Lisa Royer

Antoine Bonnefont
email: pierre-antoine.bonnefont@grenoble-inp.fr

Tristan Asset

Benjamin Rotonnelli

Juan-Jesús Velasco-Vélez

Steven Holdcroft

Simon Hettler

Raul Arenal

Benoit Pichon

Elena Savinova

Juan Velasco Velez

Cooperative Redox Transitions Drive Electrocatalysis of the Oxygen Evolution Reaction on Cobalt-Iron Core-Shell Nanoparticles

établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

transformations occurring during the harsh oxidative conditions of the OER remains a bottleneck for the development of stable and active catalysts. Here, we studied redox transformations of coreshell Fe3O4@CoFe2O4 oxide nanoparticles over a wide range of potentials by using operando nearedge X-ray absorption fine structure (NEXAFS) spectroscopy in total electron yield (TEY) detection mode. The analysis of the NEXAFS spectra reveals that the Fe3O4 core strongly affects the surface chemistry of the CoFe2O4 shell under the OER conditions. The spinel structure of the particles with Co (II) in the shell is preserved at potentials as high as 1.8 V vs. RHE, at which Co (II) is expected to be oxidized into Co (III); whereas Fe (II) in the core is reversibly oxidized to Fe (III).

TOC GRAPHICS

KEYWORDS: electrochemistry, electrocatalysis, operando NEXAFS, Oxygen Evolution Reaction (OER), core-shell nanoparticles, cobalt ferrite Anion exchange membrane water electrolysis (AEMWE) is an attractive alternative to the proton exchange membrane counterpart as it allows the replacement of iridium or ruthenium at the anode with more abundant 3d (Ni, Co, Fe, Mn) transition metal oxides (TMO) [START_REF] Thomas | Anion Conducting Poly(Dialkyl Benzimidazolium) Salts[END_REF][START_REF] Holdcroft | Sterically-Encumbered Ionenes as Hydroxide Ion-Conducting Polymer Membranes[END_REF] . TMOs with spinel structure constitute a promising class of oxygen evolution reaction (OER) catalysts due to their relatively low synthesis temperature (allowing preparation of high surface area catalysts without coalescence), and their composition-dependent and widely tunable properties thus allowing to attain high OER activity. However, the evolution of the surface structure and the composition under the OER conditions and hence the nature of the active sites are not fully understood yet. These knowledge gaps hamper building correlations between the chemical structure of materials on the one hand and their OER activity/durability on the other hand, ultimately impeding the development of active and stable catalysts for the anode of the AEMWE.

Bergmann et al. [START_REF] Bergmann | Reversible Amorphization and the Catalytically Active State of Crystalline Co3O4 during Oxygen Evolution[END_REF] studied nanocrystalline Co3O4 films during the OER using in situ X-ray diffraction and 'quasi-in situ' absorption spectroscopy (samples were freeze-quenched under potential control). They found that in the potential interval of the OER, Co (II) ions were oxidized to octahedrally (Oh) coordinated, di-µ-O(H)-bridged Co (III/IV) species resulting in a reversible formation of a sub-nanometer thick amorphous CoOx(OH)y shell. In contrast, Ortiz-Pena et al. [START_REF] Ortiz Peña | Morphological and Structural Evolution of Co3O4 Nanoparticles Revealed by in Situ Electrochemical Transmission Electron Microscopy during Electrocatalytic Water Oxidation[END_REF] studied Co3O4 nanoparticles (NPs) in situ by transmission electron microscopy (TEM) under potential control (EC-TEM) and found that this amorphization is irreversible. Also, Reikowski et al. [START_REF] Reikowski | Operando Surface X-Ray Diffraction Studies of Structurally Defined Co3O4 and CoOOH Thin Films during Oxygen Evolution[END_REF] applied operando surface X-ray diffraction to study structurally well-defined epitaxial cobalt oxide Co3O4 (111) thin films electrodeposited on Au (111). They observed fast and fully reversible Co3O4 (111)/CoOOH (001) transformation at potentials 300 mV negative of the 'onset' of the OER, and thus concluded that the observed structural transformation was potential rather than OER-driven. By comparing the OER activity of Co3O4 (111) and CoOOH (001) epitaxial crystalline films, the authors argued against di-μ-oxo bridged Co cations being responsible for the OER activity of Co oxides. For Co(OH)2 particles, Mefford et al. [START_REF] Mefford | Correlative Operando Microscopy of Oxygen Evolution Electrocatalysts[END_REF] , by using operando scanning probe and X-ray microscopy techniques, documented Co(II) into Co(III) oxidation leading to the formation of β-CoOOH under OER conditions and concluded that Co(III) at the particle surface were the OER active catalytic sites. Recently, Haase et al. [START_REF] Haase | Size Effects and Active State Formation of Cobalt Oxide Nanoparticles during the Oxygen Evolution Reaction[END_REF]

studied transformations of CoOx(OH)y

NPs with the average size ranging from 1.6 to 9.3 nm during the OER with operando hard X-ray absorption spectroscopy and density functional theory (DFT). While confirming an increase of the average cobalt oxidation state from II to III+, the authors arrived at the conclusion that during the OER, an electron 'hole' resides on oxygen (the so-called 'anion-redox' OER mechanism) ions rather than Co cations (hence Co (IV) species do not form), leading to the formation of electrondeficient 'oxyl' species (similar to what has been previously proposed for IrOx-catalyzed OER [START_REF] Pfeifer | Reactive Oxygen Species in Iridium-Based OER Catalysts[END_REF][START_REF] Saveleva | Operando Evidence for a Universal Oxygen Evolution Mechanism on Thermal and Electrochemical Iridium Oxides[END_REF] ).

From the aforementioned works, it appears that (i) the oxidation degree of the Co during the OER, namely the occurrence of the Co (II) to Co (III) and Co (III) to Co (IV) transitions, and (ii) the formation of the CoOOH phase and its reversibility, are rather controversial in the literature. This complexifies even further when addressing the Co-Fe based catalysts for the OER.

Indeed, several studies have revealed the crucial role of iron in enhancing the OER activity of Co-and Ni-based TMO 10 catalysts with further controversies regarding the reasons for this enhancement. Since iron oxide has a low activity towards the OER, it was suggested that a synergetic effect between iron and other TMs such as nickel or cobalt [START_REF] Li | Iron Doped Cobalt Fluoride Derived from CoFe Layered Double Hydroxide for Efficient Oxygen Evolution Reaction[END_REF] lies at the origin of the observed enhancement. Using Hubbard model DFT+U calculations, Wang et al. [START_REF] Wang | Deciphering the Exceptional Performance of NiFe Hydroxide for the Oxygen Evolution Reaction in an Anion Exchange Membrane Electrolyzer[END_REF] demonstrated that, for Fe-doped Ni hydroxide, a local arrangement of Fe (III) with two Ni (IV) ions plays an important role in the OER activity, and that charge transfer during the OER occurs from Fe (III) to the OER intermediates. Xiao et al. [START_REF] Xiao | Synergy between Fe and Ni in the Optimal Performance of (Ni,Fe)OOH Catalysts for the Oxygen Evolution Reaction[END_REF] also suggested a synergy between Fe and Ni where Fe (IV) catalyzes formation of an O radical intermediate and Ni (IV) catalyzes the O-O coupling. It was also argued that the presence of iron modifies the eg orbital filling [START_REF] Suntivich | A Perovskite Oxide Optimized for Oxygen Evolution Catalysis from Molecular Orbital Principles[END_REF] , generating more active materials towards the OER. DFT+U calculations were also applied to elucidate the influence of iron on the OER activity of Co3O4 [START_REF] Peng | Influence of Fe and Ni Doping on the OER Performance at the Co3O4(001) Surface: Insights from DFT+U Calculations[END_REF][START_REF] Hajiyani | Surface Termination and Composition Control of Activity of the CoxNi1-XFe2O4(001) Surface for Water Oxidation: Insights from DFT+U Calculations[END_REF] . They revealed influence of Fe on the oxidation state of Co and will be discussed in what follows. Although many studies have investigated transformations of cobalt-based catalysts during the OER, few have studied Co/Fe catalysts. Calvillo et al. [START_REF] Calvillo | Insights into the Durability of Co-Fe Spinel Oxygen Evolution Electrocatalysts via Operando Studies of the Catalyst Structure[END_REF] studied the Fe K-edge and the Co K-edge to scrutinize the chemical and structure changes of a Co-Fe spinel powder during the OER and demonstrated that the samples suffered irreversible oxidation under the OER conditions leading to the formation of a layer consisting of Co3O4, CoOOH, and Fe2O3. They also stated that these were Co (II) cations in tetrahedral (Td) sites that were experiencing changes during the OER. Saddeler et al. [START_REF] Saddeler | Influence of the Cobalt Content in Cobalt Iron Oxides on the Electrocatalytic OER Activity[END_REF] recently studied cobalt iron spinel catalysts of different compositions and due to observed changes of the Co and Fe K-edge concluded that during the OER cobalt is oxidized to Co (III) while iron maintains its Fe (III) oxidation state.

In this work, we report on the cooperative redox behavior of core-shell, cobalt iron oxide nanoparticles (Fe3O4@CoFe2O4), possessing a conductive Fe3O4 core and an OER active CoFe2O4 shell. The use of core-shell nanoparticles where Co is present only in the shell has the advantage to drastically reduce the Co loading in the electrocatalyst. Furthermore, an improved OER performance may be expected if the particle core has beneficial impact on the shell properties [START_REF] Strickler | Core-Shell Au@Metal-Oxide Nanoparticle Electrocatalysts for Enhanced Oxygen Evolution[END_REF][START_REF] Zhuang | Synthesis of Monodispere Au@Co3O4 Core-Shell Nanocrystals and Their Enhanced Catalytic Activity for Oxygen Evolution Reaction[END_REF] .

The core-shell structure with the catalytically active component localized in the shell is also very advantageous for operando investigations, since it significantly increases the surface sensitivity.

