Josiane A Kaddissy

Stéphane Esnouf

Dimitri Saffré

Jean-Philippe Renault

Efficient hydrogen production from irradiated aluminum hydroxides

Keywords: Radiolysis, Irradiation, Radiation catalysis, Hydrogen, defects, EPR, Aluminum hydroxides

Introduction

Hydrogen produced by water radiolysis in the vicinity of radioactive rocks, has been a major source of energy for development of life on the early earth. [START_REF] Lollar | The contribution of the Precambrian continental lithosphere to global H2 production[END_REF] In today's world, it may be important to sustain deep subsurface microbial communities in rock fractures. [START_REF] Lin | Radiolytic H2 in continental crust: nuclear power for deep subsurface microbial communities[END_REF][START_REF] Dzaugis | Water radiolysis and chemical production rates near solid-water boundaries[END_REF] In fact, some minerals have been known since the sixties to facilitate radiolytic processes by the so called radiation catalysis. [START_REF] Musat | Water reduction by photoexcited silica and alumina[END_REF][START_REF] Breslav | Investigation of the mechanism of radiation-catalytic processes on the synthethic zeolites by the EPR method[END_REF] The observation of radio-catalytic H 2 production on oxides has triggered many hopes concerning the possibility of radiolytically powered fuel cells. [START_REF] Petrik | Interfacial energy transfer during gamma radiolysis of water on the surface of ZrO2 and some other oxides[END_REF] In these studies, the reference material is ZrO 2 , with yields as high as 150 molecules for 100eV absorbed by adsorbed water [START_REF] Laverne | H2 production in the radiolysis of water on CeO2 and ZrO2[END_REF][START_REF] Skotnicki | Molecular hydrogen formation during water radiolysis in the presence of zirconium dioxide[END_REF] but Al 2 O 3 , SIO 2 and TiO 2 may also be quite effective. [START_REF] Yamada | Effect of alumina on the enhancement of hydrogen production and the reduction of hydrogen peroxide in the γ-radiolysis of pure water and 0.4 M H2SO4 aqueous solution[END_REF][START_REF] Yamada | Hydrogen production in the γ-radiolysis of aqueous sulfuric acid solutions containing Al2O3, SiO2, TiO2 or ZrO2 fine particles[END_REF][START_REF] Essehli | H2 production by γ and He ions water radiolysis, effect of presence TiO2 nanoparticles[END_REF] Such high yields have of course fostered in turn the development of various technological schemes for harvesting radiation in order to produce H 2 . [START_REF] Yamada | Effects of alumina powder characteristics on H2 and H2O2 production yields in γ-radiolysis of water and 0.4 M H2SO4 aqueous solution[END_REF][START_REF] Klett | H2 production through oxide irradiation: Comparison of gamma rays and vacuum ultraviolet excitation[END_REF] [ [START_REF] Ikezoe | Potential of carbon dioxide radiolysis for hydrogen production[END_REF][START_REF] Vagelatos | Application of laser fusion to the radiolytic production of hydrogen[END_REF][START_REF] Jo'm B | On the splitting of water[END_REF] For a while, the radio-catalysis on oxide surfaces has been interpreted as an exciton migration from the bulk of the material, devoid of hydrogen, to the surface hydroxyl/water groups that act as energy traps. [START_REF] Petrik | Interfacial energy transfer during gamma radiolysis of water on the surface of ZrO2 and some other oxides[END_REF][START_REF] Alam | Tuning hydrogen production during oxide irradiation through surface grafting[END_REF] Direct electron injection from the oxide to the surface water has also been identified. [START_REF] Musat | Water reduction by photoexcited silica and alumina[END_REF] In this short communication, we present data on a very efficient radiolytic H 2 production on the surface of nanostructured aluminum oxyhydroxides (AlOOH). AlOOH (Boehmite) is formed as a corrosion product during aluminum oxidation, but it is also prepared on an industrial scale by wet processes as a precursor of alumina. It was here selected as a model compound for other hydroxides and oxyhydroxides.

Materials & Methods

This part was detailed in our previous work [START_REF] Kaddissy | Radiolytic events in nanostructured aluminum hydroxides[END_REF].

Sample preparation and characterization

All oxyhydroxides samples AlOOH (Boehmite) were acquired from Sasol®, Germany and were in the highest purity available. AlOOH was studied in two different crystallite sizes (named AlOOH S and AlOOH L for small and large particles, respectively). They have already been extensively characterized in reference [START_REF] Kaddissy | Radiolytic events in nanostructured aluminum hydroxides[END_REF], and additional information are shown in the SI (Figure, S1, S2, S3 and S4). Samples were placed into humidity chambers, which contain various saturated salt solutions to generate desired levels of relative humidity, denoted as RH, water uptake was evaluated by weighing each sample periodically. Lithium chloride purchased from Sigma Aldrich with a reference number 746460-100G, Potassium carbonate purchased from Sigma Aldrich with a reference number 791776-100G and Sodium chloride purchased from Sigma Aldrich with a reference number S9625-500G were used in order to obtain relative humidity of 11, 44 and 76 % at room temperature consequently. [START_REF] Wexler | Relative humidity-temperature relationships of some saturated salt solutions in the temperature range 0 to 50 C[END_REF][START_REF] Greenspan | Humidity fixed points of binary saturated aqueous solutions[END_REF] Thermogravimetric measurements (TGA) were performed with a Mettler-Toledo TGA/DSC. Samples dedicated to H 2 quantification were irradiated in Pyrex ampules evacuated at 10 -2 mbar, filled with 0.8 mbar of ultrahigh purity helium gas and then sealed. Concerning samples dedicated to EPR analysis, Room temperature EPR sample cells were standard NMR tubes evacuated and flame-sealed.Though, samples dedicated to low temperature EPR, also irradiated at low temperature were irradiated in EPR cold finger quartz Dewar. Samples irradiated for low temperature EPR were made into pellets. It was essential to irradiate in the same vessel and analyze by EPR without creating irradiation defects in the zone analyzed by the EPR. The pellet is irradiated while it is hanged to the wire and once irradiated it is released to the bottom of the dewar where it is supposed to be analyzed by EPR as detailed in [START_REF] Kaddissy | Hydrogen production from irradiated aluminum hydroxide and oxyhydroxide[END_REF]. Dewars are filled with liquid nitrogen in order to keep the samples irradiated at 77 K. EPR measurements were conducted at Laboratoire National Henri Becquerel (LNHB), CEA-Saclay, France and Laboratoire des Solides Irradiés (LSI), Ecole Polytechnique, France. Spectra were acquired on X-Band EMX Bruker spectrometers (X-Band) with a 100 Hz field modulation. In most cases microwave power and amplitude modulation were 10 mW, 0.2 mT, respectively. The microwave frequency was measured with a frequency counter. Quantification was estimated using a hydroxyl-TEMPO sample (4-hydroxy-2,2,6,6-Tetramethylpiperidyne 1 oxyl) as a standard. The error on the conversion factor is estimated at 25%.

Irradiation experiments

Electron beam irradiations were conducted using a linear accelerator located in NIMBE, Saclay, France. The pulse-width was 10 ns, the electron energy was 10 MeV and the repetition rate was 5 Hz. No sample heating was detected. The typical dose delivered per pulse determined using the Fricke dosimeter was: 28 Gy/pulse. [START_REF] Fricke | Radation Dosimetry[END_REF][START_REF] Sutton | A Calibration of the Fricke Chemical Dosimeter[END_REF] L-α-alanine EPR dosimetry was used to determine the dose delivered in the EPR tubes and Dewars irradiated with electron beams. Most of the samples irradiated using electron beam dedicated to analyzing molecular H 2 were placed in 10 mL Pyrex ampules with valves. Only the bottom of the ampule was irradiated and was conceived to have a spherical homogeneous shape. The preliminary washing of the ampules was optimized to reduce as far as possible the hydrogen production of the empty ampules.

H 2 determination

Hydrogen released from hydrated samples irradiated using electron beam was analyzed using µ-GC (μGC-R3000 SRA instrument) (NIMBE) and Agilent 450 (LRMO) using ultrahigh purity argon (argon 6.0) as the carrier gas. A calibration curve is obtained using standard gas mixture with various concentrations of H 2 (from 100 to 1000 ppm).

Correspondance between the relative humidity and the number of water layers

The number of water layer on AlOOH surface was calculated using a specific surface of 40 m 2 /g for AlOOH L, and of 270 m 2 /g for AlOOH S, and a surface occupied by water of 5 m 2 /mg. [START_REF] Haschke | Adsorption of Water on Plutonium Dioxide[END_REF] 3

. Results and Discussion

In a dry state, AlOOH nanoparticles of 18 nm of diameter (named hereafter AlOOH L for Large) have radiolytic yields in the range of (0.05±0.02)x10 -7 mol/J. [START_REF] Kaddissy | Radiolytic events in nanostructured aluminum hydroxides[END_REF] When minute amount of water is added to the system (1% in mass, which represents less than one adsorbed water layer, see SI), this yield, calculated with respect to the total energy received by the system, reaches (7.6±0.2)x10 -8 mol/J (Figure 1). It means that such a material produces more efficiently H 2 than an equivalent mass of water. In fact, when these H 2 yields are expressed with respect to the energy directly received by the adsorbed water, as it is done currently for oxide systems, they take a leap to 134x10 -7 mol/J or 129 molecules/100 eV. (Table S1). These values are comparable to the ones measured from ZrO 2 , and, higher than the one obtained for CPG glasses. [START_REF] Rotureau | Radiolysis of confined water: molecular hydrogen formation[END_REF] To achieve such high yields, a total transfer of energy captured by the system to water and a facilitated OH bond dissociation are both required. Interestingly, these yields (Figure 1, Figure S6 and Table S1) are lower for smaller particles, (5nm, named hereafter AlOOH S). This result is quite surprising considering that smaller sizes are usually expected to favor both energy transfer processes and water adsorption (AlOOH S adsorbs ten times more water than AlOOH L see Figure S5). [START_REF] Alam | Tuning hydrogen production during oxide irradiation through surface grafting[END_REF] This raises interesting questions about the energy transfer mechanism underlying this efficient hydrogen production. Luckily, in materials like hydroxides, some reactive species can remain trapped in the solid network. Therefore, we identified by electron paramagnetic resonance (EPR) the defect patterns (Figure 2 and Table S2) i.e. various types of radicals produced after irradiation in dry (no adsorbed water detectable in thermogravimetric analysis (TGA)) and hydrated conditions (76% relative humidity which corresponds to 1.7% in mass of adsorbed water for AlOOH L and 17% in mass of water for AlOOH S) (Figure S5). For the oxidative part, O and O species can be observed in hydrated (Figure 3) and dry conditions. [START_REF] Kaddissy | Hydrogen production from irradiated aluminum hydroxide and oxyhydroxide[END_REF] The EPR g factors of these defects are not modified by the hydration. The spectra recorded and irradiated at room temperature (RT) are compared to that recorded and irradiated at 77K (Figure 2). The noise is higher in AlOOH S because of its higher water content. Spectra are normalized with respect to the mass of samples.

