A preliminary investigation into the use of molecular oxide and hydride secondary ion relationships for improvement of the ²³⁶U/²³⁸U determination on a NanoSIMS 50L

Abstract

A NanoSIMS 50L is used to investigate uranium molecular (²³⁵U¹⁶O, ²³⁶U¹⁶O, ²³⁸U¹⁶O, ²³⁵U¹H, ²³⁸U¹H, ²³⁶U¹⁶O¹H, and ²³⁸U¹⁶O¹H) and elemental (²³⁵U, ²³⁶U, and ²³⁸U) secondary ion production during sputtering of synthetic UO₂ and the NIST-610 standard to determine if: (1) the ²³⁶U¹⁶O/²³⁸U¹⁶O molecular oxide ratio performs better than the ²³⁶U/²³⁸U elemental ratio, and (2) there is co-variance between the molecular hydrides and oxides. Despite an order of magnitude greater abundance of ²³⁶U¹⁶O secondary ions (compared to ²³⁶U), the ²³⁶U¹⁶O/²³⁸U¹⁶O ratios are less accurate than the ²³⁶U/²³⁸U ratios. Further work is needed before the higher count rate of the ²³⁶U¹⁶O secondary ion can be used to obtain a better ²³⁶U/²³⁸U ratio. The second objective was undertaken because correction for the interference of ²³⁵U¹H on the ²³⁶U secondary ion species typically utilizes the ²³⁸U¹H/²³⁸U ratio. This becomes problematic in samples containing ²³⁹Pu, so our aim was to understand if the hydride formation rate can be constrained independently of having to measure the ²³⁸U¹H. We document correlations between the hydride (²³⁸U¹H and ²³⁸U¹⁶O¹H) and oxide (²³⁶U¹⁶O) secondary ions, suggesting that pursuing an alternative correction regime is worthwhile.

Introduction

Secondary ion mass spectrometry (SIMS) is routinely utilized for determining the uranium isotopic composition in a wide variety of materials. For samples containing anthropogenically perturbed uranium, the ²³⁴U/²³⁸U, ²³⁵U/²³⁸U, and ²³⁶U/²³⁸U ratios can be useful indicators of processing history (an up-to-date discussion can be found in¹). Of these uranium isotope ratios, the ²³⁶U/²³⁸U determination by SIMS is particularly challenging for a number of reasons (see discussion by²). One reason is that the ‘natural’ ²³⁶U/²³⁸U is < 10^–103, and while the ²³⁶U/²³⁸U of anthropogenically modified material can have elevated ²³⁶U/²³⁸U, the ²³⁶U/²³⁸U ratio is still typically considerably lower than that of the ²³⁵U/²³⁸U. This becomes a problem in situations where there is a limited amount of sample available for analysis (e.g. single particle analysis) because precision and accuracy in isotope ratio mass spectrometry are statistically limited by the count-rate of the minor isotope. This is compounded by the fact that the effective transmission of SIMS instruments, which can be thought of as the amount of secondary ions of the target analyte reaching the detector in comparison to the number sputtered from the matrix being analyzed, are typically a few percent at best⁴.

A separate issue that complicates the ²³⁶U/²³⁸U determination by SIMS relates to the fact that, when material is sputtered, both elemental and molecular secondary ions are formed. For the ²³⁶U/²³⁸U, formation of the ²³⁵U¹H hydride molecular species is problematic because a mass resolving power of 38,158 (defined as M/∆M) would be necessary to resolve the ²³⁶U signal independently of the ²³⁵U¹H interference. Such high mass resolving power is not routinely achievable, and even if it were, would come at the expense of secondary ion transmission through the instrument that would, in turn, exacerbate uncertainty introduced in the ²³⁶U/²³⁸U ratio by the low ²³⁶U count-rate. To circumvent this interference, it is possible to monitor the ²³⁸U¹H/²³⁸U ratio, and then apply the hydride formation rate to the observed ²³⁶U/²³⁸U using the formula ²³⁶U/²³⁸U = ((²³⁶U + ²³⁵U¹H)/²³⁸U) − (²³⁸U¹H/²³⁸U) × (²³⁵U/²³⁸U)² to obtain a corrected ²³⁶U/²³⁸U value. While this correction regime has been shown to work for uranium bearing samples that do not contains plutonium, the presence of ²³⁹Pu within the sample makes the correction regime unusable due to the fact that an MRP of 37,056 is necessary to separate ²³⁸U¹H from ²³⁹Pu.

While the ²³⁸U¹H/²³⁸U based hydride correction regime has been shown to work for samples that do not contain Pu, other possible issues relate to the fact that a comparatively high count rate of the ²³⁸U¹H is then being applied to the much lower signal at mass ²³⁵U¹H + ²³⁶U by way of the ²³⁵U/²³⁸U ratio. In theory, proper detector background and deadtime correction regimes should mitigate any issues related to the drastic differences in count rate between the various secondary ion species, but in practice, these differences could influence the ²³⁶U/²³⁸U determination. This is especially true in situations where the ²³⁶U and ²³⁸U¹H are being measured at different times during an analysis (e.g. during magnetic peak hopping) and the molecular hydride formation rate is unstable over the course of that analysis. On Fig. 1, which is a compilation from the literature of reported ²³⁶U/²³⁸U ratios plotted as a function of the reported ²³⁵U/²³⁸U ratio, it can be seen that there is a broad increase in the reported ²³⁶U/²³⁸U ratios with increasing ²³⁵U/²³⁸U. Furthermore, this increase (which can be modeled utilizing a power-law curve) broadly follows the hypothetical ²³⁵U¹H/²³⁸U ratios calculated at any given ²³⁵U/²³⁸U ratio assuming a 1% hydride formation rate. While there are obviously many nuances specific to the data from each study, the existence of this relationship between the reported ²³⁶U/²³⁸U and ²³⁵U/²³⁸U ratios suggests that, broadly speaking, the ²³⁶U/²³⁸U ratios is not adequately corrected for the ²³⁵U¹H interference during SIMS analysis.

