Nabil Mr

Pierre Badel

Pr

Flavien Balbo

Jean-François Bassereau

PR Batton-Hubert Mireille

Michel Beigbeder

Informatique Ma

Fayol

Appliquees M Mathematiques

Informatique O Batton-Hubert

Professeur Boissier

J C Formes

Professeur Genie Pinoli

N Industriel

Maitre Absi

ABSI

are considered to have susceptibilities to RTE about three times higher than those of base metals, to reect the experience on this mechanism.

Previous studies have suggested that this higher susceptibility could be due to a higher phosphorus segregation to prior austenite grain boundaries in tempered martensite than in 1 French Code for nuclear power plant construction.

Fe-P model alloy. Then four dierent techniques (X-ray Photoelectron Spectroscopy (XPS), Wavelength Dispersive Spectroscopy (WDS), APT, and STEM-EDX) are cross-compared on a Fe-P-Fe sandwich sample synthesized on purpose.

Chapter II.1 starts with a presentation of the studied steel and its fabrication then continues with a literature review on martensite and bainite structures. Then, further on RTE and its dependence to microstructure. Chapter II.2 presents the experimental methods, including the sample preparations and an adaptation of STEM-EDX data processing to the studied steel.

Chapter II.3 gives the results of the basic material characterizations undertaken for the need of this study. Chapter II.4 presents the intergranular segregation results at dierent types of grain boundaries in tempered bainitic and tempered martensitic 16MND5 type steel. At last, chapter II.5 presents the evolution the mechanical properties of tempered bainitic and tempered martensitic 16MND5 after accelerated aging. An interpretation of the relationship between microstructure, intergranular segregation, and mechanical properties is established.

At the end of this manuscript, the conclusions of the dierent results and observations are summarized. Furthermore, some perspectives for further research of this subject are proposed.

for their guidance, teaching, feedback, and encouragement throughout my doctoral research.

Without them, this thesis would not have been possible. They have been by my side throughout the whole way, I do not think that I could ask for more. In fact, I originally met Julien as my supervisor for my master's thesis in 2017, where I rst had my hands on a transmission electron microscope and had my knowledge formed by him. It was the rst time where my metallurgy classes started to feel real, instead of only having schematics. It was because of that time that I learned of my interest not just in research, as it was my rst real research experience, but also for the specic eld of materials characterization using electron microscopes that I have now spent a few years working in. Then, when I decided to continue my studies with a PhD program, they are the ones that oered me a subject and a position at EDF and Ecoles des Mines de Saint-Etienne. So once again, thank you all for guiding me in my career.

I would then like to thank my other supervisors, Frédéric and Patrick, who I did not meet prior to my thesis. I am probably not the brightest student Frédéric had, especially since I know that he had to put in extra eort with me for certain subjects. He often provided me with helpful feedback and guidance during experiments, in making presentations, and in writing papers. I would like to thank him for the brilliant ideas, such as the sandwich sample that he has provided us and the great patience he showed me. With Patrick, I think I could go on for chapters. It was not an easy approach at the beginning, but he grew on me in time. I would like to thank him for his rich experiences that provided me dierent aspects and expertise in Reactor Pressure Vessel (RPV) steel. So my deepest gratitude goes to all three of them.

I would like to express my gratitude to Prof. Grace Burke, Assoc. Prof. Sophie Cazotte, Prof. Anne-Françoise Gourgues, Assoc. Prof. Bertrand Radiguet, Bernard Marini, and Pierre Joly for their role as my defense reviewers. Thanks to your comments and constructive criticism, I have been able to edit my defense and thesis for the better.

I would like to thank the colleagues who have worked with me in the electron microscopy laboratory, Romain Badyka, Julien Tremblay, Nicolas Brynaert, Frédéric Delabrouille, and Dominique Loisnard. They have often provided me with helpful feedback and guidance during experiments and supported me when encountering diculties, especially when the machines were not working! Then, I would like to extend my thanks to all my colleagues in the metallurgy expertise laboratory and mechanical test laboratory in EDF, Vincent Barnier and Yoann Garnier at Mines Saint-Etienne, and Bertrand Radiguet at GPM Rouen. You have provided me with your expertise in dierent experiments that made my thesis more complete. I also extend thanks to my many other colleagues in the metallurgy group and at Mines Saint-Etienne who have already graduated or are still here, for making my time at EDF and at school enjoyable ones. Further, I would like to point out Maxime Mollens, a fellow PhD suerer at EDF who shared my oce during my last year. Thank you for the company, help, and support that kept me sane. I hope the best for your thesis and career.

Outside of research experience, I am also grateful to all the professors at Grenoble INP and National Tsing Hua University during my master's and undergraduate programs who helped give me a solid background in metallurgy, material characterizations, and thermal dynamics, which has allowed me to continue on in my academic career. And along those lines, thanks to all my lovely friends and family who stand by my side during my studies. You have all supported me throughout my whole academic career. I love you all! Finally, I'd like to thank Yi-Hua Wang. You have always had my back and been the most important people in my life. Thank you from the bottom of my heart.

Introduction

The nuclear energy provides a solution to stable electricity production with very low greenhouse gases emissions. Due to the nature of the nuclear chain reaction, the right connement of the produced radio nuclide is of utmost importance in nuclear energy generation, and a very high reliability of the components designed to prevent their dissemination is required in all circumstances. Therefore, most attention is paid to the evolution of the mechanical properties of the structural materials of the nuclear plants during service.

In pressurized water reactors, the main components of the primary circuit are subjected to long lifetimes (> 40 years). The operation temperature is mainly in the range of 290

• C 325 • C
and up to 345 • C locally in the pressurizer. The mechanical property evolutions during operation result from dierent aging mechanisms, including irradiation and thermal aging. The rst mechanism is directly due to the neutron ux and aects only the part of the Reactor Pressure Vessel (RPV) facing the core, the second is due to the long term holding at the operating temperatures. In the perspective of potential lifetime extensions of nuclear plants, neutron irradiation can be strongly reduced by reactor core fuel managements, while thermal aging cannot be mitigated and increases with time. Thermal aging needs therefore more attention in this context.

In the French eet, the pressure boundary material of the main components of the primary loop is the 16MND5 low alloy steel or other very close steel grades, with nominally a bainitic microstructure. However, martensite can exist as well, such as in heat aected zones of welds or in A-segregates. For materials complying with RCC-M 1 specications, the main expected aging phenomenon at the operation temperatures is Reversible Temper Embrittlement (RTE). This is a non-hardening mechanism due to the embrittlement of grain boundaries by segregation of impurities, mainly phosphorus, which results in a decrease of fracture toughness with a change of brittle fracture mode from cleavage to intergranular fracture. The phosphorus content is therefore controlled to limit this phenomenon (e.g. P < 0.008 wt%) and thermal aging embrittlement is taken into account in the structure integrity assessments. Heat aected zones INTRODUCTION tempered bainite. Bainitic boundaries (i.e. lath, block, and packet boundaries of bainite)

would have a better ability than martensitic boundaries to trap phosphorus, thus preventing it from segregating to prior austenite grain boundaries. This hypothesis was not yet veried by quantitative intergranular segregation measurements at lath, block, and packet boundaries of either microstructure, so the eect of microstructure on intergranular segregation behavior was not clearly established.

The present work is devoted to improving the knowledge on the dierence of RTE sensitivity between tempered bainite and tempered martensite in a 16MND5 low alloy steel, and more precisely to determining whether intergranular segregation strongly diers in the two microstructures. The main segregation measurement technique used for this purpose is Energy Dispersive X-ray Spectroscopy in Scanning Transmission Electron Microscopy (STEM-EDX) in order to be able to analyze all kinds of grain boundaries.

The results of intergranular segregation amount can be presented in dierent units such as fraction of a monolayer, atomic percentage, and surface concentration (atom/unit surface).

Some of these units need assumptions which are rarely veried or claried. For example, dening a fraction of a monolayer requires hypothesis of the crystallography (Miller indices) of the segregated plane. For these reasons, it is practically impossible to compare intergranular segregation quantication results from dierent sources. Direct comparisons between dierent quantication techniques are moreover seldom provided.

The most common technique for quantifying grain boundary segregation is Auger Electron Spectroscopy (AES). The analyzable areas are limited to the intergranular fracture surfaces induced by grain boundary embrittlement. This implies that all surfaces analyzed by AES have a minimum amount of segregated embrittling elements so that intergranular fracture can appear. In cases where intergranular fracture of the specimen cannot be obtained, the analysis of the grain boundaries using AES is simply not possible, which is a strong limitation of this technique.

Atom Probe Tomography (APT) has been used to study segregation especially when intergranular fracture is not seen. However, the small analysis volume and the lack of crystallography structure information is a disadvantage of APT. The analyses can however, be completed by transmission Kikuchi diraction for crystallography information. STEM-EDX has also been used to measure phosphorus intergranular segregation in low alloy steels. Depending on the dierent acquisition modes (spot, line prole, or raster scans), the everlasting diculty of beam broadening and interaction volume has not been fully solved.

The rst objective of this work is therefore to develop a methodology to quantify intergran- une ségrégation du phosphore plus élevée aux anciens joints de grains austénitiques pour les structures martensitiques que pour les structures bainitiques. Les joints bainitiques (c'est-àdire les joints de lattes, de blocs et de paquets de bainite) auraient une meilleure capacité que les joints martensitiques à piéger le phosphore, limitant ainsi la ségrégation de cet élément aux anciens joints de grains austénitiques. Cette hypothèse n'a pas été vériée par des mesures quantitatives de ségrégation aux joints de lattes, de blocs et de paquets de l'une ou l'autre microstructure, de sorte que l'eet de la microstructure sur la ségrégation intergranulaire n'a pas été clairement établi.

Le présent travail est consacré à l'amélioration des connaissances sur la diérence de sensibilité à la FRR de la bainite revenue et de la martensite revenue dans un acier faiblement allié 16MND5, en déterminant notamment si la ségrégation intergranulaire dière fortement dans les deux microstructures. La principale technique de mesure de ségrégation utilisée à cette n est la spectrométrie de rayons X à dispersion d'énergie en microscopie électronique à transmission à balayage (STEM-EDX) an de pouvoir analyser toutes sortes de joints de grains. [START_REF] Lejcek | Grain boundary segregation in metals[END_REF][START_REF] Keast | Grain boundary chemistry[END_REF]. EDX has already been used to quantify intergranular segregation in both metals and ceramics. For instance, Keast et al. [START_REF] Keast | Quantitative compositional mapping of Bi segregation to grain boundaries in Cu[END_REF] and Alber et al. [START_REF] Alber | Improved quantication of grain boundary segregation by EDS in a dedicated STEM[END_REF] worked on Bi segregation in Cu; Ikeda et al. [START_REF] Ikeda | Space Charge Segregation at Grain Boundaries in Titanium Dioxide: II, Model Experiments[END_REF] worked on Al, Nb, segregation in titanium oxide; Hu et al. [START_REF] Hu | Role of disordered bipolar complexions on the sulfur embrittlement of nickel general grain boundaries[END_REF] worked on S segregation in Ni; Zhang et al. [START_REF] Zhang | Energy dispersive spectroscopy analysis of aluminium segregation in silicon carbide grain boundaries[END_REF] worked on Al segregation in SiC;

Zheng et al. [START_REF] Zheng | Grain boundary segregation of antimony in heat aected zones during welding thermal cycles for a CrMo low alloysteel[END_REF] worked on Sb segregation in Cr-Mo low alloy steel.

STEM-EDX provides dierent advantages compared to AES:

1. It can access to any grain boundaries and not limited by the intergranular fracture facets.

2. It has access to all types of interfaces, including all types of grain boundaries, precipitate/matrix interfaces, etc.

3. It is possible to relate segregation measurements to grain boundary structure (i.e. the macroscopic 5 degree of freedom).

One of the main goals of this work is to quantify phosphorus intergranular segregation in low alloy steel using STEM-EDX. In the following of this chapter, an introduction of EDX is provided, including the details of the Cli-Lorimer method. Then a review of how STEM-EDX was used to quantify intergranular segregation and the common diculties are presented. EDX can be equipped on both SEM and TEM. The interest of using TEM instead of SEM is the smaller beam size and the very limited electron diusion, which result in very good analytical lateral resolution, i.e. nanometric or even sub-nanometric, depending on the conditions.

Furthermore, the interest of using STEM-EDX is that the convergent beam in STEM mode can be used to focus on a feature of interest or scan a dedicated area, which is not possible in conventional TEM mode. Characteristic X-rays are generated when the incident electron knock out an electron from the inner shell and excites the atom. For relaxation, an electron from the outer shell will ll in the hole while generating a photon with the same energy dierence between the two dierent shells. When analyzing the X-ray photons with dierent energies, the chemical analysis of the sample can be obtained.

An EDX system is composed of a detector (or detectors), the processing electronics, and a computer. Once these X-rays are collected, the detector generates a charge pulse proportional to the photon energies. Then the pulse is converted to a voltage and amplied to be identied electronically. At last, a digitized signal is stored in the channel assigned to the specic energy.

An illustration of the EDX system with four detectors is shown in gure I.1.1, this is also the EDX system used in this study. When a characteristic X-ray hits the detector, the energy allows the electrons of the detector to be transfered from the valence band to the conduction band, creating an electron/hole pair. The energy for the transfer for Si is about 3.8 eV at liquid N 2 temperature. The number of electron/hole pair created is proportional to the X-ray energy. θ being the elevation angle. [START_REF] Schlossmacher | Enhanced Detection Sensitivity with a New Windowless XEDS System for AEM Based on Silicon Drift Detector Technology[END_REF].

The geometry of the EDX system involves in dierent angles, that directly inuence the eciency of the system. The collecting angle Ω is the solid angle subtended at a point on the sample by the active area of the detector. It usually lies in the range of 0.3 down to 0.03 sr. For the Super-X system, the collecting angle is slightly dierent between each detector, but all of them are around 0.175 sr depending on the TEM model [START_REF] Kraxner | Quantitative EDXS: Inuence of geometry on a four detector system[END_REF]. The elevation angle θ is the angle between the normal to the detector and the horizontal line, it represents the relative location of the detectors. The take o angle α is dened as the angle between the sample surface and a normal to the center of the detector, which can vary depending of the sample tilt and the dierent position of the detectors. When the sample is at and not tilted, the take o angle α is identical to the elevation angle θ. The continuous background in the spectrum is due to the incident electrons interacting with the Coulomb eld of the sample, which can result in momentum changes causing X-rays to emit [START_REF] Williams | Transmission electron microscopy: a textbook for materials science[END_REF].

N (E) = KZ(E 0 -E) E 0 (I.1.1)
where N (E) is the Bremsstrahlung photon counts with energy E, E 0 is the accelerating voltage of the electron beam, Z is the atomic number of the ionized atom, and K is the Kramers' constant that takes multiple parameters such as collection eciency and the processing eciency of the detector and the absorption of X-rays in the specimen. From this equation, it is rare that the electron loses all its energy in one deceleration at the nucleus. In the case of an ATEM where the sample is thin and analyzed by high energy electron beam, the Bremsstrahlung X-ray can present small Gaussian peaks which are called coherent Bremsstrahlung. They are generated when electron beam proceeds through the lattice, close to a row of atoms. The energy of coherent Bremsstrahlung is given as the following [START_REF] Williams | Transmission electron microscopy: a textbook for materials science[END_REF]:

E CB = 12.4β L(1 -β(cos(90 + α))) (I.1.2)
where β is the electron velocity divided by the velocity of light (v/c), L is the real lattice spacing in the beam direction, and α is the take o angle. More than one coherent Bremsstrahlung peak can be generated because dierent Laue zones give dierent values of L. The coherent Bremsstrahlung peak intensity is greater when the beam is close to a low-index zone axis. This eect is most present in the energy range of 1 -3.5 keV, where the Bremsstrahlung background of the spectra can be very dierent due to crystal orientation [START_REF] Williams | Transmission electron microscopy: a textbook for materials science[END_REF].

Apart from coherent Bremsstrahlung, there are other artifacts that can appear on a spectrum. These are often peaks that can mislead the chemical analysis. There are common artifacts that are related to the silicon detector systems:

1. Escape peak: they are peaks that appear 1.74 keV below the true characteristic peak positions. This happens when the incoming photon uoresces a Si K α X-ray that escapes from the intrinsic region, so that the detector registers an apparent energy of (E-1.74) keV.

2. Sum peaks: these are peaks that have double the energy of the true characteristic X-ray energy. This is when two photons with the same energy arrives at the detector at the same time. It often happens when the count rate is high (high dead time), or when there is one principal element in the spectrum. CHAPTER I.1. LITERATURE REVIEW 3. Si K α peak: this peak appears in all spectra once the acquisition time is long enough. This happens when the incoming photon uoresces atoms in the dead layer (sometimes the dead layer is in Ge, then a Ge K/L peak appears). The dead layer is unresponsive to the X-ray because the electron/hole pairs recombine and do not generate pulses.

There are other artifacts related to the elements present in the TEM column and the sample holder, they are called spurious peaks. These spurious peaks can be generated prior (electrons scattered outside of the beam) or after (backscattered electrons) the electrons interact with the sample. Figure I.1.4 gives an idea of where spurious X-rays can be generated. To avoid the dierent spurious peaks, dierent sample holders are adapted for EDX analysis.

For example, the so-called high-visibility sample holder is often made of Be, where Be K α peak is dicult to detect. Also, sample holders may present carvings toward the EDX detectors to facilitate signal detection.

However, depending on the gasket or other xation used, the incident beam can also excite elements of them. Common peaks from FIB thin foil grid are Cu, Mo, Al, Cu from the sample holder itself. On the other hand, the electrons can also ionize atoms that are present in the TEM itself, including the polepieces (Fe, Cu) and the detectors (Zr, Pb) [START_REF] Kraxner | Quantitative EDXS: Inuence of geometry on a four detector system[END_REF][START_REF] Grogger | Quantitative EDXS with Super-X: Inuence fo Detector Geometry[END_REF]. These spurious peaks depend only on the dierent instruments and accessories used.

I.1.1.2 EDX Quantication by the Cli-Lorimer Method

Cli-Lorimer [START_REF] Cli | The quantitative analysis of thin specimens[END_REF] proposed the k-factor method to quantify a binary system. The weight percentage of each element C A and C B is related to the intensity (counts) in the spectrum I A CHAPTER I.1. LITERATURE REVIEW and I B , by the following equation:

C A C B = k A/B I A I B (I.1.3)
The term k A/B is often referred to as the Cli-Lorimer factor or the k factor, which is a sensitivity factor depending on the instrument (TEM and EDX systems), the acquisition parameters (accelerating voltage), and the specimen (thickness, atomic number, etc). The k factor is always relative and can be calculated between dierent pairs of elements, for example,

k A/C = k A/B × k B/C
. It is to be noted that the k factors are specic to a dedicated X-ray line (i.e. the K line or the L line). The terms I A and I B are integrated intensities after background subtraction from the acquired spectrum. When using equation I.1.3, the correct k factor in respect to the integrated intensity needs to be used. The background subtraction method will be introduced later in this section.

Another quantication method called the ζ factor method was developed based on the idea of electron probe micro-analysis where pure element standards are used. The ζ factor of a pure element A is dened as [START_REF] Watanabe | The quantitative analysis of thin specimens: a review of progress from the Cli-Lorimer to the new zeta-factor methods[END_REF]: 1.4) where ζ A is a proportional factor, intensity I A is the peak intensity of element A after background subtraction, ρt is the massthickness, C A is the concentration of element A, and D e is the total electron dose during acquisition and can be dened as:

ρt = ζ A I A C A D e (I.
D e = N e I p τ (I.1.5)
where N e is the number of electrons in a unit electric charge, I p is the beam current, and τ is the acquisition time.

Although the ζ factor method resolves several major disadvantages of the k factor method, i.e. using pure standards and providing absolute quantication, the advantages do not apply in this work. For example, preparing pure standards needs the elements of interest to exist in the pure state, which is the case for iron, but unfortunately not for phosphorus. Phosphorus is available in signicant concentration only in phosphide compounds. Also, accurately measuring beam current, which is essential in the ζ factor method, is not possible on the microscope used in this study. A review of the ζ factor method can be found in [START_REF] Watanabe | The quantitative analysis of thin specimens: a review of progress from the Cli-Lorimer to the new zeta-factor methods[END_REF], but no details are given here as it is out of the scope of this work.

Background Subtraction

The background contribution mainly comes from the Bremsstrahlung emission and needs to be removed before integrating the intensities. One of the most straight forward way to remove the background contribution to a characteristic X-ray peak is by the window method: The background intensity in window B is obtained from linear interpolation between windows B 1 and B 2 located on each side of the peak, see gure I.1.5. This method can only be used when there is no overlapping peaks. Also, this is only adapted when the Bremsstrahlung is not absorbed in the specimen. The absorption of Bremsstrahlung in the specimen results in uorescence of the characteristic X-ray peaks and creates a staircase like shape of the Bremsstrahlung background right after a characteristic X-ray peak.

Another common method to subtract the background is to simulate the Bremsstrahlung distribution using equation I.1.1 [START_REF] Kramers | On the theory of X-ray absorption and of the continuous X-ray spectrum[END_REF]. Normally this model provides a smooth curve, and is preferable when many characteristic X-ray peaks are present. There are dierent mathematical tools (i.e. Hyperspy [21]) that propose dierent models (with or without consideration of physics of X-ray production).

Once the background is removed, the peak integration is rather simple when there are no peak overlaps. The characteristic X-ray peaks can be tted by a Gaussian function. The peak position is xed, the FWHM is related to the energy resolution of the EDX system, and the peak height should be exible.

Determining k factor k factors are not constant but depend on the acquisition. One can directly calculate the k factors based on the following equation:

k A/B = (Qωα) A (Qωα) B A A A B ϵ A ϵ B (I.1.6)
where A, B stands for the dierent elements, Q is the ionization cross section, ω is the uorescence yield, α is the relative transition probability, and ϵ is the detector eciency. The detector eciency is then related to the absorption when photons travels through the window, CHAPTER I.1. LITERATURE REVIEW the Au contact layer, the Si dead layer, and the X-rays that do not arrive at the active area of the detector. The calculated k factors vary directly with the dierent assumptions made, mostly assumptions for the detector eciency or the ionization cross section.

When high accuracy is required, k factors should be determined experimentally. Standard samples should consist of a single phase and their composition should be well-characterized.

The determination process usually involves taking many spectra from dierent regions on the standard specimen. This is why the homogeneity and the stability of the specimen under electron beam should be veried. Cli and Lorimer [START_REF] Cli | The quantitative analysis of thin specimens[END_REF] used stoichiometric mineral standards to determine several k factors in respect to Si. Wood et al. [START_REF] Wood | Determination of Cli-Lorimer k factors for Philips EM400T, Quantitative Microanalysis with High Spatial Resolution[END_REF][START_REF] Wood | Experimental and theoretical determination of kAFe factors for quantitative X-ray microanalysis in the analytical electron microscope[END_REF] used single phased alloys as standards and determined k factors in respect to Fe, which is more useful to metallurgists.

Morgan et al. [START_REF] Morgan | Analysis of droplets from iso-atomic solutions as a means of calibrating a transmission electron analytical microscope (TEAM)[END_REF] and Graham et al. [START_REF] Graham | Determination of Cli-Lorimer k factors by analysis of crystallized microdroplets[END_REF] used evaporated forms of droplets as isoatomic standards to determine k factors for other elements when other types of standard samples are not available.

With an appropriate standard specimen with known composition, the k factor of a binary system can be written as k A/B = (C A /C B ) × (I B /I A ) based on equation I.1.3. However, this determined k A/B should be understood as an eective k factor k * A/B that includes absorption as a common problem. When determining the k factors, most authors uses the expression by Goldstein et al. [START_REF] Goldstein | Quantitative X-ray analysis in the electron microscope[END_REF] to correct their obtained k * A/B . This correction is presented in the follow- ing section. In dierent cases, it is necessary to measure or estimate the specimen thickness (depending on available technologies). Even today, precisely measuring the specimen thickness at the location of X-ray acquisition is not straight forward.

Horita et al. [START_REF] Horita | An extrapolation method for the determination of Cli-Lorimer kAB factors at zero foil thickness[END_REF] have proposed an extrapolation method to determine k factors by using samples with dierent thickness (often a wedge shape). This is by plotting the experimentally determined k * A/B against sample thickness and extrapolate the k factor at 0 thickness, so as to remove the absorption eect. Then they further proposed a similar idea that does not require the sample thickness [START_REF] Horita | Simplication of X-ray absorption correction in thin-sample quantitative microanalysis[END_REF]. Van Cappellen et al. [START_REF] Van Cappellen | The parameterless correction method in X-ray microanalysis[END_REF] have also proposed a method by extrapolation to determine k factor without sample thickness measurements. They plot the intensity ratio against the sum of intensities per second. Another big advantage of these methods is that they do not require numerical calculations, however, they are practical only for samples that have at least two acquisition zones with identical compositions. Horita et al. [START_REF] Horita | A new form of the extrapolation method for absorption correction in quantitative X-ray microanalysis with the analytical electron microscope[END_REF] proposed a further improvement of the extrapolation method for samples with limited regions of interests or when the thickness is uniform. They suggested tilting the specimen to vary the eective thickness to mimic a wedge-shaped specimen.

Absorption Correction

During X-ray analysis, the primary emitted X-rays may interact again with the sample. The The uorescence correction is often ignored since it is minor comparing to absorption. For example, when one dominant element absorbs the X-rays of a small amount of another element, there is only relatively small increase in the total counts of the dominant element. Further, the uoresced X-ray may not be the principle one being used for the quantication (i.e. we use the K α line for quantication but the uoresced X-ray is the L α line).

The absorption correction factor (ACF) is then the major correction factor needed. Goldstein et al. [START_REF] Goldstein | Quantitative X-ray analysis in the electron microscope[END_REF] proposed the equation I.1.7 to correct the intensity ratio after absorption:

I A I B = I A I B 0 µ ρ A spec µ ρ B spec 1 -exp(- µ ρ B spec ρt csc(α)) 1 -exp(- µ ρ A spec ρt csc(α)) (I.1.7)
where

I A I B
is the measured intensity ratio and

I A I B 0
is the absorption-corrected intensity ratio, the term µ ρ

A spec is the mass absorption coecient of X-rays from the element A in the specimen, ρ is the density at the acquisition position, t is the specimen thickness at the acquisition position, α is the take o angle of the detector.

To implement the absorption correction in the Cli-Lorimer method, the adapted equation I.1.3 should be written as:

C A C B = k A/B (ACF) A (ACF) B I A I B = k A/B (ACF) A/B I A I B (I.1.8)
Then the eective k factor k * A/B is dened as k A/B × (ACF) A/B . The term (ACF) A/B in equation I.1.8 is the ACF of element A in respect to element B. The ACF of each element was expressed by Philibert et al. [START_REF] Philibert | A Method for Calculating the Absorption Correction in Electron-Probe Microanalysis[END_REF]:

ACF i = µ ρ i spec ρt csc α 1 -exp(- µ ρ i spec ρt csc α) (I.1.9)
where i represents the dierent elements.

The mass absorption coecient term depends on the chemical composition of the specimen and is often given in cm 2 /g. Two references from Henke et al. [START_REF] Henke | X-ray interactions: photoabsorption, scattering, transmission and reection E= 50-30,000 eV, Z= 1-92[END_REF] and Chantler et al. [START_REF] Chantler | Detailed Tabulation of Atomic Form Factors, Photoelectric Absorption and Scattering Cross Section, and Mass Attenuation Coecients in the Vicinity of Absorption Edges in the Soft X-Ray (Z=3036, Z=6089, E=0.1 keV10 keV), Addressing Convergence Issues of Earlier Work[END_REF] are available on the website of National Institute of Standards and Technology and the open-source python based code Hyperspy [21] uses values from [START_REF] Chantler | Detailed Tabulation of Atomic Form Factors, Photoelectric Absorption and Scattering Cross Section, and Mass Attenuation Coecients in the Vicinity of Absorption Edges in the Soft X-Ray (Z=3036, Z=6089, E=0.1 keV10 keV), Addressing Convergence Issues of Earlier Work[END_REF].

As mentioned previously, the knowledge of sample density may not be accessible and the measurement of local thickness can be tedious. Van Cappellen et al. [START_REF] Van Cappellen | The parameterless correction method in X-ray microanalysis[END_REF] proposed a method where the knowledge of thickness is not necessary, and when analyzing stoichiometric samples, Van Cappellen et al. [START_REF] Van Cappellen | Quantitative transmission X-ray microanalysis of ionic compounds[END_REF] proposed another approach based on electroneutrality of the specimen.

CHAPTER I.1. LITERATURE REVIEW Also, there are dierent authors [START_REF] Horita | Simplication of X-ray absorption correction in thin-sample quantitative microanalysis[END_REF][START_REF] Van Cappellen | The parameterless correction method in X-ray microanalysis[END_REF][START_REF] Van Cappellen | A parameterless method to correct for x-ray absorption and uorescence in thin lm microanalysis[END_REF] that proposed parameterless methods to correct absorption and/or uorescence eects.

I.1.2 STEM-EDX for Intergranular Segregation Quantication

When analyzing intergranular segregation with STEM-EDX, there are dierent acquisition methods proposed [START_REF] Keast | Quantitative compositional mapping of Bi segregation to grain boundaries in Cu[END_REF]:

1. Spot: using a static beam to acquire a spectrum at the interface (with the interface being parallel to the electron beam). Normally this gives the best acquisition condition, and short acquisitions with good statistics. However, the problem to precisely locate the analyzing point may be an issue.

2. Line prole: acquisition with multiple spots crossing the grain boundary perpendicularly, with a dened step size. The result is the convolution of the composition distribution and the distribution of the electron beam.

3. Mapping (raster scan): mapping a 2D area containing the grain boundary on the sample.

This further decreases the surface contamination as the incident beam does not stay long on a single point. The drawback of mapping is that the statistics at each point would be degraded.

No matter which type of acquisition used, ATEM analysis faces a common problem to translating the apparent concentration to the actual concentration at the grain boundary [START_REF] Keast | Quantication of boundary segregation in the analytical electron microscope[END_REF]. The chemical composition is indeed not homogeneous in the analyzed volume, that the analyzed volume is larger than the segregated layer. This is an dierent assumption compared to the conventional bulk microanalysis.

The diculty lies in determining the interaction volume of the electron beam in respect to the segregation volume interacting with the electron beam. The interaction volume should be determined by dierent parameters including: beam diameter, beam broadening eect, and electron distribution in the beam. Depending on the local thickness of the specimen and the accelerating voltage, the incident beam broadens as a function of the thickness, making the actual interaction volume complicated to determine.

Based on the quantication method proposed by Cli-Lorimer [START_REF] Cli | The quantitative analysis of thin specimens[END_REF], Keast et al. [START_REF] Keast | Quantitative compositional mapping of Bi segregation to grain boundaries in Cu[END_REF][START_REF] Keast | Quantication of boundary segregation in the analytical electron microscope[END_REF] have proposed equation I.1.10 to include the beam interaction volume and to express their results as a grain boundary concentration of segregated solute in atom/nm 2 .

Γ i = ρ A M A i K i/M I i I M V A (I.1.10)
Where Γ i is the segregated element concentration in atom/nm 2 , ρ is the density of the analyzed area, A M and A i are the atomic mass of the matrix and the segregated element respectively, K i/M is the sensitivity factor (they used a calculated value), and I i /I M is the intensity ratio of the segregated element i and matrix M after background subtraction. V /A is the geometry factor where V is the interaction volume and G is the grain boundary area. This adapted equation solves another ambiguity of intergranular segregation. Most authors like to present segregation amount in wt%, at% [START_REF] Doig | Segregation of embrittling elements to prior austenite grain boundaries in 2•25Cr1 Mo steel[END_REF][START_REF] Faulkner | Combined quenching and tempering induced phosphorus segregation to grain boundaries in 2• 25Cr1 Mo steel[END_REF], or fraction of a monolayer [START_REF] Vatter | Measurement of grain-boundary segregation by STEM-EDX analysis[END_REF] depending on the dierent techniques used. These units often contain hypothesis like grain boundary thickness and the atomic plane of the monolayer. They vary from one author to another and sometimes are not clearly dened. This resulted in a barrier to compare results from dierent authors and techniques. By presenting results in atom/nm 2 [START_REF] Keast | Quantication of boundary segregation in the analytical electron microscope[END_REF][START_REF] Akhatova | Investigation of the dependence of phosphorus segregation on grain boundary structure in Fe-P-C alloy: cross comparison between Atom Probe Tomography and Auger Electron Spectroscopy[END_REF][START_REF] Zhang | Investigation of solute segregation behavior using a correlative EBSD/TKD/APT methodology in a 16MND5 weld[END_REF], no hypothesis is needed and the barrier to compare results directly is removed.

I.1.2.1 Diculties Encountered using STEM-EDX for Intergranular Segregation Quantication

The following describes the dierent diculties encountered for STEM-EDX quantication.

The dierent subjects are oriented specically for intergranular segregation measurements. Goldstein et al. [START_REF] Goldstein | Quantitative X-ray analysis in the electron microscope[END_REF] used single scattering approximation to describe b, then being corrected by Reed et al. [START_REF] Reed | The single-scattering model and spatial resolution in x-ray analysis of thin foils[END_REF]. The beam broadening eect b can be expressed as 1

Beam Broadening Eect

: b = 7.21 × 10 5 Z E 0 ρ A 1/2 h 1/2 (I.1.11)
where Z is the atomic number, E 0 is the beam energy in eV, ρ is the specimen density in g/cm 3 , A is the atomic weight, and h is the thickness. Z and A should be averaged when working with alloys.

Although dierent approaches were provided in literature to model the beam broadening eect, dierent authors have proposed criteria to neglect it. Zhang et al. [START_REF] Zhang | Energy dispersive spectroscopy analysis of aluminium segregation in silicon carbide grain boundaries[END_REF] calculated the ratio of interaction volume and grain boundary volume (V /V GB , considering grain boundary thickness at 1 nm) and plotted this term against specimen thickness with dierent beam diameters. These plots determined the range of specimen thickness where the beam broadening eect is negligible within their working conditions.

Keast et al. [START_REF] Keast | Quantication of boundary segregation in the analytical electron microscope[END_REF] showed that even using raster scan, the beam broadening eect should still be considered. The beam broadening eect also depends on the raster scan width [START_REF] Akhatova | Investigation of the dependence of phosphorus segregation on grain boundary structure in Fe-P-C alloy: cross comparison between Atom Probe Tomography and Auger Electron Spectroscopy[END_REF][START_REF] Williams | Transmission electron microscopy: a textbook for materials science[END_REF][START_REF] Keast | Quantitative compositional mapping of Bi segregation to grain boundaries in Cu[END_REF] nm), which is related to the magnication (2, 5, 10 MX). They show that when their specimen thickness is less then 80 nm, the beam broadening eect can be neglected regardless of the magnications used in their work. This is also noted in the work of [START_REF] Ikeda | Space Charge Segregation at Grain Boundaries in Titanium Dioxide: II, Model Experiments[END_REF]. Although larger scan widths can free us from the beam broadening eect, Alber et al. [START_REF] Alber | Improved quantication of grain boundary segregation by EDS in a dedicated STEM[END_REF] showed that when the raster scan width is small, the detection limit is improved.

Interaction Volume & Grain Boundary Area

If the electron beam is considered to be a circle with diameter d, the interaction volume without beam broadening can be seen as a cylinder π 4 d 2 t with t being the specimen thickness.

The term V /A in equation I.1.10 can be dened as π 4 d, which was used in the rst segregation measurement example [START_REF] Doig | The detection of monolayer grain boundary segregations in steels using STEM-EDS X-ray microanalysis[END_REF]. However, if beam broadening eect is taken into concern, the term V /A in equation I.1.10 can be fairly complicated. For example, if the incident beam is a Gaussian function with standard deviation σ, the geometry factor can be written as [START_REF] Keast | Quantication of boundary segregation in the analytical electron microscope[END_REF][START_REF] Doig | The detection of monolayer grain boundary segregations in steels using STEM-EDS X-ray microanalysis[END_REF][START_REF] Doig | The spatial resolution of X-ray microanalysis in the scanning transmission electron microscope[END_REF]:

V A = √ πh h 0 1 2σ 2 + βt 3 dt (I.1.12)
where t is the integration variable for the thickness h at a given point and β can be dened as the following:

β = 500( 4Z E 0 ) 2 ( ρ A ) (I.1.13)
where Z is the atomic number of the specimen, E 0 is the incident beam energy in eV, ρ is 1 The original constant by Goldstein is 6.25 × 10 5 in this equation.

the density, and A is the atomic weight.

Keast et al. [START_REF] Keast | Quantication of boundary segregation in the analytical electron microscope[END_REF] proposed an easier approach by raster scan (or simply 2D mapping). The interaction volume without considering the beam broadening eect would simply become the width of the scan perpendicular to the grain boundary. Faulkner et al. [START_REF] Faulkner | Analytical electron microscopy of thin segregated layers[END_REF] used Monte Carlo simulations to take the Gaussian distribution into account. They proposed the following equation to determine the apparent grain boundary concentration C app prole obtained along a line across the grain boundary:

C app = C bulk + 0.5(C GB -C bulk ) × erf x d + 0.5d 0 σ √ 2 -erf x d -0.5d 0 σ √ 2 (I.1.14)
where C GB is the measured solute concentration at grain boundary, C bulk is the solute concentration at bulk, x d is the distance to the grain boundary, d 0 is the width of the segregation layer, and σ is the standard deviation of the electron density distribution. Note that this is the case where there is no depletion near the grain boundary. This method was also used by other studies [4648] for measuring phosphorus and molybdenum intergranular segregation. CHAPTER I.1. LITERATURE REVIEW

High bulk concentration

When the segregated elements have high bulk concentrations (i.e. above the detection limit), overestimations can be induced. For example, Ikeda et al. [START_REF] Ikeda | Space Charge Segregation at Grain Boundaries in Titanium Dioxide: II, Model Experiments[END_REF] have performed a line prole across the grain boundary qualitatively showing that their segregated/depleted elements (Al & Nb) are measurable even far away from the grain boundary. To avoid overestimation of these elements, they proposed to perform three identical raster scans: one including the grain boundary, two others in each grain at a dened distance from the grain boundary. In Ikeda's case [START_REF] Ikeda | Space Charge Segregation at Grain Boundaries in Titanium Dioxide: II, Model Experiments[END_REF], their segregated element can be seen on the spectra from the adjacent grains. The intensity ratio of the segregated element versus the bulk element they used for the Cli-Lorimer equation is the dierence between the intensity ratio between grain boundary box spectrum and grain box spectrum, see equation I.1.15.

C excess i = (I i /I T i ) gb -(I i /I T i ) grain (I i /I T i ) grain C bulk-ICP i (I.1.15)
Where (I i /I T i ) gb and (I i /I T i ) grain are intensity ratios from the box spectrum of the grain boundary and the grain, respectively, and C bulk-ICP i is the concentration of the segregated element in the bulk measured by inductively coupled plasma. Then their results are expressed in atom/nm 2 using the same reasoning as equation I.1.10.

Channeling Eect

Cli-Lorimer method in equation I. 1.3 indicates that the characteristic X-rays emitted from the sample is proportional to the concentration. This is not the case when channeling eect is present. When analyzing crystalline materials, the Borrmann eect can inuence the Xray emission which can be higher when the crystal orientation reects the beam strongly, i.e.

when it is in strong Bragg diraction conditions. As the channeling eect on X-ray emission is not necessarily the same for all the elements, the assumption of Cli-Lorimer that X-ray emission is proportional to concentration is not valid anymore, This can cause high errors for quantication [4951].

Dierent authors [4951] have shown how channeling eect can change the X-ray intensities.

Although being a more critical problem for atomic scale EDX quantication, it was shown in [START_REF] Lugg | On the quantitativeness of EDS STEM[END_REF] that channeling eect cannot be ignored above atomic scale. However, the same authors have shown that once the STEM-EDX acquisition was done 2

• away from low-order zone axes, the channeling eect is negligible. Their results were shown in accord with simulations. In the work of Lugg et al. [START_REF] Lugg | On the quantitativeness of EDS STEM[END_REF], they further showed that channeling eect is also negligible at higher-order zone axis ( [START_REF] Bhadeshia | Bainite in steels: theory and practice[END_REF] in their work).

I.1.2.2 STEM-EDX Measurements of Phosphorus Intergranular Segregation

There were dierent studies that used STEM-EDX for intergranular segregation quantication in low alloy steel. Their results are reported in the following without considering the quantication method issues. The goal is to provide an overview of the STEM-EDX applications in this eld.

Vatter et al. [START_REF] Vatter | Measurement of grain-boundary segregation by STEM-EDX analysis[END_REF] ). Using their model [START_REF] Faulkner | Analytical electron microscopy of thin segregated layers[END_REF] for correcting the measured phosphorus intergranular segregation that will be presented in equation I.1.14, they found 1.2 at% P in the as-quenched sample, 2 at%P and > 3 at%P in the two tempered samples, respectively. Using the same approach, Song et al. [START_REF] Song | Quenching and tempering-induced molybdenum segregation to grain boundaries in a 2.25 Cr1Mo steel[END_REF] have worked on the same conditions to quantify Mo intergranular segregation.

Ding et al. [START_REF] Ding | Eect of phosphorus segregation on fracture properties of two quenched and tempered structural steels[END_REF][START_REF] Ding | Grain boundary segregation of phosphorus and molybdenum in 2•25Cr1Mo steel[END_REF] worked on quantifying P and Mo intergranular segregation in 2.25Cr-1Mo steel (0.013 wt%P, 0.91 wt%Mo). The samples were tempered at 520

• C with dierent duration.

They used the same Monte Carlo approach as proposed in [START_REF] Partridge | A comparison of auger and stem-eds quantication routines used in an investigation of intergranular segregation in long-term aged nimonic pe16[END_REF] with the hypothesis of grain boundary thickness being 1 nm.

I.1.3 Cross-comparison of Intergranular Segregation Quantication Between Dierent Techniques

Besides AES and ATEM, other techniques are used to quantify intergranular segregation, including APT, Secondary Ion Mass Spectrometry [START_REF] Christien | Quantitative grain boundary analysis of bulk samples by SIMS[END_REF][START_REF] Christien | Quantication of grain boundary equilibrium segregation by NanoSIMS analysis of bulk samples: How to quantify grain boundary segregation using NanoSIMS[END_REF], WDS [5658], etc. A review of the techniques can be found in [START_REF] Lejcek | Grain boundary segregation in metals[END_REF][START_REF] Keast | Grain boundary chemistry[END_REF].

