Paraskevas Kontis
email: p.kontis@mpie.de

Edouard Chauvet

Zirong Peng

Junyang He

Alisson Kwiatowski

Da Silva

Dierk Raabe

Cathrine Tassin

Jean-Jacques Blandin

Stéphane Abed

Rémy Dendievel

Alisson Kwiatkowski Da Silva

Catherine Tassin

Baptiste Gault

Guilhem Martin
email: guilhem.martin@simap.grenoble-inp.fr

Atomic-scale grain boundary engineering to overcome hot-cracking in additively-manufactured superalloys

Keywords: Hot cracking, grain boundaries, electron beam melting, superalloys, liquid film

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Introduction

Additive manufacturing (AM) has a great potential for the production of novel engineering components for aerospace and power generation applications, where nickel-based superalloys are predominantly used [START_REF] Babu | Additive Manufacturing of Nickel Superalloys: Opportunities for Innovation and Challenges Related to Qualification[END_REF]. However, it is very challenging to produce safety-critical components by AM with zero-crack tolerance, yet the digitalisation inherent to AM promises large gains in manufacturing and repair efficiency [START_REF] Attallah | Additive manufacturing of Ni-based superalloys[END_REF]. The AM community currently invests great efforts to 3D print well-known superalloys compositions considered as non-weldable such as IN738 [START_REF] Engeli | Processability of different IN738LC powder batches by selective laser melting[END_REF][START_REF] Zhong | Boundary liquation and interface cracking characterization in laser deposition of Inconel 738 on directionally solidified Ni-based superalloy[END_REF][START_REF] Cloots | Investigations on the microstructure and crack formation of IN738LC samples processed by selective laser melting using Gaussian and doughnut profiles[END_REF], CMSX-4 [START_REF] Ramsperger | Microstructure of the Nickel-Base Superalloy CMSX-4 Fabricated by Selective Electron Beam Melting[END_REF], CM247LC [START_REF] Carter | The influence of the laser scan strategy on grain structure and cracking behaviour in SLM powder-bed fabricated nickel superalloy[END_REF] among others [START_REF] Murr | Microstructures of Rene 142 nickel-based superalloy fabricated by electron beam melting[END_REF][START_REF] Lee | Asymmetric Cracking in Mar-M247 Alloy Builds During Electron Beam Powder Bed Fusion Additive Manufacturing[END_REF]. These alloy grades, which have been classified as non-weldable due to their Ti and Al contents [START_REF] Attallah | Additive manufacturing of Ni-based superalloys[END_REF] usually imply formation of large volume fractions of γ'-precipitates and were observed to undergo severe cracking when welded or AM built. Amongst the possible technologies to fabricate parts highly susceptible to cracking, selective electron-beam melting (S-EBM) is one of the most promising. The main advantage is the preheated powder bed (typically around 1000°C for nickel-based superalloys) resulting in the reduction of thermal stresses arising from cooling. This pre-heating however makes the thermal history of the sample more complex and sometimes difficult to control. In addition, S-EBM offers precise control over the melting strategy and hence enables tuning of the microstructure by modifying the thermal gradient and solidification velocity. Pragmatic approaches have been deployed, mainly on the weldable Inconel 718 grade, to adjust parameters to modify the direction of the main thermal gradient with respect to the building direction and the solidification velocity [START_REF] Helmer | Grain structure evolution in Inconel 718 during selective electron beam melting[END_REF][START_REF] Helmer | Additive manufacturing of nickel-based superalloy Inconel 718 by selective electron beam melting: Processing window and microstructure[END_REF][START_REF] Dehoff | Site specific control of crystallographic grain orientation through electron beam additive manufacturing[END_REF][START_REF] Dehoff | Crystallographic texture engineering through novel melt strategies via electron beam melting: Inconel 718[END_REF][START_REF] Koepf | 3D multi-layer grain structure simulation of powder bed fusion additive manufacturing[END_REF][START_REF] Koepf | Numerical microstructure prediction by a coupled finite element cellular automaton model for selective electron beam melting[END_REF][START_REF] Raghavan | Localized melt-scan strategy for site specific control of grain size and primary dendrite arm spacing in electron beam additive manufacturing[END_REF][START_REF] Raghavan | Numerical modeling of heat-transfer and the influence of process parameters on tailoring the grain morphology of IN718 in electron beam additive manufacturing[END_REF]. Successful attempts have been reported in the literature. Helmer et al. [START_REF] Helmer | Grain structure evolution in Inconel 718 during selective electron beam melting[END_REF][START_REF] Helmer | Additive manufacturing of nickel-based superalloy Inconel 718 by selective electron beam melting: Processing window and microstructure[END_REF] showed that the grain size and grain morphology can be modified by appropriate changes of the melting parameters. Dehoff et al. [START_REF] Dehoff | Site specific control of crystallographic grain orientation through electron beam additive manufacturing[END_REF][START_REF] Dehoff | Crystallographic texture engineering through novel melt strategies via electron beam melting: Inconel 718[END_REF] have demonstrated that a spatially controlled crystallographic texture within Inconel 718 components can be achieved. Such microstructure engineering approach was further investigated by Koepf et al. [START_REF] Koepf | 3D multi-layer grain structure simulation of powder bed fusion additive manufacturing[END_REF][START_REF] Koepf | Numerical microstructure prediction by a coupled finite element cellular automaton model for selective electron beam melting[END_REF] and Rhagavan et al. [START_REF] Raghavan | Localized melt-scan strategy for site specific control of grain size and primary dendrite arm spacing in electron beam additive manufacturing[END_REF][START_REF] Raghavan | Numerical modeling of heat-transfer and the influence of process parameters on tailoring the grain morphology of IN718 in electron beam additive manufacturing[END_REF].

Cracks developing during S-EBM of non-weldable alloys are often qualified as hot cracks because cracking occurs in presence of liquid films, as is the case for the grade investigated in the present work [START_REF] Chauvet | Hot cracking mechanism affecting a nonweldable Ni-based superalloy produced by selective electron Beam Melting[END_REF]. The combination of liquid films and thermal stresses arising from shrinkage and cooling leads to the development of hot cracks. Hot cracks were found to systematically propagate along high angle grain boundaries (HAGBs) while low angle grain boundaries (LAGBs) were not susceptible to hot cracking, similarly to what was reported in the welding literature [START_REF] Wang | Solidification cracking of superalloy single-and bi-crystals[END_REF]. This difference of cracking sensitivity between HAGBs and LAGBs was rationalized using the theoretical model of Rappaz et al. [START_REF] Rappaz | A new hot-tearing criterion[END_REF] that describes the last stage of solidification. Relying on the concept of repulsive (stabilization of liquid films) and attractive boundaries (dendrite coalescence), it was explained that the coalescence undercooling was larger for HAGBs than for LAGBs, which leads to liquid films stable at lower temperatures along HAGBs. The latter observation suggests that producing samples without HAGBs can be considered as a possible route to achieve crack-free parts. Körner et al. [START_REF] Körner | Microstructure and Mechanical Properties of CMSX-4 Single Crystals Prepared by Additive Manufacturing[END_REF] and Chauvet et al. [START_REF] Chauvet | Producing Ni-base superalloys single crystal by selective electron beam melting[END_REF] took advantage of the digital control of the melting strategy to grow single crystals of nonweldable nickel-based superalloys by S-EBM. Interestingly, the single crystals grown by S-EBM are free of cracks, in agreement with the observation that cracks propagate exclusively along HAGBs. However, in the work presented in ref. [START_REF] Chauvet | Hot cracking mechanism affecting a nonweldable Ni-based superalloy produced by selective electron Beam Melting[END_REF], the exact mechanism leading to cracking observed along HAGBs was still under debate, i.e. solidification cracking vs. liquation cracking. Identifying the root causes of cracking requires a detailed investigation of solutes segregating along HAGBs at the near-atomic scale. Understanding of the underlying interface decoration and decohesion mechanisms should thus help to guide strategies to avoid the development of those critical defects and allow to produce crack-free parts.

Here, we perform a detailed microstructural characterization by scanning electron microscopy (SEM) and atom probe tomography (APT) of cuboidal samples fabricated by S-EBM from nonweldable crack sensitive superalloy powders [START_REF] Murr | Microstructures of Rene 142 nickel-based superalloy fabricated by electron beam melting[END_REF], which we use to guide thermodynamic calculations. Our new insights enable us to identify the atomic-scale cause of cracking along HAGBs in the columnar microstructure formed by S-EBM. We show that cracks are caused by segregation-induced liquation at HAGBs decorated by segregated films enriched in Cr, Mo and B. Interestingly, B is originally added to enhance grain boundary cohesion. The flexibility in processing offered by S-EBM allows us to demonstrate that by controlling the interface area, in particular the grain boundary density, we can limit solute enrichment in the intergranular region and prevent critical liquation, alleviating cracking susceptibility. Increasing drastically the interface area not only helps to limit solute enrichment at HAGBs but also to contribute to better distribute thermal stresses that act as the mechanical driving force for hot cracking. This grain boundary engineering strategy is demonstrated in two new crack-free builds, respectively exhibiting an equiaxed and a fine-columnar microstructure (grain width < 100 μm). Shedding light on fundamental aspects of cracking allows us to derive atomic-scale inspired digital metallurgy design pathways to enable application of these alloys in safety-critical applications, such as blades in aero-engines.

Experimental procedures

Powder characteristics

The material investigated is a non-weldable nickel-based superalloy. The pre-alloyed powder was produced by gas atomization and provided by ERASTEEL. The powder composition was measured by thermal-conductivity-infrared for the C and O, and by inductively-coupled plasma-atomic emission spectroscopy (ICP-AES) for the other elements. The chemical composition is reported in at.% in Table 1, listing the most relevant key elements.

