domain: phys chim

text:
Hassan Denawi

Elena Nardi

Mathieu Koudia

Olivier Siri

Mathieu Abel

Roland Hayn

Magnetic Polymer Chains of Iron and Zwitterionic Quinoidal ligands on the Ag(111) Surface

On-surface polymerization of iron atoms and zwitterion quinone (ZQ) molecules on Ag(111) is studied experimentally under ultra-high vacuum and theoretically in the framework of density functional theory . The resulting one-dimensional (1D) polymer chain is a promising model system to study both magnetic and conductive properties in one dimension. Previously we have shown that such polymer synthesis is possible over large scale by a controlled codeposition of the two elements (i. e. metal and molecule) on a Ag(111) substrate (Nano Res. 2017, 10, 933). In that case, polymer chains are bound together to form a two-dimensional (2D) arrangement of spin chains influencing the magnetic properties of individual chains.

Here we show that individual chains can be obtained using a sequential deposition of first metals and then ligands by scanning tunnelling microscopy on the Ag(111) surface. Ab-initio calculations are used to compare the atomic, electronic and magnetic structures of isolated Fe-ZQ polymer chains (1D) to the previously obtained two dimensional (2D) arrangement of the polymer chains. The adsorption energy is determined using the spin-polarized generalized gradient approximation (SGGA) and the SGGA+U approximation. It yields small values of less than 530 meV per Fe. On the Ag(111) surface, the most favourable adsorption site of Fe in the polymer chain is the hexagonal-close-packed (hcp) site for the 1D polymer but it changes to the face-centred-cubic (fcc) site for the 2D polymer. Using both SGGA and SGGA+U methods, we find a small difference between the two sites: face-centred-cubic (fcc) and hexagonal-close-packed (hcp). This latter is the most stable adsorption energy when we add the Hubbard U term to the SGGA method.

INTRODUCTION

Conductive metal-organic frameworks (c-MOFs) emerged recently as promising candidates in many different application fields as they offer unique possibilities to combine conductive properties, 1,2 magnetic properties [START_REF] Denawi | Magnetic Polymer Chains of Transition Metal Atoms and Zwitterionic Quinone[END_REF][START_REF] Leuenberger | Quantum Computing in Molecular Magnets[END_REF][START_REF] Gaita-Arin | Mononuclear Lanthanide Single-Molecule Magnets Based on Polyoxometalates[END_REF][START_REF] Denawi | On-Surface Synthesis of Spin Crossover Polymeric Chains[END_REF] and catalytic properties. [START_REF] Hurtado Salinas | Reactivity of Bioinspired Magnesium-Organic Networks under CO 2 and O 2 Exposure[END_REF] Especially the prospective of electrical conductivity in MOF's attracted recently a lot of attention to these systems in nanotechnology. [START_REF] Sakamoto | The Coordination Nanosheet (CONASH)[END_REF][START_REF] Grill | Nano-Architectures by Covalent Assembly of Molecular Building Blocks[END_REF][START_REF] Barth | Engineering Atomic and Molecular Nanostructures at Surfaces[END_REF] Many studies have shown that these materials are very good candidates for use in devices for electrocatalysis, [START_REF] Hurtado Salinas | Reactivity of Bioinspired Magnesium-Organic Networks under CO 2 and O 2 Exposure[END_REF][START_REF] Miner | Electrochemical Oxygen Reduction Catalysed by Ni3 (Hexaiminotriphenylene)2[END_REF][START_REF] Zhao | Ultrathin Metal-Organic Framework Nanosheets for Electrocatalytic Oxygen Evolution[END_REF][START_REF] Ma | Metal-Organic Framework Derived Hybrid Co3O4-Carbon Porous Nanowire Arrays as Reversible Oxygen Evolution Electrodes[END_REF][START_REF] Clough | Two-Dimensional Metal-Organic Surfaces for Efficient Hydrogen Evolution from Water[END_REF] fuel cells, [START_REF] Miner | Electrochemical Oxygen Reduction Catalysed by Ni3 (Hexaiminotriphenylene)2[END_REF][START_REF] Zhao | Iron Imidazolate Framework as Precursor for Electrocatalysts in Polymer Electrolyte Membrane Fuel Cells[END_REF] and chemical sensing. [START_REF] Stassen | An Updated Roadmap for the Integration of Metal-Organic Frameworks with Electronic Devices and Chemical Sensors[END_REF][START_REF] Smith | Direct Self-Assembly of Conductive Nanorods of Metal-Organic Frameworks into Chemiresistive Devices on Shrinkable Polymer Films[END_REF][START_REF] Ko | Conductive Two-Dimensional Metal-Organic Frameworks as Multifunctional Materials[END_REF] when synthetized in layered materials. The great originality of these MOF conductive materials with respect to the insulating MOFs comes from a strong hybridization of the orbitals of the metal centers with the orbitals pi of the organic molecules giving them good conduction properties. At the same time, it imposes a state of oxidation II of the metal centers responsible for the catalytic properties but also of the magnetic properties in networks whose architecture is dictated by the organic ligand. Thanks to that it has been possible to synthesize 1D conductive MOF including magnetic atoms. 1D magnetic chains are interesting for several reasons. First of all, they would allow crucial experiments to answer fundamental questions on low-dimensional spin systems. [START_REF] García-Fernández | Exploring the Relation between Intramolecular Conjugation and Band Dispersion in One-Dimensional Polymers[END_REF][START_REF] Clair | Controlling a Chemical Coupling Reaction on a Surface: Tools and Strategies for On-Surface Synthesis[END_REF] Second, they are interesting in the field of spintronics, where not only the electron charge but also its spin is used for information processing. And third, spin chain systems are discussed for many possible spintronics applications, going from magnetic memories up to quantum computing. [START_REF] Leuenberger | Quantum Computing in Molecular Magnets[END_REF][START_REF] Gaita-Arin | Mononuclear Lanthanide Single-Molecule Magnets Based on Polyoxometalates[END_REF] Recently, it was shown that zwitterionic quinoidal molecules and metallic Fe can form, after adsorption on Ag(111) or Au(110) surfaces, a well ordered arrangement of spin chains up to micrometer. [START_REF] Denawi | On-Surface Synthesis of Spin Crossover Polymeric Chains[END_REF][START_REF] Koudia | On-Surface Synthesis of Covalent Coordination Polymers on Micrometer Scale[END_REF] The STM and LEED measurements in connection with a theoretical analysis of the obtained polymer adsorption on Au(110) [START_REF] Denawi | On-Surface Synthesis of Spin Crossover Polymeric Chains[END_REF] indicate that the adsorbed polymers adapt their lattice constants to the underlying substrate. Surprisingly, the polymer lattice constants on Au(110) and Ag(111) substrates differ by 6 per cent and such a large difference can eventually be explained by two nearly degenerate energy minima for different lattice constants corresponding to two different spin states (S=1 or S=2) as expected for spin crossover compounds. [START_REF] Denawi | On-Surface Synthesis of Spin Crossover Polymeric Chains[END_REF] However, previous theoretical studies were either focused on the electronic and magnetic structures of free polymers [START_REF] Denawi | Magnetic Polymer Chains of Transition Metal Atoms and Zwitterionic Quinone[END_REF] or treated just the adsorption on the Au(110) substrate. [START_REF] Denawi | On-Surface Synthesis of Spin Crossover Polymeric Chains[END_REF] Experimentally, only the 2D arrangement of Fe-ZQ polymer chains were reported. On the other hand, the ab-initio study of isolated free polymers indicated very interesting perspectives for these new systems, intimately related to their one dimensionality.

In the present communication, we report on two advances with respect to published work. [START_REF] Denawi | Magnetic Polymer Chains of Transition Metal Atoms and Zwitterionic Quinone[END_REF][START_REF] Denawi | On-Surface Synthesis of Spin Crossover Polymeric Chains[END_REF][START_REF] Koudia | On-Surface Synthesis of Covalent Coordination Polymers on Micrometer Scale[END_REF] First of all, the on-surface synthesis of isolated magnetic polymer chains obtained by sequential deposition and, second, a detailed theoretical analysis of the adsorption of 1D and 2D Fe-ZQ polymers on Ag(111) detailing the adsorption process and the resulting atomic, electronic and magnetic properties. Finally, electronic structure calculations allow the determination of the density of states which informs on the charge transport efficiency.

EXPERIMENTAL METHODS

The zwitterionic quinoidal ligand was prepared as described in the literature. [START_REF] Yang | First Transamination Reactions for the One-Pot Synthesis of Substituted Zwitterionic Quinones[END_REF][START_REF] Siri | Unprecedented Zwitterion in Quinonoid Chemistry[END_REF] All experiments were performed in a multi-characterization chamber under ultra-high vacuum (UHV). Zwitterion molecules were evaporated from a crucible held at 430 K. Fe atoms were deposited from an iron rod (Goodfellow) using an electron-beam evaporator. The experiments are done with a molecular deposition rate of 0.05 ML•min -1 calibrated at room temperature.

The resulting synthetic films were characterized using room-temperature scanning tunneling microscopy (Omicron VT-STM). Images were plane-corrected and analysed using the WSxM software.

