domain: chim chim.mate sde

text:
Benoit Villemejeanne

Sophie Legeai

Eric Meux

Sandrine Dourdain

Hakima Mendil-Jakani

Emmanuel Billy

ElectroLeaching-ElectroChemical Deposition (EL-ECD) of gold and palladium in a deep eutectic solvent (DES)

Keywords: Electrochemistry, Deep eutectic solvents, Precious metals recovery

Introduction

Metals recovery from end-of-life products is one of the most important challenges regarding raw materials depletion and supply but also waste generation. Especially, Waste Electrical and Electronic Equipment (WEEE) are of major concern, as they often contain significant amounts of critical, rare, or precious metals like gold and palladium [START_REF] Kaya | Electronic Waste and Printed Circuit Board Recycling Technologies[END_REF].

Currently, gold and palladium extraction from e-wastes are performed by a multistep process including pyrometallurgical and hydrometallurgical treatments [START_REF] Cui | Metallurgical recovery of metals from electronic waste: A review[END_REF][START_REF] Li | Hydrometallurgical recovery of metals from waste printed circuit boards (WPCBs): Current status and perspectives -A review[END_REF]. Hydrometallurgical steps have been used for decades but they involve reactants that can be harmful for environment and human health, e.g. cyanide leaching of gold, aqua regia or chlorine leaching of palladium [START_REF] Cui | Metallurgical recovery of metals from electronic waste: A review[END_REF][START_REF] Dawson | Recovery of platinum group metals from secondary materials. I. Palladium dissolution in iodide solutions[END_REF].

Ionometallurgy, namely the use of ionic solvents, is nowadays considered as an alternative to conventional hydrometallurgy, as the low vapor pressure and low flammability of these solvents reduce process hazards [START_REF] Galiński | Ionic liquids as electrolytes[END_REF]. Ionic solvents also have a great electrochemical stability [START_REF] Li | The electrochemical stability of ionic liquids and deep eutectic solvents[END_REF][START_REF] Gancarz | Influence of experimental conditions on the electrochemical window. Case study on bis(trifluoromethylsulfonyl)imide-based ionic liquids[END_REF] and can be considered as complexing agents. These two properties are essential to develop an electrochemical process for precious metals recovery without any solvent degradation and with low effluent generation. Recently, we studied a single step ElectroLeaching-ElectroChemical Deposition (EL-ECD) process for Au and Pd recovery using ionic liquid (IL) mixtures containing 1-Butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (C4C1Im NTf2) as diluting IL and 1-Butyl-3-methylimidazolium chloride (C4C1Im Cl) as complexing IL [START_REF] Villemejeanne | Halide based ionic liquid mixture for a sustainable electrochemical recovery of precious metals[END_REF]. This kind of melt was also used successfully for Pt recovery from fuel cell electrodes [START_REF] Balva | Environmentally Friendly Recycling of Fuel-Cell Membrane Electrode Assemblies by Using Ionic Liquids[END_REF]. High faradic yields (99 %) were obtained for Au EL-ECD using C4C1Im(NTf2)0.78Cl0.22 electrolyte. However, yield was limited to 25 % for Pd ECD, and these IL remain quite viscous (60 cP at 40 °C), expensive and not green if their whole life cycle is considered.

In this context, deep eutectic solvents (DES) may be more promising candidates than IL. Described for the first time by Abbott et al. in 2003 [10], they have same advantageous properties for EL-ECD (low vapor pressure, good electrochemical stability, complexing properties), while being less expensive and viscous [START_REF] Santana | Sustainable synthesis of natural deep eutectic solvents (NADES) by different methods[END_REF][START_REF] Zhang | Deep eutectic solvents: syntheses, properties and applications[END_REF]. They are moreover considered as greener solvents, as they are often partially biosourced and of higher biodegradability (betaine, choline) [START_REF] Płotka-Wasylka | Deep eutectic solvents vs ionic liquids: Similarities and differences[END_REF]. DES have already been successfully used for gold electrochemical recovery from electronic waste [START_REF] Abbott | Electrocatalytic recovery of elements from complex mixtures using deep eutectic solvents[END_REF][START_REF] Popescu | Recovery of silver and gold from electronic waste by electrodeposition in ethaline ionic liquid[END_REF]. Palladium electrochemical deposition (ECD) was also achieved in this new solvents family [START_REF] Soma | Palladium electrochemistry in the choline chloride-urea deep eutectic solvent at gold and glassy carbon electrodes[END_REF][START_REF] Manolova | Electrodeposition of Pd alloys from choline chloride/urea deep eutectic solvents[END_REF]. However, no author reported any DES application for direct anodic electroleaching of gold or palladium with their simultaneous recovery by electrochemical deposition at the cathode (EL-ECD process). We present here a study of such a process in choline chloride:ethylene glycol (ChCl:EG) mixture. Electrochemical stability of ChCl:EG 1:2 was first determined on different electrode materials, and electrochemical behavior of gold and palladium was studied. The speciation of leached metals was determined by Raman and UV-vis spectroscopies, allowing us to establish electroleaching and electrochemical deposition reactions. The influence of ChCl:EG molar composition on DES transport properties was then evaluated, leading to the selection of ChCl:EG 1:3 as electrolyte for the EL-ECD process. A proof of concept is presented at the end of the paper, with corresponding cathodic/anodic faradic yields, recovery rates and deposit analysis.

Experimental

Chemical reagents

Choline chloride 98% (ChCl), silver chloride 99% (AgCl), ferrocene 98% (Fc), and ferrocenium tetrafluoroborate technical (FcBF4) were purchased from Sigma-Aldrich. Ethylene Glycol technical (EG) was purchased from Technic.

Electrolytes

Electrolytes were synthetized by mixing ChCl and EG in different proportions. The solid-liquid mixture was heated around 50 °C overnight until the solution was homogeneous. Electrolytes were prepared without any atmosphere control and stored in airtight bottles. Water content of electrolytes are comprised between 0.2 and 0.8 % weight (Karl-Fischer coulometric titration).

Instrumentation

All experiments were performed at 40 °C without any atmosphere control. Cyclic voltammetry (CV) was used to study metals electrochemical behavior in ChCl:EG mixtures. A three-electrode cell (1 mL of electrolyte) connected to a Biologic VSP300 (EC-lab software) was used. The counter electrode (CE) was a platinum grid and reference electrode (RE) was a Ag I /Ag electrode (Ag in ChCl:EG 1:2 containing 10 mM AgCl). This electrode was calibrated against Fc + /Fc half wave potential (equals to 0.63V vs. SHE [START_REF] Pavlishchuk | Conversion constants for redox potentials measured versus different reference electrodes in acetonitrile solutions at 25[END_REF]) and was stable for the duration of the experiments. All potential values measured were referred to standard hydrogen electrode (SHE). At 40°C, RE has a potential of 0.15V vs. SHE. RE and CE were separated from the bulk by a fritted glass. Working electrodes (WE) were 0.5 mm-diameter wires of gold (99.99%), platinum (99.95 %) or palladium (99.95%) supplied by Metalor. A 1 mm-diameter disk of glassy carbon (GC) was also used. EL-ECD experiments were performed in two three-electrode cells presented in SI-1 (5-10 mL) and SI-2 (100 mL) under potentiostatic control with a Biologic VSP300. WE was a rectangular GC electrode and CE was a Au or Pd foil. RE was the same electrode as described before. Electrolyte was ChCl:EG 1:3 containing 25 mM of Au or Pd, dissolved by electroleaching of metals. Electrochemical reaction rate but also faradic yields were determined by gravimetric analysis using a Mettler Toledo XP6 (± 0.001 mg).

UV spectra were obtained on a Varian Cary 5000 spectrometer, using Suprasil® Quartz cells, with a 2 mmoptical length. Raman spectra were performed on a Horiba LabRAM S3000 with a Synapse detector. The laser wavelength was 632.81 nm.

Viscosity analysis were carried out with a rolling ball viscometer Anton Paar LOVIS-DMA. Electrolytes conductivity was evaluated by Potentiostatic Electrochemical Impedance Spectroscopy (PEIS) in the 1 MHz -1 Hz range, using a calibrated two-platinum plates electrode cell. Scanning Electron Microscopy (SEM) was conducted on a TESCAN Vega 3 SBU and a ZEISS LEO 1530 microscopes.

Results and discussion

Electrochemical behavior of gold and palladium

Electrochemical behavior of Au, Pd, Pt and GC electrodes in ChCl:EG 1:2 was studied by CV at 50 mV.s -1 (Figure 1), scanning first towards anodic direction. First, no Pt electroleaching was observed at 40 °C. The anodic current around 1.2 V vs. SHE observed on GC and Pt is associated to DES anodic degradation. This oxidation is attributed to EG or chloride oxidation [START_REF] Haerens | Electrochemical decomposition of choline chloride based ionic liquid analogues[END_REF].

Interestingly, DES cathodic stability depends on the electrode material, according to the following order:

GC (-1.8 V vs. SHE) > Au (-1.3 V vs. SHE) > Pt ≈ Pd (-0.8 V vs. SHE)
This reaction is associated to cholinium cation reduction [START_REF] Haerens | Electrochemical decomposition of choline chloride based ionic liquid analogues[END_REF].

