Synchrotron radiation techniques and their application to actinide materials

Research on actinide materials, both basic and applied, has been greatly advanced by the general techniques available from high-intensity photon beams from x-ray synchrotron sources. The most important single reason is that such x-ray sources can work with minute (e.g., microgram) samples, and at this level the radioactive hazards of actinides are significantly reduced. The form and encapsulation procedures used for different techniques are discussed, followed by the basic theory for interpreting the results. To demonstrate the potential of synchrotron radiation techniques for the study of lattice and electronic structure, hybridization effects, multipolar order, and lattice dynamics in actinide materials, a selection of x-ray diffraction, resonant elastic x-ray scattering, x-ray magnetic circular dichroism, resonant and nonresonant inelastic scattering, dispersive inelastic x-ray scattering, and conventional and resonant photoemission experiments are reviewed.

Figure 1

Atomic volume of the transition ($3d$), rare-earth ($4f$), and actinide ($5f$) elements as a function of electron count. Note the unusual shape of the curve for the actinide series. In the case of Eu and Yb the large expansion is due to these elements being stable in the divalent state. All other rare-earth elements have the trivalent ground state. From [69].

Figure 2

Hermetic sample holders used for investigating actinide materials with different synchrotron-radiation-based techniques. (a) Low-temperature powder x-ray diffraction ([184]). (b) Inelastic x-ray scattering in transmission geometry ([442]). (c) X-ray magnetic circular dichroism ([240]) and nonresonant inelastic x-ray scattering ([381]). (d) Inelastic x-ray scattering in reflection geometry ([268]). (c),(d) Images of ${}^{248}\mathrm{Cm}$ ($0.6\times 0.8\times 0.1{\mathrm{mm}}^3$, $m\approx 650\mathit{\mu }\mathrm{g}$) and ${\mathrm{NpO}}_2$ ($0.78\times 0.56\times 0.25{\mathrm{mm}}^3$, $m\approx 1.2\mathrm{mg}$) samples used for the studies described by [268] and [240].

Figure 3

Schematic layout of the ROBL-II beamline at the European Synchrotron Radiation Facility (ESRF), Grenoble. Insets: powder x-ray diffraction, x-ray emission spectroscopy, and x-ray absorption fine-structure stations. Adapted from [354].

Figure 4

Feynman diagrams representing the scattering amplitude. (a) First-order diagram for photon absorption with interaction $H_2^{\prime }$ or $H_3^{\prime }$. (b) First-order diagram for photon scattering with interaction $H_1^{\prime }$ or $H_4^{\prime }$. (c) Second-order diagram for photon scattering (see the text). Not shown is another second-order Feynman diagram with emission followed by absorption, which contributes to the nonresonant scattering.

Figure 5

Schematic representation of the experimental geometry for nonresonant magnetic diffraction measurements. The incident photon beam is polarized perpendicularly to the scattering plane ($\sigma$ polarization, from the initial of the German word senkrecht). $S$ is the sample, $D$ is the detector, and $A$ is the analyzer crystal allowing one to select the components of the scattered beam with polarization parallel (${\pi }^{\prime }$) or perpendicular (${\sigma }^{\prime }$) to the scattering plane. Integrated intensities of the Bragg peaks are measured as a function of the photon energy for different values of the azimuthal angle ($\rho$) defining the crystal orientation about the scattering vector (hkl). The unit vectors ${\mathbf{u}}_i$ define the reference frame. From [73].

Figure 6

Schematic representation of RIXS, a two-step process involving first the absorption of a photon and the promotion of a core electron into an empty valence state, followed by the emission of a photon with smaller energy and the filling of the core hole by an electron sitting either (a) in a core level (direct core-to-core RIXS) or (b) in the occupied valence band (direct valence-to-core RIXS). The process probes the convolution between empty (absorption step) and occupied (emission step) densities of states and leaves an electron-hole excitation in the final state. Adapted from [69].

Figure 7

Pressure dependence of the normalized unit cell volume $V(p)/V_0$ for $\alpha$-uranium ([250]), americium ([258]), and curium ([176]). Inset: typical diamond-anvil cell used for angle-dispersive, high-pressure x-ray diffraction experiments. Adapted from [176].

