Lorenzo Poggini
email: lorenzo.poggini@unifi.it

Giacomo Londi

Magdalena Milek

Ahmad Naïm

Peng Chen

Valeria Lanzilotto

Brunetto Cortigiani

Federica Bondino

Elena Magnano

Edwige Otero

Ahmad Naim

Philippe Sainctavit

Marie-Anne Arrio

Amelie Juhin

Matheieu Marchivie

Marat M Khusniyarov

Federico Totti
email: federico.totti@unifi.it

Patrick Rosa

Sub-monolayer deposit of photochromic Spin Crossover compound on HOPG

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

Introduction

Spin Crossover (SCO) metal complexes are among the most attractive systems as building blocks for spintronics, data storage and sensing devices. [1][2][3] These molecules may exist in two electronic states with different magnetic, optical and structural properties depending on the external stimuli (pressure, temperature, light-irradiation). [START_REF] Gütlich | Spin Crossover in Transition Metal Compounds I[END_REF][START_REF] Gütlich | Spin Crossover in Transition Metal Compounds II[END_REF] Their surface organization by sublimation processes onto different substrates, with controlled thicknesses from micrometres down to sub-monolayer coverage, is a powerful approach to investigate how SCO properties can be influenced by the environment at the nanoscale. [START_REF] Molnár | [END_REF][7][8][9][10][11][12][13][14][15][16][17][18] The retention of switching capability in molecular-inorganic architectures obtained by the regular assembling of SCO molecules on conductive surfaces is a mandatory step towards their integration in hybrid devices. In particular the possibility of obtaining bistable thin films Fe(II)-based spin-crossover materials, probably the family of most studied SCO, has been suggested by several recent reports. [19][20][21][22][23][24][25] Most of these studies highlighted that the direct molecular-substrate interaction can significantly modify the thermodynamics of the SCO equilibrium. While an HOPG (Highly Oriented Pyrolytic Graphite) supported SCO system has been reported to preserve its switching capability similarly to bulk. 23,26 On the other hand sub-monolayer deposits of several Fe(II) complexes show the "pinning"of their spin states and loss of their original SCO behaviour when evaporated on metallic surfaces. 9,12,[27][28][29] We recently reported the possibility of controlling the spin state of a thun layer of a SCO at room temperature by irradiating the sample with UV light. These results have been obtained by assembling a 5 nm thick film deposited on Au (111) of the [Fe(H2B(pz)2)2phen*] complex, 1, where pz is 1pyrazolyl and phen* is a diarylethene functionalized phenanthroline ligand (Fig. 1a). 25 This ligand allows a liganddriven light-induced spin change (LD-LISC) effect: a reversible cyclization of the photoactive diarylethene-based ligand is observed when this ligand maintain a specific conformation with the two aryl rings antiparallel (while is not occurring in the parallel configuration). 30 Here we attempted to move a step forward exploring the behavior of a sub-monolayer deposit (0.7 ML) of these molecules deposited via ultra-high vacuum (UHV) sublimation on HOPG substrates. In order to shed some light on the behavior of SCO systems deposited on surface as well as to further develop the multi-technique protocol we are adopting for the characterization of magnetic

2 | J. Name., 2012, 00, 1-3
This journal is © The Royal Society of Chemistry 20xx

Please do not adjust margins Please do not adjust margins molecules at the nanoscale [31][32][33][34] we coupled high resolution photoelectron spectroscopy (HR-XPS and HR-UPS) data a state of the art DFT-based modeling and a variable temperature X-Ray absorption spectroscopy-based characterization (XAS).

Results and discussion

A thin film of ~0.7ML of 1 was prepared under UHV condition by thermal sublimation of from crystalline material on a HOPG cleaved in air and gently heated up to 330K in UHV to remove possible adsorbates before the deposition. The integrity of the molecular switch on the surface was preliminarily verified by an XPS-based semiquantitative analysis (see Table S1). Within the limit of the XPS analysis (a 5% relative error) the experimental data resulted in line with the expected Please do not adjust margins Please do not adjust margins stoichiometry of the pristine 1 complex. In Figure 1 are reported the high resolution XPS spectra in the Fe2p and S2p regions of the sublimated sample on HOPG in function of temperature and light irradiation. As we can see in Figure 1b) the line shape of the Fe2p spectra evolves with the temperature variation and the reversible transition was observed for 1 on HOPG like reported in previous work. 25 In our case is evident by looking at the line shape of the Fe2p3/2 peak: in the partially LS configuration at 158K the Fe2p3/2 peak appears narrower than in the one at 297K; the latter features a broadening of the Fe2p3/2 peak probably due to coupling of the photoelectron with the partially-filled metal shell during the time of flight following ionization. 35 An additional fingerprint of the switching is in the spin-orbit splitting (ΔESO) of the Fe2p. Indeed, the ΔESO changes in the two configurations due to a different orbital population: in the HS configuration the measured transition involves eg orbitals that are empty in the LS one. This reversible transition can be followed using a deep peak fitting procedure has been adopted like previous reported by some of us 20,25,36 by monitoring the components (Figure 1b) at 708.9 eV and 721.3 eV that can be direct attributed to the LS species. We notice that this thermal driven process does not involve an alteration in the phen* ligand but only the iron coordination geometry, being due to the ligand field alteration causing the SCO effect. 37 This can be confirmed from the absence of a parallel evolution of the S2p signal centred at 165.0 eV in agreement with literature data. 25,[START_REF] Chastain | Handbook of x-ray photoelectron spectroscopy: a reference book of standard spectra for identification and interpretation of XPS data[END_REF]39 (Figure 1c); which is a direct proof that the phen* ligand retains its open conformation (phen*-o) during the thermal cycles we performed.

Further tests have been performed at room temperature to evaluate if this monolayer deposit of 1 can be converted at room temperature via UV irradiation analogously to a thick film. 25 From the direct comparison of the spectrum obtained a 297K after UV irradiation with those recorded at 297K in dark it is possible to point out that a no change of the line shape is occurring on the irradiated sample. The fitting of this spectra evidences that after the 282nm exposure on the submonolayer coverage there is not a transition promoted by an in situ UV light irradiation, in contrast on what was observed in solution, 37 in the crystalline phase 40 and in a thicker film of 5 nm deposited on Au (111). 25 We underlined that this room temperature irradiation is expected to promote the cyclization of the phen* ligand in 1 molecules that goes from the open conformation (phen*-o) to a closed one (phen*-c) 2540 as observed on similar diarylethene systems [41][42][43] this modification induces the SCO transition at RT. We already demonstrated that the XPS is sensitive to this cyclisation and to the corresponding SCO transition 25 however in this case any alteration in the Fe2p nor in the S2p lineshape has been observed after the UV exposure thus confirming the persistence of the open form (phen*-o) of the lignand. 25 This general behaviour is also confirmed by an UPS characterization performed on the same sample as reported in Figure S3. The spectra acquired, evidence contributions at -2.3 eV, -4.2 eV (shoulder), -6.5 eV, -9.4 eV and a very broad feature centred at -12.5 eV, in line with literature reports systems. 16,17,25,28 The temperature effect on the UPS spectra is visible mainly in the valence-Fermi region at -2.3 eV and at -9.4 eV in the semi-core region. However, the presence of a strong huge in the semicore (B) region of the spectra suggests that at 90 K a small HS component is still present. Upon UV irradiation, no significant energy shift is observed for the band at -2.3eV compared to the one observed at 297K, in contrast to what seen for similar diarylethene system 44,45 and for the same complex on thick film on gold. 25 The UPS spectra support what observed with XPS spectra in the Fe2p region demonstrating that in this particular case after the UV exposure no ligand cyclization occur for the diarylethene ligand. When the thermal switching occurs, a variation in the lineshape is observed in line with previous reports 17,25,28 however no quantitative hints can be easily extracted. In order to follow the thermal transition at the nanoscale, we also performed an XAS characterization. Synchrotron-based absorption techniques are unmatched tools to analyse submonolayer deposits of bistable molecular systems, providing the required sensitivity to monitor the oxidation state, 31 the spin states 8,23,31 and molecular orientation on surfaces. 46,47 Figure 2 displays the temperature evolution of the absorption spectrum at L2,3 edges of Fe of a monolayer of 1 in the 75-300 K temperature range (while data taken at additional temperatures are reported in Fig. S1 a). We have estimated the molar fraction of the HS species by fitting the experimental XAS spectra as described in the method section achieving the plot reported in Figure 3b. It can be noticed that 1 shows a spin-transition between 75 and 300 K Please do not adjust margins Please do not adjust margins (T1/2 = 160 + 15 K), reversible upon subsequent thermal treatments, and slightly shifted with respect to the SCO behaviour of the bulk crystalline compound 37 (T1/2 = 135+ 8 K) due to a more gradual SCO thermal driven transition. Although the soft X-ray induced excited spin state trapping (SOXIESST) 8,36 and the Light-Induced Excited State Trapping LIESST [START_REF] Gütlich | Spin Crossover in Transition Metal Compounds I[END_REF][START_REF] Gütlich | Spin Crossover in Transition Metal Compounds II[END_REF] effect can be observed irradiating the sample at 10K with a laser of 660 nm wavelength, the LS-HS conversion at low temperature is evident and although X-rays induce partial conversion also in this condition of low photon flux (Fig. 2c).

Both the XPS and XAS measurements at RT confirm the coexistence of LS and HS forms in the monolayer deposit, XAS suggests that the HS fraction can be estimated in about 0.87+ 4, deviating from what observed on the thicker film (4nm deposit on HOPG) where the HS fraction was 0.98+ 3.(See fig. S1 b andc). Upon cooling from 300 to 75 K the spectral features related to the LS-Fe(II) gain intensity as expected while the signal coming from the HS-Fe(II) one weakens; moreover, heating the sample back to 300 K the initial spectral line shape is restored confirming the perfect reversibility of the process. In Fig. S2 is reported the FeL3 of 0.7ML of 1 on HOPG irradiated with UV wavelength (282 nm) for 12 ours, compared with the one non-irradiated; thanks to the leastsquares interpolation employed to fit the XAS data, was possible to point out that the irradiation does not influence the spin state of the system at this coverage and on HOPG, in contradiction on what some of us reported in ref. 25 on a thicker film on Au (111).

