Article pubs.acs.org/ac
Remeasurement of
234
U Half-Life
Zsolt Varga,* Adrian Nicholl, Maria Wallenius, and Klaus Mayer European Commission, Joint Research Centre (JRC), Institute for Transuranium Elements (ITU), Postfach 2340, 76125 Karlsruhe, Germany S Supporting Information *
ABSTRACT: The half-life of 234U has been measured using a novel approach. In this method, a uranium material was chemically purified from its thorium decay product at a wellknown time. The ingrowth of the 230Th daughter product in the material was followed by measuring the accumulated 230Th daughter product relative to its parent 234U nuclide using inductively coupled plasma mass spectrometry. Then, the 234U decay constant and the respective half-life could be calculated using the radioactive decay equations based on the n(230Th)/ n(234U) amount ratio. The obtained 234U half-life is 244 900 ± 670 years (k = 1), which is in good agreement with the previously reported results in the literature with comparable uncertainty. The main advantages of the proposed method are that it does not require the assumption of secular equilibrium between 234U and 238U. Moreover, the calculation is independent from the 238U half-life value and its uncertainty. The suggested methodology can also be applied for the remeasurement of the half-lives of several other long-lived radionuclides.
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larger relative uncertainty of about 0.1% was also adapted in the evaluated and recommended half-lives by the Decay Data Evaluation Project (DDEP)10 and the Evaluated Nuclear Structure Data File (ENSDF)11 databases. For 234U, there is a higher discrepancy between the half-lives used by the radionuclide metrology community and the geochemists.12 The recommended and evaluated 234U half-life in the DDEP10 and ENSDF13 databases provided by metrology organizations is 245 500 ± 600 years, which is based on three experimental values taking into account the recommendations by Holden.14 The recommended 234U half-life was derived from the revised values of 245 000 ± 900, 245 800 ± 1300, and 245 900 ± 900 years by De Bièvre et al.24, Lounsbury and Durham,25 and Geidel’man et al.,26 respectively.14 The relative uncertainty of the combined (weighted mean) 234U half-life is 0.24%, which is much larger than that of the 235U or 238U. During the past decades, mass spectrometric techniques have mainly replaced the traditional radiometric techniques (e.g., alpha and gamma spectrometry) due to the rapid instrumental developments for age dating via the long-lived U and Th isotopes. Mass spectrometry has enabled also the remeasurement of 234U half-life with better precision. Cheng et al. redetermined the half-life of 234U using thermal ionization mass spectrometry (TIMS) in 2000.15 The method is based on the measurement of the n(234U)/n(238U) amount ratio in geological materials, which are assumed to be in secular equilibrium
ge dating is a widely used method to characterize a broad range of natural processes, such as geological and oceanographic processes or human evolution.1 230Th dating, also referred to as U/Th or 238U−234U−230Th dating, plays an important role in dating materials up to about 600 000 years.1 Its application involves the dating of carbonate sediments, bones, or teeth, the calibration of radiocarbon time scale, and establishing the absolute chronology of climate change.2−4 Age dating was also found to be the one of the most valuable signatures in nuclear forensics to determine the production date (age) of illicit uranium materials of unknown origin.5,6 The 230Th dating is based on the decay of 238U via two shortlived nuclides to 234U, which decays by alpha emission to 230Th. The equations of the radioactive decay (Bateman equations7), which are used to derive the age of the material in question, require accurate and precise knowledge of half-lives for all three radionuclides. For the present paper, all quoted uncertainties are standard uncertainties (k = 1) if not indicated otherwise. In geochronology, the most widely accepted 235U and 238U halflives are (7.0381 ± 0.0048) × 108 and (4.4683 ± 0.0024) × 109 years, respectively, reported by Jaffey et al.8 Even these very small relative uncertainties (0.068% and 0.054%, respectively) have significant contributions to the final age uncertainty. Although several databases and evaluations recommend the use of 235U and 238U half-lives from Jaffey et al., they are often applied with increased uncertainties to take into account the systematic uncertainties, which were not considered by Jaffey et al. For instance, Schön et al. doubled the 235U and 238U half-life uncertainties based on the statements by Jaffey et al. on possible systematic uncertainties.9 This approach and thus a © XXXX American Chemical Society
Received: November 18, 2015 Accepted: January 29, 2016
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DOI: 10.1021/acs.analchem.5b04370 Anal. Chem. XXXX, XXX, XXX−XXX
Article
Analytical Chemistry and behave as a closed system for 106 years or more. For such materials, the activity ratio of 234U and 238U is approximately equal to 1 (secular equilibrium); thus, the 234U half-life can be calculated using the measured n(234U)/n(238U) amount ratio and half-life of 238U. The obtained 234U half-life was 245 250 ± 245 years (0.1% relative uncertainty), which has much better uncertainty than the previously reported 234U half-lives. In 2013, using the same approach, but measured by multicollector inductively coupled plasma mass spectrometry (MC-ICPMS), an improved 234U half-life of 245 620 ± 130 years (0.053% relative uncertainty) could be achieved by Cheng et al.16 Both half-life values measured by the mass spectrometric techniques are consistent with the previously reported half-lives. However, their uncertainties are presumed to be underestimated, because they were calculated using the low uncertainty estimate of the Jaffey et al. value.8 Since the n(234U)/n(238U) amount ratio can be very precisely determined by mass spectrometry, the uncertainty of the calculated 234U half-life is dominated by the 238U half-life uncertainty.9 Both 234U half-lives by Cheng et al.15,16 are widely used by geologists, also for the sake of traceability and comparability of age results.