Figure 1

Plot of ²³⁶U/²³⁸U versus ²³⁵U/²³⁸U ratios determined by SIMS reported in the literature [data compilation can be found in the electronic appendix (supplementary table 3)]. A linear regression through the literature data (the black dotted curve) closely follows the predicted ²³⁵U¹H/²³⁸U ratio at any given ²³⁵U/²³⁸U assuming a 1% hydride formation rate (the gray solid curve).

The purpose of this study is to investigate two possible avenues for improvement of the ²³⁶U/²³⁸U ratio. One possible avenue is in use of the ²³⁶U¹⁶O/²³⁸U¹⁶O ratio instead of the ²³⁶U/²³⁸U ratio. From other studies (e.g.⁵) it is known that the ^23xU¹⁶O molecular secondary ions are typically detected in greater abundances as compared to the ^23xU elemental secondary ions. Therefore, it is possible that the increased count rate of the ²³⁶U¹⁶O relative to the ²³⁶U results in improved precision and accuracy. Use of the ²³⁶U¹⁶O molecular ion, as opposed to the ²³⁶U elemental secondary ion, to determine the abundance of ²³⁶U, relative to the other isotopes of U in a sample, has not yet been reported in the scientific literature. The second avenue is more exploratory in nature and involves an assessment of whether the pertinent (e.g. ²³⁸U¹H for correcting the ²³⁶U/²³⁸U or the ²³⁹U¹⁶O¹H for correcting the ²³⁶U¹⁶O/²³⁸U¹⁶O) hydride formation rates co-vary systematically with the uranium molecular oxide (²³⁸U¹⁶O) formation rate. If this co-variability exists, then it may ultimately be possible to constrain the magnitude of the ²³⁵U¹H and ²³⁵U¹⁶O¹H interferences on the ²³⁶U and ²³⁶U¹⁶O secondary ions independently of needing to observe the signals at masses ²³⁸U¹H and ²³⁸U¹⁶O¹H. Such an approach has not yet been attempted, or even explored, in the scientific literature. These goals are achieved by examination of UO₂ with a known uranium isotopic composition, as well as the NIST-610 standard whose isotopic composition has previously been documented, on a variety of different substrates and analytical conditions. In the end, we show that both avenues for improvement are viable if a variety of issues can be resolved.

Results: NanoSIMS data processing and presentation

The raw data from the NanoSIMS, consisting of the total number of counts observed during each of the 6.5 s cycles, was exported from the instrument and processed in Microsoft Excel. The raw data was uncorrected for the electronically programmed 44 ns electron multiplier deadtime, so this correction was applied to the raw data followed by linear interpolation of the secondary ion count rates during each cycle to the time of the magnetic field (B7) containing that cycle’s ²³⁸U, ²³⁸U¹⁶O, and ²³⁸U¹⁶O₂ secondary ion data. This was done to account for any drift in the secondary ion count rates over the course of each cycle. The linearly interpolated and deadtime corrected secondary ion counts were then utilized to calculate the various ratios of interest at each cycle. These cycle-by-cycle ratios were then averaged over the 20 cycles of data collected for each analysis. These ratios are reported in supplementary table 2a and utilized in plots 2 through 9. The error reported for each ratio is the within-run uncertainty on each ratio calculated as standard deviation of the mean value of the 20 cycles of data. In supplementary table 2b, the ratios reported are the weighted mean (calculated using Isoplot v. 3.75⁶) values for individual analyses comprising each of the different substrate and sample types. These weighted mean values were calculated using the within-run 1σ associated with each analysis, but an important note is that the uncertainty reported for these weighted mean values is at the 95% confidence level (2σ). In supplementary table 2b the mean square of weighted deviate (MSWD) value for each of the weighted means is also provided. The values in supplementary table 2a were used to construct all of the figures presented in this study.

Discussion

The primary goal of this study is to investigate two potential avenues for improvement of the ²³⁶U/²³⁸U ratio determination by SIMS. One potential avenue is by use of the ²³⁶U¹⁶O/²³⁸U¹⁶O ratio instead of the ²³⁶U/²³⁸U ratio, which is warranted considering that the uranium oxide (in this case ²³⁵U¹⁶O, ²³⁶U¹⁶O, and ²³⁸U¹⁶O) secondary ions typically exhibit higher count rates than their elemental counterparts (in this case ²³⁵U, ²³⁶U, and ²³⁸U). The second potential avenue of improvement is by searching for evidence of covariance between the ²³⁸U¹H and ²³⁸U¹⁶O¹H molecular hydride secondary ion production rates and various other combinations of the uranium elemental and molecular oxide ratios. If such co-variance were to exist, it could mean that it may ultimately be feasible to constrain the uranium hydride secondary ion formation rate taking place during an analysis independently of the assumption that the entire signal at mass 239 is composed entirely of ²³⁸U¹H. As discussed in the introduction, the approach of utilizing the ²³⁸U¹H/²³⁸U ratio to correct for the contribution of ²³⁵U¹H to the ²³⁶U/²³⁸U ratio has been shown to work in samples that do not contain Pu, but this approach cannot work for mixed U–Pu samples. Therefore, consideration of alternative means of constraining the U-hydride secondary ion formation rate during an analysis is a worthwhile endeavor.

