Julien Ramade

Emmanuel Cottancin
email: emmanuel.cottancin@univ-lyon1.fr

Marie-Ange Lebeault

Cyril Langlois

Laurent Piccolo

Michel Broyer

Matthias Hillenkamp

Jean Lermé

Florent Calvo

Michel Pellarin

Environmental Plasmonic Spectroscopy of Silver-Iron Nanoparticles: Chemical Ordering Under Oxidizing and Reducing Conditions

The chemical structure and the localized surface plasmon resonance (LSPR) of sizeselected AgxFe1-x (x=0.5, 0.8) nanoparticles (NPs), produced by laser vaporization, were investigated experimentally and theoretically. Monte Carlo simulations employing a many-bodyembedded-atom model show that small isolated Ag-Fe NPs should preferentially adopt core@shell structures with an iron core that may be deformed or off-centered while keeping a silver shell around it. Experimentally, the optical response of silica-embedded NPs was measured with a new environmental spectrophotometer based on spatial modulation and is discussed in relation with the NP chemical structure independently studied by transmission electron microscopy (TEM).

Measurements performed on as-prepared samples show that iron rapidly oxidizes when exposed to air to form a magnetite (Fe3O4) shell surrounding a purely metallic crystalline silver core. In situ optical measurements carried out successively under oxidizing and reducing atmospheres indicate that iron oxidation and reduction are reversible processes that are directly mirrored in the LSPR changes, in good agreement with optical simulations. The TEM observations, the environmental plasmonic spectroscopy measurements and the various simulations lead us to conclude that iron and silver initially adopt a segregated configuration with a silver-enriched surface and that, during oxidation, iron likely diffuses throughout the silver shell, leading to an Ag@Fe3O4 configuration, while an inverse process may occur during annealing under reducing atmosphere. Finally, we show that Ag-Fe NPs, co-deposited with alumina on a substrate kept at 400°C, offers an alternative to preserve the metallic character of iron.

Introduction

Multicomponent nanoparticles (NPs) may adopt various structures (alloys, Janus, core-shell…) [1][START_REF] Baletto | Structural Properties of Nanoclusters: Energetic, Thermodynamic, and Kinetic Effects[END_REF][START_REF] Nanoalloys | From Fundamentals to Emergent Applications[END_REF][START_REF] Ferrando | Nanoalloys : From Theory to Applications of Alloy Clusters and Nanoparticles[END_REF] and their optical properties have generated unceasing experimental and theoretical investigations over the last decades. [START_REF] Barcaro | Optical Properties of Nanoalloys[END_REF][START_REF] Cottancin | Optical Probes of The Chemical Structure in Metallic Nanoalloys[END_REF][START_REF] Cottancin | Optical, Structural and Magneto-Optical Properties of Metal Clusters and Nanoparticles[END_REF][START_REF] Cortie | Synthesis and Optical Properties of Hybrid and Alloy Plasmonic Nanoparticles[END_REF] Among all possible materials, coinage metal-based nanoalloys are of great interest as they display a strong resonance in the near UV-visible range (the so-called localized surface plasmon resonance or LSPR), the features of which depend not only on the morphology (size, shape) and environment of the NPs, but also on their internal structure that itself depends on these parameters. One primary interest of studying their optical properties lies in shaping their LSPR by tuning the relative proportion of constituents and their chemical ordering. In addition, optical spectroscopy is a nondestructive method for probing the chemical structure of the NPs and their possible chemical modifications such as oxidation or reduction for instance, both in individual NPs [START_REF] Grillet | Photo-Oxidation of Individual Silver Nanoparticles: A Real-Time Tracking of Optical and Morphological Changes[END_REF] and in NP assemblies. [START_REF] Cottancin | Plasmon spectroscopy of small indium-silver clusters: monitoring the indium shell oxidation[END_REF][START_REF] Ramade | Nano-fried-eggs: Structural, optical, and magnetic characterization of physically prepared iron-silver nanoparticles[END_REF] Moreover, the LSPR of the NP can be used as a local probe of the modifications of its immediate environment, as for example the adsorption of molecules at its surface. [START_REF] Demirdjian | Indirect Nanoplasmonic Sensing to Probe with a High Sensitivity the Interaction of Water Vapor with Soot Aerosols[END_REF] In this respect, plasmonic sensing provides a promising tool to monitor the real-time kinetics of reactions occurring at the vicinity of the NPs, [START_REF] Haldar | Core-Size-Dependent Catalytic Properties of Bimetallic Au/Ag Core-Shell Nanoparticles[END_REF][START_REF] Zadeh Adibi | Plasmonic Nanospectroscopy of Platinum Catalyst Nanoparticle Sintering in a Mesoporous Alumina Support[END_REF][START_REF] Larsson | Nanoplasmonic Probes of Catalytic Reactions[END_REF] or directly within the NPs, when one component evolves under a reactive environment. [START_REF] Cottancin | Plasmon spectroscopy of small indium-silver clusters: monitoring the indium shell oxidation[END_REF] Novel or enhanced properties can also arise owing to the LSPR and its related enhanced local field around the NP. For this purpose, a plasmonic metal is ideally combined with another material presenting a different functionality (catalytic, chemically active, magnetic, optical…). Such combinations with efficient optical absorption [START_REF] Pellarin | Plasmon Resonances Tailored by Fano Profiles in Silver-Based Core-Shell Nanoparticles[END_REF] should result in the development of new nanocomposite materials denoted as active or passive hybrid NPs with promising applications. For active hybrid NPs, the functionality of the second material involves an interaction with the LSPR that can be magneto-plasmonic, [START_REF] Armelles | Focus on magnetoplasmonics[END_REF][START_REF] Wang | Plasmonics and Enhanced Magneto-Optics in Core-Shell Co-Ag Nanoparticles[END_REF] photocatalytic, [START_REF] Zaleska-Medynska | Noble metal-based bimetallic nanoparticles: the effect of the structure on the optical, catalytic and photocatalytic properties[END_REF] or lead to enhanced fluorescence. [START_REF] Grzelak | Hybrid silica-gold core-shell nanoparticles for fluorescence enhancement[END_REF] For passive hybrid systems, which is the topic of the present work, the second material acts as the environment of the plasmonic counterpart, [START_REF] Cortie | Synthesis and Optical Properties of Hybrid and Alloy Plasmonic Nanoparticles[END_REF] and changes in its chemical or physical structure can efficiently be probed through the induced LSPR changes. [START_REF] Wadell | Drift-corrected nanoplasmonic hydrogen sensing by polarization[END_REF] This method is useful in various fields such as heterogeneous catalysis, gas sensing [START_REF] Nasir | Hydrogen Detected by the Naked Eye: Optical Hydrogen Gas Sensors Based on Core/Shell Plasmonic Nanorod Metamaterials[END_REF] or biosensing. [START_REF] Dallaire | Laser-Generated Au-Ag Nanoparticles For Plasmonic Nucleic Acid Sensing[END_REF][START_REF] Qiu | Bimetallic Au-Ag alloy nanoislands for highly sensitive localized surface plasmon resonance biosensing[END_REF] A reactive environment may induce structural modifications of the NPs that strongly affect their properties, and, in turn, their optical response. The real-time monitoring of their evolution can be directly observed at the single NP level owing to environmental transmission electron microscopy (ETEM) imaging. [START_REF] Giorgio | Environmental electron microscopy (ETEM) for catalysts with a closed E-cell with carbon windows[END_REF][START_REF] Gai | Atomicresolution environmental transmission electron microscopy for probing gas-solid reactions in heterogeneous catalysis[END_REF][START_REF] Tao | In Situ Studies of Chemistry and Structure of Materials in Reactive Environments[END_REF][START_REF] Crozier | In situ and operando transmission electron microscopy of catalytic materials[END_REF][START_REF]Controlled atmosphere transmission electron microscopy: principles and practice[END_REF] However such observations have to be combined with global environmental characterizations at the scale of larger NP assemblies in order to determine whether the processes observed on single NPs are representative for the whole sample. The ongoing development of in situ and real-time optical spectroscopy combined with ETEM techniques is essential for a better understanding of the mechanisms involved during chemical and physical rearrangements.

Recently we reported ETEM observations [START_REF] Ramade | Tracking the Restructuring of Oxidized Silver-Indium Nanoparticles Under a Reducing Atmosphere by Environmental HRTEM[END_REF] and ex-situ optical spectroscopy [START_REF] Cottancin | Plasmon spectroscopy of small indium-silver clusters: monitoring the indium shell oxidation[END_REF] on indium-silver nanoalloys. The reduction of the core-shell In-Ag@In2O3 was observed by ETEM and oxidation/reduction cycles were demonstrated through LSPR shifts. Here, we present a new setup allowing in-situ optical measurements of a NP assembly, complementary to single NP ETEM observations. The set-up is tested on iron-silver NPs, which combine a plasmonic material with a ferromagnetic transition metal, thus providing an interesting system in the field of active hybrid NPs. [START_REF] Scaramuzza | Magnetically Assembled SERS Substrates Composed of Iron-Silver Nanoparticles Obtained by Laser Ablation in Liquid[END_REF] Moreover, iron is a potential candidate for low-cost catalysis applications, [START_REF] Kharisov | Iron-based Nanomaterials in the Catalysis[END_REF][START_REF] Van Der Laan | Kinetics and selectivity of the Fischer-Tropsch synthesis: A literature review[END_REF] even though it is also very vulnerable to oxidation. Unfortunately, the Ag-Fe system at the nanoscale is not easy to stabilize. Iron (or iron oxide)-noble metal hybrid NPs have been the subject of many investigations, [START_REF] Sun | Monodisperse FePt nanoparticles and ferromagnetic FePt nanocrystal superlattices[END_REF][START_REF] Lee | Magneto-optical and optical properties of Fe-rich Au-Fe alloy films near the fcc-bcc structural transformation region[END_REF][START_REF] Lyon | Synthesis of Fe Oxide Core/Au Shell Nanoparticles by Iterative Hydroxylamine Seeding[END_REF][START_REF] Benoit | Structural and electronic properties of the Au(001)/Fe(001) interface from density functional theory calculations[END_REF][START_REF] Amendola | Coexistence of plasmonic and magnetic properties in Au89Fe11 nanoalloys[END_REF][START_REF] Amendola | Strong dependence of surface plasmon resonance and surface enhanced Raman scattering on the composition of Au-Fe nanoalloys[END_REF][START_REF] Baumgardner | Nanoparticle Metamorphosis: An in Situ High-Temperature Transmission Electron Microscopy Study of The Structural Evolution of Heterogeneous Au:Fe2O3 Nanoparticles[END_REF][START_REF] Papaefthimiou | Mixing Patterns and Redox Properties of Iron-Based Alloy Nanoparticles under Oxidation and Reduction Conditions[END_REF][START_REF] Langlois | Fully Crystalline Faceted Fe-Au Core-Shell Nanoparticles[END_REF] and some studies focused on silver-iron [START_REF] Lu | Fe@Ag core-shell nanoparticles with both sensitive plasmonic properties and tunable magnetism[END_REF][START_REF] Benelmekki | A facile single-step synthesis of ternary multicore magneto-plasmonic nanoparticles[END_REF][START_REF] Amendola | Laser generation of iron-doped silver nanotruffles with magnetic and plasmonic properties[END_REF] or silver-iron oxide with promising applications in the field of antimicrobial treatment and water decontamination. [START_REF] Luo | Improved debromination of polybrominated diphenyl ethers by bimetallic iron-silver nanoparticles coupled with microwave energy[END_REF][START_REF] Mahmoudi | Silver-Coated Engineered Magnetic Nanoparticles Are Promising for the Success in the Fight against Antibacterial Resistance Threat[END_REF][START_REF] Marková | Air Stable Magnetic Bimetallic Fe-Ag Nanoparticles for Advanced Antimicrobial Treatment and Phosphorus Removal[END_REF][START_REF] Lin | Encapsulated Fe3O4/Ag Complexed Cores in Hollow Gold Nanoshells for Enhanced Theranostic Magnetic Resonance Imaging and Photothermal Therapy[END_REF][START_REF] Moscoso-Londoño | Physicochemical Studies of Complex Silver-Magnetite Nanoheterodimers with Controlled Morphology[END_REF] It should be stressed here that both metals are immiscible in the bulk at all compositions. [START_REF] Swartzendruber | The Ag-Fe (Silver-Iron) system[END_REF] Moreover, at the nanoscale, the NPs at thermodynamic equilibrium conditions should have a surface enriched in silver because of the difference in surface energies between the two metals, namely 1.86 𝐽𝐽. 𝑚𝑚 -2 and 0.925 𝐽𝐽. 𝑚𝑚 -2 for Fe and Ag, respectively. [START_REF] Yaws | Chemical properties handbook : physical, thermodynamic, environmental, transport, safety, and health related properties for organic and inorganic chemicals[END_REF] Experimentally, depending on the synthesis method various configurations may be obtained including Janus [START_REF] Benelmekki | A facile single-step synthesis of ternary multicore magneto-plasmonic nanoparticles[END_REF] and sometimes metastable structures. [START_REF] Amendola | Laser generation of iron-doped silver nanotruffles with magnetic and plasmonic properties[END_REF] In chemical syntheses the kinetics and the nature of the surfactants strongly affects the final structure and reverse core@shell Ag@Fe NPs may also be obtained. [START_REF] Carroll | One-Pot Aqueous Synthesis of Fe and Ag Core/Shell Nanoparticles[END_REF] A different, physical route was used here for the synthesis of AgxFe1-x nanoparticles, as reported in a previous study [START_REF] Ramade | Nano-fried-eggs: Structural, optical, and magnetic characterization of physically prepared iron-silver nanoparticles[END_REF] at the specific composition x = 0.5. The NPs were generated in the gas phase by laser vaporization of bimetallic targets and then deposited onto adequate substrates. We have shown that, although simple thermodynamic considerations suggest core-shell structures with an iron core and a silver shell in the ground state, we always observe Janus-like segregated structures, termed "nano-fried-eggs". [START_REF] Ramade | Nano-fried-eggs: Structural, optical, and magnetic characterization of physically prepared iron-silver nanoparticles[END_REF] The silver part of the NP forms a pure metallic nanosphere, whereas the iron part is shown to rapidly react with the environment to form amorphous oxides or carbides.

