Mathieu François
email: mathieu.francois@thalesgroup.com

Frédéric Segonds

Mickaël Rivette

Simon Turpault

Patrice Peyre

Orcid Mathieu

Design for additive manufacturing (DfAM) methodologies: a proposal to foster the design of microwave waveguide components

Keywords: Design for additive manufacturing, laser beam melting, design method, industrial design, product development, waveguide

Additive manufacturing offers many advantages, especially in terms of creativity and design freedom. However, this emerging technology is disrupting the way design is carried out and creativity is often limited by the cognitive barriers installed through years of traditional manufacturing processes. Likewise, as this manufacturing process is relatively recent and quite unknown to designers, its specificities are not always considered during the design phase, which leads to manufactured parts happening to differ from CAD models in terms of sizing or surface quality. Consequently, microwave components nowadays manufactured layer-by-layer do not exhibit operational electromagnetic performances. In this way, it is necessary to guide designers throughout the development of a product by drawing their attention to the different steps they must consider in order to design an additive manufactured optimised part.

Introduction

For many years, microwave waveguide components have been used in communication systems and especially for antenna-feed chains. This RadioFrequency (RF) type of equipment is already widely operational in different fields such as satellite communications (SatCom), radars, space observations etc. due to their advantages in terms of low losses as well as their high energy management capabilities. In the recent years, several institutions and industries have been showing growing interest in additive manufacturing (AM) process for waveguide components [START_REF] Booth | Enhancing the Performance of Waveguide Filters Using Additive Manufacturing[END_REF][START_REF] Peverini | Selective Laser Melting Manufacturing of Microwave Waveguide Devices[END_REF][START_REF] Tchoffolo-Talom | Additive Manufacturing for RF Microwave Devices: Design, Performances and Treatments Improvement Evaluations[END_REF]. One of the greatest promises of AM can be found in exploiting the extra degrees of freedom it offers to achieve innovative design configurations unachievable by conventional techniques [START_REF] Laverne | Fabrication additive : principes généraux[END_REF]. However, additive technologies impose specific decisionssuch as orientation, part topology, support structures, materials and so onthat designers must consider during the design development to ensure an optimised part. The complexity of designing for additive manufacturing (DfAM) lies in the interdependence of these rules. It is therefore essential that the design method integrates all of this knowledge to guide designers in their choices suitable to their purpose. But how to foster microwave waveguide component design by the use of a DfAM method? This paper proposes a DfAM method that can closely guide designers in the design of additive manufactured microwave parts. In chapter two, a literature review has been carried out that we use to highlight our motivations in chapter three. Then, in chapter four, a new method for additive manufacturing RF part components fabricated by Laser Beam Melting process is proposed, followed in chapter five by the development of a three-port Kaband waveguide power divider as a case study. Conclusions and orientations of future research will bring to a close.

Literature review

First, a review of the current state of practice in AM is introduced to evaluate the manufacturing specificities to be taken into account particularly when dealing with electromagnetic requirements, followed by a presentation of its application to microwave waveguide components. Then, the different approaches employed to perform design for AM are analyzed.

2.1. Additive manufacturing 2.1.1. Specific geometrical considerations Support structures are among specificities of certain additive processes, including powder bed technologies. Their main use lies in supporting overhanging volumes to avoid a gravity-induced melt-pool collapse [START_REF] Hussein | Advanced Lattice Support Structures for Metal Additive Manufacturing[END_REF]. They are to be placed underneath every surface that is inclined by less than a critical angle, ranging from 20 to 45 degrees towards the build platform [START_REF] Leary | Optimal Topology for Additive Manufacture: A Method for Enabling Additive Manufacture of Support-Free Optimal Structures[END_REF][START_REF] Thomas | The Development of Design Rules for Selective Laser Melting[END_REF][START_REF] Vandenbroucke | Selective Laser Melting of Biocompatible Metals for Rapid Manufacturing of Medical Parts[END_REF]. For Laser Beam Melting process, supports also play a role of a heat sink, as a huge amount of thermal energy in led into the build area by the laser. To prevent residual stress from remaining after cooling and to avoid an increase of thermal stress inside the part, support structures act as a heat dissipater to transfer the heat to the manufacturing platform [START_REF] Thomas | The Development of Design Rules for Selective Laser Melting[END_REF]. Consequently, the impact of residual stress on the process is reduced. However, microwave components being related to pipes, once the fabrication of the part is completed, every support structure placed inside cavities is trapped and impossible to remove which would prevent the signal from being transmitted.

Otherwise, although manufacturing dimensional tolerances manage to be met and repeated by the use of conventional techniques, these considerations are much more complex for additive processes. Actually, their mastery is not total and it is still difficult to know and anticipate these dimensional variations [START_REF] Kempen | Dimensional Accuracy of Internal Channels in SLM Produced Parts[END_REF][START_REF] Kniepkamp | Dimensional Accuracy of Small Parts Manufactured by Micro Selective Laser Melting[END_REF]. In the RF domain, these variations are a major concern. For example, a variation of 200 microns of the crosssectioni.e 2% of the dimensionscan cause a 0.5 GHz offset on a bandwidth target of 1.5 GHz (Kaband as defined by IEEE Std 521-1984).

Part orientation

Layer-by-layer manufacture inevitably induces a 'staircase effect', owing to the finite layer thickness. This effect is all the more important for the surfaces that are neither orthogonal nor parallel to the manufacturing platform. The arithmetic roughness, Ra, generated by this geometric phenomenon can be modelled according to the formula [START_REF] Strano | Surface Roughness Analysis, Modelling and Prediction in Selective Laser Melting[END_REF]:

R a = 1 L L 0 |y(x)|dx = 1 4 L t cos a
where L t represents the layer thickness and α the angle between the manufacturing platform and the surface of the part.

However, this geometrical model seems far from representing the real surface quality obtained on a fabricated part [START_REF] Canellidis | Genetic-Algorithm-Based Multi-Objective Optimization of the Build Orientation in Stereolithography[END_REF]. It can be explained by the fact that physical phenomena cropped up during manufacture (powder aggregates) are not taken into account. However, the actual state of knowledge of the scientific community concerning these phenomena does not currently allow the construction of a mathematical model to accurately predict the surface finish.

In this context, the higher the roughness and the higher the surface resistance, resulting in power loss and attenuation constant raises [START_REF] Wang | A Rapid Estimation of the Conductor Loss in the Rectangular Waveguide with Rough Surface[END_REF]. In addition, as the frequency goes up, this phenomenon is getting bigger because the surface currents are closer to the (rough) surface and so the electric path becomes longer. Power loss can be increased by 60% compared to the same smooth surface when the average quadratic roughness is equal to skin depth [START_REF] Morgan | Effect of Surface Roughness on Eddy Current Losses at Microwave Frequencies[END_REF].

According to the distribution of the induced currents for the fundamental TE 10 propagation mode in a rectangular waveguide (Figure 1), we assume that the roughness on the larger surfaces has a bigger impact on the RF performancesboth in terms of loss and frequency offsetthan on smaller ones. Consequently, as it is often difficult to find a manufacturing orientation which could minimise the roughness on all the surfaces, the surfaces of width 'a' (Figure 1) should be worthy of more attention. Thereafter, in order to well distinguish the relative impact of each rough surface on the attenuation, the surfaces of width 'a' will be named the functional surfaces of the first order (FSFO)as we assume that roughness of these surfaces have a more significant impactwhereas the surfaces of width 'b' will be called the functional surfaces of the second order (FSSO), as shown in Figure 1.

However, surface finish in production is currently not fully controlled. To try to get the best surface finish possiblewithout considering post treatmentsvarious experimental measurements have been made. This has led to preferred orientation trends for manufacturing [START_REF] Canellidis | Genetic-Algorithm-Based Multi-Objective Optimization of the Build Orientation in Stereolithography[END_REF][START_REF] Thomas | The Development of Design Rules for Selective Laser Melting[END_REF].

Microwave waveguide components made in additive manufacturing

Theoretical interest in additive manufacturing

Since the technology can manufacture parts in a continuous way, it is then possible to dispense with assemblies and therefore interfaceswhich induce, among others, an increase in insertion loss and thus a degradation of the signal. Also, AM technologies provide superior geometric freedom and can free engineers from many mechanical constraints. Beyond simply trying to redesign existing models, it would be very interesting to exploit this design opportunity by developing complex geometries that could improve RF performances, leading to lower power loss and wider bandwidth.

Practical limitations

Consequently, a great deal of research has been done in order to evaluate the electro-magnetic performances of additively manufactured microwave waveguide components such as waveguides and filters (Tchoffolo-Talom and Turpault 2017; [START_REF] Zhang | 3D Printed Iris Bandpass Filters for Millimetre-Wave Applications[END_REF]. What emerges from these microwave-specific studies can be summarised by frequency shifts and signal amplitude loss compared to simulations, more or less important depending on the frequency band used. To try to explain these results, many factorsmore or less verifiedare brought up. Among them, dimensional tolerances of manufacture, conductivity, and roughness are widely introduced and seem to have a bigger influence. However, most of these studies focus on components whose design is very often similar to those drawn for conventional manufacturing.

In that way, other researches exploiting geometric opportunities have been performed: spherical and ellipsoidal cavities have replaced rectangular ones [START_REF] Booth | Enhancing the Performance of Waveguide Filters Using Additive Manufacturing[END_REF][START_REF] Guo | A 3-D Printed Lightweight X-Band Waveguide Filter Based on London: Springer-Verlag Resonators[END_REF], stubs have been leaned to fit for AM [START_REF] Peverini | Selective Laser Melting Manufacturing of Microwave Waveguide Devices[END_REF] and holes have been introduced into the thickness to lighten the waveguide [START_REF] Rojas-Nastrucci | Meshed Rectangular Waveguide for High Power, Low Loss and Reduced Weight Applications[END_REF]. Although the theoretical quality factor is increased with these new geometries, frequency shifts and an overall increase in loss are still observed. It seems to show that manufacturing constraints are not controlled enough. Thus, the limitations induced by AM are not fully considered during the design stage, which could partly explain the performances observed.

Design methods for AM components

Analysis of existing work through the literature reveals the lack of effective methods of design support for additive manufacturing:

(1) First, the inadequacy of effective methods of design assistance for additive manufacturing is observed.

Most of them propose a sequential approach: design process, manufacturing strategy, and manufacturing. The knowledge of the process is examined independently at each step, through the use of generic rules, favouring the 'over the wall' effect. As a result, those compartmentalised methods cannot take full advantage of AM;

(2) Second, some categories are underdeveloped compared to others which lead to unbalanced considerations during the design process.