O is a primary species in the ionization process, produced either by homolytic dissociation The concentration in O saturates with the dose, probably because it transforms progressively into O . (Figure 3)

The reaction that conducted to the formation of superoxide center or ozonide radical are recalled below:

O + O = O Equation 3 O + hole = O Equation 4 O + O = O + e Equation 5
Ozonide radical was also observed in Barium hydroxides [START_REF] Yurik | ESR investigation of hydrogen atoms stabilized in γirradiated alkaline earth hydroxides[END_REF] and in different oxides such as quartz. [START_REF] Griscom | Diffusion of radiolytic molecular hydrogen as a mechanism for the postirradiation buildup of interface states in SiO2-on-Si structures[END_REF] The following reactions have been also proposed:

O + O = O + O Equation 6
Of course, this radical can also be produced by dissociation of O 2 , but we have no signature of O 2 production in our systems (i.e. pure H 2 is produced):

O = O + O Equation 7 O + O = O Equation 8
O + e = O Equation 9Regardless of particle size, the hydration slightly decreases O production (Table 1). However, even in the hydrated case, the yields of O remain important and are stoichiometric with respect to H 2 yields presented in ND : not determined , RT room temperature, * data from [START_REF] Kaddissy | Radiolytic events in nanostructured aluminum hydroxides[END_REF] For the reductive species, two putative precursors of H 2 , H atoms and thermalized electron are observed, in EPR (Figure 2) as trapped defects. H atom doublet, separated by 50 mT is seen having an EPR g factor of 2.013 (Figure 2, AlOOH L and to a lesser extent AlOOH S). The trapped electron defect is identified only in AlOOH S as a singlet with an EPR g factor of 1.998. [START_REF] Petrik | Interfacial energy transfer during gamma radiolysis of water on the surface of ZrO2 and some other oxides[END_REF] We must notice that yields cannot be extracted from this data, as the concentration in these defects saturates very quickly with the dose (Figure 3).

Trapped H atoms and electrons have been previously observed in dry AlOOH L ( [START_REF] Kaddissy | Hydrogen production from irradiated aluminum hydroxide and oxyhydroxide[END_REF] and Figure 3), H atoms in the bulk of the material, and electrons on the surface. In the same AlOOH L material, but hydrated, only H atoms are present, with EPR properties and concentration similar to the dry material which suggests an internal localization of these species. In this case, the hydration destabilizes the electrons on the surface and may favor their recombination to produce hydrogen. In AlOOH S, the concentrations in H atoms and electrons are much smaller than in large particles and appear only in the hydrated state (Figure 2 and3). Water is obviously not expected to stabilize such defects at room temperature. However, its effect may be indirect, by favoring the diffusion of the species out of their production site and thus limiting the recombination effect by confinement observed in small dry particles [START_REF] Kaddissy | Radiolytic events in nanostructured aluminum hydroxides[END_REF][START_REF] Kaddissy | Hydrogen production from irradiated aluminum hydroxide and oxyhydroxide[END_REF] or by thermalizing them more efficiently than the surrounding material. As an alternative pathway, we can consider that these species come from the direct lysis of water on the surface and are subsequently injected in the material. In fact, the amount of adsorbed water is much higher in AlOOH S than in AlOOH L. The isotope labelling experiments that would allow to distinguish between these two hypotheses are prevented by the long equilibrium time required to control the hydration. We must also notice that, in these two pathways, water helps/allows the production of defects within the neighboring material. This observation converges with recent researches on H 2 injection in copper from neighboring water radiolysis. [START_REF] Lousada | Gamma radiation induces hydrogen absorption by copper in water[END_REF] We must also notice that this defect accumulation does not affect the structural properties of the materials (see SI, Figures S7 andS8).

In a second time, low temperature irradiations were used to stabilize and quantify the primary species produced by irradiation. At 77K, O is also the major species formed, with G values between 7 and 8 molecules/100eV for AlOOH L and AlOOH S. The ionization process is here more efficient than in water where the initial yield in holes was recently revaluated to 4.8 molecules/100eV. [START_REF] El Omar | Timedependent radiolytic yield of OH• radical studied by picosecond pulse radiolysis[END_REF] The most straightforward explanation is the lower band gap of hydroxide materials (4,5 eV), [START_REF] Alemi | Boehmite (γ-AlOOH) nanoparticles: Hydrothermal synthesis, characterization, pH-controlled morphologies, optical properties, and DFT calculations[END_REF] which is very near from the ZrO 2 band gap and much lower than that of water (>6.9 eV). [START_REF] Fang | The accurate calculation of the band gap of liquid water by means of GW corrections applied to plane-wave density functional theory molecular dynamics simulations[END_REF] As the Electron-Hole-pair-creation energy is approximatively 3 times the band gap, we can expect the formation of 7.5 holes per 100 eV. [START_REF] Alig | Electron-hole-pair creation energies in semiconductors[END_REF] Trapped H atoms are observed in both large particles and small ones at 77K (Figure 2). Their concentration saturates very quickly with the dose at low temperature, reaching 1mmol/kg for AlOOH L and 0.07 mmol/kg for AlOOH S (Data not shown). It shows that H atoms remain very reactive and thus, their mobility is only marginally lower at liquid nitrogen temperature. [START_REF] Markland | Quantum diffusion of hydrogen and muonium atoms in liquid water and hexagonal ice[END_REF] Interestingly, no trapped electrons are observed in AlOOH S at this temperature, suggesting that their observation at room temperature might result from the reaction of H atoms with hydroxyl. Therefore, the precursor of trapped electrons in aluminum hydroxides may not be free electrons but rather free H atoms.

Al ⋯ OH + H → Al ⋯ OH + e !!"# Equation 10

The annealing at room temperature of samples irradiated at 77K reveals an important decrease of H atom and oxidative defect signals, a decrease that is more pronounced in small particles than in large ones (Figure 2 and Table 1). Therefore, as the primary creation of defects observed at low temperature does not really depend on particle size, the lower H 2 production in AlOOH S compared to AlOOH L should be attributed to secondary, thermally activated recombination rather than to the initial ionization processes.

We cannot directly conclude on an excitonic transfer in our case, as it was supposed for some oxide surfaces considering exciton migration from the bulk to the surface of hydroxyl/water groups that act as energy traps. In our study, H 2 can come either from the bulk and/or from the surface. However, the low dielectric constant of aluminum hydroxides (<10) may favor excited/excitonic state formation by electron hole pairing. [START_REF] Abram | Structural and dielectric properties of hydrothermally prepared boehmite coatings on an aluminium foil[END_REF] Furthermore, excited/excitonic state formation upon irradiation is easily detected in AlOOH by cathodoluminescence, (see SI Figure S9), with light emission arising from their partial deactivation on anionic vacancies (around 420 nm) and on O defect (around 520 nm). [START_REF] Alemi | Boehmite (γ-AlOOH) nanoparticles: Hydrothermal synthesis, characterization, pH-controlled morphologies, optical properties, and DFT calculations[END_REF] Our results allow to describe more precisely this excitonic process. The oxidative counterpart of hydrogen production is here unambiguously identified as oxygen centered defects in the material, whereas it is still elusive in the case of oxides. Therefore, the exciton interaction with surface water probably corresponds to an injection of the reductive equivalent in water, while the hole remains in the materials as O or O 3 -. Such a mechanism of exciton dissociation is related to the one observed in laser photoexcited alumina, but in this case, solvated electron were observed. [START_REF] Musat | Water reduction by photoexcited silica and alumina[END_REF] However, we must not forget, that besides favoring exciton dissociation, surface water probably plays a second role in controlling reactive species diffusion and encounter, as shown by the change in defect patterns between dry and hydrated states, in AlOOH L and AlOOH S.

Al

Conclusions

From all these observations, we can draw lessons concerning the design of good radiationcatalytic materials for H 2 production and have high ionization yields. This ideal material must be easily ionized. It must provide an efficient storage of oxidative species and an optimal crystallite size for reducing/oxidant separation. And of course, it must accept water on its surface that will provide both the additional energy trapping sites, and the proper diffusion channel for reductive species.

Figure 1 .

 1 Figure 1. Hydrogen production from electron-irradiated AlOOH L and S with respect to water loading. Violet squares (AlOOH L). Cyan blue squares (AlOOH S). Black dotted line: primary radiolytic yield of liquid water.

Figure 2 .

 2 Figure 2. EPR spectra of electron irradiated at 46 kGy of AlOOH L (left) and AlOOH S (right). Two spectra for each sample are shown, one irradiated and analyzed at RT and the second irradiated and analyzed at 77 K.

  Al ⋯ OH → Al ⋯ O + H° Equation 1 or by ionization Al ⋯ OH → Al ⋯ OH + e → Al ⋯ O + H locally trapped by hydroxide + e Equation 2

Figure 3 .

 3 Figure 3. Evolution of the concentration of H radicals, O -, O 3 -and electrons plotted with respect to dose.

Table 1 (

 1 O carries one oxidative equivalent whereas H 2 molecule carries two). It is thus tempting to see in O the oxidative counterpart to H 2 production, its lower production upon hydration being due to the opening of additional dissipative/recombination pathways.

Table 1 .

