Fethi Hamdani

Improvement of the Corrosion and Oxidation Resistance of Ni-based Alloys by Optimizing the Chromium Content

This fundamental study is focused on the understanding of the influence of the chemical composition of Ni-based alloys on their corrosion and oxidation mechanisms. This work is not dedicated for a particular application. It is well known for instance that Ni-based alloys are susceptible to intergranular stress corrosion cracking (IGSCC) in primary water. Thus, Alloy600 (Ni-16Cr-9Fe), used in steam generator (SG) tubing, was replaced by higher chromium content material Alloy690 . This later shows a better resistance to IGSCC which may be linked to the growth of more protective oxide layer as chromium content is increased to 30 wt.%.

The main goal of this study is to investigate: i) the influence of chromium content, ii) impact of iron addition on the corrosion and oxidation resistance of Ni-based alloys in primary water and superheated steam at 700°C. Furthermore, analytical approach in acidic solution is conducted at room temperature. This allowed to establish a relationship between alloying elements and physical properties of the oxide layers. For this purpose, Ni-xCr (14 ≤ x≤ 30 wt.%), Ni-xCr-8Fe (x=14,22 and 30 wt.%) model alloys and industrial material Alloy600 have been studied. To characterize the oxide scales, conventional technics were used: SEM, STEM, EDX, Potentiodynamic, EIS, Chronoamperometry, Mott-Schottky. Furthermore, steam oxidation kinetics was evaluated by means of weight gain measurements.

To uncouple the effect of surface cold-work and the chemical composition of the base metal, mirror and electro polishing were carried out. In primary water, critical chromium content (20 wt.%), which corresponds to the minimum amount of chromium required to the transition from non-protective to protective and compact Cr-oxide layer, is determined. However, the analytical approach, using electrochemical technics, at room temperature elucidated the existence of optimum chromium content (26 wt.%) in terms of corrosion resistance. In superheat steam, oxidation kinetics and oxide scale characteristics showed the existence of optimum chromium content (24 wt.%) in terms of oxidation resistance. The corrosion and oxidation resistance is degraded as chromium content was increased more than optimal amount. Iron addition (8 wt.%) had a detrimental effect on the protectivess of the resulting oxide scales. Finally, this study showed that optimizing of chromium content is more appropriate method for enhancing corrosion and oxidation resistance, that increasing chromium content to high level is not necessary beneficial to those parameters. This work provides a useful knowledge to design new alternative materials. For this purpose, more investigations should be conducted to test other parameters such as: weldability, fabricability, thermal conductivity,etc.

giving me this wonderful opportunity. Your kindness, hospitality, enthusiasm, guidance and suggestion were inevitable and appreciable for this successive work. I would like to acknowledge Dr. Hiroshi Abe, assistant professor in Watanabe lab, of his constructive discussions and valuable suggestions. Thank you a lot for your support during my stay in Sendai.

My acknowledgement also goes to Dr. Takamichi Miyazaki (Tohoku University) for TEM analyses and his helpful discussion. Your patient guidance helped me to accomplish the physico-chemical characterization with appreciable accuracy. I also gave my thankfulness to Robert Di-Folco, technician in INSA de Lyon, for his contribution in the preparation of specimens for electrochemical analyses.

I would like to express my gratitude and thanks to Prof. Tatsuo Shikama and Prof. Hitoshi Mimura of Tohoku University as well as Prof. Damien Féron (CEA-Saclay) and Dr. Vincent Maurice (UPMC-Paris) for acting as reporters of this dissertation. Thank you for your time and effort. I also express my deepest gratitude and thanks to my colleagues who are in MATEIS-CorrIS laboratory and Watanabe laboratory. They gave me a lot of instructions and technical support during my experiments. You gave me wonderful and unforgettable memories especially from laboratory parties. I have been very lucky to meet you.

Finally, I would like to give my deepest thanking and gratitude to my parents, who support me and encourage me all the time. I wish also to thank my brothers and sister, many hugs to all my family members.

List of abbreviations

General context

Nuclear power plants (NPPs) are the main source of energy in France and considered as the principal source of electricity in Japan as well until march, 11 th 2011. Thus, the majority of NPPs in Japan are suspended to improve their risk management. Nowadays, numerous thermal power plants are operating as substitutes for NPPs in Japan. Fossil fuel electric production contributes in many environmental concerns such as gas emissions. Moreover, fusil fuel such as oil, natural gas and coal are finites and their exploitation has considerable negative impact on the environment. Recently, in United Nations climate change summit September 2014 hold in New-York, It was strongly recommended that actions should be forthwith undertaken to reduce gas emission and to prevent the increase of global temperature. However, renewable sources of energy such as cellulosic biofuels, geothermal energy and solar still do not meet the present demand in respect of economic issues, hence those energy sources should be investigated and developed in the future. The world's growing demand for energy and the international commitments over its production and its use in environmentally safe manner make NPPs the favourite, in terms of efficiency and economic issues, alternative source of energy. Therefore, it is necessary to improve the degradation resistance of their structural materials.

Ni-based alloys are widely used in the structural compounds for both NPPs and thermal plants, operating in severe conditions. These materials are candidates also to use in future generation of power plants and to satisfy next challenges. Improving the degradation resistance of these materials is also required to extend the design lifespan of structures. This fundamental study is focused on the influence of the chemical composition of Ni-based alloys on their corrosion behaviour in simulated primary water of pressurized water reactors (PWRs) and in superheated steam for advanced ultra-supercritical power plant [START_REF] Silvestri | Eddystone Station, 325 MW Generating Unit 1-A Brief History[END_REF][START_REF] Viswanathan | Program on Materials technology for Ultrasupercritical Coal Power Plants[END_REF][START_REF] Weitzel | Steam Generator for Advanced Ultra-Supercritical Power Plants 700 to 760C, ASME 2011 Power Conference[END_REF]. However, this work is not dedicated to a particular application. To design new structural material further investigations, taking into account the synergetic degradation for instance, must be considered as well. Moreover, analytical approach, based on electrochemical measurements, is suggested to describe at the atomic scale the protective oxide properties.

Objectives of the study

Ni-based alloys are currently used in high temperature applications due to their good corrosion resistance [START_REF] Park | Effects of solution temperature on kinetic nature of passive film on Ni[END_REF][START_REF] Abe | Oxidation behavior and cracking susceptibility of Ni-Cr alloys in dry steam and inert gas under extremely low oxygen partial pressure[END_REF]. This results from the ability of these materials to form a protective oxide layer which consists mainly of chromium oxide. In fact, the flux of species through the protective layer, such as inward and outward movement of oxygen anions and cation vacancies in sequence, is depressed as the amount of chromium in the alloys is increased to a critical threshold [START_REF] Essuman | Protective and non-protective scale formation of NiCr alloys in water vapour containing high and low-pO 2 gases[END_REF]. This is attributed to chromium enrichment in the Croxide and the decrease of nickel-hydroxide or/and oxide portion. Indeed, Cr-oxides, called passive films, are assumed to act as barriers preventing the anodic dissolution, oxidation and thus protecting the structure. This may limit for instance the Ni release from Ni-based alloys in the primary circuit and consequently reduce its activity. However, in spite of the presence of those protective films, some detrimental corrosion degradations like Stress

Corrosion Cracking (SCC) may occur in Ni-based alloys used in Light Water Reactors (LWRs) [START_REF] Lu | Characterization of microstructure, local deformation and microchemistry in alloy 600 heat-affected zone and stress corrosion cracking in high temperature water[END_REF][START_REF] Yamazaki | The effect of prior deformation on stress corrosion cracking growth of alloy 600 materials in simulated pressurized water reactor primary water[END_REF]. Some of the usually proposed mechanisms of SCC initiation rely on localized breakdown of the film: localized anodic dissolution and/or slip-dissolution model for instance [START_REF] Panter | Influence of oxide films on primary water stress corrosion cracking initiation of alloy 600[END_REF][START_REF] Rebak | Szklarska-Smialowska The mechanism of stress corrosion cracking of alloy 600 in high temperature water[END_REF][START_REF] Sui | Stress corrosion cracking on alloy 600 and alloy 690 in hydrogen/steam at 380°C[END_REF]. Hence, it is necessary to understand and optimize the properties of the rate-limiting layer to prevent the degradations. In this work attention was given to surface preparation to uncouple the possible contribution of surface cold-work. Then, exposition tests of Ni-xCr (14 ≤ x ≤ 30) and Ni-xCr-8Fe (x= 14, 22 and 30) model alloys were carried out in aqueous environments and superheated steam:

A. Aqueous corrosion

The relationship between corrosion behaviour of Ni-based alloys in simulated pressurized water reactor (PWR) environment (320°C, 14 MPa) and their chromium content is emphasized. H. Abe et al. [START_REF] Abe | Oxidation behavior and cracking susceptibility of Ni-Cr alloys in dry steam and inert gas under extremely low oxygen partial pressure[END_REF] showed that increasing chromium content reduced the corrosion rate and SCC susceptibility of Ni-based alloys in primary water. For this reason, alloy 600 (16 wt.% Cr) has been replaced by alloy 690 (30 wt.% Cr) for vapor generator tubing in PWR system. Surface observations using Scanning Electron Microscope (SEM) are performed to determine the morphology of resulting oxide scales. Further cross sectional characterization of the resulting oxides using Transmission Electron Microscope (TEM) are carried out as well. Finally, critical chromium content, corresponding to enhanced corrosion resistance, is identified. Since, oxide characteristics being unchanged with increasing chromium content more than the critical amount. Secondly, an analytical approach, based on electrochemical analysis, is suggested by investigating the passive film properties at room temperature. The passive film acts as diffusion-migration barrier, controlling the flux of species such as Ni cations and oxygen anions. Thus, the corrosion resistance depends on the nature and the structure of the film. These film characteristics change with modifying the chemical composition of the substrate. Hence, understanding the effect of alloying elements on the passivation of Ni-based alloys is necessary. From the electrochemical behaviour of Ni-Cr model alloys, the relationship between the Cr content and the properties of the passive films grown on these materials is clearly emphasized. Moreover, the existence of optimum threshold of chromium content in terms of corrosion resistance in aqueous environment is investigated. Since iron is added to Ni-based alloys in order to reduce manufacturing costs and improve their mechanical properties through solid-solution strengthening. P. Marcus et al. [START_REF] Marcus | on some fundamental factors in the effect of alloying elements on the passivation of alloys[END_REF] considered iron as a passivity promoter. Thus, the contribution of iron to the physical properties of the passive film is also investigated.

B. Steam oxidation

Ni-based alloys are candidates for use in superheated steam generators in future generations of power plants, i.e., advanced ultra-supercritical power plants [START_REF] Silvestri | Eddystone Station, 325 MW Generating Unit 1-A Brief History[END_REF][START_REF] Viswanathan | Program on Materials technology for Ultrasupercritical Coal Power Plants[END_REF][START_REF] Weitzel | Steam Generator for Advanced Ultra-Supercritical Power Plants 700 to 760C, ASME 2011 Power Conference[END_REF]. However, metal loss, internal oxidation, decarburization, and the decrease of heat transfer due to oxidation contribute to the degradation of the mechanical properties and performance of Ni-based alloys in water vapour [START_REF] Jang | Oxidation behaviour of wrought nickelbased superalloys in various high temperature environments[END_REF]. Improvement of oxidation resistance of these materials is mandatory to satisfy future challenges. Although numerous investigations have

been conducted to determine the oxidation behaviour of Ni-based alloys in dry atmospheres, relatively few oxidation studies of these materials in steam environments have been conducted to date. Steam can affect the solubility and/or diffusivity of oxygen in the alloy and thus its oxidation rate [START_REF] Jang | Oxidation behaviour of wrought nickelbased superalloys in various high temperature environments[END_REF][START_REF] Wagner | Theoretical analysis of the diffusion process determining the oxidation rate of the alloys[END_REF][START_REF] Das | Early stage SCC initiation analysis of fcc Fe-Cr-Ni ternary alloy at 288 °C: A quantum chemical molecular dynamics approach[END_REF]; therefore, detailed knowledge regarding the oxidation behaviour of Ni-based alloys in steam environments is required for accurate prediction of their oxidation rates. This second part of the thesis focused on the effect of increasing the Cr content of alloys in terms of oxidation behaviour. The critical Cr content required to form a protective scale, consisting mainly of chromia, in water vapour was reported by many authors [START_REF] Essuman | Protective and non-protective scale formation of NiCr alloys in water vapour containing high and low-pO 2 gases[END_REF]. However, the improvement of oxidation resistance by the optimization of Cr content has not been considered in previous studies. Optimal chromium content is investigated also in terms of oxidation resistance in superheated steam. To give industrial projection of this work, Alloy 600 is studied as well. Weight gain (WG) measurement was performed in this work: this robust method provides a quantitative estimation of the oxidation rate according to the power growth law of the oxides formed. Further analyses of oxide scale composition and morphology were conducted. The study of the evaluation of the WG measurements and oxide scale characteristics is an appropriate method to inspect the existence of optimum chromium content in terms of oxidation resistance in superheated steam.

Bibliographic review Chapter II

Chapter II Bibliographic review 2. Bibliographic review 2.1. Corrosion in high temperature water

Introduction

Ni-base alloys have been used for steam generator tubing (SG) as well as in various structural compounds of pressurized water reactors (PWR) and boiling water reactors (BWR). In this bibliographic review, only the degradation phenomenon of Ni base alloys in simulated PWR environment will be emphasized. These materials can suffer from general corrosion and stress corrosion cracking (SCC) in operating conditions.

 General corrosion

This type of corrosion causes the release of metallic ions in the aqueous environment which in contact with structure surface. Dissolved species will be transported by primary water to the reactor core and becomes radioactive by interaction with neutrons (e.g. 58 Ni → 58 Co) and consequently the radioactivity of the primary circuit increases. Secondly, precipitation of released cations can occur also [START_REF] Robertson | the mechanism of high temperature aqueous corrosion of stainless steels[END_REF]. This process depends on numerous parameters such as oxide properties, saturation degree in the solution and circulation rate flow [START_REF] Robertson | the mechanism of high temperature aqueous corrosion of stainless steels[END_REF]. For nickel base alloys, nickel and iron were found to be the major cations release in the solution during the corrosion process. D.H. Lister et al. [START_REF] Lister | the mechanism and kinetics of corrosion product release from stainless steel in lithiated high temperature water[END_REF] reported that solid state diffusion of Ni and Fe species, meaning through solid oxide (rate-limiting layer), to the oxide/solution interface takes place during high temperature corrosion. This can be accompanied by diffusion of species through pores present in the passive layer [START_REF] Castle | the role of diffusion in the oxidation of mid steel in high temperature aqueous solutions[END_REF] and their diffusion through grain boundaries [START_REF] Robertson | the mechanism of high temperature aqueous corrosion of stainless steels[END_REF]. It is believed that the outer layer grows by the precipitation of these species from the solution resulting in non-uniform and coarse grain layer [START_REF] Lister | the mechanism and kinetics of corrosion product release from stainless steel in lithiated high temperature water[END_REF].

The oxidation in high temperature water can be mitigated by promoting the growth of a continuous oxide with higher thermodynamic stability, that the barrier layer. Hence, the diffusion of metallic cations through this layer is considered very slow [START_REF] Boudin | Analytical and electrochemical study of passive films formed on References nickel-chromium: Influence of the chromium bulk concentration[END_REF].

 Stress Corrosion Cracking (SCC)

Ni-base alloys are susceptible to SCC in primary water [START_REF] Coriou | Stress corrosion cracking of Inconel 600 in high temperature water, 3ième colloque de métallurgie[END_REF][START_REF] Delabrouille | effect of the chromium content on the corrosion of nickel based alloys in primary water of pressurised nuclear reactors[END_REF]. J. Panter et al. [START_REF] Panter | Influence of oxide films on primary water stress corrosion cracking initiation of alloy 600[END_REF] reported cracks initiation of Alloy 600 (Ni-15Cr-8Fe) in primary water at 360°C and hydrogen partial pressure of 0.3 MPa. They proposed that the selective oxidation of Cr produces cation vacancies that transport oxygen into the substrate occurs, leading to intergranular oxidation and thus IGSCC. Hence, to decrease SCC susceptibility they suggested to perform free stress pre-oxidation in order to promote the growth of protective scale. So far, several mechanisms were proposed by authors to explain SCC process [START_REF] Santarini | Comprehensive Interpretation of CERTs: A Method for the Characterization and the Prediction of IGSCC[END_REF][START_REF] Couvant | stress corrosion cracking in PWR of austenitic stainless steel 304L, ENSM[END_REF][START_REF] Touzet | the characterization of damage in SCC by an electrochemical impedance and statistical study of multiple cracking[END_REF]. In general, the overall SCC process is divided in three phases: incubation, initiation then slow or fast propagation leading to permanent damage of the structure, i.e. the critical fracture.

It is commonly admitted by numerous authors [START_REF] Carette | Analysis and TEM examination of corrosion scales grown on Alloy 690 exposed to pressurized water at 325°C[END_REF][START_REF] Machet | XPS study of oxides formed on nickel-base alloys in high temperature and high pressure water[END_REF][START_REF] Terachi | Influence of dissolved hydrogen on structure of oxide film on alloy 600 formed in primary water of pressurized water reactors[END_REF][START_REF] Mcintyre | X-ray photoelectron studies of the aqueous oxidation of Inconel-600 alloy[END_REF][START_REF] Soustelle | PWSCC of alloy 600: a parametric study of surface film effects[END_REF] that oxide scale formed on Nibase alloys in high temperature water is a duplex layer. The inner layer is continuous and compact, consisting of chromium oxide. Nickel and iron oxides can be incorporated in this layer as spinel oxides, (Ni,Fe) (Fe,Cr) 2 O 4 , or as NiO, FeO, Fe 2 O 3 , etc. The outer layer exhibits non-uniform morphology consisting of Fe-rich crystallites, hydroxides and oxyhydroxides.

Corrosion kinetics of Ni-base alloys in aqueous environment is determined by two simultaneous phenomenon:  Evolution of consumed metal during the growth of oxides  Amount of dissolved metallic cations which is released in the solution F. Carrette et al. [START_REF] Carrette | releasing corrosion products of alloy 690 pipes of primary circuit vapor generator[END_REF] studied the oxidation kinetic of Alloy 600 using concentration profiles coupled with SIMS in primary water. According to this work, oxidation kinetics flow asymptotic-exponential rate law. However, A. Machet [START_REF] Machet | study of oxidation of stainless alloys in earliest stages in high temperature water[END_REF] concluded in his work, using nuclear reaction analysis technic (NRA), that oxidation of Alloy 600 obeys to logarithmic rate law in similar conditions. Thus, oxidation of Ni-base base alloy obeys to complex mechanisms and it seems that its modelling is difficult. But it is commonly accepted results that the formation of protective inner layer leads to significant decrease in oxidation rate.

General corrosion-passivation

Effect of chromium content

Sufficient chromium amount in Ni-base alloys has a promoting effect on the growth of protective Cr-rich oxide in high temperature water as well. T.M. Angeliu et al. [START_REF] Angeliu | the effect of chromium, carbon, and yttrium on the oxidation of nickel-base alloys in high temperature water[END_REF] indicated that oxide films are more protective with better mechanical properties when chromium content in the alloy is larger than 17 wt.%, that in high purity, deaerated hydrogenated water at 360°C . In fact, increasing Cr content from 5 to 17 wt.% led to the change film surface from Ni (OH) 2 to Cr 2 O 3 . Secondly, increasing Cr content from 17 to 30 wt.% did not significantly alter the type, composition profile or the thickness of the oxide phases formed, meaning that 17 wt.% is the critical amount of chromium which promotes the formation of dominant oxide phase. F. Delabrouille [START_REF] Delabrouille | characterisation of cracks of SCC of Ni-base alloys using MET: Effect of chromium content and environment chemistry[END_REF] observed better corrosion resistance for Ni-base alloys as chromium content is increased to a critical threshold. The exposition tests of Ni-xCr (5 ≤ x ≤ 30 wt.%) were carried out in primary water at 360°C and 0.17 MPa H 2 during 3000 hours. The critical value of Cr content was strongly dependent of surface preparation. Hence, this value is determined in the range 10-15 wt.% for ground specimens (#1200), while the critical Cr content was reported in the range 15-20 wt.% for mirror polished specimens. However, several parameters would influence also the critical Cr content, such as hydrogen concentration, water chemistry and circulation rate flow.

Generally, increasing Cr content enhances the protectiveness of passive films [START_REF] Angeliu | the effect of chromium, carbon, and yttrium on the oxidation of nickel-base alloys in high temperature water[END_REF][START_REF] Yamanaka | Proceedings of the 5th Int. Symposium on Environmental Degradation of Materials in Nuclear Power Systems -Water Reactors[END_REF]. Flux of species through the passive film is depressed as the amount of chromium in the alloys is increased. For this purpose, Alloy 600 (Ni-16Cr-8Fe) was replaced by high chromium Alloy 690 (Ni-30Cr-9Fe), hence this later shows better corrosion resistance. The limitation of anodic dissolution of species in the solution is reached with increasing Cr content to 30 wt.% [START_REF] Delabrouille | characterisation of cracks of SCC of Ni-base alloys using MET: Effect of chromium content and environment chemistry[END_REF][START_REF] Panter | study of stress corrosion cracking of Alloy 690 and Alloy600 in PWR primary water: Influence of fabrication process of steam generator pipes on the initiation[END_REF]. C. Soustelle et al. [START_REF] Soustelle | PWSCC of alloy 600: a parametric study of surface film effects[END_REF] reported that oxide formed on Alloy 690 is more enriched with Cr compared with that formed on Alloy 600 in primary water. Likewise, it was found that the thickness of oxide films was at least two orders of magnitude greater for Alloy 600.

Effect of surface preparation

The presence of high deformation degree in specimen surface provides fast diffusion path for chromium and thus it promotes the growth of Cr-rich layer as described above. Nevertheless, the increase of chromium amount in the inner layer would also imply that the preferential dissolution of Ni and Fe from Ni-base alloy substrate prevails in the first stage [START_REF] Carette | Analysis and TEM examination of corrosion scales grown on Alloy 690 exposed to pressurized water at 325°C[END_REF]. Moreover, F. Delabrouille [START_REF] Delabrouille | characterisation of cracks of SCC of Ni-base alloys using MET: Effect of chromium content and environment chemistry[END_REF] observed recrystallization zone by TEM in ground Ni-Cr specimens (#1200). Further, F. Carette et al. [START_REF] Carette | Analysis and TEM examination of corrosion scales grown on Alloy 690 exposed to pressurized water at 325°C[END_REF] revealed also the presence of nano-grains in the subsurface of Alloy 690 in primary water after exposure of mirror polished specimen (1µm diamond finish) for 2160 h. The thickness of disturbed zone, containing high dislocation density and nano-grains, is proportional to the surface cold-work degree resulting from surface preparation. It is estimated in the range 1-2 µm for emery-polished specimens [START_REF] Delabrouille | characterisation of cracks of SCC of Ni-base alloys using MET: Effect of chromium content and environment chemistry[END_REF] and in the range 100-200 nm for mirror polished specimens [START_REF] Carette | Analysis and TEM examination of corrosion scales grown on Alloy 690 exposed to pressurized water at 325°C[END_REF]. It is believed that the oxidation kinetic becomes more faster in early stage due to the presence of recrystallization zone. However, Carette model [START_REF] Carette | Analysis and TEM examination of corrosion scales grown on Alloy 690 exposed to pressurized water at 325°C[END_REF] predicts that oxidation rate decreases and then becomes negligible after the surface annealing (relaxation and metal loss). This is concordant with the parabolic rate law indicating the formation of protective layer.

