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Application of the Uranium−Helium Chronometer to the Analysis of Nuclear Forensic Materials Sean D. Gates* and William S. Cassata Nuclear and Chemical Sciences Division, Lawrence Livermore National Laboratory, Livermore, California 94551, United States S Supporting Information *

ABSTRACT: Radiochronometers are used to constrain the manufacturing and processing history of actinide materials for nuclear forensic investigations. This paper describes U−He ages and He diffusion kinetics obtained from a metallic, highly enriched uranium sample. The average U−He age is 8% older than the known casting date, which indicates that excess He is present and is likely due to incomplete degassing of pre-existing He during the casting process. Although the U−He age is older than expected, the accuracy is comparable to other chronometers that have been applied to this material. Diffusion kinetics obtained from the uranium metal indicate that He is quantitatively retained under plausible storage conditions.

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the Earth and planetary sciences to determine the ages of geologic phenomenon,10 this is the first time, to our knowledge, that the technique has been applied to fuel cycle materials. The chemical and kinetic behavior of He is sufficiently different than all other actinide series daughter products that a U−He chronometric system may provide distinctive information regarding the history of the sample. As an inert gas with low solubility11 and high diffusivity, the U−He system is more likely to be reset during fuel cycle processing than other U-series daughter isotopes. Therefore, it is reasonable to assume that U−He ages are likely to reflect the time of most recent material processing, casting, or purification. Additionally, coupling the model ages obtained from the He chronometer with those from other chronometric systems will enable more precise constraints on the history of a forensic sample and provide increased confidence in the determination of model ages. This paper presents He diffusion kinetics and U−He ages obtained from a uranium metal used in the ITWG−RR3 exercise. U−He model ages obtained from these samples are compared with other chronometric constraints on their ages and the known casting date, and the diffusion kinetics are used to constrain the retentivity of He under different storage conditions.

adiochronometers are an integral component of nuclear material forensic investigations.1,2 They provide constraints on the manufacturing and processing history of nuclear materials3−6 that may aid in attribution.2 In order for a chronometric system to yield an accurate age, two conditions must be satisfied. First, the daughter nuclides must be completely removed from the parent at the time of material production, and second, the daughter nuclides must be quantitatively retained after the production process.2 If these conditions are not met, then ages obtained from the chronometric analysis, termed model ages, may be spuriously old and young, respectively. Because one does not a priori know whether an age calculated under these assumptions is meaningful, multiple chronometric systems are generally employed to examine samples of interest.7 For example, a past study analyzing highly enriched uranium (HEU) metal from the International Technical Working Group round robin 3 exercise (ITWG− RR3) employed the 234U−230Th, 235U− 231Pa, 238U−226Ra, and 235 U−227Ac systems.8,9 It was found that the 235U−231Pa system yielded a significantly older age (∼30 years) than that determined from the other systems, all of which were within two years of the known casting date (discussed in more detail below).8,9 The “nonconcordant” 231Pa age indicates incomplete purification of 231Pa from the metal during the casting event. Thus, the use of multiple actinide series chronometers provided constraints on the efficiency of daughter product segregation during the casting process and enabled a more thorough understanding of the history of the sample, as well as increased confidence in the significance of the age.9 The focus of this study is the development of an additional chronometer of relevance to nuclear forensics investigations: the U−He system. While He age dating is routinely utilized in © XXXX American Chemical Society

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EXPERIMENTAL METHODS Sample Descriptions and Preparation. A highly enriched uranium (HEU) metal from the ITWG−RR3 exercise (ITWG−RR3−B), which has been the subject of extensive prior characterization, was selected for this study. The ITWG− Received: September 5, 2016 Accepted: November 18, 2016 Published: November 18, 2016 A

DOI: 10.1021/acs.analchem.6b03502 Anal. Chem. XXXX, XXX, XXX−XXX

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Analytical Chemistry

Figure 1. (A) The ITWG−RR3 HEU material was extracted from a hollow cylindrical casting. An optical image of sample before subsectioning is shown. Interior pieces of the metal subsample were extracted using a diamond saw for U−He analyses. (B) Scanning electron microscope backscattered electron micrograph showing uranium carbide inclusions in the metal.14

Table 1. Uranium Isotopic Composition of the ITWG−RR3−B Metal Determined by Inductively Coupled Plasma Mass Spectrometrya Atomic Ratios: ITWG−RR3−B 232

