All measurements were performed at the Stanford Synchrotron Radiation Lightsource with Si(220) crystals in the monochromator. Irradiated samples were measured in a liquid nitrogen reservoir cryostat using an ionization-type fluorescence detector. The irradiated layer was selected by tilting the samples to an angle shallow to the incident beam. Bulk samples were measured in transmission using an open-cycle liquid helium refrigerator. Thin film samples were mounted on the cold finger of a close-cycle helium refrigerator and measured in continuous scanning mode with three Ge detector channels to avoid interference from the diffraction peaks of the single crystal substrate. Spectra were self-calibrated from the bulk absorption edge values that had originally been assigned relative to a Zr foil converted to absorbance, the absorption edge jump normalized to unity, and the EXAFS extracted by approximating the smooth background above the near-edge region with a spline polynomial whose parameters were adjusted to minimize the amplitude of the Fourier transform modulus below R = 1.2 Å.

Curve-fits were performed from k = 3.2–12.5 Å⁻¹ for the irradiated samples, 2.6–14.0 Å⁻¹ for the bulk samples, and 3.3–12.5 Å⁻¹ for the films using amplitudes and phases calculated with the Feff 9 code (Rehr et al., 2010). The distances, numbers of atoms, Debye–Waller factors, and ionization energy corrections were varied, although for many spectra, the Debye–Waller factors were fixed and a number of parameters were constrained over limited ranges, often coupled to other parameters for other shells/waves. This was essential because of the disorder and high degree of correlation between the overlapping waves of the disordered structure. Here, destructive interference could marginally improve a fit by greatly increasing the amplitudes of two waves to unphysical sizes that nevertheless cancelled each other to give only a small change in their sum that was slightly close to the experimental spectrum. This same interference also necessitated the large number of waves; fitting a feature in the spectrum often caused new, relatively large features to appear in the difference because, although deceptively simple in appearance, it had originated in either a broad, anharmonic distribution or a multipeaked distribution. The curve-fits are best interpreted not literally but rather as modeling the overall U–O distribution, especially when the distances of two shells are below or only slightly larger than the spectral resolution and exacerbated when the contribution of one of them is relatively small. This consideration motivates our preference for the more qualitative visual analysis we present.

In addition to the above aspects of disorder in this system, UO_2+x presents problems specific to its EXAFS. The disorder in the U–O pairs causes rapid damping of their signals while simultaneously shifting the details of the pair distribution to higher energy, necessitating k³ weighting of the spectra. However, amplifying the high energy region of the spectrum greatly magnifies the spectral weight of neighboring U atoms because of the shift of the amplitude envelope to higher energy with increasing Z of the neighbor. This disparity in the amplitude–energy correlation of the two neighboring elements increases the uncertainty in the analysis for U–O distances beyond the limit of the nearest neighbor oxygen region at ∼3 Å.

A detailed analysis of some spectra found that this problem is exacerbated by the Ramsauer–Townsend effect (McKale et al., 1988; Hanham and Pettifer, 2001) with the high Z U that causes a phase shift around k = 3–5 Å⁻¹ where the amplitude of the U–U wave is low, which is challenging to both calculate and curve-fit. A thorough examination of the curve-fit results revealed what may be a unique problem originating in the continuously increasing U–U wave amplitude and noise with k³ weighting. Close inspection of the U–U wave in its original k dependence showed that at the initial region of the curve-fit at k = 2.6 Å⁻¹, where it is quite low in amplitude relative to the O waves, this spectral component was offset from zero while still exhibiting the high frequency corresponding to the 3.86 Å distance. This observation contradicts the presumption that the background calculated by the spline should cause the EXAFS to integrate to zero. However, χ(k) at low energy is not well defined and can include XANES features in addition to the EXAFS. The coupling of these to the U–O waves at low k in combination with the relatively minor U–U component could have caused this shift of the U wave baseline in the EXAFS. The large U–U amplitude at high k ensures that this error would be corrected in that region, but the U–U frequency connects it to the U–U wave so that, instead of the offset giving a low frequency feature, it affects the U–U wave below the main peak where the Ramsauer–Townsend phase shift occurs that also has this effect on χ(R) (McKale et al., 1988; Hanham and Pettifer, 2001). Coincidentally, it can be well fitted by U–O waves when their U–O distance corresponds to this same frequency.

