Isotopic fractionation studies of uranium and

International Journal of Mass Spectrometry 430 (2018) 57–62

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Isotopic fractionation studies of uranium and plutonium using porous ion emitters as thermal ionization mass spectrometry sources Matthew L. Baruzzini a,∗ , Howard L. Hall b , Khalil J. Spencer a , Floyd E. Stanley a a b

Los Alamos National Laboratory, Los Alamos, NM 87545, USA Department of Nuclear Engineering, University of Tennessee, Knoxville, TN 37996, USA

a r t i c l e

i n f o

Article history: Received 26 September 2017 Received in revised form 2 April 2018 Accepted 19 April 2018 Available online 22 April 2018 Keywords: Thermal ionization mass spectrometry (TIMS) Porous ion emitter (PIE) Isotopic fractionation Uranium Plutonium Nuclear forensics

a b s t r a c t Investigations of the isotope fractionation behaviors of plutonium and uranium reference standards were conducted employing platinum and rhenium (Pt/Re) porous ion emitter (PIE) sources, a relatively new thermal ionization mass spectrometry (TIMS) ion source strategy. The suitability of commonly employed, empirically developed mass bias correction laws (i.e., the Linear, Power, and Russell’s laws) for correcting such isotope ratio data was also determined. Corrected plutonium isotope ratio data, regardless of mass bias correction strategy, were statistically identical to that of the certificate, however, the process of isotope fractionation behavior of plutonium using the adopted experimental conditions was determined to be best described by the Power law. The fractionation behavior of uranium, using the analytical conditions described herein, is also most suitably modeled using the Power law, though Russell’s and the Linear law for mass bias correction rendered results that were identical, within uncertainty, to the certificate value. Published by Elsevier B.V.

1. Introduction Instrumental bias represents a significant source of error in isotope ratio mass spectrometry (IRMS); the ability to make precise and accurate isotopic ratio measurements is critical for nuclear forensic efforts. In the context of mass spectrometry, the term bias is used to describe a combination of effects, that occur in a mass spectrometer, leading to a difference between the measured and true isotope ratio(s) present in a sample. Such effects may occur during the formation, transmission, and detection of ions. In thermal ionization mass spectrometry (TIMS), mass fractionation occurs as the sample is heated by the metal filament. The rate at which each isotope evaporates from the hot metal filament is mass dependent; lighter isotopes are preferentially evaporated relative to heavier isotopes in the thermal ion source. This is a result of the higher translational velocities of lighter isotopes, for a given kinetic energy, and the tendency of heavier isotope to form stronger chemical bonds [1]. The consequence is a time-dependent variation in measured isotope ratios; the sample reservoir (i.e., the sample remaining on the filament at a given time) tends to become relatively enriched in heavier isotopes as the analysis pro-

∗ Corresponding author. E-mail address: mbaruzzini@lanl.gov (M.L. Baruzzini). https://doi.org/10.1016/j.ijms.2018.04.004 1387-3806/Published by Elsevier B.V.

ceeds. Another significant factor influencing mass bias is the size of the sample. As sample size increases, competition between analyte atoms for filament surface area also increases [2,3]. This effect is magnified in traditional single filament analysis where analyte atoms are evaporated and ionized by the same filament. The result is a substantial loss of analyte as evaporated neutral atoms, biased in favor of lighter isotopes, at relatively low filament temperatures where ionization is less likely to occur. This time-dependent behavior of measured isotope ratios hinders the accurate determination of the true isotope ratio of a sample through direct measurement because the effects of mass bias cannot be totally controlled and reproduced. In TIMS, multiple filament materials and/or geometries may be employed depending on application; fractionation effects will vary on a run-to-run and method-to-method basis. Typical mass bias for single filament TIMS analyses is on the order of a few tenths of a percent per atomic mass unit (% amu−1 ) for high mass elements (i.e., 180 amu), whereas mass bias associated with multicollector-inductively coupled mass spectrometry (MC-ICP MS) can be expected to be approximately an order of magnitude larger for the same mass range [4,5]. However, correcting for instrumental mass fractionation can be accomplished by normalizing the measured ratio of interest to a known or accepted reference ratio. Measured isotope ratios are commonly corrected for fractionation by applying one of the well known mass bias correction laws that appear in the literature. These include the Linear law [6,7],

