Introduction

One of the goals of nuclear material security is to infer the histories of nuclear facilities in order to ascertain the unauthorized production of nuclear materials1,2,3. This may involve the analysis of spent fuel from reactors, often in the form of particles. Spent fuel particulate analysis presents difficulties. The elemental and isotopic composition of spent fuel varies widely depending upon the local irradiation conditions within the reactor core. For example fuel elements near the center of the core experience greater neutron flux than those near the top or bottom or the outer edges4. This results in greater production of fission products, and also in greater transmutation of those species due to neutron capture. In addition, elemental and isotopic compositions can change significantly within a few hundred micrometers of the edge of an individual fuel pellet due to the skin effect, in which epithermal neutrons are strongly captured by 238U, resulting in copious production of Pu5,6,7,8. This in turn results in changes in the fission product distribution at the pellet edge because fission products of 239Pu have a different elemental and isotopic distribution than those of 235U.

Samples of unknown provenance could come from anywhere inside the reactor or from different reactor cycles (i.e., from different fueling/defueling events). Therefore, a collection of particles may be biased since a representative sampling is unlikely. This confounds efforts to reconstruct the core-averaged irradiation history of a batch of fuel from a given reactor cycle (i.e., the source term), and thus predict the amounts and isotopic compositions of various byproducts such as plutonium produced by the reactor. The amount of material in any given particle is limited, so analytical methods with high sample utilization are required. Because of these challenges in deriving source term information from a collection of discrete particles, techniques that yield information on many analytes simultaneously in small particles are of great value.

Given that all the particles in a collection may not come from the same source term and thus may have experienced different irradiation histories, the age of a particle of spent fuel, expressed as the time since last irradiation in a reactor, can be an important piece of information. Particle ages sort samples into coherent batches for interpretation despite the wide variation in the isotopic compositions seen in samples from the same reactor cycle or even the same fuel pellet. Radiochronometric pairs such as 241Pu–241Am give information on the age of spent fuel, however measuring the age via 241Pu decay even on relatively large particles such as those investigated here leads to high uncertainties in sample ages8. In this work we show that Sr isotopes are well suited for this purpose. Stable 88Sr and radioactive 90Sr (t½ = 28.8 year) have high fission yields, are easily measured by RIMS, and can yield sample ages.

Molybdenum and Ru are strongly produced by fission, but their isotopic compositions are more difficult to interpret with respect to their production in reactors. The isotopic composition of fission product Ru has been proposed as a burnup indicator9. Burnup is a measure of the energy generated per unit mass of fuel, and is a proxy for the total number of fissions from all fissile isotopes. In addition, Ru may be a proxy for the fraction of total fissions due to 239Pu (FPu), which increases with burnup and is higher at the pellet edge than in the center10. However, Ru and Mo undergo neutron capture in the reactor after they are produced and, together with Tc, Rh and Pd, are known to exsolve from solid UO2 to form dissolution-resistant metallic particles up to ~ 1 μm in diameter known as epsilon particles9,11,12,13,14, which can complicate interpretation.

While several techniques are in general use for spent fuel analysis, we concentrate on mass spectrometry in this discussion. (For an overview of mass spectrometric analysis in nuclear forensics see Ref.15). Mass spectrometric analysis of actinides and fission products in spent nuclear fuel have been used to ascertain reactor operating parameters such as burnup and residence time8,16,17,18. Fission product Sr has been well studied mainly in environmental analyses. Strontium-90 has been found in the environment due to the Fukushima19,20 and Chernobyl21 nuclear power plant releases, as well as from nuclear weapons testing22. Mass spectrometric detection of 90Sr must avoid isobaric 90Zr, and there are several reviews of 90Sr mass spectrometry in the literature23,24,25. The most common methods rely on dissolution and chromatographic purification of Sr to remove 90Zr, followed by analysis by Thermal Ionization Mass Spectrometry (TIMS) or Inductively-Coupled Mass Spectrometry (ICP-MS). Recently, the reaction of Zr with O2 in the collision cell of an ICP-MS has been shown to be effective in Sr isotopic analysis. This method requires dissolution but not chromatography and thus saves an analytical step. The preferential oxidation of Zr over Sr can also be exploited in a simple laser ionization mass spectrometer to perform Sr analysis without interference26.

