Marie-Hélène H Delville

Th Jaszay

Philippe Botella

Bernard Lestienne

François Cansell

Elisabeth Sellier

Jean-Pierre P Frayret

Anodic Behavior Modeling of the C-276 Alloy in Chlorinated Media Simulating the Hydrothermal Conditions of Organic Waste Treatment

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Anodic behavior modeling of the C-276 alloy in chlorinated media simulating the hydrothermal conditions of organic waste treatment

Experimental current-potential curves corrected from the contribution due to the medium oxidation are used to propose a dissolution-passivation model of the nickel base alloy C-276. This model is controlled by the major presence of nickel and shows a reaction chain mechanism with a bifurcation and two competitive determinant branches for the setup of the protection of the alloy. Considering a Langmuir-type adsorption, we formulate a current-potential law which leads, via a mathematical optimization calculation using Nelder's simplex, to the eight kinetics parameters involved in the five considered elementary steps. The respective influence of the different branches can be determined. It is used in association with the scanning electron microscopy profiles obtained at fixed potentials, to evaluate the limited reliability of the C-276 alloy as a plant reactor material for waste treatment under hydrothermal conditions, either sub-or supercritical oxidation. This evaluation relies on the comparison with the titanium T60 whose anodic behavior and performances have already been published. The determination of the kinetic parameters also underlines the role played by the oxygen source ͑H 2 O 2 ͒ on the mechanism, a role partly hidden by strict observation of the current-potential experimental curves.

The context of this study has already been stated and is briefly recalled here. [1][2][3][4] The principle is to develop elements of appreciation for an efficient choice of a material to be used in plant reactors for organic waste treatment under hydrothermal oxidation, either sub-͑temperature Ͻ 373°C͒ or supercritical ͑temperature Ͼ 373°C͒ conditions. They should also be able to orientate the choice in the case of chloride formation for pH Ͻ 5.

To our knowledge, available information on this subject and especially on nickel-based alloys, such as the C276 one, come from gravimetric measurements and corrosion facieses. 5 These studies show a high reactivity of nickel base alloys and an expected tendency to localized attacks. Despite this observation, which reveals the invalidity of these alloys, they still remain frequently used, without any attempts of a kinetic and/or mechanistic investigation. However, only such an approach can provide some comprehension of the phenomenon and lead to the identification of the right solution able to stop or at least slow down the material reactivity. The main goal of the paper is to conceive a model for the reaction mechanisms as for titanium alloys in the same experimental conditions. 1,6 It is also related to previous works that were carried out on other nickel-base alloys ͑I800͒ [START_REF] Jaszay | Proceedings of the 5th International Symposium on Environmental Degradation, Materials Nuclear Power Systems-Water Reactivity[END_REF][START_REF] Jaszay | [END_REF] and pure nickel 9 in environments simulating the conditions of primary and secondary media in PWR nuclear plants ͑for high pHs and minor quantities of chloride ions͒. The similitude of the current-potential curves led us to use the same type of model already efficient for titanium metal 6 and pure nickel by taking into account some reference works on this material generally performed in sulfuric acid media and at low temperature. [10][11][12][13]

Means of Investigation

Experimental device.-The experimental devices used for the electrochemical characterization of current-potential curves used to determine the kinetics of the dissolution-passivation processes were adapted to satisfy the constraints of working under high pressure and high temperature conditions ͓up to supercritical conditions ͑400°C, 28 MPa͔͒. 2 The essential aspects concern ͑i͒ the chemical inertness of the cell and of its equipment, ͑ii͒ the water tightness of the electrodes, and ͑iii͒ their electrical isolation ͓performed using a specific poly͑tetrafluoroethylene͒ ͑PTFE͒ sheathing͔. 1 This device has been described in other previous papers. [1][2][3][4]6 To improve the quality of the measurements, we performed a few modifications. First, long electrode bearers ͑20 cm͒ were used able to insure the acceptable tightness of the electrodes as well as their electrical isolation. Then, the welding of four external tubules on the electrochemical cell itself insures an expansion of the medium which gives rise to inlets and outlets with temperatures close to ambient. 2 As a consequence, the tightness between the PTFE sheath which isolates the electrode and the end of the electrode bearer tubing is obtained at medium temperature using a nonpolluting joint paste 6 with a high mechanical resistance. The PTFE sheathing bears no major degradation when experiments are performed in less than 24 h ͑manufacturer recommendations͒. Knowing its thermoshrinkable properties, it is possible to estimate precise areas for electrodes ͑either 1.3-3 mm diam disks or a cylindered volume of various heights͒. A passivated TA6V4 titanium alloy insures the chemical inertness of both the cell and the electrodes apertures.

