Peter Baláž

Marcela Achimovičová

Matej Baláž

Kan Chen

Oleksandr Dobrozhan

Emmanuel Guilmeau

Jiří Hejtmánek

Karel Knížek

Lenka Kubíčková

Petr Levinský

Viktor Puchý

# Michael

John Reece

Peter Varga

Ruizhi Zhang

Thermoelectric Cu-S based materials synthesized via scalable mechanochemical process

Keywords: energy materials, thermoelectrics, multinary copper sulfides, mechanochemistry, scalable solid state synthesis

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INTRODUCTION

Statistical results show that more than 60% of energy is lost in vain, most of it in the form of waste heat [START_REF] Zhang | Thermoelectric materials: Energy Conversion between Heat and Electricity[END_REF] . Over 80% of waste heat generated in industrial processes is in the temperature range of 100-300 °C, suggesting that considerable opportunities exist for the development of efficient thermoelectric materials that operate at this regime [START_REF] Long | High Thermoelectric Performance of Bornite through Control of the Cu(II) Content and Vacancy Concentration[END_REF] . Thermoelectric devices offer a viable way to generate electricity from a temperature gradient without hazardous side products. They are silent, reliable, scalable, predictable and durable. However, their applications remain limited because the best-known materials for thermoelectric devices are based on scarce, toxic and costly compounds with limited chemical stability at operating conditions. For example, the abundance of telurium is only 0.001 ppm, which is significantly lower than silver and even lower than gold and platinum. Moreover, its toxicity is high [START_REF] Ge | Low-cost, Abundant Binary Sulfides as Promising Thermoelectric Materials[END_REF] .

Several new compounds have emerged recently with high thermoelectric performance. Among them, metal chalcogenides have attracted considerable attention as potential teluriumfree alternatives [START_REF] Ge | Low-cost, Abundant Binary Sulfides as Promising Thermoelectric Materials[END_REF][START_REF] Baláž | Chalcogenide Mechanochemistry in Materials Science: Insight into Synthesis and Applications (a Review)[END_REF] . Especially copper chalcogenides appeared as potential candidates due to their advantages: earth abundant, low cost, and less toxic character of constituting components and high thermoelectric performance [START_REF] Zhang | Thermoelectric materials: Energy Conversion between Heat and Electricity[END_REF][START_REF] Suekuni | Research Update: Cu-S Based Synthetic Minerals as Efficient Thermoelectric Materials at Medium Temperatures[END_REF][START_REF] Qiu | Cu-based Thermoelectric Materials[END_REF][START_REF] Li | Processing of Advanced Thermoelectric Materials[END_REF][START_REF] Wei | Copper Chalcogenide Thermoelectric Materials[END_REF] .

As for the application of thermoelectric materials, the Seebeck coefficient (S), electrical conductivity (σ) and thermal conductivity (κ) are measured at different temperatures (T) to calculate the values of dimensionless figure-of-merit ZT:

ZT = S 2 σ/κ (1)
(κ) is a sum of lattice thermal conductivity κ L and electronic thermal conductivity (κ e ). Its ZT value determines the efficiency of thermoelectric materials. To ensure a high voltage output large S is needed, while a high σ is needed to limit losses by Joule effect. To maintain a temperature gradient low κ value is required [START_REF] Ioffe | Semiconductor Thermoelements and Thermoelectric Cooling[END_REF] . Additionally, thermoelectric devices are of interest because of their silent operation, reliability, scalability, predictability and durability.

They are used in cases when cost and energy efficiency are not so important as energy availability [START_REF] Dresselhaus | New Directions for Low-dimensional Thermoelectric Materials[END_REF] . However, their broader application is needed in future energy materials aimed to harvest waste heat and reduce of fossile fuels consumption [START_REF] Powell | Recent Developments in Earth-abundant Copper-sulfide Thermoelectric Materials[END_REF] .

In 1990s the nanostructure approaches were introduced and applied to thermoelectrics to enhance their ZT values [START_REF] Dresselhaus | New Directions for Low-dimensional Thermoelectric Materials[END_REF][START_REF] Hicks | Effect of Quantum-well Structures on the Thermoelectric Figure of Merit[END_REF][START_REF] Hicks | Thermoelectric Figure of Merit of a One-dimensional Conductor[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] Li | Defect Chemistry for Thermoelectric Materials[END_REF][START_REF] He | Advances in Thermoelectric Materials Research: Looking Back and Moving Forward[END_REF] . Moreover, when non-equilibrium procedures such as highenergy milling and/or mechanochemical synthesis (HEM/MS), melt spinning and selfsustaining heating synthesis was applied, delicate multiscale structures was obtained [START_REF] He | Advances in Thermoelectric Materials Research: Looking Back and Moving Forward[END_REF] . In the case of the application of HEM/MS [START_REF] Baláž | Chalcogenide Mechanochemistry in Materials Science: Insight into Synthesis and Applications (a Review)[END_REF][START_REF] Beyer | Mechanochemistry: The Mechanical Activation of Covalent Bonds[END_REF][START_REF] Baláž | Mechanochemistry in Nanoscience and Minerals Engineering[END_REF][START_REF] Friscic | New Opportunities for Materials Synthesis Using Mechanochemistry[END_REF][START_REF] Šepelák | Mechanochemistry: from Mechanical Degradation to Novel Materials Properties[END_REF][START_REF] Baláž | Hallmarks of Mechanochemistry: from Nanoparticles to Technology[END_REF][START_REF] Do | Mechanochemistry: A Force of Synthesis[END_REF][START_REF] Mucsi | A Review on Mechanical Activation and Mechanical Alloying in Stirred Media Mill[END_REF][START_REF] Friscic | Mechanochemistry for Synthesis[END_REF] combined with spark plasma sintering [START_REF] Bordia | Current Understanding and Future Research Directions at the Onset of the Next Century of Sintering Science and Technology[END_REF] the created nanostructures also contribute to scatter phonons and thus to suppress lattice thermal conductivity κ L . Since the invention of HEM, large quantities of nanoparticles can be prepared [START_REF] Lan | Enhancement of Thermoelectric Figure-of-Merit by a Bulk Nanostructuring Approach[END_REF] .

In this work we thus describe the properties and thermoelectric performances of several copper-based multinary sulfides. This include chalcopyrite CuFeS elements in an industrial mill [START_REF] Gock | Eccentric Vibratory Mills-Theory and Practice[END_REF] . After synthesis the produced powders were densified using spark plasma sintering (SPS) and eventually, hot pressing (HP) techniques-see SI. The properties of the products were studied by several characterization techniques and their thermoelectric performances were evaluated.

MATERIALS AND METHODS

For mechanochemical synthesis of chalcopyrite CuFeS The syntheses were carried out in an industrial eccentric vibratory ball mill ESM 656-0.5ks (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 30 kg, 80% ball filling in milling chamber, amplitude of inhomogenous vibrations 20 mm, rotational speed of the eccenter 960 min -1 , argon atmosphere. The total feed of reaction precursors was 100 g per batch. The milling was performed for different times which are mentioned in the appropriate sections.

For comparison, the syntheses were also carried out in a laboratory scale planetary mill Pulverisette 6 (Fritsch, Germany) working under the following conditions: 250 mL tungsten carbide milling chamber, tungsten carbide balls with a diameter of 10 mm and total mass of 360 g, 80% ball filling in a milling chamber, revolutions of the milling chamber 550 rpm, argon atmosphere. The total feed of reaction precursors was 5 g per batch. The milling was performed for different times which are mentioned in the appropriate section.

After completion of the milling programs, the resulting pulverized powders were shaped and densified using SPS apparatus (FCTHPD25, Germany), eventually hot pressing.

Technical details are given in SI (Table S1). The final thickness of the pellets was around 3 mm with a geometrical density in excess of 95% of the crystallographic value.

The qualitative identification of the phase compositions was performed by XRD method.

For the systems under study, several diffractometers were applied with the working conditions summarized in SI. [START_REF] Zhou | Sustainable Thermoelectric Materials Fabricated by Using Cu 2 Sn 1-x Zn x S 3 Nanoparticles as Building Blocks[END_REF] Fe Mössbauer spectroscopy was employed to clarify the magnetic ordering in chalcopyrite and to identify possible admixtures of other Fe-bearing compounds. To measure the [START_REF] Zhou | Sustainable Thermoelectric Materials Fabricated by Using Cu 2 Sn 1-x Zn x S 3 Nanoparticles as Building Blocks[END_REF]

Fe

Mössbauer spectra, the powder samples were pressed into tablets with tableting wax. The spectra were collected at room temperature and in a helium bath cryostat by Janis Research Company, Inc. (Woburn, MA, USA) at 4.2 K in the transmission mode using a [START_REF] Zhou | Sustainable Thermoelectric Materials Fabricated by Using Cu 2 Sn 1-x Zn x S 3 Nanoparticles as Building Blocks[END_REF] Co/Rh source. The calibration of velocities and isomer shift was performed with respect to an α-Fe foil at room temperature.

The electrical resistivity (ρ) and Seebeck coefficient (S) were measured simultaneously from ingots, from 300K up to 700 K under partial pressure of helium or pure N 2 flow using an ZEM-3 (Ulvac-Riko, Japan) and home made system. Also a commercial instrument LSR-3/110 (Linseis, Germany) working in the He atmosphere was used. The absolute precision and mutual veracity of above-mentioned thermoelectric measurements was verified in [START_REF] Alleno | A Round Robin Test of the Uncertainty on the Measurement of the Thermoelectric Dimensionless Figure of Merit of Co 0.97 Ni 0.03 Sb 3[END_REF] . This enabled to confirm both the relevance of the measured data and their veracity using various apparatuses. LFA 457 apparatus (Netzsch, Germany) 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 However, the sulphur atoms displaces from the center of the bonded tetrahedron, because the Fe-S bond is stronger and more anisotropic than the Cu-S bond [START_REF] Li | Thermoelectric Transport Properties of Diamond-like Cu 1-x Fe 1+x S 2 Tetrahedral Compounds[END_REF] . CuFeS 2 is known to be an antiferromagnetic semiconductor at ambient pressure. The charge carriers are p-or n-type depending on the samples, at high temperature the n-type conductivity dominates [START_REF] Teranishi | Magnetic and Electric Properties of Chalcopyrite[END_REF] .

In this respect the chalcopyrite has been reported as an interesting n-type thermoelectric material with a reported value of ZT=0.2 [START_REF] Li | Synthesis and Property Evaluation of CuFeS 2-x as Earth-abundant and Environmentally-friendly Thermoelectric Materials[END_REF] . As n-type doping procedure several approaches can be used; among all we note (i) the Fe overstoichiometry in Cu We underline that in case of chalcopyrite, which is semiconducting in nature, the optimized doping must be used to improve thermoelectric performance with higher ZT values [START_REF] Tsujii | Effect of Nanostructuring and High-Pressure Torsion Process on Thermal Conductivity of Carrier-doped Chalcopyrite[END_REF][START_REF] Tsujii | Possible Enhancement of Thermoelectric Properties by Use of a Magnetic Semiconductor: Carrier-doped Chalcopyrite Cu 1-x Fe 1+x S 2[END_REF][START_REF] Berthebaud | Thermoelectric Properties of n-type Cobalt Doped Chalcopyrite Cu 1-x Co x FeS 2 and p-type Eskebornite CuFeSe 2[END_REF][START_REF] Lefevre | Thermoelectric Properties of the Chalcopyrite Cu 1-x M x FeS 2-y Series (M = Mn, Co, Ni)[END_REF][START_REF] Vaure | Doping and Surface Effects of CuFeS 2 Nanocrystals Used in Thermoelectric Nanocomposites[END_REF][START_REF] Navratil | Thermoelectric and Transport Properties of n-type Palladium-Doped Chalcopyrite Cu 1-x Pd x FeS 2 Compounds[END_REF] .