As mentioned previously, dierent authors tend to report their measurements in dierent units. Some of those units need assumptions which are not always clearly dened, making comparison of results from dierent sources practically impossible. The target of this section is to show an overview of comparisons of intergranular segregation quantication results from dierent techniques in the literature. The examples of studies on irradiation induced intergranular segregation is not complete.

Although the problematic encountered using STEM-EDX to quantify irradiation induced intergranular segregation remains the same as the subject of temper embrittlement or other intergranular segregations. This phenomenon is out of the scope of this work.

I.1.4 Summary

Based on the dierent subjects treated in this chapter, there are dierent points that can be extracted from the current literature:

1. Regardless of the dierent advantages of STEM-EDX, quantifying intergranular segregation with STEM-EDX is not often used due to the dierent limitations, especially interaction volume and beam broadening. Dierent authors have proposed approximations, measurements, or hypotheses to ensure that their quantication results are not inuenced by these eects. This includes providing a criterion for the box width, considering the broadened beam diameter.

In addition, special attention was paid to the background subtraction method, which appeared to be of critical importance. At last, two other techniques (WDS & APT) that were used for intergranular segregation quantication are introduced.

I.2.1 Description of the Developed STEM-EDX Box Method

The following sections illustrate the dierent steps of the developed quantication method, starting from the sample preparation using FIB, then the acquisition procedure in TEM, and the data treatment procedure. Later on, validation of the method is presented.

I.2.1.1 Sample Preparation -Focus Ion Beam

In this study, all TEM specimens were prepared using FEI Helios DualBeam FIB operating As can be seen in gure I.2.1, the yellow line indicates the grain boundary apparent width before and after the alignment. When the grain boundary is parallel to the incident beam, the grain boundary appears to be a thin line, instead of a band. In some cases, the orientation of the adjacent grains can be close to zone axis, possibly causing electron channeling which might aect the EDX quantication [START_REF] Lugg | On the quantitativeness of EDS STEM[END_REF][START_REF] Chen | Energy dispersive X-ray analysis on an absolute scale in scanning transmission electron microscopy[END_REF]. Lugg et al. [START_REF] Lugg | On the quantitativeness of EDS STEM[END_REF] showed, however, that once the acquisition is 2

• o zone axis or at high-order zone axis, the channeling eect is negligible. It has been veried that the grain orientations were not at strong diraction conditions nor at low-order zone axis. Channeling eect was neglected in the EDX quantications in this study.

Once the grain boundary is aligned, it is preferable to let the thin foil stabilize for a few hours due to its magnetic nature. Then, the acquisition procedure includes EDX acquisition and thickness map acquisition. the qualitative element maps (Fe K α , P K α ) and the HAADF image of the acquisition zone.

Phosphorus grain boundary segregation is clearly seen in the P K α element map. This same procedure can be applied on any well-aligned interface and any segregated element as long as the characteristic peaks do not overlap with one another.

2 The step size depends on the STEM magnication and the number of pixels of the acquisition zone. The local thickness is needed to calculate the Absorption Correction Factor (ACF) locally so that the k factor can be corrected, see equation I.1.9. The relative specimen thickness can be determined by the low-loss spectrum using the equation

t λ = ln( I t I 0
), where t is the thickness, λ

is the electron mean free path, I t is the total area under the whole spectrum, and I 0 is the area under zero-loss peak. This implies that the electron mean free path in the specimen is needed to measure the absolute thickness. Thickness map by Energy Filtered TEM (EFTEM) was acquired using Gatan DigitalMicrograph3 [START_REF] Malis | EELS log-ratio technique for specimenthickness measurement in the TEM[END_REF] so that the local thickness of each STEM-EDX acquisition can be extracted for quantication. It consists in measuring the thickness over the inelastic mean free path (t/λ), where the mean free path is estimated to be 102 ± 10% nm for pure iron [START_REF] Iakoubovskii | Mean free path of inelastic electron scattering in elemental solids and oxides using transmission electron microscopy: Atomic number dependent oscillatory behavior[END_REF].

I.2.1.3 Determination of k factor -Iron Phosphide Sample

In order to determine k P/F e , an iron phosphide sample was used as a standard material. Its composition as measured by WDS was 58.37 wt% Fe and 29.22 wt% P. The total is not 100 wt% since there were trace amounts of other elements such as manganese. The trace elements were not all identied as the determination of the k P/F e factor is based on the P/Fe composition ratio only, so the concentrations of other elements were not needed.

A wedge shaped FIB thin foil was extracted from the iron phosphide sample at the exact location where the WDS analysis was performed. A map of the thin foil thickness was measured by EFTEM using DigitalMicrograph3 by Gatan [START_REF] Malis | EELS log-ratio technique for specimenthickness measurement in the TEM[END_REF]. Then, a matrix of EDX acquisitions was The blue boxes represent EDX acquisitions conducted at dierent thickness.

Larger foil thickness results in higher X-ray emission, as well as larger absorption. The EDX spectra obtained at dierent foil thicknesses were processed using the extrapolation method proposed by Van Cappellen et al. [START_REF] Van Cappellen | The parameterless correction method in X-ray microanalysis[END_REF], that allows the determination of intensity ratio at zero foil thickness, i.e. free from absorption eect. The ratio of X-ray line intensities (I P /I F e ) is plotted versus the total intensity of X-ray lines (I P +I F e ) so that intensity ratio at zero thickness can be determined from the y-intercept (Figure I.2.4). This procedure allows the determination of a k P/F e factor at zero foil thickness, i.e. free from the correction factors, by the following equation: The grain spectrum S Grains is obtained from:

k P/F
S Grains = B 1 + B 2 t 1 + t 2 (I.2.2)
where B 1 and B 2 are the Grain1 and Grain2 box spectra (yellow boxes in gure I.2.2 (b)) expressed in raw counts, t 1 and t 2 are the counting times corresponding to Grain1 and Grain2 boxes (i.e. number of pixels in the box multiplied by the counting time per pixel). In gure I.2.5 (a) the signal is expressed in counts per seconds to directly compare the Grains and GB spectra.

The phosphorus peak on the GB spectrum is clearly evidenced, see gure I.2.5 (b). A small amount of sulfur grain boundary segregation was also detected, but this is not discussed in this work. The background shape and the presence of spurious peaks will be discussed later. The net phosphorus K α peak was obtained by subtracting the grain spectrum from the GB spectrum (gure I.2.5 (c)). A Gaussian function was tted to the peak to determine the phosphorus peak intensity (peak area, I P in eq I.2.5). Iron peak intensity (I F e in equation I.2.5) was obtained in the same manner by tting a Gaussian function to the iron K α peak directly on the GB spectrum (gure I.2.5 (d)). The Cli-Lorimer method [START_REF] Cli | The quantitative analysis of thin specimens[END_REF], also known as the k factor method was used for quantication.

Equation I.1.8 adapted to a simple Fe-P alloy can be written as: [START_REF] Van Cappellen | The parameterless correction method in X-ray microanalysis[END_REF]. The ACF of each X-ray line (P K α and Fe K α ) was calculated based on equation I.1.9 [31]. The mass absorption coecients ( µ ρ

C P C F e = k P/F
) in cm/g are from the database of Chantler et al. [START_REF] Chantler | Detailed Tabulation of Atomic Form Factors, Photoelectric Absorption and Scattering Cross Section, and Mass Attenuation Coecients in the Vicinity of Absorption Edges in the Soft X-Ray (Z=3036, Z=6089, E=0.1 keV10 keV), Addressing Convergence Issues of Earlier Work[END_REF], accessed by Hyperspy [21] (1474.48 cm/g for P K α and 65.40 cm/g for Fe K α respectively in the Fe-P model alloy); the take-o angle (α) is designed to be 22

• in the superX conguration; this value is taken as an approximation for all four detectors that have slightly dierent take-o angles from one another. A nominal take-o angle is considered as the individual counts per detector is not accessible [START_REF] Kraxner | Quantitative EDXS: Inuence of geometry on a four detector system[END_REF].

From
X P = V A N A F e A P C P = wN A F e A P C P (I.2.6)
Where X P is the phosphorus grain boundary concentration in atom/nm 2 , N is the matrix density in nm -3 (85.5 nm -3 for iron), A F e and A P are the atomic mass of iron and phosphorus, respectively.

V A is the geometry factor, which is the ratio of the interaction volume to the area of the grain boundary. The raster scan approach in [START_REF] Hu | Role of disordered bipolar complexions on the sulfur embrittlement of nickel general grain boundaries[END_REF][START_REF] Keast | Quantication of boundary segregation in the analytical electron microscope[END_REF] was used in this study. This simplies the geometry factor (

V A

) into the width w perpendicular to the grain boundary plane; therefore the GB box width is used for w in equation I.2.6. Equations I.2.5 and I.2.6 can be easily adapted to a system where multiple elements segregate:

C i = k i/F e × ACF i/F e × I i I F e 1 + Σ i (k i/F e × ACF i/F e × I i I F e ) (I.2.7)
Where C i is the concentration of element i in wt%, k i/F e is the k factor of element i in respect to iron, ACF i/F e is the absorption correction factor of element i in respect to iron, I i I F e is the intensity ratio of the element i K α peak and Fe K α peak.

The interface concentration can be expressed in atom/nm 2 using :

X i = wN A F e A i C i (I.2.8)
Where X i is the grain boundary concentration of element i in atom/nm 2 , A i are the atomic masses of elements i, respectively. The STEM-EDX box method for intergranular segregation quantication is described above.

This section rst provides a series of Monte-Carlo simulations to verify the proposed box method. The simulations treat the long discussed question of beam broadening eect on EDX quantication by simulating the X-ray emission in dierent conditions of specimen thickness and beam diameter. A criterion of the GB box width is proposed. Then, the background subtraction validity is studied. The dierent forms of coherent Bremsstrahlung from dierent grains were compared to validate the subtraction method in equation I.2.2.

I.2.2.1 Monte-Carlo Simulations -Beam Broadening Eect & Interaction Volume

Monte-Carlo simulations of electron beam scattering and X-ray emission were carried out using the MC X-ray program [START_REF] Michaud | Mc x-ray, the monte carlo program for quantitative electron microscopy of real materials[END_REF]. The objective was to ensure that the quantication method applied in this study was valid and not inuenced by the beam-sample interaction volume.

The eect of beam diameter and beam broadening due to sample thickness were studied. The program rst allows the user to create a specimen geometry. Here, an iron thin foil containing a vertical grain boundary was created. The grain boundary is mimicked by a 0.2 nm thick Fe-P alloy layer of 7.86 g/cm 3 in density containing 6.5452 wt% of phosphorus, which corresponds to 2 atom/nm 2 of phosphorus.

During simulation, the program calculates X-ray intensities (P K α , Fe K α , Fe L α , etc.) at dierent beam locations. In this study, line proles across the grain boundary were simulated.

The electron beam shape was considered of Gaussian type. The beam diameter was dened as that containing 99.9% of the total number of electrons [START_REF] Michaud | Mc x-ray, the monte carlo program for quantitative electron microscopy of real materials[END_REF][START_REF] Hovington | CASINO: A new Monte Carlo code in C language for electron beam interactionPart I: Description of the program[END_REF]. The chosen number of electron trajectories simulated was high enough to keep statistical noise below approximately 1% of the peak height obtained on the X-ray line proles. The dierent physical models used for Monte-Carlo simulations were those set by default in the program [START_REF] Michaud | Mc x-ray, the monte carlo program for quantitative electron microscopy of real materials[END_REF].

The simulated P K α and Fe K α peak intensities were processed in the same manner as the experimental ones, i.e. using the Cli-Lorimer equation to obtain local apparent phosphorus concentrations. The k factor of the Cli-Lorimer method can be easily obtained by simulating X-ray intensities on a standard homogeneous specimen of known composition. If the standard specimen has the same thickness as the specimen of interest, no correction is required. Table I.2.2 shows the k-factor determined using a homogeneous thin foil of Fe-1 wt%P with three dierent thicknesses. These k-factors values were then used to process the X-ray intensities obtained from the simulations, i.e. by converting them into phosphorus apparent concentrations. in the specimen geometry. Line proles rather than maps were simulated here to keep the simulation time reasonable (a few minutes per prole). In addition, this procedure also allows us to easily see how the concentration prole is aected when beam or specimen conditions are changed. However, calculation of the phosphorus interface concentration (2 atom/nm 2 )

from prole peak integration is strictly equivalent, from a mathematical point of view, to the box-type method employed to process experimental data (see equation I.2.6), provided that the box chosen is wide enough to include the entire phosphorus concentration peak. diameter was set at 1 nm. It can be seen that the eect is similar to that of changing the beam diameter: peak height decreases but peak width increases with foil thickness. However, the peak area remains unchanged: 2.00, 1.99, and 1.98 atom/nm 2 are obtained, which again corresponds to the input value. This shows that beam broadening does not aect the quantication result if the GB box width (w in equation I.2.6) considered is large enough to include the entire phosphorus concentration peak. From a mathematical point of view, the unchanged peak area can be explained by the concept of convolution. The apparent phosphorus concentration prole is the convolution of the actual phosphorus concentration prole (practically a Dirac peak) with a normalized probe function [START_REF] Christien | Measuring surface and grain boundary segregation using wavelength dispersive X-ray spectroscopy[END_REF]. From the properties of the convolution product, it was shown by Risch et al. in [START_REF] Christien | Cross-sectional measurement of grain boundary segregation using WDS[END_REF] that the under-peak area of the apparent concentration prole does not depend on the shape of the probe function and always equals the under-peak area of the actual concentration prole (here 2 atom/nm 2 ). is thicker. The phosphorus signal starts to increase as the edge of the enlarged beam reaches the grain boundary. The dashed prole (thick foil case) starts to increase before the continuous prole (thin foil case). As the electron beam scans through the grain boundary, the dashed prole is broader and presents a lower peak height than the continuous prole. This is due to the larger interaction volume for the thick foil case. However, the area under peak should remain constant as shown by the simulation (gure I.2.7). This schematic also shows that the base peak width (w P , width at C ≈ 0) is twice the maximum beam diameter, i.e. the beam diameter at the exit side of the thin foil (d B ). In the box quantication method, the GB box width should be at least wider than w P to include the entire grain boundary phosphorus signal.

I.2.2.2 Validation of the Background Subtraction Method

The background subtraction approach in this study was based on subtracting the average backgrounds of both adjacent grains. The main advantage of this method is to remove the eects of coherent Bremsstrahlung and possible spurious peaks. are very dierent at low energy (1 3.5 keV). The wavy shape of the background is due to coherent Bremsstrahlung [START_REF] Williams | Transmission electron microscopy: a textbook for materials science[END_REF]. According to [START_REF] Williams | Transmission electron microscopy: a textbook for materials science[END_REF], the positions of coherent Bremsstrahlung peaks are related to crystal orientation. due to FIB preparation, Si and Zr due to SuperX detectors [START_REF] Grogger | Quantitative EDXS with Super-X: Inuence fo Detector Geometry[END_REF]. Some spurious peaks (Ga L series, Si K α , Cu K α ) can be disregarded as they are far away from the phosphorus peak that is of interest here, and do not inuence data processing. However, others (Zr L α and Pt M α ) are very close to the phosphorus peak and cause diculties in identication and quantication, see gure I.2.5 (b).

All the artifacts above considerably increase the diculty of accurate determination of phosphorus peak intensity from the GB box spectrum. Obviously, common background subtraction methods are not applicable to this work. As such, it was decided to determine phosphorus peak intensity by subtracting the average spectrum of both the adjacent grains. For this, the GB box spectrum (red box in gure I.2.2 (b)) must be symmetrical. In other words, the grain boundary must be at the center of the GB box to ensure that the two adjacent grains contribute equally in the GB spectrum. However, the two grain box spectra (yellow boxes in

I.3.1 Other Intergranular Quantication Techniques

Apart from the developed STEM-EDX intergranular segregation quantication method, there are other characterization techniques that can be used to measure surface/intergranular segregations. The following two techniques were used so that the developed STEM-EDX method can be cross-compared with them in section I.3.3.

Wavelength Disperssive Spectroscopy The principle of WDS is similar to EDX. Characteristic X-rays are emitted after inelastic scattering of the primary beam. However, the sensitivity of WDS is far better than that of EDX. Unlike EDX, WDS only captures a small fraction of the emitted characteristic X-rays, reaching a crystal. Only photons with a particular wavelength (so one element) can be diracted by the crystal and be detected. Although WDS analyzes both the signals from surface segregation and bulk, it can be adapted for surface segregation quantication. When analyzing with dierent accelerating voltages and adapting the quantication procedure, it is possible to separate the contribution of the surface segregation from the bulk. It was demonstrated that this method has excellent quantitative ability and is not as sensitive to surface contamination as AES [START_REF] Nowakowski | Measuring grain boundary segregation using Wavelength Dispersive X-ray Spectroscopy: Further developments[END_REF][START_REF] Christien | Measuring surface and grain boundary segregation using wavelength dispersive X-ray spectroscopy[END_REF].

Atom Probe Tomography With the aid of FIB, APT can be used to analyze grain boundary segregation on materials. The working principle of an APT is to evaporate atoms from a needle shape sample. A positive potential is applied on the needle shape sample and induces an electric eld at the sample surface. This potential is chosen so that the induced electric eld is too small to evaporate atoms. To control evaporation of atoms, short-duration negative electrical pulses are applied to an local electrode. When both the potentials on the sample and local electrode generates a sucient electric eld, atoms of the sample surface evaporate. This allows controlling over when surface atoms can be evaporated (only during pulses). Dierent ions or molecular ions are detected at dierent positions on the detector with dierent timeof-ight due to their chemical nature. Based on the acquired mass spectrum, the dierent ions can be identied. For more detailed information on APT analysis on intergranular segregation, including sample preparation and grain boundary characteristics, work from Akhatova et al. [START_REF] Akhatova | Méthodologie instrumentale à l'échelle atomique pour une meilleure compréhension des mécanismes de ségrégation intergranulaire dans les aciers: application au phosphore[END_REF] and Zhang et al. [START_REF] Zhang | Ségrégation intergranulaire du phosphore dans les aciers des cuves des REP[END_REF] can be referenced.

I.3.2 Fe-P Model Alloy

A rst comparative study is presented here where measurements by APT and STEM-EDX were compared. The sources of error of the STEM-EDX method were also studied.

I.3.2.1 Material & Sample Preparation

The sample used consisted of a high purity Fe-0.034 at% P-0.01 at% C model alloy that was annealed at 650

• C for 24 hours to induce phosphorus intergranular segregation. The same sample was studied by Akhatova et al. [START_REF] Akhatova | Investigation of the dependence of phosphorus segregation on grain boundary structure in Fe-P-C alloy: cross comparison between Atom Probe Tomography and Auger Electron Spectroscopy[END_REF] where two high angle grain boundaries named A1 and A2, were analyzed by APT. An EBSD orientation map of the microstructure and the positions of A1 and A2 grain boundaries are shown in Figure I.3.1 (a) [START_REF] Akhatova | Méthodologie instrumentale à l'échelle atomique pour une meilleure compréhension des mécanismes de ségrégation intergranulaire dans les aciers: application au phosphore[END_REF]. The lengths of A1 and A2 grain boundaries exceeds a few hundreds of microns, leaving enough space to prepare thin foils by FIB on the same grain boundaries. The grain boundaries were fully analyzed in [START_REF] Akhatova | Investigation of the dependence of phosphorus segregation on grain boundary structure in Fe-P-C alloy: cross comparison between Atom Probe Tomography and Auger Electron Spectroscopy[END_REF] where information including the rotation axes and the grain boundary plane, is provided. shows a HAADF image of the A2 thin foil. It can be seen that the grain boundary is straight and located close to the center. Another TEM thin foil was prepared at the A1 grain boundary in the same manner. The time interval between thin foil preparation and STEM-EDX analysis was no longer than 2 days, except for one particular case as explained later.

I.3.2.2 Results & Discussions

Multiple STEM-EDX acquisitions were performed along the grain boundary on each thin foil. The acquisition and data treatment procedure is detailed in chapter I.2. Table I

.3.1
shows the dierent data acquired on the two grain boundaries analyzed in this work and the quantication results. Fourteen acquisitions were conducted on A1 and ten were conducted on A2. The results obtained in [START_REF] Akhatova | Investigation of the dependence of phosphorus segregation on grain boundary structure in Fe-P-C alloy: cross comparison between Atom Probe Tomography and Auger Electron Spectroscopy[END_REF] using APT on the same two grain boundaries are provided. A fair agreement is found between the two techniques, although the quantication from STEM-EDX is slightly higher than that by APT; for grain boundary A1, the dierence falls into the range of the standard deviation of the series of STEM-EDX measurement series.

Measurement accuracy

The errors that are induced in this methodology can be categorized as random errors and systematic errors. The main source of random errors is by far the measurement of the phos-CHAPTER I.3. DIRECT COMPARISON OF INTERGRANULAR SEGREGATION BETWEEN DIFFERENT TECHNIQUES phorus peak intensity as iron peak intensity is higher by a factor of 10 3 approximately (table I.3.1). The relative counting error (68% condence interval) is given by [START_REF] Williams | Transmission electron microscopy: a textbook for materials science[END_REF]:

∆X P X P ∼ = ∆I P I P ∼ = √ N T N P (I.3.1)
where X P is the phosphorus grain boundary concentration, I P is the phosphorus peak intensity, N T is the total number of counts in the P energy window (1.9 2.2 keV) and N P is the number of counts in the P peak. Table I 2 ). This suggests, for the A1 grain boundary, an additional source of variability, possibly a non-homogeneous P concentration along the grain boundary [START_REF] Shen | Eect of solute grain boundary segregation and hardness on the ductile-to-brittle transition for a CrMo low-alloy steel[END_REF].

A possible source of systematic error is the foil thickness used in the ACF determination.

Local foil thickness is measured using the thickness map function proposed by Gatan DigitalMi-crograph3 [START_REF] Malis | EELS log-ratio technique for specimenthickness measurement in the TEM[END_REF]. It consists of measuring the thickness over the inelastic mean free path (t/λ),

where the mean free path is estimated at 102 nm for pure iron [START_REF] Iakoubovskii | Mean free path of inelastic electron scattering in elemental solids and oxides using transmission electron microscopy: Atomic number dependent oscillatory behavior[END_REF]. Using this method, it is reasonable to estimate a 15% error on the foil thickness measurement. However, in the thickness range covered in this work (mainly 100 150 nm, see table I.3.1), ± 15% error in thickness measurement results in only ± 2.5% in the nal P grain boundary segregation quantication.

Another possible source of systematic error is the k P/F e constant. However, in this work, as this constant was experimentally determined on a standard material in the same conditions as P grain boundary segregation measurements, this error is expected to be very low here.

Inuence of Electron Dose and Specimen Aging

It can be questioned whether the highly accelerated electrons used in TEM could result in irradiation damage in the segregated layer and hence decrease the amount of segregated solute.

To check whether this eect could occur in our analyses, two acquisitions (#3 and #4 in table I.3.1) were conducted at the same location at the same day (within nanometer positioning error due to specimen positioning and/or beam drift during acquisition). It can be seen that the phosphorus concentrations measured are not very dierent, which shows that there was no signicant eect of the electron dose received during acquisition on the phosphorus grain boundary concentration, at least in the conditions of measurement used in this work.

In addition, it can also be questioned if storing the specimen for long time at room temperature before analysis could aect the amount of solute segregated at the grain boundary.

To answer that question, acquisitions #11 to #14 on grain boundary A1 were conducted six months later than acquisitions #1 to #10. Meanwhile, the thin foil was stored under vacuum at ambient temperature. The P concentration measured for acquisitions #11 to #14 are slightly lower than the previous acquisitions #1 -#10, which might show that a small amount of phosphorus has migrated out of the grain boundary. However, the decrease observed is only slightly above the measurement accuracy. This shows that the specimen can be safely stored at room temperature before analysis, a least for weeks.

I.3.2.3 Conclusion

This rst case studied provides a direct comparison of phosphorus intergranular segregation in Fe-P model alloy. Two HAGBs containing about 2 atoms of phosphorus per nm 2 were analyzed using STEM-EDX and APT [START_REF] Akhatova | Investigation of the dependence of phosphorus segregation on grain boundary structure in Fe-P-C alloy: cross comparison between Atom Probe Tomography and Auger Electron Spectroscopy[END_REF]. The quantitative results obtained are in good agreement, which suggests that the STEM-EDX box spectrum method can provide accurate measurements for grain boundary segregation. The results of this case was published in a peer-reviewed scientic journal [START_REF] Hsu | Accurate quantication of phosphorus intergranular segregation in iron by stem-edx[END_REF].

I.3.3 Synthesized Fe-P-Fe Sandwich Sample

A second comparative study is prepared here. Measurements from four dierent characterization techniques (XPS, WDS, STEM-EDX, APT) were performed on the same specimen. The approach developed in this work was based on a Fe P Fe (iron-phosphorus-iron) sandwich specimen, where phosphorus is present at the interface as a fractional monolayer.

I.3.3.1 Material & Method

The material used as a substrate here is a disk (8 mm diameter, 0.6 mm thick) cut from a model Fe 0.0011 wt%P alloy fabricated in the laboratory. The phosphorus concentration was veried by X-ray uorescence spectrometry and WDS. It should be mentioned that trace amounts of sulfur (< 3 wt ppm) are also present in the model alloy used. The disk was polished down to colloidal silica. To ensure comparable results, a grain large enough for all techniques was identied. This is a compromise of the dierent spatial resolutions of the dierent techniques. A large grain was chosen due to the XPS beam size (selected to be at 400 µm), and the analysed volumes of other techniques were all within this grain.

BETWEEN DIFFERENT TECHNIQUES

The disc was introduced into the ultra-high vacuum chamber (10 -9 mBar) of the VG Thetaprobe XPS by Thermo Fisher Scientic (gure I.3.3 (b)). After surface cleaning using Ar + ions, the disc was in-situ annealed at 500

• C for 1 hour. The temperature was controlled using a combina- tion of a thermocouple in contact with the surface of the sample and a pyrometer. Simultaneous XPS spectra were recorded during the annealing process to ensure phosphorus segregation has been obtained on the surface. After annealing, a quantitative Angular-Resolved X-ray Photoelectron Spectroscopy (AR-XPS) analysis was conducted. The beam size of XPS was chosen to be 400 µm, which corresponds to the orange circle acquisition zone (gure I.3.2) located in one single grain. It is to be noted that sulfur segregation was also observed during annealing, although the sulfur bulk content of the substrate material is below 3 ppm. However, the presence of segregated sulfur does not aect the procedure of phosphorus quantication. As segregation of P and S was observed at the surface, it was decided to quantify both elements in this study.

After XPS analysis, the disk was transferred to the Cameca SX-veFE Electron Micro Probe Analyzer chamber for WDS analysis (gure I.3.3 (c)). The specimen was carried at atmospheric pressure during transfer, so that the formation of a surface oxide layer above the phosphorus segregation layer was inevitable. The problem of this oxide layer is treated later. However it was shown that WDS is not sensitive to nanometric oxide layers in contrast to XPS [START_REF] Christien | Measuring surface and grain boundary segregation using wavelength dispersive X-ray spectroscopy[END_REF]. The multitension method proposed by Christien et al. [START_REF] Christien | Measuring surface and grain boundary segregation using wavelength dispersive X-ray spectroscopy[END_REF] was performed with accelerating voltages of FeS 2 (Fe 46.55 wt% -S 53.45 wt%). The counting time corresponding to one single analysis was 2147 s at the peak position, and half the time at both the background positions.

Once the WDS analyses was completed, a thin layer of iron was deposited on top of the phosphorus and sulfur surface segregation layer at ambient temperature. Gatan Precision Etching Coating System (PECS) with a target of 99.99 wt% Fe (impurities are mainly Mn <800, C <200, P <200, S <150 wt ppm) was used. PECS was set to operate at 8 kV, the vacuum was optimized by ushing with argon and using a cold nger with liquid nitrogen. The pressure in the PECS chamber during deposition was about 10 -3 Pa. At rst, the sample was covered with a shutter so that the target can be cleaned. Then, the deposition was conducted CHAPTER I.3. DIRECT COMPARISON OF INTERGRANULAR SEGREGATION BETWEEN DIFFERENT TECHNIQUES in a sequence of six steps of ve minutes, expecting around 100 nm of iron deposition. To avoid too much heating of the iron target, there was a 20 minute gap between each deposition step.

It was assumed that the deposition process does not induce phosphorus long-range diusion.

At the end, the sandwich specimen was obtained with the surface segregation layer between the substrate and the deposited iron, which was used to mimic grain boundary segregation. For APT analysis, two chunks were extracted within the same grain close to the acquisition zone of WDS (white areas in gure I.3.2) by conventional lift-out method, using a Zeiss XB540 dual beam. Five APT tips were prepared by annular milling from these chunks. In all cases, the interface was nearly perpendicular to the tip axis. Its position in the needle was checked after each milling step using transmission Kikuchi diraction. When distance between interface and tip apex was smaller than 250 nm, the nal milling step was performed using a Ga ion energy of 2 keV to avoid contamination and implantation in the sample. This cleaning step was stopped when the interface was located at less than 50 nm from the tip apex. The interface composition was measured using a local-electrode atom probe 4000X HR from Cameca in voltage mode.

The tips were cooled down to 69K. The pulse fraction was 20%, the pulse repetition rate was 200 kHz, and the detection rate was kept between 0.1 and 0.25%. The phosphorus segregated interface was analyzed successfully in three of the tips. In total, more than 1.5 million atoms were detected for each tip. The software IVAS 3.8 was used for reconstructing the analyzed APT tips. Since the Fe deposited layer and the substrate have dierent evaporation elds, the reconstruction was done considering a constant cone angle, estimated from scanning electron microscope images of the tips. Typical parameters for ferritic steels were used for the reconstruction: image compression factor of 1.6 and eld factor of 4.5. Further data treatment was performed using the GPM 3D software.

It is to be noted that all the analyses are carried within the same initial grain (see gure as that presented in [START_REF] Christien | Measuring surface and grain boundary segregation using wavelength dispersive X-ray spectroscopy[END_REF] in order to extract the phosphorus and sulfur surface concentrations.

I.3.2).

Stratagem

TM is based on the model developed by Pouchou [START_REF] Pouchou | X-Ray Microanalysis of Stratied Specimens[END_REF] for electron probe microanalysis of stratied specimens. Two stratied structures were dened in Stratagem TM : the substrate is dened as iron containing 0.0011 wt%P. No sulfur was considered in the substrate as its content is below 3 wt ppm and has no eect at all on the calculations conducted using Stratagem TM .

For the rst structure, a pure phosphorus surface layer was added on the substrate. For the second structure, a pure sulfur surface layer was added on the substrate. The mass thicknesses of the surface layer in both cases were adjusted so that the calculated curve can best t the experimental points.

In the case of phosphorus segregation in gure I.3.4, the dashed line was calculated using Stratagem TM in the case when the sample surface is not enriched with phosphorus. In this case, the curve obtained depicts the contribution of bulk phosphorus only (0.0011 wt%). The continuous line shows the case where the phosphorus surface segregation mass thickness was adjusted to 16.0 ng/cm 2 , which is equal to 3.11 atom/nm 2 . The same values of I/I std were obtained in the rst and second measurements, which shows that there is no eect of surface contamination from the electron beam. As already mentioned earlier, as the specimen was in contact with room atmosphere between AR-XPS and WDS analyses, so a native oxide layer covering the specimen surface is expected. STEM-EDX observation described later indeed showed a 3 nm thick oxide layer located on top of the segregation layer. An additional curve t by Stratagem TM with a three-layer stratied structure was done, adding a layer of 3 nm Fe 2 O 3 [80, 81] on top of the segregation layer. However, the phosphorus surface mass thickness extracted from the t procedure was unchanged in this case (16.0 ng/cm 2 ), showing no inuence from the native oxide layer on the quantication of the segregated element. In the case of sulfur in gure I.3.5, the WDS measurements were more dicult than for phosphorus. The reason is that a 3 rd order K peak of iron is located close to the S K α peak.

Although its intensity is very low, it results in a signicant overestimation of the background, resulting in underestimation of the S K α peak intensity. This peak could not be completely discarded using the pulse height analyzer of the WDS spectrometer. In addition, attempts in shifting the background measurement position further from the S K α peak also resulted in background overestimation. This spurious iron peak is located on the positive side of the sulfur peak. It should be mentioned that this problem does not exist at 5 kV as this voltage is not high enough to ionize the K level of iron, so that there is no iron spurious peak in this case.

For the measurements conducted at 10 and 15 kV, the method of background measurement was changed between the rst series of measurements (square symbols in gure I.3.5) and the second one (triangle symbols in gure I.3.5) in order to obtain the upper and lower limits of the S peak intensity. For the rst dataset (squares), the conventional method was used, i.e.

the background is measured on both sides of the sulfur peak (+750 and -750). In this case, the S peak intensity is underestimated. In the second dataset (triangles), the background is only measured at the negative side of the sulfur peak (-750), i.e. opposite to the spurious iron peak. However, because of the slope of the background, this results in an underestimation of the background, i.e. overestimation of the S peak intensity. The two datasets obtained at 10 and 15 kV give the upper and lower limits of the sulfur relative intensity. The sulfur surface concentration was adjusted in StratagemTM so that the calculated curve ts the measurements obtained at 5 kV. A sulfur concentration of 21 ng/cm 2 was obtained, which is equal to 3.94 BETWEEN DIFFERENT TECHNIQUES atom/nm 2 . It is to be noted that, as expected, the curve t passes in between the two datasets at 10 and 15 kV. Christien et al. [START_REF] Christien | Measuring surface and grain boundary segregation using wavelength dispersive X-ray spectroscopy[END_REF] conducted a detailed analysis of the statistical accuracy of surface segregation measurements using WDS. Following their approach (see Eq. 6 in [START_REF] Christien | Measuring surface and grain boundary segregation using wavelength dispersive X-ray spectroscopy[END_REF]), the 68% condence intervals of the WDS measurements of P and S segregation were determined at each accelerating voltage. It was found that the statistical accuracy achieved in this study is about 1%. This was permitted by the high beam current (250 nA) and very long counting times [START_REF] Faulkner | Combined quenching and tempering induced phosphorus segregation to grain boundaries in 2• 25Cr1 Mo steel[END_REF]646

S Ref = B sub + γB dep t sub + t dep (I.3.2)
The notation in equation I.3.2 is similar as equation I.2.2. An adjustable parameter γ was needed here to obtain identical background shapes for the GB and reference spectra. This is due to the contribution of oxides to the background shape: the γ parameter makes it possible to have the same oxide contribution in the two spectra. In this case, γ is often between 1.2 and 1.5 so that the deposit spectrum background can t properly with the substrate spectrum background. Pt comes from the FIB preparation and Zr from the EDX detector. However, the presence of these spurious peak do not particularly complicate the P peak extraction. The Ag peaks are not identical on both spectra (silver is a contamination of the deposit). Again this does not aect the P and S peaks.

The net phosphorus K α peak and net sulfur K α peak were obtained by subtracting the reference spectrum from the GB one (gure I. Equations I.2.7 and I.2.8 were used to obtain the phosphorus and sulfur concentration at the interface. The k factor of sulfur k S/F e was not determined experimentally during this study. A value k S/F e = 0.786 from Sheridan et al. [START_REF] Sheridan | Determination of experimental and theoreticalkASi factors for a 200-kV analytical electron microscope[END_REF] was directly used. The mass absorption coecients for P K α , S K α , and Fe K α in pure iron are 1497.95, 1053.57, 63.99 cm/g, respectively.

Among 29 acquisitions in four thin foils, the average of phosphorus and sulfur segregation was not observed in actual grain boundary segregations [START_REF] Akhatova | Investigation of the dependence of phosphorus segregation on grain boundary structure in Fe-P-C alloy: cross comparison between Atom Probe Tomography and Auger Electron Spectroscopy[END_REF]. A possible explanation is that the iron deposit and iron substrate, although close in composition, have dierent microstructures, the deposit being nanocrystalline and highly defective, so that the evaporation eld during analysis changed at the interface. This assumption is supported by the voltage increase when entering into the substrate. This may have aected how the segregated phosphorus evaporated and contributed to delayed evaporation of phosphorous. It was decided to not go further to nd out how and why Cu enrichment was observed due to time constraints and because this result did not inuence the main comparison for phosphorus and sulfur segregations. This result is reported here for future reference. The values obtained are relatively close to each other, considering that all the methods used are very dierent in nature. The minimum and the maximum values obtained dier by 36% for phosphorus and 29% for sulfur. In general, the values obtained from the dierent methods are close to each other, i.e. no particular method was found to give results very dierent from the others. However, it can be observed that the condence intervals do not completely overlap, which suggests that the deviation between the dierent techniques may not be only related to counting statistics. This means that slight systematic biases may exist between the dierent techniques, possibly including the fact that the dierent analyses were not conducted exactly on the same part of the specimen. The results of this case is under the process to be published in a peer-reviewed scientic journal [START_REF] Hsu | Solute Interface Segregation Measurement: Cross Comparison between Four Dierent Analytical Methods[END_REF].

I.3.3.7 Conclusion

Chapter I.4

Part I Summary

In the rst part of this thesis, an overview of the literature on STEM-EDX and its use for intergranular segregation quantication has been presented. Then a new STEM-EDX method to quantify intergranular segregation has been proposed and Monte-Carlo simulations were done to validate the proposed method. At last, two cases were studied to directly compare phosphorus interface quantication results between dierent measuring techniques. The following lists out the dierent important points in this part:

1. The most common technique for intergranular segregation is AES, although it is limited to the intergranular fracture surfaces. STEM-EDX oers dierent advantages over AES and other techniques.

2. It was shown in literature that STEM-EDX has already been used for quantifying intergranular segregation in dierent systems. However, there was a common diculty related to the beam/sample interaction volume and beam broadening eect that requires dierent assumptions.

3. Quantication results from dierent sources may appear in dierent units, while needing some specic hypotheses that are rarely veried. This made direct comparison between dierent sources/techniques nearly impossible.

4. Sample preparation using FIB allows the selection of any grain boundary, so that STEM-EDX analysis is not limited by intergranular fracture nor by the level of embrittlement. 7. The k factor of P in respect to Fe (k P/F e ) was determined experimentally and the ACF was taken into account to enhance the quantication accuracy.

8. Monte-Carlo simulations were performed to further validate the proposed box method.

The ongoing consideration of beam/sample interaction volume and beam broadening effect can be ignored using the box spectrum method coupled with EDX mapping, provided the chosen GB box is wide enough (w > w P = d B , see gure I.2.8).

It was shown that under the proposed acquisition condition and sample storage condition

(under vacuum at room temperature), repeated acquisitions at the same location do not aect the results and the surface eect can be ignored.

10. Two grain boundaries from a Fe-P model alloy were analyzed by STEM-EDX and APT.

The quantication results between the two techniques are reasonably close, showing the validity of the developed method.

11. An analysis of random error from the P counts was conducted, showing that the errors are well within the measure standard deviations. The possible heterogeneity along grain boundary suggested that multiple STEM-EDX acquisitions are needed to determine the phosphorus concentration at one grain boundary.

12. A synthesized Fe-P-Fe sandwich sample was fabricated under the scope of this work to compare phosphorus measurements from dierent techniques. In-situ annealing in XPS chamber was used to generate phosphorus and sulfur surface segregation so that surface techniques AR-XPS and WDS can be used for its characterization. Then, a layer of iron was deposited to create the sandwich structure that mimics a grain boundary. Samples were thereafter extracted by FIB so that STEM-EDX and APT can be used to quantify the induced phosphorus segregation. The values obtained are relatively close to each other, considering that all the methods used are very dierent in nature. This further conrms the validity of the proposed STEM-EDX method.

Part II

Microstructure eect on intergranular segregation

Chapter II.1

Literature Review

After developing a reliable method to quantify intergranular segregation using STEM-EDX, the second objective of this work is to conduct a study on how the microstructure aects intergranular segregation behavior on bainitic and martensitic 16MND5 steel. This chapter provides a literature review rst on the 16MND5 steel, including its fabrication process and microstructure analysis. Then, an overview of the bainitic and martensitic microstructure along with their Orientation Relationships (ORs) and Misorientation Relationships (MRs) was illustrated. Further, the eect of RTE is introduced. The eect of microstructures and other metallurgical factors on RTE and intergranular segregation was given in details. At last, the mechanical aspects of bainitic and martensitic microstructure after RTE is given.

II.1.1 Reactor Pressure Vessel (RPV)

In a pressurized water reactor, the primary water is circulating under high pressure in the core located in the RPV and heated up from around 290

• C to around 325 • C during operation.
The RPV is where the chain reaction takes place and is located in a concrete container called the containment, see gure II.1.1. The RPV is one of the most important part in the nuclear power plant as it determines the lifespan of it. Being a heavy and large component in the power plant, RPV is basically irreplaceable and must remain reliable during the operation lifetime. After the forging process, there are dierent thermal treatments performed on the parts.

The thermal treatment details are extracted from [START_REF] Zhang | Ségrégation intergranulaire du phosphore dans les aciers des cuves des REP[END_REF][START_REF] Cadiou | Evolution métallurgique des pièces forgées de forte épaisseur en acier faiblement allié pour cuves de réacteurs des chaudières nucléaires PWR[END_REF][START_REF] Naudin | Modelisation de la ténaticé de l'acier de cuve REP en presence de zones de ségrégation[END_REF][START_REF] Pous-Romero | Quantitative basis for the structure and properties of a criticallyimportant pressure vessel steel[END_REF]:

The rst round of thermal treatment is called the precaution treatment.

It is a rst austenitization-quenching-tempering sequence after forging which has various roles: grain renement, descaling, reduction of hydrogen content to prevent the formation of defects, hardness mastering for machining,...etc. It is applied on the as-forged shape. The second round of thermal treatment is also an austenitization-quenching-tempering sequence to ensure that the mechanical properties of the shell can meet the standards. It is called the quality treatment.

It is applied on a shape machined in the forged blank. The two rounds of thermal treatment is presented in gure II.1.4.

