Preparation and calibration of a ²³¹Pa reference material

Abstract

A ²³¹Pa reference material has been characterized for amount of protactinium. This reference material is primarily intended for calibration of ²³³Pa tracers produced for ²³⁵U–²³¹Pa model age measurements associated with nuclear forensics and nuclear safeguards. Primary measurements for characterization were made by isotope dilution mass spectrometry of a purified ²³¹Pa solution using a ²³³Pa isotopic spike. The spike was calibrated by allowing multiple aliquots of the ²³³Pa spike solution to decay to ²³³U and then measuring the ingrown ²³³U by isotope dilution mass spectrometry using a certified uranium assay and isotopic standard as a reverse-spike. The new ²³¹Pa reference material will simplify calibration of the ²³³Pa isotope dilution spikes, provide metrological traceability, and potentially reduce the overall measurement uncertainty of model ages.

Introduction

Determining the date of the most recent processing step that resulted in separation of a special nuclear material, such as plutonium or enriched uranium, from its daughter products is one of the most diagnostic attributes than can be derived from nuclear forensic analyses. These dates are referred to as model purification ages and are calculated from the measured atomic ratio of parent–daughter nuclide pairs. The radioactive decay of ²³⁵U to ²³¹Pa has been used for determining radiometric ages of relatively young (< 200,000 a) uranium-bearing geologic materials since the 1950s [1]. More recently, ²³¹Pa–²³⁵U dating has also been utilized to measure model purification ages of uranium materials associated with the nuclear fuel cycle [2–4]. Initially, ²³⁵U–²³¹Pa dating was performed using α-counting radioactivity measurement methods but the utility of the activity-based measurements was hindered by the limited resolution of the technique. Pickett et al. [5] developed a ²³¹Pa–²³⁵U dating method that uses thermal ionization mass spectrometry (TIMS) to achieve faster and more precise measurement results. For this method, the amount of ²³¹Pa in a sample is measured by isotope dilution mass spectrometry (IDMS) using a ²³³Pa isotopic spike. Regelous et al. [6] demonstrated that ²³¹Pa IDMS measurements can be performed using multi-collector inductively coupled plasma mass spectrometry (MC-ICP-MS) instead of TIMS and noted that the greater ionization efficiency of the MC-ICP-MS method is advantageous when measuring the minute quantity (ng to fg) of ingrown ²³¹Pa that is present in most samples. Despite these advances, the difficulty of preparing and calibrating a ²³³Pa isotopic IDMS spike has been a significant barrier to routine use of ²³⁵U–²³¹Pa dating by the nuclear forensic analytical community.

The two principal methods for obtaining starting material for a ²³³Pa IDMS spike are separation from ²³⁷Np [5, 7] and thermal neutron irradiation of ²³²Th [7–10]. The ²³⁷Np nuclide has a half-life of (2.144 ± 0.007) 10⁶ a [11], decaying by α particle emission directly to ²³³Pa with a half-life of only (26.98 ± 0.02) days [12]. ²³³Pa approaches 99% of the secular equilibrium concentration with ²³⁷Np after about 180 days, which approximates the frequency with which a ²³³Pa spike can be “milked” from a ²³⁷Np “cow”. Irradiation of ²³²Th can produce ²³³Pa on-demand but requires access to a sufficiently intense thermal neutron flux and appropriate handling facilities for the irradiated material. Regardless of production method, to use ²³³Pa as an isotopic spike it must be separated from other radionuclides and then calibrated for amount of substance (mol). Once prepared and calibrated, a batch of ²³³Pa has a useful lifetime of just a few months before there is insufficient material for mass spectrometric analysis.

Calibration of ²³³Pa has traditionally been performed by reverse-IDMS using geological materials containing uranium that is assumed to be in secular equilibrium with its decay products. This calibration method requires a difficult dissolution of a silicate rock material, is fundamentally dependent on a known or precisely measured uranium concentration, and results in a complicated traceability chain for the measurements. Naperstkow et al. [10] avoided the use of rock standards and reverse IDMS by employing efficiency traced liquid scintillation counting (CNET¹), 4πβ-γ coincidence, and 4πβ-γ anticoincidence radioactivity measurement methods to calibrate a ²³³Pa solution with resulting uncertainties between 0.8 and 1% (k = 2). Although this traceable activity-based calibration was performed using sophisticated counting methods that are not routinely used outside of laboratories specializing in radioactivity measurements, an ion chamber can be calibrated for more routine activity-based ²³³Pa spike characterization. Varga et al. [4] demonstrated an indirect calibration for ²³³Pa by using γ-counting methods to measure the molality (mol g⁻¹) of ²³⁷Np in a solution that was in secular equilibrium with its ²³³Pa daughter and adding the unseparated neptunium solution directly to analysis samples. This method avoids a laborious ²³³Pa spike calibration but will typically have a relatively large uncertainty (> 2%, k = 2) due to the limits of neptunium assay measurements. More recently, Treinen et al. [13] demonstrated the use of a characterized solution of high-purity ²³¹Pa as a reverse-spike for accurate and reproducible ²³³Pa calibrations. This calibration was accomplished with less difficulty than rock standards and with uncertainties that are equivalent to, or lower than, those that can be reasonably obtained using activity measurements.