The idea of this paper is, however, to document the viability of the industrial milling process followed by the hot press treatment of mechanochemically synthesized non-doped CuFeS 2 in comparison with powders synthesized in a laboratory mill. The methods of XRD and Mössbauer spectroscopy were applied for bulk characterization.

As determined by XRD, the most prominent impurity in our mechanochemically synthesized CuFeS 2 is pyrite FeS 2 (~2.4 %) for in laboratory-milled samples and bornite Cu 5 FeS 4 (0.6-0.8 %) for both types of mechanochemical synthesis. The occurrence of these two marginal intermediate products is supported by their identification in the high temperature solid state synthesis [START_REF] Xie | Thermoelectric Performance of CuFeS 2+2x Composites Prepared by Rapid Thermal Explosion[END_REF] . Small amounts of tungsten carbide WC (1.8 %) from wear coming from milling balls was evidenced for the sample milled industrially for a much longer time (720 min) in comparison with 60 min for laboratory mill (Figure 1). The crystallite size of the powders is about 10 nm. As we were interested in the impact of the mechanochemical synthesis on different scales on morphology and crystallinity of the synthesised powder material, we chose the Mössbauer spectroscopy using [START_REF] Zhou | Sustainable Thermoelectric Materials Fabricated by Using Cu 2 Sn 1-x Zn x S 3 Nanoparticles as Building Blocks[END_REF] Fe nuclei as local probes for structural changes in chalcopyrite and for poorly crystalline admixtures. Since chalcopyrite is a strong antiferromagnet, its spectrum is characterised by Zeeman-split sextets (Figure 2), whose hyperfine parameters of these sextets correspond to tetrahedrally coordinated Fe 3+ ions in the high spin state [START_REF] Tkáčová | Reactivity of Mechanically Activated Chalcopyrite[END_REF] . The broadening of the lines at low temperatures is caused by defects [START_REF] Xie | Origin of Intrinsically Low Thermal Conductivity in Talnakhite Cu[END_REF] introduced into the structure during the mechanochemical synthesis and can be accounted for by fitting by more components with different numbers of defects among the nearest neighbors of the Fe site [START_REF] Tkáčová | Reactivity of Mechanically Activated Chalcopyrite[END_REF] . Interestingly, the sample prepared in the laboratory mill has less defects than the one synthesized in the industrial mill, although the low-temperature spectrum of the latter indicates that a certain amount of the particles contains a highly crystalline core with bulk-like properties. The roomtemperature spectra are further broadened by superparamagnetic relaxation of the nanoparticles with slightly slower Néel relaxation times than the time window of the method (10 -7 s). In both samples, admixtures of pyrite (FeS 2 ) and iron oxyhydroxides (FeOOH) were found, however, the conditions in the laboratory mill produced the chalcopyrite phase of higher purity. The highly amorphous FeOOH, likely originating from water and oxygen adsorbed in the equipment, was not detected in XRD (Figure 1) and most probably forms a surface layer of the nanoparticles. To further elucidate the influence of the high-temperature treatment (e.g. hot pressing) on the morphology and composition of the samples Mössbauer spectroscopy will be performed for both hot-pressed samples as well. We suppose that the high-temperature treatment wil reduce the amount of the impurity phases together along with reduction of strain. The temperature dependances of the electrical transport properties are shown in Figure 3a.

Most importantly, both samples exhibit similar electric transport properties. The electrical resistivity perfectly reflects the semiconducting low-doped nature of synthesized CuFeS 2 . The sign of Seebeck coefficient is changing from positive hole-like character at room temperature to negative electron-like behavior at higher temperatures (Figure 3b). The low concentration of point defects (acceptors and donors), in accordance with the variation of Seebeck coefficient, corresponds to an acceptor level accounting for p-type conductivity at low temperatures while a donor effect accounts for n-type conductivity at higher temperatures. This phenomenon is the same for both types of milling. The identical behaviour of both samples is documented also in the temperature dependence of their thermal conductivities, Figure 3c. Due to a very high electrical resistivity, the electronic contribution to the thermal conductivity is negligible. The observed substantially lower thermal conductivity compared with a pristine sample prepared by solid state reaction is due to nanostructuring of the sample.

Similarly due to nanostructuration the low temperature "dielectric" peak, typical for "pure" crystallized insulators, is completely "depressed" as well as the high temperature values.

Here, due to substantially lower phonon mean free path of heat carrying phonons, the decrease of the thermal conductivity is likely due to increased scattering similar to "point defect" likely associated with the mechanochemical synthesis. The dependence of the figureof-merit ZT on temperature is shown in Figure 3d. The ZT values for undoped CuFeS 2 are very low and of little significance for application. However, the key purpose of this study, is to demonstrate upgrading the milling process to an industrial scale, is clearly demonstrated. In this case, at 600 K the ZT value for an industrial milling is almost 2.5-times higher than in the case of a laboratory milling. Respecting the above-mentioned correlation between the doping and ZT optimization we refer to recent approach, where thermoelectric performance was enhanced by using non-doped CuFeS 2 nanocomposite created by co-milling of synthetic and natural species. An enhancement of the ZT values from 0.004 to 0.14 was obtained [START_REF] Baláž | Enhanced Thermoelectric Performance of Chalcopyrite Nanocomposite via Co-milling of Synthetic and Natural Minerals[END_REF] . Cu 2 SnS 3 belongs among ternary chalcogenides and is the most important representative of copper-tin-sulfur (CTS) family with mineralogical name mohite [START_REF] Kovalenker | Cu 2 SnS 3, a New Sulphide of Tin and Copper[END_REF] . Already 4 polymorphs have been reported until now-tetragonal, monoclinic, cubic and trigonal [START_REF] Dahman | Structural, Morphological and Optical Properties of Cu 2 SnS 3 Thin Film Synthesized by Spin Coating Technique[END_REF][START_REF] Onoda | Crystal Structure and Twinning of Monoclinic Cu 2 SnS 3[END_REF][START_REF] Han | Hydrazine Processed Cu 2 SnS 3 Thin Film and their Application for Photovoltaic Devices[END_REF][START_REF] Fernandes | A Study of Ternary Cu 2 SnS 3 and Cu 4 SnS 4 Thin Films Prepared by Sulfurizing Stacked Metal Precursors[END_REF] . Its main application field is photovoltaic [START_REF] Reddy | Review on Cu 2 SnS 3 , Cu 3 SnS 4 , and Cu 4 SnS 4 Thin Films and their Photovoltaic Performance[END_REF] , however, it has been also found as an interesting thermoelectric material [START_REF] Shen | Eco-friendly p-type Cu 2 SnS 3 Thermoelectric Material: Crystal Structure and Transport Properties[END_REF][START_REF] Nakamura | Electrical Conductivity Improved Cu 2 SnS 3 Thermoelectrics[END_REF][START_REF] Deng | Thermoelectric Properties of Non-stoichiometric Cu 2+x Sn 1-x S 3 Compounds[END_REF][START_REF] Lohani | Ultra-low Thermal Conductivity and Improved Thermoelectric Performance in Disordered Nanostructured Copper Tin Sulphide (Cu 2 SnS 3 , CTS)[END_REF] . The TE performance can be enhanced by doping with Mn 55 , Fe 56 , Zn [START_REF] Zhou | Sustainable Thermoelectric Materials Fabricated by Using Cu 2 Sn 1-x Zn x S 3 Nanoparticles as Building Blocks[END_REF] , Co [START_REF] Zhao | Cobalt-doping in Cu 2 SnS 3 : Enhanced Thermoelectric Performance by Synergy of Phase Transition and Band Structure Modification[END_REF] and Ni [START_REF] Xu | Synergistic Role of Nidoping in Electrical and Phonon Transport Properties of Cu 2 Sn 1-x Ni x S 3[END_REF] . There are many synthetic pathways to this compound, which can be divided into physical and chemical and have been nicely reviewed by Lokhande et al. [START_REF] Lokhande | Chemical Synthesis of Cu 2 SnS 3 (CTS) Nanoparticles: A Status Review[END_REF][START_REF] Lokhande | Development of Cu 2 SnS 3 (CTS) Thin Film Solar Cells by Physical Techniques: A Status Review[END_REF] .

Mechanochemical synthesis representing a one-step environmentally friendly approach has also been used for the preparation of Cu 2 SnS 3 54, 62-64 . Our research group has successfully prepared this compound from elements on a laboratory scale [START_REF] Baláž | Rapid Mechanochemical Synthesis of Nanostructured Mohite Cu 2 SnS 3 (CTS)[END_REF] , and also from binary sulfides on a larger scale [START_REF] Hegeduš | Scalable Synthesis of Potential Solar Cell Absorber Cu 2 SnS 3 (CTS) from Nanoprecursors[END_REF] . However, its application potential has not been revealed in our studies so far.

In the present study, we prepared CTS nanocrystals using mechanochemical synthesis in an eccentric vibratory mill. The XRD patterns of the elemental mixture of Cu, Sn and S taken after different time of milling are presented in Figure 4a. The XRD pattern of the powder mixture milled for 60 min already shows a significant amount of Cu 2 SnS 3 product (either cubic or tetragonal polymorph). It is not possible to certainly determine the formed polymorph from the XRD patterns of the as-milled product with very broad peaks, as the main peaks of these phases are very close [START_REF] Fernandes | A Study of Ternary Cu 2 SnS 3 and Cu 4 SnS 4 Thin Films Prepared by Sulfurizing Stacked Metal Precursors[END_REF] . However, Lohani et al. who also used ball milling to prepare Cu 2 SnS 3 nanocrystals (also starting from binary sulfides) reported the polymorph to be cubic [START_REF] Lohani | Ultra-low Thermal Conductivity and Improved Thermoelectric Performance in Disordered Nanostructured Copper Tin Sulphide (Cu 2 SnS 3 , CTS)[END_REF] . In addition to the main phase, the non-reacted Sn and CuS could still be observed in the XRD pattern of the powders treated for 60 and 180 minutes. During the next 60 minutes, there was only a slight improvement of the progress of the reaction observed. The synthesis using the scaled-up process was much less rapid in comparison with planetary ball milling using elemental precursors, which was reported to be finished in 15 minutes [START_REF] Baláž | Rapid Mechanochemical Synthesis of Nanostructured Mohite Cu 2 SnS 3 (CTS)[END_REF] . When using compounds, the process took longer, namely 60 and 240 min for planetary and eccentric vibratory milling, respectively [START_REF] Hegeduš | Scalable Synthesis of Potential Solar Cell Absorber Cu 2 SnS 3 (CTS) from Nanoprecursors[END_REF] . The laboratory-scale planetary and scaled-up eccentric vibratory ball milling have been used also for other systems, e.g. kesterite [START_REF] Hegeduš | Mechanochemical Approach to a Cu 2 ZnSnS 4 Solar Cell Absorber via a "Micronano[END_REF][START_REF] Baláž | Photovoltaic Materials: Cu 2 ZnSnS 4 (CZTS) nanocrystals Synthesized via Industrially Scalable, Green, One-step Mechanochemical Process[END_REF] and CuS synthesis [START_REF] Baláž | Ultrafast Mechanochemical Synthesis of Copper Sulfides[END_REF][START_REF] Achimovičová | Structural and Optical Properties of Nanostructured Copper Sulfide Semiconductor Synthesized in an Industrial Mill[END_REF] and were directly compared in polyvinylchloride dechlorination using eggshell [START_REF] Baláž | Simultaneous Valorization of Polyvinyl Chloride and Eggshell Wastes by a Semi-industrial Mechanochemical Approach[END_REF] , always that showing much longer time is necessary when performing the eccentric vibratory milling.