Our analysis points out that in the submonolayer deposit it is possible to quantitatively measure the thermal switchability of 1 that is comparable with what observed on thicker sample (Fig S1). However, as evident in Fig 2c both entropy and enthalpy contributions in the ML regime results altered in respect to the bulk behaviour and this could be due to an interaction with the surface. Similar effects have been observed also in bulk samples and peculiar roles are played by dilution and by crystal packing. [48][49][50] To shed some light on the absence of the diarylethene ligand cyclization upon UV irradiation when these molecules are adsorbed on HOPG we modeled the interaction of 1 with HOPG at the periodic DFT level (see DFT calculations section). We calculated four possible scenario considering the two conformer of the ligand with the arylethene rings parallel (par) and antiparallel (anti) and we included the structural effect due to the two possible spin states of Fe(II), LS and HS. The following four geometries have been optimized: 1-anti-LS, 1par-LS, 1-anti-HS and 1-par-HS. This optimization has been carried out placing the molecules on an optimized HOPG substrate[?] starting from a guess structure where the hydrogen atom of the pyrazolyl group pointing towards the surface was set at 2 Å distance from the surface and with the phenanthroline group almost parallel to the latter. According to the crystalline structure of 1 (see ESI Table S2) the geometrical environment of the iron center was conserved throughout the optimization process for all the conformers, suggesting that the deposition process on HOPG has only negligible effects on the metal ligand field. However, depending on the conformers, the thiophene groups of the diarylethene moiety rearranged their orientation (see dihedral angles, θ, in Table S1) differently. Indeed, while for 1-anti conformers the rotation of both thiophenes is substantially inhibited by the steric hindrance induced by their methyl groups, a thiophene group can rotate up to be almost parallel to the surface in the case of the 1-par conformers (see Figure 4 and Table S2). Such a rotation allows a stronger interaction of the complex with the surface and, indeed, both the phenanthroline ligand and the iron ion get closer to it with respect to the 1-anti conformers. In the light of such results, quite different absorption enthalpy, Δ𝐻 #$% &' , values are, therefore, expected for the 1-par and 1-anti conformers. The absorption enthalpy for each SCO conformer was calculated as:

Δ𝐻 #$% &' = 𝐻 )*+@-+./ &' -(𝐻 -+./ &' + 𝐻 )*+ &' ) eq.1
where

𝐻 )*+@-+./ &'
is the electronic enthalpy of the SCO adsorbed on the HOPG surface system, while 𝐻 -+./ &' and 𝐻 )*+ &' stand for the electronic enthalpy of the isolated species (see DFT calculations section).

Data reported in Table 1 clearly show that the most energetically stable conformers adsorbed on HOPG are the parallel ones with a gain for Δ𝐻 #$% &' of more than 11 kcal mol -1 with respect to Please do not adjust margins Please do not adjust margins antiparallel ones. Such result can be rationalized on the basis of the conformational rearrangements which stabilize the interaction between the HOPG surface and the SCO π electron rich periphery, i.e. the phenanthroline and the thiophene groups. Since the photoinduced mechanism occurs exclusively for the antiparallel conformers according to the Woodward-Hoffman's rules, a preferential energy-driven room temperature deposition on HOPG would lead to a preferential formation of a ML of 1-par-HS, so preventing the photocyclization and, consequently, the spin state switching from HS to LS. As a side remark, we also highlight that the LS conformers are still more stable, as expected, than their HS counterparts (0.47 and 0.93 kcal mol -1 for the parallel and the antiparallel conformers, respectively). Density of states (DOS) were computed for both the LS and HS species in their extrapolated scenario (see DFT calculations section) and reported in Figure S3 for the 1-par conformer (the 1-anti is superimposable). The overall density profile maintains all the features present in the bulk DOS for both the LS and HS species, especially for the A fingerprint valence region. 25 This outcome shows that the adsorption process does not produce severe changes in the whole structure, and, above all, in the sensitive iron ion ligand field but perfectly explain the origin of the quenching of switching capabilities at room temperature for this complex.

ΔH #$% &' (kcal mol -1 ) ΔH #$% &' (kcal mol -1 )

Conclusions

Spin-crossover molecular switch featuring a photoactive diarylethene-based ligand was successfully evaporated in ultrahigh vacuum to form a sub-monolayer on HOPG. The integrity of the complex was confirmed by HR-XPS and by XAS and DFT calculations flanked by UPS experiments explained the quenching of the switching capability of the system via UV irradiation at room temperature evidencing that the HOPG substrate stabilises the conformer of the dithienylethene ligand that cannot permit the cyclization process. On the other hand, thermally induced reversible switching has been demonstrated and the retention at cryogenic temperatures of the TLIEEST effect of these monolayer has been confirmed. Thus, this work at the same time opens new horizons for controlling magnetic properties of materials at the nanoscale down to the sub monolayer level and alert the community on the peculiar role that specific interaction with the substrate may play when dealing with multifunctional molecular systems.

Experimental

Monolayer preparation. sub-Monolayers of the [Fe(bpz)2phen*] was prepared by thermal evaporation in UHV by heating the powder with an in-house cell. Sublimation was carried out using a resistively heated quartz crucible in UHV (P < 5 × 10 -9 mbar) and the nominal thickness of the molecular films was measured by oscillating quartz microbalance. Before deposition, the crucible with solid was held at the sublimation temperature, i. e. ~ 430 K, for several hours to remove lattice solvent and any volatile contaminant. The SCO molecules were then deposited on fresh cleaved HOPG held at room temperature, by using a deposition rate of about 0.15 Å/min. HR-XPS, HR-UPS measures. XPS and UPS experiments were performed at the BACH beamline in Elettra the Italian Synchrotron Radiation Facility in Trieste. All the experiments were carried out in a UHV chamber apparatus consisting of one chamber with a base pressure in the low end of the 10 -9 mbar range, using synchrotron light as X-ray source (1077.86 eV and 46eV for XPS and UPS respectively) and hemispherical analyser by VG Scienta R3000 analyser mounting a 2Ddetector. The X-ray source is at 54.44° with respect to the analyser. XPS and UPS spectra were measured at normal emission with a fixed pass energy of 200 eV. The XPS binding energy (BE) scale was calibrated setting the C1s photoemission peak of the HOPG single crystal slab at 284.6 eV. 51 The UPS energy (E-EF) scale was calibrated subtracting both the energy used and the sample work function (obtained from XPS). In the XPS the intensity of the signal for each element corresponds to the area of the peak, calculated by standard deconvolution using for each component a mixed Gaussian (G) and Lorentzian (L) line-shapes (ratio G= 70% L= 30%) and subtracting the inelastic background by means of the linear background. The stoichiometry was calculated by peak integration, using reported cross-section in literature. 52 XAS characterization. XAS spectra have been acquired at the DEIMOS beamline of the SOLEIL Synchrotron Radiation Facility in Paris, France on a UHV compatible pumped 4He cryomagnet. All the samples have been inserted into the Cromag working in the 8-300 K range and equipped with optical windows for sample irradiation with both an X-ray beam and a 660 nm diode. Absorption spectra were measured in Total Electron Yield (TEY) detection mode to guarantee the optimal detection sensitivity. All the characterisations were performed using a low density of photons in order to avoid radiation damages. Estimation of the temperature dependence of the hs-Fe(II) molar fraction of the submonolayer coverage was performed through least-squares interpolation of its normalized L3 XAS spectra with the ones of similar [Fe(bpz)2phen] 8 complexes, featuring temperature dependent as recorded in similar experimental conditions. The photon flux per second of the 660nm laser was 10mW/cm 2 on the sample. The UV irradiation of the film was performed in situ This journal is © The Royal Society of Chemistry 20xx

Please do not adjust margins Please do not adjust margins using a deuterium lamp (20 W) equipped with a bandpass filter (282 + 5 nm).

DFT Calculations. All the calculations were performed with CP2K 5.1 suite package 53 within the DFT framework, 54,55 using a GGA revised PBE 56 exchange-correlation functional. Nonlocal functional corrections were added in order to account for the long-range dispersion van der Waals interactions (rVV10). 57 DZVP-MOLOPT-SR (double-ζ polarized molecularly optimized at short range) basis sets were chosen for all the atomic species along with normconserving Goedecker-Teter-Hutter (GTH) pseudopotentials. 57 A large energy cut-off of 550 Ry was applied to the plane-wave basis set. The HOPG (001) surface were "standalone" optimized as a four-layer slabs, each layer consisting of 288 carbon atoms, according to the graphite ABAB crystalline structure. The size of the hexagonal simulation cell were set to (29.568 x 29.568 x 60.000) Å 3 . Periodic boundary conditions were applied in the three directions, but a large vacuum space along z was taken into account to avoid spurious interactions between replicas. After the surface optimization, the interlayer AA and BB distances were 6.865 and 6.867Å, respectively. During the optimizations, the HOPG bottom layer was kept fixed to bulk positions while the topmost ones were left free to relax in order to reproduce their surface-like behavior. Geometry optimizations were performed using the BFGS algorithm and a convergence accuracy on nuclear forces of 4.5×10 -5 Hartree Bohr -1 . A convergence threshold criterion on the maximum gradient of the wavefunction in the SCF procedure of 3×10 -6 Hartree was used applying a Fermi-Dirac distribution with a broadening (electronic temperature) of 2500 K in order to facilitate the convergence. The Density of States (DOS) for each conformer extrapolated from the 1@HOPG optimized scenario were computed by performing single point calculations using a "revised" B3LYP functional, which includes an amount of 15% of the Hartree-Fock exchange, instead of the ordinary 20%. The computed DOS were convoluted with Gaussian functions with a full width half-maximum (FWHM, σ) of 0.6eV.

Figure 1 .

 1 Figure 1. Temperature dependence of the Fe2p a) and S2p b) peaks for the thick film of 1 evidencing the reversibility of the SCO behavior in function of the temperature; bottom, spectral components employed for the least squares fitting of the Fe2p XPS Binding energies (B.E.). The integrated areas is reported like percentages of each component. In brackets are reported the DESO splitting. (dark blue, blue, orange, red and cyan are respectively 158, 192, 245, 297 and 297K after 282 nm exposure).

Figure 2 .

 2 Figure 2. (a) Temperature evolution of the normalised FeL2,3 edge XAS spectra of a monolayer of 1 (empty black dots) along with high-spin Fe(II) and low-spin Fe (II) spectra (red line and blue, respectively) used as reference signals for the spectral deconvolution (green lines). Broken lines are guides to the eye. (b and c) high-spin Fe (II) thermal distribution profile (empty circles) obtained from XAS spectra taken before (b) and after (c) laser light irradiation at 4 K. In b) the red line is the fit of empty black dots by a Boltzman distribution, giving a T1/2=160+15 K. Bulk rescaled data are reported as wide coloured bands for comparison.

Figure 3 .

 3 Figure 3. Superimposed computed geometries for 1-par-LS (pink carbon atoms), 1-par-HS (green carbon atoms), 1-anti-LS (cyan carbon atoms), and 1-anti-HS (brown carbon atoms). Rust color is used for the iron ion, while hydrogen, sulphur and nitrogen atoms are white, yellow and blue, respectively.

This journal is © The Royal Society of Chemistry 20xx J. Name., 2013, 00, 1-3 | 3

Acknowledgements

The acknowledgements come at the end of an article after the conclusions and before the notes and references.