It is known that in some cases the bulk composition can be altered after the deposition, such as in the case of Al which is sensitive to evaporation when processing Ti-6Al-4V alloy by S-EBM [START_REF] Juechter | Processing window and evaporation phenomena for Ti-6Al-4V produced by selective electron beam melting[END_REF]. However, chemical analysis performed on the produced bulk samples revealed no substantial alteration of the bulk composition after S-EBM processing. The as-received powder batch exhibits mostly a spherical morphology with some satellites. The powder characteristics are summarized as follows: D50 = 75 μm, a powder bed density of 53.6% and a flow time of 16.0 ± 0.1 s for 50 g of powders going through a 2.54 mm diameter orifice (Hall flowmeter).

Selective electron beam melting

Samples with dimensions 23 x 23 x 30 mm (width x length x height) were built in an ARCAM A1 Electron Beam Melting machine operating at 60 kV accelerating voltage under a controlled pressure of He set to 2.10 -3 mbar, with the layer thickness set to 50 μm. Two different versions of the same composition were built. The first one was produced using the automatic mode while the second one was melted using the manual mode. The automatic mode resulted in a sample with relatively coarse columnar-shaped grains and it will be denoted from now as cracked columnar sample. The second sample was built with a higher scanning speed and a reduced hatch spacing resulting in a reduced linear energy (0.119 J/m²) when compared to the one employed in the automated mode (0.5-0.65 J/mm²). The significant overlap of the beam scanned multiple times over adjacent locations leads to an elongated melt pool perpendicularly to the hatching [START_REF] Helmer | Grain structure evolution in Inconel 718 during selective electron beam melting[END_REF][START_REF] Helmer | Additive manufacturing of nickel-based superalloy Inconel 718 by selective electron beam melting: Processing window and microstructure[END_REF]. This hinders epitaxial growth of new grains on the grains from the layer underneath and leads to an equiaxed microstructure [START_REF] Helmer | Additive manufacturing of nickel-based superalloy Inconel 718 by selective electron beam melting: Processing window and microstructure[END_REF][START_REF] Helmer | Grain structure evolution in Inconel 718 during selective electron beam melting[END_REF]. This sample is denoted as crackfree with equiaxed grains. All the used processing conditions were preliminary optimized to achieve dense samples (density >99.8%) with no lack-of-fusion defects. Table 2 summarizes the main parameters used to build the two samples. The building direction is denoted as Z.

A build plate made of a polycrystalline hot-rolled 10 mm thick stainless steel plate, grade EN 1.4307 was used during the production of all the samples. Although, its mechanical resistance i.e. creep, is sufficient to allow us to run stable builds, after depositing the samples it was slightly deformed. Diffusion between the substrate and the deposited material likely occurs over limited distance, however in this study only the upper parts of the samples were investigated which are not affected by this diffusion.

In each case, the build plate was heated at 1050°C and the preheating temperature was maintained at 1050°C throughout the build and the focus offset set to 20 mA during the melting steps. When operated in automatic mode, the melting parameters, such as caused by the beam power and the scanning speed, were adjusted as a function of the geometry through the use of automated functions such as the speed function or turning point function into the software EBM Control 3.2, see Table 2 for more details. In the case of the manual mode, the power and scan speed were imposed and do not depend on the geometry. In both cases, the melting strategy consisted in scanning the area defined by the CAD in a snake-like manner with a line order set to 1 and the scanning direction was also rotated by 90° after every layer. -Speed function: a function that changes automatically the scan speed as a function of the beam power. The higher the speed function, the higher the scan speed. For cuboidal samples, the scan length is constant, hence the beam power is constant.

-Turning point function: a function that further changes the beam speed to account for edge effects. To reduce the applied energy near the edge, this function is used to increase the beam speed as it comes to an edge.

-Thickness function: a function that modifies the beam speed to compensate for the lower amount of energy required in overhangs based on the distance down to powder. This function was not operating for cuboidal geometries.

Mechanical testing

Micro-specimens with a gauge length of 3 mm, a width of 1 mm, and a thickness of 0.8 mm were machined by Electron Discharge Machining (EDM) from the as-built S-EBM samples, with the load axis normal to the building direction Z. Tensile tests were performed at room temperature using an ADAMEL DY35 universal testing machine equipped with a 2kN load cell at a strain rate of 5.10 -4 s -1 . The strain was measured by digital image correlation (GOM-ARAMIS software). One side of the gauge length of the micro-tensile samples was preliminary covered with a speckle made of black and white paintings. Images were recorded during the tensile tests at a frequency of 1 Hz.

Scanning electron microscopy

The as-build samples were cut along the build direction Z and they were mechanically polished with abrasive media to a 0.04 μm colloidal silica finish for microstructural characterization. Optical microscopy was used for observations at large scale whereas a Zeiss Merlin field emission gun scanning electron microscope (FEG-SEM) was used in backscattered mode for fine microstructural observations. Electron backscattered (EBSD) analysis was performed in a Zeiss Ultra FEG-SEM operated at 20kV acceleration voltage with a step size of 2 μm. Data for maps of 1mm 2 size were collected using the TSL-OIM software. A grain was defined as a group of pixels containing at least 10 pixels, including multiple rows, and having a tolerance angle of 5°.

Atom probe tomography

In order to study the segregation of solutes at grain boundaries, specimens for atom probe tomography (APT) were prepared by following a site specific lift-out protocol outlined in Ref. [START_REF] Thompson | In situ sitespecific specimen preparation for atom probe tomography[END_REF], using a FEI Dual Beam FIB Helios 600i. The APT specimens were extracted from random high angle grain boundaries from both samples, following the procedures described in Ref. [START_REF] Kontis | On the effect of boron on grain boundary character in a new polycrystalline superalloy[END_REF]. APT specimens were analyzed using a Cameca LEAP 5000 XR instrument operating in a laser mode with pulse rate at 125 kHz, pulse energy 0.4 pJ and temperature 60 K. The commercial package IVAS 3.8.2 was used for data reconstruction and analyses. In addition, the segregation at grain boundaries as observed by APT was further analyzed by making use of the method described in Ref. [START_REF] Peng | An Automated Computational Approach for Complete In-Plane Compositional Interface Analysis by Atom Probe Tomography[END_REF].

Finally, in the case of the sample with equiaxed grains, correlative Transmission Kikuchi diffraction (TKD) and APT analysis was performed on the APT specimens to confirm the presence of a grain boundary prior to APT experiments. TKD data were obtained with a Zeiss Merlin FEG-SEM equipped with a Bruker Optimus detector. For the measurement acceleration voltage of 30kV and probe current of 1.5nA was used with a step size of 5nm at 70 fps.

Thermodynamic calculations

To evaluate the effect of the content of B, Cr and Mo on the solidification path, thermodynamic calculations were performed using the Thermo-Calc software making use of the TTNI8 database dedicated to nickel-based superalloys [START_REF] Andersson | Thermo-Calc & DICTRA, computational tools for materials science[END_REF]. Calculations of the solidification path assuming constitutive segregation based on the Scheil-Gulliver model were performed including the liquid,  and ' phases considering both, excluding and including the formation of M2B borides. No diffusion in the solid state and infinite diffusion in the liquid was assumed for the Scheil-Gulliver model.

Results

Microstructural characterization: cracked columnar sample

The first build, achieved by operating in automatic mode, is shown in Figure 1(a). A columnar microstructure develops with numerous thin grains, which progressively becoming coarser from approximately the building height of 5 mm, as evidenced by the EBSD maps in Figure 1(b-d). The sample exhibits a strong <001>-fiber texture typical of directionally solidified superalloys and FCC alloys. Cracked HAGBs are often observed (Figure 1(e))in the upper part of the build (height > 10 mm), (Figure 1(f)). The opened fracture surface in Figure 1(f) reveals a dendritic morphology typical of hot cracking [START_REF] Rappaz | A new hot-tearing criterion[END_REF], which implies that a continuous liquid film had covered almost the sample's entire cross section. Cracking only takes place at high-angle grain boundaries [START_REF] Körner | Microstructure and Mechanical Properties of CMSX-4 Single Crystals Prepared by Additive Manufacturing[END_REF] and building height greater than 10 mm in the build, where the columnar grains are wider than 100 μm. LAGBs, consisting of dislocation arrays, are systematically found to be crack-free. Importantly, cracks do not form or propagate through the final melted layer. This means that the final melted layer is the only region where the microstructure inherited from solidification is unaffected by subsequent layers or preheating at the top of the build, as revealed by Figure 2. Particles with bright contrast are often observed at cracked HAGBs in backscattered electron micrographs. Figure 3(a-c) shows a decorated HAGB between grains containing the typical /' microstructure. Atom probe tomography (APT) reveals that these particles are M2B borides, containing almost 40 at.% Mo and 20 at.% Cr as reported in Table 3, consistent with previous reports [START_REF] Chauvet | Hot cracking mechanism affecting a nonweldable Ni-based superalloy produced by selective electron Beam Melting[END_REF][START_REF] Cadel | Atom probe tomography investigation of the microstructure of superalloys N18[END_REF]. Not all HAGBs appear cracked, but most HAGBs bearing coarse borides are cracked. By contrast, LAGBs were not found to be cracked and were not decorated by M2Bborides. Figure 3(a) shows for instance cracks on either side of the region along the boundary where the boride formed and coarsened. Figure 3(d) shows that recrystallized regions exist near the borides, which are the sign of either high thermal stresses causing local plastic deformation, thereby storing dislocations that subsequently induce recrystallization, or of the coarsening of the borides [START_REF] Kontis | Microstructural degradation of polycrystalline superalloys from oxidized carbides and implications on crack initiation[END_REF][START_REF] Kontis | Influence of composition and precipitation evolution on damage at grain boundaries in a crept polycrystalline Ni-based superalloy[END_REF]. The local grain boundary composition affects the stability of the liquid film and subsequently the hot crack formation, resulting in some cases in noncontinuous cracks where isolated sections of solid bound the two grains as illustrated by The presence of borides at cracked HAGB is a strong indication that the segregated films contained a higher level of B and boride-formers such as Mo and Cr prior to boride formation. This is confirmed by the APT results in respectively. Besides, C and Si were found to segregate to the grain boundary up to 0.5 and 0.2 at.%, respectively, but no specific role on the hot cracking was observed from their presence at the grain boundary. The segregation behavior observed here is in agreement with previous reports [START_REF] Kontis | On the effect of boron on grain boundary character in a new polycrystalline superalloy[END_REF][START_REF] Bagot | An Atom Probe Tomography study of site preference and partitioning in a nickel-based superalloy[END_REF][START_REF] Alam | The early stages of ageing in the Nibased superalloy[END_REF]. Segregation of Zr and Hf at the grain boundary was not observed, instead they were found to partition within the γ', as shown in Supplementary Figure 1(a).