Based on this analysis, the sample milled for 180 min was selected as an optimum one. S2. An asterisk described the probable presence of very small amounts of monoclinic phase.

In order to test the material for its potential applications in thermoelectrics, the as-received powder was subjected to spark plasma sintering at 550 °C. The XRD pattern of the sintered sample was subjected to Rietveld refinement and the result is shown in Figure 4b. We have tried fitting the obtained XRD data in the tetragonal space group I-42m assigned to Cu 2 SnS 3 54, [START_REF] Hegeduš | Scalable Synthesis of Potential Solar Cell Absorber Cu 2 SnS 3 (CTS) from Nanoprecursors[END_REF] , in monoclinic space group C1 [START_REF] Onoda | Crystal Structure and Twinning of Monoclinic Cu 2 SnS 3[END_REF][START_REF] De Chalbaud | X-ray Powder Diffraction Data and Structural Characterization of Cu 2 GeS 3 and Cu 2 SnS 3[END_REF] and also in cubic F-43m in [START_REF] Kovalenker | Cu 2 SnS 3, a New Sulphide of Tin and Copper[END_REF] . The best fit has been obtained for the cubic phase, however, even better results were recorded when both cubic and monoclinic phase were considered, although the content of the latter was negligible. The lattice parameter a for the cubic phase was found to be 5.4314 ± 0.0002 Å, which is very close to the value 5.44 reported in [START_REF] Lohani | Ultra-low Thermal Conductivity and Improved Thermoelectric Performance in Disordered Nanostructured Copper Tin Sulphide (Cu 2 SnS 3 , CTS)[END_REF][START_REF] Palatnik | A Group of Ternary Semiconducting Compounds[END_REF] . The apparent crystallite size for the cubic Cu 2 SnS 3 was found to be 288±55 nm and the observed strain was 0.2000±0.0229.

The 2 theta values at which the three main peaks were observed are 28.42°, 47.28° and 56.10°, allow which suggest the assignment of cubic F-43m space group rather than I-42m

(by comparing the 2 theta values for both phases with those reported in [START_REF] Fernandes | A Study of Ternary Cu 2 SnS 3 and Cu 4 SnS 4 Thin Films Prepared by Sulfurizing Stacked Metal Precursors[END_REF] ). The Cu 2 SnS 3 in the same space group was reported by Lohani et al. [START_REF] Lohani | Ultra-low Thermal Conductivity and Improved Thermoelectric Performance in Disordered Nanostructured Copper Tin Sulphide (Cu 2 SnS 3 , CTS)[END_REF] . In our case, also a very small amount of monoclinic phase is most probably present. The potential phase transformation from cubic/tetragonal to monoclinic structure should be supported by the presence of the peaks at lower 2θ values [START_REF] Lohani | Ultra-low Thermal Conductivity and Improved Thermoelectric Performance in Disordered Nanostructured Copper Tin Sulphide (Cu 2 SnS 3 , CTS)[END_REF] . In Figure 4b, there is a very small diffraction peak at 16.1° marked with an asterisk, which could point to possible presence of the monoclinic phase. As the temperature of SPS was 550 °C, the cubic structure should be maintained to the large extent [START_REF] Fernandes | A Study of Ternary Cu 2 SnS 3 and Cu 4 SnS 4 Thin Films Prepared by Sulfurizing Stacked Metal Precursors[END_REF][START_REF] Oliva | Characterization of Cu 2 SnS 3 Polymorphism and its Impact on Optoelectronic Properties[END_REF] . Lohani et al. already observed 27% of the monoclinic phase after the treatment at this temperature [START_REF] Lohani | Ultra-low Thermal Conductivity and Improved Thermoelectric Performance in Disordered Nanostructured Copper Tin Sulphide (Cu 2 SnS 3 , CTS)[END_REF] .

The purity of the prepared material is quite high, with a very small amount of impurities denoted by the peaks located at 26.6° and 33.9°. The impurity has been identified as Cu 4 SnS 4 phase, similarly to a previous study [START_REF] Hegeduš | Scalable Synthesis of Potential Solar Cell Absorber Cu 2 SnS 3 (CTS) from Nanoprecursors[END_REF] . The thermoelectric properties of the sintered sample are displayed in Figure 5. The specific heat capacity was reported to be 0.44 J/gK [START_REF] Zhao | Cobalt-doping in Cu 2 SnS 3 : Enhanced Thermoelectric Performance by Synergy of Phase Transition and Band Structure Modification[END_REF] , so this value has been used for further calculations. The thermoelectric properties of the planetary ball milled Cu 2 SnS 3 have been recently reported in [START_REF] Lohani | Ultra-low Thermal Conductivity and Improved Thermoelectric Performance in Disordered Nanostructured Copper Tin Sulphide (Cu 2 SnS 3 , CTS)[END_REF] , showing the maximum ZT at 700 K to be around 0.3. We have obtained comparable result (ZT=0.26) using the scaled-up approach in this study, which further confirms that the disordered cubic F-43m structure has been obtained, although a small amount of monoclinic phase could slightly decrease the obtained ZT value. If the ordered monoclinic structure usually obtained at higher temperatures [START_REF] Oliva | Characterization of Cu 2 SnS 3 Polymorphism and its Impact on Optoelectronic Properties[END_REF] was present, the TE properties should be significantly reduced, as nicely shown in [START_REF] Lohani | Ultra-low Thermal Conductivity and Improved Thermoelectric Performance in Disordered Nanostructured Copper Tin Sulphide (Cu 2 SnS 3 , CTS)[END_REF] . In the literature, the ZT values at 700 K for undoped Cu 2 SnS 3 nanocrystals are usually around 0.2 (this can be significantly enhanced by doping as shown in [START_REF] Zhang | Role of Crystal Transformation on the Enhanced Thermoelectric Performance in Mn-doped Cu 2 SnS 3[END_REF][START_REF] Zhao | Magnetic Iron Doping in Cu 2 SnS 3 Ceramics for Enhanced Thermoelectric Transport Properties[END_REF][START_REF] Zhou | Sustainable Thermoelectric Materials Fabricated by Using Cu 2 Sn 1-x Zn x S 3 Nanoparticles as Building Blocks[END_REF][START_REF] Zhao | Cobalt-doping in Cu 2 SnS 3 : Enhanced Thermoelectric Performance by Synergy of Phase Transition and Band Structure Modification[END_REF][START_REF] Xu | Synergistic Role of Nidoping in Electrical and Phonon Transport Properties of Cu 2 Sn 1-x Ni x S 3[END_REF] ). Thus the positive input of milling action both in terms of nanostructuring and defects formation is undeniable in our case. The combination of doping and mechanochemical synthesis might be an effective combination for further improvement of Cu 2 SnS 3 thermoelectrics properties in the future.

Tetrahedrite Cu 12 Sb 4 S 13

Tetrahedrite as an Earth-abundant copper sulphide mineral with very low thermal conductivity [START_REF] Suekuni | Thermoelectric Properties of Mineral Tetrahedrites Cu 10 Tr 2 Sb 4 S 13 with Low Thermal Conductivity[END_REF] still represents continuous interest in the thermoelectric comunity [START_REF] Qiu | Cu-based Thermoelectric Materials[END_REF][START_REF] Wei | Copper Chalcogenide Thermoelectric Materials[END_REF][START_REF] Powell | Recent Developments in Earth-abundant Copper-sulfide Thermoelectric Materials[END_REF][START_REF] Chetty | Tetrahedrites as Thermoelectric Materials: an Overview[END_REF][START_REF] Baláž | Tetrahedrites Synthesized via Scalable Mechanochemical Process and Spark Plasma Sintering[END_REF][START_REF] Barbier | Structural Stability of the Synthetic Thermoelectric Ternary and Nickel-substituted Tetrahedrite Phases[END_REF] .

Moreover, its potential for application as energy material is currently expanding to be used also in photovoltaic devices [START_REF] Wang | Synthesis and Characterization of Hydrazine Solution Processed Cu 12 Sb 4 S 13 film[END_REF][START_REF] Kumar | Tetrahedrite (Cu 12 Sb 4 S 13 ) Thin Films for Photovoltaic and Thermoelectric Applications[END_REF] . To enhance its thermoelectric performance, doping of mechanochemically synthesized Cu 12 Sb 4 S 13 is a promissing possibility as can be seen from papers published recently, see e.g. [START_REF] Guler | Thermoelectric Properties and EPR Analysis of Fe Doped Cu 12 Sb 4 S 13[END_REF][START_REF] Knížek | LDA plus U Calculation of Electronic and Thermoelectric Properties of Doped Tetrahedrite Cu 12 Sb 4 S 13[END_REF][START_REF] Kumar | Thermoelectric and Electronic Properties of Chromium Substituted Tetrahedrite[END_REF][START_REF] Huang | Achieving a High Thermoelectric Performance of Tetrahedrites by Adjusting the Electronic Density of States and Enhancing Phonon Scattering[END_REF][START_REF] Tippireddy | Effect of Sn Substitution on the Thermoelectric Properties of Synthetic Tetrahedrite[END_REF] .

In this paper we present two innovative approaches for tetrahedrite:

Mechanochemical synthesis: activation energy from electrical conductivity as a function of milling time

We studied the temperature-dependent behavior of the electrical conductivity of synthetic tetrahedrite Cu 12 Sb 4 S 13 prepared by milling in an industrial mill for several different milling times. A detailed investigation of its properties is summarized in our recent paper [START_REF] Baláž | Tetrahedrites Synthesized via Scalable Mechanochemical Process and Spark Plasma Sintering[END_REF] . By fitting the linear part of the relation ln()=f(1/T), we determined the activation energies (E a ), which corresponds to three regimes of charge transport in milled samples (Figure 6a). At low temperatures (300-425 K) the activation energy changed in the range of E a = 26-37 meV, to E a =9-13 meV at medium temperatures (425-575 K), and to E a =55-71 meV at high temperatures (575-700 К) (Figure 6b). These values of activation energy are similar to the results obtained for tetrahedrite systems reported earlier [START_REF] Kumar | Thermoelectric Properties of Cd Doped Tetrahedrite: Cu 12-x Cd x Sb 4 S 13[END_REF] . The behavior of charge transport in the low and medium regimes corresponds to semiconductor behavior, showing extrinsic nature due to the highly disordered character of the crystal structure of the milled samples and saturation modes. Moreover, we observed a behavior change at the higher temperatures, showing a semiconductor to metal transition in the intrinsic mode. This transition might be caused by conduction hopping effects in the energetic band gap of Cu 12 Sb 4 S 13 because of the excitation of minority charge carriers as observed in [START_REF] Ohtaki | Electrical-transport Properties and High-temperature Thermoelectric Performance of Ca(0.9)M(0.1))MnO3 (M=Y,La,Ce,Sm[END_REF] . It is worth mentioning that depending on the milling time, the activation energies for three modes became almost saturated after 4 hours of milling with a slight decrease after 12 hours. The increase of the activation energy of carriers for three regimes can be attributed to the filling of the valence band which causes a decrease of the carrier concentration and leads to the decrease of the electrical conductivity [START_REF] Chetty | Thermoelectric Properties of Co Substituted Synthetic Tetrahedrite[END_REF][START_REF] Chetty | Thermoelectric Properties of a Mn Substituted Synthetic Tetrahedrite[END_REF] . (industrial mill).

