Aurélien Beaumais
email: aurelienbeaumais@hotmail.fr

Anthony Nonell
email: anthony.nonell@cea.fr

Céline Caussignac

Sébastien Mialle

Guillaume Stadelmann

Myriam Janin

Hélène Isnard

Michel Aubert

Thomas Vercouter

Frédéric Chartier

U atom ratio in spent nuclear fuel using double spike isotope

Introduction

During the irradiation of fuels in a reactor, two types of nuclear reactions occur, i.e., (1) fission of fertile isotopes ( 235 U and 239 Pu) that lead to the formation of lighter fission products (e.g. Cs, Sr, lanthanides including Ce and Nd, and platinum group elements) and (2) neutron capture giving rise to heavier products (i.e., actinides). Among the nuclides produced, some of them are radioactive. The precise knowledge of the energy released by radioactive decay, known as decay heat, is mandatory for radiological safety and the management of spent nuclear fuels. Among these radionuclides, the 144 Ce isotope is a fission product that significantly participates (including its short-lived product 144 Pr) to the decay heat for cooling times below 10 years.

Accurate quantification of this low abundance isotope in cooled spent nuclear fuels is thus required for two reasons: (1) to bring new constraints on neutronic calculation codes that predict the evolution of the fuel composition through time and (2) to improve the short-term management of irradiated fuels. [START_REF] Wpncs | Spent Nuclear Fuel Assay Data for Isotopic Validation[END_REF] Cerium is the second element of the lanthanide series. While most of the lanthanides are found in solution at the oxidation state +3, cerium can form Ce(III) or Ce(IV) depending on the oxidizing conditions. Naturally occurring cerium has 4 stables isotopes: 136 Ce (0.19%), 138 Ce (0.25%), 140 Ce (88.45%) and 142 Ce (11.11%), whereas in irradiated fuels, it has two main stable isotopes, 140 Ce and 142 Ce, and one low abundance radioactive isotope, 144 Ce (β -, half-life: 284.89 ± 0.04 days), that decay to form 144 Pr (β -, half-life: 17.29 ± 0.06 min) and ultimately 144 Nd. [START_REF] Bé | -A = 41 to 198[END_REF] The 144 Ce content in spent fuel depends mainly on the initial amount of fissile isotopes (enrichment) and the burn-up experienced by the fuel in the nuclear reactor ( 144 Ce production) as well as on the cooling time since the discharge of the fuel ( 144 Ce radioactive decay).

The analysis of 144 Ce content in spent fuel is usually performed by gamma-ray spectrometry using an aliquot of dissolved spent fuel solutions without extensive sample preparation.

However, the measurement uncertainty obtained with this technique remains around 3 percent or more at a 95% confidence level. [START_REF] Wpncs | Spent Nuclear Fuel Assay Data for Isotopic Validation[END_REF] Isotope dilution mass spectrometry is a method that can provide the most accurate quantification of trace element content. [START_REF] Debievre | Isotope-dilution mass-spectrometry -What can it contribute to accuracy in trace analysis?[END_REF][START_REF] Heumann | Isotope-dilution mass-spectrometry (IDMS) of the elements[END_REF] In order to reduce the measurement uncertainty of 144 Ce content (through 144 Ce/ 238 U) in spent nuclear fuels, a novel approach combining a two-step liquid chromatography, thermal ionization mass spectrometry technique and high-accuracy double spike isotope dilution method has been developed. Double spike isotope dilution mass spectrometry has previously been applied for the accurate and precise determination of (1) radionuclide ratios in nuclear fuels before irradiation, such as 166 Er/ 238 U [START_REF] Chartier | Determination of erbium in nuclear fuels by isotope dilution thermal ionization mass spectrometry and glow discharge mass spectrometry[END_REF] or in irradiated materials, such as 241 Am/ 238 U, 244 Cm/ 238 U, 90 Sr/ 238 U, 166 Er/ 238 U, 152 Sm/ 153 Eu 6-8 and (2) U and Pu content in irradiated materials using large-size dried spikes [START_REF] Jakopic | Verification measurements of the IRMM-1027 and the IAEA largesized dried (LSD) spikes[END_REF] .