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M.L. Baruzzini et al. / International Journal of Mass Spectrometry 430 (2018) 57–62

the Power law [6–8], Russell’s law [6–9], and Rayleigh’s distillation law [7–10]. Several studies of isotopic fractionation behavior during TIMS analysis have centered around creating models for correcting mass bias that are specific to the ion source (e.g., PIE, resin bead, thermal ion cavity) [11–14]. Andreasen and Sharma have concluded that isotope ratios corrected for mass fractionation using the Russell’s law are fully satisfactory given the current level of precision obtainable in TIMS analyses [14]. As precision of isotope ratio measurements continues to improve, it may become advantageous to apply fractionation models that are source specific. All fractionation laws assume that evaporation and ionization of a sample occurs in a single, homogeneous domain atop a filament. In reality, this assumption is not well justified as a sample loaded atop a filament is not a point source. A temperature gradient exists across the filament; mass fractionation behavior is temperature dependent. Recently introduced PIE techniques have been shown to address such issues. Watrous et al. have demonstrated that PIEs are very effective at containing a sample within the porous structure and do not permit sample migration across the filament [15]. The small footprint of the PIE serves to localize the analyte loading area at the center of the filament such that the instrument optics will behave as if each sample were a point source. Localized loading leads to a reduced ion energy spread as a function of voltage drop and temperature gradient across the filament surface leading greater ion transmission through the ion optics and enhanced abundance sensitivity when compared other techniques [15]. The PIE’s ability to more accurately represent a point source suggests that they may potentially reduce the effects of mass bias associated with the thermal gradient across the filament when compared to other single filament techniques. The objective of this investigation is to evaluate the fractionation effects arising from the use of PIEs as TIMS sources in the measurement of uranium and plutonium isotopic systems. Fractionation effects were evaluated according to each of the mass bias correction strategies, the Linear, Power, and Russell’s laws, introduced above and distinctions in applicability are discussed.

(∼10−5 Pa). Degassing was performed by incrementally heating the filaments to 4.5 A at a rate of approximately 0.25 A min−1 ; filaments were held at 4.5 A for 15 min. 2.3. PIE stock material and filament preparation PIE stock material was prepared by incorporating equal parts, by mass, of platinum powder, rhenium powder, and hot-melt adhesive atop a quartz glass microscope slide heated atop a laboratory hot plate to ∼120◦ C, the melting point of the hot glue. Once thoroughly integrated, the stock mixture was loaded into a specially designed extruder, heated, and expelled as a small diameter, ∼550 ␮m, rope onto a quartz glass plate. Details of extruder design and operation can be found in Ref. [16]. After cooling, sections approximately 100 ␮m in height were cut from the stock material rope, as needed, and affixed at the center of standard, high-purity zone-refined rhenium single TIMS filament assemblies via gentle heating at 1 A for approximately 5 s. The PIE stock was sintered to the filament using a GV Instruments Ltd. (now Isotopix: Middlewich) filament bake-out unit evacuated to ∼10−7 mbar (∼10−5 Pa). The filament temperature was slowly increased, 0.25 A min−1 , to 1700◦ C; filaments were held at this temperature for approximately 20 min. Filaments were allowed to cool overnight prior to sample loading. A detailed description of PIE filament fabrication has been presented by Watrous et al. [15]. 2.3.1. Sample loading Two drops, each approximately 1 ␮L, of poly(4-styrenesulfonic acid) water soluble cation exchange resin, diluted to a concentration of ∼3% by mass using 18 M deionized (DI) water, were added to each PIE. The ion exchange resin was dried by heating at 1 A for 15 s. The ion exchange resin was added to promote sample incorporation into the PIE structure. Samples were loaded directly onto each PIE in nitrate form using a 2.5 ␮L capacity pipette and dried via gentile heating at 1 A for approximately 15 s. 2.4. TIMS instrumentation