The ²³¹Pa nuclide has a half-life of (32 670 ± 520) a [11], which is sufficiently long for a batch of purified ²³¹Pa to be prepared as a calibration reference material with a shelf-life of 20 years or even considerably longer. A ²³¹Pa reference material could be utilized to perform reverse-IDMS calibrations in parallel with ²³³Pa IDMS analyses of unknown samples. This would simplify calibration of ²³³Pa isotopic tracer, increase the reliability of the IDMS measurements, and reduce uncertainties of ²³¹Pa amount measurements made on unknown samples. The preparation and characterization of such a ²³¹Pa reference material, specifically for calibration of ²³³Pa isotopic spikes, is described here. This new reference material was produced as part of an ongoing United States Department of Homeland Security program to enhance analytical capabilities for nuclear forensics. Production of the ²³¹Pa reference material and characterization measurements were performed at Lawrence Livermore National Laboratory (LLNL). Activity measurements for verification of the primary characterization value were performed at National Institute of Standards and Technology (NIST), the National Research Council of Canada (NRC), and the National Physical Laboratory in the United Kingdom (NPL).

Experimental

Figure 1 is a schematic of the process for preparation and characterization of the ²³¹Pa reference material. A purified ²³¹Pa master (M) solution and a freshly separated ²³³Pa spike (S) solution were prepared on consecutive days. Carefully weighed aliquots were taken from both M and S solutions and shipped to NIST, NPL, and NRC for activity measurements. Additional aliquots of the S solution were dispensed for analysis of ingrown ²³³U by IDMS. A subsample of the ²³¹Pa M solution was then diluted to produce the ²³¹Pa reference material (RM) solution which was dispensed to create individual reference material units. In parallel with unit production, subsamples of RM solution were spiked with the S solution. The protactinium isotopic ratios of the mixed ²³³Pa–²³¹Pa samples were measured to determinate the molality of ²³¹Pa in the RM solution by IDMS. Radioactivity measurements performed on the M and S solutions were used for verification of IDMS measurement results. Preparation of the protactinium solutions, production of the reference material units, and characterization analyses are described in further detail below. Activity measurements performed for verification of the characterization analyses are described elsewhere [13–15] with results summarized here.

Fig. 1.

²³¹Pa reference material production and characterization process. The “M Solution” is the concentrated ²³¹Pa master solution purified for this project. The “RM Solution” is a stock solution prepared for production of reference material units and the “S Solution” is the ²³³Pa spike prepared for primary calibration of the RM solution. Heavier arrows in the figure indicate material transfers and analyses performed for the primary calibration for the molality of ²³¹Pa in the RM solution. Lighter arrows indicate material transfer and analyses for verification measurements

Material preparation

An initial clean up step was performed on approximately 20 mg of ²³¹Pa stored at LLNL. This procedure, described in [16], is a precipitation of a hydrous protactinium oxide (Pa₂O₅·xH₂O) from a HF acid solution and repeated rinses of the precipitate. After this step, the protactinium was again dissolved in HF (Seastar Chemicals Inc., Vancouver, Canada)² and a subsample containing 2 mg protactinium was dried first in perchloric acid and then dried two times in concentrated HNO₃ (Seastar Chemicals Inc., Vancouver, Canada). An additional separation was then performed on this sample using a silica gel column chemistry technique described in Treinen et al. [17]. A subsample of this purified material (approximately 125 μg of ²³¹Pa) was prepared as the M solution by diluting the ²³¹Pa in a mixed solution of 2 mol L⁻¹ HNO₃ and 0.1 mol L⁻¹ HF. Aliquots of the M solution (5 mL) were transferred to Savillex perfluoroalkoxy (PFA) Teflon vials (Minneapolis, MN, USA) and shipped to NPL, NRC, and NIST for massic activity measurements. MC-ICP-MS mass scans of the purified M solution showed a n(227)/n(²³¹Pa) ratio of approximately 1 × 10⁻⁷, indicating low levels of ²³¹Pa decay products (²²⁷Ac and ²²⁷Th). Another mass spectrometric analysis of the ²³¹Pa master solution, performed 6 months after purification, indicated a n(227)/n(²³¹Pa) ratio that was 0.9% higher than expected from ingrowth alone. Based on these data, it is estimated that approximately 85% of the 227 amu contaminant, present immediately after purification, was unsupported ²²⁷Th (T_1/2 = 18.62 ± 0.09 days [18]) and the remainder was ²²⁷Ac (T_1/2 = 21.782 ± 0.003 a [19]). This excess material is not detrimental to use of the ²³¹Pa as an IDMS calibration standard, but it does represent a potentially significant source of bias for radioactivity measurements, particularly measurements performed within several months of purification.

