) have been compared through a surface science approach involving Low-Energy Electron Diffraction (LEED), X-ray photoemission (XPS), Scanning Tunnelling Microscopy (STM) and Grazing Incidence X-ray Diffraction (GIXD).

) surfaces requires specific cautions in measurement protocols.

According to photoemission, if sputtered surfaces have a composition close to the nominal one, all clean surfaces of Fe 0.85 Al 0.15 are prone to intense Al segregation in the temperature range 700-1000 K. After 1000 K, a steady state regime is reached and the impacted depth is around 2-3 nm with an average composition close to the ordered CsCl B 2 structure in agreement with the tendency of long-range order in Fe-Al. But on a structural point of view, all the surfaces behave in different ways. The (110) surface develops a 2 nm large pseudohexagonal reconstruction that is imaged in STM and that corresponds to an incommensurate in-plane modulation of the lattice parameter. The (100) surface is always (1 × 1) terminated with a marbled-like appearance assigned to an electronic and chemical contrast. At last, despite a smoothing at large scale, the (111) surface is locally rough with the development of nanometric-size three-fold protrusions/pits due to segregation-induced faceting involving (111) vicinal surfaces. The segregation trend is rationalised through ab initio calculations.

The oxidation with O 2 of all the surfaces in the Knudsen's regime at high temperature leads to a selective oxidation of Al and to the growth of alumina films of self-limited thickness

in the range of 1-2 nm. Iron stays metallic. Covering oxides are found on [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] and [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF] faces while the growth is more 3D on [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF]. Photoemission analysis of the profile of segregation shows quite distinct behaviours. Subsurfaces of [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] and [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] are depleted in Al and adopt the D0 3 structure. On the other hand, the profile of segregation is insensitive to oxidation on (100) face. All the experimental fingerprints of the oxide at [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF] and [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] orientations are very close to previous findings in particular on NiAl. At [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] surface, a two-domain alumina grows with a (18.5 × 10.5) Å2 nearly rectangular rotated unit cell as seen by diffraction with a nearly perfect (2 × 1) ox matching. While the average composition of Al 2 O 2.6 , the two oxide Al 2p components and the unit cell are twin of those of the oxide at NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF], much fewer anti-phase domain boundaries are observed probably due to the composition freedom of the subsurface provided by the random alloy. The oxide film at [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF] surface presents two (2 × 1) domains in the form of nanometric-sized orthogonal stripes; a likely explanation is the formation of a distorted θ-Al 2 O 3 structure. The lack of any oxide ordering at [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] surface is assigned to the strong tendency of this orientation to nanofacet.

Des cristaux de Fe 0.85 Al 0.15 de composition ferritique (alliage aléatoire de type A 2 ) ont été choisis comme système modèle pour étudier la dépendance en orientation de la ségrégation et de l'oxydation qui se produisent à la surface d'aciers industriels alliés à l'Al durant le recuit de recristallisation avant la galvanisation. Les trois surfaces de bas indices [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF], [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF] et [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] ont été comparées dans une approche de science des surfaces impliquant la diffraction d'électrons lents (LEED), la photoémission X (XPS), la microscopie à effet tunnel (STM) et la diffraction rasante de rayons X (GIXD) La ségrégation de carbone et la contamination à partir du vide ont constitué deux difficultés majeures à surmonter. Lors d'un recuit de la surface [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF], une ségrégation transitoire de carbone a été observée sous forme de bandes auto-orgnisées orientées suivant la direction [001] et séparées par ∼ 5 nm. Deux types de signature C 1s ont été mises en évidence et attribuées à du carbone graphitique et chemisorbé. La quantification XPS de la première suit le maximum de taux de couverture des bandes à ∼ 850 K avant de décroitre à plus hautes températures au seuil de ségrégation de l'Al. La forte réactivité des surfaces [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF] et [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] requiert des précautions spécifiques en termes de protocoles expérimentaux. D'après la photoémission, si les surfaces bombardées ont une composition proche de la valeur nominale, toutes les surfaces de Fe 0.85 Al 0.15 sont sujettes à une intense ségrégation d'Al dans la gamme de température 700-1000 K. Après 1000 K, un régime stationnaire est atteint et la zone affectée est de 2-3 nm d'épaisseur avec une composition proche de l'alliage ordonné de structure CsCl B 2 . Mais d'un point de vue structural, toutes les surfaces se comportent différemment. La surface [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] développe une reconstruction pseudo-hexagonale de 2 nm qui est imagée par STM et qui correspond à une modulation incommensurable de paramètre de maille. L'orientation [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF] est toujours terminée (1×1) avec une apparence marbrée à l'échelle atomique ce qui est attribué à un contraste électronique et chimique. Enfin, en dépit d'un lissage à grande échelle, le surface [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] est localement rugueuse et présente des structures nanométriques triangulaires dues à un facetage induit par la ségrégation sous forme de surfaces [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] vicinales. La tendance de ségrégation est rationalisée au travers de calculs ab initio.

L'oxydation par O 2 de toutes les surfaces en régime de Knudsen à haute température conduit à une oxydation sélective d'Al et à la croissance de films d'alumine d'épaisseur autolimitée de 1-2 nm. Le fer reste métallique. Des oxydes couvrants sont trouvés sur les faces [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] et [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF] alors que la croissance est plus 3D sur la face [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF]. L'analyse par photoémission du profil de ségrégation montre des comportements assez distincts. Les sous-surfaces des orientations [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] et [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] sont déplétées en Al et adoptent la structure D0 3 . D'un autre côté, le profil de ségrégation est insensible à l'oxydation sur la face [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF]. Toutes les caractéristiques expérimentales des oxydes sur les orientations [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF] et [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] sont très proches des résultats de la litérature en particulier sur NiAl. Sur la surface [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF], d'après la diffraction rasante, l'alumine croit sous forme de deux domaines ayant une maille de (18.5 × 10.5) Å2 presque rectangulaire mais tournée avec une concidence (2 × 1) ox presque parfaite avec le substrat. Alors que la composition moyenne Al 2 O 2.6 , la présence de deux composantes Al 2p oxyde et la cellule élémentaire sont des caractéristiques jumelles de l'oxyde sur NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF], beaucoup moins de parois d'anti-phase sont observées probablement en raison de la liberté de composition de la sous-surface permise par l'alliage aléatoire. L'oxyde à la surface (100) comporte deux domaines (2 × 1) sous forme de bandes nanométriques; un explication plausible est la formation d'une d'alumine de structure θ. L'absence d'ordre à la surface [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] est attribuée à la forte tendance de cette orientation à se nano-facetter.

INTRODUCTION

The industrial context

The environmental imperative of reduction of CO 2 emission (Fig. 1.1-a) leads the automotive industry to decrease vehicle mass [1]. For example, according to weight saving plan of the PSA car manufacturer, the reduction should be of 50 kg by 2020 with respect to 2015 for B class vehicles. In response to that challenge, steel industry develops generations of new highly alloyed steels that show improved formability and crash worthiness compared to the conventional grades. The use of high strength thinner gauge steel sheet results in reduction of the car weight and the fuel or electrical consumption while keeping mechanical properties and safety intact at an affordable price. A whole family of so-called Advanced High-Strength Steel (AHSS) (Fig. 1.1-b) has been developed in the recent years with a large range of mechanical properties that can be tuned with the chemical composition and multiphase microstructures resulting from precisely controlled heating and cooling processes [1]. Next to silicon and manganese, aluminium is one of the often used alloying elements for new highly alloyed steel grades. It leads not only to the improvement of elasticity limits, but also to the increase of stiffness performance due to its low density.

The manufacturing of AHSS products for automotive industry challenges industrial operations in each process step. During production process, before hot-dip galvanizing (Fig. 1.1-c), cold rolled strips undergo recrystallization annealing at ∼ 1070 K in order to remove remaining stresses and metal texture produced during the rolling operation. Despite the reducing atmosphere of the furnace (N 2 -5 vol.% H 2 ) which is suitable to thermodynamically prevent oxidation of iron, the alloying elements that are more prone to oxidation undergo oxygeninduced segregation at the surface leading to a steel sheet extensively covered by oxides such as alumina, silica or MnO x [4,[START_REF] Ollivier-Leduc | Nucleation and growth of selective oxide particles on ferritic steel[END_REF]. A strong industrial concern is that the bad wetting of these oxides by zinc [START_REF] Giorgi | Influence of annealing treatment on wetting of steels by zinc alloys[END_REF] degrades the efficiency of galvanization which is the historical method to prevent corrosion; zinc being less noble or anodic than iron, it sacrificially corrodes to protect the steel substrate. Galvanization of oxide-covered steel faces a new paradigm since it Figure 1.1: a) Worldwide convergence of objectives for CO 2 emission of cars per km [START_REF] Davis | Weight reduction, materials challenges and impact on paint process[END_REF]. b) Global formability diagram for today's Advanced High-Strength Steel grades including a comparison to traditional low-strength and high-strength steels [1]. c) Scheme of the industrial process of hot-dip galvanization of steel sheets [3].

switches from what is close to a reactive interface with a bare iron surface1 to a high-energy interface with wide bandgap oxides.

In order to improve the coatability of the steel strips, the production process can be modified via two complementary strategies which consist in (i) optimizing the conditions of the galvanization or using physical vapor deposition techniques to control adhesion at the zinc/oxide interface [3,[START_REF] Cavallotti | Role of surface hydroxyl groups on zinc adsorption characteristics on α-Al 2 O 3 (0001) surfaces: first-principles study[END_REF][START_REF] Le | First-principles study on the effect of pure and oxidized transition-metal buffers on adhesion at the alumina/zinc interface[END_REF][START_REF] Cavallotti | New routes for improving adhesion at the metal/α-Al 2 O 3 (0001) interface[END_REF][START_REF] Le | Tuning adhesion at metal/oxide interfaces by surface hydroxylation[END_REF] and (ii) modifying the morphology and composition of the oxide layer to control upstream the surface oxidation of steel [3]. The present thesis is based on the second strategy which requires a precise knowledge of the physics and chemistry underlying the formation of the oxide layer.

The research strategy

In this fundamental work, a binary FeX alloy has been examined to pinpoint the behaviour of the alloying element X. It has been chosen to study samples containing aluminium at a given composition (15 atomic per cent of Al) in the form of Fe 0.85 Al 0.15 single crystals of different crystallographic orientations for the following reasons:

• FeAl alloy as a model of alloyed-steel : obviously complex on the material side through the presence of multiple elements and its polycrystalline structure, the oxidation of steel is also complicated by the gaseous environment in which it occurs. The reducing H 2 +N 2 atmosphere used for the recrystallization annealing contains many redox couples, in particular H 2 O/H 2 . A detailed analysis of alloyed steel being far out of grasp, a tractable alternative is to study binary FeX alloys and their oxidation with only one agent, namely here O 2 .

• Surface oxidation in the form of film: alloys containing either silicon or manganese are much less easy to model since the oxidation of silicon leads to amorphous oxides while the oxidation of manganese results in different oxides corresponding to the various valences of the element. Moreover, they often appear as oxide clusters and not covering films. Instead, the Al-alloyed iron is of interest since the oxidation of FeAl crystals leads to the growth of crystalline films of aluminium oxide at surfaces with thicknesses of a few nanometres [3] which makes the system adapted to the fundamental surface science approach that is foreseen herein.

• Application as light-weight alloys: generally speaking, iron aluminides are very promising light-weight alloys [START_REF] Deevi | Nickel and iron aluminides: An overview on properties, processing, and applications[END_REF] since aluminium, which is one of the alloying elements that improves the elasticity limit of steel, increases the stiffness (elasticity limit/density ratio) performance due to its low density. The subject thus relates to other scopes of application than the automotive industry, in particular the aircraft industry. Moreover, alumina films act as corrosion barriers at low and medium temperatures.

• Ferrite phase in both model alloy and steel : Fe 0.85 Al 0.15 alloys were chosen because they nicely account for the selective oxidation observed at the surface of industrial Al-alloyed steel grades which have a similar Al content [3]. Indeed, at annealing temperatures of ∼ 1070 K, both Fe-Al alloy matrix and Al-alloyed steel correspond to the ferrite phase. Accordingly to the phase diagram, no phase transition in temperature is expected. Consequently, those alloys are test beds in applied research.

• Orientation-dependent behaviour : single crystals of similar composition are expected to allow to rationalise the effects of changes in surface orientation, in order to explain the selective oxide distribution observed at the surface of textured Al-alloyed ferrite matrices. Finally, Fe 0.85 Al 0.15 crystals of various orientations are commercially available.

In parallel to this industrial context, during the past twenty-five years, aluminium oxide thin films were extensively studied in surface science [START_REF] Wu | Preparation, characterisation and structure of Ti and Al ultrathin oxide films on metals[END_REF] for both academic and applied issues. Aluminium-based alloys were mostly used to prepare thin alumina films that were conductive enough to allow surface science analysis while being able to mimic catalyst supports.

In this context, seminal works [START_REF] Jaeger | Formation of a well-ordered aluminium oxide overlayer by oxidation of NiAl(110)[END_REF][START_REF] Libuda | Structure and defects of an ordered alumina film on NiAl (110)[END_REF] were followed by a massive number of papers dealing with the oxide-covered NiAl crystals of various compositions and orientations (see Chap. 3) until the resolution of the unusual atomic structure of the oxide film on NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] [START_REF] Kresse | Structure of the ultrathin aluminum oxide film on NiAl (110)[END_REF]. The strong contrast in affinity to oxygen of nickel with respect to aluminium insures the formation of surface alumina upon oxidation while nickel is not oxidised at all. Conversely, although they oxidise in a rather similar way than NiAl, crystals of FeAl alloys have attracted much less attention as a support of alumina thin films. A likely reason is that, in FeAl alloys, the relative affinity of iron and aluminium for oxygen is such that there are conditions in which iron is oxidised [START_REF] Graupner | Oxidation of low-index FeAl surfaces[END_REF]. Moreover, the use of a random alloy and not of a defined compound asks for the role of inward concentration gradient underneath the oxide, namely the profile of segregation, and its actual role in the film formation. Those points discouraged those who were in search of well-defined alumina thin films on iron-aluminium alloys that can be used as model surfaces. Interestingly, in line with the present work, there is nowadays a growing interest about the surface oxidation of those alloys viewed as structural materials [START_REF] Yamauchi | Influence of vacuum annealing conditions on the surface oxidation and vacancy condensation in the surface of an FeAl single crystal[END_REF].

Conversely, there is some consensus that the structures of all aluminium oxide films that are formed at the surface of Al-containing alloys in ultra-high vacuum condition bear strong similarities. Besides the case FeAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] [START_REF] Graupner | Oxidation of low-index FeAl surfaces[END_REF] and NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] [START_REF] Libuda | Structure and defects of an ordered alumina film on NiAl (110)[END_REF], the structure of the aluminium oxide grown at the Cu-9 at.% Al [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] [START_REF] Napetschnig | Ultrathin alumina film on Cu-9 at% Al (111)[END_REF] was found to be similar to that formed at the NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] surface [START_REF] Napetschnig | Ultrathin alumina film on Cu-9 at% Al (111)[END_REF] as well as the oxide formed on Al-covered Ni [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] [START_REF] Prévot | Archetypal structure of ultrathin alumina films: Grazing-incidence X-ray diffraction on Ni (111)[END_REF]. The differences of bulk atomic structure and symmetry of the used substrates (cubic-face centred or cubic centred) and of the aluminium contents question the actual role of the substrate in the final atomic structure of the oxide.

In this thesis, the orientation dependence of aluminium segregation and oxidation at the surface of Fe 0.85 Al 0.15 have been tackled with a surface science approach by combining X-ray photoemission, diffraction techniques and near-field microscopy. The low index [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF], [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] and [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] surfaces have been compared, clean and after high temperature oxidation. By restricting to ultra-high vacuum treatment, although of interest, the thickening of the oxide layer at higher oxygen chemical potential and the formation of the corresponding transient alumina structures [START_REF] Grabke | Oxidation of NiAl and FeAl[END_REF], the competition between iron and aluminium oxidation and the switch from external to internal oxidation as described by the Wagner theory [START_REF] Wagner | Reaktionstypen bei der oxydation von legierungen[END_REF] have not been addressed in this work.

Outline of the thesis

The manuscript is divided in five chapters. After the present introduction, the experimental set-up (Sect. 2.1) and techniques used (LEED: Low-Energy Electron Diffraction Sect. 2.3, XPS: X-ray Photoemission Spectroscopy Sect. 2.5, STM: Scanning Tunnelling Microscopy Sect. 2.4, GIXD: Grazing Incidence X-Ray Diffraction Sect. 2.6) are briefly introduced in Chap. 2.

Chap. 3 starts with a presentation of the phase diagram of the FeAl intermetallic alloy, the description of the corresponding common atomic structures and the question of diffusion and segregation in this material. The most common low index surfaces are then introduced with the crystallographic convention used afterwards. The emphasis is then put on surface science studies already performed on FeAl. In a second part, a state of the art of the different structures of bulk alumina is given. All previous works performed on well-crystallised oxide layers on aluminium alloys are then reviewed in particular on the well-studied nickelaluminium alloys.

Preparation of a clean surface is a prerequisite in any surface science study. Impurity contents of Fe 0.85 Al 0.15 single crystals and reactivity towards residual vacuum are two obstacles that impeded a straightforward study of the intrinsic properties of surfaces. Chap. 4 describes the transient formation of carbon stripes on the [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] surface that paralleled the aluminium segregation in the first stages of sample preparation, as well as the carbon contamination due to the residual gases in the vacuum chambers.

Once highlighted the pitfalls of surface preparation, the analysis of the intrinsic behaviour of clean surfaces is described in Chap. 5. Recrystallisation annealing of all Fe 0.85 Al 0.15 surfaces yields an intense aluminium segregation that is explored with photoemission. Dedicated modelling of the angular dependence of core level intensities (Sect. 5.1) is developed to derive the profile of aluminium concentration. A depth of a few nanometres is affected and the surface composition is close to FeAl. This surface enrichment in aluminium is accompanied by the appearance of a long-range hexagonal-like superstructure on the [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] surface which is explored by LEED and GIXD (Sect. 5.2). In parallel, [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF] and [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] surfaces seem (1 × 1) terminated. Near-field microscopy (Sect. 5.3) points at an obvious increase of terrace size of sputtered surfaces and straightening of step edges with annealing temperature. The hexagonal nanometre-sized superstructure is imaged on the [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] surface while the (100) appears flat with a marbled electronic contrast and the [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] surface is nanofacetted and rough at the atomic scale with some tendency to form locally a double periodicity. Finally, the strong trend of aluminium segregation is confirmed by ab initio calculations.

High temperature oxidation of the three orientations is addressed in Chap. 6. Analysis of core levels demonstrates that, in the present conditions, iron is not oxidised and a self-limited continuous aluminium oxide is formed. All surfaces are alternately analysed in a common way. Al 2p core levels are decomposed in metallic and oxide components through a careful fitting. Firstly, the dependence with emission angle of the ratio between metallic aluminium and iron is used to obtain the profile of segregation under the oxide. Oxidation seems to induce a subsurface depletion in aluminium except on the (100) surface. The knowledge of the actual profile of segregation is mandatory to deduce oxide film thickness and stoichiometry which turn out to be different on the three surfaces. LEED shows that all oxide films are crystalline except for [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] orientation, mainly because of the open character of the body-centred [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] surface. On the [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] surface, the complex diffraction pattern can be indexed with two domains as seen with STM exhibiting a large and nearly rectangular unit cell which is very similar to that found on NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF]. Accurate lattice parameters determination with GIXD points at a nearly coincidence on a (1 × 2) oxide supercell with traces of a superstructure due to segregation underneath. LEED and STM demonstrates that the oxide formed on [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF] surface is a twin of that formed on NiAl [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF]. Two chemical environments of oxidised aluminium are present for [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] and [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] while only one is present for [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF]. The chapter ends with a comparison of the oxides formed on all terminations with results from the literature.

Beyond a quick summary, the conclusion points at unanswered questions and tries to draw some perspectives of study.

CHAPTER 2 EXPERIMENTAL TECHNIQUES AND SET-UPS

This chapter aims at a brief introduction of the experimental set-up, the sample preparation and the characterization techniques used all along this work. The questions of orientation dependence of segregation and of oxidation at the surface of a Fe 0.85 Al 0.15 crystal were tackled on the low-index [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF], [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] and [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] surfaces using a surface science approach. The vacuum environment (Sect. 2.1) enabled the characterization of atomically clean surfaces with the following techniques:

• Low-Energy Electron Diffraction (LEED, Sect. 2.3) to explore surface crystallinity,

• Scanning Tunnelling Microscopy (STM, Sect. 2.4), to analyse the surface morphology,

• X-ray Photoemission Spectroscopy (XPS, Sect. 2.5), to determine the chemical states of elements and composition profiles.

Complementary measurements were performed at the European Synchrotron Radiation Facility (ESRF) with Grazing Incidence X-ray Diffraction (GIXD, Sect. 2.6).

The ultra-high vacuum set-up at INSP

Experiments were carried out in Ultra-High Vacuum (UHV) conditions (pressure <10 -9 mbar). UHV is essential to keep samples free of contaminants for a period long enough to be able to characterise the intrinsic properties of the surfaces. Indeed, assuming a sticking coefficient close to one, the kinetic theory of gases shows that it only takes one second at a pressure of around 10 -6 Torr to create one absorbed monolayer. This defines the Langmuir unit (L) of exposure as used hereafter which amounts to 10 -6 Torr•s (∼1.33×10 -6 mbar•s) [START_REF] Lide | CRC handbook of chemistry and physics[END_REF][START_REF] Lüth | Surface and Interfaces of Solids[END_REF][START_REF] Ibach | Electron Energy Loss Spectroscopy and Surface Vibrations[END_REF] 1 .

Aside a load-lock system for a fast entry of the samples, the experimental system used at Institut des NanoSciences de Paris (INSP) (Fig. 2.1) consists of two chambers (preparation and analysis, base pressures of 5 • 10 -11 up to 3 • 10 -10 mbar) where different in situ techniques are combined:

• photoemission spectroscopy with an Omicron EA 125 (5 channeltrons) hemispherical analyser under non-monochromatic Al-Kα (1486.6 eV) and Mg-Kα (1253.6 eV) X-ray excitations (XPS); the analysis chamber made-out of µ-metal is shielded against external magnetic field and the X-ray source is a DARX-400 from Omicron;

• near-field microscopy, herein Scanning Tunnelling Microscopy (STM) with an Omicron VT-AFM head operating under Matrix electronics;

• electron diffraction with a reverse 4 grids device (LEED; ErLEED 150 from SPECS).

The chambers are pumped by ionic pumps (Varian StarCell) with pumping speed of 500 l•s -1 (analysis) and 300 l•s -1 (preparation) associated with Ti sublimators and turbomolecular pumps (Pfeiffer, 200 l•s -1 ) back-pumped with two-stage rotary pumps (Pfeiffer 10 m 3 •h -1 ). Pressures are measured by hot filament Bayard-Alpert gauges in each chamber and by combined Pirani-Penning gauges on turbomolecular pumps. On a leak-free system, a careful bake-out of around 24-48 hours at 135 • C allows to outgas the walls of the chamber, by removing in particular adsorbed water, to reach the final pressure which composition is essentially made of hydrogen, water and carbon monoxide as checked by a Residual Gas Analyser (RGA, Pfeiffer 200 amu). Flow of ultra-pure gases (research grade O 2 and Ar) are controlled through series of leak valves connected to manifold ancillary gas pipes which are baked-out and carefully flushed several times before any use.

In the preparation chamber, the sample mounted on an Omicron plate made-out of refractory material (Ta, Mo) can be cleaned by Ar + bombardment with a gun (SPEC IQE11/35) having a fixed focalisation (spot of 1 cm 2 at sample position; beam energy around 1000 eV, incident angle 60 • from normal). The usual ion current around 10 µA allows for the removal of around one monolayer per minute assuming a sputtering yield of one. At the same position, the sample can be annealed up to high temperature (1700 K) on a home-made electron-bombardment furnace. Temperature is systematically measured directly on the supporting plate and the sample with an optical pyrometer (Impac IGA 140) with an emissivity set at 20 %; a calibration between pyrometer, thermocouple directly spot welded on the plate and heating power was performed to minimise the error on temperature determination due to emissivity. Samples are transferred between the different parts of the experimental chambers with a magnetic rod equipped with the Omicron fork. On the 5-axis manipulator of the analysis chamber, the sample can be heated up to 1100 K and analysed by XPS and LEED. The sample can be transferred from this position to the microscope via a wobble-stick.

Surface preparation and film synthesis

Fe 0.85 Al 0.15 single crystals cut along low index [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF], [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] and [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] orientations have been studied throughout this work. According to the phase diagram, such a composition corresponds to a random A 2 body centred alloy (see Sect. 3.1). The bulk composition was checked a posteriori (on (110) crystal only !) by X-ray diffraction (see Sect. 2.6) through the Vegard's law dependence of the lattice parameter [START_REF] Ellner | On the partial atomic volume of aluminum in solid solutions based on the 3d transition metals and copper[END_REF] (a = 2.8914 Å). Crystals of disk shape (φ = 6 mm, thickness 2 mm) have a miscut below 0.1 • and are polished down to the lowest achievable roughness by the supplier [26]. They have been mounted through a Ta wire inserted in a groove in the thickness of the sample and spot-welded on the support plate, letting the surface fully free.

Since segregation and sample history is an issue for random alloys (see Sect. 3.3), a common protocol of surface preparation has been adopted. Samples have been cleaned by intensive cycles of Ar + sputtering (beam energy 1000 eV) for 20-45 minutes at room temperature. From the tabulated sputter yield (normal incidence, 1000 eV Ar + ) [START_REF] Matsunami | Energy dependence of the ion-induced sputtering yields of monatomic solids[END_REF], a slight preferential sputtering of Fe (1.70 atom/ion) over Al (1.53 atom/ion) is expected at the opposite of the common belief of the literature which argues 2 about Fe enrichment. Indeed, the composition found on sputtered surface is close to the nominal one (see Chap. 5). Sputtering has been followed by a given cycle of heating: (i) ramping up to the final temperature within a couple of minutes, (ii) annealing plateau of 15-20 mins, (iii) fast cooling down. To test segregation effect, the plateau temperature has been increased from 673 K to 1273 K (see Chap. 5). However, in most cases, the annealing did not exceed 1200 K to avoid Al evaporation problems as already reported above this temperature [START_REF] Graupner | Composition and structure of the (100) and (110) surfaces of FeAl[END_REF][START_REF] Meier | Equilibration of stoichiometrically distorted Fe 1-x Al x (100) surfaces[END_REF]. Sample cleanliness and crystallographic quality were systematically checked by XPS and LEED. Bulk contamination and strong surface reactivity of bare surfaces were two major difficulties in this work as described in Chap. 4.

Surface oxidation (see Chap. 6) was achieved by introducing molecular oxygen during the annealing plateau at a pressure between 10 -7 mbar and a few 10 -6 mbar to reach a given exposure (expressed in Langmuirs) during the fixed annealing duration. Introduction of oxygen at the beginning, middle or end of the annealing plateau did not change the final results. A few tests of two-step oxidation (exposure at room-temperature followed by annealing) commonly applied to growth thin oxide films on NiAl were also performed on the (110) orientation.

Low-Energy Electron Diffraction

In surface science, Low-Energy Electron Diffraction (LEED) is the usual technique for checking the crystallographic quality, the symmetry and the reconstruction of the surface. The strong interaction between electrons of kinetic energy between 30 and 200 eV having a wavelength around the Angstrom makes this diffraction technique extremely surface sensitive. The determination of an atomic structure in diffraction experiments falls naturally into two parts [START_REF] Lüth | Surface and Interfaces of Solids[END_REF][START_REF] Ibach | Electron Energy Loss Spectroscopy and Surface Vibrations[END_REF]:

• the determination of the periodicity of the system and thus the basic unit of repetition or the surface unit mesh which requires an analysis of diffraction spot symmetry and positions;

• the location of the atoms within this unit cell which requires a careful analysis of spot intensities, and more precisely their variation with beam energy in LEED; this dynamic LEED analysis was applied in the literature to tackle the question of segregation at the FeAl surface [START_REF] Graupner | Composition and structure of the (100) and (110) surfaces of FeAl[END_REF][START_REF] Meier | Equilibration of stoichiometrically distorted Fe 1-x Al x (100) surfaces[END_REF][START_REF] Hammer | Segregation phenomena on surfaces of the ordered bimetallic alloy FeAl[END_REF][START_REF] Heinz | Surface structure and segregation of bimetallic bcc-type alloys[END_REF][START_REF] Blum | Segregation and ordering at Fe 1-x Al x (100) surfaces-a model case for binary alloys[END_REF][START_REF] Blum | Quantification of substitutional disorder and atomic vibrations by LEED-the role of parameter correlations[END_REF][START_REF] Hammer | Equilibration processes in surfaces of the binary alloy Fe-Al[END_REF].

A clean surface with large crystalline domains should be characterised by sharp spots with high contract and low background intensity. Any crystallographic imperfections or disordered phases will increase the background intensity, because of diffuse scattering from these statistically distributed defects.

Experimental set-up

A common reverse LEED optics consists in an electron gun, grids and a collector (fluorescent screen) (Fig. 2.3.1). The electron gun produces an electron beam with primary energies of ∼ 20 to 200 eV. These latter impinge on the surface of the sample at normal incidence and diffracted beams are collected in the backward direction. After a first grounded grid to produce a zone free of potential between sample and apparatus, the next one is polarised at a value close to the beam energy to get rid of inelastic electrons. The elastic ones are then re-accelerated up to several keV before reaching the fluorescent screen. According to de Broglie's relation, the wavelength λ of electrons λ( Å) ≈ 140.4/E (eV) in a LEED experiment is in the Angstrom range, i.e. the same magnitude as the interatomic distances in a solid.

LEED diffraction pattern only provides surface information originating from an area with a radius smaller than coherence length due to the instrument ∆r c :

∆r c λ 2β 1 + (∆E/2E) 2 . (2.1)
It is limited by the divergence or angular spread 2β of the beam (the so-called transverse coherence) and by the wavelength or energy spread ∆E (the so-called longitudinal coherence) given mainly by the temperature of the emitting filament. Thus for a kinetic energy of ∼ 100 eV, if the angular spread of the primary beam is ∼ 10 -2 rad, and the energy width is of ∼ 0.5 eV, the coherence length is about 100 Å which corresponds to a coherently illuminated area of ∼ 300 nm 2 [START_REF] Lüth | Surface and Interfaces of Solids[END_REF]. Therefore imperfections, in particular terrace size, will not contribute to the peak broadening above this limit.

Ewald's construction in 2D

If a low energy electron beam of wavelength λ and wavevector K i impinges on a twodimensional net of scattering centres, a number of scattered waves K s are produced within the elastic condition K i = K s = 2π/λ. The bulk Laue's conditions of diffraction on a crystal of unit cell vectors (a, b, c):

a • ∆k = 2πh b • ∆k = 2πk c • ∆k = 2πl (2.2)
would require that the wave vector transfer ∆k = K s -K i = ha * +kb * +lc * = G is a vector of the reciprocal lattice. (a * , b * , c * ) are the reciprocal space lattice vectors and (h, k, l) integers. However, the strong interaction of low kinetic electrons with matter gives rise to a limited probing depth that releases the Laue's condition perpendicular to the surface. In other words, if c is assumed to be normal to the surface and a, b are in plane, the reciprocal space seen by electrons consists of continuous rods, the so-called Crystal Truncation Rods (CTR) and the Laue's condition of constructive interference impacts only the parallel component ∆k of the wavevector transfer: ∆k = G = ha * + kb * . In terms of Ewald's sphere construction (Fig. 2.3) which is a geometrical interpretation of the Laue's conditions, scattering will be observed along directions where the CTRs drill the Ewald's sphere which is a sphere of radius K i = 2π/λ. Of course among the half space, only the scattered wavevectors K s intersecting the LEED screen will be observed. Usually in surface crystallography, the periodicity of the bulk crystal is described through a surface unit cell (a S , b S ) with the repeating unit cell vector c S normal to it; the corresponding surface indexes (h S , k S ) label the diffraction spots. The analysis of a LEED pattern [START_REF] Lüth | Surface and Interfaces of Solids[END_REF][START_REF] Ibach | Electron Energy Loss Spectroscopy and Surface Vibrations[END_REF] can provide:

• the symmetry of a superstructure (i) due to a reconstruction of the surface compared to the bulk surface unit cell (a S , b S ) or (ii) due to an adsorbed film. The unit cell lattice vectors of the superstructure is usually defined through a matrix M S from the bulk surface unit cell. In the simplest cases, it involves a dilatation (m along a S and n along b S ) and a rotation Θ and is noted (m × n)RΘ. If m, n are integers, the superstructure is said commensurate with the substrate, but incommensurate cases are not unusual. The corresponding matrix of transformation M S between "bulk" surface and superstructure unit cells is also often used to characterise this latter.

• information regarding the crystalline quality of the substrate (such as faceting, roughness etc. . . ) through spot broadening or splitting. In our case, only qualitative informa-tion can be obtained since a quantitative analysis would require a spot profile analysis apparatus.

Scanning Tunnelling Microscopy

Scanning Tunnelling Microscopy (STM) is a direct real-space imaging technique that is based on the tunnelling effect principle between a metallic tip and a sample. The tip is scanned over the surface with sub-nanometre resolution in all directions while measuring/regulating the current at the near vicinity of the surface. The strength of STM in achieving atomic resolution is the extreme sensitivity of the current on sample/tip distance. Conductive sample is a prerequisite but insulators can be imaged in the form of thin films deposited on a conductive substrate.

Instrumentation

The schematic diagram of a STM is shown in Fig. 2.4. The essential element consists of a probe tip, usually made of W or PtIr, attached to a piezodrive which involves three mutually perpendicular piezoelectric transducers along x, y, z. Upon applying a voltage, they expand or contract through piezoelectric effect (of the order of nm•V -1 ). Using the coarse motors3 and the z piezo, tip and/or sample are brought to a distance of a few angstroms at which the electron wavefunctions of the tip and sample overlap. A bias voltage applied between them causes an electrical current to flow through the vacuum junction [START_REF] Chen | Introduction to scanning tunneling microscopy[END_REF]. Sawtooth voltages that are applied on the x and y piezoelectric components enable the tip to scan the x y plane under tunnelling condition reconstructing a "topographic" image of the surface of the sample. In STM, there are two imaging modes (Fig. 2.5). At constant current, as used in this thesis, the tunnelling current is kept constant via a feedback circuit that adjusts the height while scanning. In constant-height mode, the tip moves in a horizontal x y plane, leading to a change in the tunnelling current accordingly to local topography and local electronic states of the sample.

In order to achieve atomic resolution, effective vibration isolation is critical since a typical corrugation amplitude in STM within a crystallographic plane is of the order of a fraction of Angstrom. In our microscope, this is achieved through a heavy and rigid bench for the high frequency vibrations and by a low-frequency vibration isolation stage holding the microscope based on suspension springs combined with eddy-current damping [START_REF] Chen | Introduction to scanning tunneling microscopy[END_REF]. Another important issue to be solved is the electronics and control of the STM. Since the tunnelling currents occurring in STM are typically from 0.01 to 50 nA, the current should be amplified with a low-noise circuit. Besides the current amplifier, a feedback circuit is necessary to control an equilibrium z position and control the tip-sample distance. The feedback loop is negative that is to say if the tunnelling current increases when scanning, then a voltage is applied to the z piezoelectric transducer to withdraw the tip from the sample surface, and vice versa.

Basics of STM theory

In order to understand the unprecedented resolution achieved by STM, a number of theoretical methods have been developed over the years up to atomic simulations of the whole tip/sample system. The first one is known as the elementary one dimensional model [START_REF] Chen | Introduction to scanning tunneling microscopy[END_REF]. The other two early theories are the corrugation function model, the so-called the Stoll's formula (1984) [START_REF] Stoll | Resolution of the scanning tunnel microscope[END_REF] and the s-wave-tip model developed by Tersoff andHamann (1983, 1985) [START_REF] Tersoff | Theory and application for the scanning tunneling microscope[END_REF][START_REF] Tersoff | Theory of the scanning tunneling microscope[END_REF]. Both grasp the main physics underlying the imaging i.e. the extreme sensitivity of tunnelling current on distance and the importance of density of electronic states of the sample and the tip.

In one-dimensional model, the movement of an electron of mass m having an energy E confined in one dimension by a potential barrier [U (z) = 0 if z < 0 and U (z) = U if z > 0] is described by the Schödinger's equation:

EΨ(z) = - 2 2m d 2 dz 2 Ψ(z) + U (z)Ψ(z), (2.3)
where Ψ(z) is its wave function. When E > U , the solution of Eq. 2.3 is propagative and reads:

Ψ(z) = Ψ(0)e ±ikz , (2.4)
where the wavevector is k =

√ 2m(E-U ) (p z = k). When E < U , i.e.
in the forbidden region in classical mechanics, the wave function exponentially decays with distance z since k becomes imaginary:

Ψ(z) = Ψ(0)e -kz .
(2.5)

The possibility to observe an electron at z > 0 being proportional to |Ψ(0)| 2 e -2kz is nonzero outside the potential barrier. This basic interpretation of metal-vacuum-metal tunnelling is at the basis of the calculation of the tunnelling current at a tip/vacuum/sample junction in a STM experiment (see Fig. 2.4.2) with a barrier value φ given by the work function of tip and sample (assumed to be the same herein). φ gives the minimum energy needed to remove an electron from the substrate Fermi level into vacuum; typical values of metals are in the range of 4 to 5.5 eV [START_REF] Michaelson | The work function of the elements and its periodicity[END_REF]. Under a bias voltage V applied to the sample, the junction is polarised and the tunnelling current is the probability of overlap of the wavefunction Ψ n of an electron in state n:

w ∝ |Ψ n (0)| 2 e -2kz , (2.6)
where the decay constant k = √ 2m(φ-eV ) is in the range of 1 Å-1 . The tunnelling direction of the current changes when reversing the bias. When a positive bias is applied on the sample, electrons tunnel from the tip to unoccupied states of the sample, whereas if the bias is negative, electrons tunnel from occupied states of the sample to the tip. Therefore, the bias polarity determines whether unoccupied or occupied electronic states of the sample surface are probed.

The tunnelling current is proportional to the number of states on the sample surface within an energy interval. For metals and alloys, the number is finite and proportional to the Local Density Of States (LDOS) at the set point. For semiconductors and insulators, it can be very small or even null if the bias applied is smaller than the band gap. Taking all the sample states Ψ n in the energy interval eV , the tunnelling current can be expressed as:

I ∝ E F En=E F -eV |Ψ n (0)| 2 e -2kz .
(2.7)

If the bias voltage V is small enough compared with the work function of the sample and tip, the density of states does not vary obviously within the energy interval eV . Then Eq. 2.7 can be written as the LDOS of the sample at the Fermi level and at the centre of the tip apex. LDOS is the number of electrons per unit volume per unit energy, having a given energy at a given point in space. The LDOS ρ S (z, E) can be written as:

ρ S (z, E) ≡ 1 E En=E- |Ψ n (z)| 2 . (2.8)
At (z = 0, E = E F ) within the bias voltage windows eV ,

eV • ρ S (0, E F ) ≡ E F En=E F -eV |Ψ n (0)| 2 .
(2.9)

Therefore, the tunnelling current reads:

I ∝ eV • ρ S (0, E F )e -2kz ≡ eV • ρ S (z, E F ), (2.10)
which means that a topographic STM image obtained by scanning the tip over the surface under constant tunnelling current is a contour of a constant LDOS of the surface of the sample. It is independent of the electronic states of tip.

If accounting for the whole junction including the tip electronic state by solving two separate equivalent subsystems (sample/vacuum and vacuum/tip) following the approach of Bardeen [35,[START_REF] Bardeen | Tunnelling from a many-particle point of view[END_REF][START_REF] Giaever | Energy gap in superconductors measured by electron tunneling[END_REF], the tunnelling current appears as the convolution of the Density Of States (DOS) of two electrodes:

I ∝ eV 0 ρ S (E F -eV + δ)ρ T (E F + δ)dδ.
(2.11)

ρ S and ρ T are the DOS of sample and tip and E F is Fermi level at equilibrium.

Tip preparation and image treatment

Tip is an essential component of an STM experiment since the tunnelling current is determined by the convolution of the electronic states of the sample and of the tip, and its ultimate atomic apex controls the resolution. In our experiments, reproducible STM imaging could be obtained with different W tips. They have been prepared via continuous electrochemical etching in a KOH solution (concentration ∼ 4.5 mol/L). A potential of around 7 V is applied between a W wire (Φ = 0.36 mm) partially immersed in the solution and a stainless steel ring (Φ = 40 mm) touching the surface of the solution. The overall etching reaction W(s) + 2H 2 O + 2OH -→ WO 2- 4 + 3H 2 (g) happens at the meniscus between the wire and the solution until the neck is so thin that the remaining portion of the wire falls in the solution. This generates a fresh atomic W tip. The external circuit detects the sudden increase of resistivity and stops the etching process to avoid damaging the tip apex. After thorough rinsing with deionised water and/or pure alcohol, tip shapes are optically controlled 4 and mounted onto dedicated gold coated tip holders [START_REF] Ibe | On the electrochemical etching of tips for scanning tunneling microscopy[END_REF][START_REF] Dremov | Sharp and clean tungsten tip for STM investigations[END_REF]. Tip are "cleaned" and "conditioned" in situ through pulses of increasing voltage and duration until stable and good imaging conditions are achieved in particular on steps of metallic substrates.

The obtained STM images have been treated using the Gwyddion software [START_REF]Gwyddion software[END_REF] a modular program for SPM (Scanning Probe Microscopy) data visualization and analysis. The main used image treatments are:

• a flattening of the image (tilt correction) through the average plane followed by a further interpolation line by line along the scan direction; eventually flattening is performed over selected area of the image to enhance the contrast from terraces;

• filtering through 2D Fast Fourier Transform to remove noise having specific spatial frequencies if needed;

• drift compensation between up/down images;

• 2D auto-correlation function or Fourier transform to seek for periodicity;

• line profiles and statistical analysis such as roughness or slope analysis.

X-ray Photoemission Spectroscopy

Basic principles

Photoelectron spectroscopy is based on the photoelectric effect during which electrons in a solid can be ejected by a radiation which energy exceeds the binding energies (BEs) in the material. The analysis in kinetic energy of the intensity of photoelectrons gives access to information regarding material composition and chemical states of elements. Depending on the excitation energy, laboratory photoemission can be divided into two techniques: Ultraviolet and X-ray Photoelectron Spectroscopy (UPS and XPS) respectively. XPS is also known as Electron Spectroscopy for Chemical Analysis (ESCA) [START_REF] Hüfner | Photoelectron spectroscopy: principles and applications[END_REF][START_REF] Hofmann | Auger-and X-ray photoelectron spectroscopy in materials science: a useroriented guide[END_REF]. UPS is dedicated to the analysis of the valence band.

Taking the Fermi level common to the sample and the spectrometer as an energy reference, the kinetic energy of the elastically emitted photoelectrons can be calculated from energy conservation by combining the emission (Fig. 2.7) and the energy levels involved (Fig. 2.8):

E K = hν -E B -Φ sp .
(2.12)

hν is the photon energy, E K the kinetic energy of the emitted photoelectron, E B its binding energy and Φ sp is the work function of the spectrometer. Eq. 2.12 indicates that photoemission can provide a picture of the filled states in the probed material, deep core levels in XPS and valence band in UPS. In our set-up, Φ sp was determined by using Ag 3d core level as a reference (E B = 368.2 eV).

Figure 2.7: Scheme of the main processes involved in an XPS experiment [START_REF] O'connor | Surface analysis methods in materials science[END_REF]: photoemission (left) and Auger process (right). XPS involves the emission of a single photoelectron from a given core level (1s or K shell here) via X-ray excitation. Auger emission is a three-electron process. After emission of the initial photoelectron, an other electron (L core level here) fills the vacancy and an electron of an upper orbital (L core level here) is emitted with a kinetic energy equal to the excess energy. The Auger transition, given as an example, is labelled KLL.

After photoionization, the hole created by the emitted photoelectron (Fig. 2.7) can be filled by the decay of an electron from an outer orbital followed by the subsequent emission of an electron of a higher lying orbital which kinetic energy carries the excess energy. This so-called Auger process is labelled by the three energy levels involved in the transition. For example, for a KLL series, the initial core level hole is in the K shell and the last two holes are in the L shell:

E K (KL 1 L 2,3 ) = E B (K) -E B (L 1 ) -E B (L 2,3 ) -Φ sp + ∆E rel .
(2.13)

Where ∆E rel stands for the relaxation in energy, that is involved in the Auger process. The relation (Eq. 2.13) is at the heart of Auger Electron Spectroscopy (AES) for which a series the minimum energy required to extract an electron from the Fermi level to infinity [START_REF] Oura | Surface science: an introduction[END_REF]. of relaxations follow the creation of a core hole (generally by an impinging electron or an impinging photon).

Instrumentation

The main components for a typical laboratory XPS apparatus shown in Fig. 2.9 are the X-ray source, the sample support system (manipulator), the energy analyser, the electron detector (multiplier) and the driving electronics converter. Figure 2.9: Main components for a typical XPS apparatus [START_REF] O'connor | Surface analysis methods in materials science[END_REF].

In the source, the emission of X-rays is produced by bombarding with high energy electrons (around 10 keV and 200 W in DARX-400) a cooled metallic target containing Mg or Al. For both elements, the X-ray emission spectrum due to the refilling of K-level holes is dominated by Kα 1 and Kα 2 lines [START_REF] Moulder | Handbook of X-ray photoelectron spectroscopy[END_REF][START_REF] Wagner | Handbook of X-ray photoelectron spectroscopy[END_REF]. In a non-monochromatised source, these intense lines are superimposed with:

• satellite peaks (Kα 3 , Kα 4 . . . ) which positions and relative intensities (see Tab. 2.1) are characteristic of a given anode material;

• Bremsstrahlung radiation (also called braking radiation) which is produced by the deceleration of the electrons as they strike the target;

• cross talk between anode (less than 1 % for our source) due the contamination of the anode material by the other one.

These drawbacks increases the complexity of the analysis and limit the resolution to around 0.85 eV for Al-Kα and 0.7 eV for Mg-Kα. The ionization cross section i.e. the probability of absorbing a photon and creating a hole on a given level has been calculated and are tabulated for our excitation energies [START_REF] Yeh | Atomic subshell photoionization cross sections and asymmetry parameters: 1 Z 103[END_REF]. Since our source is non-polarised and located at the "magic" angle of arccos(1/ √ 3) = 54.7 • , no assymetry in the ionization cross section have to be taken into account [START_REF] Yeh | Atomic subshell photoionization cross sections and asymmetry parameters: 1 Z 103[END_REF][START_REF] Kennedy | Photoionization of the noble gases: Cross sections and angular distributions[END_REF]. 2.1: X-ray satellite energies and intensities for given X-ray sources [START_REF] Moulder | Handbook of X-ray photoelectron spectroscopy[END_REF].

