Hacène Fouchal
email: hacene.fouchal@univ-reims.frfrance

Sharing Pseudonyms between Intelligent Transport System Stations

Keywords: Intelligent Transport System, VANETs, security, privacy, anonymity

Privacy is an important issue on any open system, in particular for connected vehicles. These vehicles send continuously messages containing their locations in order to cooperate with their neighbors about what is happening on roads.

Privacy protection is highly required to deploy C-ITS (Cooperative Intelligent

Transport Systems) in order to avoid tracking drivers. For this reason, vehicles change frequently their identity in order to become anonymous. We need to consider the authenticity of senders in order to drop messages coming from untrusted drivers who may send fake events. To do so, each trusted vehicle should sign its message using a certificate. This certificate is provided by an adapted PKI (Public Key Infrastructure) which generates certificates to all trusted vehicles. The eco-system is considered as a trusted domain. However, if a vehicle uses only one certificate, it could be tracked. since a relationship between its identity and its certificate could be easily done. For this reason, it has to use a set of pseudonym certificates (PCs). Each PC is used for a limited period of time. When this period expires, the vehicle switches to another PC. When all PCs are used, the vehicle downloads another set of PCs from the PKI. This paper proposes a method which reduces the number of PCs used by vehicles. Indeed, when a certificate is used by a vehicle, in order to introduce a confusion against any tracker, this PC will be swap with another driver PC. A tracker will be confused since the former vehicle will not be the owner of the previous PC. This swap has to be recorded on the PKI with a simple process.

Introduction

Intelligent vehicles is a hot topic either for researchers or for car industry [START_REF] Zeadally | Vehicular ad hoc networks (vanets): status, results, and challenges[END_REF]. These actors work on various issues (autonomy, safety, security, connectivity, etc,...). The connectivity issue is considered at different levels: architecture, protocols, coverage, etc Some recent studies have detailed some real deployments of such systems [START_REF] Wealwee | X communication in Europe: From research projects towards standardisation and field testing of vehicle communication technology[END_REF], [START_REF] Santa | Deployment of vehicular networks in highways using 802.11p and IPv6 technologies[END_REF] and [START_REF] Wilhelm | Ayaida A C-ITS Central Station as a Communication Manager International Conference on Innovations for Community Services[END_REF] with various mechanisms. The well known ITS-G5 (based on WiFi IEEE 802.11p) is a dedicated WiFi to connected vehicles using a short range radio [2] . In such networks, each vehicle sends continuously Cooperative Awareness Messages (CAM) [START_REF]Intelligent Transport Systems (ITS); Vehicular Communications; Basic Set of Applications; Part 2: Specification of Cooperative Awareness Basic Service[END_REF] to its neighborhood.

When a vehicle needs to notify an event, it will send another type of message denoted DENM (Decentralized Event Notification Message) [START_REF]Intelligent Transport Systems (ITS); Vehicular Communications; Basic Set of Applications; Part 3: Specifications of Decentralized Environmental Notification Basic Service[END_REF] which will be forwarded to all relevant vehicles. CAM and DENM standards are proposed by the ETSI (European Telecommunications Standards Institute). Such an ecosystem is cooperative where various applications are deployed by car manufacturers (as collision avoidance, adaptive speed, etc) and some others are deployed by road operators (as traffic jam reduction, alternative road management, etc).

All messages are broadcasted to the neighborhood and are forwarded thanks to adapted routing protocols using multi-hop forwarding algorithms [START_REF]Vehicular Communications; GeoNetworking; Part 4: Geographical addressing and forwarding for point-to-point and point-to-multipoint communications; Sub-part 1: Media-Independent Functionality[END_REF] using port selection defined in in the Basic Transport Protocol [START_REF]Intelligent Transport Systems (ITS); Vehicular Communications; GeoNetworking; Part 5: Transport Protocols; Sub-part 1: Basic Transport Protocol[END_REF] . The system is open.

It has a major flaw: anyone can send messages to its neighbors. A misbehavior driver could send a message to notify a fake event. For this reason, we need to consider the authenticity of senders in order to avoid considering messages sent by untrusted drivers. Privacy is also required in order to avoid driver tracking.

These two issues are solved by using a PKI in charge of distributing pseudonyms certificates (PC) to all trusted vehicles in the eco-system [START_REF] Verheul | Issue First Activate Later Certificates for V2X. Presentation InterCor project[END_REF]. This paper proposes a method which reduces the number of PCs used by vehicles by using a swap mechanism. Indeed, when a certificate is used by a vehicle, this PC will be exchanged with another driver PC in order to introduce a confusion for any tracker. A tracker will be confused since the former vehicle will not be the owner of the previous PC. This swap has to be recorded on the PKI with simple processes. This mechanism protects privacy and introduces a novel PC change method. It also reduces the PC costs for drivers. This paper is composed as follows: Section 2 describes some works dedicated to vehicular networks In section 3 we present our model. Section 4 details our contribution. In section 5, we present an evaluation of the proposed solution.

Section 6 concludes the study and gives some ideas about future enhancements of our proposal.

Related works

The following works are dedicated to security issues on vehicular networks.

In [START_REF] Serrai | Towards an efficient and a more accurate web service selection using MCDM methods[END_REF] a study about performances of the selection of web services in a secure environment is proposed. This scheme could be combined with a vehicular cloud solution which manages pseudonym distribution over vehicles. [START_REF] Sedjelmaci | Predict and Prevent From Misbehaving Intruders in Heterogeneous Vehicular Networks[END_REF] tackles one crucial issue about C-ITS: detecting misbehavior drivers.

The authors propose a solution based on learning the behaviors of normal drivers and preventing the abnormal ones considered as misbehaviors. This work have been extended in [START_REF] Bouali | A Distributed Detection and Prevention Scheme from Malicious Nodes in Vehicular Networks[END_REF] in order to target malicious nodes over vehicular networks.

In [START_REF] Mabrouk | Signaling Game-based Approach to Improve Security in Vehicular Networks[END_REF], the authors have applied a game-based approach to specify security troubles on vehicular networks. A closer study is presented in [START_REF] Xua | A privacy-preserving mobile application recommender system based on trust evaluation[END_REF] where the authors propose a simple mechanism to preserve privacy on mobile applications.

They use recommender systems guided by an evaluation of the trust system.

[17] has worked on two privacy-preserving mobile application recommenda-tion schemes based on a trust evaluation. They have proposed recommendations on mobile applications which are generated from trust behaviors of mobile application usage. In these two schemes, user private data can be preserved by applying the proposed security protocols and using homomorphic encryption. [START_REF] Ramassamy | Classification of usual protocols over wireless sensor networks[END_REF] proposes a classification of different protocols which could be used on such networks for security issues. Many key performance indicators have been measured for various scenarios.

