J Huyghe

V Vallet

D Lecarpentier

C Reynard-Carette

C Vaglio-Gaudard

How to get an enhanced extended uncertainty associated with decay heat calculations of industrial PWRs with the DARWIN2.3 package

Keywords: Decay heat, DARWIN2.3, uncertainty quantification, transposition, representativity factor

The decay heat is a crucial issue for in-core safety after reactor shutdown and backend cycle. An accurate computation of its value is done at the CEA within the DARWIN2.3 package. The DARWIN2.3 package benefits from a Verification, Validation and Uncertainty Quantification (VVUQ) process. The VVUQ ensures that the parameters of interest computed with the DARWIN2.3 package have been validated over experimental measurements and that biases and uncertainties have been quantified for a particular domain. For the parameter "decay heat", there are few integral experiments available to ensure the experimental validation over the whole range of parameters needed to cover the French reactor fleet (fissile content, burnup, fuel, cooling time). The experimental validation currently covers PWR UOX fuels for cooling times only between 45 minutes and 42 days, and between 13 and 23 years. Therefore the uncertainty quantification step is of paramount importance in order to increase the reliability and accuracy of decay heat calculations. This paper focuses on the strategy that could be used to answer this issue with the complement and the exploitation of the DARWIN2.3 experimental validation.

I. INTRODUCTION

The nuclear decay heat is released by both radioactive decays of unstable fuel and material structures isotopes after the reactor shutdown. The delayed fissions caused by delayed neutrons contribute significantly to the decay heat up to 100 seconds after the reactor shutdown. The decay heat reaches about 7% of the nominal power one second after the reactor shutdown [START_REF] Nutt | Spent fuel[END_REF] and is still about 1.5% of the nominal power one hour later, i.e. 40 MW for a 900MW e Pressurized Water Reactor (PWR).

The heat removal is one of the 3 key reactor safety functions, the other two being radioactivity containment and nuclear chain reaction control. The decay heat is thus an important parameter for the safety demonstration for a reactor operation under normal or accidental conditions and back-end nuclear cycle. Indeed, the decay heat is a dimensioning parameter for normal and emergency cooling systems of the nuclear core after the shutdown (up to 8 days) for a reactor in operation. It also imposes delays before the different stages of fuel discharging, storage and transportation (from 5 days to 10 years) until the reprocessing step or vitrification process and final storage (from 4 years to more than 300,000 years). Therefore, the accurate control of the decay heat calculation is essential for all the PWRs in the French reactor fleet (UOX and MOX fuels with 235 U enrichments going from 1.0 to 5.0 wt% and average plutonium contents going from 4.0 to 11.0 wt%) over a wide range of cooling times (from the reactor shutdown moment to more than 300,000 years).

The parameters required for fuel cycle applications -decay heat but also fuel inventory, activity, neutron, gamma, alpha and beta sources and spectra, radiotoxicityare provided by the DARWIN2.3 [START_REF] San Felice | Experimental validation of the DARWIN2.3 package for fuel cycle applications[END_REF] calculation package. This package is developed by the CEA with the support of its French partners (AREVA and EDF); it is the French reference for fuel cycle studies. The package has been extensively validated on a large number of experimental programs based on spent fuel chemical analyses carried out in France since 1993. It has also been validated for decay heat calculations on a more limited number of experimental programs based on elementary fission burst experiments and two integral calorimetric experiments, the MERCI-1 and CLAB experiments.

The objective of the paper is to present the methodological orientations to determine accurately the uncertainty associated with the DARWIN2.3 decay heat estimation. The determination of this uncertainty can be made either by nuclear data covariance matrix propagation or by exploiting the experimental validation through the transposition of the Calculation/Experiment (C/E) discrepancies; these two points will be explained in the next chapters, after a brief description of the DARWIN2.3 package for PWR fuel decay heat calculations. In this framework, the restriction linked to the DARWIN2.3 integral experimental validation exploitation will be illustrated. Perspectives for the estimation of an enhanced extended uncertainty associated with the decay heat calculations will be discussed at the end of the paper.

II. DARWIN2.3 PACKAGE FOR PWR DECAY HEAT CALCULATION

Description of the calculation scheme implemented in the DARWIN2.3 package

The DARWIN2.3 package is the French reference for fuel cycle studies [START_REF] San Felice | Experimental validation of the DARWIN2.3 package for fuel cycle applications[END_REF]. It is used as a reference for the validation of the industrial tool CESAR [START_REF] Vidal | CESAR5.3: An industrial tool for nuclear fuel and waste characterization with associated qualification[END_REF] for nuclear fuel and waste characterization at the AREVA La Hague reprocessing plant. It is dedicated to all fuel cycle studies for PWRs, Boiling Water Reactors, Material Testing Reactor (MTR) but also fast sodium-cooled reactors. DARWIN2.3 enables the estimation of physical quantities that characterize reactor spent fuels. In this chapter, the description of the DARWIN2.3 package is focused on the PWR application, with UOX and MOX fuels.

The PWR DARWIN2.3 calculation route is based on the chaining between the APOLLO2 [START_REF] Sanchez | APOLLO2 Year 2010[END_REF] 2D transport code and the DARWIN/PEPIN2 [START_REF] Tsilanizara | DARWIN: an evolution code system for a large range of applications[END_REF] depletion solver with two successive steps (Figure 1). The APOLLO2 calculation step solves the Boltzmann and the Bateman equations, with a simplified depletion chain, containing 162 isotopes corresponding to actinides, structural materials and 126 fissions products. The APOLLO2 calculation route uses the European JEFF-3.1.1 nuclear data library [START_REF] Santamarina | The JEFF-3.1.1 nuclear data library[END_REF], processed in a 281-group-structure Santamarina-Hfaiedh energy mesh (SHEM) [START_REF] Santamarina | The SHEM energy mesh for accurate fuel depletion and BUC calculations[END_REF]. The neutron flux is calculated in a 2D assembly geometry, using a Pij multicell model: the UP1 interface current method based on linearly anisotropic interface flux. The fuel pellets are split into four rings in order to give an accurate representation of 238 U absorption as well as fission product concentration profile. Space-dependent self-shielding, above 23 eV, is repeated at recommended burnup steps [START_REF] Jf | New modelling of LWR assemblies using the APOLLO2 code package[END_REF]. In the case of MOX assembly calculation, the UOX environment is taken into account. At the end of the APOLLO2 calculation, a library, called SAPHYB, is generated; it contains, both in the 281-group-energy structure, the fuel microscopic self-shielded cross-sections, spatially homogenized, and the 2D scalar neutron flux, tabulated versus burnup. The PWR DARWIN/PEPIN2 calculation step solves the fuel Bateman equation, under irradiation or under cooling (i.e. with no neutron flux), with a reference depletion chain containing up to 3800 isotopes. The equation solved under neutron flux (with the 4 th order Runge Kutta method) uses the selfshielded cross-sections and the 281-energy group neutron flux transmitted by the APOLLO2 code thanks to the SAPHYB. The irradiation history in DARWIN/PEPIN2 can be detailed with shutdown periods, bore concentration, moderator and fuel temperature tracking. It makes it possible to calculate precisely the depleted fuel inventory. The convolution of the fuel inventory with nuclear data leads to physical quantities such as decay heat, activity and radiotoxicity. The decay heat formula used in the DARWIN/PEPIN2 module (neglecting here the contribution of the fissions induced by delayed neutrons) is recalled in (1).

(1) where:



is the average decay energy released for a decay of the nuclide i ;

 is the half life of the nuclide i ;

 is the isotopic concentration of the nuclide i.

VVUQ process applied to DARWIN2.3 for the bias and uncertainty control

The DARWIN2.3 simulations are used to predict physical fuel cycle parameters with a quantifiable confidence and across the PWR application domain. The rigorous VVUQ process, classically used in many disciplines of science and engineering [START_REF]Predictive science academic alliance -Program-II (PSAAP-II) -Verification, Validation, and Uncertainty Quantification -Whitepaper (U)[END_REF] [10] [START_REF] Avramova | Verification, validation and uncertainty quatification in multi-physics modelling for nuclear reactor design and safety analysis[END_REF], is implemented for the DARWIN2.3 calculations, to assess the biases and uncertainties associated with the estimation of the physical parameters; it gives strength to the results for R&D and industrial applications. This process requires the following four steps [START_REF] Saint | Verification, validation and uncertainty quantification for neutronic calculation for ASTRID fast reactor detailed design[END_REF]:

-Verification: it shows that the calculation scheme does not present programming errors and gives the expected numerical results; -numerical Validation: in this step, the DARWIN2.3 results are compared to a 'reference calculation', integrating more accurate models than the calculations that have to be validated, and using the same nuclear data library. This numerical validation relies for DARWIN2.3 on several elements. It relies on the comparisons with TRIPOLI4® [START_REF] Brun | Systematic uncertainty due to statistics in Monte Carlo burnup codes : applications to a simple benchmark with TRIPOLI-4-D[END_REF] Monte Carlo calculations at step 0 (stationary conditions), before depletion; it enables to validate the APOLLO2 multigroup flux calculation and reaction rates, such as 235 U fission, 238 U radiative capture rates at step 0. The recent coupling of TRIPOLI4® stochastic transport code with the MENDEL [START_REF] Lahaye | First verification and validation steps of MENDEL release V1.0 cycle code system[END_REF] deterministic depletion solver allows to perform depletion calculations. Even though this process is not considered as a reference procedure for depletion calculation, the benchmarking between TRIPOLI4® and DARWIN2.3 has been investigated to provide first elements of modelling biases quantification [START_REF] Rizzo | Work plan for improving the DARWIN2.3 depleted material balance calculation concerning some important isotopes for fuel cycle[END_REF] for fuel cycle calculations (material balance); this work tends to show that the modelling biases are limited in comparison with the biases coming from nuclear data; -experimental Validation: it consists in comparing the calculation results of the set 'nuclear data library + calculation scheme + codes' to the values measured with integral experiments, for the decay heat and the material balance of the main actinides and the fission products involved in fuel cycle calculations and burnup credit criticality calculations; -Uncertainty and bias Quantification: it consists in associating with each parameter calculated by the DARWIN2.3 package, a controlled uncertainty over a range of applications. Generally speaking, there are two ways to achieve this goal: the first one relies on the analysis of the experimental validation results when there are enough experimental data to cover the DARWIN2.3 application domain; in this case, the transposition method is then applied, in order to transpose the Calculation-over-Experiment (C/E) discrepancies. If the experimental validation cannot be exploited for DARWIN2.3, the second way relies on nuclear data covariance propagation studies. The next chapters below are dedicated to the presentation of these two ways of uncertainty quantification applied to the DARWIN2.3 package.