Three samples of nominal UO_2.00 (Figure 1) were prepared at ITU in 2003 (Conradson et al., 2004a), at LANL in 2008 (Conradson et al., 2013), and at INL in 2012 (Pakarinen et al., 2014a; Pakarinen et al., 2014b). They were subsequently measured on different end stations at SSRL at 80–100 K using LN₂ and open cycle LHe cryostats in both transmission (LANL) and fluorescence with an ionization type detector. The EXAFS of UO_2.00-UO_2.20 at 80 K and of UO_2.0, U₄O₉, and U₃O₇ at 30, 100, and 200 K have been reported in the cited studies, with the former subjected to complete curve-fitting analysis and the latter presented only as a comparison of their χ(R) spectra supplemented by X-ray and neutron pair distribution function results. The EXAFS of the irradiated and U₄O_9-δ film samples have not been presented previously.

Polycrystalline UO_2.00 pellets for irradiation (Pakarinen et al., 2014a; Pakarinen et al., 2014b) were prepared by sintering powders followed by cooling in an Ar-6%H mixture to obtain an O/U ratio of 2. Purity and stoichiometry were confirmed by XRD. The pellets were sliced to 0.6 mm disks with a low-speed diamond saw in a radiological hood and polished to mirror finish prior to irradiating. A toroidal volume ion source (Torvis) coupled to a Pelletron tandem accelerator (University of Wisconsin-Madison) were used for irradiations with 2.6 MeV H⁺ and 3.9 MeV He²⁺ ions to fluences of, respectively, 1.4, 7.1, and 14.1 × 10¹⁷cm⁻², corresponding to 0.01, 0.05, and 0.10 displacements per atom (dpa), and 1 and 5.0 × 10¹⁵cm⁻² corresponding to 0.01 and 0.05 dpa. The sample temperature was monitored with thermocouples attached to the sample stage adjacent to the UO₂ disks. The ion beam was rastered across the specimens and the beam current and specimen temperature were recorded throughout the irradiations. For the EXAFS measurements, the pellets were mounted on the cold finger of a liquid nitrogen cryostat at a shallow angle to the incident beam and measured in fluorescence mode. At this angle, the irradiated depth exceeded the X-ray penetration depth so that only the relatively homogenous displacement dose plateau was probed while surface contribution remained small, and the peak implantation region did not contribute to the measured spectra as it would have in a purely surface measurement.

A 0.5 micron epitaxial thin film of near-stoichiometric UO₂ was grown as reported by Springell et al. (2015) and Rennie et al. (2018) by reactive DC magnetron sputtering of a depleted U target in a dedicated actinide ultra-high vacuum deposition system at the NNUF FaRMS facility at the University of Bristol, United Kingdom. The base pressure of the system was 1 × 10⁻¹¹ mbar, but during sputtering with Ar [ρ(Ar) = 7.7 × 10⁻³ mbar] a partial pressure of O₂ [ρ(O₂) = 2 × 10⁻⁵ mbar] was introduced such that the thin film deposited onto the substrate was of UO₂. The substrate used was a 10 mm³ × 10 mm³ × 1 mm³ CaF₂ single crystal substrate with a polished (100) oriented surface, sourced commercially from MTI Corp. CaF₂ was chosen due to the high degree of epitaxial alignment between CaF₂ and stoichiometric UO₂, facilitating the formation of a single crystal thin film atop the single crystal substrate. During deposition, the substrate was heated to 500 °C to further promote single crystallinity within the film. The resulting thin film crystallinity and increase in oxygen stoichiometry from the original UO₂ was confirmed ex-situ using XRD. The stoichiometry of the thin film was then tailored ex-situ by oxidative annealing at 150 °C for 30 min under a flow of 200 mbar of O₂. Ratioing of XPS peaks measured on the original surface and the subsurface region that was exposed by very mild Ar⁺ sputtering gave a value within the uncertainty for U₄O₉, with the “-δ” designating the possibility of inhibited oxygen diffusion throughout the entire film at its thickness. The limiting U₄O₉ stoichiometry has been demonstrated in tests with higher annealing temperatures and longer times (Stubbs et al., 2017; Spurgeon et al., 2019).