Au and Pd oxidation arise before DES anodic degradation (Ia) and is associated to cathodic peaks Ic on the reverse scan, corresponding to leached metals reduction. When the electrode potential is fixed at Ia, a quantitative electroleaching of metals occurs. The electrode mass loss ∆ 𝑚 is linked to the number of electrons 𝑛 exchanged (Eq. 1).

𝑛 = 𝑄𝑀 ∆ 𝑚 𝐹

Eq. 1

with M the molecular weight (g.mol -1 ), Q the electric charge (C), and F the Faraday's constant (C.mol -1 ).

Au and Pd leaching involves one and two electrons, respectively. In aqueous media (except in cyanide media), Au(I) is unstable and Au(III) is formed during Au leaching. The EL-ECD process using DES is then less energy consuming.

Leachates containing Au(I) or Pd(II) were analyzed by Raman spectroscopy (Figure 2). The observed signal at 301 cm -1 is associated to the square-planar complex PdCl4 2- [START_REF] Pandey | Force constants and bond polarizability derivatives of some XY4 square-planar type ions[END_REF]21]. This result was confirmed by UV-visible spectroscopy (Fig. 3-SI, absorbance peak at 479 nm) [21]. This complex was already identified in ChCl:EG 1:2 by EXAFS [START_REF] Hartley | EXAFS Study into the Speciation of Metal Salts Dissolved in Ionic Liquids and Deep Eutectic Solvents[END_REF]. The presence of AuCl2 - is evidenced by the signal at 329 cm -1 on the Raman spectrum [START_REF] Pan | Gold-chloride complexes in very acidic aqueous solutions and at temperatures 25-300 °C: A laser Raman spectroscopic study[END_REF]. No signal corresponding to Au(I) was clearly identified by UV-visible spectroscopy. In leachates, no Au (III) signal (322 nm [START_REF] Aldous | Electrochemical studies of gold and chloride in ionic liquids[END_REF]) was observed either (Figure SI-3). To the best of our knowledge AuCl2 -was not clearly identify in DES yet. Hence, we could attribute Ia to Reactions 2 and 3:

𝐴𝑢 + 2 𝐶𝑙 -→ 𝐴𝑢𝐶𝑙 2 -+ 𝑒 - Reaction 2 𝑃𝑑 + 4 𝐶𝑙 -→ 𝑃𝑑𝐶𝑙 4 2-+ 2𝑒 - Reaction 3
CV of 25 mM Au(I) and Pd(II) leachates were recorded on GC electrode (Figure 3). Cathodic peak Ic is observed in both solutions. When working potential is fixed to Ic peak, a yellow deposit is observable on GC in the case of Au. For Pd, a grey deposit appears. Hence, Ic peak could be attributed to Reactions 4 and 5.

𝐴𝑢𝐶𝑙 2 -+ 𝑒 -→ 𝐴𝑢 + 2 𝐶𝑙 - Reaction 4 𝑃𝑑𝐶𝑙 4 2-+ 2𝑒 -→ 𝑃𝑑 + 4 𝐶𝑙 - Reaction 5
In the case of Pd(II), Ic peak potential remains unchanged between the first and the second cycle. For Au(I), Ic peak is shifted towards more positive potential on the second cycle, compared to the first one. This is attributed to an incomplete dissolution of gold during the anodic scan (cycle 1). The second cathodic scan corresponds then to the reduction of Au(I) on Au substrate, which charge transfer kinetics appears to be faster than on GC.

Optimal composition of electrolyte: transport properties

The shape of cathodic peaks Ic on Figure 3 is characteristic of a mass-transport controlled reaction, implying that transport properties of the electrolyte are a major concern.

If mass-transport is ensured by diffusion, the current density 𝑗 is described as a function of diffusion coefficient 𝐷 (described by the Stockes-Einstein law in Eq. 3) and bulk concentration 𝐶 0 of the diffusing species (Eq. 2). Hence 𝑗 increases when viscosity 𝜂 decreases.

𝑗 = 𝑛𝐹 𝐶 0 𝐷 𝛿 ∝ 𝐶 0 𝜂 Eq. 2 𝐷 = 𝑘𝑇 6𝜋𝑟 𝐻 𝜂 Eq. 3
𝑟 𝐻 is the hydrodynamic radius (m) of the diffusing species, 𝑘 is the Boltzmann's constant (J.K -1 ) and δ is the diffusion layer thickness (m).

These equations show that current density increases as 𝜂 decreases and 𝐶 0 increases. As electrochemical reaction rate generally increases with current density (if the considered reaction is unique), a low electrolyte viscosity is preferable.

Furthermore, a high ionic conductivity σ (S.m -1 ) is desirable for this kind of process, mainly for energetic considerations. Indeed, ohmic drop 𝛥𝑈 within electrolyte during the electrolysis decreases with ionic conductivity (Eq. 4).

𝛥𝑈 = 𝑅 𝑒 𝐼 = 𝑗𝐿 𝜎

Eq. 4

with 𝑅 𝑒 the electrolyte resistance between electrodes (Ω), I the current intensity (A) and L the distance between electrodes (m).

Generally, in IL and DES, viscosity and conductivity are strongly linked. It is possible to enhance conductivity or decrease viscosity by electrolyte heating. Another way to decrease viscosity is to increase EG:ChCl molar ratio (Figure 4), EG acting like a fluidizing additive. However, as the ionic concentration decreases when EG content increases, ionic conductivity reaches a maximum for a molar ratio equals to 3. This value appears to be the best compromise to get optimal transport properties. ChCl:EG 1:3 electrolyte was then chosen to implement the EL-ECD process in a single cell.

EL-ECD of gold and palladium

As the metallic species concentration (0.025 M) is low compared to chloride content (4.2 M), the overall process will be controlled by the diffusion of metallic species. The cathodic current density will then drive the kinetics of the metal recovery (cf. Eq. 3 and Figure 1). To avoid solvent degradation and maximize faradic yield, the EL-ECD process must then be conducted under cathodic potential control. In the following study, EWE was fixed at Ic peak potential.

First experiments were carried out using the set-up presented in Fig. SI-2. The anode is a metallic plate (Au/Pd) and the cathode is a GC plate. Immersed surfaces were equal to 1 cm². The solution was unstirred to avoid deposit drop from the cathode. Table 1 summarizes the obtained experimental results. An anodic faradic yield of 100 % is reached for both Au and Pd leaching. In the case of Au, the cathodic faradic yield is also of 100 %, meaning that EL-ECD could be performed without any solvent degradation and with balanced faradic efficiencies. In contrast, the cathodic faradic yield for Pd is only 85 %, meaning that a side reduction reaction occurs simultaneously. As the working potential is fixed below 0 V vs. SHE, this reaction is assumed to be water reduction to H2. Anodic yield (%) 100 100

In both cases, the electrolysis rate v, is low. Considering a small electrolysis pilot with one cathode (S ~ 1 m²), this process would produce 10-20 g of metal per day.

To enhance mass transport of metallic species, another experiment was conducted under stirring in the set-up presented in SI-3. The corresponding results presented in Further investigations are in progress to understand parameters influence (applied potential, metal concentration, heating) on Pd deposit morphology. The influence of water content must be studied to confirm that hydrogen evolution is responsible for the poor adherence of the Pd deposit.

Conclusion

Gold and palladium ElectroLeaching-ElectroChemical Deposition (EL-ECD) in a single cell was successfully realized in ChCl:EG 1:3. Au and Pd electroleaching could be performed at low potential (< 1 V vs. SHE) with respectively 1 and 2 electrons exchanged. UV-visible and Raman spectroscopy confirmed the presence of chlorocomplexes AuCl2 -and PdCl4 2- after electroleaching. In metallic leachates and under cathodic control, EL-ECD experiments lead to quantitative anodic faradic yields. For Au, the cathodic faradic yield on glassy carbon is 100 %. For Pd, this yield is between 85 and 96 % meaning that a side reaction occurs during electrolysis, but metal deposition can be favored by stirring. The overall performance of the process using DES is much better than with ionic liquid mixtures in terms of faradic efficiency and recovery rate [START_REF] Villemejeanne | Halide based ionic liquid mixture for a sustainable electrochemical recovery of precious metals[END_REF]. This EL-ECD process is therefore of high interest in the recycling field of precious metal rich resources such as waste electrical and electronic equipment (WEEE). It could for example be applied for the refining of anodic sludges issued from pyrometallurgic treatment of printed circuit boards. One can also think about applications in electroplating industry, especially gold electroplating, as alternative to cyanide baths. The limited solvent degradation allows its recycling, which is primordial to develop a sustainable process from an economical or environmental point of view. Some parameters need however to be optimized: electrolysis rate could for instance be enhanced by decreasing viscosity or increasing metal concentration. Influence of current density and of applied potential on morphology would also need to be studied.