THEORETICAL METHOD

To determine the electronic and magnetic properties of the systems, within the framework of density functional theory (DFT) periodic calculations were performed using the Vienna Ab initio Simulation Package (VASP), [START_REF] Truhlar | Ab-initio Simulations of Materials Using VASP: Density-functional Theory and Beyond[END_REF][START_REF] Kresse | Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set[END_REF][START_REF] Kresse | From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method[END_REF] in the spin polarized generalized gradient approximation with an explicit inclusion of the Hubbard U term correction (SGGA+U) of Perdew and Wang (PW91), [START_REF] Perdew | Erratum: Atoms, Molecules, Solids, and Surfaces: Applications of the Generalized Gradient Approximation for Exchange and Correlation[END_REF][START_REF] Perdew | Accurate and Simple Analytic Representation of the Electron-Gas Correlation Energy[END_REF] for the exchange and correlation potential and the Projector Augmented Wave (PAW) pseudo potentials. [START_REF] Kresse | Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set[END_REF][START_REF] Kresse | From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method[END_REF][START_REF] Perdew | Erratum: Atoms, Molecules, Solids, and Surfaces: Applications of the Generalized Gradient Approximation for Exchange and Correlation[END_REF][START_REF] Perdew | Accurate and Simple Analytic Representation of the Electron-Gas Correlation Energy[END_REF][START_REF] Blöchl | Projector Augmented-Wave Method[END_REF][START_REF] Kresse | Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set[END_REF] The Coulomb correlation in the d shell was taken into account by a Hubbard term in the form proposed by Liechtenstein et al. [START_REF] Liechtenstein | Density-Functional Theory and Strong Interactions: Orbital Ordering in Mott-Hubbard Insulators[END_REF] The necessity of the SGGA+U method for metal-organic compounds with transition metal ions is proven by many examples as TM-ZQ, [START_REF] Denawi | Magnetic Polymer Chains of Transition Metal Atoms and Zwitterionic Quinone[END_REF][START_REF] Denawi | On-Surface Synthesis of Spin Crossover Polymeric Chains[END_REF] TM-TCNB [START_REF] Mabrouk | Possibility of a Ferromagnetic and Conducting Metal-Organic Network[END_REF] or TM-Pc [START_REF] Mabrouk | Possibility of a Ferromagnetic and Conducting Metal-Organic Network[END_REF][START_REF] Zhou | Magnetism of Phthalocyanine-Based Organometallic Single Porous Sheet[END_REF] where TM is a transition metal. The correlation energy (U) of 4 eV and exchange energy of J = 0.90 eV is taken for the Fe d orbitals. To study the polymer on the surface we use a kinetic-energy cut-off of 480 eV and the convergence criteria for the electronic step was set to 10 -4 eV. The structure was relaxed until the residual forces were smaller than 0.02 eV/Å and we used a first order Methfessel-Paxton setting with a smearing (SIGMA) of 0.2 eV. The method of Methfessel-Paxton also results in a very accurate description of the total energy. Only a single k-point, namely the -point, was used. The substrate is simulated by a 5-layer Ag (111) surface onto which we add the Fe-ZQ layer. The separation distance between the slabs (top vacuum) is set to 10 Å. It was verified that greater separation distances did not lead to significantly lower energies. The free standing polymer without surface was relaxed until the residual forces were 10 -6 eV/Å and the convergence criteria for energy was 10 -7 eV. The Brillouin zone was sampled by a k-point set of (8×1×1) for the one-dimensional (1D) free standing polymer and by a k-point set of (8×5×1) for the 2D arrangement without substrate using the Monkhorst-Pack k-point mesh. [START_REF] Pack | Special Points for Brillouin-Zone Integrations[END_REF] Figure 1 shows the atomic structure of Fe-ZQ on Ag(111) after relaxation in the most stable configuration.

RESULTS AND DISCUSSION

On-surface synthesis under UHV is a promising strategy for controlling matter at the atomic level, with important implications for the design of new one-and two-dimensional materials having remarkable electronic and magnetic properties. First, we investigate the behavior of the selected system composed by iron atoms and ZQ molecules on Ag(111).

Figures 2a,b, and c are obtained after sequential deposition of iron atoms on the Ag(111) substrate maintained at room temperature, the sample is heated to 170°C and the molecules are deposited on the Fe/Ag(111) substrate.

Step edges are decorated with Fe islands of several hundreds of atoms, of about 5 nm × 5 nm × 0.8 nm. Then the additional deposition of molecules allows the formation of needles which are 40-100 nm long and have a width of 2 nm. These needles grow on the terraces between the step edges by incorporation of Fe atoms (coming probably from the Fe islands) in between the ZQ molecules. They are composed at its periphery by 2 wires with protrusions of 7.6 Å periodicity that are compatible with the formation of 1D polymers. Between these two wires, one can observe the formation of a complex composed by a central iron atom and two ZQ molecules that is schematically shown in Figure 1d. These results clearly demonstrate the efficiency of the method, which consists of deposition of iron atoms and molecules on an Ag (111) substrate. In both cases of sequential deposition and co-deposition, the chains are oriented at 20° from the close-packed direction of the substrate with a periodicity of 7.6 Å. It is important to note that within an individual chain, there is no modulation of the height of the polymer, indicating equivalent adsorption sites for all the Fe atoms. The only difference between co-deposition and sequential deposition is the packing of the polymer chains. A (7x7) R19° epitaxial relationship is obtained in the case of co-deposition whereas individual chains separated by molecules are obtained in the case of sequential deposition.

2: (a, b and c) STM images polymeric chains obtained after sequential deposition of iron atoms on Ag(111) kept at room temperature then the sample is heated to 170°C and zwitterion molecules are deposited , (d) schematic representation of the Fe-zwitterionic quinone and (e and f) STM topography of co-deposited Fe atoms and zwitterionic quinone on the

The lattice parameters used in calculations are set in agreement with this epitaxial relationship. For the two-dimensional free-standing polymer (2D) the values of a and b are 15.30 Å and 13.24 Å, respectively, and the total magnetic moment is 2 per Fe. The local magnetic moment is 2.06 (1.94 ) for each Fe site corresponding to S = 1 for the SGGA (SGGA+U) methods, respectively, see Table 1. The objective is the study of the adsorption phenomena constituted by the Fe-ZQ polymer adsorbed on the noble metal surface Ag (111). From these calculations we derive the following trends in adsorption energies, geometric, electronic and magnetic structure. As mentioned above, there is strong experimental evidence that Fe-ZQ polymers adsorb on Ag(111) surface with high coverage under typical polymer deposition conditions. The length of the linear chains and the coverage increase with the quantity of Fe atoms. [START_REF] Koudia | On-Surface Synthesis of Covalent Coordination Polymers on Micrometer Scale[END_REF] To investigate the interaction with the substrates, geometry optimizations were carried out where the Fe atoms were placed over different sites, the top (T), bridge (B), hexagonal-close-packed (hcp)

Table 1. Lattice constants (a and b) in (Å), Magnetic Moments per Unit Cell M, and Local Magnetic Moments per Fe (M d ) at Fe Site for the free-standing polymer.

or face-centered-cubic (fcc) sites on the first layer Ag(111) as illustrated in Figure 1. The adsorption energy for Fe-ZQ on the surface is defined as E ads = E polymer/surface -E surface -E polymer . This value is confirmed by total energy calculations using spin polarized Generalized Gradient Approximation (SGGA) and inclusion of the Hubbard U term correction. The adsorption energies, total and local magnetic moments and geometric parameters of different configurations of the selected adsorption configurations were calculated (see Table 2 and3).

The adsorption energy for the stable adsorption site corresponds to the absolute minimum of the molecule moving on the surface. First, it is clear from Table 2 that the SGGA and SGGA+U methods give different results for the adsorption energy E ads and the total magnetic 2. On the other hand, the face-centred-cubic (fcc) site is the most favorable one for the 2D Fe-ZQ polymer on the surface Ag (111). However, it should be mentioned that the variation between the two different sites face-centred-cubic (fcc) and hexagonal-close-packed (hcp) is very small of only 1 … 3 meV as shown in Table 2. The adsorption energy for the most stable ferromagnetic configuration is -0.351 eV (-0.175 eV)

for the SGGA (SGGA+U) method. The total magnetic moment of M = 1.90 in the SGGA is smaller than M = 2.01 in SGGA+U method. Not surprisingly, for both configurations, SGGA gives the largest adsorption energy and smallest adsorption height. SGGA+U is a very popular functional, widely used in adsorption studies. Here SGGA+U gives an E ads of -0.175 eV, with the difference in adsorption energy between the two configurations (1D and 2D) being only 0.091 eV per Fe atom. It can also be noticed that, for the Fe-ZQ, the energy difference between two configurations with the fcc and hcp adsorption sites is ∼1-3 meV, which suggests that these two configurations are equivalent at room temperature Present calculations show that the Fe-ZQ polymer is adsorbed at the hcp site on the Ag(111) surface.