Well-defined NPs with a narrow size distribution and controlled shape and composition both for the core and the core-shell were synthesized. The synthesis consisted in a seed-mediated growth based on the thermal decomposition of metal complexes as recently reported [START_REF] Sartori | A Detailed Investigation of the Onion Structure of Exchanged Coupled Magnetic Fe3-δO4@CoFe2O4@Fe3-δO4 Nanoparticles[END_REF] . The obtained spinel Fe3O4@CoFe2O4 NPs (Figure 1 A) are homogeneous in size, shape, and composition and possess an average diameter of ~14 nm with a shell thickness of ~1.5 nm. Their diffractogram presents peaks characteristic of an inverse spinel structure (Figure S1) in which Fe (II) occupies half of the Oh sites while Fe (III) occupies the other Oh sites and the Td sites in the Fe3O4 core. In the CoFe2O4 shell with inverse spinel structure, Co (II) occupies roughly half of the Oh sites while Fe (III) is in the rest of the Oh sites and the Td sites. Hence, Co is only present in the shell while Fe (II) is only present in the Fe3O4 core. For the operando NEXAFS study, 10 μL (4.2 μg) of NPs dispersed in chloroform were drop-cast either on the surface of a Fumatech anion exchange membrane (Fumasep® FAS-50) or on the surface of an Aemion  anion exchange membrane (Ionomr Innovations Inc.) and then covered by a graphene bilayer [START_REF] Falling | Graphene-Capped Liquid Thin Films for Electrochemical Operando X-Ray Spectroscopy and Scanning Electron Microscopy[END_REF] , the latter establishing electric contact between the particles and the current collector. The shape of current-potential curves obtained with the two types of anion exchange membranes was similar (Figures 2A andS7). The membrane electrode assembly was used in the operando liquid spectro-electrochemical cell of the Innovative Station for In Situ Spectroscopy (ISISS) Beamline at Bessy synchrotron (Figure S5). A detailed description of the spectroelectrochemical cell can be found in ref [START_REF] Streibel | In Situ Electrochemical Cells to Study the Oxygen Evolution Reaction by Near Ambient Pressure X-Ray Photoelectron Spectroscopy[END_REF] . Complementary electrochemical measurements were performed in a conventional three-electrode electrochemical cell in 0.1 M NaOH electrolyte by depositing NPs on a glassy carbon (GC) disc (Figure S6). The core-shell nanoparticles exhibited OER activity of ~ 350 A/goxide at 1.65V vs. RHE (Figure S6) and this activity was multiplied by a factor of 10 if the current was normalized to the active component (cobalt mass). Their redox behavior was studied by operando NEXAFS in a wide potential interval (cf. cyclic voltammogram, CV, of Fe3O4@CoFe2O4 NPs acquired in the operando cell and presented in Figure 1 B) by monitoring the evolution of the near edge X-ray absorption fine structure (NEXAFS) spectra recorded for cobalt and iron L2,3-edges and oxygen K-edge as a function of the applied potential. The Fe, Co L-edge, and O K-edge NEXAFS spectra were collected in total electron yield mode (TEY). The sampling depth of TEY measurements is typically a few nanometers making this technique sensitive to the catalyst surface modifications during the OER.

We start our discussion with the analyses of redox transformations occurring at low electrode potentials. When the potential is decreased, a pair of anodic (PA) and cathodic (PC) redox peaks is observed in the CV at ca. 0.2 and at -0.2 V vs. the reversible hydrogen electrode (RHE), respectively (Figure 1C). The corresponding NEXAFS Fe L2,3-edges spectra measured in the interval from 1.0 down to -0.5 V vs. RHE are presented in Figure 1 C. For comparison, the cyclic voltammetry curve obtained for the core material (Fe3O4) is presented in Figure S8. The Fe L3 and L2-edge peaks are observed in the intervals 709-712 eV and 720-725 eV respectively (Figure 1 C), and are sensitive to the valence and redox state of the atoms. At 1.0 V vs. RHE, the fine structure of the Fe L3-edge shows a second contribution at 709 eV, which is attributed to Fe (II), while the main peak at 711 eV is attributed to Fe (III) [START_REF] Sassi | First-Principles Fe L2,3-Edge and O K-Edge XANES and XMCD Spectra for Iron Oxides[END_REF] . The intensity ratio between the Fe (III) and Fe (II) peaks at 1.0 V vs RHE for core-shell NPs is 0.59, slightly lower than the Fe (III)/Fe (II) intensity ratio of 0.61 observed for the Fe3O4 core NPs (Figure S9), pointing to smaller Fe (III) fraction on the surface of core-shell NPs compared to Fe3O4 NPs. The redox peaks of Figure 1B can be assigned with the help of the NEXAFS spectra. In the Fe L3-edge spectra measured at -0.2 vs. RHE (Figure 2 C), a significant increase of the Fe (II) peak and a pronounced decrease of the Fe (III) peak are clearly observed. Moreover, another shoulder at 706 eV, characteristic of the formation of FeO [START_REF] Regan | Chemical Effects at Metal/Oxide Interfaces Studied by x-Ray-Absorption Spectroscopy[END_REF] , emerges at low potentials. These changes are accentuated at -0.5 V vs. RHE. Similar changes are also seen on the L2 peaks at 720 eV, 722 eV, and 724 eV. Thus, a significant amount of the Fe (III) cations in the CoFe2O4 shell and also in the Fe3O4 core is reduced to FeO at potentials negative of the cathodic peak PC. The Co L3-edge spectrum at 1V vs. RHE (Figure S10) displays 3 contributions between 777 and 784 eV and confirms the presence of Co (II) in the shell as expected for CoFe2O4. It should be mentioned that the Co L2,3-edge spectra are not modified even for potentials as low as -0.5 V vs. RHE, suggesting that Co (II) is not reduced at these potentials (Figure S11 A) while the O K-edge spectra evidenced some changes related to the transformation of the spinel structure into the wüstite structure (Figure S11 B). Furthermore, no signature corresponding to the reduction to metallic iron was observed in the NEXAFS spectra contrary to what has been reported in some previous publications [START_REF] Accogli | Electrochemical Characterization of Magnetite (Fe3O4) Nanoaggregates in Acidic and Alkaline Solutions[END_REF] ). [START_REF] Thomas | Anion Conducting Poly(Dialkyl Benzimidazolium) Salts[END_REF] When the potential is returned to its initial value (1.0 V vs. RHE), the Fe (II)/Fe (III) ratio returns to its initial value. Consequently, the chemical transformation of Fe (III) into Fe (II) and back appears reversible. Lastly, scanning TEM high angle annular dark-field (STEM-HAADF) micrographs and electron energy loss spectroscopy (EELS) STEM mappings before (Figure 1 D, 1E and1F) and after (Figure 1 G,1H and 1I) the application of -0.5 V vs. RHE for 30 min were studied. The results provide evidence for Co redistribution inside the core-shell NPs: before the application of a potential, the NPs present a high-density contrast between the core and the shell while after reduction they present a more homogeneous distribution of Co in the entire volume of the NPs. These differences likely result from the atomic diffusion inside the core and indicate that while being chemically reversible, the redox cycling results in some structural irreversibility of the core-shell NPs. Additional TEM micrographs of the NPs before and after reduction can be found in Figures S2 andS3. The important changes observed in the Fe L2,3-edge spectra underline that the NPs probed by the soft X-ray beam are electrically connected to the graphene bilayer, confirming that this spectro-electrochemical cell design can be successfully utilized to assess changes occurring during the OER using operando NEXAFS. the application of -0.5 V vs. RHE for 30 min (G and H). F and I) Spatially-resolved EELS STEM analyses of the core-shell NP from G) (before electrochemical measurements) and from H) (after application of -0.5 V vs. RHE for 30 min), correspondingly. Cobalt is colored blue; iron -green; and oxygen -red.

