Serge Monteix

F Schmidt

Y Lemaoult

G Denis

M Vigny

EXPERIMENTAL STUDY AND NUMERICAL SIMULATION OF PREFORM INFRARED RADIATIVE HEATING

The injection stretch-blow moulding process of thermoplastic bottles requires an heating step before forming. An amorphous preform is heated above the glass transition temperature (80°C for the P.E.T.) using an infrared oven. This step is fundamental in order to determine the thickness distribution along the preform height and then insure high quality bottles.

Thus, the optimisation of the infrared oven is necessary. Various experiments have been conducted to characterise the heat source and the semi-transparent properties of the P.E.T. Measurements of air temperature inside the infrared oven and air cooling speed have been processed. These parameters have been implemented in control volume software that simulates the heating step. The surface temperature distribution of the preform has been measured using an infrared camera. Comparisons between experimental and numerical results for a rotating preform are presented.

Introduction

The injection stretch-blow moulding process of thermoplastic bottles requires a heating step before forming. An amorphous tube-shaped preform is heated above the glass transition temperature (80°C for the P.E.T.) using an infrared oven [START_REF] Rosato | Blow Moulding Handbook[END_REF]. As the P.E.T. conductivity is low (0.29 W/m/K), halogen lamps permit a rapid heating with a high flux intensity. In addition, a cooling fan is necessary in order to prevent P.E.T. thermal crystallisation that will induce nonamorphous preform. However, there are plenty of parameters such as number of lamps, distance between halogen lamps and preform, electrical power of the lamps, air cooling speed, reflectors, rotation speed,…. Therefore optimising infrared oven in order to design new plastic bottles is still a long and costly work.

The main objective of this work was to develop numerical software using control volume method that simulates the heating step of the preform. For that, we have to take into account influent parameters of the heating step such as halogen lamps characterisation and P.E.T. spectral properties. In addition, we need to measure the preform temperature. We have used an 880 LW AGEMA infrared camera (connected to real time software) in order to measure external and internal preform surface temperature distribution, heat transfer coefficient along preform height. The air temperature surrounding the preform and inside the preform is measured using thermocouples.

Heat source characterisation

Halogen lamps commonly used for the heating step are presented in figure 1. They are composed of a coiled tungsten filament, contained in a quartz tubular enclosure coated with ceramic in its back (ceramic reflector). Between the concentric cylinders, there is a neutral gas (Argon) that allows high temperature of the filament without important evaporation of the tungsten.

Spectral properties of these elements have already been measured in previous paper [START_REF] Maoult | Measurement and Calculation of Preform Infrared Heating[END_REF]. Using these data, the tungsten filament and quartz tube temperatures are calculated using a net radiation method [START_REF] Petterson | Heat Transfer and Energy Efficiency in Infrared Papers Dryers[END_REF]. In a first approach, the reflectivity of tungsten and quartz elements is neglected.

Finally, the steady state heat balance equation leads to the following system of equations (1), solving using a Newton-Raphson method:

                        0 ln 2 0 ln 2 4 * 4 * 4 T T hS T S df d T T k L T S df d T T k L T S P Q Q Q Q Q Q Q f g Q f f f Q Q Q f g Q f f f          (1)
Where P is the electrical power of the lamps; the indices f and q refer respectively to the tungsten and the quartz tube; T is the temperature, L the lamp length, d the filament diameter,  and  the average emissivity and absorptivity. At the nominal lamp power of 1 kW, this model permits to calculate a filament temperature at 2500 K and quartz tube temperature at 1000 K.

In order to measure the ceramic reflector efficiency, experiments were performed using a thermopile detector with a large spectral bandwidth [0.25-26 m]. This experimental set-up is shown in figure 2. We measured the spatial directivity of the lamps with and without ceramic reflector, moving the flux sensor around the filament. The efficiency of the reflector K eff for each angle is calculated using:

i i K eff ( * 2  (2)
The efficiency coefficient is plotted versus angle in figure 3. The average value is about 68 %. In addition, we note that the temperature of the tungsten filament has no effect.

3.Characterisation of P.E.T. spectral properties

P.E.T. spectral properties measurements were performed using a 3-mm thick sheet. These sheets were processed by injection moulding in the same conditions than tubular preforms. Thermal analysis experiments were carried out in order to measure the sheets crystallinity. Samples of 10-15 mg weight were cut away from the thick sheet. The DSC experiments were performed on a Mettler calorimeter at a heating rate of 10°C/min. The average crystallinity value of these measurements was about 5 %, corresponding to an amorphous P.E.T., which means that diffusion of the radiation can be neglected.

