Julien Granet

Muriel Sicot

Iann C Gerber

Geoffroy Kremer

Thomas Pierron

Bertrand Kierren

Luc Moreau

Yannick Fagot-Revurat

Simon Lamare

Frédéric Cherioux

¶ T Pierron

F Ch

D Malterre

Adsorption-Induced Kondo Effect in Metal-Free Phthalocyanine on Ag(111)

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

INTRODUCTION

Molecular magnetism have attracted rising attention since molecular based magnetic materials can have many technological applications in areas such as quantum computation, [START_REF] Urtizberea | A Porphyrin Spin Qubit and Its 2D Framework Nanosheets[END_REF][START_REF] Gaita-Ariño | Molecular Spins for Quantum Computation[END_REF] high-density data storage and spintronics. [START_REF] Cavallini | Magnetic Information Storage on Polymers by Using Patterned Single-Molecule Magnets[END_REF][START_REF] Cinchetti | Activating the Molecular Spinterface[END_REF][START_REF] Bogani | Molecular Spintronics Using Single-Molecule Magnets[END_REF][START_REF] Mannini | Magnetic Memory of a Single-Molecule Quantum Magnet Wired to a Gold Surface[END_REF][START_REF] Guo | A Dysprosium Metallocene Single-Molecule Magnet Functioning at the Axial Limit[END_REF] Very early in the development of the field, metallophthalocyanines (MPc) have proven to be a priviledged class of molecules to study magnetism at the nanometer scale. [START_REF] Zhao | Controlling the Kondo Effect of an Adsorbed Magnetic Ion Through Its Chemical Bonding[END_REF][START_REF] Li | Single-Molecule Chemistry of Metal Phthalocyanine on Noble Metal Surfaces[END_REF][START_REF] Niu | Exploring Single Molecules by Scanning Probe Microscopy: Porphyrin and Phthalocyanine[END_REF][START_REF] Komeda | Double-decker phthalocyanine complex: Scanning Tunneling Microscopy Study of Film Formation and Spin Properties[END_REF] Indeed, many MPc possess unpaired electrons in the gas phase and thus have non-zero magnetic moments. Besides, bis-phthalocyanines sandwiching rare-earth ions have been shown

to behave as single-molecular magnets. [START_REF] Ishikawa | Lanthanide Double-Decker Complexes Functioning as Magnets at the Single-Molecular Level[END_REF][START_REF] Ishikawa | Quantum Tunneling of Magnetization in Lanthanide Single-Molecule Magnets: Bis(phthalocyaninato)terbium and Bis(phthalocyaninato)dysprosium Anions[END_REF] Their applicative potential has already been demonstrated, for example by fabricating functional supramolecular spin valves. [START_REF] Urdampilleta | Supramolecular Spin Valves[END_REF] The attractiveness of these molecules also lies in their easy synthesis, low cost and industrial avaibility. Particularly, they can be evaporated under ultra-high vacuum (UHV) allowing the synthesis of thin films. [START_REF] Gottfried | Surface Chemistry of Porphyrins and Phthalocyanines[END_REF] In addition, the planar geometry of their π-conjugated ligand that can lie parallel to the surface on which they are adsorbed is an asset: the flatness of MPcs allows direct hybridization with the orbitals of the underlying substrate leading to the modification of surface properties and new exotic phenomena when in contact with various substrates such as ferromagnetic (FM) materials, [START_REF] Cinchetti | Activating the Molecular Spinterface[END_REF] topological insulators, supraconductors or 2D materials. [START_REF] Amsterdam | Electronic Coupling in Metallophthalocyanine-Transition Metal Dichalcogenide Mixed-Dimensional Heterojunctions[END_REF][START_REF] Kafle | Charge Transfer Exciton and Spin Flipping at Organic-Transition-Metal Dichalcogenide Interfaces[END_REF][START_REF] Padgaonkar | Molecular Orientation-Dependent Interfacial Charge Transfer in Phthalocyanine/MoS2 Mixed-Dimensional Heterojunctions[END_REF] For instance, in the case of the MPc/FM molecular spinterfaces, it has been shown that the addition of MPc increases or invert the FM spin-polarization which is a key property regarding performance of spin devices. [START_REF] Suzuki | Spin Polarization of Metal (Mn, Fe, Cu, and Mg) and Metal-Free Phthalocyanines on an Fe(100) Substrate[END_REF][START_REF] Atodiresei | Design of the Local Spin Polarization at the Organic-Ferromagnetic Interface[END_REF][START_REF] Djeghloul | High Spin Polarization at Ferromagnetic Metal-Organic Interfaces: A Generic Property[END_REF][START_REF] Delprat | Molecular Spintronics: the Role of Spin-Dependent Hybridization[END_REF] In the case of CoPc/Bi 2 Se 3 , Caputo;et al. have evidenced by angular-resolved photoelectron spectroscopy (ARPES), the modification of the topological surface states and the energy shift of the Dirac cone due to charge transfer from the molecule to the surface [START_REF] Caputo | Manipulating the Topological Interface by Molecular Adsorbates: Adsorption of Co-Phthalocyanine on Bi2Se3[END_REF] . When in contact with superconductors, magnetic nano-objects can be envisaged as qubits for quantum computing devices. In such cases, the governing factor is the strength of spin-superconductor interactions.

MPc/Pb(111) interfaces have been shown to be ideal platforms to tune locally this magnetic interaction strength by adsorbing the molecules on different sites or by continuously varying it using the interaction with an STM tip. [START_REF] Bauer | Microscopic Resolution of the Interplay of Kondo Screening and Superconducting Pairing: Mn-Phthalocyanine Molecules Adsorbed on Superconducting Pb(111)[END_REF][START_REF] Malavolti | Tunable Spin-Superconductor Coupling of Spin 1/2 Vanadyl Phthalocyanine Molecules[END_REF] Finally, optical measurements of MPc/MoS 2 heterojunctions evidenced charge transfer that is sensitive to the transition metal core. This property allows for tuneable optical absorption making those systems interesting for optoelectronic applications. [START_REF] Amsterdam | Electronic Coupling in Metallophthalocyanine-Transition Metal Dichalcogenide Mixed-Dimensional Heterojunctions[END_REF] Moreover, this flat-lying molecular adsorption configuration offers an open area to the vacuum side. This gives the opportunity to manipulate the spin-state using on-top adsorption of alkali atoms or molecules to induce electron doping. Such studies have led to the emerging research field of on surface-magnetochemistry. [START_REF] Krull | Site-and Orbital-Dependent Charge Donation and Spin Manipulation in Electron-Doped Metal Phthalocyanines[END_REF][START_REF] Ballav | Emergence of On-Surface Magnetochemistry[END_REF] In many cases, interfacial properties result from the hybridization of the highly directional d z 2orbital of the core metal atom with those of the substrate. Yet, for other MPc/inorganic interfaces, coupling can arise from hybridization with the π (p z ) orbital of the Pc ligand, as well. The filling of the π-orbital by charge transfer modifies the spin state of the molecule in comparison with the free one. As an example, it was shown that the no-spin bearing NiPc molecule acquires a 1 /2-spin of π-origin due to charge transfer upon adsorption on a Ag(100) single-crystalline surface. [START_REF] Mugarza | Spin Coupling and Relaxation Inside Molecule-Metal Contacts[END_REF][START_REF] Mugarza | Electronic and Magnetic Properties of Molecule-Metal Interfaces: Transition-Metal Phthalocyanines Adsorbed on Ag(100)[END_REF] This has been demonstrated by revealing the spectral signature which is typical of a 1 /2-spin object in interaction with an electron bath namely an Abrikosov-Suhl resonance of the differential conductance in the vicinity of the Fermi level E F using LT-STM/STS resulting from Kondo effect. [START_REF] Anderson | Localized Magnetic States in Metals[END_REF][START_REF] Kondo | Resistance Minimum in Dilute Magnetic Alloys[END_REF][START_REF] Li | Scattering Observed at a Single Magnetic Impurity[END_REF][START_REF] Madhavan | Tunneling into a Single Magnetic Atom: Spectroscopic Evidence of the Kondo Resonance[END_REF][START_REF] Komeda | Spins of Adsorbed Molecules Investigated by the Detection of Kondo Resonance[END_REF][START_REF] Ternes | Spectroscopic Manifestations of the Kondo Effect on Single Adatoms[END_REF] On the same Ag(100) surface, CuPc which possesses a 1 /2-spin state in its ground state, acquires an extra π-electron. In this last case, the molecule behaves as a two-spin system in contact with conduction electrons leading to an interesting many-body phenomenon: a triplet-singlet Kondo effect. [START_REF] Mugarza | Spin Coupling and Relaxation Inside Molecule-Metal Contacts[END_REF] Alternatively, STM and UPS measurements recorded on the CoPc/Ag(111) interface have unravelled another more complex donation/backdonation scenario: electron injection occurs from the Ag substrate to the Co-3d orbitals that is accompagnied with a back donation of electrons from the π-orbitals to the substrate. [START_REF] Toader | Site-Dependent Donation/Backdonation Charge Transfer at the CoPc/Ag(111) Interface[END_REF] Recently, it was shown by UPS that the metal-free phthalocyanine 2HPc which is a no-spin bearing molecule in the gas phase can also become charged upon adsorption on Ag(111). [START_REF] Gorgoi | Charge-Transfer at Silver/Phthalocyanines Interfaces[END_REF][START_REF] Kröger | Submonolayer Growth of H2-Phthalocyanine on Ag(111)[END_REF][START_REF] Caplins | Metal/Phthalocyanine Hybrid Interface States on Ag(111)[END_REF] We can therefore wonder if this system could also exhibit a Kondo effect as in the case of NiPc or CuPc on Ag(100). The implication of such a result would be that a purely organic phthalocyanine adsorbed on a silver surface could give rise to interesting magnetic properties without the involvement of 3d transition metal nor 4f rare-earth central ions as in previous studies. Indeed, only very few examples of pure organic systems presenting Kondo effect have been reported so far. [START_REF] Fernández-Torrente | Vibrational Kondo Effect in Pure Organic Charge-Transfer Assemblies[END_REF][START_REF] Choi | A Single Molecule Kondo Switch: Multistability of Tetracyanoethylene on Cu(111)[END_REF][START_REF] Liu | First Observation of a Kondo Resonance for a Stable Neutral Pure Organic Radical, 1,3,5-Triphenyl-6-oxoverdazyl, Adsorbed on the Au(111) Surface[END_REF][START_REF] Requist | Conductance Across the Smallest Spin 1/2 Radical Molecule[END_REF][START_REF] Esat | A Chemically Driven Quantum Phase Transition in a Two-Molecule Kondo System[END_REF][START_REF] Karan | Spin Manipulation by Creation of Single-Molecule Radical Cations[END_REF] Despite the increasing attention devoted to the abovementioned hybrid MPc/inorganic interfaces, however the spin-polarized electronic properties of the 2HPc/Ag(111) interface had been underlooked. [START_REF] Gorgoi | Charge-Transfer at Silver/Phthalocyanines Interfaces[END_REF][START_REF] Kröger | Submonolayer Growth of H2-Phthalocyanine on Ag(111)[END_REF][START_REF] Caplins | Metal/Phthalocyanine Hybrid Interface States on Ag(111)[END_REF][START_REF] Sperl | Controlled Metalation of a Single Adsorbed Phthalocyanine[END_REF] Yet, this particular system could provide a means of investigating many-body phenomena such as Kondo effect in many aspects,e.g. its intensity, spatial extension, [START_REF] Perera | Spatially Extended Kondo State in Magnetic Molecules Induced by Interfacial Charge Transfer[END_REF] quantum criticality [START_REF] Esat | A Chemically Driven Quantum Phase Transition in a Two-Molecule Kondo System[END_REF] when a 1 /2 spin in π orbital is involved rather than a 3d or 4f -orbital. It would therefore broaden our knowledge on magnetism as well as on many-body physics at the nanometer scale and at low dimensionality. [START_REF] Fernández-Torrente | Vibrational Kondo Effect in Pure Organic Charge-Transfer Assemblies[END_REF][START_REF] Choi | A Single Molecule Kondo Switch: Multistability of Tetracyanoethylene on Cu(111)[END_REF][START_REF] Liu | First Observation of a Kondo Resonance for a Stable Neutral Pure Organic Radical, 1,3,5-Triphenyl-6-oxoverdazyl, Adsorbed on the Au(111) Surface[END_REF][START_REF] Requist | Conductance Across the Smallest Spin 1/2 Radical Molecule[END_REF][START_REF] Perera | Spatially Extended Kondo State in Magnetic Molecules Induced by Interfacial Charge Transfer[END_REF][START_REF] Booth | Self-Contained Kondo Effect in Single Molecules[END_REF][START_REF] Wahl | Effect of 30 Molecular Complexes at Surfaces: Ligand Control of the Local Spin Coupling[END_REF][START_REF] Zhao | Effect in Single Cobalt Phthalocyanine Molecules Adsorbed on Au(111) Monoatomic Steps[END_REF][START_REF] Scott | Resonances in Molecular Devices[END_REF][START_REF] Tsukahara | Evolution of Kondo Resonance from a Single Impurity Molecule to the Two-Dimensional Lattice[END_REF][START_REF] Minamitani | Symmetry-Driven Novel Kondo Effect in a Molecule[END_REF][START_REF] Ziroff | Low-Energy Scale Excitations in the Spectral Function of Organic Monolayer Systems[END_REF][START_REF] Garnica | Long-Tange Magnetic Order in a Purely Organic 2D Layer Adsorbed on Epitaxial Graphene[END_REF][START_REF] Komeda | Variation of Kondo Peak Observed in the Assembly of Heteroleptic 2,3-Naphthalocyaninato Phthalocyaninato Tb(III) Double-Decker Complex on Au(111)[END_REF][START_REF] Iancu | Inducing Magnetism in Pure Organic Molecules by Single Magnetic Atom Doping[END_REF][START_REF] Lin | Two-Dimensional Lattice of Out-of-Plane Dinuclear Iron Centers Exhibiting Kondo Resonance[END_REF][START_REF] Zhang | Switching Molecular Kondo Effect via Supramolecular Interaction[END_REF][START_REF] Maughan | Ensemble Control of Kondo Screening in Molecular Adsorbates[END_REF][START_REF] Hiraoka | Single-molecule quantum dot as a Kondo simulator[END_REF][START_REF] Tuerhong | Two-Dimensional Organometallic Kondo Lattice with Long-Range Antiferromagnetic Order[END_REF] Moreover, as illustrated above, a full description of the hybrid interfaces must necessarily consider both interfacial sides. On the metal side, sizeable modifications can also be expected as already observed with other π-conjugated molecules at the interface with copper or silver surfaces. [START_REF] Caplins | Metal/Phthalocyanine Hybrid Interface States on Ag(111)[END_REF][START_REF] Temirov | Free-Electron-Like Dispersion in an Organic Monolayer Film on a Metal Substrate[END_REF][START_REF] Armbrust | Model Potential for the Description of Metal/Organic Interface States[END_REF][START_REF] Lerch | Electronic Structure of Titanylphthalocyanine Layers on Ag(111)[END_REF][START_REF] Gerbert | Formation of Occupied and Unoccupied Hybrid Bands at Interfaces between Metals and Organic Donors/Acceptors[END_REF][START_REF] Sabitova | Lateral Scattering Potential of the PTCDA/Ag(111) Interface State[END_REF] In the case of 2HPc/Ag(111), it has been shown that upon molecular adsorption, an interfacial state forms originating from the well-known bare metal Shockley state. [START_REF] Caplins | Metal/Phthalocyanine Hybrid Interface States on Ag(111)[END_REF][START_REF] Bürgi | Two-Dimensional Electron Gas at Noble-Metal Surfaces[END_REF][START_REF] Reinert | Direct Measurements of the L-gap Surface States on the (111) Face of Noble Metals by Photoelectron Spectroscopy[END_REF] Those hybrid interfacial states (HIS) are of particular importance for the understanding of contact in organic semiconductor devices and their origin are not yet fully understood [START_REF] Temirov | Free-Electron-Like Dispersion in an Organic Monolayer Film on a Metal Substrate[END_REF][START_REF] Sabitova | Lateral Scattering Potential of the PTCDA/Ag(111) Interface State[END_REF] .

