domain: spi chim

text:
Thai Le Hong

Isabelle Turque

Jean-Christophe Brachet

Jérôme Crépin

Gilles André

Quentin Barres

Raphaëlle Guillou

Caroline Toffolon-Masclet

Jean-Marc Joubert

Matthieu Le Saux
email: matthieu.le_saux@ensta-bretagne.fr

Phase transformations during cooling from the β Zr phase temperature domain in several hydrogen-enriched zirconium alloys studied by in situ and ex situ neutron diffraction

Keywords: zirconium alloys, hydrogen, β Zr to α Zr phase transformation, eutectoid reaction, in situ neutron diffraction

In hypothetical accidental conditions, zirconium-based nuclear fuel claddings can absorb high hydrogen contents (up to several thousand wppm) and be exposed to high temperatures (β Zr phase temperature range) before being cooled. This paper thoroughly investigates the microstructural and microchemical evolutions that take place in such * Corresponding author.

Introduction

In pressurized water nuclear reactors, fuel cladding tubes made of zirconium-based alloys are the first barriers that ensure the retention of radioactive fission products. Their mechanical integrity is, therefore, an important issue. Under certain hypothetical accidental conditions such as loss-of-coolant accidents (LOCA), they can be exposed to steam at high temperature (HT), beyond 700°C typically, up to 1200°C, before being cooled and then quenched in water. Above a temperature depending on the chemical composition of the material and the thermal history, the low-temperature α Zr phase with a hexagonal close-packed (hcp) structure transforms into the HT β Zr phase with a bodycentered cubic (bcc) structure [START_REF] Brachet | Influence of hydrogen content on the α/β phase transformation temperatures and on the thermal-mechanical behavior of Zy-4, M4 (ZrSnFeV), and M5™ (ZrNbO) alloys during the first phase of LOCA transient[END_REF]. Under specific conditions, the cladding material can absorb a significant amount of hydrogen at HT, up to thousand weight ppm (wppm) locally [START_REF] Chung | Embrittlement Criteria for Zircaloy Fuel Cladding Applicable to Accident Situations in Light-water Reactors[END_REF][3][4] [START_REF] Nagase | Behavior of High Burn-up Fuel Cladding under LOCA Conditions[END_REF] [START_REF] Stuckert | QUENCH-LOCA program at KIT on secondary hydriding and results of the commissioning bundle test QUENCH-L0[END_REF][7] [START_REF] Brachet | Study of secondary hydriding at high temperature in zirconium based nuclear fuel cladding tubes by coupling information from neutron radiography/tomography, electron probe micro analysis, micro elastic recoil detection analysis and laser induced breakdown spectroscopy microprobe[END_REF]. Hydrogen mainly concentrates in the β Zr phase [START_REF] Brachet | Hydrogen Content, Preoxidation, and Cooling Scenario Effects on Post-Quench Microstructure and Mechanical Properties of Zircaloy-4 and M5™ Alloys in LOCA Conditions[END_REF].

During cooling, the β Zr phase transforms back into the α Zr phase and forms the so-called prior-β Zr structure [START_REF] Woo | Transformation Characteristics of Rapidly Heated and Quenched Zircaloy-4-Oxygen Alloys[END_REF]. The mechanical strength of the cladding during and after cooling mainly results from the mechanical behavior of the residual prior-β Zr layer [START_REF] Chosson | Creep flow and fracture behavior of the oxygen-enriched alpha phase in zirconium alloys[END_REF] [START_REF] Turque | Mechanical Behavior at High Temperatures of Highly Oxygen-or Hydrogen-Enriched α and Prior-β Phases of Zirconium Alloys, Zirconium in the Nuclear Industry: 18th International Symposium[END_REF]. The mechanical behavior of the (prior-)β Zr structure principally depends on its oxygen and hydrogen contents and on the structural and metallurgical evolutions that take place during cooling from HT [START_REF] Chung | Development of an Oxygen Embrittlement Criterion for Zircaloy Cladding Applicable to Loss-of-Coolant Accident Conditions in Light-Water Reactors, Zirconium in the Nuclear Industry[END_REF][10] [START_REF] Desquines | Embrittlement of Pre-Hydrided Zircaloy-4 by Steam Oxidation under Simulated LOCA Transients[END_REF]. Several studies addressed the effect of hydrogen on the metallurgical and mechanical behavior of zirconium alloys oxidized at HT. However, most of them focused on hydrogen contents lower than 1000 wppm. For example, it was shown that the higher the hydrogen content below 1000 wppm, the lower the temperature range over which the β Zr to α Zr phase transformation takes place [START_REF] Brachet | Influence of hydrogen content on the α/β phase transformation temperatures and on the thermal-mechanical behavior of Zy-4, M4 (ZrSnFeV), and M5™ (ZrNbO) alloys during the first phase of LOCA transient[END_REF] [START_REF] Guilbert-Banti | Influence of hydrogen on the oxygen solubility in Zircaloy-4[END_REF] and the lower the material ductility at low temperature [START_REF] Brachet | Hydrogen Content, Preoxidation, and Cooling Scenario Effects on Post-Quench Microstructure and Mechanical Properties of Zircaloy-4 and M5™ Alloys in LOCA Conditions[END_REF]. Data for materials with higher hydrogen contents and cooled from HT are scarce and often limited to room temperature (RT) [START_REF] Pshenichnikov | Microstructure and mechanical properties of Zircaloy-4 cladding hydrogenated at temperatures typical for loss-of-coolant accident (LOCA) conditions[END_REF] [START_REF] Pshenichnikov | Hydride precipitation, fracture and plasticity mechanisms in pure zirconium and Zircaloy-4 at temperatures typical for the postulated loss-of-coolant accident[END_REF]. Recent results have nonetheless shown that the mechanical behavior of the (prior-)β Zr material is affected by high hydrogen contents up to approximately 3000 wppm in ways that strongly depend on temperature between 20°C and 700°C [START_REF] Turque | Mechanical Behavior at High Temperatures of Highly Oxygen-or Hydrogen-Enriched α and Prior-β Phases of Zirconium Alloys, Zirconium in the Nuclear Industry: 18th International Symposium[END_REF]. In order to interpret such results, it is necessary to have a good knowledge of the microstructural and microchemical evolutions that take place during cooling from HT. These evolutions for such high hydrogen contents are undoubtedly quite different from those observed for lower hydrogen contents due particularly to a eutectoid reaction expected to occur around 550°C according to the zirconium-hydrogen binary phase diagram [START_REF] Zuzek | Hydrogen-Zirconium)[END_REF].

This study aims to improve both experimental database and understanding of the effects of high hydrogen contents, up to 3000 wppm (20 atomic %, at%), on the metallurgical evolutions occurring in zirconium-based alloys during cooling from HT (β Zr phase domain). The effects of the alloy, the average hydrogen content, and the cooling scenario are investigated. X-ray and neutron diffraction analyses were carried out at RT after cooling by applying different scenarios, or in situ upon step-cooling from 700°C, on Zircaloy-4 and M5 Framatome cladding samples containing 320, 1100-1500 or 3300 wppm of hydrogen. The materials and the experimental procedures used in this study are described in Section 2. The results are presented in Section 3 and then discussed in Section 4. They are compared to thermodynamic predictions at equilibrium obtained using the Thermo-Calc® software together with the Zircobase database [START_REF] Dupin | A Thermo-dynamic Database for Zirconium Alloys[END_REF] [START_REF] Lafaye | Experimental investigations and thermodynamic modelling of the Cr-Nb-Sn-Zr system[END_REF], taking into account all the chemical elements constituting the material (Zr, Nb, Sn, Fe, Cr, H and O). It must be mentioned that, so far, these thermodynamic predictions had not been experimentally validated on multicomponent (multi-alloyed) systems for the highest hydrogen contents studied here.

Materials

Zircaloy-4 and M5 Framatome cladding tubes

Most specimens were prepared from stress-relieved annealed low tin Zircaloy-4 and fully recrystallized M5 Framatome (M5) cladding tube samples, with an outer diameter and a thickness of 9.5 mm and 0.57 mm, respectively. These materials initially contain 0.13-0.14 weight % (wt%) of oxygen and less than 5 wppm of hydrogen. Their nominal chemical compositions are given in wt% in Table 1. In order to investigate the effect of hydrogen, the samples were homogeneously charged with hydrogen at approximately 320, 1100-1500, and 3300 wppm. Hydrogen charging was performed in an argon/hydrogen gas mixture at 400°C to obtain ~300 wppm of hydrogen and, as already done in [START_REF] Turque | Mechanical Behavior at High Temperatures of Highly Oxygen-or Hydrogen-Enriched α and Prior-β Phases of Zirconium Alloys, Zirconium in the Nuclear Industry: 18th International Symposium[END_REF], at 800°C to reach 1100-1500 wppm or 3300 wppm of hydrogen. The samples were then cooled down to RT at a few °C/min. Hydrogen content measurements were performed using an inert gas fusion thermal conductivity technique (HORIBA EMGA-821 analyzer) on three to seven 2 mm-long ring samples extracted at different locations from the hydrogen-charged cladding samples, in order to check axial homogeneity of hydrogen. For each sample, measurements were conducted on thirds of the ring samples to verify azimuthal homogeneity of hydrogen. Homogeneity of hydrogen is satisfactory: the variation of hydrogen content along the ~66 mm-long cladding tube samples is typically from a few to a few tens of wppm. Infrared absorption analyses (LECO TC500 analyzer) showed slight oxygen uptake (approximately 0.07 wt%) after hydrogen charging at 800°C, so the samples with 3300 wppm of hydrogen contain approximately 0.2 wt% of oxygen on average.