 1 Radiolytic yields in 10 -8 mol/J calculated with respect to the energy received by the total system.

		AlOOH L	AlOOH L	AlOOH L	AlOOH S	AlOOH S	AlOOH S
		hydrated	hydrated	dry	hydrated	hydrated	dry
		77K	RT	RT	77K	RT	RT
	AlO°	70±10	16±4	23±5	80±20	4±0.5	13±3
	AlO 3 °	17±4	0.3 -1.9	0.7±0.1	18±5	0.3±0.03	0.4±0.1
				0.3*			0*
	H 2	ND	8±1	(1.2	ND	2 -4	(0.46
				trapped)			trapped)

Acknowledgements

This work has been supported by CEA, AREVA NC and AREVA TN. We thank Marie-Noëlle Amiot for EPR access as well as Bruno Boizot for EPR experimental support. We thank Vincent Dauvois and Delphine Durant for their advices and help. We are also grateful to Philippe Zeller. We thank Jean-Jacques Pielawski for his implication in this subject.


E Fischer

K Gajavalli

G Mikaelian

Experimental Study and Thermodynamic Modeling of the Ag-Cd-In System

Keywords: Ag-Cd-In, Thermodynamics, Modeling, CALPHAD

. A satisfactory agreement was obtained between the experimental data and the calculated results.

Introduction

The 80 wt.% Ag, 15 wt.% In, 5 wt.% Cd alloy (SIC alloy) is used as absorber material in most of the PWR reactors. During a severe accident (i.e. loss of cooling), the SIC alloys start to melt at 1016 K [START_REF] Steinbrück | Experiments on Silver-Indium-Cadmium Control Rod Failure During Severe Accidents Sequences[END_REF]. This does not induce any core degradation as long as the molten alloy remains inside the stainless steel cladding of the absorber rod. As the temperature increases, cadmium vapor and helium initially present in the rod cause internal pressurization (in a low-pressure scenario) until the rupture of the absorber rod stainless steel cladding. SIC liquid mixtures and vapors are then released into the core where they can degrade surrounding fuel rods and interact with the fission products released from fuel. Regarding this last point, iodine fission, product which is a major contributor to the short-to-mid-term 2 gaseous source term to environment, interacts with the Ag-In-Cd vapors. That significantly affects its speciation and then its transport in the reactor coolant system and in the containment. The thermodynamic study of the ternary Ag-In-Cd phase diagram at high temperature is a necessary step for a reliable estimate of the vaporization of the chemical elements of the absorber material to be able to predict the iodine behavior in case of a severe accident.

Several thermodynamic descriptions of the binary Ag-Cd, Ag-In and Cd-In systems, are available in literature [START_REF] Chevalier | unpublished assessment supplied to SGTE and included in the SGTE database solution v4.1 (january 2005)[END_REF][START_REF] Moser | [END_REF][START_REF] Dutkiewicz | Cd-In (Cadmium-Indium)[END_REF]. In contrast, for the ternary system at high temperature, the only experimental information available until very recently, was the melting range of the nominal composition of the absorber alloy determined by DSC [START_REF] Steinbrück | Experiments on Silver-Indium-Cadmium Control Rod Failure During Severe Accidents Sequences[END_REF][START_REF] Horrocks | Phase Diagram and Thermodynamics of the Ag-Cd-In Ternary Alloys Systems[END_REF]. Additional measurements have been performed by our team to achieve more accurate description of the system.

Firstly the mixing enthalpy of the liquid phase for five isopleth sections has been measured by silver and cadmium drop dissolution calorimetry at 723 K, and the limits of the biphasic (solid + liquid) domain were derived [START_REF] Benigni | Enthalpy of Mixing in the Ag-Cd-In Ternary Liquid Phase[END_REF].

Secondly, for three compositions, Ag 40 In 60 , Ag [START_REF] Rayson | Isopiestic Techniques Applied to Phase-Diagram Determination in the Systems Silver-Cadmium and Copper-Cadmium[END_REF] Cd 05 In 60 and Ag 28 Cd 12 In 60 , located in the 60 at.% In isopleth section, the liquidus temperatures have been measured by the so-called Interrupted-Heating Differential Thermal Analysis-IHDTA method [8]. In this thermal analysis protocol, full compositional equilibrium of the sample is approached by the application of interrupted-heating cycles near the expected liquidus temperature.

The aim of this paper is to complete the experimental work and to propose for the first time a thermodynamic modelling of the Ag-Cd-In ternary system. IHDTA is then extended to 9 ternary Ag-Cd-In compositions in order to achieve a more complete description of the liquidus surface (Section 2).

In a first step, a self-consistent set of thermodynamic descriptions of the binaries is required. For this purpose, we have reviewed the available information for the Ag-Cd (Section 4), Ag-In (Section 5) and Cd-In (Section 6) binary systems. The objective is to reassess the 3 binaries in order to represent the extension of the hcp_A3 phase in the ternary system and to be self-consistent with the current lattice stabilities of the SGTE unary database [START_REF]PURE 5.0 SGTE Pure Elements (Unary) Database[END_REF]. The second step is to perform the modeling of the ternary system (Section 7) starting from the combination of the three binary sub-systems. The ternary interaction parameters are optimized based on experimental phase diagram information and calorimetric data for ternary alloys. The optimizations were carried out by taking into account simultaneously all the selected available experimental information, equilibrium phase diagram and thermodynamic properties, with a given weight. The selection of the model parameters and the weights attached to each experimental data were changed by trial and error during the process, until a satisfactory agreement was obtained between the calculated and the experimental data.

Experimental

Materials and Methods

For each composition, silver (Alfa Aesar 99.99%), cadmium (Alfa Aesar 99.9999%) and indium (Alfa Aesar 99.9999%) shots are weighed in stoichiometric proportions. Then, these mixtures of the pure constituents are sealed in silica ampoules under argon with an oxyacetylene torch. All the sample ampoules are heat treated 1hr at 1273 K before performing the thermal analyses using a Setaram DSC 111 instrument. The heat flow sensors of this instrument, which can work up to 1103 K, are 3-D thermopiles of high sensitivity. In the experiments, one sample ampoule is inserted into the laboratory tube while an empty silica ampoule of similar weight and shape is inserted in the reference tube. The instrument is temperature-calibrated towards the melting points of Al (Koch light, 99.999%), In (Alfa Aesar, 99.9999%), Sn (Alfa Aesar, 99.9999%) and Zn (Alfa Aesar, 99.999%).

As mentioned in the introduction, the liquidus temperatures are determined using the IHDTA protocol. This method has already been employed for the accurate determination of liquidus temperatures in other systems [START_REF] Moon | Experimental and Thermodynamic Assessment of Sn-Ag-Cu Solder Alloys[END_REF][START_REF] Wu | Liquidus Temperature Determination in Multicomponent Alloys by Thermal Analysis[END_REF]. Principle of the method and its implementation to Ag-Cd-In compositions are described in our previous paper [8].

Experimental Results

To achieve a better description of the extension of the (liquid + hcp_A3) biphasic region, the liquidus temperatures of 6 new ternary compositions are determined using the IHDTA protocol (Table 1). For the sake of completeness, the liquidus temperatures of the three compositions previously studied in the 60 at.% In isopleth section [8] are also reported in Table 1.

For the binary composition, our measured value (724-727 K) is in good agreement with the DSC results of Moser et al. [START_REF] Moser | [END_REF] (728 K) and Horrocks [START_REF] Horrocks | Phase Diagram and Thermodynamics of the Ag-Cd-In Ternary Alloys Systems[END_REF] (729 K).

For the ternary alloys, discrepancies can be seen between the liquidus temperatures measured in this work and those measured by Jones [93] and Robinson [94] by Smith Thermal Analysis. As explained in [8], our thermal analysis protocol is thought to be more reliable and more weight was given to our IHDTA data while modelling the Ag-Cd-In ternary diagram. 724-727 [8] 729 [START_REF] Horrocks | Phase Diagram and Thermodynamics of the Ag-Cd-In Ternary Alloys Systems[END_REF] 752 [94] reported in [START_REF] Horrocks | Phase Diagram and Thermodynamics of the Ag-Cd-In Ternary Alloys Systems[END_REF] 728 [START_REF] Moser | [END_REF] 719.

Thermodynamic Models

Detailed crystallographic information about the different phases of the ternary system is given in Table 2. As the order-disorder formalism is not supported in the NUCLEA database [START_REF] Desgranges | Compréhension et prédiction du comportement sous irradiation neutronique d'alliages absorbants à base d'argent[END_REF] with which our optimizations will be used, simplified descriptions are chosen for the B2 and L1 2 phases.

Table 2

Crystal structure data for the solid phases in the Ag-Cd-In ternary system.

The thermodynamic models of the various phases are briefly introduced below. The Gibbs energy function °GΦ (T) = G Φ (T) -H SER is referred to the so-called "Standard Element Reference" (SER) state, H SER being the molar enthalpy of the SER state. The temperature dependence of the molar Gibbs energy of the pure elements in either stable or metastable phases, referred to the SER state, is given by the expression: G -H SER = A + BT + CT ln T + DT 2 + ET 3 + FT -1 + GT 7 + HT -9 The Gibbs energy functions of the elements are taken from the SGTE (Scientific Group Thermodata Europe) unary database [START_REF]PURE 5.0 SGTE Pure Elements (Unary) Database[END_REF]. When not available, metastable structures (necessary as reference values for the thermodynamic description of the corresponding solid solutions) are discussed separately for each phase in the following.