Measurements are carried out in a usual three-electrode cell with the specific adaptations arising from the use of hydrochloric solutions ͑pH Ͼ 1͒ along with high-temperature and high-pressure conditions ͑400°C,28 MPa͒. The working electrode ͑the alloy under study͒, the auxiliary electrode ͑a platinum wire͒, and the reference one ͑a hydrogen dynamic electrode ͑HDE͒͒ 14 are connected to a homemade potentiostat. The specificity of this setup concerns the choice of this reference electrode which prevents the use of electrochemical bridges, and the associated thermal junction problems. It is an internal electrode which can operate at high temperatures. [2][3][4]6,15 The principle of this HDE consists of the use of two platinum wires of 0.5-mm o.d. separated by less than 5 mm with an active surface of approximately 50 mm 2 . These two wires, anode and cathode ͑used as the reference electrode for measurements͒, are on the same side of the cell and are galvanostatically controlled at currents comprised between 1 and 5 mA to promote water microelectrolysis. A special attention was focused to check that this procedure had no influence on the measurements. Its potential is normalized with re-spect to the saturated hydrogen electrode ͑SHE͒ by applying the Nernst law. In this work, results are normalized with respect to the saturated calomel electrode ͑SCE͒.

The current-potential curves are analyzed with a model built on the evaluation of kinetic parameters using an optimization calculation based on the Nelder simplex method. 1,6,[16][17][18][19] The resulting interpretations of the electrochemical behavior are also illustrated by observation of scanning electron microscopy ͑SEM͒ images of the C276 alloy surfaces. They are compared to those obtained for titanium in a previous article. 2 The goal is to establish the relative capacities of these two materials to be used in the fabrication of reactors for hydrothermal oxidation processes.

Experimental conditions.-The electrochemical characterizations are performed under high-pressure and high-temperature conditions ͑up to supercritical conditions͒. Two situations are presented: ͑350°C, 28 MPa͒ and ͑400°C, 28 MPa͒.

The impurity contents of the two materials are given in Tables I and II.

These materials used as wires are placed in thermoshrinkable sheaths of PTFE ͑TER-R UL 224 quality by Gremco͒. The active surface is then polished using SiC abrasive paper up to grade 1200 and rinsed in pure deionized water under sonication. The setup of the working electrode as an anode in the electrochemical cell must be as fast as possible, especially for the air-sensitive titanium material. The two other electrodes are sheathed platinum wires. The reference electrode is always placed as close to the working one as possible.

The different aqueous solutions given in Table III are significant of those encountered in hydrothermal oxidation processes. They take into account the products resulting from the degradation of organics

C a H b X c + ͓a + ͑b + c͒/4͔O 2 → aCO 2 + ͓͑b -c͒/2͔H 2 O + cHX
Among the most dangerous pollutants, are those containing halogenated species ͑X͒. To take into account the presence of such species as well as the associated acids, we chose the hydronium and chloride concentrations given in Table III. To study the usual pH range ͑1.5-5͒, we prepared two different solutions with constant chloride contents ͑1 g/L, i.e., for example, 3 ϫ 10 -2 mol/L KCl͒, pH 1.7 and 5.1. To mimic hydrothermal oxidative conditions, we introduced an oxidative species such as 3 wt % hydrogen peroxide in the two different pH solutions. A comparison is then allowed between the two media: one with hydrogen peroxide the other with oxygen from the air. As indicated in Table III, the pH difference between the two media is very small.