(3) Third, design rules and design guidelines are specific to a process and material so inexperienced designers are quite restricted in their decisions. (4) Forth, methods often focus on a single optimisation parameter such as weight reduction or surface roughness while AM can potentially optimise much more simultaneously. (5) Last, creativity is not enough encouraged during the design development and is consequently limited by the psychological inertia of conventional process restriction [START_REF] Laverne | Assembly Based Methods to Support Product Innovation in Design for Additive Manufacturing: An Exploratory Case Study[END_REF]. Thereby, specific geometries caused by manufacturability limitations should not be considered too early in the design stage [START_REF] Kumke | A New Methodological Framework for Design for Additive Manufacturing[END_REF].

As such, how to establish a multifunctional method of Design for Additive Manufacturing while integrating the functional requirements specific to microwave guided components some of whom seem limited by additive manufacturing?

The integrated approach seems to correspond to AM because it is enough flexible to accept the interdependence of the specific rules. Design of the part is no longer constrained by the process but in keeping with the benefits of additive manufacturing. Ideal geometry comes from both the constraints of the specifications and knowledge of the chosen process. We decided to base our method on Pahl and Beitz approach, by integrating the right tools at the right time [START_REF] Pahl | Engineering Design: A Systematic Approach[END_REF]. This global concept allows designers to have an overview of the decisive choices in connection with AM they must perform throughout the design process.

DfAM method proposal

Based on the requirement list established in the previous section, we developed a DfAM framework trying to incorporate every step necessary for the good integration of additive manufacturing opportunities and limitations. This approach is shown in Figure 2.

Framework

According to Laverne's DfAM classification, the proposed method is part of the DfAM for concept assessment [START_REF] Laverne | Assembly Based Methods to Support Product Innovation in Design for Additive Manufacturing: An Exploratory Case Study[END_REF]). In addition, in accordance with the general development and systematic design procedure described by Pahl and Beitz, the suggested frame-work is divided into 4 major phases namely: problem analysis, conceptual design, embodiment design, and detail design. Then each of these phases is made up of one or several modules: task clarification and definition of requirements, preliminary study, void conceptual design, mechanical and thermal casing, and finally simulation analysis. Finally, each module is subdivided into a number of working groups within existing tools and methods are put (manufacturing process selection, design guidelines, design rules, geometrical validation etc.).

Directions for use

This section details the way of comprehending the design process and the different decision-making modules.

Task clarification and definition of requirements

The first step is based on the general concept of the traditional task clarification and definition of requirements phase of systematic engineering design process. It deals with the technical specifications, function tree, preliminary studies, external analysis etc. based on existing methods developed by [START_REF] Eder | Design Science[END_REF][START_REF] Hirtz | A Functional Basis for Engineering Design: Reconciling and Evolving Previous Efforts[END_REF][START_REF] Pahl | Engineering Design: A Systematic Approach[END_REF][START_REF] Ulrich | Product Design and Development[END_REF].

Functional specifications constitute for the design department a background document from which it will be possible to build a technical chart and a breakdown of tasks (ISO/IEC/IEEE). From the formulation of a desired functional state, the project management group must be able to define a specified or required state. This is done only after having imagined all the technical solutions (possible variants) answering the service functions initially desired. This leads to a function tree. The enumeration of the previous functions serves first of all to imagine the various possible technical solutions, then to carry out a feasibility study aimed at selecting the best solution in relation to the requirements. From the statement of all these solutions and technological characteristics, an understanding will have to be found to retain the main subsystems of each function, which is the object of a selection with justifications of exclusions, resulting in the functional specifications (ISO/IEC/IEEE). Finally, a coefficient of flexibility determines the importance of considering the various sub criteria with respect to the product to be obtained. As can be seen, this functional approach allows a challenge or a technological innovation of the project, while taking into account the future operating environment of the product. The simple logic of decomposition of the constitutive products would not allow such emergence of new ideas. Also, the external analysis needs to be examined at this stage. Flows between environmental elements (temperature, humidity level, etc.) and the product requirements to be studied: it will definitely have an influence on the process selection and sizing. Once the technical specifications are completed, the structural ones are reviewed by performing at least three major analyses. The specified state of the system, resulting from the functional decomposition [START_REF] Pahl | Engineering Design: A Systematic Approach[END_REF], will allow the various actors of the project to more easily apprehend any complex product, and thus to manage it in a more efficient way. The resulting representation is a 'breakdown structure' (National Aeronautics and Space Administration 1994), whose decomposition has to be detailed up to levels allowing an optimised realisation of all the system elementary functions. Through a matrix structure, it is possible to match the two flowcharts (technical and functional). This will serve as a basis for operating safety by listing all the elements of the system involved in the satisfaction of a particular function, and by controlling the effects of modifying one of these elements on all the functions concerned. In addition, the flows associated with the overall function performance of the product are drawn up. To do so, a classification of functional basis and flows sets are proposed by [START_REF] Hirtz | A Functional Basis for Engineering Design: Reconciling and Evolving Previous Efforts[END_REF]. The definition of flows will affect the material, the shape and sizing [START_REF] Sossou | An Additive Manufacturing Oriented Design Approach to Mechanical Assemblies[END_REF]. Finally, functional interfaces (FI) which are characterised by the relationship that two spatial regions must have to fulfil a function must be assessed. According to [START_REF] Sossou | An Additive Manufacturing Oriented Design Approach to Mechanical Assemblies[END_REF], they can be of three different natures: contact-free (for example heat dissipation), non-permanent (button, lever, etc.) or part-to-part contact. Those kinds of interactions will have an influence especially on the design space and mechanical constraints. The last working group within the task clarification and definition of requirements module consists in defining the task flowchart. This last division, also called technical chart, results from the product tree and defines the set of:

(1) Tasks induced by the product decomposition;

(2) Associated resources necessary for the study and production of the product and sub products (but absent in the final product); (3) List of requirements and specifications (R&S) to be taken into consideration throughout the project.

The technical chart is used for planning all the activities and means necessary for the good progress of the project according to the requirements and specifications of the need. A product induced task matrix can be introduced to overcome any forgetfulness as to the work to be done and on the other hand to group tasks. Once the whole requirement list and the global design space are established, preliminary studies can start.

Definition of modular structures

This second module is composed of four working groups, namely: elementary design spaces, selection of RF candidates, spatial layouts and pre-orientations.

Through the decomposition into elementary functions (waveguide, filter, polariser, orthomode, etc.) of the global function, it is possible to define a coarse design space for each of them. The dimensions of those Elementary Design Spaces (EDS) rely on the frequency bandbut it is important to mention that some of them are not fixed due to their additional degrees of freedom such as length or bending ability. The objective here is not to fix the final geometry of these functions, but to draw a primary representative idea of the dimensions. In the next stages, those elementary design spaces will be 'carved' to get an optimised geometry. Note that functions integrations should be considered here.

By means of these representations, RF candidate parts associated with an elementary functionare selected. This can be done by considering the dimensions of the part with the selected machines, specific desired characteristics in some regions incompatible with the AM technology, different materials for some parts, etc. If there are no obvious incompatibilities, the objective is to settle on all the elementary functions that compose the global function and run the third step.

Then, the RF selected partsand thus the elementary design spacesare pre-oriented and spatially arranged within the global design space to bring out the primary design of the global function. To do so, some considerations must be taken on board:

(1) The arrangement between the various elementary functions must satisfy the previously defined service function and the functional interfaces;

(2) Functional surfaces should be oriented as widely as possible in the same direction.

Once the different configurations have been defined, the objective is to identify possible manufacturing orientations for each modular structure according to the dimensions of the manufacturing machine. For microwave parts, some criteria such as surface quality of functional surfaces of the first order (FSFO) are essential (as shown in paragraph 2.1.2.). As a consequence, it would be beneficial to have manufacturing orientations where the FSFO could be built vertically. However, it sometimes induces an increase in the manufacture price. Finally, pre-oriented modular structures are obtained. If there is no suitable orientation, most of the time the selection of RF candidates should be reviewed. In this case, note that the global design space would certainly change.

It is important to mention that at this stage, external support structures are not discussed because the surfacesand so the designdo not exist yet as it is representing the volume of propagation which is purely virtual, until section 3.2.4 where it becomes tangible with the mechanical casing.

Void conceptual design

The purpose now is now to design 'the void', that is to say the volume of wave propagation. As mentioned in the previous paragraph, elementary design spaces should be 'carved' to get optimised shapes. It is a transitional step in the design of any guided propagation components because most of the product final geometry is defined here. Consequently, almost unlimited creative opportunities brought by AM have to be considered with abandon in this module to be able to break the cognitive barriers. In this way, we propose three different aspects to work on all at the same time without any specific order. One of them relates to the development of design solutions. By saying this we mean focusing exclusively on shapes/solutions. It is only about turning psychological inertia down. To do so, creativity techniques [START_REF] Rias | Design for Additive Manufacturing: A Creative Approach[END_REF], TRIZ theory [START_REF] Altshuller | Pipe Flanges and Flanged Fittings: NPS 1/2 Through NPS 24 Metric/Inch Standard[END_REF], design catalogues [START_REF] Roth | Design Catalogues and Their Usage[END_REF], feedback, nature observation, etc. are encouraged. Optimisation of RF properties working group allows ensuring the electromagnetic performances either from theoretical optimised geometries existing within the literature, a software optimisation of developed/existing design solutions.

The last one proposed is related to the AM-conformal embodiment. Existing tools such as design rules or design guidelines can:

(1) Allow design solutions imagined in other working groups to be arranged to coincide with the constraints of AM; (2) Help generate basic solution approaches to be optimised by previously introduced tools.

Also, the de-risking step is crucial before moving to the mechanical and thermal casing. In relation to the pre-orientations identified in section 3.2.2., it is necessary that the internal surfaces of the solutionsresulting from the 'carving'remain self-supported. As explained in section 2.1.1, as the part is fabricated in a continuous way, if internal support structures were placed inside the part they would be impossible to remove and so the signal would not be able to be transmitted. Note that post-processingsurface treatment and powder removingshould be considered in this void design module. Smooth section change, large radius rounded corners, etc. favour fluid flows, instead of brutal section change, sharp angles, cavities, etc.

Here again, (external) support structures are not mentioned because the void is not a physical object.

Once optimised void solutions are designed according to both RF and AM standard practice, electromagnetic simulations are completed. If they are not consistent with requirements, other void solutions must be contemplated.