A substitutional model is used for all solution phases, the excess interaction parameters being described by a Redlich-Kister-Muggianu [START_REF] Redlich | Optimization of Phase Diagrams by a Least Square Method Using Simultaneously Different Types of Data[END_REF][START_REF] Muggianu | Enthalpy of Formation of Liquid Bi-Sn-Ga Alloys at 723 K. Choice of an Analytical Expression of Integral and Partial Excess Quantities of Mixing[END_REF] polynomial, and optimized by using the Lukas et al. [START_REF] Lukas | Optimization of Phase Diagrams by a Least Squares Method using Simultaneously Different Types of Data[END_REF] computer program. The total molar Gibbs energy of the solution phases Φ is expressed under the generic form:

G Φ = G Φ,ref + G Φ,id + G Φ,exbin + G Φ,exter
In which the reference Gibbs energy is written as:

G Φ,ref = x Ag °GAg Φ + x Cd °GCd Φ + x In °GIn Φ
The ideal mixing contribution as: G Φ,id = RT (x Ag ln x Ag + x Cd ln x Cd + x In ln x In )

And the binary (G Φ,exbin ) and ternary (G Φ,exter ) contributions to the excess Gibbs energy as:

G Φ,exbin = x Ag x Cd Σ ν ν L Φ Ag,Cd (x Ag -x Cd ) ν + x Ag x In Σ ν ν L Φ Ag,In (x Ag -x In ) ν + x Cd x In Σ ν ν L Φ Cd,In (x Cd -x In ) ν G Φ,exter = x Ag x Cd x In [x Ag Ag L Φ Ag,Cd,In + x Cd Cd L Φ Ag,Cd,In + x In In L Φ Ag,Cd,In ]
where °Gi Φ is the molar Gibbs energy of the pure element i in the Φ solution, and x i the mole fraction of i. The binary ν L Φ i,j and ternary ν L Φ i,j,k interaction parameters can depend linearly on temperature.

The Gibbs energies of the A p B q binary stoichiometric compounds are expressed as:

G ApBq (T) = a + b T + p °Gref A + q °Gref B
where the a and b coefficients are respectively the enthalpy ∆ f H°2 98.15K and entropy ∆ f S °298.15K of formation of the compound. In this model, the heat capacity of a compound is given by the Neumann-Kopp additivity rule, neglecting any possible excess heat capacity. The a and b parameters are to be evaluated during the optimization process. The reference states for pure silver, cadmium and indium are the face-centered cubic (fcc_A1), close-packed hexagonal (hcp_Cd), and tetragonal (tet_A6) structures respectively. The assessed Gibbs energy parameters are collected in Table 3. The PANDAT software is used for plotting most of the figures.

4.

Ag-Cd

Phase Diagram Experimental Information

The Ag-Cd phase diagram has been extensively investigated. By means of thermal and microscopic analyses, the entire liquidus curve and the solidus curves of the α, β and η phases were determined by Rose [START_REF] Rose | On Certain Properties of the Alloys of Silver and Cadmium[END_REF], Bruni and Quercigh [START_REF] Bruni | Uber das Zustandsdiagramm der Silber Cadmium Legierungen[END_REF] and Petrenko and Fedorow [START_REF] Petrenko | Uber die Leguerungen des Silbers mit Cadmium[END_REF]. The various liquidus determinations are in rather good agreement.

Later on, Durrant [START_REF] Durrant | The Constitution of the Cadmium-Rich Alloys of the System Cadmium-Silver[END_REF] investigated the cadmium-rich part (0-41 at.% Ag) of the phase diagram by thermal and micrographic analyses, and in particular the ε and η solidus lines, and the (ε + η) field boundaries, and completed few years later [START_REF] Durrant | The ɛ, γ, and β phases of the System Cadmium-Silver[END_REF] the ε, γ, β, β' and ζ solid solution boundaries.

Hume-Rothery et al. measured the liquidus in equilibrium with the α solid solution in the 0-39 [START_REF] Hume-Rothery | The Freezing-points, Melting Points, and Solid Solubility Limits of the Alloys of Silver and Copper with the Elements of the B Sub-Groups[END_REF] and 0-16 [START_REF] Hume-Rothery | The Accurate Determination of the Freezingpoints of Alloys, and a Study of Valency Effects in Certain Alloys of Silver[END_REF] at.% Cd ranges by thermal analysis on cooling. They also derived the α solidus line and the solubility limit of the α phase in equilibrium with β by micrographic examination of the relative quantities of the 2 phases as a function of temperature.

Using X-ray diffraction, Owen et al. [START_REF] Owen | An X-Ray Study of Silver-Cadmium Alloys[END_REF] established the boundaries of the stability domains of the solid phases below 973 K. The β'(AgCd) phase is absent from their diagram.

(α + β) field boundaries at 883 K were determined by isopiestic techniques by Rayson and Alexander [START_REF] Rayson | Isopiestic Techniques Applied to Phase-Diagram Determination in the Systems Silver-Cadmium and Copper-Cadmium[END_REF] in disagreement with previous measurements.

From these studies, Hansen and Anderko [START_REF] Hansen | Constitution of Binary Alloys[END_REF] constructed the phase diagram.

Quader [START_REF] Quader | An X-Ray Study of Silver-Cadmium Alloys[END_REF] carried out an X-ray investigation to ascertain the phase boundaries at temperatures below 573 K. The presence of the β'(AgCd) phase was confirmed but without establishing its composition domain. The boundaries of the α, ζ and γ phases were in good agreement with those of Owen et al. [START_REF] Owen | An X-Ray Study of Silver-Cadmium Alloys[END_REF].

Filby and Pratt [START_REF] Filby | A Vapour Pressure Study of the Thermodynamic Properties of the Alpha, Beta, Gamma and Epsilon Silver-Cadmium Phases[END_REF] derived the boundaries of the β phase from activity measurements using a dew point technique.

Horrocks [START_REF] Horrocks | Phase Diagram and Thermodynamics of the Ag-Cd-In Ternary Alloys Systems[END_REF] validated all the invariant reactions with Smith Thermal Analysis.

Thermodynamic Experimental Information

Vapor pressure of cadmium above solid silver-cadmium alloys was measured by several researchers. Above the α phase, isopiestic method was used by Herasymenko [START_REF] Herasymenko | Thermodynamic Properties of Solid Solutions[END_REF] in the 873-1173 K temperature range, and by Masson and Sheu [START_REF] Masson | Variations in the Composition Dependence of the Activity Coefficient in Terminal Solid Solutions of Ag-Zn, Ag-Cd, and Cu-Zn[END_REF] at 1063 K, electronic spectrophotometer was used by both Scatchard and Boyd [START_REF] Scatchard | The Equilibrium of α -Silver-Cadmium Alloys with Cadmium Vapor[END_REF] and Rapperport and Pemsler [START_REF] Rapperport | Thermodynamic Measurements using Atomic Absorption[END_REF] in the 620-875 and 460-633 K temperature ranges respectively. However, Rapperport et al. did not correctly define the alloy composition and hence their data are not usable.

A dew point technique was used by Birchenall and al. [START_REF] Birchenall | The Vapor Pressures of Zinc and Cadmium over some of their Silver Alloys[END_REF] in the 793-1153 K temperature range for 3 α phase compositions, and by Filby and Pratt [START_REF] Filby | A Vapour Pressure Study of the Thermodynamic Properties of the Alpha, Beta, Gamma and Epsilon Silver-Cadmium Phases[END_REF] in the range of temperature 635-1140 K above the α, β, γ and ε phases.

The cadmium activity in the α, β, ζ, γ and ε phases was derived from EMF measurement in the 673-773 K temperature range by Olander [START_REF] Olander | Eine Elektrochemische Untersuchung von Cadmium-Silber Legierungen[END_REF].

From liquid tin solution calorimetry experiments, various authors derived the heats of formation of the solid phases at different temperatures: Kleppa [START_REF] Kleppa | Heat of Formation of Solid and Liquid Alloys in the Systems Silver-Cadmium, Silver-Indium, and Silver-Antimony at 450°[END_REF] at 723 K for the α, β, γ and ε phases, Waldman et al. [45] at 273 K and Orr et al. [START_REF] Orr | Heats of Formation of α-Phase Silver-Cadmium Alloys[END_REF] at 308 K for the α phase and Anderson [START_REF] Anderson | The Thermodynamic Properties of the Silver-Cadmium System[END_REF] at 304 K for the ζ, β' and γ phases.

Cadmium vapor pressure above the liquid phase was determined by different methods: using a dew point method by Schneider and Schmid [START_REF] Schneider | Die Dampfdrucke des Zinks und Cadmium uber ihren Binaren Flussigen Legierungen mit Kupfr, Silber und Gold[END_REF] in the 973-1123 K temperature and x Cd = 0.266-0.676 composition ranges; by mean of a silica flexible membrane at 1223 K by Van Gool [49]; using an isopiestic method by Conant and Swofford [START_REF] Conant | Solute-Solvent Interactions in Liquid Alloys[END_REF] at 773 K for silver rich alloys; using the boiling-point method by Volodin et al. [51] between 823 and 1148 K.

Using EMF measurements, the cadmium activity in the liquid was determined by Schaeffer and Hovorka [START_REF] Schaeffer | Electromotive-Force Measurements of Molten Binary Alloys[END_REF] in the 683-823 K temperature range for cadmium rich compositions, and by Houseman and Conant [START_REF] Houseman | Cadmium Activities of Silver-Cadmium Alloys Determined from Measurements on EMF Cells Involving Displacement Reactions[END_REF] at 777 K for diluted solutions of silver in cadmium.

Kleppa [START_REF] Kleppa | Heat of Formation of Solid and Liquid Alloys in the Systems Silver-Cadmium, Silver-Indium, and Silver-Antimony at 450°[END_REF] measured the heat of formation of liquid alloys at 723 K by direct reaction calorimetry.

Thermodynamic Optimization

A Calphad thermodynamic description of the Ag-Cd binary phase diagram was reported by Horrocks [START_REF] Horrocks | Phase Diagram and Thermodynamics of the Ag-Cd-In Ternary Alloys Systems[END_REF] as part of his thesis. First, this optimization is not satisfactory because the domain of non-stoichiometry of the hcp AgCd phase is too narrow whereas an accurate description of this region is of prime importance when considering that this solid solution has a large extension in the ternary. Second, the line separating the ε and (ε + η) domains, in the vicinity of x(Cd) = 0.8, is also not well reproduced. It has been thus decided to completely reoptimize this system.

