Abdellah Bouiba
email: abdellahbouiba@gmail.com

Mohammed Nabil

E L Korso
email: m.elkorso@parisnanter.fr

Toufik Boukaba
email: boukabatoufik@yahoo.fr

Robust joint relaxed maximum likelihood calibration and direction of arrivals estimation with sparse arrays

Keywords: Maximum likelihood, compound Gaussian, calibration, direction of arrivals

In this paper, we focus on the joint calibration and estimation of direction of arrivals in a data aided scenario, i.e., presence of one or more calibrators. The considered context has the following specifications: i) the antenna sensors are characterized by an unknown complex gain, ii) the array is composed of small sub-arrays largely spaced leading to a sparse noise covariance matrix and iii) observations may contain outliers or non homogeneities. Numerical simulations assess that the proposed algorithm is robust to such disturbances while performing an accurate joint calibration and direction of arrival estimation and out preforms the state of the art.

Introduction

Direction of arrivals (DOA) estimation is an important topic with a plethora of applications, e.g., wireless communication, radio-interferometer, radio-astronomy, RADAR/SAR/STAP applications, EEG localization, to cite a few [START_REF] Krim | Two decades of array signal processing research: the parametric approach[END_REF][START_REF] Vantrees | Detection, Estimation and Modulation Theory: Radar-Sonar Signal Processing and Gaussian Signals in Noise[END_REF][START_REF] Haardt | Subspace methods and exploitation of special array structures[END_REF]. In order to achieve high resolution, large systems are commonly considered. A typical example is the LOFAR (low frequency array) which consists of several thousands of elementary sensors forming a very large radiointerferometers [START_REF] Van Haarlem | LOFAR: The LOw-Frequency ARray[END_REF]. Specifically, such instrument is decomposed of several sub-arrays (50 stations for the LOFAR) each containing several antennas. In this context, the whole array is characterized by i) its geometry, leading to a sparse block diagonal noise covariance matrix. This is naturally due to the decorrelation between the noise components between sub-arrays or stations (temporally and spatially decorrelation due to the large spacing between two distinct sub-arrays) [START_REF] Pesavento | Maximum-likelihood direction-of-arrival estimation in the presence of unknown nonuniform noise[END_REF][START_REF] Ollier | Joint ML calibration and DOA estimation with separated arrays[END_REF][START_REF] Vorobyov | Maximum likelihood direction-of-arrival estimation in unknown noise fields using sparse sensor arrays[END_REF]. ii) the presence of complex gain which is due to the individual distortions of sensor outputs [START_REF] Yatawatta | On the interpolation of calibration solutions obtained in radio interferometry[END_REF][START_REF] Brossard | Parallel multiwavelength calibration algorithm for radio astronomical arraysk[END_REF]. iii) finally, the possible presence of data aided sources or calibrators is taken into account (this is a typical scenario in wireless communication [START_REF] Li | Maximum likelihood angle estimation for signals with known waveforms[END_REF][START_REF] Stoica | Training sequence design for frequency offset and frequency-selective channel estimation[END_REF] as well in radio imaging [START_REF] Van Der Veen | Signal processing tools for radio astronomy[END_REF])

Apart from the specifications listed above, it is worth-mentioning that in a high resolution scenario the Gaussian assumption of the noise is generally violated [START_REF] Yao | A representation theorem and its applications to spherically invariant random processes[END_REF]. Typical examples are high resolution radar systems, the recent large radio-interferometers and high resolution SAR imaging systems to cite a few [START_REF] Conte | Adaptive matched filter detection in spherically invariant noise[END_REF]. Recently, an interesting alternative to Gaussian noise modeling appears: the so-called compound Gaussian noise modeling [START_REF] Pascal | Covariance structure maximum likelihood estimates in compound gaussian noise: Existence and algorithm analysis[END_REF][START_REF] Zhang | MIMO radar target localization and performance evaluation under SIRP clutter[END_REF][START_REF] Breloy | Clutter subspace estimation in low rank heterogeneous noise context[END_REF]. A compound Gaussian, known also as spherically invariant random process, is composed of two component random variables: the texture parameter, a positive random variable which represents a local variation of the non homogeneities, and the speckle parameter which follows a zero mean complex Gaussian process. The multiplication of these two random parameters leads to a compound Gaussian random variable. The compound Gaussian process is known to be heavy tailed [START_REF] Yao | A representation theorem and its applications to spherically invariant random processes[END_REF] (meaning that it takes into account the presence of outliers and non homogeneities) and it encompass several well known distributions, e.g., the Gaussian distribution, the K-distribution, the student't distribution, the Weibell distributions ect. The aforementioned specification of the compound Gaussian process makes it a perfect candidate for noise modeling in a high resolution context [START_REF] Ollila | Complex elliptically symmetric distributions: Survey, new results and applications[END_REF].

Consequently, in this paper we aim at designing scalable robust joint calibration and DOA estimation. The robustness is ensured by considering the compound Gaussian noise modeling. In addition, a block coordinate descent approach is considered in order to alleviate the computational complexity cost.

Finally, it is worth-mentioning that the proposed algorithm unifies the existing work related to the calibration and/or DOA estimation in the context of sparse arrays. Specifically, i) the proposed algorithm can be considered as a robust version of the so-called modified iterative maximum likelihood algorithm designed under Gaussian assumption [START_REF] Ollier | Joint ML calibration and DOA estimation with separated arrays[END_REF] and ii) it generalizes the maximum likelihood DOA estimation in unknown noise fields using sparse sensor arrays [START_REF] Vorobyov | Maximum likelihood direction-of-arrival estimation in unknown noise fields using sparse sensor arrays[END_REF] to the case of un-calibrated sparse arrays.

The paper is organized as follows: Section 2 focuses on the data model and the noise modeling, in section 3 we expose the design of the proposed algorithm. Section 4 presents the numerical simulation results and finally, the conclusion is drawn in Section 5. Regarding the notations, scalars, vectors and matrices are represented by italic lower-case, boldface lower-case and boldface upper-case symbols, respectively. The transpose, the complex conjugate, the hermitian, the pseudo-inverse, the trace and determinant operator are represented, respectively, by (.) T , (.) * , (.) H , (.) † , tr{.} and |.|. The operators bdiag{.} and diag{.} represent a block-diagonal and a diagonal matrix, respectively.

Data Model

Model description

In the following we consider an antenna with M sensors decomposed into L small and largely spaced sub-arrays (possibly non linear). This scenario is common in radio astronomy and interferometer systems. Each sub-array is composed of M l sensors, such that L l=1 M l = M (cf. Fig. 1). The whole antenna is exposed to D far field signal sources. Part of these sources are known as calibrator sources, meaning that their positions and emitted signal sources are known (this is also known as data aided sources in the context of wireless communication [START_REF] Stoica | Training sequence design for frequency offset and frequency-selective channel estimation[END_REF]). Let us denote D K as the number of calibrator sources and D U as the number of the unknown sources, with D = D K + D U . Finally, we assume that the array (and consequently, the L sub-arrays) is not calibrated. This is mainly due to the instrumentation perturbations such as phase shifts which introduce difference between sensors gains leading to a dramatic performances loss. In this context, an accurate calibration need to be done in order to avoid the aforementioned loss.

In the next subsection, we represent mathematically the adequate parametric model associated with the above description.

Model representation

The observation vector, y(t) ∈ C M , for the t-th snapshot is then given by

y(t) = GA(θ)s(t) + n(t) (1)
where n(t) denotes the noise component which is explicated below, θ represents the DOA parameters, the steering matrix

A(θ) = [A(θ U ), A(θ K )], the signal sources s(t) = [s T U (t), s T K (t)
] T , the matrix gain G = diag(g) in which the subscripts K and U represent the known (calibrator) and unknown components, respectively. The explicit steering matrix model depends on the considered case : azimuth only estimation or elevation and azimuth estimation. This can be found in classical textbooks as [START_REF] Krim | Two decades of array signal processing research: the parametric approach[END_REF][START_REF] Vantrees | Detection, Estimation and Modulation theory: Optimum Array Processing[END_REF].