λ=
n(230Th)(t ) n(230Th)0 ≈ λ + t U 234 ‐ n(234 U)(t ) n(234 U)(t )
(3)
For the considered time span of less than four years, the error caused by the linearization is less than 0.0025% (Supporting Information). Note that λTh‑230 does not appear in eq 3, meaning that the decay of the accumulated 230Th is negligible during four years, and the 230Th amount is predominantly controlled by the 234U decay. The residual term in the linear regression (n(230Th)0/n(234U)(t) value is constant to a good approximation in the considered time span of 4 years, since the decay of 234U is also negligible due to the long half-life (Supporting Information). Therefore, eq 3 can be written as follows:
CONCEPT FOR THE HALF-LIFE MEASUREMENT The aim of the present study is the remeasurement of the 234U half-life using a novel approach. A batch of highly enriched uranium sample with a relative mass fraction, m(234U)/m(U), of approximately 1% 234U content was chemically purified from its thorium decay product at a well-known time. The purification of the material was complete, and it was verified by gamma spectrometry and by the addition of 232Th spike to the starting material and its remeasurement from the final product. After purification, the 230Th daughter product was allowed to grow-in into the material for several years. The quantity of the accumulated daughter 230Th nuclide and the n(230Th)/n(234U) amount ratio were periodically measured after a well-registered ingrowth time. As for the completely separated materials, the n(230Th)/n(234U) ratio variation is (in the initial period) approximately linearly proportional to the 234 U decay constant, and the half-life can be calculated. The measurements were performed over a time span of 3.5 years, which was sufficiently long to obtain a well-measurable quantity of the 230Th daughter product for the mass spectrometric analysis. After separation of the 230Th daughter product from its 234U parent nuclide, the 230Th starts to grow-in into the material according to the radioactive decay equation (eq 1).7
n(230Th)(t ) n(230Th)0 ≈ λ + t U‐234 n(234 U)(t ) n(234 U)0
(4)
where n(234U)0 is the amount of 234U at the time of separation (t = 0). Consequently, the n(230Th)/n(234U) amount ratio is linearly proportional to the time elapsed since the chemical separation (age, t), where the regression coefficient is equal to the decay constant. Overall, the above-described simplifications result in an error of less than 0.003% in the considered time span, which is well below the measurement uncertainties of the 230Th and 234U concentrations. Plotting the n(230Th)/n(234U) ratio as a function of time (sample age) and using linear regression, λU‑234 can be obtained as the slope (regression coefficient) of the fitted linear function, while the intercept gives the amount of residual after the chemical separation. It is noteworthy to mention that in this case λU‑234 will result in actually the almost exclusive partial decay constant (and the respective half-life) of 234 U by alpha decay to 230Th, since the 234U spontaneous fission branching of (1.6 ± 0.2) × 10−9%10 is negligible. The proposed method is similar to the 87Rb decay constant measurement by Rotenberg et al.;17 however, in our case, the time of separation is exactly known and the completeness of purification was confirmed. This also allows the use of shorter time-scale (less than 4 years compared to 30 years) for the ingrowth. The only theoretical assumption of the described method is that the sample behaves as a closed system, meaning that there is no loss or increase for either the 234U parent nuclide or the 230 Th decay product. This condition was accomplished by keeping the sample in solid form to avoid Th adsorption (U/ Th fractionation), which was also verified in our previous study.18−20
λU‐234 n(230Th)(t ) = (e−λU‐234t − e−λ Th‐230t ) 234 λ Th‐230 − λU‐234 n( U)(t ) n(230Th)0 −λ Th‐230t e n(234 U)(t )
(2)
where λ is the decay constant and T1/2 is the half-life of the radionuclide. We can simplify eq 1 considerably, due to the long half-lives of 230Th and 234U (small decay constants) and short ingrowth time (less than 3.5 years for the present study). Since the λU‑234 and λTh‑230 decay constants ((2.823 ± 0.068) × 10−6 and (9.195 ± 0.037) × 10−6 year−1, respectively10) and the considered time span are very small, their product, λt is close to 0 to a good approximation. For example, λTh‑230t is equal to 3.7 × 10−5 for t = 4 years applying the DDEP 230Th half-life and is, thus, negligible in the given time span. Thus, using the ex ≈ 1 + x and (1 − λTh‑230t) ≈ 1 approximations, eq 1 can be rewritten as follows (eq 3):
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+
ln 2 T1/2
(1)
where n(230Th)(t) and n(234U)(t) is the amount (number of atoms as a function of time) in the sample as the function of time, λTh‑230 and λU‑234 are the decay constants of 230Th and 234 U, respectively, n(230Th)0 is the residual 230Th amount after the chemical separation (t = 0), and t is the elapsed time since the separation of the radionuclides, commonly referred to as age of the sample. The decay constants can be calculated using the respective half-lives: B
DOI: 10.1021/acs.analchem.5b04370 Anal. Chem. XXXX, XXX, XXX−XXX
Article
Analytical Chemistry
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EXPERIMENTAL SECTION Instrumentation. The U and Th measurements were carried out using a double-focusing magnetic sector inductively coupled plasma mass spectrometer (ICPMS) equipped with a single electron multiplier (Element2, Thermo Electron Corp., Bremen, Germany). All measurements were carried out in low resolution mode (R = 300) using a low-flow microconcentric nebulizer operated in a self-aspirating mode (flow rate was approximately 50 μL min−1) in combination with a Teflon Scott-type spray chamber. The U concentrations and isotopic compositions were also measured for most of the samples by TIMS using a MAT261 instrument (Finnigan MAT, Bremen Germany). The gamma spectrometric measurements for the U recovery and Th separation factor calculations were performed using a well-type HPGe detector (GCW 2022 model, Canberra Industries Inc., USA) with approximately 20% relative efficiency and a resolution of