In order to characterize the properties of the transformed β Zr phase, the samples charged with hydrogen were then heat-treated for a few tens of seconds at about 1000°C in flowing steam. The protective thin oxide layer that grew at the sample surfaces during these heat-treatments allows preventing hydrogen desorption throughout the in situ neutron diffraction experiments performed under secondary vacuum at HT and presented below. The total thickness of oxide layer formed during these heat treatments is less than 10 µm. A zone enriched in oxygen with a total thickness of approximately 15 µm was observed beneath the oxide layer. This oxygen-enriched zone represents less than 2% of the whole volume of sample analyzed by neutron diffraction, so it is not expected to have a significant effect on the results. Furthermore, the oxide and oxygenenriched layers were removed from the samples before being analyzed by X-ray diffraction (XRD), since the analysis depth is limited to a few microns in this case. As shown in Section 3, the results obtained at room temperature by neutron diffraction and XRD were consistent. This confirms that the oxygen-enriched layer has no significant impact on the lattice parameters of the α Zr phase.

With the aim of studying the potential effects of the cooling scenario on the metallurgical evolutions occurring during cooling, several cooling scenarios were applied: direct quenching from 1000°C in water down to RT, slow cooling (0.1-0.4°C/s between 1000 and 500°C, and less than 0.1°C/s below) down to RT or water quenching from 600 or 700°C after cooling at about 0.4-1°C/s from 1000°C. Fig. 1 shows examples of microstructures obtained after cooling. Hydrogen content in the samples was measured after these treatments using HORIBA EMGA-821 analyzer to check the absence of significant desorption or absorption of hydrogen (the oxide layers were not removed before hydrogen analysis). at 3300 wppm step-cooled at 0.01°C/s on average from 700°C (after a prior water quenching from 1000°C).

Unalloyed Zr sheet samples

In order to isolate the effects of hydrogen and get rid of the effect of oxygen, several experiments were also performed on 1.2 mm-thick sheet samples of unalloyed zirconium refined using the Van Arkel method (ZrVA), containing only 0.01 wt% of oxygen. 24x14 mm 2 samples without additional hydrogen were heat-treated for a few tens of seconds in flowing steam at 1000°C then directly quenched in water at RT.

Hydrogen measurements using the HORIBA EMGA-821 analyzer have shown that the samples absorbed approximately 50 wppm of hydrogen during these treatments.

Other samples with the same dimensions were charged with hydrogen at approximately 3100 wppm under pure hydrogen (99.999 vol%) at 500°C. A strong gradient of hydrogen concentration was observed after this step. A homogenization heat treatment under argon (99.995 vol%) at 800°C was thus applied. It made it possible to limit hydrogen content variations within the samples to only a few tens of wppm for the average hydrogen content of approximately 3100 wppm. Finally, these samples were heat-treated at 850°C (after being encapsulated under argon to avoid oxygen uptake during heat treatment) in order to reach 100% of β Zr , then directly water quenched from 850°C or slowly cooled at an average rate of about 0.3°C/s down to 600°C before being water quenched. According to infrared absorption analyses (LECO TC500 analyzer), the ZrVA samples contain about 0.02-0.04 wt% of oxygen after these treatments.

Neutron diffraction

Metallurgical evolutions of the materials with temperature during cooling were investigated using neutron diffraction analyses. The neutron diffraction experiments were performed, without further sample preparation, on 50 mm-long Zircaloy-4 and M5 tube samples previously charged with hydrogen and heat-treated at about 1000°C. The analyses were carried out under secondary vacuum at the Léon Brillouin Laboratory (LLB, CEA, CNRS, Université Paris-Saclay, France) on the G4-1 beamline, with a monochromatic thermal neutron radiation and a neutron wavelength of 2.422 Å. A linear multi-detector with 800 cells and a pyrolytic graphite monochromator were used for collection of data in the 2θ range of 12-92° with a step-size of 0.1°, where θ is the Bragg's angle. The neutron beam was perpendicular to the tube axis. The experimental conditions allow neutrons to penetrate the whole volume of the 50 mm-long tube sample.

All the samples mentioned in Section 2.1 were analyzed at RT in order to study the effects of the alloy, the hydrogen content, and the cooling scenario on the final structure and microstructure. The samples containing 3300 wppm of hydrogen were then analyzed in situ during step-cooling from 700°C. The sample holder was made of cadmium for in situ experiments and in vanadium for experiments performed at RT.

The samples were heated at about 1°C/s up to 700°C using a furnace, then held 1h30 at this temperature and finally step-cooled down to RT. The temperature during the experiments was monitored via one thermocouple placed on the sample holder. The temperature gradient in the furnace is expected to be lower than 30°C. An average uncertainty of about ±15°C on the sample temperature is expected for temperatures above 350°C. Upon cooling, successive isothermal steps were applied, with smaller temperature steps around the expected eutectoid transition: 700, 600, 550, 540, 520, 500, 480, 350, 135, and 40°C. 2h-long steps and data acquisitions were carried out at the different temperatures, except at 700°C and 600°C for which the analyses were limited to 1h30 in order to limit the potential desorption of hydrogen as well as the diffusion of oxygen from the thin zirconia layer to the underlying metal layer at these temperatures. The cooling rate between each step was between 0.25 and 0.03°C/s, leading to a slow average cooling rate of about 0.01°C/s from 700°C to RT. Therefore, the materials could be considered to be close to their thermodynamic equilibrium conditions during the analyses.

It has been observed that the intensity of the continuous background originating from incoherent scattering tends to increase with increasing the average hydrogen content in the sample. No significant evolution of this intensity was observed during the experiments, which suggests that the hydrogen content in the samples did not evolve significantly. The absence of hydrogen desorption was also checked by measuring the hydrogen content after the experiments using the HORIBA EMGA-821 analyzer.

X-ray diffraction

The influence of hydrogen content on the lattice parameters of α Zr after cooling from the β Zr temperature domain was then investigated using XRD performed at RT on the samples previously analyzed by neutron diffraction. For this purpose, 20 mm-long tube samples were taken from the 50 mm-long Zircaloy-4 and M5 tube samples. In addition, XRD experiments were also conducted at RT on 10x10 mm 2 ZrVA sheet samples containing low oxygen content, with the aim of isolating the effect of hydrogen. In a second step, XRD analyses were carried out on some of these same samples after annealing them for 24h at 500°C in order to relax the potential residual stresses and dissolve some of the hydrides before cooling from the α Zr domain rather than from the β Zr domain. Before analysis, the samples were mounted and polished by mechanical polishing, followed by chemical etching to remove a thickness of about 100-150 µm at the sample surface, including the ZrO 2 and oxygen-enriched layers formed during heat treatment in steam and the thickness potentially strain-hardened due to polishing.

The XRD experiments were performed in Bragg-Brentano θ-θ geometry on a Bruker D8

Advance diffractometer equipped with a Lynxeye linear detector (3° opening). A monochromatic Cu Kα1 radiation with a wavelength of 1.540598 Å was employed. 6slong measurements were performed every 0.02° within the 2θ range of 25-140°. Several analyses were also conducted on a PANalytical X'Pert Pro diffractometer using an X'Celerator linear detector (2.122° opening) and a cobalt anticathode with a wavelength of 1.78897 Å. 10s-long measurements were applied with an analysis step of 0.02° within the 2θ range of 10-153°.

Electron probe microanalysis and micro elastic recoil detection analysis

Electron probe microanalyses (EPMA) were performed using a CAMECA SX100 electron microprobe on selected samples after diffraction analyses to map the main chemical elements including oxygen. Information on the EPMA measurements setup and procedure used in this study can be found in [START_REF] Brachet | Hydrogen Content, Preoxidation, and Cooling Scenario Effects on Post-Quench Microstructure and Mechanical Properties of Zircaloy-4 and M5™ Alloys in LOCA Conditions[END_REF]. In addition, micro elastic recoil detection analyses (µ-ERDA) were carried out using a nuclear microprobe at the Laboratory for Light Element Studies (LEEL, CEA, France) to quantitatively map hydrogen distribution at the microscale [9][22].

Results

Evolutions with temperature during slow cooling

The results obtained by neutron diffraction experiments on metallurgical evolutions occurring during slow cooling are presented below. They are then compared with the thermodynamic predictions at equilibrium obtained using Thermo-Calc and the Zircobase database [20][21]. The comparison will be further discussed in Section 4. Peaks related to monoclinic zirconia m ZrO2 (P2 1 /c space group) [START_REF] Gosset | In-situ X-ray diffraction analysis of zirconia layer formed on zirconium alloys oxidized at high temperature[END_REF] have been observed. As mentioned previously in Section 2.1, the oxide layer was formed during the heat treatment performed in steam at 1000°C before diffraction analysis.