Despite the high reactivity with the environment and a probable structural rearrangement, the particles retain both plasmonic and ferromagnetic properties. [START_REF] Ramade | Nano-fried-eggs: Structural, optical, and magnetic characterization of physically prepared iron-silver nanoparticles[END_REF] Beyond this first characterization essentially focused on the structural and magnetic properties of the deposited or embedded Fe0.5Ag0.5 NPs, we conduct here a detailed study for two silver compositions (50% and 80%), by investigating the chemical properties of the NPs through TEM and environmental optical spectroscopy, and interpreting the combined physico-chemical observations with the help of Monte Carlo (MC) simulations of their structural stability at finite temperature.

In the present study, NPs of two relative compositions (Ag0.8Fe0.2 and Ag0.5Fe0.5) were codeposited in a silica matrix for optical measurements in a controlled environment. In this respect, a new setup, based on the spatial modulation spectroscopy (SMS) technique, so far used for single NP spectroscopy, [START_REF] Arbouet | Direct measurement of the single-metal-cluster optical absorption[END_REF][START_REF] Billaud | Absolute optical extinction measurements of single nano-objects by spatial modulation spectroscopy using a white lamp[END_REF] and allowing the measurement of the optical absorption of embedded clusters in a reactive gaseous environment at various temperatures, was developed. The setup was used to probe the chemical ordering of iron-silver NPs under reducing or oxidizing conditions. TEM and optical characterizations were performed just after air exposure, showing that the system is segregated with a silver core surrounded by an oxidized iron shell. As will be shown below, the combination of TEM observations, environmental plasmonic measurements, optical and atomistic Monte Carlo simulations provides insight into the native structure of the NPs and its evolution during the redox cycles.

The manuscript is organized as follows. In the next section we present the modeling through Monte Carlo simulations providing information about the expected chemical ordering of the native system. After a description of the new experimental setup in section 3, TEM and optical characterizations of the NPs after air exposure are presented followed by their optical response under controlled environment. The optical responses of obtained structures implemented in optical simulations are compared to the optical spectra measured just after air exposure or after annealing under reducing atmosphere. Based on these results we propose a scenario of the evolution of the chemical ordering under reducing and oxidizing atmospheres.

Atomistic Modeling of Ag-Fe nanoalloys

Iron-silver nanoalloys are relatively poorly documented, and we have begun their investigation with some computational modeling under the ideal conditions of isolated systems. The purpose of this section is to explore the structure and finite temperature behavior of medium size nanoparticles containing approximately 1000 atoms, for compositions considered in experiments, namely 80% and 50% in silver. For such relatively large sizes, methods using an explicit description of electronic structure are not practical and we rely on semiempirical many-body potentials together with advanced Monte Carlo methods to sample the potential energy surface efficiently at finite temperature. As a first step towards understanding the fundamental behavior of Ag-Fe nanoalloys, our modeling refers to isolated nanoparticles without any contact with a substrate or a matrix.

Methods

The embedded-atom potential by Zhou and coworkers [START_REF] Zhou | Misfit-energy-increasing dislocations in vapor-deposited CoFe/NiFe multilayers[END_REF] was employed to model the nanoparticles, and parallel tempering MC simulations were undertaken to explore low-energy structures and phase changes in the temperature range extending over the melting region. The initial configurations of the nanoparticles were designed with a body-centered-cubic (BCC) iron core of cubic shape and truncated edges, on which six truncated silver pyramids with height parallel to the (001) crystallographic direction were placed following the Ag(001)/Fe(001) epitaxial relationship at 45°. Under such symmetry constraints, the number of atoms for both metals is not arbitrary, and the desired compositions are satisfied within a few percents.

The simulations were initially carried out using 32 temperatures distributed geometrically in the 200-1500 K range, allowing for occasional exchanges between random pairs of configurations from neighboring trajectories every 10 MC cycles (one cycle being equivalent to N individual moves where N is the total number of atoms). After some first simulations, the analysis of the success rates of exchange moves allows adjusting the temperature ladder, removing some of the low temperature replicas and adding others at intermediate temperatures, where thermal fluctuations are stronger. At the 80% composition in silver, the simulations were found to converge much faster by also choosing a lowest temperature of 300 K instead of 200 K, as taken at the 50% composition.

Inherent structures (IS) were located by systematically optimizing the configurations visited onthe-fly along the course of the MC trajectories. If a structure with lower energy than the existing pool was found, the Monte Carlo simulations were entirely restarted from this putative global minimum and a further quench analysis repeated after it, up to 3 of these iterations being necessary until no better candidate was found.

The final simulations consisted of 10 7 Monte Carlo cycles per trajectory, with averages accumulated after 5 x 10 6 cycles. In addition to standard thermodynamical quantities such as the internal energy 𝑈𝑈 = 〈𝐸𝐸〉 and its temperature derivative or heat capacity 𝐶𝐶 𝑣𝑣 (𝑇𝑇) = 𝜕𝜕𝑈𝑈 𝜕𝜕𝑇𝑇 � , variations in the degree of chemical ordering were quantified using the mixing order parameter 𝜇𝜇 already used to characterize nanoalloys. [START_REF] Calvo | Segregation, core alloying, and shape transitions in bimetallic nanoclusters: Monte Carlo simulations[END_REF] This parameter is defined for each configuration 𝐑𝐑 from the local connectivity of individual atoms as

𝜇𝜇(𝐑𝐑) = 𝑁𝑁 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 +𝑁𝑁 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 -𝑁𝑁 𝐹𝐹𝐹𝐹𝐴𝐴𝐴𝐴 𝑁𝑁 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 +𝑁𝑁 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 +𝑁𝑁 𝐹𝐹𝐹𝐹𝐴𝐴𝐴𝐴 (1)
𝑁𝑁 𝐴𝐴𝐴𝐴 denoting the number of A-B bonds between nearest neighbors. The parameter 𝜇𝜇 displays high positive values for phase segregated systems but much lower and, depending on composition, possibly negative values for alloyed structures. Here all bonds within 3.5 Å were considered when calculating 𝜇𝜇.

The inherent structures extracted by local optimization from the individual MC trajectories were also used for analyzing the results, as they capture the structural information but are free of thermal noise. They were sorted according to their energies {𝐸𝐸 𝛼𝛼 } at each temperature, and from the corresponding distributions the root mean square fluctuation 𝜒𝜒 was calculated. The spreading of IS distributions is reflected in the value of 𝜒𝜒, an hypothetical crystalline state being such that 𝜒𝜒 = 0 while a fluid state would exhibit large values of 𝜒𝜒. This quantity is also complementary to the conventional heat capacity because it does not include the kinetic contribution to the thermal fluctuations, all vibrations being frozen in inherent structures.

Thermodynamical equilibrium

To shed more light onto the physics of Ag-Fe nanoalloys, computational modeling of small nanoparticles containing approximately 1000 atoms and initially taken as symmetric core-shell structures were undertaken in the temperature range 200-1500 K. The main thermodynamical properties are the internal energy and the heat capacity whose variations with temperature are shown in Figure 1a and Figure 1b for the 50% and 80% silver compositions, respectively.

The extent of chemical ordering, as characterized by the mixing order parameter 𝜇𝜇 in Eq. (1), is shown as well in Figure 1c. The thermodynamical results are best analyzed by also looking at representative samples of the structures visited at different temperatures and labelled as i-iii and I-III in Figure 1c and shown in Figure 2.

The high values of the mixing parameter 𝜇𝜇 at low temperature are indicative of phase separation and are consistent with the initialization of simulations on core-shell structures. However, the parallel tempering Monte Carlo simulations were occasionally able to locate structures significantly lower in energy than the perfectly symmetric octahedral minima. In particular, for the 50% composition two types of nearly isoenergetic shapes consisting of centered (i) and offcentered (Janus-like type, ii) core-shell nanoalloys are found. At 80% silver composition, a more significant deviation from the initial structure occurs with the iron core adopting a very prolate, cigar-like structure and several isolated iron atoms dissolved in the larger silver shell (I). From the pure thermodynamical perspective, the internal energies exhibit smoothly increasing variations with temperature with marked jumps at 850 or 1000 K depending on composition. These large jumps are the manifestation of melting, which, as discussed further below, can be directly visualized on the nanoparticles themselves. However, this major phase change has no direct signature on the mixing order parameter, which shows complementary information about the extent of chemical ordering within the nanoparticles. At 50 % silver composition, 𝜇𝜇 exhibits a strong drop near 600 K, followed by a minimum at 750 K and a subsequent peak at 850 K. These features will be best interpreted from the inherent structures. At 80% silver composition the mixing parameter mildly decreases at low temperature, reaching also a minimum near 400 K, and smoothly increases across the melting range above 800 K. Inherent structures provide a more systematic connection between the finite temperature results and the underlying atomistic arrangements. The spectra of inherent structures obtained by systematic quenching along the Monte Carlo trajectories are represented in Figure 3 for the two systems. On the same line as the internal energy, the IS spectra show one main increase of about 0.1 eV/atom at the respective melting temperatures of the two systems. However, even down to room temperature the spectra have a finite broadening and show that the equilibrium phase is composed of various minima that differ more in chemical ordering rather than in global structure.