2. Experimental methods and equipment 2.1. Isotopic standards and reagents Samples were prepared from New Brunswick Laboratory certified reference material (NBL CRM) 144 plutonium isotopic standard (NBL: Argonne, IL; USA) and Institute for Reference Materials and Measurements isotopic reference materials (IRMM IRM) 199 uranium isotopic reference standard (IRMM: Joint Research Centre; Geel, Belgium). Platinum (325-mesh) and rhenium (325-mesh) metal powders as well as the water soluble poly(4-styrene-sulfonic acid) polymer ion exchange solution (Mw = 75,000, 8 wt.% in H2 O) were procured from Sigma–Aldritch (St. Louis, MO). High-purity, zone-refined rhenium filament ribbons were acquired form H. Cross Co. (Moonachie, NJ; USA). OptimaTM grade nitric acid was purchased from Fisher Scientific (Pittsburgh, PA; USA). A typical craft variety hot melt adhesive (not well characterized) was purchased from a local hardware store. 2.2. Rhenium filament preparation Filament assemblies were fabricated by spot welding strips of rhenium (0.76 × 0.03 mm) to standard filament support posts; prior to welding, filament posts and rhenium strips were cleaned via sonication in acetone and dried in a laboratory oven. The filament assemblies were then loaded into GV Instruments Ltd. (now Isotopx: Middlewich, Cheshire; UK) filament bake-out unit which was then sealed and evacuated to approximately ∼10−7 mbar

Mass spectrometric analyses were carried out using a GV Instruments Ltd. (now Isotopx: Middlewich, Cheshire; UK) IsoProbe TTM multi-collector TIMS at Los Alamos National Laboratory (LANL). This mass spectrometer is equipped with a 20-position sample turret, a single-focusing magnetic sector fitted with a 54 cm magnet, nine fully adjustable Faraday cup collectors, a Daly detector ioncounting system, and a wide aperture retarding potential (WARP) filter positioned between the main collector array and rear ion counting Daly detector. Programming and performance of the mass spectrometer was controlled via the GV Instruments IonVantage software package installed on a Dell Optiplex PC (Round Rock, TX; USA). Amplifier gains cross-calibrations are conducted on a weekly basis and automated corrections are built into the software. To ensure maximum measurement precision, the instrument was warmed under electronic conditions similar to those employed during sample analysis for at least an hour. Preliminary instrument tuning was conducted each day, prior to sample analyses, using the 187 Re+ beam from a bare rhenium filament. Fine tuning of the mass spectrometer was carried out using a low intensity beam of the major isotope present in each sample immediately preceding analysis. The liquid nitrogen cold trap was filled, as needed, to improve vacuum in the ion source housing maximizing ion transmission and reducing abundance sensitivity. 2.4.1. Mass spectrometric analysis Uranium and plutonium isotope ratio measurements were conducted using a total evaporation (TE) technique similar to the method described by Callis and Abernathey [17] and Fiedler

M.L. Baruzzini et al. / International Journal of Mass Spectrometry 430 (2018) 57–62 Table 1 Faraday cup position/nuclide assignments used during the analysis of uranium and plutonium isotopic standards. Element

Table 2 Plutonium isotope ratio data obtained from replicate analyses of CRM 144 using PIEs.

Collector position (isotope)

U Pu

Analysis

L3

L2

—

Axial

H1

H2

H3

H4

233 —

234 238

— —

235 239

236 240

— 241

238 242

— —

H5

Number

Date

Sample mass

244

1 2 3

2014-03-07 — — Mean %RSD 2014-03-20 — — — — Mean %RSD 2014-07-02 — — — — Mean %RSD

5 ng — —

et al. [18]. Static, multi-collector measurements were employed to simultaneously monitor the sample ion beams using the Faraday cup detectors, exclusively. The collector array configuration used for uranium and plutonium analyses are shown in Table 1. Individual isotope ratios were calculated for each five second integration period (i.e., one cycle). Final isotope ratio values were determined by taking the ratio of the summed signal intensities at the end of analysis. Isotope ratio measurements were conducted over a period ranging from March 2014 to July 2014. Measured isotope ratios and certificate values were decay corrected to 1 May, 2015, the data analysis date, for comparison. Half-life values used for decay corrections were obtained from the Decay Data Evaluation Project (DDEP) recommended data [19].