A necessary starting point for elucidating the structural chemistry of oxygen addition to UO₂ by EXAFS is the baseline for the reliability of the measurements themselves. This is evident in Figure 1. Three samples of nominal UO_2.00 were prepared at ITU in 2003, LANL in 2008, and INL in 2012 and were subsequently measured on different end stations at SSRL at 80–100 K using LN₂ and open cycle LHe cryostats in both transmission (LANL) and fluorescence with an ionization type detector. These all exhibited identical nodes in the real components of their χ(R) spectra and relatively small differences in their amplitudes. As discussed above, due to the continuously increasing U amplitude with k³-weighting, the amplitude variation is largest for the U contribution and also increases with increasing distance as the effects of disorder that will occur even in crystallographically single-phase stoichiometric material take effect. This distance effect is, however, relatively minor. All spectra clearly show the same pattern of features at higher R that are a fingerprint for the fluorite structure. Insofar as the region from R = 2.4–3.0 Å is free from spectral features in the fluorite structure, the small R = 2.5 Å modulus peak in the spectrum of the INL sample most likely originates from an impurity. An important point with respect to the finding of oxo-type neighbors at a very short U–O distance is the small feature at R = 1.2 Å with 0.09–0.17 modulus amplitude for this k = 2.8–13.5 Å⁻¹ transform range. For UO_2.00, this is a side lobe of the O peak. Since this is at the upper limit of frequencies removed by the background subtraction with the spline polynomial, the different backgrounds affect its amplitude more than that of the O peak with its much larger amplitude. In addition, we showed previously that the real component of this side lobe does not match that from an O neighbor (Conradson et al., 2004a). In summary, the experimental measurements for these samples are highly reliable and will have minimal to negligible effects on their analysis, with further details on the curve-fit results for these samples included as Table 1.

A means of inducing disorder without U oxidation and its insertion of adventitious, hyperstoichiometric O is ion irradiation. The 300–400 °C temperatures caused by heating from the ion beam are modest relative to the 800–1,500 °C of the pellet during operation. The resulting inhibition of the annealing of higher defect concentrations along the ion track near the surface could promote the formation of defect clusters (Weber, 1981; Guimbrètiere et al., 2012; Pakarinen et al., 2014b). Although the He²⁺ doses were most likely below the clustering threshold (Weber, 1981) and no visible signs of damage were observed with these He²⁺ doses, the p⁺ doses were sufficiently high to cause blistering of the surface and laminar fractures, despite which expansion of the lattice constants symptomatic of defect clustering did not occur. EXAFS measurements would indicate if oxygen displacements caused local composition fluctuations.

The EXAFS spectra of these UO_2.0 samples irradiated with proton and helium nucleus ion beams are shown in Figure 2. The significant reductions in amplitude of the O and especially U modulus peaks indicate that the total effects on the structure and its ordering are amplified beyond the nominal numbers of displacements. Amplitude ratio analysis showed that the very similar decrease for the highest doses of both p⁺ and He²⁺ is in both the linear and exponentially damped components of the overall amplitude envelope. This contrasts with oxidation where the decrease in the U amplitude from UO_2.00 to UO_2.20 was purely linear with increasing O stoichiometry (Conradson et al., 2004a). The induced disorder from irradiation causes both Gaussian and anharmonic broadening. In terms of local lattice distortions from O within 3 Å of the U, some of the samples exhibit negligible to minor contributions from O with a U–O distance of 1.99–2.05 Å (Table 2), but good fits of the samples with >0.01 dpa require O shells around 2.2 and 2.35 Å, as can be seen in the figure. The 0.15 Å separation is close to the 0.125 Å resolution limit for this data range. This result in combination with the difference in amplitude implies that instead of these two shells being distinct neighbors, the U–O nearest neighbor distribution that is narrow in UO_2.00 is anharmonically broadened by the strain from the displaced atoms. This would also affect the U–U distribution. Beyond these two O neighbors, complete fits of all of these spectra include an O at 2.83–2.92 Å, although this is also uniformly small. The exception is the spectrum from the lowest dose proton-irradiated sample. Although this fit includes three O shells at 3.29–3.76 Å, interference causes their sum to be quite low. Insofar as the spectrum in this region is almost identical in shape to the others, it is likely that a fit insignificantly worse than this could be obtained with a constrained fit using much smaller individual amplitudes—these neighbor shells are either not present or are much smaller than indicated by these fits. As discussed above, this spectrum serves as a caveat against using multiple, relatively large shells to model EXAFS that is much lower in amplitude than their individual contributions of the fits.