The fluctuations χ in the IS energies, depicted as insets in Figure 3 for the two systems, emphasize the thermal signatures of structural changes that were not so clear in the heat capacity. There are notably two minor peaks at 750 K and 350 K on this quantity for the 50% and 80% silver compositions, respectively, that match the temperatures at which the mixing index reaches a minimum in Figure 1c.

Typical structures sampled in the range between these temperatures and the melting points are shown in Figure 2 as labels iii and II. At 50% silver composition, the structure depicted illustrates the amorphization transition that occurs without much latent heat and could thus be considered as a second-order like phase change. At 80 % silver composition and at 400 K, the iron core appears essentially dissolved in the lattice structure imposed by the larger silver shell. Melting in this NP is sharper than at the 50% composition and, consistently with the lower melting point of silver as compared to that of iron, occurs earlier as well. The liquid phase is associated with multiple amorphous inherent structures showing iron atoms dissolved below the outermost silver layer, a feature also shared by the nanoparticle with 50 % silver. An example of inherent structure of the liquid like state of the 80 % silver NP at 900 K can be seen in Figure 2(III). Under room temperature conditions, our modeling thus predicts that isolated Ag-Fe nanoparticles preferentially adopt core-shell crystal structures. However, the iron core may not necessarily be as symmetric as the outer shell and could adopt either an off-centered position keeping a silver monolayer around it (case of the 50% composition, structure ii) or even undergo strong deformations to accommodate a significantly elongated core (case of the 80% composition, structure I). In section 4 we explore the consequences of such morphologies on the optical response for larger nanoparticles of experimental relevance and attempt to connect these predictions to measurements.

Experimental methods

Cluster Synthesis

Thin dielectric films containing bimetallic clusters with low volume concentrations have been synthesized according to the low-energy cluster beam deposition technique (LECBD) described in previous papers. [START_REF] Perez | Functional Nanostructures From Clusters[END_REF] The clusters are initially produced in the gas phase by a laser vaporization source. The second harmonic of a nanosecond Nd 3+ :YAG pulsed laser is focused on the surface of the target of desired composition that is confined in a small chamber with an aperture at the level of the nozzle in the presence of a continuous flow of helium gas (a few tens of mbar). The atomic plasma thus generated is rapidly cooled down by collisions with the inert gas, leading to nucleation and growth of small bimetallic clusters having between 2 nm and 6 nm in diameter. The particle/gas mixture then expands through the nozzle in the form of a supersonic beam into a high vacuum chamber. As laser vaporization is known to favor the growth of nanoalloys with the same average composition as the target one, [START_REF] Gaudry | Size and composition dependence in the optical properties of mixed (transition metal/noble metal) embedded clusters[END_REF] bimetallic AgxFe(1-x) particles were produced from target rods with x = 50 % or 80 % in atomic compositions. The x value given in the following corresponds to an average with some fluctuations for the produced NPs.

The charged clusters can be size-selected before deposition with a quadrupole static deviator acting as an energy selector of the ionized clusters (of about 5% of the produced clusters). Because of the almost constant velocity of the clusters, the deviator serves as a mass filter. [START_REF] Alayan | Application of a static quadrupole deviator to the deposition of size-selected cluster ions from a laser vaporization source[END_REF] The average cluster size is directly measured with a Wiley-McLaren time-of-flight (TOF) mass spectrometer located downstream of the deviator. The clusters are finally either deposited on a TEM grid (ultrathin carbon on holey carbon films supported on a copper grid) or co-deposited on a fused silica substrate

(1 cm x 1 cm, 1 mm thick) simultaneously with a transparent amorphous silica matrix (200 nm-300 nm thickness) evaporated by an electron gun. The low volume fraction of cluster matter in the thin dielectric films (a few %) prevents from significant coalescence and optical coupling between the nanoparticles. With an appropriate shadow mask, the resulting samples are composed of two adjacent areas, a first region with matrix-embedded clusters and a second region with only the matrix which serves as the reference. It should be stressed that the evaporation speed may have an influence on the porosity of the matrix, which can slightly modify its average optical refractive index.

3.2 In situ optical spectroscopy using Spatial Modulation Spectroscopy (SMS)

Principle of SMS for nanocomposite samples

In this part we briefly present a new setup that allows the measurement of the absorption of matrix-embedded clusters deposited on a transparent substrate with a low optical density and in an environment with controlled atmosphere and temperature. More precisely, we determine the absorption coefficient 𝛼𝛼(𝜆𝜆) of a nanocomposite film of thickness 𝑑𝑑 as in a conventional spectrophotometer. However, for very low optical densities, the sensitivity has to be improved.

For this purpose, we developed a new setup built on the principle of spatial modulation spectroscopy [START_REF] Billaud | Absolute optical extinction measurements of single nano-objects by spatial modulation spectroscopy using a white lamp[END_REF] that will also be suited for environmental spectroscopy experiments on single larger NPs. In SMS a light beam from a white lamp is focused on the sample surface on which NPs are dispersed in low concentration and spatially oscillates at frequency 𝑓𝑓 . Due to its absorption and scattering, a nano-object exposed to the oscillating light beam induces a modulation of the transmitted light power. The transmitted signal (denoted 𝐷𝐷𝐶𝐶) can be demodulated with a lock-in amplifier (either at 𝑓𝑓 or 2𝑓𝑓) to generate a second signal denoted 𝑋𝑋 𝑓𝑓,2𝑓𝑓 that, once normalized

as 𝑋𝑋 𝑓𝑓,2𝑓𝑓
𝐷𝐷𝐷𝐷 , leads to the absolute extinction cross-section of the object, provided the beam spot profile is fully characterized. [START_REF] Billaud | Absolute optical extinction measurements of single nano-objects by spatial modulation spectroscopy using a white lamp[END_REF] Similar experiments can be performed with matrix-embedded cluster samples by modulating the beam spot position between a region with clusters and a region without clusters in the matrix (see Figure 4a). The sample is composed of an absorbing zone with absorption coefficient 𝛼𝛼(𝜆𝜆) between 𝑥𝑥 → -∞ and 𝑥𝑥 = 0 and a transparent region between 𝑥𝑥 = 0 and 𝑥𝑥 → +∞ along the x axis. 𝑃𝑃 𝑜𝑜 (𝜆𝜆) being the incident power and 𝐼𝐼 𝑜𝑜 (𝜆𝜆, 𝑥𝑥, 𝑦𝑦) the intensity distribution of the spot on the sample plane, the relative transmitted power writes

∆𝑃𝑃 𝑃𝑃 𝑜𝑜 = 𝑃𝑃 𝑡𝑡𝑡𝑡 (𝜆𝜆) -𝑃𝑃 𝑜𝑜 (𝜆𝜆) 𝑃𝑃 𝑜𝑜 (𝜆𝜆) = � 𝑑𝑑𝑥𝑥 0 -∞ � 𝑑𝑑𝑦𝑦 𝐼𝐼 𝑁𝑁 (𝜆𝜆, 𝑥𝑥, 𝑦𝑦)𝑒𝑒 -𝛼𝛼(𝜆𝜆)𝑑𝑑 +∞ -∞ + � 𝑑𝑑𝑥𝑥 +∞ 0 � 𝑑𝑑𝑦𝑦 𝐼𝐼 𝑁𝑁 (𝜆𝜆, 𝑥𝑥, 𝑦𝑦) -1 +∞ -∞
which can be simplified as

∆𝑃𝑃 𝑃𝑃 𝑜𝑜 = -�1 -𝑒𝑒 -𝛼𝛼(𝜆𝜆)𝑑𝑑 � ∫ 𝑑𝑑𝑥𝑥 0 -∞ ∫ 𝑑𝑑𝑦𝑦 𝐼𝐼 𝑁𝑁 (𝜆𝜆, 𝑥𝑥, 𝑦𝑦) +∞ -∞
where 𝐼𝐼 𝑁𝑁 (𝜆𝜆, 𝑥𝑥, 𝑦𝑦) = 𝐼𝐼 𝑜𝑜 (𝜆𝜆,𝑥𝑥,𝑦𝑦)

𝑃𝑃 𝑜𝑜 (𝜆𝜆)
is the normalized intensity distribution (∬ 𝐼𝐼 𝑁𝑁 (𝜆𝜆, 𝑥𝑥, 𝑦𝑦)𝑑𝑑𝑥𝑥𝑑𝑑𝑦𝑦 = 1) of the spot (see also Figure 4b). If the spot position 𝑥𝑥 𝑠𝑠 (𝑡𝑡) oscillates at the frequency 𝑓𝑓 like 𝑥𝑥 𝑠𝑠 (𝑡𝑡) = 𝑥𝑥 𝑜𝑜 + 𝛿𝛿 𝑥𝑥 𝑐𝑐𝑐𝑐𝑐𝑐(2𝜋𝜋𝑓𝑓𝑡𝑡) it can be shown that:

∆𝑃𝑃(𝑡𝑡) 𝑃𝑃 𝑜𝑜 = -�1 -𝑒𝑒 -𝛼𝛼(𝜆𝜆)𝑑𝑑 �𝑈𝑈� 𝑥𝑥 𝑠𝑠 (𝑡𝑡)� with 𝑈𝑈( 𝑥𝑥 𝑠𝑠 (𝑡𝑡) = ∫ 𝑑𝑑𝑋𝑋 -𝑥𝑥 𝑠𝑠 (𝑡𝑡) -∞ ∫ 𝑑𝑑𝑦𝑦 𝐼𝐼 𝑁𝑁 (𝜆𝜆, 𝑋𝑋, 𝑦𝑦) +∞ -∞
and 𝑋𝑋 = 𝑥𝑥 -𝑥𝑥 𝑠𝑠 (𝑡𝑡). , and thus the absorption coefficient 𝛼𝛼(𝜆𝜆) related to the absorption cross-section of the NPs to be accessed through

𝑈𝑈( 𝑥𝑥

𝛼𝛼(𝜆𝜆) = - 1 𝑑𝑑 𝑙𝑙𝑙𝑙 �1 - 𝑋𝑋 𝑓𝑓 𝐷𝐷𝐷𝐷 𝑋𝑋 𝑓𝑓 𝐷𝐷𝐷𝐷 𝐴𝐴 𝑜𝑜 2 + 𝐴𝐴 1 √2 � (2)

SMS setup dedicated to environmental measurements

An overview of the SMS setup is displayed in Figure 4c. The sample is set inside a chamber under a controlled gaseous atmosphere and fixed on a heating sample holder (HSH) that can reach up to 250°C. This sample-HSH system is connected to motorized linear stages outside the reactor, allowing a 3-axes-displacement with a spatial resolution of about 0.5 𝜇𝜇𝑚𝑚 (see Figure S1). A turbomolecular pump and a gas injection system are directly connected to the reactor, allowing optical measurements under high vacuum (10 -7 mbar) or small pressures of reactive gases (up to a static pressure of a few hundreds mbar inside the reactor). Consequently, the spot profile on the sample (maintained at a given 𝑧𝑧 position) strongly evolves with the wavelength in the UV range and requires to be fully characterized so as to obtain the Fourier coefficients 𝐴𝐴 𝑜𝑜 , 𝐴𝐴 1 , 𝐵𝐵 2 and thus the absorption coefficient 𝛼𝛼 over the whole spectral range of interest. For that purpose, a razor blade stuck on a glass substrate corresponding to a total absorbing medium (𝛼𝛼(𝜆𝜆) → ∞) was used. Profile lines were then recorded for various wavelengths around the border with small oscillation amplitudes of the spot. This provided the Fourier coefficients and thus allowed a calibration curve using Eq. ( 2) to be obtained (see Figure S2, S3 and S4).

