calculations (31), the top of the valence band consists mainly of the O $2p$ and Ce $5d$ states whereas the bottom of the conduction band is dominated by Ce $4f$ states. In ThO₂, however, the unoccupied Th $5f$ states lie higher in energy so that the main weight at the bottom of the conduction band is formed by the Th $6d$ states. CeO₂ is considered a highly covalent compound and ThO₂ is not.

The spectra recorded at the $M_4$ edge of ThO₂ and CeO₂ also reveal some differences as shown in Fig. 3. Because the $M_4$ edge of ThO₂ is represented by the $3d\to 5f$ transitions and the $M_4$ edge of CeO₂ is represented by the $3d\to 4f$ transitions, the spectra were brought onto the same energy scale by setting the energy of the main maximum to 0 eV. The CeO₂ spectrum exhibits a distinct and strong high-energy satellite at ∼5.5 eV above the main line whereas only weak high-energy structures at around 2.2 eV, 4.2 eV, and 6.4 eV above the main maximum are found in ThO₂. In addition, the main line of the ThO₂ spectrum has a shoulder at ∼0.8 eV. The high-energy satellite in the CeO₂ spectrum has been discussed before (22, 32) and shown to arise from Ce $4f-$O $2p$ charge transfer as a result of strong Ce $4f-$O $2p$ hybridization and significant $4f^0$ and $4f^1{\underset{¯}{\upsilon }}^1$ configurational mixing in the ground state, where $\underset{¯}{\upsilon }$ stands for an electronic hole in the O $2p$ band. The XAS spectrum at the Ce $M_{\mathrm{4,5}}$ edges of CeO₂ was well reproduced by the AIM calculations for the Ce(IV) system. The CeO₂ spectrum appears significantly broader than that of ThO₂ because of a wider multiplet spread of the $3d^{9}4f^2{\underset{¯}{\upsilon }}^1$ configuration caused by the stronger $3d$–$4f$ interaction compared with the $3d\left(4f\right)$–$5f$ interaction in ThO₂ (figure 5 in ref. 32). The $4f$ occupancy in the ground state was found to be about 0.5 electrons, which confirms the highly covalent character of CeO₂.

Fig. 3.

XAS spectra at $M_4$ edge of CeO₂ and ThO₂.

For ThO₂, if the values for the AIM parameters previously used (33) to calculate the Th $4f$ X-ray photoemission (XPS) spectrum are adopted for calculations of the XAS spectrum at the Th(IV) $M_4$ edge, it is difficult to reproduce the high-energy (charge-transfer) satellites. This is because the emphasis in the XPS calculations was on the Th $5f-$O $2p$ hybridization and charge transfer so that the ground state of the system was described as a mixture of the $5f^0$ and $5f^1{\underset{¯}{\upsilon }}^1$ configurations (see also ref. 34). However, the Th $6d-$O $2p$ charge transfer might be more energetically favorable because the Th $6d$ states are dominant at the bottom of the conduction band of ThO₂. The charge-transfer energy is expected to be lower so that it is easier for an electron to hop from the O 2p band into unoccupied Th $6d$ states and the ground state of the system can be expressed as a mixture of the $5f^0,$ $5f^{0}6d^1{\underset{¯}{\upsilon }}^1,$ and $5f^1{\underset{¯}{\upsilon }}^1$ configurations.

Fig. 4 shows that the latter approach allows one to obtain the high-energy structures in the calculated XAS spectrum at the Th $M_4$ edge. In particular, the structure at around 3,492.5 eV appears in the calculated spectrum upon inclusion of the Th $6d-$O $2p$ charge transfer via Th 6d − Th 5f − O 2p hybridization. The multiplet poles of the calculated transitions can also be found at energies around 3,490.5 and 3,493.7 eV, although their intensities are lower in comparison with the corresponding structures in the measured spectrum. Note that the dashed curve in Fig. 4 is a HERFD-XAS spectrum corrected for self-absorption effects by using the algorithm implemented in the “XANES dactyloscope” program (https://www.cells.es/en/beamlines/bl22-claess/software). We point out that self-absorption correction algorithms used by the XAS community do introduce some uncertainty for the absorption edges with sharp and strong lines and low postedge background contribution, such as $L_{\mathrm{2,3}}$ edges of transition elements and $M_{\mathrm{4,5}}$ edges of rare earths and actinides.

Fig. 4.

Experimental and calculated XAS spectra at the Th $M_4$ edge of ThO₂. The spectra are calculated using atomic and CEF multiplet theory for the Th(IV) ion and the Anderson impurity model, respectively. The dashed curve represents the HERFD-XAS spectrum corrected for self-absorption effects (https://www.cells.es/en/beamlines/bl22-claess/software) and normalized to the maximum of the as-measured spectrum.