Mechanochemical reduction: influence of composite formation during milling on thermoelectric performance

Similarly to the ternary copper sulfide tetrahedrite Cu 12 Sb 4 S 13 , binary copper sulfide digenite Cu 1.8 S (or Cu 9 S 5 ), shows high values of figure of merit [START_REF] Ge | Low-cost, Abundant Binary Sulfides as Promising Thermoelectric Materials[END_REF] . Digenite is a part of a large Cu 2-x S family with end members chalcocite Cu 2 S and covellite CuS. Within this family digenite has the highest power factor [START_REF] Narjis | Structural and Thermoelectric Properties of Copper Sulphide Powders[END_REF] . Digenite exhibits liquid-like behavior where Cu ion migration is the key to its high ZT values [START_REF] Wei | Copper Chalcogenide Thermoelectric Materials[END_REF] . In copper metallurgy antimony-free digenite Cu 1.8 S is the desired product of Cu 12 Sb 4 S 13 decomposition because the presence of Sb worsens the properties of the final copper product. We developed a mechanochemical process for Sb removal from tetrahedrite by alkaline leaching (MELT) to produce digenite [START_REF] Baláž | Application of Attrition Grinding in Alkaline Leaching of Tetrahedrite[END_REF] . The simplified scheme behind the process can be described by hypothetical equation

where (s)-solid phase, and (l)-liquid phase. The liquid phase can be separated and solid phase forms the Cu 12 Sb 4 S 13 /Cu 9 S 5 thermoelectric nanocomposite. By controlling the conversion degree of reaction ( 2), various ratio of both sulfides in nanocomposite can be obtained.

Based on this idea and considering our previous paper [START_REF] Baláž | Tetrahedrites Synthesized via Scalable Mechanochemical Process and Spark Plasma Sintering[END_REF] where we demonstrated the possibility to synthesize non-doped tetrahedrite Cu 12 Sb 4 S 13 using an industrial mill we probed the robustness of this approach using combination both mechanochemically synthetized tetrahedrite and mechanically activated natural tetrahedrite. The combination of natural and synthetic tetrahedrites resembles the original works of Morelli´s group [START_REF] Lu | High Performance Thermoelectricity in Earth-Abundant Compounds Based on Natural Mineral Tetrahedrites[END_REF][START_REF] Lu | Natural Mineral Tetrahedrite as a Direct Source of Thermoelectric Materials[END_REF][START_REF] Lu | Rapid Synthesis of High-performance Thermoelectric Materials Directly from Natural Mineral Tetrahedrite[END_REF] . In their researches they applied the mechanochemical synthesis combining two tetrahedrites. However, the natural mineral with prevailing As over Sb was closer to the composition of tennantite Cu 12 As 4 S 13 than tetrahedrite. In our case the mechanochemical reduction according to reaction (2) creates nanocomposite of two different sulfides. After the original mineral tetrahedrite another efficient thermoelectric material formed is digenite. The samples under study are characterized in Table 1. The milling and leaching conditions of the samples listed in Table 1 are summarized in SI/2. Most importantly, the simulteneous milling and alkaline leaching should lead to modification of the thermoelectric parameters. In this respect we note that the use of natural tetrahedrite, with basically insulating character and relatively large power factor, represents a highly sensitive system that can unmask the role of electrically conducting extraneous phases via modification the thermoelectric response more clearly than highly electrically conducting matrix of ideal Cu 12 Sb 4 S 13 . Our results are shown on Figure 7. In any case we underline that our study does not represent the final optimization approach enabling industrial transfer of natural tetrahedrite to an optimized p-type electronic material, nonetheless it shows the way how, the tetrahedrite mineral can be converted to a useful thermoelectrics using a low cost, effective and throughput route. Thermoelectric data acquired on natural tetrahedrite (TELU 0) revealed that the dry milling of natural tetrahedrite (all grains are under 200 microns) leads to a material with higher electrical resistivity and lower thermal conductivity compared to the mineral (Figures 7a and7c). This can be attributed to increased interfacial scattering due to the grain size reduction (both defects and grain boundaries). The similar thermoelectric response, i.e. positive and weakly temperature dependent Seebeck coefficient of ~200 µV K -1 (Figure 7b), corroborates the semiconducting groundstate of the material.

Contrary to dry milling, the wet milling with application of leaching agent leads to a decrease of both electrical resistivity and Seebeck coefficient (Figures 7a and7b) while the thermal conductivity retained the value of dry-milled sample (Figure 7c). The essentially modified electrical properties of the wet-milled sample are consistent with: (i) either modified doping of original pristine phases or (ii) the introduction of an electrically conducting phase converting the resulting material into a composite where the electrical and thermoelectrical properties depend on the percolation behavior of the additional phase. In order to discern between these two possibilities we have intentionally performed long -term high temperature thermoelectric measurements that, in principle, unmask the role of percolation via electrically conducting precipitates as the short-time SPS sintering of the wet milled powder does not likely leads to a marked development of the conducting phase percolation network. Indeed, long-term high temperature measurements (5 days cycling between 300-700 K) led to a further decrease of the electrical resistivity (1.5 order of magnitude) and large decrease of the Seebeck coefficient at 300 K down to ~40 µV K -1 . Such low absolute values have never been observed even in highly doped tetrahedrites (S min ~ 65 µV K -1 at 300 K) and therefore can only be explained by the presence of a "guest" phase in the "host" semiconducting tetrahedrite matrix, which rules out the possibility of milling-induced doping of natural tetrahedrite. Most importantly, based on the characteristic thermoelectric power of digenite Cu 1.8 S of ~ 30 µV K - 1 at 300 K and its large electrical conductivity [START_REF] Ge | Excellent ZT Achieved in Cu 1.8 S Thermoelectric Alloys through Introducing Rare-earth Trichlorides[END_REF][START_REF] Qin | Improvements of Thermoelectric Properties for p-type Cu 1.8 S Bulk Materials via Optimizing the Mechanical Alloying Process[END_REF] , we identify the minor phase in accord with equation (2) as a low amount of digenite Cu 1.8 S phase. The highly conducting Cu 1.8 S precipitates then create the percolation pathway in the semiconducting tetrahedrite matrix, which itself has high-temperature-dependent electrical resistance. The XRD analysis of the probed samples after SPS sintering showed that this treatment leads to the crystallite size between 60-100 nm. A careful XRD phase analysis of the TELU 2 sample confirmed the presence of a small concentration (~ 1-2%) of digenite in the as-prepared sample, whereas the Cu 1.8 S characteristic peaks were significantly more pronounced on the surface of the longterm high temperature annealed sample where the higher impact of the Cu 1.8 S phase was evidenced by thermoelectric measurements. In this respect we conclude that the simultaneous milling and alkaline leaching of non-doped semiconducting natural tetrahedrite is a viable approach to modify the electronic properties via incorporation of highly conducting Cu 1.8 S species.

The samples labeled as TELU 3 and TELU 4 differ also by the procedure of ball milling, see Table 1. While TELU 3 was processed similarly as in our published paper [START_REF] Baláž | Tetrahedrites Synthesized via Scalable Mechanochemical Process and Spark Plasma Sintering[END_REF] , TELU 4 was processed by additional alkaline leaching in order to transform tetrahedrite to digenite, at least partly (see XRD pattern in SI/Figure S1). The comparative thermoelectric data, presented in Figures 7a-c, confirm that, contrary to the case of natural tetrahedrite with high electrical resistivity where small precipitate concentration can essentially influence the properties, the combination of industrially synthesized powder (TELU 3) and its subsequent chemical leaching in a planetary mill (TELU 4) does not lead to substantial modification of the robust thermoelectric properties. The polydisperse composites TELU 3 and TELU 4 posses properties defined by the dominating phase -tetrahedrite -shows similar thermal and transport properties: power factor between ~0.3 mW m -1 K -2 (300 K) and ~0.65 mW m -1 K -2 (500K) and weakly temperature dependent thermal conductivity between 1.1-1.4 W m -1 K -1 at 300-800 K which results in ZT as already published, see Figure7d. We thus conclude that the industrial milling process, enabling the synthesis of Cu 12 Sb 4 S 13 based thermoelectrics, represents a robust technological route, highly durable and resilient towards undesirable chemical errors, while the intentional chemical leaching can be used to tune the thermoelectric response of insulating natural tetrahedrite.