III. NUCLEAR DATA COVARIANCE MATRIX PROPAGATION FOR THE UNCERTAINTY ESTIMATION OF DARWIN2.3 DECAY HEAT CALCULATION

Description of the deterministic propagation method implemented in the DARWIN2.3 package

The Uncertainty Quantification is currently rigorously done by covariance propagation with a deterministic approach. The covariance is a symmetric bilinear form on a vector space of random variables. The consequence is that for a parameter of interest (Y) which can be written as a linear combination of random variables (X i ), for example , its variance is given by the formula (2).

(

) 2
When Y is not directly a linear combination of random variables, a Taylor series expansion of Y, truncated at first order, allows the application of the formula [START_REF] San Felice | Experimental validation of the DARWIN2.3 package for fuel cycle applications[END_REF]. The matrix form of the formula (2) is called the "sandwich rule" (see formula (3)), where the are the derivative of Y to (also called sensitivity coefficients).

Recently, the DARWIN2.3 package has been enriched with this covariance propagation method [START_REF] Vallet | Validation of the uncertainty propagation method for the decay heat within the DARWIN2.3 package[END_REF]. The DARWIN/PEPIN2 module which manages the sensitivity profile calculations and the nuclear data covariance propagation is called DARWIN/IncerD [START_REF] Lahaye | Comparison of deterministic and stochastic approaches for isotopic concentration and decay heat uncertainty quantification on elementary fission pulse[END_REF]. Input data are covariances taken from the European evaluation JEFF-3.1.1 for the decay data (decay periods, branching ratios, mean decay energies) and fission yields, and the CEA/Cadarache covariance matrix database COMAC-V2 [START_REF] Archier | COMAC: Nuclear Data Covariance Matrices Library for Reactor Applications[END_REF] for cross-sections. The prior calculation uncertainty ε resulting from the propagation of uncertainties of nuclear data covariances is as follows:

(3) where:

is the sensitivity vector due to nuclear data, is its transpose, is the nuclear data covariance matrix.

When the hypothesis of linearity of the decay heat parameter to the nuclear data is not straightforward, it must be checked to ensure the legitimacy of this method [START_REF] Vallet | Validation of the uncertainty propagation method for the decay heat within the DARWIN2.3 package[END_REF]; it is done by comparing the results obtained with this quadratic summation method to those produced with a different uncertainty propagation method that does not need a linearity hypothesis. This is the case of the sampling approach, implemented in the URANIE/MENDEL code system developed at CEA. URANIE [START_REF] Gaudier | URANIE: the CEA/DEN uncertainty and sensitivity platform[END_REF] is an uncertainty platform and MENDEL is the CEA new generation depletion code. MENDEL can use the same input data as the DARWIN/PEPIN2 code (same SAPHYB input files, nuclear data libraries and filiation chains). The sampling approach consists in selecting distribution laws for each random input (more often, Gaussian laws) and sampling them with a Latin Hypercube Sampling technique in order to have n realizations of each variable. Then, the MENDEL code is called n times with n different sets of input data according to the results of the sampling step. Eventually, the distribution of the decay heat is built and the moments are extracted.

Thus, the linearity hypothesis has been checked and allows the calculation of sensitivity profiles by direct perturbation and the propagation of nuclear data covariances through the DARWIN/PEPIN2 calculation. For the calculation of the sensitivity profiles of the decay heat to the cross-sections with DARWIN/IncerD, there is no accurate Boltzmann/Bateman coupling. The flux and reaction rates are performed in a previous calculation with the neutron code APOLLO2 and then stored in a file which is an input data for DARWIN/PEPIN2. When calculating the decay heat value resulting from the perturbation of a cross-section, it is the nominal value stored in the SAPHYB file that is perturbed instead of recalculating the neutron spectrum with the APOLLO2 code. However, studies showed that the impact of the coupling can be neglected on the uncertainty propagation calculation for the decay heat, for cooling times between 0.1 second and 300 years [START_REF] Vallet | Application of the bias transposition method on PWR decay heat calculations with the DARWIN2.3 package[END_REF].

An illustration of the decay heat uncertainty estimated by the deterministic approach for standard PWR fuels is given in Figure 2; the considered fuels are a UOX fuel with 3.7 wt% enriched uranium and a MOX fuel with a mean plutonium content of 9.5 wt%, both at a 50 GWd/t discharge burnup. The uncertainty is below 3.5% (1) for the UOX fuel, and below 4.5% (1) for a MOX fuel, regardless of the cooling time.

The uncertainty estimated with the stochastic approach is also presented in Figure 2. A good accuracy between the deterministic and the stochastic method is observed (the maximum discrepancy is ~0.3%). Once the sensitivity profiles are known, the main contributors to the uncertainty can be identified at a given time, as illustrated in Figure 3. In the MOX fuel case, it appears that cross-section uncertainties are responsible for about 20% of the total decay heat uncertainty at 1.0 second and for more than 90% of the total uncertainty after 10 8 seconds.

Restrictions due to nuclear data covariance matrix completeness and accuracy

The nuclear data covariance matrices play a major role on this uncertainty propagation; uncertainty propagation results highly depend on the quality, accuracy and availability of the covariance matrices.

Covariance matrices are sometimes a subject for debate for experts in nuclear data. It is often hard to know precisely how a covariance matrix was produced and measure its reliability.

It must be emphasized that more than 40,000 nuclear data -corresponding to cross sections, branching ratios, decay energies, half-lives, fission yields -are involved in decay heat calculations. In the JEFF-3.1.1 evaluation, more than 7000 nuclear data do not have uncertainties, which is about 16% of the number of nuclear data in JEFF-3.1.1. Those nuclear data are mainly branching ratios and mean energies (alpha, beta, and gamma). However we need to put something down to the parameters with no uncertainty, a value which is conservative but realistic. The other nuclear data libraries are studied and expert's advices are used for this task.

There are few covariance matrices for cross-sections or independent fission yields in the JEFF-3.1.1 library. These data are taken in the COMAC-V2 database which receives the benefit of a constant work for improvement. Even if the major part of the covariance matrices may be associated with the JEFF-3.1.1 library, some of the covariance matrices come from a different evaluation than the one giving the centered values. It is the case of the 241 Am which was re-evaluated at the CEA recently for JEFF-3.2 and whose capture cross-section was increased by about 15%. Another example is the case of the 242 Pu which is a major contributor to the decay heat uncertainty through the build-up of 244 Cm, a strong contributor to decay heat (about 40% of the total decay heat around 10 years). The covariance matrix for 242 Pu radiative capture cross-section actually comes from the ENDF/B-VII.1 evaluation. The collapsed uncertainty results in about 11% at one standard deviation and is responsible for more than 80% of the total decay heat variance of MOX fuels at 10 years of cooling. A new evaluation of the covariance matrix for this isotope would have an impact on the prior decay heat uncertainty of MOX fuels.

There is also a crucial lack of correlation matrices for independent fission yields, although they are strongly correlated by physical constraints of conservation and normalization. A subgroup at the Working Party of International Nuclear Data Evaluation Co-operation (WPEC, NEA) [START_REF] Mills | Improved Fission product yield evaluation methodologies[END_REF], whose purpose was to come up with a new methodology to produce fission yields evaluations associated with covariance matrices was proposed in 2013 and came to an end in 2016: as a conclusion, covariance matrices will be produced for the next JEFF evaluation for fission yields, based on the GEF code [START_REF] Rochman | A Bayesian Monte Carlo method for fission yield covariance information[END_REF]. Covariance matrices were also produced at the CEA, associated with JEFF-3.1.1 fission yields [START_REF] Terranova | Covariance Evaluation for Nuclear Data of Interest to the Reactivity Loss Estimation of the Jules Horowitz Material Testing Reactor[END_REF] ; its large impact on decay heat uncertainty has also been quantified in [START_REF] Terranova | Covariance Evaluation for Nuclear Data of Interest to the Reactivity Loss Estimation of the Jules Horowitz Material Testing Reactor[END_REF].

Generally speaking, the nuclear data covariance propagation is the starting point for decay heat in the Uncertainty Quantification process defined in chapter II; indeed, it enables to quantify the uncertainty associated with the DARWIN2.3 calculated decay heat, assuming that the modelling calculation bias are limited, before exploiting the experimental validation results with the representativity/transposition method. The nuclear data uncertainty propagation is also necessary to implement the representativity/transposition method, as shown in the next chapter.

IV. EXPLOITATION OF THE INTEGRAL EXPERIMENTAL VALIDATION FOR THE DARWIN2.3 UNCERTAINTY

QUANTIFICATION

Description of the experimental validation of DARWIN2.3

The current experimental validation of the DARWIN2.3 package for the decay heat is based on the following experiments:

-Elementary Fission Burst experiments [START_REF] Huynh | JEFF3 et les calculs de puissance résiduelle[END_REF]: An Elementary Fission Burst (EFB) of a fissile nuclide is the decay heat emitted by the fission of one nuclide by a neutron of a given energy (thermal or fast). Therefore in these experiments, neither the radiative capture effects among the fission products, nor the actinide contribution are taken into account. Nevertheless, these experiments provide valuable information in order to validate fission product contribution to the decay heat.