U/235U

2.16 × 10−10 a

uncertainty 5.60 × 10−11

233

U/235U

4.71 × 10−7

uncertainty 4.80 × 10−8

234

U/235U

uncertainty

1.07 × 10−2

4.30 × 10−6

236

U/235U

4.44 × 10−3

uncertainty 6.50 × 10−6

238

U/235U

7.77 × 10−2

uncertainty 8.40 × 10−5

Ref 8. 3

He atoms introduced, the measured 4He/3He ratio, and the mass discrimination. Isotope abundances were calculated at the time of admission into the mass spectrometer (t = 0), based upon polynomial regressions fit to the peak-hopping scans. All heating steps and measurements used to determine the He mass discrimination were corrected for system backgrounds. In addition to the He isotope measurements, 36Ar was measured to correct for any atmospheric contributions to 4He. It was assumed that any atmospheric gases incorporated into the sample were not fractionated (i.e., the 36Ar/He ratio is equivalent to that of the atmosphere). In order to correct for any He released from the platinum−iridium alloy packet, an empty packet was degassed using the same heating schedule. Model Age Determination. Model ages were calculated based on the sample mass, total abundance of degassed He, and α production rate given by the uranium isotopic composition (Table 1).8 All uncertainties are reported at two sigma and include propagated uncertainties from the isotopic measurements, the 3He spike calibration, and the spectrometer mass discrimination. The uncertainty on the 3He spike calibration (based on pressure, temperature, and volume uncertainties) is approximately 0.7%. The uncertainty associated with the mass discrimination is 0.6%. As these two sources of uncertainty are systematic, they are excluded from assessments of the reproducibility of the U−He ages (the internal errors). For the ITWG−RR3 sample, α production is principally derived from the 238U, 235U, and 232U decay chains. 233U and 236 U are also present in this sample, but their contribution is negligible given the concentrations and half-lives. α production from the 238U decay chain was calculated using a four-term Bateman equation (238U, 234U, 230Th, and 226Ra). 226Ra decay was modeled as resulting in the production of four α particles, as the three following nuclides in the decay chain (222Rn, 218Po, and 214Pb) have extremely short half-lives (between seconds to days). Similarly, a four-term Bateman equation was used to model the 235U decay chain (235U, 231Pa, 227Ac, and 227Th). The decay of 227Th was modeled as resulting in the production of five α particles, terminating at 207Pb. The 232U series was modeled with a two-term Bateman equation (232U and 228Th).

RR3−B sample was obtained from a hollow cylindrical log (8.6 mm thick) that was cast from scrap uranium metal of unknown age on January 14, 2004 (Figure 1A).8 The uranium isotopic composition is shown in Table 1.8 Various chronometric techniques have been applied to this sample, the results of which are discordant, ranging from April 27, 1975 ± 335.8 days to May 14, 2004 ± 25.6 days (Table 4).9 A more detailed discussion of these results will be presented in a subsequent section. α decay of uranium results in the release of α particles with kinetic energies of 4−8 MeV. These α particles will typically travel on the order of fractions of a micrometer in a material as dense as uranium.12,13 Nonetheless, to avoid biasing results toward anomalously young ages, the two samples analyzed in this study (ITWG−RR3−BA, −BB) were extracted from the interior of the bulk material using a diamond saw. Sample masses varied between 8.5 and 31.0 mg. Gas Analysis. Helium measurements were performed in the Livermore Noble Gas Laboratory using a Nu Instruments Noblesse noble gas mass spectrometer equipped with six Faraday cup detectors and four ion-counting, discrete dynode multiplier detectors. All measurements used a 15 cycle peakhopping routine on a single electron multiplier. Samples for analysis were encapsulated in high-purity platinum−iridium alloy tubes, placed under ultrahigh-vacuum conditions, and incrementally degassed using a feedback-controlled laser heating schedule. Samples were heated with a 75 W Photon Machines diode laser (λ = 970 nm) equipped with a coaxially aligned optical pyrometer for temperature control. The degassing schedule consisted of extractions at temperatures of 450−1300 °C. The samples were held at the set-point temperatures for a duration of 150 s. The released gas was purified using two SAES getters (one hot and one cold). In order to determine He abundances, a calibrated 3He spike was introduced into the processing line during each heating step. In addition, He mass discrimination was monitored throughout the course of the degassing experiment via bracketing analyses of a 3He−4He standard. The number of 4He atoms released in each heating is quantified based upon the known amount of B

DOI: 10.1021/acs.analchem.6b03502 Anal. Chem. XXXX, XXX, XXX−XXX

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Analytical Chemistry Table 2. Summary of Uranium He Diffusion Parametersa

a

sample

mass (mg)

GOF (MSWD)b

ln(Do/a2) ± 2σ (ln s−1)

Ea ± 2σ (kJ/mol)

ITWG−RR3−BA ITWG−RR3−BB av

16.3 30.9

6.8 2.7

6.9 ± 0.2 7.3 ± 3.2

220.2 ± 15.0 232.6 ± 29.9 222.7 ± 10.0

Calculated assuming spherical geometry. bGOF is goodness of fit.