Therefore, such a study might also unravel insights on the Ag hybrid interface state.

In this framework, we have investigated by LT-STM/STS, UPS and DFT, the electronic structure of adsorbed 2HPc on Ag(111) for single molecules as well as for two-dimensional selfassembled molecular networks. We demonstrate the emergence of a Kondo effect regardless of the coverage in the submonolayer regime. We think that this kind of hybrid interface with molecules comprising only C, H and N-atoms may thus be envisaged to design metamaterials composed of abundant and environmental-friendly compounds.

METHODS

The experiments were carried out in two ultra-high vacuum systems with a base pressure of 1 × 10 -10 mbar. One was equipped with a low-temperature Omicron STM operating at 5 K. The other one was equipped with a ScientaOmicron DA30-L hemispherical analyzer and a monochromatized He I (hν = 21.2 eV) UV source for ARPES. As beam damage of the molecular layers was observed on a timescale of about 20 min, duration of the measurements and sample position were adjusted accordingly. Due to angular distribution of the photoemission intensity, ultra-violet photoemission spectra were recorded at an emission angle of 45 • . [START_REF] Ziroff | Low-Energy Scale Excitations in the Spectral Function of Organic Monolayer Systems[END_REF][START_REF] Puschnig | Reconstruction of Molecular Orbital Densities from Photoemission Data[END_REF][START_REF] Gargiani | Orbital Symmetry of the Kondo State in Adsorbed FePc Molecules on the Au(110) Metal Surface[END_REF] Note that, in this geometry, the Shockley surface state of Ag(111) lying in the L-gap around the Γ point of the surface Brillouin zone is not detected [START_REF] Reinert | Direct Measurements of the L-gap Surface States on the (111) Face of Noble Metals by Photoelectron Spectroscopy[END_REF] . All spectra were normalized to the count rate at the binding energy of 0.4 eV. LEED was available on both UHV set-ups to characterize structural properties at a sample temperature of 80 K.

The Ag(111) single crystal was cleaned by repeated cycles of Ar + sputtering at an energy of 1 keV followed by an annealing to 800 K. 2HPc molecules were purchased from Aldrich and purified by column chromatography (silica gel, dichloromethane) prior to use. They were evaporated from a Knudsen cell at 565 K onto the sample held at room temperature. The STM images were recorded at a tunneling current I t and a bias voltage V b where the sign corresponds to the voltage applied to the sample. STS was acquired with a PtIr scissors-cut tip and a lock-in detection in open feedback loop conditions at a frequency of 1100 Hz and a peak-to-peak bias voltage modulation for highresolution STS of 5 mV.

The electronic structures were obtained from DFT calculations with the VASP package [72][START_REF] Kresse | Ab Initio Molecular Dynamics for Liquid Metals[END_REF][START_REF] Kresse | Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set[END_REF][START_REF] Kresse | Efficiency of Ab-Initio Total Energy Calculations for Metals and sSemiconductors Using a Plane-Wave Basis Set[END_REF] which uses the plane-augmented wave scheme [START_REF] Blöchl | Projector Augmented-Wave Method[END_REF][START_REF] Kresse | From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method[END_REF] to treat core electrons. Perdew-Burke-Ernzerhof (PBE) functional [START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF] was used as an approximation of the exchange-correlation electronic term, but PBE-D3 scheme [START_REF] Grimme | A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 elements H-Pu[END_REF][START_REF] Bučko | Improved Description of the Structure of Molecular and Layered Crystals: Ab Initio DFT Calculations with van der Waals Corrections[END_REF] was used firstly to optimize the geometry since Huang;et al. have addressed the importance of van der Waals corrections when dealing with Pc-metallic surfaces interactions. [START_REF] Huang | Understanding the Adsorption of CuPc and ZnPc on Noble Metal Surfaces by Combining Quantum-Mechanical Modelling and Photoelectron Spectroscopy[END_REF] The kinetic energy cutoff was set to 400 eV, with a gaussian smearing of 0.05 eV and using a 2×2×1 k-points grid to optimize the structures with a convergence force criterium of 0.01 eV/ Å for all allowed atoms to relax. For density of states (DOS) determinations, a 3×3×1 kpoints grid was used in conjunction with the tetrahedron method with Blöchl corrections scheme. [START_REF] Blöchl | Improved Tetrahedron Method for Brillouin-Zone Integrations[END_REF] We have confirmed that a 12 layers-slab with a vacuum height of more than 20 Å was necessary to describe accurately the intrinsic Shockley surface state of the Ag (111) surface, [START_REF] Zaitsev | Transformation of the Ag(111) Surface State Due to Molecule-Surface Interaction with Ordered Organic Molecular Monolayers[END_REF] see Fig. S3 for a band structure representation in the Supporting Information. As expected, two surface states are provided by the slab approach and the average energy of the two surface states (-86 meV) is relatively close to the experimental energy value (-63 meV). [START_REF] Reinert | Direct Measurements of the L-gap Surface States on the (111) Face of Noble Metals by Photoelectron Spectroscopy[END_REF] To mimic the individual molecule case, as well as to describe the C-phase, see definition below, a (7×7) and commensurate ([5 0; 3 6]) cell was used respectively.

RESULTS AND DISCUSSION

Structural Properties

The growth of 2HPc on Ag(111) in the submonolayer regime has been studied in previous works.

Three distinct phases form as a function of the coverage. [START_REF] Kröger | Submonolayer Growth of H2-Phthalocyanine on Ag(111)[END_REF] For self-assemblies, the unit cells have been determined. [START_REF] Kröger | Submonolayer Growth of H2-Phthalocyanine on Ag(111)[END_REF] Yet, the adsorption geometry and especially the azimuthal orientation of the molecules has only succinctly been addressed and remains elusive, particularly in self-assemblies.

Nevertheless, this information is of paramount importance to elucidate the electronic properties of the metal-organic interface. Thanks to STM images with intramolecular resolution, we were able to tackle this key point as will be explained below.

