Suzanne Vernier
email: author.suzanne.vernier@mines-paristech.fr

Jean-Michel Franchet

Christian Dumont

Nathalie Bozzolo

A mechanism leading to γ' precipitates with {111} facets and unusual orientation relationships to the matrix in γ/γ' nickel-based superalloys

 highlighted a new interaction between such precipitates and a recrystallization front passing through. This interaction resulted in γ' precipitates with a close-to-twin orientation relationship to their recrystallized host grain. Called T-type precipitates, they were revealed to be {111} bounded platelike particles. The present paper aims to clarify the mechanism whereby such precipitates form. The formation of T-type precipitates actually is part of a more global mechanism which also produces γ' precipitates slightly misoriented from their surrounding matrix (C-type precipitates) and of same size and morphology as T-type precipitates. Both T and C type precipitates display {111} facets and are evidenced in the AD730 TM , René65 and PER72 alloys, supporting the idea that the mechanism can more generally occur in all low-lattice-mismatch γ-γ' nickel-based superalloys. Finally, a scenario is proposed: T/C type precipitates form at the recrystallization front of grains sharing a <111> axis with the recovered grain they consume, and develop {111} facets and specific orientations which minimize the interfacial energy on both recrystallized and recovered sides.

INTRODUCTION

Wrought polycrystalline γ-γ' nickel-based superalloys are commonly used to manufacture aero-engine turbine disks, thanks to their outstanding mechanical properties at high temperature [1,[START_REF] Reed | The Superalloys, Fundamentals and Applications[END_REF] . Those alloys display γ grains and γ' precipitates of various sizes. The γ phase is a Face Centered Cubic (FCC) non-ordered solid solution, while the γ'-Ni3(Al,Ti) phase has a L12 ordered cubic structure. At a few micrometers in size, primary precipitates are the largest precipitates of the microstructure [START_REF] Kozar | [END_REF] . Derived from the as-cast microstructure and high temperature billet forging sequences, they are useful for the grain size control since they pin grain boundaries during subsolvus forging operations. Most of the time, primary precipitates lie on grain boundaries and are incoherent with the surrounding γ matrix, which means that there is no matching at all between the γ' and the γ crystal lattices. Yet, the interaction between a recrystallization front and an incoherent precipitate is quite easy to predict. When a moving grain boundary encounters a precipitate, its curvature is locally modified due to capillarity effects, which is interpreted as a pinning force applied on the boundary and referred to as the Smith-Zener pinning force [4] . Then, if the grain boundary is subject to sufficient driving force to counteract the pinning force, it will bypass the precipitate; otherwise it will halt at the precipitate. However, when a moving boundary meets a coherent precipitate -which means that the γ and γ' crystal lattices perfectly coincide at the γ/γ' interface [START_REF] Campbell | Elements of Metallurgy and Engineering Alloys[END_REF] -the interaction can be much more complex. Indeed, because coherent interfaces have low energy values [START_REF] Rohrer | [END_REF]7] , the maximum pinning force a coherent precipitate can enforce is twice that of an incoherent precipitate of the same size [8,9] . Then, other phenomena which also allow the grain boundary to carry on moving and which are more thermodynamically and/or kinetically interesting than the coherent precipitate bypass can occur. It was reported in the literature that a coherent precipitate may be cut-through -so that the orientation of the precipitate is changed to that of the growing grain [7,8] -or dissolved [START_REF] Cahn | Physical Metallurgy[END_REF][START_REF] Porter | [END_REF] . However, if the grain boundary driving force is not sufficient to bypass, dissolve or cut-through the coherent precipitate, the grain boundary will halt at the coherent precipitate which will then coarsen as a result of the interfacial energy equilibrium [8] . At a few hundred nanometers to few nanometers in size, secondary and tertiary precipitates are always coherent with their surrounding matrix. But much larger precipitates are also found coherent or close-to-coherent. First, Charpagne et al. evidenced large primary precipitates with the same orientation as their surrounding matrix in the case of heteroepitaxial recrystallization [12][13][14] . Second, cast-and-wrought heavily-alloyed γ-γ' nickel-based superalloys may exhibit unrecrystallized grains inherited from the ingot conversion process [START_REF] Bond | 8th Int. Symp. Superalloy[END_REF][START_REF] Minisandram | 8th Int. Symp. Superalloy[END_REF][START_REF] Crozet | Superalloys 2016 Proc. 13th Int. Symp. Superalloys[END_REF] where a high density of micrometric close-to-coherent precipitates is found. These unrecystallized grains are characterized by intragranular orientation gradients with more or less developed recovery cell structures; thus they will be called recovered grains in the following text. Yet, in the AD730 TM γ-γ' nickel-based superalloy a previous work [START_REF] Vernier | [END_REF] pointed out a new interaction between the close-to-coherent precipitates of the recovered grain and the recrystallization front passing through. This interaction sometimes led to γ' precipitates with a close-to-twin orientation relationship to their recrystallized host grain. "Close to twin orientation relationship" means that the γ' and γ cubic lattice cells conform to a 60°<111> rotation within the 8.66° tolerance given by Brandon's criterion: both the misorientation angle and misorientation axis do not deviate more than 8.66° to the 60° angle and <111> axis of the perfect twin boundary [START_REF] Vernier | [END_REF]19] . Such precipitates close to the twin orientation relationship have been called T-type precipitates and revealed to be {111} bounded plate-like particles. Their size, morphology and narrow orientation spread compared to the precipitates of the recovered grain have proved that they do not result from a simple bypass by the recrystallization front but from a specific mechanism. The aim of the present paper is to clarify this mechanism using EBSD data analyses. It is shown that the formation of T-type precipitates is part of a more global mechanism which also produces precipitates with an orientation very close to that of their surrounding matrix and of the same size and morphology as the T-type precipitates. These precipitates are called C-type precipitates and rotated by few degrees around a <111> axis they have in common with their surrounding matrix. T and C type precipitates are evidenced in the AD730 TM , René65 and PER72 alloys, supporting the idea that the studied mechanism can more generally occur in all γ-γ' nickel-based superalloys with a low-lattice mismatch. Finally, a scenario is proposed for this specific mechanism which allows a recrystallization front to get through a high density of close-to-coherent micrometric precipitates and leads to γ' precipitates with unusual morphologies and orientations.

II. EXPERIMENTAL

In the present paper, five samples are analyzed. They are derived from different thermo-mechanical conditions and from three different alloys: AD730 TM , René65 and PER72. The PER72 alloy is an equivalent of the Udimet720 alloy manufactured by the Aubert&Duval Company. All these polycrystalline γ-γ' nickel-based alloys are all heavily-alloyed, derived from the traditional cast-and-wrought route and characterized by a low lattice mismatch [12,20] . Their chemical compositions are given in Table 1.

Three samples were cut out from AD730 TM billets. Two of them were observed as-received. The third one, referred to as the "AD730 TM Lab-Forged sample", was deformed at high temperature (compression test) then solution-treated for 4 hours at 1080°C in order to complete recrystallization. Hot-deformation and solutiontreatment temperatures were both below the γ' solvus temperature which is about 1110°C. The fourth and fifth samples were cut out from René65 and PER72 billets and heat-treated for two hours at about 40° below their respective γ' solvus temperature. All the samples were ground with Si papers and polished with diamond suspensions down to 1µm. To obtain a suitable surface quality for EBSD (Electron BackScatter Diffraction), they were finally polished either by electropolishing (electrolyte: CH3OH-10% HClO4) or with a 0.02µm colloidal silica solution on a vibratory machine. Observations were carried out with a Zeiss Supra40 Field Emission Gun Scanning Electron Microscope operated at 15kV. The microscope is equipped with the QUANTAX EDS/EBSD system from the Bruker Company which is composed of an XFlash 5030 Energy Dispersive X-ray Spectrometer (EDS) and an e -FlashHR EBSD detector, both controlled by the ESPRIT® software package. Some of the EBSD data post-treatments were performed using MTEX, a freely available MATLAB toolbox [21] .

III. RESULTS AND DISCUSSION

A. T and C type precipitates in the AD730 TM alloy : the results of a single mechanism T-type precipitates have been reported in the alloy AD730 TM , in some recrystallized grains which had extensively grown into a recovered grain and which shared a <111>axis with it [START_REF] Vernier | [END_REF] . Nevertheless, Fig. 1 shows that T-type precipitates are not the only type of precipitate which can be found in such recrystallized grains. Indeed, some precipitates which are 2-3° misoriented from their host grain appear among the T-type precipitates (Fig. 1.a). These precipitates have a nearly rectangular shape in the sample section like the T-type precipitates (Fig. 1.b). Close to the orientation of their surrounding matrix, they will be called C-type precipitates in the following text. The rectangular shapes of the C-type precipitates are parallel and also parallel to those of the Ttype precipitates (Fig. 1.b). On the {111} pole figure (Fig. 1.d), the orientations of T and C type precipitates (randomly selected) are compared to those of the host recrystallized grain and the recovered grain. First, the orientations of the two precipitate types appear very homogeneous compared to those of the recovered grain selected over a much smaller area. Second, the <111> axis shared by the recrystallized and recovered grains perfectly matches with a <111> axis of the C and T type precipitates. Indeed, the three other <111> axes of the C type precipitates differ slightly from those of their recrystallized host grain, showing that the misorientation of the C-type precipitates regarding their host grain originates from a rotation of few degrees around the <111> axis they exactly have in common. Moreover, the longest sides of the rectangular shapes of the T and C type precipitates are parallel to the {111} plane trace common to the recrystallized and recovered grains. Yet, it has been evidenced in [START_REF] Vernier | [END_REF] that T-type precipitates are plate-like particles bounded by the {111} plane common to the T-type precipitates, the recrystallized grain and the recovered grain. Here, the similar morphologies and alignments of the C and T type precipitates strongly suggests that both types of precipitates are facetted by the same {111} plane, common to the recrystallized and recovered grains. Fig. 1 -C and T type precipitates coexisting in a recrystallized grain (AD730 TM Lab-Forged sample). a) EBSD map: misorientation angle to the mean orientation of the grain overlaid on the band contrast map, grain boundaries (misorientation angle threshold: 10°) plotted black and twin boundaries (60°<111> with 8.66° tolerance, following Brandon's criterion [19] ) plotted white. b) Backscattered electron image, where the γ' precipitates appear bright despite their lower atomic number because of topographic effects induced by electropolishing. Some C and T type precipitates are highlighted by blue and red arrows respectively. c) EBSD

map: orientation (IPF color code) overlaid on the band contrast map, grain boundaries plotted black and twin boundaries plotted white. d) {111} pole figure on a spherical grid (spacing: 5°), orientations of ten C-type precipitates (black crosses in c)) plotted black, orientations of ten T-type precipitates (red crosses in c)) plotted green and orientations of the yellow selection in c) plotted with the same color as displayed in c). The {111} plane trace common to the C/T type precipitates and the recrystallized matrix is displayed by a dashed line. Fig.2 -Grain full of C-type precipitates (AD730 TM billet sample). a) EBSD map: misorientation angle to the mean orientation of the grain overlaid on the band contrast map, grain boundaries (misorientation angle threshold: 10°) plotted black and twin boundaries (60°<111> with 8.66° tolerance) plotted white. b) Backscattered electron image. c) EBSD map: orientation (IPF color code) overlaid on the band contrast map, grain boundaries plotted black and twin boundaries plotted white. d) {111} pole figure on a spherical grid (spacing: 5°), orientation of the selected C type precipitates (black crosses in c)) plotted black, orientations of the yellow selections in c) plotted with the same color as displayed in c

