Peter Baláž

Emanuel Guilmeau
email: emmanuel.guilmeau@ensicaen.fr

Nina Daneu

Oleksandr Dobrozhan
email: o.dobrozhan@ekt.sumdu.edu.ua

Matej Baláž

Michal Hegedus

Tristan Barbier

Marcela Achimovičová

Mária Kaňuchová

Jaroslav Briančin

Tetrahedrites Synthesized via Scalable Mechanochemical Process and Spark Plasma Sintering

In this study, we demonstrate the use of elemental precursors (Cu,Sb,S) to synthesize tetrahedrite Cu12Sb4S13 using an industrial eccentric vibratory mill. Mechanochemical synthesis of tetrahedrite leads to the formation of covellite (CuS), skinnerite (Cu3SbS3) or famatinite (Cu3SbS4) in dependence on milling time. However, the composite product can be modified in favour of prevailing tetrahedrite when Spark Plasma Sintering (SPS) treatment is applied after milling. The as-synthesized and sintered products are composed of polydisperse nanosized particles with dimensions up to 250 nm. The thermoelectric measurements reveal a maximum value of figure-of-merit ZT = 0.67 @ 700K, as a consequence of a relatively high power factor (1.07 mW m -1 K -2 ) and a low thermal conductivity (1.12 W m -1 K -1 ). The obtained zT values for products prepared in an industrial mill are comparable to the ones synthesized by milling in

laboratory mills. The synthesis of ternary and quaternary sulphides by a scalable and industrializable milling process represents a prospective route for mass production of thermoelectric materials.

INTRODUCTION

Tetrahedrites represent the most important source of copper and antimony and are also economically attractive due to their content of silver and mercury [START_REF] Baláž | Extractive Metallurgy of Activated Minerals[END_REF]. Extractive metallurgy has been applied to selectively obtain copper and precious metals from these minerals. Several technologies have been developed like SUNSHINE in the USA and MELT in Slovakia [START_REF] Baláž | Mechanochemistry in Nanoscience and Minerals Engineering[END_REF].

However, their start-ups have been problematic as a consequence of a decline in mining and metallurgy of primary sulfidic ores.

Less than two decades were needed for tetrahedrite to be back on stage. In 2012, Suekuni et al. [START_REF] Suekuni | Thermoelectric properties of mineral tetrahedrites Cu10Tr2Sb4S13 with low thermal conductivity[END_REF] highlighted thermoelectric performance in a synthetic tetrahedrite and a new era for applications of ternary and quaternary sulphides as prospective energy materials, with tetrahedrite as a flagship has started.

Tetrahedrites form a large group of naturally-occurring sulfosalts of composition X10Y2Z4Q13

where X = Cu, Ag; Y = Cu, Mn, Fe, Co, Ni, Zn, Hg, Cd; Z = Sb, As, Bi; Q = S,Se,Te [4].

According to this formula, ten copper atoms are in the +1 oxidation state and the remaining two copper atoms are in the +2 oxidation state. Copper can be substituted by various transition metals [START_REF] Johnson | Crystal chemistry of tetrahedrite[END_REF][START_REF] Makovicky | Exploratory studies on substitution of minor elements in synthetic tetrahedrite[END_REF]. Antimony is in +3 oxidation state and sulphur is in -2 oxidation state [START_REF] Chetty | Tetrahedrites as thermoelectric materials: an overview[END_REF][START_REF] Chetty | Thermoelectric properties of a Mn substituted synthetic tetrahedrite[END_REF]. The tetrahedrite phase has a body-centred cubic (I4 # 3m) complex crystal structure which contains 58 atoms on 5 distinct crystallographic sites [START_REF] Suekuni | Thermoelectric properties of mineral tetrahedrites Cu10Tr2Sb4S13 with low thermal conductivity[END_REF]. This structure consists of three units formed by Cu in planar triangular coordination and tetrahedral coordination, and SbS3 in trigonal pyramid where Sb is coordinated by three S [START_REF] Wuensch | Confirmation of the crystal structure of tetrahedrite Cu12Sb4S13[END_REF][START_REF] Wuensch | The crystal structure of tetrahedrite Cu12Sb4S13[END_REF].

Thermoelectric power and electrical resistivity of natural tetrahedrite minerals have been reported already in the 50 th [START_REF] Telkes | Thermoelectric power and electrical resistivity of minerals[END_REF]. However, only when ultra-low thermal conductivity of tetrahedrite has been evidenced [START_REF] Suekuni | Thermoelectric properties of mineral tetrahedrites Cu10Tr2Sb4S13 with low thermal conductivity[END_REF], the number of papers on this topic dramatically increased.

Several PhD studies were initiated [START_REF] Lu | Thermoelectric Properties of Natural Mineral Based Tetrahedrite Compounds[END_REF][START_REF] Bouyrie | Identification, Synthèse et Caractérisation de Phases Tetraédrites pour la Conversion d'énergie par effets thermoélectriques[END_REF][START_REF] Chen | Synthesis and Thermoelectric Properties of Cu-Sb-S Compounds[END_REF][START_REF] Guélou | On the Structural and Physical Properties of Earth-Abundant Sulphides for Thermoelectric Applications[END_REF][START_REF] Levinský | Synthesis, Characterization and Optimization of New Thermoelectric Materials[END_REF] and several review papers were published recently [START_REF] Chetty | Tetrahedrites as thermoelectric materials: an overview[END_REF][START_REF] Chetty | Thermoelectric properties of a Mn substituted synthetic tetrahedrite[END_REF][START_REF] Candolfi | Prospective novel thermoelectric materials[END_REF][START_REF] Hébert | Searching for new thermoelectric materials: some examples among oxides, sulfides and selenides[END_REF][START_REF] Suekuni | Research update: Cu-S based synthetic minerals as efficient thermoelectric materials at medium temperatures[END_REF]. The complex crystal structure of tetrahedrite focused the understanding of the low thermal conductivity into inspecting its bonding variability. Here, copper in planar coordination between three sulphur atoms, co-operating with the lone pairs of the two antimony atoms, is characterized by large out-of-plane rattling modes, which play a decisive role in the scattering of acoustic phonons [START_REF] Suekuni | Research update: Cu-S based synthetic minerals as efficient thermoelectric materials at medium temperatures[END_REF][START_REF] Lai | From bonding asymmetry to anharmonic rattling in Cu12Sb4S13 tetrahedrites: when lone-pair electrons are not so lonely[END_REF][START_REF] Bouyrie | From crystal to glass-like thermal conductivity in crystalline minerals[END_REF][START_REF] Suekuni | Retreat from stress: rattling in planar coordination[END_REF].

There are several ways to improve the performance of thermoelectric materials. Besides the search for efficient thermoelectric materials, doping in the case of tetrahedrite is well documented [3, 7-8, 12-19, 23-39] and the nanostructuring approach plays still more and more important role in the synthesis of thermoelectrics [START_REF] Dresselhaus | New directions for low-dimensional thermoelectric materials[END_REF][START_REF] Snyder | Complex thermoelectric materials[END_REF][START_REF] Vaqueiro | Recent developments in nanostructured materials for highperformance thermoelectrics[END_REF][START_REF] Kanatzidis | Nanostructured thermoelectrics: the new paradigm?[END_REF][START_REF] Lan | Enhancement of thermoelectric figure-of-merit by a bulk nanostructuring approach[END_REF][START_REF] Heremans | When thermoelectrics reached the nanoscale[END_REF]. Here the increased phonon scattering, as a consequence of created grain boundaries and structural defects in nanostructures, leads to low thermal conductivity.

Mechanochemistry is an easy, scalable and reproducible method for the production of nanograins [START_REF] Baláž | Mechanochemistry in Nanoscience and Minerals Engineering[END_REF][START_REF] Baláž | Chalcogenide mechanochemistry in materials science: insight into synthesis and applications (a review)[END_REF][START_REF] Baláž | Chalcogenide quaternary nanocrystals for solar cells: explosive character of mechanochemical synthesis and environmental challenge[END_REF][START_REF] Baláž | Mechanochemistry of copper sulphides: phase interchanges during milling[END_REF][START_REF] Friščić | New opportunities for materials synthesis using mechanochemistry[END_REF][START_REF] Šepelák | Mechanochemistry: from mechanical degradation to novel materials properties[END_REF][START_REF] James | Mechanochemistry: opportunities for new and cleaner synthesis[END_REF][START_REF] Boldyreva | Mechanochemistry of inorganic and organic systems: what is similar, what is different?[END_REF][START_REF] Jones | Introductory lecture: mechanochemistry, a versatile synthesis strategy for new materials[END_REF][START_REF] Do | Mechanochemistry: a force of synthesis[END_REF]. Moreover, the mechanochemically synthesized (sometimes called mechanically alloyed) structures are created by a well-crystallized core of nanoparticles with disordered near-surface shell regions [START_REF] Baláž | Hallmarks of mechanochemistry: from nanoparticles to technology[END_REF], which can potentially favour a decrease in the thermal conductivity. Bulk nanostructuring approach via combination of high energy milling with hot pressing methods has been applied for the preparation of plethora nanostructured thermoelectric compounds [START_REF] Lan | Enhancement of thermoelectric figure-of-merit by a bulk nanostructuring approach[END_REF]. This combined method has been developed especially for the preparation of various non-doped tetrahedrites (Table 1). In this case, SPS treatment was mainly used for the densification of the nanopowders synthesized by mechanochemistry. More detailed insight into the thermoelectric properties of non-doped tetrahedrite produced by various synthetic and consolidation methods is given in ESI (Table S1).