Figure 7a

shows an APT reconstruction from a HAGB from the crack-free sample with equiaxed grains. TKD was performed on the APT specimen prior to the analysis, shown in Figure 7(a), and confirms the high-angle nature of the grain boundary (53° misorientation). One-dimensional composition profiles across the grain boundary show clear segregation of B, C, Mo, and Cr segregate 7.0, 0.5, 25.0 and 30.0 at.%, respectively. In this case, the amount of B, Mo and Cr at the grain boundary is higher than in the cracked columnar sample (B, Mo, and Cr segregate to the grain boundary up to 2.5, 10.0 and 30.0 at.%) and in samples of a similar grade produced through a powder metallurgical route [START_REF] Cadel | Atom probe tomography investigation of the microstructure of superalloys N18[END_REF][START_REF] Lemarchand | Investigation of grain-boundary structure-segregation relationship in an N18 nickel-based superalloy[END_REF].

Figure 8a shows a second APT analysis approximately 2 μm farther along the same grain boundary. This is also confirmed by the TKD analysis conducted prior to APT analysis. Onedimensional composition profiles across the grain boundary, as indicated by arrow #1 in Figure 8a, reveal segregation of B, C, Mo and Cr up to 4.5, 0.5, 15.0 and 26.0 at.%, respectively. It can be seen that the amount of solutes segregating to the same grain boundary changes over a distance lower than a few micrometers. In particular, in the grain boundary segment shown in Figure 8, the presence of the segregated thin film consumes grain boundary solutes resulting in lower amounts of solutes compared to the grain boundary segment being approximately 2 μm farther and that is shown in Figure 7. Similar to the columnar cracked sample Zr and Hf were found to partition to γ' and did not segregate at the grain boundary, as shown in Supplementary Figure 1(b). However, these thin discontinuous grain boundaries segregated films are not as detrimental as the hot cracks observed in the cracked columnar sample, as revealed by small-scale tensile tests performed on specimens machined from the as-produced samples. Figure 10 shows the engineering stress vs. engineering strain curves resulting from 3 tensile tests for the cracked columnar and crack-free equiaxed microstructures. The coarse-grained columnar samples show a very brittle behavior, indicative of samples that already contain critical defects. The tensile tests performed on the crack-free samples with equiaxed grain structure show a vastly improved behavior from approximately 5.0 % in the cracked columnar sample up to between 20.0 and 27.0 % engineering strain, with no tendency for early fracture, due to the absence of hot cracks.

The segregated film shown in

Figure 10: Engineering strain vs. engineering stress curves. Three micro-specimens with a gauge length of 3 mm, a width of 1 mm, and a thickness of 0.8 mm were tested for the cracked columnar microstructure and three others for the crack-free equiaxed microstructure. The load axis was normal to the building direction Z.

Thermodynamic calculations

To evaluate the influence of the content of B, Cr and Mo on the solidification path, thermodynamics calculations were performed using Thermo-Calc software making use of the TTNI8 database dedicated to nickel-based superalloys [START_REF] Andersson | Thermo-Calc & DICTRA, computational tools for materials science[END_REF]. Calculations of the solidification path based on the Scheil-Gulliver model were performed including the liquid,  and ' phases and excluding or including the formation of M2B borides, as reported in Figure 11(

Discussion

Grain boundary segregation and boride formation

Segregation to grain boundaries may originate in AM first from solidification by sweeping of solutes during grain growth as new layers are deposited, and second by solid-state diffusion as the sample is maintained at high temperature (in S-EBM a heated powder bed is used). The intergranular films get enriched in solutes, such as Cr, Mo and B, during the building process, because of remelting and most likely solid-state diffusion, particularly of fast diffusers such as B [START_REF] Kontis | On the effect of boron on grain boundary character in a new polycrystalline superalloy[END_REF]. HAGBs accommodate larger amounts of solutes than LAGBs [START_REF] Herbig | Atomic-Scale Quantification of Grain Boundary Segregation in Nanocrystalline Material[END_REF], partly due to lower their relatively higher interfacial energy [START_REF] Chan | Study of energy vs misorientation for grain boundaries in gold by crystallite rotation method-II. Tilt boundaries and mixed boundaries[END_REF].

Figure 4, Figure 7 and Figure 8 show clear segregation of B, Mo, and Cr to the grain boundaries. Under non-equilibrium conditions, such as experienced during S-EBM, thermodynamic calculations of the first solidification event predict a substantial enrichment of B, Mo and Cr in the liquid as the temperature decreases, as reported in Figure 11(c). The enrichment predicted by the Scheil-Gulliver calculations is however likely insufficient to form borides during the first solidification event, which is supported by the absence of borides in the last deposited layer. Upon several remelting events, as B gets more enriched and thus concentrated, a critical composition of boride-formers is finally reached and borides can nucleate. They can likely form in the liquid or heterogeneously in the solid state, and coarsen quickly as HAGBs are fast diffusing paths.

The small off-stoichiometric borides observed in the sample with equiaxed grains are an indication that the borides form and grow progressively during the build, and those observed here, albeit small, resulted from multiple reheating/remelting events. These small borides can thus be interpreted as early-stage variants of the larger borides observed in the coarse-grained columnar sample. The composition profile shows an enrichment of Co up to 18.0 at.% at the interface between' and the boride-precursor compared to 10.0 at.% within the ' precipitate and 5.0-10.0 at.% within the off-stoichiometric borides. This indicates outward Co diffusion from the boride towards the ' precipitate. Fully developed borides analyzed in the coarsegrained columnar sample contain only approx. 2 at.% Co, while these precursors still contain approximately 5.0 to 10.0 at.%. Also these findings support the assumption that we observed here a transient state. In cases where borides do not deplete the film in B, Mo and Cr, the high content in these boride-forming solutes in the last solidified liquid films lowers the alloy's solidus potentially significantly, as indicated by the results reported in Figure 11(a) and 11(c).

The growth of borides consumes solutes, which, as indicated by thermodynamic calculations, increases the local solidus near the boride by locally decreasing the content of solutes such as B and Mo, as proven in Figure 9. In such a case, isolated sections of solid binding between two adjacent grains appear within the liquid film, as revealed in Figure 3(a). This finding illustrates the direct influence of the local partition effects and hence of the local solute composition content on the solidification, and hence on the cracking susceptibility.

Hot cracking caused by grain boundary-segregation induced liquation

Figure 1(f) gives strong indication that cracks are caused by interfacial liquation along some of the grain boundaries and Figure 2 demonstrates that the cracks do not originate directly from the first solidification event since no cracks propagate through the last melted layer. Thermodynamic calculations demonstrate a progressive enrichment in critical solutes within the liquid film during the last stage of the first solidification event. The characterization by APT of the films observed along HAGBs confirms a significant enrichment in these same critical solutes, namely Cr, Mo and B, which can be further accentuated by both successive remelting and solid-state diffusion. This is particularly true for fast diffusing elements, such as B.

Regarding the cracking mechanism evolving during the building process, over the course of the deposition of the subsequent layers, a segregated film at a HAGB can turn into a liquid film. The drop in the solidus caused by the progressive enrichment in solute is referred to as "segregation induced liquation" [START_REF] Kou | Welding Metallurgy[END_REF]. The difference in volume between the liquid and solid phase associated with the solidification, i.e. the shrinkage effect, as well as thermal stresses caused by rapid cooling provide the mechanical driving forces for the development of hot cracks [START_REF] Babu | Joining of nickel base superalloy single crystals[END_REF]. These local thermal stresses combined with segregation-driven grain boundary liquation cause hot cracking [START_REF] Ojo | Contribution of constitutional liquation of gamma prime precipitate to weld HAZ cracking of cast Inconel 738 superalloy[END_REF][START_REF] Ojo | Heat affected zone liquation cracking in electron beam welded third generation nickel base superalloys[END_REF]. The building history of the cracked columnar sample that leads to cracking is summarised in the schematic in Figure 12. Ultimately, hot cracking requires a condition setting where concentration in the liquid reaches a critical value, which appears close to the critical composition to form borides, in combination with the solidification stresses.