Noise statistic

In an array processing context, it is commonly assumed to model the noise as a Gaussian process. This assumption is motivated by the central limit theorem. Nevertheless, with the crowing use of high resolution systems, the Gaussian assumption shows it limits due to the non applicability of the central limit theorem. Furthermore, the presence of outliers and the non homogeneity of observations clearly breaks the use of the Gaussian assumption. An interesting alternative is the so-called compound Gaussian modeling (known also as spherically invariant random process modeling). The latter generalizes a large number of distributions (possibly heavy tailed), e.g., Student's t-distribution, k-distribution, Gaussian distribution, Weibull distribution, to cite just a few. This means that considering a compound Gaussian modeling leads to a robust estimation w.r.t. to outliers (due to the consideration of heavy tailed distributions) as well being robust to all distributions represented by compound Gaussian.

A compound Gaussian process, n l (t), for the l-th sub-array, can be represent by

n l (t) = τ l (t)x l (t) (2)
where the positif random variable τ l (t) ∼ p τ l (a l , b l ), in which a and b denote hyperparameters characterizing the pdf p τ and x l (t) ∼ CN (0, Σ l ). Specific considerations need to be take into account regarding the above noise modeling -The sparse array structure, i.e., the presence of L sub-arrays, leads to specific structure of the noise covariance matrix Σ. Specifically, due to the large inter sub-array distances w.r.t. the signal wavelength, the noise is typically considered as independent from a subarray to a sub-array. This leads to a block-diagonal structure of the Σ as

Σ = bdiag(Σ 1 , . . . , Σ L ) (3) in which Σ l ∈ C M l ×M l with L l=1 M l = M .
the random variable τ l (t) follows a pdf p τ l (a l , b l ). Taking into account the true distribution of τ l leads to a complex algorithm (due to the need to estimate the hyper parameters a l and b l ) and limits the robustness efficiency (since, we have to specify the pdf, which may be unknown in some applications are in radio-astronomy and radar.) An interesting alternative is to consider deterministic but unknown realizations of τ l (t) to be estimated. -From (3) we can notice that an ambiguity exists. Consequently, we impose that Tr(Σ) = 1. This assumption does not affect the estimation accuracy of the parameter of interest which are contained in the parameterized mean [START_REF] Zhang | Maximum likelihood and maximum a posteriori direction-of-arrival estimation in the presence of SIRP noise[END_REF].

Vector of unknown parameters

Now, we are ready to specify the vector of unknown parameters, η, which is considered for the algorithm design. Specifically,

η = θ T U , s T U (1), . . . , s T U (T ), g T , τ T (1), . . . , τ T (T ), {[Σ 1 ] p 1 ,q 1 } p 1 ≥q 1 , . . . , {[Σ L ] p L ,q L } p L ≥q L T (4) with τ (t) = [τ 1 (t), . . . , τ L (t)] T .

Proposed algorithm

From ( 1) and ( 2), the likelihood function reads p(y(1), . . . , y(T

)|η) = T t=1 -exp(β(t) H Σ(t) -1 β(t)) |πΣ(t)| (5)
in which we define

Σ(t) = bdiag(τ 1 (t)Σ 1 , . . . , τ L (t)Σ L ) and β(t) = y(t) -GA(θ U )s U (t) - GA(θ K )s K (t).
Consequently, the optimization problem to be considered is

arg min η Λ(η) (6)
s.t. Λ(η) T t=1 β(t) H Σ(t) -1 β(t) -log |Σ(t)| τ (t) > 0, [Σ] p,p > 0
Maximizing (6) w.r.t. η is infeasible due to the non convexity of the objective function. In the following we propose to use a block coordinate descent algorithm in which we minimize the objective function (log likelihood) w.r.t. to a subset of η while fixing the other parameters/subsets at their previously estimated values. Then, we iterate until convergence.

Theoretical study of the convergence of such algorithm is beyond the scope of this paper and is considered as a future work.

Update of τ (t) and Σ

Equating ∂Λ ∂τ l (t) to zero and after some calculus, we obtain

τl (t) = 1 M l β H l (t)Σ -1 l β l (t) (7)
with

β l (t) = [y(t) -GA(θ U )s U (t) -GA(θ K )s K (t)] l-1 i=1 M i +1: l i=1 M i
In the same manner, equating ∂Λ ∂Σ l to zero and using [START_REF] Vorobyov | Maximum likelihood direction-of-arrival estimation in unknown noise fields using sparse sensor arrays[END_REF], we obtain after some calculus

Σl = M i T T t=1 β l (t)β l (t) H β l (t) H Σ-1 l β l (t) (8)
The fixed point equation above [START_REF] Yatawatta | On the interpolation of calibration solutions obtained in radio interferometry[END_REF], and due to its G-convexity, it is known to have a unique solution whatever is the starting point.

Update of g

We can notice that

∂Λ ∂[g] i = T t=1 y H (t)Σ -1 (t)e i e T i A(θ)s(t) + s(t)A H (θ)G H Σ -1 (t)e i e T i A(θ)s(t) (9)
in which e i is a zero element vector except the i-th element which is equal to one. Equating the above equation to zero leads to

z i = M m=1 g * m [X (i) ] m,m (10)
in which

z i = T t=1 y(t) H Σ(t) -1 e i e T i A(θ)s(t)
and

X (i) = T t=1 Σ -1 (t)e i e T i A(θ)s(t)s H (t)A(θ) H
Considering the diversity of (10) w.r.t. sensor elements, we obtain after some calculus

g = (B * ) † z * (11)
with z = [z 1 , . . . , z M ] T and [B] i,j = [X (i) ] j,j , ∀i, j = 1, . . . , M 3.3 Update of s U (t)
Again, equating ∂Λ ∂s U (t) to zero and after some calculus, we obtain

s U (t) = A(θ U ) H G H Σ(t) -1 GA(θ U ) -1 (GA(θ U )) H Σ(t) -1 (y(t) -GA(θ K )s K (t)) = ( ĀH U (t) ĀU (t)) -1 ĀH U (t) ỹ(t) (12)
in which the whitened steering matrix of the unknown and known sources are given respectively, by ĀU (t) = Σ(t) -1

2 GA U and ĀK (t) = Σ(t) -1

2 GA K , whereas, the whitened residuals reads ỹ(t) = ȳ(t) -ĀH K (t)s K (t) in which ȳ(t) = Σ(t) output : η

Numerical simulations

In the following simulations, we consider two equally powered far field sources, θ U = 30 • and θ K = 10 • , impinging on a full array composed of L = 3 linear sub-arrays. Each sub-array is uniformly linear array composed of, respectively, 5, 4 and 5 sensors with half-wavelength spacing. The inter-sub-array space is about five to six wavelengths spacing, respectively. The texture parameter is generated as Gamma distribution with a l = 0.5 and b l = 1, ∀l and we considered 20 snapshots. The amplitude and phase gain are generated uniformly on [0.5, 1.5] and [0, 2π] and the noise covariance matrix of each sub-array follows the model given in [START_REF] Zhang | MIMO radar performance analysis under K-distributed clutter[END_REF], i.e., [Σ l ] p,q = 0.9 |p-q|e j π

(p-q)

. In Fig. 1, we consider the accuracy of the direction of arrival using algorithms based on the context of sparse arrays. Specifically, [START_REF] Vorobyov | Maximum likelihood direction-of-arrival estimation in unknown noise fields using sparse sensor arrays[END_REF] considers the implementation of the maximum likelihood DOA estimation in unknown noise fields using sparse sensor arrays assuming perfectly calibrated arrays. This algorithm shows its limits due to the effect of the miscalibration represented by the calibration matrix G. Furthermore, we consider the modified iterative maximum likelihood algorithm designed under Gaussian assumption for non calibrated arrays [START_REF] Ollier | Joint ML calibration and DOA estimation with separated arrays[END_REF]. The aforementioned algorithm behaves well under Gaussian assumption but shows it limits in the case of non Gaussian environment or in the presence of outliers as shown in Fig. 1. Finally, the proposed algorithm shows it usefulness in the case of uncalibrated or mis-calibrated sparse arrays in the context of non Gaussian environment. This is also validated by a closer look at the mean square error of the calibration parameters represented in Fig. 2 (we omit the algorithm proposed in [START_REF] Vorobyov | Maximum likelihood direction-of-arrival estimation in unknown noise fields using sparse sensor arrays[END_REF] since it does not take into account the estimation of G).