4 5 6 7 8

9 10 11 12 13

Mean SD %RSD

2.5. Mass bias correction Isotope ratio data were corrected for mass fractionation via internal normalization, i.e., corrections were made on a case-bycase comparison with a known value, using the Linear law; RijC i,j

i,j

= RijM [1 + ˛L mij ]

˛L

=

v ˛u, L

=

v ˛u, L

(1)

v 1 − ˛u, mvj L

RijM [1 + ˛P ]mij

RijC

=

˛P

N /RM ) = (Ruv uv

1/muv

(2)

= RijM ( =

N /RM ] ln[Ruv uv ln[mu /mv ]

˛E

=

ˇ mj

244 Pu

1.8825601 1.8823786 1.8808832 1.8819406 0.0399261 1.8779466 1.8797532 1.8799178 1.8784558 1.8802436 1.8792634 0.0476845 1.8793285 1.8793570 1.8823587 1.8793545 1.8792706 1.8799338 0.0645141 2.6253002 0.0010115 0.0385300

2.6269894 2.6269302 2.6258635 2.6265944 0.0196982 2.6237486 2.6250593 2.6250743 2.6241599 2.6253936 2.6246871 0.0237716 2.6248152 2.6247555 2.6268088 2.6246642 2.6246399 2.6251367 0.0319370

F

=

ı mij

=

(i A/j A)M (i A/j A)N



(4)

− 1 × 1000

the subscripts, M and N, in Eq. (4) represent the measured and certified isotope ratio values; mij is the difference in isotopic masses; the superscripts i and j represent isotopes of an element, A. 3. Results and discussion 3.1. Plutonium

mi ˇ ) mj

ˇ

242 Pu

− 1,

and Russell’s law RijC

10 ng — — — —

240 Pu 244 Pu

should be emphasized that these models were empirically developed, and thus there is no theoretical basis to decide which mass bias correction law best describes fractionation behavior. Fractionation factors, F, were determined using standard delta notation (ı ‰) divided by the difference in isotopic masses;

ı

Power law;

10 ng — — — —

1.8801391 0.0014370 0.0764314



N /RM ) − 1 (Ruv uv , muv

59

(3)

for mass bias correction presented in the literature [6,9]. Here, mij is the difference in masses mi and mj of isotopes i and j; muv represents the difference in masses mu and mv of isotopes u and v; RijM and RijC are the measured and corrected isotope ratio of isotopes M is the measured i and j with masses mi and mj , respectively; Ruv N is isotope ratio of isotopes u and v with masses mu and mv and Ruv the accepted or known ratio (e.g., the certified isotope ratio) of isotopes u and v. Isotopic mass values used for calculations are from the Atomic Mass Data Center (AMDC) files [20]. The Linear and Power laws are approximations of the theoretically developed Rayleigh distillation law, each are derived using different assumptions [4]. Inspection of Eqs. (1) and (2) reveals that they are dependent on the difference between the nominal masses of the measured isotopes and not on the absolute masses. Russell’s law, Eq. (3)), however, does depend on absolute masses of isotopes that make up the ratio. As a result, Russell’s law is expected to be the most accurate. It

Multiple trials (N = 13) were conducted using NBL CRM 144 plutonium isotopic reference standard; three trials at 5 ng mass loading levels of plutonium and ten trials using 10 ng plutonium samples. Plutonium isotope ratio data, corrected for abundance sensitivity, are presented numerically in Table 2. Fig. 1 illustrates the data plotted in three-isotope space. Plutonium sample mass loading level had a significant effect on the degree of mass bias; 240 Pu/244 Pu isotope ratios exhibited average instrumental mass fractionation factors of 0.94‰ amu−1 and 1.25‰ amu−1 for 5 ng and 10 ng sample sizes, respectively. Despite the significant reduction, approximately 25%, in fractionation factor exhibited by 5 ng samples relative to 10 ng samples, the data, when plotted on a three-isotope diagram, fractionates in a highly linear fashion. Least squares regression analysis of the data yielded a trend line that extends through the ratio of certified isotope ratio values, within the stated uncertainty, reported at the 95% confidence level, with a correlation coefficient, R2 , of 0.99877. Data, plotted in three-isotope space, that falls on a straight line, the fractionation line, extending through the certificate value. This indicates that the major source of error in plutonium isotope ratios measured using PIEs is a result of mass-dependent fractionation effects, a departure from linearity would indicate mass-independent frac-

60

M.L. Baruzzini et al. / International Journal of Mass Spectrometry 430 (2018) 57–62 Table 3 Mean values for 240 Pu/244 Pu isotope ratio data corrected for mass bias using the Linear law, Power law, and Russell’s law of fractionation.