Figure 8

X-ray diffraction pattern recorded for ${\mathrm{PuCoGa}}_5$ at 5 K. Left inset: tetragonal crystallographic unit cell, with Pu and Co atoms represented by blue and red spheres, respectively. The two inequivalent Ga atoms are shown as orange and yellow spheres. Right inset: $(220)$ Bragg peak measured at 5 (black circles) and 155 K (red circles). Adapted from [125].

Figure 9

Thermal expansion coefficient for the unit cell volume of ${\mathrm{PuCoGa}}_5$ (on an expanded scale around $T_c$ in the inset). Error bars have been estimated as 5 times the statistical error provided by the Rietveld refinement and are smaller than the data symbol size. Adapted from [125].

Figure 10

(a) Refined slab contractions and (b) interstitial occupancies vs depth and three-layer periodicity. (c) Proposed model for an oxidized ${\mathrm{UO}}_2$ $(111)$ surface. U, cyan; structural O, red; surface O adatoms, magenta; interstitial O, hatched red. The surface is oxygen terminated. The $YZ$ projection of the surface unit cell is indicated by the blue dashed lines. From [380].

Figure 11

(a) Waterfall plot of fits to the integrated intensity along the full diffraction angle $2\theta$ of selected fields at 15 K. The peak at lower $2\theta$ (blue) corresponding to expansion is much larger than the peak at higher $2\theta$ (red). (b) Peak positions of the two peaks at 15 K, with filled symbols corresponding to a rising field and open symbols to a falling field. The red circles represent the smaller peak and blue squares indicate the larger one. The blue peak and its positive magnetostriction can be seen to match magnetostriction measurements using the fiber Bragg grating technique (black line), with an $\sim 150\mathrm{pp}\mathrm{m}$ expansion at the maximum 21.1 T applied field. The red dashed line is a guide for the eye. From [11].

Figure 12

Three-dimensional segmentation of the propagation-based phase contrast enhanced tomography images of a U-10Zr FIB cuboid indicating (a) the pores and (b) a composite image of pores and all three phase regions. From [395].

Figure 13

Integrated intensity of the $(003)$ superlattice Bragg peak as a function of the photon energy around the $M_5$ and $M_4$ absorption edge of U and Np in ${\mathrm{UO}}_2$ and ${\mathrm{NpO}}_2$, respectively. Data were collected in the ordered phase, with the incident beam polarized perpendicularly to the diffraction plane ($\sigma$) and the scattered photon beam polarized in the diffraction plane ($\pi$). The intensity data are corrected for self-absorption. The maxima of the intensity enhancement occur at the electric-dipole transition threshold energy and are associated with $3d_{3/2,5/2}\to 5f$ transitions. Note that the shape of the $M_4$ resonance in ${\mathrm{NpO}}_2$ is a Lorentzian squared, as predicted by [296]. Inset: sketch of the scattering geometry used to measure the integrated intensity as a function of the azimuthal angle $\rho$ describing the rotation of the sample about the scattering vector. The arrows $ϵ(\sigma ,\pi )$ correspond to the polarization direction of photons polarized perpendicularly ($\sigma$) or parallel ($\pi$) to the scattering plane. Adapted from [69].

Figure 14

Schematic representation of the projection onto the $a\text{−}b$ plane of the $3\mathbf{k}$ magnetic-dipole and electric-quadrupole ordering for (a) the longitudinal configuration and (b),(c) the two $S$ domains of the transverse configuration. The magnetic-dipole moments are represented by blue arrows, whereas the electric-quadrupole moments are shown as green ellipsoids. The red spheres represent oxygen atoms. ${\mathrm{UO}}_2$ adopts the transverse structure, whereas the electric-quadrupole longitudinal order is realized in ${\mathrm{NpO}}_2$ with zero magnetic-dipole moment. Adapted from [451].