According to Kröger;et al., at low molecular densities, 2HPc form disordered gas-like phases, referred as G-phases where the intermolecular distance changes with coverage due to substratemediated intermolecular repulsive interaction. [START_REF] Kröger | Submonolayer Growth of H2-Phthalocyanine on Ag(111)[END_REF] Upon increasing coverages to 0.5-0.89 monolayers at low temperature, they form a commensurate phase with the substrate referred as C-phase, characterized by a nearly-square unit cell which epitaxy matrix is [5 0; 3 6]. [START_REF] Kröger | Submonolayer Growth of H2-Phthalocyanine on Ag(111)[END_REF] Our LEED patterns displayed in Fig. 1(a) and Fig. 2(a) exhibiting a diffuse ring around the [00] specular beam and sharp spots, respectively are in line with those previous results. Sperl;et al. showed that 2HPc adsorb flat onto the Ag(111) substrate i.e. the Pc ligand plane adsorbs parallell to the surface plane. [START_REF] Sperl | Controlled Metalation of a Single Adsorbed Phthalocyanine[END_REF] The line formed by the two pyrrolic hydrogen atoms inside the porphyrazine core which will be referred to "the 2H-axis" hereafter, was shown to be azimuthally oriented perpendicular to 01 1 cristallographic directions of the substrate. This was later confirmed by Kügel et al. [START_REF] Kügel | Breaking Degeneracy of Tautomerization-Metastability from Days to Seconds[END_REF] In C-phase, Bai;et al. measured by STM an azimuthal angle between one vector of the unit cell and the molecular axis of about 60 • ± 3 • without specifying the orientation of the 2H-axis. [START_REF] Bai | Direct Metalation of a Phthalocyanine Monolayer on Ag(111) with Coadsorbed Iron Atoms[END_REF] In the present work, we determine the orientation of single molecules by comparing their STM appearance in Fig. 1(b) with the HOMO of the singly charged 2HPc anion calculated in ref. [START_REF] Nilson | Potassium-Intercalated H2Pc films: Alkali-Induced Electronic and Geometrical Modifications[END_REF] for which the splitted lobes are perpendicular to the 2H-axis. The specific choice of comparison with the anion is justified by the fact that the molecule gets negatively charged when adsorbed as we will discuss below. The direction of the 2H-axis of the molecules is highlighted by blue lines in Fig. 1 On the contrary, in our work, we find two adsorption orientations that can simply be explained by molecules that could rotate in the ligand plane. Fig. 1(d,e) displays the two simulated most stable adsorption configurations α and β corresponding to 2H perpendicular and parallell to 01 1 directions, respectively in good agreement with our observations. The difference of adsorption energy between these two geometries of minimum energy is only of about 0.

Kondo effect in single molecules

In previous works, it was demonstrated from UPS and two-photon photoemission (TPPE) measurements that charge transfer occurs from the Ag(111) substrate to the Pc ligand of 2HPc. [START_REF] Kröger | Submonolayer Growth of H2-Phthalocyanine on Ag(111)[END_REF][START_REF] Caplins | Metal/Phthalocyanine Hybrid Interface States on Ag(111)[END_REF] In the C-phase, this was evidenced by the occupancy of the LUMO orbital upon adsorption resulting in a state located at an energy of -0.15 eV and which has been called former-LUMO (F-LUMO) in reference to the LUMO state of the free molecule. In addition, an unoccupied HIS develops from the former Shockley-type electronic state of the bare Ag(111) surface. It originates from the steepening of the surface potential upon molecular adsorption. This nearly-free electron state has been characterized by a band onset located at an energy of +0.23 ± 0.03 eV above E F . [START_REF] Caplins | Metal/Phthalocyanine Hybrid Interface States on Ag(111)[END_REF] Knowing the abovementioned results, one can reasonably raise the following question: would self-assembled 2HPc behave like 1/2-spin in contact with a free electron bath possibly giving rise to Kondo effect? Would this effect persists for single molecules? To elucidate the arising of a Kondo effect for a single molecule as well as for a self-assembly, we performed STS and UPS on G and C-phases.

First, we address the Kondo effect in single molecules using STS and UPS. STS spectra in the enery range around E F are reported in Fig. 3(a). They were recorded with the STM tip located above molecules A, B and C' displayed in Fig. 1(c). All tunneling spectra show two main characteristics:

(i) a sharp electronic resonance in the close vicinity of E F , labeled κ in Fig. 3(a), (ii) a conductance peak located at about +52 meV, labeled ν. As no molecular nor substrate's state is expected in a range of ±10 meV around E F , we can, as a first guess, reasonably attribute the resonance at E F to Kondo effect. Yet, as other phenomena could lead to the formation of a peak in the differential conductance spectrum next to E F , a magnetic field or temperature dependency of the full width at half maximum (FWHM) of the resonance should be recorded and compared to laws governing the effect in order to unambiguously attribute its origin to Kondo effect. [START_REF] Hewson | The Kondo Problem to Heavy Fermions[END_REF][START_REF] Nagaoka | Temperature Dependence of a Single Kondo Impurity[END_REF] Alternatively, UPS can be used since a typical spectrum of a Kondo system exhibits a sharp resonance at E F at temperatures below the Kondo temperature T K . [START_REF] Hewson | The Kondo Problem to Heavy Fermions[END_REF][START_REF] Gunnarsson | Electron Spectroscopies for Ce Compounds in the Impurity Model[END_REF][START_REF] Malterre | Recent Developments in High-Energy Spectroscopies of Kondo Systems[END_REF] Upon increasing temperature, this peak is expected to broaden and decrease in intensity. [START_REF] Bickers | Self-Consistent Large-N Expansion for Normal-State Properties of Dilute Magnetic Alloys[END_REF][START_REF] Patthey | High-Resolution Photoemission Study of the Low-Energy Excitations in 4f-Electron Systems[END_REF][START_REF] Costi | Effect in a Magnetic Field and the Magnetoresistivity of Kondo Alloys[END_REF] Such a relationship with temperature is what is experimentally observed as displayed in Fig. 3 The next feature of the STS spectra to be discussed is the peak ν at E ν = 52 ± 5 meV. This side feature appears as a resonance and its intensity with respect to the zero-bias one depends on the tip location. Upon certain tip conditions (see supplementary information for further details), the Kondo resonance is not observed. In those cases, the dI/dV spectrum has an upside down hat shape as depicted in Fig. 3(a). The two step-edges are located at about ±E ν which is the standard lineshape observed when inelastic processes corresponding to vibrational excitation energies of E ν get activated. However, the side feature appears more as a resonance than as a step. According to, [START_REF] König | Zero-Bias Anomalies and Boson-Assisted Tunneling Through Quantum Dots[END_REF][START_REF] Flensberg | Tunneling Broadening of Vibrational Sidebands in Molecular Transistors[END_REF][START_REF] Paaske | Vibrational Sidebands and the Kondo Effect in Molecular Transistors[END_REF][START_REF] Chen | Phonon-Assisted Kondo Effect in a Single-Molecule Transistor out of Equilibrium[END_REF][START_REF] Roura-Bas | Nonequilibrium Transport Through Magnetic Vibrating Molecules[END_REF] it can be understood as originating from the splitting of the zero-bias resonance resulting from the electron-vibron coupling. Other Kondo organic/inorganic systems exhibit as well, such peaks of vibronic nature. [START_REF] Mugarza | Spin Coupling and Relaxation Inside Molecule-Metal Contacts[END_REF][START_REF] Mugarza | Electronic and Magnetic Properties of Molecule-Metal Interfaces: Transition-Metal Phthalocyanines Adsorbed on Ag(100)[END_REF][START_REF] Fernández-Torrente | Vibrational Kondo Effect in Pure Organic Charge-Transfer Assemblies[END_REF][START_REF] Parks | Tuning the Kondo Effect with a Mechanically Controllable Break Junction[END_REF]100 In particular, conductance spectra recorded over CuPc and NiPc on Ag(100) exhibit such fingerprints at comparable excitation energies [START_REF] Mugarza | Spin Coupling and Relaxation Inside Molecule-Metal Contacts[END_REF][START_REF] Mugarza | Electronic and Magnetic Properties of Molecule-Metal Interfaces: Transition-Metal Phthalocyanines Adsorbed on Ag(100)[END_REF] and might correspond to the activation of torsion modes. 101 According to Refs., [START_REF] Li | Scattering Observed at a Single Magnetic Impurity[END_REF][START_REF] Madhavan | Tunneling into a Single Magnetic Atom: Spectroscopic Evidence of the Kondo Resonance[END_REF] T K can be roughly determined by fitting the Kondo resonance with a Fano function lineshape expressed as, disregarding the instrumental broadening: 102,103

(q + ) 2 (1 + 2 ) ; = eV -k Γ ( 1
)
where Γ is the 1/2 FWHM such that Γ =k B T K , q the Fano asymmetry parameter and k the energy shift of the resonance from T K .

As an example, the fitting results of the dI/dV spectra recorded at the center of molecules A, B and C' are reported in Fig. 3(a) as black lines. Another set of 4 measurements is shown in Fig. S1. The mean fitted T K is T K = 130 K with a standard deviation of 20 K and q ranges from 0.3 to more than 50. The high q values indicates that the tunneling process occurs preferentially through the molecular orbital than to the conduction-electron continuum. Strong lineshape and FWHM variations are observed between the molecules. The possible influence of the adsorption configuration will be discussed below in relation to DFT calculations.

Kondo effect in self-assembly

To investigate the arising of a Kondo effect in the commensurate self-assembly, STS and UPS were carried out. Results are displayed in Fig. 4. To start with, STS was recorded over a large bias voltage range to investigate the overall electronic properties of the interface. Whereas UPS probe occupied states only, STS gives access to energy regions above and below Fermi level in a single-shot experiment enabling a direct comparison with UPS and TPPE spectra of previous studies. [START_REF] Kröger | Submonolayer Growth of H2-Phthalocyanine on Ag(111)[END_REF][START_REF] Caplins | Metal/Phthalocyanine Hybrid Interface States on Ag(111)[END_REF] The differential conductance dI/dV spectrum in Fig. 4(a) reveals distinct peaks that can unambiguously be assigned. Peaks located at about -0.12 V and -1.2 V are attributed to F-LUMO and HOMO, respectively according to ref. [START_REF] Kröger | Submonolayer Growth of H2-Phthalocyanine on Ag(111)[END_REF]104 At positive bias, the step-like feature which is typical of a nearly-free electron two-dimensional gas is assigned to the HIS. Its edge is located at +0.23 ± 0.01 V, in very good agreement with the band edge measured by TPPE. [START_REF] Caplins | Metal/Phthalocyanine Hybrid Interface States on Ag(111)[END_REF] The F-LUMO and HOMO states are also detected by UPS as indicated in Fig. S5 in the Supporting Information.

As already explained in ref.

, [START_REF] Kröger | Submonolayer Growth of H2-Phthalocyanine on Ag(111)[END_REF] explanations for the difference between the two phases will be discussed in section V.

Density of states calculated by DFT

In order to correlate spectroscopic peaks observed in STS and UPS spectra with the molecular electronic structure, we have computed the DOS of 2HPc in C-phase and projected it onto atomic orbitals. As shown in Fig. 4(d), this PDOS is dominated by p z orbitals. One peak below -1 eV corresponds to the HOMO state. Crossing E F , another prominent peak of p z character corresponds to the F-LUMO state. Although the calculated energy position of this state is upshifted compared to experiments due to a well-known drawback of standard DFT calculations that do not properly account for HOMO-LUMO gap, it remains in good agreement with experimental data and supports the identification of the electronic states of the dI/dV spectrum of Fig. 4(a).

A net charge transfer of 0.32e -of sp-orbital character occurs from the substrate to the adsorbate region. Again, this value is only qualitative since charge transfer estimated from DFT calculations depends critically on the computational details. 105 The sign of the spin is indicated in yellow/cyan. The isovalue for the electronic spin density is roughly 10 -7 e/ Å3 in both cases.

Electronic surface properties of Ag(111)

To utterly describe the organometallic interface, the Ag properties must be investigated as well.