[19] has worked on a high level trust management system for vehicular networks. Their main idea is to propose a scheme accepted by all involved vehicles in the system. [START_REF] Bourass | Secure optimal itinerary planning for electric vehicles in the smart grid[END_REF] has proposed a scheme to secure planning of electric vehicle routes within smart grids. They mainly show how to guarantee to electric vehicles to drive through secured routes. [START_REF] Boualouache | A Survey on Pseudonym Changing Strategies for Vehicular Ad-Hoc Networks[END_REF] is one of the most recent survey about pseudonyms changing mechanisms. It gives a very large overview on pseudonym certificate changes for VANETs. Most of these mechanisms focus on choosing the most appropriate location or moment to change a pseudonym for a vehicle in order to ensure privacy preservation. [START_REF] Sun | An Efficient Pseudonymous Authentication Scheme with Strong Privacy Preservation for Vehicular Communications[END_REF][START_REF] Lu | Pseudonym Changing at Social Spots: An Effective Strategy for Location Privacy in VANETs[END_REF] are one of the well known algorithms dedicated to pseudonym changes. [START_REF] Sun | An Efficient Pseudonymous Authentication Scheme with Strong Privacy Preservation for Vehicular Communications[END_REF] has proposed an efficient pseudonym authentication scheme with strong privacy preservation for vehicular communications. Compared to traditional pseudonym authentication schemes, they mainly make the size of Certificate Revocation List (CRL) linear with the number of revoked vehicles. [START_REF] Lu | Pseudonym Changing at Social Spots: An Effective Strategy for Location Privacy in VANETs[END_REF] presents an effective pseudonym changing strategy at social spots (PCS) to achieve the provable location privacy. The aim of the paper is to find the relevant location to change the pseudonym since these locations are known as crowded and are able to guarantee confusion.

In [START_REF] Boualouache | PRIVANET: An Efficient Pseudonym Changing and Management Framework for Vehicular Ad-Hoc Networks[END_REF], the authors have developed a framework for changing pseudonyms when vehicles meet some other vehicles. Even the study presented in [START_REF] Kim | UDiPP: A Framework for Differential Privacy Preserving Movements of Unmanned Aerial Vehicles in Smart Cities[END_REF] focusses on Unmanned Aerial Vehicles, the mechanism shown in the study is the preservation of privacy based on differential privacy which is applied for urban environments. [START_REF] Fouchal | Secured Communications on Vehicular Networks over Cellular Networks[END_REF] has worked on integrating security schemes for vehicles communications within various types of vehicular networks mainly on WiFI or cellular channels.

[27] has proposed an original security mechanism for vehicular networks using a cloud approach and implementing a specific blockchain.

[28] has proposed a hybrid recommender algorithm that combines users' location and preferences and the content of the items located close to such users. The locations of users are tacked and the scenarios proposed, the privacy has been investigated with low efficiency. [START_REF] Jafarnejad | Towards a real-time driver identification mechanism based on driving sensing data[END_REF] and [START_REF] Hallac | Driver identification using automobile sensor data from a single turn[END_REF] have been dedicated to clustering algorithms which are able to detect driver profiles (and behaviors) on traces collected from vehicles driving on various types of roads. They show under some conditions that the anonymity could be broken. That means drivers could be tacked even if drivers use different pseudonyms during their journey.

All these studies show that trust, privacy and cost efficiency have never been studied together. None of these studies tackles the reduction of the number of pseudonyms. As far as we know, this study is the first one which considers that the whole eco-system is able to work with the same number of pseudonym certificates and where the privacy is preserved with higher efficiency.

Security architecture

Preliminaries

In the area of C-ITS (Cooperative Intelligent Transportation System), a protocol stack has been defined and standardized by the ETSI standardisation institute in Europe [2]. A similar stack has been adopted by the USA and asian countries. Over the Transport-Networking layer (defined as geo-networking layer), the Facilities layer has been designed in order to be an efficient interface between the application layer (close to the driver and the vehicle sensors) and the Transport-Networking layer.

Usual protocols

Many types of messages are defined at this layer. We will focus in this study only on 2 main messages: CAM (Cooperative Awareness Message) [START_REF]Intelligent Transport Systems (ITS); Vehicular Communications; Basic Set of Applications; Part 2: Specification of Cooperative Awareness Basic Service[END_REF] and DENM (Decentralized Environmental Notification Message) [START_REF]Intelligent Transport Systems (ITS); Vehicular Communications; Basic Set of Applications; Part 3: Specifications of Decentralized Environmental Notification Basic Service[END_REF]. The aim behind sending CAM messages is to give dynamic information about the vehicle (i.e. position, speed, heading, etc.). A vehicle sends CAMs to its neighborhood using Vehicle-to-Vehicle (V2V) or V2I communications. Depending on the vehicle speed, the frequency of CAM messages can vary from 1 Hz to 10 Hz. A vehicle sends DENM messages in order to notify any event (i.e. accident, traffic jam, etc.). The event could be triggered automatically thanks to the connexion to the vehicle CAN Bus. In fact, some smart rules are run on the OBU and generate automatically appropriate messages. They can also be generated manually for sensitive cases as animal on the road, etc.

Privacy and authenticity

C-ITS security considers two main aspects:

• Authenticity: this aspect allows to consider only messages coming from trusted drivers.

• Privacy: this aspect allows to protect drivers data and avoid driver tracking.

In order to solve these two issues, a PKI (Public Key Infrastructure) is required. Each involved vehicle in the eco-system has to subscribe to the PKI server. The subscription is achieved by providing a long term certificate (LTC) to this vehicle (signed by a root PKI).

A vehicle could sign its messages using this LTC by means of a TPM (Trusted Platform Module) which saves securely private keys This process ensures perfectly the authenticity but not the privacy. Indeed, from an LTC we could extract private informations which give the opportunity to external observers to identify driver's information and allows to track these drivers. The usual solution to protect drivers privacy is the use of pseudonym certificates (PC) for small periods. A vehicle has a valid pool of PCs in order to be able to switch to another PC in order to derive a kind of confusion to any tracker. On Figure 1, from the location A to the location B, the vehicle uses P C1 as a pseudonym for signing its messages and uses P C2 after this location until reaching C. If the vehicle changes its PC when it is alone on the road, any tracker will be able to follow it easily since the relationship between both PCs could be established. That is why many solutions on pseudonym changes are applied when a vehicle is close to other vehicles as in [START_REF] Lu | Pseudonym Changing at Social Spots: An Effective Strategy for Location Privacy in VANETs[END_REF].

In this paper, we assume that each vehicle uploads a pool of valid PC for a long time.

Pseudonym sharing mechanism

We detail in this section our contribution. Our aim is to reduce the number of PCs used by vehicles which reduces the PC cost. We will measure this cost in the last section. Indeed, each vehicle which has used a PC for a fixed period (some minutes or some hours for instance) denoted M ax delay will swap its PC with a PC of one of its neighbors. The PC swap occurs between vehicles which drive close to each other. This process will express a kind of confusion for a tracker since a vehicle will not be the owner of its previous PC even the PC is still used. This method ensures privacy and introduces an efficient PC change mechanism. In addition, it reduces the PC cost for drivers and for the PKI.