After these treatments, a nal machining is performed, removing for example 25 mm of material on the inner surface and 15 mm on the outer surface of the shell. This eliminates regions subjected to the highest cooling rates during quenching. Once the dierent shells are prepared, they will be welded together. There is sometimes an intermediate Stress Release

Heat Treatment (SRHT) at 550 • C, then the nal round of SRHT will be performed at 610

• C for 8 hours then furnace cooled with a low controlled rate (for example -30

• C/h) in order not to reintroduce residual stresses by thermal gradients. There are two types of segregations that are very common:

1. The macro-segregations, which aect zones near the ingot axis (negative at bottom, positive at top) and have at least a centimetric size in any direction.

2. The meso-segregations, including V and A segregates: One should note that the micro-and meso-segregation denominations do not meet the usual criterion of physical scale where "micro" is used when a microscope is needed for observation.

It is possible to observe the micro-segregations by bare eye after simple polishing and nital etching due to the quite large size of the dendrites. The given classication corresponds to the mechanism of segregation.

During the forging process, the A-segregates are most likely to appear in between the internal surface to half thickness of the shell. Small micro-segregations, can be observed throughout the thickness of the shell. They are mostly enriched in molybdenum and manganese, and show an increase of hardness [START_REF] Ferguson | The eect of a-type segregation on the toughness properties of a508 class 3 forgings[END_REF]. During the welding steps, several SRHTs are performed to release the stresses induced by welding. Both the base metal, the weld, and the heat aected zones undergo these treatments.

Normally these steps only modify slightly the mechanical properties of the base metal, thanks to a temperature well below the tempering temperature, but in certain cases when the temperature is too high or the duration is too long, this can coarsen the carbides. In another case where the cooling rate is too slow, phosphorus intergranular segregation can also be induced [START_REF] Diawara | Caractérisation quantitative de la microstructure de l'acier 16MND5 des cuves de REP[END_REF][START_REF] Spink | Reversible temper embrittlement of rotor steels[END_REF].

Considering the fabrication process of the ingots, the forming of the shells, and the assembly of the shells, the microstructure of the RPV is heterogeneous. The overall microstructure of RPV shells is reported to be bainitic [9199], but the details and their eects are to be studied. The as-quenched microstructure is expected to present a microstructure gradient: mixture of martensite and bainite, then mixture of bainite and allotriomorphic ferrite from surface to half-thickness. However, dierent studies seem to not fully agree with the denition of the microstructure, and the percentage of allotriomorphic ferrite at dierent locations. Cadiou et al. [START_REF] Cadiou | Evolution métallurgique des pièces forgées de forte épaisseur en acier faiblement allié pour cuves de réacteurs des chaudières nucléaires PWR[END_REF] mentioned that there can be up to 30% of ferrite at half-thickness.

The as-received material has undergone systematic tempering treatment mentioned above.

Many [9199] suggested that the structure is mainly upper bainite and that allotriomorphic ferrite can be present once the location is close to half-thickness (where the cooling rate is the slowest).

In the remaining of the text, martensite or bainite structures denominations may be used instead of tempered martensite and tempered bainite. The material being used after tempering, the study of the aging eects is only relevant for this state. Data pertaining to the as quenched state will be duly identied. by [START_REF] Bec | Etude des transformations en refroidissement continu de produits representatifs de veines sombres observées dans des pièces forgées en acier de type 18MND5[END_REF], where the microstructure is mainly bainitic with some ferrite grain at half-thickness. Figure II.1.12: SA508 Cl.3 steel after chemical etching [START_REF] Lee | Eect of carbide distribution on the fracture toughness in the transition temperature region of an SA 508 steel[END_REF].

In gure II.1.10, the bainite seems to be similar to granular bainite that is proposed by Zajac et al. [START_REF] Zajac | Characterisation and Quantication of Complex Bainitic Microstructures in High and Ultra-High Strength Linepipe Steels[END_REF] (see gure II.1.20). The formation of granular bainite has been explained as lack of carbon [START_REF] Zajac | Characterisation and Quantication of Complex Bainitic Microstructures in High and Ultra-High Strength Linepipe Steels[END_REF] or high silicon content [START_REF] Bhadeshia | Bainite in steels: theory and practice[END_REF], which is not the case for 16MND5 type steel (Si 0.1-0.3 wt%). For the moment, most authors agree that the microstructure is mainly upper bainite for as-received 16MND5 steel.

According to the "estimated" cooling rates mentioned in [START_REF] Poitrault | Proprietés metallurgiques et mécaniques des viroles de coeur 900 et 1300 MW -Etude des vitesses de refroidissement[END_REF] and [START_REF] Ahn | Application of intercritical heat treatment to improve toughness of SA508 Cl.3 reactor pressure vessel steel[END_REF], the microstructure of RPV steel is mainly bainitic, with ferrite appearing from 1/4 thickness to half-thickness.

However, this does not t perfectly with the CCT diagram in gure II.1.8. It is to be noted that the industrial products are not homogeneous. With dierent chemical composition and grain size, these can all aect the hardenability of the RPV steel. The dierent cooling rate studied on one CCT diagram only provides an approximation. Also, the cooling rate is constant when constructing the CCT diagram, whereas the cooling rate decreases when temperature decreases during the quenching of a shell. Moreover, the cooling rates and the materials presented in CHAPTER II.1. LITERATURE REVIEW dierent studies can be based on dierent thicknesses. This is also a reason of the dierent reported microstructures and cooling rates.

Many studies of RPV steels redid austenitization followed by dierent cooling rates in order to adapt the microstructure to their studies. In can be summarized that when the cooling rate is intermediate (> 10 • C/s), the microstructure is a mixture of martensite and bainite. When the cooling rate is slow (0.5 • C/s), the structure is mainly bainitic (which is upper bainite according to the as-received microstructure studied above). Then when the cooling rate is even slower, allotriomorphic ferrite appears. Studies also modify the austenitization temperature so that the prior austenite grain size can be modied. This is often seen in studies for simulated heat aected zones with coarse or ne grains.

II.1.2 Bainitic & Martensitic Microstructures

The microstructure of a low-alloy steel is dened by how the dierent phases are arranged and the grain morphology. In the case of 16MND5 steel for RPV, the most common microstructures is bainite, but martensitic and ferritic zones can be encountered locally. In both cases, there are dierent ways to describe the microstructures. The following sections provides a review of the dierent denitions in the literature.

II.1.2.1 Martensite by Morphology

Martensitic transformation is a transformation that only includes short range displacements but no long range diusion. This is why the martensitic transformation only depends on the temperature instead of being a function of time. In a CCT diagram (see gure II.1.8), the lines Ms (martensite start) and Mf (martensite nish) indicate where the martensitic transformation begins and ends. Pure martensite can only be achieved at rapid cooling rates, for instance, higher than 100 • C/s in gure II.1.8, which is rarely done in industrial products. However, as mentioned previously, it is possible to have martensitic microstructure due to welding. During welding, the steel can be described as being quenched in metal. The cooling rate exhibits a gradient depending on the distance to the weld. Also, the meso-segregated zones (A-segregates) experience a higher hardenability due to the dierent chemical composition from the base metal.

At a ner scale, micro-segregations are also prone to martensitic transformation due to higher contents in alloying elements like manganese and molybdenum.

Martensitic structures in iron-based alloy can have dierent morphologies, i.e. lath, buttery, lenticular and thin-plate. In the case of 16MND5 type steel, the martensitic microstructure is in the form of lath due to the low carbon content, see gure II.1.13. The morphology of bainite was rst proposed by Mehl [START_REF] Mehl | Hardenability of alloy steels[END_REF]. She categorized bainite into upper and lower bainite. She described the microstructure of upper bainite as a combination of parallel, elongated ferrite grains separated by carbides in between them. The carbides are most commonly cementite (Fe 3 C) that precipitated from carbon enriched austenite during the transformation. Bhadeshia [START_REF] Bhadeshia | Bainite in steels: theory and practice[END_REF] mentioned that although dierent types of carbides can precipitate in upper bainite, they often transform into cementite during the evolution or during isothermal tempering. At last, cementite is the most common carbide found in upper bainites.

On the other hand, Mehl's denition of lower bainite is still widely used today [START_REF] Mehl | Hardenability of alloy steels[END_REF]: lower bainite has a structure of laminated ferrite in acicular shape with two kinds of carbides:

1. Interlath carbides that appear in between the acicular ferrite grains. They are precipitations from austenite during transformation which is rich in carbon. These interlath carbides are cementite (Fe 3 C).

2. Carbides in thin plate shapes that precipitates in the saturated ferrite grains, most of them have an angle of 55

• to 60

• to the elongated direction of ferrite grains. These carbides present one single crystallography orientation variant of the ferrite grains. These carbides in ferrite grains are not always cementite but can be carbides in other forms [START_REF] Bhadeshia | Bainite in steels: theory and practice[END_REF]. Lower bainite has a very similar microstructure as tempered martensite in low carbon alloys.

Tempered martensite is also a ferritic microstructure that includes dierent kinds of inter-or intra-lath carbides. One of their dierences that has been noted is that carbides in tempered martensite are normally present as several dierent variants [START_REF] Bhadeshia | Bainite in steels: theory and practice[END_REF].

Based on the denition by Mehl in 1939, others have proposed dierent categorizations of bainitic microstructures. Aaronson et al. [START_REF] Reynolds | A Summary of the Present Diffusionist Views on Bainite[END_REF] has extended the denition given by Mehl to include more kinds of bainite morphology, see gure II.1.17. The description of Mehl can be found in gure II.1.17 (c) and (d). Granular bainite is composed of irregular ferrite grains (not lath-shape) with a second phase distributed in between them. According to them, granular bainite is formed due to lack of carbon. Thus the second phase indicated previously can be any transformation product that may form from the remaining austenite during evolution. Comparing to the lath-shaped bainite, which is fairly well-dened, the main dierence for granular bainite is the lack of cementite.

II.1.2.3 Orientation Relation between Austenite, Martensite, and Bainite

The OR between prior austenite and martensite is not random. Bain [START_REF] Bain | The nature of martensite, trans[END_REF] The OR that Bain proposed results in an elastic strain so high that this relationship does

111 γ //110 α < 211 > γ // < 110 > α 12
Greninger-Troiano (GT) [START_REF] Greninger | Kinetics of the austenite to martensite transformation in steel[END_REF] 111 γ at 1

• of 110 α < 211 > γ at 2.5 • of < 110 > α 24
The ORs are based on dierent crystallographic planes and directions, which is why the number of variants are dierent. For KS OR, there are four possible close-packed planes of type {111} γ and three close-packed directions possible of type ⟨110⟩ γ among the close-packed planes with two possibilities to be parallel to ⟨111⟩ α . Similar to KS OR, the NW OR presents also four possible close-packed planes and three close-packed directions but only one possibility CHAPTER II.1. LITERATURE REVIEW to be parallel to ⟨110⟩ α . The same explanations can be applied to GT OR for the number of variants [START_REF] Lubin | Etude des mécanismes de la transformation de phase bainitique dans les aciers bas carbone[END_REF][START_REF] Slama | Étude multi-échelle et in situ des évolutions microstructurales en conditions isothermes d'aciers bainitiques en lattes[END_REF]. The relations of KS and NW are illustrated in gure II.1.22 [START_REF] Lubin | Etude des mécanismes de la transformation de phase bainitique dans les aciers bas carbone[END_REF]. ORs exist between the mother phase (austenite) and the child phase (martensite/bainite).

Although the phase transformation do not perfectly obey the theoretical ORs, the grain boundaries in the child phase also present certain characteristics.

For crystalline materials, grain boundaries are 2D crystal defects where the adjacent lattices with dierent orientation meet. There are dierent ways to categorize grain boundaries, for example, the ve degrees of freedom consist of the misorientation, two directions of the rotation axis, and two grain boundary planes, normally noted as θ[uvw]{h

1 k 1 l 1 }{h 2 k 2 l 2 }.
Here, the grain boundaries of the child phase can also present MRs, i.e. the MR between packet and block boundaries, that can be described by a misorientation angle and a rotation • . Also, there are twin blocks in that form from the same {111} γ in upper bainite.

Park et al. [START_REF] Park | Eects of boundary characteristics on resistance to temper embrittlement and segregation behavior of NiCrMo low alloy steel[END_REF] observed A508 steel and found that the Σ3 are mainly the grain boundaries with misorientations between 55

• -60

• in martensite, but other random high misorientation angle grain boundaries presents in bainite. Dierent from upper bainite, martensite packet often presents with 60

• ⟨111⟩ α twin relations [START_REF] Park | Eects of boundary characteristics on resistance to temper embrittlement and segregation behavior of NiCrMo low alloy steel[END_REF][START_REF] Bouyne | Use of EBSD technique to examine microstructure and cracking in a bainitic steel[END_REF]. Martensite blocks are high intricate but twin related grain boundaries that are formed from the same {111} γ so that shape strain can be reduced during phase transformation [START_REF] Morito | The morphology and crystallography of lath martensite in Fe-C alloys[END_REF].

Gourgues et al. [START_REF] Gourgues | Electron backscattering diraction study of acicular ferrite, bainite, and martensite steel microstructures[END_REF] also concluded that the upper bainite has a MR closer to NW/NW and that martensite has a MR closer to KS/KS. Bhadeshia et al. [START_REF] Bhadeshia | Bainite in steels: theory and practice[END_REF] conrmed that tempered bai-CHAPTER II.1. LITERATURE REVIEW nite also has NW/NW MR as there is no shape strain 3 during the slower phase transformation.

Morito et al. [START_REF] Morito | The morphology and crystallography of lath martensite in alloy steels[END_REF] suggested that grain boundaries in low carbon martensite follows KS/KS MR. Based on the block and packet boundaries indicated in gure II.1.24 the misorientation angle range of prior austenite grain boundaries can be deduced to be between 21.5 • and 46.5

• .

The lath boundaries in martensite and bainite are less discussed, they are mostly boundaries that have small misorientations. Kim et al. [START_REF] Kim | Characterization of boundaries and determination of eective grain size in mn-mo-ni low alloy steel from the view of misorientation[END_REF] found that in A508 steel, the lath in martensite have misorientations between 0.5 • -6.3

• .

II.1.3 Intergranular Segregation in Martensite & Bainite

Tempering is a thermal treatment applied for decreasing hardness and increasing toughness of the material. It is almost systematically applied to industrial pieces after quenching to optimize and homogenize their properties. Tempering is historically related to the heat treatment applied to martensitic steels. The steel is held isothermally at a temperature where austenite cannot form (typically between 400

• C and 650

• C), so that its microstructure evolves and mechanical properties change. Depending on the duration of tempering, the microstructure evolution can be described in the following stages [START_REF] Bhadeshia | Bainite in steels: theory and practice[END_REF][START_REF] Speich | Tempering of steel[END_REF]:

1. The excessive carbon in the solid solution segregates to the defects or forms clusters.

2. All excessive carbon will then precipitate into stable precipitates (commonly cementite) and all retained austenite will dissolve. Song et al. [START_REF] Song | Atomicscale investigation of ε and θ precipitates in bainite in 100Cr6 bearing steel by atom probe tomography and ab initio calculations[END_REF] observed that cementite forms in and SRHT is to obtain better mechanical properties, mainly fracture properties, than the as-quenched microstructure, but this process may also induces phosphorus intergranular segregation which may contribute to opposite eects.

3 Strain energy that opposes the transformation. [START_REF] Kameda | Combined eects of phosphorus segregation and partial intergranular fracture on the ductilebrittle transition temperature in structural alloy steels[END_REF] Step cooling in gure II.1.25 is an accelerated thermal aging treatment. The increase in DBTT due to RTE is often related to embrittle elements segregating to grain boundaries, which is also why the fracture mode changes from cleavage to intergranular fracture.

Intergranular segregation corresponds to solute atoms gathering as fractional monolayers at grain boundaries. The driving force of this phenomenon is to decrease the interfacial energy.

Intergranular segregation of various impurities can be observed in common metals and their alloys. For example, sulfur and phosphorus are common impurities that segregate at grain boundaries. RTE is a non-hardening eect that does not inuence the hardness and the yield stress [127129].

Based on gure II.1.25, RPV steel is subjected to both temper embrittlement and thermal aging during the fabrication process and operation lifetime. Phosphorus intergranular segregation in 16MND5 type steel has been widely studied [START_REF] Shen | Eect of solute grain boundary segregation and hardness on the ductile-to-brittle transition for a CrMo low-alloy steel[END_REF][START_REF] Lejcek | Grain boundary segregation in metals[END_REF][START_REF] Doig | Microanalysis of Grain Boundary Segregation in Embrittled Iron-3wt% Nickel Alloys Using STEM[END_REF][START_REF] Park | Eects of boundary characteristics on resistance to temper embrittlement and segregation behavior of NiCrMo low alloy steel[END_REF]. Evidences were conrmed in both western and eastern RPV steels [START_REF] Raoul | Eect of microstructure on the susceptibility of a 533 steel to temper embrittlement[END_REF][START_REF] Miller | Characterization of phosphorus segregation in neutron-irradiated Russian pressure vessel steel weld[END_REF][START_REF] Gurovich | Assessment of relative contributions from dierent mechanisms to radiation embrittlement of reactor pressure vessel steels[END_REF]. Miller et al. [START_REF] Miller | Characterization of phosphorus segregation in neutron-irradiated Russian pressure vessel steel weld[END_REF] mentioned that phosphorus intergranular segregation coverage in A533B steels after SRHT at 620 • C, whose phosphorus bulk content is 110 wt ppm, is about 5% before service and 7% after 30 years of thermal aging at 290

• C. In pressurized water reactors, higher temperatures of about 325

• C (outlet temperatre of the reactor) and 345

• C (pressurizer) are encountered, which can lead to higher segregation levels.

There are dierent thermal factors that can inuence the RTE process. It is shown that at a given temperature, the phosphorus grain boundary concentration increases as the aging time increases [START_REF] Nakata | Grain Boundary Phosphorus Segregation in Thermally Aged Low Alloy Steels[END_REF][START_REF] Gurovich | Inuence of structural parameters on the tendency of VVER-1000 reactor pressure vessel steel to temper embrittlement[END_REF]. Also, Spink et al. [START_REF] Spink | Reversible temper embrittlement of rotor steels[END_REF] shows that when the cooling rate after tempering decreases, the Fracture Appearance Transition Temperature (FATT) increases, indicating that the level of RTE increases when the cooling rate decreases.

Although tempering and thermal aging treatment can cause undesired eects, the term reversible in RTE indicates that the degraded mechanical properties can be restored. Viswanathan et al. [START_REF] Viswanathan | Temper embrittlement in a Ni-Cr steel containing phosphorus as impurity[END_REF] have shown that if applying a thermal treatment at 620 • C followed with quick cool- ing, the decreased toughness can be restored. However, the fracture mode remained as a mixture of cleavage and intergranular fracture for the high phosphorus content material in their study regardless of the restored toughness.

CHAPTER

Solute Concentration

Under the same thermal cycle, higher phosphorus bulk concentration induces more phosphorus intergranular segregation [START_REF] Nakata | Grain Boundary Phosphorus Segregation in Thermally Aged Low Alloy Steels[END_REF]. • C. On the other hand, they have observed DBTT shift on the A533B weld with 0.008 wt%P after aging one year at 400 • C. Viswanathan et al. [START_REF] Viswanathan | Temper embrittlement in a Ni-Cr steel containing phosphorus as impurity[END_REF] worked on a low alloy steel with only 0.0005 wt%P and showed that no embrittlement was induced after an accelerated step cooling treatment 5 . This indicates that there may be a critical phosphorus bulk concentration (here 50 ppm) or a critical phosphorus grain boundary concentration for a steel to be susceptible to RTE.

Solute Interactions

When working on model Fe-P alloys, the embrittling eect due to phosphorus intergranular segregation is obvious [START_REF] Erhart | Equilibrium segregation of phosphorus at grain boundaries of FeP, FeCP, FeCrP, and FeCrCP alloys[END_REF]. However, once the low alloy steel contains other solutes, the interaction between them and phosphorus can have an eect on the intergranular segregation behavior.

Suggested by Briant et al. [START_REF] Briant | Intergranular failure in steel: the role of grain-boundary composition[END_REF] CHAPTER II.1. LITERATURE REVIEW element (phosphorus in this study). They suggested that adding Mn in Ni-Cr steels will enhance P intergranular segregation 6 . Also, Mn is known to stabilize cementite (Fe 3 C) [137], which is a common second phase in bainitic steels. This reduces the availability of carbon for segregation.

Mulford et al. [START_REF] Mulford | Temper embrittlement of Ni-Cr Steels by phosphorus[END_REF] suggested that Ni co-segregates with P at grain boundaries in Ni-Cr steels and Ohtani et al. [START_REF] Ohtani | Temper embrittlement of Ni-Cr steel by antimony I. Embrittlement at low carbon concentration[END_REF] further found that Ni itself does not increase the DBTT of Sb2 alloy.

In other words, Ni grain boundary segregation should not induce embrittlement.

As suggested by many authors, sulfur, silicon and carbon are solutes that are in competition with phosphorus for grain boundary segregation [START_REF] Briant | Intergranular failure in steel: the role of grain-boundary composition[END_REF]140142]. While sulfur and silicon are known to be embrittle elements that can also induce intergranular segregation, carbon is known to enhance grain boundary cohesion. Erhart and Grabke [START_REF] Erhart | Equilibrium segregation of phosphorus at grain boundaries of FeP, FeCP, FeCrP, and FeCrCP alloys[END_REF] show that the intergranular fracture proportion decreases as the carbon bulk content increases in Fe-0.17 Although carbon acts as an inhibitor for intergranular fracture, it is shown that when strong carbide formers are present, the eect of carbon intergranular segregation can decreased significantly. For example, chromium is shown to have contradictory eects depending on whether chromium carbides are formed. When carbides are formed, chromium is considered to increase embrittlement since the available carbon content to compete with phosphorus segregation is decreased. Although chromium is also reported to attract phosphorus intergranular segregation [START_REF] Ustinovshikov | Eects of alloying elements, impurities, and carbon on temper embrittlement of steels[END_REF], the interaction between chromium and carbon seems more vital.

Similarly, molybdenum is also reported to have such contradictory eect depending if molybdenum carbides are formed [START_REF] Guttmann | Thermochemical Interactions Versus Site Competition in Grain Boundary Segregation and Embrittlement in Multicomponent Systems[END_REF][START_REF] Mcmahon | The inuence of Mo on P-induced temper embrittlement in Ni-Cr steel[END_REF][START_REF] Grabke | Eects of the alloying elements Ti, Nb, Mo and V on the grain boundary segregation of P in iron and steels[END_REF]. Figure II.1.29 shows that molybdenum content has nearly no eect on phosphorus intergranular segregation in carbon-free Fe-Mo-P alloy [START_REF] Grabke | Eects of the alloying elements Ti, Nb, Mo and V on the grain boundary segregation of P in iron and steels[END_REF].

Also, they showed that phosphorus can gather around Mo 2 C precipitates [144]. Dumoulin et al. [START_REF] Dumoulin | Role of molybdenum in phosphorus-induced temper embrittlement[END_REF] suggested that this contradictory relationship between molybdenum and phosphorus depends on the chemical composition, the aging temperature, and aging duration.

6 Original reference non accessible.

Grain Boundary Structure

One of the most simple grain boundary categorization is based merely on misorientation angle, where grain boundaries are categorized as Low Angle Grain Boundaries (LAGBs) and HAGBs. Typically, grain boundaries with misorientation angles smaller than 15

• are considered LAGBs as they can be regarded as an array of dislocations. Grain boundaries with misorientation angles higher than 15

• are considered HAGBs where their structures are less well-dened.

A common model to describe HAGBs is the Coincidence Site Lattice (CSL) model. Studies [START_REF] Lejcek | Grain boundary segregation in metals[END_REF] have shown that grain boundary energy is low when the coincidence of atom positions of the adjacent grains is high as there are less bonds that are broken along the boundary [START_REF] Fletcher | Crystal interface modelsa critical survey[END_REF].

The density of coincidence Σ is dened as:

Σ =

Total numbers of lattice sites in an elementary cell # of coincidence sites in an elementary cell (II.1.1)

For example, Σ3 means that one site out of three are in coincidence in the two adjacent grains. The HAGBs that can be identied using the CSL model are considered to be special grain boundaries due to their lower energy.

Based on the dierent categorizations, dierent authors tried to relate intergranular segregation measurements and grain boundary structures. Suzuki et al. [START_REF] Suzuki | Phosphorus segregation related to the grain boundary structure in an Fe-P alloy[END_REF] worked on Fe-1 wt%P alloy and suggested that the phosphorus intergranular segregations is higher at HAGBs than at LAGBs. Furthermore, the segregation level is higher at grain boundaries with high index grain boundary planes, see gure II Ogura et al. [START_REF] Ogura | Structure-dependent intergranular segregation of phosphorus in austenite in a Ni-Cr steel[END_REF] measured groove depth after picric etching on austenitic Ni-Cr steel (0.06 wt%P). They show that the phosphorus intergranular segregation is not homogeneous in different grain boundaries and that there is no phosphorus segregation at coherent twin grain boundaries. They further proposed a simplied relationship between phosphorus intergranular segregation and misorientation [START_REF] Ogura | Dependence of phosphorus segregation on grain boundary crystallography in an Fe Ni Cr alloy[END_REF]:

1. LAGBs (θ < 12 The conclusions between Suzuki [START_REF] Suzuki | Phosphorus segregation related to the grain boundary structure in an Fe-P alloy[END_REF] and Ogura [START_REF] Ogura | Dependence of phosphorus segregation on grain boundary crystallography in an Fe Ni Cr alloy[END_REF] are rather similar: HAGBs have higher phosphorus segregation than LAGBs. Williams et al. [START_REF] Williams | Quantitative characterization of the composition, thickness and orientation of thin lms in the analytical electron microscope[END_REF] observed that Σ3 are less brittle than other grain boundaries under the same thermal treatment. Leifeng et al. [START_REF] Zhang | Investigation of solute segregation behavior using a correlative EBSD/TKD/APT methodology in a 16MND5 weld[END_REF] measured phosphorus intergranular segregation using APT for 16MND5 weld. They also concluded that the phosphorus segregation level is higher at HAGBs than at LAGBs, and that Σ3 has lower segregation level than other general HAGBs. As for grain boundary planes, when both grain boundary planes have high indices, the segregation level is higher, and vise-versa. Their results conrm the conclusions from Ogura [START_REF] Ogura | Dependence of phosphorus segregation on grain boundary crystallography in an Fe Ni Cr alloy[END_REF].

CHAPTER II.1. LITERATURE REVIEW

There are other interfaces where phosphorus intergranular segregation has been reported.

Lundin et al. [START_REF] Lundin | Atom-probe study of phosphorus segregation to the carbide/matrix interface in an aged 9% chromium steel[END_REF] observed phosphorus intergranular segregation at M 23 C 6 /matrix interface in 9%Cr steel. Gurovich et al. [START_REF] Gurovich | Inuence of structural parameters on the tendency of VVER-1000 reactor pressure vessel steel to temper embrittlement[END_REF] also measured phosphorus intergranular segregation at M 23 C 6 /matrix interface in Russian RPV steel. Islam et al. [127] showed severe grooving at grain boundaries and precipitate/matrix interface after thermal aging at 520

• for 96 h for 2.25Cr- 1Mo steel. On the other hand, dierent studies [START_REF] Kameda | Combined eects of phosphorus segregation and partial intergranular fracture on the ductilebrittle transition temperature in structural alloy steels[END_REF][START_REF] Doig | Segregation of embrittling elements to prior austenite grain boundaries in 2•25Cr1 Mo steel[END_REF][START_REF] Zhai | Segregation behavior of phosphorus in the heat-aected zone of an A533B/A182 dissimilar weld joint before and after simulated thermal aging[END_REF] have also shown that phosphorus segregation at molybdenum enriched carbides at grain boundaries. However, this work focuses on grain boundary segregation and segregation at other types of interfaces is out of the scope of this study.

Up to date, the relationship between intergranular segregation and grain boundary structure showed certain tendencies. However, there are no detailed relationships between phosphorus intergranular segregation and a given grain boundary structure, i.e. one cannot estimate phosphorus grain boundary concentration when only provided with the grain boundary structure.

Tempered Martensite & Tempered Bainite

Tempered martensite and tempered bainite are two commonly observed microstructures in RPV steels. Based on dierent qualitative and quantitative measurements, the eect of microstructure is reported by dierent authors. Perhacova et al. [START_REF] Perhá£ová | Microstructural aspects of phosphorus grain boundary segregation in low alloy steels[END_REF] studied a metal with a mixture of martensite and bainite, then suggested that the intergranular segregation is slower in the as-quenched microstructure than in the as-tempered microstructure. This would be due to the fact that tempering decreases the dislocation density while dislocations act like traps for segregating solutes. However, they did not investigate the specic segregation behaviors of martensitic and bainitic areas. They have showed negative relationship between toughness and intergranular fracture percentage.

Studies have shown that phosphorus intergranular segregation prioritizes prior austenite grain boundaries and that martensite has a higher susceptibility to grain boundary segregation than bainite [START_REF] Raoul | Eect of microstructure on the susceptibility of a 533 steel to temper embrittlement[END_REF][START_REF] Park | Eects of boundary characteristics on resistance to temper embrittlement and segregation behavior of NiCrMo low alloy steel[END_REF][START_REF] Zhang | Cleavage fracture in bainitic and martensitic microstructures[END_REF][START_REF] Yang | Eect of microstructure on the impact toughness and temper embrittlement of SA508Gr.4N steel for advanced pressure vessel materials[END_REF]. Viswanathan et al. [START_REF] Viswanathan | Eect of microstructure on the temper embrittlement of Cr-Mo-V steels[END_REF] worked on Cr-Mo-V steel (250 wt ppm P) and found that after the same tempering time, the phosphorus peak height ratio is higher in martensite than in bainite. Raoul et al. [START_REF] Raoul | Eect of microstructure on the susceptibility of a 533 steel to temper embrittlement[END_REF] showed that martensitic microstructure is more sensible to intergranular fracture than bainitic microstructure for A533B steel. They suggested that this observation is related to dierent behavior of phosphorus segregation in the two microstructures. The hypothesis is that bainite has non-prior austenite grain boundaries that can trap phosphorus and prevents it from segregation to prior austenite grain boundaries. Reversely, martensite non-prior austenite grain boundaries do not trap phosphorus and it segregates mainly at prior austenite grain boundaries. In other words, the trapping eect of phosphorus in bainite is more important than in martensite.

In the study of Park et al. [START_REF] Park | Eects of boundary characteristics on resistance to temper embrittlement and segregation behavior of NiCrMo low alloy steel[END_REF], they partially conrmed the reasoning in [START_REF] Raoul | Eect of microstructure on the susceptibility of a 533 steel to temper embrittlement[END_REF]. They showed that under the same thermal treatment, phosphorus grain boundary concentration is higher in martensite (10.7%) than in bainite (7.1%) (AES results without details of peak height ratio CHAPTER II.1. LITERATURE REVIEW interpretation). Also, they performed picric acid etching on bainitic and martensitic A508 Gr.

4N Ni-Cr-Mo steels, showing that phosphorus segregation appears also at packet boundaries in fully bainitic microstructure. They concluded that phosphorus intergranular segregation prefers HAGBs and that bainite has more random high misoriented packet boundaries with no twin relations than martensite, which happens to have mainly Σ3 as high angle boundaries. Thus, bainitic microstructure has more types of grain boundaries where phosphorus segregates than martensitic microstructure.

It is to be noted that most of the intergranular segregation quantication are based on AES results [START_REF] Lejcek | Grain boundary segregation in metals[END_REF]. With the dierent limitations, the quantitative measurements are only on the intergranular fracture surfaces, which are often believed to be prior austenite grain boundaries.

Other characterization techniques that can be used to measure intergranular segregation and compare with STEM-EDX were already presented in section I.1.3.

There are few measurements of phosphorus intergranular segregation on non-prior-austenitic grain boundaries. Miller et al. [START_REF] Miller | Characterization of phosphorus segregation in neutron-irradiated Russian pressure vessel steel weld[END_REF] has discovered phosphorus intergranular segregation in lath boundaries by atom probe eld ion microscopy. Doig et al. [START_REF] Doig | Segregation of embrittling elements to prior austenite grain boundaries in 2•25Cr1 Mo steel[END_REF] also suggested that there are amounts of alloying elements segregated at bainite lath boundaries, but the amount is four times smaller than at previous austenite grain boundaries. Leifeng et al. [START_REF] Zhang | Investigation of solute segregation behavior using a correlative EBSD/TKD/APT methodology in a 16MND5 weld[END_REF] analyzed 16MND5 weld and showed phosphorus segregation at all sorts of grain boundaries.

In the literature, there are mainly evidences that phosphorus intergranular segregation prefers prior austenite grain boundaries in both martensitic and bainitic microstructure. The current hypothesis is that bainitic microstructure contains other types of grain boundaries (mainly high misorientation angle boundaries) that trap phosphorus from segregating at prior austenite grain boundaries. This is suppose to be the reason why martensitic microstructure is more susceptible to RTE than bainitic microstructure.

II.1.3.3 Thermodynamics and Kinetics Calculations of Intergranular Segregation

There are dierent models that describe intergranular segregation after thermal aging. The thermodynamic models give the equilibrium concentration depending on the phosphorus bulk content, temperature and segregation free energy. The kinetic models predicts the time variations of segregation until reaching equilibrium.

Du Plessis Thermodynamic Model for Binary System

McLean and Guttmann provided the rst thermodynamic models of segregation [START_REF] Mclean | Grain boundaries in metals. Monographs on the physics and chemistry of materials[END_REF][START_REF] Johnson | Interfacial Segregation: Papers Presented at a Seminar of the Materials Science Division of the American Society for Metals[END_REF].

Later on, Du Plessis [START_REF] Plessis | A model for surface segregation in multicomponent alloyspart I: Equilibrium segregation[END_REF] proposed another thermodynamic model based on minimizing interface energy. His model can be used for interfacial segregation when the solute atoms occupy substitution sites. Consider a system of m components (i from 1 to m) in a semi-innite volume CHAPTER II.1. LITERATURE REVIEW and an interface. The system free energy can be presented as:

G = G v + γω (II.1.2)
Where G v is the system free energy without the interface, γ is the interface energy, and ω is the molar surface in m 2 per mole. The interface energy is given as:

γ = Σ m i=1 X ϕ i (µ ϕ i -µ v i ) ω (II.1.3)
Where X ϕ i is the atomic fraction of component i in the interface, µ ϕ i is the chemical potential of component i in the interface, and µ v i is the chemical potential of component i in the volume. At equilibrium, G v is independent from the interface composition, thus

∂G ∂X ϕ i = ∂γ ∂X ϕ i = 0 ∀i (II.1.4)
In considering a binary system, equation II.1.4 can be written as:

(µ ϕ -µ v ) -(µ ϕ M -µ v M ) = 0 (II.1.5)
Where µ ϕ is the chemical potential of the solute in interface, µ v is the chemical potential of the solute in volume, µ ϕ M is the chemical potential of metal solvent in interface, and µ v M is the chemical potential of the metal solvent in volume.

Under the hypothesis of this binary system being ideal solution, where the chemical potential can be expressed as µ = µ 0 + RT ln X (R is the ideal gas constant and T is the absolute temperature in Kelvin), equation II.1.5 can be written as:

X ϕ 1 -X ϕ = X v 1 -X v exp(- ∆G kT ) (II.1.6) ∆G = -µ 0ϕ + µ 0v + µ 0ϕ M -µ 0v M
Where X ϕ is the fractional monolayer covered by segregates, X v is the bulk solute molar fraction, and ∆G is the segregation free energy per mole of solute.

In many cases, the saturation solute concentration X ϕ max at the interface in below 1, equation II.1.6 is written as two ways:

X ϕ X ϕ max -X ϕ = X v 1 -X v exp(- ∆G kT ) (II.1.7) θ 1 -θ = X v 1 -X v exp(- ∆G kT ) (II.1.8)
where θ = X ϕ /X ϕ max is called the coverage ratio of the intergranular segregation and the segregation free energy of phosphorus is dened as ∆G = ∆H -T ∆S.

Based on equation II.1.7, the unit of the dierent concentrations has to be the same. If the X ϕ max is given in the fraction of a monolayer, the result of X ϕ is also in fraction of a monolayer.

It was considered that the surface concentration (number of atoms per unit surface) is the best unit to provide quantication of intergranular segregation. This is because surface concentration does not require hypotheses on the Miller indexes of the segregation plane. Grain Size Eect on the Thermodynamic Model Grain size is one of the factors that have a direct eect on intergranular segregation. When the grain size decreases, there are more surfaces to cover in a xed volume, while the phosphorus bulk concentration remains constant.

It can be explained as when the grain size decreases below a certain value, the equilibrium phosphorus concentration decrease accordingly since the bulk phosphorus concentration is not high enough to cover all grain boundaries with the same amount as when the grain size is larger.

The thermodynamic model of equation II.1.7 should be adapted as [START_REF] Saindrenan | Endommagement interfacial des métaux: Ségrégation interfaciale et conséquences[END_REF]:

X ϕ X ϕ max -X ϕ = X v -f X ϕ 1 -X v exp(- ∆G kT ) (II.1.9)
where f is the fraction of the interfaces dened as the surface of grain boundaries in unit volume. When considering cubic grains f can be expressed as 3d 2 /d 3 . Equation II.1.9 can then be written as:

F ϕ F ϕ max -F ϕ = F v - 3 d F ϕ F tot -F v exp(- ∆G kT ) (II.1.10)
The change of notation from X to F compared to equation II.1.7 is to dierence the unit change from molar fraction to surface or volume concentration. F ϕ max is the saturation concen- tration at grain boundary, F ϕ is the concentration at grain boundary, F v is the bulk concentration, and F tot is the total atoms in the volume in atom/nm 3 . In the example for BCC iron, F tot = 85.5 atom/nm 3 . At a given temperature (325

• C for example), gure II.1.32 shows how the grain size aects intergranular segregation at equilibrium depending on the bulk phosphorus concentration. the segregation free energy used here is -39.35 kg/mol and the grain boundary saturation concentration F ϕ max is 17.29 atom/nm 2 , which is the planer density of ( 110) in BCC iron. The blue curve (%P = 80 ppm) in gure II.1.32 has a similar phosphorus bulk concentration as RPV steel. It can be seen that the equilibrium phosphorus concentration at grain boundaries depends on the grain size. In this case, phosphorus intergranular segregation concentration is constant value when the grain size exceeds ≈10 µm, but then decreases when the grain size is smaller. Here, the denition of grain size is vague. In a bainitic and martensitic steel, the grain size can be referred to as prior austenite grain size, packet size, or other smaller units. In all cases, the grain size can act as a factor that traps phosphorus and can aect the phosphorus segregation concentration.

Guttmann Model for Multicomponent System

Based on the binary model above, Guttmann [START_REF] Guttmann | Equilibrium segregation in a ternary solution: A model for temper embrittlement[END_REF] has developed a model to describe solute intergranular segregation for multicomponant system. The model assumed that all solute atoms that segregate at the grain boundary occupy the same site with or without interactions between each other. For intergranular segregation of a solute i (with m -1 solutes, i = 1, 2, ..., m -1 )in matrix M , the general expression can be written as:

X ϕ i X ϕ,max i -Σ m-1 X ϕ i = X v i 1 -Σ m-1 X v i exp(- ∆G i kT ) (II.1.15)
where X ϕ i and X v i are the concentration of solute i at grain boundary and in bulk, respectively, X ϕ,max i is the maximum concentration of solute i at grain boundary, and ∆G i is the segregation free energy per mole of solute i.

Considering the dierent solute interactions and the interactions between the solute and matrix, ∆G i is dened as:

∆G i = ∆H i -T ∆S i -2α iM (X ϕ i -X v i ) + Σ m-1 α ij (X ϕ i -X v i ) (II.1.16)
where ∆H i and ∆S i are the enthalpy and entropy of segregation of solute i, α iM is the interaction coecient between solute and matrix, and α ij is the interaction coecient between two solutes.

II.1.4 Brittle Fracture of Low Alloy Steel

Fracture mechanisms can be categorized as ductile and brittle fracture. Brittle fracture can be described as cleavage (transgranular fracture) or intergranular fracture. Cleavage refers to crack propagation along the low-index atom planes and intergranular fracture refers to crack propagation along grain boundaries. In both cases, the mechanism of fracture can be described in the following steps:

1. Crack nucleation 2. Crack propagation

Overcoming obstacles

Crack nucleation Grain boundaries serve as obstacles for dislocation movements, as dislocations pile up once arrived at grain boundaries under shear stress. The accumulated shear stress at the tip of the dislocation pile τ can thus create a crack locally or in the neighboring grain.

The minimum shear stress to nucleate a crack can be described as the following equations [START_REF] Smith | Crack Nucleation in Crystalline Solids[END_REF]:

τ > πGω (1 -ν)L F (ϕ)
(II.1.17)

F (ϕ) = 2 5 + 2cosϕ -3cos 2 ϕ (II.1.18)
where τ is the shear stress at the tip of the dislocation pile, G us the shear modulus, ω is the work needed for decohesion, L is the slip band length, and ϕ the angle between the slip band and the crack.

In the case of a single phase metal, grain boundaries serve as the principal obstacle for slip bands. Thus L is in average half the grain diameter d. This means that τ is proportional to d -1/2 according to equation II.1.17. In steels, the microstructure is often not a single phase.

Carbides and precipitates can also act as a nucleation site for cracks.

Crack propagation At this step, the crack propagates until the rst obstacle it encounters.

Base on the criteria proposed by Grith [START_REF] Grith | The phenomena of rupture and ow in solids[END_REF] During intergranular fracture, when the crack arrives at a triple junction, the propagation direction changes but still follows a grain boundary. In the case of intergranular fracture, the criterion of overcoming a triple junction can also be described in the same form as equation II.1.19 [START_REF] Grith | The phenomena of rupture and ow in solids[END_REF]:

σ tj > Eω gb πc ′ cos 4 ϕ (II.1.20)
where σ tj is the stress necessary to overcome a triple junction, ω gb is the work necessary to break the grain boundary, c ′ is the crack length at the triple junction, and ϕ is the deection angle between the crack and the triple junction (ϕ is presented as θ 1 in gure II. 1.35).