Types of phases

As shown in Fig. 2, between 700°C and 540°C for Zircaloy-4 or between 700°C and 520°C for M5, only peaks corresponding to the two phases, α Zr (P6 3 /mmc space group) and β Zr ( space group), are observed. During cooling, the intensity of α Zr peaks increases continuously while that of β Zr peaks decreases. This observation highlights the progressive transformation of β Zr into pro-eutectoid α Zr . The decrease in the intensity of the peak at 2θ = 55.6° does not reveal a decrease in the intensity of the peak corresponding to the (0002) plane of the α Zr phase, which would be an indication of a strong evolution of the texture of the α Zr phase. Actually, this (0002) peak of α Zr is convoluted to the (110) peak of the β Zr phase when the last one exists. Thus, the decrease in the intensity of the peak at 55.6° during cooling above the eutectoid reaction temperatures is considered to be mainly due to a decrease in the intensity of the (110) peak of β Zr as the result of the β Zr → α Zr phase transformation upon cooling. Indeed, the (110) peak of the β Zr phase is expected to be the most intense one of this phase from 700°C down to the temperature corresponding to the end of the eutectoid reaction.

According to the reference diffraction data of zirconium, the (0002) peak of α Zr should not be the most intense one of this phase (which may be the peak at 2θ = 58.6°).

Thus, the intensity of the (0002) peak of α Zr is supposed to increase continuously during cooling from 700°C, like the other peaks of this phase, such as , , and

. At 500°C for Zircaloy-4, no peak corresponding to the β Zr phase is observed anymore. results show that the three phases α Zr , β Zr and δ ZrH2-x coexist within a temperature range of a few tens of degree: ]540°C; 500°C[ for Zircaloy-4 and ]520°C; 480°C[ for M5.

Beyond the ±15°C uncertainty on the temperatures considered, an effect of the potential temperature gradient on the width of the temperature range over which the eutectoid transformation takes place cannot be excluded.

The evolution of the phases below 500°C for Zircaloy-4 and 480°C for M5 is illustrated in Fig. 3. In the case of M5, the diffraction diagram highlights the presence of a peak corresponding to the β Zr phase enriched in Nb between the two peaks of α Zr and . As will be discussed in Section 4, hydrogen may also contribute to the stabilization of this phase at low temperature. This metastable β Zr phase existing below the eutectoid reaction temperatures is denoted β Zr * (Nb, H) in the following so that it can be differentiated from the equilibrium β Zr phase (also enriched in both Nb and H) that only exists above the eutectoid reaction.

It can be seen that during cooling, at temperatures below 500°C for Zircaloy-4 and 480°C for M5, the intensity of δ ZrH2-x peaks continues to increase slightly, due to the decrease of the solubility limit of hydrogen in the α Zr phase and thus the additional precipitation of hydrides. Below 350°C, face-centered tetragonal (fct) γ ZrH hydrides (P4 2 /n space group) are detected in both materials. No peak corresponding to the bodycentered tetragonal ε hydrides [START_REF] Perovic | Hydride precipitation in α/β zirconium alloys[END_REF] or the hexagonal close-packed ζ hydrides [START_REF] Zhao | Blat-Yrieix, Identification and characterization of a new zirconium hydride[END_REF] is observed. β Zr * (Nb, H) γ ZrH calculations, is not observed on the diffraction diagrams obtained for M5. However, its predicted quantity (0.6 mol%) in equilibrium conditions is likely below the detection limit.

Fractions of phases

The fraction of the phases previously described has been quantitatively determined using the Rietveld refinement method [START_REF] Rietveld | A profile refinement method for nuclear and magnetic structures[END_REF] and the Fullprof software. The peaks corresponding to the sample holder have been excluded from the analysis. The refinements did not show the need to explicitly take into account the: -potential internal stresses (which could be induced by the volume changes associated with the nucleation and growth of the different phases, and by the differences in thermal expansions of these phases), -microchemical heterogeneities due to solute-element partitioning during the β Zr to α Zr phase transformation, -slight evolution with temperature of the stoichiometry of δ ZrH2-x hydrides, -potential effect of hydride morphology (needles, platelets, …), -hydrogen potentially trapped into the β Zr * (Nb, H) phase stabilized at low temperature in M5,

The α Zr (prior-β Zr ) phase resulting from the β Zr → α Zr transformation upon cooling shows a smooth "fiber" crystallographic texture [START_REF] Salcedo | après oxydation à haute température, des gaines de combustible des réacteurs à eau pressurisée[END_REF]. This is confirmed by the value of the March-Dollase preferred orientation parameter [START_REF] Dollase | Correction of intensities for preferred orientation in powder diffractometry: application of the March model[END_REF] obtained from the Rietveld analysis, which is slightly higher than 1.

In order to evaluate the potential effects of the texture of the α Zr phase on the phase fractions, Rietveld refinements have been performed by considering different preferred orientations for the α Zr phase: (100), ( 002), (101), and a combination of the three orientations. The results were not significantly different from those obtained considering an isotropic texture of the α Zr phase: the relative difference in the phase fractions is lower than 5%. Thus, in the following, considering the other sources of uncertainty, it was not necessary to explicitly take into account the texture of this phase.

The stoichiometry of δ ZrH2-x hydrides was fixed at , corresponding to the value at RT determined by thermodynamic calculations. γ ZrH hydrides were considered to be stoichiometric. The atomic fraction of Nb in the β Zr * (Nb, H) phase was fixed at 20 at% (equivalent to about 21 wt%). This fraction corresponds to the maximum amount of Nb in β Zr in equilibrium conditions at the monotectoid transition temperature derived from the Zr-Nb phase diagram.

The results in Fig. 4 indicate a good agreement between the calculated and the experimental patterns. This shows that the simplifications made for the quantitative analyses are fully justified.

Fig. 5 shows the fractions of the different phases determined as a function of temperature, for Zircaloy-4 and M5 containing about 3300 wppm of hydrogen. At 700°C, zirconium is mainly in its β Zr phase. The quantitative analyses indicate a small amount of monoclinic zirconia, approximately 1 wt%, detected at all temperatures, which is consistent with the oxide thickness formed during the heat treatment in steam at 1000°C applied to the samples before diffraction analyses.

The results show that the temperature at which the β Zr phase has fully transformed (into predicted by these calculations was taken into account for the estimation of the hydrogen content in solid solution. γ ZrH hydrides were considered to be stoichiometric.

α
Fig. 6 shows that hydrogen is entirely in solid solution at high temperature. In a few tens of °C after hydrides start to precipitate, the fraction of hydrogen in solid solution drops sharply, down to a content lower than 500 wppm. The hydrogen content in solid solution decreases gradually during cooling due to the precipitation of hydrides, down to a few tens of wppm at RT. Fig. 8 shows that, for both materials, the lattice parameter of the bcc β Zr phase increases continuously during cooling from 700°C until the end of the eutectoid transformation.

Lattice parameters

This particular evolution is discussed further below. Cizeron [START_REF] Couterne | Détermination des coefficients principaux d'expansion thermique du Zr α[END_REF] and Goldak et al. [START_REF] Goldak | Lattice Parameters, Thermal Expansions, and Grüneisen Coefficients of Zirconium, 4.2 to 1130[END_REF] for pure zirconium with almost no hydrogen.

As shown in Fig. 9, in M5, the lattice parameter of the metastable β Zr phase enriched in Nb decreases linearly with the decrease of temperature between 350 and 40°C. The average linear expansion coefficient of this phase between 40 and 350°C determined from these data is equal to 1.08•10 -5 K -1 . nevertheless, significantly smaller than that presented in [START_REF] Yamanaka | Thermal and mechanical properties of zirconium hydride[END_REF] but in good agreement with those reported in [START_REF] Maimaitiyili | The preparation of Zr-deuteride and phase stability studies of the Zr-D system[END_REF] for deuterium-charged zirconium.

The results obtained using neutron diffraction indicate that the lattice parameters of the fct γ ZrH hydrides do not change significantly during cooling below 350°C; they remain constant and equal to a = 4.653±0.001 Å and c = 4.847±0.005 Å. and M5 containing about 3300 wppm of hydrogen (and 0.2 wt% of oxygen) water quenched from 1000°C; comparison to results from Yamanaka et al. [START_REF] Yamanaka | Thermal and mechanical properties of zirconium hydride[END_REF] and Maimaitiyili et al. [START_REF] Maimaitiyili | The preparation of Zr-deuteride and phase stability studies of the Zr-D system[END_REF].