). The {111} plane trace common to the C type precipitates and the recrystallized matrix is displayed by a dashed line. Fig. 2 presents an example of a large recrystallized grain with a single T-type precipitate amongst many C-type precipitates in an AD730 TM billet. The recrystallized grain has grown by consuming a so-called substructured grain, which is a former grain mainly composed of well-defined low-misoriented crystallites with micrometric close-to-coherent precipitates located at their boundaries. It is worth mentioning here that the close-to-coherent precipitates of the substructured grain are not C-type precipitates since they do not have the aligned rectangular shapes and narrow orientation spread of the neighboring C-type precipitates (Fig. 2.b and Fig. 3). The substructured and recrystallized grains have a <111> axis close to each other (Fig. 2.d), so that the recrystallized grain is rotated around this <111> axis with respect to the substructured grain, but less rotated than what has been observed in Fig. 1. This <111> axis also coincides with the <111> axis around which the orientations of the C-type precipitates are rotated relatively to that of their host grain. Moreover, the corresponding {111} plane trace is parallel to the longest sides of the C-type precipitates, which is again consistent with C-type precipitates bounded by {111} planes.

Fig.3 -Orientations of the precipitates in the substructured grain with respect to their surrounding matrix (AD730 TM billet sample -Area highlighted in Fig.2.c). a) EBSD map: orientation (IPF color code) overlaid on the band contrast map, grain boundaries (misorientation angle threshold: 10°) plotted black and twin boundaries (60°<111> with 8.66° tolerance) plotted white. b) EBSD map: band contrast map, grain boundaries plotted black and twin boundaries plotted white. c) {111} pole figure on a spherical grid (spacing: 5°). Orientation of the precipitates (selected by blue points in b)) plotted blue, orientations of the matrix (selected by red points in b)) plotted red. Fig.4 -Change from C type to T type precipitates by twinning (AD730 TM billet sample). a) Backscattered electron image (overall view) and secondary electron image (insert at high magnification). b) EBSD map: misorientation angle to the mean orientation of the grain overlaid on the band contrast map, grain boundaries (misorientation angle threshold: 10°) plotted black and twin boundaries (60°<111> with 8.66° tolerance) plotted white. c) EBSD map: orientation (IPF color code) overlaid on the band contrast map, grain boundaries plotted black and twin boundaries plotted white. d) {111} pole figure on a spherical grid (spacing: 5°), orientations of the C-type precipitates (black crosses in c)) plotted black, orientations of the T-type precipitates (yellow crosses in c)) plotted green and orientations of the yellow selections in c) plotted with the same color as displayed in c). The {111} plane traces common to the C/T type precipitates and the recrystallized matrix are displayed by dashed lines.

A last example of C and T type precipitate coexistence in the AD730 TM alloy is presented in Fig. 4. This time, a large recrystallized grain consuming a recovered grain displays C-type precipitates in its main crystal and T-type precipitates in its twin crystals (Fig. 4.b). The two precipitate types are again rectangular in the sample section and can reach few micrometers in length. However, the rectangular shapes of the T and C type precipitates follow two different directions in space. The {111} pole figure (Fig. 4.d) reveals that the main crystal has an orientation very close to that of the recovered grain and that the longest sides of the C-type precipitates are not so far from a {111} plane trace. The twin crystals have a single <111> axis in common with the recovered grain and the longest sides of the T-type precipitates coincide with the corresponding {111} plane trace (which differs from that of the C-type precipitate). In this third example, the orientations of the C-type precipitates are very homogeneous but those of the selected T-type precipitates are somewhat more spread than observed in Fig. 1. This underlines that the mechanism leading to T-type precipitates does not produce perfect twin boundaries.

For the three cases presented above, as well as for the cases which will be presented in the following sections, the misorientation between the recrystallized grain and the recovered (or substructured) grain has been quantified by calculating the average misorientation angle (𝜃 ̅ ) at the recrystallized/recovered boundary (average on boundary segments of at least few tens of micrometers long). The values are summarized in Table 2. From Table 2, it can be noticed that recrystallized grains whose misorientation to the recovered grain is lower than ~37° show C-type precipitates only. On the other hand, recrystallized grains which are misoriented by more than ~50°

show T-type precipitates only. Between these two misorientation angles, a transition zone is observed where recrystallized grains exhibit both C and T type precipitates. So, although a more statistical analysis would be required to obtain more precise transition values, there does exist a link between the misorientation angle of the recrystallized grain relatively to the recovered grain and the precipitate type(s) which form(s).

To summarize, the C and T type precipitates are located in recrystallized grains which have grown into recovered/substructured grains. Both can display rectangular shapes in sample sections. If so, the longest sides of their rectangular shapes are up to a few micrometers in length and parallel to the trace of the {111} plane they share with their host grain. The corresponding shared <111> axis is always very close to a <111> axis of the consumed recovered/substructured grain. Thus, C and T type precipitates are both {111} bounded plate-like particles which derive from the same mechanism. The misorientation angle between the recrystallized and the recovered grains determines what precipitate type forms: while the less misoriented recrystallized grains only display C-type precipitates, the highest misoriented recrystallized grains display only T-type precipitates, and intermediate misorientations both types. Recrystallized grains with a <111> axis very close to one of the <111> axes of the recovered grain they consume originate from the Continuous Recrystallization (CRX) and the Heteroepitaxial Recrystallization (HERX) which are the two recrystallization mechanisms identified for the recovered grains of the AD730 TM alloy [START_REF] Vernier | [END_REF] . Both mechanisms produce recrystallized grains whose initial orientations are close to that of the recovered grain. As the recrystallized grain grows into the recovered grain, its misorientation with respect to the recovered grain increases because of the orientation gradients present inside the recovered grain. By growing, the recrystallized grain may also undergo annealing twinning, so that the misorientation of the recrystallization front changes from a rather low misorientation to a high one (or conversely) due to the additional 60° <111> rotation. This explains why a wide range of misorientation angles is observed at the recrystallized/recovered boundaries (Table 2).

B. Observations in other γ/γ' superalloys: René65 and PER72 alloys

In René65 and PER72 billets, recovered grains with their characteristic high density of close-to-coherent precipitates can also be observed (Fig. 5.a and Fig. 7.a). Besides, the configuration presented in Fig. 1for the AD730 TM alloy is found in the René65 billet sample too (Fig. 5): a few large recrystallized grains have grown to a large extent inside a recovered grain. These large recrystallized grains are full of micrometric precipitates with some of them well rectangular in the sample section (Fig. 5.d-e). Some of the rectangular precipitates are in twin orientation relationship to their host grain but the twin orientation relationship is imperfect because only realized within the 8.66° tolerance given by Brandon's criterion (Fig. 6). Thus, such precipitates do correspond to the Ttype precipitates as defined in the alloy AD730 TM . In the same crystal, rectangular precipitates slightlymisoriented to their surrounding matrix and parallel to the T-type precipitates are also found (Fig. 5.d-e): these precipitates are C-type precipitates. On the {111} pole figure (Fig. 5.c), one can check that the crystal hosting the T and C type precipitates has a <111> axis very close to a <111> axis of the recovered grain. Then, T and C type precipitates are rotated around this common <111> axis with respect to their host grain and the corresponding {111} plane trace coincides with the longest sides of their rectangular shapes. As observed in the AD730 TM alloy, the orientations of the two precipitate types are more homogeneous than that of the recovered grain.

Finally, CRX cells and HERX grains can be noticed at the borders of the recovered grain (black and white arrows in Fig. 5.a). No case of striking heterogeneous recrystallization with large recrystallized grains full of T/C type precipitates has been observed in the studied PER72 billet sample. It is also worth mentioning here that, in the AD730 TM and René65 alloys, all the recovered grains do not always lead to several huge statically recrystallized grains as shown throughout the paper. The reason why this phenomenon is not systematic is not understood yet but would be interesting to investigate in future research. Nevertheless, in the PER72 alloy, isolated T and C type precipitates are seen in recrystallized grains of "normal" size next to recovered grains (red and blue arrows in Fig. 7). For example, the yellow grain on Fig. 7.a contains several C and T type precipitates. This grain has a <111> axis not so far from a <111> axis of the nearby recovered grain (dashed circle in Fig. 7.b), although it is not the twin axis of the T-type precipitates. Some CRX cells and HERX grains are also seen in the recovered grains of the PER72 alloy (white and yellow arrows in Fig. 7). This means that the two recrystallization mechanisms suspected in the AD730 TM alloy as taking part to the formation of the T/C type precipitates also occur in the PER72 alloy. Fig. 7 -A

Fig.5 -C and T type precipitates resulting from the recrystallization of a recovered grain in the René65 alloy (René65 billet sample). a) and b) EBSD map: orientation (IPF color code) overlaid on the band contrast map, grain boundaries (misorientation angle threshold: 10°) plotted black and twin boundaries (60°<111> with 8.66° tolerance) plotted white. In the inserts, the black and white arrows underline a CRX cell and a HERX grain respectively. c) {111} pole figure on a spherical grid (spacing: 5°), orientations of the C-type precipitates (black crosses in b)) plotted black, orientations of the T-type precipitates (green crosses in b)) plotted green and orientations of the white selection in b) plotted with the same color as displayed in b). The {111} plane trace common to the C/T type precipitates and the recrystallized matrix is displayed by a dashed line. d) EBSD map: misorientation angle to the mean orientation of the grain overlaid on the band contrast map, grain boundaries plotted black and twin boundaries plotted white. The black arrow underlines a T-type precipitate at

recovered grain in the PER72 alloy (PER72 billet sample). a) EBSD map: orientation (IPF color code) overlaid on the band contrast map, grain boundaries (misorientation angle threshold: 10°) plotted black and twin boundaries (60°<111> with 8.66° tolerance) plotted white. b) {111} pole figure on a spherical grid (spacing: 5°), orientations of the C-type precipitates (black crosses in a)) plotted black, orientations of the Ttype precipitates (red crosses in a)) plotted green and orientations of the white selection in a) plotted with the same color as displayed in a). A {111} plane trace is displayed by a dashed line. c) EBSD map: misorientation angle to the mean orientation of the grain overlaid on the band contrast map, grain boundaries plotted black and twin boundaries plotted white. d) Backscattered electron image, where the γ' precipitates appear bright despite their lower atomic number because of topographic effects induced by electropolishing. Red, blue, yellow and white arrows highlight T-type precipitates, C-type precipitates, HERX grain and CRX cells respectively.