Resonance ionization mass spectrometry (RIMS) has several advantages over other mass spectrometric techniques for this application. First, RIMS has demonstrated very high sensitivity compared to other techniques16,27,28,29,30, making it well suited to microprobe analysis of particles. Second, RIMS has the ability to discriminate against isobars by selectively ionizing only the elements of interest while leaving isobars of other elements as undetected neutral atoms31 thus obviating the need to dissolve and separate the material, which is difficult to do on small particles. Finally, when isobars are encountered during simultaneous analysis of multiple elements, delayed ionization of one element can be used to resolve—rather than discriminate against—isobars6,32.

RIMS has long been used to measure Sr, Mo, and Ru isotopic compositions, including for example to determine isotope shifts33,34, to measure isotopic compositions in stardust grains35,36,37,38,39,40, and to develop RIMS ion imaging41. RIMS methods have also been developed to measure 90Sr with high abundance sensitivity42,43, and to perform geochronology using 87Rb-87Sr44,45.

In the present work we develop and demonstrate a RIMS method to determine Sr, Mo and Ru isotopic compositions simultaneously. The samples were six spent UO2 nuclear fuel cubes, 10 μm on a side, which were previously analyzed for U, Pu, and Am isotopic compositions by RIMS6. Sample consumption from both of these analyses was extremely low, such that nearly all of the original material is left for further analysis. We compare our spatially resolved RIMS results with previous bulk analyses of Mo and Ru in the same spent fuel samples, and we use our Sr results to determine the ages of the samples. We find that spatially resolved Mo and Ru isotopic compositions show wide variations from sample to sample and do not in general correlate with bulk measurements on the same fuel pellets, indicating that variations on the micrometer scale, likely due to diffusion and exsolution, are non-negligible. In contrast, Sr analysis shows a consistent 90Sr/88Sr ratio for all six cubes, and therefore can group samples with widely disparate actinide and fission product isotopic compositions by source term. Age determination based on 90Sr decay yields accurate ages with a precision of 0.6 years.

Methods

Samples

Powdered SrTiO3, Mo2C, and Ru metal were used as isotopic standards. The spent fuel samples were the same 10 μm UO2 cubes we previously analyzed for U, Pu, and Am isotopic composition in an earlier study6, of which the vast majority of material still remained. The samples came from the Belgian Reactor No. 3 (BR3) pressurized water reactor (PWR). This fuel had an initial enrichment of 8.26% and was discharged in September of 1980. It underwent two separate irradiations, from July 1976 to April 1978, and from June 1979 to September 1980. Thus, there were operation periods of 1.75 and 1.26 years, with a 1.2-year shutdown period in between during which the fuel sat dormant in the reactor. The reactor power level varied during operation but was between 35 and 41 MW/t most of the time. While the reactor power levels for the first and second irradiations were roughly the same, the fuel rod from which these samples were cut was moved from near the center of the core during the first irradiation period to near the edge for the second. As a result, the power experienced by these samples during the second irradiation period was approximately half of that during the first period. Figure 1 is a simplified power history experienced by the fuel in this study.

Figure 1
figure 1

A simplified history of the power experienced by the fuel pellets in this study during the two irradiation periods of the reactor.

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Sample cutting and mounting is described in detail elsewhere6,8. Two sets of three 10 μm cubes from two different fuel pellets (originally 8 cm in diameter) within the same fuel rod were cut using a focused ion beam and mounted on copper holders. One fuel pellet was halfway between the center and the top of the rod while the other was from near the rod center (axial sampling positions 2 and 3 in Ref.8). The pellet-average burnups were estimated to be 39 and 54 GWd/t based on their gamma activities. Cubes were cut from three radial positions within each pellet: two within 200 μm of the edge and one near the center.

Measurements

All RIMS measurements were made on the LION instrument at Lawrence Livermore National Laboratory. The RIMS technique and the LION instrument have been described in detail elsewhere29,46,47. A Nd:YAG laser (1064 nm, 7 ns full width at half-maximum, 1000 Hz) focused to a 1–2 µm spot volatilized material from the samples. After a variable delay, neutral gas-phase atoms were resonantly ionized with pulses from tunable Ti:Sapphire lasers aligned colinearly ~ 1 mm above the sample surface. The photoions were then accelerated into a time-of-flight mass spectrometer.