Moreover, high-precision Ce isotope measurements have been carried out for years by mass spectrometry using TIMS as an elemental (Ce + ) or an oxide (CeO -) species [START_REF] Chang | The absolute isotopic composition of cerium[END_REF][START_REF] Willbold | Determination of Ce isotopes by TIMS and MC-ICPMS and initiation of a new, homogeneous Ce isotopic reference material[END_REF][START_REF] Doucelance | What coupled cerium and neodymium isotopes tell us about the deep source of oceanic carbonatites[END_REF][START_REF] Bellot | Ce isotope systematics of island arc lavas from the Lesser Antilles[END_REF][START_REF] Willig | Accurate and precise measurement of Ce isotope ratios by thermal ionization mass spectrometry (TIMS)[END_REF][START_REF] Bonnand | Radiogenic and stable Ce isotope measurements by thermal ionisation mass spectrometry[END_REF][START_REF] Shao | High-precision cerium isotope analysis by thermal ionization mass spectrometry using the Ce+ technique[END_REF] and by MC-ICPMS [START_REF] Willbold | Determination of Ce isotopes by TIMS and MC-ICPMS and initiation of a new, homogeneous Ce isotopic reference material[END_REF][START_REF] Schnabel | La-Ce isotope measurements by multicollector-ICPMS[END_REF] on various types of geological samples not containing 144 Ce. Prior to mass spectrometry analysis by TIMS and MC-ICPMS, in order to remove the spectral and nonspectral interferences, an efficient separation of cerium from the other elements must be performed. Overall, matrix elements first need to be eliminated from the lanthanide fraction using ion exchange [START_REF] Patchett | A routine high-precision method for Lu-Hf isotope geochemistry and chronology[END_REF] or extracting [START_REF] Pin | Sequential separation of light rare-earth elements, thorium and uranium by miniaturized extraction chromatography: Application to isotopic analyses of silicate rocks[END_REF] chromatography. Then Ce purification from the other lanthanides, especially with respect to the interfering Nd, was carried out using oxidative extraction, [START_REF] Peppard | The use of dioctyl phosphoric acid extraction in the isolation of carrier-free 90Y, 140La, 144Ce, 143Pr, and 144[END_REF][START_REF] Rehkamper | Separation of Ce from other rare-earth elements with application to Sm-Nd and La-Ce chronometry[END_REF][START_REF] Tazoe | Determination of cerium isotope ratios in geochemical samples using oxidative extraction technique with chelating resin[END_REF][START_REF] Xie | A critical review on solvent extraction of rare earths from aqueous solutions[END_REF] capillary electrophoresis, [START_REF] Janos | Analytical separations of lanthanides and actinides by capillary electrophoresis[END_REF][START_REF] Vio | Separation and analysis of lanthanides by isotachophoresis coupled with inductively coupled plasma mass spectrometry[END_REF] and liquid ion exchange or extraction chromatography [START_REF] Verma | High-performance liquid and ion chromatography: Separation and quantification analytical techniques for rare earth elements[END_REF][START_REF] Chen | Chromatographic Techniques for Rare Earth Elements Analysis[END_REF] .

In this study, different separation techniques were developed to purify the cerium fraction and remove both the dominant matrix elements (e.g. U, Pu) and the interfering isotopes (e.g. 142 Nd, 144 Nd). Cerium purification was achieved in two steps: (1) U and Pu were separated from the fission products and minor actinides through gravity column liquid chromatography using a strong anion exchange resin and HCl as the mobile phase, and (2) the separation of the fission products and minor actinides was performed by high performance liquid chromatography (HPLC) using a strong cation exchange resin and 2-hydroxy-2-methylbutyric acid (HMB) as the mobile phase [START_REF] Raut | Comparative evaluation of three alphahydroxycarboxylic acids for the separation of lanthanides by dynamically modified reversed-phase high-performance liquid chromatography[END_REF][START_REF] Goutelard | Optimization conditions for the separation of rare earth elements, americium, curium and cesium with HPLC technique[END_REF] . Purification yields, decontamination factors of each separated fraction, as well as procedural blank levels were carried out on a quadrupole ICP-MS. Then, thermal ionization mass spectrometry (TIMS) was used to measure the Ce isotope ratios at high precision by a sequential method (i.e., sequential heating steps of the filaments before the proper isotopic measurement sequence) and a total evaporation method, both of which are commonly performed for the isotopic analysis of nuclear samples. [START_REF] Callis | High-precision isotopic analyses of uranium and plutonium by total sample volatilization and signal integration[END_REF][START_REF] Dubois | Isotopic analysis of rare-earth elements by total vaporization of samples in thermal ionization mass-spectrometry[END_REF][START_REF] Fiedler | Total evaporation measurements -Experience with multi-collector instruments and a thermal ionization quadrupole mass-spectrometer[END_REF][START_REF] Mialle | The use of total evaporation method using Channeltron electron multipliers by thermal ionization mass spectrometry for europium isotope ratio measurements on picogram sample amounts[END_REF] Finally, a 140 Ce/ 233 U double spike was prepared in our laboratory using certified reference materials (a 233 U solution certified for its U content and isotopic composition, and a Ce solution that had a natural isotopic composition certified only for its Ce content) in order to determine the atomic ratio 144 Ce/ 238 U at low uncertainties (around or lower than 1%) in a dissolved spent nuclear fuel solution using the double isotope dilution method. Accurate and precise isotopic compositions of both the Ce solution and the fuel sample are required to determine the atomic ratio 144 Ce/ 238 U by the double isotope dilution method and were determined by TIMS.

Materials and methods

Materials

Reagents

High purity 67-70% nitric acid and/or 33-36% hydrochloric acid (PlasmaPURE, from SCP Science, Baie d'Urfé, Canada) and ultrapure water with a resistivity of 18.2 MΩ (Milli-Q system, Millipore, Milford, USA) were mixed to obtain diluted solutions used as eluents for gravity column liquid chromatography and for ICP-MS analysis (2% HNO3). These reagents were also utilized to clean materials before use, including all Savillex TM (Teflon® PFA) vials containing the spent fuel samples and all Nalgene TM (Teflon TM FEP) bottles hosting the chromatographic eluents and the double spike solution.

The chromatographic eluent used for separating fission products and minor actinides (Am, Cm) from major actinides (U and Pu) was 10M HCl. The reducing agent HI 57% (VWR, Fontenay sous bois, France) was utilized to prepare the chromatographic eluent 10M HCl/0.1M HI for Pu elution. Finally, U was eluted using 3M HCl.