Thus, T and C type precipitates, with their characteristic {111} facets and orientation relationships, can be identified in recrystallized grains near the recovered grains of the René65 and PER72 alloys. In the same way as in the AD730 TM alloy, the recrystallized host grain has a <111> axis very close to a <111> axis of the nearby recovered grain. Such recrystallized grains are very likely to derive from the CRX and HERX which occur in the recovered grains of the three alloys studied.

C. Clarification of the mechanism leading to T and C type precipitates

1. An advantageous mechanism to overcome a high density of close-to-coherent precipitates Fig. 8 displays several large recrystallized grains which have extensively grown by consuming the nearby recovered grain. If the crystallographic orientations of these recrystallized grains (labelled by black stars in Fig. 8.a) are compared to those of the recovered grain (Fig. 8.c), it appears that all the recrystallized grainsexcept the grain N°1 in Fig. 8.ahave a <111> axis close to a <111> axis of the recovered grain they consume (less than 10° deviation). Moreover, all these large recrystallized grains show a high density of intragranular precipitates which are C and/or T type precipitates (Fig. 8.b).

On the other hand, many recrystallized grains attempting to consume a recovered grain remain very small (Fig. 9). If some of the small recrystallized grains can result from the CRX and HERX occurring in recovered grains, many of them derive from Discontinuous Recrystallization (DRX) [START_REF] Humphreys | Recrystallization and Related Annealing Phenomena[END_REF] and so have random orientations, especially those at the periphery of the recovered grain. Nevertheless, whatever the origin of the small recrystallized grains, each time the same pattern is noticed: i) recrystallized grains are small but larger than the recovery cells of the recovered grain (which are delimited by close-to-coherent precipitates); ii) small recrystallized grains are free from precipitates (except the precipitate which originated HERX); iii) some coarse close-to-coherent precipitates can be pointed out on the boundaries of the small recrystallized grains. From this pattern, a scenario explaining why these recrystallized grains remain so small may be developed. Given that small recrystallized grains are always larger than recovery cells, they must start growing by dissolving the nearby close-to-coherent precipitates. But, since no re-precipitation is observed behind the recrystallization front, at first time all the γ'-forming elements remain stored in the moving boundary. Then, the high solute concentration in the moving grain boundary decreases its mobility [START_REF] Humphreys | Recrystallization and Related Annealing Phenomena[END_REF]23] and the boundary ends up stopping at close-to-coherent precipitates. Finally, these close-to-coherent precipitates are fed by the γ'-forming elements stored in the boundary and their coarsening leads to a high pinning force, which definitely prevents the boundary from moving anymore.

The above observations suggest that the recrystallized grains having a <111> axis close to a <111> axis of a recovered grain have an advantage over a randomly-oriented recrystallized grain in consuming it. Yet, consuming a recovered grain amounts to overcoming the high Smith-Zener drag pressure exerted by its close-tocoherent precipitates. For spherical particles, the Smith-Zener drag pressure is usually described by the formula

𝑃 𝑆𝑍 = Γ. 3𝑓 2𝑟
, where Γ, 𝑓 and 𝑟 are respectively the grain boundary energy, the precipitate volume fraction and the precipitate mean radius [4] . In the present case, the drag pressure has not been precisely evaluated but, judging from the precipitate density and size, it is very likely to be quite high. In addition, the intragranular precipitates of the recovered grains are close-to-coherent and the drag pressure enforced by coherent precipitates is twice that enforced by the equivalent incoherent population [8,9] . In literature several possible mechanisms to overcome coherent precipitates have been pointed out: precipitates can be bypassed, dissolved (with a coherent reprecipitation behind the recrystallization front) [START_REF] Cahn | Physical Metallurgy[END_REF][START_REF] Porter | [END_REF] or crossed by the recrystallization front so that their orientation is changed to that of the growing grain [7,8] . However here, none of these mechanisms is observed: while many recrystallized grains stop growing very early inside the recovered grain, some recrystallized grains sharing a <111> axis with the recovered grain can grow to a large extent producing T/C type precipitates. Thus, the mechanism leading to T/C type precipitates appears as the more thermodynamically/kinetically interesting mechanism to overcome the precipitates of the recovered grain. Yet, considering that T/C type precipitates are bounded by {111} planes, this is consistent with a mechanism which minimize the energy of the system since {111} planes are known to be low energy interfaces [24] . Fig. 8

-Analysis of the heterogeneous recrystallization nearby a recovered grain (AD730 TM Lab-Forged sample). a) EBSD map: orientation map (IPF color code), grain boundaries (misorientation angle threshold: 10°) plotted black and twin boundaries (60°<111> with 8.66° tolerance) plotted white. b) EBSD map: misorientation angle to the mean grain orientation overlaid on the band contrast map, grain boundaries plotted black and twin boundaries plotted white. c) {111} pole figure on a spherical grid (spacing: 5°), orientations of the recovered grain (white selection in a)) plotted black, orientations of the grains selected by black stars in a) plotted with the same color they appear in a). Fig.9 -Recrystallized grains unsuccessful in consuming the surrounding recovered grain (AD730 TM Lab-Forged sample). a) and c) Backscattered electron images, where the γ' precipitates appear bright despite their lower atomic number because of topographic effects induced by electropolishing. b) and d) EBSD map: orientation (IPF color code) overlaid on the band contrast maps, grain boundaries (misorientation angle threshold: 10°) plotted black and twin boundaries (60°<111> with 8.66° tolerance) plotted white.

2. Involving grain boundary faceting As highlighted in [START_REF] Vernier | [END_REF] , the few T-type precipitates evidenced at the recrystallization front (black arrows in Fig. 5, Fig. 10 and Fig. 11) prove that T-type precipitates form at the recrystallization front with their characteristic orientation and facetted shape. Similarly, a C-type precipitate is seen at the recrystallization front in Fig. 12.k (black cross). Fig. 10 -A

T-type precipitate at the recrystallization front in the AD730 TM alloy (AD730 TM Lab-Forged sample). a) Backscattered electron image, where the γ' precipitates appear bright despite their lower atomic number because of topographic effects induced by electropolishing. b) EBSD map: misorientation angle to the mean orientation of the grain overlaid on the band contrast map, grain boundaries (misorientation angle threshold: 10°) plotted black and twin boundaries (60°<111> with 8.66° tolerance) plotted white. The black arrow underlines a T-type precipitate at the recrystallization front. c) EBSD map: orientation (IPF color code) overlaid on the band contrast map, grain boundaries plotted black and twin boundaries plotted white. d) {111} pole figure on a spherical grid (spacing: 5°), orientations of the red selection in c) plotted with the same color as displayed in c). The {111} plane trace common to the T-type precipitate and the selected matrix is displayed by a dashed line. Fig.11 -A T-type precipitate at the recrystallization front in the René65 alloy (René65 billet sample). a) Backscattered electron image, where the γ' precipitates appear bright despite their lower atomic number because of topographic effects induced by electropolishing. The white arrow highlights a grain boundary facet. b) EBSD map: misorientation angle to the mean orientation of the grain overlaid on the band contrast map, grain boundaries (misorientation angle threshold: 10°) plotted black and twin boundaries (60°<111> with 8.66° tolerance) plotted white. The black arrow underlines a T-type precipitate at the recrystallization front. c) EBSD map: orientation overlaid on the band contrast map, grain boundaries plotted black and twin boundaries plotted white. d) {111} pole figure on a spherical grid (spacing: 5°), orientations of the red selection in c) plotted with the same color as displayed in c), orientation of the selected T-type precipitate (green cross in c)) plotted green. The {111} plane trace common to the recrystallized and recovered grains is displayed by a dashed line. Fig.12 -{111} grain boundary facets at the recrystallization front (AD730 TM billet sample). 1 st column (a, e and i): Backscattered electron images. Secondary electron image inserted in e), the red arrows point out a twin boundary inside a precipitate. 2 nd column (b, f and j): EBSD maps -misorientation angle to the mean orientation of the grain overlaid on the band contrast maps, grain boundaries (misorientation angle threshold: 10°) plotted black and twin boundaries (60°<111> with 8.66° tolerance) plotted white. 3 rd column (c, g and k): EBSD maps -orientation (IPF color code) overlaid on the band contrast maps, grain boundaries plotted black and twin boundaries plotted white. The white arrows highlight grain boundary facets. 4 th column (d, h and l): {111} pole figures on a spherical grid (spacing: 5°), orientations of the recrystallized/recovered interface plotted with the same color as displayed in the orientation maps, orientations of the selected C-type precipitates (black crosses) plotted black. Some {111} plane traces, parallel to grain boundary facets, are displayed by dashed lines.

In the AD730 TM billet sample, small facets in the range of 0.5 to 2 µm wide can be observed on the recrystallized/recovered front (Fig. 12). Most of the facets coincide with a {111} plane trace the recrystallized and recovered grains have in common (white arrows on the orientation maps Fig. 12). On these facets, precipitates large, facetted and slightly misoriented compared to the neighboring recovered matrix are implanted (misorientation angle to the mean grain orientation maps Fig. 12). The insert in Fig. 12.e even shows, inside a precipitate implanted on a recrystallization front facet, a twin boundary being itself parallel to the recrystallization front facet. Similarly, in the René65 alloy, the T-type precipitate visible at the recrystallization front is implanted on a facet which lies on a {111} plane the recrystallized and recovered grains have in common (white arrow in Fig. 11.a).

The {111} facets of the T/C type precipitates are very unusual for γ' precipitates since coherent {100} cuboidal γ' precipitates are classically observed in nickel-based superalloys [20,25,26] . Yet, γ' precipitates always evolve so as to minimize the system free energy. For instance, the classical {100} cuboidal shape allows the minimization of the elastic strain energy occurring at the coherent interfaces due to the γ-γ' lattice mismatch. For C/T precipitates, the elastic strain energy is small since their imperfect cube-cube/twin orientation relationships require interfacial dislocations to accommodate the elastic strain. Thus, the morphology and orientations of the C/T type precipitates are mainly controlled by their interfacial energy which has to be minimized considering the recrystallized and recovered sides since C/T type precipitates form at the recrystallization front.