Catherine Combellas

Frederic Kanoufi

Fetah Jean Pinson

Frédéric Kanoufi

Fetah I Podvorica
email: fetah.podvorica@uni-pr.edu

Indirect electrografting of aryl iodides

Keywords:

published or not. The documents may come

Introduction

Many electro or photografting reactions rely on radicals that are obtained by cleavage of weak bonds, either thermally with peroxides [START_REF] Goddard | Polymer surface modification for the attachment of bioactive compounds[END_REF] (eOeO-bonds, ~40 kcal mol -1 [START_REF]Internet Bond-energy Databank (pKa and BDE)-iBonD Home Page[END_REF]), electrochemically with diazoniums [START_REF] Berisha | Electrode surface modification using diazonium salts[END_REF] (Ar-N ≡ N + , ~38.5 kcal mol -1 [START_REF] Jiang | Structure and bonding between an aryl group and metal surfaces[END_REF][START_REF] Berisha | Some theoretical and experimental insights on the mechanistic routes leading to the spontaneous grafting of gold surfaces by diazonium salts[END_REF]), photochemically with azides [START_REF] Liu | A general approach to the covalent immobilization of single polymers[END_REF] (Ar-N = N + = N -, ~37 kcal mol -1 [START_REF]Internet Bond-energy Databank (pKa and BDE)-iBonD Home Page[END_REF]). The bond dissociation energy (BDE) of alkyl and aryl iodides is somewhat higher (n-Bu-I, ~56 kcal mol -1 , Ph-I, ~65 kcal mol -1 [START_REF]Internet Bond-energy Databank (pKa and BDE)-iBonD Home Page[END_REF]) and their reduction takes place at quite negative potentials (-2.3 V/SCE for n-Hex-I [START_REF] Chehimi | Electro-and photografting of carbon or metal surfaces by alkyl groups[END_REF], -2.2 V/SCE for Ph-I [START_REF] Koefoed | Covalent modification of glassy carbon surfaces by electrochemical grafting of aryl iodides[END_REF]).

However, alkyliodides can be grafted at their reduction potential on GC, Au, Cu, Fe [START_REF] Chehimi | Electro-and photografting of carbon or metal surfaces by alkyl groups[END_REF] and Al [START_REF] Fogliazza | Powerful surface chemistry approach for the grafting of alkyl multilayers on aluminum nanoparticles[END_REF] and also at much more positive potential using a crossover reaction where the 2,6-dimethylphenyl radical (derived from 2,6-dimethylbenzenediazonium, 2,6-DMBD) cannot react with surfaces due to steric hindrance. Instead it abstracts an iodine atom from the alkyliodide to give an alkyl radical (Scheme 1, R1), which finally binds to the surface. As 2,6-DMBD is reduced at much more positive potential than alkyl iodides or alkylbromides, a potential gain of ~1.7 V and ~2.35 V was attained in the case of I(CH 2 ) 2 C 6 F 13 [START_REF] Hetemi | Electrografting of alkyl films at low driving force by diverting the reactivity of aryl radicals derived from diazonium salts[END_REF] and 6-bromohexanoic acid, respectively [START_REF] Hetemi | Surface functionalization of metals by alkyl chains through a radical crossover reaction[END_REF].

Since the BDE of iodobenzene is higher than that of alkyliodides ( [START_REF]Internet Bond-energy Databank (pKa and BDE)-iBonD Home Page[END_REF]), the formation of the phenyl radical from iodobenzene and therefore the grafting should be more difficult (Scheme 1, R2). However, when heating bis(p-chlorobenzoyl)peroxide in the presence of iodobenzene in a benzene solution, 4-chloroiodobenzene was obtained, testifying for an iodine atom abstraction [START_REF] Bunnett | Radical abstraction of iodine from aryl iodides[END_REF]. Since i) 1-iodo-2,6-dimethylbenzene is sterically hindered, and ii) the buttressing effect of two methyl groups is 1.46 kcal mol -1 [START_REF] Hetemi | Electrografting of alkyl films at low driving force by diverting the reactivity of aryl radicals derived from diazonium salts[END_REF][START_REF] Branchi | A radical and an electron transfer process are compared in their regioselectivities towards a molecule with two different C-I bonds: effect of steric congestion[END_REF], R2 should be endothermic by this value. As the entropy variation should be small for R2, R2 should be slightly endergonic.

The experiments described thereafter starting from different aryliodides demonstrate that R2 is possible.

Results and discussion

4-Iodonitrobenzene

The voltammogram of 4-iodonitrobenzene in DMF at a Pt electrode presents two close waves at ~-1.07 and -1.11 V/SCE. The first irreversible one corresponds to the transfer of 1 e -; it becomes reversible upon increasing the scan rate to 10 Vs -1 . The second one pertains to nitrobenzene that is formed through an H-atom transfer. Based on these data the following ECE mechanism [START_REF] Savéant | Single electron advances in physical chemistry transfer and nucleophilic substitution[END_REF] was proposed [START_REF] Lawless | Mechanistic studies of the decomposition of halonitrobenzene anion radicals[END_REF][START_REF] Bartak | The coupling of nitrophenyl radicals and anions to form anion radicals[END_REF][START_REF] Nelson | Cathodic reduction pathways of haloaromatics, III. Halonitrobenzenes[END_REF][START_REF] Teherani | Electrochemistry in liquid ammonia. VII. Halonitrobenzenes[END_REF][START_REF] Compton | Photoelectrochemical dehalogenation of p-halo-nitrobenzenes[END_REF][START_REF] Gallardo | Electrochemically promoted arylation of iodoaromatics[END_REF] with a slow cleavage of the radical anion: k = 1.1 s -1 [START_REF] Compton | Photoelectrochemical dehalogenation of p-halo-nitrobenzenes[END_REF]:

Upon repetitive scanning (up to 100 cycles) from -0.4 to -1.4 V/ SCE in acetonitrile, the voltammogram of 4-iodonitrobenzene on various electrodes (Au, Pt, GC) remains stable and does not indicate significant grafting. This was confirmed by IRRAS: under the above conditions, a gold plate does not present the strong characteristic signals of the NO 2 group. This is due to the slow cleavage of the radical anion (Scheme 2, R2); the nitrophenyl radical that should be responsible for the grafting of 4-nitrobenzenediazonium is formed in solution and trapped by the solvent (Scheme 2, R3) before diffusing back to the electrode. Note that 4-bromonitrobenzene that cleaves somewhat faster [START_REF] Compton | Photoelectrochemical dehalogenation of p-halo-nitrobenzenes[END_REF] can be electrografted [START_REF] Koefoed | Covalent modification of glassy carbon surfaces by electrochemical grafting of aryl iodides[END_REF]. Therefore, it is not possible to graft directly 4-iodonitrobenzene onto metals.

But if 2,6-DMBD is reduced (Ep red = -0.28 V/SCE) in the presence of 4-iodonitrobenzene, its reduction wave decreases upon repetitive scanning (Fig. 1A). After rinsing the electrode under sonication and transfer to an ACN + 0.1 M NBu 4 BF 4 solution, the characteristic reversible signal of nitrobenzene is observed at E°= -1.10 V/SCE (Fig. 1B). The indirect electrografting of the nitrophenyl group is confirmed by a redox probe experiment, IRRAS and XPS. The reversible voltammogram of Fe(CN) 6 3+ /Fe(CN) 6

2+ nearly disappears on the modified electrode (Fig. 1C). The IRRAS spectrum of the modified electrode presents two stretching vibrations of the nitrophenyl group at 1350 and 1525 cm -1 (Fig. 1D). The XPS spectrum (not shown) presents a N1s signal (7.3%) with a contribution of the nitrophenyl group at 406 eV (3%) and no iodine signal in the 620-635 eV region; the spectrum of a blank sample obtained in the absence of 2,6-DMBD does not show the latter peak but a N1s peak at 400 eV (1.3%), likely due to some contamination. The surface concentration of the modified electrode was obtained by integration of the voltammogram of the grafted nitrophenyl group (Fig. 1B): Γ = 5.4 × 10 -9 mol.cm -2 that corresponds to a film thicker than a monolayer [START_REF] Brooksby | Electrochemical and atomic force microscopy study of carbon surface modification via diazonium reduction in aqueous and acetonitrile solutions[END_REF]; it agrees with the thickness of the film measured by ellipsometry as 7.9 ± 2 nm. However, thinner layers (1.4 nm) are obtained through a single voltammetric cycle.

This indirect method should apply to all aromatic derivatives that cleave slowly to a radical upon electron transfer (DISP situation). Let us mention, for example, 4-nitrophenyl-tert-butylazosulfide (Ep red = -0.95 V/SCE, k = 4.1 × 10 -2 s -1 ) that cleaves slowly to a radical that does not react with the electrode [START_REF] Guiriec | Isomerization of azo compounds. Cleavage recombination mechanism of azosulfides[END_REF].

5-Iodo-2-aminopyridine

Diazopyridinium salts are highly unstable (their unstability decreases from 3 to 4 to 2-diazopyridinium) and must therefore be prepared in situ by diazotation of the corresponding aminopyridine Scheme 1. Iodine exchange between an aryl radical and an alkyl or aryl iodide. Scheme 2. Electrochemical reduction of 4-iodonitrobenzene [START_REF] Compton | Photoelectrochemical dehalogenation of p-halo-nitrobenzenes[END_REF]. [ [START_REF] Agullo | Formation and reactivity of 3-diazopyridinium cations and influence on their reductive electrografting on glassy carbon[END_REF][START_REF] Smida | Reductive electrografting of in situ produced diazopyridinium cations: tailoring the interface between carbon electrodes and electroactive bacterial films[END_REF], which mainly leads to the corresponding hydroxypyridine. However, electrografting is possible starting from iodonium or iodo derivatives [START_REF] Sommerfeldt | Electrochemical grafting of heterocyclic molecules on glassy carbon and platinum using heteroaromatic iodonium salts or iodo-substituted heteroaromatics[END_REF]. We have tried to graft pyridyl radicals starting from an iodo derivative rather than from a diazonium salt.

Fig. 2A presents, on the same potential scale, the voltammograms of 2,6-DMBD (Ep red = -0.28 V/SCE, Fig. 2Aa) and 5-iodo-2-aminopyridine (Ep red = -2.43 V/SCE, Fig. 2Ab) recorded separately. The peak potentials difference is ΔEp = 2.15 V. When both compounds are present in the same solution and the potential of an Au electrode is scanned repetitively between 0.3 and -0.5 V/SCE, the voltammogram decreases steadily (Fig. 2B), pointing to a grafting reaction. This reaction is confirmed by i) a redox probe experiment, ii) the IR spectrum of a modified Au plate that presents four characteristic peaks at 1676, 1658, 1475 and 1380 cm -1 (to compare with 1637, 1582, 1478, 1378 cm -1 for 5-iodo-2-aminopyridine) and iii) the XPS spectrum that presents a N1s peak at 400 eV (9.3%, to compare with 3.2% in the absence of 2,6-DMBD, already present on the untreated Au wafer), and a small amount of iodine at 619 eV (0.24%, already present on the untreated Au wafer), and iv) the thickness of the film:10.3 ± 5 nm.

4-Iodoaniline

4-Iodoaniline is reduced at Ep red = -2.0 V/SCE on Au and at a similar potential on GC with a very spread out wave. Fig. 3A,B presents the voltammograms of 2,6-DMBD in the presence of 4-iodoaniline on Au and GC electrodes. On both substrates a fast decrease of the voltammogram is attributed to the grafting of the 4-aminophenyl radical, indicating the grafting of the phenyl group. This is confirmed by the IR and XPS spectra on Au plate after only two scans that present the characteristic signals of the attached aniline groups: by IR 3367, 3236, 1600, 1513, 1281 cm -1 (by comparison: 3432, 3358, 1614, 1497, 1275 cm -1 for aniline); by XPS: N1s signal at 400 eV, (6.7%) and a small amount of iodine at 619 eV (0.29%); in the absence of 2,6-DMBD only 3.7% N1s and 2.5% iodine at 619 eV (the presence of iodine is due, as above, to the Au wafer and also to a photochemical reaction under the cool white light of the laboratory that does not occur in the presence of 2,6-DMBD). The thickness of the film measured by ellipsometry is 6.7 ± 3.0 nm.