Previously developed two-color/two-photon resonance ionization spectroscopy (RIS) schemes were used for Sr36, Mo35, and Ru48. The laser parameters are shown in Table 1. To resolve the Mo and Ru isobars at m/z 100, the ionization of Ru was delayed with respect to Sr and Mo, in a manner previously described to separate Pu isobars from U and Am6.

Table 1 RIS laser parameters.
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Only 88Sr and 90Sr are produced by fission, but we did not measure a standard containing 90Sr. Table 2 shows the measured stable Sr isotope ratios in the standard. Our RIMS measurements on natural Sr showed isotopic fractionations for the stable isotopes consistent with zero within 1σ (see supplementary information for a derivation of analytical uncertainties). RIMS fractionations in even-even isotope ratio measurements arise from transition isotope shifts that are significant compared to the bandwidth of the lasers. The data of Table 2 shows no significant fractionations. Estimates of the 90Sr transition isotope shifts relative to 88Sr are consistently much less than 1 GHz49,50. In particular, Lorenzen34 showed that the transition isotope shift for the 5s2(1S0) → 5s5p(1P1) transition used in this work is mass-dependent with a proportionality constant of ~ 0.06 GHz/amu. The 88Sr-90Sr pair is separated by 2 amu, so we expect an isotope shift of ~ 0.12 GHz. This is well within the 10 GHz bandwidth typical of our lasers and therefore we do not expect isotopic fractionation in the 90Sr/88Sr ratio due to the lasers.

Table 2 Sr isotopic standard measurements.
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In addition to the cubes analyzed here, one-gram portions of the fuel pellets were previously dissolved and analyzed by ICP-MS at Idaho National Laboratory51. The sampling favored the rims of the pellets but included significant portions of the center as well. We therefore expect isotope ratios measured this way to lie on a mixing line between center and edge compositions. Since no chemical separations were done prior to ICP-MS, not all isotopes were analyzed due to isobaric interference. We hereafter refer to these measurements as bulk analysis.

Models

ORIGEN-ARP Version 6.1 was used to model an analog to the BR3 reactor to predict approximate spent fuel composition under a variety of simplified operating histories. The Westinghouse 17 × 17 model was used with a fuel enrichment of 6%, which is the highest available in the ARP libraries. The detailed operating history was smoothed to produce a core average power of 32 MW, which was then scaled. For this analysis, we scaled the power of the core model to simulate the fuel from which these samples originated. The shutdown period was included, and the power was scaled by ½ for second irradiation period.

A pin cell model in the NEWT/TRITON sequence in the SCALE code system52 was developed based on parameters from previous studies4,53 to examine the radial dependence of isotope concentrations. The model was a pin cell separated into 99 radial regions, with smaller thickness cells near the radial edge of the pin. From the outer edge, the model had 25 cell regions with thicknesses of 10 µm, followed by 60 cell regions with thicknesses of 20 µm, with the remaining cell regions having progressively coarser thicknesses to the pin center. The pin cell was depleted with twenty constant-power time steps using the same power profile as the ORIGEN model. Output concentration and flux library files were generated for subsequent ORIGEN decay analysis to account for the time between fuel discharge and RIMS measurements.

In addition to these rigorous models which calculate abundances of all isotopes, we developed a simple method to estimate the 90Sr/88Sr ratio at discharge which considers only 88Sr and 90Sr produced by thermal neutron fission of 235U and 239Pu in the reactor, with continuous decay of 90Sr. Hereafter we refer to this as the TF (thermal fission) model. We used thermal fission yields from ENDF/B-VIII54. Neutron capture on Sr was neglected, as the relevant cross sections are only a few millibarns. The model was run for the known operation period of the reactor with a time step of one day using two different power profiles: that of Fig. 1, as well as the simpler profile used in the ORIGEN and pin cell models.

Results and discussion

RIMS analysis

Figure 2 shows a RIMS spectrum from one of the spent fuel samples obtained with the three-element laser setup described in the Experimental section. The delayed ionization of Ru with respect to Mo and Sr results in an apparent mass shift of 0.4 amu in the time-of-flight spectrum. Fission product 95,97,98,100Mo and 101,102,104Ru peaks are observed, as well as 100Ru formed by neutron capture on 99Tc followed by β− decay. Non-fission Mo peaks are seen at m/z 92, 94, and 96, and are presumed to be due to Mo contamination, but no non-fission Ru is observed (e.g., 99Ru). Strontium peaks at m/z 84, 86, 87, 88 and 90 are all visible, though only 88Sr and 90Sr are produced by fission. In addition, there are peaks at 88.4 and 90.4 amu (indicated with arrows in Fig. 2) attributable to off-resonant ionization of 88Sr and 90Sr by the time-delayed Ru ionization lasers. These peaks represent ~ 1% of the resonant Sr signal and are baseline resolved from the resonant Sr peaks.