Mechanical and thermal casing

From the previous module, oriented conceptual models have arisen. Before starting casing, Boolean operations are performed to get the external wrapping. Here again, both optimisation of mechanical/thermal properties and AM-conformal embodiment working groups should be managed at the same time. To achieve an optimised casing while respecting requirements, existing tools can be integrated. For example, lattice structures can be introduced to lighten the whole structure, to help the powder removal along, to get some specific mechanical/thermal properties, etc. Almost all the surfaces being functional, topology optimisation could possibly be considered in some cases but to a certain extent and should be subject to a precise parameterisation.

To be compliant with the constraints of AM, the same tools, as those used in the previous paragraph can be employed. The purpose of the mechanical and thermal casing is, on the one hand, to move from a conceptual model (the void) to a physical model, and on the other hand, to minimise the deformations induced by the laser. Therefore, design rules and design guidelines must be used to minimise thermal gradient concentrations (rounded edges and corners, minimal wall thickness, etc.) and to maximise the mechanical resistance (minimal wall thickness, stiffeners integration, etc.).

As soon as the mechanical/thermal casing is done in compliance with the requirements and AM constraints, microwave waveguide parts for AM are obtained. Then, supports are considered and need to be implemented before running the simulations. Once the outer surfaces requiring supportsfrom thermal and gravity points of viewhave been determined, they can be automatically or manually generated. Indeed, as the outer surfaces are not functional, support structures will not affect directly the surface quality of the wave path. However, a lack of support structures could induce some mechanical and thermal deformations resulting in dimensional variations and surface finish damaging.

Simulation analyses and final manufacturing analyses

Although manufacturability, mechanical, thermal, electromagnetic performances have normally been ensured throughout the design development by the use of standard procedure, simulations remain essential to give the final green light before manufacturing. In this context, finite elements analyses enables to validate the mechanical and thermal properties, process simulation can provide information about thermal deformations induced by the powder bed fusion, aeraulic test can give access to details about the air flow inside the part and thus about powder removal etc. If properties of the part are in step with the requirements, the manufacturing strategythat is to say layer thickness, scanning pattern, hatching space, etc.is finally adopted. Whatever the chosen strategy, the part will satisfy the mechanical constraints anyway. The objective here is therefore to propose a manufacturing strategy that maximises the mechanical properties while minimising thermal deformations. Microwave waveguide components optimised for additive manufacturing are then obtained.

If the mechanical or process simulations do not satisfy the requirements, modifications need to be operated:

(1) If it concerns thermal deformations, it is possible to move back to the step of support integration. By modifying the location or the shape of the support structures, it is then possible to minimise the thermal deformation occurring during the fabrication. If the deformations are still too important, the thermal casing must be adapted;

(2) If it concerns finite element analysis, the mechanical casing needs improvements (for example by incorporating stiffners) (3) If it concerns powder removal, the mechanical casing must be adjusted (for ex-ample by integrating holes into the shell)

Case study

For the case study, we chose to present the run of the different steps of the method through the design development of a three-port Ka-band waveguide power divider-combiner [START_REF] Awang | Microwave Systems Design[END_REF][START_REF] Brown | RF/Microwave Hybrids: Basics, Materials and Processes[END_REF]). The path followed within the methodology for this case study is shown in red in Figure 2.

Task clarifications and definitions of the requirements

As the waveguide power divider is widely used in telecommunications for dividing/combining power from 1 port to n ports [START_REF] Awang | Microwave Systems Design[END_REF][START_REF] Brown | RF/Microwave Hybrids: Basics, Materials and Processes[END_REF], function tree, functional flows, and breakdown structure will not be discussed in this section, only specific requirements. Also, the task flowchart will not be shared in this particular study.

Technical specifications

The three ports waveguide powder divider must be operational in Ka-band in signal reception (Rx), that is to say between approximatively 15 and 28 GHz. Due to its insertion into whole tactical equipment, the divider must not exceed 70 × 70 × 70 mm. Given its operational environment, that is to say corrosion and temperature variations, the part must be made of Al or Ti.

Structural specifications

Functional interfaces are defined by three different parallel flanges, two of which are located in the same plane, at least 1.5 mm apart. Vertically, plans are 70 mm apart and the projection on the lower plane of the upper flange must be located between the other two flanges. The dimensions of the flanges are designed to have standardised dimensions defined by ASME/ANSI B16.5 (ASME 2017).

Once the task clarification and the definition of the requirements are completed, the global design space is drawn (Figure 3).

Definition of modular structures

Elementary design spaces

Then, the elementary design spaces which are commensurate with the waveguides are defined. In the Ka-band in signal reception, the section of a waveguide is usually 6,318 × 12,668 mm (WR-42) with a 1 mm shell. Therefore, we decided to fix the elementary design space sections to 7 × 13 mm (it is important to remind that the objective here is to have a rough idea of what the structure would look like, not to fix the exact dimensions and geometries). Besides, the length of the EDS is adjustable, as long as it is set above λ/4 (where lambda is the wavelength of the central frequency), to allow the wave to position itself correctly without causing any harmful effects (Figure 4).

Selection of RF candidates

Considering the three EDS and the requirements, it is possible to put them all together into the global design space. Consequently, the three waveguides are selected.

Spatial layout and pre-orientation

The objective is to organise into the global design space the three EDS while respecting the requirements of the three-port Ka-band waveguide power divider-combiner, and the functional interfaces. Once these considerations satisfied, two different layouts spring up (Figures 5 and6).

To decide the best configuration between those two, it is important to consider the FSFO in red in the figures. In Figure 5, as the interfaces between the FSFO are discontinuous, it is clear that a proportion must be inclined to fulfil the condition of continuity. Therefore, all the FSFO will not have the same inclination and consequently, the same roughness. Quite the reverse, in Figure 6, the interface is continuous and so all the FSFO will be in the same direction. That is why we chose to consider the second modular structure. The pre-orientation into the manufacturing chamber would be between α (defined by the material so that the FSSO are self-supporting) and 90 degrees in relation towards the build platform, in order to preserve a minimal roughness on the FSFO (Figure 5).

Void conceptual design

Optimisation of RF properties

According to a study published by [START_REF] Suzuki | Optimum Sectional Shape of Dominant Mode Waveguide[END_REF], the section of the EDS is based on the optimised configuration of waveguide for dominant mode (Figure 7).

AM-conformal embodiment

Because the part must be self-supporting to avoid trapped support structures inside the final part, it looks clear that the modular structure in Figure 5 needs an AM conformal embodiment. As suggested within the methodology, the surfaces should then be carved into the EDS to both meet the RF requirements and be selfsupporting.

Just as we have decided to fix the cross-section according to Suzuki's configuration, the objective is then to work on the wave path. Considering the materials we have selectednamely Ti and Aland the functional interfaces, all the surfaces should be leaned between 30°(45°for Al) and 72,5°towards the build platform to be self-supporting. To determine the optimised angle in terms of RF performances, incremental simulations have been performed in ANSYS HFSS. It appears that the best results are obtained considering an angle of 68°towards the build platform. The optimised void design is shown in Figure 8. From that, we can see that all the FS remain in the same direction which proves the importance of defining the modular structure.

As all the surfaces are titled between 68 and 90 degrees towards the build platform, the whole part is self-supporting if it is positioned in the manufacturing chamber at:

(1) 90 degrees, no matter the material chosen among the candidates nominated in Section 4.1.1; (2) At α = 45 degrees for Al;

(3) At α = 30 degrees for Ti.

Although the main influence of surface quality is located on the FSFO, roughness on the functional surfaces of the second order (FSSO) also has an impact on the quality of the signal transmitted. To ensure minimum roughness on both the FSFO and FSSO but also to avoid a metallisation in post-treatments, we opt for Aluminium and fix the orientation in the manufacturing machine to 90°.

At this stage, the voidrepresenting the propagation channelis designed knowing it will be self-supporting. However, as it is not a 'physical' object but only a volume of propagation, external support structures cannot be discussed here. They will in the following step where the design becomes a part.

Mechanical and thermal casing

Once the conceptual design is performed, a 1 mm outer shell is created. As we decided to undertake to manufacture by LBM process, stiffeners are integrated into the part in order to reduce thermal deformations. As the stiffeners do not affect the waveguide properties as they are not located on the signal path. The mechanical casing of the Ka-band divider is shown in Figure 9.

Simulations and analyses

Before running simulations, support structures are integrated to the design. A finite element analysis and a LBM processassumed strain simulationare performed in ANSYS Additive Print, as shown in Figure 10. As it can be observed, the greatest displacements are located in the corners of the flanges with an estimated value of 90 microns and the global average value of displacements is around 25 microns. As the dimensional tolerances of the manufacturing process are approximatively 150 microns for Aluminium, we consider that the displacements simulated are negligible and so, acceptable.

Consequently, we consider that the part can be manufactured as designed and the final part is obtained (Figure 11), including the three flanges that need to be machined after manufacturing, to reduce insertion loss.

The development of a three-port Ka-Band waveguide power divider shows a way of taking advantage of the proposed methodology. It consists of five majors steps, all divided into different tools in relation to the design and the electromagnetic, mechanical and thermal performances, that take place in a defined order. In comparison with existing methodologies within the literature, it is formulated to integrate radiofrequency, mechanical and thermal requirements. In compliance with the research issue, an integrated approach correlated to Pahl and Beitz systematic design procedure seems to correspond to the application domain. By integrating specific tools, this approach guarantees an optimised and manufacturable radiofrequency part by considering both advantages (monolithic, multifunctional and innovative ability) and constraints of additive manufacturing (roughness, supports inside cavities, post-treatment) in relation to radiofrequency requirements.

Conclusions and future research

In this paper, previous research on DfAM has been reviewed and classified. The limitations brought to light showed the need for a new design methodology dedicated to additive manufactured microwave waveguide components. A new DfAM has been proposed to provide designers a structured framework to fully exploit AM potential while considering specific limitations. Indeed, it allows considering at the same time all the characteristics and rules related to the chosen manufacturing process, whether global or local, and the necessary parameters to be taken on board in order to guarantee the electromagnetic performances defined in the specifications. The proposed method was applied successfully to the design of a three ports Ka-band waveguide power divider.

However, the validation of the proposed DfAM method cannot be based on a single case study although all the different steps have been validated separately. Moreover, to ensure a fully optimised part, some process parameters such as laser power, scanning speed, and hatch spacing need to be considered into the method. Indeed, these process parameters can greatly impact on the final part through an increase of the roughness, important dimensional variations and deformations induced by the laser [START_REF] Calignano | Influence of Process Parameters on Surface Roughness of Aluminium Parts Produced by DMLS[END_REF][START_REF] Calignano | Investigation of Accuracy and Dimensional Limits of Part Produced in Aluminium Alloy by Selective Laser Melting[END_REF].