CRediT authorship contribution statement

Figure 1 -

 1 Figure 1 -Cyclic voltammograms obtained on Au (red), Pd (blue), Pt (green) and GC electrodes in ChCl:EG 1:2. 50 mV.s -1 . Au, Pd, Pt on left scale / GC on right scale

  These results indicate that Au and Pd electroleaching and electrochemical deposition are possible within the electrochemical stability window of ChCl:EG mixtures. Cell voltage (│EWE -ECE│ or │E(Ia )-E(Ic)│) is around 0.2 V for Au and 1 V for Pd.

Figure 3 -

 3 Figure 3 -Raman spectra of ChCl:EG 1:2 (black), ChCl:EG 1:2 + Au(I) (red) and ChCl:EG 1:2 + Pd(II) (blue)

Figure 2 - 1 -

 21 Figure 2 -Cyclic voltammograms obtained on GC electrode in ChCl:EG 1:2 (blackright scale), ChCl:EG 1:2 + 25 mM Au(I) (red-left scale) and ChCl:EG 1:2 + 25 mM Pd(II) (blue-left scale). Dotted lines correspond to cycle 1. Straight lines correspond to cycle 2. 50 mV.s -1

Figure 5

 5 Figure5presents images of the two deposits. Au deposit (A) appears more homogeneous at macroscopic scale than the Pd one (D) which is poorly adherent. However, SEM images reveal that the gold deposit is dendritic (B,C), with particles that are 1-5 µm large and 20-60 µm long. The Au deposit was easily removed from the GC plate to obtain an Au foil. Palladium nuclei are smaller than 1 µm but the deposit is heterogeneous. It presents nanometric cavities (E) and peels off the substrate (D, F), which agrees with hydrogen evolution side reaction. The thickness of the deposit could reach few hundred of µm. Large particles of Pd could further be recovered by electrode scratching. Only a thin layer of Pd remains attached to the substrate.

Figure 4 -

 4 Figure 4 -Ionic conductivity (black) and viscosity (red) of ChCl:EG (1:x) electrolytes

Figure 5 -

 5 Figure 5 -(A) Au deposit and corresponding SEM images (B) of the surface (× 5 000) and (C) of the cross-section (x 500) / (D) Pd deposit and corresponding SEM images (E) of the surface (× 5 000) and (F) of the cross-section (x 100)

  Benoit Villemejeanne: Conceptualization, Investigation, Writing -original draft, review & editing Eric Meux, Sophie Legeai, Emmanuel Billy, Hakima Mendil-Jakani, Sandrine Dourdain: Conceptualization, Supervision, review & editing

Figure 6 -

 6 Figure 6 -Au (A-C) and Pd (B-D) deposits obtained after EL-ECD experiment in SI-3 cell

Table 1 -

 1 Results of EL-ECD experiment

		Au(I)	Pd(II)
		(30 mM)	(25 mM)
	Time (h)	18	6
	Δm deposit (mg)	15.81	3.34
	Applied EWE (V vs. SHE)	0.55	-0.35
	j (mA.cm -2 )	0.1	0.35
	Qs (C.cm -2 )	6.4	6.5
	v (mg.h -1 .cm -2 )	0.7	0.5
	Cathodic yield (%)	100	85

Table 2

 2 and appears brighter than previously. The faradic yield of Pd recovery is improved (close to 100%), but the deposit is still poorly adherent and heterogeneous (Erreur !

show that process rate is increased by 2 to 3 times compared to previous experiments. Au deposit is homogeneous at macroscopic scale (Erreur ! Source du renvoi introuvable.-A)

Source du renvoi introuvable.-B).

Table 2 -

 2 Results of EL-ECD experiment in half-circle cell

		Au(I)	Pd(II)
		(40 mM)	(25 mM)
	Time (h)	2	3
	Δm deposit (mg)	43.0	26.1
	Applied EWE (V vs. SHE)	0.55	-0.35
	j (mA.cm -2 )	0.26	0.5
	Qs (C.cm -2 )	2.1	5.0
	v (mg.h -1 .cm -2 )	2.1	0.9
	Cathodic yield (%)	99	96
	Anodic yield (%)	98	100

Funding sources :

This research was supported by the CEA LITEN and EE4Precious project, ANR-20-CE08-0035-01.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.


Martina Pastorino
email: martina.pastorino@edu.unige.it.

Gabriele Moser

Sebastiano B Serpico

Josiane Zerubia

FULLY CONVOLUTIONAL AND FEEDFORWARD NETWORKS FOR THE SEMANTIC SEGMENTATION OF REMOTELY SENSED IMAGES

Keywords: CNN, FCN, feedforward networks, semantic segmentation, multiresolution satellite images

This paper presents a novel semantic segmentation method of very high resolution remotely sensed images based on fully convolutional networks (FCNs) and feedforward neural networks (FFNNs). The proposed model aims to exploit the intrinsic multiscale information extracted at different convolutional blocks in an FCN by the integration of FFNNs, thus incorporating information at different scales. The purpose is to obtain accurate classification results with realistic data sets characterized by sparse ground truth (GT) data by taking benefit from multiscale and long-range spatial information. The final loss function is computed as a linear combination of the weighted cross-entropy losses of the FFNNs and of the FCN. The modeling of spatial-contextual information is further addressed by the introduction of an additional loss term which allows to integrate spatial information between neighboring pixels. The experimental validation is conducted with the ISPRS 2D Semantic Labeling Challenge data set over the city of Vaihingen, Germany. The results are promising, as the proposed approach obtains higher average classification results than the state-of-the-art techniques considered, especially in the case of scarce, suboptimal GTs.

INTRODUCTION

The development of a supervised method for the semantic segmentation-or dense image classification-of remote sensing (RS) images at very high resolution (VHR) is a challenging problem. Current space missions allow to obtain multimodal (e.g., multiresolution, multisensor, multiband, multifrequency) satellite imagery and to reach fine spatial resolutions (up to 30 cm). Aerial imagery often have resolutions of a few centimeters. Methods based on deep learning (DL) are capable to successfully integrate this information and obtain accurate classification results [START_REF] Gbodjo | Multisensor land cover classification with sparsely annotated data based on convolutional neural networks and selfdistillation[END_REF][START_REF] Farooq | Transferable convolutional neural network for weed mapping with multisensor imagery[END_REF][START_REF] Piramanayagam | Supervised classification of multisensor remotely sensed images using a deep learning framework[END_REF]. In particular, mo-University of Genoa and Université Côte d'Azur (UCA) are part of the Ulysseus Alliance (European University). https://ulysseus.eu/. The code is available at https://github.com/Ayana-Inria/ FCN-FFNET_RS-semantic-segmentation dels based on FCNs [START_REF] Long | Fully convolutional networks for semantic segmentation[END_REF] are the state-of-the-art techniques for semantic segmentation tasks. These methods, however, need large training data sets [START_REF] Maggiolo | A semisupervised CRF model for CNN-based semantic segmentation with sparse ground truth[END_REF], which require high efforts in annotation and most often are not available for RS applications. In this case, the modeling of the information contained at different spatial resolutions (e.g., the spatial details of the finest and the robustness to noise plus outliers of the coarsest), has proven to be effective and guarantees improvements of the segmentation results in spatial precision and accuracy [START_REF] Gómez-Chova | Multimodal classification of remote sensing images: a review and future directions[END_REF].

Indeed, thanks to the operations executed by FCNs [START_REF] Long | Fully convolutional networks for semantic segmentation[END_REF], characterized by different multiscale processing stages through convolutional and pooling layers, it is possible to derive multiscale information. This is mostly contained in the hidden layers of the FCN and can be retrieved directly via skip connections. Stochastic models, such as probabilistic graphical models (PGMs) (e.g., Markov models, postulated on planar or multilayer graphs), are flexible and powerful models which can extract information from multiscale data for labeling purposes [START_REF] Li | Markov random field modeling in image analysis[END_REF][START_REF] Kato | Markov random fields in image segmentation[END_REF].

Several approaches that combine DL and models capable of making structured predictions, such as PGMs, have been studied in order to improve the accuracy of the results of semantic segmentation tasks by capturing the interactions between pixels. Methods that incorporates graphical models into a DL framework such as [START_REF] Zheng | Conditional random fields as recurrent neural networks[END_REF][START_REF] Nguyen | Context from within: Hierarchical context modeling for semantic segmentation[END_REF][START_REF] Liu | Deep learning Markov random field for semantic segmentation[END_REF] have also been considered. In [START_REF] Zheng | Conditional random fields as recurrent neural networks[END_REF], convolutional neural networks (CNNs) and conditional random fields (CRFs) are integrated in an end-toend approach where the mean-field inference for the CRF is approximated with Gaussian pairwise potentials as recurrent neural networks (RNNs). In [START_REF] Nguyen | Context from within: Hierarchical context modeling for semantic segmentation[END_REF] CRFs and FCNs are combined to model the context exhibited within the middle layers of an FCN and the mean-field inference process of a dense CRF is approximated as a multi-dimensional gated recurrent unit (GRU) layer. In [START_REF] Liu | Deep learning Markov random field for semantic segmentation[END_REF] a Markov random field (MRF) is defined by means of a CNN, namely a deep parsing network (DPN). In particular, DPN extends a CNN to model unary terms and additional layers are devised to approximate the mean field (MF) algorithm for pairwise terms.

