Morgane Mokhtari

Takeshi Wada

Christophe Le Bourlot

Jannick Duchet-Rumeau

Hidemi Kato

Eric Maire

Nicolas Mary
email: nicolas.mary@insa-lyon.fr

Corrosion resistance of porous ferritic stainless steel produced by liquid metal dealloying of Incoloy 800

Keywords:

Liquid metal dealloying is a newly available technology used to create bulk porous materials. In this study, a commercial nickel-based superalloy, Incoloy 800, was dealloyed to elaborate a fully porous ferritic stainless steel. The Mg selective dissolution in nitric acid solution acts as a passivation treatment that enhances the passive film resistance.

Corrosion tests confirm the beneficial effect of the nitric acid treatment on the Cr enrichment of the passive film thus improved the material resistance. The electrochemical characterizations show a higher effect of the size porosities on the diffusion kinetics of the electrolyte rather than on the pitting sensitivity.

Introduction

Porous bulk materials, and especially nanoporous metals, have attracted considerable attention owing to their excellent functional properties, including their high catalytic activities, sensing capabilities, and surface-enhanced Raman scattering resulting from their interconnected structure and high specific surface area [START_REF] Erlebacher | Hard materials with tunable porosity[END_REF][START_REF] Snyder | Oxygen reduction in nanoporous metal-ionic liquid composite electrocatalysts[END_REF][START_REF] Lang | Nanoporous metal/oxide hybrid electrodes for electrochemical supercapacitors[END_REF][START_REF] Chen | Nanoporous copper with tunable nanoporosity for SERS applications[END_REF]. More recently, micro/nanoporous materials have been applied as biomaterials [START_REF] Fukuzumi | Surface improvement for biocompatibility of Ti-6Al-4V by dealloying in metallic melt[END_REF][START_REF] Kato | Dealloying toxic Ni from SUS316L surface[END_REF][START_REF] Okulov | Dealloying-based interpenetrating-phase nanocomposites matching the elastic behavior of human bone[END_REF][START_REF] Okulov | Open porous dealloying-based biomaterials as a novel biomaterial platform[END_REF][START_REF] Okulov | Dealloyingbased metal-polymer composites for biomedical applications[END_REF][START_REF] Okulov | Tuning microstructure and mechanical properties of open porous TiNb and TiFe alloys by optimization of dealloying parameters[END_REF]. In most of the cases, materials with the smallest ligament size and the highest specific surface area are required. Also, the design (i.e., morphology) of ligaments must be controlled to optimize the microfluidic flow and to ensure the mechanical stability of the samples [START_REF] Ding | Nanoporous metals with controlled multimodal pore size distribution[END_REF]. Such porous structures are usually produced by molten metal foaming or metal particle sintering at the industrial scale. However, the formation of connected sub-micron pores is difficult to obtain with these techniques [START_REF] Dumée | The fabrication and surface functionalization of porous metal frameworks -a review[END_REF][START_REF] Dumée | control of porosity and pore size of metal reinforced carbon nanotube membranes[END_REF]. Electro-spinning, self-assembly and inject printing give fine microstructures, however they are slow processes with post treatment as sintering or carbonization materials to stabilize the porosity network. Note that the control of the porosity size over large scales is also not easy [START_REF] Dumée | The fabrication and surface functionalization of porous metal frameworks -a review[END_REF][START_REF] Wu | Electrospinning of Fe, Co, and Ni nanofibers: synthesis, assembly, and magnetic properties[END_REF][START_REF] Warren | Ordered mesoporous materials from metal nanoparticle-block copolymer self-assembly[END_REF][START_REF] Ko | Metal nanoparticle direct inkjet printing for low-temperature 3D micro metal structure fabrication[END_REF]. Alternatively, chemical or electrochemical dealloying are suitable for macroscopic scaled nanoporous samples with a controlled unimodal pore distribution. These techniques were initially applied to metals with noble elements such as Au, Ag, Pt, Pd, Cu and Ni [START_REF] Chen | Nanoporous copper with tunable nanoporosity for SERS applications[END_REF][START_REF] Forty | Corrosion micromorphology of noble metal alloys and depletion gilding[END_REF][START_REF] Xu | Dealloying to nanoporous silver and its implementation as a template material for construction of nanotubular mesoporous bimetallic nanostructures[END_REF][START_REF] Pugh | Formation of nanoporous platinum by selective dissolution of Cu from Cu0.75Pt0.25[END_REF][START_REF] Min | The microstructure and dealloying kinetics of a Cu-Mn alloy[END_REF][START_REF] Hayes | Monolithic nanoporous copper by dealloying Mn-Cu[END_REF][START_REF] Smith | Kinetics and mechanism of the preparation of Raney® copper[END_REF][START_REF] Sun | Fabrication of nanoporous nickel by electrochemical dealloying[END_REF]. Chemical dealloying consists on a selective dissolution of metals from binary alloy in various acids and bases solution with a control of the temperature [START_REF] Nam | Development of nanoporous copper foams by chemical dealloying of mechanically alloyed Al-Cu compounds[END_REF][START_REF] Semiz | Nanoporous Pt and Ru catalysts by chemical dealloying of Pt-Al and Ru-Al alloys for ultrafast hydrogen generation[END_REF]. In some cases, hydrogen generation is reported during chemical and electrochemical dealloying that later affects the mechanical properties of the porous material [START_REF] Sankir | Hydrogen generation from nanoflower platinum films[END_REF]. Unlike chemical dealloying, liquid metal dealloying (LMD) can be used to prepare submicron-scale porous samples with less noble metals including Ti, Fe, Cr, Nb, Mg [START_REF] Wada | Dealloying by metallic melt[END_REF][START_REF] Wada | Three-dimensional open-cell macroporous iron, chromium and ferritic stainless steel[END_REF][START_REF] Kim | Sub-micron porous niobium solid electrolytic capacitor prepared by dealloying in a metallic melt[END_REF][START_REF] Okulov | Nanoporous magnesium[END_REF] while limiting secondary reactions in the solution, as hydrogen evolution.

LMD involves selective dissolution of one of the major elements of a solid precursor alloy in a liquid metal at few hundred degrees. Because the chemical composition of the material changes with the immersion time, atomic reorganization of the matter occurs, leading to the fabrication of a new material. In parallel, the metal bath is enriched into the dissolved element. LMD mainly works via chemical interaction among elements, which is governed by their enthalpies of mixing ΔH mix [START_REF] Wada | Dealloying by metallic melt[END_REF][START_REF] Takeuchi | Classification of bulk metallic glasses by atomic size difference, heat of mixing and period of constituent elements and its application to characterization of the main alloying element[END_REF]. To better understand the mechanism of dealloying, LMD was initially applied on model precursors. For example, Wada et al. [START_REF] Wada | Three-dimensional open-cell macroporous iron, chromium and ferritic stainless steel[END_REF] created a ferritic stainless steel foam (i.e., Fe-Cr-based alloy) by applying LMD to Fe-Cr-Ni alloy precursor. In this example, Ni was the sacrificial element selectively dissolved in a liquid Mg bath. Artymowicz et al. accessed to total dealloying of a precursor, leading to porous bulk material for the concentration of the sacrificial element (Ni) in the https://doi.org/10.1016/j.corsci.2020.108468 Received 19 July 2019; Received in revised form 6 January 2020; Accepted 9 January 2020 precursor over the parting limit, approximately 20-25 at.% for facecentered-cubic (FCC)/body-centered-cubic (BCC) lattice precursors [START_REF] Artymowicz | Relationship between the parting limit for de-alloying and a particular geometric high-density site percolation threshold[END_REF]. In these previous examples, the final volume fraction of pores is predicted by the initial precursor composition alone, independent of the dealloying conditions [START_REF] Zhao | Three-dimensional morphological and chemical evolution of nanoporous stainless steel by liquid metal dealloying[END_REF][START_REF] Mokhtari | Microstructure Characterization by X-ray tomography and EBSD of porous FeCr produced by liquid metal dealloying[END_REF]. However, the temperature of the liquid metal has an exponential effect on the ligament size and an increase of the dealloying time favors the coarsening of ligaments [START_REF] Wada | Three-dimensional open-cell macroporous iron, chromium and ferritic stainless steel[END_REF][START_REF] Tsuda | Kinetics of formation and coarsening of nanoporous atitanium dealloyed with Mg melt[END_REF].