Once the photoelectrons escape from the surface of the sample into the vacuum, they are collected and separated according to their kinetic energy and subsequently converted into a spectrum. Thus the electron energy analyser is the heart of XPS system and is the critical component in determining sensitivity and resolution [START_REF] O'connor | Surface analysis methods in materials science[END_REF]. The ejected electrons first pass through a set of electrostatic lenses that refocus the beam and are then decelerated down to (or accelerated up to) the so-called pass energy E p before entering the hemispherical analyser (Omicron EA 125). The voltage difference applied between the inner and outer hemispheres acts as a band pass filter. The analyser only transmits electrons with an energy matching E p which are then collected by the detector. The resolution can be improved by reducing the pass energy (at the expense of the total number of counts), entrance slit width and the acceptance angle of the lens system. The latter also govern the probed area.

The analyser can be run in:

• at Constant Retard Ratio (CRR) by keeping constant the ratio of pass energy and kinetic energy and therefore the transmission of the analyser,

• at Constant Analyser Energy (CAE) i.e. at constant pass energy and therefore resolution throughout the whole range of binding energy. This mode was systematically used in this work and leads to a higher transmission at low kinetic energy.

The resolution of the analyser can be written approximately as: erature [START_REF] Ruffieux | Experimental determination of the transmission factor for the Omicron EA125 electron analyzer[END_REF], the transmission function of our analyser is close to the theoretical one for an hemispherical analyser i.e. T ∼ E p /E K . This value was used for all our data analysis.

∆E = E p d 2R 0 + α 2 . ( 2
In our case, the detectors are multiple-channel detectors that are placed across the exit plane of the analyser. The amplification factor is 10 8 . The small current pulse present at the output of the channeltrons (5 on our EA 125) is filtered and passed into the preamplifier unit. Then it is transmitted to a pulse counter for processing and an electron energy spectrum is produced.

Data interpretation

A typical spectrum of X-ray photoemission is made of sharp peaks corresponding to the core levels and broader lines due to the Auger transitions overlapped with a continuous background of secondary electrons due inelastic processes and Bremsstrahlung emission in a nonmonochromatic source [START_REF] Hofmann | Auger-and X-ray photoelectron spectroscopy in materials science: a useroriented guide[END_REF][START_REF] Moulder | Handbook of X-ray photoelectron spectroscopy[END_REF][START_REF] Wagner | Handbook of X-ray photoelectron spectroscopy[END_REF]. The binding energies of core levels are sensitive to the chemical state and to the environment of the emitting atoms.

Core level characteristics in a photoemission spectrum: lineshape and data fitting

Core level lines are either singlets or doublets in case of spin-orbit splitting. A vacancy created by photoionisation couples with an unpaired electron in the originally incompletely filled shell and generates a splitting of the orbital (case of p, d, f orbitals). The coupling in the final state between the spin angular momentum s and the non zero orbital angular momentum l is described by a new total electronic angular momentum j = s + l. For example, for Fe 3p orbital, the allowed values are j = 1/2; 3/2 giving rise to two photoelectron lines labelled Fe 3p 3/2 and Fe 3p 1/2 . For different orbitals, the relative peak intensity is related to the degeneracy of the final state; it is given by [2(l -1 2 ) + 1]/[2(l + 1 2 ) + 1] and summarised in Tab 2.3. Of course, no splitting is expected for a s level (l = 0). In our data fitting, theoretical ratio between the two components of a doublet was kept constant.

Core level 2p 3d 5f j Core level lineshape maybe complex due to the combination of several physical and instrumental effects [START_REF] Hüfner | Photoelectron spectroscopy: principles and applications[END_REF][START_REF] Hofmann | Auger-and X-ray photoelectron spectroscopy in materials science: a useroriented guide[END_REF]:

• X-ray excitation profile,

• broadening of the core level hole state due to its finite lifetime and thermal effect,

• surface potential inhomogeneities, surface charging of the sample, band bending in case of non-metallic sample,

• response function of the electron energy analyser.

If the X-ray source emission and the finite lifetime broadening are inherently Lorentzian, peak shapes are generally mixed with an additional Gaussian broadening, mainly due to the instrument. This latter is accounted for through a Voigt function i.e. a convolution of Gaussian G(E) and Lorentzian L(E) functions:

V (E) = A +∞ -∞ L(E )G(E -E )dE , (2.15)
where:

G(E) = ln 2 π 1 γ G exp - E 2 • ln 2 γ 2 G , (2.16)
L(E) = 1 πω L γ L ((E -E 0 ) 2 + γ L ) . (2.17)
2γ G and 2γ L are full widths at half maximum (FWHMs) of the Gaussian and Lorentzian components, E 0 the peak position and A the peak area.

But the profile may be greatly influenced by many-body phenomena such as electronhole pair excitations near the Fermi level and plasmon excitations of the cloud of valence electrons. For solids with a large DOS at the Fermi level like metals, these excitation processes lead to a skewed peak shape toward higher binding energies [START_REF] Hüfner | Photoelectron spectroscopy: principles and applications[END_REF][START_REF] Hofmann | Auger-and X-ray photoelectron spectroscopy in materials science: a useroriented guide[END_REF]. For energies of only a few electron-volts from the peak energy, where the valence band density of states may be considered roughly constant, the combined effect of these electron-hole pair excitations and the lifetime broadening is described by a formula derived by Doniach and Sunjic [START_REF] Doniach | Many-electron singularity in X-ray photoemission and X-ray line spectra from metals[END_REF]:

DS(E, α) = Aγ ds cos π α 2 + (1 -α) arctan E-E 0 γ ds [(E -E 0 ) 2 + γ 2 ds ] 1-α γ ds . (2.18)
α is an asymmetry parameter and γ ds is related to the peak FWHM. α = 0 corresponds to the Lorentzian shape. Of course, DS(E, α) should be convoluted with a Gaussian to account for instrumental broadening.

Another important feature of the spectra is the background due to inelastic electrons, which subtraction is crucial for data interpretation. The often used Shirley background assumes a background proportional to the integral up to a given kinetic energy of the actual signal; it naturally accounts for the increase in the overall measured background that happens for each subsequent core level [START_REF] Shirley | High-resolution X-ray photoemission spectrum of valence bands of gold[END_REF]. Beside this continuous background, other satellite peaks may be present due to the losses suffered by the outgoing electrons, such as quantified plasmon losses and shake-up/shake-off satellites due to the interaction with valence electrons.

During this thesis, photoemission spectra were fitted using the XPSMania macro package for Igor Pro created by F. Bruno. Peaks were fitted through Levenberg-Marquadt χ 2 minimization with Voigt profiles and with Doniach-Sunjic shape for metallic component. The background was of Shirley's type.

Quantification and intensity analysis

Through modelling of intensities, photoemission can provide a quantification of coverage, atomic density or film thickness [START_REF] Hüfner | Photoelectron spectroscopy: principles and applications[END_REF][START_REF] Hofmann | Auger-and X-ray photoelectron spectroscopy in materials science: a useroriented guide[END_REF][START_REF] Moulder | Handbook of X-ray photoelectron spectroscopy[END_REF][START_REF] Wagner | Handbook of X-ray photoelectron spectroscopy[END_REF]. For a thin layer of thickness dz buried at a depth z in a semi-infinite substrate, the photoelectron intensity I at kinetic energy E K is given by:

I ∼ F ADΩT (E K )σ(E K ) exp [-z/λ(E K ) cos Θ] n(z)dz, (2.19)
where:

• F is the average flux of X-rays on the sample,

• A is the sample area illuminated by X-rays viewed by the analyser,

• D is the detector efficiency,

• Ω is the acceptance solid angle of the analyser,

• T (E K ) is the analyser transmission function which is close to the inverse of the kinetic energy for a perfect hemispherical analyser [START_REF] Ruffieux | Experimental determination of the transmission factor for the Omicron EA125 electron analyzer[END_REF],

• σ(E K ) is the photo-ionisation cross-section of the corresponding core level,

• λ(E K ) cos Θ is the electron escape depth which depends on the collection angle Θ and the Inelastic Mean Free Path (IMFP) λ(E K ) for photoelectrons in the sample; it comes into play through an exponential damping of Beer-Lambert type;

• n(z) is the atomic density of the probed element.

Depending on the material characteristics, the value λ(E K ) were obtained herein from the TPP-2M predictive formula of Tanuma, Powell and Penn [START_REF] Tanuma | Calculations of electron inelastic mean free paths for 31 materials[END_REF][START_REF] Tanuma | Calculations of electorn inelastic mean free paths. II. Data for 27 elements over the 50-2000 eV range[END_REF][START_REF] Tanuma | Calculations of electron inelastic mean free paths: III Data for 15 inorganic compounds over the 50-2000 eV range[END_REF][START_REF] Tanuma | Calculations of electron inelastic mean free paths (IMFPS). IV. Evaluation of calculated IMFPs and of the predictive IMFP formula TPP-2 for electron energies between 50 and 2000 eV[END_REF][START_REF] Tanuma | Calculations of electron inelastic mean free paths. V. Data for 14 organic compounds over the 50-2000 eV range[END_REF][START_REF] Tanuma | Calculations of electron inelastic mean free paths (IMFPs) VI. Analysis of the Gries inelastic scattering model and predictive IMFP equation[END_REF][START_REF] Tanuma | Calculation of electron inelastic mean free paths (IMFPs) VII. reliability of the TPP-2M IMFP predictive equation[END_REF][START_REF] Tanuma | Calculations of electron inelastic mean free paths[END_REF][START_REF] Shinotsuka | Calculations of electron inelastic mean free paths. X. data for 41 elemental solids over the 50 ev to 200 kev range with the relativistic full penn algorithm[END_REF] as implemented in the QUASES-IMFP-TPP2M software [START_REF] Tougaard | QUASES-IMFP-TPP2M Software[END_REF].

While absolute intensity determination through reference sample is difficult, quantification can still be achieved by simply looking at the ratio of peak areas acquired during a given run since the ionization cross section, IMFP and transmission function are known quantities and the remaining ones F, A, D, Ω can be assumed to be constant as poorly dependent on the kinetic energy. The ratio I/T (E K )σ(E K ), called the corrected intensity, contains information related to the profile of concentration of the probed atom. The strategy of analysis depends on the sample geometry (see Fig. 5.3 for examples) and the question at hand implies the z-integration of the above equation while accounting for any damping by overlayers. Two classical cases are tackled hereafter: the homogeneous mixture and the thin film on top of a bulk.

2.5.3.2.1 Bulk alloy If an element A is homogeneously mixed with an element B in a solid solution A 1-x B x (Fig. 5.3-a), the atomic concentration of the two elements are given by n A ∼ 1 -x and n B ∼ x. Therefore, the atomic ratio x can be determined from the measured intensities I A , I B of given core levels of the elements A and B by directly integrating Eq. 2.19:

I B I A T A σ A T B σ B = x 1 -x λ AB B λ AB A , (2.20)
where T i (i = A, B) is the analyser transmission function at the corresponding electron kinetic energy, σ i the photo-ionization cross section of the core level under consideration and λ AB i the inelastic mean free path of the photoelectrons from atom i in A 1-x B x . The formula is independent of the collection angle Θ.

Thin film on a substrate

For a thin film of thickness t of material B (density n B ) on top of a semi-infinite substrate A (density n A ) (Fig. 5.3-a), the signals can be derived by integrating Eq. 2.19:

I A T A σ A ∼ n A 0 -∞ exp z/λ A A cos Θ dz × exp -t/λ B A cos Θ = n A λ A A cos Θ exp -t/λ B A cos Θ I B T B σ B ∼ n B 0 -t exp z/λ B B cos Θ dz = n B λ B B cos Θ 1 -exp -t/λ B B cos Θ . (2.21)
λ j i (i, j = A, B) corresponds to the inelastic mean free path of core level i in material j. Notice that a further damping exp -t/λ B A cos Θ of the substrate signal in the film has been added in the previous equation. The other parameters have the above defined meanings. The ratio I B /I A of intensity yields a transcendental equation that can be solved easily by dichotomy to obtain (d, n B ) from the knowledge of n A . Measurements at several collection angles allow to further constrain the modelling and check the validity of the underlying model.

Grazing Incidence X-Ray Diffraction

Grazing Incidence X-Ray Diffraction (GIXD), also known as Surface X-ray Diffraction (SXRD), was used to study the crystallography of the reconstruction and of the oxide layer on the Fe 0.85 Al 0.15 (110) surface.

Principle

The principle of GIXD (Fig. 2.11) [START_REF] Als-Nielsen | Elements of modern X-ray physics[END_REF][START_REF] Holý | High-resolution X-ray scattering from thin films and multilayers[END_REF][START_REF] Feidenhans | Surface structure determination by X-ray diffraction[END_REF][START_REF] Renaud | Oxide surfaces and metal/oxide interfaces studied by Grazing Incidence X-Ray Scattering[END_REF][START_REF] Renaud | Probing surface and interface morphology with grazing incidence small angle X-ray scattering[END_REF] is to shine a well collimated X-ray beam of wavelength λ of the order of the Angstrom at grazing incidence α i and to collect scattered/diffracted beams along the two directions, in-plane (2θ f ) and out-of-plane (α f ), leading to a wave vector transfer:

q x = k 0 [cos(α f ) cos(2θ f ) -cos(α i )] q y = k 0 [cos(α f ) sin(2θ f )] q z = k 0 [sin(α f ) + sin(α i )] k 0 = 2π/λ.
(2.22)

Figure 2.11: Grazing incidence X-ray scattering geometry [START_REF] Renaud | Probing surface and interface morphology with grazing incidence small angle X-ray scattering[END_REF]. The incident beam of wave vector k i makes a small incident angle α i with respect to the sample surface. The intensity is recorded at wide angles as a function of the angles 2θ f and α f describing the in-plane and out-of plane angles between the incident k i and scattered k f wave vectors, respectively. The sample can be rotated by an angle ω around its surface normal. 2θ is the usual total scattering angle. SXRD and GIXD correspond to large values of the scattering angles. The direction of the exit wave vector k f is defined by slits, parallel and perpendicular to the surface, behind which lies the detector, which can be punctual or linear, or even two-dimensional. Looking close to the origin of reciprocal space allows probing nanometre length structures with Grazing Incidence Small-Angle X-Ray Scattering (GISAXS) or XRR (X-Ray Reflectivity).

By scanning at fixed incidence, the position of the detector along (2θ f , α f ), it is possible to explore the reciprocal space of the sample. GIXD exploits the phenomenon of total external reflection of hard X-rays to reduce the penetration depth and to enhance the contribution of the surface compared to the bulk. Indeed, the index of refraction of matter in the hard X-rays regime n = 1 -δ + iβ is slightly lower than one (δ ∼ 10 -5 ) leading to total external reflection below the critical angle α c = √ 2δ (α c ∼ 0.1 -0.3 • ). Fresnel calculations show that the total reflection (Fig. 2.6.1-a) observed for α i < α c parallels a drastic reduction of the penetration depth Λ (Fig. 2.6.1-c) up to a value Λ c = 1/2k 0 α c and an enhancement of transmission coefficient (Fig. 2.6.1-b) due to the propagation of an evanescent wave parallel to the surface. Typically Λ c is in the range of the nanometre. Due to the time reversal principle, the same phenomenon holds true for the out-going diffracted beam i.e for α f . In a GIXD experiments, one can probe:

• the intensity of the Crystal Truncation Rods (CTRs) which originate from the spreading of the signal in between bulk Bragg peaks due to the existence of a surface; their quantitative analysis and that of in-plane structure factors allows to determine atomic positions (relaxation, rumpling etc.. . . ); this requires a precise integration of intensity;

• the presence of reconstruction which appear as extra-CTRs in between those of the substrate; they have a q z extension much larger as they originate from a finite small thickness;

• the epitaxy and eventually the atomic structure of thin films or nanoparticles.

Usually, like in LEED, a point of the reciprocal space q is defined by its coordinates (h S , k S , l S ) in the (a * S , b * S , c * S ) basis which first two components are linked to the surface unit cell (a S , b S ) of the substrate while the third component is along the surface normal c S .

Experimental set-up

The low amount of diffracting matter favors the use of a brilliant and collimated beam coming from a synchrotron source [START_REF] Als-Nielsen | Elements of modern X-ray physics[END_REF][START_REF] Holý | High-resolution X-ray scattering from thin films and multilayers[END_REF][START_REF] Feidenhans | Surface structure determination by X-ray diffraction[END_REF][START_REF] Renaud | Oxide surfaces and metal/oxide interfaces studied by Grazing Incidence X-Ray Scattering[END_REF][START_REF] Renaud | Probing surface and interface morphology with grazing incidence small angle X-ray scattering[END_REF]. GIXD experiments have been performed at the European Synchrotron Radiation Facility (ESRF, Grenoble) on the INS (In situ Nanostructure and Surface) surface diffraction end-station of the bending magnet french beamline (BM32) [72]. The X-ray optics includes mainly one mirror and a double Si crystal monochromator. The X-ray energy was set at E = 18 keV (λ = 0.6888 Å ) (i) to avoid absorption and fluorescence by the substrate and the film,(ii) to have the highest accessible range of reciprocal space and (iii) to match the maximum of intensity of the bending magnet. The incidence α i = 0.14 • was fixed just below the critical angle of Fe 0.85 Al 0.15 for total external reflection at the corresponding energy (α c = 0.173 • [START_REF]Center for X-ray optics[END_REF]) to minimise bulk signal. The X-ray beam was sagittally focused on the sample with horizontal (H = 0.4 mm) and vertical (V = 0.3 mm) sizes (Full Width at Half Maximum, FWHM), corresponding to divergences of δ H = 1 mrad and δ V = 0.13 mrad, respectively.

In the INS set-up, the sample (Fig. 2.6.2) is mounted vertically on the head of a six-circles diffractometer of "z-axis type" which holds the UHV-chamber (base pressure 1 • 10 -10 mbar) and allows for a precise positioning of the incoming beam α i and of the outgoing in-plane (2θ f ) and out-of-plane (α f ) scattered beam angles. The X-ray beam enters and exits the chamber through a large 0.5 mm thick X-ray transparent beryllium window; several slits in particular in vacuum reduces the background scattering. The alignment of the rotation axis ω of the sample normal is set by an hexapod (cradle-like settings) and rotation movement is transmitted through differential pumping. The detector arm which moves along (α f , 2θ f ) holds a 2D MaxiPix detector (1280 × 256 pixels) with pixel size of 55 µm which is put at a distance of 700 mm behind a vertical slit of 5 mm. It allows to measure directly portion of reciprocal space. Integration of signal along Region of Interests on the detector gives rise to a vertical resolution of 0.08 • for in-plane scan. The UHV chamber is equipped with several surface science facilities such as ion gun for sample cleaning, Auger spectrometer and a reflection high-energy electron diffraction set-up for a rapid analysis of reciprocal space. Samples can be annealed by electron bombardment of the molybdenum holder; the temperature is estimated by pyrometry. The clean Fe 0.85 Al 0.15 [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] surface and the oxide layers were prepared in situ following the same recipes as those used in the laboratory.

STATE OF THE ART OF ALUMINIUM METALLIC ALLOYS AND THEIR OXIDATION

This thesis focusses on the segregation and the oxidation behaviour of the low index orientations of Fe 0.85 Al 0.15 single crystals. This chapter aims at acquainting the reader to the existing literature.

Bulk order in Fe 1-x Al x alloys

Like other transition metal aluminides (such as NiAl), Fe-Al alloys have been recognised as potential candidates for a variety of high temperature structural applications (e.g. turbine blades in aircraft) due to their excellent oxidation and corrosion resistances as well as specific mechanical properties [START_REF] Deevi | Nickel and iron aluminides: An overview on properties, processing, and applications[END_REF]. The versatility of alloys stems primarily from the ability to manipulate their exact chemical composition giving profound control over their chemical and physical properties. Alloying elements may affect localised regions of strong compositional inhomogeneity, such as microstructural features (e.g. the distribution and interaction of dislocations, the cohesion of grain boundaries, or the formation and distribution of small-scale precipitates), which determine the mechanical behaviour of a material. Also, this concerns the region which mediates any interaction of a material with its environment, i.e. its surface.

The bulk phase diagram of Fe 1-x Al x alloy (x is the atomic percentage) brings out the formation of several compounds or solid solutions with different structures. In the simplified diagram of Fig. 3.1, several stable phases [START_REF] Kubaschewski | Iron-Binary phase diagrams[END_REF][START_REF] Sanchez | Reciprocal-space analysis of shortrange-order intensities by the cluster-variation method[END_REF][START_REF] Staunton | A theoretical treatment of atomic shortrange order and magnetism in iron-rich bcc alloys[END_REF][START_REF] Li | The Al-rich part of the Fe-Al phase diagram[END_REF] appear as function of aluminium content x and temperature:

• a liquid phase at high temperature,

• the γ-Fe cubic face centred (fcc) characterized by a γ-loop at low Al content (1-2%),

• the A 2 phase which is a body centred cubic (bcc) solid solution, also called random alloy in which long-range order (LRO) is absent but short-range order (SRO) is possible under certain conditions,

• the B 2 phase, a long-range ordered bcc solid solution with CsCl structure,

• five common stable compounds, namely the Heussler D0 3 phase (of BiF 3 type, bcc with LRO), (uncertain phase), FeAl 2 , Fe 2 Al 5 , FeAl 3 respectively (see Ref. [START_REF] Li | The Al-rich part of the Fe-Al phase diagram[END_REF] for the complex Al-rich part of the phase diagram). The ball models of the most relevant cubic structure with 0 ≤ x ≤ 0.5, namely A 2 , B 2 and D0 3 are shown in Fig. 3.2 and their space groups and lattice parameters are given in Tab. 3.1. At the peculiar concentration used in this study Fe 0.85 Al 0.15 , the alloy is in the random A 2 structure up to its melting point; in other words, no bulk structural transition is expected up ∼ 1700 K which allows safe high temperature annealings. The B 2 phase exists in wide range of composition 0.23 ≤ x ≤ 0.55 depending on temperature; at room temperature, it extends from x = 0.4 to x = 0.48. In the range 0.2 ≤ x ≤ 0.35, Fe-Al system adopts a LRO D0 3 structure which is derived at Fe 0.75 Al 0.15 composition from B 2 -CsCl by replacing half of the Al atoms by Fe. The evolution of the cubic lattice parameter a B with x [START_REF] Ellner | On the partial atomic volume of aluminum in solid solutions based on the 3d transition metals and copper[END_REF] was shown to follow a Vegard's law of random alloy from 2.86 Å to 2.90 Å at x = 0 -0.2 before being nearly constant up to x = 0.5 in the B 2 phase. At the composition studied herein, a B = 2.8914 Å. This evolution of parameter is marginal (1.4 %) leading to reduced problem of lattice mismatch; this also holds for the bcc sublaticce of the D0 3 structure. [START_REF] Ellner | On the partial atomic volume of aluminum in solid solutions based on the 3d transition metals and copper[END_REF].

&Ğ ůс&Ğ

Obviously, owing to the large domain of existence in x, each ordered lattice is able to incorporate excess atoms while retaining its positional translation symmetry through randomly distributed defects. The simplest ones are (i) antisites defects i.e. excess of A on B sublattice or vice-versa and (ii) vacancies. Antisites are much more energetically favorable for the FeAl B 2 structure on both side of the composition domain, Al-rich and Al-poor [START_REF] Fähnle | Theory of atomic defects and diffusion in ordered compounds, and application to B 2 -FeAl[END_REF][START_REF] Bester | Atomic defects in the ordered compound B 2 -CoAl: A combination of ab initio electron theory and statistical mechanics[END_REF]; there is nearly no vacancies. The formation enthalpy of Fe-Al alloys is quite high (0.26 eV per unit cell in Fe 0.50 Al 0.50 ) [START_REF] Blum | On the interplay of surface segregation and bulk order in binary alloys[END_REF][START_REF] Hultgren | Selected values of the thermodynamic properties of binary alloys[END_REF] demonstrating a favourable mixing trend.

Beyond composition, the degree and assumed type of order in Fe-Al alloys is temperature dependent. Two order-disorder transitions appear D0 3 ↔ B 2 , B 2 ↔ A 2 . The condition for the existence of a complete disordered solid solution is quite demanding (such as high temperature close to melting point); thus a degree of SRO always exist in A 2 Fe 1-x Al x through a correlation between each lattice site and its immediate surrounding, not only to first nearest neighbours but also to second ones [START_REF] Blum | Segregation and ordering at Fe 1-x Al x (100) surfaces-a model case for binary alloys[END_REF]. In diffraction, SRO appears through diffuse scattering that has been analysed by neutron scattering in the case of Fe 0.8 Al 0.2 to extract effective pair interactions [START_REF] Sanchez | Reciprocal-space analysis of shortrange-order intensities by the cluster-variation method[END_REF]. It turned out that second neighbour contributions are sizeable compared to first neighbour ones; Al atoms have a trend to be surrounded by Fe as first neighbours and a strong preference for Al as second neighbours at low temperature [START_REF] Sanchez | Reciprocal-space analysis of shortrange-order intensities by the cluster-variation method[END_REF][START_REF] Blum | On the interplay of surface segregation and bulk order in binary alloys[END_REF]. This trend appears obviously through the existence of B 2 and D0 3 structures in the phase diagram. The increasing presence of antisites seems to shift the order-disorder B 2 -A 2 transition from close to the melting temperature at x = 0.5 down to 750 K.

Crystallography of Fe 1-x Al x low index surfaces

For a better understanding of the following chapters, it is worth introducing the bulk truncation along the low index surfaces of the main crystal structures found in the bulk phase diagram of Fe 1-x Al x in the range x = 0 -0.5, namely A 2 , B 2 and D0 3 . As this work deals with a surface science analysis, an emphasis will be put on their surface unit cell. As usual, the surface unit cells (a S , b S , c S ) for which c S is normal to the considered face is used to describe the crystallography of a given truncation. Later on, in diffraction analysis, the reciprocal space will be defined in the surface unit cell with the corresponding (h S , k S , l S ) indexes. Hereafter, the B and S subscript will stand for bulk and surface related quantities. can also be defined by a S,P = (a S + b S )/2 and b S,P = (-a S + b S )/2; both will be used later on;

Cubic centred A 2 random alloy

• (111): a S = (-4a B + 2b B + 2c B )/3, b S = (2a B -4b B + 2c B )/3, c S = (a B + b B + c B )/2 (a S = b S = 2 √ 2a B / √ 3 = 4.72 Å)
While all atoms are coplanar on (100) and ( 110) faces (see Figs. 3.3, 3.4), the (111) surface of body centred compound is opened and atomically rough; it includes three atomic planes (Fig. 3.5-b) defining a physical monolayer. The distance between atomic planes giving the monoatomic steps (see Figs. [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF], [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF], [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] faces, respectively. The density of atoms per unit of surface is given by: n 100), ( 110), [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] faces leading to the hierarchy n S (100) < n S (111) < n S [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF]. This coverage will be used to define the monolayer for each orientations; this corresponds to 1.20 × 10 15 atm•cm -2 on (100), 1.55 × 10 15 atm•cm -2 on (111) and 1.69 × 10 15 atm•cm -2 on (110).

3.3, 3.4, 3.5-c) is a B /2 = 1.45 Å, a B / √ 2 = 2.04 Å, a B /2 √ 3 = 0.83 Å for
S = 1/a 2 B , n S = √ 2/a 2 B , n S = 3 √ 3/4a 2 B for (

CsCl B 2 ordered alloy

Compared to the A 2 cubic centred random alloy, the ordered B 2 has the same cubic structure but with one type of atom at the nodes of the cube and the other one at the centre (CsCl structure). This "centring" leads to an higher level of complexity for the low index faces as shown in Fig. 3 • (110): the (110) face is mixed with 50 % of Al and 50 % of Fe with coplanar atoms;

• (111): like for A 2 structure, the (111) is terminated by three planes alternatively made out of Fe and Al; therefore the last plane is 100 % Fe or Al and they alternate along the [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] B direction; the surface unit cell is larger than for A 2 -(110).

D0 3 Heussler Fe 3 Al phase

The bulk truncation of the D0 3 Heussler Fe 3 Al (Fe 0.75 Al 0.25 ) is even more complex than the A 2 structure (see Fig. 3.7):

• (100): the (100) bulk termination is made out of either a mixed 50 %-50 % Fe-Al plane or a pure Fe one. All atoms are coplanar. The last plane can be seen as a c(2 × 2) superstructrure of the bcc(100) surface.

• (110): [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] planes are mixed with exactly the bulk composition 75 % Fe -25 % Al.

• (111): along the [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] B direction , pure Al or Fe planes alternate with the same density following the sequence Al-Fe-Fe-Fe.

The surfaces of the Fe 1-x Al x alloy

The surface structures presented above (Sect. 3.2) are only truncations of the bulk infinite crystal. Breaking bonds to create a surface along a given crystallographic direction and reducing locally the coordination of atoms leads to atomic rearrangements such as [START_REF] Heinz | Surface structure and segregation of bimetallic bcc-type alloys[END_REF][START_REF] Desjonqueres | Concepts in surface physics[END_REF]: • normal relaxations: the interlayer spacings of top layers change but preserve the same lateral symmetry; in metals, it is usually inward for the first layer and followed by an damped oscillatory behaviour at deeper layers;

• surface reconstruction: a geometrical in-plane reordering induces a symmetry-breaking compared to bulk truncation (see Sect. 2.3).

Surface segregation is one of the driving forces of reconstructions on both ordered and disordered metallic alloys [START_REF] Bardi | The atomic structure of alloy surfaces and surface alloys[END_REF][START_REF] Vasiliev | Surface effects of ordering in binary alloys[END_REF][START_REF] Polak | The interplay of surface segregation and atomic order in alloys[END_REF]. It consists in an enrichment with a given constituent through diffusion in the vicinity of a surface. For instance, Fe 1-x Al x surfaces are always enriched in Al. For ordered alloys, such an effect can produce new ordered phases or some disordered antisite phase with respect to the bulk. Regarding random alloys with substitutional disorder, a variable concentration of enriched element can be found in near-surface layers (the so-called segregation profile which may be oscillatory) before converging towards the bulk concentration as depth increases [START_REF] Heinz | Surface structure and segregation of bimetallic bcc-type alloys[END_REF]. If the interplay between segregation, LRO, SRO and crystal structure can be quite complex (see review Ref. [START_REF] Bardi | The atomic structure of alloy surfaces and surface alloys[END_REF][START_REF] Vasiliev | Surface effects of ordering in binary alloys[END_REF][START_REF] Polak | The interplay of surface segregation and atomic order in alloys[END_REF]), the commonly accepted driving forces of surface segregation are:

• a reduction of the surface free energy; in this respect, surface energies of pure phases can serve as a guideline: that of Al surface is much lower than that of Fe for all orientations [88-90] (see Tab. 3.2);

• a reduction of surface stress due to different atomic sizes between the solvent and solute;

• a decrease of the elemental heat of vaporisation which reflects in the broken bond model the bond strength of the element under consideration;

• the reaction of one of the alloying element with an adsorbate, among which for instance oxygen; one speaks about induced preferential segregation;

• preferential sputtering may induce an artificial enrichment in one of the elements; ion bombardment is a mandatory step in the preparation of a clean surface; some authors [START_REF] Graupner | Composition and structure of the (100) and (110) surfaces of FeAl[END_REF][START_REF] Hammer | Segregation phenomena on surfaces of the ordered bimetallic alloy FeAl[END_REF][START_REF] Heinz | Surface structure and segregation of bimetallic bcc-type alloys[END_REF][START_REF] Blum | Segregation and ordering at Fe 1-x Al x (100) surfaces-a model case for binary alloys[END_REF][START_REF] Gleason | Water adsorption and thermal decomposition on FeAl (110)[END_REF][START_REF] Kottcke | Segregation-induced subsurface restructuring of FeAl (100)[END_REF][START_REF] Eltester | AES and LEED investigation of Al segregation and oxidation of the (100) face of Fe 85 Al 15 single crystals[END_REF][START_REF] Kizilkaya | Surface reconstruction of FeAl (110) studied by scanning tunnelling microscopy and angle-resolved photoemission spectroscopy[END_REF] The last comment points at the underlying question of the actual equilibrium between bulk and (sub)surface in surface science studies [START_REF] Meier | Equilibration of stoichiometrically distorted Fe 1-x Al x (100) surfaces[END_REF][START_REF] Hammer | Equilibration processes in surfaces of the binary alloy Fe-Al[END_REF] and therefore of the history of the sample after intensive cycles of preparation. In our experiments, we checked the reproducibility of the composition of the surface after sputtering/annealing through ratio of intensities of photoemission peaks (see Sect. 5.1.2.2).

However, if the large surface energy and heat of vaporisation of transition metals compared to Al favours segregation, it can be counterbalanced by a large (absolute) heat of formation of the alloy (the larger this quantity, the less favourable the interchange of constituents). This argument explains (i) why Fe-Al alloys are more prone to Al segregation than Ni-Al or Co-Al ones [START_REF] Hammer | Segregation phenomena on surfaces of the ordered bimetallic alloy FeAl[END_REF] (∆H(FeAl) = -25.1 kJ/mol, ∆H(Fe 3 Al) = -13.0 kJ/mol, ∆H(NiAl) = -58.9 kJ/mol, ∆H(CoAl) = -54.2 kJ/mol) and (ii) why Ni-Al alloys are found nearly bulk terminated compared to Fe-Al ones (see below). Finally, ordering tendency in the alloy will hamper segregation since the latter favours the occupation of neighbouring lattice sites by the same atomic species while ordering causes exactly the opposite [START_REF] Polak | The interplay of surface segregation and atomic order in alloys[END_REF].

In Chaps. 5-6, the profile of segregation (before and after oxidation) and the reconstructions on Fe 0.85 Al 0.15 (100), ( 110) and [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] surface will be analysed with core level photoemission and LEED. The following sections aim at introducing the state-of-the-art on Fe 1-x Al x surfaces.

Auger spectroscopy [START_REF] Gemmaz | Determination of the diffusion coefficient of Al in an Fe-Al alloy by Auger spectrometry[END_REF] evidenced a clear trend of Al segregation in polycrystalline Fe 0.8 Al 0.2 sample with an activation energy of ∼ 2 eV/atom assigned to the diffusion coefficient of Al. It was found that all the surface orientations of Fe 1-x Al x are characterised by Al surface segregation phenomena somewhat more pronounced for the more opened surfaces although no clear trend exist at least for FeAl [START_REF] Hammer | Segregation phenomena on surfaces of the ordered bimetallic alloy FeAl[END_REF]. This is in stark contrast with NiAl for which bulk terminations are observed. The onset of the phenomenon is around 600-800 K [28-30, 32, 93, 96] and depends on bulk composition. Most of the surface science studies on single crystals have been performed by a German group [START_REF] Graupner | Composition and structure of the (100) and (110) surfaces of FeAl[END_REF][START_REF] Meier | Equilibration of stoichiometrically distorted Fe 1-x Al x (100) surfaces[END_REF][START_REF] Hammer | Segregation phenomena on surfaces of the ordered bimetallic alloy FeAl[END_REF][START_REF] Heinz | Surface structure and segregation of bimetallic bcc-type alloys[END_REF][START_REF] Blum | Segregation and ordering at Fe 1-x Al x (100) surfaces-a model case for binary alloys[END_REF][START_REF] Blum | Quantification of substitutional disorder and atomic vibrations by LEED-the role of parameter correlations[END_REF][START_REF] Hammer | Equilibration processes in surfaces of the binary alloy Fe-Al[END_REF][START_REF] Kottcke | Segregation-induced subsurface restructuring of FeAl (100)[END_REF] from the University of Erlangen using Auger spec-troscopy and dynamic LEED, i.e. variation of spot intensities with beam energy to determine atomic positions, relaxations as well as profile of concentration in the first layers. Multiple scattering effects due to the strong electron surface interactions render the quantitative LEED analysis quite complex all the more that a coupling exists in the refinement between elementdependent vibrational amplitudes and compositions. Therefore, results should be taken with caution as it was recognised by the authors themselves [START_REF] Blum | Quantification of substitutional disorder and atomic vibrations by LEED-the role of parameter correlations[END_REF].

Fe

1-x Al x (100)
The ordered B 2 -Fe 0.53 Al 0.47 (100) (a B =2.903 Å) surface [START_REF] Graupner | Composition and structure of the (100) and (110) surfaces of FeAl[END_REF][START_REF] Hammer | Segregation phenomena on surfaces of the ordered bimetallic alloy FeAl[END_REF][START_REF] Kottcke | Segregation-induced subsurface restructuring of FeAl (100)[END_REF] is found depleted in Al after room temperature sputtering. Upon annealing at increasing temperature, Auger spectroscopy evidences an onset of Al segregation around 623 K with a fast equilibration kinetic that depends more on the annealing temperature than on the annealing time. This finding is quite general for all the studied surfaces [28-30, 32, 93, 96]. The LEED pattern (Fig. 3.8) displayed the following transitions: From Refs. [START_REF] Hammer | Segregation phenomena on surfaces of the ordered bimetallic alloy FeAl[END_REF][START_REF] Heinz | Surface structure and segregation of bimetallic bcc-type alloys[END_REF].

diffuse(1 × 1) -→ 623-683 K c(2 × 2) -→ >683 K (1 × 1) (3.
equivalent with that of Fe 0.97 Al 0.03 but with a poor contrast in the LEED pattern [START_REF] Meier | Equilibration of stoichiometrically distorted Fe 1-x Al x (100) surfaces[END_REF][START_REF] Blum | Segregation and ordering at Fe 1-x Al x (100) surfaces-a model case for binary alloys[END_REF][START_REF] Eltester | AES and LEED investigation of Al segregation and oxidation of the (100) face of Fe 85 Al 15 single crystals[END_REF]. The corresponding refined stacking and compositional models of c(2 × 2) surface region with top 4 layers are shown in Fig. 3.10-a. If an STM image of Fe 0.85 Al 0.15 [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF] surface annealed at ∼ 700 K indeed shows locally a c(2 × 2) superstructure demonstrated by the antiphase boundaries (Fig. 3.10-b [START_REF] Blum | Segregation and ordering at Fe 1-x Al x (100) surfaces-a model case for binary alloys[END_REF]), no LEED determination could be obtained for this reconstruction. The c(2 × 2) structure of Fe 0.70 Al 0.30 [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF] is quite close to that observed on Fe 0.53 Al 0.47 with a nearly full aluminium capping. It should be noted that, the same c(2 × 2) superstructure forms on Fe-Al alloys with different bulk atomic arrangements (see phase diagram Fig. 3.1), i.e. (i) for x = 0.03, 0.15 on top of a randomly occupied A 2 lattice, (labelled as c(2 × 2) I ) and (ii) for x = 0.30, 0.47 on top of a D0 3 lattice (x = 0.3) or a thick D0 3 layer (x = 0.47) (labelled as c(2 × 2) II ). This latter reconstruction is observed up to ∼ 700 K which corresponds to the phase transition from D0 3 to B 2 . These structures have been determined mainly from dynamic LEED with some Auger/STM input for decisive pieces of information in terms of composition [28-31, 92, 93].

For the Fe 0.85 Al 0.15 (100) surface above 1100 K, the faint c(2 × 2) phase is replaced by a (1 × 1) phase with an Al segregation beyond half a monolayer [START_REF] Blum | Segregation and ordering at Fe 1-x Al x (100) surfaces-a model case for binary alloys[END_REF][START_REF] Eltester | AES and LEED investigation of Al segregation and oxidation of the (100) face of Fe 85 Al 15 single crystals[END_REF]. The surface Al concentration can reach up to 75% as derived from low energy ion scattering data; the corresponding structural model although questioned later on by the same authors due to correlations in LEED analysis [START_REF] Blum | Quantification of substitutional disorder and atomic vibrations by LEED-the role of parameter correlations[END_REF] is shown in Fig. 3.11 as well as the corresponding STM image. On all (100) terminated surfaces [START_REF] Blum | Segregation and ordering at Fe 1-x Al x (100) surfaces-a model case for binary alloys[END_REF], the oscillatory behaviour of the composition was assigned to the favourable nearest neighbour interactions.

To sum up, a compositional schematic diagram of the equilibrium phases of above-mentioned Fe 1-x Al x (100) surface regions after annealing at high temperatures is shown in Fig. 3.12 [START_REF] Meier | Equilibration of stoichiometrically distorted Fe 1-x Al x (100) surfaces[END_REF] From Ref. [START_REF] Blum | Segregation and ordering at Fe 1-x Al x (100) surfaces-a model case for binary alloys[END_REF]. in terms of reconstruction, subsurface bulk structure and capping layer.

Fe 1-x Al x (110)

To our knowledge, very few studies of (110) orientation of B 2 FeAl have been reported [START_REF] Graupner | Composition and structure of the (100) and (110) surfaces of FeAl[END_REF][START_REF] Hammer | Segregation phenomena on surfaces of the ordered bimetallic alloy FeAl[END_REF][START_REF] Heinz | Surface structure and segregation of bimetallic bcc-type alloys[END_REF][START_REF] Kizilkaya | Surface reconstruction of FeAl (110) studied by scanning tunnelling microscopy and angle-resolved photoemission spectroscopy[END_REF][START_REF] Baddorf | Identification of an incommensurate FeAl 2 overlayer on FeAl (110) using X-ray diffraction and reflectivity[END_REF][START_REF] Kizilkaya | The electronic structure of ultrathin aluminum oxide film grown on FeAl (110): A photoemission spectroscopy[END_REF][START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF][START_REF] Gleason | A photoelectron spectroscopy and thermal desorption study of CO on FeAl (110) and polycrystalline TiAl and NiAl[END_REF].

Annealing at ∼ 673 K the sputtered Al-depleted surface of Fe 0.53 Al 0.47 [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] results in Al segregation with a (2 × 1) superstructure (Fig. 3.13-a) which is supposed to be a thick Fe 3 Al layer on top of FeAl [START_REF] Hammer | Segregation phenomena on surfaces of the ordered bimetallic alloy FeAl[END_REF][START_REF] Heinz | Surface structure and segregation of bimetallic bcc-type alloys[END_REF]. A higher temperatures (673-873 K or > 1073 K), a superstructure which is commensurate along the [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] direction but not along the [001] direction appears [START_REF] Graupner | Composition and structure of the (100) and (110) surfaces of FeAl[END_REF][START_REF] Hammer | Segregation phenomena on surfaces of the ordered bimetallic alloy FeAl[END_REF][START_REF] Kizilkaya | Surface reconstruction of FeAl (110) studied by scanning tunnelling microscopy and angle-resolved photoemission spectroscopy[END_REF][START_REF] Baddorf | Identification of an incommensurate FeAl 2 overlayer on FeAl (110) using X-ray diffraction and reflectivity[END_REF][START_REF] Kizilkaya | The electronic structure of ultrathin aluminum oxide film grown on FeAl (110): A photoemission spectroscopy[END_REF] (Fig. 3.13b). It is characterised by a matrix M s = 1 0.7 0 1.41 due to a quasi-hexagonal arrangement of atoms imaged in STM [START_REF] Kizilkaya | Surface reconstruction of FeAl (110) studied by scanning tunnelling microscopy and angle-resolved photoemission spectroscopy[END_REF][START_REF] Kizilkaya | The electronic structure of ultrathin aluminum oxide film grown on FeAl (110): A photoemission spectroscopy[END_REF] and limited to the last plane according to diffraction [START_REF] Baddorf | Identification of an incommensurate FeAl 2 overlayer on FeAl (110) using X-ray diffraction and reflectivity[END_REF]. Diffraction [START_REF] Baddorf | Identification of an incommensurate FeAl 2 overlayer on FeAl (110) using X-ray diffraction and reflectivity[END_REF] concludes that Fe protudes over Al. The STM image of Fig. 3.14-b is interpreted as Fe atoms surrounded by 6 Al atoms. The periodicities of the superstructure as defined by the distance between two successive Fe atoms based on STM measurements are 4.2 Å and 8.22 Å along [001] and [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] directions respectively, indicating the commensurability along [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] direction (4.1 Å for the substrate). The stoichiometry of the superstructure is close to FeAl 2 with an estimated Al concentration of the last plane of 0.67 according to Auger spectroscopy [START_REF] Baddorf | Identification of an incommensurate FeAl 2 overlayer on FeAl (110) using X-ray diffraction and reflectivity[END_REF] and X-ray diffraction (XRD) results [START_REF] Graupner | Composition and structure of the (100) and (110) surfaces of FeAl[END_REF][START_REF] Hammer | Segregation phenomena on surfaces of the ordered bimetallic alloy FeAl[END_REF]. Relaxations have been also calculated [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF].

In the intermediate regime of temperature (873-973 K), unexplained severe streaking along the [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] direction was observed in LEED by Graupner and coworkers [START_REF] Graupner | Composition and structure of the (100) and (110) surfaces of FeAl[END_REF] (Fig. 3.13-c). While these authors [START_REF] Graupner | Composition and structure of the (100) and (110) surfaces of FeAl[END_REF][START_REF] Hammer | Segregation phenomena on surfaces of the ordered bimetallic alloy FeAl[END_REF] argue that a (1 × 1) bulk terminated surface does not exist, it was observed either after annealing at ≥ 1073 K in Ref. [START_REF] Gleason | A photoelectron spectroscopy and thermal desorption study of CO on FeAl (110) and polycrystalline TiAl and NiAl[END_REF] (Fig. 3.13-d) or at annealing of around 673 K by STM in Ref. [START_REF] Kizilkaya | Surface reconstruction of FeAl (110) studied by scanning tunnelling microscopy and angle-resolved photoemission spectroscopy[END_REF] (see Fig. The more open ( 111), ( 211) and (310) surfaces of FeAl were studied only in Ref. [START_REF] Hammer | Segregation phenomena on surfaces of the ordered bimetallic alloy FeAl[END_REF]. Upon annealing the [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] orientation, in parallel to Al segregation observed through Auger spectroscopy (average concentration c Al ), a series of reconstructions has been found:

diffuse(1×1) -→ 573 K,c Al =0.6 ( √ 3× √ 3)R30 • -→ 873 K,c Al =0.7 (2.4×2.4)R30 • -→ 973 K,c Al =0.75 (3×3)+(3×6)/(6×6) (3.
2) In contrast to the other orientations, c Al increases continuously and almost linearly with temperature. This proves the existence of a severe multilayer Al segregation which can be explained already by the specific open structure of bcc [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF]. Based on LEED and average Auger compositions, it was assumed that, like on other surfaces, the (

√ 3 × √ 3)R30 • corre-
sponds to a reconstruction on a thick Fe 3 Al D0 3 slab while the (3 × 3) was assigned to a regular array of pyramids with microfacets having a lower energy. A tentative model for the close-packed microfaceted (3×3) surface is shown in Fig. 3.15-c. However, it should be noticed that the corrugated amplitude of FeAl [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] surface is comparable with the escape depth of Auger electrons increasing the uncertainty in the determination of near-surface concentration on which these conclusions are based [START_REF] Hammer | Segregation phenomena on surfaces of the ordered bimetallic alloy FeAl[END_REF].

The (210) displays a (1 × 3) reconstruction while the (310) is not stable at all and microfacets along the [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF] direction.