Then we have proceeded to P.E.T. spectral properties measurements (transmitivity, reflectivity) using a Perkin-Elmer FT-IR spectrometer. The previous thick sheets were polished in order to obtain samples of 0.3-mm thickness. The measured absorbtivity is plotted versus wavelength (figure 4). The spectral distribution radiated by the tungsten filament at temperature of 2200 K is superimposed. It appears from these experimental data that the material is transparent at short wavelengths where the intensity of the radiation is maximum. In addition, the polymer is opaque for wavelengths in the range of 8 to 12 m with an average emissivity of 0.93. This bandwidth corresponds to the one of the infrared camera.

http://dx.doi.org/10.21611/qirt.2000.026

Experimental data

Figure 5.a shows the experimental set-up developed on the basis of industrial infrared oven using in injection blow moulding machines. This device consists of six halogen lamps (Philips 1000 W-235 V SK15) describes previously, monitored by power device. The preform is fixed on a rotating support to provide homogeneous hoop temperature. Behind the preform, there is a cooling fan controlled by a DC supply. A pneumatic system allows the preform displacement inside and outside the oven.

Measurement of the air temperature inside the oven

For the measurement of the air temperature inside the oven, J type thermocouples were used. They are connected to a Keithley recorder instrument. All thermocouples are shielded with aluminium adhesive tape. They are mounted in the oven as presented in figure 5.b. In order to place a thermocouple inside the preform, the top of the preform is drilled. Average data issued from a set of measures are plotted in figure 6. In particularly, we note that the temperature of the air inside the preform, still increase after the heating stop.

Measurement of surface temperature distribution

Typical infrared thermograms for external surface temperature distribution of the preform are presented in figure 7.

However, the internal surface temperature measurement is more tedious and necessitates developing a specific process. First, we have to cut the preform in its longitudinalsection (figure 8). Then, the two half-parts of the preform are sticking together using a conductive grease to insure joining during the heating time. All the lamps are set to the same temperature, coupled with the cooling fan, during 20 seconds. Then the rebuild preform exits from the oven in front of the camera. In order to make possible the internal surface temperature measurement, one half-parts is removed (immediately after preform recovering or after a characteristic inversion time). Comparison of external and internal surface temperature measurements versus time (figure 9) provides the temperature inversion throughout preform thickness (frequency of analysis is equal to 1 frame per second).

Measurement of air forced convection heat transfer coefficient

In this section, we want to determine the air forced convection heat transfer coefficient, generated by the cooling fan along the preform height. Two different methods are developed and compared. The first one consists in measuring air-cooling speed using a hot wire anemometer (Ans Snelco). The calculated Reynolds numbers deduced from these data are in the range between 4000 and 10000 that is to say a turbulent flow. Then, we identify from the literature [START_REF] Holman | Heat Transfer[END_REF][START_REF] Incropera | Fundamentals of heat and mass transfer[END_REF][START_REF] Özisik | Heat Transfer a Basic Approach[END_REF] different classical relationships that are suitable for a cylinder in cross flow, i.e. Nu  f Re, Pr  .

The second method is based upon the preform surface temperature measured in presence of cooling flow. The following specific experimental procedure has to be observed in order to compute the heat transfer coefficient: first, a 20 seconds heating time coupled with cooling; then turn off heating and cooling in order to insure an uniform temperature throughout the preform thickness; then restart the cooling fan. Thus, the last step of the procedure allows solving analytically the energy balance integrated over the thickness if we assume that the main part of the preform is a hollow tube. For a given height, the relationship for the heat transfer coefficient h yields: http://dx.doi.org/10.21611/qirt.2000.026

  Re Ri Re T T dt T d Cp h o t 2 2 0                (3)
Where T is the thickness-average temperature, C p the P.E.T. heat capacity,  the P.E.T. specific mass, T  the thickness-average ambient temperature, R e and R i are respectively the external and internal preform radii. R i is computed using the depth penetration throughout the preform (4) over a characteristic time t, for which we have sufficient temperature data to calculate the initial slope dT dt

        t 0
of the temperature-time plot (figure10).

  t Re e Re Ri      2 ( 4
)
Where  is the P.E.T. diffusivity and  the argument of the erf function, computing assuming the surface temperature has decreased of 90% at the depth thickness. In figure 11, we present a comparison between the heat coefficient measured using both methods. The agreement between the two different methods is fair. It permits to calculate an average air cooling heat transfer coefficient of 45 W/m 2. K± 5.

All these process parameters will be useful for the numerical model assessment.

Modelling of infrared PET preform heating

Control-volume model

3D control-volume software, called PLASTIRAD, has been developed in order to compute heat transfer during the infrared-heating step. The preform is meshed using hexahedral elements so-called control volumes [START_REF] Patankar | Numerical Heat Transfer and Fluid Flow[END_REF]. The temperature balance equation including radiative transfer (thermal power absorbed by the semitransparent P.E.T. preform radiates from halogen lamps) is integrated over each control volume and over the time interval from t to t+t (5):

                      t r t t p e e e dt d n dt d n T k dt d t T c     . .     (5)
Where  e is the control-volume, q c the Fourier's flux and q r the radiative heat flux. The unknown temperatures are computed at the cell centres. Further details on the numerical procedure (view factor computation, volume source) are given in previous paper [START_REF] Monteix | Experimental Study and Numerical Simulation of Preform or Sheet Infrared Radiative Heating[END_REF].