Transmission Electron Microscopy

TEM experiments were performed with a FEI TITAN Transmission Electron Microscope (TEM) G2 operating at 300 kV and corrected for spherical aberrations of the objective lens (Cs corrector).

The oxidized or metallic state of the observed crystalline phases can be clearly discriminated by measuring the interplanar spacing. High-resolution images can be obtained in the HAADF-STEM mode because the size of the nanoprobe can be reduced down to 0.1 nm even if the microscope is not probe corrected. For these experiments, NPs were deposited on supported ultrathin amorphous carbon films (ultrathin carbon on Holey Carbon films, AGAR inc.) or Si3N4 thin films and in some cases sandwiched between two silica layers (5 nm thickness) evaporated with the electron gun.

Results and discussion

4.1 TEM characterization of the NPs after air exposure: spontaneous oxidation of iron

First TEM observations of NPs with 50% silver with a fairly large size distribution, in various environments and after air-exposure have already been reported. [START_REF] Ramade | Nano-fried-eggs: Structural, optical, and magnetic characterization of physically prepared iron-silver nanoparticles[END_REF] For uncapped NPs or NPs embedded in silica it was shown that iron and silver segregate with a quasi-spherical silver part surrounded by an amorphous iron oxide structure. The similar structure for uncapped NPs and silica-embedded NPs suggests that the contact of the NPs with the matrix has a minor influence on their morphology.

We here show results on mass-selected NPs with two different silver compositions. TEM characterizations were first performed after air exposure on size-selected NPs with 50% of silver (〈𝜙𝜙〉 = 4.5 ± 0.3 nm deduced from mass spectrometry or 𝑁𝑁 ≈ 3340 atoms) deposited on a layer of silica (2 nm) with a very low concentration to avoid any coalescence (≈ 250 NPs/𝜇𝜇𝑚𝑚 2 , equivalent bulk thickness of 0.01 nm). The low magnification image displayed in Figure 5a shows NPs with two clearly distinguishable segregated phases. The almost spherical darker parts of the NPs, corresponding to silver, were size analyzed over a population of a few hundreds NPs. The corresponding size distribution (Figure 5b) follows a log-normal distribution centered at 3.6 nm. reflects the fluctuations of x, the silver composition of mixed clusters. The iron oxide part should display the surface of a 5.7 nm diameter sphere as predicted from the spherical assumption assuming a face-centered cubic (FCC) lattice parameter of Fe3O4 of 0.839 𝑙𝑙𝑚𝑚. However, its surface analysis could not be achieved since the external boundaries are hardly distinguishable.

Yet, the large visible surfaces suggest that iron oxide wets the surface of thin films (silica or carbon) more efficiently than the silver cluster surface, [START_REF] Ramade | Nano-fried-eggs: Structural, optical, and magnetic characterization of physically prepared iron-silver nanoparticles[END_REF] although TEM tomography should be performed to ascertain this conclusion. The analysis of this sample, in which coalescence was avoided, shows that only one silver sphere exists in each NP, which further indicates that the segregation between silver and iron probably occurs before iron oxidation, in agreement with the MC simulations discussed in section 2.

HAADF-STEM and HRTEM observations were also performed for 50% and 80% silver compositions, either on uncapped NPs or on NPs sandwiched between two silica layers (2 nm below and 5 nm above). It should be emphasized that the silica evaporated with the electron gun is known to be porous. [START_REF] Cottancin | Plasmon spectroscopy of small indium-silver clusters: monitoring the indium shell oxidation[END_REF] For both concentrations the HAADF-STEM images of Figure 6a and6c clearly show two regions with different contrast in each NP due to differences in atomic number Z. The brighter almost spherical regions correspond to silver (Z=47) whereas the less defined darker ones correspond to iron (Z=26). For the 50% silver composition, an energy dispersive xray mapping performed on a single NP confirms this hypothesis (inset in Figure 6a). The observations for the Ag0.8Fe0.2 samples are in good agreement with previous observations for the Ag0.5Fe0.5 system, [START_REF] Ramade | Nano-fried-eggs: Structural, optical, and magnetic characterization of physically prepared iron-silver nanoparticles[END_REF] i.e. the silver part crystallizes in face-centered-cubic (FCC) or multiply twinned pure nanospheres, whereas the iron part forms amorphous structures that crystallize into magnetite (Fe3O4) or maghemite (γ-Fe2O3) under continuous electron beam irradiation (see Figure 6b and6d). These two iron oxides present the same FCC crystalline structure with almost identical lattice parameters (0.833 nm and 0.839 nm for maghemite [START_REF] Pecharroman | The Infrared Dielectric-Properties of Maghemite, Gamma-Fe2o3, from Reflectance Measurement on Pressed Powders[END_REF] and magnetite, 62 respectively), making them undistinguishable from one another by HRTEM observations. However, the difference between their enthalpy of formation (-811.6 kJ.mol -1 for maghemite and -1120.9 kJ.mol - 1 for magnetite [START_REF] Lemire | Chemical thermodynamics of iron, part 1 In Chemical Thermodynamics[END_REF] ) should favor magnetite. The discrimination between both structures is not essential for the present work, but it could be achieved by electron energy loss spectroscopy (EELS). [START_REF] Meng | Atomistic Insight into the Redox Reactions in Fe/Oxide Core-Shell Nanoparticles[END_REF] It is only under continuous electron irradiation that iron oxide crystallizes, while remaining amorphous if not exposed to electron irradiation, as in the samples dedicated to optical measurements. Yet, the nearly systematic presence of iron oxide at the surface is consistent with the relatively low surface energies of magnetite or maghemite [σs(Fe3O4) = 0.79 J.m -2 and σs(γ-Fe2O3) = 0.57 J.m -2 ], compared to the silver value (0.925 J.m -2 ). Also worthy of note is that silver oxide is absent. Due to its more noble character relative to iron, silver should be less reactive than transition metals such as iron. Moreover, iron oxide may protect silver from oxidation.

To conclude, the TEM observations and analyses of the NPs after air exposure show that a rapid oxidation of iron occurs at both silver compositions (50 % and 80 %), even when the NPs are protected with silica, while silver remains metallic. The NPs form a compact crystallized silver core surrounded by a not-so-well defined iron oxide shell wetting the substrate. No hematite was observed and the iron oxide preferentially crystallizes into magnetite even if the presence of maghemite cannot be completely excluded.

Optical studies 4.2.1 Optical response of AgxFe1-x NPs in silica after air exposure

The optical response of various elaborated samples of Ag-Fe NPs embedded in silica has been measured after air exposure and compared to theoretical predictions based on Mie theory and using the dipolar approximation. This last assumption is justified by the very small size of the NPs relative to the excitation wavelength, scattering being negligible with respect to absorption. In the absence of spherical symmetry, absorption cross-sections were calculated with the finite element method and using the COMSOL Multiphysics software. The dielectric functions of silver, iron and iron oxide were all taken from the literature. [START_REF] Palik | Handbook of optical constants of solids[END_REF][START_REF] Johnson | Optical-Constants of Transition-Metals -Ti[END_REF][67] FeAg Ag x Fe 1-x for various configurations: Janus (red line), off-centered spherical core-shell Fe@Ag (blue line), spherical core-shell Fe@Ag (gray line), spherical geometry assuming a stacking of silver and iron nano-domains for which the dielectric function is the weighted volumic average of both silver and iron dielectric functions (cyan line) and pure silver (black line). In this last case, the absorption cross-section of a silver sphere of 4 nm in diameter was also calculated by taking into account the decreasing of the electron mean free path in the NP (black dotted line). [START_REF] Cottancin | Handbook of Nanophysics: Nanoelectronics and Nanophotonics[END_REF] The hatched rectangular areas corresponding to the experimental positions of the resonances displayed in (a) highlight the opposing trends of the experimental and theoretical LSPR shifts with varying silver composition.

Samples of size-selected AgxFe1-x clusters embedded in silica were elaborated for optical measurements. The obtained samples have an averaged diameter of 〈∅ 𝐴𝐴𝐴𝐴 〉 = 4.0 ± 0.3 𝑙𝑙𝑚𝑚, 〈∅ 𝐴𝐴𝐴𝐴 0.8 𝐹𝐹𝐹𝐹 0.2 〉 = 4.6 ± 0.3 𝑙𝑙𝑚𝑚 and 〈∅ 𝐴𝐴𝐴𝐴 0.5 𝐹𝐹𝐹𝐹 0.5 〉 = 4.0 ± 0.3 𝑙𝑙𝑚𝑚 for x=1, 0.8 and 0.5, respectively.

The corresponding absorption spectra are displayed in Figure 7a and compared to theoretical predictions for various geometrical configurations in Figure 7b. The LSPR of silver is well marked at around 415 nm and remains stable over a few days, whereas the LSPR of mixed NPs is damped, broadened and red-shifted with increasing iron proportion, which is at variance with our calculations. For pure silver NPs, the absorption cross-section of a silver sphere of 4 nm in diameter was also calculated by taking into account the decreasing of the electron mean free path in the NP (black dotted line). [START_REF] Cottancin | Handbook of Nanophysics: Nanoelectronics and Nanophotonics[END_REF] This effect induces a broadening and a damping of the LSPR that are both in better agreement with the experimental spectrum and with the size effects experimentally observed in this size range. [START_REF] Campos | Plasmonic quantum size effects in silver nanoparticles are dominated by interfaces and local environments[END_REF] For mixed AgxFe1-x NPs, the decrease of the electron mean free path should also induce a similar effect on the LSPR regardless of the configuration, but this effect is not straightforward to implement except for the spherical core@shell configuration through the use of the Granqvist formula. [START_REF] Granqvist | Optical absorption of ultrafine metal spheres with dielectric cores[END_REF] Both calculations have been performed only for the spherical core@shell configuration (see Figure S5 in supporting information). A damping of about a factor 2 without any shift of the LSPR is observed when the shortening of the mean free path is taken into account.

Therefore, despite our theoretical spectra being less realistic due to the neglect of such phenomenological size effects, both calculations would lead to the same conclusions. Below, only calculations for Fe-Ag NPs without taking into account the decreasing of the electron mean free path are thus presented.