2.634 2014-03-07, 5ng sample Mean, 2014-03-07, 5ng sample

2.632

2014-03-20, 10ng sample 240 Pu

242

Pu/244Pu ratio

Mean, 2014-03-20, 10ng sample

Mass bias correction law

244 Pu

2014-07-02, 10ng sample

2.630

Mean, 2014-07-02, 10ng sample

Slope: 0.70305 ± 0.01051 Offset: 1.30347 ± 0.01976 R 2: 0.99877

Certificate value

2.628

mean SD %RSD Deviation from cert. value (‰)

2.626

Linear

Power

Russell

1.8890092 0.0000722 0.0038229 −0.01447

1.8890199 0.0000728 0.0038518 −0.00878

1.8890569 0.0000741 0.0039242 0.01081

2.624 0.9680

2.622

1.878

1.880

1.882

1.884

1.886

1.888

Sample data

1.890

0.9675

240

Pu/244Pu ratio

Certificate value

0.9670

ln(242Pu/244Pu)

Fig. 1. A three-isotope diagram of plutonium isotope ratio data corrected for decay and abundance sensitivity. Also plotted is the decay corrected ratio of 240 Pu/244 Pu and 242 Pu/244 Pu certificate values along with associated uncertainties.

tionation. Isotope ratio data corrected for fractionation using each of the aforementioned mass-bias correction laws are plotted in Fig. 2. The decay corrected certified 240 Pu/244 Pu isotope ratio value, 1.88904(85), is represented by the solid line; the dashed lines represent the upper and lower bounds of the uncertainty in the certificate ratio. Each of the mass-bias correction laws used herein generated isotope ratio data that, on average, were statically identical to the certified value. Mean 240 Pu/244 Pu isotope ratio values of 1.8890199(728), 1.8890092(722), and 1.8890569(741) were determined using the Power law, Linear law, and Russell’s law, respectively. The data indicate that the Power law most accurately (i.e., the smallest relative difference) describes the fractionation behavior of NBL CRM 144 plutonium isotopic standard loaded atop PIE equipped filaments with a deviation from the certificate value of −0.00878‰. Deviations from the certificate value calculated using Russell’s law and the Linear law were determined to be 0.01081‰ and −0.01447‰, respectively. Assuming that the true instrumental fractionation does follow the Power law, the error that would be introduced by correcting isotope ratio data using the Linear law would be approximately 0.0014‰ amu−1 and 0.0050‰ amu−1 using Russell’s law. Average mass bias corrected isotope ratios along with associated uncertainties are presented in Table 3. Due to the concordance between isotope ratio data corrected for mass bias using the Power, Russell’s, and Linear laws further investigation into fractionation law selection was conducted. This was accomplished by fitting a straight line to the natural logarithms of the isotope ratio data, plotted against one another, in three-isotope space, as shown in Fig. 3. The slope, 0.503543(7528), of the resultant trend line was then compared to the slopes of lines predicted by Russell’s law and the Power and Linear laws. Slope values were

0.9665

Slope: 0.503543 ± 0.007528 Intercept: 0.647285 ± 0.004753 R 2 : 0.998773

0.9660 0.9655 0.9650 0.9645 0.9640 0.629

0.630

0.631

0.632

0.633

0.634

0.635

0.636

0.637

ln(240Pu/244Pu)

Fig. 3. Natural logarithms of experimentally determined plutonium isotope ratio data plotted in three-isotope space.