The chromatographic eluent for lanthanide separation using HPLC was prepared freshly by dissolution of 2-hydroxy-2-methylbutyric acid, HMB (Sigma-Aldrich, Saint-Quentin-Fallavier, France) in ultrapure water. The pH of the mobile phase was adjusted with a 25% ammonia solution (Suprapur, Merck, Darmstadt, Germany) to respectively 3.6 and 4.5 for the 0.1M HMB and 0.2M HMB solutions. A 0.13mM Arsenazo III solution (analytical grade, Sigma Aldrich, Saint-Quentin-Fallavier, France), prepared in acetic acid (Suprapur, Merck, Darmstadt, Germany) buffer solution, was taken as the post-column complexing agent for lanthanides and actinides permitting the detection of these complexes with an UV detector.

Reference materials

To date, no certified isotopic reference material for natural Ce is available. Therefore, a monoelemental solution of Ce NIST3110 (NIST, Gaithersburg, USA) certified at 9.971 ± 0.015 mg (Ce) • g -1 of 10% HNO3 solution, (uc), with natural isotopic abundances ( 136 Ce (0.25%), 138 Ce (0.19%), 140 Ce (88.45%), 142 Ce (11.11%)) [START_REF] Berglund | Isotopic compositions of the elements 2009[END_REF] was chosen for this study.

The uranium spike employed for the double spike solution consisted of an isotopic certified reference material 233 U IRMM 040a (JRC, Geel, Belgium), approved for its 233 U content (4.0278 ± 0.0036 mol of 233 U • kg -1 of 5M HNO3 solution, (uc) and for its isotopic abundance (n( 233 U)/n(U) = 0.980430 ± 0.000029, uc). The U standard solution used in this study to evaluate the TIMS performances (internal precision, external reproducibility, accuracy) was a NIST SRM U-500 standard certified for its isotopic composition ( 235 U/ 238 U = 0.9997 ± 0.0007, uc).

Solutions to optimize the chromatographic elution and analytical conditions as well as to simulate a spent fuel sample (the elemental proportions of the fuel were simulated to verify the yield of purification of the chromatographic elution) were freshly prepared by appropriate dilution and mixture of the 1000 mg/mL individual stock standard solutions of U, Sm, Nd, Pr, Ce in 2% HNO3 (SPEX CertiPrep, Metuchen, USA), certified for elemental content.

Spent fuel samples

Two uranium and plutonium mixed oxide (MOx) spent nuclear fuel samples were analyzed.

After an irradiation period in a nuclear reactor and a cooling period of less than 10 years, targeted sections of irradiated fuel rods were cut, extracted and dissolved in hot cell facilities (ATALANTE, CEA Marcoule). Then, aliquots of diluted solutions of two spent nuclear MOx fuels were supplied to the Laboratory of Analytical development for Nuclear, Isotopic and Elemental Analysis (LANIE, CEA Saclay, France) for both elemental and isotopic characterization. The analyzed elements included actinides and fission products, and one of the challenges was to determine the 144 Ce/ 238 U ratio in these samples using the double spike isotope dilution technique.

Diluted solutions of irradiated MOx fuel samples contain mainly U (≈90 wt.%), where 238 U is the dominant isotope, and to a lesser extent Pu (≈5 wt.%) and fission products (≈4 wt.%) including lanthanides and minor actinides (≈1 wt.%) such as Am and Cm. As discussed above, Ce has two dominant and stable isotopes in such samples, 140 Ce and 142 Ce with abundances close to 50% each ( 142 Ce/ 140 Ce ≈ 0.9), and one minor and radioactive isotope 144 Ce with a low abundance <1% ( 144 Ce/ 142 Ce ≈ 0.02). Spent fuel composition models (SPRC, CEA Cadarache, France) suggest that at the time of the isotopic analysis in the LANIE lab, the MOx fuels had 144 Ce/ 238 U ratios of around 50 ppm (at./at.). The stable 144 Nd was the major isobaric interference with respect to 144 Ce, with a 144 Nd/ 144 Ce ratio around 20, while the lanthanide 144 Pr (short-lived nuclides) contribution was negligible ( 144 Pr/ 144 Ce below 5×10 -5 ).

The handling of radioactive samples (e.g., spent fuel) was carried out carefully in a dedicated laboratory using negative pressure glove-boxes equipped with leaded glass in order to minimize the analyst's exposure to radiation. All analysts systematically used active and passive radiation dosimeters in order to record and control their exposure to radiations.

Double spike solution

A double spike is a mixture of a Ce solution that has natural isotopic abundances and a 233 Uenriched solution has been prepared in order to determine the 144 Ce/ 238 U ratio in the spent fuels using the double spike isotope dilution method. The 233 U was chosen as the 233 U abundance in the samples was negligible ( 233 U/ 238 U lower than 10 -9 ). The in-house double spike 140 Ce-233 U was gravimetrically prepared using a weight scale in a negative-pressure glove-box from Ce NIST3110 and 233 U IRMM 040a (JRC, Geel, Belgium) solutions that were diluted with 4M HNO3 prepared from high-purity 69% nitric acid PlasmaPure and ultrapure water at LANIE (CEA Saclay, France). The U content and the isotopic composition of the 233 U IRMM-040a solution were certified, while for the Ce NIST 3110 solution, this was the case only for the Ce content (Table 1). As no certified values were available, the value from the IUPAC report ( 142 Ce/ 140 Ce = 0.12565 ± 0.00029; uc) representing the isotopic composition of chemical or natural materials that are likely to be encountered in the laboratory was used in this study. [START_REF] Berglund | Isotopic compositions of the elements 2009[END_REF] The accurate knowledge of the isotopic composition (Ce and U) of the double spike, or the 140 Ce/ 233 U atom ratio, is required for the accurate determination of the 144 Ce/ 238 U ratio of a spent fuel sample using the double spike isotope dilution -mass spectrometry technique. The 140 Ce/ 233 U atom ratio of the double spike was determined at 0.01082 ± 0.00002 (uc) from (1) the weighted masses of each spike solution, (2) the Ce and U content in each solution, and (3) the isotopic composition of Ce and U in the Ce NIST3110 and 233 U IRMM040a solutions, respectively. The atomic and isotopic ratios of the double spike required for the double spike isotope dilution -mass spectrometry technique are presented in the Table 1.