Figure 2
figure 2

RIMS spectrum showing Sr (red), Mo (blue) and Ru (green) isotopes in spent nuclear fuel. The arrows indicate Sr ionized non-resonantly by the Ru lasers, which were delayed relative to the Sr and Mo lasers (see text).

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Notably absent in the spectrum of Fig. 2 is Zr, which would be observable at m/z 91 (stable 91Zr) and m/z 93 (93Zr; t½ = 1.5 × 106 year). ORIGEN and pin cell models predict copious production of these two fission products, with 91Zr/88Sr and 93Zr/88Sr ratios of 1.6 and 2.0 respectively. This is borne out by the bulk analysis, which found ratios of 1.85 and 2.11, respectively. Given the age of the fuel we expect 90Zr/90Sr = 1.04 from β− decay of 90Sr, which means that both 91Zr and 93Zr are more abundant than 88Sr in this material. The ratio of m/z 88 to m/z 93 in the spectrum is > 15,000:1. This implies a discrimination factor of > 30,000 for Sr over Zr. We conclude that there is no significant interference from 90Zr on the 90Sr peak.

As noted in the Introduction, RIMS is an extremely sensitive mass spectrometric technique, and simultaneous analysis of multiple elements makes it even more so. Figure 3 shows electron micrographs of one of the samples before and after two RIMS analysis sessions that measured first U, Pu, and Am, and then Mo, Ru, and Sr isotopic compositions. The mass of the cube is ~ 10 ng, and the concentrations of Sr, Mo and Ru as measured by bulk analysis are 871(1), 3596(8), and 2340(8) μg/g respectively. The figure shows the face of the cube after 2.2 × 106 laser shots for the previous actinide analysis and an additional 1.6 × 106 shots for the present Mo, Ru, and Sr analysis (the repetition rate was 1 kHz). Some melting of the Pt weld and Cu holder and some erosion of the UO2 at the right edge of the cube is evident, however there are no visible laser pits and we cannot determine from these images how much material was consumed. It is evident however that very little material was consumed. For reference, a 10 μm cube contains 9, 26, and 23 pg of Sr, Mo, and Ru respectively.

Figure 3
figure 3

Electron micrographs of one of the sample cubes as received (a), after U, Pu, and Am isotopic analysis (b), and after further analysis for Mo, Ru, and Sr isotopic composition (c).

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We used the ORIGEN model to estimate the abundances of minor Sr and Mo isotopes to correct for the natural Sr and Mo contamination observed in the RIMS spectra. ORIGEN provides elemental and isotopic composition estimates for bulk fuel. In this case it predicts essentially zero production of 92,94Mo so these two isotopes were used to correct for Mo contamination, which was present in every sample. The amount of contamination was highly variable from sample to sample and accounted for anywhere from 1 to 43% of the total Mo observed. Like U, Mo forms a gaseous hexafluoride and can be carried along during the enrichment process, however the amount observed here is far too high to have been introduced via this route. Analysis of a low-enriched U standard (CRM-125A) indicates ~ 1–10 ppm of Mo55, while analyses of other low-enriched U materials show 10–100 pm56. Comparing ORIGEN predictions to the RIMS measurements, we estimate that up to ~ 1300 ppm of contaminant Mo is present in our samples, which is much more than can be accounted for by initial Mo content. Further, Mo present in the virgin fuel would lead to a constant Mo content in all samples, which was not observed here. The large sample-to-sample variability indicates that Mo was introduced during sample preparation and handling.

Weak production of 84,86,87Sr is expected in a PWR, but the amounts noted in two of our samples were higher than could be accounted for by irradiation. For example, ORIGEN predicts 87Sr/88Sr < 10–6, yet a robust 87Sr peak is noted in the spectrum of Fig. 2. Using the 87Sr abundance to correct for non-fission 88Sr contamination changes the 90Sr/88Sr ratio of this sample by 6.3%. The contamination correction on one other cube changed the ratio by 2.3%; the corrections on the four others were all less than 0.1%.