found to be 0.497996 and 0.500067 using Russell’s law and the Power and Linear laws, respectively. This analysis supports our conclusion that the data are best described by the Power law which provides a better fit than Russell’s or the Linear law. However, all values fall within the uncertainty in the slope value determined for the line of best fit to the data. 3.2. Uranium Repeat fractionation trials (N = 9) were conducted at 50 ng sample mass loadings of IRMM IRM 199 uranium isotopic reference material. Analytic conditions for uranium trials were similar to those employed during plutonium analyses; a key difference being the larger sample size used during uranium analysis. As expected, the relatively larger samples exhibited an increase in degree of fraction. An average fractionation factor of 1.58‰ amu−1 was determined for the 233 U/238 U isotopic ratio using Eq. (4). Uranium data, corrected for abundance sensitivity and decay, are listed in Table 4. Even though the samples were relatively heavily fractionated, data plotted on a three-isotope diagram are fit well by a straight line, R2 = 0.99746. The fractionation line projects project through

1.8910

Russell's law Power law Linear law

1.8905

240

Pu/244Pu ratio

1.8900

Russell's law (mean, 1 ) Power law (mean, 1 ) Linear law (mean, 1 )

1.8895 1.8890 1.8885 1.8880 1.8875 1.8870

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

Analysis number

Fig. 2. High precision plutonium isotope ratio data, obtained using PIE sources, corrected for mass bias. The solid line represents the certified isotope ratio; uncertainty in the certified ratio is shown by the dashed line.

M.L. Baruzzini et al. / International Journal of Mass Spectrometry 430 (2018) 57–62 Table 4 Uranium isotope ratio data results acquired from repeat measurements of IRM 199 using PIE sources.

Number

Date

Sample mass

1 2 3 4 5

2014-03-19 — — — — Mean %RSD 2014-06-10 — — — Mean %RSD

50 ng — — — —

6 7 8 9

50 ng — — —

Mean SD %RSD

0.9919459 0.0011557 0.1165124

Table 5 Mean 233 U/238 U isotope ratio data corrected for mass bias using the Linear law, Power law, and Russell’s law.

233 U

235 U

233 U

238 U

238 U

238 U

0.9913719 0.9911128 0.9917260 0.9912360 0.9919483 0.9914790 0.0314427 0.9951381 0.9917391 0.9916034 0.9916374 0.9925295 0.1518264 0.9954863 0.0006851 0.0688210

0.9951196 0.9949769 0.9953345 0.9951327 0.9955689 0.9952265 0.0206593 0.9973730 0.9952698 0.9952936 0.9953076 0.9958110 0.0905720

0.000

U/238U ratio

235

Power

Russell

0.9998750 0.0000847 0.0084747 0.00657

0.9998874 0.0000842 0.0084231 −0.00578

0.9999207 0.0000835 0.0083523 −0.03910

Sample data Certificate value

− 0.001 − 0.002

Slope: 0.58951 ± 0.07881 Offset: 0.00024 ± 0.00065 R 2 : 0.99745

− 0.003 − 0.004

2014-03-19, 50ng sample Mean, 2014-03-19, 50ng sample

− 0.005

2014-06-10, 50ng sample

1.000

Linear

0.001

1.002 1.001

Mass bias correction law

Mean SD %RSD Deviation from cert. value (‰)

ln(235U/238U)

Analysis

61

Mean, 2014-06-10, 50ng sample

−0.009 −0.008 − 0.007 −0.006 −0.005 − 0.004 −0.003 −0.002 −0.001 0.000

0.001

ln(233U/238U)

Certificate value

0.999

Slope: 0.59129 ± 0.07909 Offset: 0.40895 ± 0.07844 R 2 : 0.99746

0.998 0.997

Fig. 6. Natural logarithms of measured uranium isotopic ratio data plotted on a three-isotope diagram.