The recrystallized and recovered grains share a <111> axis. Yet, <111>twist boundaries have a much lower boundary energies than any other grain boundary type, with minima at 0°<111> and 60°<111> corresponding to the cube-cube and twin orientation relationships respectively (from [24] the energy of a <111>twist boundary does not exceed 0.5 J/m² while a random boundary can reach 1.5 J/m²). Thus, by developing <111>twist boundaries (approximately) lying on the {111} plane common to the recovered and recrystallized grains, the precipitates decrease their interfacial energy on both recovered and recrystallized sides. Finally, the γ/γ' <111>twist rotation angle which is adopted is the best compromise to minimize the total interfacial energy of the precipitate. This rotation angle is logically close to 0° or 60°, depending on the mutual misorientation of the recrystallized and recovered grains.

Regarding the formation of the {111} facets which have been noticed at the recrystallization front, two hypotheses can be considered; they are schematically represented in Fig. 13. The first one (H1) is that the recrystallization front naturally tends to develop {111} facets, and thus <111>twist portions, because of the <111> axis its shares with the recovered grain. Then, due to the supersaturation of the recrystallization front, γ'forming elements re-precipitate on these {111} facets in order to minimize the total interfacial energy of the obtained precipitates as just explained above. Coincidence Site Lattice (CSL) boundaries naturally tend to facet and the obtained facets are preferentially the crystallographic planes densely packed with coincidence sites [27,28] .

Many CSL boundaries in the FCC structure are equivalent to a <111> rotation and so present the {111} planes as densely packed CSL planes. The names of these CSL boundaries as well as their corresponding rotation angle are given in Table 3. One can notice that the <111> rotation angles of these CSL boundaries cover the whole recrystallized/recovered misorientation angle range presented in the present paper (Table 2).

In the second hypothesis (H2), the T/C type precipitates first nucleate at an initially rough recrystallization front due to solute supersaturation. This nucleus is <111> rotated with respect to the recrystallized and recovered grains so as to minimize its interfacial energy. Then, while growing, the precipitate develops its characteristic {111} facets to again minimize its interfacial energy. The γ/γ' {111} facets of the precipitate oblige the recrystallization front in turn to facet so as to bypass it.

At the moment, given the available information, deciding which hypothesis between H1 and H2 is the most likely is not possible. But, whatever the hypothesis considered, as the T/C type precipitates form at the recrystallization front but inside the recovered grain, the recrystallization front still has to bypass them to carry on growing. Because T and C type precipitates are {111} bounded plate-like particles, the classical Smith-Zener model which is used for spherical particles and, above all, which ignores the interfacial energies between the grains and the particle is not the most appropriate here. However, the work of Ringer et al. [29] on grain boundary pinning by stable cubic-shaped particles is interesting to consider. Indeed, they highlighted that the pinning enforced by a cubic or spherical particle strongly depends the "degree of particle coherency" defined by the ratio:

𝐷 𝑃𝐶 = Γ 1𝑝 -Γ 2𝑝 Γ 12
Where the grain 1 is non-recrystallized, the grain 2 is recrystallized, Γ 𝑖𝑝 is the energy of the grain i/particle interface and Γ 12 is the grain boundary energy. Ringer et al. evidenced that for a cubic (or spherical) particle the pinning force is minimal for low 𝐷 𝑃𝐶 values. On the contrary, in case of a coherent particle, the 𝐷 𝑃𝐶 is close to 1 and the pinning force is much higher. As said above, <111>twist interfaces have low energy values. Thus, considering the T/C type precipitates delimited by <111> twist boundaries whose corresponding {111} plane is common to the recrystallized and recovered grains, Γ 1𝑝 and Γ 2𝑝 are very low compared to Γ 12 , so the 𝐷 𝑃𝐶 is small and the pinning enforced is minimized. Fig. 13 -Schematic diagrams describing the two hypotheses (H1 and H2) for the formation of {111} facets at the recrystallized/recovered front.

Scenario proposed for the formation of C and T type precipitates

At this point, a scenario for the formation of T and C type precipitates can be proposed. Under hot-deformation and subsequent heat-treatments, recovered grains partially recrystallize by forming CRX and HERX grains which are low-misoriented to the surrounding recovered matrix. Recrystallized grains are also produced by DRX occurring at the periphery of the recovered grain as everywhere in the equiaxed grain areas. During an annealing stage, all these recrystallized grains start growing inside the recovered grain due to its relatively high stored energy. This first growth step is supported by the dissolution of the precipitates encountered in the recovered grain, so that the recrystallization front gets more and more saturated with γ'-forming elements. Then, there are two cases. In the first case, the recrystallization front gets so saturated that the high solute concentration decreases significantly its mobility. Thus, the recrystallization front stops at some precipitates of the recovered grain and the γ'-forming elements stored in the front feed those precipitates. Those precipitates coarsen, pin and prevent the boundary from further motion. The second case concerns the recrystallized grains sharing a <111> axis with the nearby recovered grain. These recrystallized grains mainly derive from the CRX and HERX occurring in the recovered grain. The common <111> axis can allow: H1) the formation on the recrystallization front of facets lying on the {111} common planes, then the implantation of γ'-forming elements on the {111} facets as a consequence of supersaturation; H2) the formation of precipitates facetted by the {111} common planes on a rough recrystallization front due to supersaturation, this then obliges the recrystallization front to form {111} facet in order to bypass them. Whatever the hypothesis (H1 or H2), what is sure is that the T/C type precipitates form inside the recovered grain at the recrystallization front, and develop these {111} facets combined with specific orientations to minimize their interfacial energy including both the recrystallized and recovered sides. Indeed, <111>twist boundaries have low energies with minima at 60°<111> and 0°<111>. This implies that the lowest misoriented recrystallized grains (< ~37°) lead to precipitates implanted approximately at 0°<111> on the front, the highest misoriented ones (> ~50°) lead to precipitates implanted approximately at 60°<111> on the front, and that for the intermediate misorientations both implantations are possible. The low interfacial energies on both recrystallized and recovered sides make the facetted precipitates little costly to bypass. The obtained precipitates are few degrees rotated to their host recrystallized grain (~0°<111> -C-type) or in close-to-twin orientation relationship (~60°<111> -T-type). Released from the γ' elements it contained, the recrystallization front can carry on moving inside the recovered grain and repeat the same mechanism.

Nevertheless, the scenario which is proposed here has some weaknesses. First, the reason why all the grains derived from the CRX and HERX in the recovered grain do not succeed in growing to a large extent inside the recovered grain is not understood yet. Thus, the mechanism leading to T/C type precipitates must require additional conditions to a common <111> axis to happen. Second, the reason why the γ' precipitates re-arrange inside the recovered grain and not coherently behind the recrystallization front as it is expected from the literature is unclear too. One can imagine that the γ'-forming elements precipitate around a precipitate preexisting in the recovered grain with a slight change in orientation to minimize the interfacial energy. However, no such sub-boundary has been observed into the T/C type precipitates yet. Another reason which could account for this is the enhanced γ'-forming element diffusion which occurs in the recovered grain due its highly developed network of dislocations [30] . All these points need to be clarified in future research.

IV. CONCLUSION

A previous work [START_REF] Vernier | [END_REF] has pointed out a close-to-twin orientation relationship between micrometric γ' precipitates and their host recrystallized grain in the AD730 TM γ-γ' nickel-based superalloy. The aim of the present paper is to clarify the mechanism leading to such precipitates called T-type precipitates.

This paper shows that:

1. The mechanism leading to T-type precipitates is also able to form C-type precipitates, which are micrometric γ' precipitates slightly misoriented to their surrounding matrix by a rotation of few degrees around a <111> axis. Both C and T type precipitates are found in recrystallized grains which have grown into a recovered grain and which (approximately) share a <111> axis with this recovered grain.

The recrystallized grains sharing a <111> axis with a recovered grain derive from the CRX and HERX occurring in the recovered grain.

2. The misorientation angle between the recrystallized and recovered grains determines if the precipitates are mainly C-type (< ~37°), mainly T-type (> ~50°) or both (between ~37 and ~50°).

3. Both C and T type precipitates are facetted by {111} planes whose corresponding <111> axes are common to the T/C type precipitates, the surrounding recrystallized matrix and the consumed recovered grain.

4. Like the AD730 TM alloy, the René65 and PER72 alloys can exhibit large recovered grains. In the René65 and PER72, T and C type precipitates with their characteristic shape and orientation relationships are found in recrystallized grains sharing a <111> axis with the nearby recovered grain.

Those recrystallized grains derive from the CRX and HERX mechanisms which have been also pointed out in the recovered grains of the René65 and PER72 alloys. So, the mechanism leading to T/C type precipitates may possibly occur in all the low-lattice-mismatch γ-γ' nickel-based superalloys.

5. The mechanism leading to T/C type precipitates is an advantageous mechanism to overcome the high density of close-to-coherent precipitates in a recovered grain. Thus, regarding a random recrystallized grain, recrystallized grains derived from the CRX and HERX occurring in the recovered grain are privileged for consuming it. 6. T/C type precipitates appear in the recovered grain at the recrystallization front. They grow onto {111} facets that the recrystallization front developed due to its crystallographic structure (H1), or grow directly with {111} facets on a rough recrystallized front which is then obliged to form {111} facets in order to bypass them (H2). Whatever the hypothesis, T/C type precipitates develop <111>twist boundaries with specific rotation angles (~60°<111> and ~0°<111>) in order to minimize their interfacial energy including both the recovered and recrystallized sides. Then, the low interfacial energy on both the recrystallized and recovered sides of the T/C precipitates makes them little costly to bypass. 7. However, some points of the suggested scenario remain unclear. First, as all the CRX and HERX grains formed from the recovered grain do not display T/C type precipitates, additional conditions must certainly be required for the mechanism to happen. Second, the re-precipitation in the recovered grain and not in the recrystallized grain as it is expected from the literature may be perhaps due to the enhanced diffusion occurring in the recovered grain because of its network of dislocations. [START_REF] Bond | 8th Int. Symp. Superalloy[END_REF] Bal. 3 -CSL boundaries equivalent to a <111> rotation in a FCC structure [32] CSL

TABLES

  Fig.6 -The imperfect twin orientation relationship of the T-type precipitates (René65 billet sample). a) and b) EBSD maps -misorientation angle to the mean orientation of the grain overlaid on the band contrast map, grain boundaries (misorientation angle threshold: 10°) plotted black and twin boundaries (60°<111> with Δθ tolerance) plotted white. In a) twin boundaries are plotted with 8.66° tolerance following Brandon's criterion[19] . In b) twin boundaries are plotted with 2° tolerance. c) {111} pole figure on a spherical grid (spacing: 5°). The orientations of the T-type precipitates selected in a) are plotted green, the orientations of the surrounding matrix and the corresponding perfect twin crystal (60°<111> 0° tolerance) are plotted purple and red respectively.