Mo and Ru isotopic compositions

Table 3 gives the Ru and Mo isotopic compositions measured in each sample. Figure 4 shows measured Mo isotope ratios, along with bulk analysis values and pin cell model predictions. The pin cell model provides elemental and isotopic compositions as a function of radial position within a fuel pellet. The data and models are in broad agreement for Mo: the bulk analyses and pin cell models agree within 5%. The RIMS measurements and pin cell models show the skin effect, which was also seen in actinide isotope compositions in these and similar samples6,8. The model agrees with the measured values within ~ 10%, however the model predictions and bulk analyses show very little difference between the two pellets, whereas the RIMS measurements show significant differences, particularly in the pellet centers.

Table 3 Isotope ratios measured in spent fuel samples.
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Figure 4
figure 4

Mo isotope ratios as a function of radial position within a fuel pellet as measured by RIMS (filled symbols) and bulk analysis (open stars), and as calculated by a pin cell model (dash-dot lines). 1σ error bars are included but are generally smaller than the data symbols. Bulk analyses are arbitrarily set to a position of 2000 μm from the pellet edge.

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Figure 5 plots the Ru isotopes. The skin effect is evident in both the RIMS measurements and pin cell models, however there is considerable disagreement between the three data sets. The RIMS and bulk analyses agree for 104Ru/101Ru but disagree significantly with the model. The bulk 102Ru/101Ru ratios agree well with the model but are significantly different from the RIMS values. Figure 5 also shows the 100Ru/101Ru ratio, for which there is no bulk analysis. Here the pin cell model predicts essentially no skin effect, but one of the pellets shows a dramatic increase in 100Ru/101Ru at the edge while the other does not.

Figure 5
figure 5

Ru isotope ratios as a function of radial position within a fuel pellet. See Fig. 4 caption and legend for details.

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The Mo and Ru isotopic compositions are expected to vary with position within the reactor primarily due to variations in burnup and FPu. Burnup and FPu are only loosely correlated. Burnup is related to the total number fissions, which produces both fission products and neutrons. Fission product elemental and isotopic compositions are modified by neutron capture during reactor operation. Neutron irradiation also generates 239Pu via capture on 238U, which increases FPu. In the case of Mo and especially Ru, the isotopic composition of these fission products is strongly affected by whether the fissioning isotope is 235U or 239Pu. However, the amount of 239Pu produced, and hence FPu, depends strongly on the character of the local neutron spectrum, which varies between the center and edge of a fuel pellet. Our pin cell models predict that burnup increases by a factor of about 1.3 from center to edge, but 239Pu concentration increases by a factor of 3. The same 3 × increase in 239Pu at the pellet edge has been measured in irradiated PWR fuel including some from samples taken from the same axial position as this work5,7,8. This is due to the skin effect, i.e., the strong capture of some epithermal neutrons near the edge due to resonances in the capture cross section of 238U. These epithermal neutrons are then greatly reduced in the pellet center due to the resonance self-shielding effect. This leads to higher FPu near the pellet edge that is out of proportion to the local number of total fissions, therefore burnup alone is not sufficient to predict local fission product compositions.

The effect of FPu is in some sense isolable, i.e. one can understand how isotope ratios change with FPu, and explain why Ru has been proposed as an indicator of the relative 239Pu fissions10. Figure 6 shows the expected change in the 100Mo/95Mo and 104Ru/101Ru ratios as a function of FPu alone (i.e., ignoring neutron capture on Mo and Ru). Here we normalize by the light fission product isotopes of Mo and Ru as these ratios should respond most strongly to changes in FPu. In the figure, the ratios are normalized to their values at FPu = 0. The 101Ru/104Ru ratio increases by > 60% as FPu rises from 0 to 0.35, reflecting the strong differences in the 235U and 239Pu fission yields of 101Ru and 104Ru. The measured 101Ru/104Ru and 100Mo/95Mo ratios do increase as expected at the pellet edge as seen in Figs. 4 and 5.

Figure 6
figure 6

Expected change in selected Sr, Mo, and Ru isotope ratios due solely to fission yield as a function of Pu fission fraction (FPu). Ratios are normalized to their values at FPu = 0.