What is notable about radiation-induced disorder is, vide infra, it exhibits a different motif than oxidation. There is no indication of the very short U–O distance that is the signature for an oxo/uranyl group. Spectral features below the principal O peak are only half the amplitude of those assigned to this moiety. They are well fit by the two overlapping ones for the main peak, leaving only miniscule or no residual even when a spectrum displays a shoulder of it that continues to lower R. There is therefore no evidence that the displaced oxygen atoms aggregate into U₄O₉-like domains that would be offset by O-depleted ones.

As an extension of our earlier presentation of these spectra (Conradson et al., 2004a) we have applied the shell-separation approach (Conradson et al., 2014a; Conradson et al., 2014b; Batuk et al., 2015; Conradson et al., 2020). The first step is curve-fitting the total spectrum, followed by selecting a target neighbor shell. Its χ(k) EXAFS is isolated from the others by subtracting all other U–O and U–U waves from the original energy spectrum. Its corresponding χ(R) for visualization and comparison is obtained by Fourier transforming this residual. The curve-fits are therefore not the final results but an intermediate step in the analysis. The detrimental effects of inaccuracies in the calculated amplitudes and phases, in the use of harmonic pair distributions, and in the presumed structure are therefore minimized because the objective is to reduce their spectral contributions below that of the target neighbor shell. Having previously shown that the EXAFS of these hyperstoichiometric mixed-valence compounds change with temperature from 30 to 200 K in the absence of a phase transformation, we now identify the components of the structure in which these changes originate.

An immediate observation is that the modulus amplitudes are quite low, only half or less of those from the irradiated UO₂ (Figure 3). Corroboration is provided by the original UO_2.20 spectrum (Conradson et al., 2004a) that not only displays similar amplitudes but also has the same pattern of modulus peaks as the U₄O₉ sample at 100 K, which is closest it in terms of composition and temperature. For the U, this substantial reduction is because of the amplification of the FT modulus by the continuous increase in the amplitude of the U–U wave through the high energy end of the spectrum with k³-weighting. When the damping from the disorder causes the U–U amplitude to be flat throughout the energy spectrum, as for these spectra, the modulus amplitude is only half or even less. Greater disorder builds on this amplitude reduction of the modulus such that the latter is lower for U₃O₇ than U₄O₉ at 200 K. The amplitude from the O neighbors is low because of its splitting into a multisite distribution, evident in the several peaks and shoulders and in the subsequent destructive interference between the overlapping waves.

The complexity of the overall O contribution is evident in all spectra. A feature of note is the peak or shoulder at R∼1.2 Å that is completely and consistently fit by an O at 1.65–1.73 Å for U₃O₇ and 1.68–1.69 Å- for U₄O₉ (highlighted by the green line in the figures). The numbers of this O atom calculated by the curve-fits are only a few tenths, but the inverse square distance dependence of the amplitude and small Debye–Waller factor result in its substantial amplitude in the spectrum despite its low abundance in the actual material. The close to exact correspondence of the amplitude and phase with a U–O wave and large error in fitting the side lobe in the UO₂ spectrum with O and the insensitivity of the O fit to different background parameters meet the dual criteria of sufficiency and necessity. Additional confirmation was provided by the presence of this neighbor shell in the Fourier analysis by maximum entropy calculation (Conradson et al., 2013), which also required that the amplitude and phase in the spectrum match the U–O parameters that served as input. Although distances below ∼1.7 Å are significantly shorter than in U coordination compounds, they are longer than the 1.64 Å U-oxo distance reported for α-UO₃ that therefore serves as a precedent (Greaves and Fender, 1972).