Mass spectrometers

A quadrupole ICP-MS ''X series'' mass spectrometer from Thermo Electron (Winsford, UK) was used for the elemental analysis (e.g., purification yields, blank levels). This ICP-MS is the first X series modified, with the ICP source in a glove-box, in order to handle radioactive samples as previously described. [START_REF] Favre | Understanding reactions with O-2 for Sr-90 measurements by ICP-MS with collision-reaction cell[END_REF] A thermal ionization mass spectrometer Sector 54 from GV Instruments (Manchester, UK) was used to perform cerium and uranium isotope ratio measurements. The source of the instrument is placed inside a glove-box to handle radioactive samples, as described previously. [START_REF] Chartier | Determination of Am and Cm in spent nuclear fuels by isotope dilution inductively coupled plasma mass spectrometry and isotope dilution thermal ionization mass spectrometry after separation by high-performance liquid chromatography[END_REF][START_REF] Isnard | Determination of Sr-90/U-238 ratio by double isotope dilution inductively coupled plasma mass spectrometer with multiple collection in spent nuclear fuel samples with in situ Sr-90/Zr-90 separation in a collision-reaction cell[END_REF] The source is equipped with a turret of 20 positions, where removable triple filament arrangements (side internal, central and side external) are available. Sector 54 instrument is equipped with seven Faraday cups associated with amplifiers fitted with 10 11 Ω positive feedback resistors.

The Faraday amplifier gains were calibrated daily before the analytical sessions.

Reproducibility of the electronic gains was better than 20 ppm day -1 .

Methods

Double spike isotope dilution method

The double spike isotope dilution technique made it possible to directly and very accurately find out the atomic ratio of two isotopes from two elements present in a sample. [START_REF] Chartier | Determination of Am and Cm in spent nuclear fuels by isotope dilution inductively coupled plasma mass spectrometry and isotope dilution thermal ionization mass spectrometry after separation by high-performance liquid chromatography[END_REF][START_REF] Isnard | Determination of Sr-90/U-238 ratio by double isotope dilution inductively coupled plasma mass spectrometer with multiple collection in spent nuclear fuel samples with in situ Sr-90/Zr-90 separation in a collision-reaction cell[END_REF] The 144 Ce/ 238 U ratio was determined for each spent fuel (1)

Elemental purification

Elemental purification of Ce and U is required to eliminate the matrix and the interfering elements before isotopic analysis by mass spectrometry. In spent nuclear fuel samples, uranium is the dominant matrix element, while 142 Nd, 144 Nd and 238 Pu are respectively the main isobaric interferences for 142 Ce, 144 Ce and 238 U that are involved in isotope ratios measured by mass spectrometry. In this particular study, the main challenge was to remove the high amount of 144 Nd from the very low amount of 144 Ce ( 144 Nd/ 144 Ce ≈ 20).

Separation U/Pu/Fission products + minor actinides

Chemical separations of U/Pu/Fission products + minor actinides from spent fuels were performed in a glove-box following a procedure adapted from Huntley (2001) [START_REF] Huntley | Sequential separation of americium, curium, plutonium, neptunium and uranium in various matrices from the electrometallurgic treatment of spentnuclear fuel[END_REF] using gravitational chromatographic columns filled with a strong anionic resin AG1-X8 200-400 mesh (BioRad, Hercules, CA, USA) in a hydrochloric medium. The elution conditions (acid molarity, eluted volume) were optimized using a synthetic mixture of mono-elemental solutions of U and lanthanides (Spex, CertiPrep, Metuchen, NJ, USA) simulating the composition of the spent fuel.

For this procedure, aliquots of spent fuel solutions dissolved in 8M HNO3 were evaporated to dryness at 90°C on a hot plate in a glove-box, and dissolved in 10M HCl. Then, the samples were loaded into the gravitational column and the "fission products + minor actinides" fraction (including Ce and Nd) was eluted using 5 mL of 10M HCl, while anionic chloro-complexes of U(VI) and Pu(VI) were fixed on this quaternary ammonium-type resin. The Pu was then reduced and discarded with 5 mL 10M HCl/0.1M HI, as Pu(III) cationic chloro-complexes (Huntley, 2001). Finally, U was collected using 3 mL of 1M HCl.