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Th then decays through a series of short-lived α producers (224Ra, 220Rn, 216Po, 212Bi, 212Po) until the chain terminates at stable 208Pb. Each decay of 228Th was, therefore, taken to result in the production of five He atoms. The sample also contains 14.1 ppb Pu and 3.42 ppm 237Np.14 These concentrations are orders of magnitude lower than what would be required to significantly affect the total α production (≪0.1%). Likewise, 231 Pa and 226Ra are present in disequilibrium, but their initial concentrations do not significantly (by more than 0.1%) affect the total α production rate.9 Calculation of Diffusion Kinetics. Diffusion coefficients normalized by the characteristic length scale (D/a2) were calculated for each heating step based upon the fraction of the total gas released and the extraction temperature and duration. Equations from Crank for spherical geometry, following the algorithm of Fechtig and Kalbitzer, were used.15,16 To determine the activation energy (Ea) for diffusion, linear regressions were fit to extractions that yielded reproducible D/a2 values during duplicate isothermal heating steps, and the retrograde heating steps bracketed by these measurements. The lowest temperature data from the retrograde heating cycles were neglected because the measured signals were an order of magnitude lower than other extractions and, in some instances, were not discernible above background (see Supporting Information). The metal appears to contain a distribution of diffusion length scales, potentially related to fractures imparted during sample preparation or inherent defects (discussed in more detail below). As a result, Arrhenius arrays calculated using the algorithm of Fechtig and Kalbitzer, which assumes isotropic diffusion over a single length scale, are nonlinear.16 Multidomain diffusion (MDD) models are required to reproduce the Arrhenius arrays and to simulate diffusive loss under environmental conditions of interest. For more information regarding MDD modeling, see Lovera and Richter.17 Key points are summarized here. MDD modeling is predicated on the assumption that there exists a series of discrete distribution of diffusive length scales (domains) that are degassed simultaneously during the laboratory heating experiment. During the initial heating steps, smaller domains rapidly become depleted, while larger domains retain a greater fraction of their initial gas content due to longer average diffusion distances. Eventually, the small domains are exhausted and gas diffuses solely from larger domains. During the initial degassing stage, the Arrhenius diagrams (i.e., the calculated D/a2 values) predominantly reflect gas lost from smaller domains. As degassing progresses, the Arrhenius plots increasingly reflect the kinetic characteristics of larger domains. Sample ITWG−RR3−BA was used for detailed diffusion modeling. The number of domains, the domain sizes, and the domain volume fractions in the MDD model were optimized to reproduce the Arrhenius array obtained from the incremental degassing experiment. High-temperature data above the melting point of uranium (approximately 1100 °C) were neglected in generating the MDD model. 228

RESULTS AND DISCUSSION Diffusion Kinetics. Activation energies (Ea) and the frequency factors (Do) determined from linear regressions fit to the Arrhenius arrays (see the Experimental Methods section) are shown in Table 2. The metal yields reproducible Arrhenius arrays that define an average Ea of 222.7 ± 10.0 kJ/mol. This Ea is higher than that observed in lower density uranium oxides.18 As noted above, the Arrhenius arrays are consistent with a range in diffusive length scales. A multidiffusion domain (MDD) model using four domains was constructed to fit the ITWG−RR3−BA data (Figure 2). The MDD model indicates

Figure 2. Arrhenius plot of the diffusion of He in the ITWG−RR3−B uranium metal. Orange dots indicate measured data. Blue dots are MDD model data. Dashed blue lines represent the Arrhenius arrays that describe diffusion in each of the four domains. Relative domain sizes and gas fractionations are shown to the right of the figure.

that approximately 98% of the He is retained in the largest domain (Figure 2). The other domains are at least 3 orders of magnitude smaller in size, and each contain 1.0% or less of the total He (Figure 2). This model is consistent with surficial imperfections, perhaps related to sample preparation using a diamond saw, defining the small, volumetrically insignificant domains, and the bulk of the sample defining a single, cohesive domain. The diffusion kinetics inferred from the Arrhenius plot can be used to assess the sensitivity of the U−He chronometer to thermal resetting. Fractional losses of He that would result from square-pulse heating under different temperature-duration conditions are shown in Figure 3. Regardless of domain size, the U−He system is resistant to resetting during long-term storage under environmental conditions. For example, the largest domain would only lose ∼1% of its He content if held at 400 °C for 10 years. It thus appears that resetting of the chronometer requires a high-temperature thermal event such as casting. C