As the effectiveness of the combination of mechanochemistry and SPS has already been proven at laboratory level, the aim of this work has been focused on the development of industrial milling for the synthesis of tetrahedrite Cu12Sb4S13 followed by SPS. We report in this study ZT values comparable to the ones obtained in laboratory mills (Table 1). The relationship between the phase composition, nano-microstructure and transport properties of the final products is discussed in the following.

MATERIALS AND METHODS

For mechanochemical synthesis of tetrahedrite Cu12Sb4S13, the following elemental precursors were used: copper (Merck, 99% purity, 99% particles below 70 micrometers), antimony (Alpha Aesar, 99.5% purity, 99% particles below 120 micrometers) and sulphur (CG-Chemikalien, 99% purity, 99% particles below 390 micrometers).

Mechanochemical solid-state syntheses were carried out in an industrial eccentric vibratory ball mill ESM 656-0.5 ks (Siebtechnik, Germany) working under the following conditions: 5L steel satellite milling chamber attached to the main corpus of the mill, tungsten carbide balls with a diameter of 35 mm and total mass of 25 kg, 80% ball filling in milling chamber, amplitude of the mill 20 mm, rotational speed of the eccenter 960 min -1 , argon atmosphere. The total feed of reaction precursors is 100 grams per batch. The milling was performed at different times, i.e.

1-6 h. The photographs of the mill together with the attached satellite chamber are shown in ESI (Fig. S1).

After completion of the milling programs, the resulting pulverized powder was shaped and densified using SPS (FCT HPD 25) at 723 K for 30 minutes (heating and cooling rate of 100 K/min) under a pressure of 64 MPa using graphite dies of 10 mm diameter and a slight overpressure of 30 hPa (Ar), in order to prevent both oxidation and sulphur volatilization. The final thickness of the pellets was around 8 mm with a geometrical density in excess of 95 % of the crystallographic value.

The qualitative identification of the phase composition was performed by XRD method with an X´Pert PW 3040 MPD diffractometer (Phillips) working in the 2q geometry with CuKa radiation. XRD patterns of sintered samples were collected using a D8 Advance diffractometer (Brucker, Germany) with the CuKa radiation in the Bragg-Brentano configuration. The generator was set up at 40 kV and 40 mA. The divergence and receiving slits were 0.3° and 0.1 mm, respectively. The XRD patterns were recorded in the range of 10-80° 2θ with a step of 0.05°. Rietveld refinements of XRD data of the as-prepared solid solutions were performed in the space group 𝐼4 # 3𝑚 using Fullprof software [START_REF] Rodriguez-Carvajal | Fullprof program, version 2.4.2[END_REF]. The XRD line broadening was analyzed by the refinement of regular Thompson-Cox-Hastings pseudo-Voigt function parameters. In order to obtain proper geometry set-up and to eliminate instrumental broadening, the instrumental resolution function was determined by refinement of the LaB6 standard specimen.

The JCPDS PDF database was utilized for phase identification [START_REF]Joint Committee on Powder Diffraction Standards (JCPDS), Powder diffraction file[END_REF].

The content of non-reacted elemental sulphur in the samples was determined by a simple gravimetric method using a Soxhlet extractor. The extraction thimble was loaded with wellweighed 1 g of powder sample and placed into the main chamber of the extractor. 30 mL of carbon disulphide (99.9%, Fischer Chemical) was placed into a 500 mL distilling flask and the apparatus was set up. Upon heating of the flask in a hot water bath, three cycles were run to quantitatively dissolve all sulphur present in the sample. The resulting solution cooled to room temperature was transferred into a 250 mL round bottom flask of a known mass and the solvent was distilled under vacuum. The flask was further dried at 70 o C to eliminate any traces of the solvent and re-weighed. Conversion degree a of corresponding mechanochemical synthesis was calculated based on Soxhlet analysis according to the formula:

a = 100 -((mf1-mf0)/ms0) (1)
where a is overall conversion degree, ms0 the starting amount of sulphur in the reaction mixture (g), mf1 the mass of the flask after extraction (g), and mf0 the mass of the flask before extraction (g).

XPS apparatus SPECS with PHOIBOS 100 SCD and non-monochromatic X-ray source was used. The core spectra were measured at 70 eV and the survey spectrum at 70 eV using room temperature. Basic pressure 1.10 -8 mbar with AlKa excitation at 10 kV for all spectra were acquired. For data analysis, SpecsLab2 CasaXPS software (Casa Software Ltd.) was used. All peaks were fitted with Shirley and Tougaard type baseline. Silver (Ag3d) was used for calibration of the spectrometer. Charging of samples was resolved by the calibration on carbon.

Scanning electron microscopy images were recorded using MIRA 3 FE-SEM microscope (TESCAN Czech Republic) equipped with EDX detector (Oxford Instrument, United Kingdom) or a field-emission gun scanning electron microscope (FEG-SEM; JSM-7600F, Jeol Ltd., Tokyo, Japan) operated at 10-20 kV and equipped with an energy dispersive X-ray spectrometer (EDS; INCA Oxford 350 EDS SDD, Oxfordshire, UK). EDS analyses were performed at 20 kV and 15 mm working distance. The samples were ground and polished, final polishing was done on 3-microns diamond lapping film. Cross-sections perpendicular and transversal to the applied pressure during SPS sintering were analyzed to check for potential texturization in the sintered samples. For Transmission Electron Microscopy (TEM) analyses, the samples were prepared according to the conventional procedure using thinning, dimpling and ion-milling. The sintered compacts were inserted into a brass tube with 3-mm diameter for support and fixed with epoxy resin. The samples were thinned from both sides to form around 100 microns thin discs, which were further dimpled to around 15-microns in the disc center.

Electron-transparent regions were obtained by ion milling (Gatan Pips 691, California, USA) using 3.8 kV Ar + ions at an incidence angle of 10° until perforation. Prior to TEM analyses, the specimens were coated by a thin layer of carbon to improve surface electron conductivity. TEM analyses were performed on a 200-kV probe-aberration corrected atomic-resolution scanning transmission electron microscope (JEOL ARM200 CF, Jeol Ltd., Tokyo, Japan) equipped with energy dispersive x-ray spectrometer (Jeol Centurio 100).

The electrical resistivity (ρ) and Seebeck coefficient (S) were measured simultaneously from ingots, from 300 K up to 700 K using an ULVAC-ZEM3 device under partial helium pressure.

A NETZSCH LFA-457 apparatus was used for measuring the thermal diffusivity under argon flow. The thermal conductivity (κ) was determined as the product of the geometrical density, the thermal diffusivity, and the theoretical heat capacity using the Dulong-Petit approximation.

The Wiedemann-Franz law, using a Lorenz number estimated from the relationship L = 1.5 + exp(-|S|/116), [START_REF] Kim | Characterization of Lorenz number with Seebeck coefficient measurement[END_REF] was used to calculate the lattice thermal conductivity by subtracting the electronic contribution to the total thermal conductivity (κL = κ -κe). The estimated measurement uncertainties are 6% for the Seebeck coefficient, 8% for the electrical resistivity, 11% for the thermal conductivity, and 16% for the final figure of merit, ZT [START_REF] Alleno | A round Robin test of the uncertainty on the measurements of the thermoelectric dimensionless figure of merite of Co0.97Ni0.03Sb3[END_REF].