Historically, EFBs were used to calculate the decay heat by integration over the time and summation over the major fissile nuclides of the fuel. This method has even given birth to an international ISO standard 10645:1992 for decay heat computations [START_REF]Énergie nucléaire -Réacteurs à eau légère -Calcul de la puissance résiduelle des combustibles nucléaires[END_REF]. The DARWIN2.3 experimental validation includes the analyses of the DICKENS and AKIYAMA experimental values (with cooling times between around 3 seconds and 8 hours) [START_REF] Akiyama | [END_REF][27] [START_REF] Dickens | Fission-Product Energy Release for Times Following Thermal-neutron Fission 239,241Pu between 2 and 14000s[END_REF][29] concerning 235 U or 239 Pu fission in the thermal energy range; it showed a good agreement with the experimental elementary decay heat values released with fission of a 235 U or 239 Pu (thermal and fast spectra); -The MERCI-1 experiment: this integral experiment was conducted in the French experimental reactor OSIRIS at the CEA Saclay, that consisted in measuring with a calorimeter the decay heat released at short cooling times (45 minutes to 42 days) after irradiating a PWR-UOX fuel pin (with a burnup of 3.5GWd/t and 3.7% enrichment in 235 U) [START_REF] Jaboulay | Analysis of MERCI decay heat measurement for PWR UO2 fuel rod[END_REF]. The interpretation of the MERCI-1 experiment shows a maximum discrepancy of 6% at around 12.5 hours of cooling. Between 5 and 42 days, the uncertainties are about 1% at one standard deviation. The associated uncertainty is constant and equal to 1% at two standard deviations; -CLAB experiments: they consist in calorimetric measurements of PWR-UOX entire assemblies at the Swedish facility CLAB [START_REF] Sturek | Measurements of decay heat in spent nuclear fuel at the Swedish interim storage facility CLAB[END_REF]. Measurements are available for fifteen 17x17 assemblies and twenty-one 15x15 assemblies with different fissile contents (enrichment in 235 U between 2 and 3.5%), burnup values (between 20 and 47GWd/t) and cooling times (between 12.9 and 23.2 years). The C/E discrepancies obtained with the DARWIN2.3 package are of -2.2% on average with a 3.4% uncertainty at one standard deviation. The dispersion of the results lies between +0.9% and -4.0% [START_REF] San Felice | Experimental validation of the DARWIN2.3 package for fuel cycle applications[END_REF]. Besides, no correlation was detected with the burnup or the cooling times; -Post-Irradiated Experiments (PIE) on irradiated fuel: they are based on the measurement of nuclide concentrations contributing to the decay heat also, after fuel chemical dissolution. They can also bring valuable elements for the DARWIN2.3 decay heat experimental validation [START_REF] San Felice | Experimental validation of the DARWIN2.3 package for fuel cycle applications[END_REF]. Especially at long cooling times (typically over 6 months), only a few isotopes contribute to the irradiated fuel decay heat (less than 50). The major decay heat contributors for both UOX and MOX fuels after 6 months are 144 Pr, 106 Rh, 134 Cs, 242 Cm, 137m Ba, 90 Y, 244 Cm, 238 Pu and 241 Am.

After the demonstration of the analyzed experiment representativity relatively to PWR fuel decay heat, the experimental validation has to be transposed to bring valuable information for the DARWIN2.3 Uncertainty Quantification step.

First results concerning the implementation of the representativity and transposition on the DARWIN2.3 integral experimental validation

The representativity and transposition method relies on an experimental data assimilation process. The transposition gives consistent results, when the similarity between the experiment and the "reactor" case is strong. This similarity is quantified by the representativity factor, introduced by Orlov [START_REF] Orlov | Problems of Fast Reactor Physics related to breeding[END_REF]. The representativity factor is a correlation factor corresponding to the scalar product of two sensitivity profiles of a parameter of interest to nuclear data. The representativity factor between two applications (for instance an experiment and a reactor) for a given parameter (for instance the decay heat) is described by the formula (4) where the index A stands for the reactor application and e for the experiment. The vector S A (respectively S e ) is the sensitivity to nuclear data in the reactor application (respectively the experiment), and is the covariance matrix. [START_REF] Sanchez | APOLLO2 Year 2010[END_REF] One can also define a weight (see formula ( 5)) where is the uncertainty associated with the experiment and the prior uncertainty due to nuclear data and calculated with formula [START_REF] Vidal | CESAR5.3: An industrial tool for nuclear fuel and waste characterization with associated qualification[END_REF]. The weight provides an indication of the interest of the experiment regarding to a transposition application. In the ideal case where there is no experimental uncertainty ( =0); the weight is maximum and the main source of uncertainty comes from the nuclear data. As a conclusion, the transposition method is the most efficient, that is to say leads to the largest bias and uncertainty reduction due to nuclear data covariances, when and are the closest to unity.

(

) 5
The transposition method applied to one experiment and one reactor application allows an indirect reestimation of nuclear data leading to a new calculation bias ( ) and a posterior uncertainty ( ) due to nuclear data covariances (see formulas ( 6) and ( 7)).

(6) [START_REF] Jf | New modelling of LWR assemblies using the APOLLO2 code package[END_REF] These formulas have been extended to more than one experiment [START_REF] Santos | Optimisation de l'approche de représentativité et de transposition pour la conception neutronique de programmes expérimentaux dans les maquettes critiques[END_REF][34]: [START_REF] Carmouze | The similarity/transposition theory to assess accurately MOX 15x15 used fuel inventory with DARWIN2.3[END_REF]. Indeed, the current experimental validation report of the DARWIN2.3 package is focused on 17x17 lattices. The use of the representativity/transposition method on the isotopic concentrations was allowed by a strong representativity factor (r=0.99) and led to an uncertainty reduction on nuclide concentration calculations ranging from 0 to 87%.

The second work conducted at CEA is a prospecting study on the use of the transposition for decay heat [START_REF] Vallet | Application of the bias transposition method on PWR decay heat calculations with the DARWIN2.3 package[END_REF]. The goal was to quantify to what extent a measurement at a given set of parameters (t cooling , BU) could be used through the transposition at another set of parameters (t cooling ' , BU ' ). The Figure 4 shows the representativity factor obtained as a function of the cooling time for an UOX fuel ( 235 U e%=3.7%) reactor application and one of the CLAB experiment at a cooling time of 4724 days (i.e. ~13 years) and a very similar discharge burnup. The decay heat mainly originates from both short-life fission product decays and actinide decays. One can see in this illustration that the representativity factor quickly drops under 2000 days (i.e. ~5.5 years) of cooling. Therefore it can be sensed here that it would be difficult to use the transposition to quantify biases and uncertainties due to nuclear data at a shorter cooling time than 2000 days. Bear in mind that the representativity is usually considered as satisfactory when it is close to 0.9. Another work is on progress concerning the exploitation of the MERCI-1 experiment analysis, which is the integral experiment that provides the integral experimental data at the lowest cooling times (45 min). The decay heat exclusively originates from short-life fission product decays. The representativity factor on the decay heat between MERCI-1 and a PWR standard UOX fuel ( 235 U e%=3.7%), is presented in Figure 5. The MERCI-1 fuel sample was irradiated during three cycles in the OSIRIS experimental reactor, with a mean specific power around 65 W/g, with two inter-cycle and shutdown periods; a fine irradiation history was taken into account for decay heat calculations [START_REF] Jaboulay | Analysis of MERCI decay heat measurement for PWR UO2 fuel rod[END_REF]. For the PWR standard PWR fuel, a simplified mean irradiation history was modelled, with a classical specific power (around 40W/g.) With this assumption, it is observed that the representativity is very good, even for low cooling time (5 min), as long as the burnup is close to the MERCI-1 fuel burnup (3.6GWd/t); for higher burn-up (>15GWd/t), the experiment is not representative enough to use the transposition method. Indeed, the low MERCI-1 representativity for a standard UOX spent fuel (BU>15GWd/t) is due to the contribution of 239 Pu fissions to decay heat, and thus to its associated uncertainty, from a burn-up of 15 GWd/t (see Figure 6), and increasing with the burn-up. The bias transposition will be able to be analyzed in a second step for the cases presenting a good representativity.

Figure 1 :

 1 Figure 1 : DARWIN2.3 package

Figure 2 :

 2 Figure 2: Decay heat uncertainty estimated by deterministic (DARWIN/IncerD) / stochastic (URANIE/MENDEL) approaches for UOX and MOX standard PWR fuels at a 50GWd/t discharge burnup.

Figure 3 :

 3 Figure 3: Relative contributions to the total decay heat uncertainty for the MOX case.

  prior and posterior values of the calculated quantity of interest, -and are the prior and posterior uncertainties due to nuclear data covariances for the reactor application, -is the extended representativity vector of the reactor application A, -(for several experiments (i)) -is the extended representativity matrix between experiments, -and is the experimental uncertainty for the experiment i and is the experimental correlation between the experiments i and j, -At CEA, transposition applications have been initiated for fuel cycle application in 2015. The first one concerns the transposition of C/E discrepancies on isotopic concentrations of a 17x17 square lattice PWR MOx fuel on a 15x15 square lattice PWR MOX fuel

Figure 4 :

 4 Figure 4: Representativity factor between a CLAB experiment (t=4724 days, BU=47.3 GWd/t) and an UOX fuel (BU=46.5 GWd/t).

Figure 5 :

 5 Figure 5: Representativity factor between a MERCI experiment (t=45 min or 42 days, BU=3.6 GWd/t) and a standard PWR UOX fuel for decay heat.

Figure 6 :

 6 Figure 6: Contribution of fission products coming from 235 U thermal fissions and 239 Pu thermal fissions on the decay heat uncertainty versus fuel burn-up, for a UOX spent fuel.

ACKNOWLEDGEMENT

The authors would like to thanks EDF, FRAMATOME and ORANOfor their financial support on the DARWIN2.3 calculation tool.

V. PERSPECTIVES FOR THE ESTIMATION OF AN ENHANCED EXTENDED UNCERTAINTY ASSOCIATED WITH THE DARWIN 2.3 DECAY HEAT CALCULATIONS

The recent studies of nuclear data covariance propagation performed at CEA over the last years on the decay heat of UOX and MOX fuels shows that the total uncertainty is reduced, sometimes by a factor 2, in comparison with the uncertainty estimation at the end of the 90's [START_REF] Rebah | Incertitude sur la puissance résiduelle due aux incertitudes sur les données de produits de fission[END_REF]. This is mainly due to the use of a more stringent method of uncertainty propagation and to improvements on the content of nuclear data libraries. However, this reduction emphasizes the fact that one should be careful when analyzing the results and supports the interest of keeping a critical look on nuclear data covariances.