Distribution of hydrogen and oxygen after cooling

Hydrogen maps obtained by μ-ERDA after the in situ neutron diffraction experiments show the presence of zones enriched in hydrogen, with a content up to 6000 wppm on average (about 36 at%), surrounded by hydrogen depleted zones, with a hydrogen content of about 400 wppm on average (4 at%). Comparison with oxygen maps obtained by EPMA shows that the zones depleted in hydrogen are enriched in oxygen,

Evolutions at RT as a function of hydrogen content and cooling scenario

The results presented above made it possible to quantitatively determine the phase transformations that occur during slow cooling (0.01°C/s on average), i.e. under nearequilibrium conditions, from the β Zr phase domain of Zircaloy-4 and M5 containing about 3300 wppm of hydrogen. The effects of the alloy, the hydrogen content, and the cooling scenario on these transformations have also been investigated. For that purpose, in a first step, X-ray and neutron diffraction analyses were performed at RT on:

-Zircaloy-4 and M5 cladding tube samples, as-received or charged with 320, 1100-1500 or 3300 wppm of hydrogen, step-cooled at 0.01°C/s on average from 700°C after water quenching from 1000°C, directly water quenched from 1000°C, or cooled at 0.4-1°C/s from 1000°C down to 600°C then water quenched;

-ZrVA sheet samples, as-received and directly water quenched from 1000°C, or charged with 3100 wppm of hydrogen and heat-treated at 850°C then directly water quenched or quenched from 600°C after cooling at about 0.3°C/s on average.

In a second step, the Zircaloy-4 sample with 3300 wppm of hydrogen step-cooled from 700°C and the ZrVA samples were annealed at 500°C for 24h and then slowly cooled at an average rate of 0.1°C/s down to RT. The samples were then analyzed by XRD at RT. At 500°C, zirconium is entirely in its α Zr phase. The objective was to be closer to the equilibrium hydrides fraction at 500°C.

Preprint submitted to Acta Materialia 29

Types and fractions of phases

Fig. 12 shows neutron diffraction patterns obtained at RT on Zircaloy-4 and M5 containing 320 wppm of hydrogen having undergone direct quenching from 1000°C or quenching from 600°C after cooling at 0.4-1°C/s from 1000°C. On the one hand, no peak related to δ ZrH2-x hydrides is detected after direct quenching. Only peaks corresponding to γ ZrH hydrides are observed, for both materials. On the other hand, after slow cooling from 1000°C down to 600°C then quenching, hydrides are mostly in the δ ZrH2-x phase; only a small amount of γ ZrH is observed.

The fractions of δ ZrH2-x , γ ZrH hydrides, and β Zr * (Nb, H) at RT are shown in Fig. 13 for the different hydrogen contents and cooling scenarios tested for both alloys. The ratio between the fractions of δ ZrH2-x hydrides and γ ZrH hydrides determined after direct water quenching increases with increasing the average hydrogen content. This ratio is higher for M5 than for Zircaloy-4. The faster the cooling, the higher the fraction of γ ZrH hydrides. It reaches about 15 mol% in the material containing 3300 wppm of hydrogen directly quenched from 1000°C. However, in the case of Zircaloy-4 with 3300 wppm of hydrogen, there is no significant difference in the fractions of the hydrides after direct quenching from 1000°C and quenching from 600°C after cooling at 0.4-1°C/s. As shown in Fig. 15, the same observation can be made for ZrVA containing about 3100 wppm of hydrogen: the fractions of the hydrides are in the same order of magnitude after direct quenching from 850°C and after quenching from 600°C after slow cooling from 850°C. Fig. 14 shows the amount of hydrogen remaining in solid solution in the α Zr phase estimated from the total hydrogen content in the material measured using an analyzer and the quantity of hydrogen in hydrides derived from their fraction determined by neutron diffraction. It can be seen that a significant fraction of hydrogen remains in solid solution after direct water quenching from 1000°C. In the case of the materials containing 320 or 1100-1500 wppm of hydrogen, the precipitation of hydrides is promoted by cooling at 0.4-1°C/s down to 600°C before quenching, compared to direct quenching. In the case of Zircaloy-4 containing 3300 wppm of hydrogen, the hydrogen content remaining in solid solution is not significantly modified by cooling at 0.4-1°C/s down to 600°C before quenching (no diffraction analysis was performed on M5 with the same hydrogen content heat-treated in this condition). However, after step-cooling from 700°C after quenching from 1000°C, almost all hydrogen is precipitated as hydrides (mostly in the form of the δ ZrH2-x phase) at RT; only a small fraction of hydrogen, a few tens of wppm, remains in solid solution after this cooling scenario, which is likely much closer to equilibrium conditions. Fig. 14 indicates that the amount of hydrogen in solid solution at RT after cooling increases with the average hydrogen content for the materials having undergone the same cooling scenario (direct water quenching from 1000°C or water quenching from 600°C). It can reach 850-890 wppm for an average hydrogen content of 3300 wppm. The results suggest that the ratio between the hydrogen content in solid solution and the average hydrogen content decreases with the increase of the average hydrogen content. water quenching from 600°C after cooling at 0.4-1°C/s from 1000°C (Q600), step-cooling at 0.01°C/s on average from 700°C after water quenching from 1000°C (slow). direct water quenching from 1000°C (DQ), water quenching from 600°C after cooling at 0.4-1°C/s from 1000°C (Q600), step-cooling at 0.01°C/s on average from 700°C after water quenching from 1000°C (slow). XRD patterns recorded at RT on ZrVA containing about 3100 wppm of hydrogen subjected to various cooling scenarios: direct water quenching from 850°C, direct water quenching from 850°C followed by a heat treatment for 24h at 500°C, or quenching from 600°C after cooling at about 0.3°C/s on average from 850°C.

The Zircaloy-4 sample with 3300 wppm of hydrogen step-cooled from 700°C and the ZrVA samples with 3100 wppm of hydrogen directly quenched from 850°C or quenched from 600°C were annealed at 500°C for 24h then slowly cooled down to RT.

On the one hand, this heat treatment does not significantly modify hydrides' fractions in the case of Zircaloy-4, probably because of a very small hydrogen amount remaining in solid solution after the slow cooling from 700°C. On the other hand, in the case of ZrVA, the heat treatment at 500°C leads to a significant increase in the fraction of γ ZrH hydrides, while the fraction of δ ZrH2-x is not modified. In this case, a significant amount of hydrogen may have remained in solid solution in the α Zr phase after quenching. This hydrogen is thus likely to precipitate in the form of γ ZrH hydrides during the slow cooling from 500°C (i.e. upon the second thermal treatment applied). (Nb, H) phase retained at RT is higher by about 0.4-0.6 mol% after direct quenching from 1000°C than after slow cooling (down to 600°C before quenching or step-cooling from 700°C), regardless of the average hydrogen content.

Lattice parameters

Fig. 16 shows the evolution of the lattice parameters a and c of α Zr deduced from XRD and/or neutron diffraction analyses carried out at RT as a function of the average hydrogen content for Zircaloy-4, M5, and ZrVA subjected to various cooling scenarios.

The lattice parameters' values derived from neutron diffraction and XRD data are consistent. The results in Fig. 16 show that, on the one hand, the parameter a does not significantly depend on the cooling scenario and tends to increase slightly with the average hydrogen content for the three materials tested. On the other hand, the parameter c increases considerably with the average hydrogen content, in particular for Zircaloy-4 and M5. The value of the parameter c is slightly higher after direct quenching from 1000°C (in the case of Zircaloy-4) or 850°C (in the case of ZrVA) than after quenching from 600°C after slow cooling or step-cooling from 700°C. The evolution of the lattice parameters with the average hydrogen content is smaller after slow cooling down to 600°C followed by water quenching than after direct quenching.

In the case of Zircaloy-4 containing 3300 wppm of hydrogen step-cooled from 700°C, the lattice parameters of α Zr at RT are not significantly changed after a heat treatment for 24h at 500°C followed by a slow cooling at about 0.1°C/s down to RT. However, in the case of ZrVA containing 3100 wppm of hydrogen directly quenched from 850°C, the lattice parameters of α Zr are significantly decreased after this heat treatment, and they approach those measured on the hydrogen-free sample.

Discussion

Comparison of experimental results and thermodynamic predictions

Fig. 5 compares the fractions of phases determined by neutron diffraction upon stepcooling (0.01°C/s on average) from 700°C and those predicted by the thermodynamic calculations at equilibrium, for Zircaloy-4 and M5 containing 3300 wppm of hydrogen (and 0.2 wt% of oxygen). It is shown that the experimental data are in good agreement with the thermodynamic predictions, for the equilibrium phases in particular, i.e. α Zr , β Zr , and δ ZrH2-x (Fig. 5). The largest difference between thermodynamic predictions and experimental data is observed for M5 at 700°C. It is important to recall that these calculations had not been experimentally validated for such high hydrogen contents so far. The γ ZrH hydride phase, potentially metastable, was not taken into account in the thermodynamic calculations at equilibrium. The temperatures at which the eutectoid reaction occurs, according to the neutron diffraction data, are lower by about 20-30°C compared to those predicted by equilibrium calculations. Furthermore, the temperature ranges over which this reaction takes place, according to neutron diffraction, are wider by about 35°C. This makes sense because of a hysteresis effect during cooling relative to the equilibrium temperatures. This difference would probably be more significant for faster cooling due to dynamic effects.