Iodobenzene

Its reduction on GC at Ep red = -2.23 V/SCE involves a two-electron irreversible wave corresponding to the formation of the aromatic anion that cleaves to iodine and benzene (after protonation) [START_REF] Pause | Can single-electron transfer break an aromatic carbon-heteroatom bond in one step? A novel example of transition between stepwise and concerted mechanisms in the reduction of aromatic iodides[END_REF]. However, after 100 cycles its reduction peak decreases and the grafting of phenyl groups is observed on the GC surface [START_REF] Koefoed | Covalent modification of glassy carbon surfaces by electrochemical grafting of aryl iodides[END_REF]. Considering such a difficult grafting, the indirect approach described herein should be an efficient alternative.

When iodobenzene is grafted on gold through an iodine abstraction from the 2-dimethylphenyl radical as above, the presence of phenyl groups is attested by a weak IR-ATR spectrum with aromatic bands at 1558, 1487 and 1427 cm -1 (by comparison 1570, 1471 and 1438 cm -1 for iodobenzene), these bands are not observed when the same reaction is performed in the absence of 2,6-DMBD. The thickness of the film measured by ellipsometry is 8.5 ± 4.6 nm. Therefore reaction R2 in Scheme 1 is possible in spite of its small calculated endergonicity, likely because the reaction is equilibrated and the driving force provided by the irreversible grafting reaction (ΔH = -38.5 kcal.mol -1 ) [START_REF] Berisha | Some theoretical and experimental insights on the mechanistic routes leading to the spontaneous grafting of gold surfaces by diazonium salts[END_REF].

Conclusions

The indirect electrografting of aromatic iodides owing to the 2-dimethylphenyl radical provides a valuable option when the direct grafting i) is not possible (4-iodonitrobenzene), or ii) occurs inefficiently at very negative potentials (5-iodo-2-aminopyridine, iodoaniline, iodobenzene). This reaction can also be an alternative to the grafting of diazonium salts when the latter are highly unstable or too difficult to prepare.

Fig. 1 .

 1 Fig. 1. A-C) Cyclic voltammetry on A) Au electrode (1 mm diameter, 0.1 V.s -1 ) in ACN + 0.1M NBu 4 BF 4 of 2,6-DMBD (10 mM) in the presence of 4-iodonitrobenzene (12 mM), a) first and b) second cycle; Ac) 4-iodonitrobenzene (12 mM) without 2,6-DMBD; B) Au electrode modified by 4-nitrophenyl groups; C) redox probe experiment, Ca) 2 mM K 3 [Fe(CN) 6 ] + 0.1 M LiClO 4 on a bare Au electrode and Cb) on the same modified electrode as in B); D) IRRAS spectrum of Da) Au plate modified as in B) and Db) Au plate treated with 4-iodonitrobenzene in the absence of 2,6-DMBD.

Fig. 2 .

 2 Fig. 2. A, B) Cyclic voltammetry on Au electrode (1 mm diameter, 0.1 V.s -1 ) of Aa) 2,6-DMBD (10 mM), Ab) 5-iodo-2-aminopyridine (20 mM) (recorded separately and presented on the same scale, currents are not on scale), B) DMBD in the presence of 5-iodo-2-aminopyridine (10 and 20 mM, respectively), a) first and b) second cycle and Bc) 5-iodo-2-aminopyridine (20 mM) without 2,6-DMBD. C,D) IRRAS and high resolution XPS spectrum, N1 s contribution of Ca, D) Au plate grafted by 5iodo-2-aminopyridine (20 mM) in the presence of 2,6-DMBD (10 mM); Cb) blank spectrum in the absence of 2,6-DMBD.

Fig. 3 .

 3 Fig. 3. Cyclic voltammetry on A) Au and B) GC electrodes (1 mm diameter, 0.1 V.s -1 ): a) 1st and b) 2nd scan in ACN + 0.1 M NBu 4 BF 4 + 10 mM 2,6-DMBD +20 mM IC 6 H 4 NH 2 and c) in the absence of 2,6-DMBD. Ca, D) Au plate grafted by 5-iodo-2-aminopyridine (20 mM) in the presence of 2,6-DMBD (10 mM). Ca) IRRAS spectrum, D) high resolution XPS spectrum, N1 s contribution. Cb) blank spectrum in the absence of 2,6-DMBD.

Acknowledgments

CNRS, Paris Diderot University, ANR (Agence Nationale de la Recherche) and CGI (Commissariat à l'Investissement d'Avenir) are gratefully acknowledged for their financial support through Labex SEAM (Science and Engineering for Advanced Materials and devices) ANR 11 LABX 086, ANR 11 IDEX 05 02. Dr. P. Decorse is gratefully acknowledged for XPS analyses.


Mohamed Bettayeb

Vincent Maurice
email: vincent.maurice@chimie-paristech.fr

Lorena H Klein

Linsey Lapeire

Kim Verbeken

Philippe Marcus
email: philippe.marcus@chimie-paristech.fr

Combined in situ microstructural study

Keywords: Copper, Electrochemical STM, EBSD, Grain boundary, Structure, Passivation

Introduction

Intergranular corrosion is a major form of localized corrosion limiting the durability of polycrystalline metallic materials. In aggressive environment, the corrosive attack of the grain boundary (GB) network is first initiated at the topmost surface and then can penetrate and propagate in the sub-surface, leading to degradation of the microstructure. The resistance to intergranular corrosion can be improved by GB engineering that aims at designing and producing polycrystalline materials, including micro and nanocrystalline metals, with the most resistive GB network. This requires a good knowledge of the relationships between GB type and structure and corrosion resistance that is most often developed by performing micrographic and microscopic characterizations of GB engineered materials submitted to intergranular subsurface penetrating attack . From such studies, coherent twin boundaries are considered as most resistant to intergranular corrosion [START_REF] Vinogradov | On the Corrosion Behaviour of Ultra-Fine Grain Copper[END_REF][START_REF] Cl Changliang | Improving the intergranular corrosion resistance of 304 stainless steel by grain boundary network control[END_REF]. Coherent twin boundaries are CSL (Coincidence Site Lattice) boundaries with a {111}-oriented GB plane and of 3 index, meaning that 1/3 of the lattice sites in the GB plane coincide with the lattice sites of the two grains. Among the low  CSL boundaries, only the 3 boundaries and partially the Σ9 boundaries have been reported to better resist to intergranular corrosion [START_REF] Kim | Grain Boundary Character Distribution and Intergranular Corrosion Behavior in High Purity Aluminum[END_REF][START_REF] Lehockey | On the relationship between grain boundary connectivity, coincident site lattice boundaries, and intergranular stress corrosion cracking[END_REF][START_REF] Ralston | Effect of Grain Size on Corrosion: A Review[END_REF][START_REF] Cl Changliang | Improving the intergranular corrosion resistance of 304 stainless steel by grain boundary network control[END_REF][START_REF] Kumar | Methods for making alloy 600 resistant to sensitization and intergranular corrosion[END_REF]. Higher  CSL boundaries and random boundaries, that cannot be described by a coincidence site lattice, are high angle boundaries that do not resist intergranular sub-surface attack [START_REF] Lin | Influence of Grain Boundary Character Distribution on Sensitization and Intergranular Corrosion of Alloy 600[END_REF][START_REF] Kim | Grain Boundary Character Distribution and Intergranular Corrosion Behavior in High Purity Aluminum[END_REF][START_REF] Shimada | Optimization of grain boundary character distribution for intergranular corrosion resistant 304 stainless steel by twininduced grain boundary engineering[END_REF][START_REF] Xia | Effect of single-step strain and annealing on grain boundary character distribution and intergranular corrosion in Alloy 690[END_REF][START_REF] Ralston | Effect of Grain Size on Corrosion: A Review[END_REF][START_REF] Jones | Sensitisation behaviour of grain boundary engineered austenitic stainless steel[END_REF][START_REF] Cl Changliang | Improving the intergranular corrosion resistance of 304 stainless steel by grain boundary network control[END_REF][START_REF] Kumar | Methods for making alloy 600 resistant to sensitization and intergranular corrosion[END_REF].

The relationships between the local structure at the surface termination of the grains boundaries and the resistance in the initial stages of intergranular corrosion, i.e. before penetration and propagation in the sub-surface region, have been much less studied. This is due to the difficulty of applying analytical methods sensitive to the electrochemically-induced local alterations of the topmost surface. Recently, ECSTM (Electro-Chemical Scanning Tunneling Microscopy) has been applied to microcrystalline copper to investigate in situ the local corrosion resistance at the surface termination of grain boundaries in metals [START_REF] Martinez-Lombardia | In Situ Scanning Tunneling Microscopy Study of the Intergranular Corrosion of Copper[END_REF][START_REF] Martinez-Lombardia | In Situ Scanning Tunneling Microscopy Study of Grain-Dependent Corrosion on Microcrystalline Copper[END_REF][START_REF] Chen | Grain Boundary Passivation Studied by In Situ Scanning Tunneling Microscopy on Microcrystalline Copper[END_REF][START_REF] Chen | Local passivation of metals at grain boundaries: In situ scanning tunneling microscopy study on copper[END_REF][START_REF] Bettayeb | Nanoscale Intergranular Corrosion and Relation With Grain Boundary Character as Studied In Situ on Copper[END_REF]. It was found that dissolution in the active state, i.e. in the absence of formation of a passive film, did not occur at the GB edges assigned to coherent twin boundaries whereas it did at GB edges assigned to other CSL boundaries or to random boundaries in the same conditions of early corrosive attack [START_REF] Martinez-Lombardia | In Situ Scanning Tunneling Microscopy Study of the Intergranular Corrosion of Copper[END_REF]. Very recently, a deeper insight into the GB behavior in the very first stages of active dissolution was brought using an innovative approach combining analysis of the same local microstructural region by ECSTM and EBSD (Electron Back-Scatter Diffraction) [START_REF] Bettayeb | Nanoscale Intergranular Corrosion and Relation With Grain Boundary Character as Studied In Situ on Copper[END_REF]. Random high angle boundaries as well as 9 CSL boundaries were found susceptible to the initiation of intergranular corrosion in conditions where quantities not exceeding a few equivalent monolayers of material were dissolving. For the 3 CSL boundaries the behavior was found dependent on the deviation angle of the GB plane from the exact {111} orientation with a transition from resistance to susceptibility occurring between 1° and 1.7° of deviation.