Mawsonite Cu 6 Fe 2 SnS 8

The mineral mawsonite Cu 6 Fe 2 SnS 8 (MAW) belongs to sulfosalts of copper that occur in nature within hydrothermal copper deposits in altered volcanic rocks. It is frequently associated with other binary, ternary and quaternary sulfides. Recently, thirteen Cu-S based compounds as potential termoelectric materials were identified among which MAW was mechanochemically synthesized for the first time in a laboratory mill [START_REF] Zhang | Screening for Cu-S Based Thermoelectric Materials Using Crystal Structure Features[END_REF] . The milling was performed for 96 hours and thermoelectric performance was evaluated. A figure-of-merit value ZT = 0.43 at 623 K was calculated. Thus the mineralogical curiosity named after Antarctic explorer Douglas Mawson started to interest the thermoelectric community in its effort to mimic natural minerals. Recently, the thermoelectric properties of MAW were thoroughly studied [START_REF] Siloi | Thermoelectric Properties of Minerals with the Mawsonite Structure[END_REF] . The authors in their theoretical work revealed that the low thermal conductivity of MAW is a consequence of low frequency vibration modes of Cu-ions. Good electronic transport properties and low thermal conductivity give promising thermoelectric performance characterized by a maximum ZT value of 0.5 at 750 K. However, up-scaling of MAW synthesis was documented only in our recent paper [START_REF] Baláž | Mechanochemistry for Thermoelectrics: Nanobulk Cu 6 Fe 2 SnS 8 /Cu 2 FeSnS 4 Composite Synthesized in an Industrial Mill[END_REF] . The mechanochemical solid state synthesis was performed for milling times of 5-240 min. The XRD analysis revealed that the transformation to final product proceeds via several intermediate steps where binary (CuS, SnS) and ternary (Cu 2 SnS 3 ) sulfides were identified, and finally practically only MAW is present at milling for 240 min (Figure 8). A summary of the thermoelectric measurements is shown in Figure 10. The relatively high value ZT of 0.51 at 623 K for industrially milled sample (Fig. 10f) results in a low lattice thermal conductivity 0.29 W mK -1 (Figure 10d) and moderate power factor 3.3 µW cm -2 K -2 (Figure 10c). Especially the values of κ L are encouraging because they are comparable with values for the top Cu-based sulfides such as colusite (0.3 W mK -1 at 663 K 100, 101 and tetrahedrite (0.2 W mK -1 at 673 K) [START_REF] Lu | Natural Mineral Tetrahedrite as a Direct Source of Thermoelectric Materials[END_REF] .The electrical conductivity (Figure 10a) shows typical semiconducting behaviour. In previous work [START_REF] Zhang | Screening for Cu-S Based Thermoelectric Materials Using Crystal Structure Features[END_REF] this behaviour is discussed for laboratory milled sample as a consequence of Sn deficiency. It seems that this deficiency is greater in the industrially milled sample. In conclusion, the industrially synthesized mawsonite/stannite composite represents a perspective scalable energy material for future applications. Several synthesis routes for the preparation of CZTS have been evaluated. Among them, the mechanochemical synthesis starting from Cu, Zn, Sn and S elemental precursors demonstrates a scalable approach towards the pure CZTS nanocrystals [START_REF] Hegeduš | Mechanochemical Approach to a Cu 2 ZnSnS 4 Solar Cell Absorber via a "Micronano[END_REF][START_REF] Baláž | Photovoltaic Materials: Cu 2 ZnSnS 4 (CZTS) nanocrystals Synthesized via Industrially Scalable, Green, One-step Mechanochemical Process[END_REF]105 Guided by the previously published work on kesterites, we selected several samples of industrially synthesized kesterites of which the photovoltaic properties have been reported [START_REF] Baláž | Photovoltaic Materials: Cu 2 ZnSnS 4 (CZTS) nanocrystals Synthesized via Industrially Scalable, Green, One-step Mechanochemical Process[END_REF] to perform thermoelectric measurements. With increasing milling time the samples became more amorphized and there was a gradual diminishing of the Zn peaks (Figure 11). After 360 minutes of milling, only the Bragg reflections assigned to the CZTS phase was identified [START_REF] Baláž | Photovoltaic Materials: Cu 2 ZnSnS 4 (CZTS) nanocrystals Synthesized via Industrially Scalable, Green, One-step Mechanochemical Process[END_REF] , thus the as-received powder milled for 360 min was subjected to spark plasma sintering at 600 °C, in order to evaluate the materials thermoelectric related properties. The thermoelectric performance of this sample as a function of temperature is shown in Figure 12.

It can be seen that the sample has relatively high resistivity and shows semiconducting behavior, as its electrical resistivity decreases with increasing temperature. It has a positive scaling-up the process of mechanochemical synthesis leads to the similar values than using laboratory methods conditions (Table 2). This makes the production of Cu-based sulfides as a prospective energy harvesting material for converting heat to electricity feasible. Several new concepts have been developed, which especially a combination of natural and synthetic species (tetrahedrite) and nanocomposite formation (tetrahedrite/digenite, mawsonite/stannite) offer sustainable approaches in solid state chemistry. Mechanochemical synthesis and reduction is selected as a simple, one-pot and facile solid-state synthesis route for sulfide thermoelectric materials, with capability to reduce, or even eliminate solvents, toxic gases and the need of high temperatures with controllable enhanced yields. The synthesis of a largescale nanostructured materials represents a major achievement in the field of nanotechnology.

The synthesis is environmentally friendly and essentially waste-free. The obtained results illustrate the possibility of large-scale deployment of energy-related materials. S1), details about XRD measurements, milling conditions for tetrahedrite treatment for subsequent leaching, XRD pattern of tetrahedrite after leaching (Figure S1), and accuracy factors of the Rietveld refinement (Table S2).

Figure 1 .

 1 Figure 1. XRD spectra of chalcopyrite CuFeS 2 , milling time: A-60 min (laboratory mill), B-

Figure 2 .

 2 Figure 2. Mössbauer spectra of chalcopyrite CuFeS 2 measured at 4.2 K and 296 K, milling

Figure 3 .

 3 Figure 3. Thermoelectric performance of chalcopyrite CuFeS 2 as a function of temperature:

Figure 4 .

 4 Figure 4. (a) XRD patterns of the Cu-Sn-S mixture milled for 60, 180 and 240 min in an

Figure 5 .

 5 Figure 5. Thermoelectric performances of mohite Cu 2 SnS 3 as a function of temperature,

Figure 6 .

 6 Figure 6. (a) Arrhenius dependence and (b) activation energy (E a ) as a function of the milling

Figure 7 .

 7 Figure 7. Thermoelectric performance as a function of temperature: a) electrical resistivity, b)

Figure 8 .Nanobulk Cu 6 Fe 2 SnS 8 /Cu 2 FeSnS 4

 862824 Figure 8. XRD patterns of reaction mixture after milling in an industrial mill (milling times

Figure 9 .

 9 Figure 9. Rietveld analysis for the sample milled for 240 min in an industrial mill after SPS

Figure 10 .

 10 Figure 10. Thermoelectric performance for the samples milled 4 hours in an industrial mill

Figure 11 .Cu 2

 112 Figure 11. XRD pattern of reaction mixture after milling in an industrial mill (milling times

  Seebeck coefficient indicating p-type conductivity. It is interesting to note that the Seebeck coefficient increased more rapidly in the temperature range of 475 -525 K, which could be related to the order-disorder phase transition in kesterite. A similar temperature dependence of Seebeck was reported by Isotta109 . The thermal conductivity decreases with increasing temperature, indicating phonon-phonon scattering as the main scattering effect and the sample shows low thermal conductivity. The sample shows a relatively low ZT value due to the fact that the electrical properties were not optimized. A similar ZT was reported in non-doped CZTS prepared by laboratory-scale mill104 . The results indicate CZTS can be synthesized via industrial milling.

Figure 12 .

 12 Figure 12. Thermoelectric performance of kesterite Cu 2 ZnSnS 4 as a function of temperature,

  2, mohite Cu 2 SnS 3, tetrahedrite Cu 12 Sb 4 S 13 , mawsonite Cu 6 Fe 2 SnS 8 and kesterite Cu 2 ZnSnS 4 synthesized from

  2, mohite Cu 2 SnS 3, tetrahedrite Cu 12 Sb 4 S 13 , mawsonite Cu 6 Fe 2 SnS 8 and kesterite Cu 2 ZnSnS 4 , the following precursors were

	used: copper (Merck, 99% purity), antimony (Alpha Aesar, 99.5% purity), tin (Nihon Seiko,
	99% purity), iron (Winlab, 99% purity), zinc (Aldrich, 99% purity), and sulfur (CG-

Chemikalien, 99% purity). The elemental precursors for appropriate sulfides were mixed in stoichiometric amounts. In some cases natural minerals of chalcopyrite CuFeS 2 (deposit Zhezkazgan, Kazachstan

[START_REF] Baláž | Enhanced Thermoelectric Performance of Chalcopyrite Nanocomposite via Co-milling of Synthetic and Natural Minerals[END_REF]

with the main admixture silicon oxide SiO 2 (JCPDS 01-077-1060)) and tetrahedrite Cu 12 Sb 4 S 13 (deposit Rožňava, Slovakia) with the main admixtures siderite FeCO 3 (JCPDS 01-083-1764) and silicon oxide SiO 2 (JCPDS 01-077-1060)) were used.

Table 1

 1 Description of samples applied for thermoelectric performance

	Sample	Milling	Specification
	TELU 0	__	Natural tetrahedrite (mine Mária,
			Rožňava, Slovakia)
	TELU 1	Laboratory mill	Milling of sample TELU 0
		(dry mode)
	TELU 2	Laboratory mill	Milling of sample TELU 0
		(wet mode)
	TELU 3	Industrial mill	Synthesis from elements for 2

  . The influence of changing Cu:Zn ratio in Cu 2 ZnSnS 4 leads to Cu/Zn disorder with consequences on its physical properties[106][107][108][109] . From a thermoelectric point this effect was analysed by[START_REF] Powell | Recent Developments in Earth-abundant Copper-sulfide Thermoelectric Materials[END_REF] . Also, completely replacing Zn with Cu in Cu 2 ZnSnS 4 will form Cu 3 SnS 4 , which has a disordered tetragonal structure with very low electrical resitivity110 . It seems that non-stoichiometric compositions of Cu 2+x Zn 1-x SnS 4 is key to achieving an improvement of thermoelectric performance104, 109 .

Table 2

 2 Comparison of figure-of-merit ZT for sulfides under study. /pubs.acs.org/doi/10.1021/.... and contains: experimental conditions of SPS treatment (Table

	Sulfide	Figure-of-merit ZT
		Industrial milling	Laboratory milling
	Chalcopyrite CuFeS 2	0.016@600 K (This work)*	0.007@600 K (This work)*
	Mohite Cu 2 SnS 3	0.26@713 K	0.30@723 K 54
	Tetrahedrite Cu 12 Sb 4 S 13	0.67@700 K 29	0.65@673 K 93
	Mawsonite Cu 6 Fe 2 SnS 8	0.51@623 K 68	0.43@623 K 97
	Kesterite Cu 2 ZnSnS 4	0.023@673 K (This work)	0.04@673 K 109
	*Not optimized with repect to charge carrier concentration
	ASSOCIATED CONTENT
	Supporting Information

ACKNOWLEDGEMENTS

This work was supported by the projects of the Slovak Grant Agency VEGA (2/0044/18, 2/0065/18), the Slovak Research and Development Agency APVV (VV-18-0357) and the Czech Science Foundation (18-12761S). The work was further supported by Operational Programme Research, Development and Education financed by European Structural and Investment Funds and the Czech Ministry of Education, Youth and Sport (SolidCZ.02.1.01/0.0/0.0/16_019/0000760).

"For Table of Contents Only"

One-step solid-state scalable mechanochemical approach applying elements as precursors for the synthesis of multinary sulfides and their thermoelectric performance is reported herein.