The LSPR of the mixed AgxFe1-x NPs is expected to be blue-shifted with increasing iron amount, for all Janus, centered and off-centered Fe@Ag spherical core-shell configurations. This is related to the increasing influence of iron which has a complex dielectric function. [START_REF] Johnson | Optical-Constants of Transition-Metals -Ti[END_REF] Assuming now that the effective dielectric function of the NPs is the weighted volumic average of both silver and iron dielectric functions, which is appropriate if Ag and Fe nanodomains are randomly distributed as pure nanodomains in the spherical NP, the LSPR is then expected to be strongly damped, especially for an amount of silver of 50%, which is in contradiction with experimental spectra.

Combined with TEM observations for which a single silver domain was always observed, this suggests that such an alloyed configuration is definitely unrealistic.

The difference in the behavior of the optical response with increasing iron composition between experiments and theory is most likely due to iron oxidation, as observed by TEM imaging. The progressive oxidation of a metal near a second plasmonic metal in bimetallic NPs leads to a redshift and damping of the LSPR induced by the complex dielectric function of the oxide part. [START_REF] Gaudry | Size and composition dependence in the optical properties of mixed (transition metal/noble metal) embedded clusters[END_REF] As magnetite was shown to be the most likely oxide, the evolution of the optical response of AgxFe1-

x NPs in silica computed for increasing levels of iron oxidation is reported in Figure 8, the dielectric function of magnetite Fe3O4 being extracted from Ref. 67 . Starting from Janus, centered or offcentered Fe@Ag spherical core-shell configurations, three scenarios of oxidation are proposed leading to centered or off-centered Ag@Fe3O4 spherical core-shell NPs, similarly to the structures observed by TEM. In the three cases, the LSPR is all the more red-shifted, broadened and damped that the initial composition is rich in iron and that the level of oxidation is high. Comparing with the experimental spectra obtained just after air exposure (see Figure 7a), we deduce that the NPs have an average oxidation level higher than 60% at both 50% and 80% silver compositions. After ageing the level of oxidation is even higher than 80 % (see Figure 7a).

Results after annealing

The metallic character of iron may be recovered by annealing under reducing atmosphere. For this purpose, the samples were introduced in the home-built spectrophotometer described in section 3

after their initial air exposure at room temperature. Two identical cycles of reduction/oxidation were performed in the chamber with first some annealing at 250°C for 10 to 15 minutes under H2 (5%)-N2 (95%) atmosphere and then a venting of the chamber to the atmosphere. Since the melting point of silica exceeds 1700 °C, its structure should not be drastically modified during annealing, except a slight decrease of its porosity that would hardly change its optical index. The spectra recorded after each process are displayed in Figure 9 at both 80% and 50% silver compositions. The absorption spectra after annealing were recorded after returning at room temperature in the presence of hydrogen.

Even if the spectra are broad due to size, shape and porosity dispersion in the samples, some reproducible trends over both cycles can be noticed. First, the LSPR bands are broadened and damped after air exposure and better defined after annealing under hydrogen atmosphere. But the most apparent feature is the blueshift of the LSPR after annealing and the redshift after air exposure. This is clearer at 80% silver, as the LSPR maximum is better seen (see also Figure S6 and S7). The shifts after annealing or air exposure are larger for Ag0.8Fe0.2 NPs because the amount of iron to be reduced or oxidized is smaller than for Ag0.5Fe0.5 NPs for which the damping or the reappearing of the resonance are the strongest effects. The LSPR maximum for non-oxidized Ag0.5Fe0.5 NPs is expected to be located below 400 nm whatever the configuration (see Figure 10), a threshold that is never crossed after annealing under H2 atmosphere. The reduction of iron therefore remains only partial after 10-15 minutes. Longer times or higher annealing temperatures are probably required to achieve complete reduction of the NPs. In the case of Ag0.8Fe0.2 NPs the LSPR peak position at around 400 nm is more compatible with a full reduction of iron oxide, except for the spherical core@shell configuration for which the LSPR maximum is expected near 390 nm (see Figure 10). However, this configuration is less likely, especially after annealing. absorption cross-sections for various configurations: Janus AgxFe1-x (red curves); off-centered spherical core-shell Fe@Ag (blue curves), spherical core-shell Fe@Ag (gray curves), core-shell Fe@Ag with an oblate core similar to the predicted configurations from the Monte Carlo simulations (green curves).

In Figure 10, the absorption spectra for configurations similar to the ones deduced from atomistic Monte Carlo simulations are also shown, namely configurations obtained at 300 K for 50% and 80% silver compositions and labelled i and I in Figure 2, respectively. They consist of an oblate iron core surrounded by a silver spherical shell. Their corresponding absorption spectra are very

Fe Ag

After first reducing After first reducing similar to the ones expected for an off-centered spherical core-shell Fe@Ag. This suggests that such configurations are also likely in our sample.

Nevertheless, definitive conclusions about the structure of the NPs, either just after elaboration or after reduction cannot be drawn easily only on the basis of optical spectroscopy that only allows segregated, alloyed or oxidized structures to be discriminated. To proceed further, complementary characterization techniques such as TEM or low energy ion spectroscopy [START_REF] Cottancin | Optical properties of mixed clusters: comparative study of Ni/Ag and Pt/Ag clusters[END_REF] should be performed on native NPs (before air exposure), which requires a vacuum transfer system that is currently missing. Nevertheless, no iron oxide was observed in Ag-Fe NPs deposited in ultra-high vacuum and capped with a thin layer of carbon on the order of 5 nm thick. [START_REF] Ramade | Nano-fried-eggs: Structural, optical, and magnetic characterization of physically prepared iron-silver nanoparticles[END_REF] We can thus conclude that the produced Fe-Ag NPs are not oxidized before venting.

Even without a complete characterization of the native structure, some conclusions may still be drawn on the possible evolution of the structure of the NPs during the cycles of oxidation and reduction, as sketched in Figure 11. The initial structure, expected from Monte Carlo simulations to be an Fe@Ag core-shell, should evolve to a segregated configuration with a more or less centered silver core surrounded by iron oxide, as observed through HRTEM and HAADF-STEM analyses and in agreement with the joint red-shift, broadening and damping of the LSPR.

Annealing under reducing atmosphere induces a reduction reflected by the blue-shift and narrowing of the LSPR band. This reduction is surely not complete for the 50% silver composition and the final configuration is probably more complex with three segregated phases where iron may be surrounded by silver and a remaining iron oxide domain. But other complex configurations can be envisioned at this stage. The air exposure inducing iron re-oxidation should then lead to the Ag@FexOy core-shell configuration already observed after the first step of air exposure. The second redox cycle should lead to very similar configurations as the first cycle. environments. The initial structure is assumed to be an Fe@Ag core-shell structure accordingly with atomistic MC simulations. After air exposure the NPs evolve to an Ag@FexOy core-shell configurations and the annealing under reducing atmosphere leads to a more complex structure in which silver, iron and iron oxide are all present within the NP.

Finally, in order to minimize iron oxidation, Ag0.5Fe0.5 NPs were embedded in alumina (instead of silica) with the substrate kept at 400°C during co-deposition. This technique has previously been shown to be efficient to prevent copper NPs against oxidation. [START_REF] Celep | Optical properties of copper clusters embedded in alumina: an experimental and theoretical study of size dependence[END_REF] The optical absorption spectra of this sample can be seen in Figure 12. The optical index of alumina deposited at 400 °C, varying and and and from 1.71 to 1.64 in the UV-visible range, is higher than that of silica (1.47), hence the LSPR of metallic NPs embedded in alumina is expected to be red-shifted compared to metallic NPs embedded in silica. The first spectrum, recorded just after sample elaboration, displays an LSPR centered at 396 nm in good agreement with the calculated spectra for an off-centered spherical core@shell structure or a core@shell structure with an oblate core similar to the configuration obtained from Monte Carlo simulations. Moreover, no change is observed after one day. This strongly suggests that the NPs are preserved from oxidation during a longer time when elaborated under these conditions. The slight red-shift of the LSPR after almost two years shows that oxidation exists but is considerably slowed down. Metallic Ag-Fe NPs were nevertheless not observed by TEM because, as the thickness of alumina for TEM observations needs to be very low (a few nm), the NPs near the surface rapidly oxidize. However, embedding in alumina at 400°C is probably a good alternative for elaborating transparent matrix embedded Ag-Fe NPs while keeping their metallic character. To confirm this, XPS measurements on this type of samples as already performed on copper NPs 72 will be needed. Fe@Ag (blue line), spherical core-shell Fe@Ag (gray line), and core-shell Fe@Ag with an oblate core similar to the configuration obtained from Monte Carlo simulations (green line). Lower panel: experimental absorption spectra of as-prepared AgxFe1-x NPs embedded in alumina just after air exposure at time denoted 𝑡𝑡 𝑜𝑜 (black line), at time 𝑡𝑡 𝑜𝑜 + 1 𝑑𝑑𝑑𝑑𝑦𝑦 after air exposure (blue curve) and at time 𝑡𝑡 𝑜𝑜 + 600 𝑑𝑑𝑑𝑑𝑦𝑦s after air exposure (red line).

Conclusions

In this work the optical and structural properties of silver-iron NPs were investigated at two compositions (50% and 80% in silver). Parallel tempering Monte Carlo simulations at the atomistic Fe Ag level predict that, at room temperature, such systems should preferentially adopt Fe@Ag coreshell crystal structures when isolated. From the experimental point of view, the structure of the native NPs could not be determined because of rapid iron oxidation. Nevertheless, electron microscopy characterizations have shown that the system forms, after iron oxidation, a crystallized silver core surrounded by a less clearly defined iron oxide shell crystallizing under the electron beam into magnetite. Moreover, the development of an environmental optical spectroscopy setup based on the SMS technique allowed the oxidation and reduction of the NPs to be both monitored through the LSPR modifications they induce. Such a setup should enable the monitoring of individual NPs through in operando conditions. Finally, TEM observations and optical characterizations combined with optical and Monte Carlo simulations concur to show that these metals are initially segregated with a silver-enriched surface and that oxidation induces some iron migration towards the surface. After iron reduction, which is not always complete, the system may return to its initial configuration, but optical spectroscopy alone cannot provide a conclusive evidence.

Environmental TEM measurements under controlled atmosphere as already performed on indiumsilver NPs 30 are needed to proceed further. Moreover, other characterization techniques like anomal x-ray diffraction [START_REF] Andreazza | Structure and order in cobalt/platinum-type nanoalloys: from thin films to supported clusters[END_REF] or low energy ion spectroscopy [START_REF] Cottancin | Optical properties of mixed clusters: comparative study of Ni/Ag and Pt/Ag clusters[END_REF] should also be valuable, especially if performed on NPs protected from oxidation.

ASSOCIATED CONTENT Supporting Information

Figure 1 .

 1 Figure 1. Predicted thermodynamical properties of Ag-Fe nanoalloys containing about 1000 atoms

Figure 2 .

 2 Figure 2. Half-cut structures of Ag-Fe nanoalloys at various temperatures, as borrowed from the

Figure 3 .

 3 Figure 3. Spectra of inherent structure energies {𝐸𝐸 𝛼𝛼 } of Ag-Fe nanoalloys obtained by systematic quenching of the instantaneous configurations visited along the Monte Carlo simulations. The

Figure 4 .

 4 Figure 4. (a) Principle of spatial modulation spectroscopy. A monochromatic collimated beam is

  Photodiode

Figure 5 . 3 where

 53 Figure 5. (a) TEM image of Ag-Fe NPs with 50 % of silver deposited on a 2 nm silica layer itself

Figure 6 .