The distances between metal ions (Fe) and Ag surface in the configurations with the lowest total energy are 2.62, and 2.66-3.52 Å for the cases of 2D Fe-ZQ polymers, without and with the Hubbard U correction, respectively. Since we are interested in the magnetic properties of the systems, the spin-polarized density of states projected on the Fe(II) in the adsorbed polymer with the lowest energy configurations is presented in Figure 3a-b to identify the influence of the Ag surface on the electronic structures of the adsorbates. First of all, the DOS in Fig. 3 looks very similar to the DOS of a free standing chain (not shown) besides a certain smearing of the peaks. Also the position of the Fermi level is almost not shifted showing the absence of any charge transfer between substrate and polymer chain. The electronic structure provides deep insight into the interaction between adsorbate and surface. We now analyze the densities of states (PDOS) of the Fe-ZQ polymer on Ag(111). The peak at +0 eV in the SGGA method (Figure 3a) has been shifted to -1.0 eV for the SGGA+U method. In the spin up channel, all peaks are shifted closer to the Fermi level. We observe that the spin-down d xy and the d z² orbitals are completely filled, leaving d x²-y² empty for the spin-up as shown in Figure 3

Table 2. Adsorption energies in eV for different sites of the Fe-ZQ on the Ag (111), distances between the central Fe atoms and the Ag surface are provided (d Fe-Ag , in Å), total magnetic moments (M per Unit Cell, in ), local magnetic moments of the d orbital at the TM atoms ( per TM atom, in ) for different sites of the Fe-ZQ on the Ag (111) with the SGGA and SGGA+U (U = 4 eV) methods.

Fe-ZQ

CONCLUSIONS

The conclusion that can be drawn is that the adsorption, electronic, and magnetic structure of Fe-ZQ (1D and 2D) adsorbed on Ag (111) surfaces have been obtained by the modification of the growth conditions. 1D isolated polymer chains are obtained by sequential deposition of Fe followed by ZQ deposition whereas 2D close-packed arrangements are obtained by co-deposition of the two precursors Fe and ZQ. These two configurations (1D and 2D) together with the underlying substrate had been systematically studied using the SGGA and the SGGA+U approximations within DFT calculations. The hexagonal-closepacked (hcp) and face-centred-cubic (fcc) site are the most favorable ones for the adsorption of Fe-ZQ on the Ag (111) surfaces. We have calculated the partial density of states of the Fe-3d states for the Fe-ZQ/Ag (111) system, as well as the distance between the atoms (Fe-Fe, b

Fe-N, Fe-O and Fe-Ag). Above all, our results based on electronic structures can give reasonable explanations and predictions on the existing experimental results from a theoretical level. We have shown a way to synthesize well separated magnetic chains with antiferromagnetic nearest neighbour exchange interaction [START_REF] Denawi | Magnetic Polymer Chains of Transition Metal Atoms and Zwitterionic Quinone[END_REF][START_REF] Denawi | On-Surface Synthesis of Spin Crossover Polymeric Chains[END_REF] on a metallic substrate. This new strategy will hopefully open a way to study experimentally that well-known model system of low-dimensional physics.

Figure 1 :

 1 Figure 1: Schematic representation of the 2D Fe-zwitterionic quinone on Ag(111)surface. The Fe atoms are in the hexagonal-close-packed (hcp) site, with the method SGGA+U and U = 4 eV. Left: top view, Right: side view.

Figures

  Figures 2e and 2f are obtained as previously reported 21 by co-deposition of Fe atoms

Figure

  Figure 2: (a, b and c) STM images polymeric chains obtained after sequential deposition of iron atoms on Ag(111) kept at room temperature then the sample is heated to 170°C and zwitterion molecules are deposited , (d) schematic representation of the Fe-zwitterionic quinone and (e and f) STM topography of co-deposited Fe atoms and zwitterionic quinone on the Ag (111) surface heated at 250°C.

  Figure 2: (a, b and c) STM images polymeric chains obtained after sequential deposition of iron atoms on Ag(111) kept at room temperature then the sample is heated to 170°C and zwitterion molecules are deposited , (d) schematic representation of the Fe-zwitterionic quinone and (e and f) STM topography of co-deposited Fe atoms and zwitterionic quinone on the Ag (111) surface heated at 250°C.

  moment. The hexagonal-close-packed (hcp) site is the most favorable one in the case of 1D Fe-ZQ polymer on surface Ag (111). The Fe-O (Fe-N) bond length d Fe-O (d Fe-N ) of the polymer on adsorption was calculated to be 1.88 (1.87) Å for the SGGA method. While the d Fe-O (d Fe-N ) length increases in the SGGA+U method, d Fe-O (d Fe-N ) rises from 1.88 to 1.91 Å (1.87 to 1.90 Å) respectively. The vertical distance between a Fe atom and the Ag(111) substrate, i.e. the adsorption height Fe-Ag(111) is 2.58 Å (2.68 Å) within the SGGA (SGGA+U) method, the distance between the irons atoms (Fe-Fe) is 7.65 Å for the ferromagnetic (FM) configuration. The adsorption energy for the most stable adsorption configuration is -0.525 eV (-0.263 eV) per Fe atom. The total magnetic moment M is 1.74 (1.93 ) and the local magnetic moment is 1.89 (1.96 ) per Fe, when we use the SGGA (SGGA+U) method, see Table

  and giving a magnetic moment close to 2 per Fe (S = 1).

  a

Figure 3 :

 3 Figure 3: (a and b) PDOS of the Fe-3d states in the 2D Fe-ZQ on the Ag (111) surfaces obtained from the PAW-SGGA and PAW-SGGA+U respectively.

ACKNOWLEDGEMENTS

This work was supported by the Computer resources of the Centre Informatique National de l'Enseignement Supérieur (CINES), Project No. A0020906873 and the High Performance Computing (HPC) resources of Aix-Marseille University financed by the project Equip@Meso (ANR-10-EQPX-29-01).

AUTHOR INFORMATION

Corresponding Author

*E-mail: hassan.denawi@im2np.fr (H.D.).


P Didier

G Le Coz

G Robin

P Lohmuller

B Piotrowski

A Moufki

P Laheurte

Consideration of SLM additive manufacturing supports on the stability of flexible structures in finish milling

Keywords: Selective Laser Melting (SLM), Additive Manufacturing support, machining

The supports in additive manufacturing can be used in an innovative way by being considered as supports for machining operation. This innovative use of manufacturing supports can facilitate the finishing of functional thin structures. But the flexible global workpiece-supports system can potentially cause vibrations during the machining operation. This can cause irregular surfaces with bad quality.

This study highlights the importance of additively manufactured support structures on the stability of Ti-6Al-4V parts milling by using supports as a machining fixture. Nowadays, the control of the support stiffness and mechanical properties is not proposed by specific AM software. A way to develop a numerical method to optimize the post-processing of additive manufacturing parts is to use specific lattice structures as supports. Indeed, by adjusting the topology and the beam diameter of lattices, the relative stiffness and the relative density of the global structure can be controlled. The objective of this study is to show that the stiffness of the manufacturing supports is crucial for the machining operation.

To validate this concept, milling tests are proceeded on thin-walled plates produced by Selective Laser Melting (SLM) using defined finish milling cutting conditions. Three types of results are obtained: cutting forces signals, displacements and surface qualities by confocal microscopy. The study reveals that milling can induces chatters. Also, surface qualities and dimensional deviations depend on the support choice.

The control of mechanical properties of support structures appears to be a good way to favor machining operation of flexible and thin-walled structures. Topology and dimensional parameters of supports have to be considered in preliminary design steps of the additive manufacturing digital chain.

Introduction

The growing interest in Additive Manufacturing (AM) processes and particularly in the Selective Laser Melting (SLM) technology resulted in the development of the associated techniques: "design for additive manufacturing". This offers new opportunities and considerations despite new constraints [START_REF] Thompson | Design for Additive Manufacturing: Trends, opportunities, considerations, and constraints[END_REF]. The possibilities offered of 3D printing technology make it possible to redesign products by taking advantage of these new processes [START_REF] Gibson | Additive manufacturing technologies[END_REF]. For example, in the biomedical field, it is possible to manufacture custom-made implants and prosthesis which perfectly adapt to bone anatomy [START_REF] Didier | Mechanical stability of custom-made implants: Numerical study of anatomical device and low elastic Young's modulus alloy[END_REF]. Automotive, aeronautical and aerospace industries are particularly attracted by the freedom of shapes, allowing the manufacturing of topologically optimized macro-structures [START_REF] Saadlaoui | Topology optimization and additive manufacturing: Comparison of conception methods using industrial codes[END_REF] and complex beam network, such as lattices structures [START_REF] Zhang | Selective electron beam manufactured Ti-6Al-4V lattice structures for orthopedic implant applications: Current status and outstanding challenges[END_REF]. Numerical approaches of topological optimization allow to determine the optimal distribution of material in a defined volume subjected to specific loads for the lightening of the structure. [START_REF] Bendsoe | Topology optimization: theory, methods, and applications[END_REF]. All these new possibilities lead to complex geometries and thin-walled structures.