Conclusion

Although, according to bulk properties, Fe-Al is an ordering system which should favour bulk termination, its surfaces are dominated by strong segregation effects. Al being the element with the lowest bulk binding energy, it segregates to the surface in a way that depends on the composition, bulk atomic structure, temperature and crystal orientation. The (1 × 1) termination is not the rule, except after sputtering, and a rich set of reconstructions has been observed in which a strong coupling between chemical and substitutional disorder happens. Even ordered Fe-Al compositions are prone to segregation.

Sometimes it may be hard to state whether a certain stoichiometric state or chemical order that is reached is stable or still metastable and only frozen [START_REF] Heinz | Surface structure and segregation of bimetallic bcc-type alloys[END_REF]. Transient states are often observed; through the comparison of several Fe 1-x Al x compositions, some authors [START_REF] Hammer | Equilibration processes in surfaces of the binary alloy Fe-Al[END_REF] concluded at a two-step equilibration model according to which a thermal equilibrium happens much faster between the top Al-enriched layer and the subsurface atomic slab than between this latter and the bulk. During the course of annealing, the altered layer is ruled by bulk like atomic interaction and follows the actual phase diagram in the sequence A 2 → D0 3 → B 2 .

Oxides at the surfaces of aluminium metallic alloys

In this section, the literature on the aluminium oxide thin films formed at the surfaces of metallic (alloy) substrates is briefly reviewed (see review [START_REF] Wu | Preparation, characterisation and structure of Ti and Al ultrathin oxide films on metals[END_REF]). After a starter on the necessary description of the atomic structures of the alumina polymorphs on which rely most of the surface science analysis, the emphasis is put on the most studied substrates (in particular NiAl) and the effects of orientation and reduced dimensionality on the structure of the formed ultrathin alumina films. The section ends with a summary of the common characteristics of those films.

The bulk alumina polymorphs

Alumina is a ceramic material with a high melting point (2323 K) and a large band gap (8.8 eV) that has numerous applications as a catalyst by itself, a support of catalytically active metallic nanoparticles, a soft abrasive, an electrical insulator or a tunnelling barrier [START_REF] Gitzen | Alumina as a ceramic material[END_REF][START_REF] Levin | Metastable alumina polymorphs: crystal structures and transition sequences[END_REF]. Alumina presents a great variety of polymorphs which consist in oxygen sub-lattice in which the Al cations occupy tetrahedral and/or octahedral distorted sites. The type of oxygen stacking and the differences in occupation probability of these vacancy sites determine the crystal structure. The most common polymorphs and their characteristics are gathered in Tab. 3.3; some of atomic structures are represented in Fig. 3.16. Depending upon the stacking sequence, three groups of alumina can be distinguished:

• ABAB. . . stacking: the oxygen sub-lattice has a hexagonal compact (hcp) structure; α-alumina is the most representative of this group;

• ABCABC . . . stacking: the oxygen sub-lattice has a face centred cubic structure (fcc); γ-alumina is among those;

• Disordered stacking: the oxygen sub-lattice has neither a hcp nor a fcc structure (ex: β-alumina).

The distance between oxygen atoms in the packed hexagonal planes is in the range of 2.75 Å for all the compounds. The distance between O planes is around 2. Table 3.3: Crystal structures of the most important alumina polymorphs. "Octa" and "Tetra" stands for octahedral and tetrahedral sites, respectively.

is distributed between 1.65 and 2 Å.

On a thermodynamic point of view, the most stable phase is α-Al 2 O 3 known as corundum. α-Al 2 O 3 is the final product of the dehydration sequence of trihydroxides Al(OH) 3 (gibbsite) and the aluminium oxide-hydroxides AlOOH (boehmite). During dehydration, several transient phases occur depending on the temperature. But the followed reaction pathways depend on temperature, precursors and atmosphere (vacuum/water content); reaction sequences are irreversible and all the transition aluminas are stable at room temperature. Some structures do not have an exact Al 2 O 3 stoichiometry due to partial occupancy of sites; some of them are even still debated on a crystallographic point of view.

Although being rhombohedral, α-Al 2 O 3 is often described in a hexagonal unit cell containing 18 planes of pure Al or O that stack along the [0001] direction with the sequence O-Al-Al where the distance between planes in Al-Al bilayer is 0.485 Å. The distance between successive O plane in the hcp stacking is c/6=2.165 Å. In this structure, Al atoms occupy only distorted octahedral sites with two Al-O bond lengths (1.86 and 1.96 Å). γ-Al 2 O 3 has a defect spinel structure with Al ions distributed between octahedral and tetrahedral sites. θ-Al 2 O 3 alumina is closely related to γ-Al 2 O 3 . Through a slight change of the arrangement of the Al ions in the interstices, the lattice becomes monoclinic instead of cubic. The local geometry of the ion configuration (bond lengths and angles) is the same of those of γ-Al 2 O 3 . The last alumina to mention is amorphous aluminium oxide a-Al 2 O 3 . Even if it lacks long-range order, it has a significant short-range order like in glass; it can be described as oxygen clusters with aluminium in their tetrahedral vacancies.

Surface structures of α-Al 2 O 3

On a surface science point of view, only the various surfaces of the thermodynamically stable α-Al 2 O 3 polymorph have been studied in the literature due to the availability of large scale and good quality single crystals. Studies have been reviewed in Refs. [START_REF] Renaud | Oxide surfaces and metal/oxide interfaces studied by Grazing Incidence X-Ray Scattering[END_REF][START_REF] Kelber | Alumina surfaces and interfaces under non-ultrahigh vacuum conditions[END_REF][START_REF] Woodruff | Quantitative structural studies of corundum and rocksalt oxide surfaces[END_REF]. The discussion will be restricted herein to the most stable (0001) orientation. Due to the stacking [START_REF] Goniakowski | Polarity of oxide surfaces and nanostructures[END_REF] (i.e. without a dipolar moment perpendicular to the surface that increases dramatically the surface energy). Theoretical and experimental studies agree that the (1 × 1) (0001) surface prepared in ultra-high vacuum conditions is Al terminated with a strong inward relaxation (∼ 50 % ) followed by sizeable ones for the next planes [START_REF] Guénard | Determination of the α-Al 2 O 3 (0001) surface relaxation by measurements of crystal truncation rods[END_REF]. On the other hand, hydroxylated surfaces are terminated by an OH-plane [START_REF] Eng | Structure of the hydrated α-Al 2 O 3 (0001) surface[END_REF]. High temperature annealing under vacuum leads to a series of O-deficient reconstructions: [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] has been solved by surface X-ray diffraction [START_REF] Renaud | Oxide surfaces and metal/oxide interfaces studied by Grazing Incidence X-Ray Scattering[END_REF][START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF]. It is terminated by 5 Al planes upon removal of the last two O planes of the corundum structure. The structure of the last two Al planes is very close to that of Al [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF].

sequence). Through simple electrostatic arguments, only termination (i) with only one Al plane is self-compensated on chemical and polarity points of views

(1×1) -→ 1473 K ( √ 3× √ 3)R30 • -→ (2 √ 3×2 √ 3)R30 • -→ 1573 K (3 √ 3×3 √ 3)R30 • -→ 1673 K ( √ 31× √ 31)R±9 • Only the last reconstruction ( √ 31 × √ 31)R ± 9 • [

Alumina thin films on metallic alloys

In binary alloys A 1-x B x , if the species B possesses a higher oxygen affinity compared to A, the oxidation tends to produce a BO y compound at the surface, through the so-called selective or preferential oxidation [START_REF] Wu | Preparation, characterisation and structure of Ti and Al ultrathin oxide films on metals[END_REF][START_REF] Finnis | The oxidation of NiAl: What can we learn from ab initio calculations?[END_REF]. This oxidation is accompanied by a depletion in B and enrichment in A in the near surface region. If the A 1-x B x is a defined compound, the species in excess may dissolve in the bulk to keep the stoichiometry ratio under the oxide while for a random alloy, a gradient of concentration builds up. The prototypical examples are (i) chromia on M-Cr alloys, M being Fe [START_REF] Swaminathan | Thermodynamic and kinetic aspects on the selective surface oxidation of binary, ternary and quarternary model alloys[END_REF], Co [START_REF] Zimmermann | Origin of the selective Cr oxidation in CoCr alloy surfaces[END_REF][START_REF] Demczyk | Oxidation behavior of annealed CoCr thin films[END_REF], Ni [START_REF] Wood | High-temperature oxidation of alloys[END_REF][START_REF] Latu-Romain | The role of oxygen partial pressure on the nature of the oxide scale on a NiCr model alloy[END_REF]; and (ii) alumina on M-Al alloys, M being Fe [START_REF] Grabke | Oxidation of NiAl and FeAl[END_REF][START_REF] Nakayama | Selective oxide films of a 5 % aluminum-iron alloy in a low oxygen potential atmosphere[END_REF][START_REF] Prescott | The oxidation of iron-aluminum alloys[END_REF][START_REF] Grace | Selective oxidation of Al from an Al-Fe alloy[END_REF], Ni [START_REF] Kresse | Structure of the ultrathin aluminum oxide film on NiAl (110)[END_REF][START_REF] Stierle | X-ray diffraction study of the ultrathin Al 2 O 3 layer on NiAl (110)[END_REF][START_REF] Rosenhahn | Oxidation of Ni 3 Al (111) at 600, 800, and 1050 K investigated by scanning tunneling microscopy[END_REF], Cu [START_REF] Napetschnig | Ultrathin alumina film on Cu-9 at% Al (111)[END_REF][START_REF] Yoshitake | Interface termination and band alignment of epitaxially grown alumina films on Cu-Al alloy[END_REF] and Co [START_REF] Rose | Growth of ultra-thin amorphous Al 2 O 3 films on CoAl (100)[END_REF][START_REF] Rose | High temperature oxidation of CoAl (100)[END_REF]. Single crystal alloy substrates are preferred platforms to grow well-defined epitaxial thin films and to rationalise the effect of crystallographic orientations and the interplay with segregation; they also offer the opportunity to form oxide films with atomic structures that are metastable in the bulk form or without bulk equivalent. Moreover, film thickness quite often provides enough conductivity to employ surface science characterisation techniques based on charged species.

In this thesis, the orientation dependence of the structure, the composition and the morphology of alumina thin films have been probed on Fe 0.85 Al 0.15 (100), ( 110) and ( 111) surfaces. As explained in Chap. 1, this study is motivated by the upstream control of selective aluminium oxidation on Al-alloyed steel that is detrimental during the hot-dip galvanization process [3,[START_REF] Cavallotti | New routes for improving adhesion at the metal/α-Al 2 O 3 (0001) interface[END_REF][START_REF] Le | Tuning adhesion at metal/oxide interfaces by surface hydroxylation[END_REF]. On the contrary, the use of structural alloys for high temperature applications [START_REF] Deevi | Nickel and iron aluminides: An overview on properties, processing, and applications[END_REF] is quite demanding for the formation of a stable protective alumina against corrosion [START_REF] Heuer | Alumina scale formation: a new perspective[END_REF].

Alumina ultrathin films on metallic substrates can be prepared following different strategies [START_REF] Wu | Preparation, characterisation and structure of Ti and Al ultrathin oxide films on metals[END_REF]:

• surface oxidation of Al- [START_REF] Crowell | Surface sensitive spectroscopic study of the interaction of oxygen with Al (111)-low temperature chemisorption and oxidation[END_REF][START_REF] Cai | Effect of oxygen gas pressure on the kinetics of alumina film growth during the oxidation of Al (111) at room temperature[END_REF][START_REF] Cai | Tuning the limiting thickness of a thin oxide layer on Al (111) with oxygen gas pressure[END_REF][START_REF] Popova | Comparative study of Al (111) oxidation with O 3 and O 2[END_REF] or Al-alloyed (NiAl [START_REF] Stierle | X-ray diffraction study of the ultrathin Al 2 O 3 layer on NiAl (110)[END_REF][START_REF] Ulrich | Growth of thin alumina films on a vicinal NiAl surface[END_REF][START_REF] Franchy | The oxidation of the NiAl (111) surface[END_REF][START_REF] Cai | Growth of ultrathin amorphous alumina films during the oxidation of NiAl (100)[END_REF], Ni 3 Al [START_REF] Hamm | Surface structure of an ultrathin alumina film on Ni 3 Al (111): a dynamic scanning force microscopy study[END_REF][START_REF] Kurnosikov | Atomic structure and electronic properties of Ni 3 Al (001) surface[END_REF][START_REF] Rosenhahn | The formation of Al 2 O 3 -layers on Ni 3 Al (111)[END_REF],

FeAl [START_REF] Graupner | Oxidation of low-index FeAl surfaces[END_REF][START_REF] Grabke | Oxidation of NiAl and FeAl[END_REF][START_REF] Kizilkaya | The electronic structure of ultrathin aluminum oxide film grown on FeAl (110): A photoemission spectroscopy[END_REF][START_REF] Kizilkaya | Formation of aluminum oxide thin films on FeAl (110) studied by STM[END_REF][START_REF] Xu | High temperature oxidation behaviour of FeAl intermetallics-oxide scales formed in ambient atmosphere[END_REF], CuAl [START_REF] Napetschnig | Ultrathin alumina film on Cu-9 at% Al (111)[END_REF][START_REF] Yoshitake | Interface termination and band alignment of epitaxially grown alumina films on Cu-Al alloy[END_REF][START_REF] Yoshitake | AES and LEED study of well-ordered oxide film grown on Cu-9 at.% Al (111)[END_REF] and CoAl [START_REF] Rose | Growth of ultra-thin amorphous Al 2 O 3 films on CoAl (100)[END_REF][START_REF] Rose | High temperature oxidation of CoAl (100)[END_REF]) single crystal surface,

• growing alumina on other metallic substrate such as Ni(111) [START_REF] Prévot | Sixton rectangles in the structure of alumina ultrathin films on metals[END_REF][START_REF] Nemšák | Growth of thin epitaxial alumina films onto Ni (111): an electron spectroscopy and diffraction study[END_REF], Co(0001) [START_REF] Nemšák | Depth profiling of ultra-thin alumina layers grown on Co (0001)[END_REF], Cu(111) [START_REF] Nemšák | Growth of thin epitaxial alumina films onto Ni (111): an electron spectroscopy and diffraction study[END_REF]) via (i) reactive deposition of Al in an oxidising atmosphere or (ii) postoxidation after deposition of Al followed by a thermal treatment in an oxidising agent.

In the following, the studies done on surface oxidation on aluminium metallic alloys will be briefly reviewed in connection with the present work. In particular, those studies performed on Al [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] 110), ( 100), ( 111) surfaces (Sect. 3.4.3.6) [13-16, 18, 99, 121-125, 127-130, 132-134, 137-139, 143-196] provide keys to understand the work performed herein on Fe 0.85 Al 0.15 single crystals.

Alumina grown on Al crystal

Alumina film formed on Al [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] surface via oxidation method is not well crystallised and its thickness is self-limited [START_REF] Wu | Preparation, characterisation and structure of Ti and Al ultrathin oxide films on metals[END_REF][START_REF] Crowell | Surface sensitive spectroscopic study of the interaction of oxygen with Al (111)-low temperature chemisorption and oxidation[END_REF][START_REF] Cai | Effect of oxygen gas pressure on the kinetics of alumina film growth during the oxidation of Al (111) at room temperature[END_REF][START_REF] Cai | Tuning the limiting thickness of a thin oxide layer on Al (111) with oxygen gas pressure[END_REF][START_REF] Popova | Comparative study of Al (111) oxidation with O 3 and O 2[END_REF][START_REF] Kiejna | Stability of oxygen adsorption sites and ultrathin aluminum oxide films on Al (111)[END_REF]. Indeed, the low melting temperature of aluminium (933 K) severely limits recrystallisation annealing. The self-limited thickness is often described in the frame of the Cabrera-Mott model [START_REF] Cabrera | Theory of the oxidation of metals[END_REF]. According to it, an electric field is formed across the oxide film due to the potential difference of the metal-oxide and the oxygen-oxide work functions resulting from electron tunnelling between the Fermi level of the substrate and acceptor levels of chemisorbed oxygen at the surface. The generated electric field due to this potential difference reduces the energy barrier for the migration of the ions through the oxide. But as the tunnelling current decreases with thickness, the oxidation stops at a saturating thickness.

Cai et al. [START_REF] Cai | Effect of oxygen gas pressure on the kinetics of alumina film growth during the oxidation of Al (111) at room temperature[END_REF][START_REF] Cai | Tuning the limiting thickness of a thin oxide layer on Al (111) with oxygen gas pressure[END_REF] studied the oxidation kinetics of Al [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] by molecular oxygen in the pressure range of 1×10 -8 to 5 Torr at room temperature. The kinetics for dissociative oxygen adsorption can be fitted by a Langmuir isotherm. Oxide growth rate as well as film thickness increase with gas pressure. But, film thickness saturates at ∼ 12.4 Å beyond 1 Torr of oxygen pressure [START_REF] Cai | Effect of oxygen gas pressure on the kinetics of alumina film growth during the oxidation of Al (111) at room temperature[END_REF][START_REF] Cai | Tuning the limiting thickness of a thin oxide layer on Al (111) with oxygen gas pressure[END_REF]. Oxygen populates surface and then subsurface sites [START_REF] Crowell | Surface sensitive spectroscopic study of the interaction of oxygen with Al (111)-low temperature chemisorption and oxidation[END_REF][START_REF] Kiejna | Stability of oxygen adsorption sites and ultrathin aluminum oxide films on Al (111)[END_REF] but in the explored temperature range, oxygen pressure weights more than oxidation temperature for oxide growth rate. Kiejna et al. [START_REF] Kiejna | Stability of oxygen adsorption sites and ultrathin aluminum oxide films on Al (111)[END_REF] used first-principle density-functional calculations to explore the structure of oxygen adsorption sites on Al [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF]. They found that for on-surface sites, O atoms (1 monolayer) prefer to be chemisorbed in hcp hollow sites, and for subsurface, the most stable structure is O-(1 × 1) in tetrahedral sites below the top-most Al layer. Thus these two O layers induce a very large increase in the mean interplanar distance of top-most layers that consequently deteriorate the surface crystalline structure [START_REF] Wu | Preparation, characterisation and structure of Ti and Al ultrathin oxide films on metals[END_REF][START_REF] Kiejna | Stability of oxygen adsorption sites and ultrathin aluminum oxide films on Al (111)[END_REF].

Ni x Al

Thin oxide films on Ni x Al (x = 1, 3) single crystal have been intensively studied not only per se as an alloy for high temperature applications [START_REF] Deevi | Nickel and iron aluminides: An overview on properties, processing, and applications[END_REF] but also mostly as a support in fundamental surface science studies of catalytic activity of metallic nanoparticles [START_REF] Wu | Preparation, characterisation and structure of Ti and Al ultrathin oxide films on metals[END_REF][START_REF] Bäumer | Metal deposits on well-ordered oxide films[END_REF][START_REF] Freund | Oxide ultra-thin films on metals: new materials for the design of supported metal catalysts[END_REF]. Well-ordered and crystallised alumina films can be formed on all the low index surfaces [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF], [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] 111) and ( 110) alloys have Al atoms located above Ni atoms [START_REF] Jurczyszyn | Atomic structure and electronic properties of Ni 3 Al (111) and (011) surfaces[END_REF][START_REF] Vesselli | The Ni 3 Al (111) surface structure: experiment and theory[END_REF]. Annealing the crystal to above 1070 K is required to restore stoichiometric Ni 3 Al composition after ion bombardment [START_REF] Jurczyszyn | Atomic structure and electronic properties of Ni 3 Al (111) and (011) surfaces[END_REF][START_REF] Shen | Studies of surface composition, structure and oxygen adsorption of Ni 3 Al (110) by Li + and He + ion scattering[END_REF]. [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] Alumina ultrathin film formed on a NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] surface by high temperature or two-step (exposure followed by annealing) oxidation in the low UHV exposure regimes was the one most extensively studied system [13-15, 145, 146, 148, 149, 151, 152]. The NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] surface unit cell is a centred rectangle with cmm symmetry with zigzag Ni and Al atoms in equal amount. After ion bombardment and flash-annealing to 1300 K, clean NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] surface is characterised by a rumpling: Al atoms stick out of the top-most layer by 0.2 Å and Ni atoms relax inward towards the second layer by 0.12 Å. These outward relaxed Al atoms are detected through a -0.13 eV shift on the Al 2p spectra [START_REF] Stierle | Observation of bulk forbidden defects during the oxidation of NiAl (110)[END_REF][START_REF] Stierle | Surface core level shift observed on NiAl (110)[END_REF].

NiAl

Besides the lack of Ni oxidation, photoemission shows that the oxide film thickness on NiAl( 110) is limited to two bilayers (5-11 Å by photoemission [START_REF] Jaeger | Formation of a well-ordered aluminium oxide overlayer by oxidation of NiAl(110)[END_REF][START_REF] Song | X-ray photoelectron spectroscopy and low-energy electron diffraction study on the oxidation of NiAl (110) surfaces at elevated temperatures[END_REF][START_REF] Yoshitake | Well-ordered ultra-thin Al 2 O 3 film formation on NiAl (110) by high-temperature oxidation[END_REF] and has a large band gap (6.7 eV) but lower than bulk alumina phases [START_REF] Jaeger | Formation of a well-ordered aluminium oxide overlayer by oxidation of NiAl(110)[END_REF][START_REF] Andersson | Metal-oxide interaction for metal clusters on a metal-supported thin alumina film[END_REF]. The surface unit cell of ultrathin films was determined through LEED [START_REF] Jaeger | Formation of a well-ordered aluminium oxide overlayer by oxidation of NiAl(110)[END_REF][START_REF] Libuda | Structure and defects of an ordered alumina film on NiAl (110)[END_REF] in particular in the Spot Profile Analysis of Libuda et al. [START_REF] Libuda | Structure and defects of an ordered alumina film on NiAl (110)[END_REF]. As confirmed extensively later by STM [START_REF] Libuda | Structure and defects of an ordered alumina film on NiAl (110)[END_REF][START_REF] Ulrich | Growth of thin alumina films on a vicinal NiAl surface[END_REF][START_REF] Kulawik | Atomic structure of antiphase domain boundaries of a thin Al 2 O 3 film on NiAl (110)[END_REF][START_REF] Simon | Atomically resolved force microscopy images of complex surface unit cells: Ultrathin alumina film on NiAl (110)[END_REF][START_REF] Schmid | Oxygen-deficient line defects in an ultrathin aluminum oxide film[END_REF][START_REF] Mccarty | Translation-related domain boundaries form to relieve strain in a thin alumina film on NiAl (110)[END_REF], the LEED pattern (Fig. 3.17-a, b) reveals that the oxide film is composed of two domains having a quasi-rectangular large unit cell rotated by ∼ 24 • from the [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] direction. One domain may be favoured on vicinal substrate via a stress relief mechanism [START_REF] Ulrich | Growth of thin alumina films on a vicinal NiAl surface[END_REF]. The unit cell parameters were found as a ox = 17. The initial studies concluded at a structure close to that of α-or γ-alumina through a comparison to vibrational fingerprints of Electron Energy Loss Spectroscopy with known aluminium compounds [START_REF] Jaeger | Formation of a well-ordered aluminium oxide overlayer by oxidation of NiAl(110)[END_REF], Transmission Electron Microscopy [START_REF] Klimenkov | Transmission electron microscopic investigation of an ordered Al 2 O 3 film on NiAl (110)[END_REF] or STM imaging of the compact [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] planes [START_REF] Ceballos | Structure investigation of the topmost layer of a thin ordered alumina film grown on NiAl (110) by low temperature scanning tunneling microscopy[END_REF]. Later on, a surface X-ray diffraction study [START_REF] Stierle | X-ray diffraction study of the ultrathin Al 2 O 3 layer on NiAl (110)[END_REF] pointed at the formation of a well-ordered ultrathin κ-Al 2 O 3 -like layer with a strong distorted double layer structure. This latter was assigned to hexagon-like arranged oxygen ions interacting strongly with NiAl(110) substrate. Aluminium ions occupy equally octahedral and tetrahedral sites but with two bonds that are unphysically short (Al-Al, 2.08 Å, Al-O, 1.51 Å). This model was challenged by Kresse et al. [START_REF] Kresse | Structure of the ultrathin aluminum oxide film on NiAl (110)[END_REF] who concluded that the alumina film on NiAl( 110) is related to neither bulk α-corundum nor to γ-or κ-alumina. By combining atomically resolved STM and ab initio calculations, they concluded at a bilayer film with a stacking sequence and stoichiometry of 4(Al

2+ 4 O 2- 6 Al 3+ 6 O 2- 7
), corresponding to interfacial Al (Al i ), interfacial O (O i ), surface Al (Al s ) and surface O (O s ) ions. The oxide unit cell (white rectangles in Fig. 3.18), with 16 NiAl surface unit cells beneath, is nearly commensurate along the diagonal of the oxide unit cell (yellow line). In this structure, 24 surface Al atoms are arranged nearly in hexagons (Fig. 3.18-e) together with 28 coplanar oxygen atoms (Fig. 3.18c). Among these 24 surface Al atoms, 12 are tetrahedrally coordinated and 12 pyramidally coordinated with surface O atoms (Fig. 3.18-a, f). The 16 interfacial Al atoms are in pentagonheptagon pairs (blue lines, Fig. 3. c,d); one interfacial Al atom shares one valence electron with Ni atom underlying and two valence electrons with the oxide film. In Fig. 3.18-d, the interface structure is visualised and the thickness of alumina film (Fig. 3.18-b) is around ∼ 5 Å. The average surface Al-Al distance around 3.03 Å is in accord with the well known [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF]. The proposed model matches perfectly data from the literature in particular core level shifts [START_REF] Martin | High-resolution corelevel spectroscopy study of the ultrathin aluminum oxide film on NiAl (110)[END_REF], STM [START_REF] Kresse | Structure of the ultrathin aluminum oxide film on NiAl (110)[END_REF], atomic resolved Atomic Force Microscopy [START_REF] Simon | Atomically resolved force microscopy images of complex surface unit cells: Ultrathin alumina film on NiAl (110)[END_REF][START_REF] Li | Atomic force microscopy identification of Al-sites on ultrathin aluminum oxide film on NiAl (110)[END_REF][START_REF] Simon | Atomic structure of the ultrathin alumina on NiAl (110) and its antiphase domain boundaries as seen by frequency modulation dynamic force microscopy[END_REF][START_REF] Heinke | Structure and electronic properties of step edges in the aluminum oxide film on NiAl (110)[END_REF], vibrational spectroscopy [START_REF] Jaeger | Formation of a well-ordered aluminium oxide overlayer by oxidation of NiAl(110)[END_REF][START_REF] Kresse | Structure of the ultrathin aluminum oxide film on NiAl (110)[END_REF] and diffraction [START_REF] Stierle | X-ray diffraction study of the ultrathin Al 2 O 3 layer on NiAl (110)[END_REF]. A similar structure was also observed during oxidation of Al deposits on Ni [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] [START_REF] Prévot | Archetypal structure of ultrathin alumina films: Grazing-incidence X-ray diffraction on Ni (111)[END_REF][START_REF] Prévot | Sixton rectangles in the structure of alumina ultrathin films on metals[END_REF].

( √ 31 × √ 31)R ± 9 • ) high temperature reconstruction of α-Al 2 O 3 (0001)
Martin et al. [START_REF] Martin | High-resolution corelevel spectroscopy study of the ultrathin aluminum oxide film on NiAl (110)[END_REF] extended previous photoemission analysis of this layer [START_REF] Jaeger | Formation of a well-ordered aluminium oxide overlayer by oxidation of NiAl(110)[END_REF][START_REF] Libuda | Interaction of rhodium with hydroxylated model substrates[END_REF][START_REF] Mulligan | A high-resolution photoemission study of nanoscale aluminum oxide films on NiAl (110)[END_REF]. Based on the model proposed in Ref. [START_REF] Kresse | Structure of the ultrathin aluminum oxide film on NiAl (110)[END_REF], a study via high-resolution core level spectroscopy and Density Functional Theory calculation distinguished oxygen and aluminium atoms residing at the surface and interface. As seen in Fig. 3.19 and Tab. 3.4, Al 2p 3/2 spectra can be decomposed into 4 components, corresponding to the NiAl substrate (72.5 eV), to the interfacial Al atoms between the oxide and the NiAl substrate (72.4 eV), to the interfacial Al atoms in the oxide layer (73.5 eV) and to the surface Al atoms (74.77 eV) respectively, in agreement with previous results [START_REF] Nishimura | Structure of an ultrathin aluminum oxide layer grown on a NiAl (110) substrate[END_REF]. The O 1s core level can be decomposed into two components; the weaker has a 19 % intensity of the larger component and derives from surface O atoms bounded to interfacial Al atom underneath [START_REF] Martin | High-resolution corelevel spectroscopy study of the ultrathin aluminum oxide film on NiAl (110)[END_REF].

These alumina layers on NiAl(110) possess three kinds of defects, which are oxide step edges, reflection domain boundaries and antiphase domain boundaries (Fig. 3.20) [START_REF] Libuda | Structure and defects of an ordered alumina film on NiAl (110)[END_REF][START_REF] Stierle | X-ray diffraction study of the ultrathin Al 2 O 3 layer on NiAl (110)[END_REF][START_REF] Kulawik | Atomic structure of antiphase domain boundaries of a thin Al 2 O 3 film on NiAl (110)[END_REF][START_REF] Simon | Atomic structure of the ultrathin alumina on NiAl (110) and its antiphase domain boundaries as seen by frequency modulation dynamic force microscopy[END_REF][START_REF] Simon | Atomic structure of surface defects in alumina studied by dynamic force microscopy: strainrelief-, translation-and reflection-related boundaries, including their junctions[END_REF][START_REF] Schmid | Oxygen-deficient line defects in an ultrathin aluminum oxide film[END_REF][START_REF] Hansen | Palladium nanocrystals on Al 2 O 3 : structure and adhesion energy[END_REF][START_REF] Mccarty | Translation-related domain boundaries form to relieve strain in a thin alumina film on NiAl (110)[END_REF][START_REF] Heinke | Structure and electronic properties of step edges in the aluminum oxide film on NiAl (110)[END_REF]. Oxide step edges are introduced by the atomic steps of the substrate, reflection domain boundaries separate domains orientated differently due to the 2-fold symmetry of the substrate, while antiphase domain boundaries are between domains with the same orientation, which are identified as straight (along the small oxide unit cell vector) and zigzagged (along the diagonal of the oxide unit cell) types [START_REF] Kulawik | Atomic structure of antiphase domain boundaries of a thin Al 2 O 3 film on NiAl (110)[END_REF][START_REF] Simon | Atomic structure of the ultrathin alumina on NiAl (110) and its antiphase domain boundaries as seen by frequency modulation dynamic force microscopy[END_REF]. Antiphase domain boundary occur between translation related domains which equivalent sites are related by a displacement vector that cannot be expressed as an integer multiple of the surface lattice constant. They From Ref. [START_REF] Martin | High-resolution corelevel spectroscopy study of the ultrathin aluminum oxide film on NiAl (110)[END_REF].

are believed to lower the strain energy in the film [START_REF] Kulawik | Atomic structure of antiphase domain boundaries of a thin Al 2 O 3 film on NiAl (110)[END_REF][START_REF] Schmid | Oxygen-deficient line defects in an ultrathin aluminum oxide film[END_REF][START_REF] Mccarty | Translation-related domain boundaries form to relieve strain in a thin alumina film on NiAl (110)[END_REF] and to be oxygen deficient F 2+ like centre [START_REF] Schmid | Oxygen-deficient line defects in an ultrathin aluminum oxide film[END_REF] with stoichiometry (NiAl) . They are preferential nucleation sites for metallic clusters due to their specific electronic structure [START_REF] Schmid | Oxygen-deficient line defects in an ultrathin aluminum oxide film[END_REF] leading to unoccupied states in the band gap of the oxide [START_REF] Schmid | Oxygen-deficient line defects in an ultrathin aluminum oxide film[END_REF][START_REF] Nilius | Defect-induced gap states in Al 2 O 3 thin films on NiAl (110)[END_REF][START_REF] Heinke | Local work function differences at line defects in aluminium oxide on NiAl (110)[END_REF].

Finally, another preparation method through multistep selective oxidation [START_REF] Krukowski | Anomalous hexagonal superstructure of aluminum oxide layer grown on NiAl (110) surface[END_REF] leads to an atomically flat film with a hexagonal superstructure quite different from the previously described one. Based on STM, it was assigned to α-alumina. At last, much thicker epitaxial film of γ-Al 2 O 3 (111) (several nm) can be obtained through harsher oxidative conditions at high pressure [START_REF] Zhang | γ-Al 2 O 3 thin film formation via oxidation of β-NiAl (110)[END_REF][START_REF] Zhang | Kinetics aspects of initial stage thin γ-Al 2 O 3 film formation on single crystalline β-NiAl (110)[END_REF].

NiAl(100)

Owing to the CsCl-B 2 structure, bulk truncated NiAl( 100) is either Al-or Ni-terminated. The actual structure of the clean surface depends strongly on annealing temperature and duration [START_REF] Stierle | Surface X-ray diffraction study on the initial oxidation of NiAl (100)[END_REF][START_REF] Mullins | The structure and composition of the NiAl (110) and NiAl (100) surfaces[END_REF][START_REF] Blum | Preparation-dependent surface composition and structure of NiAl (001): SPA-LEED and NICISS study[END_REF]. Blum et al. [START_REF] Blum | Preparation-dependent surface composition and structure of NiAl (001): SPA-LEED and NICISS study[END_REF] found that a defective Al terminated surface can be obtained by a prolonged annealing at temperatures lower than 500 K with a (1 × 1) LEED pattern, while the same pattern with a Ni terminated surface appears after flashing to 1400 K and rapid cooling to room temperature. Annealing at 800 K generates a c(

√ 2 × 3 √ 2)R45
• LEED pattern that is characteristic of an Al terminated missing row surface structure [START_REF] Blum | Preparation-dependent surface composition and structure of NiAl (001): SPA-LEED and NICISS study[END_REF]. However, the same pattern is also believed to be due to O, C or N contamination [START_REF] Gassmann | Preparation of a well ordered aluminum oxide layer on NiAl (001)[END_REF][START_REF] Gassmann | Investigations on phase transitions within thin Al 2 O 3 layers on NiAl (001)-HREELS on aluminum oxide films[END_REF].

Fortunately, oxide formation at NiAl(100) is unaffected by the initial composition of the surface [START_REF] Blum | Initial growth of Al 2 O 3 on NiAl (001)[END_REF] but depends mainly on oxygen pressure, temperature and annealing duration [START_REF] Frémy | X-ray photoelectron spectroscopy study of thin oxide layers formed on (001)-oriented β-NiAl single-crystal surfaces[END_REF]. All starting surfaces c( [START_REF] Frémy | X-ray photoelectron spectroscopy study of thin oxide layers formed on (001)-oriented β-NiAl single-crystal surfaces[END_REF][START_REF] Frémy | Initial stages of growth of alumina on NiAl (001) at 1025 K[END_REF] or Ni-terminated/Al-terminated (1×1) [START_REF] Gassmann | Preparation of a well ordered aluminum oxide layer on NiAl (001)[END_REF][START_REF] Gassmann | Investigations on phase transitions within thin Al 2 O 3 layers on NiAl (001)-HREELS on aluminum oxide films[END_REF] produce epitaxial θ-Al 2 O 3 -like alumina with a two-domain (2×1, 1×2) LEED pattern and a thickness close to 1 nm. This structural model was initially proposed based on lattice mismatch arguments with all the known alumina compounds [START_REF] Gassmann | Preparation of a well ordered aluminum oxide layer on NiAl (001)[END_REF] and on vibrational fingerprints in High Resolution Electron Energy Loss Spectroscopy [START_REF] Gassmann | Investigations on phase transitions within thin Al 2 O 3 layers on NiAl (001)-HREELS on aluminum oxide films[END_REF]. The corresponding structure is displayed in Fig. 3.21. The monoclinic θ-Al 2 O 3 of lattice parameters a ox = 5.64 Å, b ox = 2.91 Å, c ox = 11.83 Å, β ox = 104 • consist in fcc oxygen sublattice where Al 3+ ions occupy tetrahedral and octahedral interstices equally. This epitaxy corresponds to the Bain classical orientation relationship between the fcc oxygen sublattice and the bcc NiAl. The mismatch amounts to 2.5 % in one direction (2a NiAl = 5.78 Å) and 1 % along the other direction (b NiAl = 2.89 Å), which explains the (2×1, 1×2) observed LEED pattern very well [START_REF] Gassmann | Preparation of a well ordered aluminum oxide layer on NiAl (001)[END_REF][START_REF] Gassmann | Investigations on phase transitions within thin Al 2 O 3 layers on NiAl (001)-HREELS on aluminum oxide films[END_REF]. The structure was confirmed by X-ray diffraction [START_REF] Stierle | Surface X-ray diffraction study on the initial oxidation of NiAl (100)[END_REF] but with some strong distortions from the bulk θ-alumina; Al prefers tetrahedral sites at the interface and octahedral sites at the surface. Diffraction evidenced a Stranski-Krastanov like growth with 0.76 nm thick layer covered by 2 nm high islands.

√ 2 × 3 √ 2)R45 • [
STM imaging yields to a morphology in the form of orthogonal strips running along the [010] and [001] directions with a mean width of 27 Å and a periodicity of 45 Å [START_REF] Blum | Initial growth of Al 2 O 3 on NiAl (001)[END_REF][START_REF] Frémy | X-ray photoelectron spectroscopy study of thin oxide layers formed on (001)-oriented β-NiAl single-crystal surfaces[END_REF][START_REF] Frémy | Initial stages of growth of alumina on NiAl (001) at 1025 K[END_REF][START_REF] Blum | Growth of Al 2 O 3 stripes in NiAl (001)[END_REF][START_REF] Wang | Under-surface observation of thin-film alumina on NiAl (100) with scanning tunneling microscopy[END_REF]. This lateral anisotropy is assigned to a stress build-up due to the lattice mismatch. As shown by [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] surface depends on the preparation conditions. A clean surface is terminated by a Ni plane with Al in the second layer with double steps and has a (1 × 1) LEED pattern. When annealed up to 1300 K with a coverage of a fraction of monolayer of oxygen contamination, the surface switches to large flat Ni-terminated terraces covered by triangular islands (size 2.5 nm, height 0.8 Å) with azimuthal ordering with respect to the substrate separated by double atomic steps with an average height of 1.7 Å. Annealing at 1400 K can avoid oxygen contamination, generating Ni-terminated surface [START_REF] Niehus | Surface structure of NiAl (111) determined by ion scattering and scanning tunneling microscopy[END_REF]. Usually, the sample is annealed to 1500 K to remove oxide on NiAl [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] [START_REF] Franchy | The oxidation of the NiAl (111) surface[END_REF].

Franchy et al. [START_REF] Franchy | The oxidation of the NiAl (111) surface[END_REF] conducted high temperature oxidation experiments (at 900-1100 K) on oxygen-saturated surfaces covered by amorphous alumina obtained by exposing to O 2 at room Upon exposure of the surface at pressures of 2 × 10 -8 -1 × 10 -6 mbar (exposure∼ 8 L) at 970 K, disordered AlO x overlayer forms on top and oxygen activates Al segregation [START_REF] Shen | Studies of surface composition, structure and oxygen adsorption of Ni 3 Al (110) by Li + and He + ion scattering[END_REF]. When exposed to 2500 L (10 -6 Torr) of O 2 at 800 K followed by annealing to 1100 K, the mixture of NiO and AlO x formed at 800 K are transformed into metallic Ni and Al 2 O 3 due to the reduction of NiO and Al segregation [START_REF] Garza | Characterization of oxidized Ni 3 Al (110) and interaction of the oxide film with water vapor[END_REF]. But none of the studies above put forward a clear structural model for alumina/Ni 3 Al( 110). Yet Qin et al. [START_REF] Qin | Theory and experiments on the structure of 7 Å alumina films grown on Ni 3 Al[END_REF] proposed theoretically a κ-like structure for a 7 Å thick alumina film (i.e., three O-layers) which is produced by annealing the as-formed alumina film (exposed with 500 L of O 2 at 900 K) to 1100 K. The relaxed computed model obtained via ab initio methods is shown in Fig. 3.23. The bottom O-layer is chemisorbed on a plane of Al [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] and the film has a κ-alumina on the first two planes followed by interfacial O( 111)+Al [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] layer on top of Ni 3 Al( 110) substrate [START_REF] Qin | H 2 O-induced instability of Al 2 O 3 /Ni 3 Al (110) and Al 2 O 3 /Ni 3 Al (111) thin films under non-UHV conditions[END_REF][START_REF] Qin | Theory and experiments on the structure of 7 Å alumina films grown on Ni 3 Al[END_REF][START_REF] Jennison | Ab initio structural predictions for ultrathin aluminum oxide films on metallic substrates[END_REF]. 111) plane parallel to the (100) surface of the substrate [START_REF] Podgursky | Ultra thin Al 2 O 3 films grown on Ni 3 Al (100)[END_REF]. The corresponding very complex LEED pattern (Fig. 3.24) is explained by a hexagonal structure with a lattice constant around 3 Å with two domains perpendicular to each other. Extra-spots are assigned to a hexagonal superstructure of lattice constant 17.5 Å [START_REF] Podgursky | Ultra thin Al 2 O 3 films grown on Ni 3 Al (100)[END_REF]. Similar LEED results were previously obtained upon high temperature oxidation above 800 K [START_REF] Bardi | Initial stages of oxidation of the Ni 3 Al alloy: structure and composition of the aluminum oxide overlayer studied by XPS, LEIS and LEED[END_REF]. The 17.5 Å periodicity is assigned to simple dislocation lines that could be described as (5 × 1) reconstruction. The structure of the film depends on the annealing temperature and amorphous oxide is formed at low temperature [START_REF] Rosenhahn | Oxidation of Ni 3 Al (111) at 600, 800, and 1050 K investigated by scanning tunneling microscopy[END_REF][START_REF] Becker | Oxygen adsorption and oxide formation on Ni 3 Al (111)[END_REF]. Oxidation performed on the Ni 3 Al(111) (2 × 2) surface at high temperature (≥ 1000 K) [START_REF] Rosenhahn | Oxidation of Ni 3 Al (111) at 600, 800, and 1050 K investigated by scanning tunneling microscopy[END_REF][START_REF] Hamm | Surface structure of an ultrathin alumina film on Ni 3 Al (111): a dynamic scanning force microscopy study[END_REF][START_REF] Becker | Oxygen adsorption and oxide formation on Ni 3 Al (111)[END_REF][START_REF] Addepalli | STM atomicscale characterization of the γ-Al 2 O 3 film on Ni 3 Al (111)[END_REF][START_REF] Maroutian | Superstructures and coincidences of a thin oxide film on a metallic substrate: A STM study[END_REF][START_REF] Degen | Determination of the coincidence lattice of an ultra thin Al 2 O 3 film on Ni 3 Al (111)[END_REF][START_REF] Gritschneder | Disorder or complexity? Understanding a nanoscale template structure on alumina[END_REF] leads to a well ordered alumina with a thickness of around 5 Å including two compact planes of oxygen. The LEED pattern reveals the presence of two domains of hexagonal symmetry (lattice parameter of around 3 Å) rotated by ∼ 24 • and ∼ 37 • with respect to the substrate. This structure relationship with the substrate was assigned to a distorted γ -Al 2 O 3 [START_REF] Becker | Oxygen adsorption and oxide formation on Ni 3 Al (111)[END_REF][START_REF] Addepalli | STM atomicscale characterization of the γ-Al 2 O 3 film on Ni 3 Al (111)[END_REF] with its (111) plane parallel to the substrate. The assignment is confirmed by specific vibrational fingerprints [START_REF] Becker | Oxygen adsorption and oxide formation on Ni 3 Al (111)[END_REF].

STM imaging pointed [START_REF] Rosenhahn | Oxidation of Ni 3 Al (111) at 600, 800, and 1050 K investigated by scanning tunneling microscopy[END_REF][START_REF] Maroutian | Superstructures and coincidences of a thin oxide film on a metallic substrate: A STM study[END_REF] at the existence of two different hexagonal superstructures at the nanometric scale depending on the bias voltage. Above 3 V, a so-called "network" of b net = 2.6 nm lattice parameter appears while around 2.3 V a "dot" superstructure of b dot = 4.5 nm is observed; both of them are linked by a ( film are very uniform and without apparent defects.

√ 3 × √ 3)R30 • transformation. The
Further STM studies with atomic resolution and Spot Profile Analysis-LEED with a better reciprocal space resolution [START_REF] Degen | Determination of the coincidence lattice of an ultra thin Al 2 O 3 film on Ni 3 Al (111)[END_REF] disclosed that the "dot" superstructure is the actual real superstructure of the alumina film with an unit cell of ( √ 67 × √ 67)R47.78 • with a parameter b dot = 4.16 nm [START_REF] Degen | Determination of the coincidence lattice of an ultra thin Al 2 O 3 film on Ni 3 Al (111)[END_REF] or b dot = 4.14 nm [START_REF] Hamm | Surface structure of an ultrathin alumina film on Ni 3 Al (111): a dynamic scanning force microscopy study[END_REF] while the "network" structure is just a (1/ √ 3 × 1/ √ 3)R30 • reconstruction with b net =2.40 nm [START_REF] Degen | Determination of the coincidence lattice of an ultra thin Al 2 O 3 film on Ni 3 Al (111)[END_REF] or b net =2.39 nm [START_REF] Hamm | Surface structure of an ultrathin alumina film on Ni 3 Al (111): a dynamic scanning force microscopy study[END_REF]. More accurate imaging could be obtained via dynamic Scanning Force Microscopy (SFM) [START_REF] Gritschneder | Disorder or complexity? Understanding a nanoscale template structure on alumina[END_REF] which showed that six dark spots are arranged around the corner of the "dot" structure and the "network" structure covers the entire surface with a honeycomb-like atomic feature (Fig. 3.26) [START_REF] Gritschneder | Disorder or complexity? Understanding a nanoscale template structure on alumina[END_REF]. The commensurability of the substrate, dot structure and network structure is shown in Fig. 3.27. While the dot structure is commensurate with the (2×2) substrate (integer numbers in the transformation matrix), the network structure is incommensurate [START_REF] Degen | Determination of the coincidence lattice of an ultra thin Al 2 O 3 film on Ni 3 Al (111)[END_REF][START_REF] Gritschneder | Disorder or complexity? Understanding a nanoscale template structure on alumina[END_REF]. Finally, the main structural element of the oxide film is a lattice of hexagons (side length of 0.29 nm) that is pinned onto the 0.51 nm grid of the substrate [START_REF] Gritschneder | Disorder or complexity? Understanding a nanoscale template structure on alumina[END_REF]. It is assigned to a distorted hexagonal network of oxygen rotated by 30 • from the substrate [START_REF] Addepalli | STM atomicscale characterization of the γ-Al 2 O 3 film on Ni 3 Al (111)[END_REF]. This large scale superstructure drew some attention also as a potential candidate to grow organised array of nanoparticles through preferential nucleation [START_REF] Hamm | Bimetallic PdAu nanocluster arrays grown on nanostructured alumina templates[END_REF]. 111) substrate (0.51 nm, white), the dot (blue) and the network (red) structures of the oxide. In contrast to the network structure, the dot structure is commensurate with the substrate lattice [START_REF] Gritschneder | Disorder or complexity? Understanding a nanoscale template structure on alumina[END_REF].