Our proposal is composed of the following steps: The swap of a PC between v A and v B could occur if both vehicles are in the same coverage range. We only consider a swap between vehicles having almost the same speed. If vehicles have different speeds, it will be easier to distinguish the vehicle behaviors and to detect their features (mainly their speed). Some interesting studies about driver profile detection have been undertaken since many years and are able to detect drivers id even if they use pseudonyms as in [START_REF] Jafarnejad | Towards a real-time driver identification mechanism based on driving sensing data[END_REF][START_REF] Hallac | Driver identification using automobile sensor data from a single turn[END_REF].

The minimum speed difference has to be fixed in order to know the most relevant value to choose in order to avoir driver tracking. This value could be set with accuracy with a long evaluation study through simulations or real experimentations. In addition to that, when a swap with a neighbor has been decided to be done, it could be done within a time slot which depends on the speeds of both vehicle. When the speeds of vehicles are almost similar, we have longer periods for vehicles to be close to each other.

In Figure 2, we observe the connectivity duration between a vehicle driving at 50km/h compared to a vehicle having various speeds. When the speed of the neighbor is 60km/h, the connectivity duration is around 18 seconds but when its speed is 130km/h the connectivity duration is 5 seconds. This parameter will be considered in the algorithm of neighbor selection.

Selection of the swap instant

In our solution, a vehicle will change its PC after having used it for a minimum period of time (usually some hours). The idea is to find the best compromise between preserving privacy and getting the lowest cost of PCs. In this study we will use a fixed value denoted M ax delay (which varies from some minutes to hours) when reachable neighbors are around. Since no additional cost is required for these PCs, if the PC swap number increases, the privacy preservation increases as well. A special care should be taken about the neighbor to chose. A vehicle has to handle a list of neighbors in a continuous way. It has to consider the vehicles which are nearby for more than a stable duration (for instance one minimum duration). In fact we will avoid to swap a PC with a vehicle having a different speed from the current vehicle speed. In order to be sure that a vehicle is not very faster than ours, we will monitor the list of neighbors.

Neighbor selection algorithm

This step is the core of the contribution. Indeed, it intends to provide confusion among drivers. Our work is based on three different usual scenarios: a grouped set of vehicles driving followed one each other like a platoon; a vehicle driving through a group of vehicles faster than all of them and merging groups in one larger group coming from two roads.

Grouped vehicles

In Figure 3, two vehicle groups Group-1 and Group-2 are separated and are split into two platoons. This situation is quite usual over the highway. The PC swap is possible within the two groups. Since there is no traffic jam the groups may be kept separated for a long period. We can have the extreme vehicles (vehicle 3 in Group 1 and vehicle 14 in Group 2) of each group be connected together. In the algorithm of PC swap, we only permit to vehicles having a minimum number of neighbors to request a PC swap. Indeed, if a small group of vehicles drive together for a period of time, and if they swaps their PCs many times, it could be easy to recover their ids since the initial number of vehicles is low;

Fast vehicle through grouped vehicles

In the scenario shown in Figure 4, Figure 5 and Figure 6, we illustrate a scenario where the key swap should not considered. When we observe the red vehicle v1 which will cross the two groups because its speed is higher than the vehicles of both groups. If v1 swaps with any vehicle of both groups, it could be easily tracked through driver profile detections mechanisms when they are based on speed analysis. Indeed, some well known studies about drive profile detection could be used on drivers involved in this highway. The vehicle v1 could be isolated since its speed is higher than all others even if its PC has changed many times. For this reason, in the PC swap algorithm, the difference speed with a vehicle is used as a relevant parameter to select the neighbor.

Merging vehicles

The situation where two groups of vehicles are merging on a joining road is useful, then we take profit from this location to start swaping the PCs. Usually, the trafic road is reduced, the confusion is guaranteed if the vehicles speed differences are lower than a threshold. The same situation is observed when a road is separated into two roads, this kind of location should be exploited with efficiency for the confusion that could be introduced. On Figure 7, we observe that vehicles reaching the merging road on Figure 8 will form a new group (red vehicles and yellow vehicles) for a period of time due to their merging process.

Then we have to speed up the PC swap at this location. As a conclusion from these scenarios, any vehicle could request a PC exchange but should cooperate with a vehicle having the closest behavior to it (mainly in terms of speed). If a neighbor B has almost the same speed and behavior as a vehicle A and if A is kept in its range coverage, A and B could swap their PCs. We should also keep in mind that this swap is done no more than once between A and B otherwise, we could undo the result of the swap if we execute another swap between these two vehicles.

Key swap algorithm

The algorithm 1 describes the actions to be run by any vehicle having in its neighborhood another vehicle. According to the reception of CAM messages, one is able to know about its neighborhood. Then, each node has to update continuously its neighborhood table . The key exchange will be run only if the receiver is detected as a neighbor for a sufficient period of time in order to ensure that the exchange will succeed. Indeed, if a vehicle is met for a quick period, the exchange process may abort.

The swap of a PC between v A and v B will be achieved as follows: The vehicle v A starts the exchange process by sending a signed exchange request to the destination v B (A sends in the message its certificate). If the later accepts the request, it will respond with a message containing its proposed PC denoted P C B which is encrypted in asymmetric way using A public key contained in the certificate. When A receives the response (which is considered as an acknowledgment of the request), it will choose a PC to exchange denoted P C A and sends it to B using an asymmetric encryption mechanism. When B receives the proposed PC, it has to acknowledge the reception to A. Both vehicles have to send a notification to the PKI server to inform it about this swap. The server needs to get both notification in order to record the new owners of PCs.

Figure 9 shows the protocol to be executed by two nodes in order to ensure a secure exchange. This process could be run with another vehicle in another slot time.

PKI notification algorithm

When the key swap has been run by two vehicles, they have to notify the PKI server about the exchange. These notifications should be sent immediately if the We notice that in our eco-system we assume that drivers respect the use of the PC mainly when they have run a PC swap. Indeed, since they still have the private key of their former PC even when they have swap it, they should never use it. This issue will not be discussed in the current study.

Performance evaluation

The evaluation of our proposal is based on measuring two key performance indicators: the confusion rate and the PC cost. Let have an eco-system composed of N vehicles for a period T . The confusion rate is defined as the number of vehicles which could be identified even with different pseudonyms. The PC

Conclusion

In this paper we have proposed a simple solution to share a set of pseudonym certificates in the area of C-ITS. We have shown that this proposal has two main features:

• Reduction of certificate costs: In C-ITS, must current solutions suggest the use of a PC pool for a period. After that, a new pool is required.

• Enhancing the privacy: This solution allows to use one PC for various vehicles, which means that trackers will be confused to follow any driver.

As future works, we intend to test better the scalability of our system by launching larger simulations with various scenarios as all those described in section 4.3.

In the meantime we intend to analyse the security performances of signing and verifying processes.

Figure 1 :

 1 Figure 1: Example of a PC change

1 .

 1 Choice of the instant and location where the pseudonym change occurs 2. Selection of the more relevant neighbor 3. Effective swap of PCs 4. Notification of the PKI server 4.1. PrincipleWe consider a set V of N vehicles such as V = v 1 , v 2 , ..., v N . Each vehicle v i has a current pool of M PCs denoted P i such as P i = P C i1 , P C i2 , ..., P C iM .