Continuing the curve-fitting of the nearest neighbor O contribution consistently identifies two overlapping shells at 2.15–2.55 Å. Inspection of Table 3 shows no discernible trend in their U–O distances that are, for U₄O₉, 2.31 and 2.51 at 30 K, 2.24 and 2.40 Å at 100 K, 2.19 and 2.34 Å at 200 K, and for U₃O₇, 2.24 and 2.43 at 30 K, 2.15 and 2.32 Å at 100 K, and 2.19 and 2.34 Å at 200 K. Although fit component amplitudes larger than the spectral features being fit often indicate overdetermination of the data, that is not the situation here as the total number of O atoms they represent remains below eight and all are smaller than the modulus peak in UO₂ from its fully ordered O neighbor. Fitting the small peak at R = 2.2–2.4 Å requires a third neighbor at 2.49–2.65 Å that ranges in amplitude from negligible to almost as large as the other two. Completing that region and the next smaller peak around R = 3 Å requires additional shells through 3.5 Å. The issue of whether the metrical parameters from the curve-fits can be assigned to actual, discrete neighbor shells as in ordered systems again resides in their overlap and subsequent interference between their signals. The large numbers of neighbors occurring at 0.2–0.4 Å intervals exacerbates the uniqueness problem. The minimum in the curve-fit error is so shallow that the numbers of atoms calculated by the fits can extend over a wide range with no significant change in this metric for the quality of the fit, even when the total numbers of neighbors and the Debye–Waller factors are constrained to physically realistic values. The best interpretation is that the results represent a broad, continuous distribution across the total distance range of the curve-fits whose shape resembles the sum over the shells, often with additional broadening. Using this interpretation still assists in characterizing the structure. Two conclusions for these samples are that the only O neighbors with U–O distances less than 2.1–2.2 Å are the oxos and that the adventitious O is not inserted into discrete locations to give a locally ordered structure but define a distribution that is at least semi-continuous.

The question of whether the changes in the spectra over the 30–200 K originated in only a few U–O pairs with others being invariant or whether all of them were affected is examined by applying the shell separation method described above to the four O neighbors with U–O < 2.7–2.8 Å (Figure 4). The FT real components visualize the distances and amplitudes for each region more effectively than just the numerical parameters. The changes in the nodes caused by shifts in the U–O distances and the varying amplitudes demonstrate that the shifting of atoms throughout the continuous U–O distribution is the better scenario. O atoms are moving towards and away from the central U with no discernible correlation with temperature for both U₄O₉ an U₃O₇, and the resulting changes in amplitude modified by interference are larger than any changes in the numbers of O in those regions. The possible exception is the U-oxo pair for which the distances are relatively invariant and the amplitudes are smaller at 100 K and larger at 30 and 200 K for both compounds. The conservation of the distance is consistent with this being the strongest U–O bond and its separation from all the other U–O pairs. The behavior therefore is more like fluctuations than a transformation.

Complementing the bulk U₄O₉ is an epitaxial U₄O_9-δ film. EXAFS spectra were obtained at 10, 35, 80, 120, 160, 200, and 240 K. Beyond the two primary peaks from the nearest neighbor O and second neighbor U characteristic of the fluorite structure, the first result is that the amplitudes are much higher and the O contribution is much simpler than in the bulk materials (Figure 5). The EXAFS therefore indicates that the films are significantly more ordered, most likely because the atoms are epitaxially constrained by the substrate. The corollary to this result is that consistent with our interpretation of the bulk sample EXAFS, the pair distributions have substantial continuous character without specific well-defined atom positions and bond lengths. It is also consistent with the difficulties inherent in the crystallography of UO_2+x, even regardless of the fact that instead of determining distributions with respect to the unit cell, correlated thermal motion of atom pairs gives a short-range order different than the long-range average.

Curve-fits of the spectra, however, show that the local structure has both similarities with and significant differences from the bulk materials (Figure 5). They also illustrate the paradox that interference within the EXAFS from disorder can cause spectra that appear simple to actually be quite complicated. As with the UO_2+x spectra, a prominent peak at R = 1.2 Å is present at all temperatures, although here it is well separated from the primary oxygen feature. Insofar as the real component peak is at the same position as in the bulk sample spectra, it is well fit by an O neighbor at a somewhat longer distance, 1.70–1.75 Å, and with a larger number of atoms, ∼0.6, consistent with the larger modulus amplitudes (Table 4). The primary nearest neighbor O at R∼1.9 Å is large and narrow because, with the exception of 80 K, it has as its principal constituent a single shell at 2.35–2.37 Å. This 0.02 Å range is within the experimental error and is only a small fraction of the variation in the bond lengths of the bulk samples. Another significant difference is that complete fits of these spectra all require an O at 1.94–2.00 Å in contrast to the bulk samples, where no O were found in this region. Interference among these three overlapping neighbor shells is how the contributions of the uranyl and these primary O neighbors appear so well separated in terms of the modulus at R∼1.5 approaching 0 in χ(R). In common with the bulk samples is an O neighbor at 2.53–2.56 Å whose modulus peak is around half as high as the principal one. The total numbers of O atoms from these near neighbors are within the upper limit of 8, but the correlation between the numbers and Debye–Waller factors again causes a shallow minimum in the fits that would make tabulation of these numbers misleading by implying discrete neighbors at those locations. The qualitative depiction in the figure that shows the overlap of the neighbors provides the best interpretation of the results.