RESULTS AND DISCUSSION

Phase formation during mechanochemical synthesis

XRD patterns of stoichiometric mixtures of Cu, Sb and S precursors co-milled in an industrial mill are shown in Fig. S1. Milling times of 1-6 hours have been applied. Consecutive formation of binary and ternary sulphides is clearly evidenced (see also Table 2), as shown in our previous works on the mechanochemical synthesis of multinary sulphides for solar cells applications [START_REF] Baláž | Chalcogenide mechanochemistry in materials science: insight into synthesis and applications (a review)[END_REF][START_REF] Baláž | Chalcogenide quaternary nanocrystals for solar cells: explosive character of mechanochemical synthesis and environmental challenge[END_REF][START_REF] Baláž | Rapid mechanochemical synthesis of nanostructured mohite Cu2SnS3 (CTS)[END_REF][START_REF] Dutková | Mechanochemical synthesis, structural, magnetic and electrooptical properties of CuFeS2 nanoparticles[END_REF][START_REF] Hegedüs | Mechanochemical approach to a Cu2ZnSnS4 solar cell absorber via a "micro-nano" route[END_REF][START_REF] Baláž | Semi-industrial green mechanochemical syntheses of solar cell absorbers based on quaternary sulfides[END_REF]. Strong affinity of copper with sulphur leads to the formation of copper sulphides [START_REF] Baláž | Ultrafast mechanochemical synthesis of copper sulfides[END_REF]. In our case, small amounts of CuS and Cu2S were formed already during mixing precursors to prepare homogeneous input into the mill (Table 2). However, even after 6 hours of milling, both phases are still the most dominant. Compared to ball-milling in laboratory where the tetrahedrite phase is almost fully formed after only 5h [START_REF] Barbier | Thermoelectric materials: a new rapid synthesis process for nontoxic and high-performance tetrahedrite compounds[END_REF],

it seems that the eccentric vibratory ball-milling conditions in our study are less energetic to lead to complete crystallization of the tetrahedrite phase.

In principle, four ternary phases can exist in Cu-Sb-S system: chalkostibnite CuSbS2 (space group: Pnam), skinnerite Cu3SbS3, famatinite Cu3SbS4, and tetrahedrite Cu12Sb4S13. The corresponding free energy values DG are -138.5 kJ.mol -1 , -216,9 kJ.mol -1 , -266.6 kJ.mol -1 and -917.2 kJ.mol -1 , respectively [START_REF] Craig | Thermochemical approximations for sulfosalts[END_REF]. According to these values, the incidence of tetrahedrite and famatinite phases are the most feasible in solid-state synthesis.

We hypothesize that two parallel reactions proceed during milling. First, the thermodynamically most feasible synthesis of tetrahedrite is realized. Then, the produced nanograined and reactive tetrahedrite is forced to evolve elemental sulphur which backward reacts with tetrahedrite to form famatinite. Indeed, the co-existence of famatinite with tetrahedrite has been evidenced by the study of tetrahedrite stability relations in Cu-Sb-S system [START_REF] Tatsuka | Tetrahedrite stability relations in the Cu-Sb-S system[END_REF]. In this case, temperatures of 250-300 o C were sufficient for the formation of famatinite from partly decomposed tetrahedrite. Evidence of hot spots with temperatures several hundred degrees at contact points of milling balls with milled material has been verified in mechanochemistry many times (see e.g. hot-spot theory in [START_REF] Baláž | Mechanochemistry in Nanoscience and Minerals Engineering[END_REF]) and can play role also in our case.

In the thermoelectric community, there is a tendency to suppress famatinite because it reduces the thermoelectric performance of tetrahedrite due to its low electrical conductivity and large thermal conductivity [START_REF] Chen | Enhanced thermoelectric performance of Sn-doped Cu3SbS4[END_REF][START_REF] Suzumura | Improvement in thermoelectric properties of Se-free Cu3SbS4 compound[END_REF]. For this purpose, the seed matrix containing only natural tetrahedrite (50%) together with addition of the elemental precursors was investigated by Morreli's group [START_REF] Lu | Thermoelectric Properties of Natural Mineral Based Tetrahedrite Compounds[END_REF][START_REF] Lu | Rapid synthesis of high-performance thermoelectric materials directly from natural mineral tetrahedrite[END_REF][START_REF] Lu | High performance thermoelectricity in earth-abundant compounds based on natural mineral tetrahedrites[END_REF][START_REF] Lu | The effect of Te substitution for Sb on thermoelectric properties of tetrahedrite[END_REF][START_REF] Lu | Natural mineral tetrahedrite as a direct source of thermoelectric materials[END_REF]. In this case, famatinite as a product becomes minute. Famatinite suppression was also realized by doping of tetrahedrite and/or by SPS post-treatment after milling [26-30, 33, 56, 68, 71]. In our case, XRD patterns of co-milled reaction precursors with subsequent SPS treatment are illustrated in Fig. 1. The very good selectivity for the tetrahedrite/famatinite ratio was obtained only for sample milled for one hour. In this case, the content of tetrahedrite was over 99 wt%, while for samples milled for longer times it approximately oscillates around 80 wt%. This suggests that the famatinite phase stabilized during ball-milling is difficult to transform during subsequent fast SPS treatment.

Conversion degree of mechanochemical synthesis

The amount of non-reacted elemental sulphur has been determined by the Soxhlet method in order to evaluate the extent of mechanochemical synthesis. The data for conversion degree a calculated according to equation ( 1) are given in supplementary information (Table S2).

Definitively, the total conversion to binary and ternary sulphides is very fast, as the only small amounts of non-reacted sulphur were detected. Consequently, the conversion degree calculated for the milling interval 1-6 h is very high and approaches 98-99 %.

XPS analysis

XPS analyses were carried out to determine the composition of the surface species in mechanochemically synthesized sulphides. The XPS patterns were investigated in detail and are displayed in Figure 2 for M1 and M1S samples, and Figure S3 for M3 and M3S samples.

The spectra for Cu 2p, Sb 3d, and S 2p were recorded in a high-resolution core level mode.

Based on the binding energy values, a peak splitting (PS) was also calculated. The values of PS play a decisive role in the determination of the oxidation states of the elements on the surfaces.

XPS can especially offer resolved spectra for Cu + and Cu 2+ species, respectively [START_REF] Le | The electronic structure of the CuRh1-xMgxO2 thermoelectric materials: An X-ray photoelectron spectroscopy study[END_REF].

Bearing in mind the distribution of species in the compounds (see Figs. 1 and S2 and Table 2), the following oxidation states can be expected : Cu 1+ for famatinite [START_REF] Van Embden | Near-infrared absorbing Cu12Sb4S13 and Cu3SbS4 nanocrystals: synthesis, characterization, and photoelectrochemistry[END_REF], covellite [START_REF] Van Embden | Near-infrared absorbing Cu12Sb4S13 and Cu3SbS4 nanocrystals: synthesis, characterization, and photoelectrochemistry[END_REF] and tetrahedrite [4,[START_REF] Van Embden | Near-infrared absorbing Cu12Sb4S13 and Cu3SbS4 nanocrystals: synthesis, characterization, and photoelectrochemistry[END_REF], Cu 2+ for tetrahedrite [4,[START_REF] Van Embden | Near-infrared absorbing Cu12Sb4S13 and Cu3SbS4 nanocrystals: synthesis, characterization, and photoelectrochemistry[END_REF], Sb 5+ for famatinite [START_REF] Wang | Synthesis and characterization of hydrazine solution processed Cu12Sb4S13 film[END_REF], Sb 3+ for tetrahedrite and skinnerite [START_REF] Chetty | Tetrahedrites as thermoelectric materials: an overview[END_REF][START_REF] Chetty | Thermoelectric properties of a Mn substituted synthetic tetrahedrite[END_REF][START_REF] Wang | Synthesis and characterization of hydrazine solution processed Cu12Sb4S13 film[END_REF] and S XPS spectra for Sb 3d are depicted in Fig. 2b and Fig. S3b for milled samples (M) and in Fig. 2e and Fig. S3e for the sintered samples by SPS (MS). In all the figures, two intensive peaks can be also present as a consequence of famatinite [START_REF] Wang | Synthesis and characterization of hydrazine solution processed Cu12Sb4S13 film[END_REF].

corresponding
XPS spectra for S 2p are depicted in Figs. 2c andS3c for milled samples and in Fig. 2f and Fig. S3f for the sintered samples by SPS (MS). The values of binding energies in the region (162. 46-163.95) eV belong to the states S2p3/2 and S2p1/2 and correspond very well with the expected values for S 2-oxidation state [START_REF] Van Embden | Near-infrared absorbing Cu12Sb4S13 and Cu3SbS4 nanocrystals: synthesis, characterization, and photoelectrochemistry[END_REF][START_REF] Wan | Two-stage evaporated CuSbS2 thin films for solar cells[END_REF]. However, also small hallos can be traced for the milled samples M1 and M3 (Figs. 2c andS3c) with maximum at binding energy of ~169 eV, which is characteristic value of S 6+ oxidation state [START_REF] Naumkin | NIST X-ray photoelectron spectroscopy database[END_REF]. After SPS treatment, in samples M1S and M3S (Figs. 2f andS3f), these hallos are missing. This illustrates the positive influence of the SPS treatment on the purification and surface stability of the samples in this study.