B is usually added to superalloys to increase GB cohesion [START_REF] Tytko | Microstructural evolution of a Ni-based superalloy (617B) at 700 °C studied by electron microscopy and atom probe tomography[END_REF] and limit damage at GBs under creep conditions. However, here it acts detrimental and promotes hot cracking as it depresses the solidus temperature, hence stabilize liquid films to lower temperatures. The limited number of grain boundaries in columnar samples will tend to have a more highly concentrated and continuous films extending over several grains, which appears to be highly detrimental to the structural integrity of the build. The typical criterion for non-weldability, namely the content of (Ti+Al) [START_REF] Attallah | Additive manufacturing of Ni-based superalloys[END_REF], does not seem to apply here. In the alloy that we investigated, this criterion is superseded by the content of B, Cr and Mo found at HAGBs. Ultimately, HAGBs crack because (i) the films are continuous and extend over several mm and (ii) the local composition of the segregated films allows the liquid to remain stable to relatively lower temperatures, hence causing grain boundary liquation during the deposition of the subsequent layers. Our observations imply that a bulk-criterion may not allow to appropriately depict near-atomic-scale processes. It is also known that Zr promotes hot cracking in nickel-based superalloys produced by casting [START_REF] Heydari | Hot tearing in polycrystalline Ni-based IN738LC superalloy: Influence of Zr content[END_REF][START_REF] Zhou | Effect of grain boundary fraction on castability of a directionally solidified nickel alloy[END_REF][START_REF] Grodzki | Effect of B, Zr, and C on Hot Tearing of a Directionally Solidified Nickel-Based Superalloy[END_REF][START_REF] Zhang | Effect of Zr and B on castability of Ni-based superalloy IN792[END_REF] and AM processes [START_REF] Cloots | Investigations on the microstructure and crack formation of IN738LC samples processed by selective laser melting using Gaussian and doughnut profiles[END_REF]. Although Zr is added in the bulk composition of the investigated alloy (0.02 -0.025 at.%), APT revealed no segregation of Zr at the grain boundary. Our observation on Zr is consistent with other studies performed by Cadel et al. [START_REF] Cadel | Atom probe tomography investigation of the microstructure of superalloys N18[END_REF] and Lemarchand et al. [START_REF] Lemarchand | Investigation of grain-boundary structure-segregation relationship in an N18 nickel-based superalloy[END_REF]. By contrast, Zr was found to partition to the γ' phase for both columnar cracked and equiax crack-free samples, as shown in Supplementary Figure 1. However, in a different nickel-based superalloy, Zr was found to segregate at the grain boundary [START_REF] Cloots | Investigations on the microstructure and crack formation of IN738LC samples processed by selective laser melting using Gaussian and doughnut profiles[END_REF]. Besides, significant interactions between Zr and B were recently reported during casting [START_REF] Grodzki | Effect of B, Zr, and C on Hot Tearing of a Directionally Solidified Nickel-Based Superalloy[END_REF]. In order to rationalize the interactions between the different alloying elements in such chemically complex metallic systems, further detailed investigations are required which are outside the scope of this present work.

Strategies for additive manufacturing of crack-free superalloys components

Better understanding and quantitative mapping of solute segregation to grain boundaries allows us to derive strategies to avoid cracking in additively manufactured superalloy parts.

Modulating solute segregation at grain boundaries allows to better control liquation and better distribute the thermal stresses associated to solidification and rapid cooling. This can be achieved by controlling the total interfacial area. This means that, depending on the bulk concentration of critical solutes, one has to adjust the overall interfacial area to gain control over their segregation to HAGBs in order to avoid liquation.

Interestingly, our APT results show higher solute enrichment along HAGBs in the crack-free sample with equiaxed grains compared to the ones in the cracked columnar sample. At first sight, it could be considered as not consistent with our argument stating that increasing the interfacial area should result in a less concentrated thin segregated films in critical solutes, i.e. the ones reducing the solidus temperature. The distribution of solutes at larger interfacial are would then allow to limit critical grain boundary segregation that can lead to liquation in presence of thermal stresses. However, those results have to be considered in light of the presence of coarse micron-sized borides that consume large quantities of critical solutes such as B, Mo and Cr. In the cracked sample with columnar grains we have extracted APT specimens in the immediate vicinity of coarse borides. We show how the precipitation of borides along HAGB and the associated partitioning of grain boundary solutes into these particles can affect locally the grain boundary segregation. Our results suggest that prior to boride formation, HAGBs were likely decorated by a continuous and highly segregated film, which increases the liquation susceptibility. However, this contradicts our observations at HAGBs in the sample with equiaxed grains, where no borides and no cracks were observed, only discontinuous segregated films. In the equiaxed sample, the grain boundary enrichment in B, Cr and Mo had also slowed down as solutes are spread over a wider area and must diffuse over longer distances to reach a high local composition. Conversely to the cracked columnar sample, the grain boundary area in the equiaxed samples translates into discontinuous segregated films as evidenced in Figure 6(b). In addition, the presence of more interfaces in the equiaxed version helps to better accommodate solidification shrinkage and thermal stresses, hence the likelihood of crack initiation is significantly reduced in comparison with a microstructure made of coarse columnar grains.

It becomes apparent that a strategy for AM produced crack-free superalloys should have good control of the total interfacial area of the produced component. This will prevent from reaching the critical composition for the formation of detrimental continuous liquid films and undesirable local thermal stresses over very few interfaces.

Based on this strategy aiming at controlling carefully the interfacial area, it would be possible to produce a crack-free columnar sample, by once again taking advantage of the digital control of the melting strategy offered by S-EBM, to achieve a critical grain width that leads to crackfree samples. Figure 13 shows the evolution of grain width as a function of building height for the cracked columnar and crack-free equiaxed sample. It can be seen that for a grain width of approximately 20 μm, the equiaxed sample is crack free. Interestingly, the cracked columnar is also free of cracks over the first roughly 10 millimetres of the build which corresponds to a grain width lower than 100 microns. In other words, by producing a finer columnar microstructure with grain width < 100 μm, one should get samples free of cracks.

We have produced a third sample which was built by using a relatively low power and slow scan speed (linear energy of 0.3 J/mm²) while maintaining a line offset of 0.1 mm. The low power maintains a relatively small melt pool that hinders grain coarsening and limits grain selection. As a result, the grain width remains small, approximately 45 μm as shown in Figure 13 along the entire height of the build. An overview of this fine columnar microstructure shows no hot cracks, as revealed in Figure 14.

A possible alternative route would consist in adjusting the composition to achieve lower level of solutes along HAGBs that decrease the solidus for instance or to form a continuous layer of e.g. borides to strengthen the grain boundaries [START_REF] Kontis | On the effect of boron on grain boundary character in a new polycrystalline superalloy[END_REF][START_REF] Kolb | On the grain boundary strengthening effect of boron in γ/γ′ Cobalt-base superalloys[END_REF].

Conclusions

To conclude, we combined microstructural observations by optical and electron microscopy with near-atomic scale compositional investigation of critical microstructural features by atom probe tomography, and thermodynamic calculations to study additively manufactured builds from a non-weldable nickel-based superalloy produced by S-EBM. Our approach allowed us to provide fundamental insights into the dynamic interplay, at the nano-scale, of the local composition in critical regions, such as HAGBs, that leads to segregation-induced liquation cracking.

The new fundamental understanding of the root cause of cracking set us on the path to tune the atomic-scale distribution of critical solutes, such as B, Cr and Mo, in particular along HAGBs. This was made possible by the high level of control over the melting strategy offered by the S-EBM process. Through modifications in the melting strategy, we adjusted the geometry of the melt pool which turned the coarse-grained columnar microstructure sensitive to liquation cracking into either small grained equiaxed (grain width approximately 20 μm) or fine columnar microstructures (grain width approximately 50 μm). Increasing the interfacial area not only prevents high concentration of boride-forming elements that cause liquation, and hence avoids cracking but also helps to distribute thermal stresses over more interfaces.

Figure 1 :

 1 Figure 1: Overview of the cracked columnar sample. a) Optical micrograph of the entire height showing a graded microstructure along the building direction. b)-d) EBSD IPF-Z (building direction) maps illustrating the columnar grain width evolution along the building direction and the strong crystallographic fiber texture. e) Enlarged view of a HAGB (misorientation 26°) affected by hot cracking in the upper region of the specimen. f) Fracture surface after tensile testing giving evidence of the presence of liquid films.

Figure 2 :

 2 Figure2: Optical micrograph towards the top of the cracked columnar sample highlighting that cracks do not propagate through the last melted layer. Note that the dendritic microstructure can only be seen in the final melted region while it is erased in the underlying layer because the complex thermal history acts as a homogenization treatment.

Figure 3 (

 3 a) and Figure 3(b).

Figure 3 :

 3 Figure 3: a) Borides forming solid bridges across a high-angle grain boundary in the cracked columnar sample. b) Higher magnification backscattered electron micrograph from a cracked grain boundary of the columnar grain shape sample containing borides. c) Backscattered electron micrograph from a grain boundary of the cracked columnar grain shape sample containing borides and d) EBSD IPF-Z (building direction) map corresponding to the region denoted by the red dashed box in Figure 2c showing recrystallization in the vicinity of intergranular borides.

Figure 4

 4 obtained close to a cracked HAGB (misorientation of 26°) containing several relatively coarse borides. B, C, Mo, and Cr segregate to the grain boundary up to 2.5, 0.5, 10.0 and 30.0 at.%, respectively while Ni, Al and Co are depleted as readily visible in the composition profiles plotted in Figure 4(b) and (c)

Figure 4 :Figure 5 (

 45 Figure 4: a) Atom probe reconstruction from a random high angle grain boundary in the cracked columnar region. The γ/γ' interfaces are shown by an iso-composition surface encompassing regions in the data containing over 7.0 at.% Cr. The grain boundary is highlighted by an iso-composition surface with a threshold of 1.0 at.%. B and c) One-dimensional composition profiles across the γ'/GB/γ interface as denoted by arrow #1 in Figure 4a are plotted for the minor additions and main alloying elements. Error bars are shown as lines filled with color and correspond to the 2σ counting error.3.2 Microstructural characterization: crack-free sample with equiaxed grainsFigure5(a) shows the sample produced by adjusting the building parameters manually, with full control over the input power, scanning speed and hence melting strategy. The EBSD maps in Figure5(b-d) were obtained approximately at the same height as in Figure1, and they reveal a homogeneous microstructure with equiaxed grains exhibiting a random crystallographic texture with a maximum orientation density of only 1.8 times the random orientation distribution in the {001}-pole figure. Figure6(a) reveals only gas porosity[START_REF] Rappaz | A new hot-tearing criterion[END_REF] and no lackof-fusion-like defects, while Figure6(b) is a close-up of the typical /' microstructure within grains where no borides, no cracks or micro-voids at grain boundaries were found. However, a brightly imaging, discontinuous segregated film appears at HAGBs, shown in Figure6(b). That film was further investigated by APT.