Once the desired temperature ͑350 or 400°C͒ and the associated autogenic pressure are reached ͑this conditioning performed to maintain a monophasic domain is carried out up to 28 MPa to avoid any chlorinated compound crystallization [20][21][22] ͒, a delay necessary to reach the open-circuit potential stability ͑corrosion potential͒ is applied before the polarization. It is performed for C276 alloy at a scan rate of 0.1 mV/s, two times smaller than those used in the same conditions of pressure and temperature in previous works. 1,6,9 Therefore, with this scan rate, experiments were carried out in quasistationary state conditions, and localized attacks, which could be formed in chlorinated solutions, cannot significantly occur. In a similar way, there is a minor effect of the diffusion transport of oxygen either for titanium or C276 alloy as already known. 4,[START_REF] Jaszay | [END_REF] We, therefore, can perform current potential curves on a fixed electrode and use a steady-state model for the theoretical aspect. In order to compare the electrochemical behaviors of Ti and C276 alloys, the current potential curves of titanium were also performed at the same scan rate. Such a rate leads to limited reaction times, which, as well, guarantee the chemical integrity of the cell constituents.

SEM was performed on a JEOL JSM-840A apparatus. Samples prepared for these experiments were kept at a fixed potential for 10 h. This potential was chosen in a region where the titanium oxidation is located on a plateau; this corresponds to the beginning of a pseudo plateau for C276. Potentials are given in V/SCE vs the SCE. Current densities are given in microamperes per square centimeter.

Results

The current-potential curves ͑Fig. 1-4͒ were recorded for the two materials in the four electrolytic media under sub-and supercritical conditions. They show no significant change as compared to the results obtained when the curves were recorded with a twofold scan rate; 4,6 the quasi stationary hypothesis can be applied.

The current-potential curves of C276 all present an oxidation peak coupled with a component associated with water dissociation. This tends to mask the end of passivation and the beginning of passivity and caused us to reconstruct these curves by subtracting the oxygen-evolution current from the total current. By subtracting this water component using an extrapolation of its most oxidized part where it takes place alone, we obtained an apparent profile with an activation peak. By subtracting this water component using an extrapolation of its most oxidized part where it takes place alone, we obtained an apparent profile with an activation peak, which corresponds to the dissolution ͑or the degradation of the material by the solution͒ up to a maximum intensity where there is an inversion of the current slope. The resulting negative slope corresponds to the passivation domain where the material dissolution is slowed down.

Once the second inversion of current curve corresponding to the oxidation reduction reaction ͑OER͒ is decoupled, a plateau can be seen ͑starting at a round 0.2 V͒ which can be called a pseudoplateau because it is not a real passivity plateau. The current value is too high to consider that the material is really protected by an oxide layer, and these results are also confirmed by SEM and energydispersive spectroscopy ͑EDS͒ data, as illustrated below. A sample of this reconstituted profile is shown in Fig. 5.

As opposed to C276 alloy, titanium does not show any current peak and except at the corrosion potential, its current potential profile corresponds exclusively to a passivity plateau which is totally independent of the kinetics of diffusion. 4,6 The amplitude of this plateau, in identical reaction conditions, is much lower than that of the C276 pseudo plateau. From these observations, it comes out that C276 is electrochemically much more reactive than titanium with currents which can be 2.5 times higher than those found for titanium in the more favorable potential range ͑the plateau͒ and at least ten times in the region where the peak current is high ͑medium D 400°C, Fig. 5͒. This hierarchy is maintained for all the other cases. Whatever the nature of the material, its reactivity is increased for the lowest pHs and slows down as soon as temperature is higher than 373°C. These data underline the active participation of H + ions to the kinetics of the reactions with a detrimental influence when they are highly dissociated and/or concentrated ͑current are then higher͒. The impact of H + dissociation is largely illustrated by the current decrease as soon as the critical temperature is reached, as shown by comparison of subcritical conditions ͑Fig. 1 and 3͒ and supercritical ones ͑Fig. 2 and 4͒. This underlines once more the modifications of the fluid properties at the critical point crossing, with an attenuation of its ionic character and a strong tendency to become apolar. 23 Indeed, depending on temperature and pressure, water is a medium of tunable density, ionic product, and dielectric constant. Therefore, its solvent character can vary from highly polar at high densities ͑350°C/28 MPa͒ to nearly nonpolar at low ones ͑400°C/28 MPa͒. With a high polar character, the solubility and/or the dissociation of the ionic species like salts and acids are favored. On the opposite, in low-density water ͑400°C/28 MPa͒, aqueous corrosion processes are suppressed insofar as a greater association of the ion pairs is observed ͑lower plateau current as compared to 350°C/28 MPa͒. [START_REF] Huang | Supercritical Fluid Science and Technology[END_REF] This apolar nature is a priori less aggressive, especially when H + ions are concerned.