Conclusion

In this paper, we proposed a novel robust algorithm that, jointly, calibrate the sensors and estimate the direction of arrival in a context of sparse arrays. The proposed algorithm is based on a relaxed version of the maximum likelihood in a non Gaussian environment. To reduce the computational cost, a block coordinate descent approach has been used in which we managed to obtain closed form updates for most of the parameters. Finally, numerical simulations assess the usefulness of the proposed algorithm regarding an accurate joint calibration and direction of arrival estimation by out preforming the state of the art.

Fig. 1 .

 1 Fig. 1. Array configuration

Fig. 2 .

 2 Fig. 2. SNR vs. MSE DOA

Fig. 3 .

 3 Fig. 3. SNR vs. MSE G


Evgenia Kartsaki

Gerrit Hilgen

Bruno Cessac

Evelyne Sernagor

FIGURE 1. DREADDs in ACs makes the interpretation of functional results from DREADD-expressing RGCs more challenging. Probing retinal function with a multi-layered simulator

Introduction

evgenia.kartsaki@inria.fr

Summary

Pharmacogenetics: Control neuronal activity in-vivo, non-invasively, reversibly and fast by using the Designer Receptors Exclusively Activated by Designer Drugs (DREADDs) technique. DREADD-expressing cells' activity can be increased or reduced when the synthetic designer drug clozapine N-oxide (CNO) is added to the solution 1 .

Disclaimer: All the experimental work is done at Prof. Sernagor's lab

What is the impact on vision?

RGCs and/or ACs can express DREADDs.

The effect is not clear on experimental grounds, since these cell types "antagonize" each other.

Courtesy of Gerrit Hilgen

Retinal processing Macular's structure Simulations Our novel numerical platform, called Macular, is designed to simulate and test hypotheses in normal and impaired retinal conditions from single-cell to large-scale level. It is able to handle different visual processing circuits and allows us to visualize responses to visual scenes (movies). Macular also allows us to mimic specific pathologies or pharmacologically induced impairments that can be controlled by tunable parameters, as well as to emulate electric stimulation by prostheses. Our brain can recreate images from interpreting a stream of information emitted by ~1 million parallel channels in the retina. This ability is partly due to the astonishing functional and anatomical diversity of the retinal ganglion cells (RGCs), each interpreting a different feature of the visual scene. In addition, RGCs talk to each other during complex tasks (especially motion handling), via amacrine cells (ACs -lateral connectivity) or gap junctions.

Macular

To better understand the respective role of specific cells type in vision:

Switch them ON or OFF.

We modify pharmacologically the excitability of specific cell populations using pharmacogenetics (DREADDs technology).

We propose a computational model of specific RGCs and ACs activity, that express DREADDs.

We simulate this model using a novel simulation platform that can reflect normal and impaired retinal function from single-cell to large-scale level.

We explore the effects on the individual and collective response to different stimuli. The retina has both a feed-forward structure, from photoreceptors to bipolar cells and onwards to RGCs and a lateral structure, due to inhibitory interneurons comprising two groups; horizontal and amacrine cells. These neurons are organized into multiple functional circuits that operate in parallel and converge onto RGCs, thus allowing them to efficiently process visual information at a single and population level.

Local (single level) information can be read in the spikes emitted by a single RGC (firing rate, latency of the first spike) and non-local (population level) information is provided by the lateral connections from horizontal and amacrine cells that induce indirect interactions between RGCs.

⊛

A cell is not necessarily a biological cell, it can be a group of cells.

Stimulus convolution with a spatio-temporal kernel

Work in progress

Switching ON or OFF RGCs and/or ACs may impact the RGCs individual response but also their concerted activity to different stimuli, thus allowing us to understand how they contribute to the encoding of complex visual scenes. However, it is difficult to distinguish on pure experimental grounds the effect of CNO when both cell types express DREADDs, as these cells "antagonize" each other. Contrarily, numerical simulation can afford it.

ü We propose a computational model of the CNO effect. ü We develop a novel numerical platform to simulate and test this effect.

Perspectives: o Tune the simulator to reproduce experimental results.

o Study the CNO effect on the single-cell and population level.

o Anticipate new experiments.

[3] inhibitory excitatory

  is funded by the Leverhulme Trust (RPG-2016-315 to ES and BC) involving the Institute of Neuroscience, Newcastle University and the Biovision team, INRIA SAM. We would also like to thank the DREAM-SED service of INRIA SAM for their collaboration in the development of Macular.

Figure 3 .

 3 Figure 3. The retinal response to a movie at different layers of the retina. Left tab: RGC layer Right tab: Four panels including the stimulus and the response to it at earlier stages of retinal processing.

Figure 2 .

 2 Figure 2. 3D visualization of retinal layers. The user can view each neuronal layer of the retina and the interactions among the same or different layers in 3D. Implementation of V1 cortical activation is under development.

  is under development, in collaboration with the DREAM-SED service of INRIA SAM.


Authors: B. Chanaron, S. Kliem, D. Bestion, D. Lakehal, N. Crouzet

1) The NURESAFE objectives

Numerical simulation tools used for the design and safety evaluation of nuclear power plants (NPP) are under continuous development, improvement and validation. In this field, a key challenge is the development and consolidation of integrated simulation platforms to support safety analysis and future fission reactor designs. These simulation platforms must integrate the dynamic 3D coupling of the codes simulating the different physics of reactor problems into a common multi-physic simulation scheme in order to enhance the prediction capability of the computations used for safety demonstration of the current light water reactors (LWR) nuclear power plants and the design of innovative LWR.

In this context, the NURESAFE European project had two major objectives:

 to deliver to European stakeholders a reliable and predictive up-to-date software platform usable for safety analysis needs for LWR and to further improve the "safety culture" by developing a high level of expertise in the proper use of the most recent and most advanced simulation tools; this software capacity is the NURESIM (Nuclear Reactor SIMulation) European reference simulation platform.  to create a community that brings together the European key-players, to promote the use of an advanced scientific basis among this community and engage it in advanced and predictive simulation for LWR.

The NURESIM software platform offers:  higher fidelity methods as for example pin-by-pin resolution rather than nodal methods and innovative computational fluid dynamics methods  an integrated multi-physics environment enabled by the SALOME open-source software (http://www.salome-platform.org/). SALOME provides a generic userfriendly interface and is designed to facilitate the coupling of computing codes in a heterogeneous distributed environment as well as to facilitate interoperation between CAD modeling and codes.  a toolbox for uncertainty quantification, sensitivity analysis and model calibration:

the URANIE open-source software (http://sourceforge.net/projects/uranie/).

The NURESIM software platform was developed from 2006 to 2015 by 22 European organizations. It incorporates from now the latest advances in core physics, two-phase thermal-hydraulics and fuel modeling for present and future reactors together with, sensitivity and uncertainty tools as well as multi-scale and multi-physics features. It provides tools parallel of those of industry, with higher fidelity. These tools are usable for simulation of design basis accidents of LWRs as well as normal operation

The different physics of the NURESIM platform were validated and fully integrated into the platform using SALOME, in order to provide a standardized state-of-the-art code system to support safety analysis of current and evolving LWRs.

2) A "Situation Target" driven approach

In order to enhance the computational capacities to predict safety-relevant parameters with more accuracy and more reliability, predictive physical models, efficient solvers and codes and coupling capacities are needed. To achieve the NURESIM objectives and to demonstrate the predictive capability of the software platform, NURESAFE focused on some challenging reactor situations named "Situation Targets". As safety analysis is the main issue within the project, all these situation targets consist in some accidental scenarios. The challenging "Situation Targets" have been selected according to the required coupling between two or three different disciplines.

The following Situation Targets have been selected. They have been grouped into five categories:

1) Advanced boron dilution modeling 2) PWR main steam line break (MSLB)

 PWR application  VVER application 3) Boiling water reactor anticipated transient without scram (BWR ATWS) 4) Lost of coolant accident (LOCA) in PWR  Modeling of LOCA  Pressurized Thermal Shock (PTS) 5) BWR thermal-hydraulics scenarios, particularly behavior of the pressure suppression pool in accidental conditions

The NURESIM platform addresses these Situation Targets through predictive simulations including validation and uncertainty quantification. Therefore, NURESIM allows the reduction in uncertainty of design margins and facilitates optimization of fuel management, power uprate and lifetime extension for current reactors and facilitates the introduction of new reactor designs with enhanced performance characteristics.