Numerical simulation

We performed simulation of the heating step for a P.E. 13). Finally, a comparison between numerical and experimental data is presented in figure 14. Preliminary comparison shows a discrepancy, between computed and measured temperature. We observed that the computed temperature decreases more rapidly during the cooling step. We have to introduce a more accurate heat transfer coefficient and time dependent air temperature in order to improve the simulation.

Conclusion

Numerical simulations of P.E.T. preform heating stage have been performed successfully. Characterisations of halogen lamps and P.E.T. spectral properties have been processed in order to define assumptions necessary for describing the heat transfers inside the oven.

An original method was developed to measure the internal surface temperature of the rotating preform, using a cut-preform technique. This procedure allows measuring the so-called inversion temperature phenomenon. The forced convection coefficient due to the cooling fan was measured along the preform height using an infrared camera. In addition, the infrared oven was instrumented using thermocouples that provide the air temperature evolution inside the oven and inside the preform. The infrared camera is a powerful device in order to make quantitative temperature measurements and to assess the numerical simulations All the measured parameters have been included in the numerical model. The agreement between numerical simulations and experimental data is fair considering the simple model used for absorption (Beer-Lambert law). Future developments will include coupling between infrared heating simulations and stretch-blow moulding simulations.

Fig. 2

 2 Fig. 1 Infrared electric heaters

Fig. 3 Fig. 6 Fig. 8

 368 Fig. 3 Ceramic reflector efficiency

Fig. 9

 9 Fig. 9 Preform longitudinally cutted

  T. preform, taking into account processes parameters introduced previously. The values of the main parameters are summarised in the table below. External surface temperature distribution versus time is presented in figure 12. In addition, numerical computations allow computing temperature distribution in the preform cross-http://dx.doi.org/10.21611/qirt.2000.026

	section (figure
	Heating time (s)	Cooling time (s)	Number of lamps	Distance lamps-preform (mm)	Heat transfer coefficient (W/m 2. K)	Lamps Temperature (K)	Rotation Speed r s-1 )
	20	20	6	20	45	2400	1.2

Acknowledgements

Perrier-Vittel Company supports this work. Special thanks go to J-P. Arcens, C. Miquel and M. Farasse


Cédric Morin

Judith Monnier

Jean-Baptiste B Vaney

Gaëlle Delaizir

Andrea Piarristeguy

Christophe Candolfi

Annie Pradel

Bertrand Lenoir

Eric Alleno

Improved ZT in ball-milled and spark plasma sintered Cu15As30Te55 glass ceramics

Keywords: thermoelectric properties, chalcogenides, glass-ceramics Thermoelectric materials, ball milling, chalcogenide glass-ceramics

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

Introduction

Thermoelectric devices can be used as refrigerators (Peltier effect) or as electric power generators (Seebeck effect) since they can either pump heat or convert it into electricity. Their conversion efficiency is related to the dimensionless figure of merit ZT of the constituting materials defined by ZT = α²T/ρλ where α is the Seebeck coefficient or thermopower, ρ is the electrical resistivity, λ is the total thermal conductivity and T is the absolute temperature. This technology is currently considered for supplying low electrical power (~ 1 µW) to sensors by harvesting heat from ambient air or for medium power generation (~ 100 W) by recycling the heat wasted for instance by the exhaust pipe of cars.