Ce purification from "fission products + minor actinides" fraction

The Ce purification of the "fission products + minor actinides" fraction of spent fuels (Figure 2) was performed using high-performance liquid chromatography (HPLC). A DIONEX (Sunnyvale, CA, USA) ICS 3000 gradual dual pump was used with a LUNA SCX (Strong Cation Exchange) analytical column (250 mm of length, internal diameter of 4.6 mm) protected by a 3-mm long security guard column system positioned just in front (Phenomenex, Torrance, CA, USA). The stationary phase was silica-based and bonded with benzene sulfonic acid, with a particle size of 5 μm and having a 100Å pore size. The eluent flow rate was 1 mL min -1 and the Rheodyne injection valve (9725 i) was equipped with a 50-μl sample loop. The HPLC was hyphenated to a UV-visible detector (654 nm, Jasco UV-2070) with post-column reaction with Arsenazo III (0.1 mL min -1 ) in order to detect the separated lanthanides, as previously described (Goutelard et al., 2009). The addition of a flow rate split in the system between the column outlet and the Arsenazo III inlet, allowed the detection of lanthanides only from 10% of the flow rate and the simultaneous collection (90% of the flow rate) of the pure fractions of each of the lanthanides for isotopic analysis. The columns, injection valve, split, UV-visible detector were located inside the glove-box. Chromatographic pumps and eluents were placed outside the glove-box. Tubing and connections from the pump to the injection valve were in polyether-ether ketone (PEEK). Flow rate control of the HPLC pumps and integration of the transient UV peaks were performed with the Chromeleon Software.

At the time of sample injection into the HPLC system via a syringe into the Rheodyne valve, the elution of fission products started with an isocratic mode using 0.1M HMB at pH 3.6 to elute the heavier lanthanides (Gd-Eu-Sm) during 30 min, followed by a gradient step which involved the linear replacement during 45 min of the first eluent by a second one (0.2M HMB, pH 4.5) with a higher ligand concentration and a higher pH in order to separately elute Nd, Pr, and Ce in that order. [START_REF] Goutelard | Optimization conditions for the separation of rare earth elements, americium, curium and cesium with HPLC technique[END_REF][START_REF] Gueguen | Multi-elemental Gd, Eu, Sm, Nd isotope ratio measurements by liquid chromatography coupled to MC-ICPMS with variable Faraday cup configurations during elution[END_REF] The elution conditions (HMB concentration, pH, isocratic and gradient elution mode) were previously optimized using a synthetic mixture of mono-elemental solutions of lanthanides (Spex, CertiPrep, Metuchen, NJ, USA) simulating the lanthanide content of spent fuels. With this method, a Ce peak apex appeared more than 6 min after the Nd peak and more than 2 min after the Pr peak (Fig. 2). An aliquot of the collected Ce fractions was analyzed using a Q-ICPMS in order to check the yields of Ce and the absence of residual Nd.

Mass spectrometry measurements

Q-ICPMS

The elemental analysis, including the screening of the purified fractions to verify the purification yields, decontamination factors and measurement of blank levels, were carried out on a quadrupole ICP-MS ''X series''(Thermo Electron, Winsford, UK). Sample introduction in the plasma was performed with a quartz bead impact spray chamber and a quartz concentric nebulizer (1.0 mL min -1 ). Tuning parameters were optimized daily with a 1-ppb multi-element test solution in order to obtain the maximum count rates and stability for the 115 In and 238 U signals and the lowest oxide rate and doubly-charged ion rate.

TIMS

Cerium and uranium isotope ratio measurements were performed on a thermal ionization mass spectrometer Sector 54 from GV Instruments (Manchester, UK). One of the main bias factors impairing accuracy in TIMS is isotope fractionation occurring during the evaporation process. [START_REF] Habfast | Multiple collector techniques in high-precision thermal ionization isotope ratio determinations[END_REF] An accurate analysis of the isotopic composition of non-natural samples by TIMS can be performed with both the sequential method (i.e., comparison with a reference sample)

or with the total evaporation method. [START_REF] Dubois | Isotopic analysis of rare-earth elements by total vaporization of samples in thermal ionization mass-spectrometry[END_REF] The so-called "sequential" method was based on a procedure of sequential heating steps of the filaments, prior to the proper isotopic measurement, and these steps were pre-calibrated for a given element using a reference material with a known isotopic composition in order to obtain the isotopic reference value. The calibrated operating procedure was then carefully applied to the unknown samples assuming that there is a minimum isotope fractionation during the acquisition. The total evaporation method, based on the integration of all the ions formed during analysis, was considered to be more accurate than the sequential method since the effects of isotope fractionation on the final results were minimized. [START_REF] Callis | High-precision isotopic analyses of uranium and plutonium by total sample volatilization and signal integration[END_REF][START_REF] Dubois | Isotopic analysis of rare-earth elements by total vaporization of samples in thermal ionization mass-spectrometry[END_REF][START_REF] Fiedler | Total evaporation measurements -Experience with multi-collector instruments and a thermal ionization quadrupole mass-spectrometer[END_REF][START_REF] Mialle | The use of total evaporation method using Channeltron electron multipliers by thermal ionization mass spectrometry for europium isotope ratio measurements on picogram sample amounts[END_REF][START_REF] Richter | Improved techniques for high accuracy isotope ratio measurements of nuclear materials using thermal ionization mass spectrometry[END_REF] However, the total evaporation method become less accurate for the quantification of isotope ratios involving a minor isotope (e.g., 144 Ce/ 142 Ce of the spent fuel), due to the lower precision associated with low quantity of accumulated signal recorded for the minor isotopes.