The difference of behavior of the two alloys can also be checked from the surface morphology of samples obtained after a fixed period at constant polarization ͑see experimental conditions͒. A general feature is observed and illustrated for the two samples ͑Fig. 6 and 7͒ after treatment in medium B.

The titanium preserves an unmodified aspect as the untreated sample: absence of thick layers on the surface and absence of localized defects. The only observed imperfections are related to the preparation mode of the sample surface with more or less accentuated grooves. The C276 alloy is covered with a colorless, thick, embossed layer all over the surface. This layer exhibits a variable porosity which may induce an unstable and defective protection. On the contrary, in agreement with the current-potential curves, the unchanged aspect of titanium reveals the formation of a thin protec-tive film. This film is slightly blue/purple and is indicative of the continuous formation of the TiO 2 oxide, well-known for exhibiting highly passivating properties. 25,26

Model-Interpretation-Discussion

The establishment of a model for the dissolution-passivation of titanium and nickel-base alloys has already been examined in our previous papers. [1][2][3][4]6 Works on titanium performed in hydrogen chloride 1,6 have established current-potential profiles for passivable materials ͑a peak followed by a low-amplitude plateau͒ obtained in a stationary or quasi-stationary state which can be described by a model which uses a reaction process with a bifurcation in two competitive branches starting at a potential corresponding to the maximum current intensity. This bifurcation corresponds to the appearance of the valence 4 of titanium, whereas valence 3 is present from the beginning of the process. The formation of the plateau is linked to the valence 4 as the unique species. Therefore, we showed that the active branch is associated with the dissolution of titanium in its 3-valence state and the passive one leads to the formation of a titanium oxide layer in its 4-valence state. Their respective influences are strongly dependent on the applied potential. For pH Ͼ 1, the dissolution peak is no longer present, leaving a single plateau related to valence 4 and illustrating the disappearance of the active branch. The chain reactions model as well as the scheme of the alloy interface is presented in Schemes 1 and 2.

Since the polarization rate used for the study of C276 is slower than that used for titanium in previous papers, 1,6 a stationary regime is considered and the same approach was used to establish a model for the dissolution-passivation of C276.

We have just shown the necessity in the case of titanium to consider both the current potential curve and the valence-potential curve to build up a model of metallic materials. For C276 alloy the current-potential curves are described in Experimental. As far as the valence-potential laws are concerned, the analysis is complicated by the fact that the material is an alloy. However, according to the results already mentioned in the literature [START_REF] Jaszay | [END_REF][9][10][11][12] and in agreement with the general trend of the current-potential laws, it is reasonable to assume that in an acidic and chlorinated solution, [START_REF] Latimer | Oxidation Potentials[END_REF][START_REF] Pourbaix | Atlas d'Équilibres Électrochimiques à 25[END_REF] the material behavior is controlled by the Ni element with its two valences 1 and 2. [START_REF] Jaszay | [END_REF]9 This is also confirmed by the fact that ͑i͒ the layer formed on the material is porous and nonprotective ͑cf. Fig. 7͒ and ͑ii͒ the green solution recovered at the end of the experiment contains Cr͑VI͒ ͑orange͒, Mo͑VI͒ ͑colorless͒, Fe͑III͒ ͑yellow͒, and Ni͑II͒ ͑green͒ as usually expected for such oxidative conditions. A model based on the bifurcation scheme can then be used; this approach has already been used for I800 alloy in basic as well as neutral media. [START_REF] Jaszay | Proceedings of the 5th International Symposium on Environmental Degradation, Materials Nuclear Power Systems-Water Reactivity[END_REF] Because for nickel the dissolution in these media can lead only to Ni 2+ , the bifurcation takes place at the level of an adsorbed species with an oxidation state of +1. Each branch of the bifurcation leads to a divalent nickel but with different kinetics. To keep in mind that the dissolution-passivation model of this alloy is dominated by nickel, we will use the symbol ͓A͑Ni͔͒ in Scheme 3 to describe the fact that we work with an alloy ͑A͒ and that its behavior is controlled by Ni. To establish this model, some hypotheses are used: ͑i͒ the electrochemical steps are monoelectronic and follow a Tafel law; ͑ii͒ all the elementary, chemical, and electrochemical steps are irreversible, e.g., oriented toward the dissolution; ͑iii͒ the different steps are submitted to Langmuir isotherm conditions, leading to the coverage of the surface in the form of a monolayer by the adsorbats ͓A͑Ni͔͒ ads with no interaction with each other. ͑These conditions are not exactly respected but the resorting to more suited hypotheses does not necessarily lead to a better fit and introduced a much more complicated and often less-efficient formalism.͒ Using a minimum number of elementary steps, it is then possible to build a model with four elementary steps and seven kinetic parameters. However Rabu et al. 9 has shown that for nonalloyed nickel this model is not satisfactory and should be replaced by a model with eight parameters ͑Scheme 3͒.