Figure 2 :

 2 Figure 2: Connectivity duration vs. vehicle speed

Figure 3 :

 3 Figure 3: Example of grouped vehicles

Figure 4 :

 4 Figure 4: Before insertion of a vehicle in a platoon

Figure 5 :

 5 Figure 5: Insertion of a vehicle in a platoon

Figure 6 :

 6 Figure 6: After insertion of a vehicle in a platoon

Figure 7 :

 7 Figure 7: Two groups driving on two different roads

Figure 8 :

 8 Figure 8: Merging of two groups

Figure 9 :

 9 Figure 9: Key swap protocol

Algorithm 1 :

 1 Key exchange Algorithm 1: Begin -V : set of vehicles -v s : the sender vehicle -v r : the receiver vehicle -P C s : The sender PC -P C r : The receiver PC 2: v s and v r are in the coverage range of each other 3: v r receives an PC exchange request from v s 4: v r checks the validity v s 5: if (v s is valid ) then 6: v r sends a response R1 with P C r using asymetric encryption to v s 7: v s check the validity of R1 8: if (R1 is valid ) then 9: v s sends a response R2* with P C s using asymetric encryption to v r 10: if (R2 is valid ) then 11: v r acknowledge the reception v s ; 12: v r and v s update their PC sets accordingly; 13:v r and v s send a notification to the PKI server 14: End cost is the number of P Cs used by the eco-system during t.We have developed our proposal on the OMNET++ framework and a simple changing mechanism based on changing a pseudonym for a vehicle after it has signed a fixed number of messages. The results of our experimentation is shown below. In the Figure10and Figure 11, we have observed the behavior of vehicles during a period delta composed of 10 slot times. In each slot time we have run a classical PC change (from a local pool of each vehicle) and we have run our swap mechanism.

Figure 10 :Figure 11 :

 1011 Figure 10: Starting datel

Figure 12 :

 12 Figure 12: Rate of PC changing for 10 vehicles over 10 slots

Figure 13 :

 13 Figure 13: Rate of PC changing for 40 vehicles over 10 slots

Acknowledgement This work was made possible by EC Grant No. INEA/CEF/TRAN/A2014/1042281 from the INEA Agency for the SCOOP project. The statements made herein are solely the responsibility of the authors.


Williams Lefebvre
email: williams.lefebvre@univ-rouen.fr

Grégory Rose

Pauline Delroisse

Eric Baustert

Fabien Cuvilly

Aude Simar

Nanoscale periodic gradients generated by laser powder bed fusion of an AlSi10Mg alloy

Keywords: Laser powder bed fusion, SLM, LPBF, selective laser melting, additive manufacturing powder bed fusion, design, gradient, microstructure, aluminium, Al-Mg-Si, amorphous, clustering, atom probe tomography

A layered nanostructure is produced by laser powder bed fusion of an Al-Si10Mg alloy. Melt pools are formed of repeated Al cells exhibiting a gradient of dislocation density and nano-layers of amorphousphase enriched in Al and Si containing fine dispersions of diamond-Si nanocrystals. The high solidification rate involves the formation of a high density of solute-rich clusters in Al crystals.

Introduction

Elaboration of metallic parts by laser powder bed fusion (LPBF) or selective laser melting (SLM) of metallic powders [START_REF] Li | Selective laser melting of nano-TiB2decorated AlSi10Mg alloy with high fracture strength and ductility[END_REF][START_REF] Kruth | Binding mechanisms in selective laser sintering and selective laser melting[END_REF][START_REF] Rashed | Metallic microlattice materials: A current state of the art on manufacturing, mechanical properties and applications[END_REF][START_REF] Olakanmi | A review on selective laser sintering/melting (SLS/SLM) of aluminium alloy powders: Processing, microstructure, and properties[END_REF][START_REF] Martin | 3D printing of high-strength aluminium alloys[END_REF][START_REF] Yap | Review of selective laser melting: Materials and applications[END_REF][START_REF] Thijs | A study of the microstructural evolution during selective laser melting of Ti-6Al-4V[END_REF][START_REF] Louvis | Selective laser melting of aluminium components[END_REF][START_REF] Yadroitsev | Parametric analysis of the selective laser melting process[END_REF][START_REF] Van Den Broek | A model based reconstruction technique for depth sectioning with scanning transmission electron microscopy[END_REF][START_REF] Aboulkhair | Reducing porosity in AlSi10Mg parts processed by selective laser melting[END_REF][START_REF] Brandl | Additive manufactured AlSi10Mg samples using Selective Laser Melting (SLM): Microstructure, high cycle fatigue, and fracture behavior[END_REF][START_REF] Amato | Microstructures and mechanical behavior of Inconel 718 fabricated by selective laser melting[END_REF] offers a unique opportunity to achieve significant hardening by microstructure design. Hardening of alloys is commonly pursued by combining contributions such as lattice friction, solid solution strengthening, work hardening, Hall-Petch strengthening, and precipitation hardening. Insofar as LPBF is applied to produce end products, work hardening cannot be directly considered. Although LPBF is intrinsically a casting process, its advantage comes from the incredibly high cooling rates involved (in the range 10 3 -10 6 K/s) [START_REF] Li | Selective laser melting of nano-TiB2decorated AlSi10Mg alloy with high fracture strength and ductility[END_REF][START_REF] Qian | Additive manufacturing and postprocessing of Ti-6Al-4V for superior mechanical properties[END_REF][START_REF] Jung | Fabrication of Fe-based bulk metallic glass by selective laser melting: A parameter study[END_REF]. Whereas similar cooling rates could only be obtained using specific methods such as melt spinning, which produces thin ribbons only [START_REF] Bendijk | Characterization of Al-Si-alloys rapidly quenched from the melt[END_REF][START_REF] Hono | The microstructure evolution of a Fe73.5Si13.5B9Nb3Cu1 nanocrystalline soft magnetic material[END_REF][START_REF] Lefebvre | Role of Niobium in the nanocrystallization of a Fe73.5Si13.5B9Nb3Cu alloy[END_REF], LPBF allows for the trapping of alloy systems in complex non-equilibrium states, which can also serve as a basis for smart microstructure design by well-defined heat treatments.