Fig. 4

 4 in Fig.4.c 53.8° T Green grain in Fig.10.c Table

Table 1 -

 1 Chemical compositions of the alloys used in the present work (wt. %)

	Element	Ni	Fe	Co	Cr	Mo	W	Al	Ti	Nb	B	C	Zr
	AD730 TM [31]	Bal.	4.00	8.50	15.70 3.10	2.70	2.25	3.40	1.10	0.01	0.015 0.03
	René65

Table 2 -

 2 Average misorientation angle 𝜃 ̅ calculated at recrystallized/recovered grain boundaries

			1	13	16	4	4	2.1	3.7	0.7	0.016 -	0.05
	PER72	Bal.	0.138 14.5	16.06 2.88	1.21	2.57	5.07	-	0.016 0.017 -

ACKNOWLEDGMENTS

This work has been carried out thanks to the financial support of the ANR-Safran industrial chair OPALE.


Suzanne Vernier
email: author.suzanne.vernier@mines-paristech.fr

Jean-Michel Franchet

Maxime Lesne

Thierry Douillard

Jeremie Silvent

Cyril Langlois

Nathalie Bozzolo

Jérémie Silvent

iCHORD-SI combination as an alternative to EDS-EBSD coupling for the characterization of γ-γ' nickel-based superalloy microstructures

Keywords: Focused Ion Beam, Ion channeling, Secondary ions, EDS-EBSD coupling, Gamma -Gamma Prime nickel-based superalloy

Introduction

Due to their superior resistance at high temperature, γ-γ' nickel-based superalloys are used for the manufacturing of highly-constrained aero-engine parts [START_REF] Reed | The Superalloys, Fundamentals and Applications[END_REF]. Their mechanical properties at high temperature result from several features including the γ' phase distribution. Indeed, the γ' phase forms precipitates of different sizes which are spread inside the γ matrix, the finer precipitates ensuring the strengthening of the alloy [START_REF] Devaux | Effect of Aging Heat-Treatment on Mechanical Properties of AD730 TM Superalloy[END_REF]. But many interactions between the γ grains and the γ' precipitates also occur during hot forging operations: deformation triggers recrystallization mechanisms which closely depend on the precipitation and its evolution. For instance, precipitates may dissolve to potentially reprecipitate behind the front [START_REF] Cahn | Physical Metallurgy[END_REF][START_REF] Porter | The recrystallization of nickel-base superalloys[END_REF], pin grain boundaries [START_REF] Nes | On the Zener drag[END_REF] or act as nucleation sites [START_REF] Humphreys | Recrystallization and Related Annealing Phenomena[END_REF][START_REF] Huang | The double-edge effect of second-phase particles on the recrystallization behaviour and associated mechanical properties of metallic materials[END_REF]. Understanding these γγ' interactions enables the optimization of the forging process so as to obtain the γ' phase distribution leading to the best mechanical properties. Thus, for the γ-γ' microstructures the characterization of respective phases is a real need.

Electron Back-Scattered Diffraction (EBSD) is commonly used to characterize polycrystalline microstructures. However, in the case of the γ-γ' microstructures, this technique is not able to discriminate the γ and γ' phases because of their respective crystallographic structures, FCC and L1 2 , which lead to very similar diffraction patterns [START_REF] El-Dasher | Application of Electron Backscatter Diffraction to Phase Identification[END_REF]. Superstructure reflections, which are theoretically present in the γ' patterns and absent in those of the γ phase, have too low intensities to be detected with the conventional EBSD mapping settings (e.g. diffraction patterns of 160x120 pixels).

γ' phase is easily recognizable on BackScattered Electron (BSE) images because its higher content in light chemical elements makes it appear darker than the γ phase. The overlay of a BSE image acquired at a 0° tilt angle with an EBSD map acquired at a 70° tilt is difficult since distortions are very likely to exist between the two images even after tilt correction. In the EBSD sample configuration, BSE can be collected either by a BSE detector beneath the SEM column or by a solid-state BSE detector mounted at the topside of the EBSD camera. But in both cases the collected intensity is low, which can result in noisy images [START_REF] Schwarzer | Backscaterred Electron Imaging with an EBSD detector[END_REF]. In addition, with the solid-state detector optimal contrast settings can be difficult to find [START_REF] Schwarzer | Backscaterred Electron Imaging with an EBSD detector[END_REF]. In order to collect more intensity, some research have been done in order to use the EBSD detector itself as a BSE detector [START_REF] Schwarzer | Backscaterred Electron Imaging with an EBSD detector[END_REF]; but the technique is not widespread.

Performing Energy Dispersive X-ray Spectrometry (EDS) at the same time as the EBSD scan allows the discrimination of the phases thanks to their difference in chemical composition [START_REF] Nowell | Phase differentiation via combined EBSD and XEDS[END_REF][START_REF] Charpagne | Evidence of multimicrometric coherent γ′ precipitates in a hot-forged γ-γ′ nickel-based superalloy[END_REF]. One limit of this method is the spatial resolution of the EDS technique which depends on the chemical composition of the material as well as on the electron beam energy [START_REF] Anderson | Extension of electron microprobe techniques to biocemistry by the use of long wavelenght X-rays[END_REF][START_REF] Barkshire | High-Spatial-Resolution Low-Energy Electron Beam X-Ray Microanalysis[END_REF]. Yet, γ' precipitates as small as 100 nm must be considered in the analysis of the microstructures because they have a significant effect on the mechanisms and kinetics of recrystallization in addition to their impact on the material mechanical properties.

The present paper aims at presenting another method to discriminate the γ and γ' phases on an orientation map, also based on the chemical differences of the phases but performed with a Focused Ion Beam (FIB) microscope. This methods combines the ion CHanneling ORientation Determination (iCHORD) technique, recently developed by Langlois et al. [START_REF] Langlois | Crystal orientation mapping via ion channeling: An alternative to EBSD[END_REF] and which uses the intensity variations in Secondary Electron (SE) images to determine the crystal orientations, with the Secondary Ion (SI) signal whose intensity strongly depends on the atomic number [START_REF] Phaneuf | Applications of focused ion beam microscopy to materials science specimens[END_REF]. Acquired with the same scan electronics and without changing the sample position, SE and SI signals are can be easily superimposed, providing an orientation map with phase identification. The performances of the iCHORD-SI combination on a γ-γ' microstructure are analyzed in regards to that of the EDS-EBSD coupling. Applied filters (part 3.1), angular resolution (part 3.2), spatial resolution of the phase discrimination (part 3.3) and acquisition time (part 3.4) are discussed.

Experimental

Material

The AD730 TM alloy is a polycrystalline γ-γ' nickel-based superalloy recently designed by the Aubert&Duval Company for aero-engine applications [START_REF] Devaux | AD730TM -A new Nickel-based superalloy for high temperature engine rotative parts[END_REF]. Its chemical composition is given in Table 1. The γ phase forms the matrix of the alloy and is a Face Centered Cubic solid solution. The γ' phase forms precipitates of various sizes and has a Simple Cubic L1 2 ordered structure. The chemical composition of each phase measured on the as-received billet by EDS at 15 kV is presented in Table 2. Compression samples were machined out of the AD730 TM industrial billet. To trigger the recrystallization of the alloy and observe γ-γ' interactions, the samples were isothermally compressed below the γ' solvus (which is about 1,110°C) and water quenched. Sample sections were ground and polished with first diamond suspensions down to 1 µm then 0.02 µm colloidal silica (OPS) on a vibratory polishing machine. Hot compression led to a partially recrystallized microstructure exhibiting many microstructural features, including recrystallized/unrecrystallized grains and several γ' populations with characteristic sizes. Thus, this kind of microstructure was found relevant to discuss the performances of the iCHORD-SI combination.

The iCHORD-SI combination

The ion CHanneling Orientation Determination (iCHORD) technique has been recently developed by Langlois et al. [START_REF] Langlois | Crystal orientation mapping via ion channeling: An alternative to EBSD[END_REF] to obtain orientation maps using the ion channeling effect. Ion/matter interactions produce secondary electrons whose intensity depends on how deep the ions are channeled through the crystal, and so on the orientation of the crystallographic planes relative to the ion beam [START_REF] Phaneuf | Applications of focused ion beam microscopy to materials science specimens[END_REF][START_REF] Feldman | Materials Analysis by Ion Channeling, Submicron Crystallography[END_REF][START_REF] Yahiro | Crystallographic orientation contrast associated with Ga+ ion channelling for Fe and Cu in focused ion beam method[END_REF]. Then, if the crystal position changes relative to the ion beam, the intensity of the collected secondary electrons varies following an intensity profile which is characteristic of the crystallographic orientation of the crystal.

The experimental setup of the iCHORD technique (Figure 1.a) has been optimized so that each intensity profile corresponds to a unique crystallographic orientation. The sample is first tilted at a 40° fixed angle around an axis (e y ) which lies in its surface. Next, with a fixed azimuthal rotation step, the sample performs a complete rotation around its tilted normal (e z ) to make secondary electron intensity vary (Figure 1.c). One Secondary Electron (SE) image is acquired at each azimuthal position. Then, using the Fiji image processing software [START_REF] Schindelin | Fiji: an open-source platform for biological-image analysis[END_REF], SE images undergo tilt correction, rotation correction, are aligned and cropped all together to get a stack of aligned images. The intensity of a given point of the scanned area varies as the stack is browsed, allowing the plot of a so-called intensity profile (i.e. intensity of the point in the SE image as a function of the azimuthal rotation angle, Figure 1.b). Finally, during the post-treatment stage, intensity profiles are compared to theoretical intensity profiles stored in a database, each theoretical intensity profile corresponding to a known crystallographic orientation. The building of the theoretical profiles and the database search algorithm are precisely described in [START_REF] Langlois | Crystal orientation mapping via ion channeling: An alternative to EBSD[END_REF]. The theoretical profile which matches the best with the experimental intensity profile gives the crystallographic orientation of the point.