In a recent approach [START_REF] Pastorino | Semantic segmentation of remote sensing images through fully convolutional neural networks and hierarchical probabilistic graphical models[END_REF], DL and stochastic models are combined to incorporate multiresolution information present at different layers of the neural networks to address the semantic segmentation of RS images in the case of scarce GT. In this paper, our aim is to take advantage of multiscale information extracted by the FCN through the addition of FFNNs at different convolutional blocks of the FCNcorresponding to information at different scales. As compared to the previous approach in [START_REF] Pastorino | Semantic segmentation of remote sensing images through fully convolutional neural networks and hierarchical probabilistic graphical models[END_REF], the method developed in this paper is based on an architecture capable of integrating multiscale data without the need of ensemble learning techniques, thus making the approach end-to-end. Spatialcontextual information is favored in this framework through a supplementary convolutional layer modeling the interactions between neighboring pixels at the same resolution.

The goal of the proposed method is threefold: firstly, to take advantage of the instrisic multiscale behaviour of FCNs to integrate multiscale information through the addition of FF-NNs; secondly, to strengthen the modeling of the spatial information through an additional convolutional layer; finally, to define a loss function capable to take into account both this multiscale and spatial information within an end-to-end neural model (see Fig. 1).

METHODOLOGY

FCNs, which are networks with an encoder-decoder architecture, are characterized by an intrinsic quadtree structure: in fact, the pooling and unpooling layers of size 2 ˆ2, normally employed within each convolutional block, match the powerof-2 relation typical of the pixel grids S l pl " 1, . . . , Lq at different L levels of a quadtree [START_REF] Laferté | Discrete Markov image modeling and inference on the quadtree[END_REF].

In order to exploit this intrinsic quadtree structure, the idea is to add FFNNs at each convolutional block in the decoder of the FCN, in this case a U-Net [START_REF] Ronneberger | U-net: Convolutional networks for biomedical image segmentation[END_REF]. The objective of the FFNNs is to retrieve the multiscale information contained at different scales in the activations of the feature maps of the hidden layers of the FCN. The FFNNs are built through convolutional layers with kernels of size 1 ˆ1, in order to work with 2D data and compute pixelwise posterior probabilities.

To integrate further spatial information, a convolutional layer is added after the output layer of the FCN. Zero padding is employed to ensure that every pixel is considered. The size of the kernel defines the number of neighboring pixels that influence a pixel i and, therefore, the spatial-contextual information modeled.

The loss function, expressed in equation ( 1), is designed as a linear combination of L multiscale weighted crossentropy loss functions. The losses were computed over the pixelwise softmax [START_REF] Goodfellow | Deep learning[END_REF] of the L ´1 FFNNs (after a resampling of the GTs at the corresponding resolution) and of the final feature map of the output layer of the FCN. They can be considered as unary terms, since they only depend on the value of each pixel considered individually. The weighting factor introduced in the cross-entropy loss is inversely proportional to the number of samples of each class in the image analysed, in order to take into account the presence of imbalanced training data.

L u " ´1 L L ÿ l"1 M ´1 ÿ k"0 Pmax Pk ÿ iPS l t ik log pp ik q (1)
p ik " exp pz ik q ř M ´1 n"0 exp pz in q (2)
where M is the number of classes, p ik is the estimated output probability that pixel i belongs to class k, pz i1 , . . . , z ij q is the prediction vector, Pk is the prior probability of the k-the class, estimated as its relative frequency in the training set (k " 0, 1, . . . , M ´1), and Pmax " max k Pk . t ik " 1 only if the sample i belongs to class k, otherwise it is equal to 0. The number of samples in the l´th pixel grid S l is N l " W l ˆHl , with W l and H l being the width and the height of the pixel grid, respectively. Considering N 1 the number of pixels in the smallest grid (l " 1), corresponding to the first convolutional block of the decoder, in general, N l " N 1 ¨22pl´1q , given the power-of-2 relation between the pixel grids at consecutive convolutional blocks.

This loss function was integrated with an implicitly pairwise term, shown in equation (3), deriving from the crossentropy loss function over the pixelwise softmax of the feature map obtained by the additional convolutional layer described above:

L p " ´WL ÿ a"1 H L ÿ b"1 M ´1 ÿ k"0 t ik log ˜D´1 ÿ j"0 D´1 ÿ q"0 h j,q ¨ppa´j,b´qq,k (3)
with h j,q one of the weights of the kernel of size D ˆD, and p pa,bq,k the probability that pixel in position i " pa, bq belongs to class k. The total loss is defined as follows:

L " L u `Lp (4)
The methodology is briefly summarized in Algorithm 1.

EXPERIMENTAL VALIDATION

The proposed method was tested with the ISPRS 2D Semantic Labeling Challenge data set containing aerial images of the city of Vaihingen, Germany 1 . It is a data set of VHR images, with a spatial resolution of 9 cm and it contains six classes: impervious surfaces (e.g., roads), buildings, low vegetation, trees, cars, and clutter. The last class is of relatively limited interest, as it comprises all the surfaces not belonging to the previous five and is highly mixed. Furthermore, it accounts for only a small percentage of pixels. Following the example of previous authors [START_REF] Audebert | Beyond RGB: Very High Resolution Urban Remote Sensing With Multimodal Deep Networks[END_REF][START_REF] Liu | Dense dilated convolutions' merging network for land cover classification[END_REF][START_REF] Lv | Mfalnet: A multiscale feature aggregation lightweight network for semantic segmentation of high-resolution remote sensing images[END_REF], the results of the class "clutter" were excluded from the averaged metrics.

1 https://www2.isprs.org/commissions/comm2/wg4/benchmark/semanticlabeling/

The results herein reported were obtained with L " 4, i.e., with FFNNs attached to 3 distinct convolutional blocks of the decoder of the FCN; D, the size of the kernel of the additional convolutional layer, is equal to 2, therefore each term in the pairwise loss function contained information of a pixel and three of its neighbors, (other results were omitted for brevity). The equipment used for the experiments is an Alienware Aurora R11 with a RAM of 16 GB and a GPU NVIDIA GeForce RTX 2080 Ti.

Two training conditions were considered (shown in Fig. 2(a)-(b)): (i) the full data set with densely labeled GTs and (ii) a data set of scarce GTs, obtained by removing entire connected components from the original exhaustive GT maps and then applying morphological erosion to the remaining information [START_REF] Pastorino | Semantic segmentation of remote sensing images through fully convolutional neural networks and hierarchical probabilistic graphical models[END_REF], in order to approximate realistic GTs with isolated patches typically found in RS applications.

The experiments were conducted on both the full images, whose results are reported in Table 1, and subsections of size 1280 ˆ1280 of the original test images, to be able to compare the proposed architecture with the previous ones, whose results are collected in [START_REF] Pastorino | Semantic segmentation of remote sensing images through fully convolutional neural networks and hierarchical probabilistic graphical models[END_REF]. Table 2 shows a quantitative analysis of the results obtained in the latter case.

As it can be seen from the values reported in Tables 12, the proposed method exhibits remarkable improvements concerning the average accuracy metrics, especially when the input training data is scarce and approaches the realistic GTs available for RS applications. In particular, when compared to the previous technique [START_REF] Pastorino | Semantic segmentation of remote sensing images through fully convolutional neural networks and hierarchical probabilistic graphical models[END_REF] and a standard FCN (e.g., U-Net), the proposed approach was capable of reaching higher or similar classwise results and generally higher values for the average metrics. The comparison of the classification maps obtained with U-Net and the proposed method are shown in Fig. 3(b)-(c).

The proposed approach was further compared to a multiscale feature fusion (MFF) technique, namely a light-weight attention network (LWN-Attention2 ) [START_REF] Liu | Light-weight attention semantic segmentation network for high-resolution remote sensing images[END_REF], and to HRNet3 [START_REF] Sun | Deep high-resolution representation learning for human pose estimation[END_REF], a neural network integrating multiscale information through a set of multiresolution subnetworks connected in parallel. MFF approaches involve multiscale information through the concatenation of feature maps associated with different scales [START_REF] Liu | Light-weight attention semantic segmentation network for high-resolution remote sensing images[END_REF]. The qualitative results obtained with these two methods are shown in Fig. 3(d)-(e).

From this comparison it is possible to notice that the proposed approach obtained higher or very similar per-class recalls, and generally higher overall accuracies, recalls and F1 scores. With the sparse GTs, the new approach guaranteed an improvement in overall accuracy, recall, and F1 score of about 5% with respect to the considered state-of-the-art techniques, reaching values up to 86% of accuracy for the full images. The proposed approach also attained improved results for the classification of minority classes in the case of scarce GT data, compared to U-Net, HRNet, and the MFF method.