Among the aluminium alloys used in additive manufacturing, hypoeutectic alloys are quite common because of their good castability, high strength, and good corrosion resistance [START_REF] Olakanmi | A review on selective laser sintering/melting (SLS/SLM) of aluminium alloy powders: Processing, microstructure, and properties[END_REF][START_REF] Li | Age-hardening behavior of cast Al-Si base alloy[END_REF]. Poor ductility and anisotropy are often associated with the as-built condition, which explains why longduration high-temperature annealing is usually applied to "reset" the microstructure inherited from the LPBF processing [START_REF] Padovano | A comparative study of the effects of thermal treatments on AlSi10Mg produced by laser powder bed fusion[END_REF]. However, in the as-built condition, AlSi10Mg is known to exhibit high tensile strength and hardness compared to the same material processed by conventional casting [START_REF] Padovano | A comparative study of the effects of thermal treatments on AlSi10Mg produced by laser powder bed fusion[END_REF]. Indeed, from the as-built state, interesting properties can already be achieved for Al-Si alloys [START_REF] Brandl | Additive manufactured AlSi10Mg samples using Selective Laser Melting (SLM): Microstructure, high cycle fatigue, and fracture behavior[END_REF][START_REF] Thijs | Fine-structured aluminium products with controllable texture by selective laser melting of pre-alloyed AlSi10Mg powder[END_REF][START_REF] Lien | Ultrahigh strength and plasticity in laser rapid solidified Al-Si nanoscale eutectics[END_REF]. As illustrated in the work by Lien et al. [START_REF] Lien | Ultrahigh strength and plasticity in laser rapid solidified Al-Si nanoscale eutectics[END_REF], an excellent compromise between the strength and strain can be achieved by means of laser rapid solidification compared to classical casting applied to Al-20wt%Si modified alloys. These authors have clearly shown how the drastic refinement of the microstructure obtained by rapid solidification was responsible for this gain in strength and ductility.

Accounting for the complex gradients inherited by the LPBF process, advanced material design by heat treatments can be pursued. Physical metallurgists may hence dispose of a complex tangle of regions with significantly different compositions and microstructures at the submicron scale that they can force to evolve to achieve some target properties. In this study, much attention has been paid to the fine-scale characterisation of an AlSi10Mg alloy in the as-built state by a combination of transmission electron microscopy (TEM) and atom probe tomography (APT) analyses.

Observations by these two techniques allow for the connection of the non-equilibrium structures to the high cooling rate resulting from the LPBF process. While the repetition of a microstructural pattern in the melt pools is identified, solute clustering in the Al cells is quantitatively investigated, and the potential role of clusters in phase selection during further heat treatments is discussed.

Experimental

Materials elaboration and specimen preparation

Bulk LPBF samples were manufactured on an EOS M290 in the form of plates with dimensions of 150 mm × 35 mm × 5 mm. The build platform was maintained at 35 °C. The choice of this rather low temperature was made to avoid softening and phase decomposition during the process. The fabrication parameters were optimised by the machine manufacturer, which were a laser power of 390 W, powder layer thickness of 30 μm, hatch spacing of 0.19 mm, scanning speed of 1300 mm/s, and rotation between scans rotation of 67°. To prevent sample oxidation during fabrication, the manufacturing chamber was under protective argon gas.

For TEM/scanning TEM (STEM) and APT analyses, samples were prepared by focussed ion beam (FIB) using the in situ lift-out technique in a cross-beam NVISION-40 ZEISS. In the first step, a chunk was removed from a bulk sample with milling currents of 6.5 nA and 1.5 nA at 30 kV and welded to a copper grid with a gas injection system, which uses an organometallic gas composed of platinum and carbon. In the last step, the chunk was machined into a fine lamella with milling currents of 300 pA and 80 pA at 30 kV using Ga ions. To reduce Ga implantation and damage in the region of interest, the final step of milling of the lamella was performed at a low acceleration voltage of 2 kV.

Characterisation tools and protocols

Atom probe experiments were performed using a Cameca LEAP 4000 HR, operating in voltage mode. The voltage pulse fraction was 20% with a pulse repetition rate of 200 kHz, while the specimen temperature was set to 40 K. APT reconstructions and data mining were performed using the IVAS ® software. TEM and STEM observations were obtained with a JEOL ARM equipped with a Cscorrector of the probe forming system. The microscope voltage was set to 200 kV.

In the APT reconstructions, the level of decomposition of the aluminium solid solution was first analysed by plotting radial distribution functions (RDFs) [START_REF] Sudbrack | Direct observations of nucleation in a nondilute multicomponent alloy[END_REF]24] An RDF was plotted for a given atom type (e.g. Mg). For each atom of the selected element in the APT reconstruction, the concentrations of all elements in a shell of radius r and thickness dr around the atom were calculated (CAl(r), CMg(r), CSi(r)), and then compared to the average concentration of each of these elements in the whole APT reconstruction by calculating the concentration ratio. Hence, a clustering was indicated by an RDF value > 1, whereas a random distribution of solutes would give a value of 1.

Quantification of clustering in the Al solid solution was performed by applying the maximum separation distance (MSD) algorithm [25,[START_REF] Hyde | An Analysis of the Structure of Irradiation induced Cu-enriched Clusters in Low and High Nickel Welds[END_REF] extended to high-order nearest neighbour distances, first to Mg atoms and, second, to Si atoms. This well-established cluster search methodology for APT is described and compared with other cluster search methods in several reviews [START_REF] Marquis | Applications of atom-probe tomography to the characterisation of solute behaviours[END_REF][START_REF] Lefebvre-Ulrikson | Atom probe tomography put theory into practice[END_REF][START_REF] Gault | [END_REF]. For the sake of clarity and to allow the reader to compare the present results with the literature, the principle and limitations of the method are summarised hereafter.

MSD gathers atoms of selected species in a given cluster if they are closer than the distance dmax. Classically, MSD has been applied to first nearest neighbour (1NN) distance distributions in the literature, and this is also the case in a recent work on an AlSi10Mg alloy elaborated by LPBF [START_REF] Maeshima | Solute clustering and supersaturated solid solution of AlSi10Mg alloy fabricated by selective laser melting[END_REF].

Nevertheless, since 1NN distribution of clusters strongly overlap with the 1NN distribution of the matrix in most cases [START_REF] Maeshima | Solute clustering and supersaturated solid solution of AlSi10Mg alloy fabricated by selective laser melting[END_REF][START_REF] Lefebvre-Ulrikson | Data Mining[END_REF], applying dmax to 1NN distribution results in the selection of a significant proportion of wrong clusters (corresponding to the "noise" of the algorithm) coming from the start of 1NN distribution in the matrix, together with actual clusters (which are the "signal" of the algorithm). This problem is well documented in the literature with the support of simulations [START_REF] Gault | [END_REF][START_REF] Lefebvre-Ulrikson | Data Mining[END_REF],

and it has been proven that applying a criterion Nmin on the minimum number of solute atoms per cluster is not sufficient to retrieve a satisfying signal over noise ratio if only the 1NN distance distribution is considered. On the contrary, the reliability of the MSD algorithm is significantly improved by considering KNN (K th nearest neighbour distance) distributions with K>1 [START_REF] Lefebvre-Ulrikson | Data Mining[END_REF][START_REF] Stephenson | Cluster analysis under microscope: quantitative techniques for atom probe analysis of solute clustering in multi-component materials[END_REF].