The three ζ, ε and η solid solutions exhibit the same hcp Mg prototype, but different c/a ratios. In the composition range of the ζ and ε phases, this ratio decreases from about c/a = 1.619 to c/a = 1.555 on increasing cadmium concentration from 47 to 81 at.%. These values are very similar, and close to the ideal 1.63 value corresponding to the close packing of hard spheres. Conversely, the c/a ratio of the η phase (Cd terminal solution) raises from 1.816 to 1.886 on increasing cadmium concentration from 97 to 100 at.%, well above the ideal value. As reported in [START_REF] Horrocks | Phase Diagram and Thermodynamics of the Ag-Cd-In Ternary Alloys Systems[END_REF] for Cd, or in [START_REF] Gomez-Acebo | Thermodynamic Assessment of the Ag-Zn System[END_REF][START_REF] Kowalski | Thermodynamic Reevaluation of the Copper-Zinc System[END_REF][START_REF] Schmid-Fetzer | Is zinc HCP_ZN or HCP_A3?[END_REF] for Zn, we consider that the dissimilarity in the interatomic spacings creates an energy difference between the lattice stabilities of the ideal and "non-ideal" hcp cadmium forms.

The lattice stability of the hexagonal close-packed cadmium with a "non-ideal" c/a ratio, denoted here hcp_Cd, is taken from the SGTE unary databank [START_REF]PURE 5.0 SGTE Pure Elements (Unary) Database[END_REF]. The lattice stabilities of the metastable "ideal" Cd(hcp_A3) and the metastable Cd(bcc_A2) are estimated at the most suitable values during the optimization process, and then fixed.

The AgCd intermetallic phase is modelled as a line compound as it is only stable in a very narrow composition range as shown by [START_REF] Durrant | The ɛ, γ, and β phases of the System Cadmium-Silver[END_REF] who found the 48.7 and 50.3 at.% Cd compositions to be diphasic between 468 K and 497 K.

The γ-brass structure at high temperature and γ' related superstructure at low temperature have been described as a single Ag 2 Cd 3 phase due to the lack of experimental data. Its domain of stability on both sides of the 60 at.% Cd composition (58.6 to 61.8 at.% Cd at T = 300-850 K [START_REF] Owen | An X-Ray Study of Silver-Cadmium Alloys[END_REF], 57.6 to 61.6 at.% Cd at 773 K [START_REF] Durrant | The ɛ, γ, and β phases of the System Cadmium-Silver[END_REF]) is small justifying to consider this phase as stoichiometric.

The optimization is performed following the guidelines presented in the introduction.

Results and discussion

The Ag-Cd phase diagram calculated using the optimised set of parameters is compared with the experimental data in Fig. 1. Temperatures and compositions of invariant equilibria are compared with experimental values in Table 4.

The experimental phase boundaries determined by the different researchers show an overall good concordance. A very good agreement is also observed between calculated and experimental values across the entire system.

Nevertheless, small deviations can be seen in the temperature and compositions of the phase boundaries at the invariant reactions with the γ phase. This results from our choice to model the γ phase as a stoichiometric compound. The ζ/(ζ + γ) lines determined by both Durrant [START_REF] Durrant | The ɛ, γ, and β phases of the System Cadmium-Silver[END_REF] and Owen et al. [START_REF] Owen | An X-Ray Study of Silver-Cadmium Alloys[END_REF] are not compatible. When the global optimization was carried out, the experimental points from Owen et al. [START_REF] Owen | An X-Ray Study of Silver-Cadmium Alloys[END_REF] were found easier to reproduce and hence adopted, in the final optimisation.

The calculated ε/(ε + η) line slightly differs from the experimental points because, due to the scarce thermodynamic information on these two phases, we have chosen to restrict the number of optimized interaction parameters. The calculated formation enthalpy of the liquid phase is compared in Fig. 2 with the only measured values from Kleppa [START_REF] Kleppa | Heat of Formation of Solid and Liquid Alloys in the Systems Silver-Cadmium, Silver-Indium, and Silver-Antimony at 450°[END_REF] at high-cadmium content, with a good agreement. For the hcp (ε and ζ) and bcc_A2 (β) phases, the enthalpies calculated with our optimization lie less than 1 kJ/mol above the experimental values obtained by Kleppa [START_REF] Kleppa | Heat of Formation of Solid and Liquid Alloys in the Systems Silver-Cadmium, Silver-Indium, and Silver-Antimony at 450°[END_REF] and Anderson [START_REF] Anderson | The Thermodynamic Properties of the Silver-Cadmium System[END_REF]. This discrepancy is considered acceptable knowing the magnitude of the uncertainty in high temperature solution calorimetry experiments. The Cd chemical potential in the liquid phase, calculated at T = 773 K and 1100 K, is plotted vs. Cd mole fraction in Fig. 3 and compared to the experimental data. The highly dispersed experimental values obtained by Volodin et al. [START_REF] Volodin | Thermodynamic Study of the Silver-Cadmium System with Determination of the Upper Boundary of Existence of Liquid Alloys[END_REF], those of Schaeffer and Hovorka [START_REF] Schaeffer | Electromotive-Force Measurements of Molten Binary Alloys[END_REF], who themselves judged that their measured activities do not vary in a regular manner with concentration, and few too high values at rich Cd composition discarded by Van Gool [49] himself were not considered in the optimization. The selected data from [START_REF] Schneider | Die Dampfdrucke des Zinks und Cadmium uber ihren Binaren Flussigen Legierungen mit Kupfr, Silber und Gold[END_REF][START_REF] Conant | Solute-Solvent Interactions in Liquid Alloys[END_REF] and [START_REF] Houseman | Cadmium Activities of Silver-Cadmium Alloys Determined from Measurements on EMF Cells Involving Displacement Reactions[END_REF] are quite well fitted.

Fig. 3

Cadmium chemical potential in the liquid phase, referred to Cd L , calculated at T = 773 K and 1100 K, compared with experimental data.

The calculated formation enthalpy of the α phase (Fig. 4) is in agreement with the measured values of Kleppa [START_REF] Kleppa | Heat of Formation of Solid and Liquid Alloys in the Systems Silver-Cadmium, Silver-Indium, and Silver-Antimony at 450°[END_REF], Waldman et al. [45], and Orr et al. [START_REF] Orr | Heats of Formation of α-Phase Silver-Cadmium Alloys[END_REF]. No variation with temperature could be inferred from these three consistent sets of values. The cadmium chemical potential in the α phase, calculated at T = 700 K and 1000 K is represented in Fig. 5 and compared with all experimental data. A good agreement is obtained with the data reported by Herasymenko [START_REF] Herasymenko | Thermodynamic Properties of Solid Solutions[END_REF], Masson et al. [START_REF] Masson | Variations in the Composition Dependence of the Activity Coefficient in Terminal Solid Solutions of Ag-Zn, Ag-Cd, and Cu-Zn[END_REF] and Birchenall et al. [START_REF] Birchenall | The Vapor Pressures of Zinc and Cadmium over some of their Silver Alloys[END_REF]. The calculated curves are less compatible with the values of [START_REF] Filby | A Vapour Pressure Study of the Thermodynamic Properties of the Alpha, Beta, Gamma and Epsilon Silver-Cadmium Phases[END_REF], [START_REF] Scatchard | The Equilibrium of α -Silver-Cadmium Alloys with Cadmium Vapor[END_REF], and [START_REF] Olander | Eine Elektrochemische Untersuchung von Cadmium-Silber Legierungen[END_REF].

Fig. 5

Cadmium chemical potential in the α phase referred to Cd L , calculated at T = 700 K and 1000 K, compared with experimental data.

Fig. 6 shows the calculated cadmium partial Gibbs energy in the hcp (ε and ζ) phases and in the bcc_A2 (β) phase, compared with experimental data from Olander [START_REF] Olander | Eine Elektrochemische Untersuchung von Cadmium-Silber Legierungen[END_REF] and Filby and Pratt [START_REF] Filby | A Vapour Pressure Study of the Thermodynamic Properties of the Alpha, Beta, Gamma and Epsilon Silver-Cadmium Phases[END_REF]. It can be seen that the data series reported by the two authors are in strong disagreement, especially for the ε phase. It was also not possible to correctly reproduce the whole set of a single author. For the hcp phase, values from [START_REF] Olander | Eine Elektrochemische Untersuchung von Cadmium-Silber Legierungen[END_REF] are in better agreement with the calculation, whereas for the bcc_A2 phase, a mean value between [START_REF] Olander | Eine Elektrochemische Untersuchung von Cadmium-Silber Legierungen[END_REF] and [START_REF] Filby | A Vapour Pressure Study of the Thermodynamic Properties of the Alpha, Beta, Gamma and Epsilon Silver-Cadmium Phases[END_REF] is calculated.

Fig. 6

Cadmium chemical potential in the hcp phase (700 K, black) and in bcc_A2 phase (800 K, red) referred to Cd L , compared with experimental data.

For the two stoichiometric compounds, the calculated enthalpies of formation match quite well with the available experimental values: Ag 0.5 Cd 0.5 , ∆ f H°3 04K (J/mol) = -9645 this work (-9079 [START_REF] Anderson | The Thermodynamic Properties of the Silver-Cadmium System[END_REF]), ∆ f H°7 23K (J/mol) = -12716 this work (-9720 [START_REF] Kleppa | Heat of Formation of Solid and Liquid Alloys in the Systems Silver-Cadmium, Silver-Indium, and Silver-Antimony at 450°[END_REF]); Ag 0.4 Cd 0.6 , ∆ f Η°3 04 K (J/mol) = -7119 this work (-8326 [START_REF] Anderson | The Thermodynamic Properties of the Silver-Cadmium System[END_REF]); ∆ f H° 723K (J/mol) = -10804 this work (-10810 [START_REF] Kleppa | Heat of Formation of Solid and Liquid Alloys in the Systems Silver-Cadmium, Silver-Indium, and Silver-Antimony at 450°[END_REF], -10816 [START_REF] Filby | A Vapour Pressure Study of the Thermodynamic Properties of the Alpha, Beta, Gamma and Epsilon Silver-Cadmium Phases[END_REF]), and are not so far from the DFT calculated value ∆ f H°0 K (J/mol) = -6657 for Ag 0.5 Cd 0.5 [START_REF] Saal | Materials Design and Discovery with High-Throughput Density Functional Theory: The Open Quantum Materials Database (OQMD)[END_REF].

5.