Thus, the DARWIN2.3 experimental validation must be completed, considering the lacks of representativity of the integral experiments. Its exploitation with the representativity and transposition method must also go on, in order to provide elements to validate the order of magnitude of the nuclear data uncertainty for the DARWIN2.3 calculated decay heat on the application domain. First, the DARWIN2.3 validation could be extended with the analysis of two sets of integral decay heat measurements which have been found in the literature: GE-Morris and HEDL measurements. They are used for the validation of other international codes dedicated to decay heat computation such as SCALE/ORIGEN [START_REF] Gauld | Validation of SCALE 5 Decay Heat Predictions for LWR Spent Nuclear Fuel[END_REF] or VESTA2.1 [START_REF] Haeck | Experimental Validation of Decay Heat Calculations with VESTA 2.1[END_REF]. GE-Morris and HEDL measurements enable to cover lower cooling time ranges than the CLAB experiments, the characteristics are the following (Figure 6):

-General Electric (GE) (UOX assemblies, 3.4%<e% 235 U<4.0%, 26<BU<39GWd/t, cooling times between 3 and 8 years): San Onofre 1 and Point Beach 2 reactor units [START_REF] Judson | In-Plant Test Measurements for Spent Fuel Storage at Morris Operation -Volume 3: Fuel Bundle Heat Generation Rates[END_REF]; -Hanford Engineering Development Laboratory (HEDL) (UOX assemblies, e% 235 U = 2.55%, 25<BU<30GWd/t, cooling times between 2 and 6 years): Turkey Point 3 reactor unit [START_REF] Schmittroth | ORIGEN2 Calculations of PWR Spent Fuel Decay Heat Compared with Calorimeter Data[END_REF]; Concerning EFBs, the experimental validation could be extended as well to give elements for short cooling times with the following experiments:

-235 U th : LOTT experimental values (1973) [START_REF] Lott | Puissance Residuelle Totale emise par les Produits de Fission thermique de l' 235 U[END_REF] for cooling times between 17s and more than 100 days and NGUYEN values (1997) [START_REF] Nguyen | Gamma-ray spectra and decay heat following 235 U thermal neutron fission[END_REF] for cooling times between less than 1s and about 5 hours;

-238 U fast : AKIYAMA values (1982) for cooling times between 30s and about 11 hours and NGUYEN values (1997) for cooling times between less than 1s and about 14 hours;

-239 Pu th : FICHE values (1976) [START_REF] Fiche | Mesures Calorimetriques de la Puissance Residuelle Totale Emise par les Produits de Fission Thermique de 233 U et 239 Pu[END_REF] for cooling times between 50s and about 28 hours, JOHANSSON values (1987) [START_REF] Johansson | Integral Determination of the Beta and Gamma Heat in Thermal-neutron-induced Fission of 235 U and 239 Pu, and of the Gamma Heat in Fast Fission of 238 U[END_REF] for cooling times between about 300s and about 7 hours, and NGUYEN [START_REF] Nguyen | Decay heat measurements following neutron fission of 235U and 239Pu[END_REF] values (1997) for cooling times between about 1s and about 9 hours;

-241 Pu th : DICKENS [START_REF] Dickens | Fission-Product Energy Release for Times Following Thermal-neutron Fission 239,241Pu between 2 and 14000s[END_REF] values (1980) for cooling times between 2.7s and about 3.3 hours.

The experimental validation based on EFBs will have to be added to the experimental data assimilation process that only relies on MERCI-1 and CLAB assimilation for the moment; the objective will be to assimilate all these data at the same time, as recommended by [48] (for which only FEB data assimilation is performed), to get a final uncertainty capable to cover the largest DARWIN2.3 application domain, much wider than the current one covered by the experimental validation.

.

VI. CONCLUSION

The decay heat is a crucial issue for in-core safety and back-end cycle. In this framework, the accurate control of the decay heat calculation is needed for all the PWRs in the French reactor fleet (UOX and MOX fuels with 235 U enrichments going from 1.0 to 5.0 wt% and average plutonium contents going from 4.0 to 11.0 wt%) over a wide range of cooling times (from the reactor shutdown moment to more than 300,000 years). An estimation of the decay heat is provided by the DARWIN2.3 package. The DARWIN2.3 package benefits from the implementation of the VVUQ process. There are very few integral experiments available for decay heat to ensure the experimental validation of the DARWIN2.3 package over the whole range of parameters needed. The Uncertainty Quantification associated with the decay heat calculated by DARWIN2.3 relies today mainly on a deterministic nuclear data covariance propagation. The input data for this propagation are covariances taken from the European evaluation JEFF-3.1.1 for the decay data and fission yields, and the COMAC-V2 database for crosssections. However, these covariances are often uncompleted, considering the number of nuclear data involved in the decay heat calculation (more than 40,000). Besides, their quality and accuracy are sometimes a subject for debate for experts in nuclear data (in particular concerning fission yield correlation matrix). That is why it is needed to complete and to exploit the DARWIN2.3 experimental validation, to confirm the uncertainty level associated with the decay heat calculation. To do so, a data assimilation work, with the implementation of the representativity and transposition method, has to be done integrating the C/E discrepancies coming from both integral experiments and EFBs.


G Gutierrez
email: gaelle.gutierrez@cea.fr

C Onofri

S Miro

M Bricout

F Leprêtre

Effect of ballistic damage in UO 2 samples under ion beam irradiations studied by in situ Raman spectroscopy

The damage induced in uranium dioxide (UO 2 ) during ion irradiation at low energy was studied by micro-Raman spectroscopy. Polycrystalline UO 2 samples were irradiated by 0.9-MeV I, 2-MeV Au at 25°C and by 4-MeV Kr ions at -160°C in a wide range of fluence. In situ Raman measurements reveal similar spectra evolution no matter the ion beam used. The T 2g band centred at 445 cm -1 related to the fluorine structure reveals a broadening with the irradiation damage increase. In addition, several bands ranging from 500 to 700 cm -1 , which are attributed to sub-or sur-stoichiometric structural defects, are observed at the first time of irradiation. Their intensities rise up with the irradiation fluence increase to a similar asymptotic relative values for all the irradiation conditions. The obtained Raman kinetics are compared with data from the literature on the microstructure evolution observed by Transmission Electronic Microscopy (TEM) and on the fraction of displaced atoms determined by Rutherford Backscattering Spectroscopy in channelling mode (RBS-C).

Intro

Raman spectroscopy is an efficient technique to determine the structural evolution in materials under irradiation. Nuclear fuel [1], cladding materials [2] or matrices for high level nuclear waste management [3] have been successfully characterized by this technique. Radioactive fuel samples [4,5] as well as ion beam irradiated uranium dioxide (UO 2 ) samples [6,7] can be studied and compared.

Several papers have investigated the Raman spectra evolution of UO 2 after ion beam irradiation [1,6,7]. In addition to the standard T 2g band, additional bands in the range of 500 to 700 cm -1 are observed after sample oxidation or are induced by ion irradiation performed under vacuum [1,[4][5][6][7]. At 575 cm -1

, the LO Raman-forbidden mode in the perfect fluorite structure becomes active by the presence of disorder in the crystal due to a breakdown in the selection rules [1,8]. Two other bands at around 520 and 630 cm -1 denoted as U1 and U3 could be associated with sub-stoichiometry UO 2-x and with structural defects in the cuboctahedral symmetry of the interstitial oxygen in hyper-stoichiometric UO 2 , respectively [7,9,10].

The present study aims to investigate the effect of ballistic damage generated by ion beam irradiations in UO 2 . The damage kinetics of polycrystalline samples under ion beam irradiation was monitored in real time by using the JANNuS (Joint Accelerators for Nanoscience and Nuclear Simulation) platform in Saclay, France. In situ Raman setup with a frequency-doubled Nd: YAG (532 nm) laser is coupled with a triple beam chamber [11]. Samples were irradiated with low energy ions in order to determine the Raman spectra evolution under ballistic damage. Experiments have been performed at room temperature (25°C) with I ions at an energy of 0.9 MeV and with Au ions at 2 MeV. A complementary irradiation at low temperature (-160°C) has been also carried out with Kr ions at an energy of 4 MeV.

To follow in real time the radiation damage evolution, in situ Raman spectra have been recorded for different irradiation fluences.

Experimental procedures

UO 2 polycrystalline pellets with an average grain size of 7.6 µm were cut in discs (thickness: 500 µm) and polished on one side. An annealing at 1400°C during 4 h under an Ar-H2 (5%) was performed in order to remove the damage induced by polishing. Pellet density has been measured to be around 10.74 g.cm -3 (∼98 % of densification).

The irradiations were carried out at JANNuS-Saclay facility with 0.9 MeV I ions and 2 MeV Au ions at a controlled temperature of 25°C and with 4 MeV Kr ions at -160°C. The irradiations were performed under a vacuum lower than 10 -7 mbar in order to prevent any oxidation. Irradiation conditions and parameters calculated using the SRIM code are reported in Tab.1 [START_REF] Ziegler | The Stopping and Range of Ions in Solids[END_REF].

The JANNuS facility also includes the possibility of in situ Raman monitoring during irradiation. The experimental set up is described in [11]. Raman spectra were recorded in broad wave-number range between 200 and 900 cm -1 for virgin and irradiated samples using an Invia Reflex Renishaw spectrometer coupled with a Leica microscope. A laser power lower than 1 mW was used in order to avoid oxidation during the analysis. In situ Raman measurements after beam shut off were carried on irradiated samples with a frequency-doubled Nd:YAG (532 nm) laser and a 2400 groove/mm grating.

The Raman spectrometer has been calibrated by using silicon monocrystalline samples. Raman spectra were recorded during 120 s at each step of irradiation fluence. Raman spectrum can be recorded during ion irradiation but, in order to obtain representative data avoiding any additional evolution of the microstructure, the ion beam is stopped during the acquisitions.

The fitting module of the Wire Raman spectroscopy software (Renishaw) was used for the spectra simulation. A combination of Lorentzian (often used for crystal) and Gaussian line shape (expected for disordered materials) called Voigt profiles was used. The accuracy on band position deduced from spectrum simulation is determined at ± 1 cm -1

.

Results

The figure 1 presents the Raman spectra between 300 and 900 cm -1 in situ recorded on UO 2 samples irradiated with 2 MeV Au ions at 25°C for fluences ranging from 4.7×10 12 to 1.2×10 16 Au.cm -2

. Before irradiation (spectrum 0 in black), we observed a band centred at 445 cm -1 assigned to the triply degenerate Raman active mode (T 2g ) commonly Raman active for all the fluorine structures [14]. This band is relied to the breathing vibration of oxygen atoms around the uranium atoms in the crystalline structure. In the 500 and 700 cm -1 range, we also remark one intense band at 575 cm -1 and two bands with a smaller intensity at 520 and 630 cm -1

. The band at 575 cm -1 is associated to the first order T 1U LO scattering mode [8]. This mode is Raman-forbidden in the perfect fluorite structure and becomes active by the presence of disorder in the crystal due to a breakdown in the selection rules [1,8]. The assignment of 520 and 630 cm -1 bands is less obvious. The first one denoted as U1 is associated with sub-stoichiometry UO 2-x [1]. The third band denoted U3 is assigned to structural defects in the cuboctahedral symmetry of the interstitial oxygen in hyper-stoichiometric UO 2 [7]. This triplet band (U1, LO, U3) is already observable before irradiation highlighting the presence of defect in the virgin samples due to the preparation or to a surface oxidation [15]. As shown on Fig. , the intensity of T 2g band decreases and a broadening is observed.