Insofar as an arbitrary definition of (K, dmax,Nmin) is not expected to lead to optimum values (i.e., maximising the signal-to-noise ratio and providing a fair description of the clusters), a heuristic approach has been used to identify the optimum parameters for the algorithm [START_REF] Stephenson | Cluster analysis under microscope: quantitative techniques for atom probe analysis of solute clustering in multi-component materials[END_REF][START_REF] Miller | Precipitation in neutron-irradiated Fe-Cu and Fe-Cu-Mn model alloys: a comparison of APT and SANS data[END_REF][START_REF] Vaumousse | A procedure for quantification of precipitate microstructures from three-dimensional atom probe data[END_REF][START_REF] Kolli | Comparison of compositional and morphological atom-probe tomography analyses for a multicomponent Fe-Cu steel[END_REF]. This is done by comparing the results of cluster selection for numerous sets of parameters (K, dmax,Nmin) in the analysed volume and in its equivalent randomised volume wherein atomic positions are randomly exchanged. For cluster selection based on Mg atoms, the signal-to-noise ratio was found to be optimum for K = 5, dmax= 1.8 nm, and Nmin = 21. For cluster selection based on Si atoms, the signal-tonoise ratio was found to be optimum for K = 7, dmax= 1.0 nm, and Nmin = 39. Subsequently, the envelope method [START_REF] Miller | Atom probe tomography: a technique for nanoscale characterization[END_REF] was used to associate other atoms to the selected clusters. For this method, the envelope length was set to 1 nm and the erosion distance was 0.7 nm.

Results

Non-equilibrium features in eutectic areas and local strain hardening

After LPBF, the microstructure consists of a superimposition of melt pools containing a succession of Al cells separated by eutectic zones. Over several tens of microns, Al cells may display a similar crystalline orientation, suggesting that they belong to the same primary dendritic Al crystal.

Such observations not reported here are already vastly reported at this scale in many papers [START_REF] Brandl | Additive manufactured AlSi10Mg samples using Selective Laser Melting (SLM): Microstructure, high cycle fatigue, and fracture behavior[END_REF][START_REF] Thijs | Fine-structured aluminium products with controllable texture by selective laser melting of pre-alloyed AlSi10Mg powder[END_REF][START_REF] Casati | Aging Response of an A357 Al Alloy Processed by Selective Laser Melting[END_REF][START_REF] Delroisse | Effect of strut orientation on the microstructure heterogeneities in AlSi10Mg lattices processed by selective laser melting[END_REF]. In Figure 1, TEM observations of Al cells and eutectic zones are displayed. The specimens were selected well into the melt pools, away from thermally affected zones that can be generated by the LPBF of superior layers. All observed Al cells in Figure 1 have the same orientation, as revealed by fast Fourier transform (FFT) in high-resolution TEM. Their thickness (i.e., their smallest dimension) is approximately 400 nm. No clear precipitation could be revealed inside the Al cells at this scale, suggesting that cooling was fast enough to avoid long-range diffusion of solute elements and phase separation. On the contrary, a slow cooling rate or reheating of the material would have led to solid-state decomposition in the Al cells, along with the formation of Mg2Si and/or Si particles predicted by the ternary phase diagram. Furthermore, contrasts due to lattice distortions are visible in the Al cells in the vicinity of eutectic regions. Such distortions (indicated by white arrows in Figure 1(a)) could either be generated by coherency strain across the Al-cell/eutectic zone interface or by the volume variation of the eutectic region at the end of its solidification, which occurs after the rapid formation of Al cells. As will be shown hereafter, eutectic areas do not exhibit a lattice structure that could form a coherent interface with Al cells. Hence, lattice distortions are produced by volume variation during the solidification of eutectic regions. Complex interface structures involving both crystalline and amorphous phases have also been shown to produce dislocations in the literature [START_REF] Li | Surface reinforcements of TA15 titanium alloy with laser induced Co base multiphase composites[END_REF][START_REF] Li | Microstructure evolution, texture and laser surface HEACs of Al-Mg-Si alloy for light automobile parts[END_REF]. Such distortions are expected to contribute to the residual stress measured at the microscopic scale [START_REF] Levkulich | The effect of process parameters on residual stress evolution and distortion in the laser powder bed fusion of Ti-6Al-4V[END_REF]. By computing an FFT of the image in Figure 2(a), several spots consistent with the spatial frequency of the {111} planes of diamond Si are identified in Figure 2(b). The random orientation of these reflexions is the signature of equiaxed crystallisation of diamond Si in the eutectic area. By selecting the eutectic area for the calculation of the FFT, it was confirmed that both these spots and the diffuse circle of radius 3.2 nm -1 are generated by the eutectic region. Whereas the circle of diffuse intensity is generated by an amorphous structure, the recurrent 3.2 nm -1 frequency indicates a local ordering compatible with the formation of {111} planes of diamond Si. This is confirmed by the presence of numerous nanoclusters in Figure 2(c). Insofar as the thickness of the APT specimen rapidly reaches tens of nanometres, direct correlative analysis by APT and HR-TEM becomes inappropriate if the determination of nano-scale features such as those observed in Figure 2(a) is pursued. Hence, the structural analysis of eutectic regions has been determined in thin foils only, and

Quantification of clustering in the supersaturated solid solution

APT analyses were performed in the Al cells. The composition of the solid solution is detailed in Table 1. As expected, the rapid cooling undergone by LPBF induces a large supersaturation in the Al cells, and no precipitation could be revealed away from the heat-affected zone. Indeed, Zandbergen et al. showed that the solid solubility of Si and Mg was lower than 0.05 at% below 180 °C [START_REF] Zandbergen | Data analysis and other considerations concerning the study of precipitation in Al-Mg-Si alloys by Atom Probe Tomography[END_REF]. However, the fluctuations of solute distribution in the Al solid solution may be already identified in Figure 4(a) and affect both Mg and Si at a very fine scale. In order to clearly identify and quantify these fluctuations, RDFs [START_REF] Sudbrack | Direct observations of nucleation in a nondilute multicomponent alloy[END_REF]24] were calculated in the APT reconstruction of Figure 4 for Mg atoms and Si atoms separately. These are plotted in Figure 5. Around Mg atoms, the composition of Mg is on average significantly higher (up to 3 times higher on average), whereas a significant enrichment in Si can also be distinguished. These enrichments may extend slightly above 2 nm. Around the Si atoms, the solute distribution is also found to be non-random. Nevertheless, it is impossible to conclude from RDF calculations whether local solute enrichments correspond to one or more 12 populations of clusters. For this purpose, further quantification of clustering has been undertaken using the well-established cluster search methodology described in section 2.2. In Figure 6 at% from Table 1). Finally, the number densities of the two populations of clusters were calculated and are displayed in Table 2. The measured values are typically one order of magnitude larger than values reported in the literature of 6xxx wrought alloys (see, for instance, [START_REF] Zandbergen | Data analysis and other considerations concerning the study of precipitation in Al-Mg-Si alloys by Atom Probe Tomography[END_REF][START_REF] Torster | The influence of composition and natural aging on clustering during preaging in Al-Mg-Si alloys[END_REF]). One can also notice that we detect two more Si clusters (free of Mg) than Mg-rich clusters (containing Si). Although Si contributes to both populations of clusters, the larger number density of Si-rich clusters is consistent with the much larger supersaturation in Si in the solid solution compared to the supersaturation in Mg.

Table 2 : Number densities of solute-rich clusters in the as-built state of the AlSi10Mg alloy

Mg-rich clusters Si-rich clusters

Number density (m -3 ) (4.9±0.5) 10 23 (8.9±0.9) 10 23

Discussion

In this study, a complex periodic microstructure of AlSi10Mg designed by LPBF is described.