 6 Figure 6. TEM images after air-exposure of Ag0.5Fe0.5 NPs between two silica layers (upper

Figure 7 .

 7 Figure 7. Optical absorption spectra of as-prepared AgxFe1-x NPs embedded in silica just after air

Figure 8 .Fe 3 O 4

 834 Figure 8. Evolution of the optical absorption cross-section of AgxFe1-x NPs (x=0.5 and x=0.8)

Figure 9 .

 9 Figure 9. Cycles of in situ optical absorption measurements of AgxFe1-x NPs embedded in silica

Figure 10 .

 10 Figure 10. Absorption spectra of AgxFe1-x NPs embedded in silica (upper panel: x=0.8, lower

Figure 11 .

 11 Figure 11. Plausible evolution of the Ag-Fe NP structure under oxidizing and reducing

Figure 12 .

 12 Figure 12. Optical absorption spectra of Ag0.5Fe0.5 NPs embedded in alumina (𝜀𝜀 𝑚𝑚 = 2.17) with the substrate kept at 400 °C during co-deposition. Upper panel: theoretical absorption cross-

  𝑠𝑠 (𝑡𝑡)) can be decomposed in Fourier series as follows𝑈𝑈 𝑠𝑠 (𝜆𝜆, 𝑥𝑥 𝑠𝑠 (𝑡𝑡)) = 𝐴𝐴 𝑜𝑜 2 + 𝐴𝐴 1 cos(2𝜋𝜋𝑓𝑓𝑡𝑡) + 𝐵𝐵 2 sin(4𝜋𝜋𝑓𝑓𝑡𝑡) + ⋯The Fourier coefficients 𝐴𝐴 𝑜𝑜 , 𝐴𝐴 1 , 𝐵𝐵 2 of 𝑈𝑈� 𝑥𝑥 𝑠𝑠 (𝑡𝑡)� can be obtained if the spot profile is well characterized (see Supporting Information for details) and the transmitted signal, once demodulated with a lock-in amplifier, allows

	𝑋𝑋 𝑓𝑓
	𝐷𝐷𝐷𝐷

AUTHOR INFORMATION

The authors declare no competing financial interests.

ACKNOWLEDGMENT

Financial support from GDR 3182 Nanoalliages and European COST Action MP1302 Nanospectroscopy is gratefully acknowledged. We also thank the regional computing center CALMIP for providing generous computational resources (project p1141). The Authors also thank


G Kirstetter
email: geoffroy.kirstetter@univ-cotedazur.fr

F Bourgin

P Brigode
email: pierre.brigode@univ-cotedazur.fr

O Delestre
email: olivier.delestre@univ-cotedazur.fr

Real-Time Inundation Mapping with a 2D Hydraulic Modelling Tool Based on Adaptive Grid Refinement: The Case of the October 2015 French Riviera Flood

The vulnerability of the French Riviera territories to hydro-meteorological hazards has been highlighted by the flash flood of the 3rd of October 2015, which had catastrophic consequences. In the view of the speed and violence of these phenomena, the development of warning systems able to provide real-time flood mapping should make it possible to limit their impacts. In this context, the main objective of this work is to study the feasibility of using a 2D hydraulic modelling tool with adaptive grid refinement, the Basilisk calculation code http://basilisk.fr/, which is based on state-of-the-art finite volume methods. This code has been used to model the October 2015 flood event on one French Riviera coastal catchment, the Brague River catchment. Results obtained with Basilisk were compared with available information from post-event surveys, showing promising performances in terms of simulated peak discharges, inundation extent and water levels in the floodplain. These results highlight that forecasting inundation extents generated by flash flood events on small watersheds (less than 100 km 2 ) is possible at a moderate computational cost.

Introduction

Mostly in autumn, watersheds of French Riviera are frequently subject to flash floods due to short duration and high intensity rainfall events. This occurs on small and medium watersheds (generally less than 100 km 2 ) with steep slopes which leads to short hydrological responses, from a few minutes to a few hours. Most of the downstream parts of these watersheds are urbanized. These extreme events represent a real threat on human life and on property (private damages, activities, cars, etc.). It is thus necessary to accurately forecast the dynamic of the flood event and its associated inundation map in order to help authorities to anticipate and take appropriate decisions in a real-time crisis situation. It becomes necessary to model that type of event accurately in the description of the dynamic and of the extent of the flood. Previous works have been done in one and two dimensional hydraulic modelling. A catalogue of flood maps can be generated offline and then can be used in real-time from flow forecasting, for example using the simplified 1D hydraulic modelling setup approach presented by Le Bihan et al. [START_REF] Le Bihan | The challenge of forecasting impacts of flash floods: test of a simplified hydraulic approach and validation based on insurance claim data[END_REF], 1D/2D coupling [START_REF] Guinot | Calibration of physically based models: back to basics[END_REF] or other 2D hydraulic model approaches such as steady state modelling [START_REF] Davy | A precipiton method to calculate river hydrodynamics, with applications to flood prediction, landscape evolution models, and braiding instabilities[END_REF] and synthetic flood events generation. A recent review of several approaches can be found in Teng et al. [START_REF] Teng | Flood inundation modelling: A review of methods, recent advances and uncertainty analysis[END_REF]. On one hand, the main limitations of 1D approaches are accuracy and inability to provide a good description of the floodplain, while it provides computational efficiency that allows real-time simulations. On the other hand, high-resolution 2D approaches can provide a better representation of the flood dynamics in complex settings, but they are still very expensive in terms of computational costs and require user expertise (e.g. [START_REF] Bermúdez | Quantifying local rainfall dynamics and uncertain boundary conditions into a nested regional-local flood modeling system[END_REF], [START_REF] Nguyen | A high resolution coupled hydrologichydraulic model (HiResFlood-UCI) for flash flood modeling[END_REF]). This work aims at exploring an alternative approach, which consists in using a 2D hydraulic modelling tool based on adaptive grid refinement and shallow-water equations to provide real-time inundation mapping applied to a watershed having a short hydrological response. The main challenge lies in obtaining a dynamical description of the inundation in a forecasting context, i.e., the computational time has to stay very limited compared to the real life duration of the event. We propose to test our approach on a typical coastal watershed of the French Riviera, the Brague River catchment (68 km 2 ), on the flash flood that occurred during the rainfall event of the 3rd of October 2015. During this event, 650 billion of insured damage and 20 casualties were reported (source: http://basilisk.fr/, see also [START_REF] Pons | Semi-automatic maps for 2015 french riviera floods[END_REF]. As a first step, we describe the watershed of the Brague River and the rainfall event of the 3rd of October 2015. Then we present the open source software Basilisk, the obtained results and future work perspectives.

Figure 1: (top) Elevations of the Brague watershed, position of flood marks (Schapi [START_REF]le Service central d'hydromét méorologie et d'appui à la prévision des inondations (Schapi), service du Ministère de la transition écologique et solidaire[END_REF]), and observed damages [START_REF] Saint-Martin | Damagis: a multisource geodatabase for collection of floodrelated damage data[END_REF]. Blue points show the sections where maximum flood flows have been estimated by Amponsah et al. [START_REF] Amponsah | Integrated high-resolution dataset of high-intensity european and mediterranean flash floods[END_REF], and the estimated peak discharge values are indicated (in m 3 /s). Note that temporal series of river discharges have been estimated at four of these particular sections, noted as Basilisk stations (colored points). (bottom left) Zoom on the elevations at the Brague watershed outlet, where simulated inundation extents will be highlighted. (bottom right) Cumulated PANTHERE rainfall during the 3rd October 2015.

2 Materials and methods

The Brague River Watershed

The Brague River watershed is located in the French Riviera, near Antibes, Alpes-Maritimes (Fig. 1). It is a costal Mediterranean catchment of 68 km 2 prone to regular flash floods, with marked elevations in the upper hills of the basin and an urbanised lower part in the floodplain near the coast.

Datasets Used

Digital Elevation Model

We used the Digital Elevation Model (DEM) RGE ALTI at 1 m resolution provided by IGN (http://professionnels. ign.fr/rgealti). The DEM was aggregated at 4 m resolution for the hydraulic model.

Rainfall

We used the rainfall data from the PANTHERE product of Météo-France for the 3rd October. The PANTHERE product is derived from radar data, it has a spatial resolution of 1 km 2 and a rainfall grid is provided every 5 min. The cumulated rainfall for the 3rd October in the Brague area is illustrated in Fig. 1.

Peak Discharge Estimations and Flood Marks

Several post-event investigations were launched to understand and document the 2015 catastrophic event. In particular, a post-event study carried out within the HyMeX program results in peak discharge estimations at several locations along the main streams that flow into the Brague floodplain, as illustrated in Fig. 1. The database is open-access and described in Amponsah et al. [START_REF] Amponsah | Integrated high-resolution dataset of high-intensity european and mediterranean flash floods[END_REF]. In addition, we used several flood marks available through the open-access national platform (https://www.reperesdecrues.developpement-durable.gouv. fr, Schapi [START_REF]le Service central d'hydromét méorologie et d'appui à la prévision des inondations (Schapi), service du Ministère de la transition écologique et solidaire[END_REF]) and other observed damages documented in Saint-Martin et al. [START_REF] Saint-Martin | Damagis: a multisource geodatabase for collection of floodrelated damage data[END_REF].

Basilisk Software

Leading Equations

We used the open-source software Basilisk (http://basilisk.fr/) to model the system. Because overland flows are well-described by the Saint-Venant equations, also known as the shallow-water equations, we used this system to mimic the physics of the hydraulics process. The rigorous derivation of the Saint-Venant equations with rain can be found in Zhang and Cundy [START_REF] Zhang | Modeling of two-dimensional overland flow[END_REF]. The rain intensity is added as a source term in the mass conservation equation. The Manning friction term is added as source term in the momentum conservation equation.

Numerical Scheme

The shallow-water equations are discretized by the finite volume method. The time is discretized with time-step ∆t > 0 and the space is discretized with square cell of different size, as explained in the next section. We name ∆ the length of ridge of square cells. We use the second-order hydrostatic reconstruction scheme introduced by Audusse et al. [START_REF] Audusse | A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows[END_REF]. This scheme conserves lake-at-rest state and preserve positivity of water depth. The numerical flux is solved by the Godunov-like approximate Riemann solver developed by Kurganov and Levy [START_REF] Kurganov | Central-upwind schemes for the Saint-Venant system[END_REF]. We use a predictor-corrector scheme to increment the time and we use a simple time-splitted method to deal with the source terms like friction and rain.

Quadtree-Adaptive Grid Refinement

Many schemes solve the Saint-Venant or the Boussinesq equations on a regular Cartesian grid. This method ensures a maximal precision but at a cost of computational time, which typically scales like ∆ 3 . With this kind of method, to divide by a factor 2 the spatial resolution, we have to multiply by 8 the computational time. Here, we use the quadtree adaptive refinement approach proposed by Popinet [START_REF] Popinet | Quadtree-adaptative tsunami modelling[END_REF] to drastically decrease this factor and limit the computational burden. Basilisk provides a strategy for refinement and coarsening that is applied at each time steps by comparing a chosen scalar field obtained at different spatial resolutions. Refinement occurs when the difference between the value of the scalar field obtained as the average of the four child cells and the value of the parent cell is greater than a threshold value. Conversely, coarsening occurs when the same difference is smaller than the threshold. Thus, the threshold value can be seen as the allowable error between two levels of refinement.