The RM solution was prepared from the M solution as a stock material for production of the reference material units. A 4 g subsample of the M solution was transferred to a pre-cleaned and weighed 1 L fluorinated ethylene propylene (FEP) Teflon bottle, diluted with 650 mL of a mixed 2 mol L⁻¹ HNO₃ and 0.1 mol L⁻¹ HF solution, and homogenized by hand shaking (gravimetrically determined dilution factor is 187.279 ± 0.047, k = 2). Five (5) subsamples of the ²³¹Pa RM solution were prepared for IDMS analysis by transferring carefully weighed aliquots (0.5–1.0 g) to new pre-cleaned Savillex vials. The potential for weighing bias due to evaporation during dispensing was minimized for these subsamples (and all subsequent spike or sample aliquots for IDMS analyses) by transferring the solution using disposable low-density polyethylene pycnometers (Canus Inc., Ottawa, Canada) with capillary tips. Masses of the subsamples were determined by the difference between the pycnometer mass when filled with solution and after dispensing. At least 3 replicates weighings were performed for all mass measurements. The balance used for this work was a calibrated 5-place XPE 105 electronic balance (Metter-Toledo, Columbus, OH, USA) that was regularly checked for accuracy and linearity using a calibrated weight set.

Following preparation of the IDMS analysis samples, the RM solution was dispensed using a Hamilton MICRO-LAB 600 dispenser (Reno, NV, USA) outfitted with a new 5 mL dispensing syringe. Intake and dispensing tubing was thoroughly flushed by rinsing with a dilute HNO₃ and HF mixed solution followed by deionized water. Prior to dispensing the RM solution, approximately 30 mL of mixed 2 mol L⁻¹ HNO₃ and 0.1 mol L⁻¹ HF solution was run through the apparatus (6 dispensing cycles). The uptake tubing was then transferred to the RM solution stock bottle and 30 mL of the solution was dispensed before filling the first reference material unit. A total of 112 ²³¹Pa reference material units were prepared with each unit comprised of 5 mL of solution in a pre-cleaned and pre-weighed 30 mL FEP bottle that was previously labelled with a number corresponding to the order in which the bottle was filled. Each unit was tightly capped after receiving the solution and all units were then carefully reweighed. The reference material units were filled in a single effort lasting approximately 1 h. The mean mass of dispensed solution was 5.2978 g with an expanded uncertainty of 0.0022 g (k = 2). Individual unit bottles were packaged by wrapping the top of the bottle and cap with polytetrafluoroethylene (PTFE) Teflon tape which, in turn, was wrapped with vinyl tape to prevent loosening of the cap or unravelling of the PTFE tape. Each bottle was placed in an individual aluminized Mylar pouch along with acid-resistant absorbent pads and the pouch was then heat sealed.

A batch of ²³³Pa IDMS spike was prepared by separation from a high-purity ²³⁷Np solution (65 mg of ²³⁷Np in HCl). This separation was performed using an AG MP-1 M anion exchange resin followed by a silica gel separation, as described in [17]. The purification procedure was completed at 22:50 UTC on 27 June 2017. A 1 mol L⁻¹ HNO₃ solution is used in the silica gel separation procedure as a rinse prior to eluting the protactinium. MC-ICP-MS mass scans of this rinse solution indicated a n(²³³Pa)/n(²³⁸U) ratio of approximately 0.011 whereas ²³⁸U was not observed in the separated ²³³Pa; thus demonstrating the protactinium was quantitatively separated from uranium, including ingrown ²³³U. Mass scans of the separated protactinium also indicated a n(²³³Pa)/n(²³⁷Np) atom ratio of > 3 which corresponds to an activity ratio greater than 1.0 × 10⁸. The total integrated quantity of ²³³Pa that could grow in from this proportion of ²³⁷Np, over the course of project activities (300 days), is inconsequential (< 0.01% relative to the amount of ²³³Pa present after purification). The purified ²³³Pa was dissolved in a mixed 2 mol L⁻¹ HNO₃ and 0.1 mol L⁻¹ HF solution to produce the ²³³Pa S solution with an estimated massic activity of ≈ 30 kBq g⁻¹ at the time of preparation. On 28 June 2017 aliquots of the S solution were transferred to Savillex Teflon vials and shipped to NIST, NRC, and NPL for activity calibrations. Another 4 aliquots of the ²³³Pa solution were transferred to vials which were capped, weighed, and stored for later measurement of ²³³U.

A uranium (U) reverse-spike was prepared for high-precision IDMS measurements of ²³³U in the decayed ²³³Pa calibration samples. The starting material for the reverse-spike was CRM 112-A uranium metal assay and isotopic standard [20]. For initial preparation of the uranium solution, a 0.25 g piece CRM 112-A metal was twice cleaned in 8 mol L⁻¹ HNO₃ to remove any uranium oxide prior to weighing. The metal was then dried, weighed, and dissolved in 70 mL of a mixed 2 mol L⁻¹ HNO₃ and 0.05 mol L⁻¹ HF solution to produce a relatively concentrated master solution. A 2-stage serial dilution of this uranium master solution was performed to create the U reverse-spike with a molality of (111.80 ± 0.14) pmol g⁻¹ (k = 2).