Microchemical evolutions during cooling

As presented in Section 3.1.4, the materials show microchemical heterogeneities after cooling. As developed hereafter, the zones less rich in hydrogen and richer in oxygen must correspond to those firstly transformed into pro-eutectoid α Zr during cooling, preferentially at the former β Zr grain boundaries. The zones very rich in hydrogen and less rich in oxygen should correspond to the residual zones of β Zr that were not transformed when reaching the eutectoid reaction temperature.

These micro-chemical heterogeneities result from the partitioning of the chemical elements during the phase transformation of zirconium during cooling. Above the eutectoid transition temperature, hydrogen is distributed between α Zr zones and β Zr zones. These zones evolve during the on-cooling pro-eutectoid β Zr to α Zr phase transformation. Fig. 17 shows the evolutions, with temperature, of the hydrogen and the oxygen contents in solid solution in the α Zr and β Zr phases predicted by thermodynamic calculations at equilibrium for Zircaloy-4 containing 3300 wppm of hydrogen. The tendencies are similar for M5. The oxygen content in solid solution is higher in the α Zr phase than in the β Zr phase as a result of the α Zr -stabilizing effect of oxygen. During cooling from 700°C down to the eutectoid transition temperature, the oxygen content in solid solution decreases in both the pro-eutectoid α Zr phase and the β Zr phase, due to the β Zr to α Zr phase transformation (increase of the fraction of the α Zr phase) and the α Zrstabilizing effect of oxygen (enrichment and depletion of oxygen in the α Zr phase and the β Zr phase respectively). During cooling above the eutectoid transition temperature, the hydrogen content in solid solution increases in both the α Zr phase and the β Zr phase.

However, the hydrogen content is much higher in the β Zr phase where it can reach approximately 5300 wppm as against about 400 wppm in the pro-eutectoid α Zr phase.

These contents are in good agreement with those determined by μ-ERDA (Fig. 11) in the presumed prior-β Zr zones transformed during the eutectoid reaction and proeutectoid α Zr zones.

In the following discussion, the potential effects of internal stresses are not considered, as these stresses have not been measured. Beyond their direct effect on the lattice parameters, these stresses may play an indirect role via a potential effect on the chemical partitioning during the on-cooling phase transformation. However, if it exists, this effect of stresses on chemical partitioning does not seem to be significant, since the chemical compositions measured after cooling by EPMA and µ-ERDA are close to the thermodynamic predictions at equilibrium without taking into account stress effects.

β Zr phase

The evolution of the lattice parameter of the β Zr phase has been determined between 700°C and 520 or 480°C for Zircaloy-4 and M5 containing 3300 wppm of hydrogen.

The vast majority of the data reported in the literature on the evolution of the lattice parameter or the thermal expansion of this phase as a function of temperature are limited to temperatures superior to 900°C [START_REF] Skinner | Thermal Expansion of Zirconium between 298°K and 1600°K[END_REF][38], i.e. above the range investigated in this study. However, lattice parameter values of 3.604 Å at 627°C [START_REF] Aurelio | Structural properties and stability of metastable phases in the Zr-Nb system: Part II. Aging of bcc (β) alloys and assessment of β-Zr[END_REF] and 3.627 Å at 700°C [START_REF] Zhao | Thermal equations of state of the α, β, and ω phases of zirconium[END_REF] have been reported for pure hydrogen-free β Zr . These values are approximately 0.02 to 0.05 Å lower than those determined in this study for Zircaloy-4 and M5 containing 3300 wppm of hydrogen. This difference is probably due to the additional chemical elements, notably hydrogen, present in the materials studied.

The results in Fig. 8 show that the lattice parameter of the β Zr phase increases with decreasing the temperature between 700°C and 520 or 480°C. The contraction of purely thermal origin is thus outweighed by other effects. On the one hand, according to the thermodynamic calculations shown in Fig. 17, the oxygen content in solid solution in the β Zr phase decreases during cooling down to the eutectoid reaction temperature. Thus, the evolution of the lattice parameter of β Zr cannot be explained by the evolution of its oxygen content. On the other hand, the hydrogen content in solid solution in the β Zr phase increases continuously during cooling in this temperature range. Hence, the evolution of the lattice parameter of the β Zr phase as a function of temperature above the eutectoid reaction temperatures can be a direct result of the effect of a progressive enrichment in hydrogen of this phase upon cooling.

β Zr * (Nb, H) phase in M5

In the case of M5, a residual (metastable) β Zr phase noted β Zr * (Nb, H) has been highlighted at low temperatures. The fraction of this phase at RT is higher after direct quenching than after slow cooling. The existence of a β Zr phase enriched in Nb retained at RT in the form of stringers between α Zr laths was reported in [START_REF] Toffolon-Masclet | Study of secondary intermetallic phase precipitation/dissolution in Zr alloys by high temperature-high sensitivity calorimetry[END_REF] for Zr-2.5%Nb heat-treated for 5 min at 1045°C then slowly cooled at an average rate of 0.05°C/s. This can be explained by the fact that below 700°C, Nb diffuses very slowly, which favors the stabilization of a significant fraction of a metastable β Zr phase containing theoretically up to ~20 wt% of Nb [19][24]. It can be assumed that hydrogen has an additional effect. It should prevent the decomposition of the β Zr phase enriched in Nb by delaying the on-cooling β Zr to α Zr phase transformation as the result of its β Zr -stabilizing effect. Indeed, this decomposition involves the diffusion (partitioning) of niobium, whose rate decreases with decreasing the temperature. Moreover, hydrogen, which concentrates in the last β Zr zones to be transformed on cooling, could have an intrinsic chemical effect by stabilizing a higher proportion of the metastable β Zr phase retained until RT. Thus, this β Zr * (Nb, H) phase is expected to be enriched in both Nb and H, hence the notation used.

The Nb content is not expected to evolve in this phase between 350 and 40°C because of its very slow thermal diffusion. Therefore, it can be supposed that the evolution of the lattice parameter of this phase (Fig. 9) with temperature is mostly of thermal origin.

The value of the linear expansion coefficient of this phase estimated between 40 and 350°C, previously mentioned in Section 3.1.3, is in good agreement with the thermal expansion coefficient of the β Zr phase, which is generally determined at much higher temperatures. The values of the lattice parameter of the β* Zr (Nb, H) phase obtained in this study are higher by about 0.024 Å than those reported in [START_REF] Yan | In Situ Characterization of Lattice Structure Evolution during Phase Transformation of Zr-2.5Nb[END_REF] for Zr-2.5%Nb

analyzed by neutron diffraction during heating at 0.3°C/s between RT and 500°C and then at 0.03°C/s between 500 and 1000°C. This difference is consistent with the one observed on the lattice parameter of the β Zr phase at 700°C between M5 hydrogencharged at 3300 wppm and pure hydrogen-free zirconium, as previously mentioned in Section 4.3.

Hydrides and hydrogen in solid solution

The results have shown that, for hydrogen contents higher than about 1000 wppm, δ ZrH2-

x hydrides precipitate upon (slow) cooling from the β Zr temperature domain, mainly during the eutectoid reaction. The observed evolution, with temperature, of the lattice parameter of this phase is assumed to result from, at least, two phenomena: thermal expansion and possible evolution of their stoichiometry. In addition, the precipitation of γ ZrH hydrides has been evidenced below approximately 350°C. No evolution of the lattice parameters of γ ZrH with temperature has been observed, knowing that no such evolution has been reported so far in the literature. ε hydrides [START_REF] Perovic | Hydride precipitation in α/β zirconium alloys[END_REF] or ζ hydrides [START_REF] Zhao | Blat-Yrieix, Identification and characterization of a new zirconium hydride[END_REF] have not been observed in this study.

The coexistence of γ ZrH and δ ZrH2-x hydrides upon cooling has already been reported in the literature [START_REF] Pshenichnikov | Microstructure and mechanical properties of Zircaloy-4 cladding hydrogenated at temperatures typical for loss-of-coolant accident (LOCA) conditions[END_REF] [START_REF] Small | Observation of kinetics of γ zirconium hydride formation in Zr-2.5Nb by neutron diffraction[END_REF]. The disappearance of a large or even a total fraction of γ ZrH hydrides has been noted in [START_REF] Root | Kinetics of the δ to γ zirconium hydride transformation in Zr-2.5Nb[END_REF][46] at temperatures above 180°C on heating. The reverse phenomenon was observed during cooling from 400°C, but the fraction of precipitated γ ZrH hydrides is much lower than that estimated before heating. This was recently confirmed through in situ neutron diffraction experiments performed on the Zr-D system [47][48]. Root et al. [START_REF] Root | Kinetics of the δ to γ zirconium hydride transformation in Zr-2.5Nb[END_REF] suggested that the formation of γ ZrH hydrides is associated with the partial dissolution of δ ZrH2-x hydrides. This transformation would be energetically favorable due to the smaller elementary cell volume of γ ZrH compared to that of δ ZrH2-x , thus minimizing microstress. Bailey [START_REF] Bailey | Electron microscope observations on the precipitation of zirconium hydride in zirconium[END_REF] observed only γ ZrH hydrides in zirconium containing between 100 and 1000 wppm of hydrogen directly quenched in ice-cold salt-water or rapidly cooled down from 800°C. Pshenichnikov et al. [START_REF] Pshenichnikov | Hydride precipitation, fracture and plasticity mechanisms in pure zirconium and Zircaloy-4 at temperatures typical for the postulated loss-of-coolant accident[END_REF] suggested that, for hydrogen contents close to 100 wppm and below, the formation of γ ZrH hydrides is favored due to the low hydrogen content, which would not allow the precipitation of δ ZrH2-x hydrides. For the high hydrogen contents investigated here in this study, the formation of γ ZrH hydrides could be related to the partition of oxygen and hydrogen during the β Zr to α Zr transformation. As shown in Section 3.1.4, there are zones with very high hydrogen content surrounded by areas containing less hydrogen. Therefore, γ ZrH hydrides could preferentially form near the areas with the lowest hydrogen content.