On the other hand, many authors [START_REF] Mcintyre | X-ray photoelectron studies of the aqueous oxidation of Inconel-600 alloy[END_REF][START_REF] Tapping | the composition and morphology of oxide films formed on type 304 stainless steel in lithiated high temperature wate[END_REF][START_REF] Cissé | Effect of surface preparation on the corrosion of austenitic stainless steel 304L in high temperature steam and simulated PWR primary water[END_REF] reported that minimizing surface cold work by mirror polishing or electropolishing promotes the formation of more uniform and compact protective layer. It was proposed that the growth of adherent and uniform outer layer prevails with minimizing surface cold work [START_REF] Couvant | stress corrosion cracking in PWR of austenitic stainless steel 304L, ENSM[END_REF].

Nature of oxide scales

The nature of resulting oxide determines the corrosion behaviour of Ni-base alloys in primary water. Morphology and composition of oxide scales were investigated by numerous authors, Table . 1 gives a summary of some previous works conducted in primary water. It can be seen that the outer layer consists of crystallites of nickel ferrite and nickel hydroxide, their growth resulting from precipitation phenomenon [START_REF] Sennour | A detailed TEM and SEM study of Ni-base alloys oxide scales formed in primary conditions of pressurized water reactor[END_REF]. The precipitation of Ni hydroxide would be an intermediate step in the nucleation and growth of spinel oxide.

Crystallites size and composition depends on surface preparation, Cr content and saturation degree in the solution. In this way, Ni-rich filaments were observed for model alloys with low Cr content [START_REF] Delabrouille | characterisation of cracks of SCC of Ni-base alloys using MET: Effect of chromium content and environment chemistry[END_REF] due probably to Ni cation saturation. The inner layer is divided into a continuous layer of Ni

Growth kinetic models

Point defect model

The point defect model (PDM) describes passivity of metals and alloys [START_REF] Macdonald | the Point Defect Model for the passive state[END_REF][START_REF] Macdonald | the history of the Point Defect Model for the passive state: A brief review of film growth aspects[END_REF]. This model was developed to transfer the idea of Wagner [START_REF] Wagner | theoretical analysis of the diffusion process determining the oxidation rate of the alloys[END_REF] from oxidation to aqueous corrosion at high temperature. Indeed, it is assumed that oxide layer is a point defective phase, incorporating cation vacancies and (𝑉 𝑀 𝜒′ ) and oxygen vacancies (𝑉 𝑂 •• ), as shown in Fig.

2.

Where 𝑀 𝑀 and 𝑂 𝑂 correspond respectively to cation and oxygen in normal lattice sites, 𝑀 𝑖 refers to interstitial cations. The most important postulates and assumptions in the development of this model are:

 The presence of continuous generation and annihilation process  The electric field strength (Ɛ) is independent of voltage and distance through the film  The voltage drop across the film/solution interface linearly dependent upon the applied potential  Steady state barrier layer thickness varies linearly with voltage and pH  For p-type oxide systems (e.g. Ni/NiO and Cr/Cr 2 O 3 ), the steady current is exponentially dependent upon the applied voltage (Tafel's law).

This model provides an atomic description of growth and breakdown of the passive film. The growth kinetics is related to the inward migration of cation vacancies, generated from the anodic dissolution at oxide/solution interface, and the outward migration of anion vacancies, resulting from the formation of 𝑀𝑂 𝑥/2 (see Fig. 2). Further, semi-conductive behaviour and conductivity of the film is dependent upon type and concentration of point defects. Thus, according to this model the oxide film behaviour is directly correlated to its defective structure properties. Since the corrosion rate is limited by the slow diffusionmigration of point defects through the oxide scale formed in primary water. However, PDM does not take into account short-circuit of diffusion, such as diffusion through grain boundaries. For this reason, other models are reviewed in the following section.

Fig. 2.

Summary of the defect generation and annihilation reactions envisaged in PDM to occur at the interfaces of the barrier oxide layer on a metal [START_REF] Macdonald | the history of the Point Defect Model for the passive state: A brief review of film growth aspects[END_REF].

Robertson model

The grain boundaries-pores model of Robertson [START_REF] Robertson | the mechanism of high temperature aqueous corrosion of stainless steels[END_REF][START_REF] Robertson | the mechanism of high temperature aqueous corrosion of steel[END_REF] is illustrated in Fig. 3. This model takes into account both nano-pores (~1 nm), created by growth stresses due to difference between oxide and alloy volume, and heterogeneities due to grain boundaries. The presence of nano-pores within the oxide permits the penetration of oxygen containing species to the metal/oxide interface. This model proposes double-layer structure of the oxide scale. The inner layer consists of fine grains because it grows in constrain volume. Hence, the outer layer exhibits coarse -grained structure. This later grows by precipitation of species from the saturated external solution. As illustrated in Fig. 3, this model suggested that the outer layer consists of large crystallites and it has morphology of precipitates. Since the external solution creates concentration gradient of dissolved species and thus their outward diffusion through grain boundaries to oxide/solution interface occurs. Diffusion in the solid oxide takes place under condition of local equilibrium and charge neutrality. Charge conservation requires that the current associated with the flux of cations through the oxide is accompanied by compensating electric current from the diffusion of electrons or protons, or it could be carried by external circuit. This model proposed that the ratelimiting step is controlled by the transport of species through oxide grain boundaries for Nibase alloys [START_REF] Robertson | the mechanism of high temperature aqueous corrosion of stainless steels[END_REF]. The thickness of the inner layer varies parabolically with time and the underlying diffusion constant (D). In this case, parabolic rate constant (k p ) can be expressed as a function of underlying diffusion constant.

𝑘 𝑝 = 2𝐷 (10)
However, this model suggested that the total corrosion rate is independent of the presence of the outer layer, the degree of saturation of corrosion products and the solution flow rate. For this reason, Lister model which takes into account those phenomena is described in the following section. Fig. 3. Diffusion of species through the barrier oxide during high temperature corrosion [START_REF] Robertson | the mechanism of high temperature aqueous corrosion of steel[END_REF].

Lister Model

Lister model [START_REF] Lister | the mechanism and kinetics of corrosion product release from stainless steel in lithiated high temperature water[END_REF] explains how structure and morphology of the film can be manipulated by the level of corrosion products released in the solution. The study of the high temperature corrosion of stainless steel in saturated and corrosion-product-free water shows that once the inner layer is established the nucleation of the outer layer is suppressed and that the total corrosion rate is about the same. This reveals that the outer layer does not provide protection against corrosion (Fig. 4). Releasing process depends upon the structure of resulting oxides. If the outer layer is not formed, species which would otherwise be incorporated in the precipitated layer are not saturated in fluid flow boundary layer. This model demonstrated that the overall corrosion rate is strongly dependent of the release kinetics and thus the protectiveness of the inner layer. Furthermore, this model point out the effect of the degree of saturation with corrosion products on the release. Lister [START_REF] Lister | the mechanism and kinetics of corrosion product release from stainless steel in lithiated high temperature water[END_REF] proposed that some of cations at oxide/solution interface diffuse to the bulk solution by mass transfer and do not precipitate to form the outer layer. This has implication of the understanding of the release of corrosion products in primary water circuit.

Gardey Model

Gardey model [START_REF] Gardey | study of general corrosion of Alloy 600, 690 and 800 in primary water, contribution in the understanding of mechanisms[END_REF] is based on models proposed by Robertson [START_REF] Robertson | the mechanism of high temperature aqueous corrosion of stainless steels[END_REF][START_REF] Robertson | the mechanism of high temperature aqueous corrosion of steel[END_REF] and Lister [START_REF] Lister | the mechanism and kinetics of corrosion product release from stainless steel in lithiated high temperature water[END_REF]. This model suggested that releasing process is divided into five steps, as illustrated in Fig. 5. This mechanism is proposed according to the corrosion behaviour of electropolished specimens in experimental loop dedicated to measure the release kinetics. Multi-layer structure of oxide scale is also assumed. Where, the inner layer controls the solid-state diffusion. This later grows by selective dissolution of the substrate (1) and [START_REF] Viswanathan | Program on Materials technology for Ultrasupercritical Coal Power Plants[END_REF]. Cations diffuse then to oxide/solution interface and dissolve in the solution (3). These released cations can precipitate on the surface to form oxide precipitates, that the outer layer (4). While transport of released cations to the bulk solution can also take place [START_REF] Abe | Oxidation behavior and cracking susceptibility of Ni-Cr alloys in dry steam and inert gas under extremely low oxygen partial pressure[END_REF]. This process corresponds to the mass transfer in diffusion boundary layer. Gardey [START_REF] Gardey | study of general corrosion of Alloy 600, 690 and 800 in primary water, contribution in the understanding of mechanisms[END_REF] suggested that the corrosion rate can decrease by nano-pores blocking phenomenon due to the lateral growth of the inner layer. However, this model does not take into account the effect of the precipitates dissolution on the release kinetic.

The corrosion rate in high temperature water does not obey to a parabolic rate law, corresponding to the solid state diffusion species through a solid oxide. Hence, diffusion of species through short-circuit path, such as nano-pores and grain boundaries, as well as dissolution of precipitates can simultaneously occur. This influences the corrosion kinetics and results in deviation from the parabolic rate law.

Oxidation in superheated steam

Introduction

Although numerous investigations have been carried out to emphasize the oxidation behaviour of Ni-base alloys in dry atmospheres, few oxidation studies of these materials in steam environment were conducted so far. However, these materials are used in critical compounds such as steam generator and they are subject of accelerated oxidation rate in water vapor. In contrast with dry oxidation, steam would change oxidation processes of chromia-forming alloys in terms of oxidation mechanism, oxidation scale morphology and oxidation kinetics.

Oxidation mechanisms

In the literature, authors have been suggested various mechanisms to describe the effect of water vapour on the oxidation behaviour. J. Ehlers et al. [START_REF] Ehlers | enhanced oxidation of the 9%Cr steel P91 in water vapour containing environments[END_REF] proposed dissociation mechanism according to their study of the oxidation of 9% Cr steel in water vapour at 650°C, H 2 O (g) penetrates into the scale, probably via micro-cracks, and promotes the oxygen transport through the reaction :

H 2 O (g) = H 2 + 1/2 O 2 (1)
As illustrated in Fig. 6, new oxide forms at metal/oxide interface. The inward transport is relatively fast, that the partial pressure of H 2 O (g) in the void would approach its partial pressure in the external gas, thus an equilibrium between mixed-gas and solid oxide in the void achieves. The hydrogen produced from this oxidation reaction in the void leads to the reduction at the surface, that dissociation process, due to H 2 O-H 2 bridges. M. Nakai et al. [START_REF] Nakai | correlation of high temperature steam oxidation with hydrogen dissolution in pure iron an ternary highchromium ferritic steel[END_REF] investigated hydrogen dissolution in oxide scales formed on Fe-10Cr-0.08C ferritic steels in steam at 650°C and they revealed that incorporation of hydrogen results in the decrease of chromium cations diffusivity. This group postulated that Cr interstitial cations in chromia scales may decrease in order to hold its neutrality, meaning that dissolved hydrogen would modify defects concentration and their transport through the scale. S. Henry et al. [START_REF] Henry | characterization of chromia scales grown on pure chromium in different oxidizing atmospheres[END_REF] characterized thin chromia scales grown on pure chromium at 700 °C in oxygen and water vapor and they confirmed these statements. According to this work, the presence of water vapor causes a significant increase of cation vacancies, leading to vacancies condensation and pores formation. Furthermore N.K. Das et al. [START_REF] Das | Early stage SCC initiation analysis of fcc Fe-Cr-Ni ternary alloy at 288 °C: A quantum chemical molecular dynamics approach[END_REF] reported that diffused hydrogen in Ni matrix accelerates the penetration of oxygen. Using Tight-binding Quantum Chemical Molecular Dynamic (QCMD), they demonstrated that diffused hydrogen becomes negatively charged by electron transfer from metal atoms. This process weakens the metallic bonds resulting in fast diffusion of oxygen into the surface and interacting with metal atoms. As elucidated by these mechanisms, the effect of water vapour on the oxidation relates to modify in transport process through the oxide scale or its properties. This phenomenon may accelerate the overall oxidation rate in superheated steam. Whereas, in absence of water vapor a protective chromium-enriched spinel oxide was observed on 9-12% chromium steels in the temperature range 550-650 °C [START_REF] Quadakkers | steam oxidation of ferritic steelslaboratory test kinetic data[END_REF]. This can be linked to the slow oxygen diffusion, leading to a good balance between inward diffusion of oxidant and outward diffusion of metallic cations [START_REF] Saunders | the oxidation behaviour of metals and alloys at high temperatures in atmospheres containing water vapour: A review[END_REF]. It commonly accepted results that water vapor causes accelerated internal oxidation [START_REF] Essuman | the effect of water vapour on selective oxidation of Fe-Cr alloys[END_REF][START_REF] Essuman | enhanced internal oxidation as trigger for breakaway oxidation of Fe-Cr alloys in gases containing water vapour[END_REF]. This will be described in oxide scale morphology in the following section.

Oxide scale morphology

The penetration of H 2 O (g) molecule within the oxide scale leads to the volatilisation of species [START_REF] Surman | gas phase transport in the oxidation of Fe and steels[END_REF]. H. Asteman et al. [START_REF] Asteman | indication of chromium oxide hydroxide evaporation during oxidation of 304L at 873 K in the presence of 10% water vapor[END_REF][START_REF] Asteman | the influence of water vapor on the corrosion of chromia-forming Steels[END_REF] studied the oxidation of chromia-forming steels in presence of water vapor. They proposed that the formation of volatile-Cr-species (Eq. 2) would contribute in Cr-depletion and the breakaway type oxidation. In fact, the formation of volatile CrO 2 (OH) 2 (g) depleted the surface sufficiently so that protective scale of chromia is not formed.

Cr 2 O 3 + 2 H 2 O + 3/2 O 2 = 2 CrO 2 (OH) 2 (g) (2)
Moreover, J. Ehlers et al. [START_REF] Ehlers | enhanced oxidation of the 9%Cr steel P91 in water vapour containing environments[END_REF] observed that the vaporisation of Fe-species promotes the growth of thicker outer layer compared with that in dry environment. In fact, the lower oxygen potential in the inner layer will result in higher Fe OH 2 (g) partial pressure in outer scale regions, leading in a concentration gradient of Fe-volatile-species and consequently their outward diffusion. Fe OH 2 (g) species are unstable at high oxygen pressure in some external scale regions and form solid oxides (Fe 3 O 4 ), as illustrated in Fig. 7. However, this group concluded that chromium volatilization affects slightly the overall oxidation process. The good resistance against spallation in high temperature environment is strongly dependent of the adhesion of the oxide scale and its morphology. R. Dieckmann et al. [START_REF] Dieckmann | solution and transport of water in oxides[END_REF] reviewed briefly the effect of water vapour on transport process and they reported that dissolved hydrogen into the system preferentially segregates to the metal/oxide interface. Assuming a correlation with previous studies on the effect of hydrogen in various systems, they suggested that penetrated hydrogen weakens the metal-oxide interface. The transport of hydrogen containing species and/or their segregation to the metal/oxide interface, as described above, induces initially porous oxide scale and its failure as a result of scale cracking [START_REF] Galerie | mechanisms of chromia scale failure during the course of 15-18Cr ferritic stainless steel oxidation in water vapour[END_REF][START_REF] Jianian | high-temperature oxidation of Fe-Cr alloys in wet oxygen[END_REF]. Breakaway was found to be linked to the formation of continuous voids in 9% Cr steels at 1100 °C, using pull and indentation test [START_REF] Hou | a survey of test methods for scale adhesion measurement[END_REF]. J. Ehlers et al. [START_REF] Ehlers | enhanced oxidation of the 9%Cr steel P91 in water vapour containing environments[END_REF] further confirmed that rapid outer scale growth in wet gas in conjunction with slow chromium diffusion in the alloy lead to local equilibrium loss between solid and phases of the reacting systems. T. Sundararajan et al. [START_REF] Sundararajan | high temperature corrosion of nanoceria coated 9Cr-1Mo ferritic steel in air and steam[END_REF] studied the oxidation resistance of 9Cr-1Mo ferritic steel in air and steam at 650 °C and they reported the enhanced inward oxidation in steam. They observed, Fig. 8, that steam oxidized specimens exhibited three-layered scale with thickness of about 60 µm which is 2 to 3 times larger than that of air oxidized specimens. Furthermore, W.J. Quadakkers et al. [START_REF] Quadakkers | steam oxidation of ferritic steelslaboratory test kinetic data[END_REF] have suggested schematic illustration (Fig. 9) showing the development of the thick breakaway scale type on 9-12% chromium steels in Ar-H 2 O mixtures in the temperature range 550-650 °C. It seems that the breakdown of the protective oxide is accompanied by the fast growth of magnetite layer and inner scale consisting of chromia precipitates in FeO matrix due to oxygen inward diffusion. Gaps appeared between this duplex scales, probably due to vacancies condensation resulting from fast transport of iron cations to magnetite layer. Whereas, protective chromium-rich spinel is maintained in dry atmosphere [START_REF] Quadakkers | steam oxidation of ferritic steelslaboratory test kinetic data[END_REF].

L. Mikkelsen et al. [START_REF] Mikkelsen | high temperature oxidation of Fe-Cr Alloy in O 2 -H 2 -H 2 O atmosphere, microstructure and kinetics[END_REF] point out the growth of whiskers, consisting of pure chromia in FeCr alloys oxidized in O 2 -H 2 -H 2 O atmospheres at 900 °C. They showed that the dissociation of H 2 O (g) caused the growth of whiskers (Fig. 10). This is more pronounced in water containing environment because of the faster dissociation of water vapor compared with oxygen. The growth of whiskers would contribute in Cr-depletion in the surface.

Water vapour affects also growth stress of oxides which may have a significant contribution in spallation. M. Schütze et al. [START_REF] Schütze | parameters determining the breakaway oxidation behaviour of ferritic martensitic 9%Cr steels in environments containing H 2 O[END_REF] demonstrated that the growth stress on 9% Cr steels at 650°C in wet gas was larger than that formed in dry atmosphere by 5 orders of magnitude. This is combined with enhanced growth rate of the outer scale. In general, oxide scale formed in wet environment tends to exhibit non-protective scale due to Cr-depletion (volatilization and growth of whiskers), formation of discontinuous pores and gaps at oxide/substrate interface. This results in breakaway oxidation and faster oxidation kinetics.

Oxidation kinetics

The oxidation rate of 9% Cr steels at 650°C in gas mixtures with different H 2 O concentration was investigated by J. Ehlers et al. [START_REF] Ehlers | enhanced oxidation of the 9%Cr steel P91 in water vapour containing environments[END_REF]. Weight gain data obtained by this group in Fig. 11 shows that very small amounts of water vapour, less than 5 %.vol, are sufficient to accelerate the oxidation and induce the breakaway when water vapour is larger than 10%.vol, corresponding to the weight loss. This occurred when oxygen level is below 20 %.vol. However, the increase of oxygen to 20 %.vol leads to the growth of protective layer and the non-protective oxidation occurred only if the water vapour portion is increased to relatively high levels. The formation of Fe-volatile species, created by water vapor interaction with solid oxide, can re-deposit in some scale region where higher oxygen potential exists, resulting in the increase of the weight gain [START_REF] Ehlers | enhanced oxidation of the 9%Cr steel P91 in water vapour containing environments[END_REF]. However, only few works reported the volatilisation of nickel in NiCr systems which can be linked to higher decomposition pressure of NiO compared with that of Fe oxide [START_REF] Saunders | the oxidation behaviour of metals and alloys at high temperatures in atmospheres containing water vapour: A review[END_REF].

The failure of chromia layer is attributed to the formation of Cr-volatile species at relatively high local oxygen pressure [START_REF] Schütze | parameters determining the breakaway oxidation behaviour of ferritic martensitic 9%Cr steels in environments containing H 2 O[END_REF][START_REF] Peng | effect of grain refinement on the resistance of 304 stainless steel to breakaway oxidation in wet air[END_REF][START_REF] Asteman | evidence for chromium evaporation influencing the oxidation of 304L: the effect of temperature and flow rate[END_REF][START_REF] Halvarsson | microstructural investigation of the breakdown of the protective oxide scale on a 304 steel in the presence of oxygen and water vapour at 600 °C[END_REF][START_REF] Segerdahl | breakdown of the protective oxide on 11% Cr steel at high temperature in the presence of water vapor and oxygen, the influence of chromium vaporization[END_REF][START_REF] Yamauchi | evaporation of Cr 2 O 3 in atmospheres containing H 2 O[END_REF][START_REF] Opila | volatility of common protective oxides in high-temperature water vapor: current understanding and unanswered questions[END_REF]. K. Segerdahl et al. [START_REF] Segerdahl | breakdown of the protective oxide on 11% Cr steel at high temperature in the presence of water vapor and oxygen, the influence of chromium vaporization[END_REF] investigated 11 % Cr steel at the temperature range 450-700°C in dry and O 2 + 10 or 20 %.vol H 2 O. The vaporization of CrO 2 (OH) 2 from Cr 2 O 3 surface is also observed and thus it was reported that the oxidation behaviour is determined by the ability of the metallic substrate to supply the oxide with Cr by diffusion which depends of exposed systems. Whereas, in the absence of water vapor the alloy formed protective oxide of corundum-type solid solution (Fe 1-x Cr x ) 2 O 3 . J. Ehlers et al. [START_REF] Ehlers | enhanced oxidation of the 9%Cr steel P91 in water vapour containing environments[END_REF] have demonstrated that when haematite magnetite system grown in moist oxygen it is gas permeable, but if it formed in dry oxygen it is not. This can be correlated also to faster oxidation rate in water vapour. A. Galerie et al. [START_REF] Galerie | mechanisms of chromia scale failure during the course of 15-18Cr ferritic stainless steel oxidation in water vapour[END_REF] further showed that breakaway in the early stage of oxidation of Fe-15Cr at temperature range 800-1000 °C Ar-H 2 O gas mixtures corresponds to the separation of chromia scale from the alloy and consequent scale equilibration leading to the formation of Fe 2 O 3 oxide at the metal/oxide interface. The rapid growth of Fe 2 O 3 at the interface disrupts the chromia growth and spalling ensues. Whereas, the oxidation kinetics is depressed in dry environment due to the formation of barrier layer of chromia which continue to form and thus the protective behaviour is maintained [START_REF] Galerie | mechanisms of chromia scale failure during the course of 15-18Cr ferritic stainless steel oxidation in water vapour[END_REF]. The effect of water vapour concentration on the oxidation kinetics has been studied by numerous authors [START_REF] Źurek | The effect of water-vapor content and gas flow rate on the oxidation mechanism of a 10%Cr-ferritic steel in Ar-H 2 O mixtures[END_REF][START_REF] Cheng | effect of water vapor on annealing scale formation on 316 SS[END_REF][START_REF] Mikkelsen | high temperature oxidation of Fe-Cr Alloy in O 2 -H 2 -H 2 O atmosphere, microstructure and kinetics[END_REF][START_REF] Fujii | the mechanism of the high temperature oxidation of ironchromium alloys in water vapour[END_REF][START_REF] Pieraggi | morphological characteristics of oxide scales grown on H11 steel oxidised in dry or wet air[END_REF]. In general, the accelerated oxidation is due to breakaway type oxidation. Increasing water vapor concentrations causes the fast transition, after short exposition time, from protective to non-protective behaviour of the oxide scale.