Ag-In

Phase Diagram Experimental Information

The phase diagram of the Ag-In system was built by Hansen and Anderko [START_REF] Hansen | Constitution of Binary Alloys[END_REF] after critical analysis of available experimental investigations. It is essentially based on the results of Weibke and Eggers [START_REF] Weibke | The Ag-In System[END_REF], Hume-Rothery et al. [START_REF] Hume-Rothery | The Ag-In System[END_REF][START_REF] Hume-Rothery | The Ag-In System[END_REF], Owen and Roberts [START_REF] Owen | Factors Affecting the Limit of Solubility of Elements in Copper and Silver[END_REF] and Hellner [START_REF] Hellner | The Binary System Silver-Indium[END_REF]. The more recent works reported thereafter do not significantly modify the phase diagram of [START_REF] Hansen | Constitution of Binary Alloys[END_REF].

The maximum solubility of indium in α silver has been determined using X-Ray Diffraction (XRD) and metallographic techniques by Straumanis and Riad [64] as x In =0.194 at room temperature, and by Snyder [START_REF] Snyder | Primary Solid-Solution Phase Boundary in Silver Corner of Silver-Cadmium-Indium Ternary System[END_REF] as x In = 0.193 at room temperature and x In = 0.206 at 588 K.

A new phase diagram was constructed by Campbell et al. [START_REF] Campbell | The Silver-Indium System: Thermal Analysis, Photomicrography, Electron Microprobe, and X-ray Powder Diffraction Results[END_REF] using differential thermal analysis (DTA), XRD on powder, photomicrography, and Electron Probe Micro-Analysis (EPMA). Compositions ranging from pure indium to 75 at.% Ag were investigated. Above 723 K, the liquidus lies approximately 8 K above the one of Weibke and Eggers [START_REF] Weibke | The Ag-In System[END_REF]. The ζ phase extends to much higher indium concentration than was previously established by [START_REF] Weibke | The Ag-In System[END_REF], and this phase is still stable at room temperature over a very narrow, 70.3 to 71.0 at.% Ag, composition range. The metatectic reaction ζ -> L + Ag 2 In was observed at lower temperature.

By means of Smith Thermal Analysis, Horrocks [START_REF] Horrocks | Phase Diagram and Thermodynamics of the Ag-Cd-In Ternary Alloys Systems[END_REF] measured the invariants and 2 liquidus points of this system, in very good agreement with previously published works.

Different experimental techniques were used by Moser et al. [START_REF] Moser | [END_REF] to investigate the Ag-In phase diagram. By DSC, they determined the temperature of the phase transitions over the whole composition range. Their liquidus temperatures were in agreement with previous studies. With diffusion couples and metallography, they established in particular that the extent of the ζ phase was narrower than previously found by Campbell et al. [START_REF] Campbell | The Silver-Indium System: Thermal Analysis, Photomicrography, Electron Microprobe, and X-ray Powder Diffraction Results[END_REF]. The region of stability of the Ag 3 In phase was not investigated.

Using DTA, DSC, XRD and EPMA Bahari et al. [START_REF] Bahari | Study of the Ag-In-Te ternary System, II. Description of the Quadrilateral Ag-Ag2Te-In2Te3-In[END_REF], [START_REF] Bahari | Experimental Study of the Ternary Ag-Cu-In Phase Diagram[END_REF] confirmed the existence of Ag 3 In in the composition range between 24.3 and 30 at.% at 298 K.

Thermodynamic Experimental Information

Concerning the solid phases, the heat of formation was measured by liquid tin solution calorimetry, by Kleppa [44] for the α and ζ solid solutions at 723 K in the x In = 0.078 -0.535 composition range, and by Orr and Hultgren [START_REF] Orr | Heats of Formation of α Phase Silver-Indium Alloys[END_REF] for the α phase, dropping samples from 317 K in the bath maintained at 700 K, in the x In = 0.05 -0.17 composition range. In the α phase, both data sets are in excellent agreement.

The activity of indium in the α phase was measured by EMF and gas-solid equilibrium techniques by Alcock and Jacob [START_REF] Alcock | Thermodynamics of -Solid Solutions of Silver with Indium and Tin[END_REF] at 900 K, for compositions ranging from x In = 0.04 to 0.19, and, with an atomic absorption spectrophotometer, by Masson and Pradhan [START_REF] Masson | Measurements of Vapor Pressure of Indium over α Ag-In Using Atomic Absorption[END_REF] at 1000 K, for compositions ranging from x In = 0.0781 to 0.1817.

There is no information available in literature on the thermodynamic properties of the compounds.

The heat of formation of the liquid phase has been determined by several researchers. The employed technique, the temperature of measurements and the studied composition ranges are compiled thereafter for each study: Kleppa [START_REF] Kleppa | Heat of Formation of Solid and Liquid Alloys in the Systems Silver-Cadmium, Silver-Indium, and Silver-Antimony at 450°[END_REF], calorimetry, dissolution of solid silver in liquid indium at 723 K, x In = 0.67 -0.94; Itagaki and Yazawa [START_REF] Itagaki | Measurements of Heats of Mixing in Liquid Silver Binary Alloys[END_REF], adiabatic calorimetry at 1243 K, x In = 0.5; Beja [72] and also reported as unpublished work by Castanet et al. [START_REF] Castanet | Propriétés Thermodynamiques des Solutions Liquides Argent-Indium[END_REF], direct calorimetry at 1028 K, x In = 0.10 -0.95; Castanet et al. [START_REF] Castanet | Propriétés Thermodynamiques des Solutions Liquides Argent-Indium[END_REF], drop calorimetry at 743 K and 1280 K, x In = 0-1; Sabbar et al. [START_REF] Sabbar | The Ag-Bi-In system: Enthalpy of Formation[END_REF], drop calorimetry at 896 K, x In = 0.5.

The activities of silver and indium have been studied combining Knudsen effusion and mass spectrometry by Alcock et al. [START_REF] Alcock | A Mass Spectrometric Study of the Binary Liquid Alloys, Ag-In and Cu-Sn[END_REF] at 1300 K, for compositions x In = 0.1 -0.9, and by Qi et al. [START_REF] Qi | Thermodynamic Study of Liquid Ag-In and Ag-Ga Alloys with a Knudsen Cell-mass Spectrometer[END_REF] in the 1100 -1400 K temperature range and for compositions x In = 0.1 -0.9.

Using EMF measurements, the activity of indium has been determined by Przezdziedcka -Mycielska et al. [START_REF] Przezdziecka-Mycielska | Thermodynamic Properties of Liquid Metallic Solutions XI. The Ag-In System[END_REF] at 1000 K and for x In = 0.30 to 0.95, by Nozaki et al. [START_REF] Nozaki | Thermodynamic Studies on Liquid Silver-Indium Alloys[END_REF] from 1000 to 1200 K and for x In = 0.208 to 0.823, by Kameda et al. [START_REF] Kameda | Activities of Liquid Silver-Indium Alloys by EMF Measurements Using Zirconia Solid and Fused Salt Electrolytes[END_REF] in the range of temperature 835 -1272 K for x In = 0.20 to 0.85, and by Jendrzejczyk and Fitzner [80] between 950 and 1273 K for x In = 0.15 to 1.

Predel and Schallner [START_REF] Predel | Untersuchung der thermodynamischen Eigenschaften flussiger binaren Legierungen des Silbers und Goldes mit Gallium, Indium und Germanium[END_REF] have measured the activity of zinc in ternary Ag-In-Zn liquid alloys using EMF techniques from which they derived the activity of indium at 1000 K.

Thermodynamic Optimization

Previous CALPHAD modelling of this system by Chevalier and Fischer [START_REF] Chevalier | XXIIièmes Journées d'Etude des Equilibres entre Phases[END_REF][START_REF] Chevalier | [END_REF][START_REF] Landolt-Bornstein | Thermodynamic Properties of Inorganic Materials[END_REF], Korhonen et al. [START_REF] Korhonen | Thermodynamics of the Sn-In-Ag Solder System[END_REF] and by Moser et al. [START_REF] Moser | [END_REF] are all based on the old lattice stability of In(fcc_A1). Moreover, the Ag 3 In phase is omitted in the assessments of Horrocks [START_REF] Horrocks | Phase Diagram and Thermodynamics of the Ag-Cd-In Ternary Alloys Systems[END_REF] and Gierlotka [START_REF] Gierlotka | Thermodynamic Description Of The Quaternary Ag-Cu-In-Sn System[END_REF]. Hence, a new assessment based on the current In(fcc_A1) lattice stability [START_REF]PURE 5.0 SGTE Pure Elements (Unary) Database[END_REF] is performed in this study. The very small solubility of Ag in In(tet_A6) is not described. The Ag 2 In and AgIn 2 phases are considered as stoichiometric compounds due to their narrow phase field. The Ag 3 In should rigorously be considered as a non-stoichiometric compound since Bahari [START_REF] Bahari | Study of the Ag-In-Te ternary System, II. Description of the Quadrilateral Ag-Ag2Te-In2Te3-In[END_REF] established its rather large composition domain of stability extending between 24.3 and 30 at.% In. Nevertheless, considering that this thermodynamic modelling is mainly focused on the high temperature range relevant for nuclear safety assessment under severe accident conditions, the Ag 3 In compound, which decomposes above 473 K, is modeled as a stoichiometric compound for the sake of simplicity.

Results and Discussion

Temperatures and compositions of invariant equilibria are compared with experimental values in Table 4. The Ag-In phase diagram calculated using the optimized set of parameters is displayed in Fig. 7 with the experimental data for comparison.

Fig. 7

Ag-In calculated phase diagram compared with experimental points.