It is first necessary to consider whether the uranium isotopic data collected in this study is of high enough quality to investigate these possibilities. This can be ascertained on the basis of whether the isotope ratios behave according to the expected relationships between minor isotope count rate, within-run uncertainty, and deviation between the measured and true values. In Fig. 2, the fractional 1σ within-run uncertainty (Fig. 2a) and observed/true (Fig. 2b) versus the total number of ²³⁵U counts for the ²³⁵U/²³⁸U ratio associated are shown for each analysis of the UO₂ and NIST-610 glass. As can be seen, the within-run 1σ (Fig. 2a) and degree of deviance (Fig. 2b) both decrease exponentially with increasing count rate of the minor isotope (²³⁵U). The same is true of the ²³⁵U¹⁶O/²³⁸U¹⁶O within run 1σ (Fig. 3a) and observed/true (Fig. 3b), except that the ²³⁵U¹⁶O/²³⁸U¹⁶O exhibits a slightly lower within run 1σ, yet a slightly more scattered observed/true, as compared to the ²³⁵U/²³⁸U determination. Nonetheless the ²³⁵U/²³⁸U and ²³⁵U¹⁶O/²³⁸U¹⁶O are typically in good agreement with the solution MC-ICP-MS ²³⁵U/²³⁸U ratio for the UO₂ of 0.002153(1) and the published ²³⁵U/²³⁸U ratio⁷ for the NIST-610 glass of ²³⁵U/²³⁸U = 0.0023856(7). Similar behavior is seen in the uncorrected ²³⁶U/²³⁸U (Fig. 4) and ²³⁶U¹⁶O/²³⁸U¹⁶O ratios (Fig. 5) ratios, as well as the ²³⁴U/²³⁸U ratio (not shown in figures, but data is provided in supplementary table 2). The fact that minor isotope count-rate appears to be the major contributing factor to the precision and accuracy of the observed isotopic ratios indicates that the U isotope data collected in this study behaves in-line with what would be expected for mass spectrometric isotope data. Therefore, the dataset can be used to further investigate the two possible avenues for improvement of the ²³⁶U/²³⁸U ratio determination outlined in the preceding paragraph.

Figure 2

Plots of the fractional 1σ within-run uncertainty (a) and observed/true (b) versus the total number of ²³⁵U counts for the ²³⁵U/²³⁸U ratio associated with each analysis of the UO₂ dispersed onto the various substrates.

Figure 3

Plots of the fractional 1σ within-run uncertainty (a) and observed/true (b) versus the total number of ²³⁵U¹⁶O counts for the ²³⁵U¹⁶O/²³⁸U¹⁶O ratio associated with each analysis of the UO2 dispersed onto the various substrates.

Figure 4

Plots of the fractional 1σ within-run uncertainty (a) and observed/true (b) versus the total number of ²³⁶U counts for the ²³⁶U/²³⁸U ratio associated with each analysis of the UO₂ dispersed onto the various substrates.

Figure 5

Plots of the fractional 1σ within-run uncertainty (a) and observed/true (b) versus the total number of ²³⁶U¹⁶O counts for the ²³⁶U¹⁶O/²³⁸U¹⁶O ratio associated with each analysis of the UO₂ dispersed onto the various substrates.

It is also important to consider the factors impacting hydride formation rate during the analytical session within-which the data presented in this study was collected. ²³⁵U¹H hydride formation rate as it applies to the ²³⁶U/^238U determination on micrometer sized particles by SIMS has recently been explored by Simons and Fassett (2017), with a basic observation being that the composition of the analytical substrate upon which the particles are sitting exerts far more control over the hydride formation rate than the residual vacuum within the analytical chamber. The data presented in this study was collected during the course of a single analytical session, wherein the vacuum level within the analysis chamber remained at ~ 4.5 × 10^–9 mbar. Examination of supplementary table 2a reveals that the ²³⁸U¹H/²³⁸U ratios observed in this study range from as low as 0.00001 to as high as 0.03.

However, it is equally important to note that the ²³⁸U¹H/²³⁸U ratios for the polished UO₂ and NIST-610 glass reference material are all below 0.0003, whereas the values for the UO₂ dispersed onto the various substrates are an order of magnitude higher. This could indicate that residual volatiles adhered to the irregular surfaces created by dispersing the finely crushed UO₂ particles onto the substrates contributed to hydride formation, and/or that the substrates themselves contribute substantially to hydride formation (as suggested by Simons and Fassett, 2017). In either case, obtaining a dataset displaying a range of hydride formation rates is consistent with the goals of our study, which is to explore various hydride correction regimes. An equally important note is that there does not appear to be any statistically significant (e.g. outside of within-run uncertainty) differences in the ²³⁵U/²³⁸U or ²³⁵U¹⁶O/²³⁸U¹⁶O ratios obtained for the highly polished UO₂ and the UO₂ that was crushed and dispersed onto the various substrates.