In our AIM calculations for the Th(IV) system, the ground (final) state for the XAS process was described as a combination of the $5f^0,$ $5f^{0}6d^1{\underset{¯}{\upsilon }}^1,$ and $5f^1{\underset{¯}{\upsilon }}^1$ ($3d^{9}5f^1,$ $3d^{9}5f^{1}6d^1{\underset{¯}{\upsilon }}^1,$ and $3d^{9}5f^2{\underset{¯}{\upsilon }}^1$) configurations. The model parameters had the following values: $U_{ff}=4.0$ eV, $U_{fc}=6.0$ eV, $U_{dc}-U_{df}=2.0$ eV, $V_g=1.1$ eV, and $V_m=0.7$ eV, where $U_{ff}$ ($U_{df}$) and $U_{fc}$ ($U_{dc}$) are the $5f-5f$ ($6d-5f$) Coulomb interaction and core-hole potential acting on the $5f$ ($6d$) electron, respectively, and $V_g$ and $V_m$ are hybridization terms in the ground and final states. $V_m$ was set smaller to take into account the configuration dependence (35) of V. Whereas in the LDA + U calculations (31, 36) for ThO₂ somewhat larger values of $U_{ff}$ were applied (5 eV and 6 eV, respectively), $U_{ff}\simeq 4.0$ eV was deduced from the fit of the Th $4f$ XPS data (33). In addition, according to estimations in ref. 37, $U_{df}$ can be as large as $U_{df}\simeq U_{fc}/2.$

In the limit of $V\to 0,$ the difference between the configuration averaged energies for the ground state was $E\left(5f^{0}6d^1{\underset{¯}{\upsilon }}^1\right)-E\left(5f^0\right)={\mathit{ϵ}}_{6d}-{\mathit{ϵ}}_n=5.0$ eV and $E\left(5f^1{\underset{¯}{\upsilon }}^1\right)-E\left(5f^0\right)={\mathit{ϵ}}_f-{\mathit{ϵ}}_n=8.0$ eV and for the final state it was $E\left(3d^{9}5f^{1}6d^1{\underset{¯}{\upsilon }}^1\right)-E\left(3d^{9}5f^1\right)={\mathit{ϵ}}_{6d}-{\mathit{ϵ}}_n+U_{df}-U_{dc}=3.0$ eV and $E\left(3d^{9}5f^2{\underset{¯}{\upsilon }}^1\right)-E\left(3d^{9}5f^1\right)={\mathit{ϵ}}_f-{\mathit{ϵ}}_n+U_{ff}-U_{fc}=6.0$ eV, where ${\mathit{ϵ}}_f,$ ${\mathit{ϵ}}_{6d},$ and ${\mathit{ϵ}}_n$ are one-electron energies of Th $5f,$ $6d,$ and O $2p$ levels. The Slater integrals were scaled down to 80% of their Hartree–Fock values. The CEF parameters for the Th $5f$ shell were set to $B_0^4=-1.30$ eV and $B_0^6=0.55$ eV and for the Th $6d$ shell to $10Dq=-3.5$ eV (38). ${\mathrm{\Gamma }}_m$ was set to 0.3 eV and an additional Gaussian broadening was applied to match the experimental resolution.

These calculations gave the contributions of the $5f^{0}6d^1{\underset{¯}{\upsilon }}^1$ and $5f^1{\underset{¯}{\upsilon }}^1$ in the ground state of ThO₂ to be 20% and 11%, respectively; i.e., the occupancy of the Th $6d$ states (0.20 electrons) is larger than that of the Th $5f$ states (0.11 electrons). This result does not support the ionic character of ThO₂ and is also in agreement with the LDA + U (36) and hybrid-density functional (39) calculations that show the occupied Th 6d density of states (DOS) in the valence band of ThO₂ to be about two times higher than the occupied Th 5f DOS.

The improved resolution of the HERFD-XAS technique allows us to resolve the shoulder at ∼0.8 eV above the main maximum of the Th $M_4$ edge of ThO₂ (conventional XAS spectra in refs. 4 and 40). The origin of this shoulder becomes clear from a comparison of the experimental data with atomic and CEF multiplet theory for the Th(IV) ion in Fig. 4. The atomic multiplet calculations for the transitions between the $3d^{10}5f^0$ and $3d^{9}5f^1$ configuration in the ¹$S_0$ ground state produce a single multiplet pole whereas putting the Th(IV) ion in the cubic (O_h) CEF environment reveals CEF split states of the $3d^{9}5f^1$ configuration, thus producing the shoulder at ∼0.8 eV above the main peak in the calculated spectrum for the CEF parameter values of $B_0^4=-1.30$ eV and $B_0^6=0.55$ eV. The improvement in resolution offered by HERFD-XAS now allows probing the CEF interactions for the $5f$ shell and extracting the information about the CEF effects directly from the XAS data in the manner commonly used for the $L_{\mathrm{2,3}}$ edges of $3d$ transition metal systems.

Specifically for ThO₂, it is difficult to accurately determine the CEF strength with other techniques. For commonly used methods, such as optical and EPR spectroscopies, the ThO₂ sample is usually doped with a small concentration of another actinide ion into the ThO₂ lattice to observe the $5f-5f$ excitation pattern in the spectra. However, this may cause a local lattice distortion around the doped actinide ion, thus generating larger uncertainties in quantities derived from the fit of the spectra. For example, our determined values for CEF parameters $B_0^4$ and $B_0^6$ are somewhat larger than those obtained for Am-doped (41) and Cm-doped (42) ThO₂.

Improved energy resolution demonstrates the shape sensitivity of the actinide $M_4$ edge to the strength of the crystal-field interaction and to the degree of covalency in the chemical bonding. Therefore, as in case of the $L_{\mathrm{2,3}}$ edges of $3d$ transition metal systems, detailed analysis of the $M_{\mathrm{4,5}}$ edges spectral shapes of actinide compounds with the partially filled $5f$ shell enables characterization of the ground state and low-lying excited states that define physical properties of these compounds (for example, analysis of the results of the temperature-dependent measurements or measurements in varying X-ray polarization geometries).