Soil Conservation Service -Curve Number (SCS-CN)

To account for interception, rainfall-excess time series are estimated fromthe rainfall time series with the wellknown and widely used SCS-CN approach (USDA, [START_REF]Soil Conservation Service National Engineering Handbook, Supplement A, Section 4, Hydrology[END_REF]). For each pixel of the rainfall field, the SCS loss model is applied with a CN value of 70. We did not account for spatial variability of the CN values in the Brague catchment since the analysis carried out during the post-event study [START_REF] Lebouc | Reconstitution et analyse des débits de pointe des crues du 3 octobre 2015 dans les Alpes Maritimes[END_REF] suggested that a constant CN value of 70 was adequate for the flood event of the 3rd of October.

Simulation Setup

We used the following simulation setup:

• a uniform value of 0.05 for the Manning coefficient,

• the water height as the scalar field used for refinement and coarsening with an error threshold equal to 20 cm,

• grid cell resolutions ranging from 4 m for the highest resolution and 66 m for the lowest resolution.

To assess the computational efficiency and the feasibility of real-time inundation mapping based on real-time precipitation forecasts, we performed three different simulations on a Linux virtual machine with 16 Intel(R) Xeon(R) CPU E5-2650-v4 2.20 GHz processors, by limiting the highest grid cell resolution at 16, 8 and 4m respectively. These three simulations will be named LR (low resolution), MR (medium resolution) and HR (high resolution) hereafter. Computational times of 15, 60 and 238 min were obtained when simulating the three-hour event of the 3rd October, from 18:30 to 21:30 TU. The number of cells at the end of each simulation is respectively 98 845, 149 407 and 224 500, which explains the difference in computing time. (down) Scatter plot between absolute differences water elevation errors and the differences between elevation values due to the variable grid resolution for the three different simulations. 1). The estimated values and their uncertainty from the post-event survey reported in Amponsah et al. [START_REF] Amponsah | Integrated high-resolution dataset of high-intensity european and mediterranean flash floods[END_REF] are shown as a gray range and a black line as no timing information was available. Starting time is 18:30 TU. Vertical dashed lines showed the six time steps for which the inundation extent is illustrated in Fig. 2.

Results

Inundation Extent

Temporal Dynamic of the Reference Simulation MR

Impact of the Spatial Resolution on Simulated Flood Extent and Performances

The difference of flood simulation extents obtained with the three simulations is limited (not shown). For the three simulations, more than 89% of the available 391 flood marks are located within the simulated inundation extents (89.5%, 91.8% and 93.4% for the low, reference and high resolution simulations, respectively). Figure 3 (top) shows the general performances obtained by the three different simulations in terms of simulation of water elevation values obtained at 276 points (out the 391 flood marks) where flood marks and water elevation values are available [START_REF]le Service central d'hydromét méorologie et d'appui à la prévision des inondations (Schapi), service du Ministère de la transition écologique et solidaire[END_REF]. The highest resolution simulation (HR) produces better results than the lowest resolution simulation (LR), and the reference simulation (MR) stands in between, with median absolute difference values of 0.49, 0.49 and 0.42 m for LR, MR and HR respectively. It is interesting to note that the largest errors could be explained by significant differences between elevations of the reference DEM (4 m resolution) and elevations used during the simulation (up to 66 m for the lowest resolution), as shown in Fig. 3 (bottom), where the water elevation errors for each of the 276 points is plotted against the elevation differences. This can be explained by our choice of the refinement criteria that only takes into account the water height and not the water elevation and thus does not necessarily lead to refining areas with steep elevation gradients.

Simulated Hydrographs

Figure 4 shows the hydrographs estimated from the reference simulation for the main four watercourses that are located upstream the Brague floodplain, as illustrated in Fig. 1. Discharge values were estimated by extracting the velocity and the height of water across the grid cells belonging to vertical or horizontal cross sections, depending of the shape of the river valley. The flood event was sudden and the simulated hydrographs suggest a fast hydrological response with time to peak duration ranging froma few minutes for the Vallon des Combes to one hour for the Brague River. The maximum discharge values obtained from the reference simulation seem to be within the range of estimated values from the post-event survey, although an underestimation can be seen for the Brague River and a slight overestimation for the Valmasque River. Furthermore, we compared the simulated peak discharge values to the estimated peak discharge values from the post-event survey at ten locations shown in Fig. 1. Figure 5 confirms that the simulated discharge values along the Brague River are underestimated, while the discharge values at the locations along the Valmasque stream appear to be slightly overestimated. The peak discharge values for the Bouillide stream and the Vallon des Combes stream are in a good agreement with the values from the post-event survey.

Overall, those results suggest that the simple approach of SCS-CN used to estimate the net rainfall is sufficient to yield acceptable peak discharge estimations for this event. Nonetheless, it should be remembered that the constant CN value of 70 we used was based on a preliminary work carried out during the post-event study on this event.

Conclusions

In the French Riviera, most of the urban zones are concentrated near the coast due to the mountainous relief. Upstream areas of these urban zones are small or medium size catchment with steep slopes. Thus, the short response time of those watersheds combined to the high intensity and the short duration of autumnal rainfall event frequently result in devastating flash floods. These catastrophic extreme events are a threat to the population life and to properties and it becomes clearly necessary to have forecasting tools with a good description of the dynamic of the event. We investigated the feasibility of using a physically-based approach in order to tackle this issue. Because a standard approach was not appropriate due to too high computational times, we used a 2D approach based on adaptive mesh refinements. In this context, there is a trade-off between the levels of grid refinement, the accuracy of the results and the computational time costs. The results obtained on the Brague River watershed (68 km 2 ) show that this alternative is a promising solution to the problem raised: getting a forecast of flash flood events on watersheds of less than 100 km 2 with reasonable computational cost is possible, with good performances in terms of maximum discharges, inundation extent and water levels. Some improvements could be obtained by a treatment of the DEM to correct some elevation artefacts, and by finding another refinement criteria of the mesh adaptation, both in time and space. In addition, this study has some limitations regarding the choice of the production function (SCS-CN) and the Manning coefficient and further work is needed to investigate the impact of these hypotheses in a real-time forecasting situation. Moreover, a strategy of coupling rainfall-runoff modelling on the upper parts of the studied watershed and hydraulic modeling on the lower parts (with high stakes) might be tested to further reduce the computational costs. In future works, this general approach will be applied on the same catchment with other rainfall events and on other catchments to confirm the genericity of the approach. Complementary, the adaptive grid refinement approach will be compared with results obtained with other state-of-the art inundation modeling approaches.

Figure 2 :

 2 Figure 2: Simulated flood extents obtained with the reference simulation, from 19:15 to 20:30 TU: only the pixels with more than 20 cm of water are highlighted here.

Figure 3 :

 3 Figure 3: (top) Scatter plot between observed and simulated water elevation values for the three different simulations. The boxplots (5, 25, 50, 75 and 95th quantiles) summarizes the distributions of absolute differences.(down) Scatter plot between absolute differences water elevation errors and the differences between elevation values due to the variable grid resolution for the three different simulations.

Figure 2

 2 Figure 2 shows the temporal dynamic of the simulated flood by showing flooded areas (pixels with more than 20 cm of water) at six different time steps, starting at 19:15 TU. At this timestep, water is coming within the

Figure 4 :

 4 Figure 4: Hydrographs estimated from the reference simulation at four locations (see Fig.1). The estimated values and their uncertainty from the post-event survey reported in Amponsah et al.[START_REF] Amponsah | Integrated high-resolution dataset of high-intensity european and mediterranean flash floods[END_REF] are shown as a gray range and a black line as no timing information was available. Starting time is 18:30 TU. Vertical dashed lines showed the six time steps for which the inundation extent is illustrated in Fig.2.

Figure 5 :

 5 Figure 5: Comparison between simulated peak discharge values and minimum and maximum estimated peak discharge values from the post-event survey reported in Amponsah et al. [1] at ten locations along the four main watercourses.

Acknowledgments

The authors thank Météo-France for providing the meteorological data and IGN for the elevation data. This work is supported by the EU-funded project Risq´Eau (Interreg ALCOTRA project).


Camille Scotté

Siddharth Sivankutty

Hervé Randy A Bartels

Hervé Rigneault
email: herve.rigneault@fresnel.fr

Line-scan Compressive Raman imaging with spatio-spectral encoding

come

Line-scan Compressive Raman imaging with spatio-spectral encoding

Spontaneous Raman spectroscopy permits characterization of molecular species with high specificity in a label-free manner. Typically, the Raman inelastically scattered light is spectrally dispersed and collected onto an array detector -for several positions of the sample -resulting in a Raman hyperspectral image. This measurement of a complete vibrational Raman spectrum per spatial pixel, coupled with the weak Raman scattering cross-section and detector array noise, requires lengthy acquisition times and generates large data sets. In situations where hyperspectral measurements simply aim to map the spatial distribution of known molecules, such an acquisition process is highly inefficient. Instead of unmixing the spectral data in a post-processing step to detect molecular species and/or estimate their concentrations [1,2], higher acquisition efficiencies can be achieved by encompassing compressive techniques in the acquisition process. In Compressive Raman Technology (CRT), the measurement is directly designed to estimate quantities of interest (e.g., molecular concentrations), rather than deducing them from complete hyperspectral measurements [3][4][5][6][7][8][9]. This is achieved by replacing the array detector by a single-pixel detector combined with a fast programmable optical filter, typically a digital micromirror device (DMD). Based on the a priori knownledge of the Raman spectra of the pure molecular species contained in the sample, these filters select accurately chosen spectral components and combine them into the detector (Fig. 2). Such CRT developments have led to spontaneous Raman imaging with pixel dwell times down to 30 µs [3,10], which is orders of magnitude faster than state-of-the-art Raman hyperspectral imaging [7]. To further improve CRT, we recently demonstrated a CRT line-scan strategy based on spatial frequency-modulated illumination imaging [11], referred to as CRiSPY [12]. As opposed to recent spatial encoding approaches [13][14][15], CRiSPY does not use an spatially-resolved detector but combines both spatial and spectral information into a single-pixel detector. It encodes the 1D spatial information into temporal frequencies, by modulating modulates the illumination line with chirped cosines imprinted on a rotating disk [11,12]. In the present Letter, we explore an alternative line-scan CRT strategy that does not require an external modulator, but instead makes use of the bi-dimensionality of the DMD exploits -for the first time in CRT -the bi-dimentionality of the DMD (Fig. 2): (i) The Raman spectral information is dispersed across the λ-axis, and the DMD encodes this information with dedicated spectral filters; (ii) The spatial information along the line-focus is encoded onto the DMD x-axis, with Hadamard matrices shifted to contain only positive values. We demonstrate line-scan CRT with proof-of-concept experiments for chemically specific classification of molecular species, and give evidence that this approach is beneficial over point-scanning CRT in a number of cases.