The ion-matter interactions also create secondary ions whose intensity mainly depends on the atomic number of the excited atoms [START_REF] Phaneuf | Applications of focused ion beam microscopy to materials science specimens[END_REF]. Thus, collected by a Secondary Ion (SI) detector, the Secondary Ion signal highlights the chemical contrast of the microstructure. In the present case, the γ' phase, which contains lighter elements (Table 2), appears much brighter than the γ phase on SI images (Figure 1.d). To properly extract the γ' phase from SI data, several SI images have been acquired at different rotation angles and summed all together so as the channeling contrast of the SI images does not interfere with the chemical information. Finally, to separate the γ' precipitates from the γ matrix an intensity threshold is applied to the sum image.

Using the TESCAN Lyra3 FIB-SEM of the Orsay Physics Company, combined iCHORD and SI scans have been performed on a sample section. The FIB was equipped with a Gallium ion source and the beam setup for data acquisition was 30 kV / 48 pA. The pixel size was 36 nm and the azimuthal rotation step was 4°, which implied the acquisition of 90 SE images to achieve the complete rotation of the sample. With the same 36 nm pixel size, four SI images were also acquired at different azimuthal rotation angles.

b) Theoretical intensity profile (blue dashed line) matching with an experimental profile (red line)data of the point highlighted by a red cross on c). c) Secondary Electron (SE) image for one azimuthal position around e z (the orientation contrast arises from the ion channeling effect). d) Secondary Ion (SI) image for the same azimuthal angle (gray levels mainly depend on the chemical composition even if a slight orientation contrast is also visible).

Both SE and SI images are tilt corrected.

EDS-EBSD coupling: example of the γ-γ' nickel-based superalloys

The crystallographic lattice parameters of the γ and γ' phases are very close to each other. However, theoretically EBSD patterns of both phases do exhibit differences. Indeed, the γ' phase has an ordered structure which allows crystallographic planes with both odd and even Miller indices to diffract, contrary to the γ phase whose disordered structure leads to a systematic extinction for such planes. So, in principle, detecting the presence or the absence of the superstructure reflections should allow the distinction of the two phases with EBSD. But, the corresponding Kikuchi bands exhibit very low intensities compared to the others and would thus require the acquisition of very high signal-to-noise ratio EBSD patterns to be detected. This does not conform to the settings of commercial EBSD optimized for orientation mapping, which means a high indexing speed from noisy Kikuchi patterns (e.g. patterns of 160x120 pixels). Consequently, in practice the γ and γ' grains of same crystallographic orientation display identical patterns (Figures 2.a, 2.b and 2.c) and the EBSD indexing software is unable to decide alone whether a given diffraction pattern arises from one phase or the other. This is why extra information is needed to distinguish the two phases in an EBSD map.

The γ and γ' phases can easily be identified with the EDS technique relying on their Nickel, Titanium and Chromium contents (Table 2, Figures 2.d, 2.e and 2.f). Thus, simultaneously to the EBSD scan, EDS spectra are acquired for each point of the map. Afterward, from EDS data, Ni, Ti and Cr ratios are defined as references for each phase. The re-analysis of the EBSD data assigns to an indexed point the phase whose reference ratios are the closest to the Ni, Ti and Cr ratios quantified in this point. Finally, an EBSD map with γ/γ' discrimination is obtained (Figure 2.g). EDS-EBSD coupled acquisitions have been performed on a similar sample than that used for the iCHORD-SI acquisition, using the same 36nm pixel size. Three accelerating voltages 10kV, 15kV and 20kV were tested corresponding to a beam current in the 7-10 nA range. The EDS/EBSD system is a QUANTAX system from the Bruker Company composed of an EDS XFlash 5030 detector and an e -Flash HR EBSD detector, controlled by the ESPRIT software package. The ESPRIT software package was used for both the acquisition and the re-analysis of the EBSD data with the EDS data (semi-automated procedure). This system is installed on a Field Emission Gun scanning electron microscope (Zeiss Supra 40).

Figure 2. Principle of the EDS-EBSD coupling. a) and b) Kikuchi patterns (160x120 pixels) of the points displayed on c): M (Matrix -γ phase) and P (Precipitate -γ' phase). c) EBSD orientation map, the color code (standard triangle) displays the crystal direction parallel to the Z axis, normal to the scanned area. d) to f) EDS elemental maps. g) γ' phase obtained from the EDS-EBSD coupling method highlighted blue on the EBSD pattern quality map.

Results and Discussion

Raw data quality and applied filters

Some of the results presented in the following parts were analyzed and displayed using the free MTEX Matlab toolbox [START_REF] Bachmann | Grain detection from 2d and 3d EBSD data -Specification of the MTEX algorithm[END_REF].

During an EBSD scan, points located at grain boundaries show poor pattern quality because the diffraction patterns of the adjacent grains overlap. This explains why grain boundaries are non-indexed with the EBSD technique (Figure 3). On the other hand, with the iCHORD technique, all the points are indexed by the theoretical profile which suits the best. Then, to assess the quality of the correlation between the experimental and theoretical intensity profiles, a confidence index can be calculated. This confidence index may be defined by (1-ED) where ED means the Euclidian Distance between the two normalized profiles (this confidence index is plotted in Figure 12.a). By default, no threshold value is applied on the confidence index of the iCHORD raw dataset. That is why by default there is no zero-solution points and orientations are proposed even for points located at grain boundaries (Figures 4.e, 5.c and 6.a). This will be referred to as "grain boundary indexing" in the following.

"Grain boundary indexing" is actually an artifact of the iCHORD technique since most of the time the orientations assigned to grain boundaries are totally different from that of their surrounding grains (Figure 4.e). Those wrong orientations at grain boundaries can be explained by two effects resulting from the sample abrasion which occurs during the scan, even at beam currents as low as 48 pA. Indeed, between the first and the fourth SI image, 220 nm large precipitates have vanished (green circles on Figures 4.a and 4.b) and others have appeared. In the sample section, the largest diameter of the small precipitate population is approximatively 340 nm (Figure 4.a). This means that, if the small precipitates are initially spheres with a 340 nm diameter, at least the removal of a 40 nm layer is required to make the precipitates with a 220 nm diameter in the sample section disappear. The fourth SI image was acquired at one-third of the iCHORD experiment, so that the removed layer during the complete rotation is about 120 nm.

The first effect of abrasion is boundary raveling (Figure 4). Abrasion depends on the phasebecause the γ and γ' phases do not have the same "hardness"and depends also on crystal orientation within the same phase. That is why, after several FIB scans some γ-γ' and γ-γ grain boundary planes are revealed and an extra topographic contrast is added in SE images (yellow arrows on Figure 4.c). In fact, when the revealed grain boundary plane is exposed (or hidden) to the SE detector, bright (or dark) saturation is observed. These alternative signal saturations along grain boundaries degrade the SE images alignment (Figure 4.d) and leads to thick grain boundaries. The pixels within these thick boundaries are indexed by the closest theoretical profile, which is likely to be different from that of the adjacent grains due to the alternative signal saturations (Figure 4.e), but which may nevertheless present a good fitting (Figure 4.f and 4.g).

The second effect of abrasion is boundary displacement (Figure 5). If a grain boundary plane is tilted regarding the sample surface, then the intersection of the grain boundary plane with the observed section (i.e. the grain boundary trace) will progressively move as the matter is removed from the sample surface by the ion beam (Figure 5.b). So, a point initially in a grain can belong to the neighbor grain at the end of the iCHORD scan. The intensity profile acquired in such a point begins by the intensity profile of the first grain it belonged and ends by that of the second grain (Figure 5.d). The whole profile is assigned to a theoretical profile which, once again, is likely to be different from that of the adjacent grains (Figure 5.c), but which may nevertheless present a good fitting.

b) Fourth SI image acquired at one-third of the complete rotation. Green circles highlight small precipitates which have vanished between a) and b). c) SE image, yellow arrows showing boundary raveling due to abrasion. d) Grain boundaries obtained from SE images processing with Fiji [19]. Boundaries detected on the first ten SE images and boundaries detected on the last ten SE images plotted green and red respectively. e) iCHORD orientation map, yellow arrows showing raveling boundaries whose orientations are different from that of the neighboring grains. f) and g) Intensity profiles acquired in the grain boundary "GB" and precipitate boundary "PB" points displayed in d). Red arrows show signal saturation.

Thus, theoretical profiles can correctly fit profiles of points at grain boundaries by chance and this explains why the confidence index is not efficient to filter out the indexed grain boundary from the iCHORD raw dataset. So, another method was experimented: the microstructure edges were extracted by processing the SE images with the Fiji programs (Figure 6.b) and then stated as non-indexed points in the iCHORD dataset (Figure 6.d). This filtering is globally efficient but not perfect. Due to the FIB abrasion effects discussed above, the extracted edges can be larger than the "indexed interface". On the contrary, some small areas with inconsistent orientations still remain after filtering (black arrows Figure 6.d). Another idea to remove the "indexed boundaries" from the dataset could have been to: i) calculate the grains from the raw dataset, which would have identified artifact elongated grains along some real grain boundaries, ii) filter out those elongated grains based on a grain shape factor criterion. This idea was not investigated in this paper but may provide a finer treatment of the iCHORD raw data in the future. The following parts will present the results obtained from the iCHORD data filtered as explained above.

b) Backscattered Electron (BSE) image, showing that indexed boundaries do not correspond to real crystals but mainly to grain boundaries revealed by the ion beam. c) Edges of the iCHORD data extracted with the Fiji programs from the SE images. d) iCHORD orientation map after data filtering (i.e. where edges of the microstructure were stated as non-indexed points). Black arrows show remaining inconsistent orientations.

Angular resolution

In order to have a reference in term of crystal orientation, an EBSD scan at 20 kV has been performed on the area chosen for the iCHORD-SI combination. The obtained iCHORD and EBSD maps are very similar, though some slight discrepancies are observed at some points (black arrows in Figure 7). These discrepancies can be explained by a change in the macroscopic reference frame -since the two experiments have been carried out in two different microscopes -but also by the different angular resolutions of the two techniques. Indeed, once the sample tilted the collected backscattered electrons and secondary ions come from volumes of approximately same sizes, that are typically within the 20-40 nm range [START_REF] Joy | Beam interactions, contrast and resolution in the SEM[END_REF][START_REF] Ishitani | Objective Comparison of Scanning Ion and Scanning Electron Microscope Images[END_REF][START_REF] Cohen-Tanugi | Superior imaging resolution in scanning helium-ion microscopy: A look at beam-sample interactions[END_REF].

Figure 7. Orientations maps given by the iCHORD and EBSD techniques. The color code (standard triangle) displays the crystal direction parallel to the Z axis, normal to the scanned area. a) iCHORD orientation map. b) EBSD orientation map. Black arrows highlight some differences between the iCHORD and EBSD maps.