ECSTM was also applied on microcrystalline copper to investigate the local passivation properties at the surface termination of grains boundaries and their relation with the GB type [START_REF] Chen | Grain Boundary Passivation Studied by In Situ Scanning Tunneling Microscopy on Microcrystalline Copper[END_REF][START_REF] Chen | Local passivation of metals at grain boundaries: In situ scanning tunneling microscopy study on copper[END_REF]. The passive film formed in the Cu(I) passivation region was found to be thicker at grain boundaries than on grains and a thicker Cu(I) passive film was observed at GB edges assigned to random grain boundaries than at GB edges assigned to coherent twins [START_REF] Chen | Local passivation of metals at grain boundaries: In situ scanning tunneling microscopy study on copper[END_REF]. No metal was observed to be preferentially consumed at GB edges by transient dissolution during Cu(I) passivation. However, the relationship between local passivation behavior and GB structure could not be investigated in further detail because of the lack of detailed characterization of the GB crystallographic parameters at the local sites where passivation could be analyzed at the nanoscale by ECSTM.

Here, we report further insight into the comprehensive knowledge of the GB structuredependent passivation behavior of metals. The study was performed on microcrystalline copper passivated in the anodic oxidation range where a single Cu(I)2O oxide film is formed, as shown by ex situ [START_REF] Strehblow | The Investigation of the Passive Behaviour of Copper in Weakly Acid and Alkaline Solutions and the Examination of the Passive Film by Esca and ISS[END_REF][START_REF] Sander | In Situ Photoacoustic Spectroscopy of Thin Oxide Layers on Metal Electrodes[END_REF][START_REF] Kautek | XPS Studies of Anodic Surface Films on Copper Electrodes[END_REF][START_REF] Millet | A Correlation Between Electrochemical Behaviour, Composition and Semiconducting Properties of Naturally Grown Oxide Films on Copper[END_REF][START_REF] Feng | Corrosion Mechanisms and Products of Copper in Aqueous Solutions at Various pH Values[END_REF][START_REF] Melendres | In-situ synchrotron far infrared spectroscopy of surface films on a copper electrode in aqueous solutions[END_REF] and in situ [START_REF] De Chialvo | The Mechanism of Oxidation of Copper in Alkaline Solutions[END_REF][START_REF] Mayer | An In Situ Raman Spectroscopy Study of the Anodic Oxidation of Copper in Alkaline Media[END_REF][START_REF] Chan | Oxide Film Formation and Oxygen Adsorption on Copper in Aqueous Media As Probed by Surface-Enhanced Raman Spectroscopy[END_REF][START_REF] Maurice | In Situ STM Study of the Initial Stages of Oxidation of Cu(111) in Aqueous Solution[END_REF][START_REF] Kunze | In Situ Scanning Tunneling Microscopy Study of the Anodic Oxidation of Cu(111) in 0.1M NaOH[END_REF][START_REF] Strehblow | Initial and Later Stages of Anodic Oxide Formation on Cu, Chemical Aspects, Structure and Electronic Properties[END_REF][START_REF] Kunze | In Situ STM Study of the Effect of Chlorides on the Initial Stages of Anodic Oxidation of Cu(111) in Alkaline Solutions[END_REF][START_REF] Kunze | In Situ STM Study of the Anodic Oxidation of Cu(001) in 0.1 M NaOH[END_REF][START_REF] Kunze | In Situ STM Study of the Duplex Passive Films Formed on Cu(111) and Cu(001) in 0.1 M NaOH[END_REF] surface analysis. The innovative approach combining ECSTM and EBSD analysis of the same local microstructural area including various types of grain boundaries was applied. To our knowledge, this study is the first combining in situ characterization of the local passivation-induced topographic alterations of GB edges with local microstructural characterization of the same GB sites.

Experimental

Starting from high-purity cast electrolytic tough pitch (ETP-) copper, the microcrystalline samples were produced by cycles of cryogenic rolling and recrystallization annealing [START_REF] Martinez-Lombardia | Scanning Electrochemical Microscopy to Study the Effect of Crystallographic Orientation on the Electrochemical Activity of Pure Copper[END_REF][START_REF] Martinez-Lombardia | In Situ Scanning Tunneling Microscopy Study of the Intergranular Corrosion of Copper[END_REF][START_REF] Martinez-Lombardia | In Situ Scanning Tunneling Microscopy Study of Grain-Dependent Corrosion on Microcrystalline Copper[END_REF][START_REF] Chen | Grain Boundary Passivation Studied by In Situ Scanning Tunneling Microscopy on Microcrystalline Copper[END_REF][START_REF] Chen | Local passivation of metals at grain boundaries: In situ scanning tunneling microscopy study on copper[END_REF][START_REF] Bettayeb | Nanoscale Intergranular Corrosion and Relation With Grain Boundary Character as Studied In Situ on Copper[END_REF][START_REF] Lapeire | Effect of Neighboring Grains on the Microscopic Corrosion Behavior of a Grain in Polycrystalline Copper[END_REF][START_REF] Lapeire | Structural Dependence of Gold Deposition by Nanoplating in Polycrystalline Copper[END_REF]. Annealing was performed at 200 °C for 1 min in order to limit the grain size and to preserve a GB density suitable for the STM field of view [START_REF] Martinez-Lombardia | In Situ Scanning Tunneling Microscopy Study of the Intergranular Corrosion of Copper[END_REF][START_REF] Martinez-Lombardia | In Situ Scanning Tunneling Microscopy Study of Grain-Dependent Corrosion on Microcrystalline Copper[END_REF]. EBSD revealed a nearly random texture of the grains with a ∑3 CSL boundaries length fraction of 66%. The remaining 34% corresponded to random boundaries for the most part [START_REF] Martinez-Lombardia | In Situ Scanning Tunneling Microscopy Study of the Intergranular Corrosion of Copper[END_REF][START_REF] Martinez-Lombardia | In Situ Scanning Tunneling Microscopy Study of Grain-Dependent Corrosion on Microcrystalline Copper[END_REF]. Surface preparation was performed by mechanical polishing with diamond spray down to a final grade of 0.25 μm. The cold work layer was removed by electrochemical polishing in 66% orthophosphoric acid at 3 V for 15 s versus a copper counter electrode.

An Agilent Technologies 4500 system comprising PicoSPM base, STM S scanner, PicoScan 2100 controller, PicoStat bi-potentiostat and Picoscan software was used for ECSTM analysis [START_REF] Zuili | Surface Structure of Nickel in Acid Solution Studied by In Situ STM[END_REF][START_REF] Seyeux | In Situ STM Study of the Initial Stages of Growth and of the Structure of the Passive Film on Ni(111) in 1 mM NaOH(aq)[END_REF][START_REF] Seyeux | In Situ STM Study of the Effect of Chloride on the Growth Mechanism and Structure of the Passive Film on Nickel in Alkaline Solution[END_REF][START_REF] Maurice | In situ STM Study of the Surface Structure, Dissolution and Early Stages of Electrochemical Oxidation of the Ag(111) Electrode[END_REF][START_REF] Li | Structure and Morphology Modifications of Silver Surface in the Early Stages of Sulphide Growth in Alkaline Solution[END_REF]. The ECSTM cell exposed a working electrode area of 0.16 cm 2 and had two Pt wires serving as counter electrode and pseudo reference electrode, the latter being calibrated versus the standard hydrogen electrode (V/SHE). Tips were produced from tungsten rods of 0.25 mm diameter, electrochemically etched and coated with Apiezon wax for electrochemical insulation in the ECSTM cell. A 0.1 M NaOH(aq) aqueous solution was used as electrolyte. It was prepared from ultrapure NaOH and Millipore water (resistivity > 18 MΩ cm).

After exposure to the electrolyte at open circuit potential (-0.03 V/SHE), the samples were submitted to a voltammetry treatment in order to remove the air-formed native oxide and produce an oxide-free metallic state to start with. The potential was cycled at a sweep rate of 0.02 V s -1 down to -1.10 V/SHE, at the onset of hydrogen evolution, and backward to the value of -0.60 V/SHE. This treatment was repeated until the cyclic voltammograms (CVs) showed no cathodic peak associated with the reduction of Cu(I) to Cu(0). Two cycles were enough to fully reduce the air-formed native oxide.

The microcrystalline copper surface was then imaged in the metallic state at -0.60 V/SHE in order to include a relevant microstructure in the STM field of view and to localize GB edges of interest. Afterwards, passivation was forced by sweeping (0.005 V s -1 ) the potential up to -0.10 V/SHE in the Cu(I) passivation range. During the sweep, the tip was kept engaged but did not scan the surface so as to keep the very same local area of interest in the STM field of view.

Images of the surface in the Cu(I) passive state were then taken at -0.10 V/SHE. Next, the passive oxide film was reduced by cycling the potential (0.02 V/s) down to -1.10 V/SHE and upward to -0.6 V/SHE. For this treatment also, the tip was kept engaged without scanning the surface so as to keep the measurement localized in the very same local area of interest. Images of the surface in the reduced metallic state were then taken at -0.60 V/SHE. All ECSTM images of the surface in the initial metallic, passive and reduced states were acquired in the constant current mode. No filtering was used and the recorded images were processed with the Gwyddion software [START_REF]Gwyddion -Free SPM (AFM, SNOM/NSOM, STM, MFM …) data analysis software[END_REF]. In addition to the potential damages to the tip that are inherent to STM measurements, tip alterations could also be induced by the passivation/reduction electrochemical treatments of the surface and were observed in some of the experiments thus limiting the success of obtaining complete series of images of the same local area of interest of the surface in the metallic, passivated and reduced surface state. However, comparative analysis of the data for series of images successfully acquired showed reproducible behavior of the variations of topography measured in the grain boundary regions.

EBSD analysis of the microstructural area of interest analyzed by ECSTM required very precise

repositioning of the analyzed area. The repositioning was achieved thanks to micro marks made on the sample surface using the tip as a nano indenter after recording the last STM image. The applied procedure is described in detail elsewhere [START_REF] Bettayeb | Nanoscale Intergranular Corrosion and Relation With Grain Boundary Character as Studied In Situ on Copper[END_REF]. A digital scanning electron microscope Ultra55 from ZEISS (FEG-SEM) located at LISE (Laboratoire Interfaces et Systèmes Electrochimiques, CNRS -Université Pierre et Marie Curie) was used for EBSD analysis. The micro marks on the sample surface were first located with SE (secondary electron) images obtained at an accelerating voltage of 20 kV, a nominal beam size of 10 nm and a measured beam current of 1.5 nA. EBSD analysis was then performed on areas of about 30 × 30 µm 2 including the micro marks. A minimum step size of 0.1 µm was used for acquisition in order to optimize the post-processing for the crystallographic characterization of the grain boundaries, including at the local sites where line profile analysis has been performed by STM. The OIM ® software was used for processing the EBSD data.