DOI: 10.1021/acs.analchem.6b03502 Anal. Chem. XXXX, XXX, XXX−XXX

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Excess He may be related to the incorporation of atmospheric gases during processing or storage. For example, atmospheric He could diffuse into the melt if it were undersaturated with respect to the surrounding environment. As He has been shown to be more soluble than other atmospheric gases in liquid metals,19−21 this scenario could result in the incorporation of fractionated air. However, it is common to cast uranium under vacuum,22 and therefore this mechanism seems implausible. It is also possible that He was adsorbed on the surface of the samples. Adsorption, however, favors the heavier noble gases,23 and therefore corrections that were employed based on 36Ar (see the Experimental Methods section) would have resulted in an overcorrection for He. Consequently, atmospheric contamination of the samples does not appear to be a viable source for the observed excess He. Another possible source of the excess He is the presence of the short-lived actinides in the uranium decay chains that were not considered in the α production model. In the 238U decay chain, for instance, if the most abundant short-lived isotope, 210 Pb, was not efficiently removed during the purification or casting process, it would contribute to α production. One can place an upper bound to the contribution of this short-lived actinide to the α production of ITWG−RR3 by assuming that it was chemically purified at the date implied by the 235U−231Pa model age (April 1975), but not separated during the casting event. Under these assumptions, there would be an in-growth of 210Pb on the order of 1.0 × 108 atoms/g sample since 1975. As an excess of 7.0 × 1013 He atoms/g sample was measured, retention of 210Pb during casting cannot explain the excess He. Perhaps the most plausible source of the measured excess is He that was incompletely degassed from the melt during casting. This excess He may be derived from the scrap uranium melted for the casting or from outgassing of process components like the crucible or mold. Since the ITWG−RR3 sample was cast from scrap uranium metal from 1975 or earlier, He had accumulated from at least 29 years of decay. By extrapolating the diffusion kinetics inferred from our laboratory degassing experiment to higher temperatures, it is possible to estimate the duration for which the melt would have to be held at elevated temperatures in order to completely reset the chronometer. Under the assumption that the largest domain inferred from the MDD model (Figure 2) corresponds to ∼1 mm (the macroscopic dimension of the samples analyzed), fractional losses of He that would result from casting metals of different average dimensions (diffusive length scales) are shown in Figure 5. As previously detailed, the ITWG−RR3 scrap uranium was cast into cylinders with thicknesses on the scale of millimeters to centimeters. Typical casting conditions (e.g., temperatures of 1350−1450 °C and maximum durations of 10 h)22 appear insufficient to completely degas He from melts of such length scales (Figure 5). Although there is considerable uncertainty in this analysis, and the duration-temperature conditions shown in Figure 5 likely represent upper bounds (assuming diffusivity in the melt is higher than that inferred from an upward extrapolation of the Arrhenius array), the

Figure 3. Fractional He loss as a function of temperature and time for the largest (a0) and smallest (a3) diffusion domains. These data indicate that the U−He would not be easily reset at standard environmental conditions.

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CHRONOLOGY Two aliquots of the ITWG−RR3 material were analyzed; the masses and He abundances are detailed in Table 3. Model dates of March 25, 2003 ± 0.16 (internal) ± 0.29 (external) years and November 29, 2002 ± 0.18 (internal) ± 0.30 (external) years were obtained. Corrections to U−He ages due to atmospheric contamination and backgrounds were negligible (500 °C) processing event for a significant time duration (years). Coupling this chronometer with those previously employed for nuclear forensic applications will aid in the interpretation of unknown samples, as well as in the understanding of nuclide behavior in uranium metal during processing and purification events.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.analchem.6b03502. Complete analytical data set used to calculate the He diffusion kinetics (PDF)

Figure 5. Fractional He loss as a function of temperature and time for a diffusion domain of size 1 mm (blue) and 1 cm (red). These data indicate that residual He would likely be retained in the ITWG−RR3 sample during the casting process.

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retention of a few percent of pre-existing He is evidently probable. Assuming an initial age of 1975 for the scrap metals, the measured excess of He (7.0 × 1013 atoms/g sample) corresponds to 2.5% retention during casting, which, while consistent with the analysis outlined above, is lower than that predicted from Figure 5. This is presumably due to the assumption that the low-temperature diffusion kinetics can be extrapolated to molten uranium. Based on the measurements shown in Figure 2, it appears that the diffusion coefficient for

AUTHOR INFORMATION

Corresponding Author

*Fax: 925-422-3160. E-mail: [email protected]. ORCID

Sean D. Gates: 0000-0002-1103-4463 Notes

The authors declare no competing financial interest. E

DOI: 10.1021/acs.analchem.6b03502 Anal. Chem. XXXX, XXX, XXX−XXX

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ACKNOWLEDGMENTS This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344 with Laboratory Directed Research and Development funding (16FS025).

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REFERENCES

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DOI: 10.1021/acs.analchem.6b03502 Anal. Chem. XXXX, XXX, XXX−XXX