As labmade precursors are expensive and usually produced in low quantity, the use of commercial alloys is under consideration for the industrialization of LMD. In a previous work [START_REF] Mokhtari | Low cost high specific surface architectured nanoporous metal with corrosion resistance produced by liquid metal dealloying from commercial nickel superalloy[END_REF], the LMD process was successfully applied to a commercial Incoloy 825. The dealloyed material exhibited a porous structure highly dependent on the dealloying temperature as predicted by the literature. However, it was shown that the pore distribution was not necessarily unimodal. The results proved the feasibility of LMD on commercial material and also highlighted the good corrosion resistance of the porous materials [START_REF] Liang | The corrosion behavior of porous Ni3Al intermetallic materials in strong alkali solution[END_REF][START_REF] Jia | In vitro degradation behavior of Mg scaffolds with three-dimensional interconnected porous structures for bone tissue engineering[END_REF]. However, a lack of control of the pore size with Incoloy 825 was pointed out. In conventional metallurgy, the microstructure and the presence of inclusions or precipitates strongly depend of the chemical nature of the alloying elements [START_REF] Al-Jarba | Effect of carbon additions on the as-cast microstructure and defect formation of a single crystal Ni-based superalloy[END_REF]. Based on that idea, a lower alloyed Incoloy was selected since this may reduce the number of chemical interactions between elements during LMD. Compared to Incoloy 825, Incoloy 800 (UNS N08800) does not contain copper among others [START_REF] Dehmolaei | Microstructural changes and mechanical properties of Incoloy 800 after 15 years service[END_REF][START_REF] Sayiram | Microstructural characterization of dissimilar welds between Incoloy 800H and 321 austenitic stainless steel[END_REF]. Copper is known to form a solid solution with Ni and might play a negative role during LMD in term of porosity size control. Table 1 compares the mixing enthalpies for the main elements in a commercial Incoloy 800. Note that the exact chemical composition of our coupons will be determined by SEM-EDS later. Like Incoloy 825, a stainless-steel foam can be produced by LMD in a Mg bath from Incoloy 800. Therefore, the objectives of the current study is (i) to elaborate a fully porous Fe-Crbased alloy with two different pores and ligament sizes, (ii) to discuss the role of the dissolution of the Mg-Ni phase in nitric acid solution on the corrosion resistance of the foam and (iii) to link the pore size on the electrochemical behavior of the final product. Note that the material resulting to the LMD will be named porous materials or metallic foam.

Materials and methods

Materials synthesis

A 1.57 mm thick Incoloy 800 sheet was provided by Nilaco (Japan) and cold-rolled until 1 mm thickness. Coupons of 30 × 20 mm² were extracted and no additional heat treatment was applied before LMD. Chemical compositions of coupons were determined by EDS-SEM and are given in the results section.

In LMD, the dealloying time and temperature are the two parameters that determine the theoretical ligament thickness and the dealloyed layer thickness [START_REF] Wada | Three-dimensional open-cell macroporous iron, chromium and ferritic stainless steel[END_REF][START_REF] Mokhtari | Low cost high specific surface architectured nanoporous metal with corrosion resistance produced by liquid metal dealloying from commercial nickel superalloy[END_REF]. In this work, Incoloy 800 coupons were immersed for 1 h in liquid Mg bath either at 750 °C or 830 °C. A preliminary work shown that a dealloyed structure was obtained into the volume of the coupon before 1 h. In order to insure homogeneous ligament size, LMD was performed during 1 h. The lowest temperature was selected from the minimum of temperature required to initiate the dealloying process. For Incoloy precursor, this occurs above 750 °C [START_REF] Kim | Sub-micron porous niobium solid electrolytic capacitor prepared by dealloying in a metallic melt[END_REF][START_REF] Mokhtari | Low cost high specific surface architectured nanoporous metal with corrosion resistance produced by liquid metal dealloying from commercial nickel superalloy[END_REF]. The highest temperature was selected from our previous works dealing with dealloying of Incoloy 825 and labmade Fe-Ni-Cr precursor [START_REF] Mokhtari | Microstructure Characterization by X-ray tomography and EBSD of porous FeCr produced by liquid metal dealloying[END_REF]. After air quenching at room temperature, a bicontinuous microstructure was obtained with a matrix enriched in iron and chromium and a second phase of magnesium and nickel magnesium intermetallic compound. Then, the Mg-rich phase was chemically etched in a 3 M HNO 3 (pH -0.9) aerated aqueous solution for 16 h at room temperature (optimized treatment time). This last step finally reveals the metallic foam with an interconnected network of stainless steel ligaments.

For corrosion tests, stainless-steel ingots were also prepared from pure materials by arc melting with the same compositions as the porous samples as described in [START_REF] Wada | Three-dimensional open-cell macroporous iron, chromium and ferritic stainless steel[END_REF]. The ingots were cast into 8 mm diameter rods and surfaces were polished until 1200 SiC grit paper. These samples were used as dense materials in order to better understand the role of porosities on the electrochemical behavior of porous samples

Materials characterizations

The cross-sectional and surface morphologies of the precursor, the bicontinous structure and porous samples were investigated by scanning electron microscope (SEM; Carl Zeiss ULTRA 55, Oberkochen, Germany). An Ar ion beam polisher was used to prepare cross-sections of samples (EM-3500 Hitachi, Japan). This method was preferred to classical cross section preparation in resin to limit the deformation of the ligaments during the several polishing steps. Quantification of the pore size was done from SEM images with Fiji image analysis software [START_REF] Schindelin | Fiji: an open-source platform for biological-image analysis[END_REF]. Note that these observations are representative of the porous microstructure since the microstructure does not evolve significantly after the chemical dissolution of the Mg-Ni phase [START_REF] Chen-Wiegart | 3D morphological evolution of porous titanium by x-ray micro-and nano-tomography[END_REF].

Crystallographic structures of precursors and porous materials were defined by X-ray diffraction (XRD; Rigaku Ultima IV, Tokyo, Japan) using Cu Kα radiation (1.54 Å). Diffractograms were recorded in air at room temperature from 20°to 100°(2θ) using a step size of 0.005°. Experimental peak positions were compared to the open crystallography database (COD).

Surface chemistry of the porous surfaces were studied by X-ray photoelectron spectroscopy (XPS). The XPS spectra were recorded using a Versaprobe II PHI 5000 apparatus operated in constant analyzer energy mode (CAE; pass energy of 117.4 eV for wide scan and 58.7 eV for regions) with a monochromatized Al Kα source (1486.7 eV). The pressure of the chamber was maintained to less than 10 -7 Pa during the experiments. No sputter cleaning was performed before analysis. Spectra were acquired at 90°and referenced to the adventitious C1 s set at 284.6 eV. High-resolution windows scans (0.129 eV) were recorded on the major elements of the oxide film: O1 s (524-538 eV), Cr2p (568-582 eV), Fe2p (700-720 eV), and C1 s (278-292 eV). Data (background subtraction and peak fitting) were processed using Origin software with a Shirley background and a Gaussian peak shape. The binding energies were compared to an open-access XPS database to identify the species present on the samples [START_REF]La surface[END_REF]. In the elaboration process, the bicontinuous microstructure is merged in a nitric acid solution. In addition to dissolve chemically the Mg-Ni phase, the acidic solution plays the role of a passivation treatment on the stainless steel ligaments formed during LMD. The consequences of a passivation treatment are characterized by an Cr enrichment in the passive film and a thicker oxide layer [START_REF] Wallinder | Eis and XPS study of surface modification of 316LVM stainless steel after passivation[END_REF]. The former can be confirmed by Eq. ( 1) which quantifies the chromium ratio in the oxide layer, (Cr) ratio from XPS analysis. Cr ox and Fe ox correspond to the area of the Cr oxide peak and the Fe oxide peak, respectively (Eq. ( 1)).