Al deposited on Ni(111)

NiAl surface alloys on Ni [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] [START_REF] Prévot | Archetypal structure of ultrathin alumina films: Grazing-incidence X-ray diffraction on Ni (111)[END_REF][START_REF] Prévot | Sixton rectangles in the structure of alumina ultrathin films on metals[END_REF][START_REF] Le Pévédic | Growth of Ni-Al alloys on Ni (111): (I) formation of epitaxial Ni 3 Al from ultra-thin Al deposits[END_REF][START_REF] Le Pévédic | Growth of Ni-Al alloys on Ni (111), from Al deposits of various thicknesses: (II) Formation of NiAl over a Ni 3 Al interfacial layer[END_REF][START_REF] Le Pévédic | Formation of a well-ordered ultrathin aluminum oxide film on Ni (111): Determination of its thickness, composition and structure[END_REF] have also been used as substrates for the growth of ordered alumina thin films. Alloyed layers are obtained by progressive annealing up to 800 K of Al deposits of various amounts on Ni [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] leading to the formation of a relaxed epitaxial NiAl(110) (B 2 -CsCl structure) with three domains at 120 • (NiAl[001] Ni [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF]) on top of a 18 (111) layers of Ni 3 Al (fcc-L1 2 structure) in strained epitaxy on Ni [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF]. In the range of a few Al monolayers deposit, only the Ni 3 Al epitaxial layer is observed while above 800 K, the alloy layer decomposes and Al diffuse into the bulk of Ni.

A well-ordered alumina film is obtained through a two-step recipe, after oxygen exposure at room temperature and annealing at 1000 K of Ni 3 Al(111) alloy layer on Ni [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] [START_REF] Le Pévédic | Formation of a well-ordered ultrathin aluminum oxide film on Ni (111): Determination of its thickness, composition and structure[END_REF]. Ion beam analysis concludes at a stoichiometry close to Al 2 O 3 , a self-limited film thickness of 2.5 ML (two compact planes of oxygen) with a (5

√ 3 × 5 √ 3)R30 • LEED structure quite different from that observed on Ni 3 Al(111) (see Sect. 3.4.3.2.6
). The difference is assigned to the absence of Al in the substrate, this latter has diffused deeply in the bulk upon annealing treatment. However, LEED and STM analysis of Prévot et al. [START_REF] Prévot | Sixton rectangles in the structure of alumina ultrathin films on metals[END_REF] indicates that the actual unit cell corresponds to a sixton rectangle (18.2 × 10.5 Å2 ) inscribed into an hexagon with a ratio between the two sides of the mesh of √ 3. This value is assigned to a specific hexagonal arrangement of oxygen atoms in the plane. This hypothesis was further confirmed by an accurate X-ray diffraction determination of the atomic structure [START_REF] Prévot | Archetypal structure of ultrathin alumina films: Grazing-incidence X-ray diffraction on Ni (111)[END_REF] that found an atomic arrangment very close to that proposed by Kresse for NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] [START_REF] Kresse | Structure of the ultrathin aluminum oxide film on NiAl (110)[END_REF] within small distortions and sharing similarities with η-Al 2 O 3 . The lack of registry and of modifications of the interfacial substrate atom positions lead Prévot et al. [START_REF] Prévot | Archetypal structure of ultrathin alumina films: Grazing-incidence X-ray diffraction on Ni (111)[END_REF][START_REF] Prévot | Sixton rectangles in the structure of alumina ultrathin films on metals[END_REF] to suggest that the oxide film structure common to many substrates of different symmetries and crystalline structure is a paradigm of a free-standing oxide layer (NiAl( 110 Cu-9 at.% Al is a random alloy that crystallises in the fcc structure. When annealed at above 650 K, Al segregation generates a ( √ 3 × √ 3)R30 • superstructure, the corresponding LEED pattern and atomic model of which are displayed in Fig. 3.28 [START_REF] Napetschnig | Ultrathin alumina film on Cu-9 at% Al (111)[END_REF][START_REF] Yoshitake | Interface termination and band alignment of epitaxially grown alumina films on Cu-Al alloy[END_REF][START_REF] Ferrante | An Auger electron spectroscopy and LEED study of equilibrium surface segregation in copper-aluminum alloys[END_REF][START_REF] Yu | Surface segregation of aluminum atoms on Cu-9 at.% Al (111) studied by Auger electron spectroscopy and low energy electron diffraction[END_REF]. From Refs. [START_REF] Napetschnig | Ultrathin alumina film on Cu-9 at% Al (111)[END_REF][START_REF] Yu | Surface segregation of aluminum atoms on Cu-9 at.% Al (111) studied by Auger electron spectroscopy and low energy electron diffraction[END_REF].

Starting from this surface, oxidation at ≥ 900 K leads to an ordered alumina film with a (7/ √ 3 × 7/ √ 3)R30 • superstructure related to γ-Al 2 O 3 [100](111) [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF]Cu-9 at.%Al [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] with a thickness of ∼ 4 Å [START_REF] Yoshitake | AES and LEED study of well-ordered oxide film grown on Cu-9 at.% Al (111)[END_REF][START_REF] Nemšák | Ultra-thin oxide layer formation on Cu-9 % Al (111) surface and Pd growth studied using reflection high energy electron diffraction and Auger electron spectroscopy[END_REF]. However, at the opposite to Refs. [START_REF] Yoshitake | AES and LEED study of well-ordered oxide film grown on Cu-9 at.% Al (111)[END_REF][START_REF] Nemšák | Ultra-thin oxide layer formation on Cu-9 % Al (111) surface and Pd growth studied using reflection high energy electron diffraction and Auger electron spectroscopy[END_REF], LEED analysis and atomic resolved STM study of this layer [START_REF] Napetschnig | Ultrathin alumina film on Cu-9 at% Al (111)[END_REF] point at a crystallographic structure with properties very similar to that of films obtained on NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF]. The film is formed by three domains with a large rectangular unit cell (18.2 × 10.6 Å) rotated by 18 • and 30 • with respect to the close-packed rows of the substrate. Beyond the matching of the unit cell with the structural model proposed by Kresse [START_REF] Kresse | Structure of the ultrathin aluminum oxide film on NiAl (110)[END_REF][START_REF] Napetschnig | Ultrathin alumina film on Cu-9 at% Al (111)[END_REF] which is different from γ type alumina, a good agreement is also obtained on the atomic positions in STM (Fig. [START_REF] Kresse | Structure of the ultrathin aluminum oxide film on NiAl (110)[END_REF]. In (b,e) the primitive unit cell is drawn in black and the four rectangular building blocks are marked in white. From Ref. [START_REF] Napetschnig | Ultrathin alumina film on Cu-9 at% Al (111)[END_REF].

The chemical states of alumina/Cu-9 at.% Al [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] were probed through core level and valence band photoemission. Core levels demonstrate the inertness of Cu; only Al is oxidised. Four components of Al 2p 3/2 peak are presented after oxidation at 910 K: top Al layer of the clean alloy (E B = 72.40 eV), Al in the bulk (E B = 72.58 eV), the interface Al between alloy and epitaxial alumina (E B = 73.63 eV) and Al in the alumina (E B = 74.90 eV) [START_REF] Yoshitake | Interface termination and band alignment of epitaxially grown alumina films on Cu-Al alloy[END_REF]. The valence band spectra obtained with low energy photons at grazing emission reveal that, the position of the valence band maximum of alumina is 4.4 eV below the Fermi level of the substrate [START_REF] Yoshitake | Interface termination and band alignment of epitaxially grown alumina films on Cu-Al alloy[END_REF]. This value is considered being reasonable for Al interface termination from the reported results of first-principles calculations and similar to the well-ordered alumina on NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] [START_REF] Yoshitake | Interface termination and band alignment of epitaxially grown alumina films on Cu-Al alloy[END_REF][START_REF] Andersson | Metal-oxide interaction for metal clusters on a metal-supported thin alumina film[END_REF]. Amazingly a similar oxide structure as determined from LEED and STM has been obtained on the cubic Complex Metallic Alloy (CMA) γ-Al 4 Cu 9 (110) [START_REF] Wardé | Growth and structure of ultrathin alumina films on the (110) surface of γ-Al 4 Cu 9 complex metallic alloy[END_REF]. CMAs [START_REF] Dubois | Complex metallic alloys: fundamentals and applications[END_REF] are characterised by a unit cell containing from a few tens to several thousands atoms arranged into highly symmetric clusters; they share some similarity with quasi-crystals. Small oxide domains with the sixton rectangular unit cell (18.2 × 10.5 Å2 ) rotated by ±23.5 • have been observed after annealing at 925 K the surface oxidised at room temperature. Heptagonalpentagonal atomic arrangements characteristic of the Kresse's structure [START_REF] Kresse | Structure of the ultrathin aluminum oxide film on NiAl (110)[END_REF] appear on STM images.

CoAl(100)

CoAl crystallises in a cubic CsCl-B 2 lattice structure with a parameter of 2.86 Å [START_REF] Mehl | Structural properties of ordered high-melting-temperature intermetallic alloys from first-principles totalenergy calculations[END_REF]. The clean surface has a (1 × 1) LEED pattern with 40-100 nm wide terraces separated by 2.8 Å double atomic steps and it is enriched in Al after annealing at 1470 K for 10 min [START_REF] Rose | Growth of ultra-thin amorphous Al 2 O 3 films on CoAl (100)[END_REF][START_REF] Rose | High temperature oxidation of CoAl (100)[END_REF].

High temperature oxidation of CoAl(100) at ≥ 800 K produces a well ordered θ-Al 2 O 3 film showing a two-domain (2 × 1) LEED pattern having an epitaxial relationship identical to that of θ-Al 2 O 3 /NiAl(100) (Bain orientation, Fig. 3.30-b), thus leading to a small mismatch value of ∼ 1 % along a ox -axis and ∼ 2 % along b ox -axis directions [START_REF] Rose | High temperature oxidation of CoAl (100)[END_REF][START_REF] Gassmann | Preparation of a well ordered aluminum oxide layer on NiAl (001)[END_REF][START_REF] Gassmann | Investigations on phase transitions within thin Al 2 O 3 layers on NiAl (001)-HREELS on aluminum oxide films[END_REF]. Due to the substrate symmetry, the film presents two orthogonal domains as seen in STM (Fig. 3.30-a) with a self-limited thickness of ∼ 10 Å [START_REF] Rose | High temperature oxidation of CoAl (100)[END_REF] and has a band gap of ∼ 4.5 eV [START_REF] Rose | High temperature oxidation of CoAl (100)[END_REF][START_REF] Rose | The band gap of ultrathin amorphous and well-ordered Al 2 O 3 films on CoAl (100) measured by scanning tunneling spectroscopy[END_REF].

Besides θ-Al 2 O 3 phase, it was reported also that phase transformations occur within alumina grown on CoAl(100): (i) single γ or four cubic γ alumina leading to a (2

√ 2 × 2 √ 2)R45 • superstructure [195], (ii) intermediate phases of alumina with a c(2 √ 2 × 6 √ 2)R45
• LEED pattern, and (iii) α-like alumina [START_REF] Podgursky | Study of phase transitions within alumina grown on top of CoAl (100) surface[END_REF]. It should be noted that the phase transformations were achieved by very specific treatments [START_REF] Podgursky | The coexistence of γ (γ ) and θ alumina observed by STM and LEED on top of oxide layer grown on CoAl (100)[END_REF][START_REF] Podgursky | Study of phase transitions within alumina grown on top of CoAl (100) surface[END_REF].

Fe 1-x Al x

The surface science studies of the oxidation of Fe-Al alloys are scarce maybe because of the intense segregation phenomena observed at their surfaces (see Sect. 3.3). Moreover, they are limited to ordered phases: B 2 (CsCl) Fe 0.53 Al 0.47 [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF] [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] [START_REF] Graupner | Oxidation of low-index FeAl surfaces[END_REF][START_REF] Eltester | AES and LEED investigation of Al segregation and oxidation of the (100) face of Fe 85 Al 15 single crystals[END_REF][START_REF] Kizilkaya | The electronic structure of ultrathin aluminum oxide film grown on FeAl (110): A photoemission spectroscopy[END_REF][START_REF] Kizilkaya | Formation of aluminum oxide thin films on FeAl (110) studied by STM[END_REF]] and D0 3 Fe 0.75 Al 0.25 [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] [START_REF] Vonk | In situ x-ray study of Fe 3 Al (110) subsurface superlattice disordering during oxidation[END_REF].

On Fe 0.53 Al 0.47 [START_REF] Graupner | Oxidation of low-index FeAl surfaces[END_REF], high temperature annealings (> 773 K) (with direct exposure to oxygen or with prior oxygen adsorption) are required to achieve ordered phases. Indeed, room temperature oxidation gives rise only to an amorphous oxide. For UHV exposures, the amorphous oxide has a thickness in the range 6 Å on all orientations. Electron spectroscopies clearly demonstrate that only Al is oxidised; Fe stays in its metallic state (Fig. 3. 35-c), except at high oxidation rates for which the oxide thickness is larger (∼ 10 -30 Å). This is in agreement with the hierarchy of enthalpy of formation of the aluminium and iron oxides (∆H(Al 2 O 3 ) = -1676 kJ/mol, ∆H(Fe 2 O 3 ) = -826 kJ/mol, ∆H(Fe 3 O 4 ) = -1118.4 kJ/mol, ∆H(FeO) = -278.0 kJ/mol) [START_REF] Lide | CRC handbook of chemistry and physics[END_REF]). At room temperature, the oxygen uptake of a clean surface [START_REF] Graupner | Oxidation of low-index FeAl surfaces[END_REF] follows a two-step regime, the first one corresponding to the reaction of available Al atoms at the surface, the second to a much slower thickening of the oxide film through a Cabrera-Mott process [START_REF] Cabrera | Theory of the oxidation of metals[END_REF]. All films are found thermally unstable above 1073-1173 K, an instability assigned to Al evaporation from the interface between the oxide overlayer and the substrate.

3.4.3.6.1 Fe 0.53 Al 0.47 [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] In the range of 773-1173 K, the formation of well-ordered oxide film is observed; it grows in island mode at low exposure (10 L) before covering the whole surface (1000 L) [START_REF] Graupner | Oxidation of low-index FeAl surfaces[END_REF]. According to the authors [START_REF] Graupner | Oxidation of low-index FeAl surfaces[END_REF], the LEED pattern of the film shares some similarities with that observed on NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] although the LEED overlap is not fully convincing (see Fig. 3.17 The film thickness is evaluated around 6 ± 1 Å. Besides the two-domain diffraction spots in the LEED pattern, a streak phase (Fig. 3.31-b) is always observed (i) on surface oxidised at 773-973 K and (ii) at higher temperature but for large exposure (10 4 L) indicating a total disorder along [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] direction but a long-range order along [001] direction. No explanation was given for this structure; but a similar streak phase was observed in our measurements on the clean surface and assigned to C contamination (see Chap. 4). Only two articles [START_REF] Kizilkaya | The electronic structure of ultrathin aluminum oxide film grown on FeAl (110): A photoemission spectroscopy[END_REF][START_REF] Kizilkaya | Formation of aluminum oxide thin films on FeAl (110) studied by STM[END_REF] dealt with STM measurements on oxidised Fe 0.53 Al 0.47 (110) (Fig. 3.32). The proposed unit cell from STM measurements (18.6 × 19.4 Å2 rotated by 30 • with respect to [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] direction) is weird compared to LEED [START_REF] Graupner | Oxidation of low-index FeAl surfaces[END_REF], all the more that, according to the authors, only one domain is present on the surface. Based on earlier theoretical model of thin alumina films [START_REF] Jennison | Ab initio structural predictions for ultrathin aluminum oxide films on metallic substrates[END_REF][START_REF] Jennison | Ultrathin aluminum oxide films: Al-sublattice structure and the effect of substrate on ad-metal adhesion[END_REF], they proposed an hypothetical structure model for alumina where Al cations are arranged in nearly the same plane as O anions with Al ions situated in octahedral and tetrahedral sites in the form of zigzag and stripe structures [START_REF] Kizilkaya | Formation of aluminum oxide thin films on FeAl (110) studied by STM[END_REF]. [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF], ( 100) and [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] give rise to at least two chemically shifted Al 2p components [START_REF] Graupner | Oxidation of low-index FeAl surfaces[END_REF][START_REF] Kizilkaya | The electronic structure of ultrathin aluminum oxide film grown on FeAl (110): A photoemission spectroscopy[END_REF] (see Fig. 3.35). The major one associated with the largest binding energy (∆E B = 3 -3.6 eV) corresponds to the bulk of the Al 2 O 3 film and the minor one with the smallest binding energy (∆E B = 0.7 -1.6 eV; ∆E B (110) = 1.2 eV, ∆E B (100) = 1.2 eV, ∆E B (111) = 1.5 eV) is tentatively assigned, not to defects, but to under-coordinated atoms at the interface. The width of the peak is close to experimental resolution pointing at well defined chemical environments. However, the only available Al 2p peak fitting [START_REF] Graupner | Oxidation of low-index FeAl surfaces[END_REF] is questionable since it involves a subtraction of the metallic component prior to Shirley background subtraction and does not take into account the spinorbit splitting of the Al 2p lineshape. Finally, as shown by band structure measurements, the oxide on Fe 0.53 Al 0.47 [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] exhibits a highly two-dimensional electronic structure in accord with its small thickness [START_REF] Kizilkaya | The electronic structure of ultrathin aluminum oxide film grown on FeAl (110): A photoemission spectroscopy[END_REF].

3.4.3.6.5 Fe 0.75 Al 0.25 [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] According to the X-ray diffraction study of Ref. [START_REF] Vonk | In situ x-ray study of Fe 3 Al (110) subsurface superlattice disordering during oxidation[END_REF], the clean Fe 0.75 Al 0.25 [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] comprises a top-most atomic layer with a B 2 order on top of a bulk D0 3 ordered crystal. Upon oxidation at 573 K (1400 L), the crystalline order disappears over a depth of 2-3 nm; at the same time a thin smooth oxide is formed on the surface. While the

Common fingerprints of ultrathin oxide films formed on Alalloys

From the above brief overview of the studies of oxidation performed on some metallic Alalloys [START_REF] Wu | Preparation, characterisation and structure of Ti and Al ultrathin oxide films on metals[END_REF], a common set of conclusions can be drawn:

• the difference of electronic affinity between the alloying element and aluminium in the studied transition metal aluminides is enough to favour only the formation of an aluminium oxide layer; all chemical sensitive spectroscopies (photoemission or Auger spectroscopy) clearly rule out any trace of oxidation of the alloying elements when films [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] before and after oxidation. From Ref. [START_REF] Vonk | In situ x-ray study of Fe 3 Al (110) subsurface superlattice disordering during oxidation[END_REF].

are grown in UHV conditions i.e. in the Knudsen's regime at low exposure; only high exposure rates are needed to deplete the subsurface in aluminium and counterbalance its bulk diffusion rate resulting in the oxidation of the other alloying elements;

• an amorphous oxide is formed at room temperature following chemisorption on aluminium; the formation of well-ordered alumina layer requires a post-annealing step at high temperature (700-1200 K) or a direct oxidation at elevated temperature; in this respect, alloys with high melting temperature like NiAl or FeAl are ideal candidates;

• the film thickness is self-limited, typically to a few compact atomic plane of oxygen (∼ 5 -10 Å); thickening requires much higher oxygen activity and exposure; if determined, the stoichiometry is close to Al 2 O 3 and the last-plane is made out of oxygen atoms at the opposite of bulk α-Al 2 O 3 (0001);

• phase transitions in the film have been rarely highlighted; annealing allows to recrystallise the film, the structure of which never depends on the initial reconstruction of the substrate;

• oxidation induces segregation/depletion in aluminium in the subsurface region; bulk compounds with a narrow composition windows in the bulk phase diagram seem to be more prone to maintain a fixed composition underneath the oxide by dissolving the produced defects; but these points are poorly explored in the literature due to the lack of subsurface or bulk sensitive tools (except with ion beam measurements of Ref. [START_REF] Le Pévédic | Formation of a well-ordered ultrathin aluminum oxide film on Ni (111): Determination of its thickness, composition and structure[END_REF] or X-ray diffraction [START_REF] Vonk | In situ x-ray study of Fe 3 Al (110) subsurface superlattice disordering during oxidation[END_REF]);

• due to the structural complexity, the analysis of the LEED pattern or the interpretation of the STM images does not allow to establish a given model; but STM measurements are crucial for the determination of the topographic defects of the layer; most of the discussions on the structure of the alumina film are based on epitaxy arguments and on the similarity with bulk alumina compounds in terms of vibrational fingerprints; but the few available structural determinations (i.e. atomic positions) [START_REF] Kresse | Structure of the ultrathin aluminum oxide film on NiAl (110)[END_REF][START_REF] Prévot | Archetypal structure of ultrathin alumina films: Grazing-incidence X-ray diffraction on Ni (111)[END_REF][START_REF] Stierle | Surface core level shift observed on NiAl (110)[END_REF] point at strong distortions and/or unusual occupancy of octahedral/tetrahedral sites for Al;

• despite a blurred landscape due to the complexity of multiple domains, some structures appear to be recurrent; one can quote: (i) the large Al 10 O 13 structure with a sixton rectangular unit cell (∼ 18×10 Å2 ) historically studied and solved on NiAl(110) [START_REF] Kresse | Structure of the ultrathin aluminum oxide film on NiAl (110)[END_REF][START_REF] Stierle | Surface core level shift observed on NiAl (110)[END_REF] but presents on many substrates of different crystallographic structures, symmetries or degrees of order (NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF], γ-Al 4 Cu 9 [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF], FeAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF], Al on Ni [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF], Cu-9 at.%Al [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF]) or (i) the θ-distorted alumina assigned to the Bain epitaxy between the fcc stacking of oxygen at the substrate (NiAl(100), CoAl( 100)).

Even if we will see that the oxide layers formed on Fe 0.85 Al 0.15 (see Chap. 6) do not escape the last two cases, the random character of the alloy provides an extra degree of flexibility in terms of segregation that was poorly explored up to now. Carbon coverage can increase in two ways, reaction with gases from the environment [START_REF] Booyens | The adsorption of ethene on Fe (111) and surface carbide formation[END_REF] and segregation upon annealing [START_REF] Grabke | Equilibrium surface segregation of dissolved nonmetal atoms on iron (100) faces[END_REF][START_REF] Musket | Preparation of atomically clean surfaces of selected elements: A review[END_REF][START_REF] Panzner | The bonding state of carbon segregated to α-iron surfaces and on iron carbide surfaces studied by electron spectroscopy[END_REF][START_REF] Arabczyk | Electron spectroscopy studies on carbon segregation from a mono-crystalline α-Fe (111) specimen[END_REF]. The present concern is to study the behaviour of the Fe-Al surfaces with respect to the two phenomena, in order to find protocols to prepare clean surfaces and to keep them in this condition during specific treatments. According to litterature [START_REF] Booyens | The adsorption of ethene on Fe (111) and surface carbide formation[END_REF], the reactivity of surfaces of iron single crystals with alcene molecules is in the order Fe(100) > Fe(111) > Fe [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF]. The same hierarchy is observed for the surface oxidation of FeAl single crystal surfaces at room temperature [START_REF] Graupner | Oxidation of low-index FeAl surfaces[END_REF]. The two observations fulfil the expectation that the denser [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] surface (see Sect. 3.2.1) is the less reactive. Therefore, it is chosen herein to describe (i) the transient carbon segregation observed during the preparation of the as-received Fe 0.85 Al 0.15 [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] in conditions in which the reaction with the residual vacuum is marginal and (ii) the reaction with UHV of the more reactive Fe 0.85 Al 0.15 [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF] and [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] surfaces. Astonishingly, bulk carbon segregation was not observed on the as-received (100) and ( 111) crystals. All the surfaces were found free of other common contaminants of Fe [START_REF] Musket | Preparation of atomically clean surfaces of selected elements: A review[END_REF], such as sulphur or phosphorous but it turn out that oxygen removal after oxidation required intensive sputtering-annealing cycles.

4.1 Carbon segregation at the Fe 0.85 Al 0.15 (110) surface

Graphitic films, chemisorbed carbon and carbide

To study the segregation of carbon, the as-received Fe 0.85 Al 0.15 [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] surface was firstly degassed at ≥ 650 K and then cleaned by cycles of Ar + ion sputtering and annealing at increasing high temperatures in ultra-high vacuum. The transient phenomenon of carbon segregation was analysed through the analysis of C 1s, Al 2p and Fe 3p core level spectra (Fig. 4.1) upon annealing between 670 and 1070 K. The absence of a shoulder on the high binding energy of the metallic Al 2p component at 72 eV is a clear proof of the bulk origin of carbon since contamination from residual vacuum is always accompanied by oxidised Al species (see Fig. 4.10). The Al 2p peak can be decomposed into one spin-orbit split (0.4 eV) asymmetric Doniach-Sunjic line (Fig. 4.1-b and Sect. 6.2.1.2 for explanation and parameters) characteristic of the metallic state. At all temperatures but 870 K, the carbon spectra can be decomposed into two components with Gaussian shapes, one represented by a rather sharp peak at 282.7 eV (1-1.3 eV FWHM) and the other by a broad feature at 284.9 eV (3.5-3.9 eV FWHM). These binding energies correspond quite well to those of chemisorbed carbon and graphitic carbon that were found on Fe(100) at 282.6 eV and 284.6 eV, respectively, by Panzner et al. [START_REF] Panzner | The bonding state of carbon segregated to α-iron surfaces and on iron carbide surfaces studied by electron spectroscopy[END_REF]. The labelling [START_REF] Panzner | The bonding state of carbon segregated to α-iron surfaces and on iron carbide surfaces studied by electron spectroscopy[END_REF] comes from the similarity of lineshape between graphitic carbon and bulk graphite. Although aluminium carbide Al 4 C 3 has a C 1s signature at 282.4 eV [START_REF] Hinnen | An in situ XPS study of sputterdeposited aluminium thin films on graphite[END_REF], its formation can be ruled out since the strong charge transfer to aluminium gives rise to an Al 2p component at 74 eV that is absent in our data. In the case of the 870 K annealing, the broad C 1s component peaks at 284.3 eV (Fig. 4.1). This makes possible the existence of a contribution from iron carbide Fe 3 C associated to C 1s binding energies ranging from 283.4 eV to 283.7 eV [START_REF] Panzner | The bonding state of carbon segregated to α-iron surfaces and on iron carbide surfaces studied by electron spectroscopy[END_REF][START_REF] Arabczyk | Electron spectroscopy studies on carbon segregation from a mono-crystalline α-Fe (111) specimen[END_REF][START_REF] Wiltner | Formation of endothermic carbides on iron and nickel[END_REF][START_REF] Papastavros | Oxygen, carbon, and sulfur segregation in annealed and unannealed zerovalent iron substrates[END_REF], although it has not been possible to evidence the Fe 3p component shifted by ∼ -1.5 eV with respect to the metallic contribution, which was shown to characterise iron carbide [START_REF] Papastavros | Oxygen, carbon, and sulfur segregation in annealed and unannealed zerovalent iron substrates[END_REF].

Carbon was quantified as a function of the annealing temperature through the analysis of the ratio of I C 1s /I F e 3p and I C 1s /I Al 2p integrated peak area after profile decomposition and subtraction of a Shirley background (Fig. 4.2). The ratios have been firstly corrected from ionisation cross section and analyser transmission function (see Tab. 5.1 for used parameters). Then they have been modelled in the framework of two schematic approaches. The carbon is either assumed to be evenly distributed in the bulk of the alloy (Figs. a,c). The model of carbon homogeneously distributed in the bulk leads to values of carbon concentration (10-25 at.%) which are expected to give rise to a sizeable content of carbides, in particular by annealing at 1070 K [START_REF] Connetable | A calphad assessment of Al-C-Fe system with the κ carbide modelled as an ordered form of the fcc phase[END_REF]. Such occurrence does not corresponds to the STM observations of the next section 4.1.2. In contrast, the thin carbon film model (Fig. 4.2-b) in which graphitic carbon dominates up to form 2.5 atomic layers is reminiscent of observations made for similar carbon segregation at the surface of pure iron [START_REF] Grabke | Equilibrium surface segregation of dissolved nonmetal atoms on iron (100) faces[END_REF][START_REF] Panzner | The bonding state of carbon segregated to α-iron surfaces and on iron carbide surfaces studied by electron spectroscopy[END_REF][START_REF] Fujii | C-Fe chains due to segregated carbon impurities on Fe (100)[END_REF][START_REF] Kelemen | The interaction of surface sulfur with carbon on Fe (110)[END_REF]. The known limit of solubility of carbon in iron (Fig. 4.3-a) is such that carbon tends to segregate at low temperature to give rise to surface graphite [START_REF] Grabke | Equilibrium surface segregation of dissolved nonmetal atoms on iron (100) faces[END_REF][START_REF] Panzner | The bonding state of carbon segregated to α-iron surfaces and on iron carbide surfaces studied by electron spectroscopy[END_REF][START_REF] Fujii | C-Fe chains due to segregated carbon impurities on Fe (100)[END_REF][START_REF] Kelemen | The interaction of surface sulfur with carbon on Fe (110)[END_REF], the exact temperature range depending on the carbon content of the metal [START_REF] Grabke | Equilibrium surface segregation of dissolved nonmetal atoms on iron (100) faces[END_REF]. At low carbon content, the Fe 0.85 Al 0.15 alloy is expected to behave in a way similar to pure iron, which means that it involves bcc FeAl alloy (instead of bcc iron) and graphite [START_REF] Connetable | A calphad assessment of Al-C-Fe system with the κ carbide modelled as an ordered form of the fcc phase[END_REF]. As for the iron carbide Fe 3 C which is possibly identified at 870 K (Fig. 4.1-a), it appears in bulk iron at carbon contents higher than the limit of solubility of carbon (Fig. 4.3-b) [START_REF] Chipman | Thermodynamics and phase diagram of the Fe-C system[END_REF]. Its formation is endothermic on iron surfaces [START_REF] Wiltner | Formation of endothermic carbides on iron and nickel[END_REF][START_REF] Jiang | Carbon atom adsorption on and diffusion into Fe (110) and Fe (100) from first principles[END_REF] and it is not favoured either on Al-poor bcc FeAl alloys with low carbon content [START_REF] Connetable | A calphad assessment of Al-C-Fe system with the κ carbide modelled as an ordered form of the fcc phase[END_REF]. Therefore, carbide Fe 3 C may be observed in the presence of graphitic carbon, but as a minority component [START_REF] Panzner | The bonding state of carbon segregated to α-iron surfaces and on iron carbide surfaces studied by electron spectroscopy[END_REF][START_REF] Wiltner | Formation of endothermic carbides on iron and nickel[END_REF].

Annealing not only induced carbon segregation but also an enrichment of the surface with aluminium as testified by the increase of I Al 2p /I F e 3p ratio (Fig. 4.4). This segregation

Carbon-induced stripes 4.1.2.1 STM observation

As seen in large scale STM images of Fig. 4.5, the segregation of carbon at the Fe 0.85 Al 0.15 [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] surface upon successive anneals is accompanied by the formation of self-organised equidistant stripes of tens to hundreds of nanometres long which protude over the average surface whatever the bias voltage. In parallel, a straightening of step edges as well as an enlargement of the terrace size is observed. Below 700 K (Fig. 4.5-a), the [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] surface shows terraces that are irregular in shape. Between 690 and 760 K (Fig. 4 bulk direction (or [01] S surface direction) while straight steps form in the same direction. Upon annealing to higher temperatures (Fig. 4.5-c), the coverage of stripes increases while kinked steps rotated by 142 • from [001] B develops. The step height is found close to 2 Å in agreement with the a B / √ 2 = 2.04 Å bulk Fe 0.85 Al 0.15 expectation. Herein, the coverage of stripes is qualitatively determined by calculating the ratio between the apparent area covered by stripes and the corresponding image area. It reaches a maximum of 34 % at 950 K where the average distance between lines amounts to ∼ 5 nm, as measured through line profiles along the [START_REF] Le | Tuning adhesion at metal/oxide interfaces by surface hydroxylation[END_REF] S direction (Fig. 4.6-b inset). When annealing temperature rises to 1030 K, stripes fade out by decreasing in length leading to a surface coverage of 13 % and to larger stripe free domains in which the bare reconstructed FeAl surface is exposed (Fig. 4. 5-c,d).

On the enlarged image shown in Fig. 4.6-a, stripes appear not to be continuous from one terrace to the other. Their apparent height varies between 0.5-2.0 Å (Fig. 4.7-b). It should be noted that the height of stripes largely depends on the location of measurement, thus the results are basically indicative of a general distribution. The distance between rows is not constant. It passes through a minimum after annealing at 950 K (Fig. 4.7-a) but shows deviation up to 2 nm. Meanwhile, annealing the Fe 0.85 Al 0.15 [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] surface also triggers Al segregation (Fig. 4.4 and Chap. 5). The pseudo-hexagonal superstructure that is observed between stripes (Fig. 4.6-a) is attributed to a Fe-Al surface compound due to Al segregation, which will be analysed in detail afterwards (Sect. 5.2.1,5.3.1). Differences in contrast are observed when switching from positive to negative bias (Fig. 4.6-a,b).

The evolution of the stripes coverage as function of temperature parallels unambiguously that of the intensity of high-lying C 1s component observed at 284.3-284.9 eV (Fig. 4.1-a), with a maximum around 900 K (Figs. 4.2). Such a behaviour indicates that the stripes that are associated with graphitic carbon diffuse back partially into the substrate above 900 K as observed for CO dissociated on FeAl(110) [START_REF] Gleason | A photoelectron spectroscopy and thermal desorption study of CO on FeAl (110) and polycrystalline TiAl and NiAl[END_REF] 1 , but not the chemisorbed carbon of which intensity is about constant throughout the annealing process. A possible explanation is the competitive segregation of bulk impurities as it was already observed on Fe 0.97 Al 0.03 [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF] in the order C, Al, S as function of temperature [START_REF] Blum | Competitive surface segregation of C, Al and S impurities in Fe (100)[END_REF]; in our case, C 1s signal starts dropping around 900 K (Fig. 4.2) when the surface enriches in Al (Fig. 4.4) as on Fe 0.97 Al 0.03 (100) [START_REF] Blum | Competitive surface segregation of C, Al and S impurities in Fe (100)[END_REF]. The hierarchy of segregation is likely linked to the segregation enthalpy that are larger for C (∆H F e(110) = -117 kJ/mol [START_REF] Kelemen | The interaction of surface sulfur with carbon on Fe (110)[END_REF]) than Al (∆H F e(110) = -38 kJ/mol, present ab initio calculations for Sect. 5.4). onset of segregation of aluminium as shown by photoemission analysis of the clean surface (Sect. 5.1.2.2; Fig. 5.5). Upon further annealing, these "flower"-like spots sharpen and overlap with discrete spots aligned along the [START_REF] Le | Tuning adhesion at metal/oxide interfaces by surface hydroxylation[END_REF] S direction and giving to the pattern a streaking appearance along [START_REF] Le | Tuning adhesion at metal/oxide interfaces by surface hydroxylation[END_REF] S . These latter sign the occurrence of regularly spaced one-dimensional structures, namely the carbon stripes seen in STM. As already noticed in STM (Fig. 4.6), Al-rich reconstruction develop not only on C-free terraces (see Fig. 5.17-c) but also underneath C-stripes. However, at the maximum of C coverage around 990 K, the LEED is clearly dominated by stripe-related diffraction (Fig. 4.8-c) in the form discrete multiple spots with a regular spacing of around ∆h S 0.1 r.l.u (reciprocal lattice unit) along the [START_REF] Le | Tuning adhesion at metal/oxide interfaces by surface hydroxylation[END_REF] S reciprocal space direction; this correspond to a periodicity of around a S /∆h S 4.3 nm in good agreement with STM measurements. Finally at 1030 K (Fig. 4.8-b), the recovering of the "flower"-like spots parallels the disappearance of C-stripes seen in STM and the decay of the graphitic C 1s component. It should be stressed that, besides the mixing of C-stripes and Al-rich reconstruction, the relative contrast of the spots depends strongly on the beam energy. The streaking along the [START_REF] Le | Tuning adhesion at metal/oxide interfaces by surface hydroxylation[END_REF] S of the LEED pattern due to C-segregation resembles to that observed by Graupner et al. [START_REF] Graupner | Composition and structure of the (100) and (110) surfaces of FeAl[END_REF] between 873 and 973 K on the (110) surface of the ordered Fe 0.53 Al 0.47 alloy (Fig. 3. 13-c). Although the authors state that their sample was free of contaminants such as carbon, they did not propose any explanation of their observation.

C-induced stripes and oxidation

Some oxidation tests were performed to get rid of carbon, as in the well-known case of metallic tungsten [START_REF] Musket | Preparation of atomically clean surfaces of selected elements: A review[END_REF]. In an astonishing way, as shown by the STM images of Fig. 4.9, oxide does form on stripe-free surface. The nature of the oxide grown on a clean surface will be detailed in depth in the last chapter 6; it appears as streaked areas in Fig. 4.9. Due to imaging difficulties and transient segregation of carbon, it is not possible to say if oxygen is adsorbed underneath the C-induced stripes. But, the contrast between areas are clearly different. Because the self-organization of the stripes is indicative of strained structures with longrange order induced by strain effects in the metallic substrate and because stripes covered areas oxidise in a different way as bare terraces, a suggestion is that they stem from a surface compound containing carbon with an unknown Fe-C-Al composition. This hypothesis is more in agreement with the above XPS quantification (Fig. 4.2) that overcomes the apparent STM stripe coverage. In term of distances, our finding is larger by one order of magnitude than the C-chains already observed at the surface of Fe(100) upon segregation; in this case, the organisation is driven by repulsion between adsorbed C atoms at the monolayer level [START_REF] Panaccione | Local and long-range order of carbon impurities on Fe (100): Analysis of self-organization at a nanometer scale[END_REF].

Although the formation of stripes remains unexplained, fortunately, intensive sputteringannealing-oxidation cycles allowed to deplete enough the subsurface in carbon to obtain a Fe 0.85 Al 0.15 [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] surface free of carbon, at least at the sensitivity level of XPS, LEED and STM.

4.2 Contamination from residual vacuum on Fe 0.85 Al 0.15 [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF]

and (111) surfaces

As mentioned above, an other source of contamination is introduced by the reaction with residual gases of the chamber, mainly H 2 O and CO. The ageing at room temperature of clean ( 100) and ( 111) surfaces prepared by sputtering and annealing at 970 K has been monitored continuously during 8 h through the evolution of the Al 2p, O 1s, C 1s and Fe 3p core levels in the XPS chamber (Fig. 4.10). During the whole measurement, although slightly spoilt by the outgasing of the X-ray gun, the vacuum level was below 5 × 10 -10 mbar. After a fast transfer from the preparation to the analysis chamber, the contamination level is below the detection limit. Ageing goes with a continuous increase of C 1s and O 1s that parallels (i) the increase of a shoulder on the high binding energy side of Al 2p that is characteristic of oxidised aluminium and (ii) the damping of the metallic aluminium component. At the same time, Fe 3p lineshape poorly evolves; the signal is only damped. These evolutions are accompanied by a disappearance of the LEED pattern due to the amorphous nature of the formed film [START_REF] Graupner | Oxidation of low-index FeAl surfaces[END_REF].

These evolutions were quantified (Fig. 72 eV) and oxidised (E B 74.5 eV) components in the form of Gaussian peaks. The same was performed for the two components of C 1s at E B 283 eV and E B 286 eV. After correction from photo-ionisation cross section and analyser transmission function, ratios were converted into coverage by using the model of thin film on a semi-infinite substrate (Sect. 2.5.3.2) in a way similar to the case of carbon stripes. A hypothetical graphite layer density (2.26 g.cm -3 ) was assumed for the modelling with the following inelastic mean free paths of the photoelectrons λ graphite After an initial linear increase in coverage (slope around 1.1), a saturation seems to be reached after 400 min between 3 and 5 ML. By using the total pressure of 5 × 10 -10 mbar to estimate a total exposure and by adding carbon and oxygen coverage, an effective sticking coefficient of 0.65 can be determined. The oxygen and the parallel oxidised aluminium uptakes are larger on the (100) than on the [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] Although ill-defined, this experiment is worth being compared to previous studies of O 2 [START_REF] Graupner | Oxidation of low-index FeAl surfaces[END_REF], CO [START_REF] Gleason | A photoelectron spectroscopy and thermal desorption study of CO on FeAl (110) and polycrystalline TiAl and NiAl[END_REF] and H 2 O [91] adsorption on FeAl surfaces at low temperature, CO and H 2 O being usual components of a residual vacuum. As in those cases, there is no evidence herein that iron is oxidised as the Fe 3p profile does not evolve; there is neither a shift nor a change of lineshape. Fe stays in its metallic state. Indeed Fe 2+,3+ (FeO: E B = 55 ± 0.6 eV; [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF]. The contamination layer was modelled by graphite, and either the bulk composition Fe 0.85 Al 0.15 or the actual profile of aluminium segregation was accounted for. Coverages are given in monolayers corresponding to (100) and (111) orientations.

Fe 3 O 4 : E B = 55.1 ± 1; Fe 2 O 3 : E B = 55.9 ± 0.4 eV; FeOHO: E B = 56.2 ± 1 eV; Fehydrocarbon E B ∼ 54.1 eV) leads to a sizeable chemical shift compared to metallic iron (Fe 0 : E B = 52.9 ± 0.3 eV) [START_REF] Moulder | Handbook of X-ray photoelectron spectroscopy[END_REF][START_REF] Wagner | Handbook of X-ray photoelectron spectroscopy[END_REF][START_REF]NIST X-ray photoelectron spectroscopy database[END_REF]. Therefore, the reactive adsorption sites involve aluminium. In the case of O 2 exposure [START_REF] Graupner | Oxidation of low-index FeAl surfaces[END_REF], the change of growth regime was assigned to a Al diffusion limited growth through the Cabrera-Mott mechanism [START_REF] Cabrera | Theory of the oxidation of metals[END_REF]. Previous experiments of H 2 O adsorption on FeAl(110) [START_REF] Gleason | Water adsorption and thermal decomposition on FeAl (110)[END_REF] have shown a dissociative adsorption above 173 K leading to adsorbed hydroxyls (OH ads ) and to a desorption of molecular hydrogen above 250 K. The asymmetric O 1s core level observed in our case may reflect this mixture of chemisorbed oxygen preferentially bounded to Al (at ∼ 531 eV) and of OH ads shifted by ∼ 1.4 eV. However, this speculative interpretation is entailed by the fact that room temperature adsorption of CO on FeAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] [START_REF] Gleason | A photoelectron spectroscopy and thermal desorption study of CO on FeAl (110) and polycrystalline TiAl and NiAl[END_REF] results also in both molecular and dissociated species, the O binding to Al. Photoemission measurements combined with thermal desorption [START_REF] Gleason | A photoelectron spectroscopy and thermal desorption study of CO on FeAl (110) and polycrystalline TiAl and NiAl[END_REF] showed that the C 1s component at ∼ 285 eV is a signature of molecularly adsorbed CO while the component at lower binding energy (∼ 282 eV) is assigned to chemisorbed carbon. Quite similar fingerprints are found herein on C 1s spectra. This experiment shed light on the question of contamination related to aluminium reactivity. Although unavoidable for the time consuming STM experiments, XPS and LEED measurements on native surface were performed as fast as possible (< 30 min)3 ; in particular, segregation studies (Chap. 5) involved either a freshly prepared sample at each temperature or fast in situ annealing in the analysis chamber. As it will be detailed later on, oxide thin films (Chap. 6) were synthesised during the course of substrate recrystallisation annealing right after sputtering; moreover, oxide films turned out to be much less prone to contamination than bare surfaces.

CHAPTER 5 ALUMINIUM SEGREGATION, ATOMIC STRUCTURE AND

MORPHOLOGY OF FE 0.85 AL 0.15 (100), ( 110) AND ( 111) SURFACES

Compared to the literature dealing only with the B 2 ordered compound (see Sect. 3.3), the case of a random alloy like Fe 0.85 Al 0.15 offers an extra degree of freedom related to the gradient of composition. Once the conditions to prepare a clean surface were identified (Chap. 4), the work focused on the orientation dependence of the interplay between segregation, atomic structure and morphology of annealed surfaces. The modelling of the angular dependence of photoemission signal is developed in Sect. 5.1 to determine the profile of segregation. The corresponding surface reconstructions are explored by LEED and GIXD (Sect. 5.2) while STM is used to unravel the associated modification of surface topography (Sect. 5.2). Although the actual behaviour of surfaces seems to be rich and complex, ab initio calculations are used to rationalise some observed trends (Sect. 5.4).

Angular analysis of segregation by photoemission

The angular dependence of the escape depth λ cos(Θ) has been exploited to probe the profile of concentration of elements by changing the photoelectron collection angle Θ between the analyser and the surface normal from 0 • up to 75 • . Segregation has been quantified from the ratio of intensity of metallic Al 2p and Fe 3p core levels for two reasons:

• the proximity in kinetic energy of those two photoemission lines minimises the error due to the estimate of the transmission function of the analyser,1

• both lines belong only to the crystal and not to the sample plate or holder which is made out of Mo, W, and Ta; this caution is particularly important at grazing emission to avoid spurious signal,

• their kinetic energies maximise the probing depth,

• the ratio is poorly sensitive to forward scattering effects along the dense crystallographic directions since, regardless of short range ordering, Al and Fe occupy the same bcc lattice sites.

After substraction of a Shirley background, Al 2p and Fe 3p peaks have been integrated and corrected from the photo-ionization cross sections σ(E K ) [START_REF] Yeh | Atomic subshell photoionization cross sections and asymmetry parameters: 1 Z 103[END_REF] and the transmission function of the analyser given by T (E K ) ∼ E -1 K [START_REF] Ruffieux | Experimental determination of the transmission factor for the Omicron EA125 electron analyzer[END_REF] of our EA-125 Omicron hemispherical analyser (see Tab. 5.1). Figs. 5.4-5.7 show on all the surfaces a clear trend of enrichment in Al near the extreme surface (grazing emission conditions) after an anneal at high temperature. This trend will be analysed quantitatively hereafter. and Spin-Orbit Splitting (SOS) in the metallic state [START_REF]NIST X-ray photoelectron spectroscopy database[END_REF]; corresponding Kinetic Energy (E K ) and Photo-Ionization Cross Section (PICS) [START_REF] Yeh | Atomic subshell photoionization cross sections and asymmetry parameters: 1 Z 103[END_REF] for Al-Kα and Mg-Kα excitations.