Characterization measurements

The 4 calibration aliquots of the S solution were stored for period of 298 days, after which the samples were reweighed to correct for any change to the solution mass due to evaporation. Individual samples were then split, mixed with the U reverse-spike solution, and measured on the LLNL Nuplasma HR MC-ICP-MS (Nu Instruments Ltd, Wrexham, UK). Mass spectrometry analysis conditions for these measurements are described in Table 1. The n(²³³U)/n(²³⁸U) isotopic ratios of the spiked samples were measured on 4 May 2018, by which time greater than 99.9% of ²³³Pa initially present in the S solution had decayed to ²³³U but less than 0.0003% of the ingrown ²³³U had decayed to ²²⁹Th. Accordingly, with only a small correction for remaining ²³³Pa, uranium IDMS on these subsamples provides a quantitative value for the amount of ²³³Pa originally present in the purified solution.

Table 1.

Summarized MC-ICP-MS measurement conditions for protactinium and uranium isotopic ratio analyses of IDMS samples for the ²³¹Pa RM solution and the ²³³Pa S solution

Parameter	Pa IDMS analyses	U IDMS analyses
Instrument	Nu-plasma HR multi-collector inductively-coupled plasma mass spectrometer
Collectors	231Pa L2 Faraday cup, 233Pa axial Faraday	233U L3 Faraday cup, 238U H1
	cup	Faraday cup
Introduction system	Cetac Aridus II (Omaha, NE, USA)
Nebulizer	Cetac PFA Nebulizer
Nebulizer gas flow	0.9 L/min	0.9 L/min
Solution uptake	100 μL/min	100 pL/min
Mass bias CRM	CRM U010 [22]	CRM U010
Quality control CRM	U005-A [23] and CRMs 129-A [24]	CRM U005-A and CRM 112-A
Corrections applied	Detector baseline, instrument background, detector gains, mass bias

Revised uranium isotopic ratio values cited in [21] were used for CRMs U010 and U005-A

The molality of ²³¹Pa in the RM solution was measured by IDMS using the ²³³Pa S solution as an isotopic spike. IDMS aliquots of the RM solution were mixed with aliquots of the S solution and a final purification of the mixed solutions was performed using the silica gel method. The n(²³³Pa)/n(²³¹Pa) isotopic ratio measurements for the IDMS analyses were performed, in duplicate, approximately 7 h after purification. These measurements were made on the LLNL Nu-plasma MC-ICP-MS; details of the analysis procedure are provided in Table 1. The protactinium IDMS analyses were performed 17 days after purification of the ²³³Pa S solution, so 35% of the ²³³Pa in the spike had decayed, requiring a substantial decay correction.

Verification measurements

Massic radioactivity analyses for ²³³Pa in the S solution and ²³¹Pa in the M solutions were incorporated into the reference material production project as metrologically independent verification measurements for the molality of these nuclides. A primary ²³³Pa massic activity measurement for the S solution was made by NIST using a live-timed 4πβ-γ anticoincidence counting method (LTAC) and confirmatory measurements were made by γ-spectrometry on efficiency-calibrated HPGe detectors. Details of the methods and data reduction for these analyses are provided in [13]. NRC also performed a primary calibration of S solution using an LTAC method and performed additional activity measurements using a CNET ³H efficiency-traced liquid scintillation counting method and a Triple-to-Double Coincidence Ratio (TDCR) method [14]. Finally, the S solution massic activity was measured by NPL using a 4πβ-γ coincidence counting method (Keightley, personal communication, 7 February 2018).

Massic activity calibrations for ²³¹Pa in the M solution were performed by NRC using two LSC activity measurements methods, CNET and TDCR [14]. Activity measurements of the M solution at NIST included the CNET method and α spectrometry [15]. The NIST measurements were performed in July of 2017, shortly after the samples were received, and additional CNET measurements were made in November of 2017. ²³³Pa was added to α spectrometry samples as a yield monitor for electrodeposition of the ²³¹Pa sources and the detectors were calibrated for energy and efficiency using U, Am, and Pu electrodeposited sources. NPL did not report any measurements for the ²³¹Pa.

Results

The massic activity values for ²³¹Pa in the M solution and for ²³³Pa in the S solution that were reported by the radioactivity measurement laboratories are summarized in Table 2. Also shown in the table are values for molality of ²³³Pa in the S solution and molality of ²³¹Pa in the RM solution that were calculated from the activity data. Fitzgerald et al. [15] noted that both CNET and preliminary γ-spectrometry measurements of the ²³¹Pa master solution showed radioactivity in the samples declining for several weeks after receipt and then increasing again due to ingrowth of ²³¹Pa daughter products. This pattern indicates the presence of an unsupported radioactive contaminant. Corrections were applied to the NIST and NRC counting data for ingrowth of ²³¹Pa decay chain products and an attempt was made by NIST to perform an empirical correction for the contaminant radioactivity. This correction, however, is not likely to be sufficient due the lack of quantitative data about the amount or proportion of nuclide(s) comprising the contaminating material. NRC did not attempt to apply a correction for contaminating nuclides in the ²³¹Pa M solution.