Results and discussion

Macroscopic electrochemical behavior

Figure 1 shows a CV characterizing the macroscopic electrochemical behavior of microcrystalline copper in 0.1 M NaOH(aq). It was recorded in the ECSTM cell after reduction of the air-formed native oxide between the onset of hydrogen evolution and the Cu(I) passive range. The anodic AI peak is characteristic for the formation of a Cu(I) oxide layer and the cathodic CI peak for its decomposition to Cu(0) metallic copper [START_REF] Strehblow | The Investigation of the Passive Behaviour of Copper in Weakly Acid and Alkaline Solutions and the Examination of the Passive Film by Esca and ISS[END_REF][START_REF] Sander | In Situ Photoacoustic Spectroscopy of Thin Oxide Layers on Metal Electrodes[END_REF][START_REF] Kautek | XPS Studies of Anodic Surface Films on Copper Electrodes[END_REF][START_REF] Millet | A Correlation Between Electrochemical Behaviour, Composition and Semiconducting Properties of Naturally Grown Oxide Films on Copper[END_REF][START_REF] Feng | Corrosion Mechanisms and Products of Copper in Aqueous Solutions at Various pH Values[END_REF][START_REF] Melendres | In-situ synchrotron far infrared spectroscopy of surface films on a copper electrode in aqueous solutions[END_REF][START_REF] De Chialvo | The Mechanism of Oxidation of Copper in Alkaline Solutions[END_REF][START_REF] Mayer | An In Situ Raman Spectroscopy Study of the Anodic Oxidation of Copper in Alkaline Media[END_REF][START_REF] Chan | Oxide Film Formation and Oxygen Adsorption on Copper in Aqueous Media As Probed by Surface-Enhanced Raman Spectroscopy[END_REF][START_REF] Maurice | In Situ STM Study of the Initial Stages of Oxidation of Cu(111) in Aqueous Solution[END_REF][START_REF] Kunze | In Situ Scanning Tunneling Microscopy Study of the Anodic Oxidation of Cu(111) in 0.1M NaOH[END_REF][START_REF] Strehblow | Initial and Later Stages of Anodic Oxide Formation on Cu, Chemical Aspects, Structure and Electronic Properties[END_REF][START_REF] Kunze | In Situ STM Study of the Effect of Chlorides on the Initial Stages of Anodic Oxidation of Cu(111) in Alkaline Solutions[END_REF][START_REF] Kunze | In Situ STM Study of the Anodic Oxidation of Cu(001) in 0.1 M NaOH[END_REF][START_REF] Kunze | In Situ STM Study of the Duplex Passive Films Formed on Cu(111) and Cu(001) in 0.1 M NaOH[END_REF].

Analysis of the charge density transfer was performed for the anodic and reverse cathodic reactions by integrating the current density measured above and below the drawn baseline, respectively. The measured charge densities for the anodic and cathodic reactions were 𝑞 𝐴𝐼 = 1870±10 µ𝐶 cm -2 and 𝑞 𝐶𝐼 = 1710±10 µ𝐶 cm -2 , respectively, showing a partially reversible behavior assigned to the irreversible reaction of copper dissolution occurring during anodic polarization. The equivalent thickness of irreversibly dissolved copper (𝛿 𝐶𝑢(𝐼𝑅) ) can be calculated using Eq. ( 1) where 𝑞 is the electric charge density associated to the reaction (𝑞 = 𝑞 𝐴𝐼 -𝑞 𝐶𝐼 ), 𝑉 𝑀 the molar volume of the reacting material, 𝑧 the number of exchanged electrons, and 𝐹 the Faraday's constant.

𝛿 = 𝑞𝑉

𝑚 𝑧𝐹 Eq. (1)
One obtains a value of 0.12±0.01 nm of copper (𝑉 𝑀 𝐶𝑢 = 7.1 cm 3 mol -1 , 𝑧 = 1) being irreversibly dissolved during Cu(I) passivation. This low value amounts to about 0.6 equivalent monolayer (ML) of copper (one (111)-oriented ML of copper is 0.208 nm thick from the bulk fcc structure).

Using Eq. ( 1), the equivalent thickness of the passive oxide film (𝛿 𝑃𝑎𝑠𝑠 ) can be calculated from the electric charge density of the reduction peak (𝑞 = 𝑞 𝐶𝐼 ). Assuming the formation of a Cu(I)2O oxide film (𝑉 𝑀 𝐶𝑢 2 𝑂 = 23.9 cm 3 /mol, 𝑧 = 2 for the reduction of 2 Cu(I)), the value of 2.12±0.01 nm is obtained is in agreement with previous data reported for the Cu(I) passive oxide film formed by cyclic voltammetry [START_REF] Chen | Local passivation of metals at grain boundaries: In situ scanning tunneling microscopy study on copper[END_REF][START_REF] Strehblow | The Investigation of the Passive Behaviour of Copper in Weakly Acid and Alkaline Solutions and the Examination of the Passive Film by Esca and ISS[END_REF][START_REF] Sander | In Situ Photoacoustic Spectroscopy of Thin Oxide Layers on Metal Electrodes[END_REF][START_REF] Kunze | In Situ Scanning Tunneling Microscopy Study of the Anodic Oxidation of Cu(111) in 0.1M NaOH[END_REF].

Passivation at grain boundaries

A local area of copper where the microstructure was first imaged in situ by ECSTM at the topmost surface and then mapped by EBSD after sample transfer and repositioning of the analysis is shown in Figure 2. The EBSD maps show the micro mark made with the STM tip and used to localize the STM field of view (marked by squares). The EBSD IPF map (Figure 2(b)) shows that the STM field of view includes nine grains labelled G1 to G9. They have different crystallographic orientations except for the smaller grains G5, G6 and G8. The presence of three sub-grains labelled SGA to SGC is also evidenced in grain G2. The SGA and SGB sub-grains have the same crystallographic orientation, different from that of the matrix grain G2. The SGC sub-grain is also differently oriented from the matrix grain G2 and has the same orientation as grain G3.

In the ECSTM image (Figure 2(a)), the surface level for the sub-grains SGA to SGC is systematically measured to be lower than the one of the matrix grain G2, like previously observed [START_REF] Bettayeb | Nanoscale Intergranular Corrosion and Relation With Grain Boundary Character as Studied In Situ on Copper[END_REF]. This suggests faster pre-etching of the sub-grains during surface preparation by electrochemical polishing. It is also observed that the grain G3, of same orientation as the subgrain SGC, has a lower topographic surface level than the surrounding grains G1, G2, G8, G9

but not G4, which is also indicative of faster pre-etching during surface preparation.

The EBSD IQ map (Figure 2(c)) enables us to identify the type of grain boundaries included in the STM field of view. According to this IQ mapping analysis, the boundaries at the G1/G2, G1/G3, G1/G8, G5/G6, G3/G4, G4/G7 and G2/G7 interfaces would be of random type while all others would be grain boundaries of CSL type. Among the CSL boundaries, the boundary at the G8/G9 interface would be 9 and those at the G2/G3, G4/G5, G4/G6 and G4/G8 interfaces would be 3 boundaries. All boundaries delimiting the three sub-grains SGA to SGC from the matrix grain G2 would also be 3 boundaries.

In the ECSTM image of the topmost surface (Figure 2(a)), the grain boundary regions can be identified by the topography variations between the adjacent grains. Like previously reported [START_REF] Martinez-Lombardia | In Situ Scanning Tunneling Microscopy Study of the Intergranular Corrosion of Copper[END_REF][START_REF] Chen | Grain Boundary Passivation Studied by In Situ Scanning Tunneling Microscopy on Microcrystalline Copper[END_REF][START_REF] Chen | Local passivation of metals at grain boundaries: In situ scanning tunneling microscopy study on copper[END_REF][START_REF] Bettayeb | Nanoscale Intergranular Corrosion and Relation With Grain Boundary Character as Studied In Situ on Copper[END_REF], line profile analysis revealed that the GB regions could be characterized by the presence of a topographic gap at the interface between the adjacent grains. The sites labelled from 1 to 16 correspond to the local sites where the depth of the topographic gaps, and thus of the GB regions, could be measured in the initial metallic state, in the passive state and in the reduced metallic state. It should be noted that for several boundaries, the line profile measured between the adjacent grains did not reveal a gap sufficiently deep to ensure a reliable measurement of the depth of the GB region and its variation after electrochemical treatment.

Such shallow gaps were observed for the random boundaries at the G1/G2, G1/G3, G1/G8, G5/G6, G3/G4, G4/G7 and G2/G7 interfaces and for the CSL boundaries at the G2/G3 and G4/G5 interfaces. Their observation can be assigned to the large difference of topographic level between the adjacent grains masking, at least partially, the topography of the GB edge resolved by the STM tip. Insufficient preferential pre-etching during the electrochemical polishing pretreatment could also explain their presence.

Like previously reported [START_REF] Chen | Grain Boundary Passivation Studied by In Situ Scanning Tunneling Microscopy on Microcrystalline Copper[END_REF][START_REF] Chen | Local passivation of metals at grain boundaries: In situ scanning tunneling microscopy study on copper[END_REF][START_REF] Bettayeb | Nanoscale Intergranular Corrosion and Relation With Grain Boundary Character as Studied In Situ on Copper[END_REF], the depth of the GB region was measured from line profiles obtained by averaging 30 adjacent line scans drawn across the GB edge, covering a local distance of ~170 nm along the boundary. The results obtained for the surface in the initial metallic state, in the passive state and in the reduced metallic state are presented in Figure 3. A first examination reveals 3 types of behaviors according to the variation of the depth of the GB region after passivation (Table 1): an increased depth observed in sites 4, 12, 14-16, a decreased depth observed in sites 1-3, 6, 9-11, or an unchanged depth observed in sites 5, 7, 8, 13. An increase of the depth of the GB region can be assigned to the formation of a passive film locally thinner than on the adjacent grains. In the grain boundaries showing this behaviour, passivation would be more efficient since locally consuming less copper than the adjacent grains to form the passive oxide. Inversely, a decrease of the depth of the GB region can be assigned to the formation of a passive film locally thicker and thus to a less efficient passivation consuming more copper than on the adjacent grains by anodic oxidation. The absence of variation of the depth of the GB region in the passive state implies that the passive film is locally as thick as on the adjacent grains and thus that passivation is equally efficient. In nearly all cases the depth measured after reduction of the passive film is identical, within the uncertainty of the measurement, to that measured prior to passivation, indicating a reversible reaction at the GB edges.

Let us now discuss the results for the different grain boundaries observed in Figure 2 and start with the grain boundaries delimiting the sub-grains SGA and SGB from grain G2. These boundaries are all of 3 CSL type according to the EBSD IQ map. We observe a similar behaviour characterized by an increase of the GB depth in the passive state at sites 12 and 14

(delimiting sub-grain SGA) and at sites 15 and 16 (delimiting sub-grain SGB). However, at site 13, corresponding to another grain boundary delimiting the sub-grain SGA, no significant variation is observed. In all cases, the GB depth variation is reversible after reduction of the passive film.

The grain boundary measured at sites 2 to 6 along the G4/G8 interface is also of 3 CSL type according to the EBSD IQ map. It shows a varying behaviour since, at sites 2, 3 and 6, a significant decrease of the GB depth is measured after passivation whereas a very small increase or no variation are measured at sites 4 and 5, respectively. The depth variations measured along this boundary are either reversible (site 2 and 5) or irreversible (sites 3, 4 and 6) after reduction of the passive film. The  CSL boundary measured at sites 7 to 11 along the G4/G6 interface also shows a varying behaviour since a significant decrease of the GB depth is measured at sites 9 to 11 but not at sites 7 and 8. After reduction of the passive film, the observed depth variations are reversible. For the boundary measured at site 1 across the G8/G9 interface and of 9 CSL type according to the EBSD IQ map, the depth decrease is the largest observed after passivation and the change is reversible after reduction of the passive film.