Core

Dependence of inelastic mean free path on composition

Assuming an in-plane homogeneous sample, the quantitative analysis of photoemission data requires the knowledge of the inelastic mean free path λ(x) in Fe 1-x Al x which depends on the local composition x(z) at depth z. Unfortunately, λ(x) is not tabulated but its variation is expected to be sizeable if one compares λ(x = 0) in bulk Fe (A 2 -bcc structure) and λ(x = 1) in bulk Al (A 1 -fcc structure) that are known [START_REF] Tanuma | Calculations of electorn inelastic mean free paths. II. Data for 27 elements over the 50-2000 eV range[END_REF]. Whatever the kinetic energies, a difference up to 10 Å exists between the two materials which can be assigned at first sight to a change of electronic density between aluminium (0.18 e• Å-3 ) and iron (1.35 e• Å-3 ). To overcome this issue and to obtain λ(x), the followed strategy has been to use the TPP-2M predictive formula of Tanuma, Powell and Penn as developed in their famous series of papers Refs [START_REF] Tanuma | Calculations of electron inelastic mean free paths for 31 materials[END_REF][START_REF] Tanuma | Calculations of electorn inelastic mean free paths. II. Data for 27 elements over the 50-2000 eV range[END_REF][START_REF] Tanuma | Calculations of electron inelastic mean free paths: III Data for 15 inorganic compounds over the 50-2000 eV range[END_REF][START_REF] Tanuma | Calculations of electron inelastic mean free paths (IMFPS). IV. Evaluation of calculated IMFPs and of the predictive IMFP formula TPP-2 for electron energies between 50 and 2000 eV[END_REF][START_REF] Tanuma | Calculations of electron inelastic mean free paths. V. Data for 14 organic compounds over the 50-2000 eV range[END_REF][START_REF] Tanuma | Calculations of electron inelastic mean free paths (IMFPs) VI. Analysis of the Gries inelastic scattering model and predictive IMFP equation[END_REF][START_REF] Tanuma | Calculation of electron inelastic mean free paths (IMFPs) VII. reliability of the TPP-2M IMFP predictive equation[END_REF][START_REF] Tanuma | Calculations of electron inelastic mean free paths[END_REF][START_REF] Shinotsuka | Calculations of electron inelastic mean free paths. X. data for 41 elemental solids over the 50 ev to 200 kev range with the relativistic full penn algorithm[END_REF].

More precisely, the QUASES-IMFP-TPP2M software [START_REF] Tougaard | QUASES-IMFP-TPP2M Software[END_REF] from S. Tougaard was employed to generate the inelastic mean free paths in Fe 1-x Al x from:

• its bulk density ρ(x);

• its atomic mass M (x) = (1 -x)M F e + xM Al with M F e = 55.85 g•mol -1 and M Al = 26.98 g•mol -1 ;

• its band gap taken as zero for a metallic compound;

• the total number of valence electrons of binding energy below 30 eV as given by Tab. 5.2; basically a linear interpolation accordingly to the atomic fraction x was assumed. Regarding the dependence of the bulk density on x, a careful analysis of all the Fe-Al compounds reported in the Inorganic Crystal Structure Database (ICDS [237]) was undertaken including:

Electron spreading

• the A 2 -bcc and A 1 -fcc structures of pure Fe and Al,

• the most interesting data for A 2 -bcc random alloy and for the high temperature quenched ordered B 2 -CsCl alloys [START_REF] Ellner | On the partial atomic volume of aluminum in solid solutions based on the 3d transition metals and copper[END_REF],

• the ordered Heussler D0 3 alloys (Fe 3 Al),

• more exotic high temperature compounds of various symmetries in the Al rich zone of the phase diagram (see legend of Fig. 5.1).

The obtained data gathered in Fig. 5.1 showed a change from 2.7 g•cm -3 (Al, x = 1) up to 7.86 g•cm -3 (Fe, x = 0) that follows a robust linear dependence ρ(x) = 7.94 -5.17x g•cm -3 corresponding to a hyperbolic variation of the volume per atom V (x) ∼ ρ(x)/M (x) or of the atomic concentration n(x) ∼ M (x)/ρ(x) in Fe 1-x Al x compounds. This linear dependence will be assumed to hold even at segregated surfaces since it encompasses numerous local environments of Fe and Al.

The obtained TPP-2M inelastic mean free path are plotted in Fig. 5.2 for the usual Al-Kα (Fig. 5 [START_REF] Ellner | On the partial atomic volume of aluminum in solid solutions based on the 3d transition metals and copper[END_REF] for the A 2 (red filled circles) and B 2 (orange filled squares) structures. In the legend, the corresponding compounds as well as their space groups, their parent compounds and their Strukturbericht symbol are labelled. Data are well accounted for by a linear regression (black line) corresponding to an hyperbolic variation of the atomic volume (inset). one would expect from pure Fe and Al up to a molar fraction of x 0.8. Nevertheless, this variation was taken into account in the following analysis through a polynomial fit of the TPP-2M values (lines in Fig. 5.2). Finally, one should keep in mind that the accuracy of the TPP-2M formula is of the order of 20 % [START_REF] Tanuma | Calculations of electron inelastic mean free paths for 31 materials[END_REF][START_REF] Tanuma | Calculations of electorn inelastic mean free paths. II. Data for 27 elements over the 50-2000 eV range[END_REF][START_REF] Tanuma | Calculations of electron inelastic mean free paths: III Data for 15 inorganic compounds over the 50-2000 eV range[END_REF][START_REF] Tanuma | Calculations of electron inelastic mean free paths (IMFPS). IV. Evaluation of calculated IMFPs and of the predictive IMFP formula TPP-2 for electron energies between 50 and 2000 eV[END_REF][START_REF] Tanuma | Calculations of electron inelastic mean free paths. V. Data for 14 organic compounds over the 50-2000 eV range[END_REF][START_REF] Tanuma | Calculations of electron inelastic mean free paths (IMFPs) VI. Analysis of the Gries inelastic scattering model and predictive IMFP equation[END_REF][START_REF] Tanuma | Calculation of electron inelastic mean free paths (IMFPs) VII. reliability of the TPP-2M IMFP predictive equation[END_REF][START_REF] Tanuma | Calculations of electron inelastic mean free paths[END_REF][START_REF] Shinotsuka | Calculations of electron inelastic mean free paths. X. data for 41 elemental solids over the 50 ev to 200 kev range with the relativistic full penn algorithm[END_REF].

Photoemission modelling of intensities: the case of segregation at the surface of alloys

The basis of quantification in photoemission has been introduced in Sect. 2.5.3.2 where the cases of a homogeneous alloy (Fig. 5.3-a) and of an overlayer (Fig. 5.3-b) have been introduced.

Segregation at the surface of an alloy

The analysis of the segregation at the surface of an alloy is slightly more complex than the homogeneous mixture or a genuine thin film on top of a substrate. Indeed, signal in the compared core levels may come both from the bulk of the alloy or from its surface. Two models as sketched in Fig. 5.3 have been compared and are described as follows.

5.1.2.1.1 The homogeneous segregated layer on an homogeneous alloy Let us consider a segregated layer A 1-x L B x L on top of a semi-infinite substrate A 1-x S B x S (Fig. 5.3c). If n j i and λ j i are the atomic concentration and mean free path of element i = A, B in medium j = L, S, the photoelectron signals from elements A, B encompass contributions from the substrate and the layer and read:

I A T A σ A ∼ λ S A n S A exp -t/λ S A cos Θ + λ L A n L A 1 -exp -t/λ L A cos Θ I B T B σ B ∼ λ S B n S B exp -t/λ S B cos Θ + λ L B n L B 1 -exp -t/λ L B cos Θ . (5.1)
As reminder, Θ is the emission angle, T the analyser transmission function and σ the photoionisation cross section. If V (x) is the atomic volume at atomic fraction x, n

S A = (1 -x S )/V (x S ), n S B = x S /V (x S ), n L A = (1-x L )/V (x L ), n L B = x L /V (x L ).
If one assumes, as done in Sect. 5.1.1, that the inelastic mean free path depends on the atomic fraction x, the ratio of measured intensities reads:

I B I A T A σ A T B σ B = λ B (x S )x S V (x L ) exp [-t/λ B (x S ) cos Θ] + λ B (x L )x L V (x S ) {1 -exp [-t/λ B (x L ) cos Θ]} λ(x S )(1 -x S )V (x L ) exp [-t/λ(x S ) cos Θ] + λ(x L )(1 -x L )V (x S ) {1 -exp [-t/λ(x L ) cos Θ]} .
(5.2) From the knowledge of the substrate composition x S , the previous equation can be used to fit the angular variation of the fraction I B I A to obtain film composition x L and thickness t.

The continuous profile

The previous model is easily generalised to any continuous profile of atomic fraction x(z) (Fig. 5.3-d) by integration of the infinitesimal photo-electron signal of layer dz of element i:

dI i ∝ T i σ i n i (z) exp 0 z dz /λ[x(z )] dz. (5.3)
Using the same hypothesis as above, one obtains:

I A T A σ A ∝ 0 -∞ 1 -x(z) V [x(z)] exp 0 z dz /λ A [x(z )] dz I B T B σ B ∝ 0 -∞ x(z) V [x(z)] exp 0 z dz /λ B [x(z )] dz. (5.4)
For the sake of simplicity, a diffuse profile has been chosen to analyse our data:

x(z) = x S + ∆x exp(-z 2 /Λ 2 ), (5.5)
where x S = 0.15 is the bulk value, x S + ∆x the surface value and Λ a typical length of segregation. [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF], [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] and [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF]. The atomic fraction corresponds to an analysis of the ratio I Al 2p /I F e 3p with an homogeneous bulk material Fe 1-x Al x . Ex situ data correspond to samples annealed directly after sputtering in the preparation chamber (normal emission) and in situ data to a progressive annealing on the analysis chamber manipulator (grazing emission). The pass energy E p is different for the two sets of measurements.

Angular analysis of segregation at the surfaces of Fe

Data have been analysed with the model of homogeneous bulk material Fe 1-x Al x (Eq. 2.20) to obtain the equivalent atomic fraction x. The error bars come from a cumulative total uncertainty of 20 % on measured intensities and mean free path determination. Fig. 5.5 calls for three comments:

• strong surface enrichment due to preferential sputtering is to be excluded since normal and grazing emission data (points at T=300 K) matches within the uncertainties of measurements2 . All our estimates on all the sputtered surfaces lead to a composition of x = 0. • for all the orientations, an enrichment of the surface in Al starts around 750 K; since grazing measurements lead to higher values of composition than normal emission in the framework of homogeneous bulk alloy model4 , a profile of segregation should exist with an enrichment of the surface in Al compared to Fe. By comparing normal and grazing measurements, the surface enrichment seems to be larger and earlier in temperature on the ( 100) and ( 111) than on the [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] surface and equilibration of the near surface is faster than bulk.

• above ∼ 950 K, the profile of segregation seems to reach a steady state on a photoemission point of view since a plateau is observed.

To further confirm the Al segregation, the angular variation of the I Al 2p /I F e 3p has been measured (Fig. 5.6) between Θ = 0 • and Θ = 75 • after annealing at 1273 K in the steady state plateau value. The binding energy of Fe 3p is found at 53 eV in close agreement with literature (E B = 52.9±0.3 eV [START_REF]NIST X-ray photoelectron spectroscopy database[END_REF]) while Al 2p is found at 72 eV shifted by -0.8 eV compared to metallic aluminium (E B = 72.8 ± 0.3 eV [START_REF]NIST X-ray photoelectron spectroscopy database[END_REF]) as it is found in the case of transition metal aluminides among which FeAl [START_REF] Graupner | Oxidation of low-index FeAl surfaces[END_REF][START_REF] Gleason | A photoelectron spectroscopy and thermal desorption study of CO on FeAl (110) and polycrystalline TiAl and NiAl[END_REF]. The clear decrease of Fe signal at grazing emission was quantitatively fitted with either an homogeneous segregated layer or a diffusive continuous profile. For both models, the substrate value was kept fixed at the nominal value x S = 0.15. Fits are shown as lines in Fig. 5.7 and parameters are gathered in Tab. 5. systematic errors due to the determination of the inelastic mean free paths from the TPP-2M formula (up to δλ/λ ∼ 20 %) lead to fitted values of t or Λ roughly within the above error bars (Tab. 5.3). In parallel, uncertainties in the determination in atomic volume V (x) come into play only nearly to second order; indeed as shown by Eq. 5.2, V (x) appears only as a ratio:

V (x L ) V (x S ) = V (x 0 L ) V (x 0 S ) 1 + ∂V ∂x x 0 L - ∂V ∂x x 0 S δx + O(δx 2 ) , (5.6)
in which the slopes at point x 0 L and x 0 S partially cancel. Basically, the same argument holds for the λ-terms and for Eq. 5.4. Therefore, x L or ∆x values are poorly influenced by systematic errors on inelastic mean free path or atomic volume.

On [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] surface, the found subsurface composition over ∼ 3 nm is close to Fe 0.6 Al 0.4 ; it falls into the ordered B 2 range of stability according to the bulk phase diagram (Fig. 3.1).

For ( 100) and ( 111), the composition Fe 0.53 Al 0.47 is the Al-rich limit of CsCl B 2 phase.

Surface crystallography from LEED and GIXD

All the three surfaces of Fe 0.85 Al 0.15 crystals show a faint (1×1) or no LEED pattern right after sputtering. Upon annealing, only on the (110) face, surface segregation was accompanied by a reproducible surface reconstruction that was analysed by LEED and GIXD. The other ones ( 100) and ( 111) displayed a (1×1) like LEED pattern without the intermediate reconstruction found in the literature (Sect. 3.3).

(110) orientation

LEED analysis

Due to the centring of the rectangular surface unit cell of the A 2 bcc random alloy (see Fig. 3.4), all the h S + k S = 2n + 1 reflections with n integer are extinguished 5 . It is reminded that the indexes S and B stand for crystallographic quantities related to surface or bulk unit cell. Directly after sputtering and even after annealing at 673 K (not shown), the [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] surface has a faint (1 × 1) LEED pattern. However, on a surface free of carbon stripes (see Sect. 4.1 and Fig. 4.6), a reconstruction appears at annealing temperature above 873 K in the range of segregation of aluminium as shown by photoemission (Fig. 5.5). The corresponding LEED pattern6 shown in Fig. 5.8 has a pseudo-hexagonal "flower"-like shape around only active (1 × 1) reflections.

Combining patterns taken at low energy around the (00) S reflection (Fig. 5 However, despite distortions due to sample alignment, the matching between simulated and experimental LEED patterns (Fig. 5.9) is not fully satisfactory with an apparent incommensurability along the [START_REF] Le | Tuning adhesion at metal/oxide interfaces by surface hydroxylation[END_REF] s . This feeling is confirmed by integrated line cuts along [START_REF] Le | Tuning adhesion at metal/oxide interfaces by surface hydroxylation[END_REF] S and [01] S direction through the (11) S reflection of Fig. 5.9. While commensurability is verified along the [01] S direction (∆h S = 0.2, ×5 periodicity), peaks appear at h S = ±0.12, ±0.56 along the [START_REF] Le | Tuning adhesion at metal/oxide interfaces by surface hydroxylation[END_REF] S direction that is to say at a distance of ∆h S = 0.44 from the surface Bragg peaks. Indeed, whatever the beam energy, the superstructure spots are found only around Bragg spots. This convolution of reciprocal space nodes by superstructure ones (that verifies also the surface extinctions of {10} S and {01} S ) corresponds typically to an incommensurate modulation in direct space along [h S 0] of the atomic positions and/or of the composition of the unit cell. This is not a simple incommensurate overlayer on-top of the substrate leading to a Moiré pattern. By introducing the corresponding expansion along [START_REF] Le | Tuning adhesion at metal/oxide interfaces by surface hydroxylation[END_REF]

GIXD analysis

The LEED findings have been further confirmed by GIXD. The three main directions (h S , 0), (0, k S ) and (h S , h S ) of reciprocal space have been scanned in GIXD at l s = 0.075 on a clean surface annealed at 1050 K (Fig. 5.11 black lines). The main reconstruction peaks (grey lines) appear at (h S = 1.56 -3.56 -5.56) and (0, k S = 1.10 -1.8 -2.2 -3.8 -4.2) showing that the superstructure due to the aluminium segregation is commensurate along the [01] S but incommensurate along the [START_REF] Le | Tuning adhesion at metal/oxide interfaces by surface hydroxylation[END_REF] S . Analysis of peak width of the reconstruction peaks around integer positions both in radial and angular scans points at a nearly constant reciprocal broadening of ∆q A 0.05-0.06 Å-1 for (h S ±0.44, k S ) and of ∆q B 0.03-0.04 Å-1 for (h S ±0.22, k S ±0.2).

The corresponding coherence length of 1/∆q A 16 -20 Å and 1/∆q B 24 -33 Å is of the order of the modulation showing its disordered character as seen in STM (Sect. 5.3.1).

Besides those peaks that are similar to those of LEED, broad bumps of FWHM ∆k S 0.3 are visible at (0, k s = 2.76, 4.76, 6.76) (Fig. 5.11-b) and also along the more complex (h S , h S ) direction (Fig. 5. 11-c). Those are reminiscent of a complex modulation of the unit cell content, position and/or composition over a length a S /∆k S 14 Å.

Out-of-plane scan at the position of the most intense superstructure peak (h S = 0, k S = 2.2) (Fig. 5.12) has a strong modulation with an increasing broadening with l S . An approximative analysis of peak FWHM ∆l S in terms of size (∆l S,s ) and strain ( ∆cr cr ) effects of Williamson-Hall type ∆l 2 S = ∆l 2 S,s + ∆cr Finally, the extended reflectivity or the (0, 0, l S ) rod was measured at room temperature after sputtering and along the annealing up to 1053 K. The poor evolution of the rod up to 873 K parallels the temperature dependence of segregation of aluminium observed with photoemission (Fig. 5.5) and the smoothing of the surface seen with microscopy (Sect. 5.3.1). The shape of the rod (red curve of Fig. 5.13) points at surface relaxations and/or modulation of composition. Further analysis is needed to model the atomic profile of segregation.

(100) orientation

Starting from an annealing temperature of 673 K up to 1123 K, the LEED pattern is sharp and (1 × 1) (see Fig. 5.2.2) without any traces of reconstruction. Spot sharpen with temperature and (n×n) reconstruction can be ruled out from the Bragg angle estimated from screen-sample distance and screen size.

(111) orientation

From an annealing temperature of 773 K to 1273 K, the Fe 0.85 Al 0.15 [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] orientation has a (1 × 1) surface structure as shown in Fig. 5.15. No superstructure peak has ever been found. The marked evolution of the peak intensity with beam energy with an apparent 3-fold symmetry is due the open structure of the ( 111) surface of body-centred metal (see Fig. 3.5) and the reminiscence of the bulk extinctions. Indeed, the surface unit cell (a

S , b S , c S ) (of parameter a s = b s = a √ 2, c s = a √ 3/2
) is occupied by three atoms at coordinates (0, 0, 0), (1/3, 2/3, 1/3) and (2/3, 1/3, 2/3) leading to a structure factor with bulk extinctions when h S + 2k S + l S = 3n + 1 and h S + 2k S + l S = 3n + 2 with n integer (or h S + 2k S + l S = 3n + 2 and h S + 2k S + l S = 3n + 1). Therefore, for bulk diffraction, one over three Bragg peaks will be active along the (10l S ) and (11l S ) rod but with an offset of ∆l S = 1 between the two types of rods. Since atoms are not coplanar on the [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] surface, this conclusion partially applies to electron diffraction despite the poor penetration depth of electrons. 5.3 Morphology of the Fe 0.85 Al 0.15 [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF], ( 100) and ( 111) surfaces 5.3.1 Fe 0.85 Al 0.15 [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] As seen in Sect. 4.1.2 and in particular in Fig. 4.5, annealing the (110) surface after sputtering induces a sizeable smoothing, a straightening of the step edges and an increase of average size of terraces which become separated mostly by monoatomic height steps (as seen for instance in Fig. 4.5 and in the height distribution of Fig. 5.17-d).

As already partially evoked in Sect. 4.1.2 about carbon segregation, zooms at higher resolution let appear a long-range ordered hexagonal-like superstructure in between the carbon [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] after annealing at 973 K. stripes (Fig. 5.16-a) and also on flat terraces (Fig. 5.17-a). Because of the very complicated intensity modulations, the determination of periodicities is difficult from simple line profile (Fig. 5.16-a, Fig. 5.17-a). Fortunately, the autocorrelation function [START_REF] Ceballos | Structure investigation of the topmost layer of a thin ordered alumina film grown on NiAl (110) by low temperature scanning tunneling microscopy[END_REF] is a well-established tool for determining periodicities in complex images. It is defined as:

C(ξ, η) ∝ 1 2X 1 2Y +X -X +Y -Y [z(x, y) -z][z(x + ξ, y + η) -z]dxdy, (5.7)
where z is the mean height. After drift correction, the average periodicity measured on the autocorrelation images (Fig. 5.16-d; Fig. 5.17-b) along the three "equivalent hexagonal" directions is 2.1±0.2 nm which matches the lattice parameters of 18.6×17.2 Å2 of the "pseudo" hexagonal supercell found with LEED. The superstructure occupies the whole surface from one terrace to the other as seen in Fig. 5.17-c,d and does not appear as different domains which confirms the description with only one supercell as obtained from LEED and GIXD.

It is worth noticing the strong fluctuations of the "hexagon" sizes and shapes but with a low apparent surface corrugation of 0.05-0.1 Å (see line profiles Fig. 5.16-b, Fig. 5.17-e). Amazingly, the contrast is inverted between images taken at different polarities (Figs. 5.16-a,c) demonstrating, beyond topographic contribution, also the role of density of states, the nature of atoms and the hybridisation between Fe and Al [START_REF] Duguet | Chemical contrast in STM imaging of transition metal aluminides[END_REF]. Indeed, in a naive picture, Fe 3d electronic states are expected to be more localised and to lie more below the Fermi level than the Al sp ones which are more delocalised. But ab initio calculations of Fe 1-x Al x [START_REF] Das | Electronic structure of substoichiometric Fe-Al intermetallics[END_REF] pointed at a strong hybridisation between Fe 3d and Al sp levels with a strong local character between nearest neighbours; the density of states at the Fermi level is in fact dominated by Fe 3d levels with some contributions from Al 3p. Therefore, the perimeter of "hexagons" is probably more iron rich (Fig. 5.16-c).

Some bright protrusions are also apparent and are probably related to contamination due to the reactivity of the surface (see Chap. 4). The hexagonal superstructure seems to appear already from the lowest annealing temperature (not shown) at the onset of aluminium segregation.

5.3.2 Fe 0.85 Al 0.15 [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF] Large scale STM images of a (100) surface (Fig. 5.18) annealed at increasing temperatures exhibit a clear improvement of the roughness and a straightening of the step edges along approximatively the [10] S = [001] B direction. But the step edges are not perfectly straight along the most compact [START_REF] Le | Tuning adhesion at metal/oxide interfaces by surface hydroxylation[END_REF] S direction; they are clearly kinked. Anyway, the step height agrees perfectly with the distance between atomic planes on the (100) surface. It can be estimated through a line profile perpendicular to the step (inset of Fig. 5.18-d) or more accurately by plotting a height histogram of a given STM image as depicted in Fig. 5.19 where four terraces are clearly observed with a separation of 1.45 ± 0.07 Å (the distance between (100) atomic planes being 1.445 Å). At higher magnification, the terraces appear flat at the atomic scale (Figs. 5.20-5.21). Indeed, the roughness calculated on each image from R a = 1 N N j=1 | z j -z | where z j is the pixel height and z the average pixel heigh amounts to 0.34 ± 0.05 Å and 0.12 ± 0.02 Å respectively; it is due to an actual electronic contrast i.e. a variation of the local density of state and not to topographic contrast. However, some line profiles exhibit holes, like the 1 Å deep one on Fig. 5.21-b,c that may be due to a missing atom. Image 5.20-b is reminiscent of the only STM observation of the literature on the (1 × 1) terminated Fe 0.85 Al 0.15 [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF] showing disordered patches of protruding atoms (see Fig. 3.11 [START_REF] Blum | Segregation and ordering at Fe 1-x Al x (100) surfaces-a model case for binary alloys[END_REF]). Protrusions, like on Fig. 5.20, are likely due to adsorbate and/or atoms on the surface since they can be moved by the tip between successive scans (Fig. 5.22). [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] The smoothing of the [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] surface with increasing temperatures is even more apparent than on the two other orientations (Fig. 5.23). On large scale images, sputtering induces long range undulations with an amplitude of several nanometres and a correlation length of the order of several hundreds nanometres. Upon annealing, the roughness parameter R a drops by an order of magnitude (from 1 nm to 0.1 nm) between 785 K and 1186 K where it reaches an atomic amplitude (see Fig. 5.23-bottom). Only some residual deep pits remain on large images. However, upon increasing the magnification, the surface appears to be covered by nanometresized pits forming mainly triangular-shaped features aligned along the [START_REF] Le | Tuning adhesion at metal/oxide interfaces by surface hydroxylation[END_REF] S = [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] B and the other two equivalent directions (Fig. 5.24). Pits have a size of around 1-2 nm and are organised as pyramidal protrusions (black and yellow triangles), holes with an internal periodicity (blue and green triangles) or even chains (green ellipses). This topographic appearance can be understood if one remembers that the (111) surface of body-centred metal is already open at the atomic scale (see Fig. 3.5); it exhibits three different levels separated by a B /2 √ 3 = 0.83 Å (a B being the bulk lattice parameter). Indeed, as shown on a small scale (20 × 18 nm 2 ) image (Fig. 5.25), height distribution histogram can be decomposed into gaussian peaks corresponding to different atomic planes; their constant spacing of 0.72 Å agrees with the bulk spacing and the number of peaks corresponds to nearly two unit cells along the [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] B direction.

Fe

0.85 Al 0.15
A further analysis of the local slopes τ of pits of highest height demonstrate that they are nanopyramids with [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] vicinal side facets. As shown in Fig. 5.26, line cuts along three equivalent [START_REF] Wagner | Reaktionstypen bei der oxydation von legierungen[END_REF] S = [START_REF] Stierle | X-ray diffraction study of the ultrathin Al 2 O 3 layer on NiAl (110)[END_REF] B directions at 120 • that is to say normal to the [START_REF] Gleason | A photoelectron spectroscopy and thermal desorption study of CO on FeAl (110) and polycrystalline TiAl and NiAl[END_REF] B pyramid edge give a local slope of 8.5 • very close to the τ = 8.05 • of (433) vicinal orientation. This conclusion is further confirmed by a global analysis of local slope angles τ on image 5.24-a. The distribution with a three-fold symmetry (not shown) is dominated by small τ values around 6 -7 • with a very poor contribution from flat areas at the opposite of ( 100) and ( 110) faces. A comparison with the expected angles for vicinal [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] surfaces of type (hkk), h > k, i.e. including the [011] B direction is given as grey lines in Fig. 5.24 7 . The slope density peaks around (655), (544), (977) and (433) orientations. The three equivalent (hkk), (khk), (kkh) form nanopyramids with downhill edges along the [START_REF] Swaminathan | Thermodynamic and kinetic aspects on the selective surface oxidation of binary, ternary and quarternary model alloys[END_REF] B , [START_REF] Ulrich | Growth of thin alumina films on a vicinal NiAl surface[END_REF] B , [311] B . But the symmetric orientations 8 7 The angle between (hkk) is given by cos τ 8 The vicinal surface symmetric to (hkk), h > k still including the [011] B bulk direction has an opposite slope. Their indexes (h s k s k s ), h s < k s are given by the solution of the equation cos τ

= h+2k √ 3 √ h 2 +2k 2 .
= h+2k √ 3 √ h 2 +2k 2 = hs+2ks √ 3 √ h 2 s +2k 2 s
. A straightforward algebra give hs ks = 4k-h 2h+k . For instance, the symmetric vici- 977) are (588), [START_REF] Jaeger | Formation of a well-ordered aluminium oxide overlayer by oxidation of NiAl(110)[END_REF][START_REF] Prévot | Archetypal structure of ultrathin alumina films: Grazing-incidence X-ray diffraction on Ni (111)[END_REF][START_REF] Prévot | Archetypal structure of ultrathin alumina films: Grazing-incidence X-ray diffraction on Ni (111)[END_REF], [START_REF] Prévot | Archetypal structure of ultrathin alumina films: Grazing-incidence X-ray diffraction on Ni (111)[END_REF][START_REF] Ellner | On the partial atomic volume of aluminum in solid solutions based on the 3d transition metals and copper[END_REF][START_REF] Ellner | On the partial atomic volume of aluminum in solid solutions based on the 3d transition metals and copper[END_REF] planes. 9 This holds true for angles higher and lower than that of (211) face. Aluminium segregation may favour this nanofacetting trend as it is known for other atomically rough and non-close-packed surfaces with high surface free energy when covered with a foreign element [START_REF] Madey | Nanoscale surface chemistry over faceted substrates: structure, reactivity and nanotemplate[END_REF][START_REF] Revenant | Structural and morphological evolution of Co on faceted Pt/W (111) surface upon thermal annealing[END_REF]. For instance, when covered with oxygen or other metals, body-centred W(111)/Mo [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF], face centred cubic Ir(210)/Pt [START_REF] Zhang | γ-Al 2 O 3 thin film formation via oxidation of β-NiAl (110)[END_REF] and hexagonal compact Re(1231) spontaneously rearrange above 700 K to minimise their total surface energy by developping facets even if it involves an increase in surface area and step/kink energy contribution. Faceting on W(111) develops [START_REF] Zhang | Kinetics aspects of initial stage thin γ-Al 2 O 3 film formation on single crystalline β-NiAl (110)[END_REF] facets upon O, Pt, Pd, etc. . . adsorption [START_REF] Madey | Nanoscale surface chemistry over faceted substrates: structure, reactivity and nanotemplate[END_REF][START_REF] Revenant | Structural and morphological evolution of Co on faceted Pt/W (111) surface upon thermal annealing[END_REF][START_REF] Szczepkowicz | A comparison of adsorbate-induced faceting on flat and curved crystal surfaces[END_REF]. In those cases, the driving force for faceting is thermodynamics, since it leads to a reduced surface energy of the covered vicinal surface with respect to the flat surface. According to calculations [START_REF] Vitos | The surface energy of metals[END_REF], this is already verified in the case of bare iron; an extended (211) surface has a lower energy that the open [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] surface (E 111 F e = 2.73 J•m -2 ; E 211 F e = 2.59 J•m -2 ). But faceting is controlled by kinetics and mass transport. On body-centred (111) surfaces, one physical monolayer is required; it corresponds to three atomic [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] planes; more material leads to islanding or alloying. Most of the time the formed facets are more close-packed than the initial one and facetting keeps the symmetry of the initial surface (C 3v in the case of Fe 0.85 Al 0.15 [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF]). In our case, nano-facetting is observed upon aluminium segregation like in the case of sulphur on Fe [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] [START_REF] Lin | S-induced faceting transformations on Fe (111)[END_REF] and seems homogeneous since nano-pyramids do not coexist with planar surface. Usually, faceting by an adsorbate is limited to a given temperature window before the onset of desorption of the foreign element; above the surface flattens again. But in the present case, segregation of aluminium provides an infinite reservoir; despite the increase of temperature (Fig. 5.23), the Fe 0.85 Al 0.15 [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] smoothens but never flattens. Finally, at the opposite of metal covered W [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF], not only [START_REF] Zhang | Kinetics aspects of initial stage thin γ-Al 2 O 3 film formation on single crystalline β-NiAl (110)[END_REF] facets are observed on Fe 0.85 Al 0.15 [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF]) but vicinal of (111) maybe because of the complex interplay between segregation, formation of a surface alloy and faceting.

I t = 0.4 nA, b) U b = 1.5 V, I t = 0.4 nA, c) U b = -1.5 V, I t = 0.4 nA, d) U b = 1.6 V, I t = 0.4 nA, e) U b = 1.6 V, I t = 0.
At last, few areas appear locally flat at the atomic scale with an hexagonal periodicity along bulk directions of ∼ 8 Å which is the double of the surface lattice parameter (a S = 4.01 Å). A likely hypothesis is local ordering of the segregated aluminium atoms in a B 2 -CsCl structure in agreement with the Fe 0.5 Al 0.5 surface composition found in XPS. Indeed on the FeAl(111), the lattice spacing is 7.35 Å.

Ab initio calculations of Al segregation trend

To rationalise the segregation trend found mainly by photoemission (Sect. 5.1), ab initio calculations of mixing and segregation energies of aluminium in iron have been undertaken (J. Goniakowski, Institut des NanoSciences de Paris).

Computational methods and settings

All the calculations were performed within the Density Functional Theory (DFT) implemented in VASP (Vienna Ab Initio Simulation Package) [START_REF] Kresse | Efficient iterative schemes for ab initio total energy calculations using a plane-wave basis set[END_REF][START_REF] Kresse | Ab initio molecular dynamics for liquid metals[END_REF]. The interaction of valence electrons with ionic cores was described within the Projector Augmented Wave (PAW) method [START_REF] Blöchl | Projector augmented-wave method[END_REF][START_REF] Kresse | From ultrasoft pseudopotentials to the projector augmentedwave method[END_REF], and the Kohn-Sham orbitals were developed on a plane-wave basis set with a cutoff energy of 300 eV. Semi-core Fe 3p electrons were treated explicitly. All the calculations were spin-polarised with a ferromagnetic ordering of iron spins. Gradient-corrected PW91 [START_REF] Perdew | Atoms, molecules, solids, and surfaces: applications of the generalized gradient approximation for exchange and correlation[END_REF] exchange-correlation functional was used.

Results summarised in Tab. 5.4 show a satisfactory agreement between computational and experimental results for bulk Fe and Al. We have checked that a Γ-centred (10×10×10) Monkhorst-Pack grid for k-point sampling of the Brillouin zone of the primitive unit cell of bulk iron (a B = 2.84 Å) insures a convergence of the calculated lattice parameters (a B ) to within 0.005 Å and of cohesion energy (E coh ) to within 0.005 eV/Fe. A very similar degree of convergence is obtained with an equivalent (7 × 7 × 7) k-point sampling of the Brillouin zone of bulk aluminium (a B = 4.05 Å) unit cell. We note that the overestimation of the bulk cohesion energy of Fe is principally due to a less accurate estimation of the total energy of an isolated Fe atom, and will thus not impact directly the calculated mixing, substitution, and segregation energies.

Fe (bcc) a B ( Å) E (eV) B (GPa) calc.

2 Calculations on bulk Fe 1-x Al x (x < 0.5) phases were performed in a cubic (2 × 2 × 2) iron supercell containing 16 atoms. All the configurations were thoroughly optimised, including cell lattice parameters and all the atomic positions (residual forces smaller than 0.01 eV/ Å).

Calculations of Al segregation energies at Fe surfaces of different orientations were performed in slab geometry. In all the cases, a single Al substitution per unit cell has been considered and its energy has been evaluated as:

E sub = (E(FeAl) -(E(Fe) + E(Al))
, where E(FeAl) and E(Fe) are the total energies of Fe slab with and without an Al substitution and E(Al) is the total energy of an Al atom in bulk aluminium.

Different surface orientations required different computation settings to achieve an equivalent degree of convergence. Slabs composed of 7-9, 9-11, and 13-15 atomic layers have been used to represent [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF], ( 100) and ( 111) surfaces, respectively. With these settings the surface energies (2.45 J/m 2 , 2.53 J/m 2 , and 2.67 J/m 2 , respectively) are converged to within 0.01 J/m 2 . Differences of E sub for an Al substitution in the slab center between the thinner and the thicker slab are less than 0.01, 0.04, and 0.02 eV/atom, respectively.

Results

Calculated properties of bulk FeAl phases

We have considered the two known ordered bulk phases of Fe 1-x Al x (x < 0.5), namely Fe 0.5 Al 0.5 (B 2 ) and Fe 0.75 Al 0.25 (D0 3 ) and an additional low-concentration (Fe 0.9375 Al 0.0625 ) cubic structure with a single Al atom in the (2×2×2) cell of bulk iron (Fe 15 Al 1 = Fe 0.9375 Al 0.0625 ). Tab. 5.5 summarises the essential structural and energetic characteristics of these systems. The mixing energy was evaluated with respect to pure bulk aluminium and iron reference

a B d Al-Al E mix E' sub ( Å) ( Å) (eV/
E mix (Fe 1-x Al x ) = {E(Fe 1-x Al x ) -[(1 -x)E(Fe) + xE(Al)]} /n
, where E(Fe 1-x Al x ), E(Fe), and E(Al) are the total energies of bulk Fe 1-x Al x alloy, bulk iron and bulk aluminium, respectively and n is the number of sites in the units cell (n = 16 in the present case).

We find relatively large negative mixing energies, fully consistent with the existence of the ordered B 2 and D0 3 Fe 1-x Al x phases and in agreement with the large enthalpies of formations found in the literature [START_REF] Blum | On the interplay of surface segregation and bulk order in binary alloys[END_REF][START_REF] Hultgren | Selected values of the thermodynamic properties of binary alloys[END_REF][START_REF] Das | Electronic structure of substoichiometric Fe-Al intermetallics[END_REF]. Interestingly, since the Al-induced expansion of Fe lattice parameters is relatively small (< 1.5 %) for the considered Al concentrations (x < 0.5), we find that the mixing energies E mix , calculated without accounting for this expansion (lattice parameters fixed to bulk Fe values), are only little underestimated with respect to the fully optimised result (E mix and E mix differ by less than 4%).

As a reference, a calculation in the more diluted case (Fe 0.981 Al 0.019 ), performed in a cubic (3 × 3 × 3) unit cell (54 Fe atoms), predicts the lattice parameter of 2.839 Å (+0.001 % with respect to bulk Fe) and the mixing energy E mix = -0.014 eV/atom.

Trends in Al segregation to the surface

(1 × 1) and (2 × 2) surface unit cells (see Sect. 3.2.1) have been systematically used for (100) and ( 111) oriented surfaces, while (1 × 1) and (2 × 3) surface cells were used for the [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] orientation. As it can be seen in Tab. 5.6, in case of ( 110) and (100) orientations, the (1 × 1) unit cells produce short nearest neighbour Al-Al distances, typical for these in Fe Despite this fact, with the larger cells, we find that the calculated E sub for Al substitution in the slab center (-0.83, -0.80, and -0.89 eV/atom, for [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF], [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF], and (111) orientations, respectively) are systematically more negative compared to the estimation obtained for the bulk Fe 0.9375 Al 0.0625 phase, E sub = -0.68 eV/Al. Results obtained for Al substitutions in the slab center of the (1 × 1) unit cells (-0.69, -0.61, and -0.83 eV/Al, respectively) represent a less favourable substitution with respect to the large cells. Aside a small contribution due to a possible lack of a full convergence with respect to the slab thickness and to fine differences in the sampling of the Brillouin zone of differently oriented slabs, these results reveal a many-body character of the iron-mediated Al-Al interaction, which likely depends on the precise configuration of the Al substitutions in the subsequent coordination shells. This trend to ordering was already pointed in Sect. 3.1.

In the following, we will analyse the variation of E sub as a function of position of the Al substitutions within the slabs of different orientations. For this purpose, for each subsequent atomic layer i (i = 1 corresponds to the surface atomic layer), we define the segregation energy as

E i seg = E i sub -E c sub
, where E i sub and E c sub are substitution energies in i-th atomic layer and in the slab center, respectively. Fig. 5.4.2.2 summarises the results obtained with differently oriented slabs for both (1 × 1) and for the larger surface unit cells.

We note that, despite significantly different Al densities in calculations with the small and with the large surface unit cells, the obtained segregation profiles are qualitatively similar and that the main quantitative differences concern the surface layers only. This validates the present computational settings and shows the robustness of the calculated behaviours and trends.

For the three surfaces, we find a general oscillatory behaviour of E i seg which consists of an increase of tendency for segregation at the surface (negative E i seg ), followed by a decrease (positive E i seg ) in a sub-surface region. Underneath the sub-surface region the variations of E i seg become relatively small. In the case of ( 110) and ( 100) surfaces, both the surface and the subsurface regions consist essentially of a single atomic layer (i = 1 for the surface and i = 2 for the sub-surface region), and variations of segregation profile are strongly attenuated already for i > 3. Conversely, in case of the [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] surface, the surface region with negative E i seg extends over three surface atomic layers (i = 1 -3) and is followed by a sub-surface region composed of layers i = 4 and 5, the 5th one being particularly strongly unfavourable for Al segregation. In this case variations of segregation profile are attenuated only below the 6th atomic layer. The very different thickness of the surface region of the [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] surface can be directly linked to the very open character of this surface. Indeed, under-coordinated atoms (atoms with missing nearest neighbours (NN)) at this surface can be found down to the 3rd surface layer (4 NN, 7 NN, and 7 NN in the 1st, 2nd and 3rd surface layers, compared to 8 NN for bulk atoms). Conversely, at the ( 110) and (100) surfaces, the under-coordinated atoms are present in the 1st surface layer only (6 NN and 4 NN, respectively). Calculated E 1 seg which describe the thermodynamic bias for surface segregation show that the results obtained with small and with large surface unit cells are essentially very similar except for the (100) surface, where the segregation effect is visibly stronger at low Al coverage. This is to be assigned to the high density of surface Al in the (1 × 1)-(100) unit cell.

In the following, we focus on the results obtained in the limit of low Al concentrations (large unit cells). We find that surface segregation is the most favoured at the (100) surface (E 1 seg ∼ -0.7 eV) and that the (110) and ( 111) oriented surfaces are characterised by a similar E 1 seg of about -0.4 eV. The principal force responsible for the strong segregation at (100) surfaces is the low coordination of its surface atoms (4 NN, compared to 6 NN on the (110) surface). Interestingly, an equally low coordination of surface atoms on the (111) surface (4 NN) does not produce an equally strong segregation. It is to be assigned to a much stronger surface relaxation at the [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] surface, induced by under-coordinated atoms in the 2nd and 3rd surface layers. This strong relaxation results in particularly short surface inter-atomic distances which partially compensate the effect of lost neighbours.

Trends in Al surface adsorption energies

The adsorption energy of Al adatoms at iron surfaces of different orientations was defined as

E ads = -(E(Fe+Al) -(E(Fe) + E(Al))
, where E(Fe+Al) and E(Fe) are the total energies of Fe slab with and without Al adsorbates and E(Al) is the total energy of an isolated Al atom. Tab. 5.7 summarises the computed adsorption characteristics of Al at the three iron surfaces. [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] In all the considered cases, surface adsorption of Al atoms is thermodynamically favoured (positive adsorption energies). Moreover, since adsorption energies are larger than Al cohesive energy (Tab. 5.4), adsorption on the Fe surface is favoured over formation of 3D Al clusters. Regarding the ( 110) and ( 100) surfaces, we find that E ads increases at a higher density of surface Al, what reveals an attractive interaction between Al ad-atoms. The increase is particularly well pronounced in the case of (100) surface, where the (1 × 1)-( 100) unit cell configuration corresponds to a dense surface Al ad-layer. Conversely, the effect is small and opposite at the [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] surface, where however the distances between Al adatoms in the (1 × 1) unit cell are much larger (Tab. 5.6).

Focusing on the energetically favoured case of adsorption in dense configurations [(1 × 1) unit cells], the progressive increase of E ads along the series is to be linked to the increase of the number of first Fe and Al neighbours of the adsorbed atom [(110): 2 NN Fe and 2 NN Al, (100): 4 NN Fe and 4 NN Al, (111): 4 NN Fe and 0 NN Al). In the case of ( 111) surface E ads is likely influenced by the strong surface relaxation. Most likely it will be additionally enhanced if the surface Al layer is made more dense.

Discussion and conclusion

The composition of the sputtered Fe 0.85 Al 0.15 surface was found close to the nominal one with a slight enrichment in Al. Upon annealing of all the studied low index surfaces, photoemission evidenced a strong aluminium segregation with a similar onset of temperature around 700 K probably dictated by bulk diffusion [START_REF] Gemmaz | Determination of the diffusion coefficient of Al in an Fe-Al alloy by Auger spectrometry[END_REF]. Whatever the orientation, both models of photoemission analysis (segregated film or profile) agree with a near surface composition close to Fe 0.5 Al 0.5 with a typical affected depth of around 25 Å except on the [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] surface for which those figures are slightly different (Fe 0.6 Al 0.4 ; ∼ 40 Å; Tab. 5.3). Although in agreement on the phenomenon with the existing literature obtained mainly on FeAl (Sect. 3.3) and with the above calculations in terms of segregation and adsorption trends (Sect. 5.4), the thickness impacted by segregation is much larger than that determined previously by Auger spectroscpy or dynamic LEED measurements on FeAl [START_REF] Graupner | Composition and structure of the (100) and (110) surfaces of FeAl[END_REF][START_REF] Meier | Equilibration of stoichiometrically distorted Fe 1-x Al x (100) surfaces[END_REF][START_REF] Meier | Equilibration of stoichiometrically distorted Fe 1-x Al x (100) surfaces[END_REF][START_REF] Hammer | Segregation phenomena on surfaces of the ordered bimetallic alloy FeAl[END_REF][START_REF] Heinz | Surface structure and segregation of bimetallic bcc-type alloys[END_REF][START_REF] Blum | Segregation and ordering at Fe 1-x Al x (100) surfaces-a model case for binary alloys[END_REF][START_REF] Blum | Quantification of substitutional disorder and atomic vibrations by LEED-the role of parameter correlations[END_REF][START_REF] Hammer | Equilibration processes in surfaces of the binary alloy Fe-Al[END_REF][START_REF] Kottcke | Segregation-induced subsurface restructuring of FeAl (100)[END_REF][START_REF] Eltester | AES and LEED investigation of Al segregation and oxidation of the (100) face of Fe 85 Al 15 single crystals[END_REF][START_REF] Gemmaz | Determination of the diffusion coefficient of Al in an Fe-Al alloy by Auger spectrometry[END_REF] 10 . According to the bulk phase diagram (Fig. 3.1), the profile of composition should cross all the transitions A 2 ↔ D0 3 ↔ B 2 from the bulk to the surface. This gradient of composition was never really evidenced up to now in the Fe 1-x Al x system, probably because studies focused on ordered alloys; anyway, it was suspected in the diffraction study of Kotcke et al. [START_REF] Kottcke | Segregation-induced subsurface restructuring of FeAl (100)[END_REF] on FeAl [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF]. This segregation is accompanied:

• by the appearance of a non commensurate complex long-range structural/chemical superstructure with a pseudo-hexagonal unit cell of ∼ 20 Å on the (110) surface,

• by a (1 × 1) termination on the (100) surface,

• by an intense faceting in the form of triangular pits having vicinal [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] side facets for the [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] orientation.