Use of the ²³⁶U¹⁶O/²³⁸U¹⁶O vs the ²³⁶U/²³⁸U ratio

Comparison between Figs. 4a and 5a reveals that the ²³⁶U¹⁶O/²³⁸U¹⁶O within-run uncertainties are lower than the ²³⁶U/²³⁸U uncertainties, whereas comparison between Figs. 4b and 5b reveals that the raw ²³⁶U¹⁶O/²³⁸U¹⁶O ratios exhibit more scatter relative to the solution MC-ICP-MS value as compared to the raw ²³⁶U/²³⁸U ratios. However, it is important to note that both the ²³⁶U/²³⁸U and ²³⁶U¹⁶O/²³⁸U¹⁶O ratio must be corrected for the ²³⁵U¹H and ²³⁵U¹⁶O¹H interferences. For the ²³⁶U/²³⁸U, this is achieved by use the formula ²³⁶U/²³⁸U = ((²³⁶U + ²³⁵U¹H)/²³⁸U) − (²³⁸U¹H/²³⁸U) x (²³⁵U/²³⁸U) (see “Discussion”²). Applying this calculation to the raw ²³⁶U/²³⁸U ratios pulls the data from the greased substrates towards lower values that are, on average, closer to the solution value (supplementary table 2b). In contrast, the data from the un-greased substrates are pulled, on average, towards values lower than the solution value. In some cases, the corrected ²³⁶U/²³⁸U ratios are ≤ 0. For the polished UO₂ mounted in epoxy, the correction regime has virtually no effect on the ²³⁶U/²³⁸U whereas for the NIST-610 glass, the uncorrected ²³⁶U/²³⁸U are actually closer, on average, to the published value than the corrected ²³⁶U/²³⁸U (supplementary table 2b) which are pulled towards lower values. These observations suggest that the ²³⁵U¹H correction based on the ²³⁸U¹H signal results in a slight over-correction of the ²³⁶U/²³⁸U ratio for the data set collected in this study.

There are several possible reasons for this. One may be that the hydride formation rate at the time of the ²³⁸U¹H acquisition is higher than that at the ²³⁶U acquisition. Examination of the secondary ion count rate data does indicate that for some of the analyses (full dataset provided in the electronic appendix), the ²³⁸U¹H does increase as a function of time during the analytical session whereas in others, it remains stable or decreases. This variability in the count-rate as a function of time during the analysis is the reason why the raw secondary ion count-rates were linearly interpolated to the time of the ²³⁸U acquisition prior to additional data processing. However, the reality is that the very low ²³⁶U count rate (sometimes < 1 c/s) complicates the linear interpolation method. Equally problematic is the fact that the hydride formation rate, as constrained by monitoring the relatively strong signal at mass ²³⁸U¹H, must then applied to the considerably lower signal at mass ²³⁵U to infer the number of ²³⁵U¹H ions being produced at the time of the ²³⁶U acquisition. While other factors may be important, the ²³⁶U/²³⁸U ratio overcorrection is most likely related to the large difference between the count rates at masses 235, 236, and 239. This is especially true for those analyses where the ²³⁸U¹H increases as a function of time whereas, the ²³⁶U and ²³⁵U count rates are too low to exhibit a noticeable increase or decrease as a function time during any of the analyses.

While the ²³⁶U count rate is sometimes < 1 c/s for the analyses conducted in this study, the ²³⁶U¹⁶O count rates were typically > 10 c/s. This higher count rate results in a smaller within-run 1σ (Fig. 4a vs 5a), but as noted earlier the raw ²³⁶U¹⁶O/²³⁸U¹⁶O ratios exhibit more scatter as compared to the raw ²³⁶U/²³⁸U ratios (Fig. 4b vs 5b). As with the ²³⁶U/²³⁸U ratio, it is necessary to account for an interference on the ²³⁶U¹⁶O signal from the ²³⁵U¹⁶O¹H molecular species, which would require a mass resolving power of 40,743 to resolve. Since the dynamics of forming a secondary ion molecular species containing uranium, oxygen, and hydrogen (e.g. ²³⁵U¹⁶O¹H) would presumably be different as compared to one containing only uranium and hydrogen (e.g. ²³⁵U¹H) it would be inappropriate to use the observed ²³⁵U/²³⁸U and ²³⁸U¹H/²³⁸U to correct the observed ²³⁶U¹⁶O/²³⁸U¹⁶O ratio. Because the mass table utilized in this study (Table 1) also included the ²³⁵U¹⁶O, ²³⁸U¹⁶O, and ²³⁸U¹⁶O¹H molecular oxide and hydride species, it is possible to apply a correction according to the following equation: ²³⁶U¹⁶O/²³⁸U¹⁶O = ((²³⁶U¹⁶O + ²³⁵U¹⁶O¹H)/²³⁸U¹⁶O) − (²³⁸U¹⁶O¹H/²³⁸U¹⁶O) × (²³⁵U¹⁶O/²³⁸U¹⁶O). In principal this is similar to the equation for the elemental ²³⁶U/²³⁸U correction, except that it utilizes the molecular secondary ion species which is likely to be more appropriate for the ²³⁶U¹⁶O/²³⁸U¹⁶O corrected ratio. Applying this correction scheme does not reduce, on average, the degree of scatter exhibited by the ²³⁶U¹⁶O/²³⁸U¹⁶O ratios (supplementary table 2b) for the UO₂ dispersed onto the various substrates. However, for UO₂ mounted on the carbon sticky tab and mounted in epoxy, as well as the NIST-610 glass, the corrected ²³⁶U¹⁶O/²³⁸U¹⁶O values do move slightly closer to the ‘true’ values in comparison to the uncorrected ²³⁶U¹⁶O/²³⁸U¹⁶O ratios.