In addition, the triplet bands in the range of 500-700 cm -1 increases. The U1 and U3 bands less marked on the virgin samples are more intense after irradiation. Then, from an irradiation fluence of

10 14 Au.cm -2
, the Raman spectra do not seem to evolve any more. We must note that our Raman measurements have been performed with a 532 nm wavelength laser. In these analysis conditions, the LO band is much more intense compared to the U1 and U3 bands due to a resonance effect [16].

The U1 and U3 evolutions is more difficult to follow especially for low damage level. For that reason, in the following part, the triplet band in the 500 and 700 cm -1 range will be discussed together and referred as the defect massif.

The Raman spectra have also been in situ recorded for UO 2 samples irradiated at 25°C with 0.9 MeV I ions and at -160°C with 4 MeV Kr ions. We observed a similar evolution with an increase of the defect massif area at first step of irradiation and a decrease of T 2g band with a broadening. In order to compare the results obtained from the different irradiations, the line width (FWHM) of T 2g band, characteristic to the undisturbed fluorite lattice, is reported on Fig. 2.a as a function of the maximum displacement per atoms (dpa). It exhibits similar evolution for all the irradiated samples. Below 0.03 dpa, no significant linewidth evolution is observed. After an irradiation inducing 0.03 dpa, a broadening occurs and increases linearly with the damage. Then a stabilization at an asymptotic relative value of around 30 cm -1 is shown. In addition, a small T 2g shift (<1.5 cm -1

) to the lower frequencies is noticed for all the irradiations.

Since the defect massif is associated to the structural disorder, the ratio between its area and T 2g band area describes the damage build-up kinetics in UO 2 for different irradiation conditions. Fig. 2.b presents this ratio as a function of the maximum dpa. We observed that, as soon as the UO 2 samples are submitted to irradiation damage (first step at 0.001 dpa), the band intensity increase for all the curves. We notice a shift of massif defect evolution between the samples irradiated at 25°C and the one at -160°C. It indicates that the area increase occurs in a faster way for the irradiation performed at low temperature (Kr) than for the ones at room temperature (I, Au). A similar asymptotic relative value is achieved for all the irradiation conditions but at different damage level according to the irradiation temperature. The evolution of defect massif area is well reproduced by the multiple step damage accumulation (MSDA) model [17]. The evolutions inducing during I ions irradiation at 25°C and Kr ions irradiation at -160°C have been fitted by the following equation (Fig. 3):

                                           1 1 , 1 1 1 , exp 1 exp )) ( exp( 1 n i n n sat n D n k k k i i sat i D D G f G f f    (1)
where f D,i sat is the level of damage at saturation, n is the number of steps required for the achievement of the total disordering process, Φ i is the threshold ion fluence of the i th step, and σ i the disordering cross-section at the i th step. G corresponds to the Heaviside function H multiplied by its argument. In the MSDA model, the damage accumulation results from atomic rearrangements steps induced by microscopic and/or macroscopic events [17]. Each step is correlated to a new defect configuration, which is generated by the damage accumulation. In our case, the damage build-up is accumulated via a two-step mechanism (n = 2 in Eq. ( 1)): the first step up to 0.065 and 0.0054 dpa at an irradiation temperature of 25°C and -160°C, respectively, and the second for higher value. The first step occurs for a very small amount of damage level and is shorter for the lower irradiation temperature.

Concerning the second step, it is interesting to note that a higher disordering cross-section (σ 2 ) is determined for an irradiation at a temperature of -160°C (12.7 nm

2

) than at 25°C (3.7 nm 2

). These results indicate a faster increase of level damage for an irradiation temperature of -160°C. The level of damage at saturation (f D,2 sat ) decreases from 5.3 at 25°C down to 4.8 at -160°C. However, due to our resolution limit, this difference is not quite significant. Thus, the first step observed for very low damage level, should be, for example, the consequence of point defect evolving in clusters on the Raman spectra. However, complementary experiments are required to conclude on this point.

Discussion

The results from the different irradiation experiments highlight that, during an irradiation favouring the ballistic damage at 25°C, one damage level (dpa) seems to induce one Raman spectra. Indeed, we have observed that a broadening and an intensity decrease of T 2g band occur for all the performed irradiations. The intensity loss of the T 2g band indicates deviations from the perfect cubic fluorite structure [9]. In addition, the disorder arising from irradiation induces the relaxation of selection rules allowing a greater range of vibrational modes to contribute to Raman scattering. This could be experimentally observed by an asymmetrical broadening of the Raman band [18,19]. We do also measure a shift to lower frequencies with a value closed to our resolution limit (<1.5 µm). Similar T 2g red-shift was reported for UO 2 samples irradiated with He 2+ at 25 MeV and in self-irradiated samples [7,5]. It could highlight the defects formation (point defects, dislocations or voids) and a lattice swelling. This point will be discussed in the following part by comparing the evolution kinetics of different defects obtained by other characterizations (TEM and RBS-C).

In addition, the defect massif area, correlated with the damage build-up, increases with the irradiation doses and then reaches saturation at the dose of around 0.2-0.4 dpa (Fig. 2). The cross section analysis of an irradiated samples with He ions at 25 MeV by Raman spectroscopy highlights also a T 2g broadening correlated with a grow up of U1, LO and U3 bands area when the ballistic stopping power becomes predominant compared to the electronic one [7].The Raman spectra comparison between the irradiations performed at 25°C and -160°C indicates a faster increase of level damage for an irradiation at -160°C. It could be explained by the freezing of generated defects at low temperature and a higher recombination during the irradiation at 25°C [20]. However, a stabilization at a closed asymptotic value of T 2g linewidth and defect massif area were observed. This increase of defect massif was also reported in literature after irradiations with Kr ions at an energy of 0.2 MeV [6] and of 4 MeV [21].

Indeed, after an irradiation at 500°C with Kr ions at an energy of 4 MeV, Onofri et al. reported an increase of defect massif area up to 6 times higher than for the virgin one after an irradiation fluence of 3.10 16 Kr.cm -2 (i.e. 90 dpa) then a saturation is reached for higher fluences [21]. This ratio difference is closed to the one obtained in our study (around 5 times compared to the virgin samples). It seems to show that no matter the irradiation temperature the area ratio between defect massif and T 2g band stabilizes at a quite similar value indicating a similar measured disordered level or saturation of Raman signal. However, as no Raman measurement has been performed at lower Kr irradiation fluence by [21], we cannot conclude if this saturation is achieved for a higher damage level at a higher irradiation temperature.

Point defects generated by irradiation can cluster forming extended defects such as voids and dislocation loops. Several studies report the nucleation of dislocations loops at very low damage level [22][23][24][START_REF] Onofri | Influence of exogenous xenon atoms on the evolution kinetics of extended defects in polycrystalline UO2 using in situ TEM[END_REF][26]. For instance, Onofri et al. have in situ observed the first dislocation loops nucleation under irradiation at -180°C with 0.39 MeV Xe ions from a damage level of around 0.008 dpa [START_REF] Onofri | Influence of exogenous xenon atoms on the evolution kinetics of extended defects in polycrystalline UO2 using in situ TEM[END_REF] (Fig. 4.a).

The loop density increases with the irradiation fluence up to a saturation value, which depends on the temperature [22,23,[START_REF] Onofri | Influence of exogenous xenon atoms on the evolution kinetics of extended defects in polycrystalline UO2 using in situ TEM[END_REF]. Then, a decrease occurs due to the formation of dislocation line. Lastly, the loop density remains constant. Thus, the evolution kinetics of dislocations is very different from the one observed in the current work (Fig. 4.a). Simultaneously to the dislocation formation, voids nucleation was observed at low damage level too [27][28][29]. The bubble/cavity density increases in the first time of the irradiation and then reaches a constant value of 2 -4 × 10 24 m -3

. The voids generated in UO 2 samples under irradiation with Au ions at 4 MeV at 25°C and observed in situ by Sabathier et al. [27] were compared to our Raman spectra change. Fig. 4.b gathers the value of defect massif area during the 0.9 MeV I ions irradiation at 25°C and the void density as a function of the generated dpa.

Quite similar evolution is shown by the both techniques. The first voids observation is noticed at low damage level (0.03 dpa) which is correlated with the increase of massif defect area at our first irradiation step (0.001 dpa). Then, no significant evolution of the defect massif or of the void density was observed after an irradiation inducing around 0.3 dpa.

Lastly, Rutherford Backscattering Spectroscopy in Channelling mode (RBS-C) can characterize the fraction of displacement atoms (f D ) during irradiation. Fig. 5 presents the damage kinetics obtained by RBS-C during 0.5 MeV La ions irradiation at 25°C as function as the maximum dpa [30]. The damage fraction increase occurs for values higher than 4 dpa whereas the value of defect massif area during the 0.9 MeV I ions increases after a radiation damage of 0.03 dpa. It clearly indicates that the two evolutions are not similar. However, for UO 2 samples, ion channelling is able to measure disorder on the U sub-lattice and O sub-lattice but with different cross section. Indeed, by using the

Conclusions

In situ Raman coupled with ion irradiation at low energy have been carried out on uranium dioxide.

The results confirmed that polycrystalline samples were not amorphized by nuclear damage even for very high defect level (200 dpa). Quite similar maximum asymptotic value of the defect massif area and of T 2g band width was found for all the investigated projectiles. Only the shape evolution of defect massif area change with the irradiation temperature. Indeed, the saturation is achieved at a smaller defect level for low temperature (-160°C) than at 25°C. The study of the damage kinetics evolution induced by ion irradiations shows a good match between voids nucleation and Raman spectra changes (massif of defects). On the contrary, the evolutions kinetics of dislocations and of damage fraction obtained by RBS-C are very different from the one observed in the current work. It should indicate that the defect massif increase is linked to the formation of point defect and defect cluster evolving in the void nucleation. Future work will aim at correlating the microstructural evolution by TEM and the Raman spectra change in uranium dioxide.

ACKNOWLEDGMENTS

The staffs of the JANNUS facilities at Saclay are sincerely acknowledged for their assistance during ion irradiations. Tab. 1: Irradiation conditions used during this study and simulated by SRIM software [START_REF] Ziegler | The Stopping and Range of Ions in Solids[END_REF]. The projected range (R p ), the maximum displacement per atoms (dpa) have been simulated for a density of 10.74 g.cm -3

, in full cascade mode with threshold displacement energies of 20 and 40 eV for the O and U sub-lattices, respectively [START_REF] Soullard | [END_REF].