With this knowledge, we turn to the analyses of NEXAFS spectra acquired above 1.0 V vs. 2A shows a pair of low intensity peaks (PA,1 and PC,1) around 1.05 V vs. RHE, which are usually attributed to the Co (II/III) transition in Co3O4 or Co(OH)2 materials [START_REF] Reikowski | Operando Surface X-Ray Diffraction Studies of Structurally Defined Co3O4 and CoOOH Thin Films during Oxygen Evolution[END_REF][START_REF] Mefford | Correlative Operando Microscopy of Oxygen Evolution Electrocatalysts[END_REF] . Additionally, a cathodic peak usually attributed to the Co (III/IV) transition [START_REF] Reikowski | Operando Surface X-Ray Diffraction Studies of Structurally Defined Co3O4 and CoOOH Thin Films during Oxygen Evolution[END_REF][START_REF] Mefford | Correlative Operando Microscopy of Oxygen Evolution Electrocatalysts[END_REF] is observed at higher positive potentials, around 1.3 V vs. RHE (PC,2). The oxidation peak is hidden by the OER and is consequently barely distinguishable. Since the intensity of these CV peaks is low (compared to the peaks observed at low potentials), the changes in the NEXAFS spectra are expected to correspond to a minor oxidation change of the cations (Figure 2 B, C andD). The cyclic voltammetry curve obtained for Fe3O4 NPs does not exhibit these peaks around 1.1 and 1.4V. At 1.0 V vs. RHE, the Co L3-edge NEXAFS spectrum exhibits a shape characteristic of Co (II). By comparing this spectrum with the simulated L2,3-edges spectra of Co in Oh and Td sites [START_REF] Papaefthimiou | Nontrivial Redox Behavior of Nanosized Cobalt: New Insights from Ambient Pressure X-Ray Photoelectron and Absorption Spectroscopies[END_REF] , it is estimated that roughly 75% of cobalt resides in the Oh and 25% in the Td sites as expected for a mainly inverse spinel structure (Figure S10A). Surprisingly, when the potential is increased, in 0.2 V increments, up to 1.8 V vs. RHE (Figure 2B), the Co (II) signal is still largely present in NEXAFS spectra revealing that the spinel structure is preserved even under the OER conditions. However, it is worth noticing that the L3 peak slightly shifts to higher energies when the applied potential increases, suggesting that a small fraction of Co (II) is transformed into Co (III) (see figure S10B for comparison with the published Co (II) and Co (III) L-edge spectra). Potentialinduced changes observed at the Fe-L3 edge (Figure 2C) are more significant with (i) the characteristic Fe (II)/Fe(III) peak ratio decreasing to 0.46 at 1.8 V vs. RHE and (ii) the disappearance of the 707 eV shoulder, both evidencing oxidation of a fraction of Fe (II) present in the NPs core into Fe(III) [START_REF] Zhou | Spinel Ferrite Nanocrystals Embedded inside ZnO: Magnetic, Electronic, and Magnetotransport Properties[END_REF] . As iron in the Fe (II) oxidation state is only present in the Fe3O4 core (in the shell it is Fe (III)), we conclude that the Fe3O4 core is strongly influencing the chemical properties of the CoFe2O4 shell, as this oxidation likely results from an electron transfer from the Fe (II) in the core to compensate for the Co oxidation and reduce the Co (III) species in the shell, essentially maintaining its Co (II) state. Additionally, STEM-HAADF micrographs and EELS mappings of the NPs after the oxidation (Figure 2 E, F andG) demonstrate that the crystallinity and the presence of the Co-containing shell have been preserved even after the application of 1.75 V vs. RHE for 30 minutes. Supplementary high-resolution TEM (HRTEM) micrographs of the NPs after oxidation can be found in Figure S4. However, the NPs appear to be rougher and the edges are not as sharp as before applying the anodic potential (Figure 2E). Such roughening may be tentatively attributed to the NP restructuring driven by the migration of excess Fe (III) cations from the core to the shell of the NPs. This hypothesis is supported by the reported evidence of the inverse spinel structure Fe3O4 (magnetite) that can easily transform into -Fe2O3 (maghemite) which is a deficient spinel, with vacancies in the octahedral sublattice [START_REF] Jolivet | Iron Oxides: From Molecular Clusters to Solid. A Nice Example of Chemical Versatility[END_REF] . For example, oxidation of Fe (II) of magnetite NPs into Fe (III) by molecular oxygen involves electron hopping along with migration of Fe (III) cations through the lattice framework, generating vacancies in the octahedral sublattice (and their migration) in order to preserve the charge balance [START_REF] Jolivet | Iron Oxides: From Molecular Clusters to Solid. A Nice Example of Chemical Versatility[END_REF] .

RHE. The cyclic voltammogram shown in Figure

It is interesting to note that no changes were observed in the low excitation energy region of the O K-edge spectra when the potential was increased from 1.0 to 1.8 V vs. RHE (Figure S12). Thus, an anion redox mechanism involving the formation of an electrophilic oxygen species O I-as an OER intermediate can be discarded. On the other hand, a small peak around 714 eV emerges in the Fe L-edge spectra at E > 1.6 V vs. RHE (Figure 2 C and D) and may be tentatively attributed to the formation of Fe (IV), since broadening of the L3 peak has been shown in the literature to correspond to Fe (IV) [START_REF] Ikeno | First Principles Calculation of Fe L<SUB>2,3</SUB>-Edge X-Ray Absorption Near Edge Structures of Iron Oxides[END_REF][START_REF] Abbate | Controlled-Valence Properties of La 1 -x Sr x FeO 3 and La 1 -x Sr x MnO 3 Studied by Soft-x-Ray Absorption Spectroscopy[END_REF] . Subtracting the spectrum obtained at 1 V vs. RHE from the spectra at higher potentials (Figure 2D) better highlights this peak. The presence of this peak agrees with a cation redox OER mechanism involving possible participation of Fe (IV) in the OER active site as it was suggested by Enman et al. upon operando hard-X-ray investigation of Co(Fe)OxHy oxyhydroxide [START_REF] Enman | Operando X-Ray Absorption Spectroscopy Shows Iron Oxidation Is Concurrent with Oxygen Evolution in Cobalt-Iron (Oxy)Hydroxide Electrocatalysts[END_REF] . Note that on the core alone (Fe3O4, Figure S9), which is much less OER-active and which has been proven to be stable during oxidation [START_REF] Müllner | Stability and Catalytic Performance of Reconstructed Fe3O4(001) and Fe3O4(110) Surfaces during Oxygen Evolution Reaction[END_REF] , almost no changes are seen on the Fe L-edge under the OER conditions. This hindered Fe3O4 core compared to Fe3O4@CoFe2O4 core-shell NP oxidation may be attributed to the presence of a thin layer of -Fe2O3 on the surface of the Fe3O4 NPs acting as a passivating layer [START_REF] Ikeno | First Principles Calculation of Fe L<SUB>2,3</SUB>-Edge X-Ray Absorption Near Edge Structures of Iron Oxides[END_REF] and highlights the synergy between the Fe from the core and Co from the shell during the OER.

Considering this observation, we can conclude that in the core-shell NPs a small fraction of Fe (II) from the core, likely localized in the close proximity to the shell, is oxidized to Fe (III) to maintain the Co (II) state above 1.1 V vs. RHE. To preserve electroneutrality in the core, this Fe (III) cation probably migrates from the core towards the surface of the NPs, leaving behind a vacancy in the core and leading to a roughening of the NP surface. It is interesting to note that stabilization of the Co(II) state at high applied potential by the nearby Fe was already invoked in Refs. [START_REF] Peng | Influence of Fe and Ni Doping on the OER Performance at the Co3O4(001) Surface: Insights from DFT+U Calculations[END_REF][START_REF] Hajiyani | Surface Termination and Composition Control of Activity of the CoxNi1-XFe2O4(001) Surface for Water Oxidation: Insights from DFT+U Calculations[END_REF] dealing with DFT+U calculations of Co3O4(001) and CoFe2O4 (001) surfaces with and without an additional half or full monolayer of Fe. It was concluded that the OER active site is octahedral Co, both in the presence and in the absence of a Fe monolayer. However, while for the Fe-free surface Co is oxidized to reach a Co(IV) state [START_REF] Peng | Influence of Fe and Ni Doping on the OER Performance at the Co3O4(001) Surface: Insights from DFT+U Calculations[END_REF] , the presence of a Fe monolayer (for example, on the CoFe2O4 (001) surface) stabilizes the Co(II) state [START_REF] Hajiyani | Surface Termination and Composition Control of Activity of the CoxNi1-XFe2O4(001) Surface for Water Oxidation: Insights from DFT+U Calculations[END_REF] , while itself relaxing to octahedral sites and accepting the Fe(III) oxidation state under the OER potential. In this case, the OER catalytic cycle would involve the oxidation of a surface active site composed of Co(II) interacting with a nearby Fe(III), into Co(III). The formation of short-lived Co (IV) as it has been suggested in the literature on similar compounds [START_REF] Wang | Deciphering the Exceptional Performance of NiFe Hydroxide for the Oxygen Evolution Reaction in an Anion Exchange Membrane Electrolyzer[END_REF][START_REF] Smith | Spectroscopic Identification of Active Sites for the Oxygen Evolution Reaction on Iron-Cobalt Oxides[END_REF] cannot be fully discarded. However, considering that only a small fraction of Co (II) is transformed into Co (III) during the OER, such a scenario is quite unlikely for the core-shell NPs. Finally, these results suggest that the anion redox mechanism previously proposed for IrOx 8,9 and Co3O4 18 anodes involving electron-deficient oxygen as an active intermediate is rather unlikely.

In addition, it is worth noticing that the spinel structure is preserved in the core as both Fe (II) and Fe (III) are present in the NPs at all potentials (cf. Figure 2C) as well as in the CoFe2O4 shell, where the Co is mainly resting in the Co(II) state (cf. Figure 2B), even at high potentials where the formation of cobalt oxyhydroxyde phase has been previously found for Co3O4. [START_REF] Bergmann | Reversible Amorphization and the Catalytically Active State of Crystalline Co3O4 during Oxygen Evolution[END_REF][START_REF] Ortiz Peña | Morphological and Structural Evolution of Co3O4 Nanoparticles Revealed by in Situ Electrochemical Transmission Electron Microscopy during Electrocatalytic Water Oxidation[END_REF][START_REF] Reikowski | Operando Surface X-Ray Diffraction Studies of Structurally Defined Co3O4 and CoOOH Thin Films during Oxygen Evolution[END_REF] OER occurs on an active center comprised of Co (III) and Fe (III). However, one cannot exclude formation of active Fe (IV) species above 1.4 V vs RHE. Oxygen atoms are in red, cobalt in blue and iron in green.

To conclude, we performed an operando study using soft X-ray absorption spectroscopy over a wide potential range spanning from -0.5 V vs. RHE up to the OER interval on membrane electrode assemblies containing cobalt iron oxide spinel core-shell nanoparticles (Fe3O4@CoFe2O4) covered by a graphene bilayer. This approach turns out to be well-suited for studying redox transformations of these NPs. The work sheds light onto the interactions between the core and the shell, providing insights into the synergies that might exist between the Fe in the core and the Co in the shell. We document a strong influence of the Fe3O4 core on the redox behavior of the CoFe2O4 shell under OER conditions. Compared to previously investigated Co3O4 or Co(OH)2 NPs 3-6 , core-shell Fe3O4@CoFe2O4 NPs behave differently: most of the cobalt atoms in the shell remain in a Co (II) oxidation state in the potential region where significant OER occurs.

In addition, the presence of Co in the shell favors the oxidation of some fraction of Fe (II) into Fe (III) in the NPs core (in close proximity to the shell). Hence, these results suggest the occurrence of a cation-redox OER mechanism involving cooperative redox behavior between Co and Fe atoms. It is remarkable that the core-shell spinel structure is essentially preserved under the OER conditions but cannot withstand cathodic polarization to -0.5 V vs. RHE.