Moreover, their knowledge will help us better understand the Kondo effect. In the following, we are interested in the modifications of the Ag surface properties when a very small amount of molecules is adsorbed such as in Fig. 1(b). To begin with, we have recorded a dI/dV curve on pristine Ag(111) prior to molecular adsorption. It is shown as a grey dashed curve in Fig. 5(a).

Its lineshape and energy onset is typical of the well-known Ag Shockley surface state. [START_REF] Bürgi | Two-Dimensional Electron Gas at Noble-Metal Surfaces[END_REF]106,107 After molecular adsorption at low coverage, a dI/dV spectra have been recorded on the uncovered Ag surface in between molecules. They are quite different compared to the one observed on the pristine Ag surface and they depend strongly on the location where they were recorded. Spectra 2 to 4 are given in Fig. 5(a) as examples. The spectra can be described as a step-like lineshape with prominent peaks superimposed to it. As will be explained below, those extra peaks are eigenstates resulting from electron confinement. STM and conductance maps are shown in Fig. 5(c-f).

A strong spatially textured background between the molecules is observed for energies eV b above the Ag Shockley state energy onset E 0 . This is illustrated by the STM image recorded at -40 meV in Fig. 5(b). The effect is even better evidenced on the three conductance maps shown in Fig. 5(c-f).

Indeed, whereas the dI/dV map recorded at -0.1 V in (c) shows a constant and homogeneous background, strong variation of the conductance is observed on the flat areas of bare Ag between the molecules for the map at eV b > E 0 in Fig. 5(d-f). Moreover, it depends strongly on the energy. Due to these characteristics, we attribute these observations to the formation of standing wave patterns resulting from the scattering of the 2D nearly free electron surface state of Ag. In other words, 2HPc molecules act as electron scatterers of nanometric size. On those maps, the most surprising feature is the one observed at the center of the image as pointed by the green arrow in Fig. 5(d-f) that is reminiscent of electron confinement in closed 2D artificial hexagonal Ag nanovacancies, 108 nanoislands [109][110][111] or even 2D porous molecular networks adsorbed on coinage (111) metal surfaces. 112 What is remarkable is that, contrary to those 2D resonators that are closed structures delimited by hard walls, the pattern of this current work have been obtained with only 4 or 5 molecules that are 2 to 5 nm apart and thus forming an open structure. In the abovementioned examples of electron confinement, the potential barrier is con-sidered as continuous whereas it is obviously discontinuous in the present work. Shchyrba;et al.

showed previously partial confinement insides molecular pores with missing borders. 113 Pennec;et al. showed confinement of the Ag surface state in a U-shaped cavity formed of linear molecular walls. However, to the best of our knowledge, the formation of an open walls molecular confining cavity has not been evidenced yet and therefore deserves a keen interest.

Scattering of the surface state of (111) surfaces of coinage metals by πconjugated molecules have been previously observed. [114][115][116][117][118] When self-assembled in specific ways such as in Ref. 117 or organized in metal-organic frameworks, molecules can act as scattering walls for electrons of a two-dimensional electron gas. Quantum well arrays can thus be formed with well-defined molecular boundaries. Single π-conjugated molecular scatterer has been modeled 114 as a collection of atomic total absorbers at the position of the carbon atoms using multiple scattering expansion as developped for quantum corrals. 119 In molecular porous networks, scattering molecules are described in the framework of the boundary elements method where molecular boundaries correspond to constant rectangular potential. 116 The case of 2HPc on Ag(111) at low coverage is singular in the sense that it represents an intermediate case between the two situations cited above. Therefore, to explain the patterns observed in our work, a complementary theoretical approach might be necessary and further experimental investigations are required. This demonstrates that the 2HPc/Ag(111) interface offers the possibility to explore new fundamental aspects of quantum physics i.e. the electron scattering by an object of nanometric size composed of a collection of atomic-like scatterers covalently bonded. Besides, it holds promise for the design of tunable low-dimensional electron resonator. As will be discussed in section V, quantum confinement might have a non negligible impact on the Kondo effect.

Discussion

In this section, we would like to address the mechanism behind the variation of T K within the Gphase as well as with molecular density. In previous sections we have shown that T K for single molecules can vary by about several tens of K. In addition, it is about twice smaller in the C-phase as compared with the G-phase.

Prior to that, the question arises whether the UPS spectra of the two phases corroborate STS results? To answer this question, a quantitative extraction of T K would be necessary.

However, such analysis requires a temperature dependence of the linewidth of the Kondo peak together with theoretical calculations of the spectral function. 120 Solely based on (i) the width and intensity of the Kondo resonance which are larger for the C-phase than for the G-phase, (ii) theoretical descriptions of the variation of the spectral function [START_REF] Hewson | The Kondo Problem to Heavy Fermions[END_REF] and (iii) experimental photoemission intensity of heavy fermions systems as a function of T K , [START_REF] Hewson | The Kondo Problem to Heavy Fermions[END_REF][START_REF] Gunnarsson | Electron Spectroscopies for Ce Compounds in the Impurity Model[END_REF][START_REF] Malterre | Recent Developments in High-Energy Spectroscopies of Kondo Systems[END_REF]120 we would conclude that the C-phase has a higher T K than the G-phase. This would contradict our STS measurements. However, in the present case, a direct parallel with those available works on strongly correlated materials is not totally valid since the π-orbital is involved instead of 4f states. In addition, here, electron-vibron coupling related to vibrational energies very close to E F is present. The presence of such a coupling might result in satellite Kondo resonances at energies related to E ν and therefore might contribute to the width of the UPS spectra in the close vicinity of E F . [START_REF] Roura-Bas | Nonequilibrium Transport Through Magnetic Vibrating Molecules[END_REF] The intensity of the coupling is likely to vary between the two phases thus affecting differently the intensity and the width of the corresponding resonances. Further theoretical work is required to properly describe molecular vibrational Kondo effect and to analyze experimental UPS lineshape when charge-vibron coupling is present in a Kondo system. As a conclusion, the following discussion can only be based on T K extracted from STS.

The Kondo temperature inside the G-phase can be assumed to depend on the adsorption configuration. [START_REF] Minamitani | Symmetry-Driven Novel Kondo Effect in a Molecule[END_REF] Nevertheless, it is not supported by our DFT calculations: adsorption heights and PDOS are very similar for both α and β configurations. Comparing G and C-phase, a possible explanation could lie in the effect of intermolecular interactions. It has been shown in some Pc supramolecular assemblies that ligand-ligand interaction could engender a lifting of the molecules, reducing the molecule-substrate coupling and thus, T K . [START_REF] Mugarza | Spin Coupling and Relaxation Inside Molecule-Metal Contacts[END_REF][START_REF] Komeda | Variation of Kondo Peak Observed in the Assembly of Heteroleptic 2,3-Naphthalocyaninato Phthalocyaninato Tb(III) Double-Decker Complex on Au(111)[END_REF] However, according to our DFT calculations, the adsorption height varies only minutely between the two phases. In addition, as shown in Fig. S6 in the Supporting Information, the PDOS of the 2HPc molecule on Ag(111) at low concentration is very similar to the one of molecules in the C-phase reported in Fig. 4(d). The position of the F-LUMO varies only a little and a charge transfer of 0.27 electrons has been extracted. This is very close to the value of 0.32 electrons obtained for the self-assembly. This supposes that the coupling strength with the substrate doesn't vary much upon formation of the C-phase and can not account for the strong variation of T K .

The Ruderman-Kittel-Kasuya-Yoshida (RKKY) interaction is an alternative origin. It is an indirect spin-spin interaction mediated by the conduction electrons of the metal. Depending on distance, it favours ferromagnetic or antiferromagnetic (AFM) alignments of single magnetic moments. It has been shown that an interplay between the Kondo effect and the RKKY interaction exists in supramolecular assemblies, as well. [START_REF] Tsukahara | Evolution of Kondo Resonance from a Single Impurity Molecule to the Two-Dimensional Lattice[END_REF][START_REF] Tuerhong | Two-Dimensional Organometallic Kondo Lattice with Long-Range Antiferromagnetic Order[END_REF] The width of the Abrikosov-Suhl resonance is strongly affected or even suppressed due to the magnetic coupling between the spins. More specifically, FM RKKY interaction sharpens the resonance and, on the other hand, the AFM RKKY broadens it. 121 Unfortunately, it is very challenging to test the assumption whether RKKY interaction is responsible for the reduction of T K in the self-assembly. Indeed, in order to demonstrate it, a thought experiment would be to measure T K by STS as a function of the molecule-molecule distance for a pair of molecules to mimic the conditions of the two-impurities Kondo problem. 122 However, in such a case of a molecular pair, surface electrons would dominate the RKKY interaction due to their lower k F compared to bulk electrons and couldn't be used to conclude on the exchange coupling in the self-assembly for which the surface state has hybridized with a molecular orbital to form the unoccupied HIS. Nevertheless, one can tentitatively apply the following formula to predict the sign of the exchange coupling in the commensurate phase:

J = J 0 sin(2k F r) (2k F r) 2 ,
where k F is the Fermi wave vector of the substrate and r, the distance between the spins. The latter parameter r can be estimated from the calculated lattice parameters of the rectangular unit cell (black dashed line in Fig. 2(c)) that are equal to 1.51 nm and 1.45 nm) and k F = 12.02 nm -1 . 123 Moreover, we discard the influence of the second-nearest neighbors due to the fast decay of the exchange for bulk electrons. The result gives an AFM coupling between nearest-neighbors molecules. This would lead to an increase of T K compared with the single impurity case which contradicts our experimental findings. Therefore RKKY can not account for the decrease of T K upon formation of self-assembly.

The observed variation of T K between the two phases could be alternatively explained considering that T K is directly proportional to exp -1 ρ F J , where ρ F is the substrate's density of states at the Fermi energy and J is the exchange coupling at the magnetic impurity. [START_REF] Hewson | The Kondo Problem to Heavy Fermions[END_REF] This relationship indicates that when ρ F is reduced, T K is reduced as a result. At low molecular concentration, the uncovered substrate exhibits a Shockley surface state that participates to ρ F . In the case of the C-phase, as this state hybridizes with the LUMO state of the free molecule to form the HIS shifted above E F , ρ F is reduced in comparison with the isolated molecules and thus, would explain the decrease of T K for the C-phase.

The influence of the surface state on the Kondo resonance width has been a topic of debate for many years (see Ref. 124 and references therein). Some works on Ag(111) have suggested a minor role for surface-state electrons in the Kondo effect. 125 Only very recently, Li;et al. tackle this controversy using LT-STM/STS on Co adsorbates on Ag(111). 124 They unambiguously demonstrate the influence of the surface state on the Kondo resonance by measuring the width of the zero-bias peak as a function of the lateral distance to the impurity. The key point is that they evidenced an oscillatory dependency as a function of the distance to the magnetic impurity which periodicity matches the half Fermi wavelength of the Ag(111) surface state. Moro-Lagares;et al. obtained experimentally and theoretically a nearly linear relationship between T K and the surfacestate contribution local density of states of the substrate. 126 Besides, both works emphasize the effect of quantum confinement of the surface state. In particular, it was evidenced that in a quantum corral, the Kondo width can be significantly increased (more than three times). 124 As at low molecular density in the 2HPc/Ag(111) system, quantum confinement of the Ag surface state is also observed, it probably also plays a significant role on the high value of T K and its variation in the G-phase. The effect of the Shockley surface state on T K has also been observed on molecules such as Co-tetraphenylporphirin on Cu(111). 115 In this work, Iancu;et al. showed that molecules exposed to Cu surface state electrons exhibit a higher T K than molecules inside a self-assembled cluster. These results are in favor of our observation of a lower T K upon self-assembly.