Thus, for grain boundaries that are classified of the same  CSL type by the EBSD IQ mapping analysis, the efficiency of the passivation varies as revealed by ECSTM analysis of the increased, decreased or unchanged depths of the GB regions. Clearly these results suggest that although of the same  CSL type, the local GB structure may vary between different boundaries and also along the same boundary, modifying the local reactivity towards passivation similarly to what was observed in the initial stages of active dissolution [START_REF] Bettayeb | Nanoscale Intergranular Corrosion and Relation With Grain Boundary Character as Studied In Situ on Copper[END_REF].

Effect of GB local structure

In order to better rationalize the effect of the GB structure, the EBSD analysis was refined. At each local site where line profile analysis of the ECSTM data was performed, the misorientation angle 𝜃 and the deviation angle 𝜑 of the boundary with respect to the ideal coherent GB geometry were extracted. The results are compiled in Table 1.

At sites 1 and 2, the local EBSD analysis did not yield values of the misorientation angle consistent with a well-defined  CSL type, meaning that the GB local structure is of random type. This local random type of the structure of the boundary can thus be used to explain the locally lower efficiency for passivation and thus higher reactivity of the boundary. This result is consistent with the higher reactivity (i.e. susceptibility) of random type boundaries observed in the initial stages of active dissolution [START_REF] Bettayeb | Nanoscale Intergranular Corrosion and Relation With Grain Boundary Character as Studied In Situ on Copper[END_REF] and in later stages of sub-surface penetrating attack [START_REF] Lin | Influence of Grain Boundary Character Distribution on Sensitization and Intergranular Corrosion of Alloy 600[END_REF][START_REF] Kim | Grain Boundary Character Distribution and Intergranular Corrosion Behavior in High Purity Aluminum[END_REF][START_REF] Shimada | Optimization of grain boundary character distribution for intergranular corrosion resistant 304 stainless steel by twininduced grain boundary engineering[END_REF][START_REF] Xia | Effect of single-step strain and annealing on grain boundary character distribution and intergranular corrosion in Alloy 690[END_REF][START_REF] Ralston | Effect of Grain Size on Corrosion: A Review[END_REF][START_REF] Jones | Sensitisation behaviour of grain boundary engineered austenitic stainless steel[END_REF][START_REF] Cl Changliang | Improving the intergranular corrosion resistance of 304 stainless steel by grain boundary network control[END_REF][START_REF] Kumar | Methods for making alloy 600 resistant to sensitization and intergranular corrosion[END_REF]. Thus, random type high angle boundaries are susceptible to intergranular attack in the absence of the passive film and are not efficiently self-protected by passivation.

At sites 3 to 16, all boundaries can be classified as  CSL type in agreement with the EBSD IQ mapping analysis. The Brandon [START_REF] Brandon | The structure of high-angle grain boundaries[END_REF] and Palumbo-Aust criteria [51] define ranges of tolerance of the misorientation angle outside of which the boundary can no longer be considered as a specific  CSL. For the 3 misorientation, these ranges are 60±8.67° and 60±6°, respectively. For the sites 3 to 16, these criteria are respected and the GB structure is locally a  CSL one. Thus, the variations of the passivation behaviors measured at these sites are hereafter discussed based on the deviation angle of the GB plane, i.e. in terms of coherent vs.

incoherent local structure of the boundary.

Along the G4/G8 interface (sites 2 to 6), the largest deviation ( = 1°) with respect to the perfect  CSL geometry ( = 0°) is observed at site 6, which would explain the higher reactivity of the site and thus its lower efficiency to passivate and the formation of a locally thicker passive film. At sites 3 to 5, the deviation with respect to the perfect geometry is lower ( = 0.4-0.5°), which would imply a lower reactivity of the sites and thus their better efficiency to passivate as indicated by the observed variability of the depth variations of the GB region.

Along the G4/G6 interface (sites 7 to 11), the local deviation of the boundary with respect to the perfect geometry is 0.5° at the most. This also implies a lower reactivity and a better efficiency to passivate than at site 6, which is indeed observed at sites 7 and 8 ( = 0.3°) where no variation of the depth of the GB region is observed. At sites 9 to 11 for which the local deviation is higher ( = 0.4-0.5°), a higher reactivity and thus lower efficiency to passivate is measured as indicated by the decrease of the depth of the GB region. One can notice in Figure 2 that, in this region, the GB edge presents a kinked morphology indicative of the accumulation of misfit dislocations in the GB plane, and contributing to its deviation from the perfect geometry.

At the SGA/G2 (site 12 to 16) interfaces, the local deviation of the boundary with respect to the perfect geometry is 0.3° at the most. Note that such low values of the deviation angle  are indicative of nearly perfect coherent twins, which is also suggested by the presence of parallel GB edges at the surface (Figure 2). The lower deviated local structure of these coherent twins implies a lower reactivity and increased efficiency to passivate which is confirmed by the observed variations of the GB depth measured at sites 12 to 16, where the passive film was measured to be thinner than on the adjacent grains in most cases.

In our previous study of active dissolution of microcrystalline copper [START_REF] Bettayeb | Nanoscale Intergranular Corrosion and Relation With Grain Boundary Character as Studied In Situ on Copper[END_REF], the transition from resistance to susceptibility to the initiation of the intergranular attack of 3 CSL boundaries was observed for a deviation angle  of 1.0-1.7°. This value was concluded to correspond to the transition from resistive coherent twins to susceptible incoherent twins in the absence of formation of a passive film. The transition was explained by the presence of misfit dislocations (i.e. steps) accommodating the deviation of the boundary plane from the exact CSL plane and by the increased density of step regions introduced in the boundary plane with increasing deviation [START_REF] Bettayeb | Nanoscale Intergranular Corrosion and Relation With Grain Boundary Character as Studied In Situ on Copper[END_REF]. The present data obtained for copper passivation by formation of a Cu(I) oxide film show a transition from more efficient to less efficient passivation for a deviation angle  of 0.4-0.5°. This implies that the effect of the presence of an increasing density misfit dislocations (i.e. steps) in the boundary plane is more detrimental for the efficiency to passivate than for the resistance to dissolve.

Conclusions

The relationship between grain boundary type and structure and passivation efficiency was studied for the first time by combining ECSTM and EBSD analysis of the same microstructural area. The study was performed on microcrystalline copper in 0.1 M NaOH(aq) aqueous solution. The in situ ECSTM data show that passivation by anodic oxidation in the Cu(I) range is characterized in most cases by a decrease of the depth of GB edge region due to the formation of a passive film locally thicker than on the adjacent grains and thus to anodic oxidation being locally less efficient since consuming more copper at the grain boundaries. Cu(I) passivation is less efficient at the edges of high angle random boundaries as compared 3 CSL boundaries.

Coupling ECSTM and EBSD enabled us to address the effect of the GB fine structure on the passivation properties. For 3 CSL boundaries, a transition from more efficient to less efficient passivation was observed for a deviation angle  of 0.4-0.5° of the {111} GB plane with respect to the perfect geometry of an ideal coherent twin boundary. For lower values of the deviation angle, the GB edges would be less reactive and passivate more efficiently than adjacent grains whereas for higher values the local behaviour can be either identical to that of the adjacent grains or similar to that of random boundaries. This transition would result from the presence of misfit dislocations (i.e. steps) accommodating the deviation of the boundary plane from the exact CSL plane and from the effect of an increased density of steps introduced in the boundary plane with increasing deviation on the local anodic oxidation properties.

Figure captions

Figure 1

 1 Figure 1 Cyclic voltammogram recorded in the ECSTM cell for microcrystalline copper in 0.1 M NaOH(aq), scan rate = 20 mV/s.

Figure 2

 2 Figure 2 Local microstructure of polycrystalline copper imaged in situ by ECSTM and then mapped by EBSD after repositioning in the same area: (a) Topographic ECSTM image of the metallic state at E = -0.6 V/SHE in 0.1 M NaOH(aq) (Z range ΔZ = 15 nm, tip potential Etip = -0.9 V/SHE, tunneling current It = 1.5 nA); (b) EBSD inverse pole figure (IPF) map; (c) EBSD image quality (IQ) map. In (a) and (b), grains are labelled G1 to G9 and sub-grains SGA to SGC. The local GB sites selected for depth profile analysis are indexed 1 to 16. In (b) and (c), the squares mark the field of view analyzed by STM.

Figure 3

 3 Figure 3 Bar graph of the depth measured across the grain boundaries at the sites # 1 to 16 in Figure 2(a) in the initial metallic state at E = -0.6 V/SHE, in the passive state at E = -0.1 V/SHE and in the final metallic state at E = -0.6 V/SHE after reduction of the passive film. The symbols ↓, ↑ and ≈ denote a lower, higher or equivalent local passivation efficiency, respectively, as deduced from the variations of the GB depth after passivation.

  Figure 2

Acknowledgments

This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (ERC Advanced Grant No 741123, Corrosion Initiation Mechanisms at the Nanometric and Atomic Scale, CIMNAS).

Table

Table 1 Grain boundary crystallographic characteristics as measured by EBSD at the sites marked in Figure 2 and variation of the depth of the GB region and efficiency of Cu(I) passivation behavior with respect to adjacent grains as measured by ECSTM.

Variation of GB depth

Passivation efficiency


Abdeldjalil Aissa

El Bey

Karim Abed-Meraim

Yves Grenier

Blind separation of audio sources using modal decomposition

come

BLIND SEPARATION OF AUDIO SOURCES USING MODAL DECOMPOSITION

A. Aïssa-El-Bey, K. Abed-Meraim and Y. Grenier ENST-Paris, 46 rue Barrault 75634, Paris Cedex 13, France {elbey, abed, grenier}@tsi.enst.fr here to exploit this last property for the separation of audio sources by means of modal decomposition.

DATA MODEL

The blind source separation model assumes the existence of N independent signals s 1 (t), . . . , s N (t) and M observations x 1 (t), . . . , x M (t) that represent the mixtures. These mixtures are supposed linear and instantaneous, i.e.

x i (t) = N j=1 a ij s j (t) i = 1, . . . , M (1)
This can be represented compactly by the mixing equation

x(t) = As(t) (2)
where s(t

) def = [s 1 (t), . . . , s N (t)]
T is a N × 1 column vector collecting the source signals, vector x(t) similarly collects the M observed signals, and the M × N mixing matrix A def = [a 1 , . . . , a N ] with a i = [a 1i , . . . , a M i ] T contains the mixture coefficients. We will suppose that for any pair (i, j) with i = j, the vectors a i and a j are linearly independent. The source signals are supposed to be decomposable in a sum of modal components c j i (t), i.e:

s i (t) = l i j=1 c j i (t) t = 0, . . . , T -1 (3)
The usual source independence assumption is replaced here by a quasi-orthogonality assumption of the modal components, i.e.

c j i |c j i c j i c j i ≈ 0 for (i, j) = (i , j ) (4)
where

c j i |c j i def = T -1 t=0 c j i (t)c j i (t) * (5)
and

c j i 2 = c j i |c j i ( 6
)
Remark: Assumption (4) may be restrictive in certain applications. However, it can be relaxed in such a way to allow common modal components to different sources as shown in [START_REF] Aissa-El-Bey | Séparation aveugle sous-déterminée de sources audio par la méthode EMD (Empirical Mode Decomposition)[END_REF].