To summary, let us say the NURESIM implementation strategy comprised four steps: 1) Develop physical models and computational tools with enhanced predictive capacity 2) Integrate these tools in the SALOME software platform to get a standardized environment with the multi-physics / multi-scale functionalities 3) Develop and run tools for simulation of some challenging reactor problems or « Situation Targets » 4) Implement a methodology for verification and validation

3) Validation of the NURESIM platform

NURESAFE carried out an extensive validation program in order to ensure its predictive capacity when running reactor accidental transients and to quantify biases and uncertainties. This validation program included four components:

 Critical experiments,  Numerical validation using Monte-Carlo reference solutions for cell or lattice,  Thermal-hydraulics experiments at the different time and space scales considered in the platform,  Operating power plant measurements.

Each Situation Target included a specific sensitivity and uncertainty analysis correlated to the validation task. In order to avoid duplication, the NEA and IAEA databanks were used to contribute to the validation. The completion of the four components demonstrated the reliability of the NURESIM software platform and the accuracy of the core simulation capability that can be used by the nuclear industry.

4) The NURESIM roadmap

The roadmap of the NURESIM simulation platform in general aimed at improving the safety of light water reactors (LWR) through deterministic analysis of NPP events in the scope of the plant design basis (Design Basis Accidents -DBA). It is part of a global trend to move towards "higher-fidelity" simulation techniques in reactor analysis. Validation of the codes against experimental data was also an important objective for the roadmap.

The work under this roadmap was carried out through three successive projects as shown in figure 1. The first project, NURESIM, established the basic architecture of the platform and resulted in a first prototype of a truly integrated multi-physics simulation environment. The NURISP project was conceived as a consolidation of the platform together with an extension of the simulation capabilities towards higher-resolution both in space and time. The NURESAFE project showed the extended capabilities of the platform, demonstrated the readiness of the tool for Industrial safety applications and established the platform as a reference European tool.

5) The NURESAFE consortium

The NURESAFE partnership brought together the majority of European organizations with suitable skills in order to develop novel modeling capabilities and an advanced integrated software platform usable for predictive simulation of light water reactors. This consortium connected nuclear technology and fundamental research through the partnership gathering utilities, industry, technical support organizations (TSO), universities and research institutes. The project management ensured the tight collaboration among the partners. Thus, the consortium has the capability to share complementary expertise in order to implement an interdisciplinary competence and to develop solutions applicable to industry challenges. The NURESAFE consortium includes 22 contributors to the development:

 6 Universities or high-schools (UPM, KTH, U-PISA, UCL, LUT, ICL)  2 Large industries (EDF, AREVA)  10 Research Institutes (KIT, CEA, HZDR, PSI, JSI, VTT, INRNE, UJV, KFKI, ENEA)

 3 TSOs (GRS, IRSN ; NCBJ)  1 SME (ASCOMP)

6) The NURESAFE Sub-projects

The objective of the NURESAFE project was achieved through 4 sub-projects devoted to software development and validation. These sub-projects were designed to ensure that the NURESIM platform has all necessary physical models, multi-physics capacities and functional features necessary to accurately simulate reactor transients or normal operation. 1) Multiphysics applications involving core physics: This sub-project developed the coupled models involving thermal-hydraulics and neutronics and conducted the analysis of MSLB and BWR ATWS. 2) Multiscale analysis of core thermo-hydraulics: The objective was to develop new CFD models for LWR core analysis and to implement models in the NURESIM CFD codes. This work was conducted in a multi-scale approach. 3) Multiscale and multi-physics applications of thermal-hydraulics: Within this sub-project, the challenge problems concerning LOCA, PTS and BWR thermal-hydraulics applications were analyzed. New methods were developed and applied to the simulation of these situation targets. 4) Software platform: The goal of this sub-project was to integrate the models and software developed by other sub-projects into the SALOME software.

In addition, a comprehensive education and training program was conducted within NURESAFE in order to enable participants from the different NURESAFE partners to share models, modules and methods in order to catalyze their engagement including scientist staff of the partners, PHD students and postdoctoral associates.

6.1 Sub-project 1 (Multiphysics applications involving core physics)

The objective of this sub-project was to enhance the prediction capability of the computations used for safety demonstration of the current LWR nuclear power plants through the dynamic 3D coupling of the codes simulating the different physics of the problem into a common multi-physics simulation scheme. Within this sub-project, three physics were considered: core physics, thermal-hydraulics and fuel thermo-mechanics. Individual models, solvers, codes and coupled applications, were run and validated through modelling some Situation Targets: MSLB and one selected BWR anticipated transient without scram (ATWS). Industry-like applications were released at the end of the project:  Square lattice PWR main steam line break (MSLB),  BWR turbine trip without scram,  VVER main steam line break (MSLB), The analysis also included uncertainty quantification using the URANIE open-source software.

The MSLB transient analysis provided more accurate assessment of margins between predicted key parameters and safety criteria. The outcome of the transient simulation was evaluated with respect to the following phenomena:

 Local re-criticality,

 Maximum reactor power level. The BWR turbine trip analysis framework featuring coupled simulations combined:

 System thermo-hydraulics,  3D neutronics,  Thermo-mechanic evaluation of fuel safety parameters,  Uncertainty evaluation.

6.2 Sub-project 2 (Multiscale analysis of core thermo-hydraulics)

The objective of this sub-project was to advance the fundamental knowledge and develop new models based on detailed Direct Numerical Simulation (DNS) for momentum exchange and boiling heat transfer issues present in thermal hydraulics of Light-Water Reactors (LWRs). New benchmark data bases for fundamental and applied problems were developed. This sub-project included four work-packages.

A first work-package has been tailored to extend the existing computational multiphase flow strategies to cope with a wider range of practical applications.

The second work-package was devoted the development of novel methods for pool and convective boiling in a channel.

Within the third work-package, advanced strategies for modelling turbulent bubbly flow in a channel and in a rod bundle were analyzed. Novel ideas were explored and others further refined as to combining large-scale and small-scale prediction techniques that should in the medium term replace state-of-the-art methods that are limited to one flow regime. These novel techniques are applicable to more complex core-level thermalhydraulics situations involving boiling.

In the last work-package, the novel models and simulation techniques have been implemented in the CFD platform codes NEPTUNE_CFD, TransAT and TRIO_U, validated and delivered to end-users, including most advanced numerical simulation features and the associated modelling approaches for the physics pertinent to both PWR and BWR.

Sub-project 3 (multiscale and multi-physics applications of Thermal-hydraulics)

The objectives of the SP3 were to develop multi-scale and multi-physics simulations of LOCAs, PTS and BWR thermal-hydraulics for more accurate and more reliable safety analysis.

LOCA is usually simulated with industrial versions of thermal-hydraulics system codes such as CATHARE-2 and ATHLET. Although system codes are able to answer most safety needs, the status and limits of current methods and tools for plant analysis was reviewed during the NURISP project and areas for improvements have been pointed out.

Concerning LOCA, this sub-project aimed at developing advanced tools and methods for a multi-scale and multi-physics analysis and simulation of LOCAs including situations with deformed or ballooned rods and possible fuel relocation. Such transients are currently treated by system thermal-hydraulic codes. The addition of two-phase CFD tools and of advanced fuel models allowed revisiting these transients for more accurate and reliable predictions. Geometrical effects of ballooned rods were better understood at CFD scale; This required improving and coupling CFD to system codes or improving system codes and system codes coupled with fuel thermo-mechanics codes. Furthermore, methods of uncertainty and sensitivity analysis applied to system codes must be improved, and in this framework, a special focus was put on the issue of the quantification of the uncertainties of the closure laws. This work was based on a benchmarking of the possible methods using reflooding experimental data (FEBA and PERICLES).

PTS:

The objectives were to progress in the simulation of PTS scenarios by improving CFD modelling with analysis of new experimental data (including TOPFLOW steamwater and KAERI CCSF test). In this context, 2-phase PTS phenomenology was clearly identified and addressed in the modelling; In addition, sensitivity and uncertainty methods were applied to CFD codes and synthesis on validation and uncertainty of CFD application to reactor issues was done.

BWR:

The objectives were to progress in the simulation of two-phase thermalhydraulics issues in BWR. This includes Dry-out prediction, transient core thermalhydraulics and steam injection in pressure suppression pool. CFD codes, and subchannel codes were used, improved and validated during the project. Pertinent phenomena leading to dry-out were better identified at CFD scale. Effects controlling condensation regimes in pressure suppression pool were analyzed.