16 O 2 ,

 162 resonant reaction with He ions at an energy of 3.085 MeV, the backscattering event of4 He on O sub-lattice is increased by a factor of 15 compared to standard Rutherford elastic backscattering[31]. However, the backscattering event of4 He on U sub-lattice, proportional to Z remains around 7 times higher than for O sub-lattice. The damage evolution obtained by RBS-C analysis is more sensitive to the U than to the O sub-lattice disorder. As we clearly observed different evolution with Raman kinetics, the changes on Raman spectra seems to be more sensitivity to damage on the O sub-lattice in good agreement with the literature where the U1 and U3 bands are correlated with oxygen sub-or sur-stoichiometry, respectively[7,10, 32].

Fig. 1 :

 1 Fig. 1: In situ Raman spectra on UO 2 samples irradiated at 25°C with Au ions at an energy of 2 MeV.

Figure 2

 2 Figure 2

Fig. 2 :

 2 Fig. 2: (a) The T 2g width evolution and (b) the ratio between defect massif area and T 2g band area after irradiation with 0.9 MeV I ions and 2 MeV Au ions at 25°C. The hatched rectangles represent the reference T 2g width of virgin UO 2 before irradiation and the initial ratio.

14

 14

Figure 3 Fig. 3 :

 33 Figure 3

Figure 4 Fig. 4 :

 44 Figure 4

Figure 5 Fig. 5 :

 55 Figure 5

TABLE Table

 Table

	1
		Energy ( MeV)	Irradiation temperature (°C)	Flux (at.cm	-2 .s	-1 )	R p (nm)	Maximum dpa at 10 15 at.cm -2
	I	0.9	25	1×10 11	150	7.5
	Au	2	25	5×10 11	210	11.5
	Kr	4	-160	5×10 11	420	3


Hélène Isnard
email: helene.isnard@cea.fr

Precise isotopic and elemental characterization of spent nuclear fuel is a major concern for the validation of the neutronic calculation codes and waste management strategy in the nuclear industry. Generally, the elements of interest, particularly U and Pu which are the two major elements present in spent fuel, are purified by ion exchange or extractant resins before off-line measurements by thermal ionization mass spectrometry. The aim of the present work was to develop a new analytical approach based on capillary electrophoresis (CE) hyphenated to a multicollector inductively coupled plasma mass spectrometer (MC-ICPMS) for online isotope ratio measurements. An electrophoretic separation protocol of U, Pu and the fraction containing fission products and minor actinides (Am and Cm) was developed using acetic acid as the electrolyte and complexing agent. The instrumentation for CE was designed to be used in a glove box and a laboratory-built interface was developed for hyphenation with MC-ICPMS. The separation was realized with only a few nL of a solution of spent nuclear fuel and the reproducibilities obtained on the U and Pu isotope ratios were on the order of a few ‰ which is comparable to those obtained by thermal ionization mass spectrometer (TIMS). This innovative protocol allowed a tremendous reduction of the sample amounts classically required for analysis: sample masses from µg to ng and sample volumes from µL to nL. also a drastic reduction of the liquid waste production from mL to µL. In addition, the measurement process was shorted by at least three orders of magnitude. All of these improved parameters are of major interest for nuclear applications.

Introduction

The precise knowledge of actinides and fission products in spent nuclear fuels is mandatory in order to qualify and validate neutronic calculation codes. These codes are used to improve nuclear fuel performances, waste management and associated safety-related applications. [START_REF]Spent nuclear fuel assay data for isotopic validation[END_REF] The major analytical requirement for such topics is to obtain the best uncertainties when it comes to the concentration measurements and isotopic compositions in the spent fuel samples. [START_REF] San-Felice | [END_REF] These samples are characterized by a complex matrix with a large diversity of elements produced by neutron capture, fission or activation reactions. Diluted nuclear fuel sample solutions contain uranium (more than 95% of the elements present) and transuranium radioelements (Np, Pu, Am, Cm) as well as a variety of fission products (FP) consisting mainly of lanthanides (La, Nd, Sm, Eu, Gd, …), alkali and alkaline earth metals (Cs, Sr …) as well as transition metals (Ag, Ru, Pd,…).

Mass spectrometric techniques involving multi-collection systems have the capacity to measure isotope ratios in a very precise and accurate way. However, prior to measurements, two steps of chromatographic separation [3][4][5][6] are in most cases required to prevent spectral (isobaric, polyatomic or doubly charged) or non-spectral (matrix effects) interferences on the isotopes of interest. The first step leads to the chemical purification of U and Pu by isolating them from the FP and minor actinides (Am) collected in a third fraction (FP+ Am). This purification is generally achieved by using ion exchange or extraction resins. 7,8 The second step by High Performance Liquid Chromatography (HPLC) aims to separate certain elements of interest (for example Nd and Cs) from the complex FP fraction. 3 These complex protocols are required in order to isolate each element of interest prior to its isotopic characterization. 3,9,10 Apart from their complexity and duration, these protocols also present drawbacks such as the increased handling time of radioactive samples, the production of radioactive waste and the risk of natural contamination. Several analytical developments were designed in order to significantly limit the sample handling duration, the amount of sample required for accurate measurements and the amount of waste produced. For example, the use of ICPMS with collision or reaction cells allows the in-situ resolution of spectral interferences by using an appropriate gas selected on the basis of both thermodynamic and kinetic considerations. [11][12][13][14][15] These systems, based on collision-induced processes and reaction chemistry in a gas-filled multipole device, avoid time-consuming chemical separation of the interfering elements and reduce risks of sample contamination.

Another improvement consists in the hyphenation of HPLC with MC-ICPMS, which has also been widely developed during the last two decades. 16 In the particular case of nuclear fuel samples, several studies have evaluated the performance of HPLC-MC-ICPMS for isotope ratio measurements of U, Pu, Nd, Eu, Gd, Sm in nuclear fuel samples or simulated solutions. [17][18][19][20] After taking into account the drift phenomenon occurring when transient signals are acquired [21][22][23] , isotope ratios are measured with uncertainties on the order of or lower than 1‰. This approach is particularly attractive for reducing the analysis time and consequently the analyst's exposure to ionizing radiation. Nevertheless, considering the typical flow rates of the chromatographic systems which are usually on the order of several hundreds of microliters per minute, further developments are required to reduce the associated liquid waste volumes. Since electrokinetic methods only involve ion migration under the influence of an electric field, they enable a significant reduction of liquid waste production as well as sample consumption in the nano-or microliter range.

Very few studies have addressed the hyphenation of electrokinetic separations with ICPMS for isotope ratio measurements. Pitois et al. 24 hyphenated a capillary electrophoresis (CE) device with a quadrupole ICPMS or a magnetic sector ICPMS to perform isotope ratios at 1% uncertainty of 14 lanthanides in less than 15 min with a liquid production as low as 4 µL.min -1 and quantification limits of a few tens of ng.mL -1 . Vio et al. 25 developed a method to separate lanthanides by isotachophoresis, an electrophoretic technique used to preconcentrate the sample while separating the analytes at the same time. In this study, 13 lanthanides were separated with a sample volume of 1.3 µL containing 6.5 ng of each lanthanide. This separation was then transposed on an ITP microchip and hyphenated to an MC-ICPMS for Sm and Nd isotopic measurements. 26 The approach was extended in order to perform multielemental Nd, Sm, Eu, Gd isotope ratio measurements by stop-flow isotachophoresis. This analytical development enabled the isotope ratio measurements, within a single analytical run, of 4 elements and up to 23 isotopes with only 20 ng injected per element with isotope ratio reproducibilities better than 0.4% (k=2) and accuracies better than 0.2%. 27 In addition, Martelat et al. 28 investigated the isotopic fractionation and evaluated the analytical performances of electrokinetic separations hyphenated with MC-ICPMS for Nd isotope ratio measurements. The reproducibility obtained was lower than 0.2 ‰ regardless of the Nd isotope ratio and with 0.5 ng of sample injected for each analysis. This reproducibility was similar to that obtained with the hyphenation of LC to MC-ICPMS 19 but with significantly reduced sample volumes and liquid waste quantities.

Concerning U and Pu, CE is not commonly used to separate and purify these two elements for isotope ratio measurements by mass spectrometry, but several studies have been dedicated to the speciation of actinides and lanthanides in environmental or nuclear samples.

In these studies the separation of lanthanides and actinides have been achieved using different types of electrolytes. [29][30][31][32][33][34] The separation of different Pu oxidation states was optimized by Kuczewski et al. 32 using La(III), Th(IV), Np(V) and U(VI). The background electrolyte was 1 mol.L -1 acetic acid at a pH of 2.4 (yielding a free acetate concentration of approximately 7 mmol.L -1 ). Subsequently, the same electrolyte was used to separate different Pu species, i.e., Pu(III), Pu(IV), Pu(V) and Pu(VI).

The first objective of this study was to develop the separation by capillary electrophoresis of U and Pu from the FP fraction also containing minor actinides (Am, Cm).

The background electrolyte was chosen in order to obtain the highest difference of electrophoretic mobility between U, Pu and the FP and minor actinide fractions. The change in migration time as a function of the oxidation state of Pu was studied in order to obtain the best resolution between the U and Pu peaks and to resolve the main isobaric interference 238 U/ 238 Pu encountered in nuclear fuel samples.

The second objective was the hyphenation of CE with MC-ICPMS in order to obtain precise and accurate isotope ratios for U and Pu within a single analytical run. A mass bias correction approach was developed and validated with the use of certified isotope reference materials of uranium.

The third objective was the application of this new analytical protocol to irradiated fuel samples. The direct measurement of U and Pu by CE-MC-ICPMS was performed on several nL of a solution of mixed oxide (MOx) spent fuel. The reproducibility obtained on the U and Pu isotope ratios by this new CE-MC-ICPMS analytical approach are then compared to reference values determined by Thermal Ionization Mass Spectrometry (TIMS).

Materials and methods

Reagents and reference materials

Electrolyte solutions

For CE analysis, the background electrolyte (BGE) was prepared daily by diluting a solution of acetic acid (99.9% purity) in ultra-pure water (Millipore, Guyancourt, France). The pH was adjusted to 3.0 using an ammonia solution (25% v/v). In order to modify the electrolyte conductivity, ammonium chloride was added for the measurements performed on the spent nuclear fuel sample. For the oxidation step of Pu, a solution of concentrated perchloric acid (70%) was diluted in ultra-pure water. All chemicals were purchased from Sigma Aldrich (Saint Quentin Fallavier, France), and all the reagents used were of ultrapure analytical grade.

Prior to each analysis the capillary was successively flushed with H 2 O, HNO 3 (0.3 mol L -1 ), H 2 O, NaOH (0.1 mol L -1 ), H 2 O and the BGE in the given order for 5 min each at a pressure of 1 bar. Sample plugs of 1 cm and 5 cm were injected. The injection parameters were determined by using a small plug of a standard solution of uranium pushed at 100 mbar through the capillary to ICPMS by the background electrolyte. Once the injection step was completed, the capillary inlet was immersed in a vial containing the BGE.