SEM and TEM analysis

SEM images of mechanochemically synthesized powders are given in Fig. S4. Polydisperse distribution of grains can be observed with the tendency to form aggregated particles. The same observation was reported in [START_REF] Baláž | Hallmarks of mechanochemistry: from nanoparticles to technology[END_REF] where the obtained tetrahedrite particles decreased significantly to several micrometers in comparison with the size of tenths micrometers of the reaction precursors. By synthesis from salts in an autoclave, particles of Cu12Sb4S13 with an average diameter of 50-70 nm were obtained [START_REF] An | Selective synthesis and characterization of famatinite nanofibers and tetrahedrite nanoflakes[END_REF]. However, nanoparticles can also be detected in our case in the form of aggregated grains, with particle sizes of several hundreds of nanometers. No significant difference is observed between the two powders.

SPS treated powders after milling for 1h and 3h were further analysed by SEM to reveal the microstructural characteristics (Figure 3). The M1S sample contains only tetrahedrite, while the M3S sample is a mixture of two phases, tetrahedrite and famatinite, as already determined by XRD (see diffraction pattern in Fig. 1). The presence of the famatinite phase in the M3S sample was also investigated in more detail by TEM. Fig. 5a shows a typical famatinite grain embedded in the matrix of tetrahedrite grains.

The size of the famatinite grains is comparable to the tetrahedrite grains. The grain shown in

Thermoelectric properties

The temperature dependences of electrical conductivity (s), Seebeck coefficient (S), power factor (PF), total thermal conductivity (k) and figure-of-merit (zT) were collected on sintered samples over the temperature range 300-700 K. In Fig. 6a, the electrical conductivity of all the samples exhibits a semiconducting behaviour with a clear transition to a metal-like behaviour at 550 K. This behaviour was already reported in several other studies on pristine tetrahedrites [START_REF] Barbier | Structural stability of the synthetic thermoelectric ternary and nickelsubstituted tetrahedrite phases[END_REF][START_REF] Lu | High performance thermoelectricity in earth-abundant compounds based on natural mineral tetrahedrites[END_REF]. A marked difference can be observed between M1S sample and the four other samples.

M1S sample exhibit a lower electrical conductivity as compared to the four other samples, in agreement with the presence of famatinite in a large content in M2S, M3S, M4S, and M6S

samples. Although the famatinite phase is known as a semiconductor characterized by a low electrical conductivity [START_REF] Chen | Enhanced thermoelectric performance of Sn-doped Cu3SbS4[END_REF][START_REF] Suzumura | Improvement in thermoelectric properties of Se-free Cu3SbS4 compound[END_REF], the larger electrical conductivity in samples containing famatinite phase is likely explained by stoichiometry deviations in the tetrahedrite phase.

Indeed, variations of the composition of the crystal structure induce a change in the carrier concentration, which is supported by the marginally lower Seebeck coefficient in M2S-M6S samples on the full temperature range (Fig. 6b). In addition, the magnitude of the Seebeck coefficient at RT for the five samples remains close to the ones reported for pristine tetrahedrite [START_REF] Barbier | Structural stability of the synthetic thermoelectric ternary and nickelsubstituted tetrahedrite phases[END_REF][START_REF] Lu | High performance thermoelectricity in earth-abundant compounds based on natural mineral tetrahedrites[END_REF][START_REF] Suekuni | High-performance thermoelectric mineral Cu12-xNixSb4S13 tetrahedrite[END_REF].

The changes in electrical conductivity and Seebeck coefficient are in overall counterbalanced, leading to similar power factor values on the overall temperature for the five samples. The highest value of around 1.05 mW m -1 K -2 at 700 K is achieved for M1S and M2S samples.

Comparison with other works shows that values obtained in this work are in good agreement with the pristine tetrahedrites prepared by mechanochemical and high-temperature synthesis [START_REF] Barbier | Structural stability of the synthetic thermoelectric ternary and nickelsubstituted tetrahedrite phases[END_REF][START_REF] Kim | Preparation of tetrahedrite Cu12Sb4S13 by mechanical alloying and hot pressing[END_REF][START_REF] Sun | Powder metallurgically synthesized Cu12Sb4S13 tetrahedrites: phase transition and high thermoelectricity[END_REF][START_REF] Wang | Quick fabrication and thermoelectric properties of Cu12Sb4S13 tetrahedrite[END_REF]. The temperature dependences of the thermal conductivity are displayed in Fig. 7a. For M1S sample, the thermal conductivity increases with temperature in agreement with previous reports on pristine tetrahedrite [START_REF] Barbier | Structural stability of the synthetic thermoelectric ternary and nickelsubstituted tetrahedrite phases[END_REF][START_REF] Lu | High performance thermoelectricity in earth-abundant compounds based on natural mineral tetrahedrites[END_REF][START_REF] Suekuni | High-performance thermoelectric mineral Cu12-xNixSb4S13 tetrahedrite[END_REF]. The magnitude is comparable to the ones observed in other pristine tetrahedrites prepared by mechanical-alloying or by high-temperature synthesis [START_REF] Barbier | Structural stability of the synthetic thermoelectric ternary and nickelsubstituted tetrahedrite phases[END_REF][START_REF] Lu | High performance thermoelectricity in earth-abundant compounds based on natural mineral tetrahedrites[END_REF][START_REF] Lu | The effect of Te substitution for Sb on thermoelectric properties of tetrahedrite[END_REF][START_REF] Suekuni | High-performance thermoelectric mineral Cu12-xNixSb4S13 tetrahedrite[END_REF][START_REF] Chetty | Thermoelectric properties of Co substituted synthetic tetrahedrite[END_REF][START_REF] Yan | High thermoelectric performance balanced by electrical and thermal transport in tetrahedrites Cu12+xSb4S12Se[END_REF]. For the other four samples (M2S-M6S), the thermal conductivity decreases with the increasing temperature with an abrupt deflection at 375 K. The jump observed in the temperature dependence of the thermal conductivity around 375 K is not yet understood but may be caused by an exsolution process or reactivity between famatinite and tetrahedrite. The larger values observed in famatinite rich samples is explained by the increased electronic contribution in those samples (increased electrical conductivity) and by the enhanced lattice thermal conductivity (inset of Fig. 7a) due to the larger lattice thermal conductivity of famatinite [START_REF] Chen | Enhanced thermoelectric performance of Sn-doped Cu3SbS4[END_REF][START_REF] Suzumura | Improvement in thermoelectric properties of Se-free Cu3SbS4 compound[END_REF] as compared to tetrahedrite.

For the sample milled for 1 h (M1S), the combination of relatively high PF (1.07 mW m -1 K -2 at 700 K) and low thermal conductivity (1.12 W m -1 K -1 at 700 K) leads to the highest figureof-merit ZT (0.67 at 700 K) among the investigated samples, which is comparable with values reported for undoped tetrahedrites synthesized using laboratory mechanochemical [START_REF] Kim | Preparation of tetrahedrite Cu12Sb4S13 by mechanical alloying and hot pressing[END_REF][START_REF] Sun | Powder metallurgically synthesized Cu12Sb4S13 tetrahedrites: phase transition and high thermoelectricity[END_REF] and high-temperature synthesis [START_REF] Prem Kumar | Thermoelectric properties of Bi doped tetrahedrite[END_REF][START_REF] Suekuni | High-performance thermoelectric mineral Cu12-xNixSb4S13 tetrahedrite[END_REF][START_REF] Wang | Quick fabrication and thermoelectric properties of Cu12Sb4S13 tetrahedrite[END_REF][START_REF] Chetty | Thermoelectric properties of Co substituted synthetic tetrahedrite[END_REF].

CONCLUSIONS

In this work, tetrahedrite Cu12Sb4S13 was synthesized in an industrial vibratory mill. The milling was performed up to 6h in an argon atmosphere using Cu, Sb, and S as elemental precursors.

After milling the samples were treated by spark plasma sintering (SPS). Methods of XRD, Soxhlet analysis, XPS, SEM, EDS, TEM and thermoelectric analysis were applied to characterize properties of the synthesized products. Mechanochemical synthesis in industrial mill proceeds via several intermediate phases where skinnerite (Cu3SbS3) together with famatinite (Cu4SbS4) and tetrahedrite (Cu12Sb4S13) are prevailing. However, the product is chemically more uniform after SPS treatment. For example, the sample milled for 1 h and subsequently SPS treated is almost exclusively tetrahedrite. Soxhlet analysis showed the total conversion of the applied mechanochemical reaction. XPS analysis allowed us to discriminate between Cu 1+ , Cu 2+ , Sb 3+ and Sb 5+ species in tetrahedrite and famatinite. Nanosize particles were identified by SEM and HRTEM methods. In the latter case, dimensions around 250 nm for tetrahedrite were determined. The thermoelectric measurements performed for optimal sample (milling time 60 min) revealed a figure-of-merit value ZT of 0.67@700K as a consequence of relatively high power factor (1.07 mW m -1 K -2 ) and low thermal conductivity (1.12 W m -1 K -1 ). The obtained ZT value for tetrahedrite powders synthesized in an industrial mill is comparable to the values obtained in laboratory mills. The synthesized ternary sulphide represents a prospective material for future applications. The applied approach can serve as a scalable route for the preparation of ternary and quaternary sulphides for a wide range of applications.