Table 2.

Measured massic activity and calculated molality of ²³³Pa in the S solution, measured massic activity of ²³¹Pa in the M solutions, and calculated molality of ²³¹Pa in the RM solution

Analysis laboratory	Analysis method	S solution 233Pa massic activity (Bq g−1)	S solution molality of 233Pa (pmol g−1)
NIST	LTAC*	26,320 ± 170	0.1470 ± 0.0010
NIST	HPGe γ spectrometry	26,120 ± 570	0.1459 ± 0.0032
NRC	LTAC*	26,190 ± 370	0.1463 ± 0.0021
NRC	Coincidence counting	26,340 ± 450	0.1471 ± 0.0025
NRC	TDCR	26,310 ± 220	0.1469 ± 0.0012
NRC	CNET 1	26,040 ± 230	0.1454 ± 0.0013
NRC	CNET 2	26,130 ± 250	0.1459 ± 0.0014
NPL	Coincidence counting*	26,340 ± 180	0.1471 ± 0.0010
Analysis laboratory	Analysis method	M solution 231Pa massic activity (Bq g−1)	RM solution molality of 231Pa (pmol g−1)
NIST	α Spectrometry*	2096 ± 68	27.6 ± 1.0
NIST	CNET Corrected	2154 ± 67	28.41 ± 0.73
NIST	CNET	2175 ± 67	28.7 ± 1.0
NRC	CNET*	2193 ± 66	28.92 ± 0.98
NRC	TDCR	2266±41	29.88 ± 0.72

Molality of ²³³Pa was converted from massic activity using the evaluated ²³³Pa half-life [12] of (26.98 ± 0.2) days (k = 1). The molality of ²³¹Pa in the RM solution was calculated from the M solution massic activity using the dilution factor of 187.279 ± 0.047 (k = 2) and the evaluated ²³¹Pa half-life [11] of (32 670 ± 260) a (k = 1). All values are decay corrected to a reference time of 27 June 2017 22:50 UTC. Uncertainties are expanded uncertainties (U=k u_c) with a coverage factor (k) of 2. NIST massic activity values are from [13] for ²³³Pa and [15] for ²³¹Pa. All massic activity values for NRC are from [14] and the cited ²³³Pa activity value from NPL is from Keightley (personal communication, 7 February 2018). CNET 1 and 2 refer to analyses performed on liquid scintillation counters from different manufacturers

^*Primary or highest confidence activity measurements, as designated by the analysis laboratories

The results for the IDMS calibration of the ²³³Pa S solution are summarized in Fig. 2 and details are provided Table 3. The 8 replicate measurement results agree within uncertainties and have an observed variability of only 0.07% relative standard deviation. The mean measured ²³³Pa molality for a reference date of 27 June 2017 22:50 UTC is 0.14690 pmol g⁻¹ with an expanded uncertainty of 0.00035 pmol g⁻¹ (0.24% relative, k = 2). This value is consistent with ²³³Pa molality values derived from primary and confirmatory massic activities calibrations performed at the radioactivity laboratories.

Fig. 2.

Measurement data for molality of ²³³Pa in the S solution. All values are for a reference time of 27 June 2017 22:50 UTC. Error bars for data points are expanded uncertainties (U = k u_c) with a coverage (k) factor of 2. A mean value for the IDMS data (solid line) and an expanded uncertainty interval for the mean value (dashed lines) are included in the figure

Table 3.

IDMS sample data and measurement results for the molality of ²³³Pa in the S solution

Sample ID	233Pa S solution* aliquots (g)	U reverse-spike aliquots (g)	Measured isotope ratio n(238U)/n(233U)	Molality of 233Pa (pmol g−1)
233Pa 1A	2.0640 ± 0.0010	0.3613 ± 0.0010	132.21 ± 0.30	0.14680 ± 0.00057
233Pa 1B	2.0586 ± 0.0010	0.7128 ± 0.0010	261.35 ± 0.59	0.14690 ± 0.00048
233Pa 2A	1.7827 ± 0.0010	0.5993 ± 0.0010	254.01 ± 0.58	0.14676 ± 0.00049
233Pa 2B	2.3084 ± 0.0010	0.6633 ± 0.0010	216.67 ± 0.49	0.14705 ± 0.00049
233Pa 3A	1.6769 ± 0.0010	0.3569 ± 0.0010	160.64 ± 0.37	0.14692 ± 0.00057
233Pa 3B	2.5439 ± 0.0010	0.4086 ± 0.0010	121.31 ± 0.28	0.14683 ± 0.00055
233Pa 4A	1.9842 ± 0.0010	0.6033 ± 0.0010	229.45 ± 0.51	0.14693 ± 0.00049
233Pa 4B	2.2204 ± 0.0010	0.4804 ± 0.0010	163.19 ± 0.37	0.14700 ± 0.00052