In this case, the crack length at triple junction varies as a function of grain size d. This is a more vital criterion compared to c the initial crack length and L the length of the slip band.

The critical stage of intergranular fracture is to overcome the triple junctions [START_REF] Guttmann | Fragilité de revenu et ségrégation intergranulaire de l'antimoine et du langanese dans des aciers faiblement alliés à 2manganese[END_REF].

The three steps of brittle fracture mentioned above can be described in gure II.1.35 [START_REF] Christien | Fragilité intergranulaire de l'acier 17-4 PH en cours de vieillissement[END_REF]. Depending on the testing temperature, the fracture can be controlled by dierent steps mentioned above. Yu et al. [START_REF] Yu | On the change of fracture mechanism with test temperature[END_REF] have shown that at very low temperature (< -160 • C), the critical event that controls cleavage fracture is the nucleation step. But at higher temperatures, the critical event becomes the propagation step, which is conrmed in [START_REF] Lambert-Perlade | Mechanisms and modeling of cleavage fracture in simulated heat-aected zone microstructures of a BIBLIOGRAPHY high-strength low alloy steel[END_REF] where k is a non dimensional constant that describes the crack geometry.

Close to the crack tip, the yield stress σ y is reached, see gure II.1.36. The size of the plastic zone r p can be estimated by this relationship:

r p ≈ αak 2 ( σ σ y ) α = 1/2π plane stress α = 1/6π plane strain (II.1.22)
where α represents the stress triaxiality around the crack. It can be seen that if the hardness of a metal or the stress triaxiality increases, the size of the plastic zone decreases. To open the crack tip and continue the propagation, Orowan [START_REF] Orowan | Symposium at massachusetts institute of technology[END_REF] proposed to describe the work ω into a term of surface energy 2γ s and a term of plastic work 2γ p . The surface energy can generally be neglected but the plastic term depends strongly on it. The work term can be described as the following: [START_REF] Wood | Experimental and theoretical determination of kAFe factors for quantitative X-ray microanalysis in the analytical electron microscope[END_REF]. When the temperature increases, the yield stress of a metal decreases followed by a slight increase of γ p (which also increases the brittle fracture stress σ f ). At low temperature, the stress for cleavage is smaller than the yield stress: the fracture is brittle and absorbs little energy. Reversely, when yield stress is smaller than the cleavage stress, there is macroscopic plastic deformation before fracture. The DBTT can be dened as the temperature where these two curves intersect, see gure II.1.37. In practice, the DBTT can be dened in dierent ways. In this work, the DBTT is dened as when the absorbed energy is at 7 daJ/cm 2 (or 56 J). There are dierent metallurgy factors that can aect the DBTT by changing the brittle fracture stress or yield stress, see gure II.1.39.

ω = 2(γ s + γ p ) ≈ 2γ p = f (γ s ) (II.

CHAPTER II.1. LITERATURE REVIEW

A increase in yield strength and/or a decreases in brittle fracture stress will result in shifting he DBTT to higher temperature.

II.1.4.3 Eect of Metallurgical Factors on Brittle Fracture

Martensite and bainite are two microstructures commonly seen in industrial steels. This is also the case for RPV steels, even though martensite is often not a desired microstructure.

Bainite and martensite are dierent in many aspects that can aect their fracture properties directly.

Hardness: For the as-quenched microstructures, martensite is known to be hard but brittle compared to bainite due to the excess carbon content in the solid solution. Higher hardness can be translated into higher yield stress. This results in increasing the DBTT. In the nuclear industry, structural and pressure vessel steels are never used with as-quenched microstructure due to high residual stresses. Once a martensitic steel undergoes tempering, its hardness is likely to decrease as the excessed carbon content precipitates into carbides (see section II.1.3).

For RTE, hardness does not play a role in the evolution of fracture properties as many authors [127129] showed that thermal aging by RTE generally does not induce a softening of the material.

Grain size: Under the hypothesis that the principal obstacles for crack propagation are grain boundaries or triple junctions, the fracture stress depends on the initial crack length c ′ which is related to the grain size (see equation II. 1.20). When the grain size increases, statistically c ′ increases as well, thus the fracture stress decreases and DBTT increases. In the case where the yield stress is not inuenced by the grain size, the material with smaller grain has a higher impact toughness. As martensite blocks are smaller than bainite blocks [START_REF] Guttmann | Fragilité de revenu et ségrégation intergranulaire de l'antimoine et du langanese dans des aciers faiblement alliés à 2manganese[END_REF],

a given steel with a martensitic structure would have a higher impact toughness than with a bainitic structure for a same hardness level [START_REF] Marini | Eect of the bainitic and martensitic microstructures on the hardening and embrittlement under neutron irradiation of a reactor pressure vessel steel[END_REF]. The eect of grain size on crack propagation is also explained by Raoul et al. [START_REF] Raoul | Rupture intergranulaire fragile d'un acier faiblement allié induite par la ségrégation d'impuretés aux joints de frains: Inuence de la microstructure[END_REF]. They suggested that the stress intensity proportional to the grain size d at the triple junction is equivalent to the size of the facet.

CHAPTER II. Carbides: Apart from grain boundaries, carbides are also known as crack initiators [START_REF] Lee | Evaluation of microstructural parameters controlling cleavage fracture toughness in MnMoNi low alloy steels[END_REF][START_REF] Saario | On the Microstructural Basis of Cleavage Fracture Initiation in Ferritic and Bainitic Steels[END_REF]. Roseneld et al. [START_REF] Roseneld | Fractographic observations of cleavage initiation in the ductile-brittle transition region of a reactor-pressure-vessel steel[END_REF] observed cleavage fracture in A508 steel after step cooling. They found that if the cleavage initiation site is in a grain, residual of a MnS inclusion is seen; if the cleavage initiation site is at a grain boundary, it is related to small carbides. These small carbides are identied as Mo 2 C by Raoul et al. [5]. This shows that the second phases can also be weak spots for creak initiation.

Intergranular segregation: As mentioned previously, intergranular segregation plays an important role in intergranular fracture. With a sucient amount of segregation, the surface energy term decreases (γ s in equation II.1.23), which decreases the brittle fracture stress and increases the DBTT [START_REF] Kraxner | Quantitative EDXS: Inuence of geometry on a four detector system[END_REF][START_REF] Lee | The inuence of alloying elements on impurity induced grain boundary embrittlement[END_REF][START_REF] Gibson | Segregation-induced changes in grain boundary cohesion and embrittlement in binary alloys[END_REF].

II.1.4.4 Intergranular Fracture in Martensitic and Bainitic Microstructure

The brittle fracture of martensitic and bainitic steel at low temperature is mostly by transgranular cleavage. Dierent studies provide evidence of how phosphorus intergranular segregation aects fracture modes by decreasing grain boundary cohesion energy [START_REF] Kraxner | Quantitative EDXS: Inuence of geometry on a four detector system[END_REF][START_REF] Lee | The inuence of alloying elements on impurity induced grain boundary embrittlement[END_REF][START_REF] Gibson | Segregation-induced changes in grain boundary cohesion and embrittlement in binary alloys[END_REF]. The fracture mode changes from cleavage into a mix of intergranular fracture and cleavage when intergranular segregation is present. The relationships between intergranular segregation, change in DBTT, and intergranular fracture are studied in dierent low alloy steels with dierent microstructures after tempering embrittlement. In the following, how intergranular segregation eects the fracture properties of martensitic and bainitic low alloy steels is presented.

Intergranular Segregation & ∆DBTT

Druce et al. [START_REF] Druce | Eect of ageing on properties of pressure vessel steels[END_REF] showed that in coarse grain A533B steel, the change in DBTT is proportional to the P/Fe peak height ratio measured by AES, see gure II.1.40 [START_REF] Druce | Eect of ageing on properties of pressure vessel steels[END_REF].

CHAPTER II.1. LITERATURE REVIEW CHAPTER II.1. LITERATURE REVIEW From the studies above, phosphorus grain boundary monolayer coverage seems to directly inuence DBTT. The relationship is often reported to be linear, i.e. ∆DBTT = Const. × P gb .

Although this relationship seems straight forward and simple, there are dierent factors that were not considered. For example, Forsten et al. [START_REF] Pelli | Eect of thermal ageing on impact ductility of the nuclear reactor pressure vessel steel SA533B and its weld metal[END_REF] showed that after temper embrittling on A533B weld (80 wt ppm P), the material experienced a DBTT shift but intergranular fracture was not observed.

Shen et al. [START_REF] Shen | Eect of solute grain boundary segregation and hardness on the ductile-to-brittle transition for a CrMo low-alloy steel[END_REF] studied DBTT shift of P-doped 2.25Cr-1Mo steel (600 wt ppm) after aging at 540

• C and of untempered water quanched samples. The water quenching was performed on where P P is the AES P 120 /F e 730 peak height ratio in %, H is the Rockwell hardness, G is the ASTM grain size number of prior austenite grain. This relation has been established on a database obtained with martensitic structures. It can be seen that DBTT increases with increasing phosphorus intergranular segregation, hardness, and grain size. It highlights the synergetic eect between hardness and segregation noticed by Christien [START_REF] Christien | Synergetic eect of hardness and phosphorus grain-boundary segregation on the ductile-to-brittle transition temperature of 17-4 PH steel[END_REF] and Shen [START_REF] Shen | Eect of solute grain boundary segregation and hardness on the ductile-to-brittle transition for a CrMo low-alloy steel[END_REF]. This relationship was also conrmed by others in dierent steels [START_REF] Mulford | Temper embrittlement of Ni-Cr Steels by phosphorus[END_REF][START_REF] Mcmahon | Solute segregation and intergranular fracture in steels: a status report[END_REF].

Intergranular Segregation & Critical Fracture Stress

The DBTT shift due to RTE is often observed with the change in fracture mode from cleavage to intergranular fracture. Boasen et al. [START_REF] Boåsen | Thermal ageing of low alloy steel weldments from a Swedish nucle-ar power plant a study of mechanical properties[END_REF] observed intergranular fracture on both A533B reference (80 wt ppm P) and weld metal (130 wt ppm P) after thermal aging. Erhart et al. [START_REF] Erhart | Equilibrium segregation of phosphorus at grain boundaries of FeP, FeCP, FeCrP, and FeCrCP alloys[END_REF] showed that intergranular fracture percentage increases when phosphorus grain boundary segregation increases. Nakata et al. [START_REF] Nakata | Grain Boundary Phosphorus Segregation in Thermally Aged Low Alloy Steels[END_REF] showed that the phosphorus peak height ratio is Lee et al. [START_REF] Lee | The inuence of alloying elements on impurity induced grain boundary embrittlement[END_REF] observed a decrease in critical intergranular fracture stress when phosphorus intergranular segregation concentration increases. They also observed that when there are strong carbide formers (such as molybdenum and chromium) in the steel, this eect is more severe, which also suggested the segregation competition between carbon and phosphorus. This observation is also supported by McMahon et al. [START_REF] Mcmahon | Mechanisms of intergranular fracture in alloy steels[END_REF].

Christien et al. [START_REF] Christien | Synergetic eect of hardness and phosphorus grain-boundary segregation on the ductile-to-brittle transition temperature of 17-4 PH steel[END_REF] reported that for a maraging stainless steel, P intergranular segregation and hardness have a synergetic eect on DBTT, but P intergranular segregation itself does not change the DBTT unless the hardness is high enough. They explained this phenomena by Davidenkov diagram presented in gure II.1.44 [START_REF] Christien | Synergetic eect of hardness and phosphorus grain-boundary segregation on the ductile-to-brittle transition temperature of 17-4 PH steel[END_REF]. They assumed that the cleavage stress is independent of the yield stress and the temperature. When the material is not hard enough, the intergranular fracture stress has no inuence on DBTT. The DBTT (T 1 ) is determined by the intersection of cleavage stress and yield strength. When the material is harder, the DBTT (T 2 ) is determined by the intersection of intergranular fracture stress and yield strength. This interpretation is based on the assumption that the intergranular fracture stress decreases with increasing temperature when phosphorus is segregated at grain boundaries.

Intergranular Segregation & Microstructure

As mentioned in the previous section, the intrinsic properties of dierent microstructures can also inuence the intergranular segregation behavior and fracture properties, see section [START_REF] Druce | Eect of ageing on properties of pressure vessel steels[END_REF] shows the DBTT shift of A533B steel with dierent microstructures.

II.1.3. Figure II.1.40
It can be seen that the coarse grain microstructures are more susceptible to temper embrittlement. Viswanathan et al. [START_REF] Viswanathan | Eect of microstructure on the temper embrittlement of Cr-Mo-V steels[END_REF] showed that at comparable ∆FATT, martensitic microstructure presents higher intergranular fracture percentage than bainite. They also mention that, they did not necessarily observe intergranular fracture at high ∆FATT specimens.

Raoul et al. [START_REF] Raoul | Eect of microstructure on the susceptibility of a 533 steel to temper embrittlement[END_REF] suggested that tempered martensite is more susceptible to intergranular embrittlement than tempered bainite, and they proposed a reasoning related to phosphorus segregating to dierent types of grain boundaries (mentioned in section II.1.3). Nevertheless, their results could also be explained from a mechanical point of view. Regardless of the microstructure, the competition between cleavage and intergranular fracture depends on the critical stress, grain size, and yield stress. In their study, the prior austenite grain size remains constant (≈150 µm) in both microstructures. Their results where low hardness (bainitic) samples fracture by cleavage and high hardness (martensitic) samples fracture by intergranular fracture could actually fall into the case explained in gure II.1.44. However, this interpretation does not explain why the transition of fracture mode occurs so rapidly as a function of the cooling rate.

On the other hand, Raoul et al. [START_REF] Raoul | Rupture intergranulaire fragile d'un acier faiblement allié induite par la ségrégation d'impuretés aux joints de frains: Inuence de la microstructure[END_REF] modied the prior austenitization grain size to about 11 µm by decreasing the austenitization temperature. They discovered that the fracture mode then changes from intergranular to cleavage. This illustrates that prior austenite grain size can inuence the fracture mode by aecting the intergranular fracture stress.

II.1.5 Summary

Based on the current information gathered in literature, there are certain points that can be summarized:

1. RPV is constructed by dierent shells that are welded together, the microstructure heterogeneity can be induced during fabrication and assembly.

2. The denition of bainite morphology is not absolute, dierent authors have dened bainite in dierent ways. Most authors agreed that the as-received RPV steel is mostly likely to be upper bainite as in the denition by Mehl.

3. There are certain OR between the austenite parent phase and martensite or bainite child phase. The dierent types of grain boundaries obtained from a single austenite grain in martensite and bainite also have a certain MR. The targeted microstructures were the as-received and the tempered martensite structures. The as-received microstructure indicates the original observed microstructure at the reception of the material, which is mostly believed to be tempered bainite as mentioned in section II.1.1.2. The samples used in this study were extracted from the nozzle shell of the RPV.

II.2.2 Sample Preparation

The experimental program of this work includes characterization of the two studied microstructures, intergranular segregation investigations by STEM-EDX and AES, and dierent mechanical tests. Samples were machined from the nozzle shell of the RPV. Already shown in gure II.1.6, ghost lines appear mainly from 1/2 thickness until the internal surface. To avoid ghost lines, the specimens were extracted starting from 1/2 thickness until the external surface.

However, this is not the case for sample BSA, see gure II.2.1 (a). Mechanical specimens Plate-shape blanks with 15 mm thickness were machined so that dierent mechanical specimens can be extracted. The dimensions of the blanks were designed so that martensitic structure can be obtained by water quenching. Charpy V-notch samples and tensile test (TC6 3 ) samples were machined from these plate blanks. The dimensions of these mechanical specimens are given in appendix A.1. Once the two microstructures were obtained, they underwent dierent thermal treatments to induce dierent intergranular segregation levels. Table II [START_REF] Raoul | Rupture intergranulaire fragile d'un acier faiblement allié induite par la ségrégation d'impuretés aux joints de frains: Inuence de la microstructure[END_REF][START_REF] Chaouadi | Eect of step cooling and P-segregation to grain boundaries on the tensile and fracture toughness properties of A533B plate and A508 forging steels[END_REF][START_REF] Zhai | Segregation behavior of phosphorus in the heat-aected zone of an A533B/A182 dissimilar weld joint before and after simulated thermal aging[END_REF][START_REF] Andrieu | Mécanismes et modélisation multi-échelle de la rupture fragile trans-et intergranulaire des aciers pour Réacteurs à Eau sous Pression[END_REF]. This shortens the aging time from a few months or longer to about 10 days.

Samples for intergranular segregation quantication

The thermal treatment for as-received samples was close to a standard industrial thermal cycle. For states B and BSC, two tempering cycles were performed to ensure that they have undergone the same tempering treatment as the martensitic states. As mentioned previously, state BSA was a sample recovered from previous studies, the thermal treatment was slightly dierent than the others. On the other hand, the thermal treatment for martensitic samples was modied with a water quench after tempering so that the dierence in intergranular segregation is maximized between the full step cooling (MSC) and non aged (M) state.

II.2.3 Experimental Methodology

This section provides the experimental procedures for dierent purposes. First, the methods used for metallurgy characterizations are described. Then, the procedure for STEM-EDX acquisitions with slight modications compared to the methodology developed in the rst part (chapter I.2) of this work is described. Later on, the details for AES acquisitions are illustrated.

At last, the mechanical tests conditions are given.

II.2.3.1 Metallurgy Characterizations Microstructure Observations

To reveal the micro-segregations or ghost lines, chemical etching by FeCl 3 was performed.

The samples were polished up to 2400 grade SiC paper, then a layer of diluted FeCl 3 solution was poured on the sample surface. Cotton was used to tap lightly on the sample surface for uniform etching. Then the etching solution was removed by water followed by ethanol jet to avoid oxidation. The etching results were observed with bare eye.

To reveal the microstructure of each sample, the samples were polished up to 1 µm diamond paste. Then, 2% nitic acid was used to etch the grain boundaries. The microstructure of the samples was observed using optical microscope and SEM.

Chemical Composition Heterogeneity

Dierent from the nominal composition measured by X-ray uorescence, it was noted in [START_REF] Naudin | Intergranular fracture stress and phosphorus grain boundary segregation of a Mn-Ni-Mo steel[END_REF] that micro-segregations can be enriched with Mo, Mn, Si, Cr, and P. WDS was used to perform line proles that compare solute concentrations between micro-segregations and base metal.

Dierent micro-segregated zones were identied after chemical etching by FeCl 3 . Three line proles were analyzed by WDS. In total, the concentration of Mo, Mn, Si, Cr, and P of four micro-segregated zones were analyzed.

EBSD Investigation

Based on the results of FeCl 3 chemical etching, the EBSD acquisitions were performed out of the micro-segregation zones. The goal was to ensure that the concentration of the segregating elements remains close to the nominal composition. The EBSD mappings were used to identify the prior austenite grain boundaries so that the location of TEM FIB thin foil positions can be identied. Meanwhile, the crystal orientation information was used for further analysis of the microstructure and the relationship between intergranular segregation and grain boundary characteristics.

II.2.3.2 Intergranular Segregation Measurements by STEM-EDX

The procedure for STEM-EDX acquisitions for intergranular segregation quantication is detailed in the following:

1. Identication of prior austenite grain boundaries using EBSD: based on the MR between austenite and martensite proposed by Morito et al. [START_REF] Morito | The morphology and crystallography of lath martensite in alloy steels[END_REF] and Gourgues et al. [START_REF] Gourgues | Electron backscattering diraction study of acicular ferrite, bainite, and martensite steel microstructures[END_REF] (see gure II.1.24), grain boundaries with misorientations between 21.5 • and 46.5

• are prior austenite grain boundaries since the packet, block, sub-block, and lath boundaries are forbidden in this misorientation range.

From the EBSD acquisition of each sample, these grain boundaries can be highlighted.

An example from the sample MIA is shown in gure II.2.4 where the prior austenite grain boundaries are marked in red on the index quality map 4 . The highlighted grain boundaries do not fully reconstruct austenite grains, but it is good enough to locate positions to extract TEM FIB thin foils, which are marked in orange. The thickness map is used to extract local thickness of each acquisition so that ACF can be calculated (see equation I.1.9).

STEM-EDX acquisitions: the TEM, beam condition, and EDX acquisition parameters

were the same as mentioned in section I.2.1.2 (table I.2.1). There are multiple grain boundaries in one FIB thin foil, there were dierent priorities in analyzing the dierent grain boundaries:

(a) Prior austenite grain boundary:

It can be seen that the prior austenite grain boundary can be separated into different segments due to the ne structure in the adjacent grains. In gure II.2.6, for example, the white dots represent the position of each STEM-EDX acquisition conducted on the dierent prior austenite grain boundary segments. These dierent segments have dierent misorientation and rotation axes, in other words, they are dierent in nature.

(b) Other grain boundaries:

Clearly shown in gure II.2.6, a thin foil can contain many grain boundaries apart from the prior austenite grain boundary. These grain boundaries include lath, block and packet boundaries. This allows intergranular segregation analyses at dierent types of grain boundaries, which is one of the biggest advantage of TEM in comparison with AES and APT. In each FIB thin foil, some other grain boundaries were also analyzed. The selection of these grain boundaries was based on their vertical alignment. As mentioned in section I.2.1.2, STEM-EDX acquisition should be performed when the grain boundary is aligned parallel to the incident beam. The CHAPTER II.2. EXPERIMENTAL PROCEDURES other grain boundaries analyzed by STEM-EDX were the ones that can be aligned easily. These grain boundaries can be separated into dierent categories based on their misorientations. This will be discussed later.

Additional information and modications of STEM-EDX data processing:

The data processing for STEM-EDX acquisitions follows the same principle as detailed in section I.2.1.4. Dierent from Part I, where only phosphorus segregates at grain boundary, there are other elements (Mo, Mn, Ni) that were measured at grain boundaries. The following introduces the dierent quantication parameters for other elements. On the other hand, due to the higher bulk content of these elements, dierent considerations during data processing were raised. The details and the modications are given in the following.

(a) Quantication parameters for 16MND5 samples: Apart from the k factor of phosphorus that was determined experimentally [START_REF] Van Cappellen | The parameterless correction method in X-ray microanalysis[END_REF], no other k factors of other segregated elements was determined in this work. Table II.2.4 gives the k factors (k i/F e ) used in this work along with their sources. The values in table II.2.4 were calculated from k i/Si and k F e/Si that are from the same source for each element. Because of the determined k P/F e being close to the experimental value given in [72],

k M n/F e from the same reference was directly used. k factors from Esprit v1.9 (STEM- EDX acquisition software used in this work) and values given in the JEOL software (TEM also operating at 200 kV) were compared. It was identied that the k factors provided by JEOL are closer to the determined k P/F e and the values reported in [72].

Thus, k N i/F e and k M o(L)/F e from JEOL were used. It can be seen that for P, Mo, and Ni, once the GB box width exceeds about 10 nm, the quantication results are stabilized as in gure I.2.9. For Mn, however, a diusion prole can be observed in the line prole. Under this circumstances, the background removal by the adjacent grain boxes depends on the GB box size. This is why the Mn concentration varies with GB box size. As a result, the STEM-EDX data processing is slightly modied compared to section I. Here, it is necessary that the GB box width being as narrow as possible but still includes all signals from the apparent grain boundary concentration; and the grain boxes being as close as possible to the GB box, so that the quantication of Mn can be the closest to the real grain boundary concentration. From gure II.2.7, the GB box width should be chosen same as the peak width.

However, there were dierent barriers that do not allow selecting the most narrow GB box:

i. When the grain boundary is curved.

ii. When the grain boundary is not completely aligned parallel to the primary electron beam.

These were not a concern in Part I thanks to the easier sample conguration (model alloy with long straight grain boundaries and surface segregation interface). Due to the reasons mentioned above, the GB box was not selected manually for data processing for acquisitions on 16MND5 thin foils. A program based on MATLAB © and Python 3 was used to reallocate the curved grain boundary into a straight one and then place the GB box to t the peak width.

To do so, the program rst plots the EDX map of each element and allows selecting several points along the segregation prole manually, see gure II.2.9 (a). The red CHAPTER II.2. EXPERIMENTAL PROCEDURES crosses in gure II.2.9 (a) represent the selected points. In most cases, the Mn segregation map was used for this purpose. In some cases where there were no Mn segregation, other segregation proles can also be used for this purpose. Then, the program aligns the selected points vertically at the center of the map while shifting the dataset correspondingly, see gure II.2.9 (b).

Once the grain boundary is aligned, the spectra is summed along the Y direction.

The intensity line prole can be plotted as shown in gure II.2.9 (c). The GB and of the phosphorus K α peak is very low but the automatic tting forces a Gaussian function t. The segregation was not seen in the according EDX qualitative map.

In this case, the amount of segregation is considered to be below the detection limit and the quantication result is adjusted to 0.0 atom/nm 2 . (c) P K α peak above detection limit with correct Gaussian curve t, (d) EDX map and (e) line prole not showing segregation of phosphorus at grain boundary, (f ) P K α peak below detection limit with forced Gaussian t.

It is to be noted that for some grain boundaries, any segregation element (P, Mo, Mn, Ni) can be below the detection limit and the quantication results were adjusted to zero manually.

The intergranular segregation quantication measurement proposed here should be considered as the Gibbsian interfacial excess instead of the absolute grain boundary concentration. This is because of the proposed box method that subtracts background based on spectra from the grains (the bulk). In the case of phosphorus, the Gibbsian interfacial excess and absolute grain boundary concentration is basically the same as the phosphorus bulk concentration is below the detection limit. This is also nearly true for the other elements as their bulk concentrations, although detectable by EDX, are also quite low.

II.2.3.3 Intergranular Segregation Measurements by AES

The AES acquisitions were performed using Thermo VG Thetaprobe spectrometer by Thermo Fisher Scientic. Only three sample states were analyzed: MSC, MIA, BSC, as they were the ones most likely to have intergranular fracture surfaces (i.e. embrittle enough). The specimens were cooled down by liquid nitrogen to about -100

• C and fractured in the ultra-high vacuum chamber. The non aged samples could not be analyzed using AES because of the absence of intergranular fracture. The quantication method used in this work was developed (but not yet published) by V.

Barnier, Ecole des Mines de Saint Etienne, France. The AES is calibrated by AR-XPS so that the method does not require standard samples in the quantication procedure in contrast to the conventional methods. The results are given as a number of phosphorus atoms per unit surface.

The AES analysis was limited to phosphorus. The analysis of Mo, Mn, and Ni segregation was not possible due to the high contribution from the bulk concentration.

II.2.3.4 Mechanical Properties

Two types of mechanical tests were conducted. Charpy V-notch impact tests (Kcv) were performed to establish the transition curves to determine the DBTT. Then, uniaxial tensile tests were done to conrm that the embrittlement is not induced by hardening. The tensile test specimen was chosen to be TC6 to conserve the material. TC6 is a cylindrical specimen with 6 mm gauge diameter, the specimen dimensions can be found in appendix A.1.

The goal of the mechanical tests is to gure out if the fracture properties evolution is only due to the increase of intergranular segregation or if there is also a microstructual eect. Table II The testing temperature varies for the Charpy V-notch impact test so that the transition curve of each state can be established. After fracture, the fracture surfaces of the specimens were observed using FEI Quanta 650 SEM.

No tensile tests at ambient temperature were planned for the as received microstructure since there were already knowledge of such tests based on previous internal studies in EDF. This information was from specimens at 1/4 thickness from the internal surface, and is considered equivalent to 3/4 thickness from the internal surface. It is to be noted that these as-received samples only underwent one tempering treatment like state BSA, instead of two tempering treatments likes state B & BSC.

Chapter II.3

Material Characterization

The 16MND5 type steel analyzed during this study is from a nozzle shell and the samples were extracted from 1/2 thickness to the external surface, see gure II.1.2. This chapter provides the characterization of the analyzed 16MND5 steel and the two microstructures (as-received bainite & martensite).

II.3.1 Chemical Composition

Four sets of specimens were extracted for chemical composition measurements by X-ray uorescence and infrared absorption spectroscopy. Table II The chemical composition of the tested material is within the RCC-M requirements stated in table II.2.1. Also, it can be seen that the global composition does not vary between 1/2 thickness and close to external surface.

II.3.1.1 Local Composition Heterogeneity

As mentioned in section II.1.1.1, segregations at dierent scales are formed at dierent stages of fabrication, notably the A-segregates (or ghost lines) that are often present close to the internal shell surface and the micro-segregation that are zones where the solidication happens last. Naudin et al. [START_REF] Naudin | Modelisation de la ténaticé de l'acier de cuve REP en presence de zones de ségrégation[END_REF] performed a series of investigations on the segregated zones.

CHAPTER II.3. MATERIAL CHARACTERIZATION They showed that the ghost lines mainly locate between the internal surface and 1/2 thickness and that their dimensions vary, see gure II.1.6.

A plate-shape sample of the circumferential/radial surface was used for revealing the segregated zones by FeCl 3 chemical etching. The distribution of the segregated zones along the thickness (radial direction) was shown. This plate sample only shows the surface from 1/2 thickness to the external surface since the samples for this study were machined from the same part. The other two surfaces were also etched: short side (Axial/Radial surface), long side (Axial/Circumferential surface). From gures II.3.1 and II.3.2, it can be concluded that ghost lines are very rare in this part of the shell thickness and that the micro-segregation is most likely to have a disk shape.

Line proles using WDS were done to measure the solute concentrations in micro-segregated zones. The micro-segregated zones were identied by etching, then the line prole starts from the base metal and crosses the micro-segregated zone. Mn, Mo, Si, P, and Cr concentrations were measured for three line proles. The WDS line proles show clearly that there are composition heterogeneity at the microsegregated zones. The solute concentration increases at the micro-segregated zones: 30% of Mo, 15% of Mn, 10% of Si, and 10% of Cr. No obvious increase was observed for P due to lack of statistics. To ensure that the intergranular segregation measured by STEM-EDX were all from the same bulk composition, all FIB thin foils were extracted out of the micro-segregated zones as indicated in gure II.2.3.

II.3.1.2 Matrix composition

Solute can be consumed in the formation of the dierent precipitates in 16MND5 steel. This leads to a dierent matrix composition compared to the global composition measured by X-ray uorescence (see table II.3.1). Cazottes et al. [START_REF] Cazottes | Quantitative microstructural characterization of nuclear grade bainitic steel: Inuence of macrosegregations in full-scale forgings[END_REF] have studied the matrix composition after tempering and SRHT, see table II.3.2.

In this work, the matrix composition was also veried. A STEM-EDX map was taken on the matrix where no visible precipitates were observed. The acquired EDX map was summed into one matrix spectrum. The background of each X-ray peak was removed using Hyperspy v.4.1 [21] by the two window method introduced in section I.1.1.2. The Cli-Lorimer method was used for quantifying the matrix composition of Fe, Mn, Mo, Cr, and Ni. The eect k factors of each elements were the same from tables II.2.4 and II.2.5. Meanwhile, k * Cr/F e = k Cr/F e ×ACF Cr/F e = 1.15. The measured matrix compositions in wt% from [START_REF] Cazottes | Quantitative microstructural characterization of nuclear grade bainitic steel: Inuence of macrosegregations in full-scale forgings[END_REF] in comparison with the analyzed matrix in this work are listed in table II.3.2.

Table II.3.2: Matrix concentration in wt% of the main solutes in 16MND5 steel reported in [START_REF] Cazottes | Quantitative microstructural characterization of nuclear grade bainitic steel: Inuence of macrosegregations in full-scale forgings[END_REF] and measured in this work.

Mn

Cr Mo Ni [START_REF] Cazottes | Quantitative microstructural characterization of nuclear grade bainitic steel: Inuence of macrosegregations in full-scale forgings[END_REF] The measured matrix compositions provided in [START_REF] Cazottes | Quantitative microstructural characterization of nuclear grade bainitic steel: Inuence of macrosegregations in full-scale forgings[END_REF] are very close regardless of the dierent nominal chemical composition (table 1 in [START_REF] Cazottes | Quantitative microstructural characterization of nuclear grade bainitic steel: Inuence of macrosegregations in full-scale forgings[END_REF]). It can be seen that the nickel and chromium matrix concentration does not vary signicantly from nominal composition, while the concentration of manganese and molybdenum decreases due to the formations of dierent carbides and precipitates. The nominal composition of Mn in this work (1.3 wt%) is lower than in [START_REF] Cazottes | Quantitative microstructural characterization of nuclear grade bainitic steel: Inuence of macrosegregations in full-scale forgings[END_REF] (1.57 wt% & 1.45 wt%), which may explain the dierences in table II.3.2. Huang et al. [START_REF] Huang | Inuence de l'irradiation aux neutrons sur le vieillissement des aciers de cuves des réacteurs nucléaires à eau pressurisée[END_REF] have also measured the matrix composition of a 16MND5 steel by APT, they have obtained similar results as this work.

II.3.2 Microstructure by Morphology

As mentioned in chapter II.2, the targeted microstructures in this study were the as-received bainitic structure and the re-austenized martensitic structure. Dierent characterizations were done to study the microstructures.

For the martensite samples, the as-quenched microstructure was studied to ensure that the re-austenitization has achieved martensitic microstructure. Chemical etching by 2% nital acid and Vickers hardness tests were done. Carbide clusters at a smaller scale were also observed in STEM imaging, see gure II.3.8.

It can be seen that large carbides (hundreds of nms) form a cluster that is located only on the CHAPTER II.3. MATERIAL CHARACTERIZATION middle right, and another one that is on the top right corner of the thin foil (pointed out in blue). Some other smaller precipitates can also be seen in the STEM BF image. where carbides clusters can be seen.

Apart from the carbide clusters that can be seen in gures II.3.6 and II.3.8, smaller carbides that have nanometric size were also observed in TEM samples. It was not the main goal of this study to identify the dierent types of carbides, only qualitative EDX analysis was done. The observations were in accord with a recent study of Cazottes et al. [START_REF] Cazottes | Quantitative microstructural characterization of nuclear grade bainitic steel: Inuence of macrosegregations in full-scale forgings[END_REF].

Typical carbides such as the cementites (Fe 3 C) which are rich in Mn were observed, see gure II.3.9. Another carbide that is rich in Mo is believed to be Mo 2 C, which is a common carbide that is observed in 16MND5 steel [START_REF] Raoul | Eect of microstructure on the susceptibility of a 533 steel to temper embrittlement[END_REF][START_REF] Cazottes | Quantitative microstructural characterization of nuclear grade bainitic steel: Inuence of macrosegregations in full-scale forgings[END_REF]. Both of these carbides were observed on grain boundaries and in the grains. Another precipitate that presents a more rectangular shape is found to be AlN, see gure II.3.10. The spectra of the pink and blue boxes in the BF images show two types of precipitates.

It can be seen that the pink spectrum is enriched in Al and N whereas the blue spectrum is the molybdenum-rich carbide. Due to the overlapping of the two precipitates, the pink spectrum also shows Mn, Mo, Cr peaks. In the few analyses conducted here, AlN was only observed in the grains and always present very close to a molybdenum-rich carbide.

II.3.3 Bainite & Martensite by EBSD Analysis

Orientation maps obtained using EBSD on the non aged samples (B and M in table II. CHAPTER II.3. MATERIAL CHARACTERIZATION Diawara et al. [START_REF] Diawara | Caractérisation quantitative de la microstructure de l'acier 16MND5 des cuves de REP[END_REF] and Gourgues et al. [START_REF] Gourgues | Electron backscattering diraction study of acicular ferrite, bainite, and martensite steel microstructures[END_REF] suggested that the misorientation distribution between upper bainite and martensite can be distinguished by the ratio between the peak at From gure II.3.12, it is very obvious that the peak ratio of 54 • /59 • for the as-received bainite microstructure is higher than peak ratio for the martensite microstructure. Also, the two histograms in gure II.3.12 corresponds to the histograms presented in [START_REF] Gourgues | Electron backscattering diraction study of acicular ferrite, bainite, and martensite steel microstructures[END_REF]. Based on the chemical etched surface observation and the grain boundary misorientation distribution, it is clear that the as-received microstructure is upper bainite and that the re-austenitized microstructure is martensite.

From gure II.3.12, the dierent grain boundaries were classied into ve groups according to their misorientation angles. Group 1 (< 7

• ) is composed essentially of lath boundaries. Kim et al. [START_REF] Kim | Characterization of boundaries and determination of eective grain size in mn-mo-ni low alloy steel from the view of misorientation[END_REF] found that in A508 steel, the lath in martensite have misorientations between 0.5 • -6.3

• . Gourgues et al. [START_REF] Gourgues | Electron backscattering diraction study of acicular ferrite, bainite, and martensite steel microstructures[END_REF]. showed that based on the KS/NM MR, a block boundary can exist at 5.25 microstructures. This is expected as group 3 contains essentially prior austenite grain boundaries. For the other groups, the axes distribution is not as random. In addition, there are dierences between bainite and martensite, especially for groups 4 and 5.

The martensitic structure (gure II.3.13 (b)) shows high density of [START_REF] Mehl | Hardenability of alloy steels[END_REF] and [START_REF] Morito | The morphology and crystallography of lath martensite in Fe-C alloys[END_REF] rotation axes in groups 4 and 5. This may indicate high proportion of Σ3 as suggested in [START_REF] Park | Eects of boundary characteristics on resistance to temper embrittlement and segregation behavior of NiCrMo low alloy steel[END_REF][START_REF] Gourgues | Electron backscattering diraction study of acicular ferrite, bainite, and martensite steel microstructures[END_REF]. The similar high density of [START_REF] Mehl | Hardenability of alloy steels[END_REF] and [START_REF] Morito | The morphology and crystallography of lath martensite in Fe-C alloys[END_REF] in group 4 and 5 are the block and packet boundaries in the KS MR [START_REF] Gourgues | Electron backscattering diraction study of acicular ferrite, bainite, and martensite steel microstructures[END_REF]. When comparing gure II.3.13 (b) to the theoretical axes distribution proposed in gure II.1.24 [START_REF] Gourgues | Electron backscattering diraction study of acicular ferrite, bainite, and martensite steel microstructures[END_REF], it can be seen that the rotation axis distribution resembles the KS MR.

Dierent from the martensitic structure, the bainitic structure does not present high density of [START_REF] Mehl | Hardenability of alloy steels[END_REF] or [START_REF] Morito | The morphology and crystallography of lath martensite in Fe-C alloys[END_REF] rotation axes at any misorientation. For group 4, the high density zone seems to be in the middle of [START_REF] Mehl | Hardenability of alloy steels[END_REF] and [START_REF] Morito | The morphology and crystallography of lath martensite in Fe-C alloys[END_REF], which are rotation axis close to [221] and [331]. For group 5, the high density zone falls also at the middle of [START_REF] Mehl | Hardenability of alloy steels[END_REF] and [START_REF] Morito | The morphology and crystallography of lath martensite in Fe-C alloys[END_REF], but slightly shifted toward [START_REF] Mehl | Hardenability of alloy steels[END_REF]. The EBSD acquisition step size ranges from 250 nm to 350 nm, see table II.2.3. The misorientation angle threshold for grain construction of the EBSD maps was chosen to be 3

• .

The grain size extracted by the EBSD mapping is considered as the average size of ferritic grains, which is considered as the block size. An automatic function in MATLAB with MTEX texture and crystallography analysis toolbox developed by Bachmann et al. [START_REF] Bachmann | Texture Analysis with MTEXFree and Open Source Software Toolbox[END_REF] that calculates the equivalent radius based on the grain areas was used to obtain the ferritic grain size. Three EBSD mappings of each microstructure were analyzed and the average of the three values were taken as the ferritic grain size of each structure.

The prior austenite grain size of the two microstructures were obtained based on an iterative method that reconstructs the prior austenite grains proposed by Nyyssönen et al. [START_REF] Nyyssönen | Iterative Determination of the Orientation Relationship Between Austenite and Martensite from a Large Amount of Grain Pair Misorientations[END_REF]. To process the EBSD data, the iteration method is implemented in MATLAB with MTEX [START_REF] Bachmann | Texture Analysis with MTEXFree and Open Source Software Toolbox[END_REF]. With the EBSD acquisition step sizes and sensitivity, it was considered that the laths were not necessarily identied. TEM FIB thin foils were used to determine the lath size. The method by interceptions was also used to obtain the average lath size. Figure II.3.15 shows the ASTAR index quality map superposed with the orientation map of a martensitic thin foil. The horizontal and vertical lines with known length were drawn to calculate the intercepts. The intercepts were identied in black (horizontal) and yellow (vertical) dots. The average lath size was then calculated on both directions and averaged. It is to be noted that, not all ASTAR mappings can clearly show the laths since the misorientation between laths can be very small.

Three bainitic thin foils and ve martensitic thin foils were used to measure the lath sizes.

Table II.3.3 gives the averages of the dierent grain sizes of the two microstructures. The main focus was to at least analyze three prior austenite grain boundaries per state. Due to dierent constrains, there were nearly no other grain boundaries analyzed for samples MIA and BSA.

It was observed that four elements: P, Mo, Mn, Ni segregate at the grain boundaries.

The detailed quantication results of each acquisition along with the STEM-EDX acquisition positions on each FIB thin foil are given in appendix A.3.

II.4.1.1 Types of Grain Boundaries Analyzed in Bainite & Martensite

The categorization of the STEM-EDX analyzed grain boundaries were based solely on their misorientation angles (see gure II.3.12). In combining information of the misorientation angle and the rotation axis, it is sometimes possible to identify the grain boundaries more in detail (packet, block, or lath boundaries). See gure II.1.24 for the theoretical misorientation/rotation axis pairs from [START_REF] Gourgues | Electron backscattering diraction study of acicular ferrite, bainite, and martensite steel microstructures[END_REF]. However, if the misorientation/rotation axis pairs of the analyzed grain boundaries cannot be identied using gure II.1.24, the grain boundaries were considered as random ones.