ACKNOWLEDGEMENT

Figure 1 .

 1 Figure 1. XRD patterns of sintered samples versus milling time. Inset: relative ratio of

Figure 2 .

 2 Figure 2. High-resolution spectra of M1 (a,b,c) and M1S (d,e,f) samples: (a,d) Cu 2p, (b,e) Sb

Figure 3 .

 3 Figure 3. SEM images of sintered samples from a) 1h ball-milling (M1S) and b) 3h ball-milled

Figure 4 .

 4 Figure 4. (a) Low-magnification BF-STEM image of M3S sample showing tetrahedrite grains

Figure 8b is oriented

  Figure 8b is oriented along the [-221] zone axis as determined from the fast Fourier transform

Figure 5 .

 5 Figure 5. (a) Famatinite grain (arrow) in the matrix of tetrahedrite grains. FFT pattern in the

Figure 6 .

 6 Figure 6. Temperature dependence of (a) electrical conductivity s, (b) Seebeck coefficient S,

Figure 7 .

 7 Figure 7. Temperature dependence of (a) thermal conductivity k and (b) figure-of-merit ZT of

  This work was supported by the Slovak Research and Development Agency (project APVV-18-0357) and the Slovak Grant Agency (projects VEGA 2/0044/18, 2/0065/18). The support of the European research project COST (OC-2015-1-19345) is also acknowledged. O.D. thanks to the National Scholarship Programme of the Slovak Republic (SAIA) for his research grant performed at the Institute of Geotechnics of Slovak Academy of Sciences. The technical support

Table 1 .

 1 Figure of merit ZT of pristine tetrahedrites Cu12Sb4S13 synthesized via the combination of high energy milling and spark plasma sintering

	ZT	T (K)	High energy milling	Reference
	0.55	673	Laboratory	[3]
	0.56	673	Laboratory	[26]
	0.30	623	Laboratory	[33]
	0.76	623	Laboratory	[7,8]
	0.42	573	Laboratory	[13]
	0.65	673	Laboratory	[29]
	0.59	673	Laboratory	[14]
	0.68	623	Laboratory	[56]
	0.86	723	Laboratory	[57]
	0.67	700	Industrial	This work

Table 2 .

 2 XRD qualitative analysis of mechanochemically synthesized powders (L corresponds to low content of phase).

	Milling		Identified phase			Sample
	time (h)	Cu Sb S Cu2S CuS Cu3SbS3 Cu3SbS4 Cu12Sb4S13	name
	0	+ + + +	+				M0
	1		+	+	+	+	M1
	2		+	+	+	+	M2
	3		L	+	+	+	M3
	4			L	+	+	M4
	6				+	+	M6
	Starting from 1 hour of milling, four products of mechanochemical synthesis have been detected,
	i.e. covellite CuS (space group: P63/mmc), skinnerite Cu3SbS3 (space group: P21/c), famatinite
	Cu3SbS4 (space group: 𝐼4 # 2𝑚 ), and tetrahedrite Cu12Sb4S13 (space group: 𝐼4 # 3𝑚 ). With
	increasing milling time, the contents of CuS and Cu3SbS3 are decreasing while Cu3SbS4 and

Cu12Sb4S13 are the only present phases. Tetrahedrite starts slowly to prevail over famatinite.

Table 2 ,

 2 the presence of Cu 1+ can be connected with covellite, skinnerite, famatinite and tetrahedrite. The SPS treatment has not a detrimental effect on the presence of Cu 1+ . However, Because Cu 2+ is present only in tetrahedrite[4,[START_REF] Van Embden | Near-infrared absorbing Cu12Sb4S13 and Cu3SbS4 nanocrystals: synthesis, characterization, and photoelectrochemistry[END_REF], this satellite peak can be associated with this phase. The absence of Cu 2+ in sample M1 can be associated with the lowest content of tetrahedrite in comparison with samples M1S, M3 and M3S.

	Accordingly, the values of 953.17 eV, 933.22 eV for M1S and of 953.23 eV, 933.37 eV for
	M3S correspond with the values of PS 20.0 eV and 19.9 eV. The values of binding energies for
	both sintered samples are in good agreement with the values for Cu 1+ given in [4, 72-76]. In
	agreement with the corresponding XRD patterns in Fig. 1 and S2, and the phases reported in

2-

for all sulphidic species

[7-8, 73, 74]

.

Four samples have been selected for XPS analysis, i.e. M1, M3, M1S and M3S, where M denotes a milled sample and MS is the same sample subsequently sintered by SPS. The milling time for samples M1 and M1S was 1 hour, for samples M3 and M3S was 3 hours.

For copper atoms, the values of binding energies of 952.83 eV, 933.08 eV for M1 and of 953.10 eV, 933.09 eV for M3 were calculated by peak fitting (see Fig.

2a

and Fig.

S3a

). Comparably, PS values of 19.8 eV and 20.0 eV for both samples confirm the presence of Cu +1 state. the satellites with binding energies 942.91eV, 943.69 eV and 942.78 eV can be traced in the samples M1S, M3 and M3S (Fig.

2d, S3a and S3d

).

  to 3d5/2 and 3d3/2 states of antimony are present. Their Eb values are in the regions (539.43-540.57) eV for 3d5/2 state and (530.64-531.43) eV for 3d3/2 state. The peak separation (3d5/2 and 3d3/2) originates from spin-orbit coupling. Peaks can be connected with Sb 3+ state [77] corresponding to tetrahedrite and skinnerite. However, we hypothesize that Sb 5+

for XRF and surface analyses performed by Dr. Šestinová and Dr. Lukáčová Bujňáková is also acknowledged.

SUPORTING INFORMATION

Table S1. Thermoelectric properties of Cu12Sb4S13 tetrahedrite material obtained by the different synthetic and consolidation methods. Table S2. Soxhlet analysis of samples after milling.


Philippe Veber

Karol Bartosiewicz

Jérôme Debray

Guillaume Alombert-Goget

Omar Benamara

Vincent Motto-Ros

Maï Pham

Ana Borta-Boyon

Hugues Cabane

Kheirreddine Lebbou

Jerome Debray

Mai Pham

Franck Levassort

Kei Kamada

Akira Yoshikawa

Mario Maglione

Lead-free piezoelectric crystals grown by the micro-pulling down technique in the BaTiO3-CaTiO3-BaZrO3 system

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

Introduction

Lead-based ferroelectric materials such as lead zirconate titanate PbZr 1-x Ti x O 3 (PZT) 2,3 are the most widely used piezoelectrics because of their excellent properties. However, environmental and health issues of lead-based materials have led to an increasing interest in the development of lead-free piezoelectric materials [4][5][6][7][8] whose the expected piezoelectric response is equal or higher than that of lead-based materials. While classical lead-free piezoelectric ceramics exhibit lower performance than PZT ceramics 2,3 , among the three main families of promising lead-free piezoelectrics 4,7,9,10 , recent reports have shown outstanding piezoelectric constants up to 620 pC . N -1 in (1-x)BaTi 0.8 Zr 0.2 O 3 -xBa 0.7 Ca 0.3 TiO 3 (BCTZ) solid solution 6,7,11,12 . BCTZ solid solution properties make this system promising as alternative to lead-containing materials. Furthermore, single crystals, due to their anisotropic properties, usually display better electromechanical properties than those of ceramics.

Hence, it is expected that BCTZ single crystals would exhibit piezoelectric constants of about 1500-2000 pC . N -1 as predicted by Liu et al. 11 . Recently, growth attempt of BCTZ single crystals in BaTiO 3 -CaTiO 3 -BaZrO 3 pseudo-ternary solid-solution were reported [13][14][15][16][17][18] with various calcium (Ca) and zirconium (Zr) contents. However, high partition coefficients have been measured in these single crystals grown by Top Seeded Solution Growth (TSSG) method 15 . This phenomenon induces strong elemental content variations within the crystals and is detrimental for their piezoelectric performances.