6.4 Sub-project 4 (software platform)

The NURESIM platform is a set of codes at the state of the art, connected to the SALOME software which gives generic capabilities for pre and post processing, supervision and coupling (figure 2). The objective of this sub-project was to provide a support to developers for integration of the codes into the SALOME software and to produce and manage the successive versions of the NURESIM platform on a dedicated repository. The NURESIM software platform comprises predictive computer tools based on stateof-the-art physical models and numerical methods, supplemented by uncertainty quantification and validation against experimental data. This platform currently hosts a new generation of experimentally validated "best estimate" simulation tools. It provides an accurate representation of the physical phenomena by promoting and incorporating the latest advances in reactor and core physics, two-phase thermal-hydraulics. It has also features enabling easy coupling of some different codes through the use of a common data structure and generic functions as well as pre-processing and postprocessing functions that make the codes more user-friendly. These features are provided by the SALOME open-source software

The NURESIM platform currently includes (figure 3):

-One neutronics deterministic spectral code for cross-section generation, -One neutronics and radiation propagation Monte-Carlo code, -Three complementary core kinetics codes, -Three complementary thermal-hydraulics sub-channel codes, -Two complementary thermal-hydraulics system codes, -Three complementary CFD codes, -One Sensitivity and uncertainty quantification software (URANIE), -Two fuel thermo-mechanics codes.

Neutronics simulation can be performed for 2D lattices, 2D and 3D core configurations for light water reactors at nodal scale or pin-by-pin. The NURESIM core simulators are connected to a cross-sections generator that provides specific cross-sections for the core and transient considered. The SALOME supervision module (YACS, figure 4) provides functionalities for code integration, dynamic loading and execution of components on remote distributed computing systems, and supervision of the calculation. The computing codes are wrapped into a C++ class which provides a coupling interface, and afterward they are integrated in SALOME platform as CORBA components (the CORBA layer being automatically generated by the platform integration module). This integration technique has the advantage of not requiring an access to the source of the coupled codes. Also it provides an explicit interface to the codes, which enables the coupling in an external coupling scheme, in our case a python script or a graph. This scheme is not implicit and embedded inside the source of the codes being coupled, thus it is clearer, and the debugging is much easier.

The data exchange is facilitated by the adoption of a common format for numerical meshes and fields (the MED library, an open standard provided by SALOME platform). This feature is of high importance as it is the basic support for all the coupling schemes that can be implemented between different codes once they are integrated as SALOME components. The MED library also provides a complete set of interpolation algorithms, which has proven to be very useful when codes rely on different meshes.

The URANIE toolbox for uncertainty analysis and code calibration

Of particular importance to all simulation areas is the development of a capacity to:

 quantify the uncertainty in the evaluations,  perform sensitivity studies  calibrate parameters of physical models.

These tasks were an important part of NURESAFE work-program. URANIE is an opensource software based on the CERN ROOT toolbox.

URANIE includes also:

 the capability to a build surrogate models of codes  a simple mechanism for interfacing codes and perform studies  a C++/python interface to facilitate the implementation of new algorithms developed by different laboratories  HPC capabilities

8) Prospects

The NURESIM platform provides a simulation capacity of light water reactor design basis accidents. Compared to methods used by industry, the platform offers higher fidelity physics and coupling functionalities. This results in a better knowledge of conservatisms and margins. The scope of NURESIM is not limited to the Situation Targets analyzed within the project but it covers the range of design basis accidents and it will be able to quantitatively assess several safety relevant features like for instance:

-Boiling crisis, -Negative or positive void coefficient, -Maximum power of a fuel rod or pellet, -Low flow in some reactor channels, -Absorber rods effectiveness, -Reactivity injection accident -… In addition, the more accurate tools delivered by NURESAFE will help optimization of the new reactor designs while supporting compliance with safety related criteria and the platform has now a larger scope covering innovative design features like, for instance, highly heterogeneous cores or passive safety systems.

The NURESAFE partners (TSOs, industry, research institutes or universities) had the opportunity, within the project, to use directly the NURESIM platform, either directly or through the work made by other partners. Thus, they were able to compare their own codes and methods to those of the NURESIM platform. These actions resulted in a better knowledge of the strengths and weaknesses of the various industrial codes in use in different organizations. The advanced models and methods developed within the NURESIM roadmap are and will be available in the future for all partners which can pick-up and re-use them in their own codes. In this way, progresses made in the framework of the project can spread easily in a larger framework and it will reinforce the reliability of simulation tools used by the European Nuclear Industry.

The NURESIM platform became the tool to realize, share, compare and judge the latest advances in methods, models and codes. It will encourage collaborative work on methods beyond the state-of-the-art. As an important effort of integration of software into the SALOME platform was made during the project, most of the NURESIM software use standardized tools for pre and post-processing, and coupling capacities so that the generic tools can be mutualized and the interoperability and comparison between codes becomes easier. In this way, both regulators and industry will have from now the possibility to benefit from all the generic platform features, even if they use different software. Thus this standardized environment offered by the platform and the interoperability of codes facilitates the development of this collaborative work.

Further to the NURESAFE project, the platform will continue to break down the barriers between disciplines and federate a team of top international level experts coming from many European countries and institutions. So, the NURESIM platform will have a catalytic effect to structure teams which, on a national scale, would remain below critical mass. Their collaborative work will increase the leadership of European science for nuclear reactor simulation. The NURESAFE consortium will be a vector to share common views, methods and tools for numerical simulation of nuclear reactors within Europe. This will result in strengthening nuclear safety in these countries.

9) Acknowledgements

The present work is funded by the European Commission under the 7 th EUROATOM Framework Program within the NURESAFE Project contract No. 323263 and by the NURESAFE partners: UPM (Spain), KTH (Sweden), U-PISA (Italy), UCL (Belgium), LUT (Finland), ICL (United kingdom), EDF (France), AREVA SAS (France), KIT (Germany), CEA (France), HZDR (Germany), PSI (Switzerland), JSI (Slovenia), VTT (Finland), INRNE (Bulgaria), UJV (Czech republic), KFKI (Hungary), ENEA (Italy), GRS (Germany), IRSN (France), NCBJ (Poland), ASCOMP (Switzerland), LGI (France)

Figure 1 -

 1 Figure 1the NURESIM roadmap

Figure 2 -

 2 Figure 2 -Architecture of the NURESIM platform

Figure 3 -

 3 Figure 3-The NURESIM platform, at the end of the NURESAFE project (January 2016) 7.2 The SALOME framework The NURESIM platform is based upon the SALOME. It is an open-source project, (http://salome-platform.org), which implements the interoperability between a CAD modeler, meshing algorithms, visualization modules and computing codes and solvers. It mutualizes a pool of generic and user-friendly tools for pre-processing, postprocessing and code coupling. SALOME facilitates coupling between codes in a heterogeneous environment and promote the use of software standards. Therefore SALOME Contributes to reduce the costs and facilitates sharing models and software.

Figure 4 -

 4 Figure 4 -The YACS user interface


Keywords: UO 2, residual carbon, dissolution kinetics

UO 2 powders were synthesized thanks to oxalic precipitation (platelet morphology) and sol-gel route and completely characterized. A secondary phase was found in addition of the oxide depending on the calcination atmospheres. This phase has been identified by Raman spectroscopy as graphitic material (i.e. carbon-based secondary compound) and quantified by thermogravimetric analyses. Its amount varies with the calcination atmosphere. The presence of this secondary phase has no significant effect on the lattice parameter and its specific surface area.

Introduction

One well-known method to synthesize actinide oxides is the thermal treatment of actinide oxalates under controlled atmosphere [START_REF] Arab-Chapelet | Structural characterization of mixed uranium-plutonium co-precipitates and oxides synthesized by oxalic co-conversion route[END_REF]. Calcinations under oxygen deficient atmospheres permit to avoid over-oxidation of the final oxide. Such controlled treatments lead to actinide dioxides presenting a targeted O/M (stoichiometry of oxygen / metal) ratio close to 2.00 and usually integrating residual carbon still remaining [START_REF] Silver | Plutonium oxalates as sources of plutonium dioxide[END_REF][START_REF] Martinez | From uranium(IV) oxalate to sintered UO 2 : Consequences of the powders' thermal history on the microstructure[END_REF]. Depending on the conversion conditions (heating rate / maximum temperature / atmosphere), this carbon content varies from a few ppm to about 0.42 at. % [START_REF] Almeida | Insights into the thermal decomposition of lanthanide(III) and actinide(III) oxalates -from neodymium and cerium to plutonium[END_REF]. Up to now, this secondary phase remains uncharacterized and additional investigations are required to fully identify its structure. As a first approach, such characterizations of the residual carbon have been carried out on UO 2 synthesized in similar conditions (i.e. using oxalic conversion). For comparison purposes, UO 2 powder was also synthesized using a sol-gel route for which another amount of residual carbon is observed.