Additive manufacturing technologies also impose various constraints [START_REF] Thompson | Design for Additive Manufacturing: Trends, opportunities, considerations, and constraints[END_REF][START_REF] Hague | Implications on design of rapid manufacturing[END_REF]. For instance, the process to obtain powder for SLM technology is expensive and thus the achievable alloy compositions are limited. The control of the process allows very low porosity rates but leads to anisotropic mechanical properties and irregular surface roughness that are strongly dependent on the orientation of the parts on the substrate [START_REF] Simonelli | Effect of the build orientation on the mechanical properties and fracture modes of SLM Ti-6Al-4V[END_REF][START_REF] Leary | Surface roughness optimisation for selective laser melting (SLM): accommodating relevant and irrelevant surfaces[END_REF]. Residual stresses related to rapid cooling induce geometrical deviations [START_REF] Mugwagwa | Influence of process parameters on residual stress related distortions in selective laser melting[END_REF]. During the manufacturing processes, manufacturing supports are always used to limit strains by strengthening the overall structure and favoring a better heat diffusion during manufacturing [START_REF] Hussein | Advanced lattice support structures for metal additive manufacturing[END_REF]. However, support structures have to be removed afterward. This may take time and require manual operations causing topological defects. These defects further aggravate roughness defects.

Although additive manufacturing process makes it possible to approach the near-net shape of the product, finishing operations by chemical [START_REF] Baicheng | Study of selective laser melting (SLM) Inconel 718 part surface improvement by electrochemical polishing[END_REF], mechanical [START_REF] Salvatore | Experimental and numerical study of media action during tribofinishing in the case of SLM titanium parts[END_REF] or laser treatment [START_REF] Yung | Laser polishing of additive manufactured CoCr alloy components with complex surface geometry[END_REF] are necessary. For some surfaces, accurate dimensional qualities are required and thus finishing by milling or grinding is necessary [START_REF] Brinksmeier | Surface integrity of selective-laser-melted components[END_REF]. These treatments have already been integrated by some companies in their hybrid machining center offering additive manufacturing and milling possibilities [START_REF] Stavropoulos | Addressing the challenges for the industrial application of additive manufacturing: Towards a hybrid solution[END_REF], where material deposition and machining operation are performed in the same place. In the case of SLM process, the hybrid solutions are more complicated due to the powder deposition. Thus, the complementarity between the additive and the subtractive machines must be investigated and the repositioning methods for machining of the produced part should be considered. The concept investigated in this study is the following: considering the machining operation by milling, it is possible to consider the supports no longer as a constraint, but as an opportunity, as a customized machining fixture. The support structures are preserved in order to perform post-processing on specific surfaces, see Figure 1. This approach allows a gain of operations to obtain finished functional surfaces. This strategy eliminates the need to develop a specific clamp for a unique, custom-made, complex-shaped part. Its potential leads to the cost-effectiveness of production where post-processing is still considered to be artisanal. To achieve such a goal, several considerations need taking into account. The first technical aspect that should be considered is the appropriate positioning and the orientation of the printed part in order to make the considered surfaces accessible to the cutting tool. The second is the geometry and the stiffness heterogeneity of the global manufacturing part, including the manufacturing supports and the workpiece. These factors are unfavorable for the milling, due to the bending of the flexible part, and thus vibrations can appear between the tool and the part [START_REF] Michalik | Monitoring surface roughness of thin-walled components from steel C45 machining down and up milling[END_REF]. This situation generates dimensional deviations and low surface quality [START_REF] Seguy | Surface roughness variation of thin wall milling, related to modal interactions[END_REF]. It is then necessary to understand the vibratory phenomenon in order to anticipate, control and limit it by optimizing cutting speed and material removal rate [START_REF] Thevenot | Integration of dynamic behaviour variations in the stability lobes method: 3D lobes construction and application to thin-walled structure milling[END_REF][START_REF] Altintaş | Analytical prediction of stability lobes in milling[END_REF][START_REF] Denkena | Experimental investigation and simulation of machining thin-walled workpieces[END_REF]. Although the printed part is not adaptable because of the function that it was designed for, the supports can be optimized. They can be used to modify the mechanical properties of the part that supports the overall system, as sacrificial structures to increase the stiffness [START_REF] Smith | Sacrificial structure preforms for thin part machining[END_REF] or a mass damper to adjust the eigenfrequency of the structure [START_REF] Kolluru | A solution for minimising vibrations in milling of thin walled casings by applying dampers to workpiece surface[END_REF]. However, in the digital chain dedicated to additive manufacturing, supports are principally designed to build an unsupported overhang structure or to limit part distortion. Considering the literature review of Plocher and Panesar [START_REF] Plocher | Review on design and structural optimisation in additive manufacturing: Towards next-generation lightweight structures[END_REF], there is no previous work including the support structure optimization taking into account all the mechanical loads applied during the post-processing. Indeed, the control of their equivalent stiffness and their equivalent mechanical properties is not considered. In the same way as Hussein et al. [START_REF] Hussein | Advanced lattice support structures for metal additive manufacturing[END_REF] proposes to use lattice structures as supports to minimize the lasering time. A novel approach is to consider lattices structures as supports with the ability to control the mechanical properties of the overall additive manufacturing part, with the objective of post-processing the surfaces by milling. Thus, the present work is proposed to use lattices structures as custom-made supports directly manufactured during the process. This study highlights the influence of support stiffness on the milling operation and its effect on the quality of the finished surfaces. Side milling tests are carried out on plate samples and their manufacturing supports. Support structures with different stiffnesses are compared, using different geometrical and sizes of support structures. Cutting forces and displacements are measured using a dynamometric plate and a laser vibrometer. A correlation to the surface quality is presented.

Material and methods

Geometry and SLM additive manufacturing of the samples

Differences of stability in milling and potential vibration problems are highlighted by the design of adequate SLM samples. In the previous studies about chatters when machining, milling instability directly resulted from the thin thickness of thin-walled plates. Thevenot et al. [START_REF] Thevenot | Integration of dynamic behaviour variations in the stability lobes method: 3D lobes construction and application to thin-walled structure milling[END_REF] milled a 1-millimeter thin wall of steel plate (S235) and Seguy et al. [START_REF] Seguy | Surface roughness variation of thin wall milling, related to modal interactions[END_REF] worked with a 2017 aluminum alloy workpiece with 3 mm in thickness and 20 mm in height.

In the present work, the system is composed of two parts of Ti-6A-l4V. The main deflection of the plates is due to the open geometry of the supports and their low stiffness. Samples with two subparts are considered and the geometry of the samples is presented in Figure 2. These two parts are manufactured on a third block (unrepresented) that allows the clamping of the samples in the machining center and ensures an embedment of the samples at the base of the support-plate system. The upper rectangular-shaped plate, 3 mm thickness (l1), 9 mm high (l2) and 9 mm wide (l4), is the subpart to be finished by machining. The lower part of the samples corresponds to the manufacturing support. Its thickness is equal to (l1) and the height (l3) to 4.5 mm. As the geometrical shape is fixed, the sample stiffness is controlled by the geometry and the architecture of the supports. Two families of structures are considered in this study to cover a large range of stiffness: structures directly exported from the SLM digital chain and lattices structures, as shown in Figure 2.

The first supports are obtained with the Magics® Materialise software, dedicated to the data preparation for SLM. The Web support is composed of various vertical walls, one crossing another at the center of the surface. The Block support consists of intersecting walls with diamond-shaped perforations. The second type of supports proposed are lattice structures, made by the repetition of an elementary unit-cell. By adjusting the topology and the beam diameter, the relative stiffness and the relative density of the global structure can be controlled and numerically implemented. These mechanical properties are essential to understand the dynamic phenomenon during milling. Indeed, with the control of the truss diameter and the unit-cell size, and thus the control of the relative density, it is possible to determine its Young's modulus [START_REF] Favre | A continuous crystallographic approach to generate cubic lattices and its effect on relative stiffness of architectured materials[END_REF]. Two structures, well known in the literature, are retained in this study: the Diagonal and the Octet-truss structure [START_REF] Deshpande | Effective properties of the octet-truss lattice material[END_REF]. Two truss diameters are considered for each cell: 0.300 and 0.375 mm. The same global unit-cell dimension of 1.5x1.5x1.5 mm 3 are used and the same pattern repetition (6x2x3) in the x, y and z directions are used to define the global samples with fixed dimensions. For each structure, four samples are prepared, using the laser manufacturing parameters for the Ti-6Al-4V alloy (Power P = 200 W, laser speed v = 1650 mm/sec and hatching distance H = 80 µm).

Analysis of the first modal frequency

The sample is composed of two parts: the upper plate and the lower support that has the equivalent behavior of a bulk plate structure. Embedded in the base, the natural principal deformation is the flexion around the y-axis, as shown in Figure 2. As all the samples have the same external dimensions, they have the same first mode of vibration corresponding to the flexion around the y-axis. Since the natural frequencies of the plate increase with its rigidity, the stiffness of each sample is analyzed through the natural frequency of the first mode f1.