Figure 1 :

 1 Figure 1: A) TEM image of the Fe3O4@CoFe2O4 core-shell NPs and their size distribution, average

Figure 2 :

 2 Figure 2: A) Cyclic voltammogram of Fe3O4@CoFe2O4 core-shell NPs acquired in a spectroelectrochemical cell in 0.1 M NaOH electrolyte at 20 mV.s -1 scan rate. Area-normalized Co-L3 edge (B) and Fe-L3 edge (C)

Figure 3 :

 3 Figure 3: Proposed redox transformations on core-shell NPs depending on the applied potential. Step 1: At

Note that if the potential was scanned further negative, the CV became irreversible (not shown), which we tentatively attribute to the reduction of Fe3O4 to metallic Fe.

AUTHOR INFORMATION

Lisa Royer : lisa.royer@unistra.fr ICPEES, UMR 7515 CNRS-ECPM-Université de Strasbourg, REFERENCES


Dávid Ugi

Kolja Zoller

Kolos Lukács

Zsolt Fogarassy

István Groma

Szilvia Kalácska
email: szilvia.kalacska@cnrs.fr

Péter Katrin Schulz
email: katrin.schulz@kit.edu

Péter Dusán Ispánovity
email: ispanovity.peter@ttk.elte.hu

Irreversible evolution of dislocation pile-ups during cyclic microcantilever bending

Keywords: micromechanical testing, cantilever bending, CDD simulation, HR-EBSD, GND density

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Since the production of micron-and submicron-scale samples using a focused ion beam (FIB) and their subsequent mechanical testing became a state-of-the-art technology, the field of micromechanics has seen a rapid development. The main reason for the increased interest towards this field is three-fold: Firstly, materials at this scale exhibit remarkable features and often superior mechanical properties compared to their bulk counterparts. For instance, they generally show the 'smaller is harder' type of size effects [START_REF] Uchic | Sample dimensions influence strength and crystal plasticity[END_REF][START_REF] Greer | Size dependence of mechanical properties of gold at the micron scale in the absence of strain gradients[END_REF][START_REF] Uchic | Plasticity of micrometer-scale single crystals in compression[END_REF] and may exhibit unpredictable avalanche-like behaviour [START_REF] Dimiduk | Scalefree intermittent flow in crystal plasticity[END_REF][START_REF] Zaiser | Scale invariance in plastic flow of crystalline solids[END_REF][START_REF] Ispánovity | Dislocation avalanches are like earthquakes on the micron scale[END_REF]. Secondly, the small volume of the sample provides unique opportunities to observe specific deformation mechanisms using various experimental techniques to unprecedented detail [START_REF] Shan | Mechanical annealing and source-limited deformation in submicrometre-diameter ni crystals[END_REF][START_REF] Kiener | Work hardening in micropillar compression: In situ experiments and modeling[END_REF][START_REF] Samaee | Deciphering the interactions between single arm dislocation sources and coherent twin boundary in nickel bi-crystal[END_REF][START_REF] Máthis | On the dynamics of twinning in magnesium micropillars[END_REF]. Finally, at the micron-scale it becomes feasible to model the evolution of the whole microstructure with various physics based computational methods [START_REF] Csikor | Dislocation avalanches, strain bursts, and the problem of plastic forming at the micrometer scale[END_REF][START_REF] Zoller | Microstructure evolution of compressed micropillars investigated by in situ HR-EBSD analysis and dislocation density simulations[END_REF]. For these reasons, a range of different types of micromechanical experiments have been suggested and conducted, such as, microcompression [START_REF] Dimiduk | Size-affected singleslip behavior of pure nickel microcrystals[END_REF][START_REF] Greer | Size dependence of mechanical properties of gold at the micron scale in the absence of strain gradients[END_REF][START_REF] Volkert | Size effects in the deformation of sub-micron au columns[END_REF], microtension [START_REF] Kiener | A further step towards an understanding of size-dependent crystal plasticity: In situ tension experiments of miniaturized single-crystal copper samples[END_REF][START_REF] Kim | Tensile and compressive behavior of gold and molybdenum single crystals at the nano-scale[END_REF][START_REF] Kirchlechner | Dislocation storage in single slip-oriented cu micro-tensile samples: new insights via x-ray microdiffraction[END_REF], microshear [START_REF] Wieczorek | Assessment of strain hardening in copper single crystals using in situ sem microshear experiments[END_REF][START_REF] Guillonneau | Plastic Flow Under Shear-Compression at the Micron Scale-Application on Amorphous Silica at High Strain Rate[END_REF], microtorsion [START_REF] Fu | A tension-torsional fatigue testing apparatus for micro-scale components[END_REF], microbending [START_REF] Motz | Mechanical properties of micro-sized copper bending beams machined by the focused ion beam technique[END_REF][START_REF] Gong | Anisotropy in the plastic flow properties of single-crystal α titanium determined from microcantilever beams[END_REF] and microfatigue [START_REF] Lavenstein | Micro-scale fatigue mechanisms in metals: Insights gained from small-scale experiments and discrete dislocation dynamics simulations[END_REF][START_REF] Iyer | Cyclic deformation of microcantilevers using in-situ micromanipulation[END_REF].

In this paper the focus is on the plasticity of single crystalline metals where irreversible deformation is dominated by the collective dynamics of lattice dislocations. Here, with respect to the specimen size, two regimes of different behaviour can be distinguished. In the so-called dislocation starved regime, when the sample dimension is below approx. 1 µm, the number of dislocation lines and dislocation sources is so small, that dislocation interactions (such as annihilation, junction formation or cross-slip events) hardly take place and the plastic response and size effects are dominated by individual dislocation mechanisms (such as source activation) [START_REF] Greer | Size dependence of mechanical properties of gold at the micron scale in the absence of strain gradients[END_REF][START_REF] Shan | Mechanical annealing and source-limited deformation in submicrometre-diameter ni crystals[END_REF]. In the so-called storage regime, on the other hand, dislocation interactions do happen in an increasingly large amount during deformation, leading to the build-up of a complex dislocation network and the increase of the dislocation density [START_REF] Zhao | Critical dimension for the dislocation structure in deformed copper micropillars[END_REF][START_REF] Kiener | Work hardening in micropillar compression: In situ experiments and modeling[END_REF][START_REF] Kirchlechner | Dislocation storage in single slip-oriented cu micro-tensile samples: new insights via x-ray microdiffraction[END_REF][START_REF] Kalácska | Investigation of geometrically necessary dislocation structures in compressed cu micropillars by 3-dimensional hr-ebsd[END_REF]. The observed size effects and strain hardening can be often related to the development of strain gradients and the corresponding geometrically necessary dislocation (GND) content. Although such structures were found to develop even during uniaxial microcompression tests [START_REF] Zoller | Microstructure evolution of compressed micropillars investigated by in situ HR-EBSD analysis and dislocation density simulations[END_REF], microcantilever bending is a more natural choice to study the effect of strain gradients and the developments of GNDs since for this deformation mode strain gradients are inherently present already in the elastic regime. It is noted, that for the same reason microcantilever bending has been used successfully to study the role of strain gradients in materials with even more complex microstructure, see, e.g. [START_REF] Wang | The effect of delta-hydride on the micromechanical deformation of a Zr alloy studied by in situ high angular resolution electron backscatter diffraction[END_REF][START_REF] Kreins | Bauschinger effect and latent hardening under cyclic micro-bending of Ni-base alloy 718 single crystals: Part I. Experimental analysis of single and multi slip plasticity[END_REF][START_REF] Wimmer | Cyclic bending experiments on free-standing Cu micron lines observed by electron backscatter diffraction[END_REF][START_REF] Kapp | Structural instabilities during cyclic loading of ultrafine-grained copper studied with micro bending experiments[END_REF][START_REF] Alfreider | In-situ elasticplastic fracture mechanics on the microscale by means of continuous dynamical testing[END_REF].

The first microcantilever bending tests were carried out by Motz et al. with a focus on the multiple slip deformation of copper single crystals [START_REF] Motz | Mechanical properties of micro-sized copper bending beams machined by the focused ion beam technique[END_REF]. The experiments were later complemented by discrete dislocation dynamics (DDD) simulations [START_REF] Motz | Micro-bending tests: A comparison between three-dimensional discrete dislo-cation dynamics simulations and experiments[END_REF]. Both approaches suggested that plasticity and size effects are dominated by the development of individual dislocation pile-ups close to the neutral zone. These polarized dislocation structures also give rise to a pronounced Bauschinger effect (that is, asymmetry of the flow stress w.r.t. the loading direction) [START_REF] Kapp | Importance of dislocation pile-ups on the mechanical properties and the bauschinger effect in microcantilevers[END_REF] and induce a strong internal back stress that, for instance, has a significant influence on crack propagation during fatigue [START_REF] Eisenhut | Effect of a dislocation pile-up at the neutral axis on trans-crystalline crack growth for micro-bending fatigue[END_REF]. DDD simulations in 2D [START_REF] Tarleton | A discrete dislocation plasticity study of the micro-cantilever size effect[END_REF] and 3D [START_REF] Motz | Micro-bending tests: A comparison between three-dimensional discrete dislo-cation dynamics simulations and experiments[END_REF][START_REF] Velayarce | Influence of single and multiple slip conditions and temperature on the size effect in micro bending[END_REF] confirmed the formation of the pile-ups arranged symmetrically around the neutral zone. The role of temperature and crystal orientation on the formation of pile-ups and the corresponding size effects were also investigated experimentally [START_REF] Velayarce | Influence of single and multiple slip conditions and temperature on the size effect in micro bending[END_REF].