The slightly lower surface composition on the (110) surface found by photoemission (Fe 0.6 Al 0.4 compared to Fe 0.5 Al 0.5 on ( 100) and ( 111) surfaces) can be assigned according to ab initio calculations to a denser surface. A difference appears on the core levels. At grazing emission, Fe 3p peaks of all the surfaces overlap while, despite the poor resolution, fits conclude at a Al 2p ( 110 CHAPTER 6

OXIDES ON THE FE 0.85 AL 0.15 [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF], ( 100) AND (111) SURFACES

Film synthesis

Oxide films have been synthesised following the same protocol on all surfaces. Oxygen is introduced at a pressure in the range of p = 10 -7 -10 -6 mbar during the recrystallisation annealing plateau (15-20 mins) after sputtering. Duration was adapted to achieve a given exposure (1-1000 L) and the temperature was selected in the range 973-1173 K corresponding to the steady state regime of segregation on the bare surface (Fig. 5.5) but below the temperature at which oxide film decay is usually observed [START_REF] Graupner | Oxidation of low-index FeAl surfaces[END_REF]. On the [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] surface, the oxide film characteristics are apparently poorly dependent on the moment of oxygen introduction in the annealing plateau (not shown). Despite the high temperature that imparts the residence time of oxygen, the reactivity of aluminium is such that a full layer (on the LEED and/or STM points of view) is always reached above 100 L whatever the surface. A few tests of two-step oxidation (room temperature exposure followed by high temperature annealing) have been performed on the (110) surface giving similar results like on NiAl(110) [START_REF] Lay | Epitaxial growth of well-ordered ultra-thin Al 2 O 3 film on NiAl (110) by a single-step oxidation[END_REF][START_REF] Song | X-ray photoelectron spectroscopy and low-energy electron diffraction study on the oxidation of NiAl (110) surfaces at elevated temperatures[END_REF].

Lineshape fitting

In the absence of iron oxidation, the profile of Al 2p (Fig. 6.2) core levels has been decomposed as explained in Sect. 2.5.3.1. As in the case of the oxide on NiAl(110) [START_REF] Jaeger | Formation of a well-ordered aluminium oxide overlayer by oxidation of NiAl(110)[END_REF][START_REF] Mulligan | A high-resolution photoemission study of nanoscale aluminum oxide films on NiAl (110)[END_REF][START_REF] Martin | High-resolution corelevel spectroscopy study of the ultrathin aluminum oxide film on NiAl (110)[END_REF], three doublets are needed to describe Al 2p, one of which corresponds obviously to the metallic substrate. The spin orbit splitting of all components was kept at 0.4 eV as reported in databases [START_REF]NIST X-ray photoelectron spectroscopy database[END_REF] The good fit of the Al 2p core level of the clean surface with an unique Doniach-Sunjic profile, both in normal and grazing emission, evidences the lack of oxidation of the native surface (see Chap. 4). The binding energy E B = 71.9 eV is smaller than the metallic Al 0 in databases [START_REF]NIST X-ray photoelectron spectroscopy database[END_REF] (E B = 72.6 ± 0.3 eV) by ∆E B = -0.7 eV, a phenomenon already known in the transition metal aluminides and assigned to the bonding between the transition metal and aluminium [START_REF] Gleason | A photoelectron spectroscopy and thermal desorption study of CO on FeAl (110) and polycrystalline TiAl and NiAl[END_REF]. Comparison to values found for Al 2 O 3 (E B = 74.1 ± 1 eV [START_REF]NIST X-ray photoelectron spectroscopy database[END_REF]) or film of aluminium oxide on Al (E B = 74.4 ± 1.5 eV [START_REF]NIST X-ray photoelectron spectroscopy database[END_REF]) favours an oxidation Al 3+ state.

Finally, the assignment of the two oxide components to the surface and the interface atoms is based only on the comparison with conclusion drawn in terms of chemical environments on NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] [START_REF] Libuda | Interaction of rhodium with hydroxylated model substrates[END_REF][START_REF] Martin | High-resolution corelevel spectroscopy study of the ultrathin aluminum oxide film on NiAl (110)[END_REF] and on FeAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] [START_REF] Graupner | Oxidation of low-index FeAl surfaces[END_REF]. Indeed, at the opposite to synchrotron photoemission [START_REF] Libuda | Interaction of rhodium with hydroxylated model substrates[END_REF][START_REF] Martin | High-resolution corelevel spectroscopy study of the ultrathin aluminum oxide film on NiAl (110)[END_REF], our measurements show no relative differences between the two oxide component intensities by switching from normal to grazing emissions (Tab. 6.1). The dis-(Tab. 5.3). on the experimental ratio matches with data dispersion. At the opposite to the clean surface, no apparent segregation is found underneath the oxide layer over the probing depth of photoemission as confirmed by a fit with a continuous profile (line, Eq. 5.4).

Oxide film thickness and stoichiometry

Assuming a continuous oxide film, the oxide thickness can be obtained from ratios of areas of photoemission peaks coming from the substrate and the film. Compared to the case of a semiinfinite homogeneous substrate covered by a thin film as treated in Eq. 5.1, the segregation of aluminium underneath the oxide slightly complicates the situation. Actually, this is not really the case for [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] surface for which the profile of segregation corresponds nearly to a semiinfinite substrate on the photoemission point of view. But the formalism will be developed here for the case of oxides on (100) and ( 111) surfaces that will be treated later on in this chapter. Using the notations of Sect. 5.1.2, if the photoemission signal I L of the oxide layer L of thickness t is given by:

I L T L σ L ∼ n L λ L L cos Θ 1 -exp -t/λ L L cos Θ , ( 6
I S T S σ S ∼ 0 -∞ x(z) V [x(z)] exp 0 z dz /λ S [x(z )] dz × exp -t/λ L S cos Θ (6.2)
where λ L S is the electron mean free path of the substrate photoelectron in the oxide layer. The generalization of Eq. 6.2 to the case of Fe (term in 1 -x(z) for the concentration) and to a homogeneous segregated layer underneath the oxide is straightforward from Eqs. 5.1-5.2. Notice that the damping term in Eq. 6.2 is valid only for a continuous oxide layer. The treatment of fractional coverage is beyond the scope of our measurements and clearly does not correspond to the case of the highest (> 500 L) O 2 exposure (see below).

For all the substrate orientations, the profile of segregation found from the ratio I Al2p(metal) /I F e3p (Tab. 6.2) was kept fixed and the oxide thickness was obtained by comparing the ratio

I L T L σ L T S σ S
I S calculated from the above formula and experimental values for various combinations of core levels, namely I Al2p(oxide) /I F e3p , I Al2p(oxide) /I Al2p(metal) , I O1s /I F e3p , I O1s /I Al2p(metal) . The search was performed by dichotomy and the error bar on thickness obtained by assuming 10 % of standard deviation on the experimental value of corrected ratio. The used oxide-related electron mean free paths and density are given in Tab. 6.3. Compared to the alloy, a special care should be paid to the stoichiometry n sto in the calculation of the atomic concentration of the oxide n L ∝ n sto ρ L /M L from its density ρ L and its molar mass M L . Assuming insulating behavior, the TPP-2M predictive formula [START_REF] Tanuma | Calculations of electron inelastic mean free paths for 31 materials[END_REF][START_REF] Tanuma | Calculations of electorn inelastic mean free paths. II. Data for 27 elements over the 50-2000 eV range[END_REF][START_REF] Tanuma | Calculations of electron inelastic mean free paths: III Data for 15 inorganic compounds over the 50-2000 eV range[END_REF][START_REF] Tanuma | Calculations of electron inelastic mean free paths (IMFPS). IV. Evaluation of calculated IMFPs and of the predictive IMFP formula TPP-2 for electron energies between 50 and 2000 eV[END_REF][START_REF] Tanuma | Calculations of electron inelastic mean free paths. V. Data for 14 organic compounds over the 50-2000 eV range[END_REF][START_REF] Tanuma | Calculations of electron inelastic mean free paths (IMFPs) VI. Analysis of the Gries inelastic scattering model and predictive IMFP equation[END_REF][START_REF] Tanuma | Calculation of electron inelastic mean free paths (IMFPs) VII. reliability of the TPP-2M IMFP predictive equation[END_REF][START_REF] Tanuma | Calculations of electron inelastic mean free paths[END_REF][START_REF] Shinotsuka | Calculations of electron inelastic mean free paths. X. data for 41 elemental solids over the 50 ev to 200 kev range with the relativistic full penn algorithm[END_REF][START_REF] Tougaard | QUASES-IMFP-TPP2M Software[END_REF] was used to calculate λ L L , λ L S for bulk alumina Al 2 O 3 (corindon structure) and a fictitious material Al 10 O 13 equivalent to the oxide thin film found on NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] [START_REF] Kresse | Structure of the ultrathin aluminum oxide film on NiAl (110)[END_REF][START_REF] Prévot | Archetypal structure of ultrathin alumina films: Grazing-incidence X-ray diffraction on Ni (111)[END_REF][START_REF] Stierle | X-ray diffraction study of the ultrathin Al 2 O 3 layer on NiAl (110)[END_REF] in terms of composition, molar mass and density. Fig. 6.4 shows the calculated oxide thickness on the [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] surface for various models and all the combination of core levels. Assuming a substrate with a constant atomic fraction fixed at x S = 0.15 that is to say Fe 0.85 Al 0.15 , a striking discrepancy up to a factor two appears between the thicknesses obtained by normalizing to Al 2p (metal) or to Fe 3p. It is obviously linked to the effect of aluminium segregation which is further confirmed by simulations performed with the profile found on the clean surface or on the oxidised one (nearly equivalent to x S = 0.31). Table 6.3: Inelastic mean free paths calculated from the TPP-2M formula for photoelectrons [START_REF] Tougaard | QUASES-IMFP-TPP2M Software[END_REF] In the last case, curves overlap two by two at given oxide core level showing that the problem comes from the photoemission modelling of the oxide itself and not of the profile of segregation. Various trials with different x S values showed the robustness of this findings (not shown).

Since the film is found thinner from O 1s core levels than from Al 2p (oxide), an understoichiometry in oxygen compared to the nominal composition Al 2 O 3 is expected; the ratio of thicknesses (t 12.5 Å black/green versus t 10.5 Å blue/red points in Fig. 6.4) points at a stoichiometry of Al 2 O 2.5 . This qualitative description is confirmed by the better agreement of all curves if calculations are made for an oxide composition close to that found on NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] i.e. Al 10 O 13 =Al 2 O 2.6 (lines in Fig. 6.5). The absolute value of the film thickness (around 11.5 Å) should be taken with caution because of the uncertainties on mean free paths. Anyway, the consistency of the found thicknesses with emission angle rule out a partial coverage that would severely impacts the thickness trend. This finding validates a posteriori the treatment with the model of a continuous film and is in line with the STM observations.

The unit cell from diffraction 6.2.2.1 LEED pattern analysis

The LEED pattern of the oxide layer (Fig. 6.6) is quite complex and does not show the {11} S substrate reflections except at the lowest exposures (such as in Fig. 6.6-c, with 50 L of O 2 ) where an overlap with the pseudo hexagonal superstructure due to segregation is also visible (not shown, with 10 L of O 2 ). This agrees with a film progressively covering the whole surface. The diffraction pattern has two mirror planes crossing at the center of reciprocal space. This is compatible with a pmm symmetry which is a subgroup of the cmm rectangular centred surface unit cell. Owing to the number of spots in the reciprocal surface unit cell of the substrate (Fig. 6.6-c), the lattice parameters of the oxide should be much larger than those of the surface (a S , b S ). Fortunately, a close inspection of the LEED pattern shows that it shares some similarities with that obtained on NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] and FeAl(110) (Figs. 3.31,3.17). On those substrates, the LEED could be indexed with a rotated quasi-rectangular unit cell with two domains due to the cmm symmetry of the substrate unit cell (see Fig. 6.7). As shown in Fig. 3.17, Graupner et al. proposed to index the reflections of the oxide on FeAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] within a matrix 4 2.53 -1 3.372 similar to that obtained on NiAl(110) [START_REF] Libuda | Structure and defects of an ordered alumina film on NiAl (110)[END_REF]. Already, a direct comparison with our pattern (Fig. 6.8) shows a good qualitative overlap with the main central spots.

Based on this observation, the strategy to obtain the actual unit cell was to combine LEED and GIXD starting with the search of potential coincidences between a slightly distorted rectangular unit cell with parameters close to literature values (Tab. 6.4) and multiples of the surface unit cell of Fe 0.85 Al 0.15 [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF]. Compared to NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] and FeAl(110) (B 2 /CsCl structure), the random alloy (A 2 /bcc structure) offers in terms of symmetry an extra degree of matching due to the centring of the surface unit cell (Fig. 6.7). In other words, the matching was sought with multiples of the primitive surface unit cell (Fig. 6.7, vectors [START_REF] Le | Tuning adhesion at metal/oxide interfaces by surface hydroxylation[END_REF] S,P , [01] S,P ) both along the oxide lattice parameter a ox and b ox . Coincidence of (1×1), (1×2), (2×1), (3× 1), (1 × 3) oxide unit cells were numerically found within reasonable limits: a ox = 18.5 ± 13 %; b ox = 10.5 ± 13 %;

Ă Ždž Ε ϭϴ ď Ždž Ε ϭϬ͘ϲ α ox ~30°γ Ždž Ε ϵϬΣ Ă &Ğ ů √Ϯ Ă &Ğ ů Ε Ϯ͘ϴϵ
γ ox = 91 ± 3 • ; α ox = 26 ± 6 • . (6.
3)

The corresponding LEED patterns were simulated with the LEEDPat software [239] from Hermann and Van Hove including the two symmetric domains. Tab. 6.5 and Fig. 6.9 show the summary of the coincidences that give the best qualitative agreement between experimental and simulated LEED patterns up to ×2. Good matching (not shown) was found also for numerous (1 × 3), (3 × 1). Unfortunately, distortion on the outside of the LEED screen due to sample mispositioning and tilt did not allow to check among the found solutions the agreement on the {11} S substrate spots (Fig. 6.6-c) and therefore on the lattice parameters. This is all the more difficult than the substrate spots are often not visible. So, the unit cell was determined from GIXD measurements which is much more precise and sensitive to the substrate. [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] and the simulated one with Graupner's rotation matrix 4 2.53 -1 3.37 [START_REF] Graupner | Oxidation of low-index FeAl surfaces[END_REF].

Work

b) Corresponding real space. The grey grid corresponds to the primitive unit cell; the centred rectangular unit cell is in orange. give rise to an oxide layer covering the whole surface, radial scans before and after oxidation overlaps along the (0, k S , 0.075) direction while the superstructure peaks along (h S , 0, 0.075) at (1.56 -3.56 -5.56, 0, 0.075) are lifted by oxidation. Therefore, oxidation does not only change the profile of segregation underneath the oxide film as demonstrated by photoemission (see Sect. 6.3.1.2) but also impacts the nature of the superstructure underneath by releasing the "incommensurate" direction. Of course, new peaks appear (blue lines in Fig. 5.11) that are characteristic of the oxide layer itself.

GIXD analysis

To isolate them, a limited portion of in-plane reciprocal space at l S = 0.075 of both the clean surface (Fig. 6.10) and of the oxide layer (Fig. 6.11) has been mapped in grazing incidence diffraction through angular ω-scans. By scrutinizing Fig. 6.10-6.11, (i) obvious powder-like spurious spots due to crystal imperfection and (ii) reflections belonging to reconstructed clean surface could be excluded from the oxide reciprocal map (grey open squares in Fig. 6. 10-6.11). A set of potential oxide reflections (green circles and black squares) could be identified among which three aligned intense spots (but non-colinear with the substrate directions) are undoubtedly in-plane Bragg reflection of the oxide (double circles in Fig. 6.11; reflection 1,2,3 in Tab. 6.6). From these three, the most likely oxide unit cell parameters Table 6.5: Best (1 × 1), (1 × 2), (2 × 1), (2 × 2) oxide unit cells in coincidence with the primitive substrate unit cell that qualitatively fit the experimental LEED patterns. Parameters of the quasi-rectangular oxide unit cell (a ox , b ox , γ ox , α ox ) are defined in Fig. 6.7 with a S = 4.089 Å and b S = 2.891 Å. The rotation matrix M P between the oxide and the primitive unit cell is decomposed into a product of matrices A -1 P B P which characterise the common coincidence supercell in the basis of the overlayer (A P ) and of the substrate (B P ). The labelling of the proposed superstructures correspond to the A P matrix.

(a ox , b ox , γ ox , α ox ) and reflection indexing [(h i ox , k i ox ), i = 1 . . . 3] were sought as follows.

For a given set (a ox , b ox , γ ox , α ox ), the oxide superlattice matrix in the rectangular surface unit cell (a S , b S ) is given by (see Fig. 6.7):

M S = m 11 m 12 m 21 m 22 = a ox cos(α ox )/a S a ox sin(α ox )/b S b ox cos(α ox + γ ox )/a S b ox sin(α ox + γ ox )/b S . (6.4)
A straightforward algebra shows that a (h ox , k ox ) reflection in the oxide reciprocal unit cell corresponds to (h S , k S ) indexes in the reciprocal unit cell of the substrate through:

h S k S = a S b S a ox b ox sin γ ox m 22 -m 12 -m 21 m 11 h ox k ox , (6.5)
where the prefactor comes from the ratio of the surfaces of the unit cells. Therefore, for a given set of measured reflections [(h i S , k i S ), i = 1 . . . N ] defined in the rectangular centred substrate unit cell and indexed as [(h i ox , k i ox ), i = 1 . . . N ] in the oxide cell, the best (a ox , b ox , γ ox , α ox ) oxide unit cell can be found by minimizing: where h S (h i ox , k i ox ), k S (h i ox , k i ox ) are given by Eqs. 6.4-6.5 and ∆h S , ∆k S = 0.02 stand for typical error bars in the determination of the reflection position of our maps.

χ 2 = 1 2N N i=1 h S (h i ox , k i ox ) -h i S ∆h S 2 + k S (h i ox , k i ox ) -k i S ∆k S 2 (6.6)
The search of the unit cell relies on a proper indexing [(h i ox , k i ox ), i = 1 . . . N ] of the actual reflections. In this respect, the work performed with coincidence cells on LEED patterns is helpful but within small distortions of the unit cell, an uncertainty about the belonging of the observed reflections to a given domain remains.

To solve this, in the first step, a brute force search of minimal χ 2 for the three most obvious reflections 1-3 of Tab. 6.6 was performed (i) at fixed a ox = 18.5 Å, b ox = 10.5 Å, γ ox = 91 • close to value of the literature and for α ox = 26 ± 6 • down to 0.5 • and (ii) for indexes of -12 ≤ h i ox , k i ox ≤ 12, i = 1 . . . 3 being blind on the belonging of the reflection to a given domain. To do so, all the combinations [(h i S , ±k i S ), i = 1 . . . 3] related by the domain symmetry have been systematically tested. It turned out that a satisfactory indexing (χ 2 = 1.9 with (h i ox , k i ox ) values of Tab. 6.6) could be obtained for these three reflections within the same domain. This finding is not astonishing since it is unlikely that the three spots would be perfectly aligned without belonging to the same domain.

To confirm this, in the second step, the same brute force minimization of χ 2 was performed (i) within the boundaries of Eq. 6.3 for (a ox , b ox , γ ox , α ox ) down to 0.25 Å for the lattice parameters and 0.25 • for the angles and (ii) for (∆h ox = ±4, ∆k ox = ±4) around the previous found values. The obtained χ 2 = 0.18 confirmed the already found solution since the next ones are much worst in χ 2 = 1.13, 1.60 and with a much poorer agreement in terms of LEED pattern (not shown).

In the third step, based on this unit cell, all the potential reflections of Fig. 6 ) correspond to experimental (and calculated) positions in the substrate surface unit cell which was set at a S = 4.091 Å and b S = 2.888 Å from (020) and ( 200) bulk Bragg reflections. A, B stand for the two domains.

been indexed one by one excluding on purpose those for which the intensity is too weak or the overlap between the two domains does not allow a clear assignment. On the remaining 17 reflections [(h i ox , k i ox ), i = 1 . . . 17] (Tab. 6.6), the oxide unit cell parameters have been searched by looking for the minimum of χ 2 down to 0.01 Å and 0.02 • for parameters and angles. From the Hessian matrix of χ 2 H i,j = 1 2 ∂ 2 χ 2 ∂x i ∂x j , error bars on each fitting parameter x i could be determined as H -1

ii as well as the correlation matrix between

H -1 i,j H -1 i,i H -1 i,j
. The found solution (χ 2 = 1.2; Tab. 6.4) was:

a ox = 18.8 ± 0.2 Å; b ox = 10.68 ± 0.08 Å; γ ox = 91.2 ± 0.8 • ; α ox = 27.5 ± 0.4 • , (6.7)
with the following correlation matrix:

   
1.00 -0.12 -0.02 -0.45 -0.12 1.00 0.30 0.26 -0.02 0.30 1.00 -0.40 -0.45 0.26 -0.40 1.00

    . (6.8)
The agreement with the experimental LEED pattern (Fig. 6.12) within expected distortions further confirms the found solution. However, some LEED spots are not indexed and are assigned to double diffraction as in the case of NiAl(110) [START_REF] Libuda | Structure and defects of an ordered alumina film on NiAl (110)[END_REF] (see Fig. 3.17 which correspond to an oxide cell commensurate along 2b ox (within 0.2 %) and nearly commensurate along a ox (within 2 %). Calculations shows that the perfect coincidence supercell (1 × 2) is within the error bars of Eq. 6.7. This matching was already found from LEED analysis (B-(1 × 2) structure, Tab. 6.5 and Fig. 6.9).

Finally, the rocking width ∆ω(q) of a given oxide reflection (h S , k S ) of reciprocal space vector modulus q = (h S a * S ) 2 + (k S b * S ) 2 may originate from either a limited size of the oxide coherent domain ∆q o = 2π/d o leading to a constant q∆ω(q) broadening in reciprocal space or from in-plane mosaic spread M . Assuming uncorrelated effects, the peak broadening in reciprocal space should follows : q 2 ∆ω(q) 2 = ∆q 2 o + q 2 M 2 . As show in Fig. 6.13, the analysis of all the identified experimental in-plane oxide reflection widths ∆ω(q) yield a low mosaic spread and a coherent domain size of d o 20 nm.

Oxide surface morphology from STM

Large scale STM images of Fe 0.85 Al 0.15 [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] oxidised at 1073 K with 90 L of O 2 are presented in Fig. 6.14. Besides domains occupied by carbon stripes (see Chap. 4), the whole surface seems to be fully covered by an oxide layer with two domains showing straight line patterns (Fig. 6.15) separated by irregular boundaries [START_REF] Libuda | Structure and defects of an ordered alumina film on NiAl (110)[END_REF]252]. As determined at several locations, the average angle between the lines and the [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] B direction of the substrate is 30 ± 3 In-plane analysis of the oxide reflection widths ∆ω(q). The linear regression (green line) of q 2 ∆ω(q) 2 versus q 2 allows to unfold size and mosaic spread effects.

direction (see Sect. 4.1.2). Both angles agrees with the rotated rectangular unit cell found with diffraction within the drift effects due to room temperature STM measurements. Substrate and oxide step heights can be distinguished with a line profile through areas covered with C-stripes; the apparent height between oxide and the bottom between stripes is 2.7 ± 0.2 Å in close agreement with expected spacing between compact oxygen planes in alumina structures.

On the other hand, step heigths of FeAl are close to 2 Å (see Fig. 6.14-c); double steps of iron aluminide have never been seen like on NiAl [START_REF] Libuda | Structure and defects of an ordered alumina film on NiAl (110)[END_REF][START_REF] Heinke | Structure and electronic properties of step edges in the aluminum oxide film on NiAl (110)[END_REF]. All theses findings are in line with the existence of two domains related by the mirror plane symmetry of the substrate with a rotated unit cell as found by diffraction. Lower scale images displayed in Fig. 6.15 exhibit a periodic arrangement, but because of the very complicated intensity modulations, the determination of the constituting unit cell is difficult and requires image autocorrelation as already used for the oxide on NiAl(110) [START_REF] Ceballos | Structure investigation of the topmost layer of a thin ordered alumina film grown on NiAl (110) by low temperature scanning tunneling microscopy[END_REF]. A clear distorted rectangular mesh appears on the autocorrelation images (Figs. 6.15-b,e). Unfortunately drift prevents an accurate determination of the angle between the basis vectors as well as the vertical periodicity; on the other hand, the distance found along the scan axis of 2.2 ± 0.2 nm is close to the a ox = 18.5 Å (Sect. 6.2.2.2). Anti-phase domain boundaries are typical defects of the oxide on NiAl(110); they result from the insertion of an oxygen deficient line of atoms that releases the strain energy in the layer through a shift of ∼ 3 Å and appears in the form of straight lines along b ox or zigzag lines along the diagonal of the oxide unit cell in STM [START_REF] Libuda | Structure and defects of an ordered alumina film on NiAl (110)[END_REF][START_REF] Kulawik | Atomic structure of antiphase domain boundaries of a thin Al 2 O 3 film on NiAl (110)[END_REF][START_REF] Schmid | Oxygen-deficient line defects in an ultrathin aluminum oxide film[END_REF][START_REF] Nilius | Defect-induced gap states in Al 2 O 3 thin films on NiAl (110)[END_REF] or in Low Energy Electron Microscopy [START_REF] Mccarty | Translation-related domain boundaries form to relieve strain in a thin alumina film on NiAl (110)[END_REF]. At the opposite to rotation domains related by substrate-layer symmetries, these translation related domains do not result from impinging islands with displaced lattice but from misfit dislocation [START_REF] Schmid | Oxygen-deficient line defects in an ultrathin aluminum oxide film[END_REF][START_REF] Mccarty | Translation-related domain boundaries form to relieve strain in a thin alumina film on NiAl (110)[END_REF]; they spontaneously nucleate and grow within individual islands. They have a peculiar electronic structure in the band gap of the oxide [START_REF] Nilius | Defect-induced gap states in Al 2 O 3 thin films on NiAl (110)[END_REF] and act as favourable nucleation sites for metallic atoms or molecule adsorption [START_REF] Schmid | Oxygen-deficient line defects in an ultrathin aluminum oxide film[END_REF]. While reflection domain boundaries are quite clear in STM images of the oxide on Fe 0.85 Al 0.15 [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] (Fig. 6.14) and run in arbitrary directions [START_REF] Nilius | Defect-induced gap states in Al 2 O 3 thin films on NiAl (110)[END_REF], anti-phase domain boundaries are much less apparent and dense than on NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF]. One is visible in Fig. 6.15-c. On NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF], they appear as bright lines in topographic images above a bias of 1.5 V with a contrast that peaks at 2.5 V [START_REF] Nilius | Defect-induced gap states in Al 2 O 3 thin films on NiAl (110)[END_REF]. For those running along the short axis of the oxide unit cell and they are introduced every 8-10 nm to release strain due to the lattice mismatch along the [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] B direction (the film is incommensurate along the other [001] B direction which inhibits the development of lattice strain). The previous diffraction analysis (Sect. 6.2.2.2) concluded at a lack of lattice mismatch along 2b ox (0.2 %) and mismatch of 2 % along the a ox . A likely explanation for the lack of clear anti-phase domain boundary along this mismatched direction at the opposite of NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] is the extra-degree of structural (lattice parameter) freedom provided by the composition of the Fe 0.85 Al 0.15 alloy in the subsurface region. A similar lack but associated with an imbalance between the two rotational domains was observed on the vicinal NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] surface [START_REF] Ulrich | Growth of thin alumina films on a vicinal NiAl surface[END_REF] and assigned to the introduction of step edge and given oxide terrace size to release the oxide stress.

With respect to image 6.15-c, no difference show up after an overnight ageing (Fig. 6.15-d) demonstrating the lack of reactivity of the oxide surface at the opposite of the clean FeAl substrate. In the case of NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF], the inertness was assigned to an oxygen termination of the oxide film. Finally, very similar topographies (not shown) were found after 50 L of O 2 exposure at room temperature followed by annealing at 1073 K. After oxidation (100 L of O 2 , 973 K), an angular analysis of the three main core levels Fe 3p, Al 2p and O 1s similar to that performed on [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] surface was undertaken to study segregation (Fig. 6.16). As for [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF], there is no trace of iron oxidation (see Fig. Fit strategy similar to that developed for (110) orientation (see Sect. 6.2.1.2) was applied to (100) surface. At the opposite to (110) face, it turned out that, besides the substrate contribution, only one component was needed to account for the experimental Al 2p profile both for normal and grazing emissions (Fig. 6.17) as in Ref. [START_REF] Cai | Growth of ultrathin amorphous alumina films during the oxidation of NiAl (100)[END_REF][START_REF] Frémy | X-ray photoelectron spectroscopy study of thin oxide layers formed on (001)-oriented β-NiAl single-crystal surfaces[END_REF]212] for NiAl [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF]. On the other hand, two components were found on FeAl(100) [START_REF] Graupner | Oxidation of low-index FeAl surfaces[END_REF] and on NiAl(100) [START_REF] Ozensoy | Interaction of water with ordered θ-Al 2 O 3 ultrathin films grown on NiAl (100)[END_REF] but without taking into account the spin-orbit splitting of Al 2p in the decomposition. Fit parameters are given in Tab. 6.7. Again, the existence of only one asymmetric Al 2p component on the clean surface testifies for the cleanliness of the sample.

Oxide superstructure from LEED

A typical LEED pattern of the oxide formed at the (100) surface of Fe 0.85 Al 0.15 is shown in Fig. 6.20. It corresponds to that observed on FeAl(100) [START_REF] Graupner | Oxidation of low-index FeAl surfaces[END_REF] (see Fig. 3.33-b), on NiAl(100) [START_REF] Gassmann | Preparation of a well ordered aluminum oxide layer on NiAl (001)[END_REF][START_REF] Blum | Initial growth of Al 2 O 3 on NiAl (001)[END_REF]212] and on Fe 0.85 Al 0.15 (100) [START_REF] Eltester | AES and LEED investigation of Al segregation and oxidation of the (100) face of Fe 85 Al 15 single crystals[END_REF] with an intense streaking along the main [START_REF] Le | Tuning adhesion at metal/oxide interfaces by surface hydroxylation[END_REF] S [010] B and [01] S [001] B directions around main spots but also around half order ones. At a first sight, this matches with a two-domain (1 × 2) superstructure (see Fig. 3.33-b) that was interpreted on NiAl(100) as due to the formation of θ-alumina in Bain epitaxy [START_REF] Stierle | Surface X-ray diffraction study on the initial oxidation of NiAl (100)[END_REF][START_REF] Gassmann | Preparation of a well ordered aluminum oxide layer on NiAl (001)[END_REF][START_REF] Gassmann | Investigations on phase transitions within thin Al 2 O 3 layers on NiAl (001)-HREELS on aluminum oxide films[END_REF][START_REF] Blum | Initial growth of Al 2 O 3 on NiAl (001)[END_REF][START_REF] Frémy | X-ray photoelectron spectroscopy study of thin oxide layers formed on (001)-oriented β-NiAl single-crystal surfaces[END_REF][START_REF] Frémy | Initial stages of growth of alumina on NiAl (001) at 1025 K[END_REF][START_REF] Blum | Growth of Al 2 O 3 stripes in NiAl (001)[END_REF][START_REF] Wang | Under-surface observation of thin-film alumina on NiAl (100) with scanning tunneling microscopy[END_REF]. However, by reducing the beam energy, this streaking transforms into spot splitting, particularly visible around half integer. As already shown with much better resolution in the spot profile analysis of Ref. [START_REF] Blum | Initial growth of Al 2 O 3 on NiAl (001)[END_REF] on NiAl(100), this splitting matches with a (1 × 9) shape convolution (Fig. 6.21) corresponding to the formation of high aspect ratio oxide stripes regularly spaced by 9a S ∼ 5 nm. This will be confirmed by STM later on.

It is worth noticing that, at the opposite to the oxide on [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF], the substrate spots (Fig. 6.20; orange circles) are visible even though in STM the film apparently covers the whole surface; this is in line with a thinner film than on [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] as shown by the photoemission analysis. Finally, although the temperature of synthesis is the same of the study of Graupner et al. [START_REF] Graupner | Oxidation of low-index FeAl surfaces[END_REF] on FeAl(100), the oxide never adopts the c(6 × 6) superstructure.

Surface morphology from STM

As shown in the STM images of Figs. 6.22-a,b,c, the oxidation at high temperature gives rise to an oxide layer that covers the whole surface with small domains of which borders follow the square symmetry of the substrate. A statistical analysis of apparent height distribution shows the existence of terraces separated by a distance of 1.6 Å pointing at single step. This value is in between the distance between atomic planes along the At higher magnification (Fig. 6.23), the domains appear clearly as compact stripes with very high aspect ratio running along the [010] B and [001] B directions. Those stripes which are always limited in length by a orthogonal ones are regularly spaced by 6.9±0.2 Å (Fig. 6. 23-b,c) and packed in bunches separated by trenches with a periodicity of 5 ± 2 nm. The corrugation of the modulation due to stripes is 0.3 ± 0.1 Å. Numerous topographic defects are presented among which holes with an apparent depth of 1.6 ± 0.2 Å similar to the distance between terraces observed at large scale (Fig. 6. 22-d). This distance is therefore more in line with a physical hole in the terrace of the oxide, since the substrate step height amounts to a B /2 = 1.45 Å. Quite similar topographies have been observed on NiAl(100) [START_REF] Blum | Initial growth of Al 2 O 3 on NiAl (001)[END_REF][START_REF] Blum | Growth of Al 2 O 3 stripes in NiAl (001)[END_REF] (see Sect. 3.4.3.2) or CoAl [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF] [START_REF] Rose | Growth of ultra-thin amorphous Al 2 O 3 films on CoAl (100)[END_REF][START_REF] Rose | High temperature oxidation of CoAl (100)[END_REF][START_REF] Frémy | X-ray photoelectron spectroscopy study of thin oxide layers formed on (001)-oriented β-NiAl single-crystal surfaces[END_REF][START_REF] Frémy | Initial stages of growth of alumina on NiAl (001) at 1025 K[END_REF]212] (see Sect. 3.4.3.5) with a stripe period of ∼ 54 Å and a size/height of ∼ 26/11 Å [START_REF] Blum | Initial growth of Al 2 O 3 on NiAl (001)[END_REF][START_REF] Blum | Growth of Al 2 O 3 stripes in NiAl (001)[END_REF] for isolated ones grown at very low oxygen coverage. Stripes do not cross or coalesce as in our case. This morphology was assigned to the growth of a θ- can not be differentiated in LEED and are seen only in GIXD [START_REF] Stierle | Surface X-ray diffraction study on the initial oxidation of NiAl (100)[END_REF]. The origin of the limited stripe width was assigned to the stress build-up along the high lattice mismatch direction. Since the lattice parameter of Fe 0.85 Al 0.15 is very close to that of NiAl, the same interpretation is likely in our case. But at the opposite to exposure of NiAl(100) [START_REF] Frémy | Initial stages of growth of alumina on NiAl (001) at 1025 K[END_REF]212] at 1025 K (∼ 1000 L), the growth of alumina on iron aluminium does not seem to be accompanied with amorphous oxide domains that require prolonged annealing (and cycle of exposure) to enlarge the surface covered by stripes.

6.4 Oxide on Fe 0.85 Al 0.15 [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] 6.4.1 Photoemission analysis 6.4.1.1 Angular analysis and lineshape fitting Like for the other orientations, photoemission results favour preferential oxidation of aluminium and inertness of iron towards oxygen. Using the same procedure of decomposition than for the two other orientations (110) (Sect. 6.2.1.2) and (100) (Sect. 6.3.1.1), reasonable fits (Fig. 6.24) were obtained with two oxide components for Al 2p. From their angular dependence (Fig. 6.25, Tab. 6.8), one is assigned to oxidised aluminium close to the interface (E B = 75.3 eV) and the other to atoms closer to the interface with the substrate (E B = 73.3 eV). Fits parameters are gathered in Tab. [START_REF] Giorgi | Influence of annealing treatment on wetting of steels by zinc alloys[END_REF] Data (points) have been fitted with a model of continuous profile of segregation (lines, Eq. 5.4) which values are given in Tab. 5.3, 6.2. The orange points correspond to another measurement.

Oxide film thickness and stoichiometry

As on (110) (Sect. 6.2.1.4) and (100) (Sect. 6.3.1.3) surfaces, the modelling of the various ratios of core level intensities in terms of film thickness led to the imperious need of accounting for the profile of segregation under the oxide (lines vs symbol in Fig. 6.27). Once the analysis is corrected from this bias, a matching by pair, i.e. for a given substrate core level, is achieved. But, at the opposite of (100) orientation, thicknesses predicted for O 1s intensity are larger than those obtained from Al 2p(metal) pointing at a problem of stoichiometry of the oxide in the quantification. The effect was reversed for (110) orientation and was assigned to an under-stoichiometry in oxygen with an average composition of Al 2 O 2.5 . The present ratio of thicknesses of ∼ 1.25 obtained from O 1s, Al 2p(oxi)/Fe 3p, Al 2p(metal) points at a stoichiometry of Al 2 O 3.5 as confirmed by simulations (not shown 4 ) with a thickness around 19 Å. Finally, the decrease of the film thickness at high emission angles (Fig. 6.27) highlights a weakness of the continuous thin film interpretation which is due to the roughness of the film as it will be apparent in STM.

Oxide crystallography from LEED

Whatever the oxidation route, an ordered LEED pattern has never been observed after oxidation of the (111) surface. High temperature oxidation (973 K) with different amounts of oxygen (1, 10, 20, 100 L of O 2 ) but also room temperature oxidation followed by high temperature annealing up to 1123 K never led to any clear ordering. While covering oxide give rise to only diffuse background pointing at the lack of epitaxial oxide, small exposures led to a faint (1 × 1) pattern. Amazingly, surfaces slighly contaminated with oxygen and annealed leads to a spot splitting of {10} S and {11} S reflections that evolves with beam energy. This thickness than the overlap between the values obtained from the different core level ratios. [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] [START_REF] Graupner | Oxidation of low-index FeAl surfaces[END_REF]; the difference lies probably in the use of a defined compound in their study.

Surface morphology from STM

STM imaging supports the LEED conclusions of the lack of growth of any ordered oxide layer. Whatever the route of oxidation, the surface is rough and difficult to image. Fig. 6.29 shows a typical large scale topography where appear large three-dimensional features with a typical size in the range of several tens of nanometres and height of 7 ± 2 nm. These islands present facets inclined by 10 -15 • with respect to the surface plane and are surrounded by small features with a corrugation of 0.5 ± 0.2 nm. This surface roughness explains the lack of LEED pattern, the deviation from the thin film model for photoemission angular measurements points at a three dimensional growth of alumina.

Influence of oxygen exposure and growth mode

The thickness analysis was also performed for films grown on (110) surface at O 2 exposures ranging from 1 to 1000 L at fixed temperature (1123 K) (Fig. 6.30). In most cases, only the available normal and grazing (Θ = 60 • ) measurements were analysed at a fixed bulk composition enriched in aluminium as found above (x S = 0.31 at 500 L) and at a fixed Al 2 O 3 stoichiometry. Despite these simplifying assumptions, a clear saturation of thickness appears above 100 L while below 50 L partial coverage is suspected. Indeed, below 50 L, substrate To further assess the interplay between oxide film thickening, stoichiometry and segregation, a more systematic angular analysis as described above was undertaken on all the orientations for 1,10,100 (500) L of O 2 at a given annealing temperature. The characteristic length Λ of the fitted exponential segregation profile, the surface composition x(0) = x S +∆x, the oxide thickness t and its stoichiometry are gathered in Tab. 6.9. Of course, the use of a continuous film model on top of an in-plane homogeneous profile of segregation is questionable in the case of a partial coverage. But again the (100) orientation distinguishes from the two others. While the film thickens continuously on [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] and [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF], it seems to stabilise quickly with exposure on (100) without changing at all the profile of segregation underneath. 1 L of O 2 is enough to grow a 6.2 Å thick film very close to the final thickness of ∼ 9 Å. Assuming a θ-alumina structure as found on NiAl [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF], this corresponds to roughly 4 oxygen planes and a surface density of oxygen of 4 × 10 15 O atoms•cm -2 which is even higher than the oxygen exposure of 1 L. If stoichiometry poorly change on ( 100) and ( 111) surfaces leading to a continuous 2D films, it changes on [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] Oxidation was performed on all three faces following a common protocol (see Sect. 2.1). While oxidation of iron can be excluded in all cases (see Fig. 6.31) pointing at a preferential oxidation of aluminium, the formed oxide layers have different intrinsic characteristics that are summarised in Tab. 6.10. While the self-limited growth could be clearly explored only on the (110) orientation up to 1000 L (Fig. 6.30), STM, LEED and angular analysis of photoemission demonstrated the formation of a covering oxide of nanometre thickness on all surfaces in the range of 100 L of exposure. While a three dimensional growth happens on (111) probably due to the already complex nano-faceting found on the clean surface, flat and covering film grow on ( 110) and (100) with a thickness in the range of a few O-O interlayer spacings (∼ 2.2 Å) as found in all the alumina polymorphs (see Sect. 3.4.1)5 . However, similar values deduced from photoemission were obtained in the literature for instance on NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] [START_REF] Lay | Epitaxial growth of well-ordered ultra-thin Al 2 O 3 film on NiAl (110) by a single-step oxidation[END_REF][START_REF] Song | X-ray photoelectron spectroscopy and low-energy electron diffraction study on the oxidation of NiAl (110) surfaces at elevated temperatures[END_REF][START_REF] Yoshitake | Crystallinity and thickness control of wellordered ultra-thin Al 2 O 3 film on NiAl (110)[END_REF] or on FeAl(110) [START_REF] Graupner | Oxidation of low-index FeAl surfaces[END_REF] x(0) = x S + ∆x is the average surface composition; the corresponding bulk structure is indicated below; the arrow stands for the change from clean to oxidised surface.

The (100) face behaves differently from the two other ones. Oxidation gives rise to a thinner oxide, which diffraction spots are still present in the LEED pattern, without any strong change of the segregation profile underneath. The subsurface composition is close to Fe 0.5 Al 0.5 i.e. to the B 2 ordered alloy accordingly to phase diagram (Fig. 3.1) over a depth of 3 nm. Meanwhile, on [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] and [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] surfaces, oxidation depletes the subsurface in aluminium compared to the bare surface and pumps out aluminium from the bulk leading to a flatter but deeper profile of segregation. For those orientations, the subsurface composition gets closer to Fe 0.66 Al 0.33 in the range of stability of the ordered D0 3 alloy (Fig. 3.1); relying only on bulk stability, this would imply a transition of phase induced by the growth of the oxide. A possible explanation is a subtle minimisation of the interfacial stress between the oxide film and the subsurface of the alloy. Indeed, as shown in Tab. 3.1 and the inset of Fig. 5.1 [START_REF] Ellner | On the partial atomic volume of aluminum in solid solutions based on the 3d transition metals and copper[END_REF], the variation of the lattice parameter between x = 0 and x = 0.5 in A 2 -B 2 structures is only 1.4 % and, on a symmetry point of view, the bulk (110) truncation of A 2 , D0 3 and B 2 have quite close lattice parameters. Poorly studied in surface science, such kind of oxide-induced depletion was partly evidenced on Fe 3 Al(110) [START_REF] Vonk | In situ x-ray study of Fe 3 Al (110) subsurface superlattice disordering during oxidation[END_REF] (Fig. 3.36).

While two chemical environments can be identified for aluminium, on [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] and [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF], one closer to the surface one to the interface, only one Al 2p oxide core level is found on [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF]. Their interpretation in terms of tetrahedral (low binding energy) and octahedral (high binding energy) coordinated aluminium and the labelling of the film based on the closest bulk alumina parent polymorph was often used in the first photoemission studies on NiAl [START_REF] Jaeger | Formation of a well-ordered aluminium oxide overlayer by oxidation of NiAl(110)[END_REF][START_REF] Libuda | Interaction of rhodium with hydroxylated model substrates[END_REF][START_REF] Mulligan | A high-resolution photoemission study of nanoscale aluminum oxide films on NiAl (110)[END_REF] on FeAl [START_REF] Graupner | Oxidation of low-index FeAl surfaces[END_REF]. Although useful for very thick films, such comparisons are hazardous for few monolayers thick oxide films where coordination of atoms are strongly distorted and chemical states are influenced by the underlying substrate. This was clearly shown by the high resolution photoemission study of the oxide on NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] [START_REF] Martin | High-resolution corelevel spectroscopy study of the ultrathin aluminum oxide film on NiAl (110)[END_REF] compared to the Kresse's model [START_REF] Kresse | Structure of the ultrathin aluminum oxide film on NiAl (110)[END_REF]. Poorly discussed up to now in our study, the O 1s core level of all our oxide films (Fig. 6.31) is strongly asymmetric and can always be decomposed into two components which high binding energy one corresponds to surface species as it is always slightly enhanced at grazing emission. Finally, the stoichiometry of our films estimated from photoemission changes from sub-to over-stoichiometry in oxygen from [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] to [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF], with an stoichiometry Al 2 O 3 composition for [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF]. On a LEED point of view, only the oxide on [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] surface is "amorphous".

Comparison to the existing literature

Already addressed all along this chapter, strong similarities appeared between existing literature and our present findings on ( 110) and (100) surfaces.

Oxide at (110) surface

The unit cell found by GIXD for the oxide film on Fe 0.85 Al 0.15 is very close to the only two accurate determinations on NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] [START_REF] Libuda | Structure and defects of an ordered alumina film on NiAl (110)[END_REF][START_REF] Stierle | X-ray diffraction study of the ultrathin Al 2 O 3 layer on NiAl (110)[END_REF] and Al/Ni [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] [START_REF] Prévot | Archetypal structure of ultrathin alumina films: Grazing-incidence X-ray diffraction on Ni (111)[END_REF] (see Tab. 6.4); the film LEED pattern shares also some symmetry similarities with the other substrates such as FeAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] [START_REF] Graupner | Oxidation of low-index FeAl surfaces[END_REF], Cu-9 at.% Al [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] [START_REF] Napetschnig | Ultrathin alumina film on Cu-9 at% Al (111)[END_REF] and γ-Al 4 Cu 9 (110) [START_REF] Wardé | Growth and structure of ultrathin alumina films on the (110) surface of γ-Al 4 Cu 9 complex metallic alloy[END_REF]. According to photoemission, its stoichiometry is close to Al 2 O 2.6 , the Al 10 O 13 one found in the theoretical study of Kresse et al. [START_REF] Kresse | Structure of the ultrathin aluminum oxide film on NiAl (110)[END_REF] and detailed in Sect. 3.4.3.2.1. However, a discrepancy remains on its thickness which is found larger than a O-bilayer film. Modulo a few distortions, this structure seems to be found on support of different symmetries and structures. The actual role of the substrate in its formation is still puzzling. While Prevot et al. argue that its an archetype of free-standing oxide [START_REF] Prévot | Archetypal structure of ultrathin alumina films: Grazing-incidence X-ray diffraction on Ni (111)[END_REF] since, according to their diffraction study, it poorly affects the atomic positions of Ni [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF], but the substrate-induced strain is present on NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] and manifests through dense anti-phase domain boundaries. On Fe 0.85 Al 0.15 , the freedom of composition of the subsurface leads to a nearly perfect matching with a (1 × 2) oxide unit cell giving rise to a very low density of such linear defects in STM.