In this model, ⌰ y corresponds to the coverage ratio per surface unit and K x is defined as the rate of the elementary step x per surface unit. It consists of five elementary steps, among which are two chemical ones at the end of the reaction process. Parameters K 0 , K 1 , K 3 are the rate constants of the electrochemical steps, and

K x = K x 0 e b x E
, where ͑i͒ b x corresponds to the Tafel exponent and T the absolute temperature, ͑ii͒ E is the imposed potential, ͑iii͒ K x 0 = k x a i i a j j . . ., with k x the rate constant of the electrode heterogeneous process, a the activity of the species concerned by the process, and i the partial orders of the reaction, generally equal to 1. This model leads to two different adsorbates of valence II, thereby characterized by distinct dissolutions ͕A͓Ni͑II͔͖͒ s1 and ͕A͓Ni͑II͔͖͒ s2 . For the chemical steps of dissolution of ͓A͑Ni͔͒, K y is given by K y = k y a i i a j j . The reaction rate v j for the different steps of the model are a function of the coverage ratio ⌰ i according to

v 0 = K 0 ͑1 -⌰ 1 -⌰ 2 -⌰ 3 ͒ ͓ 1͔ v 1 = K 1 ⌰ 1 ͓2͔ v 2 = K 2 ⌰ 2 ͓3͔ v 3 = K 3 ⌰ 1 ͓4͔ v 4 = K 4 ⌰ 3 ͓5͔
For a steady state, the formation rate of a product is then identical to its disappearance rate leading to

v 0 = v 1 + v 3 , v 1 = v 2 , v 3 = v 4 .
From these equations, it is possible to determine the coverage ratios, ⍜ i

⌰ 1 = ͓1 + K 3 ͑1/K 4 + 1/K 0 ͒ + K 1 ͑1/K 2 + 1/K 0 ͔͒ -1 ͓6͔ ⌰ 2 = K 1 ⌰ 1 /K 2 ͓7͔ ⌰ 3 = K 3 ⌰ 1 /K 4 ͓8͔
The expression of the current takes into account the different rates of the electronic transfers according to

I = 2F͑K 1 + K 3 ͒⌰ 1 ͓9͔ I = 2F͑K 1 0 e b 1 E + K 3 0 e b 3 E ͓͒1 + K 3 0 e b 3 E ͑1/K 4 + 1/K 0 0 e b 0 E ͒ + K 1 0 e b 1 E ͑1/K 2 + 1/K 0 0 e b 0 E ͔͒ -1 ͓10͔
The example given in Fig. 8 illustrates the rather good correlation between the experimental curves and the calculated laws using the eight-parameter model. This result illustrates the validity of this model to evaluate the electrochemical behavior of C276 alloy as a function of the environmental factors. For example, the kinetic pa- rameters used for the experiment performed in medium C at 400°C and 28 MPa are: b 0 = 0.0296 mV -1 , b 1 = 0.0179 mV -1 , b 3 = 0.0044 mV -1 , K 0 0 = 23.6 mol s -1 cm -2 , K 1 0 = 13 mol s -1 cm -2 , K 3 0 = 1.26 mol s -1 cm -2 , K 2 = 0.98 ϫ 10 -4 mol s -1 cm -2 , and K 4 = 0.28 mol s -1 cm -2 .