Figure 15

Azimuthal angle dependence of the Stokes parameters $P_1$ and $P_2$ for the $(001)$ and $(003)$ superlattice reflections measured in ${\mathrm{NpO}}_2$ at 10 K with $E=3.846\mathrm{keV}$. The origin of the azimuthal angle $\rho$ corresponds to the $a$ axis lying in the scattering plane. The lines are calculations based on a longitudinal $3\mathbf{k}$ order of ${\mathrm{\Gamma }}_5$ electric quadrupoles with an ordered magnetic-dipole moment equal to zero. No fitting parameters are involved. Adapted from [72].

Figure 16

Top panel: azimuthal dependence of the $(201)$ Bragg reflection in ${\mathrm{URu}}_2{\mathrm{Si}}_2$. Solid (red) circles, $\sigma \pi$ channel; black squares, $\sigma \sigma$ channel. The solid (red) line is the theoretical intensity variation for magnetic dipoles ordered along $[001]$. The dashed red (dashed blue) line is the $\sigma \pi$ ($\sigma \sigma$) $\rho$ dependence of the intensity expected for $xy$ quadrupole order. Bottom panel: experimental data compared with theoretical predictions for a dipole magnetic moment with an increasing component in the $a\text{−}b$ crystallographic plane. Adapted from [435].

Figure 17

Measurements at the As $K$ edge of the integrated intensity in the $\sigma \pi$ channel of the $(0.5,0,6)$ reflection in UAs at $T=20\mathrm{K}$ as a function of the azimuthal angle around the normal to the $[001]$. Insets: geometry and schematic of the Fourier component of the magnetic structure of UAs giving rise to this reflection, where the propagation vector of the structure is $[100]$. The azimuthal angles $\mathrm{\Psi }=0°$ and 180° correspond to the $[100]$ axis lying in the scattering plane, which are defined by incident and scattered wave vectors $\mathbf{k}$ and ${\mathbf{k}}^{\prime }$, respectively. From [277].

Figure 18

Pu $L_3$ edge XANES (normalized absorbance) for a series of plutonium molecules and compounds in different formal oxidation states. (a) Gallium stabilized $\delta$-Pu metal compared to the plutonium aqua ions in oxidation states III-VI and the Pu(VII) oxohydroxide. The spectra of Pu(0)–Pu(VI) are replotted from the original data reported by [88], and data for Pu(VII) in a $2M$ NaOH solution are courtesy of M. Antonio of ANL. (b) The peak amplitude of the $\delta$-Pu alloy is suppressed by self-absorption in this opaque sample. The XANES spectra of gallium stabilized $\delta$-Pu metal is compared to a number of binary plutonium compounds, including ${\mathrm{PuO}}_2$, which represents Pu(IV). Adapted from [88], and [205].

Figure 19

Experimental and calculated HERFD-XANES spectra at the U $M_4$ edge of ${\mathrm{U}}_4{\mathrm{O}}_9$ and ${\mathrm{U}}_3{\mathrm{O}}_8$ compared to those of the reference systems ${\mathrm{UO}}_2$ and ${\mathrm{UO}}_2{(acac)}_2$. The dashed lines indicate the energy position of the main peaks corresponding to uranium(IV) and uranium(VI), respectively. From [228].

Figure 20

Distribution of U–O bonds in the average unit cell of ${\mathrm{U}}_3{\mathrm{O}}_7$ at 18 K. The structural model assumes a regular geometry of cubo-octahedral oxygen clusters. The histograms in red and green correspond to fluorite-type and additional U-O bonds, respectively. The blue diamonds and magenta squares are EXAFS results reported on by [251] and [204], respectively. From [251].

Figure 21

(a) XAS spectra of ${\mathrm{UGe}}_2$ measured at the U $N_{4,5}$ absorption edges at 5 K in a magnetic field of 4 T. (b) XMCD signal measured at different temperatures and applied magnetic fields. From [385].

Figure 22

XMCD spectra as a function of photon energy through the An $M_{4,5}$ edges in ${\mathrm{AnFe}}_2$ ($\mathrm{An}=\text{U}$, Np, Pu, Am) and elemental Cm. The spectra have been corrected for self-absorption effects and incomplete circular polarization of the incident beam. Adapted from [240].