Most microbending experiments mentioned so far focused on unidirectional loading and the formation and role of pile-ups during bending. However, it is equally important to investigate the evolution of the microstructure during reversed loading to understand the role of GNDs and strain hardening during fatigue. Plastic deformation and the corresponding dislocation motion is generally considered irreversible, however, under certain conditions it can, in fact, be reversible. A prominent example is a sequence of dislocations emitted from the same source, therefore lying on the same slip plane and piling up against an obstacle. Upon reversed loading dislocations in such a pile-up may return to their origin and annihilate, thus recovering the exact original atomic arrangement. This process was confirmed by in situ micro Laue diffraction experiments performed during low cycle bending fatigue of single crystalline copper microcantilevers with a cross section of approx. 10 × 10 µm 2 [START_REF] Kirchlechner | On the reversibility of dislocation slip during small scale low cycle fatigue[END_REF]. Generally speaking, broadening of X-ray diffraction peaks in single crystals are caused by internal misorientations due to GNDs. Kirchlechner et al. found that peak broadening and the formation of subpeaks during microbending was to a large extent reversible upon unloading [START_REF] Kirchlechner | On the reversibility of dislocation slip during small scale low cycle fatigue[END_REF]. This means that GND storage or cell formation was not observed at low cycle numbers in spite of the relatively large sample size. However, several possible origins of irreversibility were discussed such as cross-slip and dislocation-dislocation interactions with the formation of new Burgers vectors (BVs, e.g., Lomer locks) [START_REF] Kirchlechner | On the reversibility of dislocation slip during small scale low cycle fatigue[END_REF]. Stricker et al. also discussed a possible mechanism of irreversibility during which the dissolution of the pile-up after unloading leaves behind a slip step on the surface [START_REF] Stricker | Irreversibility of dislocation motion under cyclic loading due to strain gradients[END_REF].

In order to understand the formation of pile-ups and to tackle the issue of plastic reversibility/irreversibility upon reversed loading, in this paper bending of Cu microcantilevers is studied. To promote dislocation reactions, a multiple slip orientation is chosen. The evolution of the microstructure is analysed mainly using in situ highresolution electron backscatter diffraction (HR-EBSD), a cross-correlation based method that provides detailed microstructural information based on the Kikuchi patterns [START_REF] Arsenlis | Crystallographic aspects of geometricallynecessary and statistically-stored dislocation density[END_REF][START_REF] Wilkinson | Determination of elastic strain fields and geometrically necessary dislocation distributions near nanoindents using electron back scatter diffraction[END_REF]. In particular, components of the stress and distortion tensor, as well as three components of the Nye dislocation density tensor can be measured on the surface of the sample with a spatial resolution of about 100 nm. As such, this technique is especially useful for characterizing dislocation structures that develop close to the surface [START_REF] Kalácska | 3d hr-ebsd characterization of the plastic zone around crack tips in tungsten single crystals at the micron scale[END_REF]. The method can also be applied for three-dimensional (3D) reconstruction of the microstructure using FIB serial sectioning, this, however, leads to the destruction of the sample, see, e.g, [START_REF] Kalácska | Investigation of geometrically necessary dislocation structures in compressed cu micropillars by 3-dimensional hr-ebsd[END_REF]. The method was also applied for a Cu microcantilever to measure the 3D GND structure after unidirectional bending and a quite homogeneous distribution of GNDs along the cross section of the beam was found [START_REF] Konijnenberg | Assessment of geometrically necessary dislocation levels derived by 3d ebsd[END_REF].

To gain deeper physical insights into the dislocation mechanisms during microbending and to explain the findings of the HR-EBSD measurements, experiments are complemented with continuum dislocation density (CDD) simulations [START_REF] Hochrainer | A three-dimensional continuum theory of dislocation systems: kinematics and meanfield formulation[END_REF][START_REF] Hochrainer | Continuum dislocation dynamics: towards a physical theory of crystal plasticity[END_REF][START_REF] Hochrainer | Multipole expansion of continuum dislocations dynamics in terms of alignment tensors[END_REF][START_REF] Schulz | A mesoscale continuum approach of dislocation dynamics and the approximation by a runge-kutta discontinuous galerkin method[END_REF]. The advantage of this method compared to DDD simulations is that a larger volume can be modelled up to larger strains, yet, this method, contrary to even higher scale crystal plasticity approaches, can account for every individual dislocation interaction that can take place in the FCC crystal. In addition, CDD is able to model all the quantities measured by HR-EBSD, so, comparison of experiments and modelling can be done in an explicit manner, as was shown earlier for microcompression experiments [START_REF] Zoller | Microstructure evolution of compressed micropillars investigated by in situ HR-EBSD analysis and dislocation density simulations[END_REF]. As such, this method is very well suited for the aim of the present paper, that is, to understand to what extent is pile-up formation reversible, and to identify the dislocation mechanisms that are responsible for possible irreversibilities.

The paper is organised as follows. This introduction is followed by a brief crystallographic analysis of the microbending studied to make general predictions on the slip system activities. Then, section 3 introduces the experimental methods and the CDD framework followed by a detailed overview of the results obtained by both experiments and modelling in section 4. Section 5 provides an in-depth discussion of the findings and concludes the paper with a short outlook.

System analysis

In this paper the plastic bending of a Cu single crystalline microcantilever of rectangular shape and square cross section is investigated. The cantilever is oriented for ⟨100⟩{100} multiple slip, that is, edges of the beam are parallel with the edges of the cubic unit cell of the FCC lattice. The sketch of the geometry is shown in Fig. 1a where, according to the Schmid-Boas notation [START_REF] Schmid | Kristallplastizität : mit besonderer Berücksichtigung der Metalle[END_REF], the four individual slip planes are denoted by letters A-D and the slip directions (or BV directions) by numerals 1-6 (specified in Fig. 1b). On the left side, the end of the beam is fixed, that is, no displacements are allowed, whereas a displacement u D is prescribed at the right end of the cantilever that results in force F . Free boundary conditions apply on the rest of the sides. Since the cantilever is initially bent downwards, positive u D and F values refer to displacements and forces in the negative y direction. In both experimental and simulation studies cantilever size is chosen as a = 5 µm that, according to the Introduction above, is expected to be at the limit of the starved and storage regimes.

In this section we aim to make predictions about the plastic activities on the individual slip systems based on the crystal orientation and deformation mode. To this end, we, first, analyse the stresses developing during elastic bending of the cantilever. The bending moment along the z axis M (x) = F (x -l) (with l being the length of the cantilever or, equivalently, the moment arm) is linear along the x-axis and, consequently, the normal and the shear stresses read as

σ 11 (x, y) = - 12M (x) a 4 y - a 2 (1)
and

τ 12 (y) = - 6 F a 2 1 4 - y a - 1 2 2 , (2)
respectively. Figure 1c shows qualitatively the region where the magnitude of the shear stress exceeds that of the normal stress. At the fixed end of the beam, where the largest stresses occur, this region is rather thin because the ratio of the maxima of the occurring normal and shear stresses is quite large: |σ11|max |τ12|max = 4 • l/a. Accordingly, the shear stress is expected to play an inferior role during bending. Based on this analysis one can group slip systems into four categories: Group I contains slip systems where both normal and shear stresses contribute to the resolved shear stress (RSS) (A3, B4, C3, D4), Group II contains the ones where only normal stresses have contributions (A6, B5, C5, D6) and Group III comprises systems with only shear stresses playing a role (A2, B2, C1, D1). The distinction of slip systems of Group I and Group II is also motivated by the fact, that BVs 3 and 4 lie in the xz plane, so a single dislocation moving to the neutral zone during bending will have a pure screw character. As a result, dislocations in Group I are expected to cross-slip at a larger rate compared to the other two groups that may contribute significantly to irreversibility.

Methods

Experimental

A rectangular-shaped cantilever with a rounded base geometry was fabricated using a FIB in a FEI Quanta 3D dual beam scanning electron microscope (SEM). The sides of the bream cross section were measured as a z = a y = 5.0 ± 0.1 µm, and the length of the beam was L = 20.6 ± 0.1 µm. In order to avoid stress concentrations at sharp edges, circular geometry was used at the base of the cantilever with a diameter of d = 8.0 ± 0.1 µm (Fig. 2). During the loading, the indenter's bending tool was in contact with the cantilever along a straight line parallel to the cantilever's z direction, and was 2.1 ± 0.2 µm far from the free end of the cantilever which resulted in a moment arm length of l = 18.5±0.3 µm. During microsample preparation, the final FIB polishing step was operated at 30 kV and a Ga + ion current of 500 pA was used, which resulted in less than 1 • differences between the parallel sides of the cantilever and a minimal Ga + implantation. It is noted, that in total 3 microcantilevers were prepared with identical geometry and orientation, and since all of them exhibited equivalent plastic behaviour, in the paper we focus on the results obtained for a single measurement.

Micromechanical deformation

The microcantilever bending experiments were performed using a custom-made in situ microdeformation stage [START_REF] Hegyi | Micron-scale deformation: a coupled in situ study of strain bursts and acoustic emission[END_REF][START_REF] Ispánovity | Dislocation avalanches are like earthquakes on the micron scale[END_REF]. The hook-shaped bending tool was made from a tungsten needle tip by FIB machining. The deformation tool was attached to a spring with a spring constant of 1.7 mN/µm that was used to determine the acting force. During bending, the spring was moved with a constant velocity of ±5 nm/s.

EBSD/HR-EBSD

The orientation of the sample was determined using EBSD. An Edax Hikari camera was used to record the patterns with 1 × 1 binning, using an electron beam of 20 kV, 4 nA. The measurement confirmed that the sample consists of a single grain and the orientation was found to be 5.2 • inclined w.r.t. the preferred ⟨100⟩{100} orientation, as indicated in Fig. 2b (see also Suppl. Fig. S1). In order to characterise the plastic zone in the deformed cantilevers, in situ HR-EBSD was utilized on the FIBmachined surface of the cantilever. HR-EBSD is a surface technique where the diffraction patterns collected on the specimen are related to a reference pattern through image cross-correlation [START_REF] Wilkinson | High-resolution elastic strain measurement from electron backscatter diffraction patterns: new levels of sensitivity[END_REF][START_REF] Wilkinson | Strain mapping using electron backscatter diffraction[END_REF]. The special geometry of the indentation device allowed to perform some of the HR-EBSD mappings in situ, while the sample was under load. Therefore, during such mappings (which took approx. 25 minutes), the motion of the hook was paused. In other cases, HR-EBSD maps were recorded after releasing the sample, creating a unique opportunity to compare the HR-EBSD maps obtained under load and after releasing the sample to a relaxed stress state. HR-EBSD evaluation was performed using BLGVantage CrossCourt Rapide v.4.5.0.