The parameters ͑K 0 0 , K 1 0 , K 3 0 , K 2 , K 4 ͒ represent the intrinsic rates of the different elementary steps in the model. They depend on the various species observed during the process ͑diffusion adsorption/ desorption, redox processes͒ at the metal/medium interface. They do not take into account the influence of the potential ͑Tafel law͒ nor the coverage ratio of the adsorbats on the surface exposed to the solution. Therefore, these five parameters are indicators which can provide a hierarchy of the intrinsic kinetics of the different elementary steps and can also be used to quantify the effects of the variation of concentration in species or the physical factors ͑pressure, temperature͒. Apart from the general slow down of the overall kinetics as soon as the supercritical domain is reached ͓parameters are around 1.3 times higher in subcritical conditions close to the critical point ͑350°C͔͒, we observe that whatever the temperature, the relative influence of each step is preserved. Parameters are very sensitive to the pH as well as ͓H 2 O 2 ͔ variations as shown in Fig. 9, which gathers the kinetic parameters at 400°C and 28 MPa in the four different media.

When the pH increases all the parameters decrease, especially those concerning the electrochemical steps. Media A and C are characterized by the following order: K 0 0 Ͼ K 1 0 Ͼ K 3 0 and K 4 Ͼ K 2 with K 4 close to K 3 0 . This order is modified in the presence of hydrogen peroxide ͑media B and D͒ where K 3 0 Ͼ K 0 0 Ͼ K 1 0 while K 4 Ͼ K 2 is kept. There is also a strong decrease of the rate constants of the electrochemical steps especially for K 0 0 and K 1 0 with a difference of more than six decades as compared to constants in H 2 O 2 -free media ͑A and C͒, even if the current-potential in the two cases are rather similar for a given pH range. This situation therefore illustrates the tremendous influence of the potential imposed to the material in the presence of H 2 O 2 . This reactant thus plays the role of an inhibitor in the absence of polarization, in agreement with the shift of the opencircuit potential toward positive values ͓cf. ͑I,E͒ curves, Fig. 1͔. K 0 0 , K 1 0 , and K 3 0 parameters are more sensitive to pH variation in the presence of H 2 O 2 ͑⌬K over two decades͒, whereas the chemical rates K 2 and K 4 seem to be independent of the medium composition. K 4 is the highest parameter in H 2 O 2 media. The relative values of K 2 and K 4 are interesting to compare because they play a major role for the material passivity ͑reconstituted plateau of the current-potential curves͒. In all the media, the general trend is K 2 Ͻ K 4 , and this tendency is particularly relevant for understanding the role played by the chemical steps at the very end of the process on the amplification of the material degradation. This degradation also strongly depends on the imposed potential. This can explain why the currentpotential curves are comparable whether the media are oxygenated or not. Table IV gathers the calculated ratio between these parameters and underlines the constancy of the K 0 0 /K 1 0 ratio ͑1.7͒ so that the relative kinetic of the two electrochemical steps ͑the initial one and that leading to the branch concerned by v 1 and v 2 ͒ is fixed whatever the medium.

The other ratios illustrate the impact of the media composition, and we clearly retrieve the cleavage between with and without H 2 O 2 with an inversion of the predominance of the rates for the couples K 0 0 and K 3 0 , K 1 0 and K 3 0 , K 1 0 and K 2 . To exactly detect the respective influence of the different steps and the role of the two branches of the mechanism, it is possible to study the evolution of the coverage ratio ⌰ with the applied potential. They indeed represent a signature of the balance between all the elementary steps in relationship with the polarization level ͑Fig. 10 and 11͒. Profiles are similar for all the media. The free surface ͓1 -⌰ 1 -⌰ 2 -⌰ 3 ͔ decreases when the potential increases and practically reaches zero at the pseudo plateau of the currentpotential curve. This evolution corresponds to a progressive diminution of the active surface of the starting material and is concomitant with an increasing coverage by the adsorbed species, the coverage being total when ͓1 -⌰ 1 -⌰ 2 -⌰ 3 ͔ → 0.