As a consequence, the Ce and U isotopic data were acquired in static multicollection mode with Faraday cups, using (1) the total evaporation method [START_REF] Callis | High-precision isotopic analyses of uranium and plutonium by total sample volatilization and signal integration[END_REF][START_REF] Dubois | Isotopic analysis of rare-earth elements by total vaporization of samples in thermal ionization mass-spectrometry[END_REF][START_REF] Fiedler | Total evaporation measurements -Experience with multi-collector instruments and a thermal ionization quadrupole mass-spectrometer[END_REF][START_REF] Mialle | The use of total evaporation method using Channeltron electron multipliers by thermal ionization mass spectrometry for europium isotope ratio measurements on picogram sample amounts[END_REF][START_REF] Richter | Improved techniques for high accuracy isotope ratio measurements of nuclear materials using thermal ionization mass spectrometry[END_REF] for the determination of 142 Ce/ 140 Ce and 238 U/ 233 U ratios in the blends and for the qualification of the 142 Ce/ 140 Ce ratios in the reference material (Ce NIST3110), and (2) the sequential method for the determination of the Ce isotopic composition (that involved the 144 Ce minor isotope) in the spent fuel samples.

Due to the lack of an isotopic reference material for Ce, the Ce NIST 3110 solution was used as a reference material to calibrate the sequential method and the IUPAC Ce isotopic composition value was taken as a reference. [START_REF] Berglund | Isotopic compositions of the elements 2009[END_REF] When using the sequential method to measure Ce in spent fuel samples and the NIST3110 solution, 150 ng of Ce diluted in 2% HNO3 was deposited on the evaporating rhenium filament (located in the external side position of the turret). The heating process corresponded to a succession of current increases applied to the filaments until the sum of the 140 Ce + and 142 Ce + ion beams reached target voltages, followed by periods of acquisition used to control the evolution of the isotope fractionation. The acquisition method applied for the isotope ratio measurements included 4 blocks of 10 cycles, when the sum of the 140 Ce + and 142 Ce + ion beams reached 2 V. Faraday cup configurations for the Ce isotope ratio measurements are reported in Table 2. For the Ce measurements using the total evaporation method of NIST3110 solution and blends, only 50 ng of Ce diluted in 2% HNO3 was loaded on the evaporating filament. The total ion current measured on masses 140 and 142 with this methods was higher than 2 × 10 -11

A.

Approximately 50 ng of U diluted in 2% HNO3 was deposited on the evaporating rhenium filament for U measurements of U-500 and blends performed by the total evaporation method.

Faraday cup configurations for the U isotope ratio measurements are reported in Table 3. The total ion current measured on 238 and 235 (U-500) or 233 (blend) with this method was found to be higher than 10 -11 A for each mass.

Results and discussion

Ce and U purification

In the "fission products + minor actinides" fraction collected during the U/Pu/fission products separation on AG1-X8 resin, the Ce and Nd yields were determined by Q-ICPMS to be around 90%. In the collected uranium fraction, the U yield reached 90% and the residual Pu was found to be negligible. The level of U blanks was also checked by Q-ICPMS and was determined to be negligible.

In the Ce fraction collected after the fission product separation step using HPLC (Fig. 2), Ce yields reached at least 90%. Residual Nd in the Ce fraction could be neglected. The total level of procedural blanks at m/z=144 was very low, less than 1 ng, compared with the amount of 144 Ce recovered after the elemental purification steps (a few μg) and was therefore negligible with respect to the 144 Ce/ 142 Ce ratio measurements.

average 142 Ce/ 140 Ce and 144 Ce/ 142 Ce ratios were measured respectively at 0.88602 ± 0.00580 and 0.001411 ± 0.00011 for MOx 1 and at 0.87200 ± 0.00571 and 0.01828 ± 0.00014 for MOx 2 (U, k = 2). The relative differences between the two aliquots A and B were 0.16% ( 142 Ce/ 140 Ce) and 0.19% ( 144 Ce/ 142 Ce) of MOx 1 and 0.01% for both ratios of MOx 2. The relative standard deviation (1σ) of 142 Ce/ 140 Ce and 144 Ce/ 142 Ce obtained from three TIMS measurements on MOx 1 were 0.11% and 0.38%, respectively. The relative standard deviation was higher for 144 Ce/ 142 Ce compared with 142 Ce/ 140 Ce, because the signal for the 144 ion beam (15 mV) was lower compared to the signals recorded for the 142 and 140 ion beams (around 1V each).

The relative uncertainty (k = 1) of the 142 Ce/ 140 Ce ratio of MOx 1 was evaluated at 0.33% using a quadratic combination of (1) the relative standard deviation (0.11%) of the 142 Ce/ 140 Ce ratio of the MOx 1, (2) the relative combined uncertainty of the IUPAC reference value (0.23%) used to set up the sequential method, and (3) the relative difference between the IUPAC reference value and the total evaporation result (0.21%). The relative uncertainty (k = 1) of the 144 Ce/ 142 Ce ratio of MOx 1 was evaluated at 0.38% using only the relative standard deviation (1σ) of three TIMS measurements, as neither reference value nor total evaporation results were available.

These relative uncertainties were then assigned to the 142 Ce/ 140 Ce ratio and the 144 Ce/ 142 Ce ratio of MOx 2 as the ratios were of the same magnitude. These uncertainty values encompassed the relative difference observed on the measured isotope ratios between each aliquot of the two fuels and were therefore representative.