It has been shown that a certain fraction of hydrogen remains in solid solution in the α Zr phase after cooling from the β Zr temperature domain down to RT. These observations are in agreement with those of Pshenichnikov et al. [START_REF] Pshenichnikov | Microstructure and mechanical properties of Zircaloy-4 cladding hydrogenated at temperatures typical for loss-of-coolant accident (LOCA) conditions[END_REF] who reported that a part of the hydrogen, up to 400 wppm, would remain in solid solution after cooling in air from 727°C at a rate of about 5°C/s, for Zircaloy-4 containing 2250 to 4760 wppm of hydrogen on average. Trapping of hydrogen in solid solution at low temperature is not predicted by thermodynamic calculations at equilibrium.

α Zr phase

As shown in Fig. 7, the evolutions of the lattice parameters of the α Zr phase between 700°C and ~500°C in Zircaloy-4 and M5 containing 3300 wppm of hydrogen are very different from those observed in the materials with little hydrogen. Above the eutectoid reaction temperature, the value of the parameter a is higher and its decrease with decreasing temperature is more significant than those reported in [START_REF] Russell | Coefficients of Thermal Expansion for Zirconium[END_REF], [START_REF] Couterne | Détermination des coefficients principaux d'expansion thermique du Zr α[END_REF], and [START_REF] Goldak | Lattice Parameters, Thermal Expansions, and Grüneisen Coefficients of Zirconium, 4.2 to 1130[END_REF] for pure α Zr containing almost no hydrogen (< 10 wppm). In this temperature range, the parameter c increases with decreasing temperature in the case of Zircaloy-4 and M5 containing 3300 wppm of hydrogen, while it decreases in the case of pure hydrogen-free zirconium. Below 350°C, the evolutions of the parameters a and c as a function of temperature are similar to those reported in [START_REF] Russell | Coefficients of Thermal Expansion for Zirconium[END_REF], [START_REF] Couterne | Détermination des coefficients principaux d'expansion thermique du Zr α[END_REF], and [START_REF] Goldak | Lattice Parameters, Thermal Expansions, and Grüneisen Coefficients of Zirconium, 4.2 to 1130[END_REF]. These results suggest that, as for the β Zr phase, the variations of the lattice parameters of α Zr with temperature are not purely of thermal origin in the materials investigated in this study. As shown in Section 3.1.4, there is a microchemical partition between the pro-eutectoid α Zr phase and the β Zr phase during the on-cooling β Zr to α Zr transformation. Note that no significant partitioning of tin is expected in Zircaloy-4 for the conditions studied here [START_REF] Brachet | Oxygen, Hydrogen and Main Alloying Chemical Elements Partitioning Upon Alpha-Beta Phase Transformation in Zirconium Alloys[END_REF].

Fig. 17 shows that the hydrogen content in solid solution in the α Zr phase increases during cooling above the eutectoid reaction temperatures, while its oxygen content decreases. Oxygen is known to induce an anisotropic expansion of the lattice parameters of α Zr [51][52]. However, based on the results of Boisot and Béranger [START_REF] Boisot | Variations des paramètres cristallins de la solution solide a zirconiumoxygène en fonction de la teneur en oxygène[END_REF], it can be concluded that the evolution of the oxygen content determined here cannot be insufficient to explain the evolution of the lattice parameters observed. Thus, in the temperature range of 700-540°C, the decrease of the parameter a of the pro-eutectoid α Zr phase is dominated by thermal effects [START_REF] Couterne | Détermination des coefficients principaux d'expansion thermique du Zr α[END_REF][53] that outweigh the effects of the evolutions in hydrogen and oxygen contents in solid solution. Hydrogen atoms are bigger than the volume of the tetrahedral sites of the α Zr phase in which they are inserted [START_REF] Domain | Atomic-scale Ab-initio study of the Zr-H system: I. Bulk properties[END_REF][55], leading to an expansion of the α Zr lattice [START_REF] Hellouin De Menibus | Hydrogen contribution to the thermal expansion of hydrided Zircaloy-4 cladding tubes[END_REF]. Therefore, the increase of the parameter c observed during cooling between 700 and 540°C (Fig. 7) probably results from the insertion of hydrogen atoms that outweighs the contraction of purely thermal origin. In summary, the present results show a very anisotropic effect of the insertion of hydrogen atoms within the hcp lattice of the pro-eutectoid α Zr phase above the eutectoid reaction temperatures.

It has been observed that the lattice parameters of the α Zr phase at RT, in particular the parameter c, increase with increasing the average hydrogen content (Fig. 16). It is important to remind that Zircaloy-4 and M5 samples charged with hydrogen at 3300 wppm contain about 0.2-0.3 wt% of oxygen on average due to a slight oxygen uptake during hydrogen charging at 800°C (as mentioned in Section 2.1.1), while the oxygen content in hydrogen-free materials is 0.13-0.14 wt%. However, according to the results of Boisot and Béranger [START_REF] Boisot | Variations des paramètres cristallins de la solution solide a zirconiumoxygène en fonction de la teneur en oxygène[END_REF], the difference in average oxygen contents cannot simply explain the increase of 0.006-0.009 Å in the parameter c measured between the hydrogen-free samples and the samples containing 3300 wppm of hydrogen. The lattice parameters' values of the α Zr phase measured for hydrogen-free ZrVA in this study are similar to those given for pure zirconium in the Powder Diffraction File™ provided by the International Centre for Diffraction Data (a = 3.232 Å and c = 5.147 Å). The lattice parameters determined for hydrogen-free Zircaloy-4 and M5 at RT are in good agreement with those reported by Stern et al. [START_REF] Stern | Investigations of the Microstructure and Mechanical Properties of Prior-β Structure as a Function of the Oxygen Content in Two Zirconium Alloys[END_REF] for Zircaloy-4 containing 0.25 wt% of oxygen. However, they are higher than those reported in [START_REF] Pshenichnikov | Microstructure and mechanical properties of Zircaloy-4 cladding hydrogenated at temperatures typical for loss-of-coolant accident (LOCA) conditions[END_REF] for Zircaloy-4, which are, curiously, very close to the lattice parameters measured for hydrogen-free ZrVA (unalloyed). Although the lattice parameters' values are shifted, the relative increase of the lattice parameters of α Zr with increasing the average hydrogen content is consistent with the observation made by Pshenichnikov et al. [START_REF] Pshenichnikov | Microstructure and mechanical properties of Zircaloy-4 cladding hydrogenated at temperatures typical for loss-of-coolant accident (LOCA) conditions[END_REF]. This increase seems to be related to the residual hydrogen content in solid solution at RT, which is higher after direct quenching than after slower cooling, as shown in Fig. 13.

The results presented in Section 3.2.2 show that, in the case of ZrVA, the lattice parameters of the α Zr phase at RT do not evolve any more with the average hydrogen content after a heat treatment at 500°C promoting the precipitation of hydrides (Fig. 16).

In this case, the (anisotropic) expansion of the α Zr lattice observed at RT in the presence of hydrogen would, therefore, be entirely due to the residual hydrogen in solid solution.

However, in the case of Zircaloy-4 and M5, the lattice parameters of α Zr increase with increasing the average hydrogen content even after very slow cooling, for which only a very small quantity of hydrogen remains in solid solution at RT (< 100 wppm). It is difficult to imagine that this increase in the lattice parameters of α Zr is due to a direct effect of hydrogen almost entirely precipitated in the form of hydrides. It can be assumed that, in alloyed materials as Zircaloy-4 and M5, hydrogen has an indirect effect on the evolution of the lattice parameters of α Zr by inducing the enrichment, notably in oxygen, of certain zones of the matrix (partitioning) during the phase transformations occurring on cooling from the β Zr phase domain. Stern et al. [START_REF] Stern | Investigations of the Microstructure and Mechanical Properties of Prior-β Structure as a Function of the Oxygen Content in Two Zirconium Alloys[END_REF] observed such an effect of oxygen partitioning in oxygen-enriched materials cooled from the β Zr phase domain. In particular, they observed a shift and/or a doubling of XRD peaks related to the presence of microchemical (oxygen) heterogeneities.