Figure 6 (

 6 Figure 5(a)shows the sample produced by adjusting the building parameters manually, with full control over the input power, scanning speed and hence melting strategy. The EBSD maps in Figure5(b-d) were obtained approximately at the same height as in Figure1, and they reveal a homogeneous microstructure with equiaxed grains exhibiting a random crystallographic texture with a maximum orientation density of only 1.8 times the random orientation distribution in the {001}-pole figure. Figure6(a) reveals only gas porosity[START_REF] Rappaz | A new hot-tearing criterion[END_REF] and no lackof-fusion-like defects, while Figure6(b) is a close-up of the typical /' microstructure within grains where no borides, no cracks or micro-voids at grain boundaries were found. However, a brightly imaging, discontinuous segregated film appears at HAGBs, shown in Figure6(b). That film was further investigated by APT.

Figure 5 :

 5 Figure 5: Overview of the crack-free equiaxed sample. a) Optical micrograph of the entire height showing a homogeneous microstructure. b)-d) EBSD IPF-Z (building direction) maps illustrating grains with equiaxed structure. A1 and A2 are the X and Y scanning direction of the electron beam during the deposition.

Figure 6 :

 6 Figure 6: Backscattered electron micrographs from the crack-free with equiaxed grain sample: a) showing only gas pores in the microstructure and absence of intergranular cracks, b) showing a discontinuous segregated film at GBs.

Figure 8 (

 8 a) contains regions with a B content higher than 20.0 at.%, and Cr and Mo at 25-35 at.%, as revealed in Figure9(a). These are akin to off-stoichiometric boride precursors. Figures9(b-d) are two-dimensional composition maps calculated using the protocol outlined in Ref.[START_REF] Herbig | Atomic-Scale Quantification of Grain Boundary Segregation in Nanocrystalline Material[END_REF] for Mo, Cr and B, showing that, away from these precursors, Mo, Cr and B, are only enriched up to 6.0, 11.0 and 2.0 at.% respectively, 3-4 times lower than in Figure7(b) and Figure7(c). These results evidence how the consumption of solutes by the growth of the borides affects the grain boundary's composition.

Figure 7 :

 7 Figure 7: Atom probe reconstruction from a random high angle grain boundary from the crack-free equiaxed grain shape sample alongside an IPF map from TKD. The γ/γ' interfaces are shown with an isosurface with a threshold of 18 at.% Cr and the grain boundary is shown with an isosurface delineating regions containing more than 2.0 at.% B. b)-c) One-dimensional composition profiles across the γ/GB/γ' interface as denoted by arrow #1 in Figure 7a are plotted for the minor additions and main alloying elements. Error bars are shown as lines filled with colour and correspond to the 2σ counting error.

Figure 8 :

 8 Figure 8: a) Atom probe reconstruction from the cracked-free equiaxed grain shape sample and the same random high angle grain boundary as in Figure 7 and IPF map from the TKD analysis. The γ/γ' interfaces are shown with an isosurface with a threshold of 7 at.% Cr and the segregated film is shown with an isosurface at 10.0 at.% B. b)-c) One-dimensional composition profiles across the γ/GB/γ' interface as denoted by arrow #1 in Figure 8a are plotted for the minor additions and main alloying elements. Error bars are shown as lines filled with colour and correspond to the 2σ counting error.

Figure 9 :

 9 Figure 9: a) 1D composition profiles across the GB along arrow #2 across the boride precursor in Figure 8a. Error bars are shown as lines filled with colour and correspond to the 2σ counting error. b)-d) 2D compositional maps calculated inside the grain boundary plane for Mo, Cr and B. Note that the colorbar scale gives the solute content in at.%.

  a) and (b), respectively. No diffusion in the solid state and infinite diffusion in the liquid were assumed in the Scheil-calculations. The calculations allow to simulate sequential steps from the liquidus temperature to an approximate solidus temperature, giving the fraction of solid and composition of the new liquid at each temperature. The comparison between Figure11(a) and (b) shows that liquid films remain stables at lower temperatures when considering that borides are not a solidification product but rather form in the solid state. The solidus is 60°C lower when excluding borides from the calculations. The composition of the liquid as a function of the temperature of the investigated alloy is plotted in Figure11(c) as a function of the mole fraction of B, Cr and Mo respectively in orange, pink and red when assuming that borides are not a solidification product (boride not considered in the calculation). The three solutes, namely B, Cr and Mo strongly partition to the liquid, and the liquid is hence enriched in those solutes as the solidification proceeds, reaching approximately 6.0, 19.0 and 24. at.% respectively during the last stage of solidification.

Figure 11 :

 11 Figure 11: Solidification paths relying on the Scheil-Gulliver assumptions (a) without and (b) with the precipitation of M2B borides as a solidification product. Calculations performed using Thermo-Calc and relying on TTNI8 database. c) Evolution of the B-, Cr-and Mo-content as a function of the temperature in the liquid phase when considering only , ′ and liquid (excluding borides).

Figure 12 :

 12 Figure 12: Schematic summary of the microstructural and compositional evolution during the build of the sample with hot cracks.

Figure 13 :

 13 Figure13: Quantification of grain width along the building direction for cracked and crack-free samples. Results from two different cracked columnar samples were included to highlight that the grain width is reproducible from one build to another. Blue and green dashed lines represent the average grain width for the sample with equiaxed and columnar grains, respectively. Red dashed line corresponds to the critical grain width, beyond that hot cracks occur.

Figure 14 :

 14 Figure 14: Overview of the crack-free fine-grained columnar sample: optical micrograph along with detailed EBSD IPF-Z (building direction) maps and pole figure illustrating the fine columnar grains along the building direction. A1 and A2 are the X and Y scanning direction of the electron beam during the deposition.

Table 1 :

 1 Chemical composition of the powders used in the present investigation in at.%.

	Ni	Cr Mo Co	Ti	Al	Zr	Hf	B	C	Si
	Bal.	12.20 3.80 14.85	5.30	8.70	0.02-0.025 0.18-0.21 0.083 0.06-0.07 0.04

Table 2 :

 2 Summary of the main processing parameters used for building the three samples.

	Cracked columnar	Crack-free with
		equiaxed grains

Preheating Temperature, Tp (°C) 1050 1050 Linear Energy = P/v (J/mm²)

		Auto* (0.5-0.65)	0.119
	Line Order	1	1
	Focus Offset, FO (mA)	20	20
	*Power and scanning speed automatically determined by the thermal model used in the EBM Control 3.2 software which depends on the
	geometry of the parts to be built. When running the automatic mode of the EBM control 3.2 software, the scanning speed changes spatially (x,
	y, z) through the use of automated functions:

Table 3 :

 3 Chemical composition of M2B boride in the columnar grain shape sample as measured by APT (at.%).

		B	Mo	Cr	Ti	Co	Ni
	M2B	33.86±0.030 38.16±0.030 21.90±0.026 2.11±0.009 2.0±0.009	1.80±0.008

Acknowledgements

This work was performed within the framework of the Center of Excellence of Multifunctional Architectured Materials ''CEMAM'' n°AN-10-LABX-44-01 funded by the ''Investments for the Future Program''. The authors are grateful to Poly-Shape for their contribution to funding this work. We thank Uwe Tezins & Andreas Sturm for their support to the FIB & APT facilities at MPIE. We are grateful for the financial support from the Max-Planck Gesellschaft via the Laplace project for both equipment and personel (PK, AKdS). ZP acknowledges financial support from the BIGMAX project. JH is grateful for funding by the DFG through the SFB TR103. BG acknowledge financial support from the ERC-CoG-SHINE-771602.

Author contributions

P.K., B.G., J-J.B and G.M. designed the study. E.C. and G.M. 3D-printed the alloy. P.K., B.G. and D.R. prepared the atom probe specimens, processed the data and interpreted the results. Z.P. conducted the grain boundary analysis. J.H. and P.K. conducted the TKD analysis. A.K.S. performed Thermo-Calc calculations, C.T. provided support on these. B.G., P.K. and G.M. wrote the main draft of the paper. All authors contributed to the discussion of the results and commented on the manuscript.

Supplementary Figure

Supplementary


C Frétigny

J.-Y Duquesne

D Fournier
email: daniele.fournier@upmc.fr

Perturbation of the Heat Lateral Diffusion by Interface Resistance in Layered Structures

Keywords: Interface resistance, Thermal conductivity, Thermal diffusivity, Thermoreflectance microscopy

It is well established that interface resistances do usually exist in layered structures, and their values strongly depend on their origin. They may arise from different vibrational properties of the layers, nonharmonic processes at the interface, surface chemical contamination, interfacial defects, etc. Numerous studies have been published to evaluate their values, most of the time, in a perpendicular heat diffusion scheme. In this paper, the effect of interface resistances on the lateral modulated surface temperature of a layered structure for cylindrical symmetry heat diffusion is studied. The thermoreflectance microscope is a particularly convenient tool to record heat lateral diffusion from a surface modulated heated point and thus to evidence the presence of such resistance interfaces. In a first part, the theoretical model of heat diffusion in cylindrical symmetry, in a layered structure exhibiting an interface resistance between the layer and the substrate, is briefly described. In a second part, the C/I configuration (good conductive layer deposited on an insulating substrate, with an interface resistance) is investigated. Experimental results illustrate the theory. In the third part, the reverse case I/C (insulating layer deposited on a conductive substrate, with an interface resistance) is discussed. To conclude, all the cases and the ability of the lateral diffusion to recover interface thermal resistances are compared.