Table 1 NanoSIMS Analytical conditions utilized in this study. All analyses of UO₂ were conducted with a 200 pA O^-primary beam rastered over a 5 × 5 µm area. In contrast, the NIST-610 glass was analyzed using a scanning 2 nA primary beam. All analyses consisted of 6.5 s per cycle at each mass station, with a total of 20 cycles of data for each analysis.

The cause of this behavior is not known, but an important observation may be that the ²³⁸U¹⁶O¹H signal exhibits similar behavior to the ²³⁸U¹H as a function time within the analysis in that, for some analyses, the signal remains relatively stable whereas in others it increases or decreases throughout the analysis. As with the ²³⁶U/²³⁸U correction, the discrepancy between the time of data collection for the ²³⁶U¹⁶O and ²³⁸U¹⁶O¹H secondary ion species may lead to some instability in the correction regime that is not adequately accounted for using the linear interpolation method to correct for signal drift. While the uncorrected and corrected ²³⁶U¹⁶O/²³⁸U¹⁶O ratios do not result in a systematic improvement in their accuracy when compared to the corrected and uncorrected ²³⁶U/²³⁸U ratios, the basic observation that the ²³⁶U¹⁶O/²³⁸U¹⁶O ratios are associated with better within-run precision is promising. If the sources of uncertainty introduced by the hydride correction regime can be resolved, it may ultimately be feasible to take advantage of the improved ²³⁶U¹⁶O count rate. However, this will require a better understanding of the molecular oxide and hydride formation dynamics, which will be discussed in the subsequent section.

Evidence for coupling between the U molecular hydride and oxide secondary ions

As discussed in the preceding section, developing a better understanding of molecular oxide and hydride secondary ion formation may lead to an alternative (i.e. one that is not based on the ²³⁸U¹H/²³⁸U or ²³⁸U¹⁶O¹H/²³⁸U¹⁶O ratios) correction regimes for the ²³⁶U/²³⁸U ratio determination if it can be shown that the molecular hydride production rate co-varies systematically with the production rate of a non-hydride (and interference free) molecular oxide. It may also help clarify our understanding of how us of the relatively strong signal at mass 239 to correct the comparatively lower signal at mass 236 contributes to uncertainty in the final corrected ²³⁶U/²³⁸U ratios. A different situation altogether is where the material under investigation contains both U and Pu. In such an instance, having an alternative correction is especially important since ²³⁸U¹H and ²³⁹Pu would require an MRP of 37,057 to resolve from one another. In this situation, utilizing the ²³⁶U¹⁶O/²³⁸U¹⁶O ratio would not necessarily ameliorate the issue due to the fact that it would still be necessary to correct for the contribution of ²³⁵U¹⁶O¹H on the observed ²³⁶U¹⁶O signal. To do this, one could monitor the ²³⁸U¹⁶O¹H signal (as was done in this study). However, if ²³⁹Pu is present and is forming ²³⁹Pu¹⁶O molecular oxide, which would require an MRP of 39,536 to resolve from the ²³⁸U¹⁶O¹H, it would still not be possible to accurately constrain the hydride formation rate for correction of the ²³⁶U¹⁶O/²³⁸U¹⁶O ratio for the ²³⁵U¹⁶O¹H interference.

This discussion will now seek to understand whether the secondary ion molecular U hydride formation rate can be constrained independently of the signal at mass 239 (²³⁸U¹H) or 255 (²³⁸U¹⁶O¹H). While there is still considerable uncertainty in the SIMS community over the mechanisms governing molecular secondary ion formation, co-variance between different elemental and molecular oxide species has been documented and is actually the basis for certain inter-element correction regimes utilized in other disciplines (see discussion by⁸). Therefore it is possible that there will be some co-variability between either the ²³⁸U¹H/²³⁸U and/or ²³⁸U¹⁶O¹H/²³⁸U¹⁶O hydride ratios and a non-hydride molecular oxide secondary ion species (e.g. the ²³⁸U¹⁶O/²³⁸U). If this co-variability exists, it might mean that the formation rate of the non-hydride molecular oxide observed during an analysis could be utilized to infer the hydride formation rate, thus by-passing the need to use the formula ²³⁶U/²³⁸U = ((²³⁶U + ²³⁵U¹H)/²³⁸U) − (²³⁸U¹H/²³⁸U) × (²³⁵U/²³⁸U) or its modified version for the ²³⁶U¹⁶O/²³⁸U¹⁶O ratio correction. In practice, such an approach would obviously require the existence of matrix matched reference materials as well as some other analytical considerations. However, a first step is simply to examine whether there is any evidence of this co-variability. The dataset collected in this study allows us to answer this question since the UO₂ was examined across a range of different substrates and preparation routes that presumably influence both the hydride and non-hydride molecular secondary ion formation rates. Therefore, if co-variability exists, it should be evident in the dataset collected in this study.