In their high resolution photoemission analysis of the oxide on NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] based on density functional calculations, Martin et al. [START_REF] Martin | High-resolution corelevel spectroscopy study of the ultrathin aluminum oxide film on NiAl (110)[END_REF] isolated two sizeable core level shifts for oxidised Al 2p compared to metallic Al (Tab. 3.4) that were assigned to interface and surface aluminiums. Moreover, if similar oxidised Al 2p species are probably present in our study (Tab. [START_REF] Gleason | A photoelectron spectroscopy and thermal desorption study of CO on FeAl (110) and polycrystalline TiAl and NiAl[END_REF][START_REF] Martin | High-resolution corelevel spectroscopy study of the ultrathin aluminum oxide film on NiAl (110)[END_REF], leading to similar value for the interface component, the surface one is still different, demonstrating the role of the interaction with the substrate and/or a different environnement. According to ab initio calculations and experiment on NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] [START_REF] Martin | High-resolution corelevel spectroscopy study of the ultrathin aluminum oxide film on NiAl (110)[END_REF], a broader distribution of core level shifts is expected for surface aluminium atoms than for interface ones due to numerous slightly different environments; this is in close agreement with the present results on the Gaussian FWHM of the peaks (Tab. 6.1, FWHM(Al s ) = 1.3 vs FWHM(Al i ) = 0.8). Finally, our O 1s component can be fitted perfectly with two Voigt components shifted by 1.23 eV as for NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] [START_REF] Libuda | Interaction of rhodium with hydroxylated model substrates[END_REF][START_REF] Martin | High-resolution corelevel spectroscopy study of the ultrathin aluminum oxide film on NiAl (110)[END_REF] with a somehow larger ratio 0.33 compared to 0.19 in Ref. [START_REF] Martin | High-resolution corelevel spectroscopy study of the ultrathin aluminum oxide film on NiAl (110)[END_REF]. It is reminded that the high binding energy O 1s component was assigned to specific O atoms of CHAPTER 7

CONCLUSION

This work aimed at exploring the orientation dependence of aluminium segregation and oxidation at surfaces of Fe 0.85 Al 0.15 single crystals. This random bcc alloy was selected to mimic those effects at the more complex alloyed-steel surfaces. This thesis developed a surface science approach under ultra-high vacuum of the questions at hand. By using core-level photoemission, not only the chemistry of the oxide films but also the profile of segregation and film thicknesses were determined thank to the in-depth sensitivity of the technique. The atomic structure of the surfaces, and more precisely the unit cells, were explored with Low-Energy Electron Diffraction. Synchrotron Grazing Incidence X-Ray Diffraction was also used to refine the large oxide unit cell at [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] surface. Theses studies were supplemented by Scanning Tunnelling Microscopy to explore the topography of the surfaces. At last, ab initio calculations helped to rationalise the effects of orientation on the trend of segregation.

In the first step, a common protocol of preparation of clean surfaces was established. Bulk impurities as well as contamination from residual vacuum were two major difficulties to overcome. The former requires intensive cycles of surface preparation by sputtering-annealing to get rid of carbon. Although unavoidable for time consuming measurements such as STM and GIXD, vacuum contamination was avoided through fast XPS/LEED measurements. Coupled to that of aluminium, an intense carbon impurity segregation was observed only on [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] orientation in the form of self-organised stripes separated by ∼ 6 nm as found by STM and LEED. Upon annealing, two types of C 1s photoemission fingerprints were evidenced, one assigned to graphitic-like carbon and another one to chemisorbed carbon. Bulk carbide formation could not be excluded. Quantification of the graphitic component in photoemission paralleled the optimum of apparent coverage of stripes at ∼ 850 K. The latter started decaying at the onset of aluminium segregation and prevented the formation of fully covered oxide layer.

Upon annealing, all surfaces of Fe 0.85 Al 0.15 i.e. (110), ( 100) and [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] were prone to intense segregation of aluminium that is accompanied by step straightening, terraces widening and surface smoothing. Although segregation is presented on B 2 -FeAl surfaces according to the literature, the A 2 random alloy provides one more degree of freedom linked to potential phase transitions and ordering from the bulk to the surface. A special emphasis was put on the quantification of the segregation profile via photoemission. Dedicated models were developed including the variation of electron inelastic mean free paths with composition, although this turned out to be important only for the case of large aluminium atomic fraction. At the opposite of literature, sputtering seemed to slightly enrich the surface with aluminium. Segregation happened between 700 and 1000 K but the onset was much earlier at the surface than in the bulk; i.e. the surface equilibrates first. After 1000 K, a steady state regime and therefore a constant composition was reached at least on the photoemission point of view. In this regime, the impacted depth is around 2-3 nm with an atomic fraction corresponding to the ordered B 2 structure at the surface, is in agreement with the tendency of short-range order known in Fe-Al alloys. But, on a structural point of view, the three surfaces behaved drastically in different ways. Only the [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] face developed a large scale pseudo-hexagonal reconstruction, never disclosed up to now. Its unit cell of ∼ 2 nm is squeezed along one direction. According to LEED and GIXD, it is not a simple incommensurate reconstruction but in fact, it corresponds to a in-plane modulation of lattice parameter that extends up to 6 atomic planes below the surface. This yielded a strong apparent irregularity of hexagon rings in STM. On the other hand, whatever the temperature, the (100) surface was always (1 × 1) terminated with a marbled-like appearance assigned to an electronic contrast, probably due to a chemical one. At last, despite a smoothing at large distances, the [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] surface was always locally rough with the development of triangular pits involving several atomic levels with a distribution of local slopes peaking around ∼ 6 • . Assigned to the formation of vicinal [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] orientations which are dominated by [START_REF] Zhang | Kinetics aspects of initial stage thin γ-Al 2 O 3 film formation on single crystalline β-NiAl (110)[END_REF] terraces, this faceting seems to be a characteristic of the atomically rough bcc [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] orientation. But at the opposite of the literature where it is observed upon adsorption of an element that lowers the surface energy of covered [START_REF] Zhang | Kinetics aspects of initial stage thin γ-Al 2 O 3 film formation on single crystalline β-NiAl (110)[END_REF] surface compared to bare [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF], the present faceting happened upon segregation. The gain in energy should counterbalance the cost of formation of numerous under-coordinated kinks and steps. If simulations predicted a favourable Al segregation energy in the first layer of Fe with a slight oscillatory behaviour, the experimental situation on the three low index orientations appeared to be richer and more complex than expected. Theoretical work in still on-going to understand the relative stability of Al-covered Fe [START_REF] Zhang | Kinetics aspects of initial stage thin γ-Al 2 O 3 film formation on single crystalline β-NiAl (110)[END_REF] surface and bare Fe [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] surfaces.

The surfaces of Fe 0.85 Al 0.15 crystals have then been oxidised at a temperature corresponding to the steady-state regime of segregation. The used ultra-high vacuum conditions (1-1000 L) led to a selective oxidation of aluminium and to the growth of alumina films with a self-limited thickness of 1-2 nm. Iron always stayed in its metallic state. Ultrathin oxide was observed on ( 110) and (100) orientations while a three-dimensional growth happened on [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] surface. Through a decomposition of Al 2p core level into metallic and oxide states, an analysis of the profile of segregation was undertaken showing quite distinct behaviours. Subsurface of [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] and [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] orientations were found to be depleted in aluminium, but still richer than bulk; they adopt a composition close to the D0 3 phase up to the probing depth of photoemission. On the other hand, the segregation profile at the (100) surface was insensitive to oxidation and the subsurface kept its B 2 structure.

All the STM, LEED and XPS fingerprints of the oxide at [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] and (100) surfaces were very close to previous observations of the literature on NiAl, showing the recurrence of the corresponding structures and questioning the actual role of the substrate in their formation and stability. At [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] surface, a two-domain alumina film grew with a (18.5 × 10.5) Å2 nearly-rectangular rotated unit cell as determined by GIXD having a nearly perfect (2 × 1) matching with the substrate. The existence of two core level shifts for Al 2p, a stoichiometry of Al 2 O 2.6 and the symmetry of the unit cell let suppose that its structure is identical to the quite complex one identified at the surface of NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] [START_REF] Kresse | Structure of the ultrathin aluminum oxide film on NiAl (110)[END_REF] and for Al-deposit on Ni [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] [START_REF] Prévot | Archetypal structure of ultrathin alumina films: Grazing-incidence X-ray diffraction on Ni (111)[END_REF]. But its XPS thickness is larger than a simple bilayer remains unexplained. However, fewer anti-phase domain boundaries have been observed at Fe 0.85 Al 0.15 [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] than at NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF]. While the former is a way to adapt the lattice mismatch along one direction of NiAl, the capability of the random alloy to change its subsurface structure could be a way to reach this lattice matching. According to preliminary ab initio calculations, the model of Kresse is stable on Fe 0.85 Al 0.15 [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] with minor distortions. On (100) surface, (2 × 1) + (1 × 2) film was observed in the form of orthogonal stripes; a likely explanation is the formation of a distorted θ-Al 2 O 3 structure in Bain's epitaxy. This epitaxy is related to the stacking of oxygen anions that is common to all alumina polymorphs. But the existence of only one chemical shift for aluminium remains puzzling in light of the complexity of the proposed structural model on NiAl(100) [START_REF] Stierle | Surface X-ray diffraction study on the initial oxidation of NiAl (100)[END_REF] and the existence of mixture of tetrahedral and octahedral sites for aluminium in θ-Al 2 O 3 . Calculations are still on-going to see if this structure is actually stable. Finally, the lack of clear structure and the oxide film roughness observed on [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] orientation may be related to the strong tendency of this surface to nano-facet.

From the above findings, it is apparent that there is a coupling between the oxide structure, the orientation and the profile composition of the subsurface; therefore the creation and/or annihilation of point defects (antisite or vacancies) below the film is an essential part of the process of oxide growth. Tackling the problem on a theoretical point of view is already tough on NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] [START_REF] Finnis | The oxidation of NiAl: What can we learn from ab initio calculations?[END_REF]. Finally, whether the found profile is kinetically or thermodynamically driven is however still open.

Compared to the upstream context of formation of oxides at the surface of Al-alloyed steel, this study is only a first fundamental step on model single crystals. The role of oxygen activity, the nature of the oxidising agent and the switch from external to internal oxidation have been put aside by restricting to the Knudsen's regime, to O 2 and to single crystals. Indeed, not speaking about polycristalline samples and the role of grain boundaries, many studies point at a thickening of the film on single crystals at much higher oxygen activity as well as a potential oxidation of the transition metal and/or formation of mixed compounds, depending upon the kinetics [START_REF] Graupner | Oxidation of low-index FeAl surfaces[END_REF]. For instance, the growth of 80 nm thick epitaxial γ-Al 2 O 3 (111) films has been observed on NiAl(110) single crystal after oxidation in dry air [START_REF] Zhang | γ-Al 2 O 3 thin film formation via oxidation of β-NiAl (110)[END_REF][START_REF] Zhang | Kinetics aspects of initial stage thin γ-Al 2 O 3 film formation on single crystalline β-NiAl (110)[END_REF]; in their study of multistep selective oxidation of NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] under ultra-high vacuum, Krukowski and coworkers [START_REF] Krukowski | Anomalous hexagonal superstructure of aluminum oxide layer grown on NiAl (110) surface[END_REF] claimed to have grown α-alumina on NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF]. Since bulk alumina has a rich phase diagram with differences between polymorphs being just due to small variation in the relative octahedral/tetrahedral cation occupation, quite complex scenario of phase transitions upon annealing have been reported on Fe-Al polycrystalline alloys in the order γ, δ, θ up to the formation of the most stable α-Al 2 O 3 [START_REF] Grabke | Oxidation of NiAl and FeAl[END_REF]. Mirroring the bulk behaviour in the case of these "thick" films can be quite useful but with the caveat that ultrathin films can develop atomic and electronic structures with aluminium environments without any bulk counterpart [START_REF] Freysoldt | Ultrathin oxides: bulk-oxide-like model surfaces or unique films?[END_REF][START_REF]Oxide Materials at the Two-Dimensional Limit[END_REF]. For those peculiar ultrathin 2D oxides, some open surface science questions remains for Fe 0.85 Al 0.15 :

• is segregation coupled to the growth of the oxide? Is the profile thermodynamically or kinetically driven?

• why the observed oxide structures are recurrent on so many substrates? What is the actual role of the substrate in terms of stress and/or symmetry?

• what are the first steps of oxidation, the type of defects induced in the substrate and how does the structure progressively build-up depending on orientation?

• why is the film thickness self-limited? What is the rate limiting step? How does the transition to films with a "bulk-like" phase (thickening) proceed?

Figure 2 . 1 :

 21 Figure 2.1: Overview of the ultra-high vacuum system at INSP used during this thesis.

Figure 2 . 2 :

 22 Figure 2.2: Schematic of a four-grids LEED optics.

Figure 2 . 3 :

 23 Figure 2.3: Ewald's construction based on 1D reciprocal lattice points. The reciprocal space of a surface is made of Crystal Truncation Rods normal to the surface which intersections with the Ewald's sphere give the directions of the diffracted beams. CTRs are labelled here with their surface indexes.

Figure 2 . 4 :

 24 Figure 2.4: Schematic diagram of a scanning tunnelling microscope. From Ref. [35].

Figure 2 . 5 :

 25 Figure 2.5: The STM imaging modes [36]: (left) constant-current mode, (right) constantheight mode.

Figure 2

 2 Figure 2.6: Schematic diagram of metal-vacuummetal tunnelling [35]. Metals are indicated by the grey shadowing and represent the metal sample (left) and the tip (right). The middle region corresponds to the vacuum.

Figure 2

 2 Figure 2.8:Link between schematic band level alignment between sample and spectrometer and photoemission spectrum in kinetic energy. Φ s is the work function of the sample i.e. the minimum energy required to extract an electron from the Fermi level to infinity[START_REF] Oura | Surface science: an introduction[END_REF].

Fig. 2 .

 2 10 shows a wide photoemission scan of the clean and oxidised Fe 0.85 Al 0.15 surface for a Al-Kα excitation 5 with all the peaks labelled. Our work focused mainly on C 1s (E B 285 eV), Al 2p (E B 73 eV), Fe 3p (E B53 eV) and O 1s (E B 531 eV) for the quantification of segregation and chemical state analysis. To characterise iron, Fe 3p was preferred over Fe 2p despite its lower ionization cross section to minimise differences of analyser transmission function compared to Al and to maximise escape depth.

  800 700 600 500 400 300 200 100 0 Binding Energy (eV) Fe 0.85 Al 0.15 single crystal Wide scan, Al Kα source, Θ = 0 E °Figure 2.10: Al-Kα wide scan of a clean and oxidised Fe 0.85 Al 0.15 where the main photoemission core levels and Auger transitions are pointed. Notice the increase of background at low kinetic energy due to inelastic electrons.

  Figure 2.12: Fresnel quantities as function of the incident angle α i normalised by the critical angle of the substrate α c = √ 2δ for absorption β/δ=0.001, 0.005, 0.01, 0.05, 0.1: a) the reflection coefficient R = |r| 2 , b) the transmission coefficient T = |t| 2 , c) the penetration depth Λ normalised to Λ c = 1/2k 0 α c , d) the phase shift at reflection. From Ref. [71].

Figure 2 .

 2 Figure 2.13: Picture of the z-axis diffractometer INS of the BM32 beamline. The main components are indicated in the figure.

CHAPTER 3

 3

Figure 3 .

 3 Figure 3.1: Fe-Al binary phase diagram where the most important compounds (shaded area) are labelled with their Strukturbericht symbol [74, 78-80] and/or their formula.

Figs. 3

 3 Figs.3.3, 3.4, 3.5 show the bulk truncation along (100), (110) and (111) orientations of a cubic centred A 2 random alloy. As reminder, the bulk unit cell parameter of Fe 0.85 Al 0.15 is a B = 2.8914 Å[START_REF] Ellner | On the partial atomic volume of aluminum in solid solutions based on the 3d transition metals and copper[END_REF]. The surface lattice vectors (Figs. 3.3, 3.4, 3.5-a) are defined from the bulk ones (a B , b B , c B ) as: • (100): a S = a B , b S = b B , c S = c B ; • (110): a S = -a B + b B , b S = c B , c S = a B + b B (a S = √ 2a B = 4.09 Å and b S = a B = 2.89 Å); the selected surface unit cell is centred but a primitive one, rotated by 45 • can also be defined by a S,P = (a S + b S )/2 and b S,P = (-a S + b S )/2; both will be used later on;

Figure 3 . 3 :

 33 Figure 3.3: Ball model of the (100) face of cubic centred A 2 Fe 1-x Al x random alloy. The brown balls stand for the average atom and the bulk cubic unit cell vector (a B , b B , c B ) are shown with coloured arrows. a) Top view along the [001] B direction with the surface unit cell indicated by bold arrows. b) Side view along [010] B . c) View in perspective showing a monoatomic terrace with steps along the surface unit cell directions.

Figure 3 . 4 :

 34 Figure 3.4: Same as Fig. 3.3 but for the (110) orientation. a) Top view along [110] B . The primitive unit cell is shown by red arows. b) Side view along [110] B . c) View in perspective with a monoatomic step.

Figure 3 . 5 :

 35 Figure 3.5: Same as Fig. 3.3 but for the (111) orientation. a) Top view along [111] B . b) Side view along [011] B . c) View in perspective with a three consecutive monoatomic steps.

Figure 3 . 6 :

 36 Figure 3.6: Low index (100), (110) and (111) surfaces of FeAl in CsCl B 2 ordered alloy structure. The brown and blue balls stand for Fe and Al atoms, respectively and the bulk cubic unit cell vector (a B , b B , c B ) are shown with coloured arrows. Left column corresponds to top views along the [100] B , [110] B , [111] B while the right column shows a side view. The surface unit cell is indicated by black arrow.

Figure 3 . 7 :

 37 Figure 3.7: Same as Fig. 3.6 but for low index surface of Heussler D0 3 ordered alloy.

  1) with a high temperature surface average composition 1 of Fe 0.38 Al 0.62 and pure Al termination[START_REF] Kottcke | Segregation-induced subsurface restructuring of FeAl (100)[END_REF][START_REF] Wang | Atomic structure of FeAl {001}[END_REF] while the c(2 × 2) superstructure corresponds to a surface average composition of Fe 0.51 Al 0.49 based on LEED/Auger analysis[START_REF] Graupner | Composition and structure of the (100) and (110) surfaces of FeAl[END_REF][START_REF] Hammer | Segregation phenomena on surfaces of the ordered bimetallic alloy FeAl[END_REF][START_REF] Hammer | Equilibration processes in surfaces of the binary alloy Fe-Al[END_REF][START_REF] Kottcke | Segregation-induced subsurface restructuring of FeAl (100)[END_REF] on top of a thick metastable film (at least 6 layers) of D0 3 Fe 3 Al[START_REF] Kottcke | Segregation-induced subsurface restructuring of FeAl (100)[END_REF] (Fig.3.9).

Figure 3 . 8 :

 38 Figure 3.8: LEED patterns obtained after annealing a Fe 0.53 Al 0.47 (100) surface: a) at low temperature (673 K) and b) at higher temperature leading to a) c(2 × 2) and b) (1 × 1) reconstruction. From Ref. [28].

Figure 3 . 10 :

 310 Figure 3.10: Structural models of a) Fe 0.97 Al 0.03 (100)-c(2 × 2) I , c) Fe 0.70 Al 0.30 (100)-c(2 × 2) II and b) the STM image of Fe 0.85 Al 0.15 (100) with a local c(2 × 2) I (Size 100 × 100 Å2 , U b = -0.5 mV, I t = 2.1 nA). Herein sublattices with c(2 × 2) periodicity are denoted I and II, respectively. Interlayer spacings ∆d/d and atomic concentrations c i are given in figure. From Refs. [29, 32].

Figure 3 .

 3 Figure 3.11: a) Structural models of Fe 0.85 Al 0.15 (100)-(1 × 1) and b) room temperature STM image of this surface (100 × 83 Å, U b = -6 mV, I t = 0.46 nA). According to authors, a clear chemical contrast is achieved between Fe (protruding atoms) and Al (dark indentations).From Ref.[START_REF] Blum | Segregation and ordering at Fe 1-x Al x (100) surfaces-a model case for binary alloys[END_REF].

Figure 3 . 12 :

 312 Figure 3.12: The compositional schematic diagram of equilibrium FeAl(100) surface region deduced from full dynamical LEED intensity analyses. Split shadings within a layer manifest that two sublattices of c(2 × 2) symmetry are observed [29]. Schematic stacking is given below each figure: (R) randomly, (OL) overlayer, (CAP) capping, (Al-term) Al terminated. From Ref. [29].

  3.14-a).

Figure 3 .

 3 Figure 3.13: LEED patterns of Fe 0.53 Al 0.47[START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] surface after annealing at a) 673 K with a (2 × 1) pattern; b) 673-873 K or > 1073 K with a complex superstructure; c) 873-973 K with unknown streak phases along[START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] direction[START_REF] Graupner | Composition and structure of the (100) and (110) surfaces of FeAl[END_REF]. d) LEED pattern of Fe 0.60 Al 0.40[START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] annealed at ≥ 1073 K showing a (1 × 1) arrangement[START_REF] Gleason | A photoelectron spectroscopy and thermal desorption study of CO on FeAl (110) and polycrystalline TiAl and NiAl[END_REF].

Figure 3 .

 3 Figure 3.14: STM images of Fe 0.53 Al 0.47 (110) after annealing at a) 673 K showing a truncated bulk (1 × 1) surface (4.7 × 4.7 nm 2 , I t = 3.96 nA, U b = 331 mV) with some vacancies; b) at 1123 K, with a FeAl 2 superstructure on top (15 × 15 nm 2 , I t = 5.41 nA, U b = 30.2 mV). The unit cells are labeled, and the corresponding ball models are shown below. The unit cell of stoichiometric FeAl 2 is one Fe atom surrounded by six Al atoms. Only one type of atoms (Fe) is imaged. From Ref. [94].

3. 3 . 3

 33 Fe 0.50 Al 0.50[START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF], (210),(310)

Figure 3 .

 3 Figure 3.15: LEED patterns and proposed ball models of an annealed Fe 0.50 Al 0.50 (111) surface (E K = 42 eV). a) ( √ 3 × √ 3)R30 • superstructure obtained after annealing at 753 K; b) (3 × 3) superstructure formed at ≥ 973 K. Patterns have been overlapped with simulated LEED; the insets show the corresponding direct space. The atoms marked in bold represent close-packed Al microfacets forming pyramid-like microstructures. Interpreted from Refs. [30, 31].

Figure 3 . 16 :

 316 Figure 3.16: Ball models of a few bulk alumina atomic structures showing the coordination polyhedra of the cations. Red spheres stand for oxygen anions and blue ones for aluminium cations. Al cations are either surrounded by a distorted octahedron or by a tetrahedron made out of O nearest neighbours. Partial occupancy of sites is not uncommon.

  ,[START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF] of the ordered compound NiAl and Ni 3 Al[13-15, 121, 122, 132-134, 145, 146, 148, 149, 151-164, 164-166,168-188]. At the opposite of our study on a random alloy, the use of an ordered alloy sets the composition of the substrate underneath the oxide. NiAl crystallises in the CsCl B 2 structure where Ni atoms occupy the corner of a cube and the Al its centre or vice-versa (a B = 2.89 Å). Ni 3 Al adopts a cubic L1 2 -Cu 3 Au type structure (a B = 3.56 Å[START_REF] Sondericker | Atomic structure of alloy surfaces. II. Ni 3 Al {111}[END_REF][START_REF] Wang | Density functional theory study of Ni/Ni 3 Al interface alloying with Re and Ru[END_REF]) where Ni atoms occupy the centres of the faces of the cube while Al atoms are located at the corners. The relaxed surfaces of Ni 3 Al(

  9 Å, b ox = 10.55 Å, γ ox = 88.7 • ; close values have been obtained by Surface X-Ray Diffraction [121] a ox = 18.01 Å, b ox = 10.59 Å, γ ox = 91.15 • .The film is commensurate with the substrate along the[START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] direction and incommensurate along the other one [001]. Ni atoms in excess after oxidation are dissolved in the bulk of the crystal[START_REF] Jaeger | Formation of a well-ordered aluminium oxide overlayer by oxidation of NiAl(110)[END_REF][START_REF] Lozovoi | Surface energy and the early stages of oxidation of NiAl (110)[END_REF][START_REF] Lozovoi | Surface stoichiometry and the initial oxidation of NiAl (110)[END_REF][START_REF] Stierle | Observation of bulk forbidden defects during the oxidation of NiAl (110)[END_REF] or annihilated by diffusing Ni vacancies[START_REF] Finnis | The oxidation of NiAl: What can we learn from ab initio calculations?[END_REF].

Figure 3 .

 3 Figure 3.17: LEED patterns of the oxide layer on NiAl(110) [14] around a) (00) S and b) (01) S reflections, and c) on FeAl(110) [16]. They have been overlapped with a simulation with an indexing corresponding to a quasi-rectangular unit cell with two domains (blue/red points) corresponding to the matrix of 4 2.53 -1 3.37 from the rectangular surface unit cell. In Figs. a, b, several additional weak spots due to double diffraction appear, which do not coincide with the indicated oxide lattice. Interpreted from Refs. [14, 16].

Figure 3 . 18 :

 318 Figure 3.18: Top view (a) and side view (b) of alumina/NiAl(110) model based on ab initio calculation and STM. Dark blue balls are Al s atoms while violet ones are Al i atoms; larger and smaller red balls are O s and O i atoms respectively. (c) to (e) are experimental STM images. (c) -2.5 mV/1.4 nA and (d) -0.2 V/0.9 nA are conducted at room temperature while (e) -0.5 V/0.3 nA is at low temperature. (a) Two unit cells are marked by white rectangles, and the green rectangles and squares are the arrangement of surface O atoms. (c)-(d), O atoms and Al atoms are presented with red and blue circles respectively. (d) Closeup of surface structure showing the coordination of the tetrahedral and pyramidal Al atoms. From Ref. [15].

Figure 3 .

 3 Figure 3.19: High-resolution core level spectra of an ultrathin alumina film formed on NiAl(110). a) right: Al 2p spectra (recorded at 130 eV) is decomposed into 4 visible components, each with a 0.4 eV spin-orbit splitting with a ratio of 0.5. These components correspond to (1) Al atoms of NiAl substrate (light blue), (2) interfacial Al atoms between oxide and substrate (grey), (3) interfacial Al atoms in the oxide overlayer (violet), (4) surface Al atoms of the oxide (orange). a) Left: O 1s spectra (recorded at 900 eV) is fitted with two components with a 1.23 eV binding energy difference and an intensity ratio of 0.19; the less intense one originates from the O atoms with interfacial Al atoms beneath that reside more distant to the other O atoms. d)e) Evolution with photon energy of ratios of Al 2p and O 1s peaks. From Ref. [151].

Figure 3 .

 3 Figure 3.20: STM image (500 × 500 Å2 ) of an alumina film on NiAl(110) showing a step edge (S), a reflection domain boundary (R) and an antiphase domain boundary (A). Sample bias = -1.3 V, I = -0.4 nA. From Ref. [159].

Figure 3 . 21 :

 321 Figure 3.21: Structural model of θ-Al 2 O 3 /NiAl(100), showing the Bain epitaxy relationship between oxygen fcc sublattice and NiAl(100) bcc lattice, that is (001) NiAl (001) O-lat and [100] NiAl /[010] NiAl [110] O-lat . The height of θ-Al 2 O 3 unit cell is 11.83 Å. From Refs. [163, 166].

Figure 3 .

 3 Figure 3.22: Atomic resolution STM image of the oxide overlayer on NiAl(100) after 500 L of oxidation followed by 2 h of annealing at 1025 K (U b = 2 V, I t = 1 nA). The observed peridodicity matches the oxygen sublattice of the bulk θ-Al 2 O 3 structure. From Ref. [166].

Figure 3 . 23 :

 323 Figure 3.23: Top and side views of the relaxed slab (alumina/Ni 3 Al(110)) computed using Density Functional Theory. The (2 × 1) unit cell (left) is shown as a yellow rectangle. X marks the largest interstitial sites. O-ions are red balls, Al-ions are white balls and metallic Al atoms in the model substrate are in grey. From Ref. [179].

  3.4.3.2.5 Ni 3 Al(100) Oxidation on Ni 3 Al(100) surface at 1100 K with 2000 L of O 2 leads to the formation of a well ordered strongly distorted γ -Al 2 O 3 thin film (thickness ∼ 10 Å) growing with its (

  3.4.3.2.6 Ni 3 Al(111) Clean Ni 3 Al(111) surface annealed at ≥ 1000 K leads to a (2 × 2) unit cell the lattice constant of which is ∼ 5.1 Å [183-185]. The corresponding LEED pattern and structural model are shown in Fig. 3.25.

Figure 3 .

 3 Figure 3.24: Calculated LEED pattern of γ-Al 2 O 3 /Ni 3 Al(100) by considering a model of alumina consisting of two domains with hexagonal structure (holes and filled squares) with a lattice constant of 3 Å and an angle of 90 • between them and two extra domains with hexagonal structure (small holes and filled circles) with a lattice constant of 17.5 Å and angle between them of 90 • . The later can be resolved in STM observation. The square indicates the substrate unit cell [181].

Figure 3 .

 3 Figure 3.25: LEED pattern (E K = 93 eV) and real space model of the clean Ni 3 Al(111) surface. The pattern is split vertically in experimental image (left) and a schematic representation (right). The surface unit cell is indicated by a rhombus. From Ref. [183].

Figure 3 .

 3 Figure 3.26: a) AFM imaging of the well ordered oxide film on a (2 × 2) Ni 3 Al(111) surface. b) Same image, with all recognizable hexagonal features. c) The open hexagons are centred on a hexagonal lattice with 0.51 nm periodicity, which is the aluminium sublattice of Ni 3 Al substrate. From Ref. [188].

Figure 3

 3 Figure 3.27:Real space unit cells of the Ni 3 Al(111) substrate (0.51 nm, white), the dot (blue) and the network (red) structures of the oxide. In contrast to the network structure, the dot structure is commensurate with the substrate lattice[START_REF] Gritschneder | Disorder or complexity? Understanding a nanoscale template structure on alumina[END_REF].

  )-Sect. 3.4.3.2.1, Cu-9 at.%Al(111) and γ-Al 4 Cu 9 (110)-Sect. 3.4.3.4, FeAl(110)-Sect. 3.4.3.6).

3. 4

 4 .3.4 Cu-9 at.% Al[START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] and γ-Al 4 Cu 9[START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF]

Figure 3

 3 Figure 3.28: LEED pattern (left) and atomic model in real space (right) of clean Cu-9 at% Al(111) surface annealed at 953 K (E K =90 eV; the reciprocal cell of ( √ 3 × √ 3)R30• superstructure is marked. From Refs.[START_REF] Napetschnig | Ultrathin alumina film on Cu-9 at% Al (111)[END_REF][START_REF] Yu | Surface segregation of aluminum atoms on Cu-9 at.% Al (111) studied by Auger electron spectroscopy and low energy electron diffraction[END_REF].

  3.29).[START_REF] Graupner | Composition and structure of the (100) and (110) surfaces of FeAl[END_REF] surface O atoms are arranged in squares and triangles with a p2gg symmetry while 16 interface Al atoms are arranged in heptagon and pentagon pairs, which agrees exactly with the structure on NiAl(110)[START_REF] Kresse | Structure of the ultrathin aluminum oxide film on NiAl (110)[END_REF][START_REF] Napetschnig | Ultrathin alumina film on Cu-9 at% Al (111)[END_REF].

Figure 3 . 29 :

 329 Figure 3.29: Atomic resolved STM images of an oxidised Cu-9 at.% Al(111) (100 L of O 2 at 953 K). a-c) The surface O layer and d-f) the interface Al layer visible at higher tunneling resistance. The left images (a,d) display the first (incommensurate) oxide structure and the centre images (b,e) show the second (commensurate) one. As a matter of comparison, the oxide on NiAl(110) is shown on right side. The dots mark the atomic positions of the alumina calculated on NiAl[START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] [START_REF] Kresse | Structure of the ultrathin aluminum oxide film on NiAl (110)[END_REF]. In (b,e) the primitive unit cell is drawn in black and the four rectangular building blocks are marked in white. From Ref.[START_REF] Napetschnig | Ultrathin alumina film on Cu-9 at% Al (111)[END_REF].

Figure 3 .

 3 Figure 3.30: a) STM image of a CoAl(100) exposed to 10 L of O 2 at 800 K (U b = 2.00 V, I t = 0.2 nA). The two orthogonal domains of the oxide film are denoted by the red stripes. For each domain a unit cell is outlined. b) Top view model of the θ-Al 2 O 3 surface plane with lattice parameters a ox = 5.64 Å, b ox = 2.91 Å. c) Structural model of the θ-Al 2 O 3 grown on CoAl(100) where a monoclinic θ-Al 2 O 3 unit cell and the close-packed oxygen fcc lattice are highlighted. For the sake of clarity, only the octahedral occupation of Al 3+ ions are shown. From Ref. [125].

) 2 .

 2 By a simple analogy with NiAl(110), Graupner et al. claimed that the film structure involves a quasi-rectangular unit cell with two domains (due to the two-fold symmetry of the substrate) given by the matrix M s = 3

Figure 3 . 31 :

 331 Figure 3.31: LEED patterns obtained after high temperature oxidation of Fe 0.53 Al 0.47 (110) at 1123 K: a) oxidation with 1000 L of O 2 (E K = 86 eV) and b) streak phase observed after exposure to 10 4 L of O 2 (E K = 125 eV). From Ref. [16].

3. 4 . 3 . 6 . 2

 4362 Fe 0.53 Al 0.47 (100) High temperature oxidation of Fe 0.53 Al 0.47 (100) (100 L of O 2 at 773-1173 K) creates an ordered alumina with a thickness of 3-5 Å; it presents (i) a c(6 × 6) (unit cell 12.2 × 12.2 Å2 ) at 973 K and (ii) a two-domain (2 × 1) LEED pattern with a streaky structure along [010] and [001] directions at 1123 K [16] (Fig. 3.33-a,b). A very similar (2 × 1) + (1 × 2) LEED pattern was also observed on Fe 0.85 Al 0.15 (100) [93], NiAl(100) (see Sect. 3.4.3.2) and CoAl(100) (see Sect. 3.4.3.5) surfaces. In the latter case, it was assigned to the growth of a θ-Al 2 O 3 film in Bain orientation [162, 163] (see Sect. 3.4.3.2, Fig. 3.21). The thickness of alumina on Fe 0.53 Al 0.47 (100) is found around d = 3 -5 Å [16, 93].

Figure 3 .× √ 3 )

 33 Figure 3.32: STM images of a well ordered alumina film on Fe 0.53 Al 0.47 (110) surface (1000 L of O 2 at 1125 K). a) 70 × 70 nm 2 , U b = -1.25 V, I t = -0.7 nA; a tentative unit cell (18.6 × 19.4 Å2 ) is shown. b) 69 × 100 nm 2 , U b = 1.25 V, I t = 0.17 nA; the line profile goes through a step edge and a hole in the layer. c) 50 × 50 nm 2 , U t = 3.02 V, I t = 1.04 nA. A line pattern appears at positive bias. From Ref. [137].

Figure 3 .

 3 Figure 3.33: LEED patterns of the oxide layer formed by high temperature oxidation of Fe 0.53 Al 0.47 (100) with 250 L of O 2 : a) at 973 K and b) 1123 K. LEED is overlapped with a) a c(6 × 6) (matrix 3 -3 3 3 ) superstructure or b) a (2 × 1) superstructure with the two equivalent domains. Corresponding direct spaces are shown below where the grey grid corresponds to surface nodes and red dots to oxide unit cell. Interpreted from Ref. [16].

Figure 3 . 34 :

 334 Figure 3.34: LEED pattern of the oxide layer formed by high temperature oxidation (973 K, 250 L of O 2 ) of FeAl(111) overlapped with the proposed (6.4 × 6.4)R30 • reconstruction. From Ref.[START_REF] Graupner | Oxidation of low-index FeAl surfaces[END_REF].

Figure 3 . 35 :

 335 Figure 3.35: Al 2p core level spectra of Fe 0.53 Al 0.47 (110) surface. a) Comparison of clean and oxidised surfaces at normal emission; b) Spectra of the oxidised surface at normal (0 • ) and grazing (60 • ) emission, revealing a weak shoulder assigned to the existence of interfacial Al atoms; c) Comparison of Fe 3p spectra of clean and oxidised surfaces showing the lack of chemical shift. The photon energy is 150 eV. From Ref. [99].

Figure 3 .

 3 Figure 3.36: Schematic profile of composition and structure of Fe 0.75 Al 0.25[START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] before and after oxidation. From Ref.[START_REF] Vonk | In situ x-ray study of Fe 3 Al (110) subsurface superlattice disordering during oxidation[END_REF].

CHAPTER 4 TOWARDS

 4 CLEAN FE 0.85 AL 0.15 SURFACES: CARBON SEGREGATION AND SURFACE REACTIVITYThis thesis focuses on the aluminium segregation and oxidation processes at the surfaces of Fe 0.85 Al 0.15 alloy. It has been chosen to study this composition as a model system for alloyedsteel (see Chap. 1) since, in the temperature range under study (300-1100 K), the alloy matrix corresponds to the ferritic solid solution which has a body centred cubic structure (labelled A 2 in Fig.3.1) as in the case of the industrial Al-alloyed steel grades. The three low index surfaces[START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF], (100) and (111) have been considered herein; their schematic bulk truncation and surface unit cells are shown in Figs.3.3-3.4-3.5. The present chapter focuses on the preparation of atomically clean and well-crystallised surfaces which is a prerequisite of any surface science analysis of their intrinsic properties. During the course of surface preparation (described in Sect. 2.2), it turned out that the Fe 0.85 Al 0.15 surfaces were very sensitive to contamination by non metal elements, in particular carbon as any surface of pure or alloyed iron.

  4.2-c,d) or fully segregated as a film supported on the surface of the alloy (Figs. 4.2-a,b). Both models are detailed in Sect. 2.5.3.2 and are sketched in Fig. 5.3. In a first step, the bulk composition of the alloy required as a reference was assumed to be given by the nominal x = 0.15 value (Figs. 4.2-a,c). In a second step, the analysis was further refined by taking into account the actual profile of Al segregation found through the analysis of the angular dependence of Al 2p/Fe 3p ratio as developed in the next chapter 5.1 (Figs. 4.2-b,d). The question of the determination of

Figure 4 .

 4 Figure 4.1: C 1s, Al 2p and Fe 3p core level photoemission spectra recorded upon annealing of the Fe 0.85 Al 0.15 (110) surface at 670 K, 870 K, 970 K and 1070 K. XPS spectra are normalised to the maximum intensity of the main peaks. The decomposition of the lines is discussed in the text. Normal emission was used at a pass energy of E p = 20 eV.

  tot) / Al 2p C 1s (283 eV) / Al 2p C 1s (285 eV) / Al 2p C 1s (tot) / Fe 3p C 1s (283 eV) / Fe 3p C 1s (285 eV) / Fe 3p a) C film on Fe 0.85 Al 0.15 the segregation profile of Al

Figure 4 . 2 :

 42 Figure 4.2: Quantification of carbon coverage from C 1s/Al 2p and C 1s/Fe 3p ratio. a)b) Model of segregated layer and c)d) model of bulk impurities starting from a)c) the Fe 0.85 Al 0.15 bulk composition and b)d) the profile of Al segregation (see text). Coverage are given in terms of (110) monolayer. Error bars stem from uncertainties of 10 % on the ratio of intensities.

Figure 4 .

 4 Figure 4.3: a) Carbon solubility at low-carbon concentration in the α (bcc) phase of the C-Fe binary phase diagram [222]; b) C-Fe phase diagram where the dashed lines indicates the metastable Fe-Fe 3 C system [232].

  .5-b), stripes develop along the [001] B

Figure 4 . 4 :

 44 Figure 4.4: Evolution of the I Al 2p /I F e 3p ratio as function of the annealing temperature on samples showing bulk carbon segregation.

Figure 4 . 5 :

 45 Figure 4.5: STM imaging of Fe 0.85 Al 0.15 (110) upon annealing at increasing temperature: a) 690 K, 30×30 nm 2 , U b = -1.0 V, I t = 1.9 nA; inset annealed at 760 K, 67×67 nm 2 , U b = +1.7 V, I t = 2 nA; b) 950 K, 150 × 150 nm 2 , U b = -1.0 V, I t = 80 pA; c) 1030 K, 150 × 150 nm 2 , U b = -1.0 V, I t = 80 pA; d) 1070 K, 150 × 150 nm 2 , U b = -1.0 V, I t = 1.2 nA.

Figure 4 . 6 :

 46 Figure 4.6: STM image of Fe 0.85 Al 0.15 (110) annealed at a) 1030 K, U b = -1.0 V, I t = 10 pA, 75 × 75 nm 2 ; b) 760 K, stripes develop on top of an hexagonal superstructure (U b = 2 V, I t = 1.97 nA, 27 × 21 nm 2 ). The inset corresponds to the line profile shown on the image.

Figure 4 . 7 :

 47 Figure 4.7: Statistic values for a) height and b) spacing of stripes derived from STM profile fits

Figure 4 . 8 :

 48 Figure 4.8: LEED pattern evolution of a C-containing Fe 0.85 Al 0.15 (110) surface. a) After annealing at 690 K, the (1×1) is overlapped with Al-rich superstructure spots (E K = 110 eV); b) at the maximum of coverage (990 K), spots related to C-stripes are regularly spaced along [10] S direction (990 K, E k = 174 eV); c) at 1030 K, stripe spots start fading out and lead to a streaking along the [10] S direction while the superstructure diffraction spots reappear (E K = 142 eV).

Figure 4 . 9 :

 49 Figure 4.9: Comparison of the morphology of Fe 0.85 Al 0.15 (110) surface after a) oxidation at room temperature (50 L of O 2 ) followed by annealing at 1073 K and b) oxidation (50 L of O 2 ) during annealing at 1073 K. a) 200 × 200 nm 2 , U b = 1.5 V, I t = 0.92 nA, b) 200 × 200 nm 2 , U b = 1.7 V, I t = 0.1 nA. C-induced stripes appear as white features running along the [001] B direction.

4 . 11 )

 411 through the ratios of integrated intensities I C 1s /I F e 3p , I O 1s /I Al 2p and I O 1s /I Al 2p after Shirley background subtraction. The Al 2p line was decomposed into metallic (E B

  66]. Either the bulk composition Fe 0.85 Al 0.15 (Fig. 4.11a,b) or the actual profile of segregation (Fig. 4.11-c,d) were used. Only the last case will be commented below.

Figure 4 . 10 :

 410 Figure 4.10: Ageing of Fe 0.85 Al 0.15 (111) and (100) surfaces (annealed at 970 K). XPS spectra of Al 2p, C 1s, O 1s and Fe 3p are recorded as a function of time at normal emission and room temperature. The chamber pressure is below 5 × 10 -10 mbar. The left column corresponds the (111) surface and the right column to (100). The pass energy was set at 50 eV and the X-ray gun power kept constant for comparison.

Figure 4 . 11 :

 411 Figure 4.11: Quantification of the ageing contamination from C 1s/Fe 3p, Al 2p(oxi)/Fe 3p and O 1s/Fe 3p ratios on a)b) Fe 0.85 Al 0.15 (100) and c)d) Fe 0.85 Al 0.15[START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF]. The contamination layer was modelled by graphite, and either the bulk composition Fe 0.85 Al 0.15 or the actual profile of aluminium segregation was accounted for. Coverages are given in monolayers corresponding to (100) and[START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] orientations.

  .2-a) and Mg-Kα (Fig. 5.2-b) excitations for the involved core levels (Fe 2p, Fe 3p, Al 2s, Al 2p, O 1s, C 1s). Somehow the dependency of λ(x) is much more moderated than

Figure 5 . 1 :

 51 Figure 5.1: Compilation of the density ρ(x) of all the Fe-Al compounds tabulated in the ICSD database overlapped with the measurements of Ref.[START_REF] Ellner | On the partial atomic volume of aluminum in solid solutions based on the 3d transition metals and copper[END_REF] for the A 2 (red filled circles) and B 2 (orange filled squares) structures. In the legend, the corresponding compounds as well as their space groups, their parent compounds and their Strukturbericht symbol are labelled. Data are well accounted for by a linear regression (black line) corresponding to an hyperbolic variation of the atomic volume (inset).

Figure 5 . 2 :

 52 Figure 5.2: TPP-2M calculated inelastic mean free path of Fe 1-x Al x compounds using a linear regression of the material density (Fig. 5.1) and the orbital filling of Tab. 5.2 for a) Al-Kα (hν = 1486.6 eV) and b) Mg-Kα (hν = 1253.6 eV) photon excitations.

Figure 5 . 3 :

 53 Figure 5.3: Models of profile of concentration used for photoemission analysis. a) The homogeneous semi-infinite alloy A 1-x B x . b) The thin film on a substrate. c) The homogeneous segregated layer A 1-x L B x L on a semi-infinite alloy A 1-x S B x S . d) The continuous profile of segregation A 1-x(z) B x(z) .

0. 85

 85 Al 0.15On all the surfaces, Al segregation has been quantified by photoemission through the evolution of the ratio I Al 2p /I F e 3p as a function of the annealing temperature (Fig.5.5) after sputtering (1 keV Ar + , 30 min, ∼ 10 µA•cm -2 ). The thermal cycle was kept constant with an heating/cooling rate around 500 K•min -1 and a plateau temperature duration of 15 min. For those so called ex situ data, the sample was cleaned between each measurement to avoid contamination and bias due to preferential oxidation of Al by residual pressure of the chamber (see Chap. 4). Normalisation of bare spectra to background (Fig.5.4) points already at an increase of the raw intensity of the aluminium signal.

Figure 5 . 4 :Figure 5 . 5 :

 5455 Figure 5.4: Evolution with annealing temperature of Al 2p core level (normal emission Θ = 0 • ) of the various orientations of Fe 0.85 Al 0.15 . Spectra have been normalised to background.

4 6 Figure 5 . 7 :

 4657 Figure 5.7: Angular modulation of the ratio I Al 2p /I F e 3p (pass energy E p = 50 eV) corrected for the transmission function and photo-ionization cross sections. Samples have been annealed at the highest temperature 1273 K. Data (points) have been fitted with a model of continuous profile of segregation (lines, Eq. 5.4). A similar fit quality is obtained with the segregated layer model (Eq. 5.2). Black open symbols correspond to measurements at the highest temperature of Fig. 5.5.

  .8-b) and the superstructure spots around {11} S surface reflections, the nearest commensurate superstructure unit cell could be determined with the help of the LEEDPat software [239] from Hermann and Van Hove (Fig. 5.9). It corresponds to a rotation matrix 4 0 2 5 in the rectangular centred unit cell (a S , b S ) of Fig. 3.4 or 4 4 -3 7 in the primitive unit cell (a S,P , b S,P ) unit cell of Fig. 3.4. The superstructure unit cell is close to an hexagonal one with a r = 16.36 Å, b r = 16.61 Å and angle of γ r = 60.5 • . Its first lattice vector a r is aligned along the a S direction. Being commensurate, such a reconstruction leads to only one domain.