Introduction

It is well established that interface resistances are most of the time present in layered structures. Their values are strongly dependant on their origin. They are smaller in the case of a crystalline lattice difference (case of super lattices deposited on semiconductors) than in the case of microstructure differences/nature of the two layers [1,2]. These interface resistances perturb the heat diffusion in the two directions, parallel and perpendicular. Numerous studies have been published to take into account their presence, most of the time, in a perpendicular heat diffusion scheme [3,4]. The 3 omega method [5], for instance, is particularly sensitive to these interface resistances. Most of the time, several samples with different thicknesses have to be studied. With the hypothesis of the same interface resistance for all the samples, it is straightforward to find the value of the interface resistance. In this paper, we study the effect of these interface resistances on heat lateral diffusion in the case of heat-modulated diffusion and show that lateral heat diffusion could be a particularly convenient tool to evidence the presence of such resistance interfaces. In a first part, we describe briefly the theoretical model of 3D heat diffusion in a layered structure and introduce the case of an interface resistance between the layer and the substrate. In a second part, we demonstrate the influence of the interface resistance for lateral heat diffusion in the case of a good conductive layer deposited on an insulator substrate. Experimental results illustrate the theory. In the third part, the reverse case (insulator deposited on a good conductive layer with an interface resistance) is discussed.

Theoretical Approach

In order to generate heat lateral diffusion, the size of the heat source has to be small compared to the thermal diffusion length. Thermoreflectance microscopy [6][7][8] is one of the setups using a small heat source. In this experiment, the sample is illuminated with an intensity modulated focused pump beam (less than 1 µm diameter). Light being totally or partially absorbed, the light power is converted into heat which diffuses around the source. The spatio-temporal temperature field is detected at the surface of the sample with a second laser beam (probe beam) which is reflected by the heated surface. Lateral scans allow following lateral heat diffusion at 50 µm from the heat source.

In the case of a semi-infinite bulk sample (thermal conductivity

k 0 (W • m -1 • K -1 ), thermal diffusivity D 0 (m 2 • s -1
), the 3D modulated surface temperature in real space is obtained after the integration of [9] T (r, 0,ω)

= ∞ 0 Q k 0 σ 0 exp - λ 2 d 2 32 J 0 (λr )λdλ, (1)
where Q is the pump power (W) absorbed by the surface sample, d is the diameter at 1/e 2 of the Gaussian pump beam, σ 0 = λ 2 + iω D 0 is the wave vector in the Hankel space, and ω is the pulsation of the pump beam. As a result, the temperature amplitude in real space is the convolution of the Gaussian beam by a spherical thermal wave exp(-r/µ 0 ) r

, where µ 0 is the thermal diffusion length (µ 0 = 2D 0 ω ). If a layer (thickness h 2 , thermal conductivity k 2 , and thermal diffusivity D 2 ) is deposited on the substrate (thermal conductivity k 0 and thermal diffusivity D 0 ),Eq.1 becomes [9]

T (r, 0,ω) = ∞ 0 Q k 2 σ 2 k 2 σ 2 + k 0 σ 0 th(h 2 σ 2 ) k 0 σ 0 + k 2 σ 2 th(h 2 σ 2 ) exp - λ 2 d 2 32 J 0 (λr )λdλ. (2)
When an additional layer (thickness h 1 , thermal conductivity k 1 , and thermal diffusivity D 1 ) is present between the layer and the substrate, Eq. 2 becomes

T (r, 0,ω)= ∞ 0 Q k 2 σ 2 k 2 σ 2 + k 0 σ 0 1+ k 1 σ 1 k 0 σ 0 th(h 1 σ 1 ) 1+ k 0 σ 0 k 1 σ 1 th(h 1 σ 1 ) th(h 2 σ 2 ) k 0 σ 0 1+ k 1 σ 1 k 0 σ 0 th(h 1 σ 1 ) 1+ k 0 σ 0 k 1 σ 1 th(h 1 σ 1 ) + k 2 σ 2 th(h 2 σ 2 ) exp - λ 2 d 2 32
J 0 (λr )λdλ.

(

) 3
If we suppose that the intermediate layer is very thin (h 1 ≪ h 2 ), that its thermal properties are very low compared to those of the substrate and layer 2 (k 1 ≪ k 2 , k 0 ) and if we note R 1 = h 1 k 1 (the interface resistance), Eq. 3 is written as

T (r, 0,ω) = ∞ 0 Q k 2 σ 2 k 2 σ 2 + k 0 σ 0 1+R 1 k 0 σ 0 th(h 2 σ 2 ) k 0 σ 0 1+R 1 k 0 σ 0 + k 2 σ 2 th(h 2 σ 2 ) exp - λ 2 d 2 32 J 0 (λr )λdλ. ( 4
)
This expression demonstrates that, in the presence of an interface resistance R 1 ,we have just to replace k 0 σ 0 by k 0 σ 0 1+R 1 k 0 σ 0 in all the equations. Note that Eq. 4 can also be obtained directly by considering a temperature jump between the layer and the substrate proportional to the flux.

Good Thermal Conductor Layer on Insulator Substrate

In [10], we have established that the solution of Eq. 2 is achieved with the integration along a contour excluding the branch point associated with σ 0 . The solution corresponds to a sum calculated for all the poles (λ n ) and a term corresponding to the integration around the branch point:

T (r, 0,ω) ≈ A n exp(iλ n r ) √ r + B exp -εr ω D 0 r ( 5
)
with ε = exp(i π 4 ). In our case (good conductor on insulator), the second term is negligible except for extremely thin films or very low modulation frequencies.

Approximations of the poles in Eq. 2 can be numerically found. However, in the case where the ratio α = k 0 k 2 is small, they can then be found by expanding the denominator ασ 0 + σ 2 th(h 2 σ 2 ) in a power series of this parameter. The asymptotic behavior corresponds to the pole which exhibits the smallest imaginary part:

λ 2 0 =-i ω D 2 -εα ω D 0 - ω D 2 (up to the first order in α) (6)
It is then straightforward that the asymptotic lateral heat diffusion corresponds to a radial-plate-like regime with a complex diffusion length:

T (∞, 0,ω) ≈ exp ir λ 2 0 √ r = exp(-r (a + ib)) √ r (7) with h(a 2 -b 2 ) = k 0 k 2 √ ω √ 2 1 D 0 - 1 D 2 ≈ k 0 k 2 √ ω √ 2 1 D 0 (8)
and

(b 2 -a 2 + 2ab) = ω D 2 (9)
When an interface resistance is suspected, we have to replace k 0 σ 0 with k 0 σ 0 1+R 1 k 0 σ 0 in the denominator of Eq. 2. In the following, we consider that the presence of the interface resistance is a perturbation of the previous system.

The poles are now calculated with the perturbed equation:

ασ 0 (1 -R 1 k 0 σ 0 ) + σ 2 th(h 2 σ 2 ) = 0. ( 10
)
The asymptotic behavior corresponds again to the pole which exhibits the smallest imaginary part:

λ 2 0R =-i ω D 2 ⎛ ⎝ 1 + R 1 k 2 0 ω D 2 -ω D 0 h 2 k 2 ω D 2 ⎞ ⎠ -εα ω D 0 - ω D 2
(up to the first order in α).

(

) 11
The asymptotic lateral heat diffusion corresponds again to a radial-plate-like regime:

T (∞, 0,ω) ≈ exp(ir λ 2 0R ) √ r = exp(-r (a R + ib R )) √ r (12) with h 2 (a 2 R -b 2 R ) = k 0 k 2 √ ω √ 2 1 D 0 - 1 D 2 ≈ k 0 k 2 √ ω √ 2 1 D 0 = p R √ ω (13) (b 2 R -a 2 R + 2a R b R ) = ω D 2 + R 1 ω k 2 0 h 2 k 2 1 D 2 - 1 D 0 ≈ ω D 2 - R 1 ωk 2 0 h 2 k 2 D 0 = q R ω. (14)
A comparison of Eqs. 8 and 9 and Eqs. 13 and 14 shows that the measurement of the thermal conductivity is not affected by the presence of the interface resistance while the effective thermal-diffusivity measurement (1/q R ) has to be corrected to find the thermal diffusivity D 2 and R 1 .

Figure 1a, b shows the experimental data for five modulation frequencies, for a 55 nm thick aluminum layer deposited on fused silica. The thermal conductivity and

.6 ×10 -4 m 2 • s -1 , thermal conductivity-154 W • m -1 • K -1 ,a n dR i -5 ×10 -8 m 2 • K • W -1
).B o t h sets of lines are superimposed the thermal diffusivity of the layer were deduced from p and q values (Eqs. 8, 9) because the thermal properties of the substrate and the thickness of the layer are known. We can remark that the thermal conductivity (154 W • m -1 • K -1 ) is smaller than the thermal conductivity of a bulk aluminum sample (237 W • m -1 • K -1 ), while the thermal diffusivity (3.45 × 10 -4 m 2 • s -1 ) is larger (0.95 × 10 -4 m 2 • s -1 ).Itis well known that the value of the thermal conductivity decreases when the thickness of the layer decreases, but the value of the thermal diffusivity is largely overestimated. Aluminum deposition presents a very small adhesion, and an interface layer is likely. Equations 13 and 14 should then be used to determine the thermal properties of the layer and to evaluate the thermal resistance. The thermal conductivity being determined with Eq. 13, a common hypothesis is to keep the ratio k 2 /D 2 constant [11], which is equivalent to the reasonable assumption that the volumetric heat capacity is a material constant. So, it is possible to know the value of the interface resistance from Eq. 14.