Finally, S.P.J. Sanders et al. [START_REF] Saunders | the oxidation behaviour of metals and alloys at high temperatures in atmospheres containing water vapour: A review[END_REF] reviewed oxidation behaviours of chromia-forming alloys and it was concluded in this work that NiCr systems have a better self-healing ability, meaning the ability to form chromia as a result of scale cracking, in the presence of water vapour compared with that of FeCr systems. But they reported that information concerning the oxidation behaviour of NiCr systems in water vapor containing environment remains somewhat surprising limited especially that these materials are used as structural materials in high temperature applications compounds and considered as candidate materials to satisfy challenging future requirements.

Description of the oxidation behaviour of Ni-base alloys

The oxidation protection of Ni-base alloys is achieved by the establishment of chromia scales that form by the selective oxidation of Cr in high temperature environment. Some authors have reported that the oxidation behaviour of these materials in wet oxygen differ from that in dry oxygen [START_REF] Źurek | The effect of water-vapor content and gas flow rate on the oxidation mechanism of a 10%Cr-ferritic steel in Ar-H 2 O mixtures[END_REF][START_REF] Henry | characterization of chromia scales grown on pure chromium in different oxidizing atmospheres[END_REF][START_REF] Essuman | Protective and non-protective scale formation of NiCr alloys in water vapour containing high and low-pO 2 gases[END_REF][START_REF] Michalik | Effect of water vapour on growth and adherence of chromia scales formed on Cr in high and low pO 2 -environments at 1000 and 1050°C[END_REF] as discussed above. This can be attributed to dominating inward scale growth due to the fast transport of oxygen in both oxide scale and Ni-matrix. E. Essuman et al. [START_REF] Essuman | Protective and non-protective scale formation of NiCr alloys in water vapour containing high and low-pO 2 gases[END_REF] studied NiCr alloys in Ar-7%H 2 O and Ar-1%O 2 at 1050°C. They reported that the addition of water vapor tends to supress protective scale formation. The effect of water vapor takes place in the early stage of oxidation. Hence, the water vapor promotes the growth of Ni-rich-oxide, in conjunction with selective internal oxidation of chromium, in the early stage of oxidation process [START_REF] Essuman | Protective and non-protective scale formation of NiCr alloys in water vapour containing high and low-pO 2 gases[END_REF]. However, G.C. Wood et al. [START_REF] Wood | a comparison of the oxidation of Fe-Cr, Ni-Cr and Co-Cr alloys in oxygen and water vapour[END_REF] observed no difference in oxidation of NiCr alloys in Ar-10% water and oxygen. Similarly, D.M. England et al. [START_REF] England | Virkar, oxidation kinetics of some nickel-based superalloy foils in humidified hydrogen and electronic resistance of the oxide scale formed, Part II[END_REF][START_REF] England | Virkar, oxidation kinetics of some nickel-based superalloy foils and electronic resistance of the oxide scale formed in air, Part I[END_REF] studied the oxidation of a series of commercial alloys (Inconel 625, Inconel 718, Hastelloy X and Haynes 230) in air and wet hydrogen at temperature between 700 and 1100°C. The oxidation kinetics of these alloys at 1100°C was slower in wet hydrogen than in air. While, at 800°C the oxidation kinetics was faster in wet hydrogen.

Obviously, the reported deviation in oxidation behaviours is related to the different conditions under which tests were carried out, chromium content, surface preparation and resulting oxide scales nature. In fact, these parameters may be carefully considered in oxidation tests and interpreting results.

Effect of test conditions

 Temperature

The oxidation rate of Ni-base alloys must be related to the activation energy (Q), testing temperature (T) and the pre-exponential factor (K o ) in the Arrhenius equation:

𝐾 𝐶 = 𝐾 0 exp( -𝑄 𝑅𝑇 )
Where, 𝐾 𝐶 the rate constant and R is is the gas constant.

T. Ramanarayanan et al. [START_REF] Ramanarayanan | investigations on the Growth Mechanisms of α-Cr 2 O 3 on Ni-Base Alloys with and without Y 2 O 3 Dispersions[END_REF] showed that the oxidation rate of Ni base alloys increases with increasing temperature from 800 to 1100°C in low oxygen partial pressure Po 2 . N. Hussain et al. [START_REF] Hussain | high-temperature oxidation behavior of HASTELLOY C-4 in steam[END_REF] confirmed that HASTELLOY C-4 (Ni-15Cr-15Mo) exhibits similar behaviour in steam with increasing the temperature from 600 to 1200°C, Fig. 12. However, D.M. England et al. [START_REF] England | Virkar, oxidation kinetics of some nickel-based superalloy foils in humidified hydrogen and electronic resistance of the oxide scale formed, Part II[END_REF] observed a shift in the oxidation kinetics of Haynes 230 (Ni-26Cr-5.3Co) in air and wet hydrogen from 700 to 1100°C. Thus, it can be seen in Fig. 13 a crossover in the oxidation kinetics at T~ 1065°C. This is attributed to semi-conductive behaviour of chromia at high temperature. E. Young et al. [START_REF] Young | Wit, n-Type behavior of chromium (III) oxide[END_REF][START_REF] Young | Wit, the oxygen partial pressure dependence of the defect structure of chromium (III) oxide[END_REF] demonstrated that a transition from n to p-type is relatively fast and proceeds at a considerable rate at temperature above 927°C. However, a shift from p to n-type does not take place below 1500°C.

Moreover, E.J. Opila [START_REF] Opila | volatility of common protective oxides in high-temperature water vapor: current understanding and unanswered questions[END_REF] showed (Fig. 14) that chromia has a significant volatility in water vapor only at temperature above ~800°C. It is predicted that evaporation has a minor effect on steam oxidation at 700°C. Further, based on the stability of M-O bridges calculations, J.R.T. Johnson et al. [START_REF] Tobias Johnson | hydrolysis on transition metal oxide clusters and the stabilities of M-O-M bridges[END_REF][START_REF] Tobias Johnson | water adsorption and hydrolysis on molecular transition metal oxides and oxyhydroxides[END_REF] reported that CrO 2 (OH 2 ) is the most stable chromium-volatilespecie at elevated temperatures and high humidities. The considerable work of H. Asteman [START_REF] Asteman | indication of chromium oxide hydroxide evaporation during oxidation of 304L at 873 K in the presence of 10% water vapor[END_REF][START_REF] Asteman | the influence of water vapor on the corrosion of chromia-forming Steels[END_REF] demonstrated that at high temperature local breakdown of chromia occurs at the center of grains, but protective scales is maintained at grain boundaries regions where the diffusivity of Cr is sufficiently high to maintain protection. Since evaporation in center of grain is suggested as major factor controlling breakdown of protective scales. A. Yamauchi et al. [START_REF] Yamauchi | evaporation of Cr 2 O 3 in atmospheres containing H 2 O[END_REF] carried out a series of experiments on chromia in N 2 -O 2 -H 2 O mixtures at 900-1200°C. They confirmed that different evaporation mechanisms operate above ~1130°C as shown in Fig. 15. When the temperature is higher than 1130°C, evaporation reactions of chromia may involve trioxides as follows:

𝐶𝑟𝑂 3 (𝑔) + 𝐻 2 𝑂 = 𝐶𝑟𝑂 2 (𝑂𝐻) 2 (𝑔) (4)
However, increasing test temperature over certain value, depending on exposure environment, would influence the oxidation behaviour due to the change of oxide properties (e.g. semi-conductive characteristics) and different evaporation mechanism.  Oxygen partial pressure 𝑃 𝑂 2

The effect of 𝑃 𝑂 2 on the defect chemistry of polycrystalline chromia has been the subject of many studies [START_REF] Young | Wit, n-Type behavior of chromium (III) oxide[END_REF][START_REF] Young | Wit, the oxygen partial pressure dependence of the defect structure of chromium (III) oxide[END_REF][START_REF] Atkinson | transport in nonstoichiometric oxides[END_REF]. It is suggested that at low 𝑃 𝑂 2 Cr interstitials are the dominant point defects and at high 𝑃 𝑂 2 , Cr vacancies are the dominant point defects. T. Matsui et al. [START_REF] Matsui | existence of hypostoichiometric chromium sesquioxide at low oxygen partial pressures[END_REF] indicated that Cr interstitial density can be expressed as a function of 𝑃 𝑂 2 by equ. 5. It is important to highlight that this is valid only in case when Cr interstitials defects are the dominant diffusing species, meaning at low 𝑃 𝑂 2 .

[𝐶𝑟 𝑖 ⋯ ] = [ 𝐾 𝐶𝑟 𝑖 ⋯ 27 ] 1/4 𝑃 𝑂 2 -3 16 ⁄ (5)
Where [𝐶𝑟 𝑖 ⋯ ] is Cr interstitial concentration, 𝐾 𝐶𝑟 𝑖 ⋯ is the law of mass action constant. Fig. 16 shows the experimental Cr tracer diffusion data from A. Atkinson et al. [START_REF] Atkinson | transport in nonstoichiometric oxides[END_REF] work and simulated data [START_REF] England | Virkar, oxidation kinetics of some nickel-based superalloy foils in humidified hydrogen and electronic resistance of the oxide scale formed, Part II[END_REF]. It is shown that Cr interstitial concentration depends of 𝑃 𝑂 2 . It is suggested that in range 10 -35 to 10 -20 , relatively higher 𝑃 𝑂 2 , chromia oxide is stoichiometric and thus Frenkel defects may be the dominant point defects as given by nul

→ 𝐶𝑟 𝑖 ⋯ + 𝑉 𝐶𝑟 ′′′ ,
where 𝑉 𝐶𝑟 ′′′ are cation vacancies. The neutrality condition is

[𝐶𝑟 𝑖 ⋯ ] = [𝑉 𝐶𝑟 ′′′ ]
. In this range, as illustrated in Fig. 16, the diffusion of Cr should be independent of 𝑃 𝑂 2 and consequently Cr/Cr 2 O 3 is reached. Following the same line of reasoning, It is believed that in high 𝑃 𝑂 2 , such as steam, cation vacancies (𝑉 𝐶𝑟 ′′′ ) are the dominant point defect [START_REF] England | Virkar, oxidation kinetics of some nickel-based superalloy foils in humidified hydrogen and electronic resistance of the oxide scale formed, Part II[END_REF] and their concentration is given by the following equation:

[𝑉 𝐶𝑟 ′′′ ] = [ 𝐾 𝑉 𝐶𝑟 ′′′ 27 ] 1/4 𝑃 𝑂 2 3 16 ⁄ (6)
E. Essuman et al. [START_REF] Mcintyre | X-ray photoelectron studies of the aqueous oxidation of Inconel-600 alloy[END_REF] studied NiCr model alloys in Ar-O 2 -H 2 O mixtures at 1050°C. Weight Gain (WG) measurement in Fig. 17 shows that the detrimental effect of water vapor is strongly depend of 𝑃 𝑂 2 . According to further SEM characterizations of resulting scales (Fig. 18), this group suggested that the transition from protective to non-protective oxide is more likely in high 𝑃 𝑂 2 . Hence, the growth rate of non-protective Ni-rich-oxide increases substantially with increasing 𝑃 𝑂 2 [START_REF] Essuman | Protective and non-protective scale formation of NiCr alloys in water vapour containing high and low-pO 2 gases[END_REF]. A. Galerie et al [START_REF] Galerie | the Kinetic behaviour of metals in water vapour at high temperatures: can general rules be proposed?[END_REF] reported that the slow growth rate of NiO when only water vapor is the oxidant can be interpreted in terms of a slow phase boundary reaction for the insertion of oxide ions into the scale. Moreover, Cr-oxide precipitates appear in the internal scale.

Generally, for technically pertinent solution water vapor is mixed with reducing gases so that the oxide stability will be determined by equilibrium partial pressure of the particular mixtures. This mandatory to preserve the stability of possible resulting oxide for the particular gas mixture of interest [START_REF] Saunders | the oxidation behaviour of metals and alloys at high temperatures in atmospheres containing water vapour: A review[END_REF]. It is believed that the concentration of cations vacancies would increase dramatically in steam compared with that measured in gas mixtures.

Bibliographic review Chapter II

 Dissolved hydrogen Dissociation of penetrated water vapor produces hydrogen into the scale. Thus, the concentration of dissolved hydrogen depends of water vapor partial pressure 𝑃 𝐻 2 𝑂 in the test environments [START_REF] Norbyk | protonic defects in oxides and their possible role in high temperature oxidation[END_REF]. Hydrogen dissolves as proton and bound with oxide ions to form a substitutional hydroxide [START_REF] Essuman | Protective and non-protective scale formation of NiCr alloys in water vapour containing high and low-pO 2 gases[END_REF]. Fig. 19 shows defect concentration as a function of 𝑃 𝐻 2 𝑂 in M 2 O 3 (M is any trivalent metal, e.g. Cr). It seems that in high 𝑃 𝐻 2 𝑂 cation vacancies concentration increases. Consequently, for oxides growing by cation diffusion, oxidation rate would be expected to increase.

Y. Larring et al. [START_REF] Larring | HT corrosion of a Cr-5 wt % Fe-1 wt % Y 2 O 3 alloy and conductivity of the oxide scale[END_REF] studied the effect of dissolved hydrogen on chromia scale properties in different 𝑃 𝐻 2 𝑂 at 800,900 and 950°C. They suggested that protons dissolve from water vapor during the growth of Cr 2 O 3 and then they are compensated by electrons. Furthermore, this group demonstrated that measured oxide conductivity increases (Fig. 20) with increasing 𝑃 𝐻 2 𝑂 which may be a direct consequence of the decrease of the activation energy. This is in good agreement with various works [START_REF] Lister | the mechanism and kinetics of corrosion product release from stainless steel in lithiated high temperature water[END_REF][START_REF] Ehlers | enhanced oxidation of the 9%Cr steel P91 in water vapour containing environments[END_REF][START_REF] Nakai | correlation of high temperature steam oxidation with hydrogen dissolution in pure iron an ternary highchromium ferritic steel[END_REF][START_REF] Das | Early stage SCC initiation analysis of fcc Fe-Cr-Ni ternary alloy at 288 °C: A quantum chemical molecular dynamics approach[END_REF], as discussed above. The dissolved hydrogen influences the electronic properties of chromia, meaning dominant point defects nature and their concentration within the scale.

 Chromium content

Numerous authors [START_REF] Essuman | the effect of water vapour on selective oxidation of Fe-Cr alloys[END_REF][START_REF] Essuman | enhanced internal oxidation as trigger for breakaway oxidation of Fe-Cr alloys in gases containing water vapour[END_REF][START_REF] Essuman | Protective and non-protective scale formation of NiCr alloys in water vapour containing high and low-pO 2 gases[END_REF][START_REF] Yang | oxidation Behavior of Ferritic Stainless Steels under SOFC Interconnect Exposure Conditions[END_REF][START_REF] Nakagawa | corrosion behavior of ferritic steels on the air sides of boiler tubes in a steam/air dual environment[END_REF] studied the effect of chromium content on the oxidation behaviour of chromia-forming alloys in the presence of water vapor. It is a commonly accepted result that increasing the chromium content to a critical value leads to more rapid establishment of a protective chromia scale. For Ni-based alloys, Essuman et al. [START_REF] Essuman | Protective and non-protective scale formation of NiCr alloys in water vapour containing high and low-pO 2 gases[END_REF] recently reported that NiCr alloys with relatively high chromium content (25 wt.%) tend to form and maintain Cr 2 O 3 protective scales in Ar-7%H 2 O atmosphere after 72 hours of exposition, that the same as in dry atmospheres as shown in Fig. 21. They concluded also that NiO growth rates is negligible as protective chromia scale formation occurs even for alloys with relatively lower Cr content (< 25, e.g. 20 wt.%). The critical threshold of chromium content is larger in FeCr alloys compared with that of NiCr alloys. The main reason of this difference is that in wet atmospheres the growth rate of NiO is slightly faster than that of chromia, but the growth rate of Fe-oxides is orders of magnitude higher. Hence, the critical chromium content is expected to decrease with decreasing growth rate of nonprotective oxides, that Ni-oxide or Fe-oxide in this case [START_REF] Essuman | the effect of water vapour on selective oxidation of Fe-Cr alloys[END_REF][START_REF] Essuman | Protective and non-protective scale formation of NiCr alloys in water vapour containing high and low-pO 2 gases[END_REF]. It seems that critical chromium contents required to form and maintain Cr 2 O 3 is strongly depends of studied system.

A. Nicolas [START_REF] Nicolas | study of the physico-chemical evolution of substrates during the oxidation at high temperatures of Ni-Cr models alloys with low chromium content and Ni-16Cr-9Fe model alloy[END_REF] demonstrated that increasing the chromium content promotes the transition from nodular oxidation to compact-scale type oxidation, as illustrated in Fig. 22. For NiCr alloy with low Cr content, inward diffusion of oxygen-containing species takes place resulting in the formation of Cr-oxide precipitates, that the nodular-like oxide. On the other hand, increasing the Cr content promotes the coalescence of Cr-oxide precipitates into a compact scale at the oxidation front. However, the growth of compact scales can be achieved by : (i) Anionic diffusion induced by oxygen-containing species transport, this is valid only in high 𝑃 𝑂 2 , such in steam, (ii) cationic diffusion induced by the transport of Cr cation which can take place in atmospheres with low 𝑃 𝑂 2 [START_REF] Nicolas | study of the physico-chemical evolution of substrates during the oxidation at high temperatures of Ni-Cr models alloys with low chromium content and Ni-16Cr-9Fe model alloy[END_REF]. This is in good agreement with E. Essuman et al. [START_REF] Essuman | Protective and non-protective scale formation of NiCr alloys in water vapour containing high and low-pO 2 gases[END_REF] results discussed above. Since, this group observed only outward growth of compact scales, that cationic diffusion, in atmospheres containing low 𝑃 𝑂 2 . Moreover, A. Naoumidis et al. [START_REF] Naoumidis | phase studies in the Chromium-Manganese-Titanium oxide system at different oxygen partial pressures[END_REF] have found that at high 𝑃 𝑂 2 Mn can replace a substantial amount of Cr in Cr/Mn-spinel, indicating that alloying NiCr alloys with other element, such Fe, can affect their oxidation behaviour as well as the critical Cr content required to form continuous chromia scale in water vapor. Fig. 22. Schematic illustration of the transition from nodular oxidation to compact-scale type oxidation by cationic or anionic growth [START_REF] Nicolas | study of the physico-chemical evolution of substrates during the oxidation at high temperatures of Ni-Cr models alloys with low chromium content and Ni-16Cr-9Fe model alloy[END_REF].

Nodular oxidation Compact-scale type oxidation

The effect of surface cold-work on the oxidation rate was emphasized by many authors [START_REF] Ostwald | Initial oxidation and chromium diffusion, I. Effect of surface working on 9-20% Cr steels[END_REF][START_REF] Grabke | Effect of grain size, cold working and surface finish on the metal-dusting resistance of steels[END_REF][START_REF] Cooper | The effect of surface treatment on the oxidation of ferritic stainless steels used for solid oxide fuel cell interconnects[END_REF][START_REF] Rakowski | The effect of surface preparation on the oxidation behaviour of gamma TiAl-base intermetallic alloys[END_REF][START_REF] Cissé | Effect of surface preparation on the corrosion of austenitic stainless steel 304L in high temperature steam and simulated PWR primary water[END_REF][START_REF] Warzee | Effect of surface treatment on the corrosion of stainless steels in high temperature water and steam[END_REF][START_REF] Carrette | releasing corrosion products of alloy 690 pipes of primary circuit vapor generator[END_REF]. They reported that the rapid diffusion of Cr from the base metal to the oxide film occurred in the cold-worked zone of the metal substrate. This results in a significant Cr enrichment in the oxide film. C. Ostwald et al. [START_REF] Ostwald | Initial oxidation and chromium diffusion, I. Effect of surface working on 9-20% Cr steels[END_REF] investigated the oxidation behaviour of 9-20% Cr steels with different surface finishes (electropolished, polished, ground, sandblasted) in N 2 -H 2 -H 2 O mixtures gases at 600°C. In fact, they confirmed that oxidation rate tends to become slower more or less clearly with increasing the degree of surface deformation: electropolished < polished < ground < sandblasted (Fig. 23). Diffusion profiles of Cr in 20%Cr-32%Ni steel (Fig. 24) confirms that slow diffusion has taken place in electropolished specimens. The diffusion was accelerated in ground specimen leading to a significant Cr-depletion in the subsurface [START_REF] Ostwald | Initial oxidation and chromium diffusion, I. Effect of surface working on 9-20% Cr steels[END_REF]. The fast diffusion paths caused by surface deformations allow fast diffusion of Cr and thus the growth of protective oxide in early stage of oxidation process. Hence, the oxidation resistance can be improved by increasing the surface cold work by shot-peening, grinding and so on. However, the beneficial effect of the surface cold-work will be supressed by annealing process and metal loss during long term operation. The effect of surface cold-work can be correlated to the effect of cold rolling as well.  Resulting oxide scales Resulting oxide scales in water vapor would determine the oxidation behaviour. The formation of a continuous Cr-rich oxide on Ni-base alloys exposed to such environment will be considered as the rate-controlling layer and thus the oxidation resistance is expected to be improved [START_REF] Essuman | Protective and non-protective scale formation of NiCr alloys in water vapour containing high and low-pO 2 gases[END_REF]. Table .2 provides a brief summary of the nature of the oxide scales formed on Ni-base alloys in both water vapor containing and dry atmospheres at high testing temperatures. Wagner model describes theoretically the diffusion process in substrate and solid oxide phases during the oxidation of alloys [START_REF] Wagner | theoretical analysis of the diffusion process determining the oxidation rate of the alloys[END_REF]. This model is valid only for ideal conditions. In fact, the intrinsic diffusion coefficient of oxidizable element and the effective diffusion coefficient of oxygen are considered constant during the oxidation process. Furthermore, the dissociation pressure of oxides is considered null. C. Wagner [START_REF] Wagner | theoretical analysis of the diffusion process determining the oxidation rate of the alloys[END_REF] suggested that the oxidation rate is proportional to the displacement ∆X metal of the metal surface. The oxidation obeys to parabolic rate law which can be described by several parabolic rate constants:

𝑑∆𝑋 𝑚𝑒𝑡𝑎𝑙 𝑑𝑡 = 𝐾 𝐶𝑚𝑒𝑡𝑎𝑙 ∆𝑋 𝑚𝑒𝑡𝑎𝑙 → 𝐾 𝐶𝑚𝑒𝑡𝑎𝑙 = (∆𝑋 𝑚𝑒𝑡𝑎𝑙 ) 2 2𝑡 𝑑∆𝑋 𝑜𝑥𝑖𝑑𝑒 𝑑𝑡 = 𝐾 𝐶𝑜𝑥𝑖𝑑𝑒 ∆𝑋 𝑜𝑥𝑖𝑑𝑒 → 𝐾 𝐶𝑜𝑥𝑖𝑑𝑒 = (∆𝑋 𝑜𝑥𝑖𝑑𝑒 ) 2 2𝑡 (7) ∆𝑊 𝑆 = √ 𝐾 𝑝 𝑡
Where ∆𝑋 𝑚𝑒𝑡𝑎𝑙 is the metal thickness (m) consumed during oxidation for time (t), 𝐾 𝐶𝑚𝑒𝑡𝑎𝑙 is the oxidation constant of the thickness of metal consumed (m 2 .s -1 ), ∆𝑋 𝑜𝑥𝑖𝑑𝑒 is the thickness of produced oxide (m) during oxidation for time (t), 𝐾 𝐶𝑜𝑥𝑖𝑑𝑒 is the oxidation constant of the thickness of oxide produced (m 2 .s -1 ). ∆𝑊 is the weight gain (g) during the oxidation for time (t) and 𝐾 𝑝 is the parabolic constant (g 2 .cm -4 .s -1 ) which is the referential constant used by many authors to estimate oxidation kinetics. [START_REF] Feulvarch | An implicit finite element algorithm for the simulation of diffusion with phase changes in solids[END_REF] suggested modelling for nodular oxidation. A fixed grid technique is proposed in the numerical simulation. This technique is based on the finite element method in space coupled with implicit integration in time. The application of this model involves diffusion of oxygen and oxidizable elements coupled with precipitation. In fact, arbitrary number of diffusing species and precipitate phases during the nodular oxidation can be taken into account. This is mandatory for the majority of realistic problems of internal oxidation, which involves multiple diffusion of species (of oxygen and chromium, etc.) and precipitation of phases such as Cr 2 O 3 . Moreover, the identification of oxide/metal interface, in case of nodular oxidation predicted to occur in superheated steam, is not required in this model. Fig. 25 shows the results of the numerical modelling of the oxidation of steel containing 0.12 wt.% of aluminium at 800°C for 60s. The relation between the total fraction of oxygen and aluminium as well as their concentrations in the matrix is assumed to be governed by local and instantaneous thermodynamic equilibrium:

𝑃 𝐴𝑙2𝑂3 = 0 𝑎𝑛𝑑 𝐶 𝐴𝑙 2 𝐶 𝑂 3 ≤ 𝐾 𝐴𝑙2𝑂3 𝑃 𝐴𝑙2𝑂3 > 0 𝑎𝑛𝑑 𝐶 𝐴𝑙 2 𝐶 𝑂 3 = 𝐾 𝐴𝑙2𝑂3 (8)
Where 𝐶 𝑂 and 𝐶 𝐴𝑙 denotes the mass concentration, 𝑃 𝐴𝑙2𝑂3 the mass fraction of Al 2 O 3 and 𝐾 𝐴𝑙2𝑂3 denotes the solubility product of Al 2 O 3 . [START_REF] Zhou | a randomwalk-cellular automaton model of precipitation of internal oxides[END_REF] introduced an atomic model of internal oxide precipitation on the basis of the cellular automaton method, implemented by computer simulation. This group proposed an original approach to determine the transition from nodular oxidation to compact-scale type oxidation. They introduced the effect of oxide size on the precipitation kinetics. It was reported that this model can reproduce basis features of precipitation, including oxide stability dependence of particles growth rate and oxygen supersaturation dependence of both oxides precipitates size and their number density. It is demonstrated that oxide particles of higher stability are larger and grow slower. This is due to the fact that the amount of free oxygen depends on the dissociation rate, hence on the stability of the oxide. In this way, lower degree of oxygen supersaturation, lower number density of oxide particles, and bigger size of oxide precipitates. This can promote the coalescence phenomenon and the growth of more stable and compact oxide layer.

Therefore, the oxidation behaviour and the transition from non-protective to protective scale is determined considering thermodynamic stability of oxides, alloy composition, particles size and their number density.

A. Nicolas et al. model : Extended Wagner model

In this work, Wagner's analytical model has been extended to take into account the dependence of oxygen diffusion coefficient in Ni-Cr alloys and the evolution of volume fraction of the oxide precipitates in the internal oxidation zone at 950°C [START_REF] Nicolas | study of the physico-chemical evolution of substrates during the oxidation at high temperatures of Ni-Cr models alloys with low chromium content and Ni-16Cr-9Fe model alloy[END_REF][START_REF] Nicolas | the transition from internal to external oxidation of Ni -X wt.% Cr at 950°C[END_REF]. It is important to consider the precipitation phenomenon, highlighted in Feulvarch and Zhou models, which may take place in superheated steam. Wagner model is based on the competition between oxygen and chromium flux which corresponds to their diffusion coefficients, D O and D Cr respectively. However, these coefficients are considered constant in Wagner model. As a first approach, oxygen diffuses through the nodular zone which is enriched with Ni, consequently D O would be equal to diffusion coefficient of oxygen in pur nickel D O/Ni . While, D O should be strongly dependent of volume fraction of oxide precipitates in nodular zone when their size becomes more large, corresponding to greater volume fraction P. In this case, D O is expressed as a function of volume fraction P by the following equation:

𝐷 𝑂 = (1 -𝑃) 𝐷 𝑂/𝑁𝑖 (9)
This leads to non-linear version of Wagner model. In agreement with Zhou model this model gives critical value of oxide volume fraction, corresponding to the coalescence of nodular oxide in compact layer occurred. Fig. 26 shows the difference between volume factions obtained by analytical Wagner model and those calculated using 28 optical micrographies.

The criterion for the transition from nodular oxide to compact layer has been found to be between 47.5 and 64 vol.% of chromium oxide. Since only low Cr content Ni-Cr alloys were used in this work, the critical chromium content which corresponds to the volumic criterion must be investigated in superheat steam at 700°C.

Summary

The bibliographic review emphasized the oxidation behaviour of chromia-forming alloys which varies as a function of exposure environment and test conditions. So far, the oxidation behaviour of Ni-Cr systems in steam remains not clearly explained. However, many studies of the corrosion of these materials in PWR conditions were conducted. In order to discuss the results of the present study, the most important information on the degradation phenomenon of Ni-base alloy in high temperature water and steam should be highlighted.

 Corrosion in high temperature water

Corrosion rate of nickel base alloys in PWR conditions is controlled by complex mechanism divided into:

-Solid state diffusion under condition of local equilibrium and neutrality.

-Diffusion through short-circuits, such as pores and grain boundaries. -Release-precipitation phenomenon which depends on the protectiveness of the inner layer, saturation degree and fluid flow rate.

Oxide scale formed on Ni-base alloys in PWR conditions exhibits duplex-layer structure:

-Inner layer of continuous Cr-rich oxide and nodules of chromia dispersed at substrate/inner layer interface. -Outer layer consists of precipitated crystallites of nickel ferrite and nickel hydroxide.

Increasing Cr content to critical amount leads to the formation of a compact and protective layer. While, increasing Cr content over the critical level does not significantly alter the type, composition profile, or the thickness of the oxide.

Surface cold-work influences the corrosion behaviour of Ni-base alloy. Disturbed zone in the subsurface is observed. The thickness of this zone is proportional to the surface cold-work. Minimizing surface cold-work promotes the growth of more compact and uniform oxide scale.

 Steam oxidation

Presence of water vapor and hydrogen, resulting from oxidation process, degrade the protective behaviour probably due to Cr-depletion (Not reported for Ni-Cr systems), formation of porous scale, the appearance of gap at substrate/scale interface and enhanced inward growth. Water vapor influences transport phenomenon within the oxide, hence it believed that inward diffusion of oxygen is dramatically accelerated in steam. Consequently, oxidation kinetics increase substantially with increasing water vapor fraction, such as steam environment. This is linked to the transition from protective to nonprotective oxidation in early stage of oxidation and consequently the growth of the barrier layer is disturbed. When the barrier layer is established the oxidation rate is controlled by solid state diffusion of species through the solid oxide.

Multi-layer structure is observed consisting of inner Cr-rich oxide and outer Ni-rich oxide. Crenriched layer formed in steam exhibits p-type semi-conductor behaviour and thus cation vacancies are the dominant point defects.

Chromium content required to form and maintain the chromia layer is strongly dependent of test condition (temperature, oxygen partial pressure). The optimization of chromium level in steam is not discussed in the literature. Presence of surface cold work enhances the oxidation resistance by providing fast diffusion path for Cr. In the following chapter, experimental set-up and methods used in the present study will be described.

Experimental & methods

Chapter III

Experimental and methods

Studied materials

Chemical composition

In order to investigate the influence of chromium content on the corrosion and oxidation behaviour of Ni-based alloys, Ni-xCr (14 ≤ x ≤ 30) model alloys were studied. Moreover, Ni-xCr-8Fe (x= 14, 22 and 30) model alloys have been also studied to point out the contribution of iron in corrosion and oxidation processes. These model alloys are supplied by Sumitomo Metal Industries, Ltd, Japan. The studied materials were hot-rolled to plates. After homogenizing at 1230°C for 10 hours, these hot-rolled plates were solution annealed at 1180°C for 30 minutes and then water quenched. To correlate the results of the present study with industrial issues, Alloy 600 which is widely used in high temperature applications such as steam generators is studied. The chemical composition of all studied materials was determined by the supplier and given in table1 below.

Microstructure

Material coupons were mirror polished and then chemically etched for 15 seconds in the following solution: 10 ml of acetic acid (C 2 H 4 O 2 ), 5 ml of hydrochloric acid (HCL) and 10 ml of nitric acid (HNO 3 ) and at room temperature. Etched coupons were subsequently ultrasonically cleaned in pure water. Optical microscope observations (Fig. 27) of etched coupons reveal austenitic microstructure. Grain size is calculated using standard test method E112-96 (reapproved 2004) and summarized in table 2. As illustrated by this later, grain refining occurred with increasing Cr content. Alloy 600 coupons were cut from industrial pipe, shaped by a cold drawing process. Consequently, etched alloy 600 coupons exhibit fine grained structure compared with that of Ni-14Cr-8Fe model alloy.

Specimens preparation

PWR and steam oxidation tests

Plate specimens were cut and ground to 2400 grit surface finishing with emery papers. To minimize the surface cold work, three surface preparations were carried out (only one specimen side):  Mechanical polishing using 3 and then 0.3 µm alumina powder suspension.  Mechanical/chemical polishing using colloidal silica suspension.  Electro-polishing in a solution composed of: 37 ml of phosphoric acid (H 3 PO 4 ) , 56 ml of glycerol (C 3 H 5 (OH) 3 ) and 7 ml of water. The current density was adjusted at 1.4-1.9 A/cm 2 and the temperature was maintained at 0°C.

All specimens were cleaned ultrasonically in acetone before testing and then suspended in PWR autoclave and steam chamber using Ni and Pt wire in sequence, as shown in Fig. 28. After the oxidation tests, specimens were mounted in resin and metallographic cross section were prepared, polishing and mirror polishing.

Electrochemical analyses

Specimens of 1 cm 2 area with 0.5 cm thickness were cut from hot-rolled plates using electro erosion wire cutting. Then specimens were fixed to copper wire with a screw thread to allow electrical connection. Specimens were coated using cataphoretic paint and embedded in epoxy resin (cold mounting resin Mecaprex MA 2) under vacuum. Specimens were gradually grinded with emery papers down to 2400 grit surface finish and then polished with 3 µm and 1 µm diamond pastes suspension. All samples were cleaned in ethanol in ultrasonic bath and then rinsed with distilled water.

Description of steam oxidation apparatus

Fig. 29 shows the schematic of the steam oxidation testing apparatus. After the specimens were placed in the reaction chamber, this later was first purged with N 2 flow. The dissolved oxygen in the feed water was kept under 1 ppb then at 200 ppb by N 2 and N 2 /pure air mixture flow respectively. The steam generator was heated up to 400°C, the chamber to 700°C simultaneously and held for 500 hours. Steam oxidation tests were carried out at the atmospheric pressure. The testing temperature was measured continuously at three zones using thermo-couples. The deviation from the test temperature was ±1°C. Steam was continuously supplied to the test chamber by feeding deaerated water to the steam generator. The feed water flow was 5ml/min, corresponding to a steam linear velocity of 0.24 m/s. While, the feed water tank is supplied by the condensed water in the cooler. To perform weight gain measurements, the oxidation test was interrupted after 30, 100 and 250 hours. After each interruption, the atmosphere was replaced by N 2 at 200°C and then cooled down to the room temperature.

Fig. 29: Schematic of the dynamic steam oxidation apparatus.

Description of PWR autoclave

Simulated PWR tests were conducted in autoclave equipped with recirculation loop (Fig. 30), simulating industrial conditions. Before testing, autoclave chamber and recirculation loop were cleaned with demineralised water flow at 100°C. The primary water is simulated by a solution of 500 ppm boric and 2 ppm LiOH in pure water. The ion exchanger allowed to hold 500 ppm of boric acid as a maximum concentration. Specimens were set in the autoclave chamber and the oxygen in the feed water was adjusted at 5 ppb by N 2 flow. The hydrogen partial pressure was set to 0.15 bars, corresponding to a concentration of 30 cc/kg. Pressure and temperature are fixed respectively at 14 MPa and 320°C for 500 hours. Dissolved oxygen was maintained at 5 ppb by only H 2 flow during the test. Autoclave chamber was continuously supplied with pre-heated feed water flow, which is fixed as 20 L/min. After the test, the autoclave was cooled down to the room temperature and purged to extract the oxidized specimens.

Characterization techniques

For the initial microstructure characterization, grain size was determined by counting method as reported above using optical microscope Nikon ECLIPSE LV150. Image treatments were carried out using NIS-Elements D.3.0 software. Characterization of the oxide scale formed on the studied materials at micro and nano-scale was performed as well. In order to study the physicochemical properties of oxide scales formed in test environments, Scanning Electron Microscope (SEM) and Scanning Transmission Electron Microscope (STEM) were used.

Scanning Electron Microscope (SEM)

Fig. 31 shows a schematic description of SEM thereby its operating is based on electron/substrate interactions. SEM observation is achieved by electron beam, generated by electron gun, interactions with specimen surface. The main signals emitted under this impact are Secondary Electrons (SE) and Backscattered Electrons (BSE), as illustrated in Fig. 32. These electrons are collected by detectors and amplified on computer monitor. Moreover, interaction in volume leads to X-ray photons emission, which is exploited to determine the elemental composition. The accuracy of these analyses is strongly dependent of radiation energy and thus the penetration depth. The scanning is performed by subsequent lines in respect of the synchronization with electron beam flux. In the present study, SE (20 eV) were used to characterize the surface morphology of specimens after testing. the physio-chemical features of oxide scales in metallographic cross sections. BSE showed a significant difference in the contrast between oxide scales and substrate, regarding to the deviation between atomic numbers (Z). In this work, Hitachi SU70 SEM integrated with energy dispersive X-ray (EDAX) is used.

Scanning Transmission Electron Microscope (STEM)

The STEM is a tool for the characterization of the nano-structure, with the ability to provide information on elemental composition and electronic structure at ultimate resolution. Fig. 33 shows its major compounds. STEM is a microscopy technique whereby a beam of electrons is transmitted through an ultra-thin specimen, resulting in interaction with this later when it passes through. Bright field (BF) detector includes the transmitted beam and so the holes appear bright, whereas a dark field excludes the transmitted beam and holes appear dark. Each detector provides a different complementary description of specimens.

Primarily observations by SEM with conjunction with Focus Ion Beam (FIB) imaging allow selecting the adequate zone for sampling. Indeed, Hitachi FB 2200 FIB is used for sampling and thinning (0.1 µm) process by Si sputtering. JEOL JEM-2100F STEM equipped with EDAX is used for TEM observations in the present work. 3.6. Electrochemical analysis at room temperature

Electrolyte and the set-up

Electrochemical measurements were conducted in a solution of 1 mol.L -1 of sulfuric acid (H 2 SO 4 ) in pure water to limit the ohmic losses. All these measurements were carried out at room temperature (22-25°C) in deaerated solution by bubbling nitrogen (N 2 ). Conventional three electrodes cell is used which is composed of a platinum counter electrode and all potentials were measured vs a saturated mercurous sulfate electrode (653 mV vs. SHE).

Electrodes were connected to an electrochemical measurement system (Gamry instrument, Reference 600 TM Potentiostat/Galvanostat/ZRA).

Conventional technics

Potentiodynamic experiments (Polarization curves)

Polarizations curves allow the identification of the passivity potential range. Moreover, these curves point out also the passivation ability of studied materials. The current density in the passive range (I pass ) emphasizes the kinetic of electrochemical reactions. In fact, these reactions are required for maintenance and sustainability of the passive film. Secondly, the passivation ability can be predicted according to the amplitude of active current peaks, i.e. the anodic dissolution needed for the establishment of the passive film. It is commonly accepted that the wider passivation range with lower current density indicates a better efficiency of the materials in terms of passivation. Indeed, the passivation current density describes the barrier effect of the passive film [START_REF] Normand | Classical electrochemical characterization methods: description and recommendations for the analysis of metal corrosion[END_REF]. Polarization curves were obtained from polarization scan rate of 10 mV s -1 after 16 hours of immersion, corresponding to the required time to reach the thermodynamic steady state potential. The polarization scan is performed from -1 to 1.5 V versus OCP. Thus, the oxide scale formed in the air is reduced by the cathodic polarization.

Chronoamperometric analysis

This technique is selected to study the evolution of the current density when the electrochemical system is kept under potentiostatic control in the passive range. Consequently, the growth of the passive film is promoted and only the steady state current density (I SS ) is measured. This current density corresponds to the current of species migration through the film. This is necessary for the maintenance of this later. On the other hand, I SS can be correlated to the flux of charge carriers through the passive film and thus it provides an estimation of its kinetic. T. Gueshi et al. [START_REF] Gueshi | Voltammetry at partially covered electrode, PartI. chronopotentiometry and chronoamperometry at model electrodes[END_REF] have been reported that I SS can be expressed by the following equation:

𝐼 𝑠𝑠 = 𝑛𝐹𝑞𝐶 0 √𝐷 √𝜋 𝑡
Where, 𝑛 is stoichiometric number, 𝐹 is Faraday's constant, 𝑞 is the total geometric surface, 𝐷 is diffusion-migration coefficient of species, 𝐶 0 donates the concentration of species in the bulk solution and t is polarization time. This is valid for electrode with negligible coverage fraction, meaning that all the electrode area is active. I SS was measured under potentiostatic at 0.1 V/MSE during 250 min.

In order to go further the description of the surface reactivity and diffusion-migration phenomenon, using a supplementary technics is mandatory.

Electrochemical impedance spectroscopy (EIS)

EIS is a useful technique to determine the charge distribution through the passive film and its physical properties. Electrochemical impedance is measured by applying an alternative signal on the electrochemical system, AC voltage is applied and the emitted current is collected. Assuming that a sinusoidal potential X(t) is applied, the response to this potential is AC current signal Y(t), as illustrated in Fig. 34. These two signals are related by Fourier transfer function H(ω): Y(ω) = H(ω) X(ω), where X(ω) and Y(ω) are respectively Fourier transfer of X (t) and Y(t) [START_REF] Lavigne | caractérisation des films passifs pour la définition de nouveaux matériaux : Application aux plaques bipolaires métalliques des systèmes PEMFCs[END_REF]111]. Electrochemical impedance should be obtained by small excitation signal amplitude which expressed as following :

𝐸 (𝑡) = 𝐸 0 sin(𝜔𝑡 + 𝜃)
Where, 𝐸 (𝑡) is the potential at time t, 𝐸 0 is the amplitude of the signal, 𝜔 is the angular frequency (𝜔 = 2𝜋𝑓, 𝑓 𝑖𝑠 𝑡ℎ𝑒 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦) and 𝜃 is the shift in phase.

Finally, the electrochemical impedance can be expressed by a complex number Z(ω) as following :

𝑍(𝜔) = 𝐸(𝜔) 𝐼 (𝜔)
Where, 𝐸(𝜔) is the perturbation and 𝐼(𝜔) is the feedback of the electrochemical system. Z(ω) can be expressed with two equivalent form: 𝑍(𝜔) = |𝑍 (𝜔)| 𝑒 𝑖𝜃 (𝜔) or 𝑍(𝜔) = 𝑍 𝑟 (𝜔) + 𝑖 𝑍 𝑖 (𝜔) , Where, 𝑖 = √-1 , |𝑍 (𝜔)| is the impedance module, 𝑍 𝑟 is the real component and 𝑍 𝑖 is the imaginary component of the total impedance. In fact, 𝑍(𝜔) can be graphically illustrated in polar coordinates (Bode plot) or in Cartesian coordinates system (Nyquist plot). In order to determine the physical properties of the passive film, fitting impedance data to an electrical equivalent circuit (EEC) is needed. Several parameters can be calculated by the fitting, such as the polarization resistance, the capacitance and the diffusion migration resistance.

The constant phase element (CPE) is usually used in the fitting to emphasize the ratelimiting behaviour of the circuit. Moreover, this parameter stands for the possibility of non-ideal capacitance of the film. The deviation from the ideal capacitive behavior can be related to the surface heterogeneities (roughness and porosity) [112] or disturbed surface reactivity (non-uniform distribution of charges in the film) [START_REF] Jorcin | CPE analysis by local electrochemical impedance spectroscopy[END_REF]. 𝑍 𝐶𝑃𝐸 is proposed by P. Zoltowski et al. [START_REF] Zoltowski | on the electrical capacitance of interfaces exhibiting constant phase element behaviour[END_REF] according to the following definition:

𝑍 𝐶𝑃𝐸 (𝜔) = 1 𝑄(𝑖𝜔) 𝛼
Where, 𝑄 is a constant (with dimensions Ω cm 2 s -(1-α) ), α is CPE exponent, for α= 1 this circuit parameter with limiting behaviour is considered as capacitor, a resistor for α=0, Warburg element for α=0.5, and inductor for α=-1 [START_REF] Jorcin | CPE analysis by local electrochemical impedance spectroscopy[END_REF][START_REF] Zoltowski | on the electrical capacitance of interfaces exhibiting constant phase element behaviour[END_REF]. Fig. 34: Schematic of the sinusoidal excitation of the electrochemical system using AC voltage which results in emitted AC current [START_REF] Lavigne | caractérisation des films passifs pour la définition de nouveaux matériaux : Application aux plaques bipolaires métalliques des systèmes PEMFCs[END_REF].