Peter Baláž

Emmanuel Guilmeau
email: emmanuel.guilmeau@ensicaen.fr

Marcela Achimovičová

Matej Baláž

Nina Daneu
email: nina.daneu@ijs.si

Oleksandr Dobrozhan
email: dobrozhan.a@gmail.com

Mária Kaňuchová
email: maria.kanuchova@tuke.sk

Bismuth Doping in Nanostructured Tetrahedrite: Scalable Synthesis and Thermoelectric Performance

Keywords: tetrahedrite, doping, bismuth, high-energy milling, thermoelectricity

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Introduction

In the Cu-Sb-S system, several ternary copper sulphides like chalcostibnite CuSbS2, skinnerite Cu3SbS3, famatinite Cu3SbS4 and tetrahedrite Cu12Sb4S13 exist [START_REF] Skinner | Studies of sulfosalts of copper III. Phase and phase relations in system Cu-Sb-S[END_REF]. Among them, tetrahedrite, an Earth-abundant copper sulphide mineral with extraordinary thermoelectric properties [START_REF] Suekuni | Thermoelectric properties of mineral tetrahedrites Cu10Tr2Sb4S13 with low thermal conductivity[END_REF][START_REF] Suekuni | High-performance thermoelectric mineral Cu12-xNixSb4S13 tetrahedrite[END_REF], shows a continuous interest in the thermoelectric community [START_REF] Lu | High performance thermoelectricity in Earth-abundant compounds based on natural mineral tetrahedrites[END_REF][START_REF] Barbier | Structural stability of the synthetic thermoelectric ternary and nickel-substituted tetrahedrite phases[END_REF][START_REF] Chetty | Tetrahedrites as thermoelectric materials: An overview[END_REF][START_REF] Qiu | Cu-based thermoelectric materials[END_REF][START_REF] Wei | Copper chalcogenide thermoelectric materials[END_REF][START_REF] Powell | Recent developments in Earth-abundant copper-sulfide thermoelectric materials[END_REF][START_REF] Baláž | Tetrahedrites synthesized via scalable mechanochemical process and spark plasma sintering[END_REF]. The enhancement of thermoelectric performances can often be accomplished via defect engineering. In this approach, two strategies to modify/generate defects in solids are applied, i.e., band engineering and phonon engineering [START_REF] Li | Defect chemistry for thermoelectric materials[END_REF]. In the former, the power factor S 2 σ (S is the Seebeck coefficient, and σ the electrical conductivity) is enhanced by electronic band structure engineering, while in the second case, the lattice thermal conductivity κL is reduced by enhanced phonon scattering [START_REF] Li | Defect chemistry for thermoelectric materials[END_REF][START_REF] He | High performance bulk thermoelectrics via a panoscopic approach[END_REF][START_REF] He | Advances in thermoelectric materials research: Looking back and moving forward[END_REF]. Transport properties S, σ and κ are embodied in the dimensionless figure-of-merit ZT = S 2 σ/κ (where T is temperature and κ is a sum of lattice thermal conductivity κL and electronic thermal conductivity κe). Based on the macroscopically measurable parameters S, σ, and κ, the calculated figure-of-merit illustrates the efficiency of a thermoelectric material [START_REF] He | Advances in thermoelectric materials research: Looking back and moving forward[END_REF]. To ensure high voltage output and low Joule losses, high S and σ are needed. To maintain the temperature gradient between the hot and cold sides of a thermocouple, a low κ value is required [START_REF] Ioffe | Semiconductor Thermoelements and Thermoelectric Cooling[END_REF]. Thermoelectric devices are highly desirable because of their silent operation, reliability, scalability, predictability and durability. They are particularly appreciated when cost and energy efficiency are not as important as energy availability [START_REF] Dresselhaus | New directions for low-dimensional thermoelectric materials[END_REF]. However, significantly lower manufacturing costs, more use cases and increased performances are required to meaningfully convert waste heat and reduce fossil fuels consumption [START_REF] Powell | Recent developments in Earth-abundant copper-sulfide thermoelectric materials[END_REF]. Since the 1950s, doping of prospective thermoelectric materials has been the most popular way to enhance ZT values [START_REF] Ioffe | Semiconductor Thermoelements and Thermoelectric Cooling[END_REF]. Generally, doping affects the charge carrier concentration as well as serving as point-defects to enhance phonon scattering. In the 1990s, nanostructure engineering was successfully applied and later used as an alternative to enhance ZT values [START_REF] Li | Defect chemistry for thermoelectric materials[END_REF][START_REF] He | Advances in thermoelectric materials research: Looking back and moving forward[END_REF][START_REF] Dresselhaus | New directions for low-dimensional thermoelectric materials[END_REF][START_REF] Hicks | Effect of quantum-well structures on the thermoelectric figure of merit[END_REF][START_REF] Hicks | Thermoelectric figure of merit of a one-dimensional conductor[END_REF][START_REF] Vaqueiro | Recent developments in nanostructured materials for high-performance 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]. Moreover, when non-equilibrium procedures, such as high-energy milling (HEM), melt spinning (MS) and self-sustaining heating synthesis (SHS), is applied, the delicate multiscale structures/defects can be obtained [START_REF] He | Advances in thermoelectric materials research: Looking back and moving forward[END_REF]. In the case of HEM [START_REF] Beyer | Mechanochemistry: The mechanical activation of covalent bonds[END_REF][START_REF] Baláž | Mechanochemistry in Nanoscience and Minerals Engineering[END_REF][START_REF] Friscic | New opportunities for materials synthesis using mechanochemistry[END_REF][START_REF] Šepelák | Mechanochemistry: From mechanical degradation to novel materials properties[END_REF][START_REF] Baláž | Hallmarks of mechanochemistry: From nanoparticles to technology[END_REF][START_REF] Do | Mechanochemistry: A Force of Synthesis[END_REF][START_REF] Baláž | Chalcogenide mechanochemistry in materials science: Insight into synthesis and applications (a review)[END_REF][START_REF] Mucsi | A review on mechanical activation and mechanical alloying in stirred media mill[END_REF][START_REF] Friscic | Mechanochemistry for Synthesis[END_REF] combined with spark plasma sintering (SPS), the multiscale dimensionality reduction and the formed nanostructures also contribute to phonon scattering and thus, to a decrease in the lattice thermal conductivity [START_REF] Lan | Enhancement of thermoelectric figure-of-merit by a bulk nanostructuring approach[END_REF]. Doping of tetrahedrite Cu12Sb4S13 has been performed in numerous studies, see e.g., references in [START_REF] Chetty | Tetrahedrites as thermoelectric materials: An overview[END_REF][START_REF] Baláž | Tetrahedrites synthesized via scalable mechanochemical process and spark plasma sintering[END_REF]. While Cu and S positions have been doped many times, doping on Sb site has been slightly overlooked. In mineral Cu12Sb4S13 this site is usually partly occupied by As and/or Bi atoms [START_REF] Baláž | Application of attrition grinding in alkaline leaching of tetrahedrite[END_REF][START_REF] Golebiowska | Substitution of Bi for Sb and As in minerals of the tetrahedrite series from Redziny, Lower Silesia, Southwestern Poland[END_REF]. While As is a toxic element, Bi has recently expanded toward engineering fields and nanomedicine thanks to its efficiency and non-toxicity [START_REF] Shahbazi | The versatile biomedical applications of bismuth-based nanoparticles and composites: Therapeutic, diagnostic, biosensing, and regenerative properties[END_REF]. In synthetic Cu12Sb4S13, several attempts have been made to optimise its thermoelectric performance via doping with Bi. Several synthesis strategies to modify Cu12Sb4S13 thermoelectric properties with Bi doping were applied [START_REF] Goncalves | Effect of Ni, Bi and Se on the tetrahedrite formation[END_REF][START_REF] Goncalves | Fast and scalable preparation of tetrahedrite for thermoelectrics via glass crystallization[END_REF][START_REF] Goncalves | Oxidation studies of Cu12Sb3.9Bi0.1S10Se3 tetrahedrite[END_REF][START_REF] Goncalves | Towards the use of Cu-S based synthetic minerals for thermoelectric applications[END_REF]. For instance, melt-spinning method for samples preparation by application of the Taguchi method has been successfully applied, which is a statistical technique to make robust design of experiments. Moreover, the oxidation and corrosion studies revealed the possibility to use doped tetrahedrite materials under extreme conditions [START_REF] Goncalves | Oxidation studies of Cu12Sb3.9Bi0.1S10Se3 tetrahedrite[END_REF]. The simultaneous double-or triple-doping of tetrahedrite to obtain Cu12-xNixSb4-yBiyS13-zSez compounds was also studied. However, this approach complicated the elucidation of the Bi effect itself. The single-and double-doping was also performed in [START_REF] Lee | Effects of Zn/Bi double doping on the charge transport and thermoelectric properties of tetrahedrites Cu12-xZnxSb4-yBiyS13[END_REF][START_REF] Kwak | Solid-state synthesis and thermoelectric properties of tetrahedrites Cu12Sb4-yBiyS13[END_REF] where Zn and Bi dopants were used. For Cu12-xZnxSb4-yBiyS13 synthesis, HEM and HP methods were applied in this case. As mentioned in the work of Goncalves et al., other phases like famatinite and skinnerite were detected. Kumar et al. synthesised Bi doped tetrahedrites with nominal composition of Cu12Sb4-xBixS13 (x = 0, 0.2, 0.4, 0.6, 0.8) by high temperature solid state reaction method [START_REF] Kumar | Thermoelectric properties of Bi doped tetrahedrite[END_REF][START_REF] Kumar | Cu12Sb4S13) thin films for photovoltaic and thermoelectric applications[END_REF]. The best results of thermoelectric performance were achieved for samples with the lowest content of bismuth. Based on the literature, we have found several issues which were not fully investigated. First, as stated in [START_REF] Kumar | Thermoelectric properties of Bi doped tetrahedrite[END_REF], increasing Bi content in the interval (0.2-0.8) leads to the deterioration of thermoelectric properties of tetrahedrite. The highest power factor and figure of merit was obtained for the composition Cu12Sb3.8Bi0.2S13 where the lowest content of Bi was applied. The region with Bi content lower than 0.2 [START_REF] Kumar | Thermoelectric properties of Bi doped tetrahedrite[END_REF] and 0.1 [START_REF] Kwak | Solid-state synthesis and thermoelectric properties of tetrahedrites Cu12Sb4-yBiyS13[END_REF] was not examined at all. Secondly, there is no evidence in the literature of the oxidative states and/or in which compounds the Bi dopant is present in the Cu-Sb-Bi-S system. Finally, the simultaneous synthesis and doping in an industrial mill which could document sca-ling possibility of thermoelectric materials preparation was not performed for this system up until now.