Conclusions

This paper provides a detailed quantitative description of the microstructural and microchemical evolutions that take place during cooling from the β Zr temperature domain in zirconium alloys containing up to very high hydrogen contents. For that purpose, X-ray and neutron diffraction analyses were performed in situ upon slow cooling (about 0.01°C/s on average) from 700°C or post facto at RT after various cooling scenarios from 1000°C. The experiments were conducted on Zircaloy-4 and M5

cladding samples as well as on unalloyed zirconium sheet samples (in particular, with almost no oxygen), pre-charged with hydrogen at different contents up to 3300 wppm.

The distribution of chemical elements, in particular oxygen and hydrogen, in the samples was quantitatively determined after cooling by EPMA and µ-ERDA. The experimental results were systematically compared to thermodynamic predictions at equilibrium obtained using Thermo-Calc associated with the Zircobase database, taking into account all the elements constituting the materials. The main conclusions of this work can be summarized as follows:

1. In the materials containing 3300 wppm of hydrogen, the β Zr phase progressively transforms into the pro-eutectoid α Zr phase during cooling at ~0.01°C/s on average, down to 540°C for Zircaloy-4 or 520°C for M5. The lattice parameter of the β Zr phase increases significantly during cooling from 700°C to about 500°C. This is likely due to the increase of the hydrogen content in solid solution in this phase during the on-cooling β Zr to α Zr phase transformation, Therefore, α Zr , β Zr , and δ ZrH2-x phases coexist between 540 and 500°C for Zircaloy-4 and between 520 and 480°C for M5, cooled at 0.01°C/s on average.

Thermodynamic calculations at equilibrium also predict the existence of these domains but in temperature ranges higher by about 20-30°C and narrower by about 35°C, which is likely due to a cooling hysteresis effect.

3. The mole fractions of phases determined from quantitative analyses of the diffraction data obtained upon slow cooling at an average rate of 0.01°C/s are in good agreement with those predicted by thermodynamic calculations at equilibrium. It is important to notice that thermodynamic predictions had not yet been experimentally validated for the high hydrogen contents investigated in this study.

4. Hydrides mainly precipitate during the eutectoid reaction in the form of δ ZrH2-x hydrides. However, they continue to precipitate at lower temperatures due to the decrease of the solubility limit of hydrogen in the α Zr phase with decreasing temperature upon cooling. In addition, γ ZrH hydrides precipitate below 350°C for both Zircaloy-4 and M5. This phase is observed at RT in all the samples containing 320, 1100-1500 and 3300 wppm of hydrogen, after direct water quenching from 1000°C as well as after slower cooling (cooling at 0.4-1°C/s from 1000°C down to 600°C then water quenching, or step-cooling from 700°C at 0.01°C/s on average). After direct quenching, γ ZrH hydrides are in the majority compared to δ ZrH2-x hydrides. The fraction of δ ZrH2-x hydrides at RT increases with decreasing the cooling rate. The higher the average hydrogen content, the larger the ratio between the fractions of δ ZrH2-x hydrides and γ ZrH hydrides after direct water quenching. The precipitation of γ ZrH hydrides could be associated with the partitioning of oxygen and hydrogen during the phase transformation of zirconium during cooling, leading to the presence of zones with a hydrogen content up to 6000 wppm surrounded by areas containing typically a few hundreds of wppm of hydrogen.

5. A significant amount of hydrogen remains in solid solution in the α Zr phase after cooling down to RT. The higher the average hydrogen content and the faster the cooling rate, the higher the hydrogen content remaining in solid solution. For example, 850-890 wppm (~8 at%) of hydrogen is still dissolved in the α Zr phase after direct quenching from 1000°C in the materials containing 3300 wppm of hydrogen on average.

6.

For the M5 alloy, the higher the average hydrogen content or the faster the cooling rate, the more significant the mole fraction of metastable β Zr * (Nb, H) stabilized at RT.

7. After cooling from the β Zr temperature domain, the parameter c and, to a lesser extent, the parameter a of the α Zr lattice increase with increasing the average hydrogen content in Zircaloy-4 and M5 at RT. The faster the cooling rate, the higher the value of the parameter c. The lattice parameters of unalloyed zirconium (ZrVA) evolve in approximately the same way as for Zircaloy-4 and M5. After heat-treatment at 500°C for 24h followed by slow cooling at 0.1°C/s on average, the lattice parameters of the α Zr phase of ZrVA charged with hydrogen become equivalent to those of the hydrogen-free material. In this case, the expansion of the α Zr lattice in the presence of hydrogen is entirely attributed to the hydrogen remaining in solid solution after cooling. In the case of alloyed materials, i.e. Zircaloy-4 and M5, it is assumed that in addition to the direct effect of hydrogen, the expansion of the lattice parameters of α Zr is associated with an indirect effect of hydrogen, via its influence on the distribution of other elements, notably oxygen. and after slow step-cooling at 0.01°C/s on average (even if not represented, a small fraction of hydrides probably precipitates during cooling in prior-pro-eutectoid α Zr zones, which contain a few tens to a few hundreds of wppm of hydrogen).

Fig. 1 .

 1 Fig. 1. Polarized optical micrographs of transverse cross-sections of Zircaloy-4 samples heat-treated for a few tens of seconds under steam at 1000°C: (a) hydrogen-free directly water quenched from 1000°C, (b) hydrogen-charged at 320 wppm directly water quenched from 1000°C, (c) hydrogen-charged at 320 wppm cooled at 0.4-1°C/s from 1000°C down to 600°C then water-quenched, (d) hydrogen-charged

Fig. 2

 2 Fig. 2 shows neutron diffraction patterns obtained at different temperatures between

Fig. 2 .

 2 Fig. 2. Neutron diffraction patterns recorded at various temperatures between 700°C and 500°C or 480°C upon step-cooling (0.01°C/s on average) from 700°C for (a) Zircaloy-4 and (b) M5 containing about 3300wppm of hydrogen (and 0.2 wt% of oxygen) water quenched from 1000°C.

Fig. 3 .

 3 Fig. 3. Neutron diffraction patterns recorded at various temperatures between 500°C or 480°C and 40°C upon step-cooling (0.01°C/s on average) from 700°C for (a) Zircaloy-4 and (b) M5 containing about 3300 wppm of hydrogen (and 0.2 wt% of oxygen) water quenched from 1000°C.

Fig. 4 .Fig. 5 .

 45 Fig. 4. Rietveld refinement of the neutron diffraction patterns measured at RT after step-cooling (0.01°C/s on average) from 700°C for (a) Zircaloy-4 and (b) M5 containing about 3300 wppm of hydrogen (and 0.2 wt% of oxygen) water quenched from 1000°C.

Fig. 6 .

 6 Fig. 6. Evolution of the hydrogen content in solid solution as a function of temperature obtained by neutron diffraction performed in situ during step-cooling (0.01°C/s on average) from 700°C on Zircaloy-4 and M5 containing about 3300 wppm of hydrogen (and 0.2 wt% of oxygen) water quenched from 1000°C.

Fig. 7

 7 Fig.7shows the lattice parameters a and c obtained for the hcp crystal lattice of the α Zr

Fig. 7 .

 7 Fig. 7. Evolution of (a) parameter a, (b) parameter c and (c) volume of elementary cell of the α Zr phase as a function of temperature obtained by neutron diffraction performed in situ during step-cooling (0.01°C/s on average) from 700°C on Zircaloy-4 and M5 containing about 3300 wppm of hydrogen (and 0.2 wt% of oxygen) water quenched from 1000°C; comparison to data reported by Russell [32], Couterne and

Fig. 8 .Fig. 9 .

 89 Fig. 8. Evolution of the lattice parameter of the β Zr phase as a function of temperature obtained by neutron diffraction performed in situ during step-cooling (0.01°C/s on average) from 700°C on Zircaloy-4 and M5 containing about 3300 wppm of hydrogen (and 0.2 wt% of oxygen) water quenched from 1000°C.

Fig. 10 shows

 10 Fig.10shows the evolution of the lattice parameter of the fcc δ ZrH2-x hydrides. The

Fig. 10 .

 10 Fig. 10. Evolution of the lattice parameter of δ ZrH2-x hydrides as a function of temperature obtained by neutron diffraction performed in situ during step-cooling (0.01°C/s on average) from 700°C on Zircaloy-4

  et al.(2017) and vice versa. As will be further discussed in Section 4, these microchemical heterogeneities result from the microchemical partitioning between α Zr and β Zr phases that takes place during the β Zr to α Zr phase transformation. The hydrogen-depleted and oxygen-enriched zones are located at the former β Zr grain boundaries. As discussed further in Section 4, these zones likely correspond to the pro-eutectoid α Zr phase formed upon cooling from 700°C before reaching the eutectoid transition temperature.

Fig. 11 .

 11 Fig. 11. μ-ERDA map of hydrogen distribution (left) and EPMA map of oxygen distribution (right) at RT of (a) Zircaloy-4 and (b) M5 containing about 3300 wppm of hydrogen (and 0.2 wt% of oxygen) water quenched from 1000°C then step-cooled (0.01°C/s on average) from 700°C.