Future work will focus on the influence of process parameters on the surface quality and dimensional variations for both Al and Ti materials. This study will lead to the creation of a new block into the framework that should ensure a fully optimised part. In addition, the proposed methodology will be run through a more complex case study.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes on contributors

Figure 1 .

 1 Figure 1. Definition of the functional surfaces of the first (FSFO) and second order (FSSO).

Figure 2 .

 2 Figure2. Design for Additive Manufacturing method proposal applied to microwave waveguide components fabricated by Laser Beam Melting process (in red the path followed in the case study).

Figure 3 .

 3 Figure 3. Definition of the global design space and its functional interfaces.

Figure 4 .

 4 Figure 4. Definition of the three elementary design spaces: a 7 × 13 mm section with a minimal λ/4 length.

Figure 5 .

 5 Figure 5. Spatial layout of the elementary design spaces inside the global design space: Modular structure 1.

Figure 6 .

 6 Figure 6. Spatial layout of the elementary design spaces inside the global design space: Modular structure 2.

Figure 8 .

 8 Figure 8. Void conceptual design of the three-port Ka-band waveguide power divider-combiner.

Figure 7 .

 7 Figure 7. Optimised configuration of waveguide cross section for dominant mode[START_REF] Suzuki | Optimum Sectional Shape of Dominant Mode Waveguide[END_REF].

Figure 9 .

 9 Figure 9. Mechanical casing of the three-port Ka-band waveguide power divider-combiner.

Figure 10 .

 10 Figure 10. Process simulation analyses: displacements obtained after manufacturing.

Figure 11 .

 11 Figure 11. Three-port Ka-band waveguide power divider-combiner optimised for additive manufacturing through the run of the DfAM proposal.

Mathieu

  François was born in Paris, France, in 1992. In 2016, he received his MSc in Mechanics, Materials and Processes from Arts et Métiers ParisTech School of Engineering with a specialisation in Mechanics and Energetics for Aeronautical and Space Engineering. Since April 2017, he has been working as a Ph.D. candidate at Thales SIX GTS France on the design for additive manufacturing of microwave waveguide components in partnership with Arts et Métiers ParisTech School of Engineering and the French National Center for Scientific Research. The defence of his Ph.D. thesis is planned for April 2020. Frédéric Segonds is Associate Professor of Mechanical Engineering at Arts et Metiers ParisTech School of Engineering in Paris, France and member of the Product Design and Innovation Laboratory (LCPI). His research interests focus on Creativity and Design With/For/By Additive Manufacturing (CXAM and DXAM). Mickaël Rivette is Associate Professor of Mechanical Engineering at Arts et Metiers ParisTech School of Engineering in Metz, France and member of the Manufacturing Engineering and Control Laboratory (LCFC). His research interests focus on Design for Additive Manufacturing. Simon Turpault is Engineering Technologist at Thales SIX GTS France in Cholet, France. His activities focus on Materials, Processes and Additive Manufacturing. Patrice Peyre is Research Director at Arts et Metiers ParisTech School of Engineering in Paris, France and member of the Processes and Engineering in Mechanics and Materials Laboratory (PIMM) and the French National Center for Scientific Research. His research interests focus on Materials Science, Laser Processes and Additive Manufacturing.


N Mavrikakis

W Saikaly

D Mangelinck
email: dominique.mangelinck@im2np.fr

M Dumont

"Segregation of Sn on migrating interfaces of ferrite recrystallisation: quantification through APT measurements and comparison with the solute drag theory"

Keywords: grain boundary segregation, interface migration, solute drag, atom probe tomography, recrystallisation

Solute atoms play an important role in grain boundary migration phenomena, which are critical for understanding the microstructural evolution in metals. Here we investigate the segregation of Sn at migrating boundaries during recrystallisation in a ferritic Fe-Si-Sn alloy using atom probe tomography. Experimental evidence demonstrated a solute depletion zone ahead of the moving interface. The behaviour of Sn was rationalized with the Cahn solute drag theory. A difference in segregation between two investigated migrating interfaces was observed and could be explained by a variation in either binding energy, intrinsic velocity of each interface or in driving force.

Introduction

Solute enrichment at interfaces can impact remarkably grain boundary migration controlled phenomena, such as recrystallisation and phase transformations, by affecting interface mobility [1][2][3][4] .

Elements like P, Se, Sn etc. are prone to segregate on lattice defects in metals [START_REF] Lejcek | Grain Boundary Segregation in Metals[END_REF] . In particular, Sn segregation has been observed in various metals [START_REF] Aust | [END_REF][7][8][9] to strongly influence the material properties 10,11 .

The majority of experimental data on the segregation of Sn at grain boundaries 7,10,12,13 stem from Auger Spectroscopy (AES). AES is a well-suited technique for studying relatively high levels of grain boundary segregation (GBS). However, in the case of grain boundary migration phenomena that occur at a timescale of a few minutes or faster (at relatively high driving forces) and for limited diffusion length, AES may not be the most appropriate method due to its limited detectability. Hence, additional techniques capable in resolving even small interfacial enrichments are needed. Among other chemical characterization techniques available, atom probe tomography (APT) has a near-atomic scale resolution and the unique feature of analysing the chemistry of matter in the three dimensions 14 . In the recent years, the practice of APT has been gaining ground in the field of GBS [START_REF] Gault | Atom Probe Microscopy[END_REF] , since proper quantification of segregation amount is accessible through the measurement of the Gibbsian excess number [START_REF] Krakauer | [END_REF] . At the same time, it offers the possibility of investigating the morphology of nanostructural features, such as interfaces, and gives access to elemental concentration profiles. Despite the scientific interest, no previous references were found on the segregation quantification of Sn solute with APT. Moreover, very few studies have focused on the GBS at the migrating interfaces of recrystallisation.

Maruyama et. al 17 used APT to study recrystallisation under the effect of Nb solute in Fe-Nb ultra-low carbon (ULC) steels, whereas more recently Takahashi et. al 18 investigated segregation of Ti and B in interstitial-free (IF) steels. The focus of this work is to explore, the GBS behaviour of Sn solute in Fe alloys and compare it to the solute drag theory. Segregation mechanisms could be truly insightful if elucidated as a function of microstructure and grain boundary structure. Therefore, Sn segregation was analysed and quantified during the progress of static recrystallisation and in combination with grain orientation data, by employing a site-specific methodology for APT analysis.

Materials and experimental

For the proper assessment of the solute effect on recrystallisation, the study was conducted on a lab processed Fe based model alloy with 5.8% Si, 0.045% Sn (at. %), while impurities limited to a total amount of about 150 at. parts per million, realised in ArcelorMittal Global R&D Gent. Si is added to stabilize α-Fe and produce a single-phase alloy to study recrystallisation only under the solute effect.

Both Si and Sn concentrations are within the solid solubility values in α-Fe. The materials were processed with cold rolling to a total cold work -Von Mises true strain of about ε = 2 as described elsewhere 19 . Materials in the as deformed state, were subjected to a static recrystallisation annealing at 973K in a BAHR dilatometer, to achieve a partially recrystallized microstructure. Temperature was chosen as recrystallisation kinetics are easier to follow, while there is enough time for Sn to segregate at the grain boundaries 20 . Following the isothermal step, samples were quenched to room temperature in order to freeze the microstructure and to ensure that no segregation occurs during cooling.

Characterization was performed by determining the recrystallisation fractions in the annealed microstructures via quantitative metallography by applying the point count method 21 . Subsequently, grain orientations and grain boundaries (GBs) of the polycrystalline microstructure were characterized with the electron backscatter diffraction (EBSD) technique in a JEOL JSM-7001F field-emission gun scanning electron microscope (FEG-SEM). The data were then post-processed in the OIM Analysis™ platform. In the context of this work, recrystallized (RX) grains are defined as newly formed grains bounded by high-angle grain boundaries (HAGBs, θ  15 ο ) with a total internal grain orientation spread not exceeding 1.8 o . Finally, a grain shape criterion is applied, selecting grains with aspect ratios between 0.33 to 1, taking RX grains as near equiaxed in shape.

For the present study, a sample recrystallized at a volume fraction, X V = 0.45, was further characterized in APT. At this stage, recrystallisation has well progressed whilst the free/un-impinged surface area of recrystallized grains is still relatively large. We focus our study on the behaviour of general GBs at the recrystallisation front, as general GB migration is suggested to be more affected by the presence of solutes than special GBs 22 . For APT, specimens were prepared into sharp needles in a FEI Helios NanoLab 600 Dual Beam focused ion beam (FIB) -SEM, following the lift-out technique 23 . The sample preparation performed in the FIB was meticulous to keep the GB of interest as close to the tip apex as possible, by inspection with the secondary electrons. FIB and consequent APT analysis were conducted in a correlative microscopy manner. As the annular milling rate (using the Ga + beam) depends on the grain characteristics (i.e. orientation, dislocation density etc.), it was possible during FIB preparation to keep track of which grain is the RX and un-RX one, respectively. In the current case, the un-RX grains have a higher dislocation density and were observed to mill at a slower rate, compared to the RX grains. Moreover, they were rather easy to identify as they had a distinct, rougher morphology (more details are given in the Supplementary Information). APT experiments were conducted in voltage mode in a LEAP 3000XHR with a detector efficiency of 0.37, a sample base temperature of 70K and pulse fraction set at 20%. Finally, the APT data were analysed in the IVAS software after calibration of the reconstruction parameters from the obtained desorption maps [START_REF] Gault | Atom Probe Microscopy[END_REF] .

Consequently, the established method of the Gibbsian interfacial excess was followed to quantify the segregation at the interface, that yields a value of concentration insensitive to the measurement's resolution [START_REF] Krakauer | [END_REF] .