An impact hammer allows us to determine the resonance frequency of the structure. The displacements are measured by a laser vibrometer. As there is no contact between the sensor and the workpiece, the measurement is not disturbed. The frequency range of the solicitation is from 1Hz to 10 000Hz. The laser is focused in the middle of the free end of the plate. A Fast Fourier Transformation (FFT) is performed to obtain the frequency content of the vibration signal. The first modal frequency is scattered with a lower value of 743 Hz for the Diagonal with 0.3 mm diameter to 6656 Hz for the Block sample, as given in Table 1. The dispersion is slightly increased for structures with 0.3 mm in diameter (8.21 %) from that for the structures with 0.375 mm in diameter (4.59 %). Indeed, at this scale, the geometrical defects due to the process are even more important with smaller diameters [START_REF] Amani | Compression behavior of lattice structures produced by selective laser melting: X-ray tomography based experimental and finite element approaches[END_REF]. Owing to the resolution, the reproducibility of the process is validated, particularly for the Magics® supports. The reproducibility of the process can be validated for all structures.

Experimental tests of finish milling

The peripheral finish milling of the plate (thin wall) is proceeded in a Roeders RXP200DS (3000 -60000 rpm) 5 axis machining center, with an Erowa ITS50 clamping system. Side up milling operation is carried on with a TiAlN coated solid carbide tool, referenced as Belet 110-1. The tool has four teeth, a helix angle of 30° and a cutting angle between 8° and 10°. The diameter of the tool is 3 mm with a 6 mm diameter body at the end. It is assembled in a collet chuck system referenced as BIG New Baby Chuck.

The samples defined previously are clamped on a dynamometric platform, Kisler 9256C, as shown in Figure 3 (a). It allows measuring the cutting forces in three directions in the three-dimensional space.

A charge amplifier Kisler 5017B integrated with an acquisition system NI Daq and a Labview program enable the recording of the cutting force signals at a frequency of 10 kHz. The tool-machine framework is considered to be perfectly rigid compared with the workpiece which is considered flexible.

The displacements of the thin wall when machining are also measured with a laser vibrometer in the middle of the free end of the plate; the laser beam is represented Figure 3 (a). The side milling of the SLM plates is performed in finishing conditions of the conventionally produced Ti-6Al-4V alloy, with a cutting speed of 141 m/min, a feed per tooth (fz) of 14 µm/th and an axial and radial depth of cut (ae) of 1 and 0.2 mm, respectively, as seen in Figure 3 (b). It corresponds to a spindle speed (N) of 15000 rpm. Two milling passes are performed for each sample. The first pass can't be considered as constant, due to the initial surface state, including roughness and particles partially melted. The first pass can be considered as roughing. To obtain constant conditions, the presented displacements and cutting forces are related to the second pass, considered as finishing.

Surface topography is obtained after milling tests by confocal microscopy with a Leica DCM3D system. The associated software Leica Map facilitates the extraction of profiles and surfaces. These data provide Ra measurements calculated on 1 mm lengths in the same direction as the machining pass.

The topography of the surfaces can also be used to extract the difference in height between the machined surface and the rough surface.

Temporal evolution of the cutting forces, displacements and surface topographies obtained by confocal microscopy are evaluated at two different scales:

-at the global scale (all along the plate): the dynamic behavior of the structure, that depends on the solicitation position, especially at the extremities of the plate; -at the local scale (tens of micrometers): the impact of each tooth on the structure.

Results

Table 2 summarizes the overall results for all structures. This takes into account the average amplitude of displacement and force on the two machining passes, the height between the machined surface and the rough surface (in confocal microscopy) and the roughness Ra. Only the Diagonal structure with 0.3 mm diameter did not allow the acquisition of all signals due to failure of the supports during the machining operation. Globally, the more rigid the structure is, the less the amplitude of its displacement is important and the higher the cutting effort. Thus, the removal of material is more important as indicated by the difference in height the machined surface and the rough surface. Finally, the surface roughness is much smoother for more rigid structures.

In order to study more precisely the impact of the stiffness of the supports on the machining operation, three structures are studied more closely. The objective is to identify two milling regimes (stable or unstable) through two structures with far different stiffness: Block structure (f1 = 6656 Hz) and Octettruss structure with a 0.3 mm diameter (f1 = 2780 Hz). They are compared to a third one with intermediate stiffness: Octet-truss with 0.375 mm diameter (f1 = 4601 Hz).

Displacement

The displacement at the global scale is firstly considered, see Figures 4 (a),(d) and (g). It shows that whatever the stiffness of the sample, the signal has the same aspect with a stable central area, composing the majority of the signal. At the beginning and at the end of the signal, edge effects are visible with different amplitudes compared with that at the stable central area. When the three plates are compared to each other, it can be seen that the more the plate is flexible, the higher the amplitude of the signal is. The same trend is observed for the edge effect.

mm diameter structure (g) (h) (i) -Global scale

Displacement is evaluated at the local scale and in the middle of the milling pass for three tool rotations, as shown in Figures 5 (a), (d) et (g). The impact of each tooth is clearly observed, with a period of 1 ms. Four impacts correspond to a tool rotation duration of 4 ms. Furthermore, the displacement imposed by each tooth is not equivalent and is decreasing with the four successive teeth, typical to a tool run out.

The signal of the higher stiffness plate (Block) presents a 0.2 ms phase without movement, equivalent to a 0.1 mm displacement, see Figure 5 (a). The Octet-truss structure with 0.375 mm diameter is more flexible, and the signal amplitude is higher and oscillates continuously from -0.35 to 0.35 mm, as seen in Figure 5 (d). At last the Octet-truss structure with 0.3 mm diameter is less rigid with a displacement oscillating between -0.6 and 0.35 mm, see Figure 5 (g).

Cutting forces

The displacement acquired with the laser interferometer in the normal direction of the plate is correlated with the normal cutting force in the same direction Fx. For the Block structure, the most part of the signal is stable, as seen in Figure 4 (b). Edge effect can be seen at the extremities marked by a limited force at the beginning and at the end of the milling. Moreover, as seen from the displacement, the edge effect is more marked for the less rigid structure with the more perturbed signal at the extremities. However, some irregularities and punctual instabilities, not observed on the displacement signal, are observed all along the Octet-truss with 0.3 mm diameter, as shown in Figure 4 (h). For the intermediate structure, the cutting force signal remains stable but with a lower amplitude than the Block structure, see Figure 4 (e). At the local scale, the impact of each tooth is clearly identified for the Block structure, as seen in Figure 5 (b). Due to a run out of the tool, an asymmetry between different teeth is observed, as seen on the displacement. It confirms the correlation between the two signals. Figure 5 (h) shows that for the flexible sample the impact of each tooth is hardly noticeable. In terms of the amplitude, the force signal decreases with the loss of the stiffness, both locally and globally.

Topography of surface

Figure 4 also presents the surface topography on all the cutting area, obtained by confocal microscopy.

The surface quality appears completely different for the three samples. For the Block structure which is more rigid, the height variations all along the plate are small and of the order of 10 µm, see Figure 4 (c). This variation is due to the side effect, especially at the output of milling. Despite these edge effects, the global topography is regular. The surface quality of the Octet-truss with 0.375 mm diameter is less homogeneous than the Block structure as shown in Figure 4 (f). The topography of the Octettruss with 0.3 mm diameter structure is even more irregular, see Figure 4 (i). The variation reaches 30 µm and the punctual vibrations seen on the cutting force signal are also observed on the surface. These observations are consistent with the determination of Ra roughnesses presented in Table 2.

At the local scale, the surface is evaluated in the middle of each plate, as presented in Figure 5. The profiles are extracted from a length of 0.5 mm. On the Block surface, the waviness due to the cutting is clearly visible, see Figure 5 (c). On the profile, the waviness period is averaged to be 56 µm. It corresponds to the feed rate per revolution. For the more rigid Octet-truss structure with 0.375 mm diameter, the periodic waves due to the cutting are less visible, but the surface quality is not significantly affected, see Figure 5 (f). The surface is considerably more degraded for the flexible Octettruss structure with 0.3 mm diameter, where the irregularity of the cutting is evident, as seen in Figure 5 (i).

Discussion

SLM process allows a near-net-shape product but some functional surfaces still need to be postprocessed. This operation contracts additional costs and thinking for planning [START_REF] Hamilton | Planning, preparing and producing: Walking the tightrope between additive and subtractive manufacturing[END_REF]. The novel approach, considering support as custom-made machining fixture for post-machining, answers to a step between additive process and subtractive milling. It leads to study the overall workpiece, including the plate and the support structure. Milling operation can induce chatters and poor surface quality, depending on the support choice but also of the cutting parameters. Previous works [START_REF] Seguy | Surface roughness variation of thin wall milling, related to modal interactions[END_REF][START_REF] Thevenot | Integration of dynamic behaviour variations in the stability lobes method: 3D lobes construction and application to thin-walled structure milling[END_REF][START_REF] Altintaş | Analytical prediction of stability lobes in milling[END_REF] propose to determine lobes stability when side milling. In the present study, authors limit the discussion and only focus on the effect of part stiffness.