The misorientation and rotation axis information of each analyzed grain boundary was collected based on ASTAR acquisitions. The rotation axis distribution of group 4 and group 5 grain boundaries show stronger tendencies. For states B, M, and MSC, the analyzed grain boundaries fall more or less in the red zones of the rotation axis distribution, although the tendency is less clear for state BSC. For states M and MSC, rotation axes in group 5 fall in principal in the red zones close to [START_REF] Mehl | Hardenability of alloy steels[END_REF] and [START_REF] Morito | The morphology and crystallography of lath martensite in Fe-C alloys[END_REF]. For state B, rotation axes in group 4 and group 5 are mainly grouped in the red zones in between [START_REF] Mehl | Hardenability of alloy steels[END_REF] and [START_REF] Morito | The morphology and crystallography of lath martensite in Fe-C alloys[END_REF]. The analyzed grain boundaries were chosen purely randomly since the rotation axis/misorientation information of each grain boundary was not determined during STEM-EDX analysis process but after. Although gure II. From gure II.4.3, it can be seen that at the same type of grain boundary the segregation level of molybdenum and manganese are higher than that of phosphorus and nickel. Concentrations of phosphorus and nickel were often adjusted to zero (i.e. below the detection limit) Regardless of the dierent tendencies mentioned above, it can be clearly seen that all four elements segregate at dierent types of grain boundaries whatever the microstructure and thermal aging. In other words, the results show a very similar segregation behavior of bainite and martensite. This is very dierent from the hypothesis in the literature [START_REF] Raoul | Rupture intergranulaire fragile d'un acier faiblement allié induite par la ségrégation d'impuretés aux joints de frains: Inuence de la microstructure[END_REF][START_REF] Park | Eects of boundary characteristics on resistance to temper embrittlement and segregation behavior of NiCrMo low alloy steel[END_REF] that segregation in prior austenite grain boundaries is lower in bainite than in martensite, because bainite would trap segregating elements in highly misoriented grain boundaries, whereas martensite would not. Each surface analyzed by AES was considered as one prior austenite grain boundary. It can be seen that the phosphorus quantication varies between dierent austenite grain boundaries, and that the average is not necessarily same as the STEM-EDX results.

It is obvious that AES measurements have higher statistics compared to STEM-EDX quantications (only three prior austenite grain boundaries). Also, it was already noted that the quantication by STEM-EDX tends to be slightly higher than APT and XPS (which is used to calibrate AES), see section I.3.3.

II.4.2 Discussions

In this section, the eect of dierent factors on intergranular segregation are discussed. First, the eect of the grain boundary structure is presented. Then, the segregation concentration at dierent types of grain boundaries are illustrated. Further, the eect of microstructure susceptibility to intergranular segregation is discussed. At last, thermodynamic and kinetic models are proposed to explain the eect of thermal aging on intergranular segregation.

II.4.2.1 Eect of Grain Boundary Misorientation Angle

Dierent authors [START_REF] Lejcek | Grain boundary segregation in metals[END_REF][START_REF] Suzuki | Phosphorus segregation related to the grain boundary structure in an Fe-P alloy[END_REF][START_REF] Ogura | Dependence of phosphorus segregation on grain boundary crystallography in an Fe Ni Cr alloy[END_REF] boundaries have lower segregation level than general HAGBs. When comparing to the conclusions of Ogura et al. [START_REF] Ogura | Dependence of phosphorus segregation on grain boundary crystallography in an Fe Ni Cr alloy[END_REF], regardless of the slightly dierent categorization of the grain boundaries, the measurements of this work aligns with their observations (see section II.1.3.2).

To compare the dierent categorization, their observation can be summarized to Group The segregation level between dierent grain boundary groups follows: γ GB (Group 3) > Group 4 > Group 5 ≈ Group 2 > Lath (Group 1). This tendency seems to be true for P, Mn, and Ni in all the studied states, while the tendency for Mo is less obvious. This observation is very striking for states BSC and MSC.

It is clear that prior austenite grain boundaries are the most preferred grain boundaries of all segregated elements. The dierence between group 4 and 5 is mainly because group 5 includes high coincidence grain boundaries (Σ3) that sometimes present lower segregation level and decrease the average. Group 2 includes some LAGBs (misorientation < 15 • ) and group 1 MARTENSITIC 16MND5 STEEL are only LAGBs. As suggested in literature [START_REF] Ogura | Dependence of phosphorus segregation on grain boundary crystallography in an Fe Ni Cr alloy[END_REF], LAGBs have lower intergranular segregation level compared to HAGBs.

To further establish the eect of grain boundary misorientation, dierent groups of grain boundaries are discussed separately. First, STEM-EDX measurements at prior austenite grain boundaries were analyzed. It is clear that no direct link can be determined between a given misorientation angle and its segregation level. In other words, for grain boundaries that have the same misorientation angle, the segregation level of any element can vary a lot. Also, there were no tendencies observed, no clear relationship was determined.

Then, group 2, 4, and 5 grain boundaries were analyzed together. In this case, the high coincidence grain boundaries (i.e. those identied to be block boundaries) analyzed in group It can be seen that for the least segregated states (B and M), many quantication results

were adjusted to zero manually as they were below the detection limit. When removing these acquisitions that were adjusted to 0, the phosphorus intergranular concentration of these two states would be 1.29 and 0.88 atom/nm 2 instead of 0.74 and 0.34 atom/nm 2 , respectively. This indicates that phosphorus intergranular segregation at some prior austenite grain boundaries was already induced prior to thermal aging.

For the aged states (BSC, BSA, MSC, and MIA), the average concentrations of each element are very close between the three analyzed austenite grain boundaries.

Random Grain Boundaries

Based on the possible rotation axes proposed in gure II.1.24 [START_REF] Gourgues | Electron backscattering diraction study of acicular ferrite, bainite, and martensite steel microstructures[END_REF], not all analyzed grain boundaries can be identied into block, packet, or prior austenite boundaries. These STEM-EDX analyzed grain boundaries that cannot be identied are referred to as random grain boundaries.

If In group 2, the analyzed grain boundaries are close to certain theoretical rotation axes, however, their misorientation angles may not t it very well. In groups 4 and 5, there are more random grain boundaries analyzed in bainitic samples than martensitic samples. Although not all analyzed grain boundaries can be identied as packet boundaries using the theoretical MRs, it was shown that regardless of the smaller amount of random HAGBs in martensite, all four MARTENSITIC 16MND5 STEEL elements segregate in these grain boundaries as well in both microstructures.

Summary

Based on the analysis above, all four elements (P, Mo, Mn, Ni) segregate at all types of grain boundaries in both bainite and martensite. This is an observation very dierent from the hypothesis proposed in the literature. Moreover, intergranular segregation was also measured at Σ3 boundaries, which is a nding contradicting the common belief.

Among the dierent grain boundary groups, the segregation level ranks in the following manner: γ GB (Group 3) > Group 4 > Group 5 ≈ Group 2 > Lath (Group 1).

However, there does not seem to have a direct relationship between the misorientation angle/rotation axis pairs and intergranular segregation level. Further analysis would require more detailed information of grain boundary structure, including grain boundary planes.

II.4.2.3 Microstructure Susceptibility

From the segregation level of the aged states of bainite and martensite (BSC & MSC), the microstructure susceptibility to intergranular segregation can be seen. For prior austenite grain boundaries, a small microstructure eect was observed. Surprisingly, bainite seems to jects the hypothesis of martensite being more susceptible to phosphorus intergranular segregation [START_REF] Raoul | Eect of microstructure on the susceptibility of a 533 steel to temper embrittlement[END_REF][START_REF] Park | Eects of boundary characteristics on resistance to temper embrittlement and segregation behavior of NiCrMo low alloy steel[END_REF] and suggests that the relationship between higher intergranular fracture susceptibility in martensite than in bainite depends on other causes.

II.4.2.4 Trapping of Phosphorus

As shown in section II.1.3.3, segregation of phosphorus on grain boundaries can cause a depletion of bulk phosphorus content, which in turn will reduce the equilibrium segregation concentration. This is here referred to as trapping of phosphorus. This eect can be signicant when the grain size is suciently small, i.e. the grain boundary density is suciently high. It was suggested in literature that trapping of phosphorus is higher in bainite than in martensite [START_REF] Raoul | Eect of microstructure on the susceptibility of a 533 steel to temper embrittlement[END_REF][START_REF] Park | Eects of boundary characteristics on resistance to temper embrittlement and segregation behavior of NiCrMo low alloy steel[END_REF], which could explain the better resistance to RTE of bainite. In this study, an estimation of the phosphorus trapping eect in both microstructures was undertaken.

Considering the small bulk concentration in this study (X v << 1), the thermodynamic model in equation II.1.7 can be simplied as the following:

X ϕ X ϕ max -X ϕ ≈ X v exp(- ∆G kT ) (II.4.1)
In the case where the intergranular segregation is very low (i.e. X ϕ << X ϕ max ), the grain boundary concentration is proportional to the bulk concentration (i.e. X ϕ ∝ X v ). In this case, the bulk depletion due to the trapping of phosphorus in dierent types of grain boundaries will aect X ϕ proportionally. In the other case where the intergranular segregation is close to the saturation (i.e. X ϕ ⋍ X ϕ max ), the grain boundary concentration is independent from the bulk concentration.

Based on the grain size information obtained by EBSD mapping and the segregation measurements conducted on dierent types of grain boundaries, the amount of phosphorus trapped by the dierent types of grain boundaries can be calculated. The dierent grain sizes of the bainitic and martensitic microstructures were introduced in section II.3.3.

To have a simpler approach, only three types of grain were considered:

(i.e. X ϕ << X ϕ max , X ϕ ∝ X v ).
It can be considered that the trapping eect is negligible. In addition, it is to be pointed out that the same level of trapping was found in bainite and martensite. This contradicts the assumption found in literature that the trapping eect is higher in bainite than in martensite [START_REF] Raoul | Eect of microstructure on the susceptibility of a 533 steel to temper embrittlement[END_REF][START_REF] Park | Eects of boundary characteristics on resistance to temper embrittlement and segregation behavior of NiCrMo low alloy steel[END_REF].

One could argue that the lath grains should present as plate instead of elongated fries. If this is the case, the lath boundary density would be It can be seen that the diusion coecient of phosphorus between the two sources showed a dierence of a few orders of magnitude. The diusion coecient determined by Druce et al. [START_REF] Druce | Eect of ageing on properties of pressure vessel steels[END_REF] was a value extrapolated from previous studies at higher temperatures. In [START_REF] Druce | Eect of ageing on properties of pressure vessel steels[END_REF], their segregation measurements by AES after isothermal aging at lower temperatures (around 400 • C to 500

• C) t this extrapolated coecient, which gives it more reliability.

Based on the calculated diusion coecients in table II.4.12, the diusion distance for the dierent thermal treatments can be calculated by:

x i = D i t (II.4.2)
where D i is the diusion coecient of each element and t is time in second. Table II The available solute quantity Q can be calculated by:

Q i = 2 × x i × C i (II.4.3)
where C i is the matrix concentration in atom/nm 3 (see table II.3.2). The phosphorus matrix concentration is considered to be identical to the bulk concentration (0.008 wt%). Table II that even in the case of phosphorus, segregation is probably controlled by thermodynamics, not the kinetics. However, when using D M atsuyama P from [START_REF] Matsuyama | Tracer diusion of P in iron and iron alloys[END_REF], the available solute quantities calculated are signicantly below the measured segregation concentrations for the step cooling and isothermal aging cases. This situation is impossible and shows that the diusion coecient from Matsuyama et al. [START_REF] Matsuyama | Tracer diusion of P in iron and iron alloys[END_REF] is not adapted to the material studied in this work.

It is to be mentioned that the approach followed here is only approximative for step cooling as it assumes that segregation occurs entirely during the last isothermal step of the step cooling treatment, which is obviously not the case. So this approach certainly overestimates the probability of kinetics limitation. In summary, it was assumed that the segregation is mainly governed by thermodynamics.

Thermodynamic Model of Intergranular Segregation

Using the thermodynamic models mentioned in section II. Here, the segregation measurements in this work are transformed into monolayer so that the expression in θ = X ϕ /X ϕ max can be used. The assumption is that one monolayer has a density s = 19.41 atom/nm 2 which corresponds to s = (N v at ) 2/3 , where N v at is the number of atom per unit volume in the material (N v at = 85.5 atom/nm 2 ). When considering the (110) plane of iron, the plane density is about 17.29 atom/nm 2 , which remains close to the previous value of 19.41 atom/nm 2 . It is to be noted that monolayer in the thermodynamic models are considered as the eective monolayer. In reality, available sites for segregation can appear in multiple layers of atoms close to the grain boundaries [START_REF] Domain | Solute segregation at (100) and (110) tilt GB in Fe at the atomic scale[END_REF].

The denition of segregation free energy (∆G) is simplied: it was assumed to vary between elements, but not to depend on temperature. Also, there were no solute interactions taken into account. The segregation free energy is adjusted for the dierent cases described below. Table II.4.15 shows the segregation free energy (∆G) in kJ/mol and saturation concentration (X ϕ max )

for each element obtained from the t procedure in the dierent cases. rough. This indicates that the intergranular fracture may be somehow related to the decohesion of small particles along the grain boundaries. Rough intergranular fracture surfaces of similar materials were also observed in previous studies [START_REF] Viswanathan | Eect of microstructure on the temper embrittlement of Cr-Mo-V steels[END_REF][START_REF] Andrieu | Mécanismes et modélisation multi-échelle de la rupture fragile trans-et intergranulaire des aciers pour Réacteurs à Eau sous Pression[END_REF][START_REF] Naudin | Intergranular fracture stress and phosphorus grain boundary segregation of a Mn-Ni-Mo steel[END_REF], which is dierent from the smooth surface observed in [START_REF] Raoul | Eect of microstructure on the susceptibility of a 533 steel to temper embrittlement[END_REF][START_REF] Lee | The inuence of alloying elements on impurity induced grain boundary embrittlement[END_REF]. An elongated bed seen at the center of gure II.5.5 is often observed to be a previous site of Mn rich inclusion based on the EDX qualitative analysis by SEM on the residuals.

The inclusion itself is often lost during fracture. This observation is true for both bainite and martensite specimens before and after thermal aging. This observations is similar to [START_REF] Roseneld | Fractographic observations of cleavage initiation in the ductile-brittle transition region of a reactor-pressure-vessel steel[END_REF].

II.5.2 Relationship between Intergranular Segregation and Fracture Properties

Based on the results from the mechanical properties mentioned above and the phosphorus intergranular segregation quantication detailed in chapter II.4, an interpretation of RTE is illustrated in this section.

Widely studied in the literature, RTE reduces toughness, which manifests as an increase of DBTT and a change in the fracture mode. In 16MND5 type steel, phosphorus is a known embrittling element that segregates to grain boundaries during thermal aging, which has further become an indicator of RTE level. Based on higher DBTT changes and higher percentage of intergranular fracture, studies have shown that martensite has higher susceptibility to RTE [START_REF] Raoul | Eect of microstructure on the susceptibility of a 533 steel to temper embrittlement[END_REF][START_REF] Park | Eects of boundary characteristics on resistance to temper embrittlement and segregation behavior of NiCrMo low alloy steel[END_REF][START_REF] Zhang | Cleavage fracture in bainitic and martensitic microstructures[END_REF][START_REF] Yang | Eect of microstructure on the impact toughness and temper embrittlement of SA508Gr.4N steel for advanced pressure vessel materials[END_REF].

From this study, no obvious microstructural eect was observed on intergranular segregation behavior. Phosphorus intergranular segregation is most present at prior austenite grain boundaries of bainite and martensite, but it was also measured on all other types of grain boundaries in both microstructures (see chapter II.4). It was also seen that bainite shows similar, or even higher susceptibility to phosphorus intergranular segregation after thermal aging than martensite, which is dierent from the hypothesis given in the literature [START_REF] Raoul | Eect of microstructure on the susceptibility of a 533 steel to temper embrittlement[END_REF][START_REF] Park | Eects of boundary characteristics on resistance to temper embrittlement and segregation behavior of NiCrMo low alloy steel[END_REF], that bainite is less susceptible to phosphorus intergranular segregation.

The measured phosphorus intergranular segregation and the mechanical properties from Charpy V-notch impact tests are presented in gure II.5.6. When comparing the eect of step TEMPERED BAINITE cooling (orange in gure II.5.6), bainite shows higher susceptibility to phosphorus intergranular segregation but smaller ∆DBTT was observed. Also, bainite shows nearly no intergranular fracture regardless of the higher phosphorus concentration at prior austenite grain boundaries.

On the contrary, martensitic states present higher intergranular fracture percentage with lower phosphorus intergranular segregation concentration with respect to bainitic states. Here, the critical intergranular fracture stress of bainite and martensite are assumed to be the same.

The STEM-EDX phosphorus measurements of the dierent states were used to complete gure II. and the Charpy V-notch impact test results, the fracture properties of martensite and bainite are clearly dierent. For martensite, only a small amount of phosphorus grain boundary concentration is needed to induce intergranular fracture. This is most likely due to its high cleavage resistance. For bainite, on the other hand, intergranular fracture was barely observed regardless of its higher phosphorus grain boundary concentration. This may be due to its lower cleavage resistance. From the results mentioned above, it can be concluded that the microstructure susceptibility to RTE is not only due to the phosphorus intergranular segregation level but also related to the intrinsic mechanical properties of the dierent microstructures.

Chapter II.6

Part II Summary

The studied 16MND5 steel was characterized and the following provides a summary:

1. The nominal composition of the studied material do not show heterogeneity along the thickness range where the dierent samples were extracted (1/2 thickness to external surface).

2. Micro-segregated zones were observed in the studied thickness range (1/2 to 3/4 thickness), but nearly no A-segregates were observed. The micro-segregated zone presented enrichment of Mn, Mo, Si, and Cr; and the hardness is locally more elevated.

3. The matrix composition measured using EDX provided similar results as previous studies and showed that Mn, Mo are consumed in dierent precipitation formations.

4. The microstructure of the studied materials was veried using chemical etching and EBSD. The two methods shows that the targeted microstructure (bainite & martensite)

were obtained after the dedicated heat treatments.

5. EBSD analyses showed dierent ORs for martensite (KS OR) and bainite (NW OR) and that the grain boundary misorientation distribution are dierent as well between the two microstructures.

6. The grain sizes of the dierent types of grains (prior austenite grain, ferritic grain, and lath) in bainite and martensite were obtained using EBSD analyses and TEM imaging.

Based on the dierent factors (microstructure, types of grain boundaries, thermal aging) and the obtained mechanical properties, the following conclusions can be drawn:

1. Four elements: phosphorus, molybdenum, manganese, nickel are shown to segregate at grin boundaries in 16MND5 by STEM-EDX in the investigated aging conditions. All four elements segregate at all dierent types of grain boundaries in tempered bainite and in tempered martensite. This was not previously reported in the literature.

CHAPTER II.6. PART II SUMMARY 2. Among the analyzed grain boundaries, the relationship between the segregation level and 4. Based on the estimation of available solute quantity, the dierent states are at equilibrium and their segregation process was governed by thermodynamics.

5. Thermodynamic models proposed by Mclean and Guttmann were used to t the measured intergranular segregation data. It was presumed that phosphorus, manganese, and nickel segregate at the same available sites. However, it was not possible to determine the grain boundary saturation concentration (X ϕ max ) and the segregation free energy (∆G i )

separately. On the contrary, molybdenum seems to segregate at a dierent site with a low saturation concentration (X ϕ max ). Moreover, P, Mn, and Ni shows correlated increase while Mo lacks relations with either. This provides a reason why phosphorus segregation concentration barely exceeds 3 atom/nm 2 (lower than 0.2 monolayer) even after longterm thermal aging. It is most likely due to the competition with other segregated elements.

6. Bainite presents smaller ∆DBTT while having higher phosphorus intergranular segregation concentration at prior austenite grain boundaries. However, due to its lower resistance to transgranular cleavage compared to martensite, intergranular fracture was barely observed at the aged state (BSC). For martensite, on the other hand, only a small amount of phosphorus is needed to induce intergranular fracture due to its high cleavage resistance. It can be seen that phosphorus intergranular segregation is not the only factor that inuences microstructure RTE susceptibility.

Conclusions & Perspectives

A novel box-type STEM-EDX method was developed to quantify intergranular segregation.

The spectrum background removal was performed by subtracting average background from the adjacent grains, in a way that spurious peaks and the Bremsstrahlung background can be completely removed. Monte-Carlo simulations were done to show that this method is independent from the everlasting problems of beam broadening and beam interaction volume when respecting a criterion: the GB box width should be at least twice the broadened beam diameter. The STEM-EDX method was rst validated on two grain boundaries of a Fe-P model alloy already analyzed by APT. The phosphorus quantication results on the two grain boundaries by the two techniques fall within the standard measuring error. Furthermore, a synthesized Fe-P-Fe sandwich sample was fabricated so that phosphorus interface segregation can be measured by four characterization techniques. First, phosphorus surface segregation was induced so surface techniques XPS and WDS can be applied. Then iron was deposited onto the surface to mimic a segregated grain boundary so that STEM-EDX and APT can be used. Good agreement was found between the results of the four techniques, which validated the developed STEM-EDX method.

The STEM-EDX method was then applied to 16MND5 type steel with tempered bainitic and tempered martensitic microstructures. It has been shown that with dierent thermal aging processes, phosphorus, manganese, molybdenum, and nickel segregate to all types of grain boundaries in both microstructures. Results have shown that prior austenite grain boundaries are the most susceptible and lath boundaries are the least susceptible to segregation. Other grain boundaries show intermediate levels of segregation. Also, it has been shown that high coincidence boundaries (i.e. Σ3) present segregation with a concentration not necessarily much lower compared to other grain boundaries. Packet boundaries could not be strictly identied from their misorientation and rotation axis, so the specic segregation behavior of packet boundaries could not be characterized.

For prior austenitic grain boundaries, no particular relationship between the segregation level and the misorientation angle was observed. However, the lower segregation tendency for grain boundaries below 20

• of misorientation was conrmed. The dierent analysis showed that there is little microstructural eect on phosphorus intergranular segregation. In other words, the segregation behaviors in tempered martensite and tempered bainite are similar which is very dierent from the hypothesis given in the literature. Also, the phosphorus intergranu-CONCLUSIONS & PERSPECTIVES lar segregation level remained very low (≈3 atom/nm 2 ) even after step cooling or long term isothermal aging. This may be due to the site competition with nickel and manganese.

The trapping eect, i.e. the bulk depletion of phosphorus due to grain boundary segregation, was estimated in both tempered martensitic and tempered bainitic microstructures. It was shown that the total phosphorus content segregated at the dierent types of grain boundaries does not exceed 25% of the nominal content (80 wt ppm). It was concluded that this eect is not expected to strongly aect the phosphorus segregation behavior.

Among the four segregated elements, it was observed that P, Mn, and Ni are most likely in site competition during thermal aging, while Mo occupies dierent sites. In addition, it was observed that segregation of Mo is essentially independent of aging temperature. This suggested that Mo may have a low grain boundary saturation concentration and that saturation is obtained even at high temperature. Assuming that equilibrium segregation is reached after the dierent heat treatments conducted, thermodynamic models were proposed to t the dierent measurements and explain the dierent relationships between the four elements. It was observed that very dierent assumptions and input parameters could give satisfactory ts of our experimental data. This implies that these models should not be used for prediction outside the temperature range investigated here (400

• C 650 • C).
The shifts in DBTT were measured after aging for the two microstructures investigated (tempered martensite and tempered bainite). It was conrmed that ∆DBTT is higher for tempered martensite than tempered bainite. When combining the results of ∆DBTT and intergranular segregation measurements, it has been shown that the higher RTE susceptibility of tempered martensite is mainly due to its higher resistance to cleavage, implying that only a small amount of phosphorus is needed at the grain boundary to induce intergranular fracture.

Tempered bainite, on the contrary, although having similar or even higher phosphorus grain boundary concentration, has a lower cleavage resistance resulting in lower susceptibility to intergranular fracture.

This work provided a reliable STEM-EDX intergranular segregation quantication method and further applied measurements on tempered bainitic and tempered martensitic 16MND5 type steels that underwent dierent thermal aging. For decades, microstructure RTE susceptibility conclusions were often drawn directly from fracture properties (i.e. ∆DBTT). These have led to a hypothesis that is proven inaccurate by this work: dierences of phosphorus intergranular segregation do not play an important role in the microstructure eect on RTE, but the intrinsic mechanical property does. The RTE susceptibilities of dierent microstructures should be further studied.

Further studies on the critical brittle fracture stress should be performed on the same samples so that a relationship between phosphorus intergranular segregation and fracture mode may be established. It is also encouraged to have more detailed analysis on grain boundary structure (especially grain boundary planes) so that the relationship between grain boundary structure and segregation can be further studied. For future references, the thermal aging cycles should remain as simple as possible (i.e. long duration isothermal aging) to facilitate comparisons and results interpretation. Keywords: Scanning transmission electron microscopy, energy dispersive X-ray analysis, wavelength dispersive microanalysis, X-ray photoelectron spectroscopy, Auger electron spectroscopy, atom probe tomography, pressure vessel steel, intergranular segregation, phosphorus, reversible temper embrittlement, bainite, martensite, thermal aging Abstract:

Conclusions & Perspectives

Phosphorus intergranular segregation in low alloy steels is known to decrease brittle fracture stress and induce intergranular fracture, which causes reversible temper embrittlement. In the nuclear industry, nominally bainitic steels are subjected to this phenomenon and the question of microstructure susceptibility has been raised as literature shows that tempered martensite is more susceptible than tempered bainite. The objective of this study is to understand if this result is related to a different segregation behavior of the two microstructures. The first part of our work establishes a segregation quantification method using STEM-EDX, that was cross-compared with four other analytical techniques. Then, a comparative study of intergranular segregation in tempered bainitic and martensitic 16MND5 steel after different aging treatments is conducted based on the developed analytical method. The results show small microstructural influence on segregation. Phosphorus, nickel, manganese and molybdenum were observed at all types of grain boundaries in both microstructures. The segregation concentrations are higher in prior austenitic grain boundaries than in other types of boundaries. Taking account of the segregation amount in different types of boundaries, the phosphorus bulk depletion is shown negligible. Finally, using Charpy tests, we confirm the lower susceptibility of tempered bainite to thermal aging by temper embrittlement and conclude that this is not related to a different segregation behavior from tempered martensite. Mots-clefs: Microscopie électronique en transmission, spectrométrie de rayons X à dispersion d'énergie, microsonde, spectrométrie photoélectronique X, spectrométrie Auger, sonde atomique tomographique, acier de cuve, ségrégation intergranulaire, phosphore, fragilisation de revenu réversible, bainite, martensite, vieillissement thermique Résumé:

La ségrégation intergranulaire du phosphore est connue pour diminuer la contrainte de rupture fragile des aciers faiblement alliés et induire une rupture intergranulaire, phénomène appelé fragilité de revenu réversible. Dans l'industrie nucléaire, les aciers faiblement alliés trempés-revenus, nominalement bainitiques sont soumis à ce phénomène en service et la question de l'effet de microstructure a été soulevée car la littérature montre que la martensite est plus sensible que la bainite. L'objectif de cette étude est de comprendre si ce comportement est lié à une ségrégation différente dans les deux microstructures. La première partie de notre travail établit une méthode de quantification de ségrégation par spectrométrie de rayons X en microscopie électronique en transmission (STEM-EDX), que nous comparons ensuite à quatre autres techniques. Cette méthode est appliquée pour mener une étude comparative de la ségrégation intergranulaire dans l'acier 16MND5 trempé-revenu bainitique ou martensitique. Les résultats montrent une faible influence de la microstructure sur la ségrégation. Du phosphore, du nickel, du manganèse et du molybdène sont observés dans tous les types de joints de grains dans les deux microstructures. Les ségrégations sont plus élevées dans les anciens joints de grains austénitiques que dans les autres types de joints. L'effet de piégeage est considéré comme négligeable. Enfin, nous confirmons, avec des déterminations de températures de transition de résilience, la plus faible susceptibilité de la bainite revenue à la fragilité de revenu réversible et concluons que cela n'est pas lié à un comportement de ségrégation différent de celui de la martensite revenue.

140 II. 3 . 2 FeCl 3

 140323 scale) at 325 • C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 II.1.33 Kinetics of phosphorus grain boundary segregation concentration in α-iron at 325 • C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 II.1.34 Observation of cleavage propagation being stopped by high angle grain boundaries in bainite [166]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 II.1.35 Schematic graph representing the three steps of fracture [169]. . . . . . . . . . . . 108 II.1.36 Schematic graph representing the plastic zone in front of the crack tip. . . . . . . 109 XIII LIST OF FIGURES II.1.37 DBTT is dened as the temperature where yield stress and brittle fracture stress are identical. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II.1.38 Typical experimental DBTT curve, showing no sharp change between ductile and brittle fracture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II.1.39 Inuence of yield strength and brittle fracture stress on DBTT. . . . . . . . . . . II.1.40 Linear relationship between DBTT and phosphorus peak height ratio from AES with dierent microstructures [162]. . . . . . . . . . . . . . . . . . . . . . . . . . II.1.41 DBTT increases as phosphorus grain boundary monolayer coverage increases for A533B steel plate, adapted from [181]. . . . . . . . . . . . . . . . . . . . . . . . . II.1.42 Dierent factors that changes with aging time: (a) phosphorus grain boundary concentration measured by AES, (b) hardness, (c) ∆DBTT [2]. . . . . . . . . . . II.1.43 Intergranular fracture proportion increases as phosphorus monolayer coverage increases on 16MND5 type steel that has a similar composition of A-segregates [184].115 II.1.44 Davidenkov diagram of low and high hardness metals, variation of cleavage stress, intergranular fracture stress, and yield strength versus temperature [3]. . . . . . . II.1.45 Relationship between critical fracture stress and phosphorus monolayer coverage on 16MND5 type steel that has a similar composition of A-segregates [184]. . . . II.1.46 Linear relationship between fracture stress and fracture mode in 2.25Cr-1Mo steel [187]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II.2.1 Schematic gure of a shell for RPV. (a) dierent directions of the shell, the radial direction is also referred to as the thickness, (b) schematic view of how the dierent samples are located along the thickness (radial direction). . . . . . . . . II.2.2 The table and curve for step cooling. . . . . . . . . . . . . . . . . . . . . . . . . . II.2.3 Etched surface of sample M to reveal micro-segregations that was used for locating EBSD acquisition positions for TEM FIB thin foil extraction. . . . . . . . . . . . II.2.4 Prior austenite grain boundaries identication. Grain boundaries with misorientation between 21.5 • and 46.5 • are highlighted in red, the orange highlights indicate the location of the three TEM thin foils and the prior austenite grain boundary they were extracted from. . . . . . . . . . . . . . . . . . . . . . . . . . II.2.5 The H bar xation for TEM FIB thin foils. . . . . . . . . . . . . . . . . . . . . . II.2.6 Index quality map of Precession assisted crystal orientation mapping (PACOM) (ASTAR) acquisition for a MIA thin foil, prior austenite grain boundaries with misorientation angle between 21.5 • -46.5 • are marked in red. . . . . . . . . . . . II.2.7 Example of line proles of the segregated elements and the GB box width eect on the quantication results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II.2.8 How dierent segregation proles can aect the box method. (a) a Dirac peak, (b) a Gaussian peak, (c) a Gaussian peak with diusion prole. . . . . . . . . . . XIV LIST OF FIGURES II.2.9 Selection of GB and grain boxes by a MATLAB © code developed in this work : (a) select several points (red crosses) on curved grain boundary to align it, (b) grain boundary after aligning the selected points, (c) select boxes based on Mn intensity prole, dark gray box is the GB box, light gray boxes are the grain boxes.134 II.2.10 An example of STEM-EDX data processing on 16MND5 steel (state BSC). The GB spectrum is superposed with the grain spectrum, showing clear P, Mo, Mn, and Ni segregation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 II.2.11 Gaussian function tting results of STEM-EDX data treatment : (a) EDX map and (b) line prole showing clear segregation of phosphorus at grain boundary, (c) P K α peak above detection limit with correct Gaussian curve t, (d) EDX map and (e) line prole not showing segregation of phosphorus at grain boundary, (f ) P K α peak below detection limit with forced Gaussian t. . . . . . . . . . . . 136 II.2.12 Fracture surface in AES ultra-high vacuum chamber showing a mixture of cleavage and intergranular fracture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 II.3.1FeCl 3 etching to reveal segregated zones on surface CR. . . . . . . . . . . . . . . etching to reveal segregated zones: (a) zoom in for micro-segregations on surface CR (orange box in gure II.3.1, (b) etching of the short side (AR surface) and the long side (AC surface), blue arrow marks out a ghost line. . . . . . . . . 141 II.3.3 HV0.01 hardness and WDS line proles of three micro-segregated zones. . . . . . 142 II.3.4 Optical micrograph of nital etched surfaces to reveal grain boundaries and carbides of (a) as-quenched martensite, (b) tempered martensite (sample M). . . . . 144 II.3.5 Optical micrograph of nital etched surfaces to reveal grain boundaries and carbides of (a) intermediate aged martensite (sample (MIA), (b) martensite after step cooling (sample MSC). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 II.3.6 Optical micrograph of nital etched surfaces to reveal grain boundaries and carbides of (a) tempered as-received bainitic microstructure (sample B), (b) asreceived bainitic microstructure after step cooling (sample BSC). . . . . . . . . . 146 II.3.7 Backscattered electron SEM micrograph of nital etched surfaces to reveal grain boundaries and carbides of (a) as-received bainitic microstructure (sample B), (b) as-received bainitic microstructure after step cooling (sample BSC). . . . . . 146 II.3.8 STEM BF image of a FIB thin foil of the as-received bainitic microstructure where carbides clusters can be seen. . . . . . . . . . . . . . . . . . . . . . . . . . 147 II.3.9 STEM-EDX qualitative analysis on dierent types of carbides, showing Fe 3 C and carbides rich in molybdenum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 II.3.10 STEM-EDX qualitative analysis on AlN, the two spectra correspond to the pink and blue box indicated in the BF image. One shows the spectrum of AlN and the other shows the spectrum of molybdenum-rich carbide. . . . . . . . . . . . . 148 II.3.11 Orientation map of (a) as-received bainitic microstructure, (b) martensite. . . . . 149 XV LIST OF FIGURES II.3.12 Grain boundary misorientation distribution histogram of (a) as-received microstructure, (b) martensite. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II.3.13 Rotation axis distribution in the dierent misorientation ranges dened for (a) as-received bainitic microstructure (sample B), (b) martensite (sample M). . . . . II.3.14 Prior austenite grain reconstruction of (a) bainite, (b) martensite. . . . . . . . . II.3.15 ASTAR indexation quality map superposed with orientation map of a martensitic FIB thin foil to determine lath size by the interception method. . . . . . . . . . . II.4.1 Rotation axis distribution of each state where the rotation axes of each STEM-EDX analyzed grain boundaries are marked. . . . . . . . . . . . . . . . . . . . . II.4.2 Indicative scale of the segregation level of the dierent samples due to the complex thermal treatments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II.4.3 Summary of how the dierent elements segregate at dierent types of grain boundaries in dierent samples, the segregation quantications are presented in atom/nm 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II.4.4 Average of total segregation in atom/nm 2 at each type of grain boundary of each sample. Solid color: sum of P+Mn+Ni, transparent color: Mo. . . . . . . . . . . II.4.5 Concentration of each element at dierent types of grain boundaries for the different states. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II.4.6 Segregation concentration in atom/nm 2 of each element against grain boundary misorientation angle for STEM-EDX analyses of prior austenite grain boundaries. II.4.7 Segregation concentration in atom/nm 2 of each element against grain boundary misorientation angle. The grain boundaries corresponds to those of gure II.4.9. . II.4.8 Graphical presentation of the average intergranular segregation at each prior austenite grain boundaries analyzed of each state. . . . . . . . . . . . . . . . . . II.4.9 Comparison between the theoretical rotation axes [121] and the STEM-EDX analyzed grain boundaries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II.4.10 Intergranular segregation level in atom/nm 2 at prior austenite grain boundaries in aged bainite & martensite. The AES measurements of BSC & MSC are indicated in white dots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II.4.11 Trapping of phosphorus at dierent types of grain boundaries for (a) non-aged bainite, (b) bainite after step cooling. . . . . . . . . . . . . . . . . . . . . . . . . II.4.12 Trapping of phosphorus at dierent types of grain boundaries for (a) non-aged martensite, (b) martensite after step cooling. . . . . . . . . . . . . . . . . . . . . II.4.13 Illustration of the available solute quantity. . . . . . . . . . . . . . . . . . . . . II.4.14 McLean thermodynamic model tting the measured segregation concentrations: (a) P, (b) Mo, (c) Mn, (d) Ni. Black curves: saturation set at one monolayer; blue curves: saturation set at 0.21 for Mo and 0.5 for the others. . . . . . . . . . XVI LIST OF FIGURES II.4.15 Guttmann multicomponent thermodynamic model tting the measured segregation concentrations: (a) P, (b) Mo, (c) Mn, (d) Ni. Note that the McLean model is still used for Mo. Black curves: saturation set at one monolayer; blue curves: saturation set at 0.21 for Mo and 0.5 for the others. . . . . . . . . . . . . . . . . II.4.16 Correlation between segregated elements in aged bainite (BSC), only prior austenite grain boundaries are considered. Small dot: each STEM-EDX acquisition; big dot: average of all STEM-EDX acquisitions. . . . . . . . . . . . . . . . . . . . . . II.4.17 Correlation between segregated elements aged martensite (MSC), only prior austenite grain boundaries are considered. Small dot: each STEM-EDX acquisition; big dot: average of all STEM-EDX acquisitions. . . . . . . . . . . . . . . . . . . . . . II.5.1 Charpy V-notch impact test to determine DBTT for (a) bainite: ♦ for B, • for BSC, (b) martensite: ▲ for M, ♦ for MIA, ■ for MSC. . . . . . . . . . . . . . . . II.5.2 Fractographs of Charpy V-notch impact tests for states (a) B fractured at -50 • C, (b) M fractured at -120 • C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II.5.3 Fractograph of Charpy V-notch impact tests for states (a) BSC fractured at -25 • C, (b) MIA fractured at -100 • C, (c) MSC fractured at -80 • C. Intergranular fractured surfaces are circled in orange. . . . . . . . . . . . . . . . . . . . . . . . II.5.4 Fractograph of Charpy V-notch impact test showing the rough intergranular fracture surface (state MSC fractured at -60 • C). . . . . . . . . . . . . . . . . . . . . II.5.5 Fractograph of MSC Charpy V-notch impact test showing fracture initiated at an inclusion (fractured at 80 • C). . . . . . . . . . . . . . . . . . . . . . . . . . . . II.5.6 Eect of thermal aging on phosphorus intergranular segregation and ∆DBTT of bainite & martensite. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II.5.7 Interpretation of the microstructure eect on intergranular fracture. . . . . . . . A.1 STEM-EDX acquisition locations on the FIB thin foils of B. . . . . . . . . . . . . A.2 STEM-EDX acquisition locations on the FIB thin foils of BSC. . . . . . . . . . . A.3 STEM-EDX acquisition locations on the FIB thin foils of BSA. . . . . . . . . . . A.4 STEM-EDX acquisition locations on the FIB thin foils of M. . . . . . . . . . . . A.5 STEM-EDX acquisition locations on the FIB thin foils of MIA. . . . . . . . . . . A.6 STEM-EDX acquisition locations on the FIB thin foils of MSC. . . . . . . . .

  ular segregation by STEM-EDX without being inuenced by the assumption on the analyzed volume. The second objective is to conduct a comparative study of intergranular segregation and RTE in bainitic and martensitic microstructures of 16MND5 type steel. It is based essentially on the developed STEM-EDX methodology and Charpy V notch impact tests to measure the shifts of Ductile-to-Brittle Transition Temperature (DBTT) (∆DBTT) due to an acceler-INTRODUCTION ated aging treatment. This manuscript is separated into two parts corresponding to the two objectives. In Part I, chapter I.1 presents a literature review of the Cli-Lorimer STEM-EDX quantication method, and a summary of STEM-EDX application on intergranular segregation quantication. At last, the comparisons of intergranular segregation quantication by dierent characterization techniques are reviewed. Following this state of the art, chapter I.2 describes the developed STEM-EDX methodology in details, starting from the sample preparation and the acquisition parameters. Then, the proposed data treatment to obtain quantication in concentration per unit surface is presented. Finally, the developed STEM-EDX method is compared to other techniques. It is rst compared to APT results on grain boundaries of a INTRODUCTION Introduction L'énergie nucléaire fournit une solution de production électrique stable avec de très faibles émissions de gaz à eet de serre. Le bon connement des radionucléides générés est crucial et une très grande abilité des composants conçus pour empêcher leur dissémination est requise en toutes circonstances. Par conséquent, la plus grande attention est accordée à l'évolution des propriétés mécaniques des matériaux de structure des centrales nucléaires au cours de leur fonctionnement. Dans les réacteurs à eau sous pression, les principaux composants du circuit primaire sont soumis à de longues durées de vie (> 40 ans). La température de fonctionnement est principalement de l'ordre de 290 • C 325 • C et jusqu'à 345 • C localement dans le pressuriseur. Les évolu- tions des propriétés mécaniques au cours du fonctionnement résultent de diérents mécanismes de vieillissement, dont l'irradiation et le vieillissement thermique. Le premier mécanisme est directement dû au ux neutronique et n'aecte que la partie de la cuve du réacteur située face au c÷ur, le second est dû au maintien de longue durée aux températures de fonctionnement. Dans INTRODUCTION Des études antérieures ont suggéré que cette susceptibilité plus élevée pouvait être due à

Figure I. 1 . 1 :

 11 Figure I.1.1: An illustration of the Super-X EDX system showing only two of the four detectors,

I. 1 . 1 . 1

 111 The X-ray Spectrum A typical EDX spectrum is shown in gure I.1.2. The spectrum shows a continuous background with dierent characteristic X-ray peaks. The characteristic X-ray peaks are Gaussian with a xed Full Width at Half Maximum (FWHM) related to the energy resolution of the EDX system used[START_REF] Williams | Transmission electron microscopy: a textbook for materials science[END_REF]. The X-rays are usually collected in the energy range well below the primary energy (100 to 300 keV depending on the microscope).

Figure I. 1 . 2 :

 12 Figure I.1.2: A typical EDX X-ray spectrum including the Bremsstrahlung background and the characteristic X-ray peaks.

  Figure I.1.3 show a general form of the Bremsstrahlung X-ray as a function of energy, which is also essentially CHAPTER I.1. LITERATURE REVIEW the background of the acquired EDX spectrum. The vertical lines are the characteristic X-ray peaks of dierent elements.