Owing to their inherent disordered nature, chalcogenide glasses harbor extremely low thermal conductivity (~0.2 W.m -1 .K -1 ) which is, however, at the expense of good electrical property with very large electrical resistivity (typically ~ 100 Ω.m) [START_REF] Parthasarathy | Effect of pressure on the electrical resistivity of bulk Ge 20 Te 80 glass[END_REF][START_REF] Dariush | Seebeck coefficient of tellurite-vanadate glasses containing molybdenum[END_REF] . Upon metal substitution, their electrical resistivity can be nevertheless reduced by several orders of magnitude (~ 1 mΩ.m). Since they display large Seebeck coefficients (~ 500 µV K -1 ) [START_REF] Dariush | Seebeck coefficient of tellurite-vanadate glasses containing molybdenum[END_REF] , they have been considered as potential thermoelectric materials for room temperature applications [START_REF] Pereira Goncalves | Conducting glasses as new potential thermoelectric materials: the Cu-Ge-Te case[END_REF][START_REF] Gonçalves | Chalcogenide Glasses as Prospective Thermoelectric Materials[END_REF][START_REF] Gonçalves | Semiconducting glasses: A new class of thermoelectric materials?[END_REF] . Modifying the composition of these glasses is nonetheless insufficient to ensure a large thermoelectric figure of merit competing with state-of-the-art materials such as crystalline Bi 2 Te 3 , which displays ZT = 1 at 300K. This ascertainment led to the partial crystallization approach of the glassy phase, which in the Cu-As-Te system, yields glass -ceramics materials with a complex multiscale nano/microstructure displaying ZT values of up to 0.08 at 300K [START_REF] Vaney | A comprehensive study of the crystallization of Cu-As-Te glasses: microstructure and thermoelectric properties[END_REF] . In such glass-ceramic materials prepared from the peculiar Cu 15 As 30 Te 55 glass composition, the promoted crystalline phase is the metastable β-As 2 Te 3 phase which by itself, is an interesting thermoelectric material with maximum ZT of 0.3 at 300 K upon proper optimization [START_REF] Vaney | High-Temperature Thermoelectric Properties of Sn-Dopedbeta-As 2 Te 3[END_REF] . However, our recent study on glass-crystal composites (Si 10 As 15 Te 75 (glass) and Bi 0.4 Sb 1.6 Te 3 (crystal)) [START_REF] Vaney | Effective medium theory based modeling of the thermoelectric properties of composites: comparison between predictions and experiments in the glass-crystal composite system Si 10 As 15 Te 75 -Bi 0.4 Sb 1.6 Te 3[END_REF] , combining experiments and generalized effective medium theory-based (GEMT) calculations of the thermoelectric properties [START_REF] Landauer | The Electrical Resistance of Binary Metallic Mixtures[END_REF][10][START_REF] Webman | Thermoelectric power in inhomogeneous materials[END_REF][START_REF] Mclachlan | An equation for the conductivity of binary mixtures with anisotropic grain structures[END_REF][START_REF] Mclachlan | Electrical Resistivity of Composites[END_REF] , ruled out the possibility for a composite to reach ZT values larger than any of its component. Nonetheless, the GEMT was in most cases verified in composites which were constituted by mixtures of micrometric phases and very seldom checked on mixtures of nanometric phases, for which interface effects cannot be neglected. Hence, a reduction to the nanoscale of the typical size of the phases in the Cu-As-Te -As 2 Te 3 glass -ceramic material was undertaken in the present work in order to determine whether improved thermoelectric properties could be achieved. To this end, high energy ball-milling was carried out in order to decrease the size of the Cu 15 As 30 Te 55 glass particles, prior to the crystallization process obtained by Spark Plasma Sintering [START_REF] Vaney | A comprehensive study of the crystallization of Cu-As-Te glasses: microstructure and thermoelectric properties[END_REF] . Our results show that the influence of the particle size reduction to the nanoscale on the thermoelectric properties can be still well understood within the EMTs. The maximum ZT value of the composite is nonetheless strongly enhanced due to a fraction of crystalline phase larger than that achieved in non-ball-milled samples.

Experimental procedures

Synthesis and ball milling of the Cu 15 As 30 Te 55 glass powders

The Cu 15 As 30 Te 55 glass composition was synthesized by the conventional meltquenching technique. A series of stoichiometric composition using highly-pure As (Ingots, Goodfellow, 99.99%), Te (Pellets, 5N+, 99.999%) and Cu (Beads, Sigma-Aldrich, 99.999%) were melted at 1123 K in a silica tube sealed under secondary vacuum and water-quenched [START_REF] Vaney | A comprehensive study of the crystallization of Cu-As-Te glasses: microstructure and thermoelectric properties[END_REF] .

The resulting ingots (~2 g) were hand-ground in an agate mortar, then analyzed by powder Xray diffraction (PXRD) on a Bruker D8 diffractometer (Cu Kα radiation) equipped with a Vantec 1D detector and by differential scanning calorimetry (DSC, TA Q100) in order to check that they are identical before being combined in a single batch. This Cu 15 As 30 Te 55 glass batch was dispatched in several 4g samples and milled using a Fritsch P7 premium planetary The ball-to-powder ratio (BPR) was 15/1, with stainless balls of 2 mm in diameter. A first batch was incrementally ball-milled up to t BM = 360 min by sampling 20 mg of powder from the vial inside a Ar-filled glove box at t = 2, 8, 20, 45, 90, 180 and 360 min. This sampled powder was used to record a PXRD pattern (with a sample holder protecting the powder from the air), to carry out a scanning electron microscopy (SEM) investigation and for DSC measurements with a 10 °C min -1 heating rate. Three other batches were ball-milled without interruption during t BM = 20, 45, 130 min. They were also characterized by PXRD (with a low noise single-crystalline Si sample holder) and by DSC. These two different ball milling conditions (with and without interruptions) may slightly influence the temperature inside the vial and consequently the crystallization kinetics, even if large majority of the energy is provided by the chocks.

Spark Plasma Sintering (SPS)

The elaboration conditions of the different Cu 15 As 30 Te 55 pellets are summarized in Table 1 and are described below. The Cu 15 As 30 Te 55 powders milled for different durations (t BM = 0, 20, 45, 130 and 360 min) were sintered by SPS using a Dr. Sinter 505 Syntex apparatus to obtain glass-ceramic materials. It is noteworthy that for this specific SPS equipment, there is no way to bridle the intensity delivered by the generator (up to 1500 A).