In line-scan CRT, both spatial (along the line-focus) and spectral information is encoded in the signal measured onto the singlepixel detector. The aim is to estimate the relative abundances (proportions) of a set of Q molecular species (with known Raman spectra) in each of the N resolved points along the illumination line (Fig. 1). We denote P as the number of DMD patterns along the x-axis (p = 1...P), Q as the number of pure chemical species present in the sample (q = 1...Q), M as the number of spectral filters (m = 1...M) and L as the number of resolved energy bins along a Raman spectrum (l = 1...L). The N × Q matrix C is the quantity to estimate, i.e., the spatial distribution of the pure chemical species proportions. Each element of C, c q (x n ), specifies the proportions of the q th pure chemical species contained in the resolved point x n of the illumination line. The P × N matrix A contains the P patterns displayed along the DMD x-axis. The L × M matrix F contains the M spectral filters f m . The Q × L matrix S contains the known Raman spectra of the pure chemical species. The measurements matrix, H, contains the number of counts measured when displaying binary masks onto the DMD. Each mask is formed by the Kronecker product of a row of A and a column of F (Fig. 2). Each column of H is recorded by keeping the spectral filter fixed, and scanning through the rows of A to obtain a complete set of spatial projections. Assuming the generated signal is linear to the excitation intensity and ignoring constant terms, the measurement process can be expressed as:

H = ACSF = ACG T (1)
where G T = SF.

Spatial patterns Spectral filters Proportions Measurements

Pure spectra

H A C S F Fig. 1. Visual representation of Eq. 1, with Q = M = 2.
Although the spatial and spectral dimensions could be considered conjointly, we handle them distinctly in this Letter. In the spectral domain, the filters f m are calculated from the pure Raman spectra s q with the same optimisation procedure as in [6]. In the spatial domain, we choose the matrix A to be a modified Hadamard matrix with positive coefficients (S-matrix). The S-matrix of size N is obtained by removing the first row and column of a Hadamard matrix of size N + 1, and changing the ones to zeros and minus ones to ones [16]. It is square (P = N), invertible, and its binary nature complies with the DMD design and its use at fast frame rates. For each line, we perform the estimation in two steps. First, we estimate a spatial line image of Raman intensities, for each spectral filter. In other words, we seek to estimate the global matrix CG T , which elements η m (x n ) represent the Raman intensity in each pixel x n , for the spectral filter f m . Since our measurements are shot-noise limited [7] and that η m (x n ) ≥ 0, we perform this estimation using the classical EM algorithm (Richardson-Lucy), which seeks to maximize the Poisson likelihood under positivity constraints [17][18][19]. By reducing the estimation variance on the object pixels where the positivity constraint applies For relatively sparse objects, its gives better performances in terms of mean-square error as compared to least-square estimation (data not shown), for relatively sparse objects [20][21][22]. We will report more precisely on this effect in a forthcoming publication. The resulting estimate is denoted ηm (x n ). After a transpose operation, the estimation of the species proportions reduces to a 1D CRT problem [6]:

ηT (x n ) = Gc T (x n ) (2) with η(x n ) = ( η1 (x n ), ..., ηM (x n )) and c(x n ) = (c 1 (x n ), ..., c Q (x n )). If G T G
is not singular, the proportions along each line are finally estimated via least-square estimation [6]:

ĉT (x n ) = G G -1 G ηT (x n ) (3)
The 2D image is built after performing these two estimation steps for each line of the sample.

A simplified schematic of the experimental setup is depicted in Fig. 2. On the illumination side, a continuous wave laser operating at 532 nm (Verdi, Coherent Inc) is spectrally filtered and expanded. The beam is brought to a line focus onto the sample plane with a combination of cylindrical lens, plano-convex lens and microscope objective (Nikon 20x, 0.5 NA). On the detection side, the scattered light from the object is relayed onto a confocal slit. A combination of dichroic mirror and notch filter ensures only the Raman signal is retained. Next, it is dispersed with a blazed grating (600 mm -1 , Thorlabs), and the spatially dispersed wavelength components are imaged onto the DMD (V-7001, Vialux -1024 × 768 mirrors). The DMD λ-axis, in conjunction with the grating, acts as a programmable spectral filter. Since the line focus is imaged onto the DMD (≈ 22.5 demagnification), its x-axis offers control over the corresponding spatial dimension of the object [Inset Fig. 2]. When the DMD pixels are in the 'ON' state, the signal impinging on these pixels is deflected into a photon-counting PMT (H7421-40, Hamamatsu), while the rest is sent into a beam dump. A piezoelectric stage scanner (P517, Physik Instrumente GmBH) holding the sample is used to scan the y-axis, yielding 2D images. In this configuration, the spatial resolution along x-is limited by the imaging system and the size of one DMD mirror. In the experiments, the DMD mirrors are binned 2-by-2 along x-, resulting in an equivalent spatial resolution of about 1.2 µm. The line length on the illumination plane, together with cropping from diverse optical elements, limits the field-of-view along x-to about 220 µm. On the DMD plane, the spatial extent of the line image only represents 1/3 of the entire DMD size, but the S-patterns are displayed over the full DMD x-range (P = 511). In the y-direction, the spatial resolution is about 1.5 µm (extent of the line focus on the sample). The spectral resolution is estimated to 40 cm -1 , limited by the grating and the imaging system. This allows to bin the DMD mirrors 8-by-8 along λ-. Spatial calibration was performed by scanning a bead of known size and matching its profile onto the DMD. The effective FOV was estimated by recording the Raman signal from a spatially homogeneous sample (microscope glass slide) and scanning it along the DMD x-axis.

The first experiment consisted in acquiring Raman line images with no spectral selectivity ( f lm = 1∀l, m) of two mixtures of beads (Sigma Aldrich). 30 µm polystyrene beads (PS), 20 µm polymethylmethacrylate (PMMA) and 12 µm melamin resin (MR) were dispersed in two different manners Fig. 3(b): (A) in a sparse way, onto a CaF 2 coverslip; (B) in a dense way, onto a glass coverslip. The total laser power on the illuminated line was set to 3.6 mW (1.1 × 10 -5 W/µm 2 ), so that the total count rate lies in the linearity regime of the detector (1.5 × 10 6 Hz). Fig. 3(a) shows the signal obtained upon the projection of each S-pattern for 10 ms, averaged over 50 measurements, and Fig. 3(b) the associated estimated Raman line images. The signal along the lines of sample B is higher due to the presence of more chemical species along x-[Fig. 3(a,c)]. No further post-processing was performed, except from the removal of some systematic periodic artefacts on the estimated images, arising from yet unindentified technical issues. , with same irradiance and integration times. This is formally equivalent to scanning the sample plane with a point-focus. Visually, the line-scan measurements seem superior to the raster-scan measurements, but this disparity is more striking for the sparse sample A than for sample B. The difference in image quality is quantitatively confirmed by the SNR values on the central pixels of a PS bead (Fig. 4 (e-g)), defined as SNR PS = ĉ(x PS ) /σ PS , where ĉ(x PS ) and σ PS are the mean and standard deviation of the estimated proportions, respectively. On the PS pixels, the SNR improvement over raster-scanning is about 3 for object A, and 1.5 for object B. To better assess the efficiency of the presented line-scanning technique over point-scanning, we compare the estimation variances of the corresponding Raman line images, with no spectral selectivity (Fig. 5). For sample A, the variance on the object is lower for line-scanning than for raster-scanning. For example, on the PS bead along central line of the sample, the variance σ 2 is about 3 times lower, leading to a SNR improvement of √ 3 (SNR on pixel i: SNR i = η(x i ) /σ i ). On the PMMA bead 1, the variance is about 6 times lower for line-scanning, while for PMMA bead 2, it is only about 2 times lower. For sample B, line-scanning leads to a relatively uniform variance along the line which is similar to raster-scanning. This leads to a limited SNR improvement. These results are consistent with the CRT results of Fig. 4. They show that, in terms of SNR, line-scanning seems mostly beneficial for the lines along which the sample is sparse for the sparse sample A, and brings a limited improvement to the denser sample B. This stems from the shot-noise limited nature of our measurements [7]. Here, the noise scales with the square-root of the number of photons arising from the illuminated pixels across the line [23]. In addition, the signal from pixel x n may be affected by photon noise coming from the average Raman signal along the entire line. This results in an object-dependent SNR improvement, which is expected to increase for sparser objects [20][21][22][23]. This is in contrast to measurements where detectors exhibit signal-independent additive noise [16] : In this case, the same S-multiplexing strategy would lead to an SNR improvement of √ N/2 , i.e. of 10 times, for both objects. The precise mechanisms for the dependence of SNR improvement due to the sparsity of the sample are out of the scope of this paper and will be investigated in more details in a forthcoming publication These aspects will be investigated in more details in a forthcoming publication. From this short analysis, we surmise that our line-scan CRT approach would bring a SNR advantage over point-scanning CRT, and thus be faster, when samples are relatively sparse or when the experimental configuration exhibits signal-independent noise contributions. We emphasize that the spectral filtering induced by CRT renders the samples more sparse, and thus further improves the SNR, as long as the chemical species spectral overlap is limited. The SNR and speed gain will then depend on the spatial and spectral structure of the sample along the multiplexed line.

In this Letter, we have demonstrated a simple approach for line-scan CRT with S-multiplexing, with proof-of-concept experiments. While a line-scan strategy includes some drawbacks such as non-uniform illumination profile [24] or potential loss in spatial or spectral resolution, we surmise line-scan CRT to be beneficial over point-scanning CRT for SNR for relatively sparse objects in many circumstances. While the mentioned speeds do not compete with point-scanning CRT, they are expected to be faster with approaches such as compressive-sensing [25,26]. In addition, the results could further be improved by filters design and optimisation taking into account the spatial and spectral domain conjointly.

Fig. 2 .

 2 Fig. 2. (a) Schematic of the experimental setup. L 1 -L 6convex lenses with focal lengths 50 mm, 150 mm, 150 mm, 150 mm, 100 mm, 150 mm and 50 mm, respectively. L 7 -comof 2 lenses that image the DMD into the PMT with × 3 de-magnification. L cyl -cylindrical lens with focal length mm, D -dichroic mirror, S -confocal slit, G -amplitude grating, PMT -photomultiplier tube. (b) The spectral axis gives access to the Raman spectrum, and allows to project optimized spectral filters. (c) The spatial axis gives access to the spatial information along the line focus.

Fig. 3 .

 3 Fig. 3. (a) Signal after projection of S-patterns along each line x-, for sample A and B. (b) Estimated images obtained with the EM algorithm. (c-d) Cross-sections along the dotted lines of (a, b). Results are averaged over 50 measures, and cropped to show only the FOV. Scale bar = 30µm. x-: Line-scan axis, y-: Piezo-scan axis. Colorbars units: counts.

Fig. 4 .

 4 Fig. 4. (a) Reference spectra and associated spectral filters, for sample A. (b) Estimated proportion maps with line-scan. (c-f) Visualization of proportion maps of PS (red), PMMA (green) and MR (blue), for line-scanning and raster-scanning.

Funding

  Centre National de la Recherche Scientifique (CNRS), Institut Carnot STAR (IRAC 2018), Aix-Marseille University A * Midex (noANR-11-IDEX-0001-02 and A-M-AAP-ID-17-13-170228-15.22-RIGNEAULT), ANR grants France Bio Imaging (ANR-10-INSB-04-01), France Life Imaging (ANR-11-INSB-0006) infrastructure networks, Plan cancer INSERM PC201508 and

Fig. 5 .

 5 Fig. 5. Variance images (50 measurements), for line-scanning and raster-scanning. (a-b): sample A. (c-d): sample B. (e-f) Cross-sections along the dotted lines of (a-d).

Acknowledgements

The authors ackowledge fruitful discussion with P. Réfrégier and F. Galland.

Disclosures

Hervé Rigneault has financial interest in Lightcore Technologies SA, Marseille.