Figure I. 1 . 3 :

 13 Figure I.1.3: General form of the Bremsstrahlung X-ray, the dashed line shows the generated X-rays and the solid line shows what is detected. The spikes indicates the characteristic X-ray lines detected [16].

Figure I. 1 . 4 :

 14 Figure I.1.4: Schematic diagram of where spurious X-rays can be generated [16].

Figure I. 1 . 5 :

 15 Figure I.1.5: Schematic of how to subtract background on a spectrum: (a) the window B beneath the characteristic peak of Cu K α , (b) linear interpolation between B 1 and B 2 to obtain the background intensity in window B [16].

  original Cli-Lorimer equation (equation I.1.3) is under the assumption where these secondary interactions do not occur. To more accurately quantify using the k factor method, corrections for absorption and uorescence are needed. This means that the k factor in equation I.1.3 should CHAPTER I.1. LITERATURE REVIEW be replaced by the eective k factor (k * A/B ) that includes the k factor and the correction factors.

Figure I. 1 .

 1 Figure I.1.6 shows an illustration of the beam broadening eect, where the incident beam diameter is d and the broadened beam diameter D can sometimes be dened as d + b, where b is the diameter change due to broadening eect.

Figure I. 1 . 6 :

 16 Figure I.1.6: Illustration of the beam broadening eect when an electron beam of diameter d travels through a specimen with thickness h and the diameter broadens to D = d + b. Adapted from [12].

  Figure I.1.7 [10] illustrates how the interaction volume can be simplied.

Figure I. 1 . 7 :

 17 Figure I.1.7: Illustration of the interaction volume when a raster scan is used in the case of quantifying intergranular segregation [10].

Figure I. 1 . 8 :

 18 Figure I.1.8: P intergranular segregation quantication results in 9 wt%Cr ferritic steel doped with dierent P content by AES & STEM-EDX from [61], unit as fraction of a monolayer of (110) plane.

Figure I. 1 . 9 :

 19 Figure I.1.9: Histogram of P intergranular segregation in 9 wt%Cr ferritic steel doped with 0.06 wt%P by AES & STEM-EDX from [39].

Figure I. 1 . 11 :

 111 Figure I.1.11: Mean STEM-EDX and AES results on P intergranular segregation in A533B and 2.25Cr-1Mo steels after dierent tempering duration [63]. The error bars indicates 1 standard deviation for both techniques.

  Thanks to the sample preparation procedure mentioned above, the thin foil can be placed nearly at the center of the TEM sample holder and the identied grain boundary is located at the center of the thin foil. A double tilt/rotation TEM sample holder was used to align the grain boundary parallel to the eucentric tilt axis. Next, the tilt was adjusted to vertically align the grain boundary, i.e. parallel to the primary electron beam, see gure I.2.1.

Figure I. 2 . 1 :

 21 Figure I.2.1: Schematic image of aligning grain boundary to eucentric tilt and aligning grain boundary vertically for STEM-EDX acquisitions. The thickness of the yellow line indicates the apparent grain boundary thickness before and after alignment.

CHAPTER I. 2 .

 2 Figure I.2.2: Example of STEM-EDX acquisition on a grain boundary of a Fe-P model alloy: (a) STEM HAADF image of the thin foil with the EDX acquisition zone marked in white, (b) HAADF image and EDX qualitative Fe K α and P K α maps, the red and yellow boxes indicate the zones considered for spectrum extraction during data treatment.

  QUANTIFICATION OF INTERGRANULAR SEGREGATION performed. Figure I.2.3 shows an illustration of the wedge thin foil and acquisition matrix.

Figure I. 2 . 3 :

 23 Figure I.2.3: STEM BF image of the wedge shape thin foil of iron phosphide standard material.

QUANTIFICATIONFigure I. 2 . 5 :

 25 Figure I.2.5: Example of STEM-EDX data processing on a Fe-P model alloy grain boundary: (a) superposed GB spectrum (corresponding to the red box in gure I.2.2 (b)) and grain spectrum (corresponding to the two yellow boxes in gure I.2.2 (b)), (b) zoom on (a) at the energy range close to the P K α peak, (c) the P K α peak after subtraction (GB spectrum minus Grains spectrum) tted by a Gaussian function, (d) the Fe K α and Fe K β peaks from the GB spectrum (corresponding to the red box in gure I.2.2 (b)) tted by a Gaussian function.

CHAPTER I. 2 .

 2 DEVELOPMENT OF A STEM-EDX BOX METHOD FOR THE QUANTIFICATION OF INTERGRANULAR SEGREGATION I.2.2 Verication of the Developed STEM-EDX Box Method

Figure I. 2 .

 2 Figure I.2.7 shows the calculated phosphorus concentration line proles across the grain boundary for three dierent specimen thicknesses: 50, 100, and 150 nm, respectively. The beam

Figure I. 2 . 6 :

 26 Figure I.2.6: Beam size eect. Phosphorus concentration line proles across the grain boundary calculated using Monte-Carlo simulation for three dierent beam diameters (sample thickness = 100 nm). The areas under peak are the same regardless of beam diameter and correspond to the input phosphorus grain boundary concentration of 2 atom/nm 2 .

Figure I. 2 . 7 :

 27 Figure I.2.7: Thickness/beam broadening eect. Phosphorus concentration line proles across the grain boundary calculated using the Monte-Carlo simulation for three thin foil thicknesses (beam diameter = 1 nm). The areas under peak are the same regardless of the beam broadening eect and correspond to an input phosphorus grain boundary concentration of 2 atom/nm 2 .

Figure I. 2 . 8 :

 28 Figure I.2.8: Schematic of an electron beam scanning through a sample with a grain boundary parallel to the electron beam. Two cases are presented: a thin sample (continuous line) and a thick sample (dashed line).

Figure I. 2 .

 2 10 shows two spectra from each of the adjacent grains (the yellow boxes in Figure I.2.2 (b)). The shapes of the two spectra

Figure I. 2 .

 2 Figure I.2.11 shows two spectra from two dierent boxes of the same grain. Exactly the same peaks of coherent Bremsstrahlung are obtained. On the other hand, gure I.2.12 shows four spectra from the four dierent grains (corresponds to the two analyzed grain boundaries in section I.3.2). Dierent coherent Bremsstrahlung peaks are obtained for each grain. Those observations are consistent with the fact that coherent Bremsstrahlung is related to crystal orientation[START_REF] Williams | Transmission electron microscopy: a textbook for materials science[END_REF].

Figure I. 2 . 10 :

 210 Figure I.2.10: Spectra of the two adjacent grains of a grain boundary from the Fe-P model alloy shown in gure I.2.2 (b). Coherent Bremsstrahlung at low energy (1 3.5 keV) and several spurious peaks are visible. The spurious peaks of Pt and Zr are close to 2 keV and cannot be identied clearly because of the presence of coherent Bremsstrahlung.

Figure I. 2 . 11 :

 211 Figure I.2.11: Spectra obtained from two dierent boxes of the same grain. The two curves overlap completely. The orange curve is shifted 5 cps upwards for clarity.

Figure I. 2 . 2 (Chapter I. 3 Direct

 223 Figure I.2.2 (b)) do not necessarily need to be the same size when expressed in cps as in gure I.2.5 (b).Figure I.2.5 (a) shows that, when the grain and GB spectra are superposed, the two backgrounds match nicely and the peaks of the segregated elements can be evidenced.

  The instrument can contain multiple crystals and acquire multiple characteristic X-rays at the same time. Due to this nature, the sample atness for WDS analysis is important. The background subtraction is simpler compared to EDX as normally there is only one peak per spectrum. The background is obtained from interpolating the background measurements on the left and right side of the CHAPTER I.3. DIRECT COMPARISON OF INTERGRANULAR SEGREGATION BETWEEN DIFFERENT TECHNIQUES peak. A linear background is assumed and removed, which is similar to the window method for conventional EDX background removal, see gure I.1.5 (b)).

Figure I. 3 . 1 :

 31 Figure I.3.1: TEM thin foil preparation from the Fe-P model alloy, (a) EBSD orientation map of the full sample surface, grain boundaries A1 and A2 are originally analyzed by APT in [40], (b) SEM micrograph of the A2 grain boundary showing four preparation sites for APT tips, the TEM thin foil was extracted close to these sites, marked in yellow, (c) STEM HAADF image of the full thin foil where the grain boundary is straight and close to the center of the sample.

  Figure I.3.2: Optical micrograph of the polished Fe-P substrate. A large grain is identied and the dierent acquisition zones for each technique are marked. The grain boundaries are highlighted in black, the bright line is a scratch on the surface used for locating the grain of interest. XPS zone corresponds to the size of the primary X-ray beam, WDS zone is a 3×3 matrix of point analyses that covers 100×100 µm, TEM zones correspond to four FIB thin foils, APT zones are two chunks that result in ve APT tips. The TEM thin foils and APT chunks are out of scale in this image.

Figure I. 3 . 3 :

 33 Figure I.3.3: Schematic of the experimental procedure followed in this work.

5, 10 ,

 10 and 15 kV, and currents of 180, 250, and 233 nA in respect to each voltage. The electron beam was defocused at 10 µm. Analyses were conducted on a grid of 3x3 points (50 µm apart). The WDS acquisition locations are indicated in green in gure I.3.2. Two large pentaerythritol (PET) crystals with a 2d value of 8.75 Å were used. Considering the low segregated amount, the exact peak positions of P and S, expressed in 10 5 sin(θ), were determined on a standard material before acquisition at each accelerating voltage. The peak positions of phosphorus are 70407, 70407, 70404 and the peak positions of sulfur are 61381, 61395, 61364 at 5, 10 and 15 kV respectively. The peak intensity was obtained by measuring the counts at the peak maximum and then removing the background. The background positions, expressed in 10 5 sin(θ), were on the left (-750) and right (750) side of the peak positions. The acquisition was repeated twice at the same positions to ensure that the surface contamination due to the electron beam has no eect. The standard materials used for this study are InP (In 78.76 wt% -P 21.24 wt%) and

Four

  TEM thin foils (gure I.3.3 (e)) were prepared using the method mentioned in section I.2.1.1. The nal thicknesses of the thin foils were around 100 nm. The positions of thin foil extraction of the thin foils were random but all very close to the WDS acquisition zone and inside the XPS zone, indicated in red in gure I.3.3. The STEM-EDX acquisitions (gure I.3.3 (f )) were performed using the developed method in section I.2.1.2.

Figure I. 3

 3 Figure I.3.4: WDS measurements. Phosphorus relative intensities (log scale) versus accelerating voltage. Squares: rst round acquisition. Triangles: second round acquisition. Lines: curves calculated using Stratagem TM . Dashed line: only the phosphorus bulk content is considered (0.0011 wt% P). Continuous line: both phosphorus bulk content (0.0011 wt% P) and a phosphorus surface concentration of 16.0 ng/cm 2 = 3.11 atom/nm 2 are considered.

Figure I. 3

 3 Figure I.3.5: WDS measurements. Sulfur relative intensities (log scale) versus accelerating voltage. Square: rst round acquisition. Triangle: second round acquisition. Line: curve calculated using Stratagem TM with a sulfur surface concentration of 21 ng/cm 2 = 3.94 atom/nm 2 .

  Figure I.3.6: STEM-EDX acquisition on the sandwich sample. (a) STEM BF image of one of the thin foils, the EDX acquisition zone is marked in black. (b) BF image and EDX element maps of Fe, P, S, and O. Orange arrow points out the native oxide layer on the sample surface; blue arrow points out the oxide layer between each deposit steps.

Figure I. 3

 3 Figure I.3.8 (a) and (b) shows the comparison between the GB spectrum and the reference one. The background shapes obtained are very similar, which allows correct background removal. A peak from Pt M α and Zr L α is found very close to P K α . As detailed in chapter I.1,

  Figure I.3.8: STEM-EDX data treatment: (a) superposed GB spectrum (corresponding to the red box in gure I.3.6 (b)) and reference spectrum (corresponding to two yellow boxes in gure I.3.6 (b)), (b) zoom in of (a) at the energy range close to P K α and S K α peaks, (c) P K α and S K α peaks after background subtraction (GB spectrum minus reference spectrum) tted by a Gaussian function, (d) Fe K α and Fe K β peaks from the substrate spectrum (corresponding to the left yellow box in gure I.3.6 (b)) tted by a Gaussian function.

  Figure I.3.9 shows the 3D reconstruction of one of the APT tips. In the rst reconstruction, only ions of P + and molecular ions PO + 2 are represented, revealing clearly the phosphorus- enriched interface. In the second reconstruction, ions and molecular ions of oxygen are presented, showing one oxide layer in the iron deposit and another layer at the interface. It has to be mentioned that S segregation cannot be quantied with APT in this system since the interface is highly enriched in oxygen and the main S isotope has a mass of 32 Da so that S + is overlapped with O + 2 and S ++ is overlapped with O + . The mimicked grain boundary segregation values of phosphorus atoms were obtained using cumulative concentration proles as shown in gure I.3.10. When there is no enrichment at the interface, the cumulative prole of silver (blue line in gure I.3.10) increases in the deposit then remained nearly horizontal starting from the interface. Sliver was chosen to represent the non-segregated agent due to its nature of being purely a contamination in the deposit. When enrichment is present at the interface, the slope of the phosphorus prole (orange line in gure I.3.10) increases between the iron deposit and the substrate. Similarly, the oxygen cumulative prole (green line in gure I.3.10) shows the two oxide layers with the changes in slope.

Figure I. 3 . 9 :

 39 Figure I.3.9: 3D reconstruction of one of the APT tips where phosphorus segregation is evident at the interface and oxide layers in the iron deposit and at the interface.

Figure I. 3

 3 Figure I.3.10: APT measurement. Cumulative concentration proles of phosphorus, oxygen, and silver atoms determined from a cylindrical region perpendicular to the interface.

  Figure I.3.11: Phosphorus concentration prole in at% from the APT analysis. The data is from the same tip as in gure I.3.10.

Figure I. 3 . 12 :

 312 Figure I.3.12: Cumulative concentration proles of phosphorus and copper atoms determined from a cylindrical region perpendicular to the interface.

APT 4 . 6 ± 0. 8 -

 468 In this part, quantication of phosphorus and sulfur intergranular segregation on a Fe-P-Fe sandwich sample was conducted using dierent analytical techniques, including surface techniques (XPS and WDS) and cross-section techniques (STEM-EDX and APT). Attention was paid to express the quantications of the dierent methods in the same manner, i.e. surface/interface concentration in atom/nm 2 , so as to allow direct comparison between them. All measurements were performed within the same grain surface of the specimen as close as possible to each other, to keep possible specimen related variations to a minimum. Despite the more complex structure of the Fe-P-Fe sample than a real grain boundary (because of the native oxide layer), the sandwich structure allowed for measurements by dierent techniques at dierent stages of the sample fabrication.

  Figure II.1.1: Schematic presentation of nuclear power plant with pressurized water reactor [82].

Figure II. 1 . 2 :

 12 Figure II.1.2: Schematic presentation of RPV, adapted from [83].

Figure II. 1 . 3 :

 13 Figure II.1.3: Images of the forging process of RPV shells. Adapted from [8486].

Figure II. 1 . 4 :

 14 Figure II.1.4: Illustration of the thermal treatments for RPV shells[START_REF] Zhang | Ségrégation intergranulaire du phosphore dans les aciers des cuves des REP[END_REF]. Note that the base metal do not undergo the weld but it undergoes the SRHT after welding.

Figure II. 1 . 5 :

 15 Figure II.1.5: Solidication structure of an ingot [85, 87].

CHAPTER II. 1 .

 1 LITERATURE REVIEW (a) V-segregates happen late during casting and are the results of general settling of the equiaxed crystal. This mostly happens in the center, the volume contraction causes the intermittent fall of the equiaxed crystals. Then the solute enriched liquid part lls the created voids. The voids are elongated downwards since the crystals are not supported by the dendrites. The V-segregates are often with high porosity or loose structure if the liquid above is insucient to ll the voids. V-segregates are normally removed by piercing before forging. (b) A-segregates (also called ghost lines) at the periphery. They are channels remaining in the mushy zone near the end of the columnar zone where solute enriched liquid begins to ascend in front of the dendrites. The average size of the largest A-segregates is about 1 mm along the radial direction after forging. 3. The micro-segregations can be observed almost in all the volume (at the exception of planar solidication areas). They are formed at the interdendritic spaces where the solute enriched liquid is last solidied. The size of micro-segregation is the size of a dendrite, which can change signicantly according to the local solidication rate (coarser dendrites are in the last solied zone near the hot top of the ingot).

Figure II. 1 .

 1 Figure II.1.6 are chemical etching of 16MND5 type steel done by Naudin et al.[START_REF] Naudin | Modelisation de la ténaticé de l'acier de cuve REP en presence de zones de ségrégation[END_REF]. It can be seen that the ghost lines can be identied from the internal surface to the half thickness.

Figure II. 1 . 6 :

 16 Figure II.1.6: Chemical etching to reveal A-segregates (ghost lines) in 16MND5 type steels, the schematic image shows the plate extraction directions. Adapted from [84].

Figure II. 1 . 7 :

 17 Figure II.1.7: Mertensitic microstructure observed close to fusion boundary of a A508 steel [88].

Figure II. 1 . 8 :

 18 Figure II.1.8: CCT diagram of the studied 16MND5 material. Adapted from [102].

Figure II. 1 . 9 :

 19 Figure II.1.9: Two 16MND5 as-received microstructure worked in [86].

Figure II. 1 . 10 :

 110 Figure II.1.10: Two 16MND5 as-received microstructure: (a) at half-thickness (Ferrite proeutectoïde stands for proeutectoid ferrite, Amas de carbures stands for carbide clusters), (b) at internal surface (Inclusions sphériques stands for spherical inclusions, which are most likely MnS in 16MND5). Adapted from [89].

Figure II. 1 . 11 :

 111 Figure II.1.11: SA508 Cl. 3 steel after chemical etching [97, 98].

Figure II. 1 . 13 :

 113 Figure II.1.13: SEM micrograph of 16MND5 type steel as-quenched martensitic microstructure after chemical etching from (a) [106], (b) [107].

Figure II. 1 . 14 :

 114 Figure II.1.14: Representation of martensitic microstructure with dierent types of boundaries [109].

Figure II. 1 . 15 :

 115 Figure II.1.15: Optical micrographs of nital acid (3%) etched martensite with dierent carbon contents: (a)Fe-0.0026 wt%C, (b)Fe-0.18 wt%C, (c)Fe-0.38 wt%C, (d)Fe-0.61 wt%C [110].

Figure II. 1 .

 1 Figure II.1.16 shows a micrograph of a lower bainitic structure of a low alloy steel that ts the description of Mehl above.

Figure II. 1 . 16 :

 116 Figure II.1.16: Micrograph of lower bainitic structure of a low alloy steel [104].

Figure II. 1 . 17 :

 117 Figure II.1.17: Schematic presentation of bainite morphology proposed by Aaronson et al. [112], in which white phase is ferrite, and dark phases are carbides: (a) nodular bainite, (b) columnar bainite along a prior matrix grain boundary, (c) upper bainite, (d) lower bainite, (e) grain boundary allotriomorphic bainite, (f ) inverse bainite.

Figure II. 1 . 19 :

 119 Figure II.1.19: Bainite morphology categorization system proposed by Bramtt and Speer [114].

Figure II. 1 . 20 :

 120 Figure II.1.20: Schematic presentation of bainite morphology proposed by Zajac [103]: (a) granular bainite, (b) upper bainite, (c) degenerated upper bainite, (d) lower bainite, (e) degenerated lower bainite.

1 - 10 ] α . By a rotation of 45 •

 11045 has proposed a structural transformation relationship between austenite and martensite. In gure II.1.21 (a) and (b), a Body-centered Tetragonal (BCT) structure can be identied in the Face-centered Cubic (FCC) structure of austenite. BCT structure is similar to Body-centered Cubic (BCC) structure but with a compression in the [001] direction and an elongation in the other ⟨001⟩ directions. Bain presents the OR of austenite and martensite as (001) γ //(001) α and [100] γ //[along the axis [001] γ , the austenitic crystal orientation becomes the ferritic CHAPTER II.1. LITERATURE REVIEW crystal. Then the Bain strain transforms the BCT cell to a BCC cell as in gure II.1.21 (c) and (d).

Figure II. 1 . 21 :

 121 Figure II.1.21: Representation of Bain structure that describes the structure transformation between austenite and martensite. (a) a FCC lattice of austenite, (b) a BCT structure identied in FCC austenite, (c) BCT austenite, (d) BCC martensite [104].

Figure II. 1 . 22 :

 122 Figure II.1.22: Illustration of ORs: (a) KS, (b) NW [119].

Figure II. 1 .

 1 Figure II.1.23 shows the[START_REF] Kim | Improved Mechanical Properties of the A 508 Class 3 Steel for Nuclear Pressure Vessel Through Steelmaking[END_REF] α pole gure with variants from a single prior austenite grain acording to Bain, KS, and NW ORs. GT OR is in between the two so its 24 variants should be added in between the red dots and the blue squares[START_REF] Lubin | Etude des mécanismes de la transformation de phase bainitique dans les aciers bas carbone[END_REF][START_REF] Slama | Étude multi-échelle et in situ des évolutions microstructurales en conditions isothermes d'aciers bainitiques en lattes[END_REF].

Figure II. 1 . 23 :

 123 Figure II.1.23:[START_REF] Kim | Improved Mechanical Properties of the A 508 Class 3 Steel for Nuclear Pressure Vessel Through Steelmaking[END_REF] α pole gure of variants in prior austenite grain based on dierent ORs[START_REF] Lubin | Etude des mécanismes de la transformation de phase bainitique dans les aciers bas carbone[END_REF].

CHAPTER II. 1 .

 1 LITERATURE REVIEW axis. The notation of MRs for grain boundaries in martensite or bainite the notation includes two ORs, for example KS/KS means taking one variant of the KS OR as reference then calculate the misorientation and rotation axis pair between the reference and the other 23 variants.Gourgues et al. [121]2 have studied A533B steel with martensite and upper bainite structures using EBSD. They suggested that block boundaries could nucleate from the same {111} γ and that packet boundaries nucleate from two dierent {111} γ . They calculated the theoretical misorientation/rotation axis pairs for KS and NW ORs, i.e. giving MRs of KS/KS and NW/NW. These are shown in gure II.1.24.

Figure II. 1 . 24 :

 124 Figure II.1.24: Theoretical misorientation/rotation axis relationships provided in [121] and adapted axes distributions.

  upper bainite during tempering at 500 • C. The duration of tempering can inuence the size of precipitated carbides, they enlarge as the tempering time increases. The enlargement of carbides can cause irreversible embrittlement. II.1.3.1 Reversible Temper Embrittlement (RTE) RTE is a phenomenon that decreases grain boundary cohesion and is often analyzed through the resulting embrittlement. In BCC steels, the reduction of toughness is observed by DBTT shift and by the fracture mode changing from cleavage to intergranular fracture. RTE can be caused by long and relatively low temperature tempering applied systematically on industrial products, or by thermal aging during operating lifetime. Figure II.1.25 shows the dierent time and temperature ranges for heat treatments 4 . The original goal of tempering treatment

Figure II. 1 . 25 :

 125 Figure II.1.25: Dierent temperature ranges for steel heat treatments 4 [126].

Figure II. 1 .

 1 [START_REF] Goldstein | Quantitative X-ray analysis in the electron microscope[END_REF] shows the relationship between phosphorus bulk concentration and equilibrium phosphorus intergranular concentration measured by AES in Fe-P alloy aged at 500• C[START_REF] Erhart | Equilibrium segregation of phosphorus at grain boundaries of FeP, FeCP, FeCrP, and FeCrCP alloys[END_REF]. It can be seen that when the bulk phosphorus content is above 0.1 wt%, the equilibrium phosphorus grain boundary concentration is nearly at saturation.

Figure II. 1 . 26 :

 126 Figure II.1.26: Equilibrium phosphorus grain boundary concentration (aged at 500 • C) versus the bulk phosphorus concentration for Fe-P alloys [134].

  in gure II.1.27, solute in an alloy can interact with each other in dierent ways with the embrittling elements. Dierent solutes can cosegregate (Mn, Ni), repulse (C), or attract (Cr) the embrittling elements at grain boundaries.

Figure II. 1 . 27 :

 127 Figure II.1.27: Periodic table showing how dierent solute atoms interact with P segregation [136].

Figure II. 1 .

 1 Figure II.1.27[START_REF] Briant | Intergranular failure in steel: the role of grain-boundary composition[END_REF] suggested that Mn and Ni are elements that co-segregate with embrittling

  wt%P model alloy aged at 600 • C, see gure II.1.28.

Figure II. 1 . 28 :

 128 Figure II.1.28: Intergranular fracture proportion decreases as carbon bulk content increases in Fe-0.17 wt%P model alloy aged at 600 • C [134].

Figure II. 1 . 29 :

 129 Figure II.1.29: Molybdenum content has no inuence in phosphorus intergranular segregation in carbon-free steels [144].

. 1 .

 1 30 (a). It can be seen in gure II.1.30 (a) that the closed markers, which indicate higher P concentration, are mostly with high index planes. Although AES measurements were only conducted on one side of the grain boundary fracture, they suggested that phosphorus intergranular segregation tends to stay on the high index plane during fracture, see gure II.1.30 (b).

Figure

  Figure II.1.30: Relationship between grain boundary structure and phosphorus intergranular segregation by Suzuki et al. [147]. (a) phosphorus peak height ratio measured for dierent grain boundary planes, (b) dierent types of grain boundary planes with low and high index. Square markers on grain boundary planes represent phosphorus segregation.

A

  Fe-P binary case close to 16MND5 low alloy steel can be used to calculate the intergranular segregation concentration at equilibrium using the McLean model (P = 80 wt ppm). The segregation free energy of phosphorus ∆G calculated by ∆H = -22.9 kJ/mol and ∆S = 27.5 J/molK [160]. The saturation concentration of a grain boundary is considered equal to the number of possible sites in (110) plane of α-iron [6]. Thus, X ϕ max = √ 2 (0.286) 2 = 17.3 atom/nm 2 ; Figure II.1.31 shows the expected phosphorus concentration at grain boundary in α-iron, determined from equation II.1.7.

Figure II. 1 . 31 :

 131 Figure II.1.31: Equilibrium phosphorus grain boundary segregation concentration in α-iron at dierent temperatures.

Figure II. 1 . 32 :

 132 Figure II.1.32: Thermodynamic model of intergranular segregation considering grain size (log scale) at 325 • C.

Figure II. 1 . 33 :

 133 Figure II.1.33: Kinetics of phosphorus grain boundary segregation concentration in α-iron at 325 • C.

Figure II. 1 . 34 :

 134 Figure II.1.34: Observation of cleavage propagation being stopped by high angle grain boundaries in bainite [166].

Figure II. 1 . 35 :

 135 Figure II.1.35: Schematic graph representing the three steps of fracture [169].

Figure II. 1 . 36 :

 136 Figure II.1.36: Schematic graph representing the plastic zone in front of the crack tip.

Figure II. 1 . 37 :

 137 Figure II.1.37: DBTT is dened as the temperature where yield stress and brittle fracture stress are identical.

Figure II. 1 . 38 :

 138 Figure II.1.38: Typical experimental DBTT curve, showing no sharp change between ductile and brittle fracture.

Figure II. 1 . 39 :

 139 Figure II.1.39: Inuence of yield strength and brittle fracture stress on DBTT.

Figure II. 1 . 40 :

 140 Figure II.1.40: Linear relationship between DBTT and phosphorus peak height ratio from AES with dierent microstructures [162].

Figure II. 1 . 41 :

 141 Figure II.1.41: DBTT increases as phosphorus grain boundary monolayer coverage increases for A533B steel plate, adapted from [181].

14 ×Figure II. 1 . 42 :

 14142 Figure II.1.42: Dierent factors that changes with aging time: (a) phosphorus grain boundary concentration measured by AES, (b) hardness, (c) ∆DBTT [2].

  proportional to DBTT and intergranular fracture percentage. Similar eect was observed by Naudin et al.[START_REF] Naudin | Intergranular fracture stress and phosphorus grain boundary segregation of a Mn-Ni-Mo steel[END_REF] on a synthesized 16MND5 type steel that has a similar composition of Asegregates. They also showed that once the phosphorus intergranular segregation increases, the intergranular fracture proportion increases, see gure II.1.43.

Figure II. 1 . 43 :

 143 Figure II.1.43: Intergranular fracture proportion increases as phosphorus monolayer coverage increases on 16MND5 type steel that has a similar composition of A-segregates [184].

Figure II. 1 . 44 :

 144 Figure II.1.44: Davidenkov diagram of low and high hardness metals, variation of cleavage stress, intergranular fracture stress, and yield strength versus temperature [3].

Figure II. 1 . 45 :

 145 Figure II.1.45: Relationship between critical fracture stress and phosphorus monolayer coverage on 16MND5 type steel that has a similar composition of A-segregates [184].

Figure II. 1 . 46 :

 146 Figure II.1.46: Linear relationship between fracture stress and fracture mode in 2.25Cr-1Mo steel [187].

Figure II. 2 . 1 (Figure II. 2 . 1 :

 2121 Figure II.2.1 (a) shows a schematic view of a RPV shell, the shell thickness is 275 mm for this work. To better describe the samples preparation details, the directions of the shell are dened in gure II.2.1 (b). Due to the cooling rate gradient, there are dierent microstructures along the thickness. In general, the as-received microstructure is dened as the microstructure at 1/4 thickness from the internal surface. In this study, samples were extracted from 3/4 thickness from the internal surface, see gure II.2.1 (b). It was assumed that 1/4 thickness and 3/4 thickness from the internal surface have very similar microstructure (same cooling rate). The martensitic microstructure was fabricated during this work by re-austenitization at 900 • C for one hour followed by water quench. The cooling rate exceeds 100 • C/s to ensure that the whole sample is martensitic. The details of the 1 RCC-M version in 1983.

Figure II. 2

 2 Figure II.2.1 (b) shows a schematic view of where the dierent samples were extracted.The as-received microstructure was dened to be specimens machined from 3/4 thickness from the internal surface, which was believed to have the same fabrication condition (same cooling speed) as 1/4 thickness from the internal surface. The martensitic microstructure specimens were fabricated by re-austenitization, thus the origin of the material is less vital. They were extracted randomly in between 1/2 thickness and the external surface. Sample BSA come from a previous study2 and was extracted at 1/4 thickness (61 mm) from the internal surface.

  Leftover of the mechanical specimen machining was used for STEM-EDX and AES analysis. The STEM-EDX samples were also used for microstructure observation (see section II.3.2). The AES specimens are rectangular bars (1.5 × 1.5 × 15 mm) for in-situ fracturing.II.2.2.2 Thermal TreatmentThe re-austenitization to obtain martensitic microstructure was based on the CCT diagram in gure II.1.8. It can be seen that it requires cooling rate that exceeds 100 • C/s for full martensitic microstructure. The austenitization temperature was selected to be 900 • C for one hour by salt bath. The cooling rate by water quenching was measured by inserting a thermocouple at the center of the blanks. The austenitization and water quenching process was performed in four batches with 7 blanks per batch. Two instrumented blanks were used to control the cooling rate of each batch, one at the fourth quench among the seven, one at the last quench. The cooling rates were kept above 100 • C/s for all batches to ensure that all the blanks are martensitic.

Figure II. 2 . 2 :

 22 Figure II.2.2: The table and curve for step cooling.

  Figure II.2.3 shows an example of the etched sample surface (state M), revealing the micro-segregation in darker lines. The EBSD acquisition position is marked in red.

Figure II. 2 . 3 :

 23 Figure II.2.3: Etched surface of sample M to reveal micro-segregations that was used for locating EBSD acquisition positions for TEM FIB thin foil extraction.

Figure II. 2 . 4 :

 24 Figure II.2.4: Prior austenite grain boundaries identication. Grain boundaries with misorientation between 21.5 • and 46.5 • are highlighted in red, the orange highlights indicate the location of the three TEM thin foils and the prior austenite grain boundary they were extracted from.

Figure II. 2 . 5 :

 25 Figure II.2.5: The H bar xation for TEM FIB thin foils.

Figure II. 2 .

 2 Figure II.2.6 shows an index quality map of one of the MIA thin foils from ASTAR. The misorientation criterion highlights the prior austenite grain boundary in red. The blue arrows in gure II.2.6 mark out the parts of the prior austenite grain boundary being outside the 21.5• -46.5• range, these portions of grain boundaries were also considered as prior austenite grain boundaries for grain boundary continuity.

Figure II. 2 . 6 :

 26 Figure II.2.6: Index quality map of ASTAR acquisition for a MIA thin foil, prior austenite grain boundaries with misorientation angle between 21.5 • -46.5 • are marked in red. The blue arrows show the portions of the grain boundary having misorientation outside the range of 21.5 • -46.5 • . White dots represent the positions of the STEM-EDX acquisitions conducted on dierent segments of the prior austenite grain boundary.

2 . 1 . 4 .

 214 The details are given in the next paragraph.

Figure II. 2 . 7 :Figure II. 2 . 8 :

 2728 Figure II.2.7: Example of line proles of the segregated elements and the GB box width eect on the quantication results.

Figure II. 2 . 9 :

 29 Figure II.2.9: Selection of GB and grain boxes by a MATLAB © code developed in this work : (a) select several points (red crosses) on curved grain boundary to align it, (b) grain boundary after aligning the selected points, (c) select boxes based on Mn intensity prole, dark gray box is the GB box, light gray boxes are the grain boxes.

Figure II. 2 .

 2 Figure II.2.11 shows the dierent cases where the phosphorus K α peak is tted with a Gaussian function.

Figure II. 2 .

 2 Figure II.2.11 (a) shows a case where the phosphorus K α peak is clearly visible. The Gaussian function ts perfectly and phosphorus segregation is clearly seen in the EDX qualitative map. Figure II.2.11 (b) shows a case where the signal-to-noise ratio

Figure II. 2 . 11 :

 211 Figure II.2.11: Gaussian function tting results of STEM-EDX data treatment : (a) EDX map and (b) line prole showing clear segregation of phosphorus at grain boundary,

Figure II. 2 .

 2 Figure II.2.12 shows a typical fracture surface with a mixture of cleavage and intergranular fracture. Multiple intergranular fracture surfaces were analyzed, see the indicated points in gure II.2.12.

Figure II. 2 . 12 :

 212 Figure II.2.12: Fracture surface in AES ultra-high vacuum chamber showing a mixture of cleavage and intergranular fracture.

Figure II. 3 .

 3 Figure II.3.1 shows the etching results on the CR surface. The as-received bainitic microstructure is located at 68.75 mm (3/4 thickness) from the external surface, marked with black dashed line. Numerous gray lines were revealed and the blue arrow points out the most likely ghost line on the etched surface. Others were considered as micro-segregations. The orange box marks out the zoomed-in image in gure II.3.2 (a) where the thin micro-segregations can be better seen.

Figure II. 3 . 1 :

 31 Figure II.3.1: FeCl 3 etching to reveal segregated zones on surface CR, the black dash line marks out 69 mm from the external surface which represents the as-received microstructure location. The blue arrow marks the most likely ghost line on the surface and the orange box marks out the zone in gure II.3.2.

Figure II. 3 Figure II. 3 . 2 :

 332 Figure II.3.2 (a) shows a zoom on gure II.3.1 (orange box). It can be seen that the microsegregations are thin along the radial direction (up to 1 mm) and elongated along the circumferential direction. The micro-segregation seems to be elongated also in the axial direction as shown in gure II.3.2 (b) where part of the etched short and long side are presented. The blue arrow in gure II.3.2 points out a possible ghost line.

  Figure II.3.3 shows the HV 0.01 hardness line proles and the WDS line proles of the ve elements. The rst line prole crosses two micro-segregated zones while the second and third prole only cross one.

Figure II. 3 . 3 :

 33 Figure II.3.3: HV0.01 hardness and WDS line proles of three micro-segregated zones. The blue case crosses two micro-segregations while the green and orange cases cross only one.

  Figure II.3.4 (a) shows the nital etched surface of the as-quenched sample. The black dots of a few micron in size were considered as artifacts during CHAPTER II.3. MATERIAL CHARACTERIZATION etching. It can be seen that the microstructure presents a lath structure without the presence of carbides. This resembles the typical lath martensite structure as mentioned in section II.1.2.1, see gure II.1.13. Lack of carbide further conrms the displasive transformation from austenite to martensite where no carbon diusion can take place.

Figure II. 3 Figure II. 3 . 4 :

 334 Figure II.3.4 (b) shows the nital etched surface of the tempered sample (sample M in table II.2.2). Tempering treatment provides time where the excess amount of carbon in martensite can diuse. Small carbides were observed in the tempered microstructure.

Figure II. 3 Figure II. 3 . 5 :

 335 Figure II.3.5 (a) and (b) show the micrographs of the aged martensite samples (MIA & MSC). It can be seen that the thermal aging treatment (SRHT and step cooling) may induce additional carbide precipitations compared to tempered martensite, although comparison of optical micrographs of etched specimens might be misleading. This suggests that precipitation is not complete after tempering. However, the microstructure between the two aged samples (MIA & MSC) remains unchanged. The change in carbide precipitates between tempered martensite and the two aged samples is also consistent with the decrease in hardness of about 15 HV after thermal aging shown in the last chapter of this study (see table II.5.1).

Figure II. 3 Figure II. 3 . 7 :

 337 Figure II.3.6 (a) and (b) show the etched surface of the tempered as-received bainitic microstructure before and after step cooling (samples B & BSC). It can be seen that there are carbide clusters located within the ferritic grains. In the work of Diawara et al. [89], it can be seen that retained austenite and martensite islands (M-A constituents) can be observed in the as-quenched microstructure. The carbon content is higher in M-A constituents than in the bainitic grains. It is known that the tempering treatment dissolves M-A constituents and forms carbides [89, 104]. Figure II.3.6 is similar to the other as-received microstructures reported in the literature, see gures II.1.9 and II.1.10 (a). Also, there were no microstructure evolutions observed between gure II.3.6 (a) and (b), showing that step cooling does not eect the microstructure.

Figure II. 3 . 8 :

 38 Figure II.3.8: STEM BF image of a FIB thin foil of the as-received bainitic microstructure

  Figure II.3.9 corresponds to the carbide cluster that is located on the top right in gure II.3.8.

Figure II. 3 . 9 :

 39 Figure II.3.9: STEM-EDX qualitative analysis on dierent types of carbides, showing Fe 3 C and carbides rich in molybdenum.

2 . 3 )

 23 Figure II.3.11: Orientation map of (a) as-received bainitic microstructure, (b) martensite.

Figure II. 3 . 13 :

 313 Figure II.3.13: Rotation axis distribution in the dierent misorientation ranges dened for (a) as-received bainitic microstructure (sample B), (b) martensite (sample M).

  These are rotation axes close to [332] and [443]. When comparing to the theoretical axes distribution in gure II.1.24, the rotation axis distribution determined here for bainite falls closer to NW MR. As mentioned in section II.1.3.3, grain size plays a role in the thermodynamic model of segregation, see gure II.1.32. To understand if the analyzed samples fall into the region where grain size aects the equilibrium segregation concentration, the size of dierent types of grains in the bainitic and martensitic microstructures are analyzed based on the EBSD maps and TEM observations.

Figure II. 3 .Figure II. 3 . 14 :

 3314 FigureII.3.14 (a) shows the reconstruction of the as-received bainitic structure, and gure II.3.14 (b) shows the reconstruction of the martensitic structure. Here, the prior austenite grain size was determined by interceptions. Vertical and horizontal lines of 50 µm apart were drawn on the EBSD map. The length of each line corresponds to the size of the EBSD maps (view eld in table II.2.3) and the number of intercepts were calculated. For the martensitic microstructure, the obtained prior austenite grain size is similar to the result obtained by Pous-Romero et

Figure II. 3 . 15 :

 315 Figure II.3.15: ASTAR indexation quality map superposed with orientation map of a martensitic FIB thin foil to determine lath size by the interception method.

  Figure II.4.1: Rotation axis distribution of each state where the rotation axes of each STEM-EDX analyzed grain boundaries are marked. Black: acquisition at the proper category; Red: assumed prior austenite grain boundaries; Yellow: other grain boundaries with misorientation measuring errors. The color maps are the axes distributions obtained from EBSD acquisitions of each state.

Figure II. 4 . 2 :

 42 Figure II.4.2: Indicative scale of the segregation level of the dierent samples due to the complex thermal treatments.

Figure II. 4 . 3 :

 43 Figure II.4.3: Summary of how the dierent elements segregate at dierent types of grain boundaries in dierent samples, the segregation quantications are presented in atom/nm 2 .

Figure II. 4 .

 4 Figure II.4.4 shows the average of total segregation in atom/nm 2 at each type of grain boundary of each state. The rst part (solid color) of each bar is the sum of P+Mn+Ni and the transparent colors indicate the amount of Mo. It is to be noted that very few grain boundaries other than prior austenite grain boundaries were analyzed for states BSA and MIA. They are removed from the comparisons.

Figure II. 4 . 4 :

 44 Figure II.4.4: Average of total segregation in atom/nm 2 at each type of grain boundary of each sample. Solid color: sum of P+Mn+Ni, transparent color: Mo.

Figure II. 4

 4 Figure II.4.4 clearly demonstrate the dierent levels of segregation obtained in the dierent grain boundary categories. Similar to the observation from gure II.4.3, molybdenum segrega-

3 &Group 4 >

 34 Group 5 (without Σ3) > Group 1. Also, segregation level at Σ3 boundaries is lower compared to general HAGBs. When considering the groups dened in this work, gure II.4.5 shows a dierent presentation of the data gathered in gure II.4.3.

Figure II. 4 . 5 :

 45 Figure II.4.5: Concentration of each element at dierent types of grain boundaries for the different states.

  Figure II.4.6 shows the segregation level of each element among the four aged states (BSC, BSA, MIA, MSC) versus the misorientation angle of each analyzed grain boundaries. The data points in gure II.4.6 are not only in the range of 21.5 • -46.5 • due to the measurements of the assumed prior austenite grain boundaries.

Figure II. 4 . 6 :

 46 Figure II.4.6: Segregation concentration in atom/nm 2 of each element against grain boundary misorientation angle for STEM-EDX analyses of prior austenite grain boundaries. Data points out of the range of 21.5 • -46.5 • are the assumed prior austenite grain boundaries.