Results and discussion

Fig. 1 shows the microstructure within the region of interest of the sample characterized by EBSD. The fact that the grains were adjacent to each other is convenient as the deformed matrix (un-RX) in front of the GBs is comparable (i.e. in terms of orientation, local dislocation density etc.). The misorientations of the migrating interfaces are θ = 48.2 o about the [4 2] axis of rotation for grain 1 (GB1) and θ = 27.5 o [ 32] for grain 2 (GB2). Finally, by examining these two grains on Fig. 1a, their alignment with a shear band of the as deformed matrix may indicate that most likely both grains nucleated at a deformation shear band [START_REF] Humphreys | Recrystallization And Related Annealing Phenomena[END_REF] . The chemical analysis of the two interfaces is shown in Fig. 2, with the volumes obtained by APT displayed for GB1 (Fig. 2a) and for GB2 (Fig. 2b). Sn atoms are represented as green spheres and are observed to decorate the GBs, whereas for clarity only a portion of the Fe and Si atoms are represented as pink and sky-blue points, respectively. We note that some Si segregation was also observed at the migrating GBsfurther discussion is made in the text (and more details are given in the Supplementary Information). Fig. 2c shows the concentration profiles for Sn solute as measured in the two GBs and the integral profiles obtained from these profiles by the method defined in ref. 25 are shown in Fig. 2d. 13 reported a value of 138 times the bulk. These values compare well with the present study if one also takes into account that the timescale for segregation was much greater in the previous works and thus, a higher interfacial segregation can be expected.

Unfortunately, there are no relevant data found in literature on Sn segregation for shorter times. GBS studies of Nb 17 and Ti, Mn 18 in Fe during recrystallisation, revealed Gibbsian excess numbers of comparable magnitude, ranging between 0.4 and 1.0 at. nm -2 .

Meanwhile, in Fig. 2c it is interesting to observe that the experimental concentration profiles for both interfaces as measured in APT display some interesting peculiarities. Although there is some scatter in the data (σ = ± 0.035 at. %) it can be observed that the Sn profile has an asymmetric character, exhibiting a minimum in Sn concentration at the vicinity of the GB. This minimum is at the side of the un-RX matrix, as shown by the direction of GB migration in Fig. 2. It is thus ahead of the moving interface, since the growth occurs from the RX grain towards the un-RX matrix. These observations are in accordance with the theoretical concentration profiles predicted by the solute drag theory 1,3 .

The most prevailing theoretical description of solute drag is the one from Cahn 3 , while Hillert and Sundman expanded it for the case of interphase boundary 26 . In the classical solute drag theories it is assumed that the interface migrates with a steady velocity V and that the segregation profile is not changed during the boundary migration (steady state). According to Cahn, the concentration profile across the migrating interface is calculated by considering the flux of atoms across the boundary given by (

where x is the position from the centre of the boundary (x = 0 at the GB), C(x) is the concentration of solute, E(x) is the interaction energy of solute-grain boundary and D(x) a diffusion coefficient of the solute, normal to the boundary, as defined by Cahn and will be so forth referred to as trans-interface diffusion coefficient.

The general solution of Eq. 1 is the following 3 (2)

for D constant it can be simplified to:

Whereas for a non-moving interface, V = 0, equation (1) simplifies to (4) where is the bulk concentration of solute. According to CSD, solutes exert a drag force , on a migrating boundary that first increases with velocity (low velocity limit) until a maximum at = 1;

then it decreases (high velocity limit) and has an inflection point at . The unified expression to estimate the drag force valid for both the low and high velocity extremes is given by 3 :

(

with and parameters that are approximately inversely proportional to diffusivity 3 . The CSD theory was applied on the experimental concentration profiles, using the wedge-shape model of binding energy, ( ) [3]. In this approach, the binding energy exhibits a linear variation from the minimum value, E 0 (negative for the case of solute adsorption) at x = 0, to a null value at the GB limit (E(x) = 0 for x = ± δ/2). Velocity under the effect of Sn was experimentally estimated (with EBSD) from the average recrystallized (RX) grain size evolution as a function of annealing time, as = 220 nm s -1 at X V = 0.45. Finally, regarding the trans-interface diffusion coefficient, ( ), it has been generally accepted that ( ) is more closely related to the bulk than the GB diffusion coefficient [27][28][29] .

This diffusion coefficient is expected to be higher than the bulk diffusion coefficient of Sn in α-Fe, = 1.27•10 -1 m 2 s -1 • 20 . Following other authors in literature 30,28 , it is assumed that the trans-interface diffusion coefficient is the product of the bulk diffusion coefficient and a numerical factor: , with 5. The parameters of the CSD model were adjusted to fit the experimentally obtained Gibbsian interfacial excesses at the two migrating interfaces taking T = 973K, C 0 = 0.045 at. % and an interface half-width δ = 2.5 nm. The interface width is certainly overestimated compared to a value of about 1 nm usually used for migrating interfaces. However, considering that APT induces some broadening of the concentration profiles, a convolution effect results in a larger apparent segregation width 31,32 .

Two approaches were followed to determine the variables E 0 and V for each C(x), as the measured interfaces revealed varying segregated content of Sn. The first approach assumes that the interface velocities at the two GBs are similar and equal to the mean interface velocity ( = 220 nm s -1 ). In this case the ratio is held constant and the fit is done for each grain boundary to determine the value of , on the basis that binding energy may vary along the boundary and for different grain boundary structures, potentially due to changes in atomic structure 33 . For the given parameters and used in the CSD model, the values of binding energies, 0 were estimated at about -29.1 ± 1.0 kJ mol -1 and -26.7 ± 1.9 kJ mol -1 for GB1 and GB2 respectively. A higher interaction energy for GB1 could be related to boundary misorientation that is higher for GB1 than for GB2, such misorientation dependence has been previously reported 34,35 . The values are reasonable as compared to the ones available in literature. Seah has estimated the binding energy of Sn in Fe-Sn to be around -20 kJ mol -1 7 , while on a similar study to the present one, for Nb in Fe-Nb, a binding energy was estimated about -28.9 kJ mol -1 36,28 . It is noted that in the study of Maruyama et al. the Nb concentration at migrating boundary is found at similar levels with the present results for Sn.

In the second approach, the value was held constant to the mean value estimated for the two interfaces (E 0 = -27.9 kJ mol -1 ) while the ratio is used to fit the experimental results by varying the intrinsic velocity at the interface, to account for the condition that the two GBs are moving at different velocities 37 . The velocities were estimated as = 170 nm s -1 for GB1 and = 270 nm s -1 for GB2. The estimated velocity of GB1 is slightly lower than the estimated mean velocity ( = 220 nm s -1 ), whereas that of GB2 is higher. The result of the fit using the CSD is shown in Fig. 3a-b, essentially the fit after both procedures lead to the same result. There is a very reasonable agreement with the APT experimental profiles. The influence of interface velocity can be evaluated in the two GBs as a consequence of solute drag for either boundary, as shown in the fitted profiles in Fig. 3c. The drag force exerted by Sn solutes (at T=973K) was estimated using Eq. 5 for the given values of diffusivity and binding energy. By substituting in Eq. 5 with the fitted values of intrinsic velocities from the APT analysed migrating boundaries, the solute drag forces on these boundaries can be estimated as . • 0 8 J m -3 for 170 nm s -1 (GB1) and .6• 0 8 J m -3 for 270 nm s -1 (GB2). These values are not far from the maximum drag force of 2. • 0 8 J m -3 for = 1 that is predicted for GB velocities

of the order of 1200 nm s -1 . The present experimental conditions (i.e. strain in the as-deformed state, annealing temperature) correspond to the low velocity limit of CSD theory. Therefore, the boundary with a lower excess (GB2) migrates at a higher velocity than the average grain growth kinetics and thus, the drag force from the solute will be stronger. Regarding the effect of Si atoms on the migrating boundaries (segregation shown by the APT data); its effect is considered to be of secondary importance as Sn has been shown to be the element that essentially retards boundary migration during recrystallization 38 (more details are given in the Supplementary Information).

Considering now the comparison to the solute drag theory, it needs to be born in mind that the Cahn theory assumes a steady-state condition that is the ideal case. Nevertheless, the majority of the literature applies it as it simplifies the mathematical description of boundary migration process. On the other hand, the non-steady state case is less treated in the literature. Recently Zhang et al. 39 discussed the appropriacy of a steady-state assumption with a theoretical phase-field method approach, their calculations showed that the steady-state assumption may overestimate the solute concentration at the migrating boundary. In the current work, besides the mathematical simplicity, the steady-state assumption is considered to be a reasonable case as the experimental and theoretical profiles fit well for reasonable values of the intrinsic boundary variables ( ).

Finally, the complexity of the deformed structure also needs to be considered. Since the driving force of recrystallisation is not constant [START_REF] Humphreys | Recrystallization And Related Annealing Phenomena[END_REF] and it varies with the heterogeneities of the deformed lattice as the motion of the boundary proceeds 40 , the difference in excess number at the GB could also be affected by the growth history of the two interfaces. Moreover, the experimental profiles of Fig. 3a-b are observed to fit better to the theory for the un-RX side of the interface. This could be related to a higher diffusion coefficient in the not recrystallized structure compared to the recrystallized grain, as a higher dislocation content could enhance diffusion via dislocation pipes 41 . In order to illustrate such an effect, Eq. 2 has been applied with a diffusion coefficient 3 times higher for the un-RX grain ( 600 nm 2 s -1 ) than for the RX one ( 200 nm 2 s -1 ). Fig. 4 shows that a better fit can be obtained by such a treatment than for a constant ( 400 nm 2 s -1 ), especially concerning the un-RX side of the interface. However further work will be needed to really quantify the difference in diffusivities between the two grains.

Conclusions

The present work gives an insight of solute drag acting on moving interfaces from the experimental point of view and in comparison, with well-established physical interpretations of the phenomena. Sn solute segregation was measured quantitatively at the grain boundaries of Fe alloys by means of APT.

The application of a site-specific methodology, using the combination of EBSD, FIB and APT characterization assisted in the quantification of interfacial segregation of Sn and link to grain boundary structure. The values of Sn segregation were obtained for two GBs during static recrystallisation and the profile of Sn concentration at the migrating interface was well described by the steady state solute drag theory expressed by Cahn. The Gibbsian excess number of solutes at two migrating interfaces yielded that the segregation amount varied. This difference could be explained by a variation in grain boundary binding energy, intrinsic velocity at which each interface migrates or driving force. For the studied conditions, the solute drag effect of Sn at the moving grain boundaries during static recrystallisation is suggested to be strong, with Sn expected to reduce greatly the mobility of general GBs.

Appendix B. FIB preparation for APT

Table A.1 shows the Gibbsian excess values, Γ i of the segregation elements. Sn atoms are clearly observed to segregate at both GBs, while relatively small enrichment of Si atoms is also observed especially at GB1. GB1 also has some C segregation that was harder to visualise in GB2. The Si enrichment factor at the grain boundary may be considered inconsequential at this stage, with .