As theoretically predicted by Burton et al. 19 , effective partition coefficients of elements depend on the growth rate. The growth velocities employed in the micro-pulling down (µ-PD) technique, with an order of magnitude about mm.min -1 , are substantially larger than those used for flux growth, which usually range within a few tenth of mm.h -1 . Hence, effective partition coefficients are expected to be different in between these two growth methods. Moreover, as experimentally referenced 1,20,21 , effective partition coefficients tend to be 1 in solid solutions and dopant distribution in oxides or semiconductors for high pulling speeds.

In the present paper, to the best of our knowledge, we report for the first time the crystal growth by the µ-PD technique of BCTZ solid solution. Two attempts performed at different pulling rates at v=9 mm.h -1 then v=6 mm.h -1 for the first fibre and at v=15 mm.h -1 for second fibre are presented. BCTZ crystal habit and evolution of grains orientation towards single orientated crystal with (001) direction is highlighted via Laue pattern measurements along the as-grown crystal fibres. Longitudinal and transversal chemical characterizations of the fibres through Electron Probe Micro-Analysis (EPMA)

were investigated. Substantial lower effective partition coefficients of Ca and Zr in µ-PD grown crystals were calculated and discussed with those calculated in already reported 15 TSSG-grown crystals. Strong chemical inhomogeneity is highlighted through Laser-Induced Breakdown Spectroscopy (LIBS). Dielectric and piezoelectric measurements performed on sub-centimetric polycrystals with millimetre-sized grains are presented and their electromechanical performances are compared to the those of orientated single crystals with close compositions reported in the literature 17,18 .

3.

Experimental procedure

Chemical and physical analysis

Castaing Electron Probe Microscopy Analysis (EPMA) were performed with a CAMECA SX-100 apparatus with a wavelength dispersive spectrometer working at 15 kV. Reference samples 14 for quantitative analysis of elements were chosen in order to reach an experimental relative accuracy of %Zr=%Ca=±0.3mol.% per single analysis point in the investigated concentrations range.

LIBS-based imaging setup was used to image the distribution of Ca and Zr in the different sections of as-grown fibres. LIBS is an all-optical analytical technique, allowing the mapping of metallic elements in various type of solid matrices [22][23][24] . During the analysis, the sample surface is scanned, through single laser pulses, in a pixel-by-pixel manner inducing the breakdown and sparks of the material. The light radiation emitted by the plasma is collected by an optical system and analysed using a spectrometer equipped with an intensified charge-coupled device (ICCD) camera. BCTZ samples were analysed using Nd:YAG laser with pulse energy of about 600 µJ operating at 100 Hz, and a lateral resolution (i.e. distance between two consecutive laser shots) of 12 µm. The spectrometer was configured in the spectral range from 310 nm to 350 nm in order to detect intense lines of both Ca (318.6 nm) and Zr (343.8 nm). The intensity calibration of the LIBS intensities was performed from the profiles obtained with EPMA.

The dielectric and piezoelectric measurements were performed on samples, which were poled under DC electric field by the increasing field method (up to 1.5 or 2kV.cm -1 ) at room temperature. Prior poling samples were prepared by electroding the major faces of crystals using silver paste. The piezoelectric properties were recorded with an impedance analyzer (4294A Agilent) 24 h after poling.

The d 33 values were measured by Berlincourt method with a Pennebaker Piezo d 33 meter (Model 8000). The temperature dependence of dielectric constant and dielectric losses were characterized in order to determine temperature phase transitions. The experiment were realized using an environmental chamber (Pyrox), which allows to measure the dielectric constants every 2° between -40 °C to 180°C at 1kHz.

Electromechanical parameters of the thickness mode were deduced from the measurement of the complex electrical impedance as a function of the frequency around the fundamental thickness-mode resonance. The experimental setup was composed of an HP4395 spectrum analyzer (Agilent Technologies Inc., Palo Alto, CA) with its impedance test kit and specific spring clamping. For the corresponding theoretical simulations of the electrical impedance, the Krimholtz-Leedom-Matthaei (KLM) model 25,26 was used. This one-dimensional model is based on an equivalent electrical circuit scheme allowing a numerical calculation of a multilayer structure behavior including the piezoelectric layer and the two electrodes. Identifications of the effective thickness coupling factor ( ) and the relative dielectric permittivity at constant stress ( ) are performed with a fitting process of the experimental complex electrical impedance. The two other electromechanical coupling coefficients for the transverse modes (k 31 and k 32 ) were determined from the measurement of the resonant (f r ) and antiresonant (f a ) frequencies on the basis of IEEE standards 27 .

X-ray diffraction (XRD) patterns were collected on a Bragg-Brentano θ-θ geometry diffractometer Bruker D8 Advance working with Cu anticathode (40 kV, 40 mA), 0.3° slits and Ni filter. The data were collected over an angular range of 2θ = 5°-90° with a 0.006° step. XRD patterns were studied using the known space groups of BaTiO 3 [START_REF]Ternary Compounds, Organic Semiconductors[END_REF] . Using a conventional notation for perovskite compounds, the pseudo-cubic Miller indices will be hereafter written using "pc" indices.

Laue back-scattering patterns were recorded using an Image Plate (Fujifilm) sensor after a 16-minute stationary crystal irradiation with a collimated (0.7mm) polychromatic X-ray beam supplied by a tungsten anticathode working at 35 kV and 40 mA (Seifert ID3003 generator). The polished samples were held on a goniometric head and set perpendicular to the X-ray beam using an autocollimator.

OrientExpress software [START_REF] Ouladdiaf | [END_REF] was used for pattern indexing.

Synthesis and crystal growth

Synthesis of initial load was prepared from BaCO 3 , CaCO 3 , TiO 2 , ZrO 2 raw powders with 99.99%purity from Fox Chemicals GmbH. Based on previous works [13][14][15] , growth attempts were carried out with a self-flux composed of an excess of CaO and TiO 2 . As for BaTiO 3 growth 30,31 , the thermodynamics effect due to fluxes CaO and TiO 2 aims at decreasing the crystallization temperature of BCTZ solid phase with respect to effective partition coefficients of elements. Initial load with (Ba 0.883 Ca 0.117 )(Ti 0.996 Zr 0.004 )O 3 exact composition represents the global solid solution including the solvent and the solute to be grown. So that 100% of Ba and Ca cations are in A site and 100% of Ti and Zr cations are in B sites of the ABO 3 perovskite structure.

Crystal growth was performed using the micro-pulling down technique [START_REF] Lebbou | Fiber crystal growth from the melt[END_REF][START_REF] Fukuda | Crystal Growth Processes Based on Capillarity: Czochralski, Floating Zone, Shaping and Crucible Techniques[END_REF][34][35] . BCTZ single crystal fibres were pulled from inductively heated iridium crucible which is placed on an iridium after-heater and surrounded by a zirconia and alumina ceramics assembly located in a gas proof tubular silica chamber [START_REF] Lebbou | Fiber crystal growth from the melt[END_REF][START_REF] Fukuda | Crystal Growth Processes Based on Capillarity: Czochralski, Floating Zone, Shaping and Crucible Techniques[END_REF][34][35] . Early attempts were undertaken with a conical-shaped iridium crucible with a 600-µm capillary at its bottom. Contrary to liquid TiO 2 , which exhibits a poor wettability 36 and acts, here, as the main part of the self-flux, we observed that BCTZ liquid solution displays a high wettability. This leads to severe creeping of the solution along the outer surface of the crucible (Figure 1a to d) whatever the heating powers used until load solidification within the crucible. Therefore, a crucible with a 3-mm wide cylindrical die with 5 openings has been chosen with a concave shape at its bottom in order to prevent the solution creeping (Figure 1e to h). Two growth experiments were carried out in Ar-O 2 (2% vol.) atmosphere at different pulling rates v=15 mm.h -1 for the first fibre and v=9 mm.h -1 then to v=6 mm.h -1 for the second fibre. As no BCTZ seeds was available with sufficient length, growths were performed onto an iridium rod with a needle-shaped tip.