CONCLUSIONS

As a conclusion, we have studied the electronic properties of the metal-free phthalocyanine 2HPc adsorbed on Ag(111) surfaces by means of scanning tunneling and photoelectron spectroscopies and compared the experimental results with DFT calculations. We have evidenced a partial filling of a molecular π state lying next to the Fermi level. The presence of this extra π-spin in the molecule leads to the emergence of a Kondo effect at low temperature for single molecules as well as for molecules arranged in a 2D self-assembly.

The fact that we deal with a metal-free phthalocyanine offer many future prospects. In other words, the absence of a metal ion at the center of the molecule is the asset of this system. Indeed, it has been shown that this metal free central cavity of 2HPc can be manipulated by STM in many ways: tautomerization [START_REF] Kügel | Breaking Degeneracy of Tautomerization-Metastability from Days to Seconds[END_REF] , partial or total deshydrogenation or direct Ag metalation can be induced. [START_REF] Sperl | Controlled Metalation of a Single Adsorbed Phthalocyanine[END_REF] Therefore, one can envisage to investigate the influence of such modifications on the Kondo physics. As an example, a 2HPc molecule can be transformed into an AgPc molecule in the self-assembly [START_REF] Sperl | Controlled Metalation of a Single Adsorbed Phthalocyanine[END_REF] and study the effect on T K . In that case, T K is likely to change through the modification of the local coupling with the substrate via the up or down-lifting of the molecules or the RKKY interaction between neighbouring molecules.

Besides the STM manipulation-based approach, local modification of the electronic and magnetic properties of 2HPc can be obtained by on-surface synthesis such as chemical doping or metallation upon adsorption of alkali or metallic atoms under UHV. [START_REF] Krull | Site-and Orbital-Dependent Charge Donation and Spin Manipulation in Electron-Doped Metal Phthalocyanines[END_REF][START_REF] Bai | Direct Metalation of a Phthalocyanine Monolayer on Ag(111) with Coadsorbed Iron Atoms[END_REF] Using Li dopants, the charge transfer could be locally modulated and the molecular spin could be tuned [START_REF] Krull | Site-and Orbital-Dependent Charge Donation and Spin Manipulation in Electron-Doped Metal Phthalocyanines[END_REF] . In another study, Bai;et al. showed that 2HPc react strongly with Fe atoms to form FePc molecules on Ag(111). [START_REF] Bai | Direct Metalation of a Phthalocyanine Monolayer on Ag(111) with Coadsorbed Iron Atoms[END_REF] This on-surface metalation process was theoretically shown to be energetically favorable for M=Co, Ni, Mn on 2HPc/Ag(111). 127 It would be particularly interesting to study the

  (b). Our STM images reveal that 2HPc not only adsorb with 2H-axis perpendicular to 01 1 directions (i.e. along 2 11 directions) as observed in literature[START_REF] Sperl | Controlled Metalation of a Single Adsorbed Phthalocyanine[END_REF][START_REF] Kügel | Breaking Degeneracy of Tautomerization-Metastability from Days to Seconds[END_REF] but also parallell (within an angle error of ±2 • ). Molecules marked as C and C' in Fig. 1(b) are representative of the two configurations. Likewise in Fig. 1(c), molecules A and B adsorb in the same configuration as molecule C. In their recent work, Kügel and coworkers demonstrate that the only way to obtain a 2H-axis along one of the 01 1 direction is to start with a molecule which 2H-axis is perpendicular to one 01 1 direction and induce tautomerization by applying a bias voltage pulse U such that |U | > 0.45 V when the tip is located above the molecule. It is claimed that the absence of 2H-axis along 01 1 directions can be explained by a high difference in energy with the configuration where the 2H-axis lies perpendicular to 01 1 .

Figure 1 :

 1 Figure 1: The Structure of 2HPc/Ag(111) in G-phase. (a) LEED pattern recorded at an electron energy of 15 eV. (b,c) High-resolution STM topographic images of 2HPc molecules on Ag(111). Tunneling bias conditions: V b = 1 mV, I t = 200 pA. The close-packed 01 1 directions of the Ag(111) are indicated by white lines in (b). The numbered crosses in (c) indicates the location where the STS spectra displayed in Fig.3(a) and Fig.5(a) were recorded. Cyan lines in (b) indicate the direction of the 2H-axis (see text) of the molecules. (d,e) Top views of the DFT calculated relaxed most stable adsorption geometries.

2

 2 eV. Molecules A, B and C would therefore correspond to the α-case (Fig.1(d)), whereas molecule C' would correspond to the β-case (Fig.1(e)). From these models, one can see that the transition from one geometry to the other can occur simply via a rotation of the molecule by 30 • . In our work, we found compelling evidences that such rotation can happen. In Fig.S4in the Supporting Information, two time sequences issued from pairs of STM images recorded successively show molecules that rotate without external stimuli other than the scanning tip governed by the tunneling parameters V b , I t with V b much smaller than the bias voltage threshold necessary to induce tautomerization. For the particular coverage shown in Fig.1(b), the ratio of parallell to perpendicular configurations is 1/3 leading to the conclusion that the perpendicular geometry is the most stable one.In the STM image of the C-phase displayed in Fig.2(b), each molecule exhibits a pair of splitted lobes. Assuming that they are perpendicular to the 2H-axis as in the case of molecules in G-phase, the azimuthal angle δ with respect to the close-packed directions of Ag(111) as sketched in Fig.2(b) can be determined. The measured value of δ is 65 • ± 3 • similar within the angle error to the azimuthal orientation of the experimentally most stable adsorption configuration α.The structural model of the molecules self-organized as a C-phase obtained by DFT calculations is shown in Fig.2(c). The angle δ = 62 • is in excellent agreement with the experimental value validitating this model to further extract the projected density of states (PDOS). The extra insight we get from this STM analysis is that molecules in the less stable configuration such as molecule C' in Fig.1 (b) undergo an azimuthal rotation of about 30 • upon self-assembling. Therefore, one expects the ratio between the two configurations to increase when increasing the coverage in favor of α configuration. However, this analysis is out of the range of this paper.

Figure 2 :

 2 Figure 2: The Structure of 2HPc/Ag(111) in C-phase. (a) LEED pattern recorded at an electron energy of 14 eV. (b) Corresponding STM topographic image. Tunneling bias conditions: V b = -1.8 V, I t = 200 pA. The close-packed 01 1 directions of the Ag(111) are indicated by a black star. Cyan lines indicate the direction of the 2H-axis of the molecules (see text). (c) Top view of the simulated relaxed adsorption geometry. Rectangles in dashed line represent the unit cells in (a) reciprocal and (b,c) direct space.

Figure 3 :

 3 Figure 3: Electronic properties of 2HPc/Ag(111) in G-phase. (a) Dotted lines are dI/dV spectra recorded with the tip on top of molecules labeled A,B and C' in Fig.1(c). Set point is: V b = 1 mV, I t = 200 pA. The dashed blue line is a dI/dV spectrum recorded on a 4 th molecule (not in Fig.1(c)). Set point : V b = 25 mV, I t = 200 pA. The full grey line was recorded further away from the molecules on bare Ag surface at the position indicated by the grey cross in Fig. 1(c). The Fano fits represented by the black lines yields: A: q = 1.73, K = -7.99 meV and Γ = 11.78;B: q = 7.22, K = -6.25 meV and Γ = 12.39;C': q = 54, K = -1.16 meV and Γ = 9.8. A vertical shift was added for clarity. (b) UPS spectra recorded at T= 9 K, 80 K and 285 K and on bare Ag(111) substrate at T= 9 K (black line) and at an emission angle of 45 • .

  the presence of an occupied F-LUMO state results from the charge transfer from the Ag surface to the molecule. Hence, both our STS and UPS experiments show that the molecule is negatively charged in agreement with these previous results. As well as for single molecules, a resonance at E F was obtained using STS and UPS techniques. Bringing forward the same arguments as for the case of single molecules, one can conclude that this resonance is the experimental signature of the Kondo effect. A high-resolution STS spectrum in Fig.4(b) exhibits, as in the case of single 2HPc, an extra peak at about 50 meV leading to the conclusion that electron-vibron coupling is not hindered by intermolecular interactions inside the self-assembly thus resulting in a vibrational Kondo effect. Once again, this is corroborated by the inelastic electron tunneling spectrum shown in blue line in Fig.4(b) recorded over the Pc ligand and exhibiting the characteristic symmetric two-step like lineshape. The Kondo temperature T K obtained by fitting the STS spectra recorded over 7 molecules inside the supramolecular network ranges from 57 to 69 K as displayed in Fig.S2. It is about twice smaller than for single molecules. Possible

Figure 4 :

 4 Figure 4: Electronic properties of 2HPc/Ag(111) in C-phase. (a,b) dI/dV spectra recorded over the center of one molecule in the self-assembly. Set point are (a) V b = -1 V, I t = 100 pA, (b) V b = 1 mV, I t = 200 pA for top curve and V b = 50 mV, I t = 200 pA for bottom curve. A vertical shift was added for clarity. The Fano fit represented by the black line superimposed to the top curve in (b) yields: q = 21, K = -0.35 meV and Γ = 5.0. (c) UPS spectra recorded at T= 9 K, 80 K, 285 K and on bare Ag(111) substrate at T= 9 K at an emission angle of 45 • . (d) Computed density of states projected (PDOS) onto atomic orbitals of 2HPc on Ag(111), (e) from left to right: spin density distribution of neutral, anionic 2HPc species in the gas-phase and adsorbed on Ag(111).

Figure 5 :

 5 Figure 5: Electronic properties of Ag in G-phase. (a) dI/dV spectra recorded on Ag(111) between molecules in solid lines and on a pristine Ag(111) surface in dashed line. Numerical labels 2 to 4 correspond to the position of the tip marked by a matching colored cross in Fig.1(c) and Fig.S4(b). Tunneling bias conditions: V b = -1.8 V, I t = 200 pA. (b) STM topographic image. Tunneling bias conditions: V b = -40 mV, I t = 200 pA, (c-f) dI/dV maps recorded at -100 mV,-40 mV,+10 mV and +30 mV, respectively. Tunneling current I t = 200 pA.

  127. Bao, D.-L.; Zhang, Y.-Y.; Du, S.; Pantelides, S. T.; Gao, H.-J. Barrierless On-Surface Metal Incorporation in Phthalocyanine-Based Molecules, J. Phys. Chem. C 2018, 122, 6678-6683.

Kondo physics in the MPc/2HPc hetero-molecular arrays as a function of MPc concentration.

Overall, any combination of the above cited manipulation strategies might be used. For these reasons, this system offers an exceptionnaly rich playground for investigating the molecular Kondo physics. This material is available free of charge via the Internet at http://pubs.acs.org.