Figure 23

The ratio $3⟨T_z⟩/⟨S_z⟩$ between the expectation values of the magnetic-dipole term and the spin moment along the quantization direction as a function of the $5f$ occupation number $n_f$. The symbols represent experimental data obtained from an analysis of XMCD spectra at the $M_{4,5}$ actinide edges for compounds with different physical properties and crystallographic structure (circles for C-15 cubic Laves phases, upside-down triangles for the NaCl-type structure, standard triangles for hexagonal lattice, and squares for orthorhombic cells). Theoretical estimates are shown for intermediate coupling (IC) (solid lines), Russell-Saunders (dashed line), and $jj$ (dotted line) coupling approximations. All the calculated values refer to the free-ion ground state except for the $f^6$ configuration, where $J$ mixing with the first excited state is taken into account; otherwise, the ratio cannot be determined, since all quantities would be zero for the ground state. Adapted from [264].

Figure 24

XAS (solid black lines) and XMCD spectra as a function of photon energy through the Pu $M_5$ (red line) and $M_4$ (blue line) edges in ${\mathrm{PuCoGa}}_5$. Adapted from [266].

Figure 25

XMCD measurements for ${\mathrm{UCu}}_2{\mathrm{Si}}_2$ and ${\mathrm{UMn}}_2{\mathrm{Si}}_2$ performed at temperatures of 10 and 300 K, respectively. The positions of the electric-dipole and quadrupolar transitions are marked. From [119].

Figure 26

XMCD signal at the $M_4$ edge from three different Pu materials: the localized system PuSb ([199]), the heavy-fermion superconductor ${\mathrm{PuCoGa}}_5$ ([266]), and the bandlike system ${\mathrm{PuFe}}_2$ ([448]).

Figure 27

U $N_4$-edge RIXS spectra of ${\mathrm{UO}}_2$ at $T=15\mathrm{K}$. Data were taken with a photon energy of 778 eV for $\sigma$ linear polarization, as shown in the inset. The red lines show the RIXS spectrum calculated for the ${\mathrm{U}}^{4+}$ $5f^2$ configuration and crystal-field parameters consistent with inelastic neutron scattering. The blue lines show the underlying multiplet peaks (without line broadening) of the crystal-field excitations around 180 meV and those for the ${}^3{F}_2$ multiplet around 550 meV. Adapted from [239].

Figure 28

NIXS spectra for ${\mathrm{UO}}_2$ at the uranium $O_{4,5}$ edges measured with a fixed final energy of 9.689 keV at different values of the scattering vector $Q$. Data at different $Q$ values are normalized to the peak intensity of the feature centered at about 104 eV. Adapted from [74].

Figure 29

Difference between the experimental NIXS spectra measured at the uranium $O_{4,5}$ edges in single-crystal ${\mathrm{UO}}_2$ with a momentum transfer direction $\mathbf{Q}=\mathbf{Q}/Q$ along $[001]$ and $[111]$. Calculations assuming a ${\mathrm{\Gamma }}_5$ triplet crystal-field ground state and a crystal-field potential strength compatible with inelastic neutron scattering experiments are indicated by the solid line. Adapted from [382].

Figure 30

NIXS measurements of the U $O_{4,5}$ edge of ${\mathrm{URu}}_2{\mathrm{Si}}_2$ for $Q=9.6{\AA }^{-1}$ and corresponding calculations for $5d^{10}$$5f^2\to 5d^9$$5f^3$. (a) Simulation of $S(\mathbf{Q},w)$ of U crystal-field states for $J=4$ in $D_{4h}$ symmetry for the two directions $\mathbf{Q}\parallel [001]$ (red) and $\mathbf{Q}\parallel [100]$ (blue). Insets: the corresponding electron densities. (b) NIXS data for momentum transfers $\mathbf{Q}\parallel [100]$ (blue) and $\mathbf{Q}\parallel [001]$ (red) at $T=25\mathrm{K}$. (c) Dichroism at 25 K in a percentage defined as the difference $I(\mathbf{Q}\parallel [100])-I(\mathbf{Q}\parallel [001])$ relative to the peak height $R_1$ as defined in the isotropic spectrum. The data (black dots) and calculations (green lines) for the crystal-field states are provided with the correct sign of the directional dichroism. Here the data points have been convoluted with a Gaussian of 0.5 eV FWHM. From [383].