Experimental section 2.1. Synthesis of UO 2 powders

Oxalic synthesis route

The oxalic conversion is usually reported to synthetize actinide oxides [START_REF] Grandjean | Structure of mixed U(IV)-An(III) precursors synthesized by co-conversion methods (where An = Pu, Am or Cm)[END_REF][START_REF] Hingant | Preparation of morphology controlled Th 1-x U x O 2 sintered pellets from low-temperature precursors[END_REF]. This process is based on an oxalic precipitation followed by a calcination step under controlled atmosphere. In this study, UO 2 is obtained by uranium (IV) oxalic precipitation. In details, uranium (IV) solution was prepared by catalytic reduction of uranium (VI) nitrate by H 2 on a Pt/Si support. Hydrazinium nitrate (N 2 H 5 + ) was used as an anti-nitrous agent to stabilize the uranium to its lowest oxidation states (i.e. +IV). The uranium precipitate was obtained by mixing oxalic acid and the U (IV) solution. Concentrations were fixed in order to reach in the precipitator a final concentration of nitric acid equal to 2M and an oxalic excess of 0.05M. In this conditions, tetravalent actinides form an oxalate of formula An IV (C 2 O 4 ) 2 .6H 2 O [START_REF] Abraham | Actinide oxalates, solid state structures and applications[END_REF]. This oxalate has a monoclinic structure and crystallizes as agglomerate square-plates [START_REF] Tamain | Crystal growth and first crystallographic characterization of mixed uranium(IV)-plutonium(III) oxalates[END_REF]. Obtained-precipitate was filtered off and rinsed with a water/ethanol mixture (10/90) before being air dried.

Sol-gel route

Articles referring to the sol-gel method lead to the synthesis of microspheres [START_REF] Vaidya | Sol-gel process for ceramic nuclear fuels[END_REF][START_REF] Jeong | UO 3 intermediate particle preparation using the Sol-gel process[END_REF]. In this paper, to synthesize powders, protocols were modified as follows. A 1.7 M U(+VI) monometallic nitrate solution was obtained through dissolution of uranyl nitrate UO 2 (NO 3 ) 2 in pure water. This metal nitrate solution was mixed with urea (CO(NH 2 ) 2 ) and HMTA (hexamethylenetetramine) solution at low temperature (~5°C). Urea acts as a complexing agent of U(VI) preventing from premature precipitation of this cation when HMTA is added. The ratio [urea] / [U] and [HMTA] / [U] used was respectively 1.74 and 1.71. Once urea and HMTA were dissolved into the cold uranyl solution, the solution was stirred and heated at 80°C. HMTA was decomposed at high temperature causing an increase in pH and hydrolysis of uranium. In few minutes, solution jellified. At room temperature, this gel was washed with NH 4 OH allowing the elimination of the remaining organic matter provided by the reagents. The washed gel of UO 3 was dried at 250°C for 20 hours to remove residual ammonium nitrate and moisture.

Thermal treatments

Thermal treatments were performed for all precursors (oxalate and UO 3 ) up to 1127 K with a heating rate of 20 K.min -1 . Compounds were maintained at this temperature for 90 min then cooled down to room temperature. Different calcination atmospheres were used in order to obtain in all cases UO 2 powders. Considering oxalate powder, it was then divided into two equal batches: one was calcined under reducing atmosphere Ar/H 2 (96/4) and the other one was calcined firstly in oxidizing atmosphere followed by the same calcination under reducing conditions Ar/H 2 (96/4). The UO 3 gel was calcined under Ar/H 2 (96/4).

Characterization

XRD Analysis

XRD (X-Ray Diffraction) analyses of the synthesized powders were performed using a D8 Bruker Advance diffractometer (LynxEye detector) using Cu-K radiation (λ=1.5418 Å) especially equipped for radioactive material measurements. Gold was added as an internal standard to calibrate the angular positions of the observed XRD lines. Each powder pattern was recorded within an angular range from 5° to 80° in 2theta, with steps of 0.02° and a counting time of 0.6s per step. The lattice parameters were determined by Le Bail refinement using the TOPAS software (TOtal Pattern Analysis Solutions) from BRUKER AXS [START_REF]DIFFRACplus TOPAS/TOPAS R/TOPAS P Version 2.1 and www[END_REF] where only the profile parameters (cell dimensions, peak shapes, background, zero point correction) were refined. The microstrains and average crystallite sizes were calculated with the fundamental parameters method [START_REF] Cheary | Fundamental parameters line profile fitting in laboratory diffractometers[END_REF]. The percent of microstrains in a structure can increase with incorporation of impurities in the cell or substitution of atoms.

Specific surface area measurements

N 2 adsorption-desorption isotherm was measured at the boiling point of nitrogen (-196 °C) using a Micromeritics Gemini 2375 equipment. The amount of adsorbed gas is correlated to the total specific surface area of the particles including pores in the surface. The specific surface area was calculated by the Brunauer-Emmett-Teller (BET) 5 points method [START_REF] Fagerlund | Determination of specific surface by the BET method[END_REF] from around 1 g of each powder.

SEM Observations

A scanning electron microscope (SEM) available in ATALANTE facility was used: a JEOL T 330A, installed in a hot cell (8 cm steel) for highly radioactive samples, allows secondary electron imaging. Previously, samples were deposited on a carbon substrate, and then metallized with gold for 4min.

Raman spectra

A Horiba Jobin-Yvon LabRam HR Evolution Raman spectrometer was used in conjunction with a nuclearized superhead (Optique Peter, Lyon, France) mounted on a support with an objective turret (10×, 20× and 50×). A YAG laser (532 nm) with output power adjustable from 0.5 to 100 mW was used to provide low-excitation-beam power levels. The superhead was mounted in glove box, while the Raman spectrometer and laser were installed outside with a fiber-optic signal transmission line. The microscope objective used was 20× and the acquisition time was 1200 s. Raman spectra were obtained from 20 mg samples. The beam has a diameter equal to 2 µm. Contrary to what has been previously observed by Tyrpekl et al. [START_REF] Tyrpekl | Low temperature decomposition of U(IV) and Th(IV) oxalates to nanograined oxide powders[END_REF], the laser intensity was sufficiently low to avoid an oxidizing of UO 2 to U 3 O 8 or UO 3 compounds.

TGA-µGC

The ratio of residual carbon remaining in the powder after calcination was estimated by thermogravimetric analysis (TGA) coupled with gas chromatography measurements (µGC). Analyses (Netzsch STA 449 thermogravimetric analyzer) were carried out on samples under air up to 1000°C. CO 2 and CO releases were monitored. Approximately 50 mg of powder were used per analysis to obtain a representative value of residual carbon in the samples.

Dissolution

All the dissolutions described in this work consisted in dissolving 300 mg of synthetized UO 2 powder in 15 mL of nitric acid 1.5 mol.L -1 . Solution was stirred at 300 rpm and maintained at 323.15 K. 1 h static dissolutions were performed in a batch of 20 mL. The aim of these dissolution experiments was to isolate the residual carbon of our powders. In addition, the different dissolution kinetics were also recorded using UV-visible spectroscopy. The device used was a Varian Cary 50 from Agilent Technologies. Dissolution of UO 2 in nitric media consisted in oxidizing U(+IV) to U +VI O 2 (NO 3 ) 2 [START_REF] Sharratt | Dissolution rates of uranium dioxide sintered pellets in nitric acid systems[END_REF]. In UV-visible spectroscopy, the band of the U(+VI) present in solution appears near 415 nm. From pre-established standards and the Beer-Lambert law, it is possible to convert the absorbance into concentration of uranium (VI) in solution. A 10 % error bar has to be applied to experimental concentration data due to the use of optical fibers and the range of analyzed concentrations (i.e. from 2 to 18 g.L -1 ).

Results and discussion

3.1.