To decorrelate orientation variations due to a change in the macroscopic reference frame (used to define the Euler angles) from that due to the angular resolution of the techniques, intragranular misorientation has been analyzed. Grains have been defined as groups of pixels with a neighbor-to-neighbor misorientation angle lower or equal to 10°, and misorientation to the mean grain orientation values have been calculated. Based on the misorientation to the mean grain orientation, the deformed grains can be easily distinguished from the newly recrystallized ones on both the EBSD and iCHORD maps (Figure 8.a and 8.b). Deformed grains have a high orientation spread because of lattice distortions induced by deformation. On the contrary, recrystallized grains have a very homogeneous orientation and have theoretically no deviation of individual pixel orientation from the mean grain orientation. Thus, the misorientation measured between neighboring pixels in a recrystallized grain is representative of the angular resolution of the technique. This way, from the orientation variations observed in Figure 8.c and 8.d, the angular resolution is estimated to be about 0.75° for EBSD and a bit less than 1.5° for iCHORD. This difference in angular resolution makes that the 10° grain threshold does not lead exactly to the same grains for the iCHORD and EBSD datasets, and this accounts for the differences in misorientation to mean orientation values observed between Figures 8.a and 8.b. However, the misorientation profiles plotted in Figure 8.e and 8.f demonstrate that even if small discontinuities (< 1.5°) are very roughly captured by the iCHORD technique due its angular resolution, similar grain substructures are globally revealed by both techniques.

Spatial resolution of the phase discrimination

Figure 9 shows that the SI images can resolve the γ' precipitates down to 150 nm, which means all the precipitates of the studied microstructure including the smallest ones judging from the BSE image in Figure 9.a (the differences between the BSE and SI image arise from the ion beam erosion which occurred between the first SI image and the BSE image acquired after the iCHORD scan). The resolution of the SI images is related to the volume from which the collected secondary ions come: typically some tens of nanometers [START_REF] Ishitani | Objective Comparison of Scanning Ion and Scanning Electron Microscope Images[END_REF][START_REF] Tescan | Secondary Ion TESCAN Detector[END_REF]. To evaluate the performance of the SI signal, three EDS-EBSD maps have been acquired at 10 kV, 15 kV and 20 kV on an area where precipitate sizes were similar to that analyzed with the SI signal. For each EDS-EBSD map, the exposure time per pixel was adapted to get an X-ray spectrum with 3,000 counts for each point of the map. Indeed, 2,000 to 3,000 counts per spectrum are empirical values leading to a signal-to-noise ratio large enough for a semiquantitative analysis of the EDS spectrum. With Figure 10 one can check that for the chosen exposure times, the quality of the diffraction patterns was sufficient to perform EBSD, even at 10 kV which is a quite low accelerating voltage for the technique.

The chemical contrast resulting from the three EDS scans is presented in Figure 11. As expected, the higher is the accelerating voltage, the lower the γ' precipitates are resolved. Indeed, if the X-ray absorption in the sample is neglected, for a 0° tilted sample the maximum escape depth of the X-rays can be estimated using the formula proposed by Anderson and Hasler [START_REF] Anderson | Extension of electron microprobe techniques to biocemistry by the use of long wavelenght X-rays[END_REF][START_REF] Gauvin | A Universal Equation for the Emission Range of X Rays from Bulk Specimens[END_REF]:

, where is the average maximum escape depth of the X-rays (µm), is the density of the material (g.cm -3 ), the incident electron beam energy (keV) and the critical excitation energy (keV). Considering approximate atomic compositions for the γ and γ' phases, ranges for the maximum escape depth at a 0° tilt are given in Table 3. Tilting the sample at 70° impacts the shape of the X-ray emission volume regarding the sample surface [START_REF] Nowell | Improved EDS Performance at EBSD Geometry[END_REF]. This implies that the maximum escape depth is in fact a bit smaller for a 70° tilt than for a 0° tilt. Nevertheless, Figure 11 shows that for a 70° tilt EDS at 10 kV is the only appropriate configuration to properly resolve the 150-340 nm precipitates (although the results are a bit affected by the sample relief). In addition, as the volume from which the collected X-ray arise is deeper than that of the backscattered electrons, once the sample tilted at 70° EDS data are slightly shifted compared to EBSD data [START_REF] Nowell | Improved EDS Performance at EBSD Geometry[END_REF]. The shift is highlighted by green arrows in Figure 1. This problem does not exist with the iCHORD-SI combination since SE and SI emission volumes have nearly the same sizes. The γ' phase discriminations obtained from the processing of the iCHORD-SI and EDS-EBSD data are presented in Figure 12. The resolution of the iCHORD-SI map (Figure 12.a) is slightly degraded compared to that of the original SI images (e.g. Figure 9.b). Indeed, the evolution of the precipitates resulting from the abrasion of the sample surface as well as the treatment applied to SI data (alignment, sum and threshold adjustment) are responsible for the slight degradation. Regarding the EDS-EBSD method, as implemented in the ESPRIT software, the γ' phase discrimination (Figure 12.b-d) is not done for the non-indexed points since no crystallographic structure is assigned to the non-indexed points. Yet the non-indexed points appear more numerous for low accelerating voltages (e.g. 10 kV). Moreover, the Ni, Ti and Cr ratios defined for Figure 12.b-d seem to be more adapted to the large precipitates than to the small ones which are consequently less resolved by the phase discrimination. In fact, the large and small precipitates do not form at the same temperature during the forming process, and thus may have somewhat different chemical compositions. But, above all, the resolution of small precipitates is subjected to the so-called "matrix effect" (i.e. the affection of the measured precipitate composition by that of the matrix located below), which goes worse and worse as the accelerating voltage increases due to the interaction volume. Different routes could be possible to improve the spatial resolution of the final EDS-EBSD discrimination, for instance: the adaptation of the composition ratios for each precipitate size, or the correction of the matrix effect. However, this would require EDS spectra with much higher signal-to-noise ratio and so the sacrifice of the acquisition speed.

Acquisition and processing times

As said above, for each EDS-EBSD map performed for the study the exposure time per pixel has been adapted so as to cumulate 3,000 counts per point. Consequently, acquisition time must increase as the accelerating voltage decreases (Table 4). The time given in the "Processing time / pixel" column corresponds to the time required by the ESPRIT software to re-analyze the EBSD data considering the EDS data with the defined Ni, Ti and Cr reference ratios.

For the iCHORD-SI acquisition, relatively low scanning speeds were chosen to get a good signal-to-noise ratio while limiting the sample abrasion by the ion beam. The chosen scanning speeds lead to 0.010ms/pixel and 0.032ms/pixel for the SE and SI images respectively (Table 4). These times do not include the time required for the stage rotation which may be automated. The time given in the "Processing time / pixel" column corresponds to the average time the iCHORD algorithm takes to assign a theoretical profile to an experimental intensity profile. However, with the iCHORD technique, the number of acquired points is twice bigger than the number of effectively analyzed points. In fact, the analyzed area must be an area common to all the SE images after their alignment. Yet, SE images are square images acquired at different rotation angles and this makes the corners of the images unusable after the alignment. This explains why the effective analyzed area is much smaller than the original image size. This drawback could be fixed in the future by controlling the scan coils of the microscope to automatically perform a scan rotation at each stage rotation step. From total times approximatively spent per pixel reported in Table 4, it appears that performing the iCHORD-SI method is equivalent to perform an EDS-EBSD coupling at 20 kV (taking into account that the acquired points are twice numerous than that effectively analyzed ones).

Discussion

EBSD patterns give essential details on the crystallography of the phases and on the crystal orientations, with an angular resolution typically in the range of 0.5°. On the other hand, the current version of the iCHORD technique is adapted to get a good overview of the microstructure of a material with a know crystallographic structure: the 1.5° angular resolution is enough to study the grain sizes and orientations as well as the recrystallization state of the microstructure.

Regarding the EDS technique, EDS spectra bring more than a chemical contrast as SI images do and so enables a semi-quantitative analysis of the chemical composition of the phases. Thus, numerous possibilities for the re-analysis of the EBSD data combined with the EDS spectra are possible afterward.Nevertheless, the spatial resolution of the EDS technique strongly depends on the accelerating voltage: the smaller is the accelerating voltage, the better is the spatial resolution. But decreasing the accelerating voltage must be compensated by a significant increase in the exposure time, in order to have a signal-to-noise ratio good enough for a semi-quantitative analysis of the spectra (about 30 ms x2 for an EDS at 10 kV). By resolving γ' precipitates as small as 150 nm, SI images have provided a spatial resolution as good as the EDS acquisition performed at 10 kV. But the total time per pixel is approximately three times smaller for the iCHORD-SI combination at 30 kV than for the EDS-EBSD at 10kV. Indeed, the exposure time represents a very large part of the total time spent for an EDS-EBSD map. Besides, long exposure times such as that applied at 10 kV make the electron beam drift more significant during the EDS-EBSD maps. On the other hand, for the iCHORD-SI combination, the time dedicated to the data acquisition (SE and SI images) is very short compared to the time needed to process the data (attribution of a theoretical profile to the experimental intensity profile). This makes the time spent on the microscope much smaller for an iCHORD-SI map than for an EDS-EBSD map, whatever the accelerating voltage used for the EDS-EBSD acquisition. In addition, the different escape depths of the BSE and X-ray signals leads to a slight misalignment of the EBSD and EDS data because the sample is tilted at 70°. This does not occur for the iCHORD-SI data combination since SE and SI have arise from volume with approximately the same size. But, the main drawback of the iCHORD-SI combination is the abrasion of the sample surface by the ion beam. Abrasion leads to boundary raveling and boundary displacement but also to the potential loss of the smallest grains and precipitates of the microstructure during the scan. This makes the iCHORD-SI combination a quite destructive technique which cannot be performed twice on exactly the same area. However, two ideas can be proposed to make the technique less destructive than what presented in the present paper. First, the number of acquired SE images can be decreased: it has been shown in [START_REF] Langlois | Crystal orientation mapping via ion channeling: An alternative to EBSD[END_REF] that 30 SE images with a 12° rotation step allow a correct description of the microstructure. Second, the scanning speeds could have been increased and denoising algorithms used to enhance the signal-to-noise ratio of the acquired images. Thus, like the EDS-EBSD coupling, the iCHORD-SI combination has disadvantages and advantages. But by resolving precipitates down to 150 nm on an orientation map within a very reasonable time, this method is really interesting for the γ/γ' microstructures which displays a multimodal distribution of γ' precipitates from few micrometers to some tens of nanometers.