Supporting Information Available


M Laurençon

T De Rességuier
email: thibaut.de-resseguier@ensma.fr

D Loison

J Baillargeat

J N Domfang Ngnekou

Y Nadot

Effects of additive manufacturing on the dynamic response of AlSi10Mg to laser shock loading

Keywords: AlSi10Mg, Selective Laser Melting, laser shocks, dynamic response, spall fracture

Effects of additive manufacturing on the dynamic response of AlSi10Mg to laser shock loading

Introduction

In the ongoing development of additive manufacturing (AM) processes, the characterization of physical properties and mechanical performances of the materials thus produced has become a key issue. Indeed, they offer many industrial possibilities by pushing back the technological locks linked to classical manufacturing processes. Among other things, they enable the design of geometrically complex engineering parts and offer new solutions for the most sophisticated applications, accounting for economic and ecological issues as they reduce tooling and loss of costly materials while saving energy. Several reviews summarized the concerns regarding additive manufacturing technologies [START_REF] Frazier | Metal Additive Manufacturing: A review[END_REF][START_REF] Gardan | Additive manufacturing technologies: state of the art and trends[END_REF][START_REF] Mawale | Additive layered manufacturing: State-of-the-art applications in product innovation[END_REF]. The materials obtained by these new processes come with specific microstructure and unconventional mechanical behaviour. While their response to quasi-static loads has now been widely characterised, their dynamic behaviour, especially at very high strain rates, is still largely open to question.

Aluminum alloy AlSi10Mg is a hypoeutectic alloy widely used in transportation field and for aeronautical applications. Indeed, it constitutes a very attractive combination of lightness, good physical properties, mechanical performances, and ability to be processed. Moreover, this alloy is one of the rare aluminum alloys produced by AM nowadays, more particularly by Selective Laser Melting (SLM, also referred as Additive Layer Manufacturing). Thus, advanced work has been performed to characterise its properties inherited from AM process and investigate its mechanical behaviour under quasi-static loading [START_REF] Trevisan | On the Selective Laser Melting (SLM) of the AlSi10Mg Alloy: Process[END_REF][START_REF] Tang | Inclusions, porosity and fatigue of AlSi10Mg parts produced by Selective Laser Melting[END_REF][START_REF] Fella | Selective Laser Beam Melting of AlSi10Mg alloy[END_REF][START_REF] Martinez | AlSi10Mg parts produced by Selective Laser Melting (SLM)[END_REF][START_REF] Kempen | Mechanical Properties of AlSi10Mg Produced by Selective Laser Melting[END_REF]. However, very few studies have been reported yet on its dynamic behaviour, using Hopkinson bars or plate impacts, focusing on texture transition [START_REF] Asgari | On dynamic mechanical behavior of additively manufactured AlSi10Mg_200C[END_REF] or elastic-plastic response and spall fracture [START_REF] Zaretsky | Dynamic response of AlSi10Mg alloy fabricated by selective laser melting[END_REF]. This latter work by Zaretsky et al. provided the yield strength (so called Hugoniot Elastic Limit, HEL) in compression as well as the dynamic tensile strength (so called spall strength) by measuring the free surface velocity profiles of impact-loaded AlSi10Mg targets obtained by SLM, compared to casted ones. Post-recovery fracture surfaces were observed by means of microscopy. The results reveal significantly higher dynamic properties for SLM alloy than for the one obtained by casting, as well as a ductile-brittle transition observed at strain rates comprised between 1 s -1 and 5×10 3 s -1 .

Among a variety of shock loading techniques, high power pulsed lasers provide access to very high strain rates and allow easy sample recovery for post-shock analysis (e.g. [START_REF] De Rességuier | Spall fracture and twinning in laser shock-loaded single-crystal magnesium[END_REF] and references therein), compared to more conventional techniques based on explosives or gas guns. High intensity irradiation of the target surface produces the ablation and vaporization of a thin layer of material into a plasma cloud that expands in free directions thus driving a short compressive pulse in the sample. In this work, laser-driven shocks were generated in AlSi10Mg targets obtained by different SLM processes. Then their yield strength, spall strength, and fracture behaviour were correlated to microstructural features associated with AM.

Materials

Sample manufacturing

Samples were cut from 2 different productions of AlSi10Mg by SLM. The first bar, referenced as P1, was manufactured with a 400 W fiber laser, according to a meander laser scanning strategy in XY plan [START_REF] Koutny | Influence of scanning strategies on processing of Aluminum alloy EN AW 2618 using Selective Laser Melting[END_REF], with a scan speed of 1300 mm/s. The stack of layers was performed along the Z axis on a product support maintained at constant temperature of 200 °C, with a rotation of 67° between each layer of about 30 μm width. The second bar, referenced as P2, was produced in intentionally degraded conditions, from a powder supplied by TLS Technik™ with a 350 W fiber laser, on a platform maintained constantly at 150 °C in order to minimise residual stresses. The scanning strategy followed a meander pattern at a scan speed of 930 mm/s. The layering was performed by rolling (instead of scraping for P1 production) with a rotation angle of 90° between each layer of 50 μm width. Both productions were submitted to stress relaxation heat treatments. P2 bars were heat treated during 1 h at 210°C whereas P1 production was maintained at 300 °C during 2 h. At the end of these heat treatments, both productions respect the standard NF EN 1706:2010, exhibiting the same chemical composition given in Table 1 [START_REF] Domfang Ngnekou | Fatigue properties of AlSi10Mg produced by Additive Layer Manufacturing[END_REF]. P2 production contains flaws in the form of pores that lead to 2.25 % of porosity, while P1 bars are 0.89 % porous. Specimens were cut as 15x15x1 mm plates for P2 material and as 1 mmthick disks of 15 mm diameter for P1, using electrical discharge machining. Then, they were polished mechanically to reach thicknesses comprised between 400 μm and 950 μm.

Structure of the material

The material microstructure is largely governed by SLM parameters [START_REF] Fella | Selective Laser Beam Melting of AlSi10Mg alloy[END_REF][START_REF] Martinez | AlSi10Mg parts produced by Selective Laser Melting (SLM)[END_REF]. The main architectural entity inherited from SLM process is the melt pool (Fig. 1) that follows the laser track and results from atomic segregation during the melting and resolidification of adjacent segments within the powder bed. Due to multi-layering and complex heat transfers associated with SLM process, melt pools have a dissymmetric shape (Fig. 1). Indeed, melt pools formation and layering imply the remelting of neighbouring, already formed melt pools due to interpenetration and overlap. This leads to a pronounced dissymmetry with a convex contour opposite to the building direction (bottom contour along -Z in Fig. 1) and two concave contours in the +Z direction of layering (top contours in Fig. 1). Inside these melt pools, grains grow epitaxially from the fusion line towards the center of the pools, due to temperature gradient during cooling, and are consequently strongly anisotropic. In some cases, grains can be extended over several melt pools as the stacking implies the remelting of adjacent zones previously solidified. The microstructure inside columnar grains reveals a very fine dendritic cellular network consisting of α-Al matrix surrounded by Al-Si eutectic phase [START_REF] Domfang Ngnekou | Fatigue properties of AlSi10Mg produced by Additive Layer Manufacturing[END_REF][START_REF] Domfang Ngnekou | Influence of defect size on the fatigue resistance of AlSi10Mg alloy elaborated by selective laser melting (SLM)[END_REF]. Due to SLM process, the material may develop different defects mainly in the form of porosity. Among these, lacks of fusion (Fig. 1) are characterised by irregular-shaped cavities that can reach mm-sizes. They are generally located at melt pools boundaries and they usually result from a too high scan speed combined to a low laser intensity, a too elevated hatch spacing (distance between two adjacent laser paths), or even an inadequate scanning strategy [START_REF] Aboulkhair | Reducing porosity in AlSi10Mg parts processed by selective laser melting[END_REF][START_REF] Stef | Mechanism of porosity formation and influence on mechanical properties in selective laser melting of Ti-6Al-4V parts[END_REF]. More commonly, metallurgical porosity is homogeneously distributed in the material, its formation being favoured by the high temperature of manufacturing inside the melt pool and by the pre-existing porosity of the powder grains (from gas atomisation).

Determination of density and sound velocity

As will be recalled next, the shock response of materials involves their sound velocity and density. To determine the density, two methods were used. The first one consists in measuring the mass on a precision balance and the theoretical volume calculated with specimen dimensions

+𝐳 ⃗ -𝐳 ⃗

measured with a profilometer. The second one is based on mercury pycnometry, where measurements of the mass of the empty pycnometer 𝑚 0 , the mass of the pycnometer filled with mercury 𝑚 𝑙 , the mass of the pycnometer with the specimen in it 𝑚 𝑠 and the total mass with both mercury and the specimen 𝑚 𝑠𝑙 provide the specimen density 𝜌 0 as

𝜌 0 = 𝜌 𝑙 (𝑚 𝑠 -𝑚 0 ) (𝑚 𝑙 -𝑚 0 )-(𝑚 𝑠𝑙 -𝑚 𝑠 ) (1)
where 𝜌 𝑙 = 13540 𝑘𝑔/𝑚 3 is the density of mercury in the testing conditions. The final density 𝜌 0 for both productions, reported in Table 2, was obtained by averaging these measurements. P1 production presents a higher density than P2, as this latter contains more flaws in the form of porosity.

Longitudinal sound velocity 𝑐 𝐿 was measured for both materials (Table 2), using the pulse-echo method [START_REF] Xiao | Measurement methods of ultrasonic transducer sensitivity[END_REF]. The 6482 m/s value measured in the P1 samples was found to agree well with the mean value of 6710 m/s reported by Zaretsky et al. [START_REF] Zaretsky | Dynamic response of AlSi10Mg alloy fabricated by selective laser melting[END_REF], in a similar alloy of slightly higher density (2656 kg/m 3 ). Unexpectedly, our measured velocity was found to be independent of sample orientation with respect to building direction, like also reported in ref. [START_REF] Zaretsky | Dynamic response of AlSi10Mg alloy fabricated by selective laser melting[END_REF]. Because of difficulties encountered for measuring the transverse sound velocity 𝑐 𝑇 , the bulk sound velocity in our specimens was estimated by assuming the same variation of 49 % between longitudinal and transverse sound velocities reported in ref. [START_REF] Zaretsky | Dynamic response of AlSi10Mg alloy fabricated by selective laser melting[END_REF], and by accounting for the 24 % variation of 𝑐 𝐿 between P1 and P2 materials. Results are presented in Table 2.

Experimental setup

Laser shock experiments have been performed in two different facilities. In both cases, a high power pulsed laser is focused on a spot of a few mm-diameter in the sample surface, which produces the ablation of a thin layer of material and the formation of a plasma cloud. Plasma expansion towards the laser source drives, by reaction, a short compressive pulse which propagates from the irradiated spot into the metal. The velocity of the sample free surface, opposite to the loaded spot, is recorded with a Velocity Interferometer System for Any Reflector (VISAR) [START_REF] Barker | Laser interferometer for measuring high velocities of any reflecting surface[END_REF]. A continuous laser of 0.532 μmwavelength is focused at the free surface of the sample. The Doppler shift due to the motion of that surface is used to produce interference fringes providing the surface velocity.

A first set of low pressure shots was performed with a tabletop laser at Institut Pprime [START_REF] De Rességuier | Use of laser-accelerated foils for impact study of dynamic material behaviour[END_REF], delivering a pulse of 1.06 μm-wavelength, about 20 J-energy and 25 ns-duration focused on a spot of 4 mm-diameter. A water drop was put on top of the irradiated surface to confine the plasma expansion, in order to increase both the amplitude and the duration of the resulting pressure pulse [START_REF] Berthe | Shock waves from a water-confined lasergenerated plasma[END_REF], about 2.5 GPa and 50 ns, respectively. Such loading conditions allowed the investigation of the elastic-plastic behaviour of the alloy (Section 4.1). VISAR measurements were performed with a fringe factor of 0.542 km.s -1 .