Table A.2 gives the solute-boundary binding energies and diffusion coefficients at 700ºC of Sn and Si in bulk α-Fe. With these data the solute drag forces, P i can be estimated; for the GB velocity regime in this study P Si is one order of magnitude lower than P Sn . For the present conditions the drag force from Sn solutes is of the order of 10 8 J m -3 , while the drag from Si is much weaker of about 10 6 J m -3 due to a lower solute-boundary binding energy and faster diffusion coefficient for Si in α-Fe 1,2 .

Additionally, in a previous comparative work that was focused on the recrystallization evolution, a reference model alloy of Fe-5.8 at.%Si was used to evaluate the effect of the addition of Sn 3 , where it is shown that the material's behavior, during recrystallization, changed dramatically with the addition of Sn. Hence, it is considered that the Si effect on the migrating interfaces is expected but is considered to be negligible compared to the Sn solute effect as demonstrated in the recrystallization kinetics in 3 .

Fig. 1a illustrates

  Fig.1aillustrates the kernel average misorientation (KAM) map where RX from un-RX regions can

Figure 1 .

 1 Figure 1. Partially recrystallized microstructure, a) Kernel Average Misorientation (KAM) map, with

Figure 2 .

 2 Figure 2. APT volumes with the atom distribution for Sn, Fe and Si. Sn segregates at the grain

Figure 3 .

 3 Figure 3. Concentration profiles from APT in comparison to the Cahn's solute drag model. a) for

Figure 4 .

 4 Figure 4. The experimental concentration profile for GB1 fitted to the Cahn's solute drag model using

Figure A. 2

 2 Figure A.2 APT volumes with the atom distributions at GB1 and GB2 after heat-treatment at 700ºC

Figure A. 3

 3 Figure A.3 The concentration profiles across the migrating recrystallisation interfaces (GB1 and GB2),

Table 1 .

 1 Grain boundary crystallographic information as obtained from the EBSD orientation mappings and the values of interfacial segregation for Sn as analysed with APT.

		Euler angles	Grain	general GB,	Interfacial excess of
		(φ 1 , Φ, φ 2 )	boundary	θ [hkl]	Sn (at nm -2 )
	Grain 1	13 o , 32 o , 40 o	GB1	48.2 o [4 2]	0.60 ± 0.08
	Grain 2	49 o , 27 o , 21 o	GB2	27.5 o [ 32]	0.41 ± 0.06
	Un-RX matrix	30 o , 55 o , 45 o
	The Gibbsian excess of Sn atoms at the interface was found for GB1 as	0.60 ± 0.08 at. nm -2
	while GB2 showed a lower amount of	0.41 ± 0.06 at. nm -2 . For means of comparison with

literature, the excess number is converted into at. %, equivalent Sn monolayer, by dividing the excess number by the density of (110) iron plane. The measured Sn excess then equals 3.5 and 2.4 at. % for GB1 and GB2, respectively, that corresponds to a GB enrichment factor, of about 78 and 53 times the bulk concentration. Earlier studies with AES, reported segregation levels at 700ºC for Sn at GBs of Fe-Sn alloys. Seah and Hondros 7 measured a Sn enrichment factor, of 46 to 122 times the bulk concentration, while Lejček et al.

Table A .

 A 1 Grain boundary segregation values for the various elements.

	Grain boundary		[hkl]	Segregation excess number, Sn C	(at nm Si	-2 )
	GB1	48.2	o [124]	0.60 ± 0.08		0.27 ± 0.05	3.77 ± 0.28
	GB2	27.5	o [234]	0.40 ± 0.06		0.44 ± 0.03	1.83 ± 0.25
	Table A.2 Trans-interface diffusion coefficients at 700ºC and grain boundary binding energies used in the drag force
					calculation.
			4.0•10	-16	m	2 s	-1	4
			4.2•10	-12	m	2 s	-1	2
			-27900	J mol	-1	this work
			-9000	J mol	-1	1

Acknowledgements

This project (ANRT -Project n o 1073-2015) was possible with the support of National Association of Research and Technology and the funding from ArcelorMittal Maizières Research SA. Special thanks to Dr. G. Da Rosa for fruitful discussions. The authors would also like to acknowledge the support in the experimental part, from Dr. A. Campos and Dr. M. Cabié of Centre Pluridisciplinaire de Microscopie électronique et de Microanalyse (CP2M) as well as Dr. M. Descoins of Institut Matériaux Microélectronique Nanosciences de Provence (IM2NP), Marseille. Declarations of interest: none

Appendix A. FIB preparation for APT

The RX -unRX grains demonstrated a different milling response as a result in the very different dislocation density within these two grains; the un-RX side had a rougher morphology during milling (Fig. 1b). The final prepared tip contained the GB in an off-centre configuration making it easier to compare at the end of the APT analysis the SE images to the obtained 3D-atom volume.


Yuichi Hirai

Investigation Anna Wrona-Piotrowicz

Conceptualization Janusz Zakrzewski

Arnaud Brosseau

Rémi Métivier
email: remi.metivier@ens-paris-saclay.fr

Clémence Allain
email: clemence.allain@ens-paris-saclay.fr

Mechanofluorochromism of pyrenyl acrylates with different substitutional position and steric hindrance

Keywords: solid-state luminescence, pyrene dye, organic materials, mechanofluorochromism, polymorphism

Pre-proof

Mechanofluorochromism of pyrenyl acrylates with different substitutional position and steric hindrance

Introduction:

Emission color change upon mechanical stimulation, so-called mechanofluorochromism (MFC), and has attracted attention especially in the last ten years. A growing number of MFC molecules including organic and organometallic compounds has been reported, [START_REF] Gawinecki | 4-Tert-Butyl-1-(4'-dimethylamino-benzylideneamino)pyridinium Perchlorate (BDPP): A Novel Fluorescent Dyes[END_REF][START_REF] Sagara | n a l P r e -p r o o f Luminescent Molecular Assemblies: An Emerging Class of Materials[END_REF][START_REF] Nagura | Distinct Responses to Mechanical Grinding and Hydrostatic Pressure in Luminescent Chromism of Tetrathiazolylthiophene[END_REF][START_REF] Hariharan | Self-Reversible Mechanochromism and Thermochromism of a Triphenylamine-Based Molecule: Tunable Fluorescence and Nanofabrication Studies[END_REF][START_REF] Lin | Excimer-Monomer Photoluminescence Mechanochromism and Vapochromism of Pentiptycene-Containing Cyclometalated Platinum(II) Complexes[END_REF][START_REF] Ito | Mechanical Stimulation and Solid Seeding Trigger Single-Crystal-to-Single-Crystal Molecular Domino Transformations[END_REF] and stress-sensitive dyes/polymer composites have also been developed as MFC materials. [START_REF] Crenshaw | Deformation-Induced Color Changes in Melt-Processed Photoluminescent Polymer Blends[END_REF][START_REF] Calvino | Approaches to Polymeric Mechanochromic Materials[END_REF] Fluorescent planar cores with mobile branches, such as π-aromatic systems with rotational alkyl groups, are generally recognized as promising chemical structures to host MFC properties. Our groups have explored the synthetic diversity of pyrene derivatives and demonstrated the fluorescence properties both in solution and in the solid state. [START_REF] Flamholc | A New Class of Pyrenyl Solid-State Emitters: 1-Pyrenyl Ynones. Synthesis via the Friedel-Crafts Route, Molecular and Electronic Structure and Photophysical Properties[END_REF][START_REF] Wrona-Piotrowicz | Efficient Synthesis of Pyrene-1-Carbothioamides and Carboxamides. Tunable Solid-State Fluorescence of Pyrene-1-Carboxamides[END_REF][START_REF] Piotrowicz | Aerobic Palladium(II)-Catalyzed Dehydrogenative Heck Reaction in the Synthesis of Pyrenyl Fluorophores. A Photophysical Study of β-Pyrenyl Acrylates in J o u r n a l P r e -p r o o f Solution and in the Solid State[END_REF][START_REF] Wrona-Piotrowicz | Friedel-Crafts-Type Reaction of Pyrene with Diethyl 1-(Isothiocyanato)Alkylphosphonates. Efficient Synthesis of Highly Fluorescent Diethyl 1-(Pyrene-1-Carboxamido)Alkylphosphonates and 1-(Pyrene-1-Carboxamido)Methylphosphonic Acid[END_REF] The solid-state fluorescence of pyrene derivatives is getting more common recently, and several examples of MFC with planar/branch structural features have been reported. [START_REF] Sagara | Material Design for Piezochromic Luminescence: Hydrogen-Bond-Directed Assemblies of a Pyrene Derivative[END_REF][START_REF] Sagara | Stimuli-Responsive Luminescent Liquid Crystals: Change of Photoluminescent Colors Triggered by a Shear-Induced Phase Transition[END_REF][START_REF] Ito | Tricolor Mechanochromic Luminescence of an Organic Two-Component Dye Visualization of a Crystalline State and Two Amorphous States[END_REF][START_REF] Ma | Mechanically Induced Multicolor Switching Based on a Single Organic Molecule[END_REF][START_REF] Sagara | A Water-Soluble Mechanochromic Luminescent Pyrene Derivative Exhibiting Recovery of the Initial Photoluminescence Color in a High-Humidity Environment[END_REF][START_REF] Hirai | Mechanofluorochromism of Pyrene-Derived Amidophosphonates[END_REF] Therefore, it is of great interest to establish a new library of organic MFC materials by investigating their dynamic photophysical properties in solid state. As a series of our reported pyrene derivatives, we here focused on C-1-and C-4-alkenylated pyrenes with and without tert-butyl groups for their solid-state blue/green fluorescence properties up to 0.35 quantum yields. [START_REF] Piotrowicz | Aerobic Palladium(II)-Catalyzed Dehydrogenative Heck Reaction in the Synthesis of Pyrenyl Fluorophores. A Photophysical Study of β-Pyrenyl Acrylates in J o u r n a l P r e -p r o o f Solution and in the Solid State[END_REF] Since these fluorescent molecules bear a planar unit with chain-like side groups, the emission color change is expected to be accompanied by intermolecular arrangement changes. In addition, systematic MFC study on the J o u r n a l P r e -p r o o f compounds w/ and w/o specific chemical groups and positional isomers would provide a clue to correlate the steric structures and MFC properties.