In Fig. 6a, it can be seen that there is a weak positive correlation between the uncorrected ²³⁶U/²³⁸U and the observed ²³⁸U¹H/²³⁸U ratio. However, the vast majority of the datapoints are clustered towards lower ²³⁸U¹H/²³⁸U ratios, whereas the data points with higher ²³⁸U¹H/²³⁸U are also those with the highest levels of within-run uncertainty on the uncorrected ²³⁶U/²³⁸U. The lack of a strong positive correlation between the uncorrected ²³⁶U/²³⁸U and the observed ²³⁸U¹H/²³⁸U ratio is not surprising given the observations made in the preceding section, that correction of the ²³⁶U/²³⁸U using the ²³⁸U¹H/²³⁸U ratio did not uniformly improve the ²³⁶U/²³⁸U determination. Unsurprisingly, in Fig. 6b there is no positive correlation between the uncorrected ²³⁶U/²³⁸U ratios and the observed ²³⁸U¹⁶O/²³⁸U ratio. As discussed earlier, it is likely that scatter in the ²³⁶U/²³⁸U ratios induced by the low count rate of the ²³⁶U secondary ion supersedes any relationships that may exist between the ²³⁵U¹H and ²³⁸U¹H hydrides (which should be one-to-one). It is also unclear whether the magnitude of the hydride interference induced shift in the uncorrected ²³⁶U/²³⁸U ratios, away from their true values, co-varies with the rate of formation of a non-hydride molecular oxide secondary ion (Fig. 6b).

Figure 6

Plots of the ²³⁶U/²³⁸U observed/true (and associated 2σ uncertainties) versus the observed ²³⁸U¹H/²³⁸U (a) and ²³⁸U¹⁶O/²³⁸U (b) ratios.

In contrast to the lack of any correlations between the ²³⁶U/²³⁸U and the observed ²³⁸U¹H/²³⁸U or ²³⁸U¹⁶O/²³⁸U ratios observed on Fig. 6, there does appear to be a stronger relationship between the uncorrected ²³⁶U¹⁶O/²³⁸U¹⁶O ratios and the ²³⁸U¹⁶O¹H/²³⁸U¹⁶O (Fig. 7a) and ²³⁸U¹⁶O/²³⁸U ratios (Fig. 7b). On Fig. 7a, it can be seen that the uncorrected ²³⁶U¹⁶O/²³⁸U¹⁶O ratios are skewed towards higher values with increasing ²³⁸U¹⁶O¹H/²³⁸U¹⁶O, which is the expected behavior. It is therefore unclear why the application of a correction regime based on the ²³⁸U¹⁶O¹H/²³⁸U¹⁶O and ²³⁵U¹⁶O/²³⁸U¹⁶O ratios results in corrected ²³⁶U¹⁶O/²³⁸U¹⁶O ratios that are more deviated from the solution ²³⁶U/²³⁸U value of 0.00002576(4) than the corrected ²³⁶U/²³⁸U ratios. In supplementary table 2b, it can be seen that the corrected ²³⁵U¹⁶O/²³⁸U¹⁶O ratios are actually associated with higher uncertainty and more scatter than the ²³⁵U/²³⁸U ratios despite the higher count rate of the ²³⁵U¹⁶O secondary ion in comparison to the ²³⁵U secondary ion. Therefore, one possibility is that this higher degree of scatter in the ²³⁵U¹⁶O/²³⁸U¹⁶O translates into scatter in the final corrected ²³⁶U¹⁶O/²³⁸U¹⁶O when using the formula ²³⁶U¹⁶O/²³⁸U¹⁶O = ((²³⁶U¹⁶O + ²³⁵U¹⁶O¹H)/²³⁸U¹⁶O) − (²³⁸U¹⁶O¹H/²³⁸U¹⁶O) × (²³⁵U¹⁶O/²³⁸U¹⁶O). While the uncorrected ²³⁶U/²³⁸U ratios do not vary systematically with a non-hydride molecular species, examination of Fig. 7b reveals that the uncorrected ²³⁶U¹⁶O/²³⁸U¹⁶O do vary with the ²³⁸U¹⁶O/²³⁸U ratio. This implies that formation of the hydrogen-bearing molecular oxide secondary ion is at the expense of the ²³⁸U¹⁶O molecular oxide, which is confirmed by examination of Fig. 8a where it can be seen that the ²³⁸U¹⁶O¹H/²³⁸U¹⁶O ratio deceases with increasing amounts of the ²³⁸U¹⁶O molecular species compared to the ²³⁸U elemental secondary ion. Similar behavior is observed for the ²³⁸U¹H/²³⁸U on Fig. 8b, where it can be seen that the ²³⁸U¹H molecular species decreases with increasing ²³⁸U¹⁶O production.

Figure 7

Plots of the ²³⁶U¹⁶O/²³⁸U¹⁶O observed/true (and associated 2σ) versus the ²³⁸U¹⁶O¹H/²³⁸U¹⁶O (a) and ²³⁸U¹⁶O/²³⁸U (b) ratios.

Figure 8

Plots of the ²³⁸U¹⁶O¹H/²³⁸U¹⁶O (a) and ²³⁸U¹H/²³⁸U (b) ratios versus the ²³⁸U¹⁶O/²³⁸U ratio.