= + Cr

Cr Cr Fe ratio ox ox ox [START_REF] Erlebacher | Hard materials with tunable porosity[END_REF] From XPS analysis, the passive film thickness (ξ ox ) can be also estimated by Eq. ( 2). In this relation, the passive film thickness is supposed to be an oxide over-layer.

= ⎡ ⎣ ⎢ + ⎤ ⎦ ⎥ λ ln I I ξ * 1 ox Cr ox Cr met , , (2)
Table 1 Mixing enthalpies of the major alloying elements in Incoloy 800 with Mg, ΔH mix, Mg-M (after [START_REF] Takeuchi | Classification of bulk metallic glasses by atomic size difference, heat of mixing and period of constituent elements and its application to characterization of the main alloying element[END_REF][START_REF]Incoloy alloy 800[END_REF]).

Element Fe Cr Ti Si Ni Composition at.% > 38 20-25 < 0.5 < 1 28-34 ΔH mix, Mg-M /kJ mol -1 +18 +24 +16 -26 -4
where λ is the medium free path length for photo-electrons from Cr. The common value of 1.7 nm is used in this work [START_REF] Wallinder | Eis and XPS study of surface modification of 316LVM stainless steel after passivation[END_REF]. I Cr,ox and I Cr,met are the measured intensities on XPS curves of the chromium oxide and metal peaks, respectively. Electrochemical characterizations were performed in a classical three-electrodes cell connected to a potentiostat (VP300, Biologic France). Working electrodes consisted on metallic samples. Potentials were measured versus the mercury-mercurous sulfate reference electrode (MSE) (E MSE = +0.65 V/SHE). A platinum wire of 7.2 cm² played the role of counter electrode. The experiments were performed at room temperature (∼295 K) in aerated and stagnant 0.1 M NaCl aqueous solution (pH 6.5). Before immersion in the corrosive solution, the samples were stored in the laboratory atmosphere for 8 days to obtain a mature oxide film (relative humidity at 60 %, temperature at 25 °C). In solution, electrochemical measurements were performed as follow: (i) open-circuit potential (OCP) measurement for 2 h, (ii) potentio electrochemical impedance spectroscopy (PEIS) measurements at the OCP in the frequency range of 100 kHz to 30 mHz with 9 points per decade using a 20 mV/s peak-to-peak sinusoidal voltage, and (iii) linear sweep voltammetry (LSV) measurements from -0.20 V vs. OCP to 1.00 V vs. MSE at 1 mV/s. All the measurements were performed at least two times. Because the deviation of the results was minimal, only one curve is provided for each measurement.

Results and discussion

Precursor characterization

SEM images of Incoloy 800 show a homogeneous microstructure with few heterogeneities randomly dispersed (Fig. 1). The chemical composition of Incoloy 800 is reported in Fig. 1(b). Nickel, Iron and Chromium concentrations are at 30.1 at.%, 47.3 at.%, and 21.2 at.%, respectively. Two minor elements were also detected: Si at 0.8 at.% and Ti at 0.8 at.% EDS maps of the three major elements (i.e., Ni, Fe and Cr) confirm the monophase microstructure without local enrichment. Distribution of two minor elements (Si and Ti) was also analyzed since they can form inclusions and later play a role in the dealloying process and pore size (Fig. 1(a)). Few Ti-rich inclusions of approximately 10 μm in size were detected as observed otherwise for Incoloy 800 [START_REF] Dehmolaei | Microstructural changes and mechanical properties of Incoloy 800 after 15 years service[END_REF][START_REF] Sayiram | Microstructural characterization of dissimilar welds between Incoloy 800H and 321 austenitic stainless steel[END_REF]. On XRD diagrams, the Incoloy matrix presents the expected FCC microstructure (Fig. 1(c)) and any Ti-based secondary phase was identified on XRD diagram suggesting a total volume of Ti-rich phase less than 1 vol. %.

Dealloyed microstructures

Liquid Metal dealloying is a chemical process in liquid metal where the precursor losses a part of its matter. For the Incoloy 800, nickel dissolves in Mg bath during LMD. Consequently, a size reduction of the sample might be expected. In Fig. 2(a), the macroscopic appearance of samples before and after LMD are compared. Whatever the temperature of liquid Mg bath, the geometry of the sample is not modified while the size shrink is limited to 1 %-3 %. On one hand, this indicates that the dealloying not drastically changes the apparent volume. On the other hand, this method allows to form porous material (i.e., lighter material) keeping the initial aspect of the material.

Fig. 2(b) shows the typical bicontinuous microstructure produced at 830 °C with a homogeneous reparation of Fe and Cr in the ligaments. In the Mg-Ni phase, the chemical composition is equivalent to the eutectic one [START_REF] Kim | Sub-micron porous niobium solid electrolytic capacitor prepared by dealloying in a metallic melt[END_REF]. Note that similar microstructure was observed at 750 °C. A particular attention paid on Fig. 2(c) and (d) highlights the role the temperature on the size of ligaments. On one hand, this confirms that the chemical composition of minor alloying elements in the precursor plays a significant role on the ligament growth. On the other hand, the temperature of liquid Mg plays a determinant role in the characteristic length of the ligaments [START_REF] Wada | Three-dimensional open-cell macroporous iron, chromium and ferritic stainless steel[END_REF]. The volume fraction of pores (i.e., the Mg phase in dual phases microstructure) can be estimated from the grayscale difference between the stainless-steel ligaments and the Mg phase. Regardless of the microstructure, the porosity volume is at approximately 28 % ± 3 %, which is consistent with the theoretical porosity (29 %) discussed in [START_REF] Mokhtari | Microstructure Characterization by X-ray tomography and EBSD of porous FeCr produced by liquid metal dealloying[END_REF] for such kind of material. Fig. 2(b) and (c) show a reservoir shape for pores with only a modification of the dimension with the temperature of dealloying. The ligament thicknesses were evaluated from the SEM images using 2D granulometry [START_REF] Schindelin | Fiji: an open-source platform for biological-image analysis[END_REF]. This analysis is usually underestimating the ligament and pores sizes, therefore, a correction factor equal to 4/π should be used to compare these values to 3D analysis [START_REF] Han | Analysis of the proportionality constant correlating the mean intercept length to the average grain size[END_REF]. Table 2 reports the average ligament and pore sizes measured after dealloying at 750 °C and 830 °C. After the chemical etching in nitric acid of the bicontinuous microstructure, the macroscopic aspect as well as the ligament design are not modified in the metallic foam [START_REF] Mokhtari | Microstructure Characterization by X-ray tomography and EBSD of porous FeCr produced by liquid metal dealloying[END_REF]. SEM-EDX analysis (inset of Fig. 2(e)) confirms the chemical homogeneity of the ligaments in the volume of the sample (Fe 67.7 Cr 29.5 Ti 1.0 Si 1.8 (at.%). Note that Ni and Mg contents were below the detection limit confirming the efficiency of the nitric acid treatment in the dissolution of Mg-Ni phase. The atomic ratio of Fe to Cr in the porous sample is equal to 2.2 which is almost equal to that in the precursor (Fe/Cr = 2.3). Therefore, Fe and Cr atoms were fully preserved in the ligaments during dealloying and chemical treatment. The porous stainless steel structures presents a bcc crystal lattice (Fig. 2(f)). On diagram, no sigma phase was detected despite the high Cr content. This chemical composition associated to bcc crystal structure is close to commercial stainless steels such as SUS447J1 stainless steel making them porous alloys with several industrial applications [START_REF]HongChao stainless steel[END_REF].