Mott-Schottky analysis

To describe the semi-conductive behaviour of passive films, mott-Schottky (M-S) analysis is conducted. The validity of this analysis is based on the assumption that double layer capacitance (C dl ) is much higher than the space charge capacitance (C SC ). Thus, the total capacitance is:

1 𝐶 𝑇 = 1 𝐶 𝑑𝑙 + 1 𝐶 𝑠𝑐 , when C SC << C dl , C T is equal to C SC (1/ C dl is negligible) [115].
The impedance is measured at different applied potential is the passive range using a single frequency. Then, the capacitance is derived from the imaginary component of AC capacitance impedance ( 𝐶 = -1 𝜔𝑍 𝑖

) [START_REF] Kong | A study of the passive films on chromium by capacitance measurement[END_REF]. The calculated C is a function of applied voltage (C -2 = f (V)). The selection of the frequency is crucial for the capacity determination. Hence, this later has to be greater than the characteristic frequencies of reactions related to redox species present in the solution [START_REF] Lavigne | caractérisation des films passifs pour la définition de nouveaux matériaux : Application aux plaques bipolaires métalliques des systèmes PEMFCs[END_REF]. According to the literature, the passive film formed on Cr-oxide forming materials behave as p-type semi-conductor. Thus, predominant charge carriers are cation vacancies (𝑉 𝐶𝑟 , 2-𝑉 𝐶𝑟 , 3-),) [START_REF] Kong | A study of the passive films on chromium by capacitance measurement[END_REF][START_REF] Paola | Semi-conducting properties of the passive film on stainless steel[END_REF]. Hence, their concentration can be calculated by the following expression [START_REF] Paola | Semi-conducting properties of the passive film on stainless steel[END_REF][START_REF] Fattah-Alhosseini | The smiconducting properties of passive films formed on AISI 316L and AISI 321 stainless steels: A test of point defect model[END_REF]:

1 𝐶 𝑠𝑐 2 = 2 𝜀𝜀 0 𝑒𝑁 𝐴 (𝐸 -𝐸 𝐹𝐵 - 𝑘 𝐵 𝑇 𝑞 )
Where C sc is the space charge capacitance, ε is the dielectric constant of the passive film (25 for chromium oxide [START_REF] Fattah-Alhosseini | The smiconducting properties of passive films formed on AISI 316L and AISI 321 stainless steels: A test of point defect model[END_REF]), ε 0 is the vacuum permittivity (8.85 x 10 -14 F/cm), q is the electron charge (1.602 x 10 -19 C), N A is the acceptor density (cm -3 ), E FB is the flat band potential from the extrapolation of the linear fitting to C 2 =0, K B is the Boltzmann constant (1.38 x 10 -23 J/K), T is the absolute temperature. M-S analysis was obtained by measuring the capacitance response at 1 kHz. The potential was scanned in the positive direction from -0.1 to 0.45 V/MSE with voltage scan rate of 50 mV s -1 .

Chapter IV

Aqueous Corrosion

Corrosion in High Temperature Water

Corrosion behaviour of Ni-based alloys in simulated pressurized water reactor (PWR) environment (320°C, 14 MPa) will be discussed in this section. The presence of surface coldwork may alter the corrosion mechanism of these materials in high temperature water. Therefore, minimizing surface cold-work is carried out. Fine emery-polishing, mirrorpolishing with colloidal silica and electro-polishing are conducted to minimize possible contribution of surface cold-work in the corrosion process and on resulting oxides morphology. In this way, the effect of chromium content on the corrosion behaviour of studied materials in high temperature water is clearly emphasized. This was reached by investigating the corrosion behaviour of Ni-Cr model alloys with Cr content in the range 14-30 wt. %. Surface observations using SEM are performed to determine the morphology of resulting scales. Further cross sectional characterization of the physico-chemical characteristics of resulting oxides using TEM are carried out as well.

Minimizing surface cold-work

Fig. 35 indicates that cold-work in emery-polished Ni-16Cr surface before the oxidation test remains relatively larger compared with that in mirror and electro-polished specimens. In fact, minor deformations due to the surface preparation remain in the subsurface of mirror and electro-polished specimens. After the oxidation test, TEM diffraction patterns (Fig. 36) confirm the presence of perturbed zone (~ 1 µm), named hardened layer, with high deformation density in emery-polished subsurface. In fact, the presence of high dislocations density leads to the recrystallization during the test and consequently nano-grains appear, providing fast diffusion path for chromium. However, F. Delabrouille [START_REF] Delabrouille | characterisation of cracks of SCC of Ni-base alloys using MET: Effect of chromium content and environment chemistry[END_REF] reported that surface deformations tend to weaken the role of chromium in the development of protective Cr-oxide layer on Ni-15Cr-9Fe, which corroded in primary water. Hence, the growth of this layer did not take place for this material, instead oxygen penetrated in the base metal to form Cr rich-oxide particles. Conversely, cold-work free surface presented compact Cr-oxide layer [START_REF] Delabrouille | characterisation of cracks of SCC of Ni-base alloys using MET: Effect of chromium content and environment chemistry[END_REF]. Thus, surface cold-work influences significantly the corrosion mechanism.

Surface observations (Fig. 37) show the presence of tetrahedral and octahedral crystallites (randomly distributed) on the surface of oxidized specimens. In contrast with the distribution of crystallites formed on mirror and electro-polished surfaces, those formed on emery-polished surface display bimodal size distribution (micro and nano-crystallites) as shown in Fig. 38. The distribution of the nano-crystallites is more or less uniform. SEM surface observations indicate that minimizing surface cold work with mirror and electropolishing results in noticeable decrease of crystallites density as well as their size for all studied materials which is in good agreement with TEM observations (Fig. 39). Minimizing surface cold-work by mirror-polishing promotes the growth of continuous thin film (~ 10 nm) beneath the outer layer of crystallites. While the presence of surface cold-work leads to the formation of thicker inner oxide (~ 100 nm) and oxygen penetration. Secondly, the average size of the crystallites precipitated on emery-polished surface by dissolutionprecipitation phenomenon [START_REF] Lister | the mechanism and kinetics of corrosion product release from stainless steel in lithiated high temperature water[END_REF], 1 µm, are magnitudes larger than those precipitated on mirror-polished surface, 50 nm, according to TEM observations (Fig. 39). These observations are in good concordance with previous studies [START_REF] Mcintyre | X-ray photoelectron studies of the aqueous oxidation of Inconel-600 alloy[END_REF][START_REF] Tapping | the composition and morphology of oxide films formed on type 304 stainless steel in lithiated high temperature wate[END_REF][START_REF] Cissé | Effect of surface preparation on the corrosion of austenitic stainless steel 304L in high temperature steam and simulated PWR primary water[END_REF]. Fig. 37 shows that electropolished surface of Ni-14Cr exhibits smaller crystallites that those formed on mirrorpolished surface of this metal. In fact, S. Gardey [START_REF] Gardey | study of general corrosion of Alloy 600, 690 and 800 in primary water, contribution in the understanding of mechanisms[END_REF] reported that electro-polishing can induce the prior (before the exposition test) formation of Cr-oxide, 2nm thick, which may limit the dissolution rate in the early stage. Finally, the oxide film formed on cold-work-free surface prevents the anodic dissolution of species and thus limits the precipitation on the surface, indicating the barrier effect of this resulting oxide layer. In order to dissociate the effect of surface cold-work, prior passivation and the influence of chromium content on the oxidation behaviour of Ni-based alloys, only mirror-polished surface are exploited in the following section.

Emery-polished Mirror-polished Electro-polished

Ni-14Cr

Ni-22Cr

Ni-30Cr Fig. 37. Surface observation using SEM of specimens exposed to PWR environment (320°C, 14 Mpa, DH=30 cc/kg) for 500 hours.

Base metal

Cr-oxide

Effect of chromium content -Identification of the critical value

Fig. 40 shows that the surface of oxidized Ni-xCr specimens (14 ≤ x < 20 wt.%) exhibits relatively high density of large crystallites with average size 1-3 µm, randomly distributed. In this range of Cr content, it seems that the density of crystallites decreases gradually with increasing Cr content. STEM-EDX analyses shown in Fig. 41, indicate that the crystallites consist of iron (40 %), oxygen (40%) and Ni (20%). This outer layer of crystallites is not compact, meaning it is unlikely that this layer acts as protective oxide. Compact and continuous inner layer (~10 nm thick) covers the surface of the metal, consisting of very small oxide grain because it grows in retrain volume as it is illustrated in TEM cross section (Fig. 39). This layer is notably enriched with chromium due to its selective oxidation in the subsurface (Fig. 41), reaching 32 wt.% for Ni-16Cr, as opposed of the oxide particles that have grown by precipitation from the solution. Density and size of crystallites decrease noticeably with increasing Cr content to 20 wt.%. This can be linked to the formation of more efficient inner layer which may limit considerably the release kinetics of cations and consequently decreasing the precipitation rate on the surface. Precipitation phenomenon results in the growth of crystallites is controlled by the degree of saturation of species in the boundary layer, corresponding to the saturation of Ni cation released by the specimen and Fe cations released by the stainless steel autoclave. It is important to highlight that some released cations at oxide/solution interface diffuse to the bulk solution by mass transfer and do not precipitate [START_REF] Lister | the mechanism and kinetics of corrosion product release from stainless steel in lithiated high temperature water[END_REF]. In general, it is well known that the overall corrosion rate is strongly dependent of the release kinetics due to the fast diffusion of species through the rate limiting layer [START_REF] Lister | the mechanism and kinetics of corrosion product release from stainless steel in lithiated high temperature water[END_REF].

The growth of protective inner layer on Ni-20Cr results in the decrease of the number density of crystallites of NiFe 2 O 4 spinel oxide [START_REF] Panter | Influence of oxide films on primary water stress corrosion cracking initiation of alloy 600[END_REF][START_REF] Carette | Analysis and TEM examination of corrosion scales grown on Alloy 690 exposed to pressurized water at 325°C[END_REF][START_REF] Gardey | study of general corrosion of Alloy 600, 690 and 800 in primary water, contribution in the understanding of mechanisms[END_REF][START_REF] Marchetti-Sillans | general corrosion of Ni-base alloys in aqueous environment at high temperature: Approach for the understanding of mechanisms[END_REF][START_REF] Sennour | characterization of the oxide films formed at the surface of Ni-base alloys in pressurized water reactors primary coolant by transmission electron microscopy[END_REF] precipitated on the surface. The inner layer may limit the outward solid state diffusion of Ni species as described by PDM model above [START_REF] Macdonald | the history of the Point Defect Model for the passive state: A brief review of film growth aspects[END_REF] (bibliographic chapter). Secondly the release kinetics can be reduced by nano-pores blocking phenomenon due to lateral growth of the inner layer formed on Ni-20Cr [START_REF] Gardey | study of general corrosion of Alloy 600, 690 and 800 in primary water, contribution in the understanding of mechanisms[END_REF]. Hence, the presence nano-pores provide short-circuit path for the diffusion of species accompanied by their dissolution and precipitation to form the crystallites. The protective behaviour can be probably correlated to high Cr-enrichment in the surface of this material. The decrease of the number density of crystallites is observed for all materials with Cr content larger than 20 wt.%, Indicating that this amount of chromium is sufficiently high to ensure the growth of barrier layer and its maintenance. Consequently, the flux of species through this barrier layer, which is governed by diffusionmigration phenomenon, is depressed as the amount of chromium is increased to the critical threshold. Thus, it is postulated that 20 wt.% of Cr is the critical amount of Cr content required for the improvement of the corrosion resistance. Hence, it is suggested that the oxide layer formed on high Cr content Ni-Cr systems (over 20 wt.%) being unchanged in physico-chemical properties [START_REF] Delabrouille | characterisation of cracks of SCC of Ni-base alloys using MET: Effect of chromium content and environment chemistry[END_REF]. This conclusion is in good agreement with F. Delabrouille work [START_REF] Delabrouille | characterisation of cracks of SCC of Ni-base alloys using MET: Effect of chromium content and environment chemistry[END_REF] who reported that the critical value is in the range of 15-20 wt.% using Ni-Cr mirror-polished specimens.

Low-magnification High-magnification

Conclusion

Emery-polished surface showed oxygen penetration in the base metal. Moreover, the presence of hardened layer promoted the dissolution of cations and thus the precipitation of macro-crystallites. Minimizing surface cold-work with colloidal silica-polishing promoted the formation of more compact and uniform protective passive films. While, electropolishing caused probably prior Cr-enrichment on the surface which may alter the oxidation process in the early stage. This phenomenon would improve the oxidation resistance resulting in synergetic effect between chromium content and surface treatment. In primary water, it is suggested that 20 % Cr is the critical amount of chromium required to form and maintain protective scale on cold-work free surface of Ni-Cr systems. Hence, it is assumed that oxide films formed on Ni-xCr alloys ( x > 20 wt.%) being unchanged in physico-chemical properties.

Oxide scale formed in primary water is an ultra-thin film (at nano-scale), therefore its characterization using SEM or STEM for instance is unlikely appropriate. Electrochemical characterization of the film is then conducted at room temperature. This provides analytical

µm 2 µm

Oxygen penetration

approach on growth and maintenance mechanisms of the passive films at atomic scale. Hence, the film acts as barriers against the movement of species and thus its physicochemical characteristics are the key issue. To investigate the existence of an optimal amount of chromium, a relationship between chromium content and the electrochemical behaviour of the studied materials is established. Secondly, the impact of iron addition is also investigated in the following section of the manuscript.

Electrochemical behavior of passive films

Determination of the passivation ability

As previously mentioned, chromium plays a key role in the passivation behavior of numerous alloys. It is often considered as a passivity promoter [START_REF] Marcus | Surface science approach of corrosion phenomena[END_REF]. In Fig. 42, the polarization curves obtained for different Ni-Cr binary alloys reveal effectively that the reactivity in active-passive transitions decreases with increasing the Cr content. Once the active dissolution had occurred, the passive film is established. For all the studied alloys, the passive current density appears independent of the potential, indicating the effective barrier effect of such formed oxide layers. Focusing on the passivation domain, polarization curves indicate that the passivation potential range seems independent of the Cr content while the passive current density rely on the Cr content. The passive current density (i pass ) for Ni-16Cr is the highest probably due to the presence of a significant hydroxide or a largely non-stoichiometric oxide as a result of competitive dissolution phenomena between Ni and Cr [START_REF] Bojinov | Electrochemical study of the passive behavior of Ni-Cr alloys in borate solution -a mixedconduction model approach[END_REF]. The formation of Ni-rich oxide (in crystallites) in primary water confirms this competitive dissolution takes place. Since Cr 2 O 3 is the main network of the oxide which is predicted to form on alloys with bulk Cr content more than 16 wt.%. [START_REF] Boudin | Analytical and electrochemical study of passive films formed on References nickel-chromium: Influence of the chromium bulk concentration[END_REF], the passive current density decreases suggesting a better barrier effects. Increasing the Cr content to 18 and 22 wt.% leads to the decease of i pass . This can be linked to the transition between (Cr,Ni)-oxide to an Cr-oxide inner layer [START_REF] Bojinov | Electrochemical study of the passive behavior of Ni-Cr alloys in borate solution -a mixedconduction model approach[END_REF]. For Ni-26Cr, i pass reaches its minimum while it increases slightly for Ni-30Cr.

To confirm this tendency, EIS experiments were performed at 0.1 V/MSE. EIS data plotted on Fig. 43 show that the passive film formed on Ni-16Cr exhibits the smallest pseudocapacitive loop while it becomes larger with increasing Cr content, indicating that the corrosion resistance is enhanced [START_REF] Metikoš-Huković | Some aspects in designing passive alloys with an enhanced corrosion resistance[END_REF]. The evolution of the dominant capacitive behavior is effectively associated with the increase of polarization resistance [START_REF] Wu | The semi-conductor property and corrosion resistance of passive film on electroplated Ni and Cu-Ni alloys[END_REF]. According to the polarization curves, the Nyquist plot for Ni-26Cr exhibits the largest capacitive loop, indicating better corrosion resistance than Ni-18Cr and Ni-22Cr, which may be attributed to more stoichiometric oxide with less point defects concentration. For Ni-30Cr, the capacitive behavior of the film degrades which can be correlated to the decrease of activation energy barrier. This may promote the anodic dissolution. Activation energy barrier is known to decrease with the decreasing coordination of Cr atoms on the surface. Thereby, it is predicted that coordination of atoms varies in the reverse order to the surface density of metal atoms and thus the amount of Cr content [START_REF] Marcus | on some fundamental factors in the effect of alloying elements on the passivation of alloys[END_REF]. Second reactivity at -300 mV/MSE (Fig. 42) is observed for Ni-30Cr which can be associated to the hydrogen evolution [START_REF] Kong | A study of passive films on chromium by capacitance measurement[END_REF][START_REF] Lavigne | The effect of nitrogen on the passivation mechanisms and electronic properties of chromium oxide layers[END_REF]. Hydrogen evolution occurs due to the chemical recombination reaction (2H ads = H 2 ) followed by hydrogen permeation into the film [START_REF] Kong | A study of passive films on chromium by capacitance measurement[END_REF][START_REF] Lavigne | The effect of nitrogen on the passivation mechanisms and electronic properties of chromium oxide layers[END_REF]. In order to investigate a synergic effect between Fe and Cr, ternary alloys Ni-Cr-Fe (with 8 wt.% of iron) are also studied in the present paper. It is commonly accepted that Fe exhibits a low metal-metal bond strength which is predicted to enhance substantially the passivity [START_REF] Marcus | on some fundamental factors in the effect of alloying elements on the passivation of alloys[END_REF]. Nevertheless, the polarization curves (Fig. 44) indicate that the presence of Fe causes modifications within the passivation behavior. For example, it is responsible for a noticeable increase of i pass . This may be related to a lower activation energy barrier for dissolution [START_REF] Marcus | on some fundamental factors in the effect of alloying elements on the passivation of alloys[END_REF], indicating the selective dissolution of Fe cations.

Moreover EIS data shown in Fig. 45 report that the pseudo capacitive loop are smaller with the presence of Fe in Ni-Cr systems. This experimental result clearly indicates that iron addition degrades the protective properties of the passive films. This discrepancy in the behavior is due to the significant changes in the nature and structure of the passive film. In fact, it is believed that Fe cations are incorporated in the passive film and migrate through this later to film/solution interface. Consequently, Fe cations contribute in anodic dissolution or/and formation of Fe-hydroxides.

EIS data fitting: characterization of the passive film

Fitting to Electrical Equivalent Circuits (EEC) provides more detailed understanding of ongoing process at electrode/solution interface. EIS data were satisfactorily fitted to an EEC composed of parallel combination of Q and R-Z d in series with electrolyte resistance (R s ), as illustrated in Fig. 46. Parameters Q and R t represent the electrode capacitance and charge transfer resistance respectively. The constant phase element (CPE, with an impedance of 𝑍 = 1/𝑄(𝑗𝜔) 𝛼 ) stands for the possibility of non-ideal capacitance of the film. The deviation from the ideal capacitive behavior can be related to the surface heterogeneities (roughness and porosity) [112] or disturbed surface reactivity (non-uniform distribution of charges in the film) [START_REF] Jorcin | CPE analysis by local electrochemical impedance spectroscopy[END_REF]. (Z d, R d ) and τ d refer to migration resistance and corresponding relaxation time respectively. Theoretically the diffusion-migration phenomenon illustrates the mixed electronic-ionic conductor behavior of passive films and it is given by Buck et.al [START_REF] Buck | Diffusion-Migration impedance for finite, one-dimensional transport in thin layer and membrane cells, an analysis of derived electrical quantities and equivalent circuits[END_REF][START_REF] Grzeszczuk | Analysis of charge transport impedance in the reduction of thin films conducting polyaniline in aqueous trichloroacetic acid solution[END_REF] as following:

𝑍 𝑑 = √𝜏 𝐶 0 √𝑗𝜔 coth √𝑗𝜔𝜏 + √𝜏 ′ (𝑡 𝑒 -𝑡 𝑖 ) 2 𝐶 0 ′ √𝑗𝜔 tanh √𝑗𝜔𝜏 ′ (1)
𝑍 𝑑 = 𝑅 𝑑 √𝜏 𝑑 𝑗𝜔 coth(√𝜏 𝑑 𝑗𝜔) (2)
Where τ and τ' are the relaxation time of transport, 𝐶 0 and 𝐶 0 ′ , the transport capacitance, t e and t i are the transference numbers for electron and ions respectively. It is assumed that the transport phenomenon is dominated by equal transference numbers for electron t e and ion t i . In other words, the ionic conductivity is equal to the electronic conductivity which simplifies equation 1. The equation 2 was obtained by the resolution of the general diffusion equation with the flux equal to zero at the interface, i.e. restricted migration. The calculated equivalent circuit parameters are listed in table . 3. The mathematical error (χ 2 ) is the order of 10 -3 which is acceptable according to the literature [START_REF] Cui | Electrochemical deposition and characterization of poly (3,4ethylenedioxythiophene) on neural microelectrode arrays[END_REF]. 861 For all the Ni-Cr binary alloys, α (Q exponent) is close to 1, which confirms the capacitive behaviour of passive films. In rough tendency, Q increases with increasing Cr content. R t and R d reveal electronic exchange resistance at the interface and the transport resistance thought the film respectively. Both of those parameters increase with increasing the Cr content as well. Fitting of Ni-16Cr impedance data to EEC reveals high mathematical error (χ 2 ). This is probably due to the fact that EEC calculations take into account only one oxide network for the migration impedance while the passive film grown on Ni-16Cr may be highly hydrated or non-stoechiometric. Conversely, fitting parameters such as Q and R d emphasize a transition in the behaviour, probably from defective to protective oxide film, at 26 wt.% of Cr. However, Q and R d values calculated for Ni-18Cr and Ni-22Cr are in the same order of magnitude while those parameters became significantly greater for Ni-26Cr, meaning that the corrosion resistance is enhanced. The critical threshold is identified as 20 wt.% in primary water. This discrepancy is probably due to the fact that primary water is slightly alkaline but the electrochemical analyses are conducted in acidic solution. Thus, solubility and transport of activated corrosion products are different. Secondly, the diffusion of species through the passive film is thermally activated phenomenon which may be accelerated in primary water. However, only migration of species takes place under the electrochemical gradient, corresponding to electric strength field and charge carriers distribution through the film, at room temperature.

In the presence of Fe, R d and R t decrease and thus the corrosion resistance is degraded. Q is also significantly modified suggesting a truly different passive film/electrolyte interface. It is reported that the protective film on Ni-based alloys is mostly chromia inner oxide (Cr 2 O 3 ). Fe cations diffuse roughly at the same rate as Cr which can be related to the fact that the ionic radius of cation Cr 3+ , 0.062 nm, are very close to ionic radius of Fe 3+ , 0.065 nm [START_REF] Sabiouni | Diffusion of iron in Cr 2 O 3 : polycrystals and thin films[END_REF]. Henceforward as discussed above (section 3.1), it is suggested that Fe is incorporated in the film and its outward movement results in the formation of less protective Fe-oxide or hydroxide.