Figure 5 . 8 :

 58 Figure 5.8: LEED patterns of a clean Fe 0.85 Al 0.15 (110) surface annealed at 1123 K. Beam energies are indicated in figure. The active and extinguished bulk spots are shown as orange circles and squares, respectively.

Figure 5 .

 5 Figure 5.9: a) Overlap between LEED pattern of Fig. 5.8 with the proposed commensurate superstructure. The inset shows the overlap close to the origin of the reciprocal space. Red and blue boxes correspond to line cuts shown in Fig. 5.10. Notice the discrepancy along [10] S . b) Corresponding direct space. The grey grid stand for the nodes of the (1 × 1) rectangular unit cell (a S , b S ). The red dots are the nodes of the superstructure with basis vectors a r (red) and b r (green).

Figure 5 . 10 :

 510 Figure 5.10: Line cuts of the LEED pattern of Fig. 5.9 along a) [10] S (red box) and b) [01] S (blue box). c) Convolution of the nodes of substrate reciprocal space with a modulation of unit cell shown as inset (see text).

cr 2 l 2 (

 22 inset of Fig.5.12) leads to a variation of lattice parameter of ∆cr cr 0.2 and a domain size of c S /∆l S,s 8 Å i.e. around 6 atomic layers.

10

 10

Figure 5

 5 Figure 5.11: In-plane radial diffraction scans (l = 0.075) of a clean Fe 0.85 Al 0.15 (110) surface annealed at 1050 K (black line) and after oxidation at the same temperature with 500 L of O 2 . a) (h S , 0, 0.075), b) (0, k S , 0.075), c) (h S , h S , 0.075).Grey lines points at peaks due the clean surface reconstruction and light blue ones to new peaks due to the oxide layer.

2 ∆Figure 5 . 12 :

 2512 Figure 5.12: Out-of-plane l S scan on the reconstruction peak (h S = 0, k S = 2.2) of the clean Fe 0.85 Al 0.15 (110) surface. The inset shows a Williamson-Hall plot of peak width.

Figure 5 .

 5 Figure 5.13: (0, 0, l S ) rod evolution of a sputtered Fe 0.85 Al 0.15[START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] surface during annealing at increasing temperature.

Figure 5 . 14 :

 514 Figure 5.14: LEED patterns of a Fe 0.85 Al 0.15 (100) surface annealed at 973 K. The surface is (1 × 1) as indicated by spot indexes.

Figure 5 .

 5 Figure 5.15: Evolution with beam energy of the LEED pattern of Fe 0.85 Al 0.15 (111) after annealing at 973 K.

Figure 5 . 16 :

 516 Figure 5.16: High resolution STM images of the Fe 0.85 Al 0.15 (110) surface annealed a) at 823 K (33 × 17 nm 2 , U b = 2.0 V, I t = 1.77 nA; notice the presence of residual carbon stripes which appear as white lines) and b) line profile shown in Fig. a, c) at 1073 K (53 × 28 nm 2 , U b = -1.3 V I t = 0.23 nA). c) 2D autocorrelation of image c.

Figure 5 .

 5 Figure 5.17: a) High resolution STM images of the Fe 0.85 Al 0.15 (110) surface annealed at 1150 K (30 × 30 nm 2 , U b = 2.3 V, I t = 0.2 nA). b) 2D autocorrelation of the image-b. c) Large scale image (100 × 100 nm 2 , U b = 2.1 V, I t = 0.2 nA). d) Height histogram of image-c. e) Line profiles shown in image a.

Figure 5 . 18 :

 518 Figure 5.18: Large scale STM images (500 × 500 nm 2 ) of the Fe 0.85 Al 0.15 (100) surface after annealing at three different temperatures: a) 1051 K (U b = 1.5 V, I t = 0.4 nA), b) 1078 K (U b = 0.9 V, I t = 0.1 nA), c) 1178 K (U b = -0.9 V, I t = 0.3 nA). d) Line profile drawn on the image c.

Figure 5 .

 5 Figure 5.19: a) STM image of the Fe 0.85 Al 0.15 (100) surface after annealing at 1078 K (200 × 200 nm 2 , U b = 0.9 V, I t = 0.1 nA. b) Corresponding histogram of the height of each pixel throughout the entire STM image.

Figure 5 .

 5 Figure 5.20: a) STM image (60 × 60 nm 2 ) of the Fe 0.85 Al 0.15 (100) surface after annealing at 913 K (U b = 0.2 V, I t = 0.8 nA). b) Line profile corresponding to the black line in the STM image.

Figure 5 .

 5 Figure 5.21: STM images a) 50 × 50 nm 2 and b) 15 × 15 nm 2 of the Fe 0.85 Al 0.15 (100) surface after annealing at 1051 K (U b = 1.6 V, I t = 0.4 nA). c) Line profile corresponding to the black line in the STM image.

Figure 5 . 22 :

 522 Figure 5.22: Successive STM images on a "clean" Fe 0.85 Al 0.15 (100) (50 × 50 nm 2 , U b = 0.6 V, I t = 0.3 nA). The arrows indicate the feature changing from one image to the other. The triangle is used as a reference.

Figure 5 . 23 :

 523 Figure 5.23: STM images (700 × 700 nm 2 ) of the Fe 0.85 Al 0.15 (111) surface for different annealing temperatures as indicated in the figure. A typical line profile is drawn under each image and the roughness parameter R a is also indicated. a) U b = -1.6 V,

Figure 5 .

 5 Figure 5.24: a) STM image (38 × 38 nm 2 , U b = -1.5 V, I t = 0.4 nA) of the Fe 0.85 Al 0.15 (111) surface annealed at 973 K representing various topographical features regularly reproduced. c) Local slope τ distribution of image a. The values for (111) vicinal surfaces of type (hkk) with h ≤ 9 and k < h are pointed.

Figure 5 .

 5 Figure 5.25: a) STM image (20 × 18 nm 2 , U b = -1.6 V, I t = 0.5 nA) of the Fe 0.85 Al 0.15 (111) surface annealed at 1173 K. b) Corresponding height histogram with its fit with several equidistant peaks.

Figure 5 .

 5 Figure 5.26: STM images of the Fe 0.85 Al 0.15 (111) surface (17 × 17 nm 2 , U b = -1.2 V, I t = 0.4 nA) annealed at 785 K. The line profiles are represented on the right with the same colour code.

Figure 5 . 27 :

 527 Figure 5.27: Ball model (brown spheres) of body-centred (111) vicinal surfaces normal to the [011] direction. Green balls stand for missing atoms of full (111) surface.

Figure 5 . 28 :

 528 Figure 5.28: Same as Fig. 5.27 but for face-centred cubic material.

Figure 5 .

 5 Figure 5.29: View in perspective of the (211) body-centred surface showing a step edge and protruding atom rows.

Figure 5 . 30 :

 530 Figure 5.30: High resolution STM images of the Fe 0.85 Al 0.15 (111) surface annealed at 785 K. a) 23.5 × 11.5 nm 2 , U b = -1.6 V, I t = 0.4 nA, b) 17 × 17 nm 2 , U b = -1.6 V, I t = 0.5 nA, c) Line profile corresponding to the black line of figure-a.

0. 5

 5 Al 0.5 (B 2 ) alloy. The larger surface cells [(2 × 2) and (2 × 3)] enable an accommodation of Al-Al distances equal to or larger than these in the diluted bulk case Fe 0.9375 Al 0.0625 (bcc), where the Al substitutions are spaced by d Al-Al = 5.70 Å. (110)

  Figure 5.31: Layer-resolved profiles of segregation energies of Al substitutions in Fe slabs of different orientations.

  ) component narrower and more symmetric than on the other orientations pointing at a better defined chemical environment (Gaussian FWHM (110) 0.76 eV; (111) 0.84 eV; (100) 0.90 eV). Finally, theoretical work is on going to rationalise the observed faceting on the[START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] surface.

Figure 5 . 32 :

 532 Figure 5.32: Comparison at grazing emission of the profile of the a) Al 2p and b) Fe 3p core level of the three orientations after annealing in the regime of Al segregration. Despite a slight oxidation, the (100) Al 2p is shifted and broader.

Fig. 6 .

 6 Fig.6.1 shows an angular analysis of the main three core levels after oxidation: Fe 3p, Al 2p and O 1s. The presence of O 1s and the strong enhancement of the Al 2p shoulder at grazing emission compared to the metallic component at E B = 72 eV points at the formation of an aluminium oxide layer on top of the substrate. In parallel, as shown by the perfect overlap of Fe 3p profile before and after oxidation (Fig.6.31), there is no visible evolution of the chemical state of iron even at grazing emission i.e. at the interface between the oxide and the substrate.

Figure 6 .

 6 Figure 6.1: Evolution of the a) Fe 3p, b) Al 2p and c) O 1s core levels as a function of the emission angle for a (110) oxidised surface (500 L of O 2 , 1123 K). Data have been normalised to the same background at low binding energy. High pass energy E p = 50 eV was used for a faster acquisition.

Figure 6 . 3 :

 63 Figure 6.3: Comparison of angular variation of the corrected ratio I Al 2p metal /I F e 3p (pass energy E p = 50 eV) for the metallic components in the as-prepared (110) surface (filled squares) and after oxidation as indicated in figure (open circles). Dedicated angular measurements are compared to more punctual normal/grazing measurements; the chosen error bars of 10 % on the experimental ratio matches with data dispersion. At the opposite to the clean surface, no apparent segregation is found underneath the oxide layer over the probing depth of photoemission as confirmed by a fit with a continuous profile (line, Eq. 5.4).

2 :

 2 Results of the fit of the angular variation of Al 2p (metal)/Fe 3p area ratio for surfaces oxidised with the highest amount of oxygen (pass energy E p = 50 eV with a) a segregated layer (Eq. 5.2, Fig. 5.3-c) or with b) a continuous profile of segregation (Eq. 5.4, Fig. 5.3-d). The error bars stem from 10 % uncertainties on the corrected ration I Al 2p /I F e 3p . composition x(z) in Fe 1-x Al x (see Sect. 5.1.2.1) and when the Al signal for the substrate S is used:

  of various core levels at Al-Kα and Mg-Kα excitation in: a) bulk alumina Al 2 O 3 (molar mass M L = 101.95 g•cm -3 , density ρ L = 3.99, number of valence electrons n V = 24), and in b) the oxide found on NiAl(110) namely Al 10 O 13 (molar mass M L = 95.56 g•cm -3 , density ρ L = 4, number of valence electrons n V = 21.6).

  Emission angle Θ (deg) x S = 0.31 / x S = 0.15 / profile clean Al 2p (ox) / Fe 3p O 1s / Fe 3p Al 2p (ox) / Al 2p (met) O 1s / Al 2p (met)

Figure 6 . 4 :

 64 Figure 6.4: Thickness of the oxide layer (1123 K, 500 L of O 2 ) on the[START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] surface calculated from ratios of core level areas as indicated in the figure. The atomic fraction of Al of the substrate is fixed at that of the bulk x S = 0.15 (full lines) or to the segregation found under the oxide x s = 0.31 (markers, Tab. 6.2) or to the profile of segregation found on the clean surface (dotted lines). The film composition is fixed at Al 2 O 3 (see text).

110 )Figure 6 . 5 :

 11065 Figure 6.5: Calculated oxide thickness on the (110) surface for various film stoichiometry (Al 2 O 3 (points) and Al 13 O 10 (lines)) at fixed substrate composition of x S = 0.31 corresponding to the found segregation underneath the oxide.

Figure 6 . 6 :

 66 Figure 6.6: LEED patterns of the oxide film on Fe 0.85 Al 0.15 (110) (oxidation at 1123 K with 50 L of O 2 ): Beam energy a) 45 eV, b) 57 eV, c) 109 eV. The substrate surface {11} S reflections are circled in orange; the {10} S ones are missing due to the centring of the rectangular surface unit cell of random A 2 alloy. The reciprocal surface direction [10] S [110] B and [01] S [001] B are shown. Faint traces of C stripes appear also on patterns along the [10] S direction.

Figure 6 . 7 :

 67 Figure 6.7: Scheme of the direct space unit cells used in the analysis of the LEED pattern of the oxide film on Fe 0.85 Al 0.15 (110). The oxide unit cell is quasi-rectangular with lattice parameters a ox , b ox and angle γ ox ; it is rotated by angle α ox from the [10] S [110] B direction. The surface unit cell of the random alloy can be defined as rectangular centred (orange, vectors a S = [10] S , b S = [01] S ) or as primitive (red, a S,P = [10] S,P , b S,P = [01] S,P ). The angle between [10] S,P , [01] S,P is 35.26 • and a S = a S,P + b S,P , b S = a S,P -b S,P .

Figure 6 .

 6 Figure 6.8: a) Comparison between experimental LEED pattern of the oxide on Fe 0.85 Al 0.15[START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] and the simulated one with Graupner's rotation matrix 4 2.53 -1 3.37[START_REF] Graupner | Oxidation of low-index FeAl surfaces[END_REF].

Fig. 5 .

 5 Fig. 5.11 compares in-plane reciprocal scans along the main axis ((h S , 0, 0.075) in Fig. 5.11-a; (0, k S , 0.075) in Fig. 5.11-b; (h S , h S , 0.075) in Fig. 5.11-c) before and after high temperature oxidation. If, accordingly to STM, XPS and LEED, the chosen exposure of 500 L of O 2 give rise to an oxide layer covering the whole surface, radial scans before and after oxidation overlaps along the (0, k S , 0.075) direction while the superstructure peaks along (h S , 0, 0.075) at (1.56 -3.56 -5.56, 0, 0.075) are lifted by oxidation. Therefore, oxidation does not only change the profile of segregation underneath the oxide film as demonstrated by photoemission (see Sect. 6.3.1.2) but also impacts the nature of the superstructure underneath by releasing the "incommensurate" direction. Of course, new peaks appear (blue lines in Fig.5.11) that are characteristic of the oxide layer itself.

Figure 6 . 9 :

 69 Figure 6.9: Comparison between experimental and simulated LEED patterns (left) for the superstructures of Tab. 6.5. Blue and red points correspond to the two domains. Red and green vectors correspond to a ox and b ox . The right pictures show the direct space overlap between the grey grid which corresponds to the primitive unit cell and the (n × m) oxide supercell (red points). The substrate rectangular centred unit cell is shown in orange in Fig. a.

  r.l.u)

Figure 6 . 11 :

 611 Figure 6.11: The same as Fig. 6.10 but for the oxide on Fe 0.85 Al 0.15 (110). The double circled spots have been used for unit cell indexing; they are perfectly aligned (see text).

Figure 6 . 12 :

 612 Figure 6.12: Overlap of the simulated LEED pattern obtained from the GIXD oxide unit cell. a) E K = 45 eV, b) E K = 120 eV. Discrepancies are due to distorsion and sample tilt.

2 )Figure 6 .

 26 Figure 6.13: In-plane analysis of the oxide reflection widths ∆ω(q). The linear regression (green line) of q 2 ∆ω(q) 2 versus q 2 allows to unfold size and mosaic spread effects.

Figure 6 . 14 :

 614 Figure 6.14: STM images of the Fe 0.85 Al 0.15 (110) surface after annealing at 1073 K in 2 × 10 -7 mbar O 2 for 10 min (90 L): a) 400 × 400 nm 2 , U b = 2.0 V, I t = 0.4 nA. b) 200 × 145 nm 2 , U b = 2.0 V, I t = 0.4 nA. c) Line profile from image-a.

Figure 6 . 15 :

 615 Figure 6.15: STM images of the Fe 0.85 Al 0.15 (110) surface after annealing at 1073 K for 10 min in 2 × 10 -7 mbar O 2 for 10 min (90 L) for (a) and (b) and for 5 min (50 L) for (c), (d) and (e). a) 100 × 62 nm 2 , U b = 2.0 V, I t = 0.04 nA and b) corresponding 2D autocorrelation image. c) 80 × 80 nm 2 , U b = 2.0 V, I t = 0.02 nA. d) 52 × 25 nm 2 , U b = 1.7 V, I t = 0.01 nA. e) Corresponding 2D autocorrelation image.

6. 3

 3 Oxide on Fe 0.85 Al 0.15 (100) 6.3.1 Photoemission analysis 6.3.1.1 Angular analysis and lineshape fitting

Figure 6 . 16 :

 616 Figure 6.16: Evolution of the a) Fe 3p, b) Al 2p and c) O 1s core levels as a function of emission angle for a (100) oxidised surface (100 L of O 2 , 973 K). Data have been normalised to the same background. Pass energy is E p = 50 eV.

  6.31); the uptake of oxygen is only accompanied by aluminium oxidation as seen by the appearance of a shoulder on the high binding energy side of the Al 2p peak.

2 Figure 6 . 18 :

 2618 Figure 6.18: Comparison of angular variation of the corrected ratio I Al 2p metal /I F e 3p (pass energy E p = 50 eV) for the metallic Al component of the as-prepared (100) surface (1273 K; filled circles) and after oxidation (973 K, 100 L of O 2 ; open circles). Data (points) have been fitted with a model of continuous profile of segregation (lines, Eq. 5.4) which values are given in Tab. 5.3 and 6.2. Similar fit quality is obtained with the segregated layer model (Eq. 5.2).

Figure 6 . 19 :

 619 Figure 6.19: Thickness of the oxide layer (973 K, 100 L of O 2 ) on the (100) surface calculated from ratios of core levels as indicated in figure. Calculations assume a bulk like homogeneous substrate (x S = 0.15, lines) or take into account the actual profile of segregation (markers). The layer stoichiometry is Al 2 O 3 .

  [001] B direction in Fe 0.85 Al 0.15 (a B /2 = 1.45 Å) and the spacing between the closed-pack oxygen plane in the θ-Al 2 O 3 structure proposed in the case of NiAl(100) (d Oplane = 1.91 Å).

Figure 6 . 20 :

 620 Figure 6.20: LEED patterns of the oxide film on Fe 0.85 Al 0.15 (100) (oxidation at 973 K with 100 L of O 2 ): Beam energy a) 65 eV, b) 96 eV. The substrate surface {10} S reflections are circled in orange.

Figure 6 . 21 :

 621 Figure 6.21: Overlap between (1 × 2) and (1 × 9) superstructures including the two domains with the experimental LEED pattern of Fig. 6.20-a.

Figure 6 . 22 :

 622 Figure 6.22: STM images of the Fe 0.85 Al 0.15 (100) surface after exposure to 10 L of O 2 at 973 K. a) 700 × 700 nm 2 , U b = -1.1 V, I t = 0.2 nA, b) 300 × 300 nm 2 , U b = -1.1 V, I t = 0.2 nA, c) after exposure to 100 L of O 2 at 973 K, 500 × 500 nm 2 , U b = -1.0 V, I t = 0.3 nA. d) Corresponding height histogram of image c).

Figure 6 .

 6 Figure 6.23: STM images of the Fe 0.85 Al 0.15 (100) surface after exposure to O 2 at 973 K. a) 100 L, 200 × 174 nm 2 , U b = -1.0 V, I t = 0.3 nA, b) 10 L, 60 × 60 nm 2 , U b = -1.2 V, I t = 0.2 nA, c) 100 L, 50 × 27 nm 2 , U b = -0.8 V, I t = 0.1 nA.

2 Figure 6 .

 26 Figure 6.26: Segregation under the oxide at the (111) surface from the angular variation of the corrected ratio I Al 2p metal /I F e 3p (pass energy E p = 50 eV) in the as-prepared (111) surface (1273 K; filled triangles) and after oxidation (973 K, 100 L of O 2 ; open triangles). Data (points) have been fitted with a model of continuous profile of segregation (lines, Eq. 5.4) which values are given in Tab. 5.3, 6.2. The orange points correspond to another measurement.

111 )Figure 6 . 27 :

 111627 Figure 6.27: Thickness of the oxide layer (973 K, 100 L of O 2 ) on the[START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] surface calculated from ratio of core levels as indicated in the figure. Calculations assume a bulk-like homogeneous substrate (x S = 0.15, lines) or take into account the actual profile of segregation (markers). The layer stoichiometry is fixed at Al 2 O 3 .

  is typical for a facetting of the surface along a direction 12 S which is known to occur when adsorbates are present on an open (111) of body-centred metal (like W[START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] [START_REF] Madey | Nanoscale surface chemistry over faceted substrates: structure, reactivity and nanotemplate[END_REF][START_REF] Revenant | Structural and morphological evolution of Co on faceted Pt/W (111) surface upon thermal annealing[END_REF]). The driving force is the lower surface energy of the covered vicinal surface over the clean open[START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] one. But the reproducibility of such LEED pattern and the lack of local analysis does not allow to further comment this observation.

Figure 6 . 28 :

 628 Figure 6.28: Traces of surface faceting observed after high temperature annealing of a Fe 0.85 Al 0.15 (111) surface slightly contaminated with oxygen.

Figure 6 . 29 :

 629 Figure 6.29:STM image of the Fe 0.85 Al 0.15[START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] surface after oxidation at 973 K and 100 L of O 2 (500 × 500 nm 2 , U b = -1.7 V, I t = 1.7 nA).

Figure 6 . 30 :

 630 Figure 6.30: Evolution of film thickness with O 2 exposure for film synthesised at high temperature (1123 K) on (110) surface. Normal and grazing measurements are compared for all the combinations of core levels for different experiments. Film composition and photoemission parameters have been fixed at those of Al 2 O 3 with a fixed substrate bulk composition of x S = 0.31.

6. 6

 6 Discussion 6.6.1 Comparison of the oxide on the various orientations of Fe 0.85 Al 0.15

Figure 6 .

 6 Figure 6.31: (Left) Overlap of Fe 3p core levels for all clean and oxidised surfaces as indicated in figure. Even for surface sensitive geometry (grazing emission Θ = 60 • ), no oxidation of iron is observed. Spectra have been normalised to the same background and peak intensity. (Middle) Same for Al 2p but after normalization on the metallic component. (Right) Overlap of O 1s core levels after normalization.

  6.1), their chemical shift are much larger (∆E B (NiAl) = 1; 2.27 eV versus ∆E B (Fe 0.85 Al 0.15 ) = 1.68; 3.23). If a part of the shift is due to a different metallic reference (E B (Al 0 2p , NiAl) = 72.5 eV; E B (Al 0 2p , Fe 0.85 Al 0.15 ) = 72 eV)

Table

  .14) E p is the pass energy, d is the slit width, R 0 is the mean radius of the hemispheres, and α is the half entry angle of electrons. Tab. 2.2 gathers typical parameters used for quick/wide scans (E p = 50 eV) and for better resolved (E p = 20 eV) scans. As determined in the lit-

	E p	Slit width Scan range Calculated analyser ∆E Step size Dwell time
	(eV)	(mm)	(eV)	from supplier (eV)	(eV)	(s)
	XPS broad scan 50	6 ∼ 1 -1300	1.5	0.5	0.2
	XPS narrow scan 20	6	∼ 20	0.6	0.05	0.5

Table 2 .

 2

2: Typical scan parameters and resolution used along this work.

Table 2 .

 2 3: Relative peak intensity of doublets due to spin-orbit splitting in photoemission.

  Ϭ͘ϱ ů Ϭ͘ϱ &ĞͲďĐĐ ĂͿ ďĐĐͲ Ϯ ďͿ Ϭ ϯ ͬ,ĞƵƐƐůĞƌ &Ğ ϯ ů с &Ğ Ϭ͘ϳϱ ů Ϭ͘Ϯϱ ĐͿ Ϯ ͲƐů Figure 3.2: Ball models of the main atomic structure of iron rich Fe 1-x Al x intermetallics. Fe atoms are in brown and Al atoms in light blue. Al 0.15 Fe 0.75 Al 0.25 (Fe 3 Al) Fe 0.5 Al 0.5 (FeAl)

	Composition Fe 0.85 Structure type Fe bcc bcc	D0 3	CsCl
	Space group	I(m3m)	I(m3m)	F (m3m)	P (m3m)
	Lattice parameter ( Å) 2.8665	2.8914	5.80	2.90

Table 3 .

 3 1: Atomic structure of the iron rich Fe 1-x Al x intermetallics. Lattice parameters are from Ref.

Table 3 .

 3 2: Surface energies of several orientations for Al and Fe. Calculated values with the full charge density within the full potential linear muffin-tin orbitals are from Ref.[START_REF] Vitos | The surface energy of metals[END_REF] while experimental values are from Ref.[START_REF] Tyson | Surface free energies of solid metals: Estimation from liquid surface tension measurements[END_REF].

		Structure Surface Theory (J.m -2 ) Experiments (J.m -2 )
	Al	fcc	(111)	1.199	1.143, 1.160
		(4.049 Å) (100)	1.347
			(110)	1.271
	Fe	bcc	(110)	2.430	2.417, 2.475
		(3.001 Å) (100)	2.222
			(211)	2.589
			(310)	2.393
			(111)	2.733

claimed at preferential sputtering of Al (without clear proof although predicted ones are similar

[START_REF] Matsunami | Energy dependence of the ion-induced sputtering yields of monatomic solids[END_REF][START_REF] Seah | A quantitative framework for the analysis of surfaces by AES and XPS[END_REF]

!) leading to a depletion in Al at the surface (see Sect. 5.1.2.2).

  surface (Sect. 3.4.3.1) and single crystal alloy surfaces, such as NiAl and Ni 3 Al(110),

	(100), (111) (Sect. 3.4.3.2), Cu-9 at.% Al(111) (Sect. 3.4.3.4), CoAl(100) (Sect. 3.4.3.5) and
	FeAl(

  2-(Al 19 O 28 Al 28 O 32 ) 2+

Table 5 .

 5

	barns)

E B (eV) SOS (eV) E K (eV) E K (eV) PICS (barns) PICS (1: Typical core levels involed in the present study of Fe 0.85 Al 0.15 : Binding Energy (E B )

Table 5 .

 5

	Formula	Z	Atomic structure	s+p (hbe) s+p (lbe)	d	f	Total
	Fe	26	[Ne] 3s 2 3p 6 4s 2 3d 6	8	2	6	0	16
	Al	13	[Ne] 3s 2 3p 1	0	3	0	0	3
	Fe 1-x Al x -13x + 26	-	8(1 -x)	x + 2	6(1 -x) 0 -13x + 16
	Fe 0.85 Al 0.15	24.05	-	6.8	2.15	5.1	0	14.05

2: Orbital filling used as input of QUASES-IMFP-TPP2M software to determine the inelastic mean free paths in Fe 1-x Al x . s+p(hbe) and s+p(lbe) stand for the number of electrons per formula unit in s and p orbitals of highest and lowest binding energies. d and f correspond to electrons from d and f orbitals. Basically, a linear interpolation between Fe and Al was used for the alloy. The total number of valence electrons used in the TPP-2M formula is given in the last column.

  .53 atom/ion) with normal incident 1 keV Ar + ions[START_REF]A simple sputter yield calculator[END_REF] would slightly favour preferential Fe sputtering and the enrichment of the surface in Al as observed herein. But this conclusion should be taken with caution since our sputtering geometry (at 30 • incidence) and our target (Fe 0.85 Al 0.15 ) are different. Finally, the systematic come back to the same I Al 2p /I F e 3p value demonstrates that sputtering is efficient enough to remove the segregated layer 3 .

19 ± 0.05, close to the nominal value of x = 0.15. Estimates of the sputtering yield with the formula of Matsumani et al. [27] of Fe target (1.70 atom/ion) and of Al target (1

Table 5 .

 5 4: Calculated and experimental characteristics of bulk iron and aluminium: lattice parameter a B ( Å), cohesion energy E coh (eV), and bulk modulus B (GPa).

					Al(fcc) a B ( Å) E (eV) B (GPa)
		.836	5.06	186	calc.	4.052	3.43	72
	exp.	2.867	4.29	170	exp.	4.050	3.34	76

Table 5 . 5

 55

	atom) (eV/atom)

: Calculated characteristics of bulk Fe 1-x Al x (x < 0.5) phases: lattice parameter a B ( Å), distance between Al atoms in the (2 × 2 × 2) unit cell : d Al-Al , mixing energies: E mix (eV/atom) and E mix (eV/atom). See text for details.

Table 5 .

 5 6: Distances between Al substitutions d Al-Al ( Å) in the different surface unit cells used in the calculations.

	(1 × 1) 2.84, 4.01 2.84, 2.84 4.01, 4.01
	(2 × 2)	-	5.67, 5.67 8.02, 8.02
	(2 × 3) 8.51, 8.02	-	-

Table 5 .

 5 7: Adsorption energies (eV) of Al adatoms at differently oriented Fe surfaces obtained with different surface unit cells.

			(100) (111)
	(1 × 1) 4.04 4.54 4.69
	(2 × 2)	-	3.90 4.78
	(2 × 3) 3.86	-	-

  both for Al 0 and Al n+ . Metallic Al 0 component was accounted for by a Doniach-Sunjic profile (Eq. 2.18) while a Voigt function (Eq. 2.15) was used for the two extra oxide components. Similar values of the asymmetry parameter of the metal peak (Eq. 2.18) were found on the clean and oxidised surfaces. Shirley background subtraction and fit were done outside the range of X-ray source satellites (see Sect. 2.5.2). As in the following, the Lorentzian broadening (Eq. 2.17) of peaks was found very close to the emission width of Al-Kα (0.85 eV; see Sect. 2.5.2). Instrumental contribution to the peaks broadening as well as sample-related ones were included through the convolution with a Gaussian (Eq. 2.16). The obtained parameters are gathered in Tab. 6.1.

			Al 2p (110)	igure 6.2: Line shape
		3000	decomposition of the Al 2p core level for the (110) orientation. (Top panel) Clean surface an-900 L O 2 Θ = 60˚F clean Θ = 0˚ 900 L O 2 Θ = 0˚ nealed at 1123 K (nor-
		2500		mal emission); (Bot-tom and middle pan-
	Intensity (Arb. units)	2000		els) Surface oxidised at the same temperature with 900 L of O 2 (nor-mal and grazing emis-sion). Three spin or-bit split components are needed to fit accurately the data (points) for the oxide layer (see text). Only one is required for
		1500		the clean surface. Fit
				parameters are given in
				Tab. 6.1. Spectra have
				been collected at a pass
				energy E p = 20 eV pro-
		1000		viding the best resolu-tion. Spin-orbit split-
		80 79 78 77 76 75 74 73 72 71 70 69 Binding Energy (eV)	ting was fixed at 0.4 eV for all components.

Table 6 .

 6 .1) the normalization to the substrate signal I S has to take into account the profile of segregation and its damping in the oxide layer. If the segregation is described as a continuous profile of

	Model	Parameter	(100)	(110)	(111)
	Film	Thickness t ( Å) Layer atomic fraction x L	26 ± 3 0.51 ± 0.02 0.31 ± 0.01 0.34 ± 0.01 75 ± 41 46 ± 12
		Length Λ ( Å)	29 ± 5	> 130	62 ± 22
	Profile	Variation of atomic fraction ∆x 0.39 ± 0.03 0.16 ± 0.01 0.20 ± 0.01
		Surface atomic fraction x s + ∆x 0.54 ± 0.03 0.31 ± 0.01 0.35 ± 0.01

Table 6 .

 6 4: Aluminium oxide unit cell parameters at the surface of metallic substrate as determined in the literature.

	Commensurate	[11] S		[11] S		[11] S		sixton rectangle		-	(1 × 2)
	M S	4 2.53	-1 3.37		4.03 2.54	-1.10 3.32		-		-		4 2.53	-1 3.37	4.08 3.01	-1.25 3.24
	γ ox (deg) α ox (deg)	88.67 24.1		91.15 24.01		91.84 -		90 -		88.66 24.1	91.2 27.5	±0.8 ±0.4
	b ox ( Å)	10.55		10.59		10.93		10.53		10.62	10.68	±0.08
	a ox ( Å)	17.89		18.01		17.9		18.23		18.01	18.8	±0.2
	a B , (a S × b S ) ( Å)	2.887	4.083 × 2.887	2.887	4.083 × 2.887	2.895	4.094 × 2.895	3.524	2.491 × 2.491	2.906	4.110 × 2.9064	2.888	4.091 × 2.888
	Substrate	NiAl(110)	B 2 -CsCl	NiAl(110)	B 2 -CsCl	NiAl(110)	B 2 -CsCl	Al/Ni(111)	A 1 -fcc	FeAl(110)	B 2 -CsCl	0.85 Al 0.15 (110)	A 2 -bcc
		SPA-LEED-[14]		GIXD-[121]		DFT-[15]		GIXD-[19]		LEED-[16]	GIXD-This work Fe

  Superstructure a ox ( Å) b ox ( Å) γ ox ( Å) α ox (deg) Coincidence Superlattice Matrix M P = A -1 P B P

	A-(1 × 1)	16.03	9.59	88.44	26.80	1.0 6.0 -4.0 2.0	=	1 0 0 1	-1	1 6 -4 2
	B-(1 × 2)	18.51	10.69	90.6	27.94	1.0 7.0 -4.5 2.0	=	1 0 0 2	-1	1 7 -9 4
	C-(2 × 1)	17.88	9.59	91.39	23.85	1.5 6.5 -4.0 2.0	=	2 0 0 1	-1	3 13 -4 2
	D-(2 × 1)	16.65	9.59	92.25	22.97	1.5 6.0 -4.0 2.0	=	2 0 0 1	-1	3 12 -4 2
	E-(2 × 2)	20.34	10.70	93.31	25.24	1.5 7.5 -4.5 2.0	=	2 0 0 2	-1	3 15 -9 4
	F-(2 × 2)	19.75	10.69	90.14	28.38	1.0 7.5 -4.5 2.0	=	2 0 0 2	-1	2 15 -9 4
	G-(2 × 2)	19.22	10.62	93.51	31.76	0.5 7.5 -4.5 1.5	=	2 0 0 2	-1	1 15 -9 4
	H-(2 × 2)	19.11	10.70	93.96	24.59	1.5 7.0 -4.5 2.0	=	2 0 0 2	-1	3 14 -9 4

  .8.

		80	78	76	74	72	70	68
		Al 2p (111)
			clean Θ = 0˚
		2000	100 L O 2 Θ = 0˚ 100 L O 2 Θ = 60˚F composition of the Al 2p igure 6.24: Line shape de-
								core level for the (111) ori-
								entation. (Top panel) Clean
	Intensity (Arb. units)	1500 1000						surface annealed at 973 K (normal emission); (Bottom panels) Surface oxidised at the same temperature with 100 L of O 2 (normal and grazing emission). Three spin orbit split components are needed to fit accu-rately the data (points) for
								the oxide layer (see text).
								Fit parameters are given in
		500						Tab. 6.8. Spectra have been
								collected at a pass energy
								E P = 20 eV providing the
								best resolution.
		80 79 78 77 76 75 74 73 72 71 70 69 68
			Binding Energy (eV)

Table 6 .

 6 which further oxide thickening should be tested above 100 L. = x S + ∆x 0.42 ± 0.03 0.45 ± 0.03 0.5 ± 0.03 0.31 ± 0.01 Al 2 O 2.8±0.2 Al 2 O 2.6±0.2 Al 2 O 2.5±0.2 = x S + ∆x 0.5 ± 0.03 0.51 ± 0.03 0.55 ± 0.03 0.54 ± 0.03 Al 2 O 2.5±0.2 Al 2 O 2.9±0.2 Al 2 O 3±0.2 = x S + ∆x 0.5 ± 0.03 0.41 ± 0.03 0.27 ± 0.03 0.35 ± 0.03 Al 2 O 2.8±0.2 Al 2 O 3.5±0.2 9: Results of angular analysis of photoemission performed on oxide films grown at various exposures. Error bars stem from cumulative uncertainties of 10 % on measured ratios and on average of thickness over emission angle.

	(110)@1123 K

Table 6 .

 6 after oxidation at high temperature; lower values are found in the case of twosteps oxidation process. 10: Comparison of the characteristics of the oxide films obtained at Fe 0.85 Al 0.15 surfaces.

	Orientation	(110)	(100)	(111)
	Thickness ( Å)	∼ 11	∼ 9	∼ 18.5
	Stoichiometry	Al 2 O 2.5	Al 2 O 3	Al 2 O 3.5
	E B Al 2p oxide (eV)	73.5 / 75	75	73.4 / 75.3
	Unit cell	Rotated rectangular	(1 × 2)-like	no LEED
		with 2 domains	with 2 domains	-
	Λ ( Å)	38 → ∞	26.5 → 29	25.4 → 62
	x(0) = x S + ∆x	0.42 → 0.31	0.5 → 0.54	0.5 → 0.35
	Fe-Al structure	B 2 → D0 3	B 2 → B 2	B 2 → D0 3
	Morphology	Flat film	Elongated	Rough
		with two domains	stripes

An interfacial alloy is formed between zinc and iron.

No correction from gauge ionisation sensitivity was accounted for in this study.

Without convincing proofs!

Which are actually piezoelectric motors that work on the slip/stick principle when actuated with a sawtooth voltage.

Symmetric and short apexes are preferred although this is not a guarantee of good imaging conditions.

This source was systematically used during this work.

Over the probing depth of Auger transitions of Al and Fe at 68 eV and 47 eV.

As we will see in Chap. 6.2.2.1, it is difficult to determine precisely such a large unit cell with a conventional LEED.

Desorption is unlikely owing to the low vapor pressure of graphite and the strong Fe-C bond

.

For instance, pass energy in XPS was increased to reduce counting time.

The maximum of error is obtained at low kinetic energy, which is not the case of the Al

2p and Fe 3p core levels.

This findings is at odd with several references[28,

[START_REF] Hammer | Segregation phenomena on surfaces of the ordered bimetallic alloy FeAl[END_REF][START_REF] Heinz | Surface structure and segregation of bimetallic bcc-type alloys[END_REF][START_REF] Blum | Segregation and ordering at Fe 1-x Al x (100) surfaces-a model case for binary alloys[END_REF][START_REF] Gleason | Water adsorption and thermal decomposition on FeAl (110)[END_REF][START_REF] Kottcke | Segregation-induced subsurface restructuring of FeAl (100)[END_REF][START_REF] Eltester | AES and LEED investigation of Al segregation and oxidation of the (100) face of Fe 85 Al 15 single crystals[END_REF][START_REF] Kizilkaya | Surface reconstruction of FeAl (110) studied by scanning tunnelling microscopy and angle-resolved photoemission spectroscopy[END_REF] of the literature which report, or more precisely assume, a preferential sputtering of Al without any clear experimental proof !

With a sputtering yield of ∼ 1.5, an ion beam current of ∼ 10 µA•cm -2 allows to remove 6 × 10 15 atoms•min -1 which corresponds to a few monolayers. Therefore, a 30 min sputtering is in principle enough to remove the 2-4 nm thick segregated layer (see below).

In this model, the ratio of intensity is independent of the emission angle (Eq. 2.20).

An A 2[START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] surface as determined from photoemission should lift these extinctions. But this seems to be blurred by the complex surface superstructure described hereafter.

The[START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] LEED pattern of native surface decays upon ageing under vacuum (see Sect.4.2)

Grasping oscillatory behaviour of composition found in the first layers of FeAl (see Sect. 3.3) and predicted by the present calculations (Sect. 5.4) is well beyond the sensitivity of our measurements.

Error bars stems from various references of[START_REF]NIST X-ray photoelectron spectroscopy database[END_REF].

Although the agreement is not really demonstrated in the article (see Fig.

3.17-c) !

That will appear on[START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] films also!

In the simulations, only the stoichiometry and molar mass were changed at fixed density and mean free paths since the structure of the oxide is unknown. But the latter parameter impacts much more the actual

Absolute values should be taken with caution due to uncertainties on inelastic mean free path and on the use of a continuous models of analysis. Nevertheless, the accuracy of profile of segregation and of stoichiometry are much better since they result from ratio.

Atomic structure Fe -[Im-3m; W-bcc; A 2 ] Fe 1-x Al x [Im-3m; W-bcc; A 2 ] Fe 1-x Al x -[Pm-3m; CsCl; B 2 ] Fe 0.8 Al 0.2 -[Im-3m; W-bcc; A 2 ] Fe 0.75 Al 0.25 -[Im-3m; W-bcc; A 2 ] Fe 3 Al -[Fm-3m; Heusler; D0 3 ] FeAl -[Pm-3m; CsCl; B 2 ] Fe 5.3 Al 7.7 -[I-43m; Cu 5 Zn 8 ] Fe 7 Al 11 -[P 1 ] Fe 5 Al 8 -[I-43m; Cu 5 Zn 8 ] Fe 6.41 Al 12.59 -[P -1 ] Fe 2 Al 5.4 -[Cmcm; Fe 3 Al 5 ] Fe 4 Al 13 -[C12/m1;FeAl 3 ] Fe 2 Al 5.6 [Cmcm; Fe 3 Al 5 ] FeAl 3. 2 [C12/m1; Fe 3 Al 5 ] Fe 3 Al 9.75 [C12/m1; Fe 3 Al 5 ] Fe 52.16 Al 204.04 [P6 3 /mmc; Fe 23 Al 96 ] Fe 2 Al 9 [P12 1 /a1; Fe 2 Al 9 ]

igure 5.6: Evolution with emission angle Θ of Al 2p and Fe 3p core levels of ( 110), [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF] and [START_REF] Renaud | Atomic structure of the α-Al 2 O[END_REF] tributions of environments for the surface aluminium oxide atoms may explain the larger broadening compared to the interface atoms.

Segregation under the oxide from angular analysis

From the previous core level decomposition, the aluminium enrichment underneath the oxide formed at the [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] surface was obtained from the angular evolution (Fig. 6.1) of the ratio of areas of metallic Al 2p and Fe 3p components. The case of an oxide film synthesised with a high exposure (1123 K, 500 L of O 2 ) was selected to ensure a covering layer. The template found at low pass energy E p = 20 eV (Tab. 6.1) was kept fixed to analyse angular data at lower resolution (E p = 50 eV). Compared to the bare surface (Fig. 6.3), a flat profile and a nearly constant composition are found over the typical probing depth of laboratory photoemission.

To further quantify it, an approach similar to that developed for bare surface (Sect. 5.1.2.1) was employed by fitting the experimental results of Fig. 6.3 (open circles) with the models of (i) an homogeneous segregated layer (Eq. 5.2, Fig. 5.3-c) or of (ii) a continuous diffusive profile (Eq. 5.4, Fig. 5.3-d; line). The bulk atomic fraction i.e. far from the oxide/metal interface was kept at x S = 0.15. In principle, any signal of the substrate should be further damped in the oxide overlayer through a term that accounts for the partial coverage of the oxide, if any, and for its thickness. Fortunately, since Al 2p and Fe 3p core levels are very close in binding energies (Tab. 5.1), their inelastic mean free paths in the alumina layer are the same (Tab. 6.3); both signals are damped in a similar way, an effect which is cancelled through their ratio of intensities.

Not surprisingly, the typical length of the segregated layer (Tab. 6.2) which is obtained is much larger than the probing depth of photoemission with a large uncertainty. Nevertheless, the composition of the subsurface of the substrate under the oxide is enriched in aluminium x L x S +∆x 0.31 but at a lower level than in the case of a bare surface x L x S +∆x 0.42

Segregation under the oxide from angular analysis

In a similar way to the (110) orientation, by using the previous decomposition of peaks, the aluminium segregation under the oxide was probed through the angular variation of the metallic components I Al 2p metal /I F e 3p (Fig. 6.18). At the opposite to the (110) orientation (Fig. 6.3), the strong increase of corrected ratio I Al 2p metal /I F e 3p at grazing emission parallels the findings on the clean surface (Fig. 6.18 open versus filled points). A quantitative analysis with the model of an homogeneous segregated layer under the oxide or with the case of a damped profile (see Sect. 6.2.1.3 and Sect. 5.1.2.1 for explanations) pointed at segregation parameters (x L , Λ, ∆x) quite similar to those found on the clean surface (Tab. 6.2 versus 5.3).

The composition at the interface with the oxide is still very close to Fe 0.5 Al 0.5 .

Oxide film thickness and stoichiometry

The strategy used to determine the oxide thickness from ratio of different photoemission core levels follows exactly that developed for the (110) orientation (see Sect. 6.2.1.4). But in contrast to the (110) orientation for which the profile of segregation was found to be flat but different from bulk composition, the thickness quantification on the (100) requires to account for the actual profile of segregation. Indeed without it, i.e. with fixed bulk composition (x S = 0.15), an enormous discrepancy by a factor 3 appears between values obtained by normalizing to Fe 3p or Al 2p (metal). This difference is wiped out if segregation is accounted for (markers versus line in Fig. 6.19). Surprisingly, all determinations of thicknesses agree around a value around t = 8.5 Å if the stoichiometry of the films is taken as Al 2 O 3 . In other words, the small mismatch found in the case of (110) (Fig. 6.4) 3 and assigned to a composition Al 10 O 13 is not found. Finally, the lack of variation of thickness with angle corroborate the modelling with a thin continuous film.

Segregation under the oxide from angular analysis

Like for the two other orientations (110) (Sect. 6.2.1.3) and (100) (Sect. 6.3.1.2), the profile of segregation was obtained from the modelling of the angular profile of the I Al 2p metal /I F e 3p intensity ratio (Fig. 6.25). As shown in Fig. 6.26, the profile of segregation is flatter under the oxide than on the clean surface. Indeed, the thickness of the segregated layer is larger than on the bare surface and with an interfacial composition still enriched in aluminium but equal to x S + ∆x x L ∼ 0.31.

the O-surface planes, the remaining atoms contributing to the other component. All these findings let suppose that the structure of the oxide film formed at the surface of Fe 0.85 Al 0.15 [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF] is close to that found on NiAl [START_REF] French | Composition and surface structure of the (0001) face of α-alumina by low energy electron diffraction[END_REF]. Only its thickness is larger than a simple bilayer film. and lattice parameters very close. In the present case, the subsurface composition of the clean and oxidised Fe 0.85 Al 0.15 is close to Fe 0.5 Al 0.5 the bulk structure of which is again B 2 CsCl. The common explanation is given through the already evoked Bain's epitaxy between the fcc oxygen stacking in θ-alumina and the substrate (Fig. 3.21). Diffraction data of Stierle et al. concluded at 7.5 Å thick θ-alumina with strong distorsion with a preference of tetrahedral coordinated sites at the interface and octahedral at the surface. But, if our photoemission analysis indeed resulted in the expected Al 2 O 3 stoichiometry and a similar thickness (9 Å), the only one chemical state for Al 2p and probably two for O 1s were put forward. This finding is in accord with previous works on NiAl [START_REF] Pan | Stability of FeAl (110) alloy surface structures: a first principle study[END_REF] [START_REF] Cai | Growth of ultrathin amorphous alumina films during the oxidation of NiAl (100)[END_REF][START_REF] Frémy | X-ray photoelectron spectroscopy study of thin oxide layers formed on (001)-oriented β-NiAl single-crystal surfaces[END_REF]212] but questions the proposed θ-alumina structure which involves a mixture of tetrahedral and octahedral aluminium sites.

Oxide at (111) surface

The lack of clear crystallised thin film, the sub-stoichiometry in Al and the three dimensional growth prevents any relevant comparison to known literature.

ABBREVIATIONS