In this work, the relation between the temperature of liquid Mg bath and the size of the ligaments follows the same trend that described by Wada et al. [START_REF] Wada | Three-dimensional open-cell macroporous iron, chromium and ferritic stainless steel[END_REF] and Tsuda et al. [START_REF] Tsuda | Formation Mechanism of Porous Metals During Liquid Metal Dealloying Process[END_REF]: higher the temperature, larger the ligaments will be. For Incoloy 800, an increase of 80 °C of the bath temperature enhances about 2.5 times the average ligament size and average pore size (Table 2). However, the ligament and pore sizes remain significantly lower after 1 h of immersion than those obtained after dealloying a labmade precursor (Table 2) [START_REF] Mokhtari | Microstructure Characterization by X-ray tomography and EBSD of porous FeCr produced by liquid metal dealloying[END_REF]. The main difference between the commercial Incoloy 800 and the labmade product stays in the presence of minor alloying elements as Ti or Si (respectively 0.6 at% and 0.8 at% in FCC phase in the precursor). As suspected with the absence of porosity control on Incoloy 825, the presence of alloying elements in the precursor plays a negative role in the pores and ligaments size. In the mechanism of dealloying in liquid Mg bath, the Ni dissolution at the dealloying front requires surface diffusion of the remaining Fe, Cr, and minor elements if applicable [START_REF] Wada | Three-dimensional open-cell macroporous iron, chromium and ferritic stainless steel[END_REF]. Table 1 gave the mixing enthalpy energies of different metallic element with Mg. If diffusion of Si in Mg phase is expected thermodynamically, the higher negative enthalpy for Fe suggests that it will remain in the stainless

Table 2

Average ligament and pore diameters (∅) determined from 2D images after LMD of Incoloy 800 precursor. For comparison, the 2D values for a labmade precursor dealloyed under similar conditions in a previous study [START_REF] Mokhtari | Microstructure Characterization by X-ray tomography and EBSD of porous FeCr produced by liquid metal dealloying[END_REF] are also provided.

Incoloy 800 LMD 1 h @ 830 °C Incoloy 800 LMD 1 h @ 750 °C (Fe 80 Cr 20 ) 70 Ni 30 LMD 1 h @ 820 °C [START_REF] Mokhtari | Microstructure Characterization by X-ray tomography and EBSD of porous FeCr produced by liquid metal dealloying[END_REF] Average ligament ∅ 2.5 ± 1.0 μm 1 ± 0.2 μm ∼4 μm Average pore size ∅ 1.3 ± 0.5 μm 0.5 ± 0.1 μm ∼2.4 μm steel ligaments and slow down the dealloying rate resulting in ligaments [START_REF] Mokhtari | Low cost high specific surface architectured nanoporous metal with corrosion resistance produced by liquid metal dealloying from commercial nickel superalloy[END_REF]. Further investigations should be performed on this point to better understand the effect of each elements on that process.

Passive film composition: role of Mg dissolution in nitric acid solution

In LDM technology, the porous materials are obtained after dissolution of the Mg-Ni phase in nitric acid solution. Since this occurs under the natural diffusion of nitric acid, stainless steel ligaments are in contact with the aggressive solution for at least 16 h at the surface of the foam and for shorter times in the volume. For Wallinder et al. [START_REF] Wallinder | Eis and XPS study of surface modification of 316LVM stainless steel after passivation[END_REF], the corrosion resistance of a stainless steel increases after a nitric acid immersion. This was attributed to a Cr enrichment at the metal surface. These authors also noted that the nitric acid concentration, treatment time, and temperature had greater effects on the passive film thickness than on the Cr content in the film. Therefore, the use of the nitric acid solution in LMD process has two consequences: (i) to dissolve the Mg-Ni phase and to reveal the porous microstructure and (ii) to perform a passivation treatment on the stainless steel surface. Instead of to describe the passive film on porous materials, ingots with the same chemical composition were used for XPS analysis. This solution was preferred to limit the contribution of Mg-Ni phase oxide on the bicontinuous microstructure (before nitric acid treatment) and to avoid roughness contribution on the metallic foam (after nitric acid treatment). According to [START_REF] Wallinder | Eis and XPS study of surface modification of 316LVM stainless steel after passivation[END_REF], the chemical composition of the oxide film on our foam may be constant in surface and volume whereas its thickness should change from the extern to intern part of the sample due to different time of exposure to nitric acid. Note that further experiments are required to fully valid this assumption and also to differentiate the thickness evolution of the passive layer in the foam since the diffusion/ convection of species in the foam may affect the chemical etching efficiency.

Fig. 3 shows the XPS windows scans for Fe 2p, Cr 2p, and O 1s recorded on the ingots before chemical etching and after the passivation treatment (limited to 1 h). On both conditions, metallic elements and oxidized species coexist. For iron, the metallic state is located at 706.9 eV whereas the broad peak at 710.2 eV is attributed to iron oxide Fe (II). No clear identification was achieved in the Fe (II) to distinguish the hydroxyl species to oxide. For chromium, the metallic peak Cr (0) and the oxide peak Cr (III) are located at 573.9 eV and 575.7 eV, respectively. In addition, an hydroxide peak Cr(III) is also identified at 577.1 eV. According to the database, the peak positions of Cr (III) refer to Cr 2 O 3 at 575.7 eV and Cr(OH) 3 at 577.1 eV [START_REF]La surface[END_REF]. The presence of the oxide-hydroxide layer is confirmed by the identification of OH -groups and O in the oxide state in the oxygen spectrum. After nitric acid etching, the oxygen peak shows an increase of the oxide contribution as confirmed by the increase of the oxide contribution in chromium peak in Fig. 3(b). The chromium contents in the passive films were evaluated with Eq. ( 1). (Cr) ratio is approximately 41 % without nitric acid treatment and increased to up to 67 % after 1 h of immersion in the acidic solution. Before passivation, the oxide layer is at about 1.2 nm and it increases to 1.5 nm after immersion in nitric acid solution. Thus, the increase of (Cr) ratio and the oxide thickness strongly suggest a better corrosion resistance for the metallic foam than the bicontinuous microstructure [START_REF] Wallinder | Eis and XPS study of surface modification of 316LVM stainless steel after passivation[END_REF]. Note that the comparison of corrosion resistance performances between the metallic foam and the precursor materials are out of scope here.

Corrosion properties

Fig. 4 presents the OCP, the polarization curves and the impedance spectroscopy diagram of ingots in absence or presence of passivation treatment. Whatever the sample, OCP curves stabilize at about -0.45 V MSE after 1000 s in the electrolyte. PEIS diagrams recorded after 1 h of immersion show the polarization resistance increase with the passivation treatment. The Nyquist diagrams in Fig. 4(c) contain only one pseudo capacitive loop. An equivalent electrical circuit was then used to model the passive film/electrolyte interface for the two samples (Fig. 6(a)). In this circuit, R e is the electrolyte resistance and the time constant (R//CPE) is associated to the passive film response where R a is the polarization resistance, and Q a is a Constant Phase Element (CPE, Eq. ( 3)). The use of a CPE (defined by Q a and n a ) instead of an ideal capacitor (C a )was imposed by the surface heterogeneities (roughness, charge distribution) and the cylindrical geometry of the ingots [START_REF] Lavigne | Cerium insertion in 316L passive film: effect on conductivity and corrosion resistance performances of metallic bipolar plates for PEM fuel cell application[END_REF].

= - Z f Q π f ( ) [ . (2 ) ]
= π R π 1 2 ( . Q ) 1 2 C a a a 1/na (4)
The fit results in Table 3 show a decrease of Q a with an increase of n a after the ingot passivation. Pseudo-capacitances calculated with Eq. ( 4) are equal of 475 μF.cm² and 145 μF.cm² for the polished and passivated surface, respectively and are proportional to the space charge capacitance and the double layer capacitance (Table 3). These values are somehow higher than the usual one for stainless steel passive film because of the cylindrical shape of the samples and also the roughness induced by SiC1200 polishing [START_REF] Fattah-Alhosseini | Passivity of AISI 321 stainless steel in 0[END_REF]. However, the decrease of the pseudo capacitances with the passivation treatment confirms the enhancement of the oxide properties as detected previously on XPS spectrum by the Cr enrichment of the surface and also in terms of stabilization of defects [START_REF] Carmezim | Capacitance behaviour of passive films on ferritic and austenitic stainless steel[END_REF]. Further experiments are planned to determine the modification of the number of defects and identify the presence of a p-type or n-type capacitor based on Mott-Schottky analysis. Here, the most explicit parameter is R a , which increased 10 times after the nitric acid treatment and is directly linked to the chromium content in the passive film (Fig. 4(d)). Consequently, the current in the passive region on polarization curves (Fig. 4(b)) decreases as less energy is required to maintain the passivity state in presence of a strong chromium oxide layer.