DISCUSSION AND CONCLUSION

A new end-to-end approach for the semantic segmentation of RS images based on FCNs, FFNNs and a spatial loss function is proposed in this paper. The experimental results demonstrate the effectiveness of the proposed approach for the semantic segmentation of RS images, with remarkable improvements in the overall accuracy and average recall as compared to previous architectures, especially in the case of scarce GT data. This confirms the possibility to obtain classification improvements when integrating the intrinsic multiscale information extracted by FCNs across their layers and by addressing local spatial-contextual information.

Future work may involve the extension of this methodology to the multisensor case, with optical and radar images acquired by different missions and therefore with different spatial resolutions, frequencies, and bands. Moreover, the model may be combined with transfer learning techniques to allow predictions on data sets different-in features and complexitywith respect to the ones used for training. This would allow the use of the proposed methodology on data sets with poorer GT information, for example the ones related to disaster management.

Fig. 1 .

 1 Fig. 1. Overall architecture of the method.

Algorithm 1 FCNFig. 2 .

 12 Fig. 2. GT images used to train the proposed architecture: (a) full, (b) sparse. Classes: buildings (blue), impervious (white), vegetation (cyan), trees (green), cars (yellow), unlabeled (black).

Fig. 3 .

 3 Fig. 3. GTs and classification results: (a) GT and classification maps from (b) U-Net, (c) the proposed method, (d) LWN-Attention[START_REF] Liu | Light-weight attention semantic segmentation network for high-resolution remote sensing images[END_REF], and (e) HRNet[START_REF] Sun | Deep high-resolution representation learning for human pose estimation[END_REF]. Classes: buildings (blue), impervious (white), vegetation (cyan), trees (green), cars (yellow).

Table 1 .

 1 Test-set results with full images. Precision and recall are averaged over the classes.

		Architecture	buildings impervious vegetation trees cars overall acc. recall precision F1 score
	Full GT	U-Net [14] HRNet [17] Proposed method LWN-Attention [16]	0.86 0.89 0.96 0.96	0.91 0.89 0.91 0.93	0.79 0.50 0.80 0.71	0.90 0.86 0.89 0.81 0.91 0.81 0.89 0.61	0.89 0.79 0.91 0.89	0.87 0.80 0.88 0.82	0.85 0.81 0.87 0.88	0.86 0.81 0.88 0.85
	Sparse GT	U-Net [14] HRNet [17] Proposed method LWN-Attention [16]	0.87 0.84 0.94 0.94	0.93 0.75 0.78 0.82	0.64 0.82 0.80 0.65	0.87 0.76 0.69 0.49 0.87 0.90 0.85 0.60	0.82 0.77 0.86 0.81	0.81 0.72 0.86 0.78	0.84 0.79 0.85 0.83	0.83 0.75 0.86 0.80

Table 2 .

 2 Test-set results with cropped images. Precision and recall are averaged over the classes.

		Architecture	buildings impervious vegetation trees cars overall acc. recall precision F1 score
		U-Net [14]	0.92	0.83	0.71	0.92 0.74	0.85	0.83	0.84	0.83
	Full GT	HRNet [17] Proposed method FCN+PGM [12]	0.89 0.92 0.84	0.81 0.85 0.81	0.42 0.73 0.68	0.92 0.63 0.93 0.73 0.92 0.86	0.77 0.86 0.81	0.73 0.83 0.82	0.76 0.85 0.72	0.74 0.84 0.77
		LWN-Attention [16]	0.91	0.97	0.61	0.88 0.64	0.85	0.80	0.82	0.81
	Sparse GT	U-Net [14] HRNet [17] Proposed method FCN+PGM [12] LWN-Attention [16]	0.96 0.84 0.90 0.94 0.91	0.65 0.77 0.79 0.68 0.75	0.47 0.68 0.70 0.49 0.44	0.89 0.48 0.80 0.29 0.89 0.68 0.86 0.74 0.87 0.51	0.76 0.77 0.82 0.76 0.76	0.69 0.68 0.79 0.74 0.70	0.81 0.74 0.81 0.75 0.74	0.75 0.71 0.80 0.75 0.72

https://github.com/syliudf/LWN-Attention

https://github.com/HRNet/HRNet-Semantic-Segmentation


V Baietto

Georgenthum

T Jailin

N Tardif

J Desquines

M Coret

M.-C Baietto

V Georgenthum

Experimental study and modelling of the phase transformation of Zircaloy-4 alloy under high thermal transients

Keywords: Fast thermal transients, Phase transformation, Dilatometry, Zircaloy-4

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The thermo-mechanical properties of materials are strongly related to their microstructure. Subsequently, the study of the allotropic phase transition has been of great interest for structural materials, especially the ones used at high temperatures [START_REF] García De Andrés | Application of dilatometric analysis to the study of solid-solid phase trans-515 formations in steels[END_REF][START_REF] Elmer | Phase transformation dynamics during welding of Ti-6Al-4V[END_REF]. Many previous researchers have shown the impact of the thermal kinetic on the phase transition of materials. However, due to experimental difficulties, few studies were devoted to the analysis of the material phase transition under high heating rates, the great majority focusing on low heating rates or high cooling rates [START_REF] Ahmed | Phase transformations during cooling in alpha + beta titanium alloys[END_REF][START_REF] Nurveren | Evolution of transformation characteristics with heating / cooling rate in NiTi shape memory alloys[END_REF]. This present work aims at introducing some new results about the phase transition of the Zircaloy-4 alloy upon very high heating rates.

Zircaloy-4 is widely used in Pressurized Water Reactor (PWR) as fuel cladding material. Improving the validity range of its thermo-mechanical behavior is an important challenge in the nuclear safety domain. This is especially true in accidental situations, where the loading conditions can be very intense. The Loss Of Coolant Accident (LOCA) and the Reactivity Initiated Accident (RIA) are the two design basis accidents studied for PWR. Heating rates below 100 • C/s are expected on the claddings during a LOCA. It can exceed 1000 • C/s during the post-Departure from Nucleate Boiling (DNB) phase of a RIA [START_REF] Bessiron | Modelling of clad-to-coolant heat transfer for RIA applications[END_REF]. In both accidents the temperature of the cladding can reach upwards of 1000 • C.

Zircaloy-4 presents an allotropic phase transformation (a ! b) between 800 • C and 1000 • C upon heating at equilibrium. Its crystallographic structure transforms from a hexagonal closed packed structure, below 800 • C, to a body centered cubic structure around 1000 • C [START_REF] Banerjee | Phase Transformations: Examples from Titanium and Zirconium Alloys[END_REF]. Between these two temperatures a two phases mixture is present within the material. Since the metallurgical state of the material has a strong impact on its mechanical properties [START_REF] Forgeron | Experiment and Modeling of Advanced Fuel Rod Cladding Behavior Under LOCA Conditions: Alpha-Beta Phase Trans-535 formation Kinetics and EDGAR Methodology[END_REF][START_REF] Holt | The beta to alpha phase transformation in Zircaloy-4[END_REF][START_REF] Mittemeijer | Analysis of the kinetics of phase transformations[END_REF][START_REF] Jailin | Thermo-mechanical behavior of Zircaloy-4 claddings under simulated post-DNB conditions[END_REF][START_REF] Jailin | Mechanical Behavior of As-Fabricated 550 Zircaloy-4 Claddings Under the Simulated Thermo-Mechanical Post-11 DNB Conditions of a Reactivity Initiated Accident (RIA)[END_REF] many authors have devoted their studies to the impact of the thermal kinetic on the phase transition. Forgeron et al. [START_REF] Forgeron | Experiment and Modeling of Advanced Fuel Rod Cladding Behavior Under LOCA Conditions: Alpha-Beta Phase Trans-535 formation Kinetics and EDGAR Methodology[END_REF], for instance, investigated the phase 35 transformation of Zircaloy-4 and M5 alloy in equilibrium, heating and cooling conditions. They used calorimetry and dilatometry techniques to study the effect of the thermal transient for rates up to 100 • C/s. Others methods have also been used, such as in-situ synchrotron X-ray diffraction (SXRD) or resistivity 40 tests [START_REF] Nguyen | Microstructure Changes during Fast b Cycles of Zirconium Alloys[END_REF][START_REF] Kaddour | Experimental determination of creep properties of zirconium alloys together with phase transformation[END_REF].

The general literature agrees on the point that the phase transformation is delayed toward higher temperatures as the heating rate increases. However, the phase transition of Zircaloy-4 has not been investigated for heating rates above 100 • C/s. This can 45 be explained by the difficulty of reproducing experimentally well-controlled fast thermal transients. Accurate temperature measurement is difficult at very high heating rates. The extrapolation of the existing transition models [START_REF] Forgeron | Experiment and Modeling of Advanced Fuel Rod Cladding Behavior Under LOCA Conditions: Alpha-Beta Phase Trans-535 formation Kinetics and EDGAR Methodology[END_REF][START_REF] Massih | Transformation kinetics of zirconium alloys under nonisothermal conditions[END_REF] to heating rates greater than 100 • C/s is then not straightforward.