Correlation between Mott-Schottky analysis and Defect flux

From a PDM point of view, the increase of R d may be considered as a result of slow defect transport rate within the film. For passive films, the electric field strength and charge carriers density are known to be the main driving forces governing transport phenomena [START_REF] Fattah-Alhosseini | The smiconducting properties of passive films formed on AISI 316L and AISI 321 stainless steels: A test of point defect model[END_REF][START_REF] Sikora | Nature of the passive film on nickel[END_REF][START_REF] Young | Anodic oxide films on tantalum electrodes[END_REF]. It is commonly admitted that the properties of the film are governed by rates of generation, annihilation and transport of ionic point defects in order to maintain the neutrality of the film and thus its stability [START_REF] Bojinov | Coupling between ionic defect structure and electronic conduction in passive films on iron, chromium and iron-chromium alloys[END_REF][START_REF] Wu | The semi-conductor property and corrosion resistance of passive film on electroplated Ni and Cu-Ni alloys[END_REF]. It is then essential to understand the transport mechanism through the oxide films in order to predict material behavior and its dependence on the alloying elements content. Thus, complementary methods were used: chronoamperometric (Figs. 47a and47b) and Mott-Schottky (Figs. 48a and48b) measurements. These methods provide quantitative estimations of the flux of point defects and charge carriers density respectively. On the chronoamperometric curves, the steady state current density is assessed after 1000s of polarization for all studied materials (Figs 47a,47b). The steady state current density (i ss ) is attributed to migration of point defects within the film which is required for its maintenance, as described by the PDM [START_REF] Macdonald | An electrochemical impedance analysis of passive films on nickel (111) in phosphate buffer solution[END_REF]. Moreover, mobility and/or concentration of point defects are the main parameters controlling their flux. From the relationship between i ss and point defects migration, the steady state flux of majority point defects (J 0 ) can be expressed as [START_REF] Wu | The semi-conductor property and corrosion resistance of passive film on electroplated Ni and Cu-Ni alloys[END_REF]:

J 0 = -i ss /me (3)
Where m is metal charge and e is electron charge These chronoamperometric results are consistent with EIS results. Indeed, it is observed that as lower the flux of point defects which is correlated to lower i ss as higher the measured impedance. The evolution of R d is directly connected to the evolution of J 0 . Ni-26Cr exhibit the greatest R d and the lowest J 0 , suggesting that the point defect flux is slow and the consummation of point defects at metal/passive film interface or at passive film/electrolyte interface is favored. The presence of Fe in passive films increases the dissolution kinetic (Fig. 47b) providing higher point defect density. It suggested that more defective layers grow on Ni-Cr-Fe alloys, which is consistent with the increase of i ss and low values of R d .

To determine charge carriers concentration (N q ) and semiconductor type, Mott-Schottky analyses have been performed (Figs. 48a,48b). According to the negative slope of M-S plots [START_REF] Fattah-Alhosseini | The smiconducting properties of passive films formed on AISI 316L and AISI 321 stainless steels: A test of point defect model[END_REF], passive films behave as p-type with excess of cation vacancies. This analysis allows to determine the dopant density using the following equation [START_REF] Soustelle | PWSCC of alloy 600: a parametric study of surface film effects[END_REF]:

1 𝐶 𝑠𝑐 2 = 2 𝜀𝜀 0 𝑒𝑁 𝐴 (𝐸 -𝐸 𝐹𝐵 - 𝑘 𝐵 𝑇 𝑞 ) for p-type semiconductor (4)
Where, C sc is the space charge capacitance, ε is the dielectric constant of the passive film (25 for chromium oxide [START_REF] Moffat | An Electrochemical and X-Ray Photoelectron Spectroscopy Study of the Passive State of Chromium[END_REF]), ε 0 is the vacuum permittivity (8.85 x 10 -14 F/cm), q is the electron charge (1.602 x 10 -19 C), N A is the acceptor density (cm -3 ), E FB is the flat band potential from the extrapolation of the linear fitting to C 2 =0, K B is the Boltzmann constant (1.38 x 10 -23 J/K), T is the absolute temperature. The semiconductor type depends on the predominant defects present in the film. In the present work, the passive film is assumed as homogeneous principal Cr 2 O 3 network and acceptors, i.e. Cr vacancies (𝑉 𝐶𝑟 , 2-𝑉 𝐶𝑟 , 3-), are assumed to be predominant over Ni vacancies (𝑉 𝑁𝑖 2-) [START_REF] Bojinov | Electrochemical study of the passive behavior of Ni-Cr alloys in borate solution -a mixedconduction model approach[END_REF][START_REF] Cunha Belo | Semiconducting properties of passive films formed on nickel-base alloys type Alloy 600: influence of the alloying elements[END_REF][START_REF] Lavigne | The effect of nitrogen on the passivation mechanisms and electronic properties of chromium oxide layers[END_REF]. However, chromia can be n-type in primary water. This is linked to the weak equivalent oxygen pressure in the aqueous hydrogenated water. Indeed, n-type Cr 2 O 3 , which is independent of oxygen activity, is favored [START_REF] Marchetti | Photoelectrochemical study of nickel base alloys oxide films formed at high temperature and high pressure water[END_REF]. Meaning, chromium interstitials (𝐶𝑟 𝑖 °°°) are the predominant point defects. Acceptor density is calculated from the experimental slope and listed in Table . 3. Calculated N A in the present study are larger those measured for passive films formed on pure chromium, reported in the range 10 19 -10 22 cm -3 in the literature [START_REF] Kong | A study of passive films on chromium by capacitance measurement[END_REF]. This can be associated to the different electrolyte or to the substitution of Cr cations by Ni cations having a different oxidation state, which both may influence the nature of the film and its electronic properties [START_REF] Fattah-Alhosseini | The smiconducting properties of passive films formed on AISI 316L and AISI 321 stainless steels: A test of point defect model[END_REF][START_REF] Gesmundo | Application of wagner's theory to the parabolic growth of oxides containing different kinds of defects[END_REF]. From Table 3, it is worth mentioning that increasing Cr content and alloying the materials with Fe have a direct consequence on acceptors density. The passive film formed on Ni-26Cr may show better corrosion resistance, because N A is distinctly depressed. Additionally, Brett et al. [START_REF] Alves | characterization of passive films formed on mild steels bicarbonate solution by EIS[END_REF] suggested that the decrease of N A reduces the susceptibility of film breakdown and pitting initiation, because defects are potential sites where these processes are supposed to occur. These deductions are concordant with the results from the EIS data above. Since the increase of R d is correlated to the decrease of acceptors density. Based both on the physical and electronic properties, it is believed that at 26 wt.% of Cr content a transition from defective to protective passive film is reached. As a result of the Fe presence, N A increase due to the change of the crystallographic defect structure of the film and its nature [START_REF] Bojinov | Coupling between ionic defect structure and electronic conduction in passive films on iron, chromium and iron-chromium alloys[END_REF]. These observations confirm that iron is incorporated in the film and its diffusion through Cr-oxide results in greater cation vacancies density and thus higher conductivity [START_REF] Gesmundo | Application of wagner's theory to the parabolic growth of oxides containing different kinds of defects[END_REF] which is concordant with also EIS data above. Furthermore, it has been reported that the increase of N A results from the high hydration degree of the film [START_REF] Metikoš-Huković | Some aspects in designing passive alloys with an enhanced corrosion resistance[END_REF][START_REF] Kong | A study of passive films on chromium by capacitance measurement[END_REF] leading to the increase of its conductivity. The consequence is a significant degradation of passive films properties, those formed on Ni-16Cr and Ni-Cr-fe alloys, in terms of corrosion resistance [START_REF] Metikoš-Huković | Some aspects in designing passive alloys with an enhanced corrosion resistance[END_REF][START_REF] Kong | A study of passive films on chromium by capacitance measurement[END_REF].

Finally, The E FB values of passive films formed on Ni-Cr and Ni-Cr-Fe materials with Cr content greater than 16 wt.% are more positive that those formed on Ni-16Cr and Ni-16Cr-8Fe. These values are roughly constant and correspond to the E FB values measured for pure chromium oxide [START_REF] Lavigne | The effect of nitrogen on the passivation mechanisms and electronic properties of chromium oxide layers[END_REF]. The shift of E FB toward the positive direction with increasing Cr content more than 16 wt.% proves also the occurrence of adsorption (hydration of films) in Ni-16Cr and Ni-16Cr-8Fe [START_REF] Kong | A study of passive films on chromium by capacitance measurement[END_REF].

Conclusion

This section of the manuscript concerns the study of effect of Cr content and iron addition on the passivity characteristics of Ni-based alloys in acidic solution at room temperature. It was demonstrated that the corrosion resistance of these materials is controlled by the physical and electronic properties of the passive films, the following conclusions were achieved:

 Using electrochemical technics, the existence of optimum threshold of chromium content (26 wt.%) in terms of aqueous corrosion resistance is emphasized.

 Increasing Cr content more than 26 wt.% has a detrimental effect on the properties of the passive film. This is due to the fact that the surface reactivity is increased.

 The discrepancy between the critical chromium threshold identified in primary water (20 wt.%) and that in acidic solution (26 wt.%) is probably due to test conditions, that both solution and test temperature.

 Selective dissolution of iron in Ni-Cr-Fe specimens led to the degradation of corrosion resistance. In fact, alloying Ni-Cr alloys with Fe may change the nature, the structure and the semiconductor features of the passive films.

The oxidation kinetics of Ni-based alloys in primary water considerably slower than in superheated steam at 700°C as will be described in the following section. Henceforth, the corrosion test in primary water results in the growth of a continuous ultra-thin film (at nanoscale) on cold-work free surface. The oxidation rate is strongly related to the test temperature, as it is described in the bibliographic review below. Increasing the test temperature allowed the acceleration of the oxidation process. Consequently, the growth of thicker (at micro-scale) oxide scales take place. Although, test conditions in steam induced a significant change in the physical properties of the oxide scale as well as its morphology.

Oxidation kinetics and characteristics of resulting oxide provided further information on the oxidation behaviour of Ni-base alloys as a function of their chemical composition in high temperature environment.

Chapter V Steam Oxidation

Steam oxidation

Oxidation of Ni-based alloys in superheated steam at 700°C will be discussed in this chapter. It is admitted that the presence of water vapor would influence the oxidation behaviour of these materials. Therefore, detailed knowledge of high temperature oxidation and rigorous prediction of oxidation kinetics in wet environment is required. To uncouple the effect of surface deformation, due to surface preparation, and chemical composition of studied materials on the oxidation behaviour, minimizing surface cold-work is carried out. This lead to a realistic evaluation of the oxidation kinetics. The effect of increasing chromium content is term of oxidation is emphasized. This is achieved by investigating the oxidation behaviour of Ni-Cr model alloys with Cr content in the range 14-30 wt.%. Secondly, the effect of iron addition (8 wt.%) in term of oxidation is investigated in this chapter as well. Although, it is commonly accepted that iron play important role in solid solution strengthening. Its impact on the oxidation behaviour remains not clearly explained. The effect of the chemical composition on the oxidation behaviour is evaluated considering both WG measurements and oxide scale features. Finally, to obtain industrial projection of the present fundamental study, the commercial Alloy 600 (Ni-16Cr-8Fe) is tested, providing adequate comparison with model alloy (Ni-14Cr-8Fe).

Minimizing surface cold-work

Attention is given to surface preparation to minimize possible effect of surface coldwork on the oxidation. For this purpose fine emery-polishing, mirror-polishing and electropolishing are carried out. Hence, the oxidation resistance can be improved by increasing cold-work degree by grinding, shot-peening and so on, as reported in bibliographic review. However, the beneficial effect of surface cold-work will be supressed be annealing process and metal loss during long-term operation. Hardness test data of as received Ni-16Cr (Fig. 49) reveal that deformation density remains greater in emery-polished compared with that in mirror and electro-polished surfaces. Weight grain measurement (Fig. 50) indicates that both mirror and electro-polished specimens exhibit faster oxidation rate compared with that of emery-polished specimens (see the order of magnitude in the scale). Furthermore, surface and cross sectional observations using SEM (Figs. 51 and52) confirm that the oxidation rate is depressed in emery-polished specimens as well. In fact, the rapid diffusion of Cr from the base metal to the oxide film takes place in the cold-work zone located in emery-polished specimens subsurface. This results in significant Cr enrichment in the surface, leading to growth and maintenance of Cr-enriched oxide. Secondly, the local strain gradient in the cold-work zone, named hardened layer, causes the recrystallization at high temperature resulting in the appearance of nano-grains. Consequently, the finer grain, the faster mobility of Cr, the higher density of nucleation sites, and the faster growth of Crrich layer. These statements are in good agreement with those reported by many authors [START_REF] Ostwald | Initial oxidation and chromium diffusion, I. Effect of surface working on 9-20% Cr steels[END_REF][START_REF] Grabke | Effect of grain size, cold working and surface finish on the metal-dusting resistance of steels[END_REF][START_REF] Cooper | The effect of surface treatment on the oxidation of ferritic stainless steels used for solid oxide fuel cell interconnects[END_REF][START_REF] Rakowski | The effect of surface preparation on the oxidation behaviour of gamma TiAl-base intermetallic alloys[END_REF][START_REF] Cissé | Effect of surface preparation on the corrosion of austenitic stainless steel 304L in high temperature steam and simulated PWR primary water[END_REF][START_REF] Warzee | Effect of surface treatment on the corrosion of stainless steels in high temperature water and steam[END_REF][START_REF] Carrette | releasing corrosion products of alloy 690 pipes of primary circuit vapor generator[END_REF], as discussed in the bibliographic review. Moreover, the misfit of dislocation can play the role of an efficient sink to eliminate point defects [START_REF] Bertrand | Chemical Evolution in the Substrate due to oxidation: A Numerical Model with Explicit Treatment of Vacancy Fluxes[END_REF].

True-oxidation characteristics become visible with mirror-polishing and electropolishing, according to SEM observations (Figs. 51 and52). On the other hand, A. Machet [START_REF] Machet | study of oxidation of stainless alloys in earliest stages in high temperature water[END_REF] reported that electro-polishing can induce prior Cr-enrichment in the surface (before the test). This linked to the selective oxidation of Cr during the anodic dissolution in electropolishing solution. Hence, prior formation of Cr-rich oxide can affect the weight gain measurements in early stage of oxidation. This may further alter the identification of the optimal Cr content. This phenomenon will be recalled in the following section. In contrast of fine emery-polishing, it seems that mirror-polishing and electro-polishing are accurate methods to minimize surface cold-work. Therefore, to uncouple the effect of surface deformation and that of chemical composition, only WG measurements and physicochemical characteristics of oxide scale formed on mirror and electro-polished specimens will be discussed in the following sections of this manuscript.

Optimization of chromium content

Weight gain measurements

To evaluate the oxidation kinetics, power rate law is assumed. Hence, WG data shown in Fig. 50 are modeled considering the following equation:

log ( 𝛥𝑚 𝐴 ) = C + n . log(t) (1)
Where 𝛥𝑚 𝐴 ⁄ is the weight gain per unit area (mg/cm 2 ) and 𝑡 is the time of exposition (h). From a linear fitting in double-logarithmic scale, n-values are calculated and given in Fig. 53. Knowing that ground surface of these specimens has a minor contribution in WG, mirrorpolished and electro-polished surface provided almost the overall WG. n-value corresponds to the oxidation behaviour of studied model alloys and provide an estimation of the oxidation kinetic for a long-term exposition. Fig. 53 shows that oxidation kinetics varies as a function of chromium content and it may be divided into:

 Parabolic rate kinetics (n-value = 0.5) This oxidation kinetics is observed for mirror-polished specimens with 14%, 28% and 30 % of chromium. According to Wagner model [START_REF] Wagner | theoretical analysis of the diffusion process determining the oxidation rate of the alloys[END_REF], high temperature oxidation of Ni-base alloys may obey to the parabolic rate law. These materials usually exhibit outward growth of the oxide which implies that its growth rate is limited by the diffusion of cation vacancies [START_REF] Guillou | Influence of Hydrogen and Water Vapour on the Kinetics of Chromium Oxide Growth at High Temperature[END_REF].  Deviation from the parabolic rate law (n-value < 0.5) This oxidation kinetics is observed for [START_REF] Castle | the role of diffusion in the oxidation of mid steel in high temperature aqueous solutions[END_REF][START_REF] Coriou | Stress corrosion cracking of Inconel 600 in high temperature water, 3ième colloque de métallurgie[END_REF][START_REF] Panter | Influence of oxide films on primary water stress corrosion cracking initiation of alloy 600[END_REF]24 and 26). This deviation is observed for all electro-polished specimens as well. Ni-24Cr and Ni-26Cr, mirror polished and electro-polished respectively, exhibit the lowest n-value indicating the formation of more efficient barrier layer. Fitting error calculated for some electro-polished specimens is magnitudes greater than that calculated for mirror-polished specimens. This can be linked to prior Cr-enrichment and surface roughness of specimens. Consequently, the identification of the optimal Cr content using WG data with relatively high accuracy requires further characterisations of the oxide scale according to the present study. As a first approach, the optimal Cr content is postulated as 24 wt.% for mirror-polished specimens.

In the present study WG data showed a deviation form parabolic rate law in steam. This in good agreement with many studies [START_REF] Nicolas | study of the physico-chemical evolution of substrates during the oxidation at high temperatures of Ni-Cr models alloys with low chromium content and Ni-16Cr-9Fe model alloy[END_REF][START_REF] Feulvarch | An implicit finite element algorithm for the simulation of diffusion with phase changes in solids[END_REF][START_REF] Zhou | a randomwalk-cellular automaton model of precipitation of internal oxides[END_REF][START_REF] Nicolas | the transition from internal to external oxidation of Ni -X wt.% Cr at 950°C[END_REF]. This can be linked to the fact that intrinsic diffusion coefficient of oxidizable element and effective diffusion coefficient of oxygen are considered constant in Wagner model. Furthermore, this model does not take into account the volume fraction of particules in reaction zone, such as Cr-oxide precipitates, and their coalescence phenomenon [START_REF] Feulvarch | An implicit finite element algorithm for the simulation of diffusion with phase changes in solids[END_REF][START_REF] Zhou | a randomwalk-cellular automaton model of precipitation of internal oxides[END_REF][START_REF] Nicolas | the transition from internal to external oxidation of Ni -X wt.% Cr at 950°C[END_REF] which ensures the formation of the barrier layer.

Oxide scale characteristics

Surface observations of oxidized specimens (Fig. 54) show the presence of nodules. Number density of nodules tends to decrease gradually with increasing Cr content. Fig. 55 reveals that these nodules appear alike after 30 hours of exposition. It seems also that oxidation rate is depressed at grain boundaries region (Fig. 54). In fact, the oxide scale formed at grain boundaries zone is thinner than that formed on the grain and thus a gap appears between these oxide scales. This results is due to the fact that the grain boundary provides a path for the rapid diffusion of Cr, leading to the establishment of protective and compact Cr-oxide layer [START_REF] Lozano-Perez | The role of cold work and applied stress on surface oxidation of 304 stainless steel[END_REF][START_REF] Pearce | High temperature oxidation of cold worked and annealed Alloy 800 at low oxygen pressure[END_REF][START_REF] Otsuka | Scaling of austenitic stainless steels and nickel base alloys in high-temperature steam at 973 K[END_REF]. Cross section observations of mirror and electropolished specimens respectively in Fig. 56 and 57 indicate that the characteristics of the resulting oxide scale are strongly dependent of chromium content, as described below:

 14 ≤ Cr content ≤ 22 wt.% Nodular internal oxidation occurs in this range of chromium content. It is believed that dissolved hydrogen in metallic oxides and dissociation process in steam may modify the defect concentration and thus accelerate the penetration of oxygen in the early stage [START_REF] Ehlers | enhanced oxidation of the 9%Cr steel P91 in water vapour containing environments[END_REF][START_REF] Das | Early stage SCC initiation analysis of fcc Fe-Cr-Ni ternary alloy at 288 °C: A quantum chemical molecular dynamics approach[END_REF][START_REF] Essuman | the effect of water vapour on selective oxidation of Fe-Cr alloys[END_REF][START_REF] Essuman | enhanced internal oxidation as trigger for breakaway oxidation of Fe-Cr alloys in gases containing water vapour[END_REF][START_REF] Sundararajan | high temperature corrosion of nanoceria coated 9Cr-1Mo ferritic steel in air and steam[END_REF][START_REF] Essuman | Protective and non-protective scale formation of NiCr alloys in water vapour containing high and low-pO 2 gases[END_REF]. Henceforth, nodular oxidation occurs due to the fact that anionic inward diffusion of oxygen-containing species is fast and flux of chromium is not sufficient to promote the coalescence of Cr-oxide precipitates into a compact and continuous oxide layer [START_REF] Nicolas | study of the physico-chemical evolution of substrates during the oxidation at high temperatures of Ni-Cr models alloys with low chromium content and Ni-16Cr-9Fe model alloy[END_REF][START_REF] Nicolas | the transition from internal to external oxidation of Ni -X wt.% Cr at 950°C[END_REF]. This implies that the oxide growth rate, for specimens with Cr content in the range of 14-22 wt.%, in the superheated steam is governed by the inward diffusion of oxygen-containing species which may be the origin of the deviation from the parabolic rate law. Though oxidation kinetics deviate from the parabolic rate law, a compact oxide layer does not necessary formed. According to SEM cross sectional observations, it is concluded that mirror and electro-polished specimens exhibit almost the same oxide scale characteristics. Hence, only characteristics of oxide scales formed on mirror-polished specimens will be discussed in the following section. This series of specimens is selected due to accuracy of its WG data as well.

Ni-28Cr Ni-28Cr

Ni-30Cr Ni-30Cr 50 µm 50 µm 50 µm 50 µm STEM/EDX line analyses of Ni-16Cr bellow (Fig. 58) show that the outer layer contains pure nickel. W. Gao et al. [START_REF] Gao | Oxidation behaviour of Ni 3 Al and FeAl intermetallics under low oxygen partial pressures[END_REF] have been reported that the formation of pure nickel (nodules and layer) is attributed to the internal oxidation which results in large compressive stress in the internal reaction zone where Ni is simultaneously ejected in order to release the stress. This occurs in the early stage of oxidation process, hence nodules of metallic nickel were observed after 30 hours test (Fig. 55).  Cr content = 24 and 26 wt.% Compact-scale oxidation type takes place. Since, the volume fraction of Cr nodular oxide increases gradually with increasing Cr content to 24 wt.% leading to a better balance between the flux of oxygen and that of chromium [START_REF] Saunders | the oxidation behaviour of metals and alloys at high temperatures in atmospheres containing water vapour: A review[END_REF][START_REF] Nicolas | the transition from internal to external oxidation of Ni -X wt.% Cr at 950°C[END_REF]. Consequently, a transition occurs through coalescence from nodular to a compact scale oxide. This is due to the fact that oxygen mobility in Cr-oxide is slower than in the Ni matrix [START_REF] Essuman | enhanced internal oxidation as trigger for breakaway oxidation of Fe-Cr alloys in gases containing water vapour[END_REF][START_REF] Nicolas | study of the physico-chemical evolution of substrates during the oxidation at high temperatures of Ni-Cr models alloys with low chromium content and Ni-16Cr-9Fe model alloy[END_REF]. Secondly, L. Zhou et al. [START_REF] Zhou | a randomwalk-cellular automaton model of precipitation of internal oxides[END_REF] reported that free oxygen depends on the dissociation rate of Cr-oxide particles, hence its stability. In this way, lower degree of oxygen supersaturation, bigger size of stable oxide precipitates and lower number density of oxide particles formed. Consequently, transition at 24 % Cr from nodular oxide to a continuous and stable Cr-enriched layer, probably Cr 2 O 3 , by coalescence is achieved (see Figs. 56 and59) [START_REF] Zhou | a randomwalk-cellular automaton model of precipitation of internal oxides[END_REF][START_REF] Nicolas | the transition from internal to external oxidation of Ni -X wt.% Cr at 950°C[END_REF]. STEM/EDX mapping analysis (Fig. 60) reveals the formation of Cr-rich oxide at Ni-oxide/metallic nickel interface. Despite, Cr-enrichment did not significantly occur at Ni-oxide/metallic nickel interface for materials with lower Cr content (that < 24 wt.%), it is believed that this layer exists of all studies materials.