The porous materials were characterized in the same way as the ingots. OCP are slightly more anodic than those of the ingot materials (Fig. 5(a)). This nobler behavior was also observed on the corrosion potentials on potentiodynamique curves in Fig. 5(b). This may come from the longer passivation treatment that enhances the passive film properties as the morphology difference between the samples. However, polarization curves in Fig. 5(b) show the decrease of the corrosion resistance of the porous microstructures with the detection of localized corrosion initiation at approximately 0.25 V MSE irrespective of the pore size. The effects of the porosity on the surface reactivity are also detected on PEIS diagrams (Fig. 5(c)). For the two metallic foams, the spectrum presents a slope at approximately 45°in the high frequency domain. In addition, a second slope at 45°is detected on the 1.3 μm pore sample at low frequency. Note that the amplitude of the spectrum

Table 3

Impedance fitting parameters for polished or passivated ingots and porous materials. The fit quality criterion is given by χ²/|Z| (lower it is, better the fit will be) and were lower than 0.53.

Sample

Re ( ± 10) Ω.cm² are lower than for plain samples which is online with the polarization curves that indicated higher surface reactivity. The high frequency impedance slope at ∼45°is characteristic to porous materials and can fluctuate between 22°and 45°according to the defect properties [START_REF] Wang | Impedance studies of nickel hydroxide microencapsulated by cobalt[END_REF][START_REF] Karunathilaka | The impedance of the alkaline zinc-manganese dioxide cell. I: variation with state of charge[END_REF]. Simulation of porous samples have been proposed by Keiser et al. [START_REF] Keiser | Abschätzung der porenstruktur poröser elektroden aus impedanzmessungen[END_REF] and latter De Levie et al. [START_REF] Levie | Electrochemical response of porous and rough electrodes[END_REF] who used a transmission line model. In their works they considered cylindrical semi-infinite, not connected and parallel pores (Eq. ( 5)) [START_REF] Samuel | Simulated impedance of diffusion in porous media[END_REF][START_REF] Barcia | Application of the impedance model of de Levie for the characterization of porous electrodes[END_REF][START_REF] Cericola | Impedance spectroscopic studies of the porous structure of electrodes containing graphite materials with different particle size and shape[END_REF].

Z c = Z pore,F Z a = (R//CPE) a Q p ( ± 0.1 × 10 -4 ) F.s a-
= Z R jω C π r coth L R ω C π r . ,
Where R ion,p is the ionic resistance per unit of pore (Ω. cm -1 ), C p is the electric double layer capacitance (F.cm²), r is the pore radius (cm), L is the pore length (cm). The transmission line was then modified to account the pore size distribution on the impedance in absence of diffusion [START_REF] Hitz | Experimental study and modeling of impedance of the her on porous Ni electrodes[END_REF][START_REF] Song | Electrochemical impedance spectroscopy of porous electrodes: the effect of pore size distribution[END_REF]. Barcia et al. [60] attended to quantify the characteristic length and radius as well as the number of independent pores. They highlighted that the number of pores and their average radius cannot be determined for semi-infinitely deep defects [START_REF] Barcia | Further to the paper "Application of the impedance model of de Levie for the characterization of porous electrodes" by Barcia et al[END_REF]. In addition to geometrical considerations, the surface reactivity of the pore walls has also to be considered and faradic processes (Z pore,F , Eq. ( 6)) can occur and consequently modify the impedance of cylindrical pores given by the transmission line model [START_REF] Ogihara | Theoretical and experimental analysis of porous electrodes for lithium-ion batteries by electrochemical impedance spectroscopy using a symmetric cell[END_REF].

= + ⎛ ⎝ ⎜ + ⎞ ⎠ ⎟ Z R R jω R C π r coth L R j ωR C πr R . ( 1
Where R ct,p is the pore charge transfer resistance (Ω. cm -1 ) while the other parameters were defined in Eq. ( 5). In Eqs. ( 5) and ( 6), the capacitance C p can be replaced by the constant phase element defined by Q p and n p in the case of a non-ideal surface as previously done (Eq. ( 3)). Also, these two equations refer to the impedance of one pore which is assumed in first approximation for the two porous microstructures.

In this study, the structures are characterized by interconnected pores randomly oriented in the volume. The open represent at approximately 30 % of the surface for the two samples (estimation based on ImageJ using a threshold calculation on Fig. 2(e)). Consequently, the oxide film on ligaments at the surface act on the definition of the material reactivity. At the corrosion potential, the impedance of stainless-steel porous samples is equivalent to the cathodic impedance in parallel to anodic impedance and in series with the solution resistance (R e ). The cathodic impedance corresponds to pores contributions (Z pore,F ) while the anodic impedance is related to the space charge capacitance on the ligaments (Q a , n a or C a ) and the charge transfer resistance (R a ) at the external surface of the samples [START_REF] Barcia | Application of the impedance model of de Levie for the characterization of porous electrodes[END_REF]. In the case of the 1.3 μm pore specimen, a Warburg W element was added to take into account the diffusion at low frequency.

Electrical equivalent circuits are schemed in Fig. 6(b) and (c) for the 1.3 μm and 0.5 μm pores samples respectively. In first approximation, the pore length, L, is equal to the thickness of the two samples (i.e., 1 mm) since this is the preferential dealloying orientation. The pore radius, r, corresponds to the values given in Table 2 for each material. Experimental and fitted Nyquist curves are plotted in Fig. 5(c) while Table 3 reports the fit results. The resistance of the electrolyte (R e ) depends on the material structure. Compare to rod electrodes, R e is multiplied by 10 and 100 for 0.5 μm and 1.3 μm porous samples, respectively. This enhancement with the pore sizes is attributed to the modification of the contact number and surface between the ligaments since all the experiments were performed in the same solution. Therefore, having larger pores reduces the contact surface between ligaments and contributes to the increase of R e [START_REF] Keiser | Abschätzung der porenstruktur poröser elektroden aus impedanzmessungen[END_REF]. The ionic resistance R ion,p depends on the porosity design and the largest pores lead to the highest resistance. This results is somehow surprising as R ion,p should increase with the pore length [START_REF] Ogihara | Theoretical and experimental analysis of porous electrodes for lithium-ion batteries by electrochemical impedance spectroscopy using a symmetric cell[END_REF]. This finding has to be linked to the detection of Warburg impedance at low frequency for the 1.3 μm pore sample. Indeed, the ionic resistance in Eq. ( 6) was defined originally for linear pores which is not the case here. The tortuosity of the pores and the ratio between the reservoir mouth and body affects the diffusion of species. Therefore, the volume of pores for the 1.3 μm samples is higher and the diffusion of species is easier. In the case of the 0.5 μm sample, the smaller ionic resistance comes from a more compact structure at the scale of the species diffusion as also supported by a greater value of for n p (0.85 for 0.5 μm and 0.72 for 1.3 μm samples). The estimation of the pore capacitance from Q p , n p and R ct,p (Eq. ( 4)) gives 49 μF.cm² and 44 μF.cm² for 0.5 μm and 1.3 μm pore sizes, respectively. These values are in the order of magnitude of the double layer capacitance and does not change with the dimension of the pores. R ct,pore is almost constant whatever the electrode (Table 3). This means that the physical properties of the pore walls are independent to the porosity size. As previously mentioned, the reactivity of the outer part of the ligaments has also to be consider since it represents ∼70 % of the outer surface of the sample. This is approximated by R//CPE and RW//CPE circuits for the small and large pore samples, respectively. The capacitance of the external surface of the samples is estimated with Eq. ( 4) considering Q a , n a and R a (Table 3). The capacitance C a (Eq. ( 4)) decreases with the pore shrinkage (4.1 μF. cm -2 and 0.35 μF. cm -2 for large and small pores respectively). Actually, the value of C a corresponds to the space charge capacity in the case of large pores. However, C a spreads to the usual values for the 0.5 μm sample which suggests that the oxide film is under the influence of the submicrometric pores and their effect on the local chemistry of the solution. The pore dimensions influence also R ct,s where tiny holes lead to a lower resistance. The use of the transmission line model enabled to distinguish the two porous structures in terms of surface reactivity. However, further microstructural analyses are required to describe better the pore interconnection in the volume, the tortuosity of the diffusion paths. Indeed, Cooper al. demonstrated that impedances for open systems with reservoir geometries deviate from the classical cylindrical pore model (see Fig. 2 in [START_REF] Samuel | Simulated impedance of diffusion in porous media[END_REF]).