Results and discussion

Longitudinal chemical analysis of as-grown fibres

Centimetre-sized fibres were obtained (Figure 2). The dark colour of BCTZ fibres is assumed to be induced by the partial pressure of O 2 (2 vol.%) used in the silica growth chamber as previously observed on air-annealed BCTZ single crystals with similar compositions 15 . It corresponds thus to the natural colour of stoichiometric BCTZ single crystals similar to those of BaTiO 3 30,31 and CaTiO 3 37 single crystals while BaZrO 3 38 crystals are colourless. Unlike µ-PD congruent melting crystals [39][40][41][42][43] grown with a steady diameter at constant temperature, we noted a decreasing of the BCTZ freezing temperatures inducing the diameter shrinking at constant temperature as the first fibre pulling proceed (Figure 2a). This is correlated to the slopes of the liquidus and solidus curves of BCTZ phase diagram, which is assumed to be similar to BaTiO 3 -CaTiO 3 system 44 due to the low Zr content employed (i.e. 0.4mol.%) in the present work. Therefore, an accurate decreasing ramp of the heating power was achieved in order to maintain a constant diameter. We note that diameter variation as well as meniscus height variation, which could varies up to 2 mm, as observed for the first fibre pulled at v=15mm.h -1 (Figure 2a), lead to a Peclet number much higher than 1, featuring thus the Marangoni convection as the dominating transport mechanism [START_REF] Epelbaum | Fiber crystal growth from the melt[END_REF] . A more tricky decreasing heating power process was achieved for lower pulling velocities at v= 6mm.h -1 . Except a drop-melt at the early stage of the crystal growth induced by a slight overheating of the liquid solution, a second fibre with a nearly constant 3-mm diameter has been obtained (Figure 2b). EPMA longitudinal chemical analysis performed at the centre along the fibre axis revealed fluctuations of chemical contents with, nonetheless, a nearly steady evolution of the average Ca and Zr contents all along the fibre grown at v=15 mm.h -1 (Figure 3a). Chemical fluctuations are attributed to thermal instabilities and the large-sized meniscus height, which have a pronounced effect on the chemical segregation in the longitudinal direction during the micro-pulling down process [START_REF] Epelbaum | Fiber crystal growth from the melt[END_REF] . On the contrary, the end of the second fibre grown with a lower pulling velocity v=6mm.h -1 shows lower chemical fluctuations suggesting a steadier growth as featured by the constant 3-mm wide diameter (Figure 3b). However, Ca and Zr contents, respectively, increases and decreases more strongly with respect to the pulled length (Figure 3b). They follow the same segregation trend but in a lower extent than those measured in TSSG-grown crystals 15 . Indeed, effective partition coefficients have been calculated from EPMA analysis performed at the early beginning of both fibres for v=9 mm.h -1 and v=15 mm.h -1 and give respectively, 0.90 and 0.95 for Ca, 2.5 and 1.3 for Zr. We emphasize thus they depends on the growth velocity employed for BCTZ system (Figure 4). LIBS chemical imaging calibrated with respect to EPMA measurements overall the surface of polished samples highlighted the distribution of Ca and Zr elements in the fibres (Figure 5). While Ca distribution evolves roughly smoothly, Zr content follows either erratic distribution with sharp concentration drops at high pulling speed and it segregates along well-defined streaky stripes with several hundred micrometres size, more particularly at lower pulling velocities (Figure 5). Some stripes exhibit high and non-uniform Zr content whereas the other ones exhibit a low Zr content. Due to the very high thermal gradients [START_REF] Yoon | [END_REF][47][48][49][50] (ranging in between 200 and 500°C.mm -1 at the nozzle of the die) and fast pulling velocities employed with µ-PD technique, we assume a simultaneous crystallization of two demixing perovskite solid solutions from a two-phase region of the BCTZ phase diagram, as existing in BaTiO 3 -CaTiO 3 system 44 below 1595°C. Indeed, this temperature is typically in the temperature range where the µ-PD growths occurred regarding the pyrometric measurements (1485°C to 1570°C) performed on saturation temperatures in this system where a spinodal decomposition at high temperature has been highlighted with BCTZ flux-grown crystals 15 .

On the one hand, stripes cannot be ascribed to potential eutectic lamellar microstructure which is usually observed, in the order of few micrometres, at eutectic composition in pseudo-binary, or beyond, systems [START_REF] Jackson | Kinetics processes: Crystal Growth, Diffusion, and Phase Transitions in Materials[END_REF] . Eutectic composition in BaTiO 3 -CaTiO 3 system corresponds to the chemical formula Ba 0.77 Ca 0.23 TiO 3 (BCT). Considering the low Zr content in the crystals of the present work, we can reasonably assume that the eutectic composition in BCTZ system is close to this composition. The BCT eutectic composition, which melts congruently, has been grown by Czochralski [START_REF] Kuper | [END_REF] and Laser Heated Pedestal Growth 53 . In the latter, similar or higher thermal gradients can be achieved such as those established with the in micro-pulling down technique. In both cases, as-grown single crystals are clear and transparent and do not present any streaky growth or series of stripes.

On the other hand, as well-known, Ca and Ba cations can only enter A-site of the ABO 3 perovskite matrix, Zr and Ti cations can only enter the B-site. For instance, when Zr content increases in the crystal, Ti content automatically decreases, because of same crystallographic site occupation.

However, an increasing of Ca content within crystals simultaneously to the decreasing of Zr content is not self-explanatory regarding the crystallographic sites. So that, the only thermodynamic possibility is the existence of two solid solutions, which have crystallized below the spinodal surface. Hence, the crystallization path does not follow the at-equilibrium liquidus and solidus surfaces as for steady fluxgrowth. The crystallization path for high pulling speed (15mm.h -1 ) crosses more or less vertically the phase diagram for reaching directly a two-phase region due to the high thermal gradient in the mmsized meniscus. This led to effective partition coefficients closer to 1 than those reported for steady flux-grown crystals. Concerning the crystallization path for lower pulling speed (6mm.h -1 ), we assume that the thermodynamic path follow a steep out-of-equilibrium liquidus surface, leading to different effective partition coefficients which tend, in some extent, to get closer to those calculated with fluxgrown crystals close to the equilibrium. Besides, it is worth noticing that BaTiO 3 -CaTiO 3 phase diagram does not exactly correspond to the real phase diagram where the growth took place. Indeed, BaTiO 3 -CaTiO 3 -BaZrO 3 phase diagram must be slightly different because of the little Zr amount (i.e. 0.4mol.%) in the liquid solution. So that the spinodal surface should be slightly modified.

Nevertheless, the low amount of Zr employed allows us to consider that both phase diagrams should exhibit the same main features.

We conclude that the effective segregation phenomenon in BCTZ grown by µ-PD is not completely compensated by the fast kinetics of the growth in between 6 and 15 mm.h -1 but they are drastically reduced compared to those measured in TSSG-grown crystals. Higher pulling rate should be applied in order to reach partition coefficients equal to 1 as observed for the Edge-defined Film-fed Growth of LiNb x Ta 1-x O 3 solid solution where a pulling speed about 42 mm.h -1 was used and as calculated for µPD-grown Ti 3+ :Al 2 O 3 crystals 54 in order to achieve a constant Ti 3+ -dopant distribution. Nevertheless, it appears that it would be at the expense of chemical homogeneity throughout the BCTZ samples.

Transversal chemical analysis of as-grown fibres

Transversal chemical analysis on two 3-mm wide cross sections located at 19mm and 27mm of the fibre pulled at 6 mm.h -1 depicted on Figure 2 were performed by both EPMA (Figure 6) and LIBS (Figure 7).

Elemental segregation phenomenon is also observed where the core of the fibre is Zr-rich contrary to its periphery, which is Ca-rich. This trend is similar to that which is observed in TSSG-grown BCTZ crystals 15 or in rare earth-doped garnet 41,[55][56][57] grown by µ-PD where strong increasing or decreasing of dopant content is observed from the rim towards the core of fibres. LIBS confirmed this phenomenon where central zone exhibits Zr-rich and Ca-poor contents whereas the other zones, at the rim of the fibre, display the reverse tendency. Laue patterns were recorded on different sample locations all along the fibres. Experimental patterns were indexed with P4mm space group and lattice parameters above mentioned. As growth attempts were performed on Ir rods, the beginning of fibres exhibits invariably a highly polycristalline structure with micrometre-sized grains. As the pulling length increases, sub mm-sized grains arises with preferential orientation along (110) pc and (001) pc directions (Figure 9a andb). Finally, the end of fibres exhibit large mm-sized single crystal grains with predominantly (001) pc orientation (Figure 9b andc), which corresponds, unsurprisingly, to the more stable growth orientation usually used for the crystal growth in perovskite systems 58 . It is worth mentioning that stripes highlighted by LIBS characterization tend to be oriented along (001) pc direction. As Laue patterns were recorded with a circular 0.7mm-wide beam on zones containing both Zr-rich stripes and Zr-poor stripes, they displayed clearly single crystal features.

These features indicate that the significant drops and variations of Ca and Zr contents from one stripe to another do not affect considerably the single crystal nature of the analysed zones. On the one hand, Laue experiments confirm the crossover of the BCTZ solid solution across a wide range of compositions as previously reported 13 . On the other hand, the presence of two solid solutions remains not excluded. Indeed, two solid solutions can grow each on the other with good lattice-matched epitaxy because of their close compositions, as already seen in lead-free systems with Morphotropic Phase Boundary 4,7,59-61 and Phase Convergence Region 6,11 . Nevertheless, they would be undistinguishable on Laue patterns due to their very similar lattice parameters and structures 15 as well as their mixing at the nanometre scale [62][63][64] .