In agreement with surface observation (Fig. 54), FIB cross section in the grain boundary zone of Ni-16Cr (Fig. 61) shows that the transition from nodular oxide to compact oxide is likely to occurs in this zone even for Ni-xCr (x < 24 wt.%). STEM/EDX analysis (Fig. 62) confirms the growth of continuous Cr-enriched oxide and Cr depletion beneath grain boundaries. This is due to the fact that grain boundary provide fast diffusion path for Cr [START_REF] Lozano-Perez | The role of cold work and applied stress on surface oxidation of 304 stainless steel[END_REF][START_REF] Pearce | High temperature oxidation of cold worked and annealed Alloy 800 at low oxygen pressure[END_REF][START_REF] Otsuka | Scaling of austenitic stainless steels and nickel base alloys in high-temperature steam at 973 K[END_REF]. This leads to establishment and maintenance of more uniform Cr 2 O 3 [START_REF] Asteman | indication of chromium oxide hydroxide evaporation during oxidation of 304L at 873 K in the presence of 10% water vapor[END_REF][START_REF] Asteman | the influence of water vapor on the corrosion of chromia-forming Steels[END_REF]. Therefore, fine-grained structures may exhibit a better oxidation resistance than coarsegrained structures [START_REF] Otsuka | Scaling of austenitic stainless steels and nickel base alloys in high-temperature steam at 973 K[END_REF]. Since the grain size becomes finer with increasing Cr content (Fig. 63), it is believed that synergetic effect between grain size and Cr content takes place during the oxidation process.

 Cr content > 26 wt.% Duplex compact scale is observed also as chromium content is increased over 26 wt.% (Fig. 56). However, STEM/EDX analyses (Fig. 64) show that Ni-30Cr exhibits metallic nickel zone beneath the continuous Cr-enriched layer formed in the subsurface. This can be linked to the outward diffusion of Cr in this material. Henceforth, increasing the Cr content more than the optimal value leads to a transition from internal to external diffusion. Since metallic nickel is not ejected but a diffusional phenomenon probably takes place leading to the growth of nickel oxide (Figs. 56 and64) and thus the weight gain increased. It is suggested that rate-limiting layer in this case is defective, so oxygen diffuse through this layer. Oxygen flux does not oxidize the metallic nickel beneath Cr-rich layer. In spite of that, oxygen continues to diffuse into the substrate, selective oxidation of Cr occurs and nodular oxide of Cr ensues. This can be linked to the fact that oxygen partial pressure required for thermodynamic stability of Cr-oxide is magnitudes lower than that needed to form Ni-oxide, 10 -32 versus 10 -18 atm at 700°C and 1 mole of oxygen according to ELLINGHAM diagram. This can be correlated also to the presence of metallic Ni on the surface of Ni-xCr (x < 30 wt.%) specimens due to the formation of Cr-rich oxide at Ni-oxide/metallic nickel interface, leading to barrier effect and thus the presence of relatively low oxygen partial pressure into the nodules.

Finally, the oxidation behaviour is strongly dependent of the Cr content as illustrated in schematics below (Fig. 65). When the Cr content is lower than the optimal value nodular oxidation occurs. While a coalescence of Cr-oxide precipitates and the formation of a continuous layer is achieved with increasing Cr content to the optimal value. The growth of continuous Cr-enriched oxide is ensured by increasing the Cr content more than the optimal value, at least to 30 wt.%, but Cr-depletion occurs and metallic nickel zone appears beneath this layer. However, fast diffusion of Cr at grain boundary zone ensures local growth of Crrich oxide for all studied materials. The average atomic % of Cr and O in the rate-limiting layer (Cr-enriched oxide layer) of Ni-24Cr and Ni-30Cr, as shown in Fig. 59

Effect of iron addition

Fig. 66 shows that WG increases considerably with Fe addition for all Ni-xCr-8Fe alloys. n-values are calculated using power law kinetics. n-value corresponds to the oxidation behaviour of studied model alloys and provides an estimation of the oxidation kinetic for a long-term exposition. In term of oxidation kinetics (Fig. 67), n-value increases slightly for Ni-14Cr-8Fe and Ni-30Cr-8Fe compared with those of Ni-14Cr and Ni-30Cr respectively. On the other hand, n-value increases dramatically for Ni-22Cr with Fe addition. Nodules are not observed on the surface of oxidized Ni-Cr-Fe specimens (Fig. 68). Oxidation rate is depressed at grain boundary zone which is in good agreement with Ni-Cr surface observations. The ejection of metallic nodules does not occur in Ni-Cr-Fe. This is probably due to the relaxation of the compressive stresses by the formation of cation vacancies resulting from the fast outward diffusion of Fe cations. In fact, with increasing Cr content the volume fraction of Cr-nodular oxide becomes greater leading to better balance between the inward diffusion of oxygen and outward diffusion of Ni and Fe cations and thus the fast growth of Ni-oxide and Fe-oxide takes place in the outer layer (Figs. 69 and70) [START_REF] Galerie | mechanisms of chromia scale failure during the course of 15-18Cr ferritic stainless steel oxidation in water vapour[END_REF][START_REF] Nicolas | study of the physico-chemical evolution of substrates during the oxidation at high temperatures of Ni-Cr models alloys with low chromium content and Ni-16Cr-9Fe model alloy[END_REF]. This explains the significant increase of n-value of 22Cr-8Fe compared with 14Cr-8Fe in respect with test duration. SEM-EDS line analyses (Fig. 70) confirm the presence a duplex outer oxide scale consisting of Ni-rich oxide and Fe-oxide as discussed above, that Fe diffuses to oxide/environment interface, tends to form Fe-oxide and subsequently the ejection of cation vacancies occurred. Furthermore, these SEM-EDS analysis reveal the presence of a continuous metallic nickel layer in the grain zone and it is suggested that its oxidation results in the formation of Ni-oxide. Although, relaxation of compressive stress is postulated to occur by annealing of cation vacancies, stress gradient remains in the reactive zone located in the subsurface leading to the ejection of metallic nickel in the early stage of oxidation process. In contrast with morphology of oxide scales formed on Ni-Cr alloys, Figs. 69 and70 show the presence of pores in the outer layer of oxide scales formed on Ni-xCr-8Fe (x=14 and 22) specimens. This can be linked to the volatilisation of Fe-species and vacancy condensation [START_REF] Ehlers | enhanced oxidation of the 9%Cr steel P91 in water vapour containing environments[END_REF][START_REF] Surman | gas phase transport in the oxidation of Fe and steels[END_REF][START_REF] Quadakkers | steam oxidation of ferritic steelslaboratory test kinetic data[END_REF]. This can affects growth stresses of oxide which may have a significant contribution in spallation phenomenon [START_REF] Schütze | parameters determining the breakaway oxidation behaviour of ferritic martensitic 9%Cr steels in environments containing H 2 O[END_REF]. However, characteristics of oxide scales formed on Ni-30Cr-8Fe are similar to those formed on Ni-30Cr. This is probably due to the formation a continuous Cr-oxide in Ni-30Cr which acts as a barrier against the outward diffusion in the early stage and thus Fe addition does not influence the oxidation behaviour of this material. The purpose of this comparison is to give industrial projection of this present fundamental study. Specimens of Alloy600 were machined from pipes shaped by colddrawing, named as received specimens (AR). Secondly, these specimens were solution annealed in order to minimize to cold-work degree resulting from the fabrication process. Thus, weight gain increases substantially after Solution Annealing (SA) (see Fig. 71). Calculated n-value (Fig. 72) confirms the acceleration of oxidation kinetics after the solution annealing of specimens as well. For this comparison WG data of solution annealed specimens is taken into account in order to uncouple the effect of the cold-work. n-value of alloy600-SA is greater than that of Ni-14Cr-8Fe. This can be attributed to the difference in the chemical composition and error measurements. However, similar characteristics of both oxide scales formed on Ni-14Cr-8Fe and Alloy600-SA are observed (Fig. 73). Gaps appear at outer oxide/metallic nickel interface (Fig. 74 a) and breakaway oxidation (Fig. 74 b) occurs in Alloy600-SA. It seems that the transport of hydrogen containing species and/or their segregation to the outer oxide/metallic nickel interface [START_REF] Galerie | mechanisms of chromia scale failure during the course of 15-18Cr ferritic stainless steel oxidation in water vapour[END_REF][START_REF] Jianian | high-temperature oxidation of Fe-Cr alloys in wet oxygen[END_REF] accompanied by vacancy condensation [START_REF] Quadakkers | steam oxidation of ferritic steelslaboratory test kinetic data[END_REF] induce initially porous oxide scale and its failure as result of scale cracking. Whereas, WG measurement (Fig. 71) does not show weight loss, indicating that breakaway oxidation type is limited and does not affect significantly the overall oxidation rate. Cold-work existing in Alloy600-AR promotes the growth of continuous and compact Crrich layer (Fig. 73) which is in good agreement with WG measurements discussed above.

It is demonstrated, based on this comparison that this fundamental study conducted on model alloys can be projected on the industrial material, such as Alloy 600 and Alloy 690. Hence, small deviation in the oxidation behaviour between those materials is deduced.

Summary

The effect of chromium content and iron addition on the oxidation behaviour of model nickel base alloys in steam (700°C, 500h) was emphasized in this chapter. Attention was given to surface preparation to uncouple the effect of the alloying element and surface coldwork. The following conclusions were achieved:

 Reducing the hardened layer by mirror polishing is an accurate method to emphasize the influence of alloying elements on the oxidation rate. While, electro-polishing results probably in prior establishment of Cr-oxide layer. This affects significantly the oxidation rate in the early stage of oxidation. However, SEM cross section views show similar oxide morphology, indicating that the hardened layer is efficiently reduced by mirror polishing, e.g. alumina powder down to 0.3 µm. It is important to highlight that slight cold-wok remains in the subsurface after these surface finishes.

 In agreement with the literature, oxidation rate of model alloys studied in the present investigation indicated that increasing the Cr content enhanced the oxidation resistance. This is attributed to the increase of volume fraction of nodular oxide and its coalescence into continuous barrier layer.

 Weight gain measurements and a meticulous characterisation of oxide scales elucidated the presence of an optimal Cr content (24 wt.%). Increasing Cr content to the optimal value allowed the growth and the maintenance of continuous Crenriched oxide. When the Cr content is larger than the optimal value a transition from internal to external diffusion and the appearance of Cr depleted zone beneath the rate limiting layer occurred simultaneously. Therefore, it is assumed that the Crcontent beneath this layer is not enough for its maintenance and consequently the  The oxide scale formed on Ni-Cr-Fe systems [START_REF] Silvestri | Eddystone Station, 325 MW Generating Unit 1-A Brief History[END_REF][START_REF] Carette | Analysis and TEM examination of corrosion scales grown on Alloy 690 exposed to pressurized water at 325°C[END_REF][START_REF] Machet | XPS study of oxides formed on nickel-base alloys in high temperature and high pressure water[END_REF], in water vapor containing environment, exhibit pores, condensation of pores and gaps which is not observed in Ni-Cr systems in the present study due to the formation of more compact NiO. This can be explained on the basis of higher decomposition pressure of NiO compared with Fe-oxides, meaning that oxygen bridges are maintained between the oxide and metal [START_REF] Boudin | Analytical and electrochemical study of passive films formed on References nickel-chromium: Influence of the chromium bulk concentration[END_REF]. Thus, the volatilisation of Ni-oxide which may cause the formation of pores does not occur. Since, pores are not observed in the internal zone as well, it is believed that NiO plays important role as barrier layer, preventing the increase of oxygen partial pressure and thus chromium evaporation. Hence, the formation of Whiskers [START_REF] Robertson | the mechanism of high temperature aqueous corrosion of stainless steels[END_REF] is not observed indicating that evaporation of Cr-species is minor or does not occur in Ni-Cr systems oxidised in steam at 700°C.

 Oxidation rate in grain boundaries zone is depressed and thus it is suggested that grain fining can be an effective measure to improve the oxidation resistance in steam environment. In fact, the grain size becomes finer with increasing Cr content, synergetic effect between grain size and Cr content takes place in the oxidation process. This is linked to the fact that grain boundary provide fast diffusion path for chromium.

 Fe addition (8 wt.%) degrades Ni-base alloys properties in term of oxidation resistance. The presence of Fe accelerates significantly the oxidation rate of Ni-22Cr as the equilibrium between inward and outward diffusion of species takes place at this Cr level. However, the presence of Fe does not alter the oxidation behaviour of Ni-30Cr due to the establishment of Cr-oxide layer in the early stage which acts as barrier against the outward diffusion of Fe cation. Secondly, Fe diffuses to oxide/environment interface, tends to form Fe-oxide, the ejection of cation vacancies occurred subsequently and thus relaxation of compressive stress is achieved by annealing process. Finally, Fe addition causes the formation of pores in the outer layer probably due the evaporation of Fe-oxide and condensation of cation vacancies.

 The comparison between the oxidation behaviour of Ni-14Cr-8Fe and Alloy600-SA demonstrates that this fundamental study conducted on model alloys can be projected on some industrial materials. Hence, small deviation in the oxidation behaviour between those tested materials is deduced.

Final conclusion

Chapter VI

Final conclusion

The influence of the chemical composition of Ni-based alloys, especially chromium content, on their aqueous corrosion and steam oxidation behaviour is elucidated in this thesis. Attention was given to surface preparation to minimize the possible effect of surface coldwork. The main conclusions are summarized below, along with the key contribution.

Aqueous corrosion

The growth of more uniform and protective passive film (ultra-thin film) prevails with minimizing surface cold-work in primary water. Electro-polishing caused probably prior Crenrichment on the surface which may alter the oxidation process in the early stage. This phenomenon would improve the oxidation resistance resulting in synergetic effect between chromium content and surface treatment. Thus, mirror-polishing (using colloidal silica) is suggested as more appropriate method to uncouple the effect of surface cold-work and chromium content.

In primary water, it is suggested that 20 % Cr is the critical amount of chromium required to form and maintain protective scale on cold-work free surface of Ni-Cr systems. Hence, it is assumed that oxide films formed on Ni-xCr alloys (x > 20 %) being unchanged in physicochemical properties.

The analytical approach, using electrochemical technics at room temperature, emphasized the existence of optimum threshold of chromium content (26 wt.%) in terms of aqueous corrosion resistance. Increasing Cr content more than 26 wt.% has a detrimental effect on the properties of the passive film. This probably due to the fact that the surface reactivity is increased. The discrepancy between the critical chromium threshold identified in primary water (20 wt.%) and that in acidic solution (26 wt.%) is probably due to test conditions, that both solution and temperature. Iron addition (8 wt.%) led to the degradation of corrosion resistance. In fact, alloying Ni-Cr alloys with Fe may change the nature, the structure and the semi-conductor features of the passive films.

Steam oxidation

In agreement with the effect of surface cold-work on the aqueous corrosion in primary water, reducing the hardened layer by mirror polishing (using alumina powder) is conducted in steam oxidation test. The oxidation rate investigated in the present study indicated that increasing the Cr content enhanced the oxidation resistance. This is attributed to the increase of volume fraction of nodular oxide and its coalescence into continuous barrier layer. Weight gain measurements and a meticulous characterisation of oxide scales elucidated the presence of an optimal Cr content (24 wt.%). Increasing Cr content to the optimal value allowed the growth and the maintenance of continuous Cr-enriched oxide.

When the Cr content is larger than the optimal value a transition from internal to external diffusion and the appearance of Cr depleted zone beneath the rate limiting layer occurred simultaneously. Therefore, it is assumed that the Cr-content beneath this layer is not enough for its maintenance and consequently the growth of defective oxide takes place. Oxygen penetrates to the substrate through metallic nickel zone and the formation of Croxide precipitates ensues.

Fe addition (8 wt.%) degrades Ni-base alloys properties in term of oxidation resistance. The presence of Fe accelerates significantly the oxidation rate of Ni-22Cr as the equilibrium between inward and outward diffusion of species takes place at this Cr level. However, the presence of Fe does not alter the oxidation behaviour of Ni-30Cr due to the establishment of Cr-oxide layer in the early stage which acts as barrier against the outward diffusion of Fe cation. Secondly, Fe diffuses to oxide/environment interface, tends to form Fe-oxide, the ejection of cation vacancies occurred subsequently and thus relaxation of compressive stress is achieved by annealing process. Finally, Fe addition causes the formation of pores in the outer layer probably due the evaporation of Fe-oxide and condensation of cation vacancies.

Oxidation rate in grain boundaries zone is depressed and thus it is suggested that grain fining can be an effective measure to improve the oxidation resistance in steam environment. In fact, the grain size becomes finer with increasing Cr content, synergetic effect between grain size and Cr content may takes place in the oxidation process. This is linked to the fact that grain boundary provide fast diffusion path for chromium.

The comparison between the oxidation behaviour of Ni-14Cr-8Fe and Alloy600-HT demonstrates that this fundamental study conducted on model alloys can be projected on some industrial materials. Hence, small deviation in the oxidation behaviour between those tested materials is deduced.

Key contribution

This work contributes in the understanding of the effect of alloying elements on the hightemperature oxidation of Ni-based alloys by avoiding the synergetic effect with surface coldwork. This pioneer study emphasizes that the optimization of Cr content is more appropriate method for improving the corrosion resistance of nickel base-alloys and thus increasing the lifetime of structural compounds and enhance their integrity in high temperature environments. Hence, this study revealed the existence of optimal Cr content for best corrosion resistance. Increasing Cr content more than the optimal amount led to the degradation of the protective scale properties.

Future work

To investigate the existence of optimum chromium content in primary water in terms of corrosion resistance, electrochemical measurement in-situ in autoclave is required. Hence, the resulting oxide scales on Ni-based alloys in this environment are ultra-thin films (<10 nm). Evaluation of the passivation characteristics in the early stage, by means of local electrochemical probe, must be carried out to understand the degradation of the protectiveness of the passive film, i.e. the corrosion resistance, as chromium content is increased more than the optimal amount. It is suggested that increasing chromium content more than the optimal amount results in promoted active dissolution of chromium atoms and thus its amount decreases in the passive film. Concentration of dissolved metal ions in the solution must be evaluated, that as a function of chromium content in the matrix. However, the effect of alloying elements on the growth mechanism, which may be the key issue, stills not clearly understood. Secondly, short time exposition tests to humid gas at 700°C, using thermogravimetry (TG), should be conducted to understand the oxidation mechanisms of studied materials, particularly Ni-30Cr, in the early stage. Based on these investigations, the proposed oxidation model of Ni-xCr (14 ≤ x ≤30 wt.%) alloys in superheated steam can be fully approved. This fundamental study is not dedicated to a particular application, hence synergetic degradations, such as stress corrosion cracking, are not considered. Additionally, further investigations on weldability, fabricability, thermal conductivity, etc must be conducted also to design new alternative structural material for a particular application. L'impact de l'état de surface sur le processus de corrosion et l'oxydation a été mis en évidence. Les polissages miroir et électrochimique ont été réalisés afin de découpler l'effet de l'écrouissage développé en subsurface, induit par la préparation de surface, et la composition chimique de l'alliage.

Improvement of the Corrosion and Oxidation

La teneur en chrome limite à partir de laquelle l'alliage a un comportement satisfaisant en corrosion a été déterminé à 20% dans le milieu primaire. Cependant les analyses électrochimiques ont décelé l'existence d'une teneur en chrome optimal à 26%. La cinétique d'oxydation des alliages modèles ainsi que la morphologie des oxydes formés sur ces matériaux dans le milieu vapeur surchauffée ont indiqué l'existence d'une teneur en chrome optimal à 24%. Une dégradation des propriétés des films d'oxydes a été observée en augmentant la teneur en chrome au-dessus de l'optimum. En résumé, ce travail se préoccupe de l'optimisation de la teneur en chrome, méthode plus adéquate, pour l'amélioration de la résistance à la corrosion et l'oxydation des alliages base nickel.

3 Fig. 1 .

 31 Fig. 1. Schematic view of the oxide scale that forms during the exposition of Ni-base alloys in PWR water.

Fig. 4 .

 4 Fig. 4. Growth model of oxides formed on stainless steel in high temperature water : a) in saturated solution, then b) corrosion-product-free water and c) in corrosion-product-free, then d) saturated solution [45].

Fig. 5 .

 5 Fig. 5. The release mechanism according to Gardey model [37].

Fig. 6 .

 6 Fig. 6. Schematic illustration showing transport of water vapour molecules through the scale and oxygen transfer across in-scale void via ''H 2 O-H 2 bridge'' [46].

Fig. 7 .

 7 Fig. 7. Schematic illustration showing proposed mechanism for transport of Fe from inner to outer part of the scale via volatile species Fe OH 2 (g) [46].

Fig. 8 .Fig. 9 .

 89 Fig. 8. Cross section microstructure and EPMA elemental mapping of C, Fe, Cr, and Si (brightness degree indicates distribution and concentration of elements) for the 650 °C/100 h 9Cr-1Mo ferritic steel: (a) in dry air and (b) steam [72].

Fig. 10 .

 10 Fig. 10. SEM micrograph of the oxide whisker formation on FeCr specimen grown for 70 h in H 2 /Ar containing 1 % water at 900 °C [61].

Fig. 11 .

 11 Fig. 11. Effect of O 2 and H 2 O content on the weight gain after 24 h oxidation of 9% Cr steel at 650°C in N 2 -H 2 O-O 2 gas mixture. Specimens were mirror polished prior to oxidation [46].

Fig. 12 .

 12 Fig. 12. Oxidation kinetics of Alloy C-4 exposed at 600 ≤ 1200°C, for 1-400 hr in steam [80].

Fig. 13 .

 13 Fig. 13. A comparison of the ln (parabolic rate constant K g ) vs. 1000/temperature for samples of Haynes 230 oxidized in air with those oxidized in humidified hydrogen [77].

Fig. 14 .