The quantity measured by IDMS was the molality of ²³³U in the decayed S solution (pmol ²³³U g⁻¹). Corrections for solution evaporation and undecayed ²³³Pa were applied to the IDMS data to yield molality of ²³³Pa at the reference time of 27 June 2017 22:50 UTC. Uncertainties are expanded uncertainties (U=ku_c) with a coverage factor (k) of 2. All mass values are corrected for air buoyancy

^*Correction factors for ²³³Pa sample aliquots were applied to compensate for relatively small evaporative losses (from 0.3 to 1.0%) that occurred over the interval between dispensing and aliquoting for IDMS (298 d). These factors were calculated as the quotient of the solution mass at the time of initial dispensing and the solution mass immediately prior to aliquoting for IDMS analyses

The molality of ²³³Pa in the S solution was a key variable for the protactinium IDMS measurements made to determine the molality of ²³¹Pa in the RM solution. The ²³¹Pa IDMS results are shown in Fig. 3 with details provided in Table 4. These results are also highly repeatable and have an observed variability of only 0.07% relative standard deviation. The mean molality of ²³¹Pa in the RM solution is 27.55 pmol g⁻¹ with an expanded uncertainty of 0.12 pmol g⁻¹ (0.35% relative, k = 2). The activity-based molality value calculated from alpha spectrometry measurements (Table 2) is essentially indistinguishable from the IDMS data. Activity-based molality values calculated from the LSC-based measurement methods range from 3 to 8% higher than the IDMS value.

Fig. 3.

Molality of ²³¹Pa in the RM solution. All values are for a reference time of 27 June 2017 22:50 UTC. Error bars for data points are expanded uncertainties (U = k u_c) with a coverage factor (k) of 2. A mean value for the IDMS data (solid line) and an expanded uncertainty (k = 2) interval for this mean value (dashed lines) are included in the figure

Table 4.

IDMS sample data and measurement results for the molality of ²³¹Pa in the RM solution

Sample ID	231Pa RM solution aliquots (g)	233Pa spike aliquots (g)	Measured isotope ratio* n(233Pa)/n(231Pa)	Molality of 231Pa (pmol g−1)
231Pa 1	0.6318 ± 0.0010	3.0843 ± 0.0010	0.016894 ± 0.000046	27.56 ± 0.13
231Pa 2	1.0531 ± 0.0010	3.5580 ± 0.0010	0.011701 ± 0.000048	27.54 ± 0.11
231Pa 3	0.7848 ± 0.0010	3.4152 ± 0.0010	0.015067 ± 0.000047	27.55 ± 0.14
231Pa 4	0.5688 ± 0.0010	3.4580 ± 0.0010	0.021023 ± 0.000044	27.58 ± 0.12
231Pa 5	0.8931 ± 0.0010	3.1462 ± 0.0010	0.012203 ± 0.000055	27.53 ± 0.16

For IDMS calculations, the molality of ²³³Pa in the S solution was decay corrected to the time of final purification for the protactinium IDMS mixes, 14 July 2017 18:20 UTC. Uncertainties are expanded uncertainties (U=ku_c) with a coverage factor (k) of 2. All mass values are corrected for air buoyancy

^*A correction factor (0.99936 ± 0.00059) was applied to measured n(²³³Pa)/n(²³¹Pa) ratios to account for mass spectrometer efficiency differences between ²³³Pa and ²³³U. The correction factor was calculated based on the relative proportion of ²³³U that grew in over the interval between purification and the mass spectrometer measurements and an observed transmission efficiency difference between uranium and protactinium (8.7%). This transmission difference was empirically determined based on the bias between the measured n(²³³Pa)/n(²³¹Pa) ratio of a mixed solution and the n(²³³U)/n(²³¹Pa) ratio of the same solution after the decay of ²³³Pa

The measured masses of RM solution dispensed to the ²³¹Pa reference material units have a maximum difference of only 3.1 mg (excluding a single outlier unit) which is only 0.06% of the 5.3 g of solution dispensed to each unit. The 0.35% relative expanded uncertainty for the molality of ²³¹Pa in the RM solution is much greater than the relative difference in solution masses. As a result, the variability in the mass of RM solution dispensed to individual reference material units corresponds to trivial differences in the calculated amount of ²³¹Pa in each unit and this variability does not significantly increase the uncertainty for the amount ²³¹Pa. Accordingly, a single value and uncertainty for amount ²³¹Pa can be applied to every unit in the production run. This value, of (145.96 ± 0.51) pmol (k = 2), was calculated using the mean buoyancy-corrected mass of solution aliquots dispensed to the units and uncertainty components for the range of observed masses and for a correction applied to compensate for solution evaporation during dispensing. The uncertainty for the ²³¹Pa amount value for the reference material units was estimated in accordance with international guidance for measurement uncertainty [25, 26] and includes all significant sources of uncertainty. A detailed uncertainty budget for the calculated amount of ²³¹Pa is provided in Table 5.