The major impetus for exploring an alternate correction regime that does not rely on the direct measurement of the ²³⁸U¹H secondary ion species is that the commonly used correction regime relying on the equation ²³⁶U/²³⁸U = ((²³⁶U + ²³⁵U¹H)/²³⁸U) − (²³⁸U¹H/²³⁸U) × (²³⁵U/²³⁸U) cannot be used in a situation where the sample contains ²³⁹Pu. A secondary goal is to assess whether it may be possible to mitigate scatter in the corrected ²³⁶U/²³⁸U and ²³⁶U¹⁶O/²³⁸U¹⁶O ratios that arises from the low count rates of the ²³⁶U and ²³⁸U¹⁶O secondary ion species as well as the magnification of uncertainty that arises when the ²³⁵U/²³⁸U and/or ²³⁵U¹⁶O/²³⁸U¹⁶O is used to apply the hydride formation rate determined by the ²³⁸U¹H/²³⁸U and/or ²³⁸U¹⁶O¹H/²³⁸U¹⁶O ratios to the signals at mass ²³⁶U and/or ²³⁶U¹⁶O. Both goals require a practical assessment of how the various secondary ion species behave. As explained above, molecular oxide and hydride production rates do appear coupled. In theory, this coupling could be applied to the analysis of an unknown by taking an approach similar to the reference materials based calibration curves that are widely utilized in SIMS. For example, in considering that the ²³⁸U¹H and ²³⁸U¹⁶O¹H production rates are coupled to the UO/U ratio, one approach might be to establish this relationship using standards of known ²³⁶U/²³⁸U and that are matrix matched to the unknown in question, and then use the curve to apply a correction to the observed ²³⁶U/²³⁸U or ²³⁶U¹⁶O/²³⁸U¹⁶O during an analysis of the unknown based on that analyses’ observed ²³⁸U¹⁶O/²³⁸U ratio. The dataset does not currently exist to further evaluate such an approach. Application of a correction regime derived from the UO₂ dataset cannot be appropriately applied to the NIST-610 measurements since these were made using a different primary beam condition. However, the observations made in this study certainly give promise to the possibility that a correction regime for hydride formation independently of having to measure the ²³⁸U¹H species is worth pursuing.

Conclusions

Consideration of the NanoSIMS data for the ²³⁵U, ²³⁶U, and ²³⁸U elemental, the ²³⁵U¹⁶O, ²³⁶U¹⁶O, and ²³⁸U¹⁶O molecular oxide, as well as the ²³⁸U¹H and ²³⁸U¹⁶O¹H molecular hydride secondary ions for UO₂ of known isotopic composition mounted in a variety of forms as well as the NIST-610 glass reference material supports the following conclusions:

• 1. The higher count rate of the ²³⁶U¹⁶O, in comparison to the ²³⁶U, results in ²³⁶U¹⁶O/²³⁸U¹⁶O ratios with lower within-run uncertainties in comparison to the ²³⁶U/²³⁸U ratios. However, the ²³⁶U¹⁶O/²³⁸U¹⁶O ratios are more scattered than the ²³⁶U/²³⁸U ratios. Therefore, additional work is necessary to identify the cause(s) of this scatter and thus take advantage of the higher count rates afforded by the molecular oxide secondary ion species.

• 2. Use of the ²³⁸U¹H/²³⁸U and ²³⁸U¹⁶O¹H/²³⁸U¹⁶O ratios to correct for the molecular hydride interferences of ²³⁵U¹H on ²³⁶U and ²³⁵U¹⁶O¹H on ²³⁶U¹⁶O does not uniformly improve the ²³⁶U/²³⁸U or ²³⁶U¹⁶O/²³⁸U¹⁶O ratio determination. The lack of uniform improvement appears to be related to the fact that the ²³⁸U¹H/²³⁸U and ²³⁸U¹⁶O¹H/²³⁸U¹⁶O ratios tend to behave consistently (i.e. they either decrease, remain stable, or increase) within the individual analyses whereas the ²³⁶U/²³⁸U and ²³⁶U¹⁶O/²³⁸U1⁶O are considerably more scattered. When combined with the fact that the comparatively large signals for ²³⁸U¹H and ²³⁸U¹⁶O¹H must be applied to the considerably lower ²³⁶U and ²³⁶U¹⁶O signals by way of the ²³⁵U/²³⁸U or ²³⁵U¹⁶O/²³⁸U¹⁶O ratio, the result is a magnification in the amount of deviance exhibited by the corrected ²³⁶U/²³⁸U and ²³⁶U¹⁶O/²³⁸U¹⁶O ratios.

• 3. Examination of the relationships between the various elemental, molecular oxide, and molecular hydride secondary ion ratios suggest that it may be eventually possible to model hydride (both the ²³⁵U¹H and ²³⁵U¹⁶O¹H) formation rates as a function of the non-hydride molecular oxide production rates taking place within a particular analysis. This conclusion is based on the existence of co-variance between the molecular hydride and oxide production rates. However, more work is needed to further assess this possibility.

Methods

Description of materials and mounting techniques

The UO₂ analyzed in this study was produced by calcination of UO₃ (produced via internal gelation as described in⁹) spheres at 600 °C for 5 h followed by sintering at 1,700 °C for 3 h in a reducing atmosphere (Ar w/4% H₂). A large microsphere (≥ 500 µm diameter) of this sintered material was randomly selected from the batch and coarsely crushed before being crudely dispersed onto the various substrates utilized for NanoSIMS analysis by using a pair of stainless-steel tweezers. A small shard of the crushed material was also routed for uranium isotopic measurements via solution multi collector-inductively coupled plasma-mass spectrometry (MC-ICP-MS) which will be described in the subsequent paragraph. For NanoSIMS analysis, the substrates consisted of a polished carbon planchet (Ted Pella, Inc), a silicon wafer (Nova Electronic Materials), high purity (> 99.99%) platinum foil (Aldrich), a polished aluminum billet, and a carbon sticky tab (Ted Pella, Inc). Each of the substrates was observed to produce a ²³⁸U secondary ion signal ≤ than the detector background of 0.01 c/s (averaged over 5 min). Each of the substrates (except the sticky tab) were prepared to receive the UO₂ in two ways. One way was completely bare such that the particles were only adhered to surface electrostatically. The other way was with a thin coating of Apiezon-L grease. The grease coating was applied by smearing a small quantity of it onto the substrate followed by use of a cotton cleanroom wipe to smoothen and remove the bulk of the grease such that only a thin veneer of grease remained on the substrate.