Observations have been focussed on the microstructures formed in regions where the cooling rate is expected to be maximum and where no evidence of reheating (by melting of superior layers) was provided. In addition, much attention has been paid to detail both the composition and structure of the eutectic regions at high resolution. In the literature, the characterisation of eutectic regions of Al-Si alloys in the as-built state more often provide two-dimensional chemical mappings by energy dispersive x-ray spectroscopy coupled with SEM, TEM, or STEM observations [START_REF] Rao | The influence of processing parameters on aluminium alloy A357 manufactured by Selective Laser Melting[END_REF][START_REF] Chen | Strength and strain hardening of a selective laser melted AlSi10Mg alloy[END_REF][START_REF] Yan | Microstructure and mechanical properties of aluminium alloy cellular lattice structures manufactured by direct metal laser sintering[END_REF][START_REF] Wu | Microstructure and strength of selectively laser melted AlSi10Mg[END_REF]. Although significant microstructural information was revealed by these techniques (cell size, texture, eutectic decomposition, etc. ), APT is necessary to detect the fine-scale distribution of elements induced by the LBPF process at the nanometre scale. In addition, it is mandatory to compare the information accessible by APT with observations at the same scale using (S)TEM to relate compositional variations to the structure of the material. By combining these techniques, new information is provided in the present work that highlights the potential of microstructural design of alloys by LPBF.

First, it is demonstrated that LPBF allows trapping of the AlSi10Mg system in an amorphous state in eutectic regions. This is clearly attributed to the very fast cooling associated with the LPBF elaboration process. Similarly, in the case of surface laser processing, the formation of amorphous phases has also been reported and attributed to the short existing time of the melt pool [START_REF] Li | Surface reinforcements of TA15 titanium alloy with laser induced Co base multiphase composites[END_REF][START_REF] Li | Laser/argon-arc strengthening of titanium alloy surface with Deloro matrix composites[END_REF]. The amorphous matrix observed at high resolution contains large concentrations of both Al and Si, as indicated by the composition profiles in Figure 3. However, more indications about the eutectic regions were given by APT: i) Mg and Si composition varied gradually from the core of the eutectic region towards the surrounding Al cell; ii) composition profiles are not consistent with equilibrium compositions predicted by the phase diagram of the Al-Mg-Si system. Correlating these APT results

with HR-TEM observations confirm that, in eutectic regions, fast cooling enables rapid crystalline ordering at the nanometre scale, accompanied by insufficient long-range diffusion of solute elements. Inside the amorphous matrix, phase separation is shown to start by a short-range ordering compatible with the diamond-Si structure. Some Si nanocrystals are indeed visible in the HR-TEM.

APT analysis of a eutectic region also revealed a local enrichment consistent with the formation of a Mg2Si precipitate. Nevertheless, as they are likely to form without any specific orientation with respect to the Al cells, they are not expected to give any obvious contrast in TEM unless their long axis is by chance oriented along the direction of observation. Short-range diffusion therefore enables the start of a solid-state decomposition, which is rapidly stopped during the LPBF process. The fast cooling rate, thus, locally retains a nanostructure, which is usually obtained by methods that enable high cooling rates such as melt spinning [START_REF] Bendijk | Characterization of Al-Si-alloys rapidly quenched from the melt[END_REF][START_REF] Hono | The microstructure evolution of a Fe73.5Si13.5B9Nb3Cu1 nanocrystalline soft magnetic material[END_REF][START_REF] Lefebvre | Role of Niobium in the nanocrystallization of a Fe73.5Si13.5B9Nb3Cu alloy[END_REF].

The contraction associated with the rapid solidification of eutectic areas is shown to involve local strain hardening in adjacent Al cells, as shown in Figure 1. This strain hardening was observed locally in the direct vicinity of eutectic zones and was not found to extend to more than 100 nm distant from eutectic zones on average. This local strain of Al cells at the location of the Alcell/eutectic region interface was systematic in our observations. Inside a melt pool, this results in the formation of a repeated pattern consisting of a eutectic area surrounded by Al crystals, for which the level of strain hardening gradually decreases towards their core.

Inside the Al-cells investigated by APT, a significant supersaturation of the solid solution was observed (Table 1), in agreement with previous works [START_REF] Maeshima | Solute clustering and supersaturated solid solution of AlSi10Mg alloy fabricated by selective laser melting[END_REF][START_REF] Li | A selective laser melting and solution heat treatment refined Al-12Si alloy with a controllable ultrafine eutectic microstructure and 25% tensile ductility[END_REF]. In their paper [START_REF] Maeshima | Solute clustering and supersaturated solid solution of AlSi10Mg alloy fabricated by selective laser melting[END_REF], Maeshima and Ohishi investigated the solid solution of an AlSi10Mg alloy. By applying the MSD algorithm, they found that clustering mainly concerned Mg atoms, whereas Si was not found to form either Si clusters or to participate in Mg clusters. Nevertheless, based on their calculation of first nearest neighbours only, this quantification was inevitably strongly affected by a low signal-to-noise ratio, as discussed in detail in some reference work and reviews on the topic [START_REF] Marquis | Applications of atom-probe tomography to the characterisation of solute behaviours[END_REF][START_REF] Lefebvre-Ulrikson | Data Mining[END_REF][START_REF] Stephenson | Theory of Solute Clustering in Materials for Atom Probe[END_REF] and in the experimental section above. In the present work, by following a well-established heuristic protocol for cluster selection [START_REF] Stephenson | Cluster analysis under microscope: quantitative techniques for atom probe analysis of solute clustering in multi-component materials[END_REF][START_REF] Kolli | Comparison of compositional and morphological atom-probe tomography analyses for a multicomponent Fe-Cu steel[END_REF][START_REF] Marceau | Quantitative atom probe analysis of nanostructure containing clusters and precipitates with multiple length scales[END_REF][START_REF] Lefebvre-Ulrikson | Correlative Microscopy by (Scanning) Transmission Electron Microscopy and Atom Probe Tomography[END_REF], the type of clusters present in the solid solution in the as-built condition has been clearly established. Cluster analysis revealed that two populations of clusters exist: i) Mg-Si coclusters with a Mg:Si ratio equal to 2 or above, and ii) Si-rich clusters free of Mg, with a Si content above 50 at%. These findings confirm that, despite the rapid cooling rate intrinsic to LPBF, shortrange clustering already occurs in the supersaturated solution of Al cells.

The presence of these clusters obviously plays an important role in the further precipitation of hardening phases if the microstructure is later submitted to a T5-type heat treatment, that is, involving no prior solution treatment but just a low-temperature ageing. Mg-rich clusters are expected to promote the formation of the equilibrium β-Mg2Si phase predicted by the ternary phase diagram. Meanwhile, the Si-rich clusters, which are twice the number of Mg-rich clusters, are expected to favour the formation of diamond-Si, as predicted by the ternary phase diagram.