Samples and isotope reference materials

ACS Paragon Plus Environment Analytical Chemistry

Three certified isotope reference materials of uranium (IRMM 184, IRMM 186 and IRMM 187) were employed in this study. IRMM 184 and IRMM 187 were used to evaluate the analytical performances and to validate the mass bias correction approach proposed in this work. IRMM 186 was the U isotopic standard used to perform external mass bias correction and its 235 U/ 238 U certified ratio (0.0307711(92)) was used as a reference. The standard solutions were prepared by evaporating aliquots of the IRMM 184 and 187 stock solutions and the dry extract was dissolved in adequate volumes of BGE. For IRMM 186, used for mass bias correction, the dry extract was dissolved in 2% nitric acid solution. The standard solution of IRMM 186 was used for signal optimization prior to analysis.

Two solutions of plutonium were used, one for the preliminary separation tests and one for the validation of the mass bias correction approach. The former was an enriched 242 Pu solution (97.61%) conditioned in ultrapure 4M nitric acid. The second was a reference solution conditioned in the same media and used in the laboratory for quality control. Isotope ratios were qualified by TIMS using the total evaporation technique.

The spent nuclear fuel sample was solution of a MOx fuel diluted in nitric acid (8 M) and sent from a dedicated facility to the Laboratory of Analytical development for Nuclear Isotopic and Elemental Analysis in Saclay for isotopic and elemental characterization.

Instrumentation

A schematic description of the complete instrumental system and all the instrumental settings for CE and the interface with MC-ICPMS are presented in the Supporting information section S1. The electrophoretic system was composed of a high-voltage generator applying the electric field to the capillary and a laboratory-built CE module adapted for manipulation in a glove box. In order to pressurize the CE module during the injection and separation steps, an MFC was used. A schematic description of this specially designed CE module setup for the separation is presented in Supporting information section S1. The hyphenation to the MC-ICPMS was achieved using a Mira Mist CE nebulizer (Burgener, Mississauga, Ontario, Canada). The MFC was used to deliver the makeup solution at a flow rate of 10 µL min -1 . A specifically designed low volume cyclonic spray chamber (20 mL) was used at the interface.

It was composed of 2 nebulizer inlets with an angle of 45° between them 27 : one for the Mira Mist CE nebulizer and one for a Micro Mist nebulizer, with a nominal flow rate of 100 µl.min -1 used to inject a standard during the separation in order to perform mass bias correction.

The isotope ratios were determined using a Neptune Plus MC-ICPMS (Thermo Scientific, Bremen, Germany) modified to accommodate a glove box around the ion source. The operating parameters and Faraday cup configuration are detailed in the Supporting information section S1. A special configuration was used for analysis of the spent nuclear fuel sample with a first setup used for the acquisition of the Pu isotope signals and a second setup used for the acquisition of the U isotope signals. Mass bias was corrected using the Intra Injection Sample Standard Bracketing (IISSB) approach, first introduced for Nd isotope ratio measurements by dual inlet Liquid Chromatography-MC-ICPMS. 19

Results and discussion

Development of U-Pu separation

A simulated nuclear fuel sample containing La (III), Lu(III), Am(III), U(VI) and Pu in different oxidation states was used in order to determine the migration time for each species and to establish the optimal concentration of acetic acid in the electrolyte. This sample was prepared by evaporation of two solutions: a solution containing La, Lu, U and Pu in nitric acid and a Pu solution treated with perchloric acid in order to oxidize Pu in its Pu(VI) state. Am was found as 241 Am, produced by β -decay of 241 Pu present in the Pu solutions used for these tests. After evaporation the residues of the two solutions were dissolved in 0.25M acetic acid and mixed to obtain a concentration of approximately 50 µg.g -1 for each element. Migration of all the species occurred in less than 70 minutes using a concentration of acetic acid lying between 0.25 and 0.5 M at a pH of 3.

Figure 1 presents the electropherogram obtained after injecting the simulated nuclear fuel sample. Four different Pu species were observed on the electropherogram. Plutonium is known to reach equilibrium with several oxidations states coexisting in solution, the relative abundance of the oxidation states depending on the chemical conditions. [START_REF] Cleveland | The Chemistry of Plutonium[END_REF] In our case, the four different species observed could be species containing Pu(III), Pu(IV), Pu(V) and Pu(VI).

The migration time of La(III), Lu(III), Am(III) and Pu(III) was around 35 minutes. Pu(III) comigrated with the lanthanides, in accordance with the similarity between the chemical behavior of An(III) and Ln(III). It was only present at a very low concentration and was formed by disproportionation and/or reduction of Pu(IV). The migration time for Pu(VI) was around 42 minutes. Pu(VI) migrated before U(VI) which appeared around 50 minutes. The behavior of the hexavalent state of Pu was similar to the one observed by Gräser et al. [START_REF] Graser | [END_REF] Another Pu species with a migration time equal to U(VI) and a low concentration was also observed. This species was probably Pu(V), formed by alpha reduction of Pu(VI). Pu(IV) migrated last with a migration time of 60 minutes. A deformation of the Pu(IV) peak was also seen and was believed to be caused by plutonium hydrolysis. The migration order observed here was Pu(III)>Pu(VI)>Pu(V)>Pu(IV). This migration order was interpreted by calculating the degree of complexation of Pu, knowing the pH, the total acetic acid concentration and the reviewed stability constants of Pu(III), Pu(IV) and Pu(VI) with acetate from the literature. [START_REF]NIST Standard Reference Database 46 v8, NIST Critically Selected Stability Constants of Metal Complexes Database[END_REF][START_REF] Nebel | [END_REF] The stability constants of Np(V) were used for Pu(V) as they were expected to be of the same order of magnitude. It was found that the speciation in our system was remarkably close to the one calculated by Kuckzewski et al. 32 , owing to the very small difference in the free acetate concentration between the two studies.

As the complexation was controlled by the free ligand concentration, the migration order was the same in both studies.

After the optimization of the electrolyte composition using the simulated sample, separation and resolution of isobaric interferences between Am, Pu and U in a MOx fuel sample was performed. The separation between Pu and Am, for which isobaric interferences occur at m/z=241, 242 and 244 in nuclear fuel samples, can be realized if Pu is present as Pu(IV) or Pu(VI). For the major interference in nuclear fuel samples between 238 Pu and 238 U, with a 238 U/ 238 Pu ratio generally higher than 500 in nuclear fuel samples, Pu(VI) is the most adapted oxidation state to totally resolve this isobaric interference and to avoid the peak tailing of 238 U on 238 Pu. An oxidation step was therefore performed prior to the injection. The sample solution was evaporated and the dry extract was dissolved in 1-M perchloric acid and heated to evaporate the latter, in order to oxidize the Pu into its Pu(VI) state. [START_REF] Graser | [END_REF] This process was repeated twice to ensure complete oxidation. The sample was finally dissolved in diluted perchloric acid (0.002 M) to preserve its stability over time.

Subsequently, the concentration of acetic acid in the electrolyte was increased in order to obtain a time difference between the migration peaks of Pu(VI) and U(VI) larger than 5 min. This was a mandatory step because the Faraday cups in our instrument could not be configured to detect all Pu and U isotopes with a single configuration. The time required to switch between Pu and U configurations was around 3 min. Therefore, the electrolyte concentration was increased to 0.4M in order to obtain a sufficient difference of migration time between Pu(VI) and U(VI), rendering it possible to change the detector configuration between Pu and U peak migration.

Figure 2 presents the electropherogram obtained after injecting a nuclear fuel sample solution. 50 µl of a 8M HNO 3 solution of MOx nuclear fuel was evaporated to dryness, treated with perchloric acid and after two steps of evaporation finally diluted in 50 µL of 0.002M perchloric acid before injection. The injection volume was around 5nL which corresponded to injected quantities of U, Pu and Am of approximately 0.7, 0.05, and 0.003 ng, respectively. The electropherogram shows that the separation of Am(III), Pu(VI) and U(VI) was sufficient to perform direct measurements of U and Pu isotope ratios with a gap time between the Pu and U migration times of approximately 8 min, thus allowing the Faraday cups configuration to be switched from C2 to C3 at the end of the Pu migration peak.

Mass bias correction approach and validation

In this part, the validation of the analytical approach for mass bias correction was performed on certified isotopic standards. In LC-MC-ICPMS, the introduction of the reference isotopic standard to perform IISSB mass bias correction was performed using a Tjunction located between the separation column and the ICPMS interface. In CE-MC-ICPMS, this configuration is not possible due to the fact that a specific nebulizer is used to perform the separation until the extreme end of the capillary. Therefore, a cyclonic spray chamber with two nebulizer inlets was utilized in this study to allow the injection of the reference isotopic standards while the CE separation was running. 26 The injection of the standard could be performed at any time during the separation.

The uranium isotopic standard (IRMM 186) solution was introduced five minutes before the injection of the sample, i.e., before the migration peak of Am. The second standard was injected at the end of the separation when the contribution of the baseline of the last migration peak was negligible. The data treatment methods were evaluated by injection of reference isotopic standard as samples. Different methods of data treatment have been intensively compared including point by point (PbP), linear regression slope (LRS) 39 and peak area integration (PAI). 39,40 The LRS and PAI methods are used for transient signals because they correct the isotope ratio drift. 39,40 These methods have been used and compared in our particular case. In the PAI method the background was taken into account by subtracting the baseline 30s before the migration peak and an integration window of 95% was chosen. 19,40 As the LRS method does not require the selection of a specific percentage of the peak area 39 , 100% of the peak zone was considered.

Table 1 presents the results obtained on five injections of IRMM 184 reference isotopic standard and five injections of IRMM 187 reference isotopic standard. The injection volume was around 230 nL which corresponds to a quantity of injected U around 35 ng. Mass bias was corrected with the IISSB approach for all ratios using the 235 U/ 238 U ratio value of the IRMM 186 standard and using an exponential law. Data on the bracketing standard and simulated sample were evaluated using the same data treatment method. Comparing the different data treatment methods, better reproducibilities were obtained with the LRS method, particularly when the signal intensity was lower than 5 mV. This observation is in agreement with previous studies performed by hyphenating separative techniques and MC-ICPMS. 20,27 The 235 U/ 238 U and 234 U/ 238 U isotope ratio values for IRMM 184 and IRMM 187 obtained with the LRS method were in agreement within uncertainty with the certified ratio value of the isotopic standard. For the IRMM 184 standard 236 U/ 238 U ratio was not evaluated considering the very low abundance of 236 U. For the 236 U/ 238 U isotope ratio of the IRMM187 standard, abundance sensitivity and hydrides rate are taken into account. They were evaluated at the beginning of the analytical session and were equal to 2x10 -6 ( 237 U/ 238 U) and 5.6x10 -6 (239/ 238 U) respectively. The relative difference between corrected 236 U/ 238 U ratio value obtained with the LRS method and the certified value was around 6‰.The usefulness of the IISSB approach using the LRS method of data treatment was thus demonstrated for CE-MC-ICPMS applications in the nuclear field.