Table 5.

²³¹Pa reference material uncertainty budget for amount of ²³¹Pa contained in each unit

Uncertainty component	Description	Assessment type	Ui %
b231Pa	Measurement repeatability; standard uncertainty of 5 independent measurements for 231Pa molality of RM solution.	A	0.032
b233Pa	Measurement repeatability; standard uncertainty of 8 independent measurements for 233Pa molality of S solution.	A	0.023
bC112-A	IDMS tracer; standard uncertainty for uranium molality of diluted CRM 112-A solution used as U reverse-spike.	B	0.090
Decay	Decay correction; uncertainties associated with the 233Pa half-life and the interval between initial 233Pa purification and IDMS measurements.	B	0.035
Efficiency	Transmission efficiency; uncertainty of correction factor to compensate for differing mass spectrometer transmission efficiencies between uranium and protactinium during IDMS measurements.	B	0.030
MIDMS	Aliquot mass; uncertainty component associated with mass measurements of solution aliquots for IDMS.	B	0.085
Munit	Unit Unit mass; uncertainty component encompassing the maximum difference in the mass of dispensed solution aliquots and potential evaporative loss during dispensing.	B	0.027
MassSpec	Mass Mass spectrometry; estimated uncertainty associated with mass spectrometry including potential differences in mass fractionation of protactinium and uranium in MC-ICP-MS, blank corrections, background corrections, and collector efficiencies.	B	0.086
RU010	CRM U010; standard uncertainty of n(235U)/n(238U) ratio for CRM used to calibrate the mass spectrometer.	B	0.051
Remainder	Remainder correction; estimated uncertainty for 233U measurements resulting from the proportion of 233Pa remaining in IDMS samples after 10 half-lives.	B	0.008
Relative combined standard uncertainty		0.173%
Relative expanded uncertainty (k = 2)		0.35%

Assessment Type A denotes evaluation by statistical methods and Type B denotes evaluation by other methods. u_i % is the percent relative standard uncertainty for the indicated uncertainty component. The uncertainty model presented in this table was calculated using the GUM Workbench software (Metrodata GmbH, Weil am Rhein, Germany)

Discussion

The goal of this project was to produce a ²³¹Pa reference material characterized for amount of ²³¹Pa. Although this material is not being provided as a Certified Reference Material (CRM) per the definition in [27], the production project was planned and executed to satisfy the quality requirements for CRMs as outlined in international guidance documents [28, 29]. General requirements for a high-quality analytical reference material include stability, homogeneity, and metrological traceability. Additionally, characterized attribute values should have GUM-compliant uncertainties [24] and independent verification of the attribute values should be performed, when possible.

Stability of the ²³¹Pa reference material units is an important consideration. Protactinium typically occurs in solution as the pentavalent cation, Pa(V), and has long been known to form colloids that adsorb onto container walls [30]. This tendency could result in highly variable characteristics for a production run of a protactinium reference material. To mitigate the potential for this source of variability, the ²³¹Pa RM solution was prepared as a mixture of 2 mol L⁻¹ HNO₃ and 0.1 mol L⁻¹ HF. Sub μg g⁻¹ concentrations of Pa(V) are reasonably stable in H NO₃ solutions of greater than 1.0 mol L ⁻¹ and Pa(V) is highly soluble in HF solutions, even in relatively dilute solutions (e.g. 3.9 g L⁻¹ in 0.05 mol L⁻¹ HF) [31]. Furthermore, the authors have observed that protactinium in a 2 mol L⁻¹ HNO₃ and 0.1 mol L⁻¹ HF mixed solution shows no apparent change in molality of protactinium for durations of greater than 1 year. Although it is anticipated that the ²³¹Pa will remain in solution, it is also expected that the solution in the reference material units will change in molality due to evaporative losses of the aqueous solution from the container. To ensure that the ²³¹Pa reference material will remain fit-for-purpose over the long-term, the units are characterized for amount of ²³¹Pa and each unit is contained in a weighed Teflon bottle (bottle mass values to be provided with units). With these values, a user can utilize the RM solution as received, dilute the solution in the unit container with an appropriate acid solution, or perform a quantitative transfer of the ²³¹Pa.

It is difficult to envision a mechanism that would produce unit-to-unit heterogeneity in the ²³¹Pa reference material production run. The separated protactinium used to prepare the RM solution was essentially monoisotopic and mass spectrometric analysis of the material did not indicate the presence of significant quantities of parent elements for protactinium nuclides, such as uranium or neptunium. Considering the purity of the starting material and the fact that ²³¹Pa is the only isotope of protactinium with a half-life greater than 27 d, it can be stated, with a high degree of confidence, that the characterized reference material units are monoisotopic and therefore isotopically homogeneous.