50

In this work, dilatometry tests were carried out on as-received Zircaloy-4 claddings with heating rates up to 2000 • C/s. Special care was taken to the thermal and the kinematic measurements. The dilatometry conclusions were supported by micrographs. Finally, a phase transformation model based on the 55 kinetic equation of Leblond [START_REF] Leblond | A new kinetic model for anisothermal metallurgical transformations in steels including effect of austenite grain size[END_REF] was identified, reproducing the measurements on Zircaloy-4 samples from equilibrium to 2000 • C/s.

The first section deals with the experimental setup, the methods and the phase transition model. The experimental results

60

and the identification of the model are presented in the second section. The third section discusses the important features that have to be taken into account to perform a dilatometry test at high thermal slope. An updated model is also proposed to reproduce the phase transition under fast heating rates.

Experimental setup and methods

Specimen and device

Stress-free dilatometry experiments were performed using a GLEEBLE-3500 device [START_REF] Mondelin | Procedia Engineering Surface integrity prediction in finish turning of 15-5PH stainless steel[END_REF]. Specimens were cut from Stress Relieved Annealed (SRA) Zircaloy-4 (Zr-4) claddings (see the chemical composition in Table 1). The microstructure of the as-received material is composed of thin and elongated grains and presents a texture having the hci direction at +/-30 • from the radial direction of the tube [START_REF] Li | The effect of hydride morphology on the failure strain of stress-relieved Zircaloy-4 cladding with an outer surface pre-crack under biaxial stress states[END_REF]. The samples have an initial eccentricity of between 1 and 3% [START_REF] Campello | Identification of the steady-state creep behavior of Zircaloy-4 claddings under simulated Loss-Of-Coolant Accident conditions based on a coupled experimental/numerical approach[END_REF].

Sn

Fe O Cr C Zr 1.29 0.21 0.13 0.11 0.016 bal. Specimens were 100mm long tubes, with an external diameter of 9.5mm and a wall-thickness of 0.57mm. Custom jaws enabled heating rates up to 2800 • C/s to be reached by Joule heating, with perfect axisymmetric thermal distribution. A picture of a sample mounted on the device is given in Figure 1.

One side of the sample is fixed and the other one is free along its axial direction. The distance between the jaws is 40mm. In order to have a constant emissivity on the sample outer surface during the experiments, the specimens were pre-oxidized during two days in a furnace at 470 • C under air environment.

A uniform oxide layer of 2.5µm was thus obtained, keeping the material texture and the material state unchanged. 30mm were then sandblasted on each end of the tubular sample to have a good electric conduction with the jaws.

Tests processing

Two kinds of tests were performed to investigate the impact of the heating rate on the phase transformation. A first batch of specimens was used to study the phase transformation by dilatometry. The test procedure of these experiments is depicted in Figure 2. The sample was first heated at 400 • C. After a 10 seconds plateau, the thermal transient was applied until A second batch of specimens was used to perform metallurgical analysis by optical microscopy. Similarly to the first tests 100 the samples were first heated at 400 • C. Then, after a 10 seconds hold, the thermal transient was applied until a "quenching" temperature T q directly followed by a rapid cooling down by cutting off the power. A cooling rate of around -50 • C/s was thus obtained. An example of a temperature record obtained is given 105 in Figure 3 for a test carried out with a heating rate of 100 • C/s, until a quenching temperature of 910 • C.

The two kinds of tests were performed under primary vacuum (around 0.6mbar) to prevent the sample oxidation. This test was carried out with a heating rate of 100 • C/s till a temperature T q = 910 • C (pyrometer measurements).

Thermal measurement 110

A scheme of the device and the means of measurements is given in Figure 4.

The temperature was controlled during the tests at the center of the sample using a Metis M322 pyrometer (wavelength of l = [1.45 -1.65] µm, spot size of 2.5 mm). Radiometric must remain constant during the tests. Even under secondary vacuum (around 10 -3 mbar) a thin oxide layer develops on the sample surface at temperatures above 800 • C. On as-received material this leads to a significant change of the emissivity that distorts the pyrometer measurements. It is then convenient to pre-oxidize the samples with a thin oxide layer so that additional oxidation no longer modifies the emissivity during the tests. The samples were hence pre-oxidized with a uniform 125 oxidation layer that stabilizes the emissivity during the tests. The emissivity of the pre-oxidized samples was evaluated to be 0.955 +/-0.015 and remained unchanged during 20min at 1100 • C. The pyrometer leads to an accuracy of around 0.7% of the temperature.

130

A type K thermocouple (diameter wires of 0.18mm) was spot-welded at the center of the specimen to obtain an additional thermal measurement during the temperature plateau and identify the emissivity of the sample. Due to a eutectic point between Nickel and Zirconium around 950 • C, a thin square of Tantalum (thickness of 0.025mm) was inserted between the sample and the thermocouple.

The axial thermal profile on the sample was estimated by Near InfraRed Thermography (NIRT) [START_REF] Rotrou | Near infrared thermography with silicon FPA -Comparison to MWIR and LWIR thermography[END_REF][START_REF] Campello | Validation of a multimodal set-up for the study of zirconium alloys claddings' behaviour under simulated LOCA conditions[END_REF]. This full-field method links the digital level intensity I of an image (i.e. the gray level of each pixel) to the temperature T using a radiometric model based on Planck's law:

T = K 1 ln ✓ K 2 I + 1 ◆ . (1)
In this model, two constants, K 1 and K 2 , are identified using the pyrometer data during the thermal transient. Using a high speed camera Phantom V710 at 2000Hz, an axial thermal profile was characterized on the specimens during the transient and the plateau.

Thermal expansion measurements

The diametrical expansion was measured at the mid section of the specimen by contour detection method [START_REF] Réthoré | Curve and boundaries measurement using Bsplines and virtual images[END_REF]. One high speed camera Phantom V710 1MPx (1 px ' 23µm) recorded pictures during the tests and a 200mm macro optic (NIK AF MICRO-NIKKOR 200MM F/4 D IF-ED) was mounted on the camera. The software UFreckles [22] was used to perform the images analysis. In order to avoid problems of radiation 155 at high temperatures the sample was lighted using a blue LED ring (wavelength of l = 470nm), and a pass band filter of the same wavelength was mounted on the optic [START_REF] Grant | High-temperature strain field measurement using digital image correlation[END_REF] (cf. scheme of the setup in Figure 4). The dilatometry measurements are performed in a 3mm long portion of the tube, as presented in 160 Figure 5. This method allows a subpixel precision and leads to an accuracy on the thermal expansion less than 1µm. An optical dilatometer (KEYENCE LS-7600) was also used to obtain an additional measurement of the diametrical expansion with an accuracy of around 5µm. The length of the mea-165 surements area of the dilatometer is around 6mm. Maximal frequencies of 2000Hz and 7500Hz could be obtained for the dilatometer and the high speed camera, respectively. Both means of measurements led to comparable results but the contour detection method led to less noisy data. Therefore, contour 170 detection measurements were used to compute the phase fractions.

Phase fraction computation

The lever rule is usually used to compute the phase fraction from the dilatometry curves. The principle of the method is de-175 scribed in Figure 6. In order to get proper results the dilatometry curves are first smoothed using a Gaussian filter. The authors point out that due to its nature, the lever rule method does not enable an accurate estimation of the phase content in the boundaries of the dual phase domain (i.e. from 0 to 10% and 180 from 90 to 100% of b phase).

Kinetic model

The kinetic model of Leblond [START_REF] Leblond | A new kinetic model for anisothermal metallurgical transformations in steels including effect of austenite grain size[END_REF] is used to model the (a ! b) phase transformation. This model enables reproducing anisothermal transformations, including diffusion con- trolled transformations and martensitic transformations. The Leblond's evolution equation is given by:

d f b dt = f eq (T ) -f b t(T ) , (2)
where f eq (T ) is the fraction of b at equilibrium at the temperature T and t(T ) represents the characteristic time of transformation, i.e. at a temperature T , f b tends towards f eq (T ) in a time equal to t(T ).

It is usual and convenient to describe t(T ) by an Arrheniustype equation such as:

t(T ) = h k 0 .e -E R.T i -1 , (3)
where k 0 is a kinetic prefactor, E is an activation energy and R is the perfect gas constant. Two constants, k 0 and E, have finally to be identified. It is chosen to represent the equilibrium function f eq with the equation of Forgeron [START_REF] Forgeron | Experiment and Modeling of Advanced Fuel Rod Cladding Behavior Under LOCA Conditions: Alpha-Beta Phase Trans-535 formation Kinetics and EDGAR Methodology[END_REF] that is:

f eq (T ) = 1 -e -[C.(T -T 0 )] n , (4)
where C = 1/ (T 63.2% -T 0 ), T 63.2% is the temperature corresponding to 63.2% of b phase at equilibrium, T 0 is the temperature at the beginning of the transformation at equilibrium and n is an exponent to adjust. For Zircaloy-4:

C = 1.135 10 -2• C -1 , T 0 = 809 • C and n = 2.187.
The parameters of the model (Equation 2) are identified using the dilatometry measurements by minimizing the cost function defined such as:

er 2 (l) = [U exp -U num (l)] 2 , ( 5
)
where l is the set of parameters to identify, U exp are the raw experimental values of thermal expansion and U num are the numerical values of thermal expansion. U num is computed as:

U num = U a (T ).(1 -f b ) +U b (T ). f b , (6)
where U a and U b are the asymptotic linear trends of the measured displacement in the a and b domain, respectively.