Figure 31

Phonon dispersion curves at $T=300\mathrm{K}$ along high-symmetry directions in $\delta$-Pu stabilized by 0.6 wt % Ga alloying ($a=0.4621\mathrm{nm}$). The experimental data are shown as circles [black longitudinal ($L$) modes, red and blue transverse ($T$) modes]. The branches $T_1$ and $T_2$ propagating along the $[0\xi \xi ]$ direction are polarized along $⟨011⟩$ and $⟨100⟩$, respectively. The solid curves are the fourth-nearest-neighbor Born–von Kármán (BvK) model fit. The dashed curves are calculated dispersions for pure $\delta$-Pu based on dynamical mean-field theory (DMFT) ([99]). Adapted from [455].

Figure 32

Phonon energy (top panel) and linewidth (bottom panel) dispersions on epitaxial ${\mathrm{U}}_{1-x}{\mathrm{Mo}}_x$ thin film alloys. Transverse (longitudinal) acoustic modes are shown as blue squares (red circles) for the alloy with 23 at. % Mo. Theoretical results from a virtual crystal approximation for an alloy with 25 at. % Mo are shown as dashed white lines. The full spectral function is plotted as a ${\log }_{0.6}$ color map to rescale the intensity divergence at gamma. All directions are within the parent Brillouin zone. Bottom panel: raw linewidths ${\mathrm{\Gamma }}_0$ displayed as gray squares (TA) and circles (LA). Deconvoluted linewidths ${\mathrm{\Gamma }}_d$ are shown by dashed blue (TA) and red (LA) trend lines. Adapted from [79].

Figure 33

$4f$ PES spectra for one-, two-, three-, five-, and nine-monolayer (ML) Pu thin films. The experimental results (dots) show a gradual increase in the main-to-satellite intensity ratio with increasing layer thickness [experimental data from 157]. The arrows $A$ and $B$ indicate the energy positions of the main and satellite peaks, respectively, which are only well separated in the case of the most localized case of one ML. The experimental spectra are compared to Anderson impurity calculations (drawn lines) with the hybridization parameter $V=0.25$, 0.35, 0.4, 0.45, and 0.55 eV for an increasing number of MLs ([417]). The spectrum for nine-ML Pu resembles that of $\delta$-Pu metal, whereas one-ML Pu resembles Am. From [417].

Figure 34

Uranium $4f$ core-level x-ray photoemission spectra recorded for (left panel) $\mathrm{U}(\mathrm{IV})$ in ${\mathrm{UO}}_2$, (center panel) $\mathrm{U}(\mathrm{V})$ in ${\mathrm{U}}_2{\mathrm{O}}_5$, and (right panel) $\mathrm{U}(\mathrm{IV})$ in ${\mathrm{UO}}_3$. The relative energy between the satellite peak and the $4f_{5/2}$ ($4f_{7/2}$) emission line is used as a marker for the oxidation state of the uranium atoms. From [156].

Figure 35

ARPES spectra and comparison with the results of band-structure calculations for single crystals of UN. (a) Symmetrized ARPES spectra measured along the $X\text{−}W\text{−}X$ line. Dashed curves are guides for the eye. (b) Simulation of ARPES spectra based on the band-structure calculation treating all U $5f$ electrons as itinerant. From [137].

Figure 36

Angle-integrated spectra showing the difference between photoemission spectroscopy taken with the energy tuned near the $N_5$ edge at 737 eV and the off-resonance condition of 725 eV. The $5f$ enhancement shows the weight of the signal in ${\mathrm{UGa}}_2$, where the $5f$ electrons are essentially localized, is $\sim 1\mathrm{eV}$ below $E_{\mathrm{F}}$, whereas in the heavy-fermion system ${\mathrm{UPd}}_2{\mathrm{Al}}_3$ they are basically at $E_{\mathrm{F}}$. From [136].