ABSTRACT

This paper introduces new algorithms for the blind separation of audio sources using modal decomposition. Indeed, audio signals and, in particular, musical signals can be well approximated by a sum of damped sinusoidal (modal) components. Based on this representation, we propose a two steps approach consisting of a signal analysis (extraction of the modal components) followed by a signal synthesis (pairing of the components belonging to the same source) using vector clustering. For the signal analysis, two algorithms are considered and compared: namely the EMD (Empirical Mode Decomposition) algorithm and a parametric estimation algorithm using ESPRIT technique.

A major advantage of the proposed method resides in its ability to separate more sources than sensors. Simulation results are given to compare and assess the performances of the proposed algorithms.

INTRODUCTION

The problem of blind source separation consists of finding independent source signals from their observed mixtures without a priori knowledge on the actual mixing matrix.

The source separation problem is of interest in various applications [START_REF]Blind estimation using higherorder statistics[END_REF] such as the localization and tracking of targets using radars and sonars, separation of speakers (problem known as "cocktail party"), detection and separation in multiple access communication systems, independent components analysis of biomedical signals (EEG or ECG), multispectral astronomical images etc. This problem has been intensively studied in the literature and many effective solutions have been proposed so far [START_REF]Blind estimation using higherorder statistics[END_REF]. Nevertheless, the underdetermined case where the number of sources is greater than the number of sensors (observations) remains relatively poorly treated, and its resolution is one of the open problems of blind source separation. In the case of non-stationary signals (including the audio signals), certain solutions using time-frequency analysis of the observations exist for the underdetermined case [START_REF] Nguyen | Separating more sources than sensors using time-frequency distributions[END_REF][START_REF] Jourjine | Blind separation of disjoint orthogonal signals: demixing n sources from 2 mixtures[END_REF]. In this paper, we propose an alternative approach using modal decomposition of the received signals [START_REF] Huang | The em-pirical mode decomposition and Hilbert spectrum for nonlinear and non-stationary times series analysis[END_REF][START_REF] Flandrin | Empirical mode decomposition as a filter bank[END_REF]. More precisely we propose to decompose a supposed locally periodic signal which is not necessarily harmonic in the Fourier sense into its various modes. The audio signals and more particularly the musical signals can be modeled by a sum of damped sinusoids [START_REF] Boyer | Audio modeling based on delayed sinusoids[END_REF] and hence are well suited for our separation approach. We propose

SEPARATION USING MODAL DECOMPOSITION

Based on the previous model, we propose an approach in two steps consisting of:

• An analysis step: in this step, one applies an algorithm of modal decomposition to each sensor output in order to extract all the harmonic components from them. We compare, for this modal components extraction two decomposition algorithms that are the EMD (Empirical Mode Decomposition) algorithm introduced in [2, 3] and a parametric algorithm which estimates the parameters of the modal components modeled as damped sinusoids.

• A synthesis step: in this step we group together the modal components corresponding to the same source in order to reconstitute the original signal. This is done by observing that all modal components of a given source signal 'live' in the same spatial direction. Therefore, the proposed clustering method is based on the component's direction evaluated by correlation of the extracted (component) signal with the observed antenna signal.

Signal analysis using EMD

A new nonlinear technique, referred to as Empirical Mode Decomposition (EMD), has recently been introduced by N.E. Huang et al. for representing non-stationary signals as sum of zero-mean AM-FM components [START_REF] Huang | The em-pirical mode decomposition and Hilbert spectrum for nonlinear and non-stationary times series analysis[END_REF]. The starting point of the EMD is to consider oscillations in signals at a very local level. Given a signal z(t), the EMD algorithm can be summarized as follows [START_REF] Flandrin | Empirical mode decomposition as a filter bank[END_REF]:

1. Identify all extrema of z(t).

2. Interpolate between minima (resp. maxima), ending up with some envelope e min (t) (resp. e max (t)).

3. Compute the mean m(t) = (e min (t) + e max (t))/2.

4. Extract the detail d(t) = z(t) -m(t).

Iterate on the residual m(t).

By applying EMD algorithm to the i th mixture signal x i which is written as

x i (t) = N j=1 a ij s j (t) = N j=1 lj k=1 a ij c k j (t) one obtains estimates c k j (t) of components c k j (t).

Parametric signal analysis

In this section we present an alternative solution for signal analysis. For that, we represent the source signal and hence the observations as sum of damped sinusoids:

x k (t) = L l=1 α l,k z t l ( 7
)
where α l,k represents the complex amplitude and z l = e d l +iω l is the l th pole where d l is the negative damping

[H(x k )] n 1 n 2 def = x k (n 1 + n 2 )
, D being a window parameter chosen in the range T /3 ≤ D ≤ 2T /3. We use of Kung's algorithm given in [START_REF] Kung | Spacetime and singular-value decomposition based approximation methods for the harmonic retrieval problem[END_REF] that can be summarized in the following steps:

1. Form the data Hankel matrix H(x k ).

Estimate the

2L-dimensional signal subspace U (L) = [u 1 . . . u 2L ] of H(x k
) by means of the SVD (u 1 . . . u 2L are the principal left singular vectors of H(x k )).

3. Solve (in the least squares sense) the shift invariance equation

U (L) ↓ Ψ = U (L) ↑ ⇔ Ψ = U (L)# ↓ U (L) ↑ (8)
where Ψ = Φ∆Φ -1 , Φ being a non-singular 2L × 2L matrix and ∆ = diag(z 1 , z * 1 , . . . , z L , z * L ). () # denotes the pseudo-inversion operation and arrows ↓ and ↑ denote respectively the last and the first rowdeleting operator.

4. Estimate the poles as the eigenvalues of matrix Ψ.

Estimate the complex amplitudes by solving the least squares fitting criterion

min α x k -Zα 2 ⇔ α = Z # x k (9)
where x k = [x k (0) . . . x k (T -1)] T is the observation vector, Z is a Vandermonde matrix constructed from the estimated poles and α is the vector of complex amplitudes.

Signal synthesis using vector clustering

For the synthesis of the source signals one observes that thanks to the quasi-orthogonality assumption, one has:

x|c j i c j i 2 def = 1 c j i 2    x 1 |c j i . . . x M |c j i    ≈ a i
where a i represents the i th column vector of A. We can then associate each component c k j to a space direction (vector column of A) that is estimated by

a k j = x| c k j c k j 2
Two components of a same source signal are associated to the same column vector of A, Therefore, we propose to gather these components by clustering the vectors a k j into N classes. One will be able to rebuild the initial sources up to a constant by adding the various components within a same class.

Source pairing and selection

Let us notice, that by applying the approach described previously (analysis plus synthesis) to all the antenna outputs x 1 (t), • • • , x M (t), we obtain M estimates of each source signal. The estimation quality of a given source signal varies significantly from one sensor to another. Indeed, it depends strongly on the matrix coefficients and, in particular, on the signal to interference ratio (SIR) of the desired source. Consequently, we propose a blind selection method to choose a 'good' estimate among the M we have for each source signal. For that, we need first to pair the source estimates together. This is done by associating each source signal extracted from the first sensor to the (M -1) signals extracted from the (M -1) other sensors that are maximally correlated with it. The correlation factor of two signals s 1 and s 2 is evaluated by s 1 |s 2 s 1 s 2 . Once, the source pairing achieved, we propose to select the source estimate of maximal energy, i.e.

s i (t) = max j {E j i = T -1 t=0 | s j i (t)| 2 , j = 1, • • • , M } (10)
where E j i represents the energy of the i th source extracted from the j th sensor. One can consider other methods of selection based on the dispersion around the centroid of each class, the number of components of each source estimate, etc.

Discussion

We provide here some comments to get more insight onto the proposed separation method:

• Over-determined case: In that case, one is able to separate the sources by left inversion of matrix A. The latter can be estimated from the centroids of the N clustering classes (i.e., the centroid of the i th class represent the estimate of the i th column of A).

• Estimation of the number of sources: This is a difficult and challenging task in the underdetermined case. Few approaches exist based on multi-dimensional tensor decomposition [START_REF] Lathauwer | ICA techniques for more sources than sensors[END_REF] or based on the clustering with joint estimation of the number of classes [START_REF] Frank | The data analysis handbook[END_REF]. However, these methods are very sensitive to noise, to the source amplitude dynamic and to the conditioning of matrix A. In this paper, we assume the number of sources known (or correctly estimated).

• Number of modal components: In the parametric approach, we have to choose the number of modal components L needed to well approximate the audio signal. Indeed, small values of L lead to poor signal representation while large value of L increases the computational cost. In fact, L depends on the 'signal complexity' and in general musical signals require less components (for a good modeling) than speech signals. In section 4 we illustrate the effect of the value of L on the separation quality.

• Hybrid separation approach: It is most probably that the separation quality can be improved using signal analysis in conjonction with spatial filtering. Indeed, it has been observed that the separation quality depends strongly on the mixture coefficients. Spatial filtering can be used to improve the SIR for a desired source signal and consequently its extraction quality. This will be the focus of a future work.

SIMULATION

We present here some simulation results to illustrate the performance of our blind separation algorithms. For that, we consider a uniform linear array with M = 3 sensors receiving the signals from N = 4 audio sources (except for the third experiment where N varies in the range [START_REF] Huang | The em-pirical mode decomposition and Hilbert spectrum for nonlinear and non-stationary times series analysis[END_REF][START_REF] Nguyen | Separating more sources than sensors using time-frequency distributions[END_REF]).

The angles of arrival of the sources are chosen randomly. formance obtained by our algorithm using EMD and the parametric technique with L = 30. As a reference, we plot also the NMSE obtained by pseudo-inversion of matrix A [10] (assumed exactly known). It is observed that both EMD and parametric based separation provide better results than those obtained by pseudo-inversion of the exact mixing matrix. The plots in figure 2 illustrate the effect of the number of components L chosen to model the audio-signal. Too small or too large values of L degrade the performance of the method. In other words, it existe an optimal choice of L that depend on the signal type. In figure 3, we present the separation performance loss that we have when the number of sources increases from 2 to 6 in the noiseless case. For N = 2 and N = 3 (overdetermined case) we estimate the sources by left inversion of the estimate of matrix A. In the underdetermined case,

CONCLUSION

This paper introduces a new blind separation method for audio-type sources using modal decomposition. The proposed method can separate more sources than sensors and provides, in that case, a better separation quality than the one obtained by pseudo-inversion of the mixture matrix (even if it is known exactly). For the signal analysis step of the proposed method, two algorithms are used and compared using respectively the EMD and the ESPRIT-like technique for the estimation of the poles of the modal components modeled as damped sinusoids.

  factor and ω l is the angular-frequency. (•) represents the real part of a complex entity. For the extraction of the modal components, we propose to use the ESPRIT-like (Estimation of Signal Parameters via Rotation Invariance Technique) technique that estimates the poles of the signals by exploiting the row-shifting invariance property of the D×(T -D) data Hankel matrix

Fig. 1 .

 1 Fig. 1. NMSE versus SNR

Fig. 2 .

 2 Fig. 2. NMSE versus L: SNR=10 and 30

Fig. 3 .

 3 Fig. 3. NMSE versus N (noiseless case)