For each ball-milling time t BM , 3 samples were elaborated for reproducibility concerns. 0.7 g of powder was introduced in an 8 mm diameter graphite die. The sintered temperature was checked by a thermocouple located in the wall of the die. In order to follow the evolution of the crystallization, 3 dwell times were applied (0, 10 and 20 min) at 423 K. An initial pressure of 50 MPa was implemented for t BM = 0, 130 and 360 min. Given the larger number of crystallized phases obtained as compared to a previous study [START_REF] Vaney | A comprehensive study of the crystallization of Cu-As-Te glasses: microstructure and thermoelectric properties[END_REF] , the following ball-milled samples (t BM = 20 and 45 min) and another reference sample (t BM = 0 min) were sintered under a higher pressure of 80 MPa. However, as it will be discussed below (see t BM = 0 min in Table 1), the applied pressure is not a significant parameter in this study compared to other parameters. In the case of t BM = 0 min, an extra sample was synthesized with a 30 min dwell time under 80 MPa. In the following, the powder obtained from hand-ground Cu 15 As 30 Te 55 glass (t BM = 0 min) will be considered as a reference in this work. Figure 1 shows a representative SPS cycle used to elaborate glass-ceramics. The temperature rises at a heating rate of 90 K min -1 up to T = 390 K. At this temperature, the heating rate is decreased to 45 K min -1 to reach the dwell temperature of 423 K. As shown in Fig. 1 (a), an overshoot (T max ) can be seen before the set-temperature plateau. At the end of the dwell time, the sample undergoes a natural cooling. The density d of the samples was measured using the Archimedes's method and is presented in Table 1. An average density of d = 6.28 ± 0.05 g.cm -3 over all the samples can be deduced. The standard deviation of 0.05 g.cm -3 is equal to the uncertainty of the measurement. Thus, there is no significant variation in the density with the duration of the initial ball-milling or the SPS parameters.

Transport properties of SPS glass-ceramics

Electrical resistivity measurements were directly performed on the SPS pellets with parallel faces using the van der Pauw technique [START_REF] Rouleau | Measurement system of the Seebeck coefficient or of the electrical resistivity at high temperature[END_REF] . The thermal diffusivity a was measured by the laser flash technique (Netzsch LFA 427) between 300 and 380 K. A piece of the sample was used to measure the heat capacity C p from room temperature up to 400 K with a Netzsch Pegasus DSC apparatus, in order to calculate the thermal conductivity ߣ = ܽ × ܥ × ݀ where d is the experimental density.

The Seebeck coefficient was measured between room temperature and 400 K on a parallelepiped-shaped (about 1 × 1 × 8 mm 3 ) sample cut with a diamond wire saw. These . Measurement uncertainties are estimated to be 3% for Seebeck coefficient, 5% for electrical resistivity, 10% for thermal conductivity and 15% for ZT [START_REF] Alleno | Invited Article: 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] .

Finally, the samples used for the Seebeck coefficient measurements were hand-ground and PXRD was performed in the 2θ range 20-60° in order to determine the nature of the crystalline phases stabilized in the glass-ceramics. The amount of residual glass was estimated by integrating the area under the main XRD peak around 2θ = 29.58°, normalized to the high angle background. Moreover, the amount of α-As 2 Te 3 , β-As 2 Te 3 , AsTe and Cu 1.4 Te crystalline phases in the SPS samples was evaluated from Rietveld refinements.

Results and discussion

Structural, microstructural and thermal characterizations of ball milled Cu 15 As 30 Te 55 glass

Figure 2 shows SEM micrographs corresponding to the glass particle size reduction after ball-milling. After 2 minutes, the particle size is reduced from hundreds of microns (Fig. 2a) to about 10-20 µm (Fig. 2b). After 20 and 360 minutes (Fig. 2c and2d), the SEM picture shows very small particles typically less than 1 µm. However, some larger particles, up to 5 µm, are still present. Larger magnification (Fig. 2e-g) indicates that these particles are aggregates of grains smaller than 100 nm.

Ball-milling effects in the Cu 15 As 30 Te 55 glass samples were also followed by PXRD.