A correlation can be established between the stiffness of the workpiece and the plate displacement in flexion. The more flexible the structure is, the greater its bending displacement. This trend is confirmed by the evolution of the average displacement (in the stable area) according to its first modal frequency, as seen in Figure 6. The curve shows a nonlinear increase of the average displacement with the decrease of f1. This amplification can be explained by the growing proximity between f1 and the excitation frequency of the tool tooth, corresponding to 1000 Hz. Nevertheless, the information obtained from the displacement signals is not sufficient to confirm the effective cutting of the material. In contrary to the displacement signal, a decrease of the cutting force amplitude is observed with the loss of stiffness. The decreasing amplitude of the signal indicates a less effective cutting of the material for the least rigid structure. The more the plate is flexible, the larger its deflection is, and thus less material is cut by the tool. This non-cutting phenomenon is even more pronounced when the axial depth of cut is small. Indeed, in these cutting conditions, the scale of the deflection and the radial depth of cut (ae) are the same. The previous tendencies are supported by the surface profiles, as shown in Figure 7. These data, acquired by confocal microscopy, demonstrate the difference of heights between the manufactured rough surface and the finished surface. After two passes of 0.2 mm, the height difference gap should theoretically be 0.4 mm. For the Block sample, the most rigid of all the studied structures, the real average total depth of cut is 0.3 mm. For the Octet-truss structure with 0.3 mm diameter, the difference does not exceed 0.1 mm. Thus, the deflection of the flexible parts has also considerably affected the cutting considering the dimensional expected results. The irregularities and singularities noted all along this flexible Octet-truss plate can indicate cutting instabilities due to vibratory problems. Indeed, the more flexible structures have a first modal frequency close the excitation frequency. Hence, vibration problems inducing irregular and bad cutting are more remarkable for these samples.

Other phenomena have also appeared during the machining of the plates. On the global displacement signals, edge effects are visible when the tool is cutting the extremities of the plate. When the mechanical solicitation is positioned on the sides of the sample, the flexion is amplified, and the displacement at the solicited extremity is larger than the displacement at the center of the plate. This phenomenon is even more marked when the plate is flexible. Indeed, edge effects are often observed in side milling of thin-walled plates [START_REF] Thevenot | Integration of dynamic behaviour variations in the stability lobes method: 3D lobes construction and application to thin-walled structure milling[END_REF]. As mentioned previously, despite the laser is at the center of the plate, the perturbation is detectable and increases with the reduction of the stiffness of the structures. Moreover, an asymmetry between the teeth has been detected from cutting force and displacement signals, defined as a runout. It can be explained by a tiny manufacturing defect of the tool, especially observed in micro milling, where cutting tool depth of cut (ae, f) is small. This phenomenon results in a regular waviness for the Block sample where the resultant surface is from the action of the most eccentric tooth, as shown in Figure 5 (a). For the Octet-truss with 0.3 mm diameter sample, the surface is more chaotic, and the milling waviness is not visible, as seen from Figure 5 (g).

The trochoidal movement of the tool teeth is combined with the oscillation of the flexible plate which results in particularly degraded surface topography. This is due to the increasing deflection of the plate with the decreasing of the equivalent rigidity of the support structures. Hence, the final surface quality also depends on the architecture of the lattice structures. The support structures made by AM, when they used as machining supports, have a major role on the final surface quality of the parts. Their equivalent stiffness, or more generally their mechanical property also allows the control of the final dimensions of the AM finished parts. Lattices structures, although less rigid than the Block structure, allow to adjust mechanical behavior of the global workpiece when submitted to the dynamic solicitation of the milling operation. Indeed, contrary to traditional supports designed to build overhang surface during the additive process, lattices structures stiffness can be controlled by a numerical method. For example, lattices structures can be submitted to simple procedure of numerical homogenization [START_REF] Xu | Design of lattice structures with controlled anisotropy[END_REF], replacing the complex support structure with a simplified geometry with equivalent mechanical properties. Considering the natural shape of the generative designed part, see Figure 1, the use of controlled supports really makes sense. They could allow the anticipation and the choice of the supports architecture, by analytical model [START_REF] Favre | A continuous crystallographic approach to generate cubic lattices and its effect on relative stiffness of architectured materials[END_REF] coupled with Finite Element Analysis of the part-support system. In that way, the process could be optimized to define support architecture and mass as a tuned mass damper. Moreover, sacrificial supports, not necessarily useful for AM, could be added to stabilize the peripheral milling of flexible parts, as used in other domains [START_REF] Smith | Sacrificial structure preforms for thin part machining[END_REF]. For example, additional lattice buttresses defined as sacrificial structures can temporarily increase the stiffness of part when milling interested surface before being removed.

Others possibilities exist with numerical tools and FEA modelization. In that way, a coupled analyticalnumerical model of the cutting forces could help for the supports design basis [START_REF] Moufki | Prediction of cutting forces from an analytical model of oblique cutting, application to peripheral milling of Ti-6Al-4V alloy[END_REF][START_REF] Moufki | Thermoviscoplastic modelling of oblique cutting: forces and chip flow predictions[END_REF].

Conclusions

The study proposes a novel approach considering supports as a custom-made machining fixture for machining operation. To demonstrate the concept, experimental tests of finish milling have been done on plate structures on their supports, manufactured by SLM additive process. The equivalent stiffness of the overall workpiece varies with the geometry and architecture of the manufacturing supports. Lattice structures and supports from commercial SLM software were used to cover a large range of stiffness. Cutting forces, displacement and surface topology were measured. With two principal observations, the study highlights the importance of the choice of manufacturing supports in terms of stiffness on the milling of SLM workpiece:

• Even under finishing conditions, milling can induce chatters, depending on the support choice.

The correlation between the displacement and the cutting forces confirms a more and more irregular and ineffective cutting with the loss of stiffness of the supports. • Surface qualities and dimensional deviations depend on the support structures. Vibration phenomena amplify the cutting instability, especially for the most flexible structures, whose first modal frequency is close to the excitation frequency of the teethed tool.

The actual associated digital chain does not allow optimal control of the mechanical behavior of the supports. This makes the lattice structures an excellent candidate for numerical analysis of manufacturing supports in the way to use it as custom-made machining supports. Indeed, they allow a choice of equivalent stiffness and mechanical properties. This study also opens up the possibility of numerically predicting the dynamic behavior of the part-support system in order to include the finishing operations in the design of additive manufacturing.

Figure 1 -

 1 Figure 1 -Machining operation of an additive manufactured part with consideration of supports as a machining fixture.

Figure 2 -

 2 Figure 2 -Geometry of the two types of sample: lattice structures and AM software structures

Figure 3 -

 3 Figure 3 -(a) Experimental procedure implemented, (b) Cutting schema of finishing pass and associated parameters and (c) Manufactured sample presenting the milling pass.

Figure 4 -

 4 Figure 4 -Normal displacements, normal cutting force and surface topography for the Block structure (a) (b) (c), the Octettruss with a 0.375 diameter (d) (e) (f) and the Octet-truss with a 0.3 mm diameter structure (g) (h) (i) -Global scale

Figure 5 -

 5 Figure 5 -Normal displacements, normal cutting force and surface topography for the Block structure (a) (b) (c), the Octettruss with a 0.375 diameter (d) (e) (f) and the Octet-truss with a 0.3 mm diameter structure (g) (h) (i) -Local scale

Figure 6 -

 6 Figure 6 -Evolution of the average displacement amplitude and cutting force according to the first modal frequency

Figure 7 -

 7 Figure 7 -Profile between rough and cut surfaces for (a) Block structure and (b) Octet-truss 0.3 mm diameter structure, acquired by confocal microscopy

Table 1 -

 1 Average of the first modal frequency of each structure and dispersion

	Structure	f1 (Hz)	Relative deviation (%)	Damping η
	Diagonal with
	0.300 mm	743	8.21	0.0024
	diameter
	Diagonal with
	0.375 mm	1459	4.59	0.0018
	diameter
	Octet-truss
	with 0.300 mm	2780	5.52	0.0022
	diameter
	Octet-truss
	with 0.375 mm	4601	2.04	0.0012
	diameter
	Block	6656	2.72	0.0018
	Web	4551	1.14	0.0011

Table 2 -

 2 Summary of machining test results: displacement amplitude, cutting force, height difference between machined and rough surface and roughness Ra

	Structure	f1 (Hz)	Average displacement amplitude (mm)	Average cutting force amplitude (N)	Minimum & maximum force (N)	Height difference: rough-machined surfaces (µm)	Ra (µm)
	Diagonal with
	0.300 mm in	743	/	/	/	35.5	5.09
	diameter


Arnaud Grignard
email: agrignard@media.mit.edu

Tri Nguyen-Huu
email: tri.nguyen-huu@ird.fr

Benoit Gaudou
email: benoit.gaudou@gmail.com

Doanh Nguyen-Ngoc
email: doanhnn@tlu.edu.vn

Arthur Brugière

Tu Dang-Huu

Quang Huynh

Nghi

Trong Nguyen

Kent Khanh

Larson

Huynh Quang Nghi
email: hqnghi@ctu.edu.vn

Khanh

Kent Larson

CityScope Hanoi: interactive simulation for water management in the Bac Hung Hai irrigation system

Keywords: Agent-Based Model, CityScope, GAMA platform, interactive simulation, Bac Hung Hai, irrigation system

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

I. INTRODUCTION

Irrigation systems contribute worldwide to the provision of a wide range of services on which the survival and well-being of humanity depends. They are of primary importance in Vietnam where about 90% of the water used is for irrigation and aquaculture 1 and where agriculture is the largest employer and a major contributor to the national GDP and to the income of the low-salary households. Nevertheless, irrigation systems have recently been subjected to several issues including increasing demand, pollution, under-investment, depletion of sources or environmental changes. Climate change is impacting water availability and increasing peak rainfall but also increasing the intensity of droughts [START_REF] Bernstein | Climate change 2007: Synthesis report: An assessment of the intergovernmental panel on climate change[END_REF]. As an example, the Bac Hung Hai irrigation system, which lies in the Red River Delta, is currently heavily affected by environmental pollution, with hundreds of sewers flowing into the river. With a large area crossing four provinces, it constitutes an irrigation canal for hundreds of thousand hectares of agricultural land, but the pollution caused for many years by Bac Hung Hai irrigation system seriously affects the life, activities, and production of millions of inhabitants.