  Figure II.4.8: Graphical presentation of the average intergranular segregation at each prior austenite grain boundaries analyzed of each state.

  Figure II.4.9 rst presents the possible packet rotation axes proposed in [121] in dierent grain boundary groups, the dierent point colors represent the dierent MRs. Then the rotation axis distributions of the STEM-EDX analyzed grain boundaries in dierent groups of dierent states are presented. The block boundaries identied in group 5 are removed from gure II.4.9.

Figure II. 4 . 9 :

 49 Figure II.4.9: Comparison between the theoretical rotation axes [121] and the STEM-EDX analyzed grain boundaries. Block boundaries identied in group 5 are removed from the rotation axis plots.

  be slightly more susceptible to phosphorus intergranular segregation compared to martensite, which is exactly the opposite from what the literature[START_REF] Raoul | Eect of microstructure on the susceptibility of a 533 steel to temper embrittlement[END_REF][START_REF] Park | Eects of boundary characteristics on resistance to temper embrittlement and segregation behavior of NiCrMo low alloy steel[END_REF][START_REF] Zhang | Cleavage fracture in bainitic and martensitic microstructures[END_REF][START_REF] Yang | Eect of microstructure on the impact toughness and temper embrittlement of SA508Gr.4N steel for advanced pressure vessel materials[END_REF] suggested.

Figure II. 4 .Figure II. 4 . 10 :

 4410 Figure II.4.10 shows the averaged segregation level at prior austenite grain boundary of states BSC & MSC.

FigureFigure II. 4 . 12 :

 412 Figure II.4.11: Trapping of phosphorus at dierent types of grain boundaries for (a) non-aged bainite, (b) bainite after step cooling.

Figure II. 4 . 13 :

 413 Figure II.4.13: Illustration of the available solute quantity.

Figure II. 4 . 14 :

 414 Figure II.4.14: McLean thermodynamic model tting the measured segregation concentrations: (a) P, (b) Mo, (c) Mn, (d) Ni. Black curves: saturation set at one monolayer; blue curves: saturation set at 0.21 for Mo and 0.5 for the others.

Case 3 :

 3 This case corresponds to site composition between P, Mn, and Ni, i.e. those three elements share the same type of sites. Here, the multicomponent model proposed by Guttmann[START_REF] Guttmann | Equilibrium segregation in a ternary solution: A model for temper embrittlement[END_REF] in equation II.1.15 was considered for these three elements. On the other hand, binary system from the McLean model was used for molybdenum, which is considered to segregate to dierent sites. CHAPTER II.4. INTERGRANULAR SEGREGATION IN BAINITIC AND MARTENSITIC 16MND5 STEEL element (P, Mn, Mo, and Ni) at each portion of prior austenite grain boundaries were plotted against each other. Figures II.4.16 and II.4.17 shows the correlation between two elements (six possible combinations) in bainite and in martensite. Each small dot represents an analyzed portion of prior austenite grain boundary, the big dot represents the average value.It is clearly shown that P concentration increases as Mn or Ni concentration increases in both bainite and martensite. There also seems to be relationship between Mn and Ni but it is less evident in martensite than in bainite. On the other hand, Mo shows no relationship at all with either of the elements in both microstructures.

Figure II. 4 . 16 :

 416 Figure II.4.16: Correlation between segregated elements in aged bainite (BSC), only prior austenite grain boundaries are considered. Small dot: each STEM-EDX acquisition; big dot: average of all STEM-EDX acquisitions.

martensitic microstructure ( 70 •Figure II. 5 . 2 :Figure II. 5 . 3 :

 705253 Figure II.5.2: Fractographs of Charpy V-notch impact tests for states (a) B fractured at -50 • C, (b) M fractured at -120 • C.

Figure II. 5 .

 5 Figure II.5.4 shows a zoomed fractograph of the intergranular fracture surface. It can be seen that instead of having smooth surfaces that mark out the grains' morphology, the surfaces are

Figure II. 5 . 4 :

 54 Figure II.5.4: Fractograph of Charpy V-notch impact test showing the rough intergranular fracture surface (state MSC fractured at -60 • C).

Figure II. 5 . 6 :

 56 Figure II.5.6: Eect of thermal aging on phosphorus intergranular segregation and ∆DBTT of bainite & martensite.

Figure II. 5 .

 5 Figure II.5.7 plots the critical fracture stress versus the phosphorus grain boundary concentration schematically. When assuming that the cleavage fracture stress is independent from the temperature and phosphorus intergranular segregation level, the critical cleavage fracture stress of bainite and martensite can be dened (blue dashed lines). Martensite has higher cleavage fracture stress than bainite because of its smaller carbides and the dierent carbide distribution. Meanwhile, the critical intergranular fracture stress can be considered to decrease as the phosphorus grain boundary concentration increases (red solid line). Once intergranular fracture is induced, more phosphorus segregation decreases more the critical fracture stress.

  This result has a similar tendency as reported by Naudin et al.[START_REF] Naudin | Intergranular fracture stress and phosphorus grain boundary segregation of a Mn-Ni-Mo steel[END_REF]. The green line in gure II.5.7 shows how the bainitic critical fracture stress changes with phosphorus grain boundary concentration. Similar to the rst part of the martensitic one (yellow line), no intergranular fracture was observed for state B (0.74 atom/nm 2 ) while small amount of intergranular fracture was observed for state MSC (3.35 atom/nm 2 ).

Figure II. 5 . 7 :

 57 Figure II.5.7: Interpretation of the microstructure eect on intergranular fracture.

53 • 3 .

 533 grain boundary misorientation follows roughly what was concluded by the literature: (a) HAGB > LAGB (misorientation threshold at 15 • ) (b) Group 3 (γ GB) & Group 4 (46.5 • -) > Group 5 (> 53• ) ≈ Group 2 (7 • -21.5 • ) > Group 1 (lath boundaries) Unlike what was suggested in the literature, segregation of phosphorus and other elements were observed at Σ3 boundaries. However, there was no clear relationship between grain boundary misorientation/rotation axis with intergranular segregation level, further studies can focus on the relationship with grain boundary planes to have further analysis. Trapping of phosphorus by the two microstructures (tempered bainite & tempered martensite) is estimated based on an approximation (X v << 1) for the thermodynamic model. It was shown that bainitic and martensitic microstructures traps about 20% of phosphorus in total after aging at dierent types of grain boundaries. Moreover, the segregation level at prior austenite grain boundaries for aged states (BSC & MSC) remained nearly the same based on measurements by STEM-EDX and AES. The eect of microstructure on the behavior of phosphorus intergranular segregation is not obvious, which is very dierent from the assumption given in the literature.

  Une nouvelle méthode a été développée pour quantier la ségrégation intergranulaire par STEM-EDX en exploitant des régions d'acquisition rectangulaires (boîtes). Le spectre moyen acquis sur les grains adjacents est soustrait du spectre acquis sur une zone englobant le joint de grains pour éliminer les pics parasites et le bruit de fond et ne conserver que la contribution de la ségrégation. La quantité de soluté ou impureté analysée est projetée sur la surface du joint.Des simulations Monte-Carlo ont été menées pour montrer que cette méthode est indépendante des problèmes d'élargissement du faisceau et de volume d'interaction du faisceau lorsqu'elle respecte un critère : la largeur de la boîte relative au joint de grain doit être supérieure à deux fois le diamètre du faisceau élargi. La méthode STEM-EDX a d'abord été validée sur deux joints de grains d'un alliage modèle Fe-P déjà analysés par SAT. Les résultats de quantication du phosphore sur les deux joints de grains par les deux techniques sont dans l'erreur de mesure.En outre, un échantillon sandwich Fe-P-Fe a été fabriqué an que la ségrégation interfaciale du phosphore puisse être mesurée par quatre techniques de caractérisation. La ségrégation du phosphore a d'abord été induite en surface an que les techniques de surface XPS et WDS puissent être appliquées. Du fer a ensuite été déposé sur la surface pour imiter un joint de grain ségrégé an que les méthodes STEM-EDX et SAT puissent être utilisées. Un bon accord a été trouvé entre les résultats des quatre techniques, ce qui conrme la validité de la méthode STEM-EDX développée.La méthode STEM-EDX a ensuite été appliquée à un acier de type 16MND5 de microstructure de type bainite revenue ou martensite revenue. On observe que le phosphore, le manganèse, le molybdène et le nickel ségrègent à tous les types de joints de grains dans les deux microstructures. Les résultats ont montré que les anciens joints de grains austénitiques sont les plus sensibles et que les joints de lattes sont les moins sensibles à la ségrégation. D'autres joints de grains présentent des niveaux intermédiaires de ségrégation. En outre, les joints de coïncidence élevés (c'est-à-dire Σ3) présentent une ségrégation pas toujours beaucoup plus faible que celle d'autres joints de grains. Les joints de paquets n'ont pas pu être identiés de façon able à partir de leur désorientation et de leur axe de rotation, de sorte que leur comportement vis-à-vis de la ségrégation n'a pas pu être caractérisé.Pour les anciens joints de grains austénitiques, aucune relation particulière entre le niveau de ségrégation et l'angle de désorientation n'a été observée. Cependant, la tendance à une plus faible ségrégation pour les joints de grains désorientés de moins de 20 degrés a été conrmée.CONCLUSIONS & PERSPECTIVESLes diérentes analyses ont montré qu'il y a peu d'eet microstructural sur la ségrégation intergranulaire du phosphore. En d'autres termes, les ségrégations sont similaires dans la martensite revenue et la bainite revenue, ce qui contredit une hypothèse avancée dans la littérature pour expliquer la diérence de sensibilité au vieillissement thermique de ces microstructures.De plus, le niveau de ségrégation intergranulaire du phosphore est resté très faible même après un traitement de refroidissement étagé ou un vieillissement isotherme de longue durée à 400• C (∼3 atom/nm 2 ). Cela peut être dû à une compétition de site du phosphore avec le nickel et le manganèse.L'eet de piégeage, c'est-à-dire l'appauvrissement en phosphore de la matrice dû à la ségrégation aux joints de grains, a été estimé dans les microstructures martensitiques et bainitiques.La teneur totale en phosphore ségrégé aux diérents types de joints de grains ne dépasse pas 25% de la teneur nominale (80 ppm en poids). Il en a été conclu que le piégeage ne devrait pas aecter fortement le comportement de ségrégation du phosphore.Parmi les quatre éléments ségrégés, il a été observé que le phosphore, le manganèse et le nickel sont très probablement en compétition de site pendant le vieillissement thermique, tandis que le molybdène occupe des sites diérents. De plus, il a été observé que la ségrégation de molybdène est pratiquement indépendante de la température de vieillissement. Cela suggère que le molybdène pourrait avoir une faible concentration de saturation aux joints de grains, atteinte même à haute température.En supposant que la ségrégation d'équilibre est atteinte après les diérents traitements thermiques eectués, des modèles thermodynamiques ont été proposés pour ajuster les diérentes mesures et expliquer les diérentes relations entre les quatre éléments. Il a été observé que des hypothèses et des paramètres d'entrée très diérents pouvaient donner des ajustements satisfaisants de nos données expérimentales. Cela implique que ces modèles ne doivent pas être utilisés pour des prévisions en dehors de la plage de température étudiée ici (400• C 650 • C).Le décalage de température de transition ductile-fragile a été mesuré après vieillissement pour les deux microstructures étudiées (martensite revenue et bainite revenue). Il a été conrmé que le décalage est plus élevé pour la martensite revenue que pour la bainite revenue. L'examen des résultats de décalage et des mesures de ségrégation intergranulaire suggère que la sensibilité à la FRR plus élevée de la martensite revenue est principalement due à sa meilleure résistance au clivage. Ceci implique qu'une faible ségrégation de phosphore sut à induire une rupture intergranulaire. La bainite revenue, au contraire, a une résistance au clivage plus faible qui conduit à une moindre susceptibilité à la rupture intergranulaire, bien que la concentration de phosphore aux joints de grains soit similaire.Le présent travail a fourni une méthode able de quantication de la ségrégation intergranulaire par STEM-EDX qui a été appliquée sur des aciers 16MND5 de structure bainitique revenue ou martensitique revenue dans diérents états de vieillissement thermique. Pendant longtemps, les eets de microstructure sur la fragilité de revenu réversible ont été déterminés par l'évolution des propriétés de rupture telles que la température de transition de résilience lors de traitements CONCLUSIONS & PERSPECTIVES ou vieillissements thermiques. Elles ont conduit à une hypothèse que les résultats du présent travail ne valident pas : les diérences de ségrégation intergranulaire du phosphore ne jouent pas un rôle important dans l'eet de microstructure (bainite ou martensite) sur la fragilité de revenu réversible ; en revanche, la valeur absolue de la contrainte critique de rupture par clivage paraît déterminante. L'étude des facteurs microstructuraux de la sensibilité à la FRR demande encore à être approfondie.Dans de futurs travaux, la contrainte critique de rupture fragile devrait être déterminée sur les mêmes échantillons an de la relier à la ségrégation intergranulaire de phosphore. Il serait également souhaitable d'avoir une analyse plus détaillée de la structure des joints de grains, en déterminant en particulier la nature cristallographique des plans de joints, pour améliorer la connaissance de la relation entre structure des joints et ségrégation. Les cycles de vieillissement thermique les plus simples possibles sont à privilégier (i.e. vieillissement isotherme de longue durée) pour faciliter les comparaisons et l'interprétation des résultats.

Figure A. 1 :

 1 Figure A.1: STEM-EDX acquisition locations on the FIB thin foils of B.

  . Adapted from [102]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13 SEM micrograph of 16MND5 type steel as-quenched martensitic microstructure after chemical etching from (a) [106], (b) [107]. . . . . . . . . . . . . . . . . . . . 83 II.1.14 Representation of martensitic microstructure with dierent types of boundaries [109]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 II.1.16 Micrograph of lower bainitic structure of a low alloy steel [104]. . . . . . . . . . . 85 II.1.17 Schematic presentation of bainite morphology proposed by Aaronson et al. [112]. 86 II.1.18 Schematic presentation of upper bainite formation: (a) BI, (b) BII, (c) BIII [113]. 87 II.1.19 Bainite morphology categorization system proposed by Bramtt and Speer [114]. 87 II.1.20 Schematic presentation of bainite morphology proposed by Zajac [103]. . . . . . . 88

				83
		II.1.15 Optical micrographs of nital acid (3%) etched martensite with dierent carbon
			contents: (a)Fe-0.0026 wt%C, (b)Fe-0.18 wt%C, (c)Fe-0.38 wt%C, (d)Fe-0.61
			wt%C [110
		Introduction	1
		I Development of intergranular segregation quantication method-ology based on STEM-EDX	9
		I.1	Literature Review	11
	II.1.9	Two 16MND5 as-received microstructure worked in [86]. . . . . . . . . . . . . . .

I.1.1 Energy Dispersive X-ray Spectroscopy with Scanning Transmission Electron Microscopy (STEM-EDX) . . . . . . . . . . . . . . . . . . . . . . . 12 I.1.1.1 The X-ray Spectrum . . . . . . . . . . . . . . . . . . . . . . . . 13 I.1.1.2 Energy Dispersive X-ray Spectroscopy (EDX) Quantication by the Cli-Lorimer Method . . . . . . . . . . . . . . . . . . . . . 15 I.1.2 Scanning Transmission Electron Microscope -Energy Dispersive X-ray Spectroscopy (STEM-EDX) for Intergranular Segregation Quantication 20 I.1.2.1 Diculties Encountered using STEM-EDX for Intergranular Segregation Quantication . . . . . . . . . . . . . . . . . . . . . . . 21 I.1.2.2 STEM-EDX Measurements of Phosphorus Intergranular Segregation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 I.1.3 Cross-comparison of Intergranular Segregation Quantication Between Dierent Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . terialII.1.10 Two 16MND5 as-received microstructure. Adapted from [89]. . . . . . . . . . . . II.1.11 SA508 Cl. 3 steel after chemical etching [97, 98]. . . . . . . . . . . . . . . . . . . II.1.12 SA508 Cl.3 steel after chemical etching [96]. . . . . . . . . . . . . . . . . . . . . . XII LIST OF FIGURES II.1II.1.21 Representation of Bain structure that describes the structure transformation between austenite and martensite. . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 II.1.22 Illustration of ORs: (a) KS, (b) NW [119]. . . . . . . . . . . . . . . . . . . . . . 90 II.1.23 [100] α pole gure of variants in prior austenite grain based on dierent ORs [119]. 90 II.1.24 Theoretical misorientation/rotation axis relationships provided in [121] and adapted axes distributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 II.1.25 Dierent temperature ranges for steel heat treatments 4 [126]. . . . . . . . . . . . 93 II.1.26 Equilibrium phosphorus grain boundary concentration (aged at 500 • C) versus the bulk phosphorus concentration for Fe-P alloys [134]. . . . . . . . . . . . . . . . . 94 II.1.27 Periodic table showing how dierent solute atoms interact with P segregation [136]. 95 II.1.28 Intergranular fracture proportion decreases as carbon bulk content increases in Fe-0.17 wt%P model alloy aged at 600 • C [134]. . . . . . . . . . . . . . . . . . . . 96 II.1.29 Molybdenum content has no inuence in phosphorus intergranular segregation in carbon-free steels [144]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 II.1.30 Relationship between grain boundary structure and phosphorus intergranular segregation by Suzuki et al. [147]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 II.1.31 Equilibrium phosphorus grain boundary segregation concentration in α-iron at dierent temperatures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 II.1.32 Thermodynamic model of intergranular segregation considering grain size (log

  Le premier objectif de ce travail est donc de développer une méthodologie pour quantier la ségrégation intergranulaire par STEM-EDX sans être inuencé par l'hypothèse sur le volume analysé. Le deuxième objectif est de réaliser une étude comparative de la ségrégation intergranulaire et de la FRR dans les microstructures bainitiques et martensitiques de l'acier de type 16MND5. Elle s'appuie essentiellement sur la méthodologie STEM-EDX développée et sur des essais de résilience pour mesurer les décalages de la température de transition ductile-fragile dus à un traitement de vieillissement accéléré. Ce manuscrit est séparé en deux parties correspondant aux deux objectifs. Dans la partie I, le chapitre I.1 présente une revue de littérature sur la méthode de quantication de Cli-Lorimer par STEM-EDX, et sur son application pour

	INTRODUCTION
	Chapter I.1
	Literature Review
	Part I
	Development of intergranular segregation
	quantication methodology based on
	STEM-EDX
	le chapitre II.5 présente l'évolution des propriétés mécaniques du 16MND5 constitué de bainite
	revenue ou de martensite revenue lors d'un vieillissement accéléré. Une interprétation de la
	relation entre la microstructure, la ségrégation intergranulaire et les propriétés mécaniques est
	proposée.

Les résultats de ségrégation intergranulaire peuvent être présentés dans diérentes unités physiques telles que la fraction d'une monocouche, le pourcentage atomique et la concentration de surface (nombre d'atomes par unité de surface). Certaines de ces unités nécessitent des hypothèses qui sont rarement vériées et ne sont parfois pas explicitées. Dénir une fraction de monocouche nécessite par exemple des hypothèses sur la cristallographie (indices

de Miller)

du plan de joint. Pour ces raisons, il est pratiquement impossible de comparer les résultats de quantication de ségrégation intergranulaire provenant de diérentes sources. Des comparaisons directes entre diérentes techniques de quantication sont par ailleurs rarement fournies.

La technique la plus courante pour quantier la ségrégation des joints de grains est la spectrométrie d'électrons Auger (AES). Les zones analysables sont les zones de rupture intergranulaire. Cela implique que toutes les surfaces analysées par AES ont une quantité minimale d'éléments fragilisants ségrégés an qu'une fracture intergranulaire puisse apparaître. Dans les cas où la rupture intergranulaire de l'éprouvette ne peut être obtenue, l'analyse des joints de grains par AES n'est tout simplement pas possible, ce qui constitue une forte limitation de cette technique. La sonde atomique tomographique (SAT) a été utilisée pour étudier la ségrégation, notamment lorsqu'une rupture intergranulaire ne peut pas être obtenue. Cependant, le petit volume d'analyse et le manque d'informations sur la structure cristallographique sont des inconvénients. Cette technique peut toutefois être complétée par de la diraction de Kikuchi en transmission pour les informations cristallographiques. La spectrométrie de rayons X à dispersion d'énergie en microscopie électronique à transmission à balayage (STEM-EDX) a également été utilisée pour mesurer la ségrégation intergranulaire du phosphore dans les aciers faiblement alliés, selon diérents modes d'acquisition (mesure ponctuelle, prol de ligne ou balayages 2D) . La diculté induite par la taille du INTRODUCTION faisceau, son élargissement lors de sa propagation, et par le volume d'interaction n'a pas été entièrement résolue, de sorte que les quantications de ségrégations interfaciales ne sont pas toujours ables. la quantication de la ségrégation intergranulaire. Il passe également en revue les comparaisons de quantication de ségrégation intergranulaire par diérentes techniques de caractérisation. A la suite de cet état de l'art, le chapitre I.2 décrit en détail la méthodologie de mesure par STEM-EDX développée, de la préparation de l'échantillon et des paramètres d'acquisition jusqu'au traitement des données pour obtenir une quantication en concentration par unité de surface. Enn, la méthode STEM-EDX développée est comparée à d'autres techniques. Elle est d'abord comparée à la SAT sur les joints de grains d'un alliage modèle Fe-P. Ensuite, quatre techniques diérentes (spectrométrie de photoélectrons induits par rayons X (XPS), microsonde de Castaing (WDS), sonde atomique tomographique (SAT) et spectrométrie de rayons X à dispersion d'énergie en microscopie électronique à transmission à balayage (STEM-EDX) sont comparées sur un échantillon sandwich Fe-P-Fe synthétisé à dessein. Le chapitre II.1 débute par une présentation de l'acier étudié et de sa fabrication et se poursuit par une revue de littérature sur les structures martensitiques et bainitiques, puis sur la fragilité de revenu réversible et sa dépendance à la microstructure. Le chapitre II.2 présente les méthodes expérimentales, y compris les préparations d'échantillons et une adaptation du traitement des données STEM-EDX à l'acier étudié. Le chapitre II.3 donne les résultats des caractérisations métallurgiques de base entreprises pour les besoins de notre étude. Le chapitre II.4 présente nos résultats de ségrégation intergranulaire sur diérents types de joints de grains dans les microstructures de bainite revenue et de martensite revenue de l'acier 16MND5. Enn, A la n du manuscrit, les conclusions de nos travaux sont présentées et des perspectives de recherches ultérieures sur le même sujet sont proposées.

Intergranular segregation may embrittle metallic alloys, and cause intergranular fracture

[START_REF] Kraxner | Quantitative EDXS: Inuence of geometry on a four detector system[END_REF]

. The most common technique for intergranular segregation measurement is AES

[START_REF] Lejcek | Grain boundary segregation in metals[END_REF]

.

AES is a sensitive surface technique that requires specimens being fractured under ultra high vacuum to avoid surface contamination. This means that it can only analyze intergranular fractured surfaces. In other words, only grain boundaries that have exceeded a certain amount of embrittling segregated elements can be analyzed by AES.

Apart from AES, Analytical Transmission Electron Microscope (ATEM) equipped with EDX and/or Electron Energy Loss Spectroscopy (EELS) shows great interest for the quantication of intergranular segregation

1

  It was not possible here to use a Mo grid due to the Mo L α peak overlapping with the P K α peak.

	CHAPTER I.2. DEVELOPMENT OF A STEM-EDX BOX METHOD FOR THE
	QUANTIFICATION OF INTERGRANULAR SEGREGATION
	The TEM used in this study is a FEI Tecnai OSIRIS that operates at 200 kV. The setting of
	the beam was done to obtain a beam current of 0.5 nA and a beam size of about 1 nm. With
	the thin foil thickness at approximately 100 nm, this beam condition results in about 30 kcps
	during acquisition. The beam condition was adjusted depending on the thin foil thicknesses to
	respect 30 kcps during acquisition. All STEM-EDX acquisitions were performed by Esprit v1.9
	developed by Bruker. The acquisitions were done using the hypermap function that maps an
	area of choice based on a STEM BF or HAADF image. The mapping size is approximately 161
	× 50 -80 nm, giving a pixel size of 0.157 or 0.114 nm 2 . It is to be noted that the pixel size was
	deliberately chosen much smaller than the beam size. The acquisition time is usually around
	20 to 40 minutes for the entire map. The drift correction option in Esprit was used. The drift
	observed during the acquisitions was around 30 nm on average. Acquisitions with drifts that
	exceeds Esprit correction range are removed. Table I.2.1 shows the acquisition parameters used
	in this work.
	Table I.2.1: STEM-EDX acquisition parameters used in this work.
	Parameter	Values
	Accelerating voltage	200 kV
	Beam size	≈1 nm
	Beam current	≈0.5 nA
	STEM magnication	630/900 kx
	EDX software	Esprit v1.9
	EDX function	Hypermap with drift correction
	EDX map resolution	1024 pixels
	EDX map size	y = 161 or 114 nm; x = 50 -80 nm
	EDX step size	0.6 or 0.11 nm
	EDX acquisition time	≈20 -40 mins
	EDX map total counts	≈ 47,000,000 counts
	Figure I.2.2 shows a simple example of EDX acquisition obtained on an iron grain bound-
	ary containing segregated phosphorus. This acquisition was obtained on a Fe-P model alloy
	described later (see section I.3.2). The grain boundary is aligned vertically and the acquisition
	zone is marked out in white in the STEM BF image (gure I.2.2 (a)). Figure I.2.2 (b) shows

  equations I.2.3 and I.2.4 we obtain C P in wt%:

	C P =	I P I F e I F e 1 + k P/F e × ACF P/F e × k P/F e × ACF P/F e × I P	(I.2.5)
	The phosphorus grain boundary concentration was nally obtained using (adapted from
	equation I.1.10 [36]):

Table I .

 I 2.2: k factor (P in respect to Fe) calculated using Monte-Carlo simulation on a Fe-1 Figure I.2.6 shows the calculated phosphorus concentration line proles across the grain boundary for three beam diameters with a specimen thickness of 100 nm. The simulated phosphorus concentration was expressed as a weight fraction (left axis) and converted into a number of phosphorus atoms per unit volume (right axis). As expected, beam size aects the

	wt%P sample
	Thickness	Simulated k factor
	50 nm	0.71
	100 nm	0.76
	150 nm	0.81

width of the concentration peak but does not change the area under peak: values of 1.99, 2.00 and 2.00 atom/nm 2 were obtained, corresponding to the input value of 2 atom/nm 2 specied

Table I .

 I 3.1: Phosphorus intergranular segregation quantication results by STEM-EDX compared with APT results from[START_REF] Akhatova | Investigation of the dependence of phosphorus segregation on grain boundary structure in Fe-P-C alloy: cross comparison between Atom Probe Tomography and Auger Electron Spectroscopy[END_REF][START_REF] Akhatova | Méthodologie instrumentale à l'échelle atomique pour une meilleure compréhension des mécanismes de ségrégation intergranulaire dans les aciers: application au phosphore[END_REF] for two grain boundaries of model Fe-P alloy.(1): Acquisitions #3 and #4 of A1 grain boundary were conducted at the same location. (2): Acquisition from #11 to #14 of A1 grain boundary were conducted six months later than acquisitions from #1 to #10.

					P peak	Fe peak				P		P GB
								Local			GB box	P GB
	GB	#	intensity in the GB box (cps)	intensity in the GB box (cps)	k factor (k P/F e )	thickness (nm)	ACF P/F e	concentration in GB box (wt%)	width (nm)	concentration (atom/nm 2 )	concentration by APT (atom/nm 2 )
		1	0.114	110.5		110	1.17	0.10%	11.8	1.89
		2	0.11	103.2		110	1.17	0.11%	13.2	2.22
		3	(1)	0.092	84.8		160	1.25	0.12%	12.7	2.3
		4	(1)	0.098	84.6		160	1.25	0.13%	12.6	2.42
		5	0.078	84.2		160	1.25	0.10%	11.3	1.75
		6	0.147	87.8		160	1.25	0.18%	10.1	2.8
		7	0.06	89.9		160	1.25	0.07%	12.9	1.43
	A1	8	0.112	92	0.79	160	1.25	0.13%	12.7	2.58
		9	0.099	92.2		160	1.25	0.12%	12.4	2.23
		10	0.099	94		160	1.25	0.11%	11.8	2.07
		11	(2)	0.054	64.8		140	1.22	0.09%	14	1.91
		12	(2)	0.054	74.4		140	1.22	0.08%	14.8	1.75
		13	(2)	0.067	87.6		140	1.22	0.08%	14	1.74
		14	(2)	0.042	77.8		140	1.22	0.06%	19.3	1.7
		Average								2.06 ± 0.38 1.7 ± 0.35
		1	0.043	53		100	1.15	0.08%	23.9	2.95
		2	0.084	103.1		100	1.15	0.08%	22	2.75
		3	0.096	111.5		100	1.15	0.09%	20.3	2.69
		4	0.096	131.2		90	1.14	0.07%	20.9	2.32
		5	0.103	133.1		90	1.14	0.08%	23.4	2.73
							0.79
	A2	6	0.098	144.5		90	1.14	0.07%	23.1	2.37
		7	0.078	107.9		90	1.14	0.07%	22.5	2.45
		8	0.069	103.1		90	1.14	0.07%	23.1	2.33
		9	0.085	123.8		80	1.12	0.07%	26.4	2.75
		10	0.085	111.4		80	1.12	0.08%	25.6	2.96
		Average								2.63 ± 0.24 2.2 ± 0.17

  .3.2 shows the counting data and counting error for each measurement conducted in this study. The relative counting error lies approximately between 5% and 10%. Table I.3.2: Counting data and relative counting errors for each measurement on the two Fe-P model alloy grain boundaries. It should be noted that, for the A2 grain boundary, the calculated counting errors (0.14 to 0.27 atom/nm 2 ) are in good agreement with the standard deviation (0.24 atom/nm 2 in table I.3.1) of the series of measurements. For the A1 grain boundary, however, the standard deviation (0.38 atom/nm 2 in table I.3.1) of the series of measurements is signicantly higher than the counting error (0.09 to 0.16 atom/nm

	CHAPTER I.3. DIRECT COMPARISON OF INTERGRANULAR SEGREGATION
	BETWEEN DIFFERENT TECHNIQUES
						(atom/nm	2 )
		1	9319	299812	0.059	1.66 ± 0.1
		2	11664	358366	0.051	1.97 ± 0.1
		3	7495	193388	0.059	2.03 ± 0.12
		4	7893	190412	0.055	2.14 ± 0.12
		5	5666	171306	0.073	1.55 ± 0.11
		6	9457	158646	0.042	2.47 ± 0.1
		7	4951	206843	0.092	1.27 ± 0.12
	A1	8	10271	234225	0.047	2.28 ± 0.11
		9	7902	203908	0.057	1.97 ± 0.11
		10	7496	196009	0.059	1.83 ± 0.11
		11	4377	175101	0.096	1.68 ± 0.16
		12	5778	270836	0.09	1.55 ± 0.14
		13	10801	415777	0.06	1.54 ± 0.09
		14	4760	249456	0.105	1.50 ± 0.16
		1	3536	138406	0.105	2.60 ± 0.27
		2	4254	169346	0.097	2.43 ± 0.24
		3	5050	189048	0.086	2.37 ± 0.2
		4	5107	216124	0.091	2.05 ± 0.19
		5	10322	406255	0.062	2.41 ± 0.15
	A2	6	9793	430973	0.067	2.10 ± 0.14
		7	6825	278722	0.077	2.17 ± 0.17
		8	5016	223811	0.094	2.06 ± 0.19
		9	5701	234707	0.085	2.43 ± 0.21
		10	4683	176974	0.09	2.61 ± 0.23

GB #

N P (counts) N T (counts) ∆X P X P X P ± ∆X P

  It was assumed that the surface of this grain can be considered a plane of given Miller index and that the segregation over the surface of that grain is homogeneous. Under this assumption, the analyzed volume of the dierent techniques was chosen to be as close to each other as possible (see gure I.3.2), i.e. the WDS zone is within the XPS analyzed surface and the TEM FIB thin foils and APT tips are beside and very close to the WDS analyzed zone.

I.3.3.3 Quantication by Angular Resolved-XPS AR-XPS analysis was conducted on the specimen surface after one hour of in-situ annealing at 500 • C. Analyses were done at six dierent emission angles θ: 25 • , 35 • , 45 • , 55 • , 65

  • , and • . The quantication method for AR-XPS was developed by V. Barnier, Ecole des Mines de Saint Etienne, France, and published in[START_REF] Hsu | Solute Interface Segregation Measurement: Cross Comparison between Four Dierent Analytical Methods[END_REF]. The idea is that the peak intensity ratio of P 2P and S 2P in respect to Fe 3P have a linear variation with 1/cosθ with the slope being proportional to the sulfur and phosphorus concentration. The obtained phosphorus and sulfur WDS acquisitions, the multi-tension method proposed by Christien et al.[START_REF] Christien | Measuring surface and grain boundary segregation using wavelength dispersive X-ray spectroscopy[END_REF] was applied. The relative intensity I/I std of phosphorus and sulfur are plotted in gure I.3.4 and gure I.3.5, respectively. I is the intensity (expressed in counts/s/nA) of the P K α and S K α line and I std is the intensity of the same line measured on the standard material. As expected,

	surface concentrations are: X XP S P	= 3.38 ± 0.11, X XP S S	= 3.05 ± 0.08 atom/nm 2 .
	I.3.3.4 Quantication by Multi-Voltage WDS

For the relative intensity of both elements increases as the acceleration voltage decreases, indicating that the surface is enriched in both phosphorus and sulfur. Two series of measurements were conducted corresponding to square and triangle symbols in gures I.3.4 and I.3.5. These data points were tted by a commercial software Stratagem TM , following the same procedure

Table I

 I

	.3.3 presents a summary of the phosphorus segregation quantication results of each
	technique.
	Table I.3.3: Phosphorus & sulfur segregation quantication results of sandwich specimen using
	AR-XPS, WDS, STEM-EDX, and APT.
	Technique	P concentration (atom/nm 2 )	S concentration (atom/nm	2 )
	AR-XPS	3.40 ± 0.11	3.00 ± 0.08
	WDS	3.11 ± 0.03	3.68 ± 0.04
	STEM-EDX	4.2 ± 0.6	3.9 ± 0.4

  II.1.1.2 Microstructure of RPV SteelConsidering the thickness of the forged shells, dierent studies have reported cooling rate gradients during water quenching considering the dierent location in respect to the thickness in the shell. Kim et al.[START_REF] Kim | Improved Mechanical Properties of the A 508 Class 3 Steel for Nuclear Pressure Vessel Through Steelmaking[END_REF] found cooling rates of 0.65

• C/s and 0.37 • C/s at quarter and half thickness of a 300 mm thick shell. Poitrault [101] reported that the cooling rate between 800 • C and 600 • C close to extreme surface of the 275 mm shell is about 3 • C/s, 0.4 • C/s at quarter thickness, and 0.3 • C/s at half thickness. Figure II.1.8 [102] shows a typical CCT phase diagram of forged 16MND5 shell as a reference.

  II.1. LITERATURE REVIEWAlthough phosphorus intergranular segregation due to thermal aging is a well-known cause of RTE, most studies focused on measuring the changes in mechanical properties of RTE (see section II.1.4.4), without necessary relating them to phosphorus intergranular segregation. The following section discusses the metallurgical factors that play a role in phosphorus intergranular

	segregation in low alloy steels.
	II.1.3.2 Metallurgical Eects on Intergranular Segregations
	As mentioned previously, tempering is a common treatment applied to bainitic and marten-
	sitic low alloy steels and can induce intergranular segregation of embrittle impurities. Depending
	on dierent metallurgical factors, the behavior of intergranular segregation of the impurities
	can be inuenced. This section provides a summary of the dierent metallurgical factors that
	can aect intergranular segregation.

  (see equation II.1.19), a crack cannot propagate catastrophically if the stress σ is not high enough.

	σ >	Eω πc	(II.1.19)

where σ is the tensile stress applied on the crack, E is the Young's modulus, and c is the initial crack length.

CHAPTER II.1. LITERATURE REVIEW Overcoming obstacles When the crack encounters its rst obstacle (mostly a grain boundary), the propagation direction changes. During transgranular fracture, the crack arrives at a grain boundary and continues on the direction of the new cleavage plane. Lambert-Perlade et al.

[START_REF] Lambert-Perlade | Mechanisms and modeling of cleavage fracture in simulated heat-aected zone microstructures of a BIBLIOGRAPHY high-strength low alloy steel[END_REF]

observed that high angle grain boundaries in bainite stopped the crack from propagating, see gure II.1.34. Similar phenomenon was also observed in the work of Andrieu et al.

[START_REF] Andrieu | Mécanismes et modélisation multi-échelle de la rupture fragile trans-et intergranulaire des aciers pour Réacteurs à Eau sous Pression[END_REF]

.

  LITERATURE REVIEW tip applied on a crack of length 2a, the stress at a distance r from the crack tip can be described

	as:
	σ r = kσ	a 2r	(II.1.21)
			. In this work, the
	test temperatures are all above -160 • C, meaning that the brittle fracture process is controlled
	by crack propagation.
	II.1.4.1 Plastic Correction at Crack Tip

Equations II.1.

[START_REF] Watanabe | The quantitative analysis of thin specimens: a review of progress from the Cli-Lorimer to the new zeta-factor methods[END_REF]

and II.1.20 are only valid in purely elastic models. However the stress at the crack tip creates a plastic zone in front of it. If we consider a stress σ that opens the crack CHAPTER II.1.

  1. LITERATURE REVIEWRegarding how grain size aect RTE, Nikolaeva et al.[START_REF] Nikolaeva | Grain boundary embrittlement due to reactor pressure vessel annealing[END_REF] worked on Cr-Ni-Mo low alloy steel and they showed that the DBTT shift after thermal aging is proportional to austenite grain size. Khan et al.[START_REF] Khan | Inuence of prior austenite grain size on the degree of temper embrittlement in Cr-Mo steel[END_REF] worked on 2.25Cr-1Mo steel (130 wt ppm P) with dierent austenite grain size (tempered martensite structure), they have observed that with larger austenite grain size, the proportion of intergranular fracture increases and the critical intergranular fracture stress decreases.

  .2.2 gives all the conditions for the dierent states. It can be seen that samples of both microstructures underwent the tempering treatment, no as-quenched microstructure was analyzed by STEM-EDX in this work. The thermal aging treatment was decided to be an accelerated cycle called step cooling, see gure II.2.2. This is a cycle similarly reported in

Table II . 2

 II2

		Accelerating	Beam	Step	Kikuchi pattern	Exposure	View	Acquisition
	Acquisition
		Voltage (kV)	current (nA)	size (nm)	resolution (pixel)	time (µs)	eld (µm)	points
	B	20	3	250	80×80	650	450×400	2,880,000
	BSC	20	3	250	80×80	650	450×400	2,880,000
	BSA	30	66	350	120×120	6,616	350×350	1,000,000
	M	30	66	350	120×120	6,616	350×350	1,000,000
	MIA	30	66	350	120×120	6,616	200×200	326,530
	MSC	30	66	350	120×120	3,283	300×300	734,572

.

[START_REF] Christien | Synergetic eect of hardness and phosphorus grain-boundary segregation on the ductile-to-brittle transition temperature of 17-4 PH steel[END_REF]

shows the acquisition parameters. Table II.2.3: Acquisition parameters for EBSD.

Table II .

 II 2.4: k factors and their source for dierent intergranular segregated elements in

		16MND5 steel.
		P	Ni	Mo(L)	Mn
	k i/F e	0.790	1.125	2.601	0.919
	Source	Determined experimentally in this work	JEOL	JEOL	Sheridan et al. [72]

Table II

 II High bulk content: In Part I, a Fe-P model alloy and a Fe-P-Fe sandwich sample with simple composition were used. In the case of 16MND5 steel, the other segregated elements have higher bulk content, i.e. 1.32 wt% for Mn, 0.70 wt% for Ni, and 0.52 wt% for Mo. The box method developed in Part I was originally designed to remove background contribution from the adjacent grains. Regardless of the bulk content, as long as the GB box size exceeds twice the beam size at exit (d B in gure I.2.8), the intergranular segregation quantication remains constant as the GB box contains all signals from the analyzed grain boundary (gure I.2.9).The box size eect was also studied for STEM-EDX acquisitions on 16MND5 thin foils. Figure II.2.7 shows an example of EDX counts proles across a grain boundary for P, Mo, Mn, and Ni, as well as the eect of GB box width on the quantication of segregation.

		CHAPTER II.2. EXPERIMENTAL PROCEDURES
	(b)
	.2.5 shows the mass absorption coecient µ/ρ of the dierent elements with
	the 16MND5 steel composition (see table II.2.1). These mass absorption coecients
	were used to calculate the ACFs, see equation I.1.9
	Table II.2.5: Mass absorption coecient (µ/ρ in equation I.1.9) in cm/g of the characteristic
	X-ray lines of the quantied elements in 16MND5 steel.
	Fe K α	P K α	Ni K α	Mo L α	Mn K α
	µ/ρ (cm/g) 122.19 1403.11 198.79 1010.44 124.98

Table II .

 II 2.6: AES acquisition summary of the four states.

	State	Acquisition condition	# Sample	# Analyzed facets
	MSC	10 kV, 5 nA	1	18
	MIA	10 kV, 5 nA	2	29
	BSC	10 kV, 5 nA	1	10

Table II.2.6 shows a summary of the AES analysis.

  .2.7 lists the dierent mechanical tests and testing temperatures of each microstructure.

	Table II.2.7: Summary of mechanical tests for dierent microstructures and dierent aging
	states.
	Microstructure	Type of test	Aging state	Temperature
			B	Varies
	Bainite	Kcv	BSC	Varies
			M	Varies
		Kcv	MSC	Varies
			MIA	Varies
	Martensite		M	20	• C
		TC6	MSC	20 • C
			MIA	20 • C

  • , with a rotation axis of ⟨110⟩. However, this block boundary does not seem to be frequent in the cases present in this study. Group 3 (21.5 • -46.5 • ) is expected to contain only prior austenite grain boundaries as already explained in section II.2.3.2 [108, 121]. Group 2, 4, and 5 contain block and packet boundaries, as well as prior austenite grain boundaries. Figure II.3.13 shows that rotation axes are very randomly distributed in group 3 for both

Table II .