Influence of carbon presence on UO 2 structure

Structural description

The oxalate U(C 2 O 4 ) 2 .6H 2 O precipitate was divided in two batches calcined in two different atmospheres : Ar/H 2 (96/4) and Air + Ar/H 2 (96/4) in a two-step calcination process. For both compounds, the XRD patterns of powders correspond to a sole fluorite-type UO 2 structure. Within the XRD detection limits, there are thus no additional phases. Table 1 gathers structural parameters of the different uranium oxides and the associated specific surface area (measured by BET method). A variation of lattice parameters and lattice volume with the calcination atmosphere is observed. Concerning oxide obtained after a double calcination, this post-calcination evolution of lattice parameter is explained by a slight sur-stoichiometry of the compound which results from the calcination in air + Ar/H 2 . This oxygen over-stoichiometry can be explained by the former formation of U 3 O 8 [START_REF] Barbu | The cold pressing behavior of uranium dioxide and triuranium octoxide mixed powders[END_REF] (O/U = 2.67) when compound was firstly calcined in flowing air and the difficulty to obtain a perfect stoichiometry (i.e. 2.00) during the second calcination in reductive atmosphere Ar/H 2 . UO 2 obtained by sol-gel route has a lattice parameter close to the perfect value (i.e. 5.471). Similar lattice parameter was obtained for the UO 2 synthesized after calcination in Ar/H 2 atmosphere of the oxalate. Concerning the powder obtained after a single calcination of the oxalate, crystallite sizes determined from the XRD diagram are about 160 nm. In the case of the double calcination air + Ar/H 2 , this value is multiplied by 2. This bigger crystallite size is due to the crystalline growth with the calcination time [START_REF] Podor | In Situ HT-ESEM observation of CeO 2 grain growth during sintering[END_REF]. Indeed, UO 2 resulted from the double calcination has undergone a calcination time twice longer than the UO 2 obtained after a single calcination. Despite these different crystallite sizes, the specific surface areas, determined by BET method, were similar for both UO 2 obtained by oxalic conversion and equal to 1 m²/g. The specific surface area is higher in the case of the oxide made by sol-gel route (2 m²/g), which can be explained by its different morphology (cf 3.1.4). This difference in specific surface areas may explain the better reduction of UO 3 leading to a perfect UO 2 in the case of the oxide made by sol-gel route compared to the slight oxygen sur-stoichiometry of the UO 2 obtained by the double calcination of oxalate (reduction of U 3 O 8 ) due to an higher reactivity of the calcination gas in the case of the sol-gel precursor. The microstrains of the synthetized oxides were similar. Indeed, in the case of the both single calcination, the value of microstrains were close to 0.10% and this value is equal to 0.6% in the case of the powder obtained after a time of calcination twice longer.

Raman spectra

After dissolution of the UO 2 powder obtained by calcination of oxalate in Ar/H 2 atmosphere, some non-soluble black particles remained in the nitric acid solution whereas UV-spectroscopy showed that all uranium present in the starting oxide was dissolved. This solid phase was collected by filtration and analyzed through Raman spectroscopy. Four bands characteristic of a graphitic material [START_REF] Wang | Raman spectroscopy of carbon materials: Structural basis of observed spectra[END_REF] are visible on the spectrum (figure 1). One of the main bands at 1350 cm -1 corresponds to the D-band (D for defect or disorder) and is commonly present for all sp 2 carbon systems. This band is absent for graphene perfect structures [START_REF] Jorio | Raman spectroscopy in graphene related systems[END_REF]. Another intense band distinctive of C-C bonds in graphitic materials in presence of impurities appears at 1620 cm -1 . This D'-band cannot exist without the previous one and has a weaker intensity [START_REF] Raza | Graphene nanoeletronics -Metrology, synthesis, properties and applications[END_REF]. This band is generated by the splitting of a band at 1583 cm -1 into two vibration modes [START_REF] Yan | Characterization of graphene by Raman spectroscopy[END_REF]: one D' -band at 1620 cm -1 and one G -band at 1583 cm -1 , due to the presence of impurities which interact with the band of graphene. The G -band refers to the fingerprint of singlelayered graphene. On figure 1, the G -band is not visible probably hidden by the other broad signal. The band at 2680 cm -1 is called G'-band or 2Dband and is an overtone of the Gband [START_REF] Childres | New developments in photon and materials research[END_REF]. In the case of graphene materials, the intensity of the G' -band is supposed to be higher or equal to the intensity of the band at 1583 cm -1 [START_REF] Ferrari | Raman spectrum of graphene and graphene layers[END_REF]. The small intensity at 2680 cm -1 explains the fact that the band at 1583 cm -1 is hidden by the wide D'band in the 1500 -1750 cm -1 range. The band at 2947 cm -1 is also reported as D+G mode for graphitic materials and Bokobza et al. [START_REF] Bokobza | Raman spectra of carbon-based materials (from Graphite to Carbon Black) and of some silicone composites[END_REF] explain that its intensity increases with the amount of disorder. Therefore, according to the Raman spectroscopy, the black residual solid collected after dissolution is a graphitic phase containing impurities and presenting some crystallographic defects. This material could result from the thermal decomposition of oxalate generating carbon monoxide and its disproportionation according to equation 3.1 [START_REF] Glasner | Remarks on the thermal decomposition of plutonium (IV) oxalates[END_REF].

Eq 3.1

UO 2 samples analyzed by Raman spectroscopy are illustrated in figure 1 and present characteristics bands at 445 cm -1 typical of the fluorite UO 2 structure, attributed to the triplet degenerated T2g Raman-active vibration [START_REF] Butler | Characterisation of uranium oxides by micro-Raman spectroscopy[END_REF].

Another band at 575 cm -1 is described as the "fingerprint" of the quasi-perfect fluorite structure [START_REF] Manara | Raman spectra of stoichiometric and hyperstoichiometric uranium dioxide[END_REF], its intensity is linked to the presence of oxygen vacancies in the fluorite structure [START_REF] Desgranges | A possible new mechanism for defect formation in irradiated UO 2[END_REF]. The most intense band at 1150 cm -1 corresponds to an overtone of the precedent one [START_REF] Livneh | Effect of pressure on the resonant multiphonon Raman scattering in UO 2[END_REF]. The comparison of the two UO 2 powders obtained with oxalic route reveals an increase in intensity of the 445 and 1150 cm -1 bands and a decrease in intensity of the 575 cm -1 for the oxide synthesized after a single calcination. This phenomenon is characteristic of a deviation from the perfect cubic structure [START_REF] He | Raman spectroscopic studies of defect structures and phase transition in hyperstoichiometric UO 2+x[END_REF] due to over-oxidation. It confirms data obtained by XRD analyses concerning the little over-oxidation (i.e. O/U = 2.02) of UO 2 from double calcination. For both this samples, the characteristic bands of the previously described graphitic phase (i.e. 1350 and 1615 cm -1 ) appear and an evolution is observed with the calcination atmosphere. Band intensities are highest for the single calcination under Ar/H 2 (96/4) sample. A dozen of spectra were recorded on both samples showing a variation of the ratio of the intensities of bands 1375 cm -1 (carbon phase) and 1150 cm -1 (UO 2 phase) according to the area under consideration. This ratio is in a range between 0.69 and 0.51 in the case of the sample which undergone a simple calcination under Ar/H 2 (96/4). For the second sample, this ratio varies from 0.37 to 0.20. The average ratio for simple calcination and double calcination UO 2 are respectively 0.62 and 0.28. This evolution allows concluding about a heterogeneous distribution of the carbon phase in both samples and a highest inclusion of carbon when oxalate is calcined only in Ar/H 2 . UO 2 obtained by sol-gel method was also analyzed; the typical spectra of UO 2 were found and the presence of the graphitic material was again observed by Raman spectroscopy, it is however impossible to say if there is more or less carbon than the material obtained by oxalic route after an oxidizing/reducing calcination.