To minimize the potential for temporal changes to the molality of ²³¹Pa in the RM solution, preparation of the solution, preparation of the IDMS characterization samples, and production of the reference material units were performed during a single work day with all 112 units dispensed over a relatively short period (1 h). Variability that could be caused by differential protactinium contamination was minimized by performing preparation and production work in a class 10 000 clean facility, using only new precleaned labware for all stages of the project, and using high-purity reagents for preparation, production, and analysis (double distilled acids, 18.2 MΩ cm water). Finally, variability in the amount of material transferred to the units was constrained by use of a high-precision automated dispenser and verified by carefully weighing of all unit bottles before and after dispensing.

Metrological traceability [27] for amount of ²³¹Pa was maintained for the two main stages of the calibration process. First, the molality of ²³³Pa in the spike solution was measured by a primary IDMS analysis method [32, 33] which took advantage of the relatively rapid decay of ²³³Pa to the long-lived ²³³U nuclide (Fig. 4a). This allowed for a certified uranium assay and isotopic reference material (CRM 112-A) to be used as an isotopic spike. All masses for the analyses were measured on a calibrated balance that was verified against calibrated weight sets during project activities. Mass spectrometric measurements were corrected for instrumental bias using replicate measurement of an appropriate uranium isotopic reference material (CRM U010). A value for the molality of ²³³Pa in the S solution, at the time of the ²³¹Pa IDMS analyses, was calculated by using the evaluated half-life for ²³³Pa to perform the appropriate decay correction from the time of purification. For the second stage of the calibration process (Fig. 4b), the traceable molality of ²³³Pa in the S solution was utilized for IDMS analyses of ²³¹Pa in the RM solution. All masses for the ²³¹Pa IDMS sample preparation were also measured on a calibrated balance that was verified using calibrated check weights. An isotopic standard for protactinium is not feasible, so mass spectrometric measurements were calibrated using the CRM U010 isotopic reference material. Although the MC-ICP-MS mass fractionation behavior of uranium and protactinium are likely to differ, these differences tend to be small for neighboring elements [34] and an estimated uncertainty component for potential bias in the mass spectrometry results was included in the budget for the attribute value. Finally, the average mass for the ²³¹Pa RM solution distributed to each unit was determined from multiple replicate weighings of each sample unit on a calibrated balance.

Fig. 4.

Schematic of the traceability chain for amount of ²³¹Pa. The diagram indicates the direct relationship between measurements necessary for calibration of the ²³³Pa S solution (a) and the ²³¹Pa reference material (b)

The molality of ²³³Pa in the S solution, as measured by IDMS, was independently verified by activity-based analyses performed at NIST, NRC, and NPL, providing a high level of confidence in the calibration of this material. Values for molality of ²³¹Pa in the RM solution calculated from LSC-based massic activity measurement on the M solution are, however, higher than those measured by IDMS. Observations from mass spectrometry on the ²³¹Pa M solution and the activity measurements themselves provide an explanation for this discrepancy. Mass spectrometric scans of the ²³¹Pa Master solution following the final purification procedure (prior to shipment for activity measurements) showed a small, but measurable, proportion of nuclides at 227 amu, probably ²²⁷Th and ²²⁷Ac daughter products. The presence of unsupported radioactive contaminants was also observed in LSC and γ spectrometry measurements made at NIST shortly after the samples were received. Calibration methods that measure total activity (i.e. LSC based methods CNET and TDCR) must be corrected for radioactive contaminants and for ingrowth of decay chain products from the time of purification. Due to limited data available to the radioactivity laboratories, developing a correction for the unsupported daughter products was not performed or could only be poorly constrained. As expected, this contamination resulted in elevated massic activity values from the LSC-based measurement methods used at NIST and NRC. The α spectrometry measurements performed at NIST had the advantage that only alpha particle energies characteristic of ²³¹Pa decay were measured, so these results were not affected by the presence of small proportions of unsupported decaychain products. The calculated value for the ²³¹Pa molality of the RM solution based on the α spectrometry measurements is essentially identical to the IDMS results, providing independent verification of the characterized value.

Conclusion

The molality of ²³³Pa in the S solution prepared for calibration of ²³¹Pa in the RM solution was precisely measured using a primary analysis method (i.e. IDMS) and independently verified by massic activity measurements at 3 metrology laboratories. This uniquely well characterized ²³³Pa material enabled high-precision primary measurements of the molality of ²³¹Pa in the RM solution used to prepare units of the ²³¹Pa reference material. The molality of ²³¹Pa was independently verified by α spectrometry massic activity measurements performed at NIST. Individual units were carefully prepared from the RM solution resulting in a metrologically traceable reference material that is suitable for calibration of ²³³Pa spikes that are produced by analytical laboratories on an as-needed basis. The relative expanded uncertainty for amount of ²³¹Pa in each reference material unit is 0.35% which should allow for reliable ²³³Pa spike calibrations and similarly well constrained measurements of ²³¹Pa for determination of ²³⁵U–²³¹Pa model ages.