Fig. 12 .

 12 Fig. 12. Neutron diffraction patterns recorded at RT on (a) Zircaloy-4 and (b) M5 containing about 320 wppm of hydrogen after water quenching from 1000°C or cooling at 0.4-1°C/s from 1000°C down to 600°C then water quenching.

Fig. 13 .

 13 Fig. 13. Phase mole fractions of γ ZrH hydrides, δ ZrH2-x hydrides, and β Zr * (Nb, H) (the fraction of α Zr is not represented; it is such that the total of the fractions of the phases is 100%) in the material at RT determined by neutron diffraction for (a) Zircaloy-4 and (b) M5 containing various hydrogen contents and having undergone various cooling scenarios from 1000°C: direct water quenching from 1000°C (DQ),

Fig. 14 .

 14 Fig. 14. Percentages of hydrogen in γ ZrH hydrides, δ ZrH2-x hydrides, and in solid solution (in α Zr and/or β Zr * (Nb, H)) in the material at RT determined by neutron diffraction for (a) Zircaloy-4 and (b) M5 containing various hydrogen contents and having undergone various cooling scenarios from 1000°C:

Fig. 15 .

 15 Fig. 15. XRD patterns recorded at RT on ZrVA containing about 3100 wppm of hydrogen subjected to

Fig. 13

 13 Fig. 13 shows the evolution of the mole fraction of the β Zr * (Nb, H) phase at RT,

Fig. 16 .

 16 Fig. 16. Evolution of the lattice parameters of the α Zr phase as a function of the average hydrogen content obtained at RT by neutron diffraction and XRD on (a) Zircaloy-4, (b) M5, and (c) ZrVA subjected to various cooling scenarios: direct water quenching from 1000 or 850°C, direct water quenching from 1000or 850°C followed by a heat treatment for 24h at 500°C, water quenching from 600°C after cooling at

Fig. 17 .

 17 Fig. 17. Evolution with temperature of (a) the hydrogen content and (b) the oxygen content in solid solution in the α Zr phase and the β Zr phase determined from thermodynamic calculations at equilibrium, for Zircaloy-4 containing about 3000 wppm of hydrogen (and 0.2 wt% of oxygen).

  outweighing the opposite thermal (contraction) effect. The parameter a of the α Zr lattice decreases with decreasing temperature above the eutectoid transformation temperatures, but the parameter c increases and reaches its maximum value at the eutectoid transition temperatures. These anisotropic evolutions of the lattice parameters of the α phase can be explained by the competition between the effect of thermal contraction and that of the increase in the hydrogen content in solid solution in the α Zr phase in this temperature range. The first effect is preponderant on the evolution of the parameter a. The second one is preponderant on the evolution of the parameter c. Despite this anisotropic evolution of the lattice parameters of α Zr , the elementary cell volume of the crystal lattice decreases during cooling in these temperature ranges, and the effect of thermal contraction outweighs the effect of chemical segregation at the level of the crystal lattice volume. 2. Below 540°C for Zircaloy-4 and 520°C for M5, both containing 3300 wppm of hydrogen, the residual β Zr phase rapidly transforms into α Zr . δ ZrH2-x hydrides extensively precipitate via a eutectoid reaction: β Zr ⟶ α Zr + δ ZrH2-x in the case of Zircaloy-4, β Zr ⟶ α Zr + β Zr * (Nb, H) + δ ZrH2-x in the case of M5. The decomposition of β Zr is not complete in the case of M5: residual β Zr enriched in Nb and H, noted β Zr * (Nb, H), remains at low temperatures.

Fig. 18 summarizes

 18 Fig.18summarizes the main microstructural and microchemical evolutions, highlighted

Fig. 18 .

 18 Fig. 18. Schematic representation of the metallurgical and microchemical evolutions occurring during cooling from the β Zr temperature domain down to RT, in Zircaloy-4 and M5 containing 3300 wppm of

Table 1

 1 Chemical compositions (in wt%) of the studied materials in as-received conditions (i.e. before hydrogen charging).

	Material	Sn	Fe	Cr	Nb	O	H	Hf	Zr
	Zircaloy-4	1.3	0.2	0.1	< 0.005	0.13	< 0.0005 < 0.006	balance
	M5 Framatome	< 0.005	0.04	< 0.005	1.0	0.14	< 0.0005 < 0.006	balance
	Van Arkel Zr	-	0.05	-	-	0.01	0.003	2.2	balance

  Zr + δ ZrH2-x for Zircaloy-4 and α Zr + δ ZrH2-x + β Zr the case of M5 compared to Zircaloy-4. The fraction of δ ZrH2-x hydrides in the material at RT is about 34±0.4 mol% for Zircaloy-4 and 36±0.4 mol% for M5, which is

*

(Nb, H) for M5) is lower by a few tens of °C in consistent with the fact that both alloys contain approximately the same amount of hydrogen on average (about 23±0.05 at%). In the case of M5, a small fraction of approximately 1.8±0.2 mol% of β Zr * (Nb, H) is detected for temperatures below 480°C.

For both Zircaloy-4 and M5, the fraction of γ ZrH increases slightly during cooling from 350°C down to 40°C, but it remains low. In the case of M5, it is about 0.8±0.2 mol% at 350°C and 1.7±0.2 mol% at 40°C. In the case of Zircaloy-4, it is approximately 0.5±0.2 mol% at 350°C. It is about 3.1±0.2 mol% at 40°C, a little bit higher in comparison with M5.

  3°C/s from 1000 or 850°C, or step-cooling at 0.01°C/s on average from 700°C after water quenching from 1000°C; comparison to data reported by Pshenichnikov et al.[START_REF] Pshenichnikov | Microstructure and mechanical properties of Zircaloy-4 cladding hydrogenated at temperatures typical for loss-of-coolant accident (LOCA) conditions[END_REF] for Zircaloy-4.

		0.4-1 or 0.
	Direct quenching Slow cooling Black symbols: neutron diff.	after 24h at 500°C		Direct quenching Quenching from 600°C Step-cooling
	Grey symbols: XRD				Direct quenching	Black symbols: neutron diff.
					Quenching from 600°C	Grey symbols: XRD
					Step-cooling	Full symbols: after 24h at 500°C
	(a) 3.236 3.238 4000 Average hydrogen content (wppm) Pshenichnikov et al. (2015) (Å) 1000 2000 3000 3.226 Pshenichnikov et al. (2015) (b) a 3.228 3.23 3.232 3.234 after 24h parameter at 500°C	3.226 3.228 3.23 3.232 3.236 3.238 Black symbols: neutron diff. Grey symbols: XRD (Å) Full symbols: after 24h at 500°C 3.234 0 a parameter Average hydrogen content (wppm) 1000 2000 3000 4000 Pshenichnikov et al. (2015) Pshenichnikov et al. (2015)
				0	1000	2000	3000	4000
	1000	2000	3000	Average hydrogen content (wppm) 4000	after 24h
	Average hydrogen content (wppm)			at 500°C
			(c)
	Thermodynamic				Pshenichnikov
	calculations				et al. (2015)
	00 200 300 400 500 600 700
	Temperature (°C)
		Preprint submitted to Acta Materialia	37

  of the microstructures obtained at RT after direct water quenching from 1000°C

	hydrogen; comparison
		Temperature
				β Zr
				All chemical element
				in solid solution
	700°C
		Prior-β Zr grain
	Cooling	boundary	H O	Pro-eutectoid α Zr enriched in O and depleted in H (and in Fe, Cr and/or Nb) depleted in O and enriched in H Non-transformed β Zr
					(and in Fe, Cr and/or Nb)
	~ 500-				Start of the
	550°C				eutectoid reaction
		Quenching	Slow cooling
	20°C
					Time
		α Zr ≈ 69-71 mol%		α Zr ≈ 61-63 mol%
		with ~7.2-7.5 at% of H in solid sol.	with ~0.3-0.7 at% of H in solid sol.
		+ δ ZrH2-x ≈ 13-15 mol%		+ δ ZrH2-x 34-36 mol%
		+ γ ZrH ≈ 14-15 mol%		+ γ ZrH 1.7-3.1 mol%
		+ for M5: β Zr	* (Nb, H) ≈ 2.2 mol%	+ for Zircaloy-4: Zr(Fe, Cr) 2 < 1 mol%
					+ for M5: β Zr	* (Nb, H) 1.8 mol%
					+ Zr(Fe, Nb) 2 < 1 mol%
	Preprint submitted to Acta Materialia	52

Acknowledgements

The authors thank F. Damay from LLB (CEA, CNRS), P. Berger and C. Raepsaet from LEEL (CEA), P. Bossis from DEN-DMN (CEA), C. Cobac, T. Guilbert, A. Lequien, G. Nony, J. Roubaud and S. Urvoy from DEN-SRMA (CEA), J.D. Bartout from MINES ParisTech, F. Couturas and M. Dottor from ICMPE (UPEC, CNRS), and EDF and Framatome, for their contributions to this work. This work was funded by the French Nuclear Institute in the framework of the GAINES project.