Any mitigation measure against these issues needs to be sustainable with respect to the very diverse uses of the water, the changing conditions upstream and downstream, and the somewhat conflicting objectives carried out by land-use/agricultural planning on one hand and urbanization and society wellbeing on the other hand. Any management solution of the irrigation system should thus not only be assessed considering the system as a simple physical set of channels and gates transporting water, but rather as a whole socio-environmental system. This induces the need of innovative tools to support decisions and consultation, able to integrate all the social, environmental and economic aspects of the system in a single object, that can be the object of experiments to answer whatif (such management policy is applied) and how-to (reach a sustainable state related to such indicators) questions and can favour participation and interactions between the various stakeholders, decision-makers and users.

In this context, Agent-Based Modelling (ABM) appears as an invaluable leverage. ABM is based on the design of models representing the behaviour of a system as an emerging feature of computational entities (agents) in interaction in a simulated environment [START_REF] Macal | Tutorial on agent-based modeling and simulation[END_REF], [START_REF] Treuil | Modélisation et simulation à base d'agents: exemples commentés, outils informatiques et questions théoriques[END_REF]. This approach has become the approach of choice to represent socio-environmental systems (such as irrigation systems [START_REF] Gaudou | The maelia multi-agent platform for integrated analysis of interactions between agricultural land-use and low-water management strategies[END_REF], [START_REF] Balbi | Multi-agent agroeconomic simulation of irrigation water demand with climate services for climate change adaptation[END_REF]), especially when they require the inputs of different disciplines to be designed. This approach is also well-adapted to design participatory simulations, where human beings can control an artefact agent in the simulation [START_REF] Taillandier | Participatory modeling and simulation with the gama platform[END_REF], [START_REF] Page | Kilt: a modelling approach based on participatory agent-based simulation of stylized socio-ecosystems to stimulate social learning with local stakeholders[END_REF].

This CityScope Hanoi project aims at exploring the usage of Agent-Based Modelling coupled with a tangible and interactive interface in order to ease the decision-making process of the management of an irrigation system, facing mainly issues of pollution and water scarcity. The full setup will be based on an Agent-Based Model2 developed using the GAMA Platform [START_REF] Taillandier | Building, composing and experimenting complex spatial models with the GAMA platform[END_REF] to represent the water flow, the various land use evolution and the pollution emitted in the system. This model will be integrated in the CityScope framework [START_REF] Alonso | Cityscope: a data-driven interactive simulation tool for urban design. use case volpe[END_REF]. The chosen case study is the Bac Hung Hai irrigation system close to Hanoi, in the Red River Delta, Vietnam.

The paper is organized as follows. Section II will first present the Bac Hung Hai irrigation system. Section III will present some related works. The Agent-Based Model is presented in Section IV and the interactive table in Section V. Section VI summarizes the preliminary results. Finally, Section VII concludes the paper and discusses some perspectives.

II. CASE STUDY

The Bac Hung Hai irrigation system lies in the centre of the Red River Delta. Its North-West area covers a part of Hanoi city. It is bounded by four rivers: Duong river (North, 67 km), Luoc river (South, 72 km), Thai Binh river (East, 73 km), and the Red river (West, 57 km) (cf. Fig. 1). Its area is 214.932 ha: 192.045 ha inside dykes and 22.887 ha outside. It plays an important role in the economic development of the region by: (1) providing irrigation to 110.000 ha of rice, crop and tree lands; (2) bringing water for livestock, poultry, and aquaculture (12.000 ha); (3) providing water for more than three million people and industrial zones (4.300 ha); (4) controlling flooding inside the dyke area to protect people's livelihoods and agricultural production. According to the report of Bac Hung Hai Company in July 2019, water pollution in the system is one of the main issues identified by managers, users and stakeholders.

III. STATE OF THE ART

A. Hydrology modelling

The Bac Hung Hai irrigation system is located in the Red River delta. Modelling the water flow in delta areas is not an easy task, as the slope is almost zero (preventing the use of models at the scale of the basin, such as SWAT in [START_REF] Gaudou | The maelia multi-agent platform for integrated analysis of interactions between agricultural land-use and low-water management strategies[END_REF]). Even the direction of the flow can depend on the sea tide, or the season. This explains the very low number of works about the water flow modelling in this irrigation system. The only one we are aware of is a modelling using the Mike 113 software [START_REF] Pham | Modeling water flow in Bac Hung Hai Irrigation System[END_REF]. This approach is able to provide good results when calibrated with real data. Nevertheless, it cannot be used in an interactive mode, with users changing the river network (by opening and closing a gate for example) or the withdrawal processes (by modifying the land use).

We thus decided to implement an ad hoc model in GAMA which should fulfil our two main constraints: (i) it can adapt to any change in the river network, (ii) it allows to visualize easily quantitative and qualitative results. We have decided to not implement a model of water flow in river sections similar to Mike 11's one, as it is not easy to visualize both the quantity and quality of water in river sections (increasing the size of the river when the flow is huge is not really easy to perceive on an interactive table). So we develop a much less precise model, based on discrete water elements moving on the network. It allows us to display the quantity with the number of water agent and the quality with different colours.

B. Interactive simulation

The key idea of interactive and tangible simulations is to use a tangible support to display the simulation (sandbox, 3D printed map...) and to allow users to interact with it in an intuitive manner. First examples were mainly dedicated to landscape modelling and evolution [START_REF] Petrasova | Tangible modeling with open source GIS[END_REF]. Several studies have shown the benefits of such tangible objects to help the user to think spatial information and dynamics (see Chapter 1 of [START_REF] Petrasova | Tangible modeling with open source GIS[END_REF]), improving thus the learning and understanding processes [START_REF] Woods | Pilot study using the augmented reality sandbox to teach topographic maps and surficial processes in introductory geology labs[END_REF].

First Agent-Based Models linked to a tangible interface were mainly dedicated to urban simulations such as [START_REF] Lebrun | A model for managing interactions between tangible and virtual agents on an RFID interactive tabletop: case study in traffic simulation[END_REF]. Later the CityScience research group (of the MIT Media Lab) has developed several projects [START_REF] Alonso | Cityscope: a data-driven interactive simulation tool for urban design. use case volpe[END_REF], [START_REF] Grignard | Cityscope Andorra: a multi-level interactive and tangible agent-based visualization[END_REF] to give the possibility to visualize the link between urban planning and organization, mobility modes and traffic. [START_REF] Emery | Marrakair: une simulation participative pour observer les émissions atmosphériques du trafic routier en milieu urbain[END_REF], [START_REF] Pham | HoanKiemAir: simulating impacts of urban management practices on traffic and air pollution using a tangible agent-based model[END_REF] focus on the link between traffic (in particular related to vehicle numbers and states) and air pollution.

CityScope Hanoi is thus an instance of the CityScope framework, but applied for the first time to an environmental case study, including water flow, water pollution, land use water withdrawal and pollution emission.

IV. MODEL

We present in this section the key elements of the CityScope Hanoi model, developed using the agent-based modelling and simulation platform GAMA [START_REF] Taillandier | Building, composing and experimenting complex spatial models with the GAMA platform[END_REF], providing only the key parts of the standard O.D.D. (Overview, Design concepts, Details) protocol [START_REF] Grimm | The ODD protocol: A review and first update[END_REF].

A. Overview of the model

The model aims at exploring the combined impacts of various land use organization and water management on the water quantity and quality in the Bac Hung Hai irrigation system. The main question tackled by the model is: how to reach a sustainable state of the Bac Hung Hai irrigation system that fulfil the needs and well-being of the human population?

B. Description of the model entities

The model is composed of three main parts: the hydrological sub-model, the land use sub-model and the pollution submodel, which are deeply interconnected. The main entities and their links are summarized in Fig. 2.

In this project, we have decided to implement a discrete water flow model to improve the simulation visualization: the water is represented by a set of individual water agents moving on a network of river agents. The water "mobility" is impacted by a set of gate agents located at the intersection of rivers. These gate agents can be either opened or closed (allowing or preventing the water flow) and they can be source (resp. sink) and create (resp. take out) water agents for the river network.

The land use sub-model manages the 2 types of entities related to the land use and its evolution: landuse and cell agents. Each of them is characterized by a land use type attribute. Among the 2 entities, cell agents manage the link with the rivers. They withdraw water and create pollution. In addition, cell agents type is set by data coming from the user (through the scanner, see section below). landuse agents are mainly used for display purpose and to manage dryness.