Yet, for the study of polycrystals, a technique performed within a reasonable time is of particular interest since it allows a more statistical analysis of the microstructure.

Finally, Figure 13 shows the complete result of the iCHORD-SI combination, that is the γ' phase discriminated from the SI data overlaid on the orientation map obtained with the iCHORD technique. Black and white arrows prove the interest of the phase discrimination for the studied microstructure by highlighting two metallurgical phenomena based on the γ' precipitation: the so-called Smith-Zener pinning [START_REF] Nes | On the Zener drag[END_REF] enforced by precipitates as small as 150-340 nm on the grain boundaries and the heteroepitaxial recrystallization which starts by the nucleation of a coherent γ shell around a γ' precipitate [START_REF] Charpagne | Evidence of multimicrometric coherent γ′ precipitates in a hot-forged γ-γ′ nickel-based superalloy[END_REF][START_REF] Charpagne | Heteroepitaxial Recrystallization Observed in René 65 TM and Udimet 720 TM : a New Recrystallization Mechanism Possibly Occurring in All Low Lattice Mismatch γ-γ′ Superalloys?[END_REF].

Conclusions

Because the γ and γ' phases cannot be identified by the EBSD technique alone, other methods are needed to characterize the γ-γ' microstructures.

The EDS-EBSD coupling uses the chemical information provided by the EDS technique to discriminate the γ and γ' phases on an EBSD map. The iCHORD-SI combination, which is an original method performed with a FIB microscope is based on the same idea: the iCHORD technique, recently developed by Langlois et al. [START_REF] Langlois | Crystal orientation mapping via ion channeling: An alternative to EBSD[END_REF], provides the crystallographic orientations based on the ion channeling contrast on Secondary Electron (SE) images while the chemical contrast of the Secondary Ion (SI) images is used to identify the γ' phase.

The performances of the iCHORD-SI combination on a partially recrystallized γ-γ' microstructure have been assessed using the EDS-EBSD coupling as a reference. The conclusions are the following:

-By default the iCHORD technique indexes each point of the map with the theoretical profile which suits the best to collected intensity profile. Orientations indexed at grain boundaries are most of the time inconsistent and result from boundary raveling and/or progressive boundary displacement induced by the ion beam. Thus, iCHORD data have to be treated to erase from the dataset the false orientations attributed to pixels on/along grain boundaries. -The angular resolution of the iCHORD technique (about 1.5°) is a bit less good than that of the EBSD technique (about 0.50-0.75°). Nevertheless, this angular resolution is sufficient to succeed in catching most of the grain substructures. -Unlike EDS and EBSD data, no misalignment between the SE and SI data are observed since secondary electrons and secondary ions come from volumes of similar sizes which are typically in the 20-40 nm range. -Resolving γ' precipitates down to 150 nm, the spatial resolution of the SI images is as good as that of EDS performed at 10 kV. -However, the total time required per pixel (acquisition and processing) for an iCHORD-SI map is approximately three times smaller than that required for an EDS-EBSD map at 10 kV with 3,000 counts per spectrum. In addition, the iCHORD-SI acquisition time is much decreased compared to the EDS-EBSD method, and most the required time is spent in the processing of the experimental intensity profiles which is performed offline. -The iCHORD-SI combination is a quite destructive method but the ion beam abrasion can be somewhat limited by reducing the number of acquired SE images and/or by adapting the scanning speeds, which may not degrade the quality of the results. In this way, the iCHORD-SI combination is an interesting option for the γ/γ' microstructures which have a multimodal distribution of γ' precipitates from few micrometers to some tens of nanometers. Beyond superalloys, the iCHORD-SI combination may be used for any crystallographic system, where the phase discrimination is difficult/impossible by EBSD and where there is a sufficient contrast in atomic number between the phases.

Figure 1 .

 1 Figure 1. Principle of the iCHORD-SI combination. a) Experimental setup in the FIB microscope.b) Theoretical intensity profile (blue dashed line) matching with an experimental profile (red line)data of the point highlighted by a red cross on c). c) Secondary Electron (SE) image for one azimuthal position around e z (the orientation contrast arises from the ion channeling effect). d) Secondary Ion (SI) image for the same azimuthal angle (gray levels mainly depend on the chemical composition even if a slight orientation contrast is also visible). Both SE and SI images are tilt corrected.

Figure 3 .

 3 Figure 3. Grain boundaries with the EBSD technique. EBSD orientation map, non-indexed points plotted white. Black arrows highlight non-indexed points at grain boundaries.

Figure 4 .

 4 Figure 4. Boundary raveling resulting from FIB abrasion. a) First SI image acquired at the initial sample position.b) Fourth SI image acquired at one-third of the complete rotation. Green circles highlight small precipitates which have vanished between a) and b). c) SE image, yellow arrows showing boundary raveling due to abrasion. d) Grain boundaries obtained from SE images processing with Fiji [19]. Boundaries detected on the first ten SE images and boundaries detected on the last ten SE images plotted green and red respectively. e) iCHORD orientation map, yellow arrows showing raveling boundaries whose orientations are different from that of the neighboring grains. f) and g) Intensity profiles acquired in the grain boundary "GB" and precipitate boundary "PB" points displayed in d). Red arrows show signal saturation.

Figure 5 .

 5 Figure 5. Boundary displacement resulting from FIB abrasion. a) SE image showing at the center a grain with no boundary raveling.b) Grain boundaries obtained from SE images processing with Fiji. Boundaries detected on the first ten SE images and boundaries detected on the last ten SE images plotted green and red respectively. The white arrow suggests the boundary plane trace has moved between the beginning and the end of the iCHORD scan. c) iCHORD orientation map. d) Intensity profiles acquired in the "1", "GB" and "2" points displayed in c). "1", "GB", and "2" are plotted red, black and blue respectively.

Figure 6 .

 6 Figure 6. iCHORD data and applied filters. a) Orientation map from the raw iCHORD dataset, all the points are indexed by default. b) Backscattered Electron (BSE) image, showing that indexed boundaries do not correspond to real crystals but mainly to grain boundaries revealed by the ion beam. c) Edges of the iCHORD data extracted with the Fiji programs from the SE images. d) iCHORD orientation map after data filtering (i.e. where

Figure 8 .

 8 Figure 8. Angular resolution of the iCHORD and EBSD techniques. a) Misorientation to mean grain orientation map calculated from the iCHORD dataset (misorientation angle threshold: 10°), grain boundaries plotted white. b) Misorientation to mean grain orientation map calculated from the EBSD dataset (misorientation angle threshold: 10°) grain boundaries plotted white. c) and d) Misorientation profile along the pink line in the recrystallized grain shown in a) and b) for the iCHORD and EBSD techniques respectively. e) and f) Misorientation profile along the red line in the non-recrystallized area shown in a) and b) for the iCHORD and EBSD techniques respectively.

Figure 9 .

 9 Figure 9. γ' phase from the raw SI signal, comparison with the BSE signal. a) BSE image acquired after the iCHORD-SI scan at 0° tilt. b) First SI image of the iCHORD-SI scan.

Figure 10 .

 10 Figure 10. EBSD pattern for the different EDS-EBSD settings -160x120 pixels patterns. a) EDS-EBSD coupling at 10 kV. b) EDS-EBSD coupling at 15kV. c) EDS-EBSD coupling at 20kV.

Figure 11 .

 11 Figure 11. γ' phase from the raw EDS signal, comparison with the BSE signal. a) BSE image, γ' phase appears dark because of its content in light elements and the sample relief. b), c) and d) Overlay of the Ni, Ti and Cr elemental maps obtained at 10 kV, 15 kV and 20 kV respectively. Ni, Ti and Cr elemental maps are plotted blue, green and red which reveals the γ' phase as light blue.Table3. Estimation of the maximum X-ray escape depth at a 0° tilt using Anderson and Hasler's formula.

Figure 12 .

 12 Figure 12. γ' phase discrimination obtained after SI and EDS-EBSD data processing. a) γ' phase resulting from the SI data overlaid on the iCHORD confidence index map. b), c) and d) γ' phase resulting from the EDS-EBSD data overlaid on the pattern quality map, and corresponding to the EDS-EBSD acquisitions at 10 kV, 15 kV and 20 kV respectively. Non indexed points are displayed black.

Figure 13 .

 13 Figure 13. Results of the iCHORD-SI combination. The γ' phase is plotted dark grey and overlaid on the orientation map. Black and yellow arrows highlight grain boundary pinning and heteroepitaxial recrystallization respectively.

Table 1 .

 1 Composition of the AD730 TM nickel-based superalloy (wt% )[START_REF] Devaux | AD730TM -A new Nickel-based superalloy for high temperature engine rotative parts[END_REF].

	Element	Ni	Fe	Co	Cr	Mo	W	Al	Ti	Nb	B	C	Zr
	AD730 TM Base	4.00	8.50 15.70 3.10	2.70	2.25	3.40	1.10	0.01 0.015 0.03

Table 2 .

 2 Compositions of the γ and γ' phases measured on the as-received billet by EDS at 15 kV (wt% -semiquantitative values obtained without using a suitable standard -average values over an area of few µm²).

	Element	Ni	Fe	Co	Cr	Mo	W	Al	Ti	Nb	B	C	Zr
	γ phase	54.6	5.1	9.9	19.8	3.1	2.1	2.3	2.5	0.6	NA	NA	NA
	γ' phase	70.7	1.5	5.1	3.6	0.3	0.9	6.0	10.6	1.4	NA	NA	NA

Table 4 .

 4 Acquisition and processing times for each method.

	Method	Settings	Acquisition time	Pixels acquired	Processing time /	"Total time" / pixel
			/ pixel	/ Pixels analyzed	pixel
	EDS-EBSD	10 kV	36 ms x 2 frames	1	1 ms	36x2 + 1 = 73 ms
		(42 kCts)
		15 kV	15 ms x 2 frames	1	1 ms	15x2 +1 = 31 ms
		(100 kCts)
		20 kV	8.3 ms x 2 frames	1	1 ms	8.3x2 + 1 ≈ 18 ms
		(182 kCts)
	iCHORD-SI	30 kV /48 pA	-SE image : 0.010 ms	2	17 ms	(0.010x90 + 0.032x4)x2 +
			x 90 images			17 ≈ 19 ms
			-SI image : 0.032 ms
			x 4 images

Acknowledgments

The authors gratefully acknowledge the Orsay Physics Company (Fuveau, France) for the access to a FIB-SEM microscope and for their help to perform the iCHORD technique with it. This work received the financial support of the ANR-Safran industrial chair OPALE.

Data availability

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