0.996 0.995 0.994 0.990

0.991

0.992

0.993

0.994

0.995

0.996

0.997

0.998

0.999

1.000

1.001

233

U/238U ratio

Fig. 4. Uranium isotopic ratios, corrected for decay and abundance sensitivity, plotted in three-isotope space. The ratio of 233 U/2 38U and 235 U/238 U certificate values and associated uncertainties are also plotted.

the certified value within the stated uncertainty, reported at the 95% confidence level. These data, plotted in three-isotope space, along with the fractionation line and pertinent fitting parameters are illustrated in Fig. 4. Because sample runs exhibited a relatively high degree of fractionation, Russell’s law was expected to most satisfactorily account for uranium fractionation behavior. Analysis of the data, however, revealed that all mass bias correction laws investigated herein rendered average 233 U/238 U isotope ratio values that were statistically identical to that of the decay corrected 233 U/238 U certificate value,

0.99988(30). Mean isotope ratio data corrected for fractionation and residual bias are presented in Table 5. Data corrected for fractionation using the Power law rendered the most accurate result with a −0.00578‰ deviation from the certificate value. Deviations of 0.00657‰ and −0.03910‰ from the certificate value were calculated using the Linear and Russell’s laws, respectively. Fractionation corrected data are illustrated in Fig. 5. Fractionation law selection was further tested in a manner similar to that described for plutonium in Section 3.1 of this work. Fig. 6 illustrates the natural logarithms of the raw isotope ratio data plotted on a three-isotope diagram. The slopes of the trend lines predicted by Russell’s law and the Power and Linear laws were calculated to be 0.59748 and 0.60003, respectively. Slopes predicted by each of the empirical laws were statistically identical to the slope of the regression line fit to the natural logarithms isotope ratio data, 0.58951(7881), yielding no definitive conclusion.

1.0015

Russell's law Power law Linear law

1.0010

Russell's law (mean, 1 ) Power law (mean, 1 ) Linear law (mean, 1 )

233

U/238U ratio

1.0005 1.0000 0.9995 0.9990 0.9985 0

1

2

3

4

5

6

7

8

9

10

11

12

Analysis number Fig. 5. High precision uranium isotope ratio data, obtained using PIE sources, corrected for mass bias using the Linear, Power, and Russell’s laws. The solid line represents the certified isotope ratio; uncertainty in the certified ratio is shown by the dashed line.

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4. Conclusions Analysis of NBL CRM 144 plutonium and IRMM IRM 199 uranium isotopic standards using PIE sources have yielded isotope ratio values that are in excellent agreement with the certificate values, once corrected for mass fractionation using each of the massbias correction laws presented in this work. We have determined that the commonly employed empirical mass bias correction laws presented in the literature have proven adequate for correcting mass-induced fractionation behavior of uranium and plutonium samples associated with the use of PIEs as TIMS sources. The suite of plutonium and uranium samples, analyzed under the analytic conditions described herein, exhibited consistent characteristics across analytes with the Power law most accurately describing fractionation behavior. Additional efforts are required to fully understand the effects that sample size and isotopic composition may have on mass bias associated with PIEs. Furthermore, efforts to optimize the analytical procedure should be put forth to minimize instrumentally induced mass bias in order to maximize the accuracy and precision of isotope ratio data measured using PIEs. Acknowledgements The authors gratefully acknowledge the support provided by the U.S. Department of Homeland Security under Grant Award Number, 2012-DN-130-NF0001-02. The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of the U.S. Department of Homeland Security. The authors would also to express their gratitude for the support provided by the U.S. Department of Energy/National Nuclear Security Administration Office of Nonproliferation and Verification Research and Development and the U.S. Department of Energy through the LANL/LDRD Program. This manuscript has been reviewed and approved under LA-UR-16-23969. References [1] H.C. Urey, The thermodynamic properties of isotopic substances, J. Chem. Soc. (Resumed) (1947) 562–581. [2] D.M. Wayne, W. Hang, D.K. McDaniel, R.E. Fields, E. Rios, V. Majidi, The thermal ionization cavity (TIC) source: elucidation of possible mechanisms for enhanced ionization efficiency, Int. J. Mass Spectrom. 216 (1) (2002) 41–57, URL http://www.sciencedirect.com/science/article/pii/S1387380602005511. [3] R.L. Edwards, J.H. Chen, G.J. Wasserburg, 238 U–234 U–230 Th–232 Th systematics and the precise measurement of time over the past 500,000 years, Earth Planet. Sci. Lett. 81 (2) (1987) 175–192, URL http://www.sciencedirect.com/ science/article/pii/0012821X87901543.

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