The thermal properties of the layer are estimated to be:

k 2 =154 W • m -1 • K -1 and D 2 =0 . 6× 10 -4 m 2 • s -1
and the value of the interface thermal resistance to be

R 1 = 5 × 10 -8 m 2 • K • W -1 .
In conclusion, when an interface resistance is present (weak adhesion, for instance) the heat is more confined in the layer than expected and a high value of the thermal diffusivity is deduced from the "reduced" model of the lateral heat diffusion. In this case, the second model taking into account the resistance has to be used.

Poor Thermal Conductor Layer on Good Thermal Conductor Substrate

In this case, layer 2 affects the spatio-temporal temperature field mainly around the heat spot [12]. The lateral diffusion being weak in the layer, a spherical thermal wave is developed in the substrate which heats the surface through the thin layer far from the center. In this case, the contribution of the layer to the lateral heat diffusion is a perturbation with respect to the substrate one. If the thickness of the layer is small, Eq. 2 can be developed:

T (r, 0,ω)= Q ⎡ ⎢ ⎣ 1 k 0 σ 0 + th(h 2 σ 2 ) k 2 σ 2 1 -k 2 σ 2 k 0 σ 0 2 1 + k 2 σ 2 k 0 σ 0 th(h 2 σ 2 ) ⎤ ⎥ ⎦ exp - λ 2 d 2 32 J 0 (λr )λdλ (15) T (r, 0,ω)= Q 1 k 0 σ 0 + h 2 k 2 1- k 2 σ 2 k 0 σ 0 2 exp - λ 2 d 2 32 J 0 (λr )λdλ (16)
Up to the first order, the contribution of the layer is linear with respect to h 2 . When an interface resistance is suspected, we have just to replace 1 k 0 σ 0 by 1 k 0 σ 0 + R 1 in Eq. 16. Then, the following equation has to be taken into consideration:

T (r, 0,ω) ≈ Q 1 k 0 σ 0 + R 1 + h 2 k 2 1 - k 2 2 σ 2 2 (1 + 2R 1 k 0 σ 0 ) k 2 0 σ 2 0 exp - λ 2 d 2 32 J 0 (λr )λdλ. (17)
An interface resistance behaves always as an insulator layer, but in this case this is apparent in the mathematical expression of Eq. 17. Its contribution appears mainly near the heating spot and disrupts the perpendicular diffusion scheme (Fig. 2a,b). In a previous article [12], we have studied the behavior of asymptotic lateral diffusion and demonstrated that an insulating layer deposited on a good conductor affects very slightly the heat lateral diffusion. The presence of a thermal resistance will have the same effect, and it is practically not possible to extract its value from the lateral behavior of the heat.

Conclusion

The presence of an interface resistance affects differently the behavior of the heat lateral diffusion depending on the contrast of thermal properties of the substrate and the layer.

In the case of a good conductor deposited on an insulator, the heat is more confined in the layer than expected and an overestimated value of the thermal diffusivity is deduced from the "reduced" model of the lateral heat diffusion. This is a "thermal signature" of the thermal resistance. In this case, a model which takes into account the resistance has to be used, and it is possible to obtain both the thermal properties of the layer and the value of the thermal resistance. In the opposite case (insulator on good conductor), there is little evidence of the presence of the thermal resistance on the lateral behavior of the heat diffusion. The interface resistance affects clearly the perpendicular diffusion, and its presence can be seen only close to the heating spot.

Fig. 1

 1 Fig. 1 Thermoreflectance microscope (a) amplitude and (b) phase signal for 55 nm thick Al layer on a semi-infinite fused silica substrate, recorded at five frequencies (75, 150, 300, 450, and 600) kHz. Symbols experimental points. Lines fits obtained with effective values (thermal diffusivity-3.45 × 10 -4 m 2 • s -1 and thermal conductivity-154 W • m -1 • K -1 ) or with the corrected values (thermal diffusivity-0.6 ×10 -4 m 2 • s -1 , thermal conductivity-154 W • m -1 • K -1 ,a n dR i -5 ×10 -8 m 2 • K • W -1).B o t h sets of lines are superimposed

Fig. 2

 2 Fig. 2 Calculated thermoreflectance microscope (a) amplitude and (b) phase signal. Influence of an interface resistance of 10 -8 m 2 • K • W -1 between a 80 nm Ti layer and a silicon substrate at 80 kHz modulation frequency. The equivalent resistance value of the Ti film is Req = 4 × 10 -9 m 2 • K • W -1 . Dotted line Ti layer on silicon without interface resistance. Dashed line Ti layer on silicon with the interface resistance. Full line bare silicon substrate


Ghassen Halouani
email: ghassen.halouani@gmail.com

Frida Ben

Rais Lasram
email: frida.lasram@gmail.com

Myriam Khalfallah
email: m.khalfallah@fisheries.ubc.ca

Dirk Zeller
email: d.zeller@fisheries.ubc.ca

Daniel Pauly
email: d.pauly@fisheries.ubc.ca

RECONSTRUCTION OF MARINE FISHERIES CATCHES FOR TUNISIA (1950-2010)

The reconstructed total domestic marine catches for Tunisia's fisheries, including large-scale and small-scale commercial catches and recreational catch, as well as major discards, have been estimated for the 1950-2010 period, and increased from approximately 14,500 t•year -1 in the 1950s to over 98,800 t•year -1 in the 2000s. The estimated total domestic catches within Tunisia's EEZ are 1.13 times the national data. Foreign flag industrial catches were estimated to increase from almost 7,800 t in 1950 to a peak of just under 19,200 t in 1975, and then decline to 560 t in 2010. Domestic landings were obtained from official reports of the department of fisheries at the Tunisian agricultural ministry and from the Tunisian National Institute of Statistics. Foreign flag catches and domestic discards were estimated based on independent studies and recreational catches were reconstructed based on information provided by the Tunisian Federation of Sport Fishing and other surveys.

INTRODUCTION

Tunisia is a North African country, part of the Maghreb. It has a total area of approximately 164,000 km 2 and is bordered by Algeria in the west, Libya in the southern-east and the Mediterranean Sea in the north and the east. Relative to its size, Tunisia has a long coastline, which is indented by three important embayments: the Gulf of Tunis in the north, of Hammamet near the center and the Gulf of Gabès in the south.

Tunisia can be divided into three main geographical regions according to climate, quality of soils and topography, i.e., the North, the Center and the South [START_REF] Nelson | Tunisia, a country study[END_REF]. The northern region is isolated from the rest of the country by the Atlas Mountains and is characterized by heavier rainfall and richer soils than the rest of the country; thus, most of Tunisia's agriculture production originates from the North. The Center, in contrast, has poorer soils with little vegetation and insufficient rainfall, and its littoral forms what is called Sahel, i.e. "the Coast". Its agriculture emphasizes wheat and other grains, pasture and the intensive cultivation of olive. The South includes chotts, i.e. salt marshes, oases with date palms, but mainly sand desert, i.e., the Sahara [START_REF] Nelson | Tunisia, a country study[END_REF]). The climate is mostly Mediterranean except in the southern part of the country, the Sahara, where there is extreme diurnal variation in temperature. Tunis, the capital and main city of the country since the 13 th century, is situated in the north-east of Tunisia [START_REF] Nelson | Tunisia, a country study[END_REF]Boularès 2012).

A 2013 census estimated the Tunisian population at 10.8 million (www.ins.nat.tn). Various people settled on the Tunisian coast, e.g., Phoenicians, Romans, Turkish, Arabs, etc. The French colonized the country until its independence in 1956. Habib Bourguiba became the first president of the new Tunisian republic. In 1987, a coup d'état brought a second president to Tunisia who was overthrown, following the events which initiated the "Arab Spring" of 2011 (Boularès 2012).

The sea and fish are extremely important in the Tunisian culture and traditions, particularly due to the geography of the country.

The Tunisian fishing industry

Tunisia has a wide continental shelf of over 66,000 km 2 , and in 2005, it claimed an Exclusive Economic Zone (EEZ), of 102,300 km 2 (Official journal of the Tunisian Republic 2005; www.seaaroundus.org) (Figure 1). The large extension of soft bottoms has contributed to the development of artisanal and industrial fisheries in the Gulf of Gabès, where over 40% of total landings are generated [START_REF] Najar | Evolution des profils des debarquements de poissons dans la region de Gabès[END_REF].

The artisanal sector, consisting of a fishing fleet of around 10,300 boats (in 2008), is well developed along the Tunisian coast, and it is mainly performed by about 4,500 small boats, of which 66% were motorized (in 2008); they use a wide variety of fishing techniques and target high value species.

However, for the last few decades, the number of artisanal boats has been decreasing because of the development of industrial fisheries.

Data collection is made by officials on a daily basis in each fishing port, who control the size and the quantities of fishes caught by each boat before allowing them to sell the fish at the wholesale market.

Considerable catch amounts are exported, mainly to European markets. Indeed, after olive oil, marine products (i.e., fresh and frozen fish, cephalopods and other seafood) are Tunisia's most important export products.

MATERIAL AND METHODS

Total landings were assembled by sector, year and group of species, for the 1977-2010 time period, from official reports of the Tunisian Department of Fisheries. For the period from 1950 to 1976, we used data from national Statistical Bulletins. However, the earlier statistical data do not have the same level of detail. Notably, they did not use the same taxonomic breakdown and reporting format from one year to the next, often due to transfers of management responsibilities. Thus, alternative information sources (e.g., scientific reports, local expert knowledge) were used to improve on the earlier statistics. Then, official data and those reported by FAO on behalf of Tunisia were compared to evaluate the quality of data transfer. Finally, the official data were used as the reported baseline because it has overall a better taxonomic disaggregation than the FAO data.