The characterization of the microstructure is given using the elements of the stress tensor, the net GND density and the GND density tensor, defined by Nye as:

α ij = t b t i l t j ρ t , (3)
where index t represents a slip system, ρ t is the density on that system and b t and l t is the Burgers vector and line direction of dislocations, respectively. From the elements of the distortion tensor β ij = ∂ j u i with u being the displacement field, accessible by HR-EBSD, three components of the tensor α follow as [START_REF] Wilkinson | Strain mapping using electron backscatter diffraction[END_REF]:

α i3 = ∂ 1 β i2 -∂ 2 β i1 , i = 1, 2, 3. (4)
According to Eq. ( 3) the α i3 components are a sum in which all types of dislocations not parallel with the xy plane have a contribution. This means that, in principle, from the α i3 values themselves one cannot asses the amount of dislocations with different type t, that is ρ t . If, however, there is a dominant type of BVs in the population, then the sum in Eq. ( 3) will be dominated by that term and the B i = α i3 vector is nearly parallel with b t i (for the geometrical interpretetaion of the meaning of the signs of the Nye tensor components see Fig. 2). Exactly this was found earlier for Cu micropillars [START_REF] Zoller | Microstructure evolution of compressed micropillars investigated by in situ HR-EBSD analysis and dislocation density simulations[END_REF] as well as for bulk Cu samples [START_REF] Lipcsei | Statistical analysis of dislocation cells in uniaxially deformed copper single crystals[END_REF]. Here we thus apply the same method described in [START_REF] Zoller | Microstructure evolution of compressed micropillars investigated by in situ HR-EBSD analysis and dislocation density simulations[END_REF] to determine the dominant BV type at every measurement point of the HR-EBSD.

TEM

Bright field (BF) imaging was performed on a Cs-corrected (S)TEM Themis TEM with 200 kV electron beam. One lamella with a surface normal ⃗ n ∥ [001] was removed from the sample after the deformation experiment using a Thermo Fisher Scios 2 Dual Beam microscope. In order to determine the proportion of dislocations with different BVs in the sample, 5 different tilt positions were used. In the [001] zone condition all the dislocations were visible, whereas under (200), ( 220), ( 020) and (2 20) two-beam conditions dislocations with slip directions 1+2, 5, 3+4 and 6 (cf. Fig. 1b), respectively, were not seen. This allowed us to validate the HR-EBSD measurements, however, the TEM foil could only be extracted from somewhat beneath the surface.

Simulation 3.2.1. Dislocation density based continuum model

The dislocation motion in the 3D space can be described for homogenised ensembles of curved dislocation lines by the kinematically closed Continuum Dislocation Dynamics (CDD) formulation derived by Hochrainer et al. using a higher-dimensional space preserving information about the dislocation orientations [START_REF] Hochrainer | A three-dimensional continuum theory of dislocation systems: kinematics and meanfield formulation[END_REF][START_REF] Hochrainer | Continuum dislocation dynamics: towards a physical theory of crystal plasticity[END_REF][START_REF] Hochrainer | Multipole expansion of continuum dislocations dynamics in terms of alignment tensors[END_REF]. The CDD formulation used here is based on the framework in [START_REF] Schulz | A mesoscale continuum approach of dislocation dynamics and the approximation by a runge-kutta discontinuous galerkin method[END_REF] and incorporates two coupled problems. In the external problem the stress field is calculated for a given plastic state and in the internal problem the microstructure evolution is derived for a given stress field yielding plastic deformation. These two problems are thus coupled via the plastic slip, which is assumed to be the sole result of collective dislocation motion.

The microstructure is described by different dislocation densities and a curvature density on the individual slip systems, whereby following [START_REF] Sudmanns | Data-driven exploration and continuum modeling of dislocation networks[END_REF] we distinguish between mobile dislocation density, yielding plastic deformation, and immobile dislocation network density, contributing to the material hardening. The mobile dislocation density is again additively decomposed into its statistically stored dislocation (SSD) and geometrically necessary dislocation (GND) parts, whereby the screw and edge character of the GND density is divided. A visualisation of the degrees of freedom of the CDD formulation used is given in [START_REF] Zoller | Microstructure evolution of compressed micropillars investigated by in situ HR-EBSD analysis and dislocation density simulations[END_REF].

The microstructure evolution also incorporates activities of dislocation sources covered by the homogenised model introduced in [START_REF] Zoller | Analysis of single crystalline microwires under torsion using a dislocation-based continuum formulation[END_REF], dislocation multiplication mechanisms including cross-slip and glissile reactions according to [START_REF] Sudmanns | Dislocation multiplication by cross-slip and glissile reaction in a dislocation based continuum formulation of crystal plasticity[END_REF], dislocation network formation due to Lomer reactions and annihilation processes due to collinear reactions given in [START_REF] Sudmanns | Data-driven exploration and continuum modeling of dislocation networks[END_REF]. Depending on the local stresses and dislocation configuration, the Lomer junctions can unzip again, whereby the link lengths of dislocation segments connected to Lomer junction, here called Lomer arms, influence the critical stress for unzipping [START_REF] Rodney | Structure and strength of dislocation junctions: An atomic level analysis[END_REF][START_REF] Shin | Formation and strength of dislocation junctions in fcc metals: A study by dislocation dynamics and atomistic simulations[END_REF]. Following [START_REF] Zoller | Microstructure evolution of compressed micropillars investigated by in situ HR-EBSD analysis and dislocation density simulations[END_REF], the link length distribution of these stabilised Lomer arms are modelled by a Rayleigh distribution with an expected value equal to to average link length, which is assumed to scale with the averaged dislocation distance. The constitutive law for the dislocation velocity takes internal stresses into account including short-range dislocation stress interactions represented by a back-stress term given in [START_REF] Groma | Spatial correlations and higherorder gradient terms in a continuum description of dislocation dynamics[END_REF][START_REF] Schmitt | Internal stresses in a homogenized representation of dislocation microstructures[END_REF] and eigenstresses of the dislocations according to [START_REF] Schulz | Analysis of dislocation pile-ups using a dislocationbased continuum theory[END_REF]. The hindrance of dislocation motion due to interaction with forest dislocations from other slip systems within the averaging volume are considered by a yield stress term based on [START_REF] Franciosi | Latent hardening in copper and aluminium single crystals[END_REF]. The resulting plastic slip on the individual slip systems is described by the Orowan equation [START_REF] Orowan | Zur kristallplastizität[END_REF]. The formulation used focuses on small deformations and the stress-strain relation describes physical linearity using the cubic symmetry of the elasticity tensor. The Cauchy stress tensor inserted in the static momentum balance ensures the macroscopic equilibrium condition.

Numerical implementation

The CDD formulation used was implemented into a two-scale numerical framework based on [START_REF] Schulz | A mesoscale continuum approach of dislocation dynamics and the approximation by a runge-kutta discontinuous galerkin method[END_REF] using an own customised version of the parallel finite element software M++ [START_REF] Wieners | Distributed point objects. a new concept for parallel finite elements[END_REF][START_REF] Wieners | A geometric data structure for parallel finite elements and the application to multigrid methods with block smoothing[END_REF]. A finite element approach is applied with hexahedral elements and linear ansatz functions for the displacements in the external problem as well as an implicit Runge-Kutta discontinous Galerkin scheme with full upwind flux and constant ansatz functions for the dislocation and curvature densities in the internal problem. Simplifying but found to be numerically efficient, both scales are meshed with the same spatial resolution. The time is discretised by an implicit midpoint rule with a fixed time step.

Simulation parameters

The main parameters of the CDD formulation are summarized in Table 1.

It should be noted that due to the lack of data for the dislocation reaction coefficients in the case of copper under bending, the exact choice of the dislocation reaction constants is uncertain and the values were assumed to be equal to the modelled gold under torsion in [START_REF] Zoller | Classification of slip system interaction in microwires under torsion[END_REF]. The initial microstructure is assumed to consist of a total dislocation density of ρ Tot = 7.2 × 10 13 m -2 , which is homogeneously distributed on all slip systems. Since the degree of connectivity of the initial dislocation network is unknown, it

Results

Microstructure characterisation

The cantilever was first bent in one direction (along the y axis in the negative direction), followed by reversed loading up to a similar extent. The measured plastic response of the sample is shown in Fig. 3, where stresses and strains are normalised according to the theory of elastic bending and the corresponding literature [START_REF] Motz | Mechanical properties of micro-sized copper bending beams machined by the focused ion beam technique[END_REF][START_REF] Demir | The mechanical size effect as a mean-field breakdown phenomenon: Example of microscale single crystal beam bending[END_REF][START_REF] Husser | The role of geometrically necessary dislocations in cantilever beam bending experiments of single crystals[END_REF], as:

σ b = 16F a 2 (5)
and for the bending strain the ratio of the vertical displacement u D and the moment arm l is considered:

ε b = u D /l. (6)
(For the corresponding force-displacement curve see Suppl. Fig. S2.) During the first bending, a clear strain hardening can be observed until the maximum plastic bending strain (measured after elastic unloading) of ε p,b ≈ 5.5% is reached. Upon reversed loading, the Bauschinger effect is clearly seen as well as a significantly stronger strain hardening compared to the initial direction. To reach the terminal plastic strain of ε p,b ≈ -6% in the reverse direction requires an approx. 70% larger bending stress compared to the initial direction. HR-EBSD measurements were performed seven times during the course of the experiment at stages denoted by roman numerals (I)-(VII). Measurements (II) and (IV) were carried out in situ under load, which explains the slight drops in the stress due to relaxation phenomena. The other five scans were performed at zero applied stress, that is, after releasing the sample. After each HR-EBSD scan the sample surface gets slightly contaminated that causes the deterioration of the EBSD pattern quality of subsequent scans at the same area. To eliminate the negative consequences of this effect a few tens of nm thick layer was removed by FIB from the sample surface after each scan with the same setting as was applied in the final polishing step during the cantilever preparation. To perform this, the sample had to be dismounted from the device after every scan and then had to be re-mounted again (the colouring of the different parts of the stress-strain curve is meant to reflect this detail of the experiment). A slight misorientation of the sample is unavoidable during this process, which explains the slight drop in the yield stress after measurement (VI). This artefact, however, is not expected to play any role in the general trends of the behaviour to be discussed in the following. It is noted that between measurements (IV) and (V) only elastic unloading and the weak FIB-polishing discussed above took place which allowed us to check the influence of these two processes on the microstructure.