In Fig. 3, a + 0.6° shift in 2-theta for the main broad peak is noticeable around 29°, between the non-ball-milled glass and the 20 minutes ball-milled glass. This shift is too large to be ascribed to an artifact such as a sample displacement (max 0.1°). It can be noticed that this shifted peak is located at the same angle as a diffraction line of the crystallized phase. It could be due i) to a structural transformation of the initial glass into another polyamorph as already observed in other chalcogenide glasses [START_REF] Andrikopoulos | Pressure dependence of the Boson peak in glassy As 2 S 3 studied by Raman scattering[END_REF][START_REF] Calvez | Te-As-Se glass destabilization using high energy milling[END_REF] , ii) to the emergence of nanometric crystalline domains, considering the low stability (T c -T g ) of the glass (~ 30K 6 ) where T c and T g are the crystallization and glass transition temperatures, respectively. Other evidences for this glasstransformation will be further discussed below. PXRD also highlights crystallization phenomenon which occurs during ball milling. After 45 min of ball-milling, some diffraction lines appear at 29.58° and 44.89° (Fig. 3). While they cannot be observed at t BM = 90 min, they appear again at t BM = 130 min and become more intense for longer t BM . Thus, the onset of crystallization is ambiguous when considering only the XRD data. By combining the former data with the DSC data (see Fig. 6), the beginning of crystallization can be better determined to occur between t BM = 45 min and t BM = 90 min. These diffraction lines at 29.58° and 44.89° are characteristic of one of the As 2 Te 3 crystalline phases. Due to their very low intensity, it is difficult to distinguish the α-As 2 Te 3 from the β-As 2 Te 3 crystalline polymorphs based solely on PXRD data. Nevertheless, the presence of the diffraction line near 45° is in favor of the metastable β-As 2 Te 3 form, which is likely to appear under out-of-equilibrium ball-milling conditions in this specific glass composition [START_REF] Vaney | A comprehensive study of the crystallization of Cu-As-Te glasses: microstructure and thermoelectric properties[END_REF] .

The DSC curves, evidencing the temperatures of the glass transition, crystallization and phase transformation, are plotted in Figure 4 for all the incremented t BM . The DSC curve of the reference Cu 15 As 30 Te 55 sample (t BM = 0 min) shows an endothermic glass transition at T g = 403 K and a first crystallization peak at T c1 = 440 K. This crystallization peak is shifted to higher temperature in comparison to our previous study [START_REF] Vaney | A comprehensive study of the crystallization of Cu-As-Te glasses: microstructure and thermoelectric properties[END_REF] . This enlightens the importance of the particle size on the crystallization phenomenon which occurs in the present case at the surface of the particles as already discussed in [START_REF] Vaney | Stabilization of Metastable Thermoelectric Crystalline Phases by Tuning the Glass Composition in the Cu-As-Te System[END_REF] . Upon ball milling, T g decreases to 399 K for t BM = 90 min (Table 2). For larger t BM (samples are partially crystallized), the glass transition is hidden by the first crystallization peak. The first exothermic crystallization peak which extends from 440 K to 465 K in the reference sample (t BM = 0 min), is shifted to lower temperatures with t BM (Table 2) in accordance with the decrease of the particle size [START_REF] Neuville | From glass to crystal: Nucleation, growth and phase separation: from research to applications[END_REF] . A second weak peak is also observed between 465 K and 480 K in the reference sample (t BM = 0 min). Upon increasing the ball milling durations, this peak separates into two components, which both shift towards lower crystallization temperatures. In order to assess the crystalline composition, three 90 min interrupted ball-milled Cu 15 As 30 Te 55 samples were heat-treated at a temperature higher than the maximum of each three DSC peaks i.e. at 438, 459 and 478 K respectively, (black dots in Figure 4) and their PXRD patterns were recorded. The results are displayed in Fig. 5. The diffractogram recorded on the 438 K heat-treated sample can be indexed with metastable β-As 2 Te 3 as the major phase and AsTe as a secondary phase. The first crystallization peak observed in the DSC thermograms corresponds to the crystallization of these two phases, in good agreement with a previous work [START_REF] Vaney | A comprehensive study of the crystallization of Cu-As-Te glasses: microstructure and thermoelectric properties[END_REF] . The second diffractogram at 459 K shows appearance of diffraction lines corresponding to the Cu 1.4 Te rickardite phase. Thus, the second crystallization peak can be ascribed to the crystallization of the rickardite phase. Finally, the third diffractogram (Fig. 5) obtained after a heat-treatment at 478 K, shows diffraction peaks related to the α-As 2 Te 3 and Cu 1. 4 Te phases indicating that the third DSC peak corresponds to a β-to α-As 2 Te 3 phase transition. For t BM = 180 and 360 min, the intensity of the second and third crystallization peaks hardly varies while the intensity of the first peak dramatically decreases as seen in Fig. 4. This reduction in intensity could be related to the partial crystallization of the glass particles into the β-As 2 Te 3 crystalline phase upon ball-milling as evidenced by the PXRD patterns shown in Fig. 3.

Based on the area A of the first crystallization peak, a glass transformation degree f was defined and plotted in Fig. 6:

F o r P e e r R e v i e w 9 ݂ = 100 × ሺ௧ ಳಾ ୀሻିሺ௧ ಳಾ ሻ ሺ௧ ಳಾ ୀሻ (1)
A sharp increase in the glass transformation degree for small t BM is likely to arise from a transformation of the initial glass. As previously mentioned, this could be related to a nanostructuration of the grains. Nonetheless, the presence of a plateau following this sharp increase gives a highly non monotonous character to these variations. These are in favor of a glass-to-glass transformation (polyamorph), in agreement with both the shift of the main PXRD broad peak at 2θ ~ 29° and the change in the glass transition temperature T g . For t BM > 45 -90 min, the increase in the glass transformation degree corresponds to the onset of the crystallization process during ball-milling and the presence of pre-existing crystallites, in good agreement with PXRD patterns (Fig. 3).