This coverage results from the adsorption of three intermediates: ͕A͓Ni͑I͔͖͒ ads1 , ͕A͓Ni͑II͔͖͒ ads2 , and ͕A͓Ni͑II͔͖͒ ads3 . The ratios ⌰ 1 and ⌰ 3 are weak and the associated adsorbed intermediates have a very short lifetime with a highly degrading nature of the branch leading to ͕A͓Ni͑II͔͖͒ ads3 . The regular progression of ⌰ 2 toward an overall coverage corresponds to a branch which is a priori more protective where the intermediate ͕A͓Ni͑II͔͖͒ ads2 exhibits a much higher lifetime when the potential increases. The profiles of ⌰ 1 and ⌰ 3 are relatively close for oxygen-free media ͑A and C͒ with ⌰ 3 slightly higher than ⌰ 1 . On the contrary, we observe that ⌰ 1 = 50 ⌰ 3 in the presence of hydrogen peroxide. However, their values are so small that their impact is quasi eclipsed as compared to that of ⌰ 2 .

The influence of H 2 O 2 is observed at the very beginning of the reaction chain because ͑i͒ there is an increase of ⌰ 1 and a stabilization of ͕A͓Ni͑I͔͖͒ ads1 , the starting point of the bifurcation, and ͑ii͒ there is a shift of the positioning of the current-potential curves. H 2 O 2 also decreases the impact of the more degrading branch without having too much influence on the other one. Slowing down the dissolution of ͕A͓Ni͑II͔͖͒ ads2 , it induces the formation of the observed plateau to which it is tempting to associate the establishment of a passive behavior. However, the amplitude of the plateau prevents any conclusion of this type. The coverage linked to ⌰ 2 is not of good quality, as illustrated by the SEM images ͑Fig. 7͒, as well as the coloration of the solutions after the experiments. These results are far from those obtained in the case of titanium in the same conditions 1,6 for which the formation of a very stable semiconductor oxide related to passivity plateaus exhibiting low amplitudes ͑ten times smaller than those of C276͒ are evidenced.

Conclusion

The model of the electrochemical reactivity of C276 a nickel base alloy has been established on the basis of a bifurcation scheme composed of two branches, in conditions similar to those used in hydrothermal oxidation processes. This model has proven to be a pertinent tool not only to establish but also to quantify the vulnerability of such a material in these conditions, this vulnerability being mainly due to the nickel dissolution. Both the degree of polarization ͑especially in the presence of H 2 O 2 ͒ and the pH are the two main parameters. Indeed, in the presence of H 2 O 2 , an anodic overpotential may generate dramatic situations. In the same way, the pH decrease implies an increase of the alloy dissolution. This is related to the bad characteristics of the layer formed on the surface of the material. Despite a quasi overall coverage in the plateau range of the reconstituted current-potential curve, this layer is not able to insure an efficient protection of the alloy in such hydrothermal oxidative conditions. As a comparison, in the same conditions, the titanium is recovered by a titanium oxide layer which is quasi inert and constitutes a material of choice for the use in supercritical reactors.

As for titanium, a decrease, although small, of the C276 reactivity toward dissolution has been evidenced above the critical point. It is linked to the evolution of the fluid physical-chemical properties. Nevertheless, this decrease does not basically modify the negative behavior of this alloy.

Figure 1 .

 1 Figure 1. Anodic current-potential curves of alloy C-276 in the four electrolytic solutions ͑a͒ media A and C and ͑b͒ media B and D, at 350°C and 28 MPa. 0.10 mV/s polarization rate.

Figure 2 .

 2 Figure 2. Anodic current-potential curves of alloy C-276 in the four electrolytic solutions ͑a͒ media A and C and ͑b͒ media B and D, at 400°C and 28 MPa. 0.10 mV/s polarization rate.

Figure 3 .

 3 Figure 3. Anodic current-potential curves of T60 titanium at 350°C and 28 MPa, in the four electrolytic solutions A, B, C, and D. 0.10 mV/s polarization rate.

Figure 4 .

 4 Figure 4. Anodic current-potential curves of T60 titanium at 400°C and 28 Pa, in the four electrolytic solutions A, B, C, and D. 0.10 mV/s polarization rate.