It can be seen that, excepting [START_REF] Bahari | Study of the Ag-In-Te ternary System, II. Description of the Quadrilateral Ag-Ag2Te-In2Te3-In[END_REF], there is an overall good agreement between the liquidus temperatures measured by the different authors. Significant discrepancies with the results of Bahari [START_REF] Bahari | Study of the Ag-In-Te ternary System, II. Description of the Quadrilateral Ag-Ag2Te-In2Te3-In[END_REF] are observed in the indium-rich region. According to our experience on this system, a possible explanation could be the sluggish diffusion in the hcp_A3 solid solution in equilibrium with the liquid making the liquidus detection by DSC uncertain, particularly in the In-rich region where the liquidus temperatures are low. It must be stressed that the liquidus temperatures measured later by the same authors [START_REF] Bahari | Experimental Study of the Ternary Ag-Cu-In Phase Diagram[END_REF] are in better agreement even if they are still somewhat above the other values. The experimental values are relatively well reproduced by the assessment. Nevertheless, the calculated liquidus is slightly higher than most of the experimental values in the 750-850 K area, and similar disagreements are observed in this range for the optimizations of [START_REF] Horrocks | Phase Diagram and Thermodynamics of the Ag-Cd-In Ternary Alloys Systems[END_REF], [START_REF] Moser | [END_REF], [START_REF] Gierlotka | Thermodynamic Description Of The Quaternary Ag-Cu-In-Sn System[END_REF]. When trying to better reproduce this range, the calculated liquidus is then lowered between 500 and 750 K and the agreement with the experimental points is degraded in this last range, this is the case with the assessment from [START_REF] Korhonen | Thermodynamics of the Sn-In-Ag Solder System[END_REF].

The extent of the hcp field according to the consistent works of Weibke and Eggers [59] and Moser et al. [START_REF] Moser | [END_REF] contradicts the results of Campbell et al. [START_REF] Campbell | The Silver-Indium System: Thermal Analysis, Photomicrography, Electron Microprobe, and X-ray Powder Diffraction Results[END_REF]. The narrower extent of the hcp domain at high temperature reported by [START_REF] Weibke | The Ag-In System[END_REF] was found to be compatible with the thermodynamic description, and thus selected for the new assessment. According to Campbell et al. [START_REF] Campbell | The Silver-Indium System: Thermal Analysis, Photomicrography, Electron Microprobe, and X-ray Powder Diffraction Results[END_REF], the (Ag 2 In + hcp) domain would be asymmetrical but this shape is judged unlikely by [START_REF] Okamoto | Ag-In (Silver-Indium)[END_REF]. The optimization based on the experimental points from Weibke and Eggers [START_REF] Weibke | The Ag-In System[END_REF] for the (Ag 2 In + hcp) silver rich domain leads to a symmetric shape, the hcp composition reaches 42 at.% In at the metatectic temperature of 477 K. In the calculated phase diagram, the hcp solid solution is not stable at room temperature and decomposes by the eutectoid reaction hcp fcc_A1 + Ag 3 In. The boundaries of the (fcc_a1 + hcp) diphasic domain determined by Moser et al. [START_REF] Moser | [END_REF] have been discarded along with their other points, which seem always shifted relative to the other works. For this domain, the value of the solubility of indium in fcc_A1 is calculated in better agreement with the data measured by [64][START_REF] Snyder | Primary Solid-Solution Phase Boundary in Silver Corner of Silver-Cadmium-Indium Ternary System[END_REF][START_REF] Campbell | The Silver-Indium System: Thermal Analysis, Photomicrography, Electron Microprobe, and X-ray Powder Diffraction Results[END_REF], than with those from [START_REF] Hume-Rothery | The Ag-In System[END_REF] and [START_REF] Owen | Factors Affecting the Limit of Solubility of Elements in Copper and Silver[END_REF]. However, further investigations are needed to clarify the solid phase equilibria in the 20 -50 at.% In range at low temperature.

The calculated enthalpy of formation of the liquid phase is compared in Fig. 8 with the experimental values. No clear temperature dependence of the mixing enthalpy arises from the experimental data.

The silver and indium chemical potentials, calculated at T = 1000 K and 1300 K in the liquid are shown in Fig. 9. A good agreement is observed with most of the experimental data, excepting those of Nozaki et al. [START_REF] Nozaki | Thermodynamic Studies on Liquid Silver-Indium Alloys[END_REF], which are higher than all other measured values, and those of Predel et al. [START_REF] Predel | Untersuchung der thermodynamischen Eigenschaften flussiger binaren Legierungen des Silbers und Goldes mit Gallium, Indium und Germanium[END_REF], obtained by extrapolation of Ag-In-Zn ternary data and which are lower. These two sets of data have not been taken into account in the optimization.

The enthalpy of formation calculated for the α phase at 723 K is in close agreement with the experimental data, whereas for the ζ phase, the calculated values are slightly less exothermic than the experimental data obtained by Kleppa [START_REF] Kleppa | Heat of Formation of Solid and Liquid Alloys in the Systems Silver-Cadmium, Silver-Indium, and Silver-Antimony at 450°[END_REF] and Orr and Hultgren [START_REF] Orr | Heats of Formation of α Phase Silver-Indium Alloys[END_REF] (Fig. 10).

The In chemical potential in the α phase calculated at T = 950 K is reported in Fig. 11. The experimental data from Alcock et al. [START_REF] Alcock | Thermodynamics of -Solid Solutions of Silver with Indium and Tin[END_REF] and Masson and Pradhan [START_REF] Masson | Measurements of Vapor Pressure of Indium over α Ag-In Using Atomic Absorption[END_REF] are quite well fitted. The Gibbs energies of the compounds have been entirely estimated by the optimization. The calculated enthalpies of formation can be compared with DFT calculations at 0 K: Ag 0.75 In 0.25 , ∆ f H°2 98K (J/mol) = -6574 this work, -5384 [START_REF] Curtarolo | ORG: A Distributed Materials Properties Repository from High-Throughput Ab Initio Calculations[END_REF], -4728 [START_REF] Saal | Materials Design and Discovery with High-Throughput Density Functional Theory: The Open Quantum Materials Database (OQMD)[END_REF], Ag 0.666 In 0.333 , ∆ f H°2 98K (J/mol) = -7892 this work, -4699 [START_REF] Curtarolo | ORG: A Distributed Materials Properties Repository from High-Throughput Ab Initio Calculations[END_REF], -4536 [START_REF] Saal | Materials Design and Discovery with High-Throughput Density Functional Theory: The Open Quantum Materials Database (OQMD)[END_REF], Ag 0.333 In 0.666 , ∆ f H°2 98K (J/mol) = -4166 this work, -4014 [START_REF] Curtarolo | ORG: A Distributed Materials Properties Repository from High-Throughput Ab Initio Calculations[END_REF], -3859 [START_REF] Saal | Materials Design and Discovery with High-Throughput Density Functional Theory: The Open Quantum Materials Database (OQMD)[END_REF]. The order of magnitude is consistent for Ag 0.75 In 0.25 and Ag 0.333 In 0.666 . Contrariwise, for the composition Ag 0.666 In 0.333 , the DFT calculations do not predict a stable compound. The thermodynamic description could be improved with additional experimental thermodynamic properties for the three compounds.

6.

Cd-In

A Calphad assessment of the Cd-In system has been published by Dutkiewicz et al. [START_REF] Dutkiewicz | Cd-In (Cadmium-Indium)[END_REF]. It is based on the old lattice stability for the unary In(fcc_A1) [START_REF]PURE 5.0 SGTE Pure Elements (Unary) Database[END_REF]. To achieve compatibility with our new Ag-In binary description, the interaction parameters for the fcc_A1 and tet_A6 phases are re-evaluated here. The calculated phase diagram is presented in Fig. 12 and the invariant temperatures compared in Table 4. The fcc_A1 phase field cannot be correctly fitted with the new lattice. It is not expected that this discrepancy, which occurs around room temperature, can significantly affect the calculations at high temperatures.

7.

Ag-Cd-In

Experimental Information

The fcc_A1(Ag)/(fcc_A1(Ag) + hcp_A3) line was established by Snyder [START_REF] Snyder | Primary Solid-Solution Phase Boundary in Silver Corner of Silver-Cadmium-Indium Ternary System[END_REF] combining XRD and metallographic techniques at room temperature and at 588 K.

Horrocks [START_REF] Horrocks | Phase Diagram and Thermodynamics of the Ag-Cd-In Ternary Alloys Systems[END_REF] determined the liquidus at 1098.5 K by differential scanning calorimetry for an alloy of control rod composition 80Ag-5Cd-15In wt.%, which is in complete agreement with other literature values 1095 ± 25 K [START_REF] Petti | Silver-Indium-Cadmium Control Rod Behaviour in Severe Reactor Accidents[END_REF], 1100 ± 10 K [92], 1104 K [START_REF] Steinbrück | Experiments on Silver-Indium-Cadmium Control Rod Failure During Severe Accidents Sequences[END_REF]. He reported liquidus arrest temperatures of ternary silver alloys measured by Jones [93] between 513 and 517 K in the Cd/In = 1/3 section, and by Robinson [94] between 696 and 721 K in the x In = 0.6 section. The solidus for the control rod composition is given at 998 K [START_REF] Horrocks | Phase Diagram and Thermodynamics of the Ag-Cd-In Ternary Alloys Systems[END_REF] and at 1016 K [START_REF] Steinbrück | Experiments on Silver-Indium-Cadmium Control Rod Failure During Severe Accidents Sequences[END_REF].

The enthalpy of mixing in Ag-Cd-In liquid alloys along five isopleth sections corresponding to the ratios Cd/In = 1/1, Cd/In = 1/4, Cd/In = 1/9 and Ag/In = 1/4, Ag/In = 1/19 was measured by Benigni et al. [START_REF] Benigni | Enthalpy of Mixing in the Ag-Cd-In Ternary Liquid Phase[END_REF] using drop calorimetry at 723 K. The liquidus line at this temperature was tentatively drawn from the slope changes on the partial mixing enthalpy curves (Table 1). The liquidus was also investigated by conventional DTA/DSC and the solvus compositions were also determined by optical micrograph and scanning electron microscopy on equilibrated and quenched samples by Decreton [START_REF] Decreton | Contribution Expérimentale à l'Etude Thermodynamique des Systèmes Ag-Zr et Ag-Cd-In[END_REF]. His values are reported in Table 1 in comparison with this work and the liquidus temperatures reported in [8]. The main objective of the additional experimental work reported in this paper (Table 1) was to complete the previous work by investigating the Cd-rich part of the ternary diagram poorly investigated up to now.