 II 3.3: Summary of the dierent grain sizes in bainitic and martensitic 16MND5 steel studied in this work. EDX method that was developed in Part I was applied on 16MND5 type steel that has dierent microstructures and dierent aging state, see table II.2.2. The dierent analyzed states have systematically undergone tempering treatment, the bainitic and martensitic microstructures mentioned in this chapter are tempered bainite and tempered martensite. The intergranular segregation quantication results are presented in this chapter. First, the results of STEM-EDX and AES measurements are presented. Then, the discussions on the eect of dierent microstructural factors and thermal aging are elaborated.

	Chapter II.4
	Intergranular Segregation in Bainitic and
	Martensitic 16MND5 Steel
	Prior austenite grain (µm) 19.3 9.1 It can be seen that the martensite (with re-austenitization at 900 Ferrite grain (µm) Bainite 4.2 Martensite 3.1 • C for 1h) has smaller grain Lath (µm) 0.62 0.44 sizes for all types of grains. The STEM-II.4.1 Intergranular Segregation Measurements
	Table II.4.1 gives a summary of the number of FIB thin foils per state and the number of
	STEM-EDX acquisitions per type of grain boundaries. Multiple acquisitions were done only on
	the prior austenite grain boundaries; for all other grain boundaries, one acquisition was done
	per grain boundary.
	Table II.4.1: Summary of FIB thin foils & STEM-EDX acquisitions for 16MND5 steel samples
		at dierent aging state.
	State	#FIB thin foil	#Prior austenite GB	#acquisition γ GBs #acquisition other GBs #acquisition lath boundaries
	B	4	3	23	27	17
	BSC	4	3	22	25	23
	BSA	3	3	22	2	4
	M	3	3	13	17	11
	MIA	3	3	24	0	0
	MSC	3	3	24	22	9
	Total	20	18	128	93	64

  Quantication of Segregation in Each Group of Grain BoundariesAs shown in gure II.4.1, the analyzed grain boundaries were separated into ve categories based on their misorientation angles. The average intergranular segregation quantications of P, Mo, Mn, and Ni for each category of grain boundaries are presented in tables II.[START_REF] Kameda | Combined eects of phosphorus segregation and partial intergranular fracture on the ductilebrittle transition temperature in structural alloy steels[END_REF].2, II.4.3, • -21.5 • ): According to [121], this group contains some of the packet boundaries. Meanwhile, there are also grain boundaries in this group CHAPTER II.4. INTERGRANULAR SEGREGATION IN BAINITIC AND MARTENSITIC 16MND5 STEEL that fall in the usual denition of LAGBs (misorientation <15 • ). Table II.4.3: Intergranular segregation quantication in atom/nm 2 at group 2 boundaries for all states. The numbers before the quantication results indicate the number of acquisitions not adjusted to zero (i.e. above the detection limit). Group 3 (misorientation between 21.5 • -46.5 • ): prior austenite grain boundaries based on the misorientation criteria of Morito et al. [108] and Gourgues et al. [121]. Grain boundaries that are very likely to be prior austenite grain boundary based on grain boundary continuity are also included, see the blue arrows in gure II.2.6. All these grain boundaries above are referred to as prior austenite grain boundaries further in this work. Table II.4.5: Intergranular segregation quantication in atom/nm 2 at group 4 boundaries for all states. The numbers before the quantication results indicate the number of acquisitions not adjusted to zero (i.e. above the detection limit).

	46.5	• -56	•	# acquisitions		P	Mo	Mn	Ni
	B			13	11/13	0.83 ± 0.46 12/13 4.09 ± 1.72 12/13 2.01 ± 0.86 9/13 0.43 ± 0.31
	1.24 provides the theoretical misorientation/rotation axis pairs, the identication of analyzed grain boundaries in group 2, 4, and 5 were not straightforward. More detailed categorization of these grain boundaries is presented in discussion. II.4.1.2 II.4.4, II.4.5, and II.4.6. The values highlighted in gray represent the number of valid EDX peak Gaussian t over the total number of acquisitions. The criterion of valid Gaussian t was shown in section II.2.3.2. The average concentration for each element at each group of grain boundaries were calculated including the measurements below the detection limit. 1. Group 1 (misorientation below 7 • ): Lath boundaries. These grain boundaries also fall into the typical denition of LAGBs (misorientation <15 • ). Table II.4.2: Intergranular segregation quantication in atom/nm 2 at lath boundaries for all states. The numbers before the quantication results indicate the number of acquisitions not adjusted to zero (i.e. above the detection limit). Lath # acquisitions P Mo Mn Ni B 16 3/16 0.09 ± 0.20 11/16 2.08 ± 2.08 11/16 0.76 ± 0.69 0/16 0.00 ± 0.00 BSC 24 4/24 0.12 ± 0.29 15/24 1.08 ± 1.14 19/24 0.85 ± 0.64 8/24 0.19 ± 0.29 BSA 4 3/4 0.85 ± 0.67 4/4 2.82 ± 1.34 4/4 2.37 ± 0.77 3/4 0.79 ± 0.70 M 11 1/11 0.05 ± 0.17 7/11 1.14 ± 1.06 11/11 1.41 ± 0.42 5/11 0.24 ± 0.29 MIA 0 --------MSC 9 4/9 0.35 ± 0.45 4/9 1.47 ± 1.29 9/9 1.29 ± 0.58 6/9 0.42 ± 0.36 • -21.5 • # acquisitions P Mo Mn Ni B 6 1/6 0.09 ± 0.21 5/6 2.63 ± 2.29 6/6 1.25 ± 0.54 0/6 0.00 ± 0.00 BSC 9 7/9 0.80 ± 0.51 6/9 3.06 ± 3.60 9/9 2.60 ± 1.29 7/9 0.59 ± 0.40 BSA 0 --------M 2 1/2 0.51 ± 0.72 2/2 1.90 ± 0.24 2/2 1.99 ± 1.67 1/2 0.35 ± 0.49 MIA 0 --------MSC 4 3/4 0.79 ± 0.53 4/4 4.56 ± 1.31 4/4 3.26 ± 0.78 4/4 0.69 ± 0.18 3. Although the number of acquisitions are high, only three prior austenite grain boundaries were analyzed per state. Table II.4.4: Intergranular segregation quantication in atom/nm 2 at prior austenite grain boundaries for all states. The numbers before the quantication results indicate the number of acquisitions not adjusted to zero (i.e. above the detection limit). γ # acquisitions P Mo Mn Ni B 21 12/21 0.74 ± 0.69 21/21 4.14 ± 1.08 21/21 2.77 ± 0.75 12/21 0.39 ± 0.36 BSC 22 22/22 3.35 ± 0.96 22/22 4.00 ± 1.42 22/22 4.35 ± 0.85 22/22 1.19 ± 0.33 BSA 22 22/22 2.48 ± 0.79 22/22 4.43 ± 2.10 22/22 3.49 ± 1.00 21/22 1.42 ± 0.47 M 13 5/13 0.34 ± 0.50 13/13 4.10 ± 0.75 13/13 3.37 ± 0.69 2/13 0.08 ± 0.20 MIA 24 22/24 1.15 ± 0.55 24/24 4.07 ± 1.18 24/24 3.35 ± 0.79 18/24 0.50 ± 0.34 MSC 24 23/24 2.60 ± 0.15 24/24 4.41 ± 1.90 24/24 5.29 ± 0.83 22/24 1.10 ± 0.51 4. Group 4 (misorientation between 46.5 • -56 • ): According to [121], this group con-tains most of the packet boundaries based on theoretical MR calculation. There are also random HAGBs. BSC 9 8/9 1.61 ± 0.88 9/9 3.09 ± 1.64 9/9 3.43 ± 1.26 8/9 0.94 ± 0.40 BSA 0 --------M 5 1/5 0.21 ± 0.47 3/5 1.35 ± 1.33 4/5 1.53 ± 1.00 0/5 0.00 ± 0.00 MIA 0 --------MSC 5 4/5 1.72 ± 1.13 5/5 2.46 ± 1.40 5/5 3.76 ± 1.58 5/5 1.05 ± 0.42 5. Group 5 (misorientation above 56 • ): According to [121], this group contains most 2. Group 2 (misorientation between 7 7 of the block boundaries and includes the special boundaries like Σ3.

  Table II.4.6: Intergranular segregation quantication in atom/nm 2 at group 5 boundaries for all states. The numbers before the quantication results indicate the number of acquisition not adjusted to zero (i.e. above the detection limit). Due to the complexity of thermal aging (see table II.2.2), the comparison between the different states is not direct. State B although being non-aged, should be compared to state MIA due to the similar SRHT. State BSC and state MSC can be compared as the step cooling treatment is believed to erase dierences created by previous thermal cycles. State BSA represents a simpler case of isothermal aging, which is mainly compared to state BSC. Figure II.4.2 shows an indicative segregation level for the dierent states.

	56	• -63	•	# acquisitions		P	Mo		Mn		Ni
	B			11	8/11	0.72 ± 0.48 11/11 4.56 ± 1.85 11/11 2.28 ± 1.01 7/11 0.41 ± 0.34
	BSC		6	6/6	1.21 ± 0.59 6/6 3.51 ± 1.81 6/6 2.86 ± 1.29 5/6 0.59 ± 0.35
	BSA		2	1/2	0.59 ± 0.83 2/2 4.13 ± 0.12 2/2 2.73 ± 0.52 2/2 0.89 ± 0.39
	M			10	0/10	0.00 ± 0.00 8/10 1.90 ± 1.38 10/10 1.99 ± 0.57 2/10 0.14 ± 0.31
	MIA		0	-	-	-	-	-	-	-	-
	MSC		13	6/13	0.48 ± 0.63 10/13 2.71 ± 3.62 13/13 2.85 ± 1.10 10/13 0.62 ± 0.41

  on non-aged states (B & M). Then the concentration increases after thermal aging in both microstructures, less Gaussian ts were adjusted to zero. When comparing the dierent groups of grain boundaries, the segregation level at prior austenite grain boundaries (misorientation between 21.5• -46.5 • ) is higher than the others. Following this tendency, the segregation level between dierent types of grain boundaries is roughly: group 3 > group 4 > group 5 ≈ group 2 > group 1. A more detailed categorization of the dierent types of grain boundaries will be illustrated later. The segregation is shown to be increasing after dierent thermal aging treatments. Figure II.4.3 shows the dierent states where B can be compared with MIA and BSC can be compared to MSC. As predicted in gure II.4.2, phosphorus segregation increases due to the dierent aging treatments. The same trend can be observed for manganese and nickel. For molybdenum, on the other hand, it has lower susceptibility to thermal aging since the segregation level is not necessary higher in states that underwent step cooling. It is suspected that the segregation behavior of molybdenum is dierent from the other three elements.

  have suggested that intergranular segregation can be related to grain boundary structure, see section II.1.3.2. In this work, the structure of the analyzed grain boundaries were not fully determined. Only the misorientation angle and rotation axis ), the measurements of this work accord with the conclusions of Leifeng et al.[START_REF] Zhang | Investigation of solute segregation behavior using a correlative EBSD/TKD/APT methodology in a 16MND5 weld[END_REF]: segregation level is higher at general HAGBs than at LAGBs, and Σ3

	MARTENSITIC 16MND5 STEEL
	When only considering the categorization of HAGB and Low Angle Grain Boundary (LAGB)
	(misorientation threshold at 15 •
	are accessible.

Table II .

 II 5 were removed and will be discussed later. Figure II.4.7 shows the segregation level of each element of the two aged states (BSC & MSC) against the misorientation angle of each analyzed CHAPTER II.4. INTERGRANULAR SEGREGATION IN BAINITIC AND MARTENSITIC 16MND5 STEEL II.4.2.2 Eect of Dierent Types of Grain Boundaries In the following, segregation at dierent types of grain boundaries of the six states are discussed. First, prior austenite grain boundaries of all six states are compared. Then, states BSA and MIA are removed due to lack of data. The segregation level at other types of grain boundaries are then discussed. Only grain boundaries that can be identied based on the theoretical misorientation/rotation axes in gure II.1.24 are categorized in block, or packet boundaries. Others remained categorized as random grain boundaries that were analyzed. Prior Austenite Grain Boundaries Three austenite grain boundaries were analyzed per state and multiple STEM-EDX acquisitions were performed on dierent portions of each austenite grain boundary. See appendix A.3 for the detailed acquisition positions. Table II.4.8 gives the average segregation of each element at each prior austenite grain boundary. The segregation level for phosphorus and nickel remained low for non-aged states and sometimes even aged states. There were certain acquisitions where the Gaussian t of the EDX peak was adjusted to 0 manually (see gure II.2.11 for not valid Gaussian t). The number of acquisitions adjusted to zero (i.e. below the detection limit) are also listed in table II.4.8. 4.8: Average of intergranular segregation at each analyzed prior austenite grain boundary in atom/nm 2 . Three prior austenite grain boundaries of each state were ana- lyzed (i.e. three FIB thin foils). Highlighted values are the average of the three prior austenite grain boundaries of each state.

		CHAPTER II.4. INTERGRANULAR SEGREGATION IN BAINITIC AND
						MARTENSITIC 16MND5 STEEL
	State	# acquisitions	# adjusted	# adjusted	P	Mo	Mn	Ni
			P to 0	Ni to 0
		8	5/8	5/8	0.62 ± 0.87 4.46 ± 1.05 2.45 ± 0.83 0.27 ± 0.39
		9	4/9	4/9	0.58 ± 0.57 4.06 ± 1.25 2.77 ± 0.65 0.35 ± 0.33
	B	4	0/4	0/4	1.32 ± 0.20 3.68 ± 0.65 3.43 ± 0.39 0.72 ± 0.11
			9/21	9/21	0.74 ± 0.69 4.14 ± 1.08 2.77 ± 0.75 0.39 ± 0.36
		9	0/9	0/9	3.48 ± 0.63 3.32 ± 0.38 4.11 ± 0.57 1.19 ± 0.26
		6	0/6	0/6	3.10 ± 1.18 3.95 ± 1.96 4.06 ± 0.75 1.19 ± 1.40
	BSC	7	0/7	0/7	3.41 ± 1.22 4.91 ± 1.40 4.91 ± 1.05 1.19 ± 0.41
			0/22	0/22	3.35 ± 0.96 4.00 ± 1.42 4.35 ± 0.85 1.19 ± 0.33
		8	0/8	0/8	2.54 ± 0.34 5.14 ± 1.71 4.28 ± 0.89 1.50 ± 0.31
		6	0/6	1/6	2.17 ± 0.43 4.24 ± 1.16 3.06 ± 0.62 1.29 ± 0.73
	BSA	8	0/8	0/8	2.66 ± 1.22 3.87 ± 2.90 3.03 ± 0.90 1.44 ± 0.39
			0/22	1/22	2.48 ± 0.79 4.43 ± 2.10 3.49 ± 1.00 1.42 ± 0.47
		6	2/6	4/6	0.59 ± 0.58 4.21 ± 0.67 3.17 ± 0.36 0.09 ± 0.22
		1	1/1	1/1	0	4.74	3.44	0
	M	6	5/6	5/6	0.14 ± 0.35 3.88 ± 0.86 3.56 ± 0.95 0.09 ± 0.22
			8/13	10/13	0.34 ± 0.50 4.10 ± 0.75 3.37 ± 0.69 0.08 ± 0.20
		6	1/6	3/6	0.95 ± 0.63 3.58 ± 1.05 3.56 ± 1.19 0.48 ± 0.54
		8	0/8	1/8	1.58 ± 0.37 4.38 ± 1.03 3.66 ± 0.43 0.57 ± 0.27
	MIA		1/10	2/10	0.93 ± 0.45 4.12 ± 1.37 2.97 ± 0.61 0.46 ± 0.26
			2/24	6/24	1.15 ± 0.55 4.07 ± 1.18 3.35 ± 0.79 0.50 ± 0.34
		7	1/7	2/7	1.50 ± 1.27 4.26 ± 2.82 4.29 ± 0.47 0.86 ± 0.66
		8	0/8	0/8	2.64 ± 1.11 3.46 ± 1.26 4.96 ± 0.51 1.16 ± 0.51
	MSC	9	0/9	0/9	3.31 ± 0.84 4.52 ± 1.19 5.86 ± 0.69 1.31 ± 0.33
			1/24	2/24	2.60 ± 0.15 4.41 ± 1.90 5.29 ± 0.83 1.10 ± 0.51

  This is why the standard deviation of manganese remains low compared to molybdenum. For phosphorus and nickel, the maximum and minimum values are sometimes very dierent but the box sizes remained small. This indicates that apart from certain extreme CHAPTER II.4. INTERGRANULAR SEGREGATION IN BAINITIC AND MARTENSITIC 16MND5 STEEL was assumed that these grain boundaries are Σ3. It can be seen in table II.4.9 that there was no P intergranular segregation measured at these boundaries in state M. However, the Mo and Mn segregations are signicant. Also, Ni segregation, although only measurable on two out of the six Σ3 boundaries, presented a pretty high segregation level. It seems that when there was low intergranular segregations (state M only underwent tempering followed by rapid cooling), Σ3 boundaries were not the preferred segregation locations for phosphorus, but intergranular segregation of other elements were measured.For state MSC, on the other hand, 11 grain boundaries fell in the red zone close to ⟨111⟩ (gure II.4.1) that were considered as Σ3 boundaries. Among them, seven acquisitions were adjusted to 0 for P concentration. The other four cases have an average of phosphorus segregation at 0.[START_REF] Hovington | CASINO: A new Monte Carlo code in C language for electron beam interactionPart I: Description of the program[END_REF] atom/nm 2 , which is close to half of the amount in prior austenite grain boundaries but less than in group 2 and 4 boundaries. In these 11 Σ3 boundaries, the segregation level of the manganese and nickel remained close to the average of group 5. Molybdenum concentration shows signicant heterogeneity: one case up to 13.49 atom/nm 2 with two cases adjusted to 0. Block boundaries with extreme high Mo content do not show lower segregation level of other elements. This would suggested that Mo segregates at dierent sites from the other elements. According to Park et al. [107], bainite has more packet boundaries with high misorientation angle and martensite has more Σ3 boundaries. This is the reason why martensite would trap less phosphorus in non-prior austenite grain boundaries and would then be more susceptible to RTE. There was no Σ3 analyzed in bainitic structure in this work, but from the few Σ3 analyzed in state MSC, it is clearly shown that phosphorus can also segregate at Σ3 after thermal aging and that the hypothesis in [107] is not necessarily valid. ⟨110⟩ and two in state MSC close to 49.5 • ⟨110⟩ and 60 • ⟨110⟩, see the ones in red in table II.4.9. The one in state M has high manganese segregation at 2.37 atom/nm 2 , but no other elements were measured. For state MSC, one has no phosphorus segregation and another has phosphorus concentration at half the level as of prior austenite grain boundary (2.6 atom/nm 2 ). Also, the Mo, Mn, and Ni segregation levels in the two cases in state MSC were high. This indicates that although high coincidence grain boundaries may present smaller segregation level, it is not the only factor that aects the intergranular segregation behavior.

	There were other block boundaries identied in gure II.4.1, including one in state M close
	to 60 • This was a conclusion mentioned by Ogura et al. [149].
	Lath Boundaries
	The rotation axis of group 1 grain boundaries are spread in the rotation axis distribution
	gure without forming clusters, see gure II.4.1. It can be seen that the segregation at lath

boundaries are the lowest among all types of grain boundaries regardless of the microstructure. This is most likely due to the better-ordered grain boundary structures of these LAGBs. While LAGBs are mainly formed by dislocations, their structures are better ordered than general random HAGBs.

  considering only the misorientation, grain boundaries in groups 2 and 4 are maybe packet boundaries. Although not being able to strictly identify packet boundaries based on gure II.1.24, rotation axes in group 4 form clusters that are close to theoretical rotation axes, see gure II.4.9.

  The grain boundary density (grain boundary area per unit volume) is 3/d for isotropic grains and 2/d for fries grains, where d is the grain size. The concentration of trapped phosphorus (in atom/nm 2 ) can be easily obtained by multiplying the grain boundary density d the phosphorus grain boundary concentration. This trapped phosphorus concentration can then be converted into wt ppm and compared to the nominal phosphorus content (80 wt ppm).The considered phosphorus intergranular segregation concentration of each type of grain boundary were the average values from the dierent tables: prior austenite grain from tableII.4.4, lath boundaries from table II.4.2, and the average of tables II.4.3, II.4.5, and II.4.6 was used for other grain boundaries. Table II.4.10 shows the amount of phosphorus trapped in the dierent types of grain boundaries in bainite and in martensite before and after step cooling. The segregation measurements for lath boundaries present large standard deviations (see table II.4.2), so the trapping at lath boundaries maybe overestimated. The percentage of trapped phosphorus was calculated using a total phosphorus concentration of 80 wt ppm. The calculation was not done for states BSA and MIA due to the lack of segregation measurements at dierent types of grain boundaries. Table II.4.10: Phosphorus trapped in dierent types of grain boundaries in bainite & martensite. .11 and II.4.12 show the pie charts of the trapped phosphorus based on table II.4.10. It can be seen that the amount of phosphorus trapped in the dierent types of grain boundaries is around 5 to 10% of the total bulk content in non-aged states. This percentage raises to 20 to 25% for aged states. The results are similar between bainite and martensite.

									MARTENSITIC 16MND5 STEEL
			Grain	GB density	P grain boundary		Trapped phosphorus
	State	Grain boundary type	size (d)				concentration
			(µm)	(m	2 /m	3 )	(atom/nm	2 )	(atom/nm	3 )	(at ppm)	(wt ppm)	(%)
		Prior austenite GB	19.3	3/d	155440	0.74		0.00012		1.3	0.7	0.9%
	B	Other GB	4.2	3/d	714286	0.64		0.00046		5.3	3.0	3.7%
		Lath boundaries	0.6	2/d	3225806	0.09		0.00029		3.4	1.9	2.4%
		Prior austenite GB	19.3	3/d	155440	3.35		0.00052		6.1	3.4	4.2%
	BSC	Other GB	4.2	3/d	714286	1.21		0.00086		10.1	5.6	7.0%
		Lath boundaries	0.6	2/d	3225806	0.12		0.00039		4.5	2.5	3.1%
		Prior austenite GB	9.1	3/d	329670	0.34		0.00011		1.3	0.7	0.9%
	M	Other GB	3.1	3/d	958466	0.12		0.00012		1.3	0.7	0.9%
		Lath boundaries	0.4	2/d	4504505	0.05		0.00023		2.6	1.5	1.8%
		Prior austenite GB	9.1	3/d	329670	2.60		0.00086		10.0	5.6	7.0%
	MSC	Other GB	3.1	3/d	958466	0.82		0.00079		9.2	5.1	6.4%
		Lath boundaries	0.4	2/d	4504505	0.35		0.00158		18.4	10.2	12.8%
	1. Prior austenite grain (group 3): isotropic form Figures II.4Considering equation II.4.1, a decrease of the bulk phosphorus content by 20% results in a
	2. Other grain (group 2, group 4, group 5): isotropic form decrease of the grain boundary concentration by 20% at maximum, i.e. in the case where the
	grain boundary concentration is low
	3. Lath (group 1): elongated form like fries

Table II .

 II 4.11: Diusion coecients of the segregated elements from dierent sources.The diusion coecients dened in dierent sources are mostly measured at temperatures that are higher than the thermal treatments in this work. This calculation still gives an indication of the solute diusion in order to understand if the intergranular segregation process was controlled by thermodynamics or kinetics. TableII.4.12 shows the dierent diusion coecients in m 2 /s adapted to the thermal treatments in this work. Table II.4.12: Diusion coecients in m 2 /s of each element at dierent temperatures of the thermal treatment in this work. The sources of D 0 and ∆G are listed in table II.4.11.

		Element	D 0 (m 2 /s) Q (kJ/mol)		Source
			3200000	434	Matsuyama et al. [195]
		P
			0.0000025	200	Druce et al. [162]
		Mo	0.00013	229	Kucera et al. [196]
		Mn	0.000149	234	Nohara et al. [197]
		Ni	0.00014	246	Hirano et al. [198]
		State(s)	Temperature ( • C)	D M atsuyama P	D Druce P	D M o	D M n		D N i
	Tempering	M	645	6.45×10 -19	1.04×10 -17	1.21×10 -17	7.21×10	-18	1.41×10 -18
	SRHT	B, MIA	610	6.77×10 -20	3.68×10 -18	3.69×10 -18	2.14×10	-18	3.92×10 -19
	Step cooling	BSC, MSC	468	8.14×10 -25	1.99×10 -20	9.35×10 -21	4.76×10	-21	6.37×10 -22
	Isothermal aging	BSA	400	6.59×10 -28	7.49×10 -22	2.19×10 -22	1.02×10	-22	1.13×10 -23

Table II .

 II 4.13: Diusion distance in nm of each element for dierent thermal treatments. For step cooling, only the last isothermal step was taken into account.The available solute quantity represents the solute surface concentration that is able to segregate to the grain boundary over a certain time at a given temperature. The concept of available solute quantity is illustrated in gure II.4.13. When the calculated available solute quantity is larger than the measured segregation, this means that there is no kinetics

		CHAPTER II.4. INTERGRANULAR SEGREGATION IN BAINITIC AND
					MARTENSITIC 16MND5 STEEL
		State(s)	Temperature ( • C)	Duration (s)	x M atsuyama P	x Druce P	x M o x M n x N i
	Tempering	M	645	24300	125	503	543	419	185
	SRHT	B, MIA	610	28800	44	326	326	248	106
	Step cooling	BSC, MSC	468	360000	0.5	85	58	41	15
	Isothermal aging	BSA	400	288000000	0.4	464	251	172	57
								.4.13
	gives the diusion distance in nm of each element.

limitation or, in other terms, the segregation is governed by thermodynamics. If the available solute quantity is equal or close to the measured segregation concentration, segregation may be limited by kinetics.

Table II .

 II 4.14: Available solute quantity in atom/nm 2 of each element for dierent thermal treat- ments. For step cooling, only the last isothermal step was taken into account.

		State(s)	Temperature ( • C)	Duration (s)	Q M atsuyama P	Q Druce P	Q M o Q M n Q N i
	Tempering	M	645	24300	3	12	162	729	181
	SRHT	B, MIA	610	28800	1		8	97	432	104
	Step cooling	BSC, MSC	468	360000	0.01		2	17	72	15
	Isothermal aging	BSA	400	288000000	0.01	11	75	299
	The available solute quantity for molybdenum, manganese, and nickel are way higher than
	the measured intergranular segregation (never higher than 14 atom/nm	2 ) for all the dierent
	thermal treatment, see gure II.4.3. This indicates that there is no kinetics limitation to grain
	boundary segregation and hence the intergranular segregation of these three elements are limited
	by thermodynamics. In other words, the segregation concentration measured corresponds to
	equilibrium.
										.4.14
	gives the available solute quantity in atom/nm	2 of each element.

Dierent from the other segregated elements, the phosphorus matrix concentration is very low (80 wt ppm), which results in much lower available solute quantities. When using D Druce P from

[START_REF] Druce | Eect of ageing on properties of pressure vessel steels[END_REF]

, the calculated available solute quantities are higher than the measured segregation for all states except for the step cooling states. However, the calculated value for the step cooling cases (Q

Druce P = 2 atom/nm 2 )

is very close to the measured values (BSC: 3.35±0.96 & MSC: 2.60±0.15 atom/nm 2 ). Since the available solute quantity calculation only took the last isothermal treatment of step cooling into account, Q Druce P is underestimated. This suggests

  1.3.3, the equilibrium concentration of the segregated elements can be calculated as a function of temperature. Under the hypothesis of all states have achieved equilibrium based on the dierent thermal treatments, only the last temperature at the last step of the treatments is considered for each sample, see table II.2.2. Only measurements at the prior austenite grain boundaries were taken into account as they are the most segregated for all elements and present the most possible data. All the states (B, BSC, BSA, M, MIA, MSC) were considered. Phosphorus intergranular quantication in a similar material from Druce et al.[START_REF] Druce | Eect of ageing on properties of pressure vessel steels[END_REF] and measurements by AES given in tableII.4.7 were also considered. The points in gures II.4.14 and II.4.15 correspond to the dierent available experimental data.

Table II

 II The McLean model (equation II.1.8) was used with X ϕ max = 1 for all the elements.No site competition was considered. In other words, each element can independently achieve the given saturation concentration X ϕ max . This case corresponds to the black lines in gure II.4.14. The t for P, Mn, and Ni is reasonable, but completely o for Mo. TableII.4.15 shows the values of the segregation free energies for the dierent elements obtained from the be extremely dicult to obtain because of very slow kinetics.On the other hand, the case of Mo is dierent. It is clear from the experimental points of gure II.4.14 (b) that the equilibrium concentration of Mo (about 0.21 monolayer) does not vary with temperature. This shows that the intergranular segregation sites are saturated at any temperature. This observation also suggests that Mo segregates to dierent sites from the other elements, which is in agreement with a previous ab-initio study on tilt boundaries by Domain et al.[START_REF] Domain | Solute segregation at (100) and (110) tilt GB in Fe at the atomic scale[END_REF].

	CHAPTER II.4. INTERGRANULAR SEGREGATION IN BAINITIC AND
	MARTENSITIC 16MND5 STEEL
	experimental data would
	.4.15: Segregation free energy (∆G) in kJ/mol and saturation concentration (X	ϕ max ) for
	each element obtained from the t procedure in dierent cases.
		Model	X ϕ-P, Ni, Mn max	X ϕ-Mo max	∆G Mn ∆G Ni ∆G Mo ∆G P
	Case 1		1	1	-21	-13	-30	-43
	Case 2	McLean	0.5	0.21	-27	-17	-70	-49
	Case 3		1	1	-22	-17	-30	-45
	Case 4	Guttmann	0.5	0.21	-33	-25	-65	-55
	Case 1: t procedure.
	Case 2: The same McLean model was used, but dierent values of X ϕ max were considered.
	For P, Mn, and Ni, a value of X ϕ max = 0.5 was considered. By re-adjusting the values of the free
	energies (see table II.4.15), it was possible to obtain a very good t as well (blue curves in gure

II.4.14 (a), (c), and (d)). This shows that X ϕ max and ∆G cannot be independently determined from the t procedure, as two dierent sets of input parameters both result in a good t of the experimental values. Additional measurements at lower temperature would be needed to allow independent determination of X ϕ max and ∆G for P, Mn and Ni, but these additional

Table II .

 II 5.2: DBTT and intergranular fracture ratio for dierent states When taking the higher hardness of this state into account, the DBTT at equivalent hardness should be even lower. This indicates that tempered martensite has better fracture toughness than tempered bainite prior to thermal aging. Nevertheless, a higher ∆DBTT between the non-aged state and the step cooling state was observed for the

	Sample	DBTT (	• C)	% Intergranular fracture	Specimen fracture temperature ( • C)
	B	-38		0%		All temperatures
	BSC	-21		<10%		-25
	M	-115		0%		All temperatures
	MIA	-77		30%		-100
	MSC	-45		>50%		-80
	For bainite studied in this work, the DBTT for the non-aged state (gure II.5.1 (a)♦) is -38 •
	which is slightly lower than previous measurement in [188] (-24	• C). There was nearly no DBTT
	shift observed for the bainitic microstructure (∆DBTT = 17	• C), showing a low susceptibility
	to RTE.
	It can be seen that non-aged martensite (gure II.5.1 (b)▲) has the lowest DBTT (-115 • C)
	regardless of the higher hardness.

  5.7. The yellow line in gure II.5.7 represents how the martensitic critical fracture stress decreases with phosphorus grain boundary concentration. For state M, only transgranular cleavage was observed for low phosphorus concentration (0.34 atom/nm 2 ). Then, the yellow line decreases until the red line because intergranular fracture was observed for state MIA (1.15 atom/nm 2 ) and the intergranular fracture percentage increases for state MSC (2.60 atom/nm 2 ).

la perspective d'extensions potentielles de la durée de vie des centrales nucléaires, l'irradiation neutronique peut être fortement réduite par la gestion du combustible du c÷ur des réacteurs, tandis que le vieillissement thermique ne peut être atténué et augmente avec le temps. Le vieillissement thermique nécessite donc plus d'attention dans ce contexte.Dans le parc français, le matériau de paroi soumise à la pression des principaux composants de la boucle primaire est l'acier faiblement allié 16MND5 ou des aciers de nuances très proches, à microstructure nominalement bainitique. Cependant, de la martensite peut également être présente, dans les zones aectées thermiquement des soudures ou dans les ségrégations en A.Pour les matériaux conformes aux spécications du code RCC-M, le principal phénomène de vieillissement attendu aux températures de fonctionnement est la fragilité de revenu réversible (FRR). Il s'agit d'un mécanisme non durcissant dû à la fragilisation des joints de grains par ségrégation d'impuretés, principalement le phosphore, qui se traduit par une diminution de la ténacité, avec un mode de rupture fragile passant du clivage à la rupture intergranulaire. La teneur en phosphore est donc contrôlée pour limiter ce phénomène (par exemple P < 0,008% en poids) et la fragilisation par vieillissement thermique est prise en compte dans les analyses d'intégrité de structure. Les zones aectées thermiquement sont considérées comme ayant des sensibilités à la FRR environ trois fois plus élevées que celles des métaux de base, pour reéter l'expérience sur ce mécanisme.

In their work, crystallography packet meant block and morphology packet meant packet in gure II.1.14.

CONCLUSIONS & PERSPECTIVES

Acknowledgements

First, I would like to thank Prof. Frédéric Christien, Julien Stodolna, and Patrick Todeschini

CHAPTER II.1. LITERATURE REVIEW Kinetics Model When considering a binary system where the solute is homogeneously distributed in the volume at the initial state, McLean [START_REF] Mclean | Grain boundaries in metals. Monographs on the physics and chemistry of materials[END_REF] provides a kinetics model that can describe the evolution of atomic faction of solute at interface with time:

Where k is a constant that is 1 for free surface segregation, and 2 for intergranular segregation, D is the diusion coecient of the solute, δ is the interface thickness, X ϕ 0 is the segregation amount at t = 0, and X ϕ ∞ is the segregation amount at equilibrium. When t is short, meaning that X ϕ 0 is far from the equilibrium value, equation II.1.11 can be expressed as:

Here, X v is expressed in atomic fraction, thus the result X ϕ is also in atomic fraction. If X v is expressed strictly in concentration, as in atoms per cubic centimeter (atom/cm 3 ) or gram per cubic centimeter (g/cm 3 ), then equation II.1.12 can be expressed as:

Where the result X ϕ is also strictly a surface "concentration, expressed in atoms per area (atom/cm 2 ) or gram per area (g/cm 2 ). On the other hand, the need to dene interface thickness δ is removed in equation II. 1.13.

At the same temperature as the Fe-P binary example given above (325 • C), the time needed to achieve the phosphorus equilibrium concentration at grain boundaries can be calculated using equations II.1.11 and II.1.13. Again, no direct link can be observed. It is not possible to predict the segregation level for a given misorientation angle without quantitative measurements. However in this case, the same tendency as Ogura et al. [START_REF] Ogura | Dependence of phosphorus segregation on grain boundary crystallography in an Fe Ni Cr alloy[END_REF] is observed. Comparison of gures II.4.6 and II.4.7 shows that segregation level of grain boundaries < 20 • is less than grain boundaries between 20 • -50

• , and segregation level of grain boundaries > 50 • falls in between the two. Also, gure II.4.7 shows that martensite presents similar segregation level as bainite at boundaries being not prior austenite ones. This is again a striking result in comparison with the hypothesis given in literature.

Summary

From gure II.4.5, it can be seen that the segregation level has a clear tendency with the misorientation angles that segregation levels are higher in general HAGBs than at LAGBs. This agrees with Zhang et al. [START_REF] Zhang | Investigation of solute segregation behavior using a correlative EBSD/TKD/APT methodology in a 16MND5 weld[END_REF] and Ogura et al. [START_REF] Ogura | Dependence of phosphorus segregation on grain boundary crystallography in an Fe Ni Cr alloy[END_REF]. However, from gures II.4.6 and II.4.7, it can be seen that there is no direct link between the grain boundary misorientation angle and the segregation level. In other words, it would not be possible to provide the segregation level for a given misorientation angle. For more detailed analyses, determination of grain boundary planes would be necessary. values and the adjustments to zero for cases that were below the detection limit, the standard deviation remained low.

Block Boundaries & Σ3

Based on the theoretical MRs proposed in [START_REF] Gourgues | Electron backscattering diraction study of acicular ferrite, bainite, and martensite steel microstructures[END_REF], there are only a few combinations for block boundaries. There were multiple STEM-EDX analyses in group 5 (

Summary

From the segregation level measured at prior austenite grain boundaries of the aged states and the estimation of phosphorus trapping, it is concluded that the behavior between bainite and martensite does not show big dierences. This observation was unexpected but also provides a direct proof that the hypothesis given in the literature does not seem correct. This further suggests that the microstructure susceptibility to RTE depends on other factors apart from embrittling elements segregating at grain boundaries.

II.4.2.5 Eect of Thermal Aging

Intergranular segregation was induced by SRHT and step cooling in both bainitic and martensitic microstructures. It was clear that all four segregating elements (P, Mo, Mn, Ni)

were measured on all types of grain boundaries in both microstructures (bainite, martensite), and that P, Mn, and Ni segregation level increases after thermal aging. From gure II.4.4, it was concluded that among the four segregated elements, Mo is less sensible to thermal aging compared to the others.

In this section, how thermal aging inuences intergranular segregation is discussed. Only measurements at prior austenite grain boundaries of each state were considered. The solute diusion distance was calculated to determine the available solute quantity for intergranular segregation. This value was used to check whether segregation was limited by kinetics, i.e. time of diusion. Assuming that the segregation of all four elements was governed by thermodynamics, i.e. not limited by kinetics, the dierent thermodynamic models mentioned in section II.1.3.3 were applied to t the segregation measured data.

Kinetic Limitation

The thermal treatments performed in this study remained complex (see table II.2.2) due to time limitation.

Step cooling instead of isothermal aging was chosen to induce grain boundary segregation because of its shorter duration. The goal of the kinetics calculation is to verify if the dierent states were at equilibrium after the dierent thermal treatments. To facilitate the calculation, only the duration of the last isothermal step of each treatment was considered, no cooling process was taken into account. In the case of step cooling, for example, only the last temperature and duration was taken into account (i.e. 468

• C for 100 hours) in the calculation.

The general formula for diusion coecient can be written as

, where D 0 is the diusion constant and Q is the activation energy. Diusion constants and activation energies from dierent sources were used to compare the results, table II.4.11 shows the dierent D 0 and Q from the dierent sources.

MARTENSITIC 16MND5 STEEL

Equation II.1.15 can be adapted for P, Mn, and Ni as:

, with k = M n, N i, P Again in cases 3 and 4, the values of X ϕ max and ∆G for P, Mn, and Ni cannot be determined independently from the t procedure (here arbitrary values of X ϕ max was assumed and values of ∆G were extracted from the t procedure). In addition, the two models (McLean and Guttmann) can t the experimental data nicely, so that it remains dicult to ascertain a possible site competition between P, Mn, and Ni. For Mo, on the contrary, the assumption of achieving saturation (X ϕ max = 0.21) has largely optimized the t results. This leads to the understanding that McLean model with imposed X ϕ-Mo max = 0.21 may be the better t for Mo.

When focusing only on phosphorus, the concentration barely exceeds 3 atom/nm 2 (lower than 0.2 monolayer) even for states after step cooling (BSC & MSC) and isothermal aging after long time (BSA & data points from Druce et al. [START_REF] Druce | Eect of ageing on properties of pressure vessel steels[END_REF]). This is most likely due to segregation of other elements at the grain boundaries that occupies the same sites (Mn & Ni). Even though the dierent states were considered at equilibrium based on the available solute quantity calculation mentioned above, phosphorus alone does not achieve the saturation concentration.

Summary

Based on the calculation of the available solute quantity, it is clear that the segregation of Mn, Mo, and Ni was governed by thermodynamics for all states. When considering the simplication in the calculation (where only the last isothermal plateau of step cooling was taken into account), phosphorus segregation of all states are also most likely to be governed by thermodynamics.

Two thermodynamic models were used to t the segregation data points. It is shown that the saturation concentration (X ϕ max ) and the segregation free energy (∆G i ) cannot be determined independently. It is also suggested that molybdenum segregates at dierent sites than the other three elements (P, Mn, Ni). Although site competition of P, Mn, and

Ni cannot be surely determined, it is very likely since the phosphorus grain boundary concentration remains very low even after long isothermal aging.

II.4.2.6 Correlation Between Dierent Segregated Elements

From gure II.4.4, when considering measurements at prior austenite grain boundaries, molybdenum intergranular segregation seems less susceptible to microstructure, types of grain boundaries, and thermal aging. In addition, the analysis of data using the thermodynamic models of McLean and Guttmann suggested that molybdenum segregates at dierent sites from other elements. The correlations between the concentrations of dierent solutes at the grain boundaries are discussed in the following. Here, only measurements at prior austenite grain boundaries on the aged states (BSC & MSC) were used as the other data showed too low segregation levels and not enough statistics.

To understand the correlation between dierent solutes, the measured concentrations of each Among the dierent analyzed prior austenite grain boundary portions, the grain boundary characteristics change, meaning that the number of available site changes from one grain boundary to another. The correlations observed in gures II.4.16 and II.4.17 suggest that P, Mn, and Ni indeed segregate to the same grain boundary sites: when a given grain boundary oers a high number of segregation sites, a correlated increase of P, Mn, and Ni concentration is observed. On the other hand, the absence of correlation between Mo and the other elements suggests that this element segregate to dierent sites. This is in agreement with ab-initio simulations by Domain et al. [START_REF] Domain | Solute segregation at (100) and (110) tilt GB in Fe at the atomic scale[END_REF] showing that Mo segregates preferentially to sites in tension in the grain boundary, in contrast to P segregating to sites in compression.

Chapter II.5

Fracture 2 No tensile test at ambient temperature was performed.

It can be seen that the tensile strength has decreased a little due to dierent thermal aging treatments for martensitic microstructure. Also, the martensitic samples are slightly harder than the bainitic ones even after an apparently long enough tempering treatment. The odd high value that appears for state M was unexpected. This may be related to the observation that carbides were not as well-formed than after aging as mentioned in section II.