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In addition, fission produces neutrons for capture on fission products, which changes isotope ratios as capture cross sections can vary widely among isotopes. For example, the thermal neutron capture cross sections for 104Ru and 101Ru are 1.5 and 16.8 barns54, so that the 104Ru/101Ru ratio is expected to decrease with increasing burnup due to faster depletion of 101Ru (ignoring capture on precursor nuclei, which are all short-lived in this case). This is opposite to the expected effect from FPu, in which 104Ru/101Ru increases with burnup.

These descriptions are conceptual, but can be quantified by modeling. The estimated overall FPu for our samples is ~ 0.1551, which corresponds to an increase in the 101Ru/104Ru ratio of ~ 30% in Fig. 6, however because FPu changes over the course of the irradiation, Ru produced early in the irradiation will have a different isotopic composition than Ru produced later, so the effect must be integrated over the irradiation history. Similarly, Ru produced early will be subject to greater neutron capture, which must also be integrated over the irradiation history. This is accounted for in the pin cell models plotted in Figs. 4 and 5. In general, the agreement between the models and the bulk data is within 5%, except for the 101Ru/104Ru ratio which differs by > 30%. However, the RIMS microprobe data, which sampled 1–2 μm regions of the 10 μm fuel samples, shows much more variability than predicted by the models or seen in the bulk measurements. Microscale variability has been seen in unirradiated UO2 fuel, in which the 235U/238U ratio can vary by factors of several on the micrometer scale57,58,59. While we do not know whether our samples had similar variability prior to irradiation, such large differences in the initial 235U enrichment from spot to spot could possibily lead to wide variations in burnup and FPu, and hence in the fission product isotopic compositions, and are not accounted for in the reactor models.

The observed microscale variability of Mo and especially Ru isotopic compositions may also be influenced by the fact that these metals, along with Tc, are known to exsolve from UO2 solid solution to form metallic particles up to ~ 1 μm in diameter. These are known as epsilon particles because they have the ε-ruthenium crystal structure11,12, and are not accounted for in the reactor models. Depending on where and when this process occurs, the chemical and isotopic compositions of the particles could vary as contributions from precipitation and fission become diffusion-limited. The isotopic composition of the metals in the particles would still be subject to alteration by neutron capture, however. The probe size for the RIMS analyses was ~ 2 μm, which is smaller than the 10 μm cube and could have sampled particle-rich or particle-poor regions. This may account for the observed difference between the RIMS and bulk analyses, since epsilon particles are resistant to acid dissolution and would not be represented in the bulk analyses. For example, it may account for the behavior of the 100Ru/101Ru system, which shows a dramatic difference between the two pellets (Fig. 5). The low 100Ru/101Ru ratio observed near the center of one of the pellets may be due to a Tc-poor particle present under the probe beam during that particular analysis, so that relatively little 100Ru was produced after the particle formed. The unusual irradiation history of these samples makes interpretation difficult, since diffusion would have stopped and restarted many times (Fig. 1).

Sr isotopic composition

Figure 7 shows the measured 90Sr/88Sr ratios along with the values predicted by the pin cell model as a function of the sample position within the fuel pellets. The 90Sr abundance from the pin cell model was decayed 40.8 years to account for the known cooling time of the samples (i.e., the time since they were discharged from the reactor). Here the model predicts essentially no change in the 90Sr/88Sr ratios as a function of the sample position or burnup. The burnups in Fig. 7 refer to the center of the pellet; the predicted burnup at the pellet edge is ~ 1.3 × higher, such that a range of burnups from 39 to 70 GWd/t are represented in the models. Even so, the pin cell model predicts no difference in the 90Sr/88Sr ratios for any of the samples, and the predictions are in excellent agreement with the measured values, which do not show the microscale variability seen in Mo and Ru.

Figure 7
figure 7

Measured 90Sr/88Sr (symbols) and pin cell model prediction (line). Uncertainties on the measured values are 1σ. The pin cell model predictions for 39 and 54 GWd/t are nearly identical so only one is shown (39 GWd/t). The pellet center is at 4000 μm, the edge is at zero.