Experimental results

Dilatometry results

Around 20 dilatometry tests were performed following the procedure described in Figure 2. The heating rates imposed varied from 50 to 2000 • C/s (see Table 2). For the experiments carried out with imposed heating rates greater than 100 • C/s, a decrease of the heating rate was observed during the phase transformation. The phase transition domain is characterized in Figure 8 by the loss of linearity in the coefficient of thermal expansion (CTE).

Identification of the model

The equilibrium (Figure 8) and the tests performed with a heating rate ranging from 50 to 500 • C/s are used to identify the model described in section 2.6. The equilibrium parameters (C, T 0 and n) are re-identified to allow some flexibility to the identification algorithm and to take into account uncertainties. Finally, five parameters are identified: C, T 0 and n of Equation 4and k 0 and E of Equation 3. The final values are given in Table 3.

C ( • C -1 ) T 0 ( • C) n ln(k 0 ) E (kJ.

Metallurgical analysis

The as-received microstructure of the samples is presented in Figure 11. The material is composed of thin and elongated grains as usually found in the literature [START_REF] Li | The effect of hydride morphology on the failure strain of stress-relieved Zircaloy-4 cladding with an outer surface pre-crack under biaxial stress states[END_REF].

Metallurgical analysis were performed after three different 260 heating transients of 50, 100 and 1200 • C/s. These experiments followed the procedure describes in Figure 3. Examples of optical micrographs are given in Figure 12.

After quenching at 910 • C the microstructure strongly differs from the one of the as-received material. For the three heat-265 ing rates, grains are small and equiaxed. It can be deduced that recrystallization occurred. It is in good agreement with the recrystallization kinetics expected from [START_REF] Hunt | Recrystallization of zircaloy-4 during transient heating[END_REF][START_REF] Chaieb | Comportement anisotherme et rupture des gaines combustibles en alliages de zirconium. Application à la situation d'accident d'insertion de réactivité (RIA)[END_REF]. Some micro a needles are precipitated within the grains for the experiment performed at 50 • C/s. Fewer a needles are observed for 270 the experiment performed at 100 • C/s. No ones are observed for the test performed at 1200 • C/s. These micro a needles are characteristic of ex-b grains at high temperature. Though a quantitative estimation of the phase fraction is not possible with these micrographs, a qualitative comparison can be done.

275

No, or few b grains were present for the experiments performed at 1200 • C/s. Some b grains must have been formed in the material for the experiments performed at 50 and 100 • C/s.

At 950 • C the grains still have the same morphology. However many micro a needles appear within many grains. It is

Analysis and discussions

If one wants to perform dilatometry tests with fast heating transients (i.e.> 50 • C/s), two important aspects have to be taken 310 into account in the test setup : the measurement of the temperature and the thermal heterogeneity on the thermal expansion measurement area.

The measurement of the temperature

The use of thermocouples to measure the temperature during 315 thermal transients may be inadequate. Systematic error has to be taken into account due to the intrusive nature of this measurement technique, especially for fast thermal transients. This systematic error is favored by high heating rates and large thermocouples wire diameter. Figure 13 shows a comparison be- It is also worthy to analyse the values of CTE obtained at different heating rates. The CTE should not be dependent of the 330 heating rate without activation of metallurgical phenomenon (i.g. phase transformation or elements dissolution) in the material. Such a dependence is observed when using thermocouples to measure fast thermal transients.

For the tests supporting the present study, the CTE in the a 335 domain is found to be equal to 9.6.10 -6 ± 0.9.10 -6• C -1 and the CTE in the b domain is found to be equal to 1.32.10 -5 ± 1.5.10 -6• C -1 (cf. Table 2). These values were found relying on the pyrometer temperature measurements. No impact of the thermal slope was observed on the CTE.

Homogeneous temperature area

The thermal measurements can usually be considered as local, if a thermocouple or a pyrometer are used. Conversely, the thermal expansion measurements are usually performed over a more or less important area (cf. Figure 5). As a consequence, the thermal expansion recorded corresponds to the average value within this area. It is then important to notice that a thermal heterogeneity in the sample may lead to significant errors in the phase fraction computation. This is because the phase transition may not occur simultaneously throughout the area where the thermal expansion measurements are performed.

It follows that the phase fraction obtained cannot be linked to the temperature measured locally.

To study the impact of a heterogeneous temperature in the thermal expansion measurements area a bar of Zircaloy-4 hav-355 ing a length L is numerically simulated. The CTE of the a and b phases are set equal to 9.6.10 -6• C -1 and 1.33.10 -5• C -1 , respectively. Forgeron's model (Equation 4) is used to simulate the phase transition. The bar is heated from room temperature to 1200 • C with a parabolic axial thermal distribution. Five lev-360 els of heterogeneity are simulated. The phase fraction is then recomputed in the whole area using the lever rule method. The results are presented in Figure 14. For thermal heterogeneity of {5, 10, 20, 50, 100} • C the maximal differences in the phase fraction measured with the reference are around {1.5, 3, 7, 18, 365 32}%, respectively. The estimation of the thermal heterogeneity in the thermal expansion measurements area, by full-field method for instance, is then necessary to avoid an averaging effect.

The thermal distribution on the samples in the dilatometry 370 tests was estimated using the NIRT method. Figure 15 shows an example of an image obtained with the associated thermal profile. A homogeneous temperature area of about 7mm was observed at the center of the sample, with an acceptable thermal heterogeneity of 5 • C. The temperature and the diametrical 375 expansion were measured in this area. The temperature variation through the section was estimated to be lower than 4 • C by finite element calculations (cf. Appendix A). It has then a small impact on the phase fraction computation (< 1.5%). putation. More details of the modelling are given in Appendix A. The calculations show that the mechanical deforma-385 tion is negligible compared to the total deformation and do not affect the phase fraction computed by the lever rule method.

Taking into account the saturation effect

The impact of the heating rate on the phase transformation kinetics appears to saturate above 500 • C/s, at least within the 390 uncertainties range of our means of measurement. Figure 16 shows the phase fraction obtained for the tests performed with heating rates varying from 500 to 2000 • C/s. These curves were computed using the lever rule method described in section 2.5. 2). The circle marks represent the function F 500 (T ).

To take into account this saturation effect a function F 500 was 395 defined to model the phase transformation kinetics for heating rate above 500 • C/s. The same shape of Equation 4 was used so that:

F 500 (T ) = 1 -e -[C 2 .(T -T 2 )] n 2 , ( 7
)
where C 2 , T 2 and n 2 can be linked to C, T 0 and n. The identified function F 500 is depicted with the circle marks in Figure 16 and 400 the three associated parameters are given in Table 4.

C 2 ( • C -1 ) T 2 ( • C) n 2 1.36.10 -2
865.4 4.18 The Equation 2 can now be updated such as:

d f b dt = 8 > > > < > > > : f eq (T ) -f b t(T ) if f b > F 500 (T )
F 500 (T ) -f b dt otherwise.

(8)

Summary and conclusions

The phase transition of Zircaloy-4 cladding was evaluated during fast thermal transients. Around 20 dilatometry tests were performed with heating rates ranging from 50 to 2000 • C/s. It is shown that special care must be taken to the thermal measurements and the thermal homogeneity in the thermal expansion measurements area. A careful use of thermocouples is recommended during "fast" thermal transients. The thermal heterogeneity must also be accurately determined in the thermal expansion measurements area to avoid an averaging effect that may distort the dilatometry curves.

The tests evidenced several facts: (i) from equilibrium to 500 • C/s the temperature at which the transformation starts shifts towards the high temperatures with increasing heating rates, (ii) above 500 • C/s the heating rate effect saturates, (iii) the temperature at which the transformation ends (around 960 • C) does not seem to be impacted by the heating rate.

A kinetic model based on Leblond's equation was identified.

A function of saturation was added and the equilibrium equation was re-identified using the equilibrium data of [START_REF] Forgeron | Experiment and Modeling of Advanced Fuel Rod Cladding Behavior Under LOCA Conditions: Alpha-Beta Phase Trans-535 formation Kinetics and EDGAR Methodology[END_REF]. This model is able to reproduce the phase transition of Zircaloy-4 claddings from equilibrium to heating rate till 2000 • C/s and probably above considering the observed saturation of kinetic aspects. Further analysis will have to be conducted in order to use this model under cooling. Experiments were carried out to perform metallurgical analysis. The micrographs confirmed that the transition in the pure b domain is expected at a temperature that is not significantly affected by the heating rate of about 960 • C. The optical micrographs showed also a high fraction of b phase at 950 • C for experiments performed at 50, 100 and 1200 • C/s. It is in good agreement with the phase fraction found in the dilatometry experiments. Furthermore, all the results of this study are in good agreement with the creep results of [START_REF] Jailin | Thermo-mechanical behavior of Zircaloy-4 claddings under simulated post-DNB conditions[END_REF] performed in post-DNB conditions.