In order to minimize the number of standards injected during the separation we evaluated the possibility to correct Pu isotope ratios using the mass bias factor determined from U certified isotopic standards. A Pu sample with known 239 Pu/ 240 Pu= 0.2864(3), previously evaluated in the laboratory by TIMS using the total evaporation technique was injected in the capillary. The separation conditions were the same as those previously defined for the U-Pu separation by CE. Six independent injections were performed and the average 239 Pu/ 240 Pu ratio corrected using β-values of the IRMM 186 injected before and after the Pu peaks was equal to 0.2863 with a relative standard deviation of 0.01% at k=2. This value was in very good agreement with the reference value obtained by TIMS. The strategy to correct the Pu isotope ratio using the β-value of a uranium standard was therefore demonstrated to be consistent to obtain U and Pu isotope ratios values with an uncertainty around 1‰ required for nuclear application. 42 Page 14 of 25 ACS Paragon Plus Environment Analytical Chemistry

U and Pu measurements on an irradiated nuclear fuel sample

The developed analytical procedure was applied to a MOx spent nuclear fuel sample solution.

The 8M HNO 3 solution was evaporated and treated with perchloric acid as previously described and then diluted in order to obtain a solution in 0.002M perchloric acid. The injection volume was around 20 nl which corresponded to injected quantities of U, Pu and Am around 4, 0.3 and 0.02 ng, respectively. The quantities were chosen in order to obtain signals higher than 1 mV on all isotopes of U and Pu. Mass bias correction was performed using the IISSB approach with the 235 U/ 238 U ratio value of the IRMM 186 reference isotopic standard.

U isotope ratio measurements

Table 2 presents the results obtained on U isotope ratios along with the values of Apex signals for U isotope migration peaks. The reproducibilities evaluated as the standard deviation expressed at k=2 were equal to 1.6‰, 6.2‰ and 3.8‰ for 235 U/ 238 U, 234 U/ 238 U and 236 U/ 238 U ratios, respectively. The major 235 U/ 238 U was in agreement with the ratio obtained by TIMS after chemical separation with relative difference between the two methods of 1.5‰. The 234 U/ 238 U ratio was also in agreement within uncertainty with the ratio obtained by TIMS with relative difference of -7.7‰. For the 236 U/ 238 U ratio there was a bias around 13‰ between the two methods due to the fact that abundance sensitivity and hydride formation were not evaluated for each injection but at the beginning of the analytical session. Abundance Page 15 of 25 ACS Paragon Plus Environment Analytical Chemistry sensitivity is the major source of correction for such ratio and must be more properly corrected. This will be investigated in future work. 2 and is lower than 3.5‰ for all ratios. All Pu isotope ratios values were in agreement within uncertainties between the two methods and no significant bias was detected in particular for the two interfered 238 Pu/ 239 Pu and 241 Pu/ 239 Pu ratios demonstrating the satisfactory separation obtained between 238 Pu and 238 U, and between 241 Pu and 241 Am.

Pu isotope ratio measurements

Comparison with an off-line analytical protocol

The reproducibilities obtained on U and Pu isotope ratios were on the order of a few ‰ and comparable with those obtained with the conventional analytical protocol after chemical separation by ion exchange resin and off-line thermal ionization mass spectrometric measurements. Table 3 compares the present on-line analytical approach with the "conventional" off-line protocol in terms of waste quantity, element masses required per analysis, sample volumes and times of analysis. The conventional protocol was developed in our laboratory for analysis of nuclear fuel samples 3 and the values presented here are comparable with those obtained by similar analytical protocols in other nuclear laboratories. 43- Page 16 of 25 ACS Paragon Plus Environment Analytical Chemistry 45 We observed a very significant decrease in term of analyzed quantities (from µg to ng), liquid waste volumes (from mL to µL) and sample volumes (from µL to nL). Moreover, the time of analysis was three times shorter. These reductions are very significant for nuclear applications.

Conclusion

This study aimed to demonstrate the capability of capillary electrophoresis hyphenated to MC-ICPMS to perform isotope ratio measurements of both U and Pu in nuclear fuel samples at sub-nanogram amounts of material per element and in a single analytical run. Instrumental developments were carried out to design a laboratory built module for CE that could be easily used in a glove box. Furthermore, a laboratory-developed interface was also used for hyphenation with MC-ICPMS.

The first part of the study was dedicated to the development of the separation of Am, U and Pu in order to prevent isobaric interferences for U and Pu isotope ratio measurements. A study of the migration time of all Pu states was performed. The concentration of the electrolyte was chosen in order to have time between the migration peaks of U and Pu to change the detector configuration of the MC-ICPMS necessary to detect every U and Pu isotope.

In the second part of the study, the method of Intra Injection Sample Standard Bracketing (IISSB) was adapted with the use of a home made spray chamber with two nebulizer inlets.

One inlet was dedicated to the MiraMist nebulizer containing the separation capillary and the second one to a Microflow nebulizer for the injection of a reference isotopic standard during the separation. The reproducibilities obtained on the U and Pu isotope ratios were on the order of a few ‰ which is comparable to those obtained by TIMS.

These analytical developments demonstrated that considerable gains could be obtained in terms of sample amounts, handling time, and waste production in the case of elemental and isotopic characterization in irradiated nuclear fuel samples. Further perspectives of this work include the adaptation of the analytical procedure to other fission products and actinides of interest present in nuclear samples as well as the application of isotope dilution for elemental characterization. These analytical developments could be of interest other fields where isotope ratio measurements are required.

Page 18 of 25 ACS

 25 Paragon Plus Environment Analytical Chemistry Table1: 235 U/ 238 U, 234 U/ 238 U and 236 U/ 238 U isotope ratios obtained on two uranium isotopic standards (IRMM 184 and 187) by CE-MC-ICPMS. Two different methods of data treatment (linear slope regression (LRS) and peak area integration (PAI)) are compared. Mass bias is corrected with the IISSB method using the IRMM 186 reference standard solution. Apex signals of 235 U, 234 U and 236 U are indicated. Standard deviations of the n measurements are expressed at k=2. *a represents the accuracy evaluated by the relative difference between the measured and the reference values of the isotopic standard. Standard deviation of the n measurements are expressed at k=2.

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 25

Table 2

 2 presents the results obtained on Pu isotope ratios along with the values of Apex signals for Pu isotope migration peaks. The reproducibility evaluated as the standard deviation expressed at k=2 was better than 1‰ for 240 Pu/ 239 Pu, 241 Pu/ 239 Pu and 242 Pu/ 239 Pu ratios and around 4‰ for the 238 Pu/ 239 Pu ratio in relation to intensity lower than 15 mV on the 238 Pu isotope. The bias between the value obtained with this new protocol and the values acquired by TIMS after chemical separation by anion exchange resin 3 is presented in Table

239 Pu 240 Pu/ 239 Pu 241 Pu/ 239 Pu 242 Pu/ 239 Pu

	Page 21 of 25		Analytical Chemistry
			235 U/ 238 U		234 U/ 238 U 235 U/ 238 U	236 U/ 238 U 234 U/ 238 U	236 U/ 238 U
	IRMM 184		Spent fuel MOX
	Certified value TIMS value (uncertainty) 0.0072623(22) Apex signals		0.0000528(31) 0.001320(3) 100 -236 mV	0.000261(2) 0.0000002 2.0 -4.5 mV	0.000331(2) 2.6 -6.1 mV
	Apex signals CE-MC-ICPMS, LRS (2σ, ‰, b*‰) n=4 40 -42 mV	0.15 -0.19 mV 0.001318 (1.6‰, -1.5‰)	-0.000259 (6.2‰, -7.7‰)	0.000335 (2.6‰, 13‰)
	SLR (2σ ‰, a* ‰) n=5 0.0072559 (0.6‰, -0.9‰)		0,0000530 (19.2‰, 3.7‰)	-
	PAI (2σ ‰, a* ‰) n=5 0.0072559 (0.6‰, -0.9‰)		0.0000263 (770‰, 50‰)	-
	IRMM 187
	Certified value		0.047325(14)		0.00038700(16)	0.000071965(39)
	Apex signals	480 -680 mV Spent fuel MOX		3.9 -5.4 mV	0.8 -1.1 mV
	SLR (2σ ‰, a* ‰) n=5 0.047329 (1.2‰, 0.08‰) TIMS value (uncertainty)		0.0003875 (1.2‰, 1.2‰) 0.1164(4)	0.0000715 (6.6‰, 6.0‰) 0.9122(18) 0.3600(8)	0.3543(7)
	PAI (2σ ‰, a* ‰) n=5 Apex signals	0.047345 (1.2‰, 0.4‰)		0.0003838 (2.0‰, 8.2‰) 9 -14 mV	0.0000603 (67.4‰, -162‰) 70 -105 mV 27 -42 mV	27 -42 mV
	CE-MC-ICPMS, LRS (2σ ‰, b*‰) n=5	0.1160 (4.2‰, 3.4‰) 0.9122 (0.4‰, 0.04‰) 0.3592 (1.0‰, -2.2‰) 0.3543 (0.8‰, 0.08‰)
					22
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238 Pu/

Table 2 :

 2 Results of uranium and plutonium isotope ratios obtained by CE-MC-ICPMS on a spent nuclear fuel sample. Apex signals for 238 Pu, 240 Pu, 241 Pu, 242 Pu, 235 U, 234 U and 236 U are indicated. *b represents the bias evaluated by the relative difference with the reference values obtained by TIMS after ion exchange resin separation. 1 the conventional protocol consist of a separation step by anion exchange chromatography and off-line measurements by TIMS. 4 *2 for concentration of U and Pu in a solution of MOx nuclear fuel samples around 250 ppm and 18 ppm of U and Pu respectively. *3 including redox cycle, separation and isotope ratio measurements.

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*

Table 3 :

 3 Comparison of the "conventional" protocol with the new analytical approach developed in this work in terms of waste, quantity of elements, sample volume and analysis time.