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The insensitivity of the Sr ratio to burnup and skin effect is due to two main factors. First, unlike Mo and Ru, the 90Sr/88Sr ratio is insensitive to FPu. The 90Sr/88Sr ratios produced by thermal neutron fission of the two isotopes differ only slightly: 1.617 for 235U fission vs. 1.582 for 239Pu fission. The change in the 90Sr/88Sr ratio over a range of FPu from 0 to 0.35 is less than 0.4%, as shown in Fig. 6. We therefore do not expect the 90Sr/88Sr ratio to show a significant skin effect. Second, the thermal neutron capture cross sections of 88Sr and 90Sr are very low, only 9 and 15 mb respectively, compared to 100–1300 mb for the Mo and Ru isotopes. We therefore do not expect neutron capture to have a significant effect, and estimates of the cooling time based on various models with and without neutron capture bear this out (below).Table 3 gives the 90Sr/88Sr ratios. The mean square weighted deviation (MSWD) of the six 90Sr/88Sr ratios is 0.8, indicating that the samples are statistically indistinguishable. This is in strong contrast to the Mo and Ru isotopic compositions, whose MSWDs range from 11 to > 300 (the upper 95% confidence limit for MSWD for six measurements is 2.5660. Similar scatter was seen in previous actinide measurements on these same six samples6. Based solely on the actinide data the samples could not be confidently assigned to the same source term, however the Sr data ties them together. Figure 8 plots 240Pu/239Pu and 90Sr/88Sr ratios as a function of 235U/238U for all six samples, using Pu and U analysis from our previous work6. The 235U/238U ratio serves as a rough indicator of burnup, and thus of the irradiation conditions within the reactor. The 240Pu/239Pu ratios correlate inversely with 235U/238U as expected, since higher 235U consumption leads to greater neutron capture on 238U and drives the production of Pu, which over time, leads to production of 240Pu via neutron capture on 239Pu. However, the scatter about the correlation line is considerable and is far outside the uncertainties in the measurements. In the absence of additional information, one cannot be certain that all six particles belong to the same source term. For example, even if they all are from the same reactor, they could represent more than one fueling / defueling event. The 90Sr/88Sr ratios measured in the same samples form a tight group and are independent of burnup as shown in Fig. 8. The Sr analysis establishes that all six samples belong to the same source term. In collections with particles representing multiple source terms, Sr analysis allows particles to be grouped and interpreted appropriately. However, one caveat is that Sr isotope ratios could not distinguish between samples from two different reactors if they had fuel cycles that started and stopped at the same time (within some uncertainty, in this case about half a year—see below) and were run with similar power profiles.

Figure 8
figure 8

240Pu/239Pu and 90Sr/88Sr vs. 235U/238U in six samples of spent fuel. Pu and U data are from ref.1. Uncertainties are 1σ.

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The independence of the 90Sr/88Sr ratio on burnup and FPu is well explained by the similarity of the 235U and 239Pu fission yields and the low neutron capture cross sections as a consequence of the closed neutron shell at n = 50. Barium-138 is also neutron magic (n = 82), and the 137Ba/138Ba ratio shows nearly the same independence in bulk measurements61 (here the 137Ba is radiogenic from 137Cs, which is also neutron magic). Strontium, Ba and Cs are known to form co-precipitates with metal oxides within irradiated fuel14. These precipitates dissolve along with the fuel meat and are represented in bulk analyses, but they may be encountered in microprobe measurements. However, strontium oxide is readily soluble in UO262. Therefore, little fission product strontium is expected to segregate into these precipitates, and microprobe analysis should be largely unaffected by them.

Sample age estimates

The uniform nature of Sr production across the reactor makes it a robust chronometer. A sample age can be calculated from the measured 90Sr/88Sr ratio in spent fuel according to:

$$t=\frac{-\mathrm{ln}\left(\frac{R}{{R}_{0}}\right)}{\lambda }$$
(1)

where t is the age, R is the measured 90Sr/88Sr ratio at time t, R0 is the initial ratio, and λ is the 90Sr decay constant (0.02407 year-1). Unlike traditional parent/daughter chronometers such as 241Pu/241Am, the initial 90Sr/88Sr ratio must be known to calculate an age. Simply using the relative thermal fission yields of 90Sr and 88Sr as an estimate of R0 gives an age consistent with the irradiation period, as shown below. An estimate of the cooling time can also be obtained setting R0 to the 90Sr/88Sr ratio at discharge calculated by reactor modeling.