Conclusions

In this paper, liquid metal dealloying (LMD) was applied on a commercial Incoloy 800 to create a stainless steel foam.

Microstructural, surface analyses and electrochemical characterizations were performed to evaluate the metallurgical properties of the stainless foam generated by this process. Mains results are summarized as follow:

-Porosity size depends on the temperature of the liquid metal bath.

Higher the temperature is, bigger the ligament size and the porosities will be. However, this is not strongly modifying the porosity ratio. -In comparison to pure precursor, the presence of minor alloying elements in Incoloy 800 has effect on the foam ligament size and porosity. -The Mg phase etching by nitric acid solution leads to a Cr enrichment of the passive film that improves the corrosion resistance of the porous material. -Pores increase the sensitivity to localized corrosion. However, no effect of the pore size on the pitting sensitivity was detected. -Diffusion processes in the metallic foam have been detected for the sample with the highest porosity size.

Finally, our results demonstrate the potential of the LMD process to inexpensively produce free-standing fully porous ferritic stainless steel for use as selective membranes and for structural and functional products such as electrodes, supports, filters, etc.

Fig. 1 .

 1 Fig. 1. (a) SEM micrograph of polished surface of Incoloy 800 (precursor sample) and elemental maps of Ni, Fe, Si, Cr, Ti. (b) Chemical composition analysis by EDX based on the previous list of elements and (c) XRD pattern of Incoloy 800 (precursor sample) with its austenitic phase.

Fig. 2 .

 2 Fig. 2. (a) Morphological comparison of the Incoloy 800 sample before and after dealloying, (b) EDX maps (Mg, Cr, Fe) of the bicontinuous structure. Cross-sectional SEM micrographs after Mg immersion after 1 h at (c) 830 °C and (d) at 750 °C. (e) SEM observations after dissolution of Mg by chemical etching in nitric acid solution (chemical composition of the porous structure obtained by SEM-EDS in in-window capture). (f) XRD pattern of the two porous materials and identification of a ferritic stainless steel phase.

Fig. 3 .

 3 Fig. 3. Windows XPS spectrum for Fe 2p, Cr 2p, and O 1s on the ingot sample (a) before and (b) after nitric acid treatment. The red line represents the experimental data, the gray line is the curve envelope, and the other colors are the contribution of the metal, oxide and hydroxide peaks (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).

Fig. 4 .

 4 Fig. 4. (a) OCP curves, (b) LSV curves, (c) Nyquist diagram, and (d) Bode diagram recorded in aerated and stagnant 0.1 M NaCl solution at room temperature to understand the effect of acid nitric treatment on corrosion resistance. Experiments performed on ingot sample (bulk sample with the same composition as samples obtained after LMD and etching (i.e. (Fe 67.7 Cr 29.5 Ti 1.0 Si 1.8 )).

Fig. 5 .

 5 Fig. 5. (a) OCP curves (b) LSV curves, and (c) PEIS curves on bulk and porous samples. Experiments were realized on ingot sample after nitric acid treatment (ingot) and on porous samples with a pore size of 1.3 μm and 0.5 μm. Measurements in aerated and stagnant 0.1 M NaCl solution (room temperature).

Fig. 6 .

 6 Fig. 6. Electrical models for a) the polished and the passivated rod, b) the 0.5 μm pore sample and c) the 1.3 μm pore specimen.

Acknowledgements

This work was supported by ICC-IMR (Tohoku University, Japan), Région Rhone-Alpes [CMIRA 138249], the Erasmus+ program, and the French Ministry of Research.

Data availability statement

The raw/processed data required to reproduce these findings cannot be shared at this time due to technical or time limitations.

Declaration of interests

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

Appendix A. Supplementary data

Supplementary material related to this article can be found, in the online version, at doi:https://doi.org/10.1016/j.corsci.2020.108468.


Morgane Mokhtari

Christophe Le Bourlot
email: christophe.le-bourlot@insa-lyon.fr

Jérôme Adrien

Sylvain Dancette

Takeshi Wada

Jannick Duchet-Rumeau

Hidemi Kato

Eric Maire

Cold-rolling influence on microstructure and mechanical properties of NiCr -Ag composites and porous NiCr obtained by liquid metal dealloying

Keywords: dealloying, X-ray tomography, nanoindentation, Ni, cold rolling, porous Highlights

teaching and research institutions in France or abroad, or from public or private research centers.

Introduction

Nanoporous metals have attracted considerable attention for their excellent functional properties [START_REF] Erlebacher | Hard materials with tunable porosity[END_REF][START_REF] Snyder | Oxygen reduction in nanoporous metal-ionic liquid composite electrocatalysts[END_REF][START_REF] Lang | Nanoporous metal/oxide hybrid electrodes for electrochemical supercapacitors[END_REF][4]. Properties at the nanoscale differ significantly from those of their dense, bulky counterparts. The earlier and most well-known technique used to prepare such nanoporous metals is dealloying in aqueous solution. Nanoporous noble metals including Au, Ag, Pt, Pd and Cu have been successfully prepared from binary alloy precursors such as Au-Ag, Ag-Al, Pt-Cu,

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Pd-Co, Cu-Mn and Cu-Al [4][START_REF] Forty | Corrosion micromorphology of noble metal alloys and depletion gilding[END_REF][START_REF] Xu | Dealloying to nanoporous silver and its implementation as a template material for construction of nanotubular mesoporous bimetallic nanostructures[END_REF][START_REF] Pugh | Formation of nanoporous platinum by selective dissolution of Cu from Cu0.75Pt0.25[END_REF][START_REF] Min | The microstructure and dealloying kinetics of a Cu-Mn alloy[END_REF][START_REF] Hayes | Monolithic nanoporous copper by dealloying Mn-Cu[END_REF][START_REF] Smith | Kinetics and mechanism of the preparation of Raney® copper[END_REF]. Regarding less noble metals, unstable in aqueous solution, the previous process is impossible as they oxidize immediately when coming into contact with water. To overcome this limitation, a new dealloying method using a metallic melt instead of aqueous solution was recently developed [START_REF] Wada | Dealloying by metallic melt[END_REF]. The liquid metal dealloying method is a selective dissolution phenomenon of a bi-alloy solid precursor: one component (referred to as the soluble component) being soluble in the metallic melt while the other (referred to as the targeted component) is not. When the solid precursor is immersed in the metallic melt, only atoms of the soluble component dissolve into the melt inducing a spontaneously organized bi-continuous microstructure formed by the targeted and sacrificial phases (the atoms of the sacrificial phase in solution in the melt phase). After cooling down to room temperature, this sacrificial phase can be removed by selective chemical etching to obtain the final nanoporous materials with the targeted composition. Because this is a water-free process, it has enabled the preparation of nanoporous structures with less noble elements such as pure Ti, Fe, Cr, Nb, Si and C [START_REF] Wada | Dealloying by metallic melt[END_REF][START_REF] Wada | Nano-to submicro-porous b-Ti alloy prepared from dealloying in a metallic melt[END_REF][START_REF] Chen-Wiegart | 3D morphological evolution of porous titanium by x-ray micro-and nanotomography[END_REF][START_REF] Wada | Three-dimensional open-cell macroporous iron, chromium and ferritic stainless steel[END_REF][START_REF] Kim | Sub-Micron Porous Niobium Solid Electrolytic Capacitor Prepared by Dealloying in a Metallic Melt[END_REF][START_REF] Wada | Bulk-Nanoporous-Silicon Negative Electrode with Extremely High Cyclability for Lithium-Ion Batteries Prepared Using a Top-Down Process[END_REF][START_REF] Yu | Three-dimensional bicontinuous porous graphite gerenated in low teperature metallic melt[END_REF].