Higher pressure loads were needed to study spall fracture (Section 4.2). They were obtained in the LULI2000 facility of the Laboratoire pour l'Utilisation de Lasers Intenses (LULI, France), using a Nd: YAG laser pulse of 1.053 μm-wavelength, about 800 J-energy and 5 ns-duration focused on a 5 mm-diameter spot. To avoid laser breakdown in air at high intensity, samples were shot in secondary vacuum, which also prevented oxidation during shock-induced heating. In addition to the VISAR measurements of the free surface velocity (with a fringe factor of 1.895 km/s), transverse shadowgraphy was implemented to visualize fragmentation and debris ejection, using two ultra-fast cameras in alternate synchronisation (Fig. 2) providing one image every µs with an ultra-short exposure time of 5 ns to ensure minimum motion blur. In order to study the effects of SLM process on the shock response of AlSi10Mg alloy, specimens were irradiated along their stacking direction (both +Z and -Z) and normally to this Z direction of layering (Fig. 3). Post-recovery specimens were observed using optical, Scanning Electronic Microscopy (SEM) and Field Emission Gun (FEG) microscopes. Observations were made on fracture surfaces and on cross sections after being coated in a resin and polished mechanically (without etching).

Results and discussion

As stated in section 3, two sets of different laser shock experiments, involving shots of low and high intensity, were performed to study the elastic-plastic response to dynamic compression (Section 4.1) and the damage and fracture (spall) behaviour under high rate tensile loading (Section 4.2).

Hugoniot Elastic Limit

The main parameters of the low intensity shots are listed in Table 3. The corresponding VISAR records are presented in Fig. 4. After a transit time increasing with sample thickness, the first wave to emerge at the probed surface is called the elastic precursor which accelerates that surface to a velocity 2𝑢 𝐸 of about 60 m/s. It is followed by a slightly slower plastic compression wave inducing a more progressive acceleration to the peak velocity, which decreases with sample thickness due to pressure decay with increasing propagation distance. Then, the free surface decelerates upon arrival of the unloading wave, before a new acceleration after a "round trip" of the reflected wave back to the loaded surface then forth to the probed surface, with a reverberation period of about 2𝑒/𝑐 𝐿 , where e is the specimen thickness. Based on free surface velocity profiles, the Hugoniot Elastic Limit (HEL) 𝜎 𝐸 is derived from the particle velocity 𝑢 𝐸 behind the elastic precursor [START_REF] Antoun | Spall Fracture[END_REF]:

𝜎 𝐸 = 𝜌 0 𝑐 𝐿 𝑢 𝐸 (2)
Results are listed in Table 3 and plotted in Fig. 5. Overall, the HEL, is observed to follow a decreasing trend with the increase of specimen thickness as classically observed in various materials (e.g. review in ref. [START_REF] Billingsley | The decay of the Hugoniot Elastic Limit[END_REF]). Similar decay of 2𝑢 𝐸 was reported in the same AlSi10Mg alloy under plate impacts [START_REF] Zaretsky | Dynamic response of AlSi10Mg alloy fabricated by selective laser melting[END_REF], for a wider range of specimen thicknesses from 310 μm to 4.05 mm. Those impact-based values are in very good quantitative agreement with the velocities measured in our P1 specimens (Fig. 6), while results from the P2 specimens, where density and sound velocity are lower due to degraded manufacturing conditions, cannot be directly included in the comparison (see next).

P2 specimens present lower HEL values than denser P1 samples, at identical thicknesses and regardless of the direction of loading. Thus, the presence of pores, combined to detrimental building parameters, seems to lower the elastic limit of the material under dynamic compression, which is consistent with previous results in 25 % porous tantalum specimens obtained by SLM and impacted by thick tantalum projectiles accelerated with a gas gun [START_REF] Gray | Structure/property characterization of spallation in wrought and additively manufactured tantalum[END_REF].

The HEL does not significantly depend on loading directions, as inferred from the similar values recorded in orthogonally loaded samples (P2-XY) and in those shocked along their Z stacking direction (P2-Z). This is in good agreement with results in ref. [START_REF] Zaretsky | Dynamic response of AlSi10Mg alloy fabricated by selective laser melting[END_REF] that did not present any effect of the loading direction on HEL values. Nevertheless, the decay of the elastic precursor with propagation distance seems faster in samples loaded along the Z direction than normally to that direction, leading to a significant gap in thick specimens (Fig. 5). If this decay is assumed to be enhanced by the presence of defects located preferentially at melt pools boundaries, such gap is qualitatively consistent with the number of these boundaries across a given thickness, higher in a Z-cut specimen (Fig. 3a) than in a XYcut sample (Fig. 3b).

Spall fracture

Fig. 7 shows the free surface velocity profiles recorded in the high intensity laser experiments, corresponding to the parameters presented in Table 4. In this case of higher loading pressures, the elastic precursor is overdriven, i.e. the shock front (including both elastic and plastic compression), which propagates faster than 𝑐 𝐿 , does not split into two waves, so that the HEL cannot be determined from the records. On the other hand, unlike in Fig. 4, the deceleration from the peak velocity is interrupted by a reacceleration, followed by damping oscillations around a finite, approximately steady velocity, with no reloading after a "round trip" throughout the sample thickness. This is typical of spall fracture occurring inside the specimen, at some finite depth beneath the free surface (spall plane), where the interaction of the incident unloading wave with the rarefaction wave reflected from that surface induces tensile stresses [START_REF] Antoun | Spall Fracture[END_REF]. When this local tension exceeds the dynamic tensile strength (spall strength) of the material, it is relaxed by crack opening, which produces a recompression wave. Subsequent reacceleration of the free surface is called the spall pulse, and the spall strength 𝜎 𝑅 can be classically inferred from the amplitude ∆𝑢 𝑓𝑠 of the velocity pullback from the peak velocity to the spall pulse (see Fig. 7), using a common, so-called acoustic approximation [START_REF] De Rességuier | Spall fracture and twinning in laser shock-loaded single-crystal magnesium[END_REF][START_REF] Antoun | Spall Fracture[END_REF]:

𝜎 𝑅 = 1 2 𝜌 0 𝑐 𝑏 ∆𝑢 𝑓𝑠 (3)
The strain rate can be determined as

𝜀̇= 1 2𝑐 𝑏 ∆𝑢 𝑓𝑠 ∆𝑡 (4)
where

∆𝑢 𝑓𝑠
∆𝑡 is the rate of velocity decrease during the deceleration part of the records. Measurements reveal significantly higher spall strengths for P1 specimens than for P2 specimens. This is consistent with the fact that, as previously reported in different materials [START_REF] Glam | Dynamic fracture and spall in aluminum with helium bubbles[END_REF][START_REF] Wang | Spall failure of aluminum materials with different microstructures[END_REF], the resistance to spall damage usually decreases with increasing porosity. More generally, P2 specimens have been built in degraded conditions, with a larger stripe distance between two laser tracks in a same layer (50 μm) as well as a higher angle between laser track directions of successive layers (90° against 67°), which differences are likely to be detrimental to the material cohesion.

Spall strength appears to be almost identical for both directions of shock loading, either parallel or normal to the stacking direction Z. This is consistent with results for the same alloy under plate impacts [START_REF] Zaretsky | Dynamic response of AlSi10Mg alloy fabricated by selective laser melting[END_REF], for which spall strengths are reported to be similar in both loading directions, about 1.75-1.80 GPa, in good quantitative agreement with the values measured in our P1 samples at slightly higher strain rates.

Fragmentation profiles obtained by transverse shadowgraphy are presented in Fig. 8, for P1 and P2 samples subjected to high pressure laser shocks. They show the formation and subsequent ejection in vacuum of one or several spalled layers followed by secondary fragments. Due to late breaking at the periphery of the loaded zone, under shear and tensile stresses, the curvature of the free surface is seen to increase over the first µs. The position of the centre of the free surface is observed to increase linearly with time, which provides the mean (basically constant) flight velocity of the fastest fragments, given to the right of each sequence. Logically, these mean velocities are found to agree well with those measured at the end of the VISAR records of Fig. 6, when free surface velocities reach a final, roughly constant value. They are significantly higher in the P1 specimen than in the P2 samples. This discrepancy is mainly attributed to the faster pressure decay during pulse propagation throughout more porous samples, leading to lower shock breakout pressures and lower free surface velocities. Fragmentation profiles seem smoother and more homogeneous in P1 (Fig. 8a) than in P2 samples (Fig. 8b and8c), where more irregularities and sharp angle changes are observed. This suggests a more chaotic fragmentation in P2 material, as will be confirmed next by SEM images. Microscopy observations of recovered specimens (Fig. 9-13) show spall craters in their free surface, both as front views (SEM) and cross sections (optical micrographs). Overall, the craters are very different in P1 and P2 materials. While they present very homogeneous and nicely circular contours in P1 samples (Fig. 9a and Fig. 10a), they are more chaotic in P2 specimens (Fig. 11a and Fig. 12a), which is consistent with the fragmentation profiles above, with irregular shapes and multiple islets still attached to the samples. Higher magnification SEM suggests that such islets are related to the presence of flaws, such as lacks of fusion (arrow in Fig. 12a).

Fracture surface morphology indicates two distinct types of spalling behaviour, either "intrapool", where cracks propagate within the melt pools, or "interpool", where cracks clearly follow melt pool boundaries. Indeed, the higher concentration of flaws such as lacks of fusion, pores or inclusions at these boundaries, as well as a high gradient of microstructure in this zone [START_REF] Fella | Selective Laser Beam Melting of AlSi10Mg alloy[END_REF][START_REF] Martinez | AlSi10Mg parts produced by Selective Laser Melting (SLM)[END_REF], probably provide preferential sites for voids/cracks nucleation. In samples loaded normally to the Z direction (Fig. 3b), the plane of maximum tension (spall plane) seldom coincides with melt pool boundaries, so that fracture is almost fully intrapool (Fig. 12), with cracks that might follow grains orientations (as suggested in Fig. 12b). In contrast, in samples loaded along the building direction (Fig. 3a), interpool fracture dominates. Because melt pools are dissymmetric (Fig. 1), results depend on the orientation. Upon shock loading along -Z (opposite to the stacking axis), fracture in the spall crater is almost fully interpool, resulting in smooth, convex surfaces corresponding to the bottom of the melt pools (Fig. 9), 745 m/s 613 m/s 601 m/s while a combination of both modes is observed after shock loading along +Z (Fig. 10, where intrapool damage is pointed in red and interpool in yellow). This dependence on orientation can be explained by the melt pool geometry ahead of the tensile front (Fig. 14). After a laser shock along -Z, when this front reflecting from the free surface meets the convex surface of the melt pool, fracture starts at these weak frontiers. As they are almost collinear with the tensile front, spallation propagates along these surfaces, relaxing tensile stresses. In the reverse configuration whereby specimens are loaded along +Z, the tensile front first meets the triple point where damage initiation is more difficult because of the local microstructure and the broader angles with the melt pools boundaries. Thus, spallation only starts beyond this point, in the form of intrapool fracture. Next, the decreasing angle formed between the melt pool boundaries and the tensile front becomes favourable to crack propagation, so that additional interpool fracture occurs, leading to the separation of the rest of the melt pool and leaving a smooth concave surface in the crater (Fig. 10 and11).