In addition to the crushed UO₂ mounted on the various greased and ungreased substrates, a cross-sectioned and polished sphere taken from the same batch was also analyzed. This sphere was mounted in Buehler Epothin2 epoxy followed by use of silicon-carbide and diamond based abrasives (down to ¼ µm grit) to produce a flat surface that was then coated in 50 nm of Au using a Cressington 208 HR sputter coater outfitted with an MTM-20 thickness controller prior to analysis on the NanoSIMS 50L. A shard of the NIST-610 glass reference material was also analyzed. It was prepared in the same way as the cross-sectioned and polished UO2. The U isotopic composition of the NIST-610 glass, determined via multiple techniques, has previously been reported by⁷ as follows: ²³⁴U/²³⁸U = 0.00000945(5), ²³⁵U/²³⁸U = 0.0023856(7), and ²³⁶U/²³⁸U = 0.00004314(4).

NanoSIMS analysis

The various sample formats (greased and ungreased substrates containing crushed UO₂ as well as the polished UO₂ and NIST-610 glass) were all analyzed using a NanoSIMS 50L (described in¹⁰) at Oak Ridge National Laboratory in August of 2019. The instrument used in this study was equipped with the Hyperion-II radio-frequency plasma oxygen ion source (described in¹¹). For the U isotopic measurements, the NanoSIMS primary column was tuned through use of the L1 and L0 lenses and D1 aperture to achieve a ~ 1 µm diameter 200 pA beam of O− ions on the sample surface. The exception to this beam current is for analyses on the NIST-610 glass, which only contains ppm levels of U. For these analyses, the L1 and L0 lenses were tuned to achieve a 2 nA beam. The NanoSIMS 50L entrance and aperture slits were tuned, in conjunction with the quadrupole lens, to achieve a mass resolving power of ~ 7,000 (m/∆m) at ~ 40% relative transmission. While the NanoSIMS 50L used in this study is equipped with seven moveable detector positions (each one consisting of an inter-changeable electron multiplier and Faraday cup), mass dispersion is insufficient at the mass ranges used in this study to be able to analyze the various U isotopes within the same magnetic field. Therefore, individual analyses were conducted using a peak hoping approach with the detector and magnetic field configuration outlined in Table 1. The secondary ion imaging capability was utilized to identify the locations where individual analyses were performed within a broader region of interest (typically 50 × 50 µm area). Following a minor tuning of the secondary ion extraction and steering optics to account for slight topographical variations between analysis positions, data were collected as the primary beam was scanned over a 5 × 5 µm area using the Cameca ‘isotopes’ acquisition mode for twenty cycles (each cycle lasting 6.5 s; total analysis time ~ ≈ 70 min including magnet cycling and settling times). Prior to starting the analyses reported in this study, detector noise levels were observed to be within the instrument’s factory specifications (< 0.01 c/s averaged over five minutes). The data exported from the NanoSIMS for processing (described in “Discussion”) was in the form of counts/cycle and was uncorrected for detector deadtime.

Solution MC-ICP-MS

As mentioned in “Use of the ²³⁶U¹⁶O/²³⁸U¹⁶O vs the ²³⁶U/²³⁸U ratio”, an aliquot (consisting of a single shard) of the crushed UO₂ was also analyzed via MC-IPC-MS to obtain its uranium isotopic composition. The UO₂ was digested in 0.5 mL of 4 M HNO₃ for ~ 2 weeks at ambient conditions before analysis on a Thermo Scientific NeptunePlus MC-IPC-MS equipped with a jet interface and nuclear package. During analysis ²³⁴U, ²³⁵U, ²³⁶U, and ²³⁸U were placed on adjacent Faraday cups connected to 10¹¹ and 10¹³ Ω electronically calibrated amplifiers using a 0.3 gain calibration card. The tau factor as well as a 20-min Faraday cup baseline measurement were performed. Sample solutions were introduced with a ~ 52 µL min⁻¹ Elemental Scientific Inc. integrated PFA nebulizer into a quartz Elemental Scientific Inc. Apex Omega. The instrument sensitivity was ~ 1.4 V of signal per nanogram of uranium. The UO₂ sample was analyzed in conjunction with other unknown samples (all having depleted ²³⁵U/²³⁸U isotopic compositions) using a standard sample bracketing method with 2% HNO₃ washout blanks placed before each standard/sample. Mass fraction corrections were determined with New Brunswick Laboratory Program Office Certified Reference Material U010. Unknown solutions were corrected for mass fractionation, instrument blank, baseline, and gain using established protocols in the Nuclear Analytical Chemistry and Isotopics Laboratory at Oak Ridge National Laboratory. Controls of IRMM 183, IRMM 184, and Oak Ridge National Laboratory WRM were analyzed throughout the sequence to monitor instrument operation. Final calculated isotopic values were provided with Guide to Uncertainty in Measurement¹² compliant uncertainties. This resulted in the following isotopic ratios and 2σ uncertainties for the UO₂: ²³⁴U/²³⁸U = 0.0000086(2), ²³⁵U/²³⁸U = 0.002153(1), ²³⁶U/²³⁸U = 0.00002576(4).