Materials and Methods

For mechanochemical synthesis of doped tetrahedrite Cu12Sb4-xBixS13(x = 0.025, 0.05, 0.1, 0.15, 0.2) the following precursors were used: copper (Merck, Darmstadt, Germany, 99% purity, 99% particles below 70 μm), antimony (Alfa Aesar, Kandel, Germany, 99.5% purity, 99% particles below 120 μm), bismuth (Sigma Aldrich, Taufkirchen, Germany, 99.99% purity, 99% particles below 152 μm) and sulphur (CG-Chemikalien, Laatzen, Germany, 99% purity, 99% particles below 390 μm). Mechanochemical solid-state syntheses were carried out in an industrial eccentric vibratory ball mill ESM 656-0.5ks (Siebtechnik, Mülheim an der Ruhr, 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 30 kg, 80% ball filling in milling chamber, amplitude of the inhomogeneous vibration 20 mm, rotation speed of the eccenter 960 min -1 , argon atmosphere. The total feed of reaction precursors was 100 g per batch. Bi was added in the amounts 0.025, 0.05, 0.1, 015 and 0.2 atoms per 4 atoms of Sb in tetrahedrite formula (XBi). The milling was performed for 1 h for all samples. The photograph of the mill is shown in ESI (Figure S1). After completion of the milling programs, the resulting pulverised powders were shaped and densified using SPS (FCTHPD25, Rauenstein, Germany) at 723 K for 30 min (heating and cooling rate of 100 K min -1 ) under a pressure of 64 MPa using graphite dies of 10 mm diameter and a slight over pressure of 30 hPa (Ar), in order to prevent sulphur volatilisation. The final thickness of the pellets was around 8 mm with a geometrical density above of 95% of the crystallographic value. The qualitative identification of the phase composition of the sintered samples was performed by XRD method with an X´Pert PW 3040 MPD diffractometer (Phillips) wor-king in the 2θ geometry with CuKα radiation. XRD patterns of as-received (milled) samples were collected using a D8 Advance diffractometer (Bruker, Karlsruhe, Germany) with the CuKα 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 2θ = 10-80° with a step of 0.05°. Rietveld refinements of XRD data of the as-prepared samples were performed using Diffrac plus TOPAS software (version 6, Bruker, Karlsruhe, Germany). The JCPDS-PDF database was used for phase identification [START_REF]Joint Committee on Powder Diffraction, Powder Diffraction File (PDF)[END_REF]. XPS spectrometer SPECS PHOIBOS 100 SCI (SPECS Surface Nano Analysis GmbH Berlin, Germany) and non-monochromatic X-ray source were used. The core spectra were measured at 70 eV and the survey spectrum at 30 eV at room temperature. Basic pressure was 1.10 -8 mbar. Al Kα excitation at 10 kV for all spectra were acquired. For data analysis, SPECSLab2 CasaXPS software (CasaSoftware 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. The sample with the highest Bi addition (XBi = 0.2) was investigated using scanning and transmission electron microscopy (SEM and TEM). SEM analyses of polished cross-section were performed on a field-emission source microscope (FEG-SEM; JSM-7600F, Jeol Ltd., Tokyo, Japan) operated equipped with an energy dispersive X-ray spectrometer (EDXS; INCA Oxford 350 EDXS SDD, Oxfordshire, UK). Samples for SEM/EDXS analyses were prepared by grinding and polishing, finally using 3-micron diamond lapping film. TEM/EDXS analyses were performed on a conventional microscope operated at 200 kV (JEM 2100, Jeol Ltd., Tokyo, Japan) equipped with EDXS spectrometer. For TEM analyses, smaller fragments of the sintered compacts were initially fixed between two silicon supports using epoxy resin. Then, the composite was mounted into brass tube with 3-mm diameter and prepared further using the conventional approach including thinning, dimpling and finally ion-milling (PIPS 691, Gatan Inc., Pleasanton, CA, USA) using 3.8 kV Ar+ ions at an incidence angle of 10° until perforation. Prior to TEM analyses, the specimens were coated by 3 nm layer of carbon to improve surface electron conductivity (PECS 68s, Gatan, Pleasanton, CA, USA). The electrical resistivity ρ and Seebeck coefficient S were measured simultaneously from ingots, from 300 K up to 700 K using an ZEM-3 (Ulvac-Riko, Ikonobe-cho, Japan) under partial helium pressure. LFA 457 apparatus (Netzsch, Selb, Germany) was used to measure 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 (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 from 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 [START_REF] Alleno | A round robin test of the uncertainty on the measurement of the thermoelectric dimensionless figure of merit of Co0.97Ni0.03Sb3[END_REF].

Results

Phase Analysis and Structural Parameters

XRD patterns of the sintered samples are displayed in Figure 1. The main phase corresponds to tetrahedrite Cu12Sb4S13 (space group of I 3m), with a large proportion of famatinite Cu3SbS4 clearly visible. These two phases are present in all Bi-doped samples. The broad diffraction peaks indicate that the crystallised domains are rather small, estimated from Rietveld refinement at 72-119 nm and 61-114 nm for tetrahedrite and famatinite, respectively. Traces of skinnerite Cu3SbS3 were only detected for the most heavily Bi-doped samples (x = 0.15 -0.2). In these samples, the presence of Cu4Bi4S9 phase can be also hypothesised in agreement with the results by Chen et al. [START_REF] Chen | Synthesis and Thermoelectric Properties of Cu-Sb-S Compounds[END_REF]. This multiphase behaviour can be suppressed in favour of tetrahedrite by cationic doping on Cu position (see e.g., References in 10) and/or by prolonged high energy milling with subsequent SPS treatment [START_REF] Barbier | Thermoelectric materials: A new rapid synthesis process for nontoxic and high-performance tetrahedrite compounds[END_REF]. The quantitative phase relations among the synthesised Cu-Sb-S phases determined by the Rietveld refinement are shown in Figure 2. For x = 0.025, a maximum content of 87% tetrahedrite is observed, with 21% of famatinite and 8% of skinnerite. These estimated values are in agreement with the Gibbs free energy values, which measures the feasibility of solid phase formation: i.e., ∆G = -917.2 kJ mol -1 , -266.6 kJ mol -1 and -216.9 kJ mol -1 for tetrahedrite, famatinite and skinnerite, respectively [START_REF] Craig | Thermochemical approximations for sulfosalts[END_REF]. The influence of Bi on Sb substitution on the phase distribution is clearly demonstrated. With increasing the amount of bismuth, more famatinite and skinnerite phases are formed at the expense of tetrahedrite. This is in agreement with the results of triple cationic (including Bi) and anionic substitution of high-temperature synthesised tetrahedrite published by Goncalves et al. [START_REF] Goncalves | Effect of Ni, Bi and Se on the tetrahedrite formation[END_REF]. Famatinite and skinnerite phase formation was also previously observed during the synthesis of tetrahedrites [START_REF] Lee | Effects of Zn/Bi double doping on the charge transport and thermoelectric properties of tetrahedrites Cu12-xZnxSb4-yBiyS13[END_REF][START_REF] Kumar | Thermoelectric properties of Bi doped tetrahedrite[END_REF]. In our previous work on pristine tetrahedrite [START_REF] Baláž | Tetrahedrites synthesized via scalable mechanochemical process and spark plasma sintering[END_REF], the formation of famatinite at the expense of tetrahedrite was observed only for long milling durations. In analogy with a high temperature treatment [START_REF] Tatsuka | Tetrahedrite stability relations in Cu-Sb-S system[END_REF], this phase can be formed by the reaction of elemental sulphur with tetrahedrite. In the present study, the phase formation relationship is more complex due to the presence of bismuth. It remains questionable whether Bi remains in its elemental form and/or is substituted in tetrahedrite and/or famatinite as Bi 3+ or Bi 5+ oxidation state. For example, the reaction of bismuth with sulphur to form Bi2S3 is thermodynamically feasible (∆G = -139,3 kJ mol -1 ) [START_REF] Vaughan | Chemistry of Metal. Sulfides[END_REF] and therefore cannot be excluded at least as a reaction intermediate. In agreement with Chen et al. [START_REF] Chen | Theory-guided synthesis of an eco-friendly and low-cost copper based sulfide thermoelectric material[END_REF], the occurrence of Bi 3+ in Cu4Bi4S9 structure can be hypothesised. The identification of bismuth oxidation states in the reaction products is further elucidated by using the more sensitive method of X-ray Photoelectron Spectroscopy (XPS), see part 3.2. The values for the unit cell volume VT and VF of tetrahedrite Cu12Sb4S13 and famatinite Cu3SbS4, respectively are displayed in Figure 3 as a function of the Bi content XBi. Unambiguously, a monotonous decrease of the parameter VT for tetrahedrite is observed for XBi = 0.025 -0.10 with a subsequent irregular increase for XBi = 0.15 -0.20. The necessity to apply higher Bi content for cell expansion was reported by Kumar et al., who observed an increase in tetrahedrite lattice parameter a for XBi = 0.2 -0.8 [START_REF] Kumar | Thermoelectric properties of Bi doped tetrahedrite[END_REF]. The irregular increase of the lattice constant for Bi-doped tetrahedrite was also documented in [START_REF] Kwak | Solid-state synthesis and thermoelectric properties of tetrahedrites Cu12Sb4-yBiyS13[END_REF]. The situation for famatinite is much more straight-forward: starting from XBi = 0.05, the parameter VF continuously increases. To summarize, the lattice expansion is documented for both phases at the higher Bi content (XBi = 0.15 -0.20). Generally, the lattice expansion is a consequence of an external intervention into the crystal structure, e.g., by high energy milling and/or atomic substitution [START_REF] Zhao | Lattice expansion and grain boundary excess volume of nanocrystalline Se prepared by mechanical milling[END_REF]. Both approaches were applied in our case: milling was performed constantly for one hour, and Bi was incorporated in various amounts. The ionic radii of Bi 3+ and Bi 5+ are equal to 96-117 nm (depending on coordination number) and 76 nm, respectively [START_REF] Lide | CRC Handbook of Chemistry and Physics: A Ready-Reference of Chemical and Physical Data[END_REF]. Antimony site (where bismuth has to be incorporated) is in Sb 3+ state for tetrahedrite and skinnerite and in Sb 5+ state for famatinite [START_REF] Chetty | Tetrahedrites as thermoelectric materials: An overview[END_REF]. The corresponding values of Sb ionic radii are 76 nm for tetrahedrite and skinnerite and 60 nm for famatinite, respectively. To elucidate the pre-sence of oxidation states of Bi and Sb in the synthesised samples, X-ray photoelectron spectroscopy (XPS) analyses were performed.

XPS Analysis

The XPS patterns were investigated in detail and are displayed in Figure 4. The spectra for Sb 3d and Bi 4f were recorded in a high-resolution core level mode. Based on the binding energy values, a peak splitting (PS) was also determined. The following oxidation states can be expected: Sb 3+ for tetrahedrite and skinnerite [START_REF] Chetty | Tetrahedrites as thermoelectric materials: An overview[END_REF], Sb 5+ for famatinite [START_REF] Wang | Photoelectrochemical properties of Bi2S3 thin films deposited by successive ionic layer adsorption and reaction (SILAR) method[END_REF] and Bi 3+ and Bi 5+ for Bi-doped samples. XPS spectra for antimony are depicted in Figure 4a for the sintered sample with no-minal Bi content, XBi = 0.2. Two intensive peaks corresponding to 3d5/2 and 3d3/2 states are present. Peak at Eb = 539.82 eV can be connected with Sb 3+ state corresponding to antimony oxidation state in tetrahedrite and skinnerite [START_REF] Baláž | Tetrahedrites synthesized via scalable mechanochemical process and spark plasma sintering[END_REF][START_REF] An | Selective synthesis and characterization of famatinite nanofibers and tetrahedrite nanoflakes[END_REF]. Peak at 530.82 eV corresponding to Sb 5+ is related to famatinite [START_REF] Wang | Photoelectrochemical properties of Bi2S3 thin films deposited by successive ionic layer adsorption and reaction (SILAR) method[END_REF], which is present in 21% as determined by XRD (see Figure 2). XPS spectra for bismuth are depicted for the same sample in Figure 4b. The peaks for Bi4f5/2 and Bi4f7/2 are shown. Peak-splitting value PS = 5.2 eV deduced from Eb = 159.38 eV and Eb = 164.58 eV respectively is characteristic of Bi 3+ oxidation state [START_REF] Wang | Photoelectrochemical properties of Bi2S3 thin films deposited by successive ionic layer adsorption and reaction (SILAR) method[END_REF][START_REF] Helal | Controlled synthesis of bismuth sulfide nanorods by hydrothermal method and their photocatalytic activity[END_REF]. However, bismuth in Bi 3+ state for these two peaks creates only ~62% of the total peak area. In the centre of XPS Bi4f spectrum, the third peak is also present. This peak corresponds to non-consumed bismuth in zero-valent form (Bi 0 ) and accounts for the rest of the total peak area.