Ce and U isotope ratios of blends

The measurement of the 142 Ce/ 140 Ce and 233 U/ 238 U ratios was performed twice on two different mixtures (blends A and B with varying amounts of sample and spike) by TIMS using the total evaporation method. The relative difference with regard to the 142 Ce/ 140 Ce and 233 U/ 238 U ratios obtained from the repeated measurements of the same blend was less than 0.2% which was consistent with the typical combined uncertainties found for total evaporation measurements in our lab (0.2%, k= 2). Then, the average of the 2 analyses obtained for each of the blends A or B for each isotope ratio was separately taken into account to solve the double spike isotope dilution equation.

144 Ce/ 238 U atom ratio in spent fuels by double spike isotope dilution -mass spectrometry

The 144 Ce/ 238 U atom ratio of the dissolved solutions of spent fuel was determined from the double spike isotope dilution equation and the associated expanded combined uncertainty was evaluated by the error propagation of each contributing term following a Kragten approach (Table 6). [START_REF] Kragten | Calculating standard deviations and confidence-intervals with a universally applicable spreadsheet technique[END_REF] The average 144 Ce/ 238 U atom ratios of dissolved fuel solutions were quantified at 58.8 ± 0.7 ppm (at./at.) (U, k= 2) for MOx 1, and 34.7 ± 0.4 ppm (at./at.) (U, k= 2) for MOx 2, corresponding to a relative expanded combined uncertainty of 1.1 % each. The results obtained on the final 144 Ce/ 238 U atom ratios of dissolved fuel solutions using the two different blends (A and B) presented a relative difference lower than 0.3% for both MOx fuels thus confirming the consistency of the uncertainty estimation.

The relative contributions of the main sources of uncertainty were determined (Fig. 3) and it appeared that the main uncertainty contribution to the 144 Ce/ 238 U atom ratio came from the uncertainty of the low 144 Ce/ 142 Ce ratio measured in the spent fuel sample which accounted for approximately 50% of the expanded combined uncertainty. Among the other main uncertainty contributors of the expanded combined uncertainty, the 142 Ce/ 140 Ce ratio measured by TIMS using the sequential method in the fuel made up 10-15%, the 142 Ce/ 140 Ce ratio measured by TIMS using the total evaporation method in the blend represented 16-19%, while the 140 Ce/ 233 U and 142 Ce/ 140 Ce ratios in the double spike accounted for respectively 9-10% and 6-9%.

This study demonstrates that our new method allows the determination of 144 Ce/ 238 U ratios at a few tens of ppm with expanded combined uncertainty of around 1% (k= 2) in MOx samples, which represents a significant improvement compared with the measurement uncertainty of several percent at a 95% confidence level obtained for 144 Ce content with gamma-ray spectrometry.

Conclusion

A new double spike isotope dilution combined with the mass spectrometry method was developed in order to determine the 144 Ce/ 238 U ratio at a few tens of ppm in spent nuclear fuel (MOx) with a relative expanded uncertainty of around 1 % at k = 2This was at least three times lower compared to those obtained with the classical and well-established gamma-ray spectrometry technique. This new method required (1) the use of a 140 Ce-233 U double spike which was specifically developed at the LANIE laboratory, (2) the development of Ce purification using two-step liquid chromatography, and (3) the development of Ce isotope measurements by thermal ionization mass spectrometry using both the total evaporation method for the qualification of Ce NIST3110 and blend analysis, as well as the sequential method, calibrated with the IUPAC reference value, for spent nuclear fuel sample analysis.

The main issue in this study was how to quantify the low 144 Ce content, since the uncertainty of the 144 Ce/ 142 Ce ratio measured in the spent fuel sample accounted for approximately half of the final combined uncertainty associated with the 144 Ce/ 238 U ratio measurement. In order to improve the uncertainties associated with this low-abundance isotope, the use of newgeneration mass spectrometers, especially ones equipped with high-ohm amplifiers (10 12 or 10 13 ohm instead of 10 11 ohm amplifiers) can be considered.

This new technique is therefore a robust alternative to the classical methods. With reduced uncertainties, it one that will better constrain the validation of neutronic calculations that predict the evolution of the fuel composition with time. It should also improve the decay-heat quantification and the short-term management of irradiated fuels.

Conflicts of interest

There are no conflicts to declare.

Significance to JAAS

We have developed a new method for the determination of 144 Ce/ 238 U atom ratio at a few tens of ppm with expanded uncertainty of around 1% (k= 2) in spent nuclear fuels using a double spike isotope dilution technique associated with thermal ionization mass spectrometry measurements employing both the total evaporation and the sequential methods. This represents a significant improvement compared to measurement uncertainties obtained for 144 Ce content at a level of several percent with gamma-ray spectrometry. The accurate quantification of the 144 Ce content in spent nuclear fuel is necessary to validate the neutronic calculations, in particular for decay heat purposes.

  from two aliquots of the sample (A and B), and (2) from two aliquots of the mixture of the spent fuel sample with the 140 Ce/ 233 U double spike (blends A and B). Finally, the 144 Ce/ 238 U ratio in the sample can be determined according to the isotopic balance equation: for sample, Sp for double spike and M for sample-double spike mixture (i.e., blend). The ratios ( 140 Ce/ 142 Ce)S and ( 144 Ce/ 142 Ce)S of the spent fuel samples were measured by TIMS using the sequential method, while the ratios ( 140 Ce/ 142 Ce)M and ( 238 U/ 233 U)M of the blends were measured by TIMS using the total evaporation method. The determination of the ( 140 Ce/ 142 Ce)SP, ( 238 U/ 233 U)SP and ( 140 Ce/ 233 U)SP ratios of the double spike is described in Section 2.1.4. The procedural flowchart for the double spike isotope dilution method is presented in Figure1. Ultimately, the absolute 144 Ce content in the spent fuel diluted solution was deduced from the U content determined by single isotope dilution mass spectrometry techniques with a relative expanded uncertainty of around 0.4% at k = 2 (not shown in this article).