Optimization and discussion

Horrocks [START_REF] Horrocks | Phase Diagram and Thermodynamics of the Ag-Cd-In Ternary Alloys Systems[END_REF] calculated the Ag-Cd-In system by only combining the three optimized binary descriptions. Desgranges [START_REF] Desgranges | Compréhension et prédiction du comportement sous irradiation neutronique d'alliages absorbants à base d'argent[END_REF] reported a ternary isothermal section calculated at 623 K from a Calphad modelling. Ternary excess Gibbs energy parameters are added in the fcc_A1 and hcp_A3 phases to represent the continuous biphasic (fcc_A1 + hcp_A3) phase field extending from the Ag-Cd to the Ag-In binary borders, which does not exist in Horrocks's sections.

In this work, at first, excess ternary parameters were optimized for the liquid and hcp_A3 phases, based on the experimental data from [START_REF] Decreton | Contribution Expérimentale à l'Etude Thermodynamique des Systèmes Ag-Zr et Ag-Cd-In[END_REF], [START_REF] Benigni | Enthalpy of Mixing in the Ag-Cd-In Ternary Liquid Phase[END_REF], [8] and this work. For the liquidus temperatures, a high weight was given to the data from the two latter experimental investigations relying on the IHDTA protocol. In this protocol, as discussed in detail in [8], conditions much closer to equilibrium are approached, reducing the uncertainty of the liquidus temperature measurements.

Then, these parameters were fixed, and for the fcc_A1 phase, which is present in the Ag-rich area on the one hand, and in the In rich area on the other hand, positive ternary interaction terms are evaluated to counteract a high solubility of Cd in the Ag rich phase, in order to well reproduce both the extents of the fcc_A1 and (fcc_A1 + hcp_A3) domains in accordance with Snyder [START_REF] Snyder | Primary Solid-Solution Phase Boundary in Silver Corner of Silver-Cadmium-Indium Ternary System[END_REF] results at 300 K and 588 K, and the liquidus and solidus temperature at the SIC composition.

The excess ternary interaction parameters are reported in Table 3. The calculated and measured integral and partial enthalpies of mixing in the liquid are compared in Fig. 13 a-j. The agreement is fair for the integral enthalpy values. Regarding the Ag partial values for Cd/In = 1/4 (fig. 13d) and Cd/In = 1/9 (fig. 13f) and for x Ag > 0.2, the discrepancy could be due to several reasons. Firstly, a fraction of the difference between the fit and the experimental data can be explained by the uncertainty on the measurement of the silver partial enthalpy, estimated to be around 0.5 kJ.mol -1 [START_REF] Benigni | Enthalpy of Mixing in the Ag-Cd-In Ternary Liquid Phase[END_REF]. Secondly, from a general point of view, silver dissolution in Ag-Cd-In liquid is a rather slow process. Kleppa [START_REF] Kleppa | Heat of Formation of Solid and Liquid Alloys in the Systems Silver-Cadmium, Silver-Indium, and Silver-Antimony at 450°[END_REF] already highlighted this point in reporting his experiments of solid silver dissolution in liquid cadmium. Moreover, as the solubility limit is approached by successive additions of silver samples, the driving force for Ag dissolution gradually decreases and the kinetics slows down. It is hence possible that dissolution of the last samples could be incomplete. Calculated isopleth sections at Cd/In=1/3, x In = 60 at.%, and x Cd = 60 at.% compared to experimental data, and isothermal sections at 821 K, 746 K, 723 K, 673 K, and 593 K are presented in Fig. 14 a-c, and Fig 15 a-e respectively, showing a good agreement with the experimental data. The calculated isothermal section at 723 K (Fig. 15 c), optimized by taking into account the more recent liquidus temperature determination reported in this paper and in [8], exhibits a significant discrepancy with our previous results [START_REF] Benigni | Enthalpy of Mixing in the Ag-Cd-In Ternary Liquid Phase[END_REF] and [START_REF] Decreton | Contribution Expérimentale à l'Etude Thermodynamique des Systèmes Ag-Zr et Ag-Cd-In[END_REF]. In our experimental study of the system, we have tried to gradually improve the accuracy of the liquidus temperature determinations, starting firstly by a rather indirect approach based on the examination of the partial enthalpy curves [START_REF] Benigni | Enthalpy of Mixing in the Ag-Cd-In Ternary Liquid Phase[END_REF], secondly by classical DTA/DSC [START_REF] Decreton | Contribution Expérimentale à l'Etude Thermodynamique des Systèmes Ag-Zr et Ag-Cd-In[END_REF], for which we put in evidence some limitations in this ternary system [8] and finally by IHDTA. The boundary between the monophasic fcc_A1 and biphasic (fcc_A1 + hcp_A3) domains at 588 K from Snyder [START_REF] Snyder | Primary Solid-Solution Phase Boundary in Silver Corner of Silver-Cadmium-Indium Ternary System[END_REF] is well reproduced (Fig. 15e). At room temperature, the extent of the hcp_A3 phase field by [START_REF] Snyder | Primary Solid-Solution Phase Boundary in Silver Corner of Silver-Cadmium-Indium Ternary System[END_REF] is questionable, because the AgCd and Ag 3 In compounds are known to be stable in the binary systems at this temperature.

With the global description, the temperature of fusion of the control rod alloys of nominal composition is calculated at 1099 K, compared to 1095 ± 25 K [START_REF] Petti | Silver-Indium-Cadmium Control Rod Behaviour in Severe Reactor Accidents[END_REF], 1100 ± 10 K [92], 1098.5 K [START_REF] Horrocks | Phase Diagram and Thermodynamics of the Ag-Cd-In Ternary Alloys Systems[END_REF], 1104 K [START_REF] Steinbrück | Experiments on Silver-Indium-Cadmium Control Rod Failure During Severe Accidents Sequences[END_REF], and the solidus temperature is calculated at T = 1002 K, compared to 998 K [START_REF] Horrocks | Phase Diagram and Thermodynamics of the Ag-Cd-In Ternary Alloys Systems[END_REF] and 1016 K [START_REF] Steinbrück | Experiments on Silver-Indium-Cadmium Control Rod Failure During Severe Accidents Sequences[END_REF].

8.

Conclusion

The thermodynamic assessment of the Ag-Cd-In ternary system based on the exhaustive compilation of literature data and recent experimental investigations [START_REF] Decreton | Contribution Expérimentale à l'Etude Thermodynamique des Systèmes Ag-Zr et Ag-Cd-In[END_REF] [7], [8] has been carried out. It also takes into account new experimental data related to the liquidus temperatures in cadmium-rich region which are reported in this paper. The liquidus temperatures for ternary compositions have been determined by using the IHDTA protocol. It has been shown in [8] that this method, operating closer to equilibrium conditions, considerably reduces the uncertainty in the liquidus determination for this system.

The obtained dataset of thermodynamic parameters allows a general good agreement between experimental and calculated results on the binary Ag-In, Ag-Cd and In-Cd subsystems and on the ternary system, at high temperature, in compositions domains where liquid phase is present. It is required to add ternary interaction parameters in the excess Gibbs energy expressions of the solution phases to fit the mixing enthalpy of the liquid and the extents of the (hcp_A3 + liquid) and (fcc_A1 + liquid) biphasic domains which have been experimentally determined. Additional experimental investigations such as thermodynamic data of the solid phases could be of high interest to increase the accuracy of the ternary excess interaction parameters of the hcp_A3 and fcc_A1 solid solutions.

Fig. 1 :Table 3 :Table 4 :

 134 Fig. 1: Ag-Cd calculated phase diagram compared with the experimental points.

Fig. 2

 2 Fig. 2 Calculated enthalpy of formation of the Ag-Cd liquid, bcc_A2 and hcp phases compared with the experimental values (referred to Ag fcc_A1 and Cd hcp_Cd ).

Fig. 4

 4 Fig. 4 Calculated enthalpy of formation of the α phase compared with experimental data, (referred to Ag fcc_A1 and Cd hcp_Cd ).

Fig. 8

 8 Fig. 8 Calculated enthalpy of formation in the liquid phase compared with the experimental values (referred to liquid).

Fig. 9

 9 Fig. 9 Ag and In chemical potentials in the liquid calculated at T = 1000 K and 1300 K compared with the experimental values (referred to liquid).

Fig. 10

 10 Fig. 10 Calculated enthalpy of formation in the α and ζ phases at 723 K compared with experimental data (referred to Ag fcc_A1 and In L ).

Fig. 12

 12 Fig. 12 Cd-In phase diagram recalculated from the optimized parameters, compared to the experimental points from Heumann and Predel [89], and Rosina [90].

Fig. 13 a

 13 Fig. 13 a-j Calculated integral and partial enthalpy of mixing in the liquid phase, compared to the experimental data from Benigni et al. [7].

Fig. 14 a

 14 Fig. 14 a-c Calculated isopleth sections at Cd/In=1/3, x In = 60 at.%, and x Cd = 60 at.%, compared to the experimental data.

Fig. 15 a

 15 Fig. 15 a-e Isothermal sections calculated at 821, 746, 723, 673 and 593 K, compared to the experimental data.

Table 1 Liquidus temperatures measured in this and our previous works for various compositions and comparison with literature data. Experimental methods: IHDTA this work and [8], DTA [95], isothermal calorimetry (see text) [7], Smith Thermal Analysis [6, 93-94], DSC [4] and [9].

 1

	Alloys composition / at. %	This and our previous works	Literature data
	Ag	Cd	In	T liquidus / K	T liquidus / K
	4.5	23.9	71.6		513, 517 [93] reported in [6]
	7.5	23.1	69.4	602±3 [95] 592-595 This work	517 [93] reported in [6]
	8	60	32	660-663 This work
	28	60	12	820-823 This work
	15	70	15	746-749 This work
	18	60	22	744-747 This work
	20	20	60	671-674 This work
	37	3	60	-	721 [94] reported in [6]
	34	6	60	-	709 [94] reported in [6]
	32	8	60	708±3 [95]
	31	9	60		703 [94] reported in [6]
	28	12	60	685±3 [95] 676-679 [8]	696 [94] reported in [6]
	35	5	60	716±3 [95] 712-715 [8]
	40	0	60	730±3 [95]

Acknowledgements:

The authors wish to thank the GDR CNRS No.3584 TherMatHT where fruitful discussions started and led to collaborations on the present project.