In some applications such as electron or heat transportation, great strength along a particular may be desired thus leading to anisotropy in the structure and subsequently in the electrical, thermal or mechanical properties. However no practical methods have thus far been suggested to induce such an anisotropy [START_REF] Sivula | Photoelectrochemical water splitting with mesoporous hematite prepared by a solutionbased colloidal approach[END_REF].

The study of the microstructure of these porous materials is not easy because it requires 3D information. The relationship between the microstructure and the mechanical properties of these materials made by liquid metal dealloying has also not yet been clarified.

Nanoporous Ni, already prepared by dealloying from Ni-Mn, Ni-Cu, Ni-Al [START_REF] Hakamada | Preparation of nanoporous Ni and Ni-Cu by dealloying of rolled Ni-Mn and Ni-Cu-Mn alloys[END_REF][START_REF] Sun | Fabrication of Nanoporous Nickel by Electrochemical Dealloying[END_REF][20] in aqueous solution, is directly obtained as a foam. It is therefore not possible to introduce anisotropy after employing a dealloying process such as this. In the present study, we prepare Ni 90 Cr 10 with the liquid metal dealloying method using an Ag bath. The possibility of introducing anisotropy in the microstructure by cold rolling the dealloyed material before etching the sacrificial phase is studied. The microstructure of the obtained samples is determined using 3D XRCT and its morphological characteristics are quantified. This is linked to the measurement of the mechanical properties of the NiCr-Ag composite and (in one case only) of the porous material.

Materials and methods

The elements selection strategy for designing the dealloying reaction is based on the interaction (enthalpy of mixing) between atoms, which is described in detail in [START_REF] Wada | Dealloying by metallic melt[END_REF]. A Ni-Cr-Cu alloy (the precursor) and an Ag melt were used in this work. (Ni 90 Cr 10 ) 60 Cu 40 ingots were prepared using arc melting and tilt casting, as described in [START_REF] Wada | Three-dimensional open-cell macroporous iron, chromium and ferritic stainless steel[END_REF]. The resulting cylinder was cut

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into slices 1cm in diameter and 1mm thick. The dealloying step was carried out on these slices with a temperature of 1293K for 30min in an Ag melt bath. Before selective etching some dealloyed metallic composite samples were cold-rolled to introduce morphological anisotropy by co-deformation. Three sets of samples were prepared: (i) Non-rolled samples (NR), (ii) samples rolled in one direction (1D) and (iii) samples rolled in two perpendicular directions (2D); the cold-rolling process was performed with a 70% reduction in thickness. The selective etching step was carried out using highly concentrated nitric acid to dissolve the solid-state solution of Ag, resulting in micro-to nano-porous Ni 90 Cr 10 .

Each of the composite samples was cut with a precision micro-cutting machine into a rectangular rod with 0.5-1 mm sides and 1 cm in length and then polished into a tip shape for Xray tomography measurement conducted on a easytom tomograph (RX Solutions, France). The polychromatic X-ray source was operated with a LaB 6 cathode at a voltage of 100 kV. The 488 X-Ray projections were collected on a flat panel detector with an exposure time of 10s. The reconstructed 3D images were obtained using the commercial software provided with the tomograph. The full volumes were reconstructed with a voxel lateral isotropic size of 0.3µm and analyzed with Fiji free software [START_REF] Schindelin | Fiji: an open-source platform for biological-image analysis[END_REF]. The "local thickness" function was used to calculate the phase thickness distribution of each phase. The "find connected area" and a homemade plugin were used to measure the connectivity and the specific surface (the surface being approximated using the marching cube algorithm).

Nanoindentation tests were performed using a Nanoindenter G200 device. On each sample 9 indents were performed with (1)a maximum depth of 2µm using a Berkovich diamond tip on composite samples and (ii)a maximum load of 150mN applied in 5 steps with a 70µm diameter cylindrical steel flat punch on porous samples.

The results were analyzed with the Nanosuite software and were calibrated with a fused silica sample. In order to detect a possible mechanical anisotropy induced by rolling, indentation was performed perpendicular to the thickness and along the thickness of the samples.

Results and discussion

Microstructural characterization of NiCr-Ag composites

1. 1 Qualitative images

Fig. 1 shows one reconstructed slice for each sample extracted from the reconstruction and the associated threshold outline used for the analysis. The quality of these pictures is affected by the fact that Ag and Ni are high X-ray absorbing elements, implying the use of high energy X-rays. In such conditions, image quality is not at its best on a standard laboratory tomograph. Note also that despite the fact that we used one of the smallest possible source sizes

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available on the market for such a laboratory device, the size of the microstructure of our samples is so small that the resolution is barely enough for a perfect analysis. Despite these remarks, a number of comments can be made. The two phases are clearly visible in Fig. 1. The lighter phase corresponds to the Ag phase while the darker one corresponds to the NiCr phase. . This is consistent with the imposed cold rolling process, the amount of anisotropy in the 1D sample (along its rolling direction) being expected to be higher than in the 2D sample.

1. 2 Volume fraction and phases thickness

Tomography analysis gives access to the volumic fraction (%vol) of the different components while atomic ratios are given by the stoichiometry of the design precursor.

Table 1 shows the measure of the %vol of the NiCr phase ratio. The %at amount of NiCr included in the precursor was 60%. The %vol is directly extracted from the thresholded images.

Given the bad quality of these images, the precision of the measurement is not very good (estimated to about +/-2%). All ratios measured are rather close to 60 %, which also validate the measurement process (as cold rolling does not affect volume fractions). Fig. 2(a) exhibits the phase thickness distributions of NiCr and Ag phases for the non-rolled sample. As already mentioned in literature for a similar process [START_REF] Liu | A general dealloying strategy to nanoporous intermetallics, nanoporous metals with bimodal, and unimodal pore size distributions[END_REF], the phases display a unimodal thickness distribution. The average phase thickness is around 4 µm for the NiCr and 5µm for the Ag. Fig.

2(b) and (c)

show the influence of cold rolling on the phase thickness distribution respectively for NiCr and Ag phases. Fig. 2(b) presents an almost constant NiCr phase average thickness with a slightly wider distribution for cold-rolled samples. Fig. 2(c) seems to exhibit a small effect of cold rolling on the Ag phase: the isotropic sample presents a smaller average phase thickness than cold-rolled ones. Further investigations are needed to better understand this result, the quality of the raw images prevents any graphical explanations from being given.

1. 3 Connectivity and specific surface

For various applications where the transport of electrical charges is a key property (such as capacitors), it is important to have a perfectly connected structure and a high specific surface [START_REF] Erlebacher | Hard materials with tunable porosity[END_REF][START_REF] Snyder | Oxygen reduction in nanoporous metal-ionic liquid composite electrocatalysts[END_REF][START_REF] Lang | Nanoporous metal/oxide hybrid electrodes for electrochemical supercapacitors[END_REF][4]. The connectivity for all samples is close to 1 for both phases. This result shows that our sample made by dealloying is a bi-continuous structure as mentioned in Wada et al. [START_REF] Wada | Dealloying by metallic melt[END_REF]. We then demonstrate here that the cold rolling process does not break the ligaments and that the bicontinuous structure is preserved.