Dielectric and electromechanical characterization

Five polycrystalline sub-centimetre-sized samples with large millimetre-sized grains were analysed.

The sample size is : n°1 (6,68 x 2,08 x 0,66 mm 3 ), n°2 (8,39 x 2,06 x 0,63 mm 3 ), n°3 (3,58 x 1,71 x 0,52 mm 3 ), n°4 (9,81 x 1,47 x 0,47 mm 3 ) and n°5 (8,15 x 1,61 x 0,72 mm 3 ). As highlighted by LIBS measurements, samples are chemically inhomogeneous. So that sample compositions are given for information purposes only in Table 1. That illustrates a macroscopic trend of their average content, which nevertheless allows it to be corroborated to their macroscopic electromechanical behaviour since their ferroelectric and piezoelectric features reflect long-range order effects. Dielectric Dielectric and piezoelectric results are in good agreement with literature regarding (001) pc -oriented low-Zr content BCTZ single crystals 17,18 . The polycristalline samples of the present works exhibit similar or slightly higher d 33 coefficient whatever the compositions and pulling speeds considered.

However, we noted that k 31 and k 32 , which should be strictly equal for isotropic ceramics, display slightly different values. That emphasizes the texture of polycrystals, which display preferential grains orientation as revealed by Laue experiments. The higher dielectric constant    / 0 was obtained for the sample n°3 corresponding to the beginning of the second fibre where drop melt occurred (see 4.1).

Laue analysis have shown that this sample is strongly polycrystalline and features average isotropic value of the dielectric constant as well as very close values of k 31 and k 32 . Other textured samples display, with (110) and (111) rough crystallographic direction, lower dielectric constants. For the five considered samples, electromechanical thickness coupling factor (k t ) are between 36% and 41% and the variation of the dielectric constant does not impact significantly this property.

Besides, it is well known that piezoelectric response in single crystals is both compositional and domain size dependent. Considering the results of chemical and Laue crystallographic characterization above mentioned, we assumed that the high growth kinetics and thermal gradients in the micro pulling down technique induces a high rate of defects, leading to a high rate of domain walls pining. The generation of smaller domain sizes may be enabled, as already seen by Wada et al. in BaTiO 3 grain oriented ceramics 65,66 and single crystals [67][68][69] , enhancing thus the piezoelectric response of µ-PD crystals compared to that of steady TSSG-grown single crystals with same composition.

Conclusion

Centimetre-sized BCTZ solid solution fibres with large millimetre-sized grains were successfully grown by the micro-pulling down technique. This technique enables the achievement of enhanced control of elemental distribution all along the BCTZ fibres for pulling velocities ranging from 6 to 15 mm.h -1 . Ca and Zr partition coefficients close to one were obtained and have been significantly

Conflicts of interest

There are no conflicts to declare 7.

Figure 1 :

 1 Figure 1 : (a) Conical-shaped iridium crucible with a 600-µm capillary die; (b) Ir rod with needle-shaped tip and Ir conical crucible before connexion; (c) Connexion of the Ir rod with the liquid solution and (d) creeping of the liquid solution along the outer surface of the Ir conical crucible. (e) Iridium crucible with a 3-mm wide cylindrical die, with a concave end and 5 capillary holes; (f) Connection of the Ir rod with the liquid solution; (g) and (h): beginning of pulling. No liquid solution creeping is observed.

Figure 2 : 1 ,

 21 Figure 2 : Fibres obtained at pulling rates: (a) v=15 mm.h -1 , (b) v=9 mm.h -1 in the first part from Z=0 to Z=10 mm and v=6 mm.h -1 in the second part from Z=10 to Z=30 mm.

Figure 3 :

 3 Figure 3 : Ca and Zr longitudinal content profile as a function of length of fibres pulled at (a) v=15 mm.h -1 (from z=0.0 to 15.1mm) and (b) v=6 mm.h -1 (from z=21.9 to 30.0mm). Dashed lines display the average Ca and Zr contents.

Figure 4 :

 4 Figure 4 : Effective partition coefficients of µ-PD grown fibres (orange triangles) compared to effective partition coefficient reported for flux grown crystals 15 (blue circles) for (a) Ca and (b) Zr. Dashed grey lines display targeted k eff =1.

Figure 5 : 1 .

 51 Figure 5 : LIBS chemical imaging for Ca and Zr on samples obtained from fibres pulled at (a) 15 mm.h -1 and (b) 6mm.h -1 . (c) Molar contents have been normalized regarding EPMA profile performed along the dashed line of the fibres grown at 6mm.h -1

Figure 6 :

 6 Figure 6 : EPMA transversal chemical analysis for Ca and Zr in two cross section of 3-mm wide fibres pulled at 6mm.h -1 at (a) z=19mm (Dashed lines display the average transversal Ca content) and at (b) z=27mm

Figure 7 :

 7 Figure 7 : LIBS transversal chemical imaging for Ca and Zr obtained on two cross sections of a 3-mm wide fibre pulled at 6mm.h -1 and located at (a) Z=19mm and (b) Z=27mm4.3 X-rays diffraction and Laue analysis

Figure 8 :

 8 Figure 8 : XRD patterns on BCTZ crushed sample exhibiting a tetragonal structure with double peaks at 245° featuring (002) and (200) crystallographic plans for (a) fibre n°1 and (b) fibre n°2.

Figure 9 :

 9 Figure 9 : Laue patterns along growth direction: (a) mm-sized grains displaying (110) pc orientation in the middle of fibre n°1 and (b) two grains slightly tilted with both (001) pc orientation at the end of fibre n°2 . (c) Stereographic projection along (001) pc (end of fibre n°2)

  measurements performed at various frequency confirm the pure ferroelectric behaviour and the tetragonal structure at room temperature of BCTZ samples as illustrated on Figure 10 with sample n°1 with (Ba 0.889 Ca 0.111 )(Ti 0.995 Zr 0.005 )O 3 average macroscopic composition. For this sample, the Tetragonal-Cubic transition (T-C) is observed at 113°C and the Orthorhombic-Tetragonal (O-T) transition near to -20°C.

Figure 10 :

 10 Figure 10 : Dielectric constants measurements at various frequencies of poled sample n°1 with (Ba 0.889 Ca 0.111 )(Ti 0.995 Zr 0.005 )O 3 average composition. T-C and O-T correspond to, respectively, tetragonal-cubic transition at 113°C and orthorhombictetragonal phase transition at -20°C.

  decreased compared to those obtained for classically TSSG-grown crystals. Chemical characterization performed through EPMA and LIBS measurements highlighted chemical fluctuations within single crystals. (001)-oriented stripes-like zones exhibiting high or low Zr/Ca contents alternatively suggest the coexistence of two perovskite solid solutions with close compositions without being detrimental to the single crystal nature of the characterized zones. Dielectric and electromechanical characterization displayed Curie temperatures up to 113°C, d 33 up to 242 pC.N -1 and the highest k t around 41%, which are in good agreement with single crystals with close compositions. These results obtained by the micro pulling down technique open the way of growing lead-free solid solutions with improved chemical and domain size control leading to optimal and competitive piezoelectric performances.

Table 1 :

 1 Chemical and electromechanical properties of BCTZ samples grown by µPD compared to (001) pc -oriented BCTZ single crystals with close compositions

	Sample n°	Pulling speed (mm.h -1 )	Average composition	   / 0 k t (%) k 31 (%) k 32 (%)	d 33 (pC.N -1 )	T c (°C)	Reference
	1	15	(Ba 0.889 Ca 0.111 )(Ti 0.995 Zr 0.005 )O 3	755	41.0 15.5 22.2	172	113 This work
	2	15	(Ba 0.885 Ca 0.115 )(Ti 0.995 Zr 0.005 )O 3	670	36.1 16.8 14.4	242	105 This work
	3	9	(Ba 0.882 Ca 0.118 )(Ti 0.996 Zr 0.004 )O 3	1160 39.3 16.4 16.1	123	112 This work
	4	6	(Ba 0.899 Ca 0.101 )(Ti 0.979 Zr 0.021 )O 3	770	36.6 16.7 16.0	152	107 This work
	5	6	(Ba 0.896 Ca 0.104 )(Ti 0.993 Zr 0.007 )O 3	605	35.8 14.8 17.4	186	107 This work
	(001) pc -oriented	-	(Ba 0.798 Ca 0.202 )(Ti 0.994 Zr 0.006 )O 3	-	-	-	-	232	125

Acknowledgment

The authors acknowledge the Intelum project (Marie Skłodowska-Curie grant agreement n° 644260) for financial support of this work. Ruben Vera and Erwann Jeanneau from Diffraction Centre Henri Longchambon of University Claude Bernard Lyon 1 are acknowledged for XRD experiments.

8.