We here report the MFC of C-1-and C-4-alkenylated pyrenes ((E)-Ethyl-3-(Pyren-1yl)acrylate: 1, (E)-Ethyl-3-(Pyren-4-yl)acrylate: 2, respectively) to investigate the positional effect of substituents on mechanical properties. C-4-Alkenylated pyrene with tert-butyl groups in 2,7-positions ((E)-Ethyl-3-(2,7-Di-tert-butylpyren-4-yl)acrylate: 3) is also introduced to investigate the steric effect on MFC properties. The target molecules were prepared following the reported synthetic methods. [START_REF] Piotrowicz | Aerobic Palladium(II)-Catalyzed Dehydrogenative Heck Reaction in the Synthesis of Pyrenyl Fluorophores. A Photophysical Study of β-Pyrenyl Acrylates in J o u r n a l P r e -p r o o f Solution and in the Solid State[END_REF] As-synthesized powder samples are defined as pristine condition. To study the spectroscopy of the ground form, a quartz plate was directly scratched with a pestle immediately after grinding of the powder (Figure 1). Photophysics in the solid state has been reinvestigated compared to our previous work to take into account the mechanofluorochromism of these compounds and their solid-state back reactions.

J o u r n a l P r e -p r o o f

Results and Discussion:

In order to gain insights on the molecular electronic transitions responsible for light absorption in this series of compounds, we performed DFT and TD-DFT calculations on 1-3 at the B3LYP/6-31+G(d,p) level of theory using an implicit IEFPCM solvent model for CHCl3. The electronic transitions and corresponding involved molecular orbitals of 1-3 in chloroform solution calculated by time-dependent DFT are depicted in Figure 2, Figure S1 and Table S1 (Supporting Information). For the frontier molecular orbitals HOMO and LUMO, the electron density is not only localized on pyrene but also on the acrylate group. The C-1/C-4 substitutional positions show different π-conjugation of the The solid-state excitation/emission spectra of 1-3 are summarized in Figure 3. Green or blue fluorescence of pristine 1-3 is observed as reported before (Figure 3, black line).

Upon mechanical grinding, all of these compounds were found to show MFC (Figure 3, J o u r n a l P r e -p r o o f blue line). In order to take into account the spectral shape modification upon mechanical stimulation, fluorescence color change was estimated using the mean wavelength shift (Δλ = λmean,groundλmean,pristine, Δλ < 0: hypsochromic shift, Δλ > 0: bathochromic shift)

with λmean defined by equation ( 1):

𝜆 𝑚𝑒𝑎𝑛 = ∫ 𝜆×𝐼 𝐹 (𝜆)𝑑𝜆 ∞ 0 ∫ 𝐼 𝐹 (𝜆)𝑑𝜆 ∞ 0 , (1)
where IF(λ) is the intensity of the emission spectra. The difference of the mean wavelengths before and after grinding is estimated to be Δλ = -22, +28 and +18 nm (Δν = +750, -1050, -650 cm -1 ) for 1, 2 and 3, respectively (Table 1). According to the crystal information file (CIF), [START_REF] Piotrowicz | Aerobic Palladium(II)-Catalyzed Dehydrogenative Heck Reaction in the Synthesis of Pyrenyl Fluorophores. A Photophysical Study of β-Pyrenyl Acrylates in J o u r n a l P r e -p r o o f Solution and in the Solid State[END_REF] 1 forms strong intermolecular interactions due to the close faceto-face π-π stacking (< 3.5 Å) and small distances between the center of gravity in neighboring parallel pyrene units (dcenter-center = 4.02 Å), which represents the large overlapping of pyrene moieties (see Figure S2 in Supporting Information). The hypsochromic shift of 1 upon grinding can be explained by the isolation of these molecules with decreased intermolecular interactions. [START_REF] Suenaga | Heat-Resistant Mechanoluminescent Chromism of the Hybrid Molecule Based on Boron Ketoiminate Modified Octasubstituted Polyhedral Oligomeric Silsesquioxane[END_REF] On the other hand, 3 avoids overlapping of the tert-butyl groups, resulting in larger distances between pyrene units (dcenter-center = 6.19 Å). New intermolecular interactions created upon grinding may cause the bathochromic MFC of 2 and 3. [START_REF] Ito | Reversible Mechanochromic Luminescence of [(C6F5Au)2(μ-1,4-Diisocyanobenzene)[END_REF][START_REF] Seki | Luminescent Mechanochromism of Gold N -Heterocyclic Carbene Complexes with Hypso-and Bathochromic Spectral Shifts[END_REF] When comparing the relative contribution of two excitation bands in visible (425-450 nm) and ultraviolet regions (~ 360 nm), which were J o u r n a l P r e -p r o o f attributed to the aggregated and monomer conformations in the ground state, respectively, [START_REF] Piotrowicz | Aerobic Palladium(II)-Catalyzed Dehydrogenative Heck Reaction in the Synthesis of Pyrenyl Fluorophores. A Photophysical Study of β-Pyrenyl Acrylates in J o u r n a l P r e -p r o o f Solution and in the Solid State[END_REF] the former is less pronounced after mechanical grinding than in pristine form. Therefore, the aggregated conformers such as preformed dimers in the ground state of pristine forms is partially dislocated by mechanical grinding. J o u r n a l P r e -p r o o f [a] All samples were treated at room temperature.

[b] Total shift Δλ = λmean,groundλmean,pristine.

Since the fluorescence color recovery was observed for 2 and 3, we followed the back reaction behavior to consider the molecular rearrangement in solid state (Figure 3 and Table 1). The ground samples were let sit at room temperature for 30 min (Figure 3, red line) and at 50˚C for another 30 min (Figure 3, green line), and the corresponding emission spectra were recorded to consider the solid-state back reactions. The little spectral change in 1 at room temperature and at 50˚C indicates the existence of another stable and relaxed conformation with reduced intermolecular interactions. On the contrary, the main emission band of the pristine form of 2 (~ 470 nm) recovers in 30 min at room temperature and the relative contribution of the emission bands at 510 nm decreases at the same time. Further heating at 50˚C gives an intermediate spectrum between ground form (blue line) and 30 min after grinding at room temperature (red line). 3 showed limited back reaction at room temperature and another 30 min of heating at 50˚C gave additional spectral shift; however, the original spectral profile was not recovered.

J o u r n a l P r e -p r o o f

Therefore, the bulky tert-butyl groups are considered to hinder the rearrangement of the original molecular conformation in solid state.

For further investigation of the photophysical properties, time-resolved fluorescence measurements of 1-3 were conducted at three distinct emission wavelengths. The fluorescence decays in pristine form were re-measured by using a quartz cell with 0.2 mm-deep hole in order to avoid any mechanical stimulation. Global analysis was successfully converged using a discrete multi-exponential decay model for all sets of three decays of each sample. The estimated lifetimes τ, corresponding pre-exponential factors a and fractions of intensity f are summarized in Table 2 (see Table S3 in supporting information for full sets of data).

Four components were necessary to fit the fluorescence decays at any emission wavelengths for 1-3. Despite more sophisticated models exist, such as distributions of decay times which may cover the wide variety of molecular species and packings modes, [START_REF] Métivier | Characterization of Alumina Surfaces by Fluorescence Spectroscopy. Part 1. Grafting a Pyrene Derivative on γ-and δ-Alumina Supports[END_REF] we decided to adopt a sum of four discrete exponentials to fit the obtained decay curves, since this robust model gave satisfactory fits and provided useful information about the excited-state kinetics of 1-3.

J o u r n a l P r e -p r o o f Before grinding, the fast decay components of 2 and 3 (τ ≤ 4. mentioned sample with green fluorescence is described as 1-green, and the newly found blue-fluorescent form is denoted as 1-blue hereafter. Unfortunately, the quality of crystals for 1-blue was not enough to perform single crystal X-ray analysis. According to the powder X-ray diffraction (XRD) measurements, 1-green was identified as previously reported orthorhombic crystal system with strong π-π interactions, while 1-blue showed distinct diffraction patterns (Figure 4d). another 30 min at 50˚C), and corresponding pictures of pristine/ground forms under UV irradiation (λex = 365 nm). c) Fluorescence decay curves of 1-blue pristine (λem = 480 nm, solid blue line), 1-green pristine (λem = 530 nm, solid green line) and 1 ground (λem = 510 nm, dashed blue line) excited at 360 nm. d)

Experimental powder X-ray diffraction patterns of 1-blue (blue line) and 1-green (green line), and simulated one (black line) of 1 based on the previously reported CIF file (Co tube, λ = 1.79026 Å). [START_REF] Piotrowicz | Aerobic Palladium(II)-Catalyzed Dehydrogenative Heck Reaction in the Synthesis of Pyrenyl Fluorophores. A Photophysical Study of β-Pyrenyl Acrylates in J o u r n a l P r e -p r o o f Solution and in the Solid State[END_REF] Contrary to the constant contribution of the longest decay-time (τ1 = 12 ns) of pristine 1green at all emission wavelengths, the longest component (τ1 = 9.2 ns) of pristine 1-blue is more dominant at longer λem region but still in minor fraction of intensity (see Table S4 in Supporting Information). The contribution of the shorter components (≤ 2.4 ns) also decrease when λem increases (f = 0.98 and 0.82 at 450 and 510 nm, respectively). Thus, 1-blue may be dominated by the blue-emitting monomer with a small fraction of preformed aggregated form as is the same for 2 and 3 in pristine form. Therefore, the crystal packing structures of 1-blue, 2 and 3 are expected to be similar with small contribution of face-to-face contacts, and the preformed-aggregated-like molecules would be formed under the condition of grinding. Indeed, 1-blue exhibited bathochromic shift under grinding like 2 and 3, and the structureless spectral profile centered at around 510 nm is also quite similar to that of 1-green in ground form (Figure 4, highlighted with green bar). The original fluorescence of 1-blue was not recovered due to the slight J o u r n a l P r e -p r o o f thermal back reaction at room temperature, and further heating at 50˚C (Figure 4, green line) didn't accelerate the back reaction anymore. The emission lifetimes and even the contribution of emitting species and the fraction of intensity exhibited quite similar trends among these polymorphs in ground form (Table S4 and Figure 4c). Therefore, 1-green and 1-blue are considered to form the same metastable conformations in amorphous phase, whatever the initial structure is. The series of pyrene derivatives potentially possess metastable molecular conformations close to the forms obtained by mechanical grinding, which has also been described as polymorphs-driven MFC in some studies. [23- 25] We here summarize the results by categorizing the properties into three types; i) blue form (1-blue, 2-3 pristine) dominated by monomers (short τ ≤ 4.4 ns) and minor proportion of preformed aggregates, ii) green form (1-green) which allows the formation of dynamic excimers with rise-times (a < 0) and iii) ground form (1-3 ground) with randomized monomers and long-lived dimers (τ ≥ 23 ns).