Figure 1 :

 1 Figure 1: Flow chart representing the analytical procedure performed for the determination of 144 Ce/ 238 U atom ratios in spent fuel samples. Abbreviations: S, for sample; M, for mixture (i.e.,

Figure 2 :

 2 Figure 2: Chromatogram illustrating the separation of Nd (and other fission products and

Figure 3 :

 3 Figure 3: Diagram representing the contribution of the uncertainty of each component

Table 4 :

 4 Average Ce and U isotope ratios determined for reference materials by thermal ionization mass spectrometry (TIMS) in order to estimate the external reproducibility of the total evaporation (TE) method and the sequential (seq.) method. Here, n is the number of measurements performed. The IUPAC reference value for a natural Ce solution was used(Berglund and Wieser, 2011). The isotope ratio (IR) accuracy was expressed as 100 × (IRmeasured -IRreference or certificate) / IRreference or certificate.

		Average	Expanded	Relative expanded	Relative standard	Relative difference
		value	uncertainty	uncertainty	deviation	between aliquots
						A and B
			k = 2	k = 2	1σ
	MOx 1
	142 Ce/ 140 Ce (n=3)	0.88602	0.00580	0.65%	0.11%	0.16%
	144 Ce/ 142 Ce (n=3)	0.01411	0.00011	0.76%	0.38%	0.19%
	MOx 2
	142 Ce/ 140 Ce (n=2)	0.87200	0.00571	0.65%		0.01%
	144 Ce/ 142 Ce (n=2)	0.01828	0.00014	0.76%		0.01%

Table 5 :

 5 Average Ce isotope ratios of spent fuels determined from two aliquots (A and B) by TIMS (Sector 54) according to the sequential method for the two different MOx samples. Here, n is the number of measurements performed. The relative difference between the isotope ratios (IR) of aliquots A and B is expressed as 100 × (IRA -IRB) / IRB. The explanation for the estimation of the expanded uncertainties (U) can be found in the text.

	Sample	144 Ce/ 238 U	Expanded	Relative expanded
			combined	combined
			uncertainty	uncertainty
			k= 2	k=2
	MOx 1	34.7 × 10 -6	0.4 × 10 -6	1.1%
	MOx 2	58.8 × 10 -6	0.7 × 10 -6	1.1%

Table 6 :

 6 144 Ce/ 238 U atom ratios determined in spent fuel using the double spike isotope dilution mass spectrometry technique. The expanded combined uncertainties (U) were expressed using a coverage factor (k) of 2, providing an interval with a 95% confidence level. Expanded combined uncertainties U were determined following a Kragten approach.

Ce/ 238 U ratio of aliquot A from MOx 1 spent fuel by the double spike isotope dilution-mass spectrometry technique. Abbreviations: S, for sample; Sp, for spike; M, for Mixture.

Acknowledgements

We thank the CEA GESTN and SINET programs for funding this research work.

Ce and U isotope ratios determination by TIMS

Ce and U isotope ratios of reference materials

The 142 Ce/ 140 Ce ratios of the Ce NIST3110 solution were measured by a TIMS Sector 54 using both total evaporation and sequential methods. The average 142 Ce/ 140 Ce ratio for Ce NIST3110 solution was found to be 0.125911 ± 0.000040 (n=8, 1σ) by the total evaporation method, and 0.125690 ± 0.000055 (n=7, 1σ) for 7 independent measurements using the sequential technique (Table 4). The respective relative external reproducibility was 0.03 % (RSD, 1σ) for the total evaporation method and 0.04% (RSD, 1σ) for the sequential technique. The averages of the 142 Ce/ 140 Ce ratios obtained with both methods were in good agreement with the IUPAC reference value ( 142 Ce/ 140 Ce = 0.12565 ± 0.00029; uc). [START_REF] Berglund | Isotopic compositions of the elements 2009[END_REF] The average 142 Ce/ 140 Ce ratio obtained using the sequential method was very close to the IUPAC reference value (bias of 0.03%) as the analytical procedure was designed to reach this value. The average 142 Ce/ 140 Ce ratio obtained using the total evaporation method was slightly higher (bias of 0.21%) but still remained consistent with the uncertainty of the IUPAC reference value.

The 235 U/ 238 U ratios of the NIST U-500 standard solution were measured by TIMS Sector54 using the total evaporation and the average 235 U/ 238 U ratio obtained (0.9999 ± 0.0004, SD, 1σ, n=22), corresponding to an external reproducibility of 0.04% (RSD, 1σ), and were found to be in good agreement with the reference value 0.9997 ± 0.0007 (1σ) (Table 4).

Ce isotopic compositions of spent fuels

The measurement of 142 Ce/ 140 Ce and the 144 Ce/ 142 Ce ratios were determined by TIMS for each aliquot (A and B) of the spent fuel samples using the sequential method due to the low abundance of 144 Ce (