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Table 2 gives the specific surface of the samples, bulk NiCr density was calculated with atomic fraction and density found in literature [START_REF]Properties and Selection: Nonferrous Alloys and Special-Purpose Materials[END_REF]. Both the NiCr and Ag phases have the same volumic specific surface. The specific surface is slightly decreases with cold rolling. The measured values are rather low compared to the Ni based alloy made by dealloying in aqueous solution (about twice as high) but our ligament size is about 400 times higher [START_REF] Detsi | Mesoporous Ni 60 Fe 30Mn10 -alloy based metal/metal oxide composite thick films as highly active and robust oxygen evolution[END_REF]. Nanoporous Au from a 15nm to 70nm ligament size and low density give a specific surface of around 72 10 4 m²/kg that is higher than our samples but with smaller ligament sizes [START_REF] Lakshmanan | Surface area of nanoporous gold: Effect on temperature[END_REF]. For a material elaborated by dealloying, our specific surface is low but still higher than macroporous Ni [START_REF] Detsi | Mesoporous Ni 60 Fe 30Mn10 -alloy based metal/metal oxide composite thick films as highly active and robust oxygen evolution[END_REF][START_REF] Zhu | Application of Porous Nickel-Coated TiO2 for the Photocatalytic Degradation of Aqueous Quinoline in an Internal Airlift Loop Reactor[END_REF]. For this set of samples, we did not particularly target small ligament sizes but this would be perfectly feasible using this dealloying process. A decreasing phase ratio, dealloying time or dealloying temperature will give smaller ligaments and therefore a higher specific surface. These curves are rather typical of bulk materials [START_REF] Oliver | An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments[END_REF] and are similar for each indent, highlighting the reproducibility of the measurement. The maximum indentation depth of 2µm is smaller than the ligament thickness (4µm) but the interaction area should be considered as 10 times the indentation depth so it is considered to be large enough for sampling a representative part of the sample [29]. Oliver et al explain how the Young's modulus could be extracted from such load-displacement curves [START_REF] Oliver | An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments[END_REF] Fig. 3(b) shows the evolution of the Young's modulus measured along thickness vs the perpendicular modulus for different cold rolling conditions. The dashed line corresponds to equality between the two (expected for an isotropic sample). Theoretical Ag and Ni values from literature are also plotted [START_REF]Properties and Selection: Nonferrous Alloys and Special-Purpose Materials[END_REF]. Because of the small amount of Cr in the NiCr phase and because the Ni and Cr Young's moduli are close to each other, we assumed that the Young's modulus of the NiCr phase could be assimilated to that of Ni [START_REF]Properties and Selection: Nonferrous Alloys and Special-Purpose Materials[END_REF]. All NiCr-Ag measured moduli are between 130 and 180 GPa, higher than Ag but lower than Ni. Moreover, the values are closer to Ni than to Ag, which is consistent with the phase fractions. Dispersion of the nanoindentation results is shown by error lines. The dispersion is small, around 6 GPa, and almost constant, which is consistent with the similar load-displacement curves showed in Fig. 3(a). The NR sample exhibits very similar indents independently of the tested direction while 1D and 2D coldrolled samples present higher moduli values on the sample thickness than on the sample surface. This confirms that cold rolling indeed induces a mechanical anisotropy, and that the quantity of anisotropy can be controlled by the cold rolling step. Further analyses are needed to quantify this process.

2 Mechanical characterization of NiCr-Ag composites

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3 Dissolution of NiCr-Ag 1D

1 Microstructural characterization

On NiCr-Cu precursor alloy, some SEM-EDX measurement were done, SEM-EDX maps show an homogeneous monophase alloy. Fig. 4 shows a comparison of an NiCr-Ag before and after the chemical etching of the Ag phase. SEM-EDX analysis on the two phases (Fig. 4(a)) confirms an clear separation between the phases, with no silver within the NiCr phase, and vice versa. After chemical etching (Fig. 4(b)), the silver phase has been removed, and a surface average of the SEM-EDX analysis shows no trace of residual silver. Finally, the size and morphology of the foam ligaments after dissolution seem consistent with what is visible before dissolution, because the addition of Chromium in the Nickel create a passivated layer that protect the phase. the sample is nearly completely porous, some white points could be noticed, perhaps due to some residual sacrificial phase. As mentioned for the Au sample, the propagation of the dissolution front appears to be planar from outside to inside and the propagation of nitric acid looks faster at the tip than at the side of the sample [29]. Because of the different thermal expansion coefficient between the two phases we can expect some residual thermal-stress between the two phases. The dissolution of the sacrificial phase would therefore relax this stress, even if this relaxation is likely to be small. The image quality is again not good enough to conclude on the tendencies.

2 Mechanical characterization

Table 3 displays the average Young's moduli and standard deviations measured on a composite and porous 1D sample both perpendicular and along the thickness. For the porous sample, the modulus along the thickness (9.8 GPa) is larger than that one measured on the surface (8.1 GPa). This shows the possibility of introducing anisotropy in mechanical properties at the porous state as this anisotropy seems to be preserved after dissolution. To our knowledge, there is no such comparable measurement in literature. For a three-dimensionally ordered macroporous (3DOM) nickel, with smaller pore (1.2µm), smaller ligaments size and lower density (0.26), Young's moduli measured by nanoindentation were 2GPa [30]. This seems rather consistent with the 9 GPa measured on our denser Ni foam. ( )

r r p ρ D + ρ B = E E * * 2 (2)
When applying the B and D values suggested in [33], moduli become E P =18 and E A =20

GPa, perpendicular and along the thickness, which is in better agreement with our measurements.

Conclusion

NiCr-Ag composites were prepared using dealloying by immersing Ni-Cr-Cu precursors into a Ag metallic melt bath. One sample was cold-rolled in one direction, another in two perpendicular directions with a thickness reduction of 70% and one was non-rolled. The Ag phase of the one direction cold-rolled sample was then etched. The results of X-ray tomography show that the %at fraction of the precursor will determine the %vol faction of the bi-continuous structure. The NiCr and Ag particle size distribution were independent to cold rolling conditions.

The material remains bi-continuous although the cold rolling process indicates a mechanical anisotropy. NiCr-Ag composites present Young's modulus values between those expected for Ni and Ag. Indentations perpendicular to the thickness and along the thickness give similar moduli for the non-cold rolled sample, but is different for those which are cold-rolled. The difference in Young's moduli is measured to be preserved at the porous state after etching. The introduction of anisotropy into the microstructure and the mechanical properties of the composites was well preserved after etching at the porous state.

Fig. 1 (

 1 Fig. 1(a) shows quite randomly oriented ligaments while Fig. 1(b) and (c) show ligaments oriented in one direction and (c) is more oriented than (b). This is consistent with the imposed

Fig. 3 (

 3 Fig. 3(a) shows load-displacement curves registered during nanoindentation experiments.

Fig. 5

 5 Fig. 5 shows one reconstructed slice for each sample extracted from the reconstruction with (a) the composite sample also shown in Fig. 1(c), Fig. 5(b) and (d) display the same sample after 15min immersed in nitric acid and (c) after 30min in nitric acid respectively. In Fig 5(c),

  proposed the equation[START_REF] Erlebacher | Hard materials with tunable porosity[END_REF] to link the Young's modulus (E p ) and density (ρ p ) of a porous material with the modulus (E) and density (ρ) of its bulk constituent. C and n are constant values[31]. are constant parameters, depending on the morphology of the porous sample[32]. Using C=1 and n=2, as suggested in[32] for open-cell foams, this model predicts E P =54GPa and E A =58GPa for the indents perpendicular and along the thickness respectively. This is much larger than our measurements. Molecular dynamic simulations [33] also found that nanoporous gold does not follow the Gibson and Ashby relation and these authors proposed a new model described in equation (2) with ρ r as the porous to bulk density ratio, and B and D are constants calculated from their data.

Acknowledgements

The authors gratefully acknowledge the French ministry of research for the provision of the salary grant of MM.

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[29] J. H. Westbrook, H. Conrad, The Science of hardness testing and its research applications, American Society for Metals, 1973