Figure 4 presents the HR-EBSD based evaluation of the microstructure for the final stage (VII). In panel (a) the von Mises stress σ vM calculated from the components of the stress tensor (the elements of which are accessible with HR-EBSD, as mentioned in Sec. 3.1.2) is plotted.

The GNDs are also required to accommodate the lattice rotation due to plastic bending along the z axis that is shown in panel (b) (note that the orientation changes rather smoothly, no sharp jumps can be observed that would correspond to simple low angle grain boundaries). Indeed, the total GND density [panel (c)] shows a welldeveloped inhomogeneous distribution of dislocations resembling a cellular structure also seen in bulk samples [START_REF] Kalácska | Comparison of the dislocation density obtained by hr-ebsd and x-ray profile analysis[END_REF][START_REF] Lipcsei | Statistical analysis of dislocation cells in uniaxially deformed copper single crystals[END_REF]. The components of the Nye tensor α i3 show extended regions with non-zero net BV [panels (d-f)]. Panel (h) shows the result of the BV analysis introduced in Sec. 3.1.2. As seen, large areas characterised by a single dominant BV (e.g., at the base of the cantilever almost exclusively dislocations of type 3 are found) are alternating with regions with more complex microstructure. The figure also differentiates between different signs of the BVs. As seen visually and also supported by the histogram in panel (g), for every BV type one direction is strongly preferred, that is, the microstructure is highly polarised due to the lattice rotations (that is, strain gradients), as expected. In order to eliminate measurement artefacts at the sample edges, the histogram is calculated for the central area of panel (h) (denoted with dashed line and also shown in a magnified view in panels (k) and (l)) where most of the GNDs are accumulated.

TEM experiments

BF images made from the [001] zone axis and (220) two-beam conditions are shown in Fig. 5. For the other BF images taken from the same area see Suppl. Fig. S3. In Fig. 5a a well-developed cellular dislocation structure is seen with a large number of dislocations even in the cell interiors. Similar conclusions can be drawn from the images taken at the (200) and (020) two-beam conditions (Suppl. Figs. S3a andS3b). However, under (2 20) and (220) conditions, the contrast of most dislocations disappear (as seen in Fig. 5b and Suppl. Fig. S3c). Based on these observations and the discussion of Sec. 3.1.3 it can be concluded that the majority of the dislocations found in the lamella had [ 110] or [110] type BVs, that is, of type 5 and 6 or, equivalently, Group II. This finding is in good agreement with the HR-EBSD evaluation, as in Fig. 4l 80 % of the dislocations were found to fall into this group.

Evolution of the microstructure

Figure 6 is concerned with the evolution of the dislocation microstructure during bi-directional bending. Panel (a) shows the GND densities and the dominant BV types for stages (I)-(VII) shown in Fig. 3 (for the corresponding components of the Nye tensor and the GND densities see Suppl. Figs. S4 andS5). As seen, in the initial state no specific dislocation structure can be recognized, the measured densities of BV type 4 are due to the noisy background. As stress starts to increase at stages (II) and (III) a dislocation pile-up gradually builds up with a majority of dislocations with BV type 5 in the central region. Note, that the structure is strongly polarised, so the thin region with BV type 5 extending in the [ 110] direction is practically a low-angle grain boundary separating the base of the beam from the bent part. Although the BV type 5 also points in the [ 110] direction, the slip planes are not perpendicular to the xy plane and the structure exhibits a width of approx. 1 µm, so this structure is clearly not a simple pile-up in a single glide-plane but the constituent dislocations are rather expected to have originated from sources outside the plane of the pile-up.

Upon reversed loading this structure gradually dissolves during stages (IV)-(V), first close to the top/bottom surface, and then a lot of additional GNDs accumulate throughout the cross section of the cantilever during stages (VI)-(VII). Accordingly, the total number of GNDs initially start to drop until stage (V) and then increase to a much higher value compared to stage (III) as seen in panel (b) of Fig. 6. In the meantime the polarisation of the microstructure reverses as all present BVs change their signs.

The final dislocation structure is rather complex, with the dominant BV alternating quite quickly in space. This complexity suggests a large number of dislocation interactions taking place between different slip systems during reversed bending. This and the large increase in the GND density explains the high strain hardening during this phase and the enhanced bending stress (450 MPa compared to 200 MPa of the initial bending). The results are in a very good agreement with the general predictions of Sec. 2 as the great majority of dislocations fall into Groups I and II.

As it was mentioned earlier, between stages (IV) and (V) only elastic unloading and a slight FIB polishing were performed. According to Fig. 6 the microstructures in the two cases show identical features in BV distributions and GND content, so we conclude, that elastic unloading and the FIB polishing have negligible effects on the microstructure observed by HR-EBSD.

To explore the origin of the GNDs, high quality SEM images were made on the top and bottom surfaces of cantilevers that were fabricated identically to the in situ sample. This was required because the re-deposition due to the consecutive FIB polishing steps (performed between each deformation stage because of the degradation of the EBSD pattern quality as mentioned before) masked these fine patters and it was not possible to record them afterwards on the original sample. We assume that identical slip traces would have been found if the FIB polishing was not essential to keep the EBSD mapping quality as high as possible. On the top side a characteristic checkered pattern was visible that corresponds to slip traces of dislocations gliding on different {111} planes (Suppl. Fig. S6).

Simulation

To get deeper insights into involved slip systems during the cantilever bending, the experiments are complemented by CDD simulations. Considering the simulation parameters as described in Sec. 3.2.3, we analyse the GND density evolution with respect to a given loading over the system. For a single loading cycle as shown in Fig. 7 (top), the resulting GND density evolution is given in Fig. 7 (bottom) for all 12 slip systems. It is noted, that due to computational limitations the bending amplitude in the simulations is approximately three times smaller than in the experiments. As such, in this section we aim mostly at a Applying the slip system denomination as given in Fig. 1, it can be observed that the slip system activity can be distinguished between the three different slip system groups introduced in Sec. 2. Group III is found to be almost inactive. Based on the system analysis, this group comprises slip systems that see mainly shear stresses during elastic loading while Groups I and II contain systems with predominantly normal or solely normal stress contributions to the resolved shear stress on the respective systems. The GND density evolution reflects the loading and unloading paths by a wavy course. This occurs very similarly for the two active slip groups. Looking into the loading for a half cycle (up to the maximum negative loading, shown as stages 1-7), it can be seen how the change of the loading direction results in a highly nonlinear GND evolution showing slightly higher values for Group I compared to Group II.

Looking closer into the two active slip system groups, the character of the dislocation content is analysed. Fig. 8 depicts the composition of screw and edge components for the active slip system groups. The comparison shows that the composition is different: for Group I the amount of screw dislocations is lower compared to the amount of edge dislocations and their ratio is approximately constant all over the simulation time. For Group I, on the other hand, the amount of screw dislocation density is higher compared to the edge dislocation density. This difference is probably due to the effect mentioned in Sec. 2, that is, dislocations in Group I have pure screw character in the neutral zone which leads to much higher cross-slip probabilities. This process can at the same time explain the lack of screw dislocations in Group I and the excess in Group II.

The contour plot of the whole cantilever in Fig. 9a re-veals the location of the slip activity and the occurring dislocation density pileups. The spatial distribution of GND density emerges mainly in the region close to the clamped edge due to the stress concentration. At the maximum loading, 95% of the GND density can be found in the region x/l ≤ 0.4. Averaged over cross section, the maximum averaged values can be found at x/l ≈ 0.1. High density values are found close to the neutral axis. In direct proximity to the clamped edge as well as in the transition zone to almost GND-free regions there are distinctive pileups found along the diagonal in the xy plane. For the regions of high activity, the tensor components α i3 are given in Fig. 9b. Focusing on the composition of the dislocation density with respect to the different slip system groups, we observe a complex interplay of the two active groups, see Fig. 9c. Here, elements with densities lower then ρ GND < 10 12 m -2 are neglected in the evaluation and are coloured in blue.

The evolution of the α 13 component over the stages 1-7 is given in Fig. 10. This shows the reversal of the signs, i.e., the change in polarisation during the evolution as required by the reversed strain gradients.

Finally, it shall be emphasised that the results show a significant Bauschinger effect during reverse loading based on the dislocation density evolution. The results show the formation, stabilisation and resolution of dislocation pileups as a result of the complex interplay between the different slip systems and their stress interaction.