Also similar to the bulk samples are O shells at longer distances that give the features above R = 2.6 Å, including the modulus structure around R = 3 Å on the side of the principal U contribution at R = 3.7 Å. Consistent with the discussion of the coupling of the Ramsauer–Townsend resonance to the background and the U–O waves, these are not only larger but much more variable. This scenario could explain the larger errors in the U–U distance in the 200 and 240 K spectra where the higher temperature results in a larger Debye–Waller factor and lower amplitude while the amplitude of the O shell fitting this region increases. It could be expected that the effects of this offset would also modify the O contribution. If, however, they simply matched the first low-frequency oscillation of the U–O wave they would combine with the number of atoms/Debye–Waller factor correlation that, in these disordered structures with overlapping shells, is non-trivial to deconvolute. We will therefore omit discussion of the results for the O neighbors at the longer distances found by the curve fits.

Examination of the spectra in Figure 5 indicates that, if the features around R = 3 Å are excluded, the O near neighbor contributions do not show significant changes with temperature as occur in the bulk material. However, subtracting the principal O at 2.36 Å gives a different result (Figure 6). Examination of the modulus and real components of these residuals shows that for 10–120 K, the three modulus peaks are in the same positions, although somewhat lower for 10 and 120 K, and the highest is shifted 0.1 Å higher at 80 K. This pattern is repeated for the real component except that the peak at R = 1.8 Å has flattened at 120 K. In contrast, the moduli for 160 K and 240 K have a different shape for R = 1.5–2 Å, and at 200 K it goes to zero at R = 1.8 Å. This departure from the low temperature pattern without establishing a separate trend is repeated in their real components.

Further assignment of these changes in the spectra with temperature to the specific neighbor shells was performed by the same method as used for the bulk samples’ isolation and direct comparison of the real components of χ(R) of the individual neighbor shells (Figure 7). This procedure also gives a result for the U₄O_9-δ films that is significantly different from the bulk samples. The principal O neighbor with the 2.36 Å U–O distance is essentially invariant over this entire temperature range. Corroborating the curve-fit results, the O neighbors at 1.72 and 2.55 Å also exhibit minimal changes in their distances. Insofar as the spectral features associated with these neighbors are anomalously high in the 80 K spectrum, it is unclear whether their display of, respectively, the highest and lowest amplitudes in these data indicate a shift in the structure at this temperature or are related to the noise level. The 1.72 Å feature does divide into higher and lower amplitude sets, but randomly across the three extremes. This leaves the 1.97 Å neighbor as the source of the changes observed in the total residual for 160 K and above, which is the observed result. The 10, 35, and 80 K spectra exhibit almost identical positions in their extremes, with the amplitude for 10 K being slightly lower. The 120 K spectrum begins to depart from the others with a lower amplitude and small shifts in position, as do the 160 and 200 K spectra, with the shifts going in different directions. By 240 K, the difference from the others is substantial. This behavior parallels the reduction in the amplitude of this feature with increasing temperature found by the curve fits (Figure 5). To the extent that the results in Figure 6 are larger over a greater width, there could be amplification via the interference with the other shells despite their separation that is much larger than the experimental resolution. Alternatively, and more likely, is that although the multiple shell fits appear overall complete, this particular shell with U–O ∼ 2.0 Å has an anharmonic distribution that increases beginning at ∼100 K and ultimately almost eliminates its contribution by 200 K. This scenario that does not involve displacements of the O into the other neighbor positions would be consistent with the absence of an increase in their amplitudes corresponding to the decrease in this one.