Glass-ceramics elaborated by SPS

In order to evaluate the effect of the ball-milling time on both the devitrification process and the thermoelectric properties, four series of Cu 15 As 30 Te 55 samples, ball-milled during various times (20, 45, 130 and 360 min) were sintered by SPS and compared to the reference sample sintered from hand-ground glass powder (t BM = 0 min). During the sintering, a competition may occur between the glass particle sintering through a viscous flow mechanism and the crystallization phenomenon that occurs at the same time since the thermal stability of this specific glass composition is rather low (∆T = 38K), as discussed previously [START_REF] Vaney | A comprehensive study of the crystallization of Cu-As-Te glasses: microstructure and thermoelectric properties[END_REF] .

Microstructures

The microstructures of three characteristic sintered glass-ceramics obtained for t BM = 0, 20 and 360 min are presented in Fig. 7. The grain size after the SPS process on handground samples is around 10 µm, whereas the grain size after the SPS process on the 20 minutes ball-milled sample is around 200 nm. The same grain size is observed for t BM = 360 minutes. Ball-milled samples display the same microstructure and thus, cannot be differentiated by this feature. EDX maps reveal some differences in the chemical homogeneity of the non-ball-milled and ball-milled samples (t BM = 0 and 20 minutes). While Te and As elements are well distributed within the matrix for both samples, Cu element is found as aggregates with micrometric size in the sample t BM = 0 min (Fig. 7g). These aggregates, corresponding mostly to the crystallization of the Cu 1.4 Te rickardite phase, are more homogeneously distributed in the sample t BM = 20 minutes for comparison (Fig. 7h). As will be further discussed, the fraction of crystalline phases is the critical parameter that best characterizes the samples. Rietveld refinements were performed to evaluate the relative crystalline phase fractions, which are presented in Table 1. A glass rate was defined by integrating the area under the main XRD peak around 2θ = 29.58°, normalized to the high angle background around 2θ = 59°. These evolutions of the crystalline phase fractions are in good agreement with the evolution of the glass transformation degree plotted in Fig. 6. For short t BM (< 45 min), the large fraction of β-As 2 Te 3 phase is correlated to the first glass-to-glass transformation. Indeed, it appears that this glass-to-glass transformation yields a glass reorganization which favors the germination of the metastable β-As 2 Te 3 phase at the sintering stage. On the other hand, for longer t BM , the crystallization, which occurs during ball-milling, favors larger fractions of the α-As 2 Te 3 phase at the SPS stage. The larger amount of energy provided by long t BM finally favors the crystallization of the most thermodynamically stable phase, α-As 2 Te 3 . Figure 9 gathers all the densified samples regardless of the sintering pressure (50 or 80 MPa). Since no distinction can be made between the samples, this parameter has no or a negligible influence on the phase fractions. Regarding the glass rate in the glass-ceramics, no trend can be noticed in the plot of the normalized glass rate versus t BM .

Volume fractions of crystals and "glass rate"

Thermal and electrical transport properties

Figure 10 shows the Seebeck coefficient, the electrical resistivity, the thermal conductivity, and ZT of the SPS glass-ceramics as a function of t BM . All the data shown here were measured at 400 K and are also summarized in Table 1. On the one hand, the evolution of the Seebeck coefficient with the ball-milling time mimics the evolution of the β-As 2 Te 3 crystalline fraction up to t BM = 45 min. For longer t BM , the Seebeck coefficient weakly varies despite the decrease of the β-As 2 Te 3 fraction. This arises from the increase of the α-As 2 Te 3 phase fraction, which also presents good thermoelectric properties [START_REF] Vaney | High Thermoelectric Performance in Sn-Substituted alpha-As 2 Te 3[END_REF] . Although the values of the thermal conductivity present a high variability in the non-ball-milled sintered samples, similarly to the Seebeck coefficient, they are correlated to t BM and to the crystalline phase fractions, e.g. they decrease in the ball-milled samples. For long ball-milling times, the values weakly varies since the α-As 2 Te 3 and β-As 2 Te 3 phases display similar values of thermal conductivities (1.0 W m -1 K -1 and 1.4 W m -1 K -1 , respectively) [START_REF] Vaney | High-Temperature Thermoelectric Properties of Sn-Dopedbeta-As 2 Te 3[END_REF][START_REF] Vaney | High Thermoelectric Performance in Sn-Substituted alpha-As 2 Te 3[END_REF] . An effect of the numerous interfaces created by the fine microstructure (~ 200 nm) on the phonon transport cannot as well be excluded to explain this trend. Note that (i) the variability for t BM = 0 min can probably be related to the extremely variable remaining glass fraction for these samples (Fig. 9); (ii) the fact that the thermal conductivity reaches 1.8 W.m -1 .K -1 , while the thermal conductivity of the Cu 15 As 30 Te 55 parent glass is about 0.22 W.m -1 .K -1 , or that of the α or β-As 2 Te 3 crystalline phase does not exceed 1.0 W m -1 K -1 24 and 1.4 W m -1 K -1 , respectively [START_REF] Vaney | High-Temperature Thermoelectric Properties of Sn-Dopedbeta-As 2 Te 3[END_REF] could be explained by the presence of additional metallic phases, namely the Cu 1.4 Te rickardite [START_REF] Kobayashi | Metallic binary copper chalcogenides with orthorhombic layered structure[END_REF] and AsTe [START_REF] Jr | Electrical and structural properties of annealed As-Te and As-Te-I semiconducting glasses: surface and bulk effects[END_REF] .