Figure 9 shows calculated sample ages compared to the known operation period of the reactor. We used 235U thermal fission yields from ENDF/B-VIII54 to estimate R0 in Eq. (1) as 1.618(19). This method requires no assumptions or reactor models, only the tabulated fission yields and 90Sr half-life. There is no significant difference in the calculated ages of samples from pellet centers or edges, as expected from the statistical indistinguishability of the measured Sr ratios. The difference in calculated ages of the 39 GWd/t and 54 GWd/t pellets was only 0.1 years, against 1σ errors of 0.7–0.8 year for individual measurements. For irradiation times short compared to the half-life of 90Sr, the age determined this way should correspond to some time during the irradiation period. The mean calculated age for the six samples is 42.9(6) year, which lies exactly midway between the irradiation start and stop (45 and 40.8 year respectively). Ages derived from 241Pu-241Am chronometry on similar 10–20 μm samples from the same reactor are also consistent with the known age8, however they have much larger analytical uncertainties and scatter than the 90Sr ages.

Figure 9
figure 9

Sample ages determined using 235U thermal fission yields for 90Sr and 88Sr to calculate the initial 90Sr/88Sr ratio. Blue bands represent the two periods of operation of the reactor (See Fig. 1). Open symbols correspond to samples from pellet centers; filled symbols from pellet edges. Uncertainties are 1σ.

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In general, the sample age calculated using the fission yields alone corresponds to the cooling time plus roughly half of the irradiation period. In this case, since we know the reactor history and cooling time, we used reactor modeling to estimate the 90Sr/88Sr ratio at discharge, which was then used in Eq. (1) to calculate the cooling time irrespective of the irradiation time. This allows us to compare models. The 90Sr/88Sr ratio changes due to both production and decay during the irradiation, and all three models showed it decreasing by 10% during the 1550-day irradiation period as burnup proceeds. For comparison, decay alone would change the ratio by only 6.6% over the same period. Figure 10 shows the results for the ORIGEN, pin cell, and TF models. Here the 90Sr/88Sr ratios of the six samples were averaged to give a single age estimate for each model. All three model ages are in excellent agreement with the known cooling time of 40.8 year. In particular, the simple TF model is in agreement with the more sophisticated models.

Figure 10
figure 10

Cooling times calculated from various reactor models. The known cooling time of 40.8 years is indicated by the dashed line. Uncertainties are 1σ.

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The agreement between the TF and more rigorous models validates the assumption that neutron capture on Sr—which is accounted for in the ORIGEN and pin cell models but omitted in the TF model—is negligible. The TF model is also robust with respect to FPu, which is implicit in the other models but is adjustable the TF model. Changing FPu from zero to 0.25 changes the cooling time estimate by only 0.1 year. We used a constant FPu of 0.15, which is consistent with the fraction determined from bulk analysis51. The TF method is also robust with respect to the details of the power history of the reactor. The actual power experienced by these samples was far from constant and quite atypical for a PWR power reactor, as shown by Fig. 1. However, running the TF model at a constant power for each of the two irradiation periods changed the cooling time estimate by only 0.35 year.

Conclusions

RIMS analysis of spent nuclear fuel consumes very little material and gives isotopic information on a variety of elements. The methods described here for fission products and elsewhere for actinides6 measure the isotopic compositions of three elements simultaneously, thereby further reducing material consumption. The Mo and Ru isotopic compositions show the skin effect but are not always in agreement with bulk measurements or models, possibly due to exsolution from the UO2 matrix and formation of epsilon particles, which makes interpretation difficult.

RIMS allows direct measurement of 90Sr without isobaric interference from the daughter product 90Zr, and provides a means to correct for contamination with non-fission Sr. Because the 90Sr/88Sr ratio is insensitive to both FPu and neutron capture, it does not vary as a function of sample position or burnup. This is in strong contrast to the isotopic compositions of actinides and other fission products measured in these same samples, which showed considerable variation. As a result, Sr analysis can be used to group samples by source term (i.e. reactor cycle for a given reactor), which can otherwise be difficult. Further, 90Sr/88Sr serves as a robust chronometer and is easily measured with precision sufficient to constrain the midpoint of the fuel irradiation accurately to within 0.6 year (1σ), even with the unusual power history experienced by these samples. Cooling time can be estimated by knowing the 90Sr/88Sr ratio at discharge, which is obtained from reactor modeling. The models explored here span a range from a very simple fission-only model to a relatively complicated spatially resolved pin cell model, and all yield cooling times in excellent agreement with the known value of 40.8 year.