Conclusions:

In conclusion, we reported the mechanofluorochromism of pyrene-derived acrylates. C-4-alkenylated pyrene (2) and one with bulky tert-butyl groups in 2,7-position (3) showed monomer-like emission in pristine form due to the lack of columnar face-to-face stacking.

Experimental Section

Compounds 1-3 were synthesized and purified according to the earlier published procedure. [START_REF] Piotrowicz | Aerobic Palladium(II)-Catalyzed Dehydrogenative Heck Reaction in the Synthesis of Pyrenyl Fluorophores. A Photophysical Study of β-Pyrenyl Acrylates in J o u r n a l P r e -p r o o f Solution and in the Solid State[END_REF] Pristine powders were prepared by repeated crystallization from hexanes Computational calculations: The geometry of compounds 1-3 was fully optimized using J o u r n a l P r e -p r o o f the Becke-3-Lee-Yang-Parr (B3LYP) [START_REF] Becke | Density-functional thermochemistry. III. The role of exact exchange[END_REF] exchange functional with the 6-31+G(d,p) basis set, including IEFPCM solvent model for CHCl3, as implemented in the Gaussian 16 software package, Revision B.01. [START_REF] Frisch | Gaussian 16, Revision B.01[END_REF] The absence of negative frequencies was checked to ensure true energy minima. Franck-Condon energy transitions, oscillator strengths, and involved molecular orbitals were calculated using the time-dependent DFT formalism (TD-DFT) with the same functional and basis set.

DSC measurements were performed on a DSC 25 Discovery series (TA Instruments) instrument, with a 10°C/min scan rate.

CRediT author statement

Figure 1 .

 1 Figure 1. Chemical structures and an illustration of sample preparation of ground pyrenederived acrylates (1-3) for spectroscopy.

J o u r

  n a l P r e -p r o o f acrylic chain with the pyrenyl moiety of 1 and 2, and tert-butyl groups at 2,7-positions slightly vary the electron density distribution of 2 and 3. For the three compounds, the first electronic transition S0S1 corresponds to a HOMOLUMO transition, associated with a high oscillator strength. Comparison of the data for the three compounds corroborate the lowest energy absorption band of 1 and similar photophysical properties between 2 and 3 observed for isolated molecules in CHCl3.[START_REF] Piotrowicz | Aerobic Palladium(II)-Catalyzed Dehydrogenative Heck Reaction in the Synthesis of Pyrenyl Fluorophores. A Photophysical Study of β-Pyrenyl Acrylates in J o u r n a l P r e -p r o o f Solution and in the Solid State[END_REF]

Figure 2 .

 2 Figure 2. Optimized geometry and HOMO and LUMO orbitals involved in the S0-S1 transitions for compounds 1 (left), 2 (middle) and 3 (right), obtained by DFT and TD-DFT calculations at the B3LYP/6-31+G(d,p) level (IEFPCM CHCl3 solvent model).

Figure 3 .

 3 Figure 3. Excitation/emission spectra of a) 1, b) 2 and c) 3 in solid state (black: pristine, blue: ground, red: 30 min after grinding at RT, green: another 30 min at 50˚C, λex = 360 nm, λobs = 520 nm), and corresponding pictures of pristine/ground forms under UV irradiation (λex = 365 nm). Arrow indicates the shift upon mechanical grinding.

  4 ns) correspond to the vast majority of emitting species (a2 + a3 + a4 = 0.99) and fluorescence intensity (f2 + f3 + f4 ≥ 0.93), which represents the blue-emitting monomers due to the larger proportion in shorter wavelength. On the other hand, relatively large contribution of longer decay lifetime (τ1 = 12 ns) accompanying a fast decay component (τ4 = 0.85 ns) with a negative pre-exponential factor (a4 = -0.17) is recognized for 1, which represents the dynamic excimer formation. Preformed aggregates caused the large contribution of τ2 (5.6 ns) in J o u r n a l P r e -p r o o f the red part of the spectrum (f2 = 0.52-0.75 at λem = 500-560 nm). Much longer emission decay-times (τ = 26, 23 and 28 ns for 1, 2 and 3, respectively) appear after mechanical grinding without detectable rise times (eventually with rise times much shorter than the time-resolution of our instrument), which indicates the formation of another excited species such as preformed excimers. The two short components (τ3 and τ4 ≤ 3.1 ns), appearing as rise times at longer emission wavelength in the pristine form of 1, contribute as decay times in its ground form. It would be related to the decreased intermolecular interactions as already mentioned. Two short components of 2 and 3 (τ3 and τ4, pristine form) arising from the blue-emitting monomers are also identified after grinding. Because of the remained shoulder bands in shorter wavelengths and the fast back reaction after grinding (Figure3band 3c, blue lines), the formation of aggregated molecules would be partially and temporarily allowed for 2 and 3, which was initially in monomeric conformation with large dislocation between neighbouring pyrene units. The further redshifted emission spectra of molten samples without shoulder bands (FigureS4band S4c in Supporting Information, black lines) also support that the mechanical grinding does not fully convert the molecular arrangements.Interestingly, a blue-emissive powder of 1 was also identified by fast recrystallization from dichloromethane, which showed similar fluorescence as pristine 2 and 3 with J o u r n a l P r e -p r o o f structured narrow emission bands at around 470 nm (Figure4bblack line). The as-

Figure 4 .

 4 Figure 4. Excitation/emission spectra of a) 1-green and b) 1-blue (λex = 360 nm, λobs =

J o u r

  n a l P r e -p r o o fThe bathochromic shift of these compounds upon grinding indicated the increased intermolecular interactions. C-1-alkenylated pyrene was found to form two types of polymorphs (1-blue and 1-green) with monomer-like and dynamic-excimer-like emission in pristine condition. A pair of bathochromic and hypsochromic shift upon grinding resulted in quite similar spectroscopic features with slight back reactions which suggested the same metastable conformation in amorphous phase whatever the starting state. Further investigation based on crystallography would greatly advance these MFC studies in terms of fundamental understandings and molecular designs for colourcontrolled MFC.

( 1 -

 1 green) and evaporation of the dichloromethane solutions obtained by chromatography (2 and 3), respectively. Optical Measurements: Emission and excitation spectra of pristine powder samples were recorded on a HORIBA Jobin-Yvon Fluorolog FL3-221 spectrometer using a short path length optical quartz cell (20/C/Q/0.2, Starna), and the spectra were corrected for the J o u r n a l P r e -p r o o f response of the detector system. The pristine powder was ground using an agate mortar, and the resulting amorphous solid adhered on a pestle surface was immediately transferred to a quartz plate to record the spectra and minimize the effect of back reaction at room temperature. Fluorescence decay profiles were obtained by time-correlated single-photon counting (TCSPC) method with titanium:sapphire laser (Tsunami, Spectra-Physics) pumped by a doubled Nd:YVO4 laser (Millennia Xs, Spectra-Physics). Light pulses at 720 nm was selected by an acousto-optic crystal at a repetition rate of 4 MHz, and then doubled at 360 nm by nonlinear crystals. Fluorescence photons were detected at 90˚ through a polarizer at the magic angle and monochromator, by means of a Hamamatsu MCP R3809U photomultiplier, connected to a SPC-630 TCSPC module from Becker&Hickl. The instrumental response function was recorded before each decay measurement with a fwhm (full width half maximum) of 860 ps. The fluorescence data were analyzed using the Globals software package developed at the Laboratory for Fluorescence Dynamics at the University of California, Irvine, which includes reconvolution analysis and global non-linear least-squares minimization method. Crystallography: Powder XRD patterns were recorded on a Bruker D2 PHASER with a Si single crystal plate (Co tube, λ = 1.79026 Å).

Yuichi Hirai :

 Hirai Conceptualization, Investigation, Visualization, Writing -Original Draft Anna Wrona-Piotrowicz: Investigation Janusz Zakrzewski: Conceptualization Arnaud Brosseau: Resources, Validation Rémi Métivier: Conceptualization, Supervision, Writing -Review & Editing Clémence Allain: Conceptualization, Supervision, Writing -Review & Editing, Funding acquisition J o u r n a l P r e -p r o o f

Table 1 .

 1 Sample state and corresponding mean emission wavelength

	Sample state [a]	1	2	3
	Pristine / nm	557	500	506
	Ground / nm	535	528	524
	30 min at RT /nm	537	514	519
	30min at RT + 30min at 50°C /nm 534	522	518
	Total shift Δλ at RT [b] /nm	-22	+28	+18

Table 2 .

 2 Emission decay time-constants (τ) and corresponding pre-exponential factors (a) and fraction of intensity (f). (λex = 360 nm, λem = 530/500 nm for 1, λem = 500/500 nm for 2, λem = 500/510 nm for 3, in solid state before/after grinding). * shows a small component (absolute value < 0.01) required to obtain a satisfactory fit.

		τ 1	τ 2	τ 3	τ 4
		(a 1 , f 1 )	(a 2 , f 2 )	(a 3 , f 3 )	(a 4 , f 4 )
	1	12	5.6	2.5	0.85
	pristine	(0.13, 0.26)	(0.76, 0.70)	(0.11, 0.04)	(-0.17, -0.02)
	1	26	9.3	3.1	0.46
	ground	(0.03, 0.17)	(0.29, 0.54)	(0.43, 0.26)	(0.25, 0.02)
	2	11	4.4	2.1	0.15
	pristine	(0.02, 0.05)	(0.51, 0.68)	(0.43, 0.27)	(0.05, *)
	2	23	8.0	2.1	0.41
	ground	(0.04, 0.26)	(0.20, 0.47)	(0.36, 0.21)	(0.40, 0.05)
	3	8.4	3.1	1.3	0.33
	pristine	(*, 0.06)	(0.15, 0.40)	(0.35, 0.39)	(0.49, 0.14)
	3	28	13	4.1	0.61
	ground	(0.14, 0.35)	(0.44, 0.54)	(0.27, 0.10)	(0.15, *)

Acknowledgements

We would like to appreciate Dr. Pasko Oleksandr (SATIE, CNRS ENS Paris-Saclay) for the powder X-ray diffraction measurements, and Laurent Michely and Dr. Davy-Louis Versace (ICPME, Thiais) for the DSC measurements. Y. H. gratefully acknowledges support from the Japan Society of the Promotion of Science (JSPS). R.M. and C. A. acknowledge ERC funding 'MECHANO-FLUO' (St-G 715757) project. This work was performed using HPC resources from the "Mésocentre" computing center of CentraleSupélec and École Normale Supérieure Paris-Saclay supported by CNRS and Région Île-de-France (http://mesocentre.centralesupelec.fr/).

Declaration of interests

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