It is worth noting that the phase transformation kinetic is influenced by the metallurgical state of the material. Nguyen [START_REF] Nguyen | Microstructure Changes during Fast b Cycles of Zirconium Alloys[END_REF] for instance, observed significantly faster phase transformation on recrystallized Zircaloy-4 than the same alloy in a stress relieved annealed metallurgical state. Additional testing is required to quantify the influence of the different parameters that may be coupled to the phase transformation (residual stress, lattice defects, initial microstructure...).

A.1. Coupled thermal-electrical calculation

The sample and the thermocouple are modelled using 8-node linear brick elements "DC3D8E". The cladding is modelled with an eccentricity of 3% [START_REF] Campello | Identification of the steady-state creep behavior of Zircaloy-4 claddings under simulated Loss-Of-Coolant Accident conditions based on a coupled experimental/numerical approach[END_REF] as schematized in Figure 17 5. These values are set to represent at the first order Zircaloy-4 and Chromel for the sam-475 ple and the thermocouple, respectively. Figure 18 presents the finite element modelling.

Property

Sample TC Specific heat (J.kg -1 .K -1 ) 375 600 Thermal conductivity (W.m -1 .K

Figure 17.b shows the circumferential thermal distribution obtained for a heating rate of 100 • C/s. The temperature variation within the section is around 4 • C. It has then an accept-480 able impact on the phase fraction computation, lower than 1.5% (cf. Figure 14).

Furthermore, the calculation enables obtaining a first order estimation of the inertia effect of the thermocouple. At 1000 • C and for a heating rate of 100 • C/s, the temperature in the vicin-485 ity of the thermocouple is 20 • C lower than the temperature obtained at the opposite side of the tube. The authors point out that the inertia effect would be more important with a more realistic representation of the welding point. set using the mean value of thermal expansion obtained during the dilatometry experiments. The phase transformation is simulated using the Equation [START_REF] Holt | The beta to alpha phase transformation in Zircaloy-4[END_REF]. Thereby, the contraction obtained during the phase transformation is modelled. The sample is heated at different heating rates using the experimental The phase fraction is computed at the end of the calculation using the lever rule method at the middle of the sample in an area 5 mm long. A difference lower than 1.5% is obtained 510 compared to the true phase content present at the middle of the sample.

Figure 1 :

 1 Figure 1: Picture of a sample mounted on the device.

Figure 2 :

 2 Figure 2: Temporal evolution of the thermal loading applied during the dilatometry tests.

Figure 3 :

 3 Figure 3: Example of a thermal response of a specimen from the second batch. This test was carried out with a heating rate of 100 • C/s till a temperature T q = 910 • C (pyrometer measurements).

Figure 4 :

 4 Figure 4: Scheme of the setup.

Figure 5 :

 5 Figure 5: (a) Picture of a sample; (b) example of an image obtained with the high speed camera. The diametrical expansion is computed between the red lines by contour detection method and between the orange lines with the optical dilatometer.

Figure 6 :

 6 Figure 6: Scheme of principle of the lever rule method. The phase fraction of b is computed such as f b = AB/AC.

215

  Exp. no. dT/dt CTE a CTE b ( • C/s) (10 -6 • C -1 ) (10

Figure 7 .Figure 8

 78 Figure 8 depicts examples of dilatometry curves obtained. Equation 4 models the equilibrium function f eq .The phase transition domain is characterized in Figure8by the loss of linearity in the coefficient of thermal expansion (CTE).

  230

Figure 7 :

 7 Figure 7: (a) Pyrometer measurements for a test carried out with a heating rate imposed at 2000 • C/s. (b) Evolution of the heating rate for several specified values. The values on the right correspond to the heating rates imposed during the tests.

Figure 8 :

 8 Figure 8: Examples of dilatometry curves. The equilibrium curves were obtained using the Equation 4. An offset along the y axis is added on the dilatometry curves for a better readability.

Figure 9

 9 Figure9compares some dilatometry curves obtained experimentally to the ones obtained with the model. The fraction of b obtained for different heating rates with the model is given in Figure10.a. The authors remind that the b fraction is not reliable between 0 and 10% and between 90 and 100%. It can be observed that for all the tests the end of transformation occurs around 960 • C. It is in good agreement with the results of[START_REF] Jailin | Thermo-mechanical behavior of Zircaloy-4 claddings under simulated post-DNB conditions[END_REF]. On the other hand the temperature at which the transformation starts increases with the heating rate. The equilibrium curve re-

  255

Figure 9 :

 9 Figure 9: Examples of dilatometry curves obtained (full lines) and results of the model (circle marks). An offset along the y axis is added on the dilatometry curves for a better readability.

320

  tween the pyrometer and a thermocouple measurements, for a test carried out with a heating rate of 100 • C/s till 1100 • C. It is observed that the values given by the thermocouple are around 25 • C lower than the pyrometer ones during the transient. The use of radiometric measurements becomes then necessary to 325 avoid such errors. The inertia effect of the thermocouple can be estimated at the first order by finite element calculations as presented in Appendix A.

Figure 10 :

 10 Figure 10: (a) Fraction of b obtained. The black dashed curve corresponds to the equilibrium of [7], the full lines correspond to the model computed with the true experimental thermal data. The heating rates correspond to the set points. (b) Evolution of the temperature at which the phase fraction of b is equal to 50% as a function of the heating rate (results of the model).

Figure 11 :

 11 Figure 11: Optical micrograph of the as-received material (polarized light, radial cut).

380 4 . 3 .Figure 12 :

 4312 Figure 12: Optical micrographs for the experiments performed at: (a) 50 • C/s, (b) 100 • C/s, (c-e) 1200 • C/s (polarized light, radial cut).

Figure 13 :

 13 Figure 13: Comparison between the pyrometer and a thermocouple (type K, Wires diameter of 0.18mm) at 100 • C/s.

Figure 14 :

 14 Figure 14: Impact of a quadratic thermal heterogeneity on the thermal expansion measurements. 5 values of thermal heterogeneity are presented for a bar of length L.

Figure 15 :

 15 Figure 15: Results obtained by NIRT (a) Example of an image obtained with the high speed camera (temperature computed by NIRT); (b) Axial thermal profile extracted from the red line.

Figure 16 :

 16 Figure 16: The full lines represents the evolution of f b for the experiments carried out with heating rates above 500 • C/s (Exp. no. D12 to D20 in Table2). The circle marks represent the function F 500 (T ).

  .a. The model is composed of 61626 elements and 6 elements are 465 used through the cladding thickness. All the degrees of freedom are prescribed at one extremity of the sample and the other one has unconstrained displacements along the axial direction. The sample is heated by Joule heating from 20 • C to 1100 • C. Several heating rates are tested from 1 to 2000 • C/s. The in-470 ternal and external radiation is modelled. The convection is neglected, assuming that the experiments take place under vacuum. The material properties used to model the sample and the thermocouple are given in Table

E = 116. 1 -

 1 59 ⇥ 10 -3 .T (K) [GPa].

500

  temperature profiles measured by Near InfraRed Thermography (cf. Figure 15.b). A temperature variation of 4 • C is imposed through the thickness. The jaws are cooled during the experience so the temperature at the extremities of the sample was set at 20 • C. The Figure 19.a shows the axisymmetric model and the Figure 19.b shows the axial thermal profile imposed to the cladding at the end of the test.

Figure 19 :

 19 Figure 19: Thermo-mechanical modelling: (a) axisymmetric model; (c) axial thermal profile imposed to the cladding at the end of the test. The experimental points are obtained by NIRT and a polynomial function is used to fit the experimental points.

Table 1 :

 1 Stress relieved annealed Zircaloy-4 composition (in wt%).

Table 2 :

 2 Dilatometry tests performed with the associated values of heating rates, and coefficients of thermal expansion (CTE).

	-6 • C -1 )

Table 3 :

 3 Identified parameters of Equations 3 and 4.

Table 4 :

 4 Parameters of the function F 500 (T ).

Table 5 :

 5 Material properties used to model the sample and the thermocouple (TC).

measurement is not intrusive but is very sensitive to the emissivity. The sample emissivity has to be known accurately and

characteristic of a high b phase content within the material at this temperature.

Acknowledgments

The authors acknowledge with thanks financial support of this work from EdF and Institut Carnot Ingénierie@Lyon.

Appendix A. Finite element modelling of the experiments

Data availability

The raw and processed data of the current study are available from the corresponding author on request.

Two modellings are performed to simulate the dilatometry experiments. A coupled thermal-electrical calculation is carried out to estimate the temperature variation through the cladding 455 thickness and the inertia effect of the thermocouple. A thermomechanical calculation is performed to assess the impact of the mechanical deformations on the phase fraction computation. Both modellings are carried out using the Abaqus commercial software.

A.2. Thermo-mechanical calculation

An axisymmetric calculation is also performed to estimate the impact of the mechanical deformations on the phase fraction computation. The model is composed of 7020 elements "CAX4R" and 10 elements are used through the cladding thickness. The coefficient of thermal expansion of the material is