Discussion

In this paper a systematic analysis of collective dislocation phenomena has been performed for microcantilever bending. The experimental investigations are mostly based on the HR-EBSD technique that, as shown above, provides an exceptionally detailed access to the dislocation microstructure. It does not only deliver, among others, the spatial distribution of the GND density close to the sample's surface, but also three individual components of the Nye tensor that can be used to estimate the spatial distribution of BV types and their signs. We emphasise, that such a detailed analysis of the evolution of the dislocation microstructure was not possible before. Yet, this information, although very rich compared to other available methods, is far from complete. For instance, the microstructure at the surface (where the measurements are carried out) may differ from that of the sample interior and HR-EBSD cannot distinguish between the slip planes the dislocations are lying on. Therefore, the experiments were complemented by CDD simulations, that in principle are capable of modelling the evolution of the complete dislocation microstructure in the microsample, and provides access to all these missing information. As such, they help in understanding and evaluating the experimental results and the physics behind cantilever bending.

Our most important finding is related to the formation of the dislocation pile-ups and their irreversibility during bending. As explained in detail in the introduction, it has been argued that on the micron-scale dislocation pile-ups are often reversible, that is, they practically dissolve upon unloading. While this may be true for samples significantly smaller than studied here or for different orientations, here a completely different picture is found. During the first bending phase a structure similar to a set of simple planar pile-ups form, but when it comes to reversed loading the structure becomes highly complex with the GND density being distributed all along the microcantilever cross section and its base. The reason is, that the GNDs cannot fully escape the sample upon unloading, rather the majority of them gets stuck in the sample due to dislocation reactions, as seen in the experiments (bottom panel of Fig. 6) and simulations (Fig. 7) as well. This is evident from the evolution of the available components of the tensor α, too, where the change in sign (that is, polarisation) initiates from the top and bottom parts of the cantilever, and reaches its neutral axis only at larger reversed strains (see Fig. 10) This means, that GNDs at the neutral axis are rather stable, e.g., due to cross-slip or other shortrange dislocation effects which produce junctions and keep them pinned. Nonetheless, as the reversed strain increases, the sign of the Nye tensor components ultimately change, and the structure gets polarised in the opposite direction. This process explains the strong strain hardening and the Bauschinger effect observed with both methods. The first one is the result of the accumulation of a large dislocation content due to reactions (a large portion of which are GNDs) and the other is due to the strong polarisation of the microstructure and related internal stresses, as proposed earlier [START_REF] Mughrabi | Dislocation clustering and long-range internal stresses in monotonically and cyclically deformed metal crystals[END_REF].

It is important to emphasise the correspondence between experiments and CDD simulations. Of course a one-by-one comparison is not possible due to some differences between the two systems (such as the different geometry at the cantilever base, slight misorientation, imperfections of the sample and loading device, etc.) and due to the lower bending amplitudes applied in the simulations but the qualitative similarities between the results are evident. Not only the mechanical response and the GND density evolution, but also the evolution of the available Nye-tensor components show good accordance. In addition, both experiments and simulations predict that predominantly dislocations of Group I and II dominate the plastic response. Thus, CDD yields here a deeper insight into the dislocation mechanisms that play a role during the bending process.

The results demonstrate how different the plastic deformation is during the first and second half cycle of the microbending. During the first half cycle a fully polarised rather simple GND structure forms which upon reverse loading gets excessively complex sue to the processes described in the previous paragraph. This phenomenon may play a key role in the formation of dislocation patterns specific for fatigue (such as ladder structures in persistent slip bands). The present study also pushes forward the applicability of HR-EBSD to investigate the evolution of the microstructure during plastic deformation in several aspects. (i) We validated the HR-EBSD measurements with TEM analysis and also showed their robustness by proving that the results were not sensitive to elastic unloading and a slight FIB polishing of the surface. (ii) The qualitative similarities with the CDD underline the physical feasibility of the HR-EBSD results. (iii) Although HR-EBSD measurements can only be performed on the cantilever surface, CDD simulations can supplement our conclusions about the processes within the cantilever.

(iv) The applied BV analysis is consistent with the CDD simulations which has broadened the capabilities of HR-EBSD measurements and calls for further applications on materials with more complex microstructure.

In conclusion, in the considered size regime, we provided an in-depth in situ analysis of how irreversible pileup formation leads to the development of a complex polarised dislocation microstructure during cyclic loading. This approach opens new perspectives on understanding other microscopic mechanisms during fatigue and, thus, will assist improving corresponding engineering design concepts.

the Hungarian Academy of Sciences. The authors would like to thank L. Illés for the FIB preparation of the TEM lamella. Furthermore, the financial support of this work in the context of the German Research Foundation (DFG) project SCHU 3074/3-1 is gratefully acknowledged. The simulation work was performed on the computational resource HoreKa funded by the Ministry of Science, Research and the Arts Baden-Württemberg and DFG, Germany.

Figure 1

 1 Figure 1: a) Considered system geometry and the slip planes of the FCC sample. b) Specific vectors corresponding to the slip planes and the BVs. c) The schematics highlights with blue the region on the front face of the cantilever where the shear stresses are larger than the compressive stresses.

Figure 2 :

 2 Figure 2: Experimental conditions to achieve bi-directional bending deformation. (a): The intended geometry and crystal orientation as well as the definition of the coordinate system used throughout the paper. (b): Orientation of the undeformed cantilever indicated on the inverse pole figure (IPF) triangle based on EBSD measurements. The cantilever was found to be of a single crystal with a slight 5.2 • mismatch between the actual and the preferred orientation along the z axis. (c): SEM image of the cantilever before testing. The custom made W bending tool is also shown.

Figure 3 :

 3 Figure 3: Bending stress-bending strain curve of the microcantilever. The bending experiment was performed in 6 steps, this is indicated by the different colours. HR-EBSD scans were conducted at the initial state and after each step, as indicated by the roman numerals (I)-(VII). The four sketches illustrating the state of the cantilever are to help the interpretation of the figure and the arrows represent the bending direction prior to the actual measurement. For the corresponding force-displacement curve, see Suppl.Fig. S2.

Figure 4 :

 4 Figure 4: Results of the HR-EBSD microstructural analysis for stage (VII). (a)-(c): Components of the von Mises stress tensor σ vM , rotation tensor ω 12 and the GND density ρ GND . (d)-(f) Components α i3 of the Nye dislocation density tensor. (g): Histogram of the number of dislocations N (obtained as N = ρ GND d 2 , where d is the step size of the EBSD scan) for different BV types. (h): Distribution of the dominant BVs, colours indicate the BV type, and the darkness corresponds to the GND density, as shown by the 2D colourbar. The rectangles with dashed and solid lines indicate the areas for the BV analysis and the TEM foil, respectively. (i)-(l): Insets showing the magnified views of panels (c) and (h) of the areas of the BV analysis and TEM foil.

Figure 5 :

 5 Figure 5: TEM micrographs showing the dislocation content of the region indicated with solid line in panels c) and h) of Fig. 4. a) BF in zone [001], b) BF in (220) two-beam condition.

Figure 6 :

 6 Figure 6: Evolution of the dislocation microstructure. (a) Distribution of the dominant BVs at subsequent deformation steps. Black dotted lines mark the areas where BV statistics were collected. (b) The number of dislocations N of various BV types as a function of the deformation stage.

Figure 7 :

 7 Figure 7: CDD simulation of bi-directional bending. (a): Cycle of bending moment based on the displacement driven loading and (b): resulting GND density evolution for the 12 different slip systems grouped according to Sec. 2.

Figure 8 :

 8 Figure 8: Comparison of the composition of the screw and edge dislocation density for the active slip system groups.

Figure 9 :

 9 Figure 9: Distribution of GNDs at stage 7 of the CDD simulations. (a): The spatial distribution of the GND density, (b): contour plots of the tensor components α i3 and (c): the dominant slip system groups over the cantilever beam.

Figure 10 :

 10 Figure 10: Evolution of α 13 over the loading stages 1-7.

Table 1 :

 1 Main parameters of the CDD formulation

	Parameters	Values	References
	Anisotropic	C 1111 = 168 GPa [64, 65] used in
	elastic	C 1122 = 121 GPa Eq. (5) in [46]
	constants	C 2323 = 75 GPa
	Isotropic	µ = 40 GPa	Eqs. (15) & (17)
	elastic	ν = 0.367	in [46], derived
	constants		following [66]
	BV length	b = 0.254 nm	[67]
	Drag coefficient B = 5 × 10 -5 sPa [68], [46] Eq. (14)
	Interaction	a self = 0.3	[69], [46] Eq. (17)
	matrix	a copl = 0.152
		a Hirth = 0.083
		a Lomer = 0.326
		a gliss = 0.661
		a coll = 0.578
	Backstress	D = 3.29 2π 2 (1-ν)	[58], [46] Eq. (15)
	Cross-slip	β = 10 5	[70]
	probability
	Activation	V act = 300 b 3	[71]
	volume
	Initial stress	τ III = 28 MPa	[68], [54] Eq. (20)
	for Stage III
	Dislocation	c gliss = 0.06	[72], [52] Eq. (13)
	reaction	c Lomer = 0.09
	coefficients	c coll = 0.003
	is assumed that the initial total dislocation density consist
	half of mobile and half of network dislocation density. The
	applied external load is displacement-controlled at a rate
	of | uD | = 0.1 ms -1 .

Acknowledgements

Financial support from the National Research, Development and Innovation Fund of Hungary is acknowledged under the young researchers' excellence programme NKFIH-FK-138975 (D.U., K.L., I.G. and P.D.I), under the bilateral S&T cooperation 2019-2.1.11-T ÉT-2020-00173 (D.U. and P.D.I.) and under the ÚNKP-21-4 New National Excellence Programme of the Ministry for Innovation and Technology (D.U.). S.K. was funded by the French National Research Agency (ANR) under the project No. "ANR-22-CE08-0012-01" (INSTINCT). This paper was also supported by the János Bolyai Research Scholarship (Zs.F.) of

Data availability

Experimental data related to the HR-EBSD measurements and scripts for preparing figures of the manuscript are available at https://doi.org/10.5281/zenodo.7970022.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix. Supplementary Material Supplementary Figures.

Supplementary Figures