Microstructural Analyses with SEM and TEM

Backscattered images of the sample with XBi = 0.2 recorded at lower and higher magnification (Figure 5a,b) show that the sample is composed of three main phases with different grey shades implicating different average Z-values (Zskinnerite > Ztetrahedrite > Zfamatinite). Chemical composition analyses with SEM/EDS (Figure 5c) have confirmed that the main phase (matrix) with medium grey contrast is tetrahedrite (Cu12Sb4S13), grains with the darkest contrast are famatinite Cu3SbS4, whereas the grains with the brightest contrast are skinnerite Cu3SbS3. The three phases are fairly homogenously distributed in the sample (Figure 5a) and, at first view, it appears that the average size of grains is in the micron-range, i.e., significantly larger than the diffraction domain size determined from Rietveld refinement. A closer observation of the microstructures recorded at higher magnifications (Figure 5b) reveals that some areas with uniform colour that belong to the same phase are typically composed of smaller grains with sizes well below micron as expected with nano-sized pores at the grain boundaries due to the SPS processing. In addition, nano-sized inclusions with brighter contrast are typically observed within the tetrahedrite matrix. SEM/EDS has shown the presence of a small fraction of Bi only in spectra recorded from skinnerite-rich areas, whereas signal from Bi was below SEM/EDS detection limit in tetrahedrite and famatinite areas. The presence of Bi in skinnerite particles is in agreement with the results of XRD and XPS which showed that the presence of Bi enhances the formation of skinnerite where Bi is in Bi 3+ form. Quantification of Bi in SEM/EDS spectra from skinnerite grains showed around 3-4 at% of Bi, however, these results probably underestimate the amount of Bi in skinnerite due to the small (μm 3 ) interaction volume that also includes grains without (or with a significantly lower amount of) Bi in the analysis. Besides areas with uniform phase distribution (as shown in Figure 5a,c), SEM ana-lyses revealed few remnants of unreacted initial Sb-and Sb/Bi-rich initial particles with typical diffusion-type microstructure around these particles that developed during SPS. The presence of elemental Bi from XPS most probably stems from these unreacted par-ticles (see ESI, Figure S2, Table S1). The sample was analysed with TEM, depicted in Figure 6a, showing a typical situation where a skinnerite grain is surrounded by tetrahedrite grains and nano-sized pores trapped at the grain boundaries. Famatinite grains were not found in the TEM sample indicating that the sample was most likely prepared from the tetrahedrite matrix region, where the presence of brighter nanoparticles is observed in SEM. Selected area electron diffraction (SAED) analysis of a tetrahedrite grain oriented along the [111] zone axis is shown in Figure S3 (see ESI). TEM/EDS analysis was used to analyse chemical composition of the phases. It has been shown that skinnerite contains in average 43.0 at% of S, 42.8 at% of Cu, 9.5 at% of Sb and 4.7 at% of Bi. The analyses indicate that Bi replaces Sb at its regular sites in skinnerite, as expected. TEM/EDS analyses did not unambiguously confirm the presence of Bi in tetrahedrite, as the amount of Bi was at the detection limit, i.e., below 1 at%.

Thermoelectric Performance

The temperature dependence of the electrical conductivity (σ), Seebeck coefficient (S) and power factor (PF = S 2 σ) collected over the temperature range of 300-700 K is shown in Figure 7. The electrical conductivity, σ, increases with temperature up to 500 K with a subsequent decrease, while the Seebeck coefficient S increases over the full temperature range. The positive sign of S confirms p-type carrier of all Bi-doped samples. The decrease in the electrical conductivity with increasing Bi content can be explained by the rising presence of famatinite [START_REF] Chen | Theory-guided synthesis of an eco-friendly and low-cost copper based sulfide thermoelectric material[END_REF]. Moreover, the high thermal conductivity of famatinite contributes further to the loss of thermoelectric performance [START_REF] Lu | Natural mineral tetrahedrite as a direct source of thermoelectric materials[END_REF]. Overall, as the amount of "non-tetrahedrite phases" increases with Bi content, see Figure 2, the sample with the lowest Bi content (XBi = 0.025) exhibits the highest values of σ, S and consequently PF. The sample doped with the highest Bi content (XBi = 0.2) showed the lowest values of electrical conductivity (3.7 × 10 4 S m -1 at 300 K, 5.2 × 10 4 S m -1 at 500 K and 4.4 × 10 4 S m -1 at 700 K). It should be noted that the increase of Bi content does not affect much the values of Seebeck coefficient which are equal to 87 μV/K at 300 K and 142 μV K -1 at 700 K. This suggests that bismuth in tetrahedrite remains in 3+ oxidation state. The U shape of the electrical conductivity is classically observed for tetrahedrites presenting the same magnitude of Seebeck coefficient (i.e., carrier concentration) [START_REF] Suekuni | High-performance thermoelectric mineral Cu12-xNixSb4S13 tetrahedrite[END_REF][START_REF] Lu | High performance thermoelectricity in Earth-abundant compounds based on natural mineral tetrahedrites[END_REF]. The material is here in an intermediate regime between a degenerate semiconductor and semiconductor. Therefore, the relatively high values of PF are achieved for the sample with the hi-ghest Bi content (XBi = 0.2) which reaches 0.28 mW m -1 K -2 at 300 K and 0.85 mW m -1 K -2 at 700 K. Such values are in good agreement with other works on Bi-doped tetrahedrites [START_REF] Goncalves | Fast and scalable preparation of tetrahedrite for thermoelectrics via glass crystallization[END_REF][START_REF] Kumar | Thermoelectric properties of Bi doped tetrahedrite[END_REF]. As the carrier concentration seems unchanged with varying Bi content (similar Seebeck coefficient), the decrease of PF values for Bi-substituted samples are most likely due to additional secondary phases (famatinite, skinnerite) acting as scattering barriers for the mobility of carriers. The temperature dependences of the total (κ) and lattice (κL) thermal conductivity are shown in Figure 8. The decrease in κ as the Bi content increases is mainly explained by the decrease of the electronic contribution caused by a reduced electrical conductivity. To summarise, the temperature dependence of the figure of merit, ZT, is the highest for undoped Cu12Sb4S13 tetrahedrite (ZT~0.67 at 700 K) suggesting a degradable effect of Bi doping on the thermoelectric performances of the explored system due to the decrease in electrical conductivity.

Conclusion

Elemental precursors Cu, Sb, Bi and S were successfully used to synthesise Bi-doped tetrahedrite Cu12Sb4-xBixS13 (x = 0.02 -0.20) in an industrial mill. High-energy milling, in duration of one hour followed by spark plasma sintering, led to several phases like tetrahedrite, famatinite and skinnerite, and their nanoscale dimensions have been determined. Among them, tetrahedrite Cu12Sb4S13 is prevailing with content up to 87% as determined by Rietveld refinement. Special attention was devoted to Bi presence which was doped in amounts x = 0.02 -0.20 for Cu12Sb4-xBixS13. Using XPS and SEM/EDS methods, Bi was found in +3 oxidation state and mainly concentrated in skinnerite phase where it acts as a stabilising agent. However, SEM analyses revealed few remnants of unreacted Sb-and Sb/Bi-rich particles with typical diffusion-type microstructure around these particles that deve-loped during SPS. The presence of elemental Bi detected by XPS most probably stems from these unreacted particles. The most prominent effect of the simultaneous milling and doping on the thermo-electric properties is a decrease in the total thermal conductivity (κ) with increasing Bi content, in relation with the increasing amount of famatinite and skinnerite contents. The lowest value of κ was achieved for x = 0.2 (1.1 W m -1 K -1 at 675 K). However, this sample also manifests the lowest electrical conductivity, σ, along with unchanged values for Seebeck coefficient (S) resulting in a decrease in the figure-of-merit values. This illustrates the degradation effect of Bi doping on the thermoelectric properties of tetrahedrite, as well as demonstrating that complex microstructures are not always beneficial for the thermoelectric performance. A trade-off between electrical conductivity and Seebeck coefficient must be considered in order to retain a competitive power factor and thus benefit from a lower thermal conductivity. In the present case, significant amounts of second phases are very detrimental to the thermoelectric performances despite interesting microstructural features. Supplementary Materials: The following are available online at www.mdpi.com/xxx/s1, Figure S1: Eccentric industrial vibratory mill with attached satellite milling chamber. Figure S2: (a) Sample area with two partially reacted Sb-inclusions. (b) SEM/EDS analysis of the right particle has revealed that the brightest part is mostly metallic Sb with some Bi and perhaps also Cu. The XPS signal of elemental Bi probably stems from these unreacted particles, which probably formed by alloying of Sb with Bi and Cu during high-energy milling prior to the SPS densification. The texture radiating from the central part of the particle (marked by dashed line) formed during SPS processing. 1-4 mark the EDS point analyses, the results are shown in Table S1.;

Figure 1 .

 1 Figure 1. XRD patterns of sintered samples with nominal Bi content, XBi = 0.025, 0.05, 0.10, 0.15 and 0.20.

Figure 2 .

 2 Figure 2. Phase distribution of tetrahedrite Cu12Sb4S13, famatinite Cu3SbS4 and skinnerite Cu3SbS3 for sintered samples as a function of the nominal Bi content, XBi.

Figure 3 .

 3 Figure 3. Unit cell volume of tetrahedrite Cu12Sb4S13, VT and famatinite Cu3SbS4, VF for sintered samples as a function of the nominal Bi content, XBi.

Figure 4 .

 4 Figure 4. High resolution XPS spectra of antimony Sb 3d (a) and bismuth Bi 4f (b) for sintered sample with nominal Bi content, XBi = 0.2.

Figure 5 .

 5 Figure 5. Backscattered SEM images of the sample with a nominal Bi content, XBi = 0.2 at (a) lower and (b) higher magnification revealing the presence of three main phases with different average atomic densities (Z). (c) EDS spectra recorded from areas with different contrasts reveal detectable amounts of Bi only in skinnerite.

Figure 6 .

 6 Figure 6. (a) TEM image and (b) EDS analysis of the XBi = 0.2 sample show that Bi is preferentially incorporated into skinnerite.

Figure 7 .

 7 Figure 7. Temperature dependence of (a) electrical conductivity σ, (b) Seebeck coefficient S, and (c) power factor PF of sintered samples. Nominal Bi content, XBi: see Figure.

Figure 8 .

 8 Figure 8. Temperature dependence of (a) thermal conductivity, and (b) dimensionless figure of merit, ZT of sintered samples as a function of nominal Bi content, XBi: see Figure. Inset shows the lattice component, κlat of the total thermal conductivity.

Figure

  Figure S3: (a) Conventional TEM image with marked edge of the TEM sample, hole (brightest part of the image) and nano-pores in the thin part of the sample. Tetrahedrite (Ttr) grain oriented along the [111] zone axis is marked in the image as revealed from (b) experimental and indexed SAED patterns.

Funding: This research was supported by the projects of the Slovak Grant Agency VEGA (2/0044/18) and the Slovak Research and Development Agency APVV (VV-18-0357). The support of COST Action CA18112 MechSustInd (www.mechsustind.eu), supported by the COST Association (European Cooperation in Science and Technology, www.cost.eu) is also acknowledged. We acknowledge Mr. G. Guelou for English editing.

Data Availability Statement:

Conflicts of Interest: The authors declare no conflict of interest.