Moreover, if a heat treatment is applied at moderate temperature (i.e., in the 120-170 °C range) with or without pre-ageing (i.e., below 100 °C), a sequence of metastability implying the formation of Guinier Preston-zones or β'' precipitates could be observed [START_REF] Zandbergen | Data analysis and other considerations concerning the study of precipitation in Al-Mg-Si alloys by Atom Probe Tomography[END_REF][START_REF] Torster | The influence of composition and natural aging on clustering during preaging in Al-Mg-Si alloys[END_REF][START_REF] Edwards | The precipitation sequence in Al-Mg-Si alloys[END_REF][START_REF] Geuser | 3D atom probe investigation of the early stages of precipitation in an Al-Mg-Si alloy[END_REF]. Hence, a T5-type heat treatment may result in precipitation hardening, involving precipitates commonly observed in the Al-Mg-Si system (i.e., β'', β', or β-Mg2Si) together with diamond-Si particles, which formation will be favoured by the existence of Si nanocrystals in eutectic regions and Si-rich clusters in the matrix. A detailed and systematic study of precipitation hardening kinetics starting from the as-built condition, which falls outside the scope of this paper, are required to reveal the hierarchy of phases to be formed and the associated mechanical properties for T5-type hardening treatments. It must also be mentioned that T5-type heat treatments have already been shown to produce significant hardening compared to T6-type heat treatments (involving a prior solution heat treatment) in other alloy systems [START_REF] Montero Sistiaga | Changing the alloy composition of Al7075 for better processability by selective laser melting[END_REF].

Insofar as processing parameters may play a critical role in the final designed microstructure, further investigations are required to identify the exact correlations between these parameters and the particular microstructural features revealed by this work. These include the existence of an amorphous phase together with Si nanocrystals in eutectic regions and the strain regions in Al cells in the vicinity of eutectic regions. As a particularly important parameter, the temperature of the platform was set to 35 °C to avoid significant phase decomposition and softening, which are expected to occur if this temperature is raised to 180-200 °C, as would typically be done to minimise residual stress in large pieces of material in the as-built state. A low temperature of the platform clearly promotes a high cooling rate and formation on nano-scale periodic gradients, but may be detrimental for residual stress [START_REF] Zhao | Comparison of residual stresses obtained by the crack compliance method for parts produced by different metal additive manufacturing techniques and after friction stir processing[END_REF].

Conclusion

Elaboration of alloys by means of SLM/LBPF offers new ways to guide the microstructural design. One of the main advantages of this method is its high cooling rate, which allows the trapping of alloy systems in non-equilibrium states. Such states can later serve as the basis of smart design using further heat treatments or can lead to unusual properties in the as-built state. In this study, the fine microstructure inherited by the LPBF of an AlSi10Mg alloy was investigated. By means of various microscopy tools, the repetition of a periodicity has been revealed, which implies several scales (from hundreds of nanometres for Al cells to atomic clusters). High-resolution observations have revealed the existence of a glass state in eutectic areas, wherein short-range ordering of the diamond-Si structure could be observed. In these eutectic regions, early stages of phase separation could also be demonstrated by the presence of Si nanocrystals and by the existence of complex compositional fields determined by APT. The apparent very fast solidification of eutectic regions is found to involve a local strain in adjacent Al cells, which extends up to 100 nm on average. The recurrence of this observation produces the repetition of a periodic pattern inside former melt pools (eutectic regions first, surrounded by strain-hardened Al crystals, followed by strain-free Al crystals).

The supersaturated aluminium solid solution retained by the LPBF process was quantitatively investigated by APT. Two populations of clusters were identified: Mg/Si co-clusters and Mg-free Si clusters. Determining the role that these clusters may play in the selection of phases and on subsequent hardening during a precipitation treatment (T5 type) would require further investigation.

Figure 2 (

 2 Figure 2(a) shows the observation of a eutectic zone in the high-resolution TEM (HR-TEM).

Figure 1 :

 1 Figure 1 : (a) Bright FieldTEM image displaying Al cells separated by eutectic zones. White arrows point out lattice distortions in the vicinity of eutectic regions. (b) Large-angle annular dark field STEM image showing preferential location of dislocations in Al cells at the vicinity of eutectic regions.

Figure 2 :

 2 Figure 2 : Al-Si10Mg alloy in the as-built condition. (a) HR-TEM of a eutectic zone surrounded by two Al cells oriented along a [001] zone axis. This region dominated by an amorphous contrast contains nanocrystals as indicated by circles. (b) FFT of the whole image in (a). A diffuse circle of radius 3.2 nm -1 consistent with the spatial frequency associated with (111) planes of Si diamond structure is observed. A discontinuous circle drawn by symmetric spots of similar spatial frequencies is superimposed with the diffuse circle. (c) Enlarged HR-TEM view of the eutectic area. Circles highlight local ordering in the amorphous region.

Figure 3 :

 3 Figure 3 : APT analysis of a eutectic zone in the as-built state. (a) 3D reconstruction displaying only Si atoms (green points) and an isosurface of 25.5 at% of Si (green surface between region II and III). (b) Composition profiles calculated across the Si isosurface shown in (a). Three zones named I, II and III are identified.

Figure 4 :

 4 Figure 4 : APT analysis performed in an Al cell of the Al-Si10Mg alloy in the as-built condition. Mg and Si atoms are shown in the APT reconstruction.

  (a,b), clusters selected by considering the neighbourhood of Si or Mg atoms are displayed. The Mg:Si ratio as a function of the cluster size in Mg-rich clusters is plotted in Figure 6(c).Although the largest clusters exhibit a Mg:Si ratio close to 2, large discrepancies are observed for 13 smaller ones, with a significant Mg enrichment in some. On the contrary, Si-rich clusters do not contain Mg atoms in proportions superior to the nominal composition. Consequently, the Mg enrichment shown by the RDF calculated around the Si atoms is attributed to the Si atoms present in the Mg-rich clusters. For comparison, the composition in the Si-rich clusters is plotted as a function of their size, as shown in Figure6(d). The Si composition is larger than 50 at% on average. This corresponds to a drastic enrichment compared to the average content of Si in the solid solution (~3

Figure 5 :

 5 Figure 5 : Radial distribution functions calculated around (a) Mg or (b) Si atoms extracted from an APT analysis performed in an Al cell of the Al-Si10Mg alloy in the as-built condition.

Figure 6 :

 6 Figure 6 : Solute clusters selected by the cluster search algorithm applied on Si atoms (a) and Mg atoms (b) extracted from APT data. (c) Mg:Si ratio in clusters shown in (b). (d) Fraction of Si in clusters shown in (a).

Table 1 :

 1 Composition of the solid solution of the Al-Si10Mg alloy in the as-built condition

		Al	Si	Mg
	Composition (at%)	96.78 ± 0.01	3.08 ± 0.01	0.14 ± 0.01

Acknowledgements

P. Delroisse acknowledges the financial support of the FRIA, Belgium. A. Simar acknowledges the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement n716678). Juan Guillermo Santos Macías is acknowledged for providing the LPBF samples from his PhD thesis and useful discussions about them.

confirm that their data are available