The interpool fracture mode leaves clear traces of the melt pools, either concave or convex as discussed above, in the spall crater. These traces include different orientation angles related to the stacking strategy, either 0-67°-134° in P1 samples (Fig. 9 and 10) or 0-90° in P2 samples (Fig. 11). Although such different orientations might coexist in one XY section (Fig. 1), they also result from multiple spall at increasing depths beneath the free surface (see Fig. 9b and11b). Indeed, the reflection of a triangular pressure pulse can produce such multiple spall [START_REF] Rinehart | Scabbing of metals under explosive attack: multiple scabbing[END_REF], as stress relaxation accompanying an early fracture may not prevent a later, deeper one due to further tension. Another evidence of such successive spall fractures is illustrated in Fig. 10c, where secondary (interpool) cracks are observed locally deep below the main crater. Finally, the spall craters after shock loading along the Z direction show a peripheral ring (Fig. 9a, Fig. 10a) where damage is mainly intrapool, compared to the centre showing mainly interpool fracture. Cross sections of these crater edges (Fig. 13) clearly show that both regions correspond to two different spall planes at increasing distance from the free surface. Thus, a first spalled layer was formed through intrapool fracture, about 50 µm-deep beneath the free surface. Then, further tension produced secondary spallation at deeper melt pools boundaries, except in the peripheral ring, due to additional relaxation by lateral release waves.

This process of multiple spall partially accounts for the similar spall strength values recorded under both loading directions (Table 4). Indeed, the first fracture to occur is the closest to the free surface, typically 50 µm deep below that surface in our test conditions, where the tensile front has not met favourable melt pool boundaries yet, even in the case of shock loading along the Z direction. Therefore, this first fracture is likely to be mainly intrapool, regardless of the direction of shock application. Because the spall strength inferred from the free surface velocity is related to the relaxation provided only by this first fracture, it is logically found to be independent on the loading direction. Finally, higher magnification images of the fracture surface in sample P1-Z-500-2 shocked along the +Z axis reveal small ductile dimples in both interpool and intrapool damage types (Fig. 15), with slightly more elongated dimples in intrapool regions. Thus, spall fracture involves the nucleation, growth and coalescence of microvoids in both cases. This indication that both intrapool and interpool spalling processes result from the same ductile behaviour is another possible cause for the fact that the spall strength does not significantly depend on loading directions (Table 4). The small dimple size (sub-μm-order) suggests that damage nucleation might occur along the denditric network, as Tradowsky et al. showed in their study of tensile properties of AlSi10Mg obtained by SLM [START_REF] Tradowsky | Selective laser melting of AlSi10Mg: Influence of post-processing on the microstructural and tensile properties development[END_REF]. On the other hand, our observations do not seem to corroborate the transition from a ductile to a brittle fracture behaviour reported at high strain rate in impact-loaded AlSi10Mg obtained by SLM [START_REF] Zaretsky | Dynamic response of AlSi10Mg alloy fabricated by selective laser melting[END_REF]. This may be due to the higher shock-induced heating in our case of higher loading pressures. From the peak free surface velocity of about 900 m/s, using Hugoniot data of Al, assumed to provide rough estimations for AlSi10Mg, shock breakout pressure can be evaluated as about 7 GPa, which would correspond to a temperature increase of about 70 K [START_REF] Kinslow | High-Velocity Impact Phenomena[END_REF]. However, stronger heating can be expected inside the sample before shock pressure decay during propagation up to the free surface. Such temperature rise, although moderate, might partially inhibit the transition mentioned above, but more work is needed to clarify this issue.

Conclusion

Thin specimens of SLM-produced AlSi10Mg alloys were subjected to laser-driven shocks to investigate their mechanical response at extremely high strain rates. Experiments were performed on two different materials associated with two distinct sets of building parameters, leading to different values of sound speed and initial porosity. Both the yield strength (Hugoniot elastic limit) and spall strength (resistance to high-rate tensile loading) measured in the alloy of higher quality are in very good quantitative agreement with those reported under plate impact loading. Both values are significantly lower in the alloy produced in degraded building conditions. In particular, flaws directly inherited from the SLM process such as lacks of fusion have a significant influence on the decay of the elastic precursor with propagation distance and on the fracture behaviour, leading to spall craters of irregular contours and surfaces. Although the spall strength is found to be roughly independent on loading orientation with respect to building direction (like reported under plate impacts), this orientation is shown to affect drastically the fracture surface morphology, due to the major role of the melt pool boundaries in the initiation and development of spall damage, leading to a combination of "interpool" and "intrapool" fracture modes. However, at a microscopic scale, both modes seem to result from a ductile behaviour involving the nucleation, growth and coalescence of voids leaving dimples in the fracture surface. Thus, the ductile-to-brittle transition reported under plate impacts was not observed under laser shock loading, possibly because of greater shock-induced heating in our experimental conditions.

Fig. 1 .

 1 Fig. 1. 3D Reconstruction of optical micrographs showing the typical microstructure of SLM-produced AlSi10Mg alloy (after polishing, without etching). Melt pools are visible in their length on the top view, while the cube sides show them in their height (along the z axis) and width (along the x and y axes). The cube side length is 5.5 mm.

Fig. 2 .

 2 Fig. 2. Schematic of the LULI2000 laser shock experimental setup.

Fig. 3 .

 3 Fig. 3. Schematic of laser irradiation (a) along the stacking direction Z and (b) along a direction normal to the Z axis.

Fig. 4 .

 4 Fig. 4. Free surface velocity profiles of (a) P1 samples loaded along Z axis, (b) P2 samples irradiated along Z axis and (c) P2 samples irradiated orthogonally to Z axis. Samples are referenced with their thickness in μm.

Fig. 5 .

 5 Fig. 5. Hugoniot Elastic Limit of laser shock-loaded AlSi10Mg produced by SLM. Material reference, loading direction and sample thickness in μm are indicated on each bar.

Fig. 6 .

 6 Fig. 6. Velocity 2𝑢 𝐸 measured in SLM-produced AlSi10Mg samples of increasing thickness: red squares refer to laser-shock loading of the P1 alloy, while black circles result from plate impacts [10].

Fig. 7 .

 7 Fig. 7. Free surface velocity profiles recorded in (a) P1 samples, (b) P2 samples. Shots are referenced with the direction of shock application and sample thickness in μm.

Fig. 8 .

 8 Fig. 8. Transverse shadowgraphs recorded at 1μs, 2μs, 3μs and 4μs from left to right, in (a) P1-Z, (b) P2-Z and (c) P2-XY samples with the mean velocity of the main spalled layer.

Fig. 9 .

 9 Fig. 9. Scanning Electron Micrographs of the spall crater in sample P1-Z-500-1 shocked along the -Z axis (a, b), and optical micrograph of a cross section of the sample (c).

Fig. 10 .

 10 Fig. 10. Scanning Electron Micrographs of the spall crater in sample P1-Z-500-2 shocked along the +Z axis (a, b), and optical micrograph of a cross section of the sample (c). Arrows and circles show both intrapool (red) and interpool fracture (yellow).

Fig. 11 .

 11 Fig. 11. Scanning Electron Micrographs of the spall crater in sample P2-Z-500-1 shocked along the +Z axis (a, b), and optical micrograph of a cross section of the sample (c).

Fig. 12 .Fig. 13 .

 1213 Fig. 12. Scanning Electron Micrographs of the spall crater in sample P2-XY-500-1 shocked along the normal to the building direction (a, b), and optical micrograph of a cross section of the sample (c). The white arrow points to a lack of fusion.Fracture is mainly intrapool, except for some interpool cracks at boundaries of propitious location and orientation.

Fig. 14 .

 14 Fig. 14. Schematic description of the interaction between the tensile front propagating upwards from the free surface (blue dotted line) and the melt pool boundaries, after shock loading along -Z (left) or +Z (right), at two successive instants (top then bottom).

Fig. 15 .

 15 Fig. 15. SEM-FEG images of P1-Z-500-2 fracture surface in interpool (a, a') and intrapool (b, b') regions.

Table 1 .

 1 Material composition (wt %) in NF EN 1706:2010 standard.

	Element	Al	Si	Fe	Mg	Mn	Ti	Zn	Cu, Ni, Pb, Sn
	Proportion Bal.	9.0-11.0	<0.55 0.2-0.45 <0.45 <0.15 <0.1	<0.05

Table 2 .

 2 Density and sound velocity of the AlSi10Mg alloys from SLM processes P1 and P2 (see text for details).

	Material	Density 𝝆 𝟎 (kg/m 3 )	Longitudinal sound velocity 𝒄 𝑳 (m/s)	Bulk sound velocity 𝒄 𝒃 (m/s)
	P1	2646	6482	5345
	P2	2610	4910	4049

Table 3 .

 3 Main experimental parameters and results for the low intensity shots shown in Fig.4. The irradiated spot diameter is 4 mm and the pulse duration is about 25 ns.

	Specimen reference	Material	Sample thickness (μm)	Direction of loading	Laser energy (J)	Laser intensity (GW/cm²)	2𝒖 𝑬 (m/s)	Hugoniot Elastic Limit (HEL) 𝝈 𝑬 (MPa)
	P1-Z-500	P1	500	Z	17	7.87	63	540
	P1-Z-600	P1	600	Z	16	5.90	55	468
	P1-Z-650	P1	650	-Z	16	6.64	60	514
	P2-Z-500	P2	500	Z	16	6.61	65	416
	P2-Z-600	P2	600	-Z	16	6.06	65	416
	P2-Z-700	P2	700	Z	17	4.49	42	269
	P2-Z-950	P2	950	+Z	15	3.95	34	218
	P2-XY-500	P2	500	┴ Z	16	6.13	66	423
	P2-XY-600	P2	600	┴ Z	17	7.09	61	391
	P2-XY-900	P2	900	┴ Z	18	6.27	61	391

Table 4 .

 4 Main experimental parameters and results for the high intensity shots shown in Fig.3. Laser pulse duration is 5 ns and the irradiated spot diameter is 5 mm.

	Specimen reference	Material	Sample thickness (μm)	Direction of loading	Laser energy (J)	Laser intensity (GW/cm²)	∆𝒖 𝒇𝒔 (m/s)	𝝈 𝑹 (GPa)	𝜺̇ (𝟏𝟎 𝟔 s -1 )
	P1-Z-400-1	P1	400	+Z	757	789	271	1.88	2.35
	P1-Z-400-2	P1	400	+Z	702	735	277	1.92	3.30
	P1-Z-500-1	P1	500	-Z	785	815	280	1.94	2.49
	P2-Z-500-1	P2	500	+Z	696	713	239	1.24	2.01
	P2-XY-500-1	P2	500	┴ Z	686	726	241	1.25	2.34

μm

Acknowledgements

The authors thank the Thales Group and Cyril Dupuytrent for supporting this work, as well as Zodiac Aerospace for providing the materials. The authors also gratefully acknowledge everyone within Laboratoire pour l'Utilisation des Lasers Intenses and Institut Pprime, Département Physique et Mécanique des Matériaux, équipe Endommagement et Durabilité who contributed to these experiments.

Data availability

The raw/processed data required to reproduce these findings cannot be shared at this time as the data also form part of an ongoing study.


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Laurianne L Canario

Long-term effects of selection for prolificacy and kit growth on rabbit performance and behaviour

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


Alexandre Dore

Mathieu Lihoreau

Yvon Billon

Laure Ravon

Jean Bailly

Jean-François Bompa

Edmond Ricard

Hervé Aubert

Dominique Henry

Laurianne L Canario

Millimetre-wave radars for the automatic recording of sow postural activity

  L'archive ouverte pluridisciplinaire