ATG-µGC

Carbon content of UO 2 powders was estimated by TGA-µGC analyses. As mentioned after the Raman investigation, the carbon content of powders synthesized by oxalic route is dependent on the calcination atmosphere. Two types of carbon were evidenced: a first peak emission appeared in the range of 250 -650 °C corresponding to the elimination of the carbon included as CO 2 absorbed on the powder. The second emission, between 650 and 1000°C, corresponds to the combustion of the graphitic carbon observed by Raman spectroscopy. Quantities of elemental carbon found by µGC are 0.12 w. % and 0.07 w.% for the single and the double calcination respectively. The ratio between these two values is close to the value found by Raman spectroscopy (i.e. 0.62 compared to 0.28). The carbon dioxide signature band at 1480 cm -1 [START_REF]The Raman spectra of carbon dioxide in liquid H 2 O and D 2 O[END_REF] was observed for any of the three UO 2 by Raman spectroscopy due to the weak presence on the surface of oxides and a weaker Raman response of this phase. Moreover, this band may be hidden by both the intense graphitic bands at 1350 and 1615 cm -1 . In the case of the oxide obtained via the sol-gel route, the quantity of elemental carbon was 0.11 w.%. This carbon comes from the decomposition of organic compounds (urea and HMTA), which were not totally eliminated during the washing step.

Powder morphologies

SEM micrographs in figure 2 present the powder morphology of the different uranium oxides. The powder obtained by sol-gel route is composed of one to four hundred micrometers agglomerates of particles measuring several hundred nanometers in diameter. Concerning oxides obtained by oxalic route, morphologies obtained were agglomerates of square-plates. The square-plate sizes are exactly the same for both compounds and vary between 4 and 8 µm. Differences are observed at the level of the crystallite size. For the compound formed after single calcination, crystallite sizes ranging from 150 to 400 nm are observed, while for the oxide obtained after a double calcination crystallites have a size ranging from 300 to 800 nm. These values are in agreement with the data found by XRD analyses. It is observed for this last compound an intergranular porosity which can be due to the reduction of U 3 O 8 to UO 2 : indeed, U 3 O 8 structure presents a 30% greater lattice volume than UO 2 [START_REF] Ganguly | Characterisation and quality control of nuclear fuels[END_REF]. The porosity then induced could not be erased during this reductive calcination because of a too low temperature or a too short calcination time. An increase in porosity should induce an increase in the specific surface area. However, crystallite growth from the second calcination induces a decrease in the specific surface area. A competition between porosity and crystallite growth may then explain the similar values of specific surface areas of the two powders.

Discussion on the effect of carbon content on UO 2 characteristics

Raman spectroscopy demonstrated the presence of two distinct phases heterogeneously distributed: a UO 2 powder and a graphitic phase composed of carbon only. However, is the carbon totally present in this second phase, or is a part of this carbon present in the cell of the UO 2 as crystal defects? Assuming an incorporation of carbon into the UO 2 structure would have an effect on the value of the lattice parameters and the microstrain rates, focusing on our structural parameters values (table 2) for different carbon contents may answer this question. It has already been published [START_REF] Mukhtar | Co-precipitation synthesis and characterization of nanocrystalline zinc oxide particles doped with Cu 2+ ions[END_REF][START_REF] Pakharukova | Coppercerium oxide catalysts supported on monoclinic zirconia: Structural features and catalytic behavior in preferential oxidation of carbon monoxide in hydrogen excess[END_REF] that there is a relation between an incorporation of atoms in a cell and the structural parameters calculated. Authors reported that an increase in the incorporation atom rate leads to an increase in the lattice parameters but also in the microstrain percent that is characteristic of a cell distortion or interparticle interactions. Weak microstrain values were obtained in all of the samples synthesized and the three values were close to the one of an ideal UO 2 (i.e. with no microstrain in the UO 2 cell). Therefore, it is possible to conclude that only a very small amount or none of the residual carbon would have entered inside the UO 2 cell. However, a slight variation in microstrain rates between our three samples follows the same variation of the carbon content despite the fact that most of this carbon content forms the graphitic phase. Moreover, if an O sur-stoichiometry may have similar effect on the microstrain rates, it can be observed in the sample resulting from the double calcination and presenting the lowest lattice parameter (i.e. the biggest O sur-stoichiometry) the weakest microstrain rates. Therefore, such little O sur-stoichiometry seems to have no effect on microstrain rates. It is then possible to conclude that some of the residual carbon may have entered inside the UO 2 cell but only a very little amount as all of the microstrain rates observed are very low. So far it has not been possible to quantify this amount.

Oxide compounds resulting from oxalic route lead to the same specific surface area implying that the amount of carbon has no effect on this parameter. The difference in surface specific areas between UO 2 obtained by sol-gel and oxalic route can be explained by their different morphologies.

Dissolution kinetics of these materials

Dissolution kinetics are reported in figure 3. The dissolution of powders obtained by oxalic route appears similar for both powders. Comparing these data to the SEM micrographs, porosity is likely to promote the penetration of nitric acid at the interface with the solid and to increase the dissolution kinetics. On the contrary, the increase of crystallite sizes could reduce the density of grain boundaries and limit the access of nitric acid, resulting in a decrease of the dissolution kinetics. Up to now, an effect of porosity or crystallite size on the dissolution kinetics was not quantified in the scientific literature. In our study these two effects compensate each other, leading to similar dissolution kinetics for the two UO 2 obtained by oxalic route, despite the single and double calcinations. Corollary, no effect of the carbon content on dissolution kinetics could be detected. It is not possible to isolate the role of the carbon content on kinetic dissolution. Finally, the two different synthesis routes conduced to uranium oxides presenting different dissolution kinetics. This result can be attributed to the different morphologies (size or form of agglomerates, crystallite size, porosity…) exhibited by these uranium oxides.

4.

Conclusion

To conclude, this study shows that the amount of residual carbon has no significant effect on the UO 2 oxide lattice parameters. A large part of this residual carbon has been identified as a graphitic phase presenting crystalline defects. This phase is not homogeneously distributed in the powder which is in agreement with the fact that carbon comes from the disproportionation of carbon monoxide (from the decomposition of oxalate). It has been possible to conclude than a little amount of the carbon may have entered inside the UO 2 cell on the basis of the evolution of the microstrain rates. Nevertheless, no quantification was possible. To reduce the carbon content in the powder, an oxidizing/reducing calcination cycle may be applied. However, such a treatment would have an effect on the morphology of the final oxide increasing the crystallite size and intergranular porosity. Finally, no effect of the residual carbon on dissolution kinetics could be highlighted.

FiguresFigure 1 :

 1 Figures

Figure 2 :

 2 Figure 2: Raman spectroscopy of the three UO 2 powders and of the dissolution residues.

Figure 3 :Figure 4 :

 34 Figure 3: SEM micrographs of UO 2 powders in secondary electron mode: (a) and (b) refer to calcination in flowing Ar/H 2 , (c) and (d) refers to double cycle of calcination air + Ar/H 2 and (e) and (f) refer to the UO 2 obtained by sol-gel route calcined under Ar/H 2 .

Table 1 : Structural parameters for three UO 2 powders of from different calcination atmospheres and different synthesis routes.

 1

	Precursors route	Oxalate single calcination	Oxalate double calcination	Sol-gel single calcination
	Calcination atmosphere	Ar/H 2 (96/4)	Air	Ar/H 2 (96/4)	Ar/H 2 (96/4)
	Bearing time at 1127 K(min)	90	90	90	90
	Lattice parameter (Å)	5.4704 (1)		5.4686 (1)	5.4694 (1)
	Lattice volume (Å 3 )	163.7(1)		163.5 (1)	163.6 (1)
	Average crystallite sizes (nm)	167 (3)		351 (7)	164 (2)
	Rp (%)	7.97		7.22	3.63
	Rwp (%)	10.21		9.06	4.59
	GOF	3.86		3.68	1.89
	Microstrain (%)	0.0977(45)		0.0651(25)	0.1036(37)
	Specific surface area (m 2 /g)	1 ± 0.2		1 ± 0.2	2 ± 0.2

Table 2 : Lattice parameters and carbon content of the UO 2 powders

 2

	Precursors route	Oxalate single calcination	Oxalate double calcination	Sol-gel single calcination
	Microstrains (%)	0.0977 (45)	0.0651 (25)	0.1036(37)
	Lattice parameter (Å)	5.4704 (1)	5.4686 (1)	5.4694 (1)
	Carbon content (at. %)	0.26	0.15	0.24
	3.2.

Acknowledgements

The authors are thankful to G.Jouan (DRCP/SECA) for SEM imageries. This research was partly funded by AREVA NC, France. The authors specially thank C.Lavalette (AREVA) for encouraging this PhD work and for fruitful discussions.