 14 Fig. 14. Partial pressure of primary volatile species calculated from each oxide at 1 atm total pressure: 0.5 atm O 2 , 0.5 atm H 2 O [70].

Fig. 15 .

 15 Fig. 15. Arrhenius plots of the evaporation rates of chromia in N 2 -19.7% H 2 O and N 2 -2.4% O 2 -19.7% H 2 O atmospheres [69].

Fig. 16 .

 16 Fig. 16. A plot of the lattice tracer self-diffusion data, ln (D Cr ) vs ln (𝑃 𝑂 2 ) at 1100°C [85].

Fig. 17 .

 17 Fig. 17. Weight change versus time during isothermal oxidation of a Ni-10Cr model alloy in various atmospheres at 1050°C [74].

Fig. 18 .

 18 Fig. 18. SEM cross-section images of the Ni-10Cr model alloy after 72 h isothermal oxidation in various atmosphere at 1050°C [74].

Fig. 19 .

 19 Fig. 19. Example of defect compositions in M 2 O 3 versus water vapor partial pressure at constant 𝑃 𝑂 2 ; numbers along line donates slopes [88].

Fig. 20 .

 20 Fig. 20. Conductivity of chromia vs. reciprocal absolute temperature of samples oxidized in air with different water vapor pressure at 900°C. The conductivity was measured in air containing 0.1 % H 2 O [89].

Fig. 21 .

 21 Fig. 21. SEM cross-section images of Ni-25Cr model alloy after isothermal oxidation at 1050°C in : (a) Ar-20%O 2 and (b) Ar-7%H 2 O [74].

Fig. 23 .

 23 Fig. 23. Weight gain of the 9% CrMo (left) and the 20%Cr-32%Ni steel (right) after oxidation for 1 h [94].

Fig. 24 .

 24 Fig. 24. Diffusion profiles of the 20%Cr-30%Ni steel with different surface finishes after 1 h oxidation in H 2 -H 2 O at 600°C [94].

Fig. 25 .

 25 Fig. 25. Distribution of the total mass fraction of aluminium along the diagonal of 2D mesh at time t = 60s [105].

Fig. 26 .

 26 Fig. 26. Surface and volume fraction of internal oxide as a function of depth on Ni-0.2%Cr (a) and Ni-5%Cr alloys at 950°C [107].

  b

Fig. 27 :

 27 Fig.27: Optical microscope observations of chemically Etched coupons: (a) Ni-14Cr and (b) Ni-30Cr.Table 2: Calculated grain size of studied materials using standard test method E112-96 (reapproved 2004). Materials Grain size (µm)

Fig. 28 :

 28 Fig. 28: Photo of specimens suspended in testing device: (a) PWR autoclave and (b) steam oxidation chamber.

Fig. 30 :

 30 Fig. 30: Schematic of the simulated PWR environment autoclave.

Fig. 31 :

 31 Fig. 31: Schematic description of Scanning Electron Microscope (SEM).

Fig. 32 :

 32 Fig. 32: Schematic representation of the electron beam/surface interaction.

Fig. 33 :

 33 Fig. 33: Schematic description of Scanning Transmission Electron Microscope (STEM).

Fig. 35 .

 35 Fig. 35. Hardness test performed on Ni-16Cr before the oxidation test, loading forces were: 0.1, 0.25, 0.5, 1, 2, 3, and 4 N simultaneously.

Fig. 36 .

 36 Fig. 36. Diffraction patterns of the base metal (orange) and the perturbed zone (green) of emery-polished Ni-16Cr exposed to PWR environment (320°C, 14 MPa, DH=30 cc/kg) for 450 hours.

Fig. 38 .Fig. 39 .

 3839 Fig. 38. SEM Surface observations of Ni-16Cr specimen (emery-polished) exposed to simulated PWR environment (320°C, 14 Mpa, DH=30 cc/kg) for 450 hours.

Fig. 40 .

 40 Fig. 40. SEM surface observation of Ni-Cr specimens (mirror-polished) exposed to simulated PWR environment (320°C, 14 Mpa, DH=30 cc/kg) for 500 hours.

Fig. 41 .

 41 Fig. 41. STEM-EDX line analysis of the oxide scale formed on Ni-16Cr (emery-polished) exposed to simulated PWR environment (320°C, 14 Mpa, DH=30 cc/kg) for 450 hours.

Fig. 42 .

 42 Fig. 42. Polarization curves of Ni-Cr alloys in 1 mol/L H 2 SO 4 electrolyte.

Fig. 43 .

 43 Fig. 43. Nyquist plots and the fitting (dashed lines) of the passive film formed on Ni-Cr alloys in 0.1 V/MSE.

Fig. 44 .

 44 Fig. 44. Polarization curves of Ni-Cr-Fe alloys in 1 mol/L H 2 SO 4 electrolyte.

Fig. 45 .

 45 Fig. 45. Nyuist plots and the fitting (dashed lines) of the passive film formed on Ni-Cr in 0.1 V/MSE and Ni-Cr-Fe alloys in 0.2 V/MSE.

Fig. 46 .

 46 Fig. 46. Electrical equivalent circuit used to fit the impedance data.

Fig. 47a .

 47a Fig. 47a. Chronoamperometric response of Ni-Cr alloys in 1M H 2 SO 4 at 100mV/MSE.

Fig. 47b .

 47b Fig. 47b. Chronoamperometric response of Ni-Cr-Fe alloys in 1M H 2 SO 4 at 100mV/MSE.

Fig. 48a .

 48a Fig. 48a. Mott-Schottky plots of the passive films formed on Ni-Cr alloys

Fig. 49 .

 49 Fig. 49. : Hardness test performed on as received Ni-16Cr, loading forces were: 0.1, 0.25, 0.5, 1, 2, 3, and 4 N simultaneously.

Fig. 50 :

 50 Fig. 50: Weight gain measurement for NiCr model alloys exposed to superheated steam at 700°C for 500 hours: (a) emery-polished (#2400), (b) mirror polished (c) Electro-polished.

Fig. 51 :Fig. 52 :

 5152 Fig. 51: SEM observations of surfaces and cross section of Ni-16Cr oxidized in superheated steam at 700°C during 500h: (a) and (d) emery-polished ,(b) and (c) mirror polished, (c) and (f) electro-polished specimens.

Fig. 53 :

 53 Fig. 53: Summary of n-values considering a power growth law of the oxide scale: (a) mirrorpolished and (b) electro-polished specimens.

Fig. 54 .

 54 Fig. 54. SEM surface observations of oxidized Ni-Cr specimens in superheated steam at 700°C for 500 h: (a) mirror-polished specimens and (b) electro-polished specimens.

Fig. 55 .

 55 Fig. 55. SEM surface observations of oxidized Ni-16Cr (mirror-polished specimen) in steam at 700°C during 30 hours: (a) tilt = 0° and (b) tilt = 70°.

Fig. 56 .

 56 Fig. 56. SEM micrographs of metallographic cross-sections of for mirror polished specimens exposed to superheated steam at 700°C for 500 hours.

Fig. 57 .Fig. 58 .

 5758 Fig. 57. SEM micrographs of metallographic cross-sections of electro-polished specimens exposed to superheated steam at 700°C for 500 hours.

Fig. 59 .Fig. 60 .

 5960 Fig. 59. STEM/EDX line-scan profile of Ni-24Cr (mirror polished surface) exposed to superheated steam at 700°C for 500 hours.

Fig. 61 .

 61 Fig. 61. FIB cross section of Ni-16Cr observed using SEM with tilt 70° (mirror polished surface) exposed to superheated steam at 700°C for 500 hours.

Fig. 62 .

 62 Fig. 62. STEM/EDX line-scan profile of Ni-16Cr (mirror polished surface) exposed to superheated steam at 700°C for 500 hours.

Fig. 63 .Fig. 64 .

 6364 Fig. 63. Grain size of studied materials as a function of Cr content calculated using standard test method E112-96 (reapproved 2004).

Fig. 65 .

 65 Fig. 65. Schematic representation of the oxidation behaviour of Ni-Cr model alloys exposed to superheated steam at 700°C for 500 hours as a function of Cr-content in Ni-xCr: (a) x < 24 wt.%, (b) 24 ≤ x ≤ 26 wt.% and (c) x > 26 wt.%.

Fig. 66 .

 66 Fig. 66. Weight gain measurement for Ni-Cr and Ni-Cr-Fe model alloys, mirror polished specimens, exposed to superheated steam at 700°C for 500 hours.

Fig. 67 .

 67 Fig. 67. Calculated n-values considering a power growth law of the oxide scale.

Fig. 68 .Fig. 69 :

 6869 Fig. 68. SEM surface observation of oxidized Ni-Cr and Ni-Cr-Fe specimens in superheated steam at 700°C for 500h.

Fig. 70 .

 70 Fig. 70. : SEM-EDS line-scan profile of Ni-14Cr-8Fe (mirror polished with alumina powder down to 0.3 µm) exposed to superheated steam at 700°C for 500 hours.

4 .

 4 Oxidation behaviour of industrial Alloy 600 and model alloy (Ni-14Cr-8Fe)

Fig. 71 .

 71 Fig. 71. Weight gain measurement for Ni-14Cr-8Fe and Alloy 600, mirror polished specimens, exposed to superheated steam at 700°C for 500 hours.

Fig. 72 .

 72 Fig. 72. Calculated n-values for Ni-14Cr-8Fe and Alloy600, as received (AR) and heat treated (HT) considering a power growth law of the oxide scale.

Fig. 73 .Fig. 74 .

 7374 Fig. 73. SEM micrographs of metallographic cross-section of for mirror polished specimens, Ni-14Cr-8Fe and Alloy600 (as-received and heat-treated), exposed to superheated steam at 700°C for 500 hours.

  oxide takes place. Oxygen penetrates to the substrate through metallic nickel zone and the formation of Cr-oxide precipitates ensues.

  Resistance of Ni-based Alloys by Optimizing the Chromium ContentFethi HAMDANI Résumé Cette étude fondamentale est dédiée à la compréhension de l'influence de la composition chimique, notamment la teneur en chrome, des alliages base de nickel sur leur mécanismes de corrosion et d'oxydation. La corrosion sous contrainte intergranular (CSCIG) est un mode de dégradation qui affecte de nombreux alliages au sein des réacteurs à eau pressurisé. En particulier, les alliages base nickel tubes des générateur de vapeur (GV). La sensibilité à la CSC est désormais dépend de la teneur en chrome, ce qui a conduit au remplacement de l'alliage 600 (Ni-16Cr-9Fe) par l'alliage 690 (Ni-30Cr-9Fe). Cependant le bon comportement de l'alliage 690 en termes de résistance à la corrosion restes mal défini.L'objective de cette thèse est double : i) déterminer l'effet de la teneur en chrome, ii) contribuer à la compréhension de l'effet de fer étant un élément d'addition sur la résistance à la corrosion et l'oxydation généralisée des alliages base nickel en milieu primaire assimilé et en vapeur surchauffée à 700°C. Par ailleurs, des analyses électrochimiques pertinentes dans la température ambiante ont été mené afin d'établir une corrélation entre les propriétés physiques de film passive susceptible de protéger le matériau et de la teneur en chrome. Des alliages modèles binaires Ni-Cr, à teneur de chrome varie entre 14 et 30 % en poids, des alliages ternaires Ni-Cr-8Fe et l'alliage 600 ont été étudies. L'aspect expérimental de cette étude repose sur des techniques conventionnelles: SEM, STEM, EDX, Potentiodynamique, EIS, Chronoamperometrie, Mott-Schottky. La cinétique d'oxydation en vapeur surchauffée a été déterminée en mesurant l'apport de masse.

Table . 1

 . . Properties (composition and morphology) of oxide scales formed on nickel base alloys in primary water.

	690	325°C	SIMS, XPS,	30	Outer layer : NiFe 2 O 4 (stainless	[26]
		[H 2 ]= 33 cc/Kg	GIXRD,		steel autoclave) and NiCr 2 O 4 (Ti
		2160 h	TEM		autoclave)
					Inner layer: Cr 2 O 3
	690	325°C	STEM,EDX,	30	Outer layer : Ni (1-x) Fe (2+x) O 4 +	[38]
		P(H 2 )=0.29±0.02	SEM		Ni(OH) 2 , y H 2 O
		bar			Inner layer : Ni (1-x) Fe x Cr 2 O 4
		164 and 858 h			Interface inner layer : nodular
					Cr 2 O 3
	690	325°C	TEM	30	Outer layer : crystallite of NiFe 2 O 4	[41]
		P(H 2 )=0.29 bar			Inner layer : (Ni,Fe)Cr 2 O 4
		66-858			-Nodules of Cr 2 O 3 dispersed at
					alloy/oxide interface
	Ni-Cr 360°C	TEM-EDX,	5-30	 Cr content < 15 wt.%	[33]
		P(H 2 )= 0.17 bar	SEM		Outer layer : NiFe 2 O 4 + Ni-rich
		3000 h			filament, few microns
					Inner layer : Cr-rich oxide (25
					wt.% Cr), 100-200 nm
					 Cr content > 20 wt.%
					Outer layer: Crystallites (50 wt.%
					Cr), 50 nm
					Inner layer: Cr-rich oxide (90
					wt.%), 5-10 nm.
	600	360°C	XPS,STM	16	Outer layer: Ni(OH) 2	[39]
		[H 2 ] = 35 cc/kg			Inner layer: Cr(OH) 3 + Cr 2 O 3
		0.4-8.2 min
	600	360°C	SEM,TEM,	16	Outer layer : NiFe 2 O 4	[22]
		P(H 2 )=0.3 bar	SIMS		Inner layer: Ni (Cr,Fe) 2 O 4 + Cr-
		300 h			enriched layer (5 nm)
	690	325°C	SEM,TEM,	30	Outer layer: NiFe 2 O 4 + Ni(OH) 2	[40]
		P(H 2 )=0.29 bar	XPS		Inner layer : Ni (1-x) Fe (x+y) Cr (2-y) O 4
		858 h			-Presence of nodular Cr 2 O 3 in
					Metal/inner layer interface
	Alloy	Test conditions	Technique Cr wt.%	Resulting oxides	Ref.
	600	325°C	SEM,	16	Outer layer : NiFe 2 O 4	[37]
	690	[H 2 ]= 25-30 cc/Kg	EDAX,	30	Inner layer : Cr-rich layer
		> 48 H	XPS, SDL
	600	360°C	TEM, SEM	16	Outer layer: NiFe 2 O 4	[22]
	690	P(H 2 )= 0.3 MPa	SIMS	30	Inner layer : mixt spinel	[35]
		300 h			Ni(Fe,Cr) 2 O 4
					Metal/oxide inner layer: Cr-oxide
					(5 nm)

  In general, oxide phases which can formed on Ni-base alloys in high temperature oxidation are oxide (such as, Cr 2 O 3 , NiO) or/and spinel oxides (such as, NiCr 2 O 4 , (Cr,Al) 2 O 4 ). But the formation of volatile hydroxides is not reported in the oxidation of Ni-base alloys. Chromium is the major alloying element which influences the nature and the chemical composition of oxide scales. Moreover, alloying Ni-base alloys with other elements, such as Mn or Nb, has a significant effect on the nature of oxides as well. The oxide scale formed on Ni-base alloys in relatively high temperature oxidation consists of a duplex-layer: Inner layer : compact and/or precipitates (Cr 2 O 3 , NiCr 2 O 4 )

	NiCr	Ar-4%H 2 -7H 2 O	SEM	25	Cr 2 O 3		[102]
		1050°C
		72h
	Ni-16Cr-	He-O 2	SEM	16	Inner layer : Cr 2 O 3	[92]
	9Fe	950°C			Outer	layer :	Ni-rich
		1000h			cristallites
	SY 625 Ar-7.5 H 2 O	SEM	22	Outer layer : Cr 2 O 3	[103]
		900-1000°C			Inner layer : CrNbO 4
		48h
	Alloys	Test conditions	Technique Cr (wt.%) Resulting oxides	Ref.
	Ni-Cr	Ar-7H 2 O	SEM	10-25	Outer layer: NiO	[74]
		1050°C			Inner layer: NiCr 2 O 4 +Cr 2 O 3
		72h
	Hastello	Steam	XRD	15	Outer layer: MnCrO 3 +	[80]
	y	1200°C			NiCr 2 O 4 + NiCrMnO 4 +
	C-4	400h			FeCr 2 O 4
					Inner layer : Cr 2 O 3
	Haynes 230	Wet hydrogen: P O2 (H2/H2O) =3.3 10 -21	XRD	26	Cr 2 O 3 + Mn 1.5 Cr 1.5 O 4	[77]
	Hastello	800°C		24	Cr 2 O 3 + FeCr 2 O 4
	y X	1000 hours
	Ni-Cr-Al Oxygen 0.1 atm	SEM	2-30	 Low Cr content	[101]
		1000-1200°C			Outer layer: NiO + Ni
		20h			(Cr,Al) 2 O 4
					Inner layer : Cr 2 O 3 + Al 2 O 3
					 High Cr content
					Outer layer : Cr 2 O 3
					Inner layer : Al 2 O 3

Table. 2. brief summary of the nature of the oxide scales formed on Ni-base alloys in both water vapor containing and dry atmospheres at high testing temperatures.  Outer layer : Ni-rich oxide (NiO) 2.2.3. Oxidation models 2.2.3.1 Wagner Model

  2.2.3.2 E. Feulvarch et al. model E. Feulvarch et al.

Table 1 :

 1 Chemical composition (wt %) of materials used in the present study.

	Materials	C	Mg	Si	P	S	Cr	Mn	Fe	Ni
	14Cr	0.006	0.008 <0.008	0.002	<0.001 13.89	0.049	0.014	Bal.
	16Cr	0.006	0.008 <0.001	0.002	<0.001	15.7	0.049	0.015	Bal.
	18Cr	0.003	0.003	0.005	0.001	<0.001 17.73	0.047	0.017	Bal.
	20Cr	0.008	0.005	0.009	0.001	<0.001 19.79	0.045	0.018	Bal.
	22Cr	0.004	0.003	0.007	0.001	<0.001 21.87	0.046	0.019	Bal.
	24Cr	0.004	0.003	0.008	0.001	<0.001 23.76	0.047	0.027	Bal.
	26Cr	0.003	0.008	0.007	0.001	<0.001 25.51	0.046	0.022	Bal.
	28Cr	0.006	0.001	0.006	0.001	<0.001 27.55	0.045	0.024	Bal.
	30Cr	0.003	0.002	0.012 <0.0001 <0.001 29.67	0.044	0.029	Bal.
	14Cr-8Fe	<0.001	0.001	0.02	0.001	<0.001	14.69	0.05	7.81	Bal.
	16Cr-8Fe	<0.001	0.001	0.02	0.001	0.001	15.86	0.05	7.82	Bal.
	22Cr-8Fe	<0.001 0.001	0.02	0.001	0.001	21.58	0.05	7.84	Bal.
	30Cr-8Fe	<0.001 0.002	0.02	0.001	0.001	29.35	0.05	7.85	Bal.
	Alloy 600	0.15	-	0.5	-	0.15	15.5	1.0	7	Bal.

Table 2 :

 2 Calculated grain size of studied materials using standard test method E112-96 (reapproved 2004).

	Materials	Grain size (µm)
	14Cr	179.6
	16Cr	189.06
	18Cr	110.44
	20Cr	106.8
	22Cr	85.51
	24Cr	86.37
	26Cr	89.8
	28Cr	71.42
	30Cr	75.5
	14Cr-8Fe	108.94
	16Cr-8Fe	95.26
	22Cr-8Fe	91.16
	30Cr-8Fe	72.86
	Alloy 600	72.8

Table 3 .

 3 Calculated equivalent circuit elements obtained by using EC-Lab software.

	EC element	16Cr 16Cr-8Fe	18Cr	22Cr	22Cr-8Fe 26Cr	30Cr	30Cr-8Fe
	0.694 Q(μF.s α-1. cm -2 ) 13.454 R s (Ω.cm 2 )	0.565 32.91	0.653 0.598 14.725 15.327	0.682 28.44	0.539 12.267 16.836 0.625	0.614 19.78
	α	0.935	0.983	0.955 0.959	0.924	0.977	0.953	0.995
	R t (10 5 Ω.cm 2 ) 3.564 R d (10 4 Ω.cm 2 ) 2.164	0.241 1.069	2.269 2.154 1.592 1.634	1.772 1.565	5.475 3.825	4.673 2.517	3.569 1.957
	τ d (s) χ 2 (10 -3 )	96.86 7.342	96.25 8.759	94.49 97.91 2.319 3.259	97.58 1.348	97.52 1.389	95.67 2.876	98.36 4.

Table 3 .

 3 Charge carriers densities and flat band potentials of passives films.

	Material	16Cr	16Cr-8Fe	18Cr	22Cr	22Cr-8Fe	26Cr	30Cr	30Cr-8Fe
	N q (10 23 cm -3 ) 2.93	3.24	6.14	19.1	21.7	1.4	1.88	2.23
	E FB (mV MSE )	470	550	580	610	610	620	570	610

  and 64, respectively, is estimated according to STEM/EDX analysis. The O/Cr atomic ratio of the Crenriched layer formed in Ni-24Cr is estimated at 1.43 and that formed in Ni-30Cr at 1.85. As stoichiometric chromia may exhibit O/Cr ratio of 1.5, these results indicate the growth of a nonstoichiometric and defective oxide in Ni-30Cr. In the present test conditions, i.e. steam and test temperature (700 °C), cation vacancies (𝑉 𝐶𝑟 ′′′ ) are the dominant point defect in the rate-limiting layer[START_REF] England | Virkar, oxidation kinetics of some nickel-based superalloy foils in humidified hydrogen and electronic resistance of the oxide scale formed, Part II[END_REF][START_REF] Young | Wit, n-Type behavior of chromium (III) oxide[END_REF][START_REF] Young | Wit, the oxygen partial pressure dependence of the defect structure of chromium (III) oxide[END_REF]. Whereas, 𝑉 𝐶𝑟 ′′′ in Ni-30Cr are not annealed efficiently at Croxide layer/metallic nickel interface and thus 𝑉 𝐶𝑟 ′′′ concentration increases. This result in fast transport of point defects due to the increase of concentration gradient and consequently the conductivity of Cr-oxide layer increases. Meaning oxidation resistance is degraded. In respect of the present study the optimal Cr content for the presented exposure environment is identified as 24 wt. %, where the oxidation rate is notably slowed and a protective continuous barrier layer is well-established.

Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication/2015ISAL0012/these.pdf © [F. Hamdani], [2015], INSA de Lyon, tous droits réservés

Acknowledgements

This work has been started in MATEIS-CorrIS laboratory in INSA de Lyon (France). So first I would like to give my honest appreciation to my advisor Prof. Bernard Normand for offering me this project and giving me guidance. I wish to acknowledge also Dr. Benoit Ter-Ovanessian, assistant professor in INSA de Lyon, for his help and support to shape this work into its final form. This thesis has been enrolled in the doctoral double degree program with Tohoku University (Japan). My Japanese advisor Prof. Yutaka Watanabe welcomed me warmly and supported me so much during my stay in his laboratory. Thank you so much for