Figure 5 .

 5 Figure 5. Anodic current-potential curves of alloy C-276 at 400°C and 28 MPa, in media D decoupled from the water oxidation component. 0.10 mV/s polarization rate.

Figure 6 .

 6 Figure 6. ͑a͒ SEM image of the surface area of a T60 titanium placed in a TA6V alloy cell in media B, at 350°C and 28 MPa after 10-h polarization. ͑b͒ Chemical analysis of the area.

Figure 7 .

 7 Figure 7. ͑a͒ SEM image of the surface area of a C276 placed in a TA6V alloy cell in media B, at 350°C and 28 MPa after 10-h polarization. ͑b͒ Chemical analysis of the area.

  Scheme 3.

Figure 8 .

 8 Figure 8. Illustration of the concordance between the anodic experimental points ͑᭺͒ and the anodic simulated curve ͑-͒ of the corrected anodic current-potential curve of C-276 alloy in media C at 400°C and 28 MPa. 0.10 mV/s polarization rate.

Figure 9 .

 9 Figure 9. Kinetic parameters K 0 0 , K 1 0 , K 3 0 , K 2 , K 4 at 400°C and 28 MPa in the four different media A, B, C, and D.

Figure 10 .

 10 Figure 10. Evolution of the species coverage ratios with the potential for C276 at 400°C and 28 MPa in ͑a͒ media A and ͑b͒ media B: ͑छ͒ 1 -⌰ 3 -⌰ 4 , ͑ᮀ͒ ⌰ 1 , ͑᭝͒. ⌰ 2 , and ͑᭺͒ ⌰ 3 . Inset in ͑b͒ is a magnification of the evolution of ⌰ 3 .

Figure 11 .

 11 Figure 11. Evolution of the species coverage ratios with the potential for C276 at 400°C and 28 MPa in ͑a͒ media C and ͑b͒ media D: ͑छ͒ 1 -⌰ 3 -⌰ 4 , ͑ᮀ͒ ⌰ 1 , ͑᭝͒. ⌰ 2 , and ͑᭺͒ ⌰ 3 . Inset in ͑b͒ is a magnification of the evolution of ⌰ 3 .

Table I . Chemical composition of C-276 alloy.

 I

	Element	Ni	Mo	Cr	Fe	W	Co	Mn
	Mass %	57	17	16	4	3	2	1

Table II . Impurities in parts per million contained in titanium T60.

 II

	Impurity	O	Fe	N	C	H	Si
	ppm	2000	1980	195	190	60	50

Table III . Characteristics of the media used at high pressure and high temperature.

 III

		pH measured at	Composition of the
	Medium	21°C	medium in H 2 O 2 and Cl -
	A	5.10	͓KCl͔ = 0.0292 mol/L
	B	4.77	H 2 O 2 /KCl:3 wt % H 2 O 2 and 0.0292 mol/L Cl -
	C	1.71	͓HCl͔ = 0.0289 mol/L
	D	1.69	H 2 O 2 /HCl:3 wt % H 2 O 2 and 0.0289 mol/L Cl -

Table IV . Ratios between the kinetic parameters in the eight pa- rameters model for the four different media at 400°C and 28 MPa.

 IV

			Medium
	Ratio	A	B	C	D
	K 0 o /K 1 o K 0 o o /K 3 K 1 o o /K 3 o /K 2 K 1 o /K 4 K 3 K 4 /K 2	1.58 182.9 115.5 9.3 ϫ 10 4 0.34 2.36 ϫ 10 3	1.66 8.3 ϫ 10 -5 5.0 ϫ 10 -5 9.1 ϫ 10 -4 0.0148 1.22 ϫ 10 3	1.82 18.73 10.3 13.3 ϫ 10 4 4.5 2.86 ϫ 10 3	1.81 4.9 ϫ 10 -5 2.7 ϫ 10 -5 6.14 ϫ 10 -4 2.0 1.11 ϫ 10 3

z E-mail: delville@icmcb-bordeaux.cnrs.fr

Acknowledgments

The authors want to gratefully acknowledge the APESA, the ECODEV program of the CNRS, Anjou Recherche and CNIM, and the région Aquitaine for their financial support.