The Tunisian department of fisheries has applied correction factors to the landings data since the end of the 1970s in order to take into account subsistence and unreported commercial catches, which amount to considerable quantities of fishing products sold directly to hotels and restaurants or in local markets without being accounted by the statistical agents. These correction factors account for 42% of total commercial catches in the artisanal fishery, 17% in the trawl fishery and 15% in the small pelagic fishery. These correction factors are still used today with the same coefficients. Tunisia should be applauded for the foresight of using adjustment factors, something used also by some other countries to account for unmonitored subsistence and commercial catches (e.g., [START_REF] Khalfallah | Proposition d'amélioration du système de Statistiques de la Pêche en Tunisie : Cas du Golf de Tunis[END_REF], but not all [START_REF] Salsabil | Contribution à l'étude qualitative et quantitative des rejets de chalutage dans la région nord de la Tunisie. Résultats des campagnes de prospection 2002-2008[END_REF][START_REF] Zeller | Synthesis of under-reported small-scale fisheries catch in Pacific-island waters[END_REF].

Reported commercial fishery

The artisanal sector is multi-species and multi-gear. It includes non-motorized and motorized boats (length <12m). The industrial fishery involves trawlers, lampara, i.e., a type of purse seines fishing with lights and targeting small pelagic fishes, longliners and other purse seiners which target both demersal and pelagic resources. In the national data that were used in this study as the reported baseline, landings were classified by gears. However, due to the incoherence of the gear classification among the national data, for the 1950-2010 periods, landings had to be reclassified into the appropriate gear categories based on the targeted species.

Recreational fishery

With the sophistication of the recreational fishing gears, which became cheaper and more affordable to a wider public, the recreational fishery in Tunisia is gaining in popularity. However, there is almost no data or studies on fisheries catches by this sector. The most important organization of the recreational fishery is the Tunisian Federation of Sport fishing, which was created in 2005 for better controls and regulations, as well as promotion of activities within the sector, e.g., underwater fishing, line fishing, etc. This organization thus became a hub for recreational fishing clubs of the country (www.ftps.org.tn). To estimate recreational fishery catches, we used information from previous works on recreational fishing in Tunisia, surveys of recreational fishers, as well as information provided directly by the Tunisian Federation of Sport Fishing.

Based on the number of recreational fishers who are members of Tunisian recreational fishing clubs in 2013 and on the recreational fishing effort, i.e., numbers of trips per season and mean catch per trip, we estimate the recreational catch for the year 2013, when the fishing clubs had 3,000 members (Tunisian Federation of Sport fishing pers. comm.). Earlier catches were interpolated between the 2013 estimate and a catch of zero in 1960, assuming that recreational fishing started in the early 1960s.

There are two different fishing seasons for this sector: summer (June/July/August) and "nonsummer". Recreational fishers go fishing on average twice a week in summer and once a month in "non-summer". However, on average each fisher returns empty-handed following 3 trips out of 5 in summer and 1 trip out of 5 in "non-summer". During the trips where there are catches, the average catch amount per trip per fisher in summer is 3.5 kg and in "non-summer" 1.8 kg [START_REF] Khalfallah | Proposition d'amélioration du système de Statistiques de la Pêche en Tunisie : Cas du Golf de Tunis[END_REF].

Following [START_REF] Khalfallah | Proposition d'amélioration du système de Statistiques de la Pêche en Tunisie : Cas du Golf de Tunis[END_REF] Industrial discards included mainly discards of trawlers. These discards were estimated based on the results of scientific surveys of the National Institute of Marine Sciences and Technology (INSTM), and other scientific reports [START_REF] Gharbi | Rapport sur les résultat des prospections réalisées dans le golfe de Gabès du 14 au 16 novembre 2001[END_REF][START_REF] Jarboui | Etude des rejets du chalutage benthique sur les côtes tunisiennes[END_REF][START_REF] Salsabil | Contribution à l'étude qualitative et quantitative des rejets de chalutage dans la région nord de la Tunisie. Résultats des campagnes de prospection 2002-2008[END_REF]). These estimates were made separately for the northern and eastern coast of Tunisia, as well as for the southern coast including the Gulf of Gabès.

Discards of the artisanal fishery were estimated by [START_REF] Harrabi | Analyse des captures principales, accessoires et des rejets des filets droits destinés à la pêche des crevettes, des céphalopodes et des poissons dans la région côtière Mahrès[END_REF] for the east coast of Tunisia, i.e., regions of Monastir and Mehdia, during the 2000s. Based on these estimates, the percentages of discards by gear compared to the total landings were calculated (Table 1). These estimates were then applied to the entire period, from 1950 to 2010.

Table 1. Percentages of artisanal discards by gear from total landings for Tunisia [START_REF] Anon | Reports and documents n 2-78[END_REF][START_REF] Harrabi | Analyse des captures principales, accessoires et des rejets des filets droits destinés à la pêche des crevettes, des céphalopodes et des poissons dans la région côtière Mahrès[END_REF].

Fishing gear Discards (%)

Monofilament fishing net 2

Trammel net for shrimp 38

Trammel net for cuttlefish 22

Species disaggregation

Taxonomic disaggregations for each of the artisanal and industrial commercial fisheries were available for the periods 1978-1982 and 1995-2010 in reports of the Department of Fisheries. We calculated the percentages of each taxa group for the years 1978 and 1982 and applied these percentages to the total industrial landings for the 1950-1977 and 1983-1994 time periods, respectively. As the fishery for shrimp, which generates copious discards, began only in 1978, the discard percentages were adjusted to exclude this fishery before 1978.

The taxonomic disaggregation of artisanal discards and recreational catches, which includes individual species, was pooled to the family level. Then, the percentage of each family was applied to the artisanal catches for the 1950-2010 time period, while the percentages of families for the recreational catches were adjusted according to the popularity of some species of fish among recreational fishers.

Foreign fishing

Foreign industrial catches were estimated separately and were obtained from reports supplied by the National Institute of Marine Sciences and Technology (INSTM; [START_REF] Anon | Reports and documents n 2-78[END_REF]. Similarly, the Discards taxonomic desegregation of foreign (industrial) catches was brought up to a family level. Then we applied the percentages of families to the foreign catches.

RESULTS

Reconstructed marine fisheries catches were estimated for Tunisia for the 1950-2010 time period.

Although the FAO catches were sometimes higher than the national data, they have the very similar trajectories (Figure 2). However the national data have a better taxonomic disaggregation, and they were thus used as the baseline, to which previously unreported small-scale and large-scale commercial, recreational, and illegal foreign catches, as well as major discards were added (note that subsistence catches as well as unreported commercial catches are implicitly included in the reported data because of the application of correction factors, and thus are deemed "reported"; see above).

The estimated total domestic catches are 1.13 times the official reported landings. Catches increased steadily from 13,000 t in 1950 to the peak of 111,200 t in 1988 (Figure 2a). Catches then leveled out and averaged 95,200 t•year -1 from 1990-2010. Reconstructed total catch was dominated by the industrial sector with 66%, followed by artisanal (34%) and recreational (0.1%; Figure 2a). Discards contributed 11% of the catch with almost 92% coming from the industrial sector and only 8% from artisanal. The main fish families of the reconstructed total domestic catch are Clupeidae (24%), Sparidae (13%) and Carangidae (8.4%) followed by Mullidae (7.2%), Scombridae (5.1%) and Octopodidae (5.1%; Figure 2b).

Foreign flag industrial landings were estimated to increase from almost 7,800 t in 1950 to a peak of just under 19,200 t in 1975, and then decline to 560 t in 2010. Catches were dominated by Clupeidae (29%), Sparidae (14%), Carangidae (11%), Mullidae (8.8%) and Octopodidae (6.2%).

In the 1970s, the Government of Tunisia started to invest heavily in the fishery sector, which led to the intensification of fishing effort. By the late 1980s, first signs of overexploitation became visible, i.e., landings decreased while fishing effort was still increasing. This led to the reinforcement of the fisheries regulations. Thus, between the mid-1990s to the mid-2000s, the fishery recovered.

Our estimations of artisanal and industrial discards as well as recreational catches remain conservative. For the discards, we did not take into account all type of gears, e.g., pelagic trawl or purse seiners. Estimates of recreational catches were based only on catches by fishers, who are members of the Tunisian Federation of Sport Fishing, i.e., independent anglers are excluded.

Overall, fisheries management in Tunisia is well developed. The correction factors applied to the different fisheries take into account subsistence and unreported commercial catches. However, these factors have been put in place at the end of the 1970s and need to be updated [START_REF] Khalfallah | Proposition d'amélioration du système de Statistiques de la Pêche en Tunisie : Cas du Golf de Tunis[END_REF]. , 1950-2010, by a) fisheries sector, plus discards shown separately, with landings reported nationally overlaid as line graph (note that recreational catches are too small to be visible); and b) by main taxonomic group. Note the 'others' category includes 44 additional taxonomic groups, family level or higher (see Appendix Table 2).

  , we consider (A) number of recreational fishers in 2013; (B) number of trips per fisher in summer; (C) number of trips per fisher in "non-summer"; (D) recreational catch amounts per trip per fisher in summer; (E) recreational catch amounts per trip per fisher in "nonsummer"; and (F) total estimated recreational catch amounts in 2013, i.e., F = A•[(B•D) + (C•E)] .

Figure 1 .Figure 2 .

 12 Figure 1. Exclusive Economic Zone (EEZ) and shelf area (to 200 m depth) of Tunisia.

ACKNOWLEDGEMENTS

We acknowledge support from the Sea Around Us, a scientific initiative supported by The Pew Charitable Trusts and the Paul G. Allen Family Foundation.