The pollution sub-model is based on a collection of pollutants agents for every agriculture's elements: static_pollution, which represent land pollution, and polluted_water, for water. Each static_pollution is generated from polluted_water (in an area of 4 km) in order to reduce the water pollution and negatively impact the landuse agents.

C. Description of the model processes

Within each simulation cycle, the first element to be scheduled is the water management. During this step, all the river agents' internal water level is recomputed from the water and polluted_water agents located on it. The river agents' water level is used to drive the move of the water agents: when a water has reached an intersection between rivers, it will have a higher probability to go on the river with the lowest level of water. Once each river's water level has been recomputed, the source gate agents will generate some new water agents for the water network at the location of these gates, and the sink gate agents will remove from the simulation all the water and polluted_water which arrived at those locations.

The second computing process of each cycle is the interaction between the water agents (in rivers) and the cell agents. The first processed interaction is with the clean water which may be polluted depending if the travelled landuse is already polluted. After that, the polluted_water will have the same process, but start with a chance to generate 8 static_pollution in an area of 3 kilometers around.

The third process is about the water move. In this process, the water and polluted_water agents will follow the same steps one after the other. Water agents, first, move following the river network (influenced by the water level in the river agents, computed at the beginning of the cycle) and, with a fixed probability, may evaporate (i.e. been remove from the simulation).

The fourth process is the disappearance of the static_pollution agents which slowly dissolve until a threshold where they are naturally removed.

Finally, each landuse agent slowly dries up with a fixed amount (set by the user).

D. Input data

The simulations are initialized using a set of shapefiles of the Bac Hung Hai irrigation system (summarized in Fig. 3). This dataset is composed of (i) a shapefile (of polygons) representing the shape of the four main rivers surrounding the irrigation system, used to initialize the main_river agents, (ii) a shapefile (of polylines) with the linear shape of the interior irrigation channels, used to initialize the river agents, (iii) a shapefile (of points) containing the location of the main inflow and outflow points of the system, used to initialize the eye_candy agents. For all these agents, only the geometry is read from the shapefile. As far as the gate are concerned, agents are created from a dedicated shapefile of points, and the gate type is read from the shapefile attribute table (specifying whether it is a source or a sink). All these data files have been provided by the Bac Hung Hai Irrigation System Company.

As far as the landuse agents are concerned, they are created from the opendata shapefile of the village administrative areas 4 .

The overall environment of the simulations is a rectangle of 73 km x 57 km, corresponding to the dimensions of the shapefile used to create the main_river agents. Finally, the land use type of each cell comes from the Lego interactive table (described in the next section) as a JSON 4 The data come from the GADM website http://gadm.org/.

file describing for each cell of the grid its current land use type.

E. Outputs

The display of the simulation (Fig. 4) is first made of two contextual elements (in the sense that they do not have any impact in the simulation): the surrounding rivers and the in and out flows. This allows users to recognize the area and to identify flows direction.

All the agents of the simulation are displayed, except the cell agents. Landuse agents are displayed instead as they represent a real area in the system. The idea was that the display of a grid of square cells would have appeared unrealistic to Irrigation Systems managers. In addition, it would not be coherent to display precise rivers with their real shapes while the land use only displayed on a square shape. Finally, a legend on the left provides information about how the land uses are represented on the map (which colour) and how they are encoded with the black and white code located behind each Lego block. This legend provides also information about the gates' colour depending on their type (source, sink, or nothing).

V. INTERACTIVE TABLE

The model described previously is integrated in the CityScope framework 5 .

A. Principle of the interactive table

The model is displayed on a table (from a ceiling-mounted projector). On this table are 64 square blocks of Lego organized as an 8 × 8 matrix. Figure 6 presents a picture of the table with the Lego blocks. These Lego blocks can be manipulated: they can be removed, exchanged with another Lego block or be rotated.

Each Lego block is white on the top to be used as a screen for the simulation. But on the other side, it presents a black and white code (like a minimalist QR code), that is read and interpreted by a camera located inside the table. The CityScope framework comes with a Python scanner able to interpret this code, transform the information in a JSON file and send it to the GAMA simulation. In the simulation, a dedicated agent has been created (of species NetworkingAgent) to manage these data. When it receives the JSON file, it will parse it and assign to each cell and gate agent its new land use and closure status. Finally, the landuse agents reflect this change of land use (Fig. 5).

B. Description of the hardware

In addition to the ceiling-mounted projector connected to a computer executing the simulation, the main hardware element is the interactive table 6 . The table is composed of a top transparent board with a white mask plaque that has been cut to let space to Lego blocks.

In order to improve the quality of the footage taken by the camera and ensure the correctness of the code identification, the sides and bottom boards of the table are black and opaque. Inside the table are located a camera (specifications require a camera with a resolution of at least equals to 1080P), and a set of LEDs, to provide the light necessary for the camera. 6 The interactive table specifications are available from the CityScope webpage https://cityscope.media.mit.edu/.

The camera is plugged on a computer with a specific software scanner in charge of analysis its pictures.

C. Scanner

The scanner is a Python open-source software 7 . It takes the images provided by the camera, and identifies for each Lego pixel (the size of a 1×1 Lego block) if it is black or white 8 . It then aggregates the Lego pixels in blocks, each of them corresponding to 1 cell in the simulation and sends the corresponding JSON file to the dedicated agent, using the UDP communication protocol. For each cell, there are 2 data: the id number corresponding to the code, e.g. 1 could be all the blocks are black, 2 there is only 1 block white and 3 black ones (independently to position of this white block). The second information is a rotation code. For example the configuration with 1 white block and 3 black ones can appear with 4 different positions: the white block can be on the topright, top-left, bottom-right, or bottom-left location. In the 4 cases, the scanner will send the same id number, but with a different rotation number. We thus use this id number of the land use and the rotation number to set whether a gate is close or open.

VI. RESULTS

A first positive result of the project is that the interactive table has been presented to a wide audience during the exhibition for the 60th anniversary of Thuyloi University (Fig. 7). It has been a great opportunity to make it tested by academics, industrialists (e.g. the head of the Bac Hung Hai Irrigation Ltd, the company managing the system) and students. The feedback were really positive as people were easily able to understand what happens in the simulation, and how to interact with it. Although, the simulation appears limited for the moments in terms of possible actions to perform, this test is a first preliminary proof of correctness of the model: at least it does what it is expected to do (e.g. filling the system with industry will increase the pollution...). Now, as far as the simulation itself is concerned, and even if we cannot calibrate it with real data in terms of hydrology, we can already observe some interesting patterns. In particular, source gates definitely play a key role in the simulation results: when an industry is located close to a source, it will produce much more pollution and will affect much more the system, than an industry located elsewhere.

An indirect interesting result is that, even if the previous observation can easily be understood with the rules of the model, it forces us to think whether it occurs in the real irrigation system. Improving the accuracy of the model could require more field study or interactions with experts to evaluate whether this is only a simulation artefacts or a real phenomenon.

The model thus already succeeds in raising questions and promoting interdisciplinary and cross-sectorial interactions.

VII. CONCLUSION

In this paper, we have presented a tangible and interactive Agent-Based Model to support decision-making and interaction around irrigation systems management alternatives and have demonstrated its interest in the path to design more sustainable solution. We also illustrate the applicability of the CityScope framework in an agriculture context. Even very promising, this model definitely needs to be improved, in particular to better take into account the link between drought and pollution.

In this model, we focused on the land use change as a way to organize and manage the space. It could be interesting to investigate now the possibilities to be more subtle (and, then, realistic) on the actions players can do on the system: as an example, players could build, repair, or destroy dykes, simply change the crop on the fields, rather than being able to change from rice to industry and back to vegetables.

Fig. 1 .

 1 Fig. 1. Map of the Bac Hung Hai irrigation system.

Fig. 2 .

 2 Fig. 2. Class diagram of the main entities of the model.

Fig. 3 .

 3 Fig.3. Input data used to initialize the simulations: village-level administrative area (grey), in and outflow (purple), the main rivers (light blue surfaces), the main channels (dark blue lines), and gates (green disk).

Fig. 4 .

 4 Fig. 4. Screenshot of the simulation.

Fig. 5 .

 5 Fig. 5. Interaction principle: from Lego block to land use types.

Fig. 6 .

 6 Fig. 6. Illustration of the top board of the table with the Lego blocks.

Fig. 7 .

 7 Fig. 7. Interactions and discussion around the tangible interface.

more than 94% in

for agriculture and livestock. Source: https://data. worldbank.org/indicator/ER.H2O.FWAG.ZS?locations=VN.

The model is distributed as an open-source software. It is available on its GitHub repository https://github.com/CityScope/CSL Hanoi.

Mike 11 website: https://www.mikepoweredbydhi.com/products/mike-11.

CityScope official website: https://cityscope.media.mit.edu/.

The scanner is available from its GitHub repository https://github.com/ CityScope/CS CityScoPy.

This limitation to black and white is a safety policy, the scanner could definitely recognize much more colours, but the error rate will be much higher.

ACKNOWLEDGEMENT

The CityScope project has been initiated at the MIT Media Lab. CityScope Hanoi has been funded by the CityScience group at MIT Media Lab and the JEAI WARM team, UM-MISCO/Sorbonne University (SU)/IRD and Thuyloi University (TLU).