On the other hand, the resistivity values are subjected to a larger sample-to-sample variability, which probably masks the evolution of this property. The values for all the samples vary in an interval (± 0.60 mΩ cm) around the average value of 1.5 mΩ cm but weakly influence the ZT values. This variability stems from: (i) the differences in crystalline phases fractions; (ii) the likely different carrier concentrations of the As 2 Te 3 phases, known for severely impacting their electrical properties, especially in the case of α-As 2 Te 3 26 .

The figure of merit ZT follows the variations in the Seebeck coefficient: it goes through a maximum for short t BM , and weakly changes for longer t BM . Again, this evolution mimics the evolution of the β-As 2 Te 3 phase fraction, which improves the thermoelectric properties of the glass-ceramics. This result is in full agreement with our previous work on the partial crystallization of the Cu 15 As 30 Te 55 glass composition which enabled an increase in the ZT values from 0.08 to 0.14 at 365K by crystallizing the metastable β-As 2 Te 3 phase 6 . Indeed, this phase was shown to display good thermoelectric properties at 400 K with ZT = 0.4 [START_REF] Vaney | High-Temperature Thermoelectric Properties of Sn-Dopedbeta-As 2 Te 3[END_REF] . In

Conclusions

In this study, the effect of ball-milling and crystallization from the Cu 15 As 30 Te 55 parent glass on the thermoelectric properties of the corresponding glass-ceramic materials are presented. The partial crystallization of glass remains an interesting and original way to stabilize new crystalline phases. Thanks to ball-milling, the grain size is reduced to less than 100 nm. PXRD and DSC measurements indicate that the first stages (t BM < 45 min) induce a glass-to-glass transformation followed by the crystallization of the β-As 2 Te 3 phase which occurs after t BM = 130 min for interrupted ball-milling. Upon sintering, the grain size increases up to 200 nm in every ball-milled sample. Four crystalline phases, namely α-As 2 Te 3 , β-As 2 Te 3 , AsTe and Cu 1.4 Te, were evidenced in the different samples in various proportions.

The fraction of the metastable β-As 2 Te 3 phase is maximum for short t BM (20 -45 min), i.e. for samples which underwent the glass-to-glass transformation (in comparison to non-ball-milled samples). These samples exhibit the largest thermoelectric figure of merit ZT up to 0.3 at 400K, a value nearly doubled when compared to the non-ball-milled glass-ceramics. 1 for the SPS conditions) glass-ceramics as a function of t BM . The solid lines represent the mean of transport properties for each t BM. The grey area is plotted to recall that the corresponding samples were partially crystallized after ball-milling. Tg (K) 402.9(5) 402.2(5) 401.0(5) 400.2(5) 400.3(5) 398.7 [START_REF] Gonçalves | Semiconducting glasses: A new class of thermoelectric materials?[END_REF] 397.0(5) 394.1(5)

T c (K) 440( 1) 420( 1) 414( 1) 412( 1) 411( 1) 411( 1) 404( 1) 403( 1) 411( 1) 410( 1) 407

4 machine

 4 equipped with 80 mL stainless steel jars at a speed of 500 rpm (round per minute).

  out using a homemade apparatus based on the differential method 14

Figure 8 20 , 20 ,

 82020 Figure8shows a typical PXRD pattern of a sintered glass-ceramic sample (t BM =

Figure 9

 9 Figure 9 presents the evolution of the crystalline fractions and the glass rate as a

13 the

 13 present work, the effect of short ball-milling time leads to an increase in the ZT max value, from 0.15 for the best non-ball-milled sample to 0.3 at 400K for t BM = 20 min.

Figure 1 :

 1 Figures captions

Figure 2 :

 2 Figure 2: SEM micrographs of Cu 15 As 30 Te 55 powder obtained after different duration of ball milling t BM = 0 (a), 2 (b), 20 (c) and 360 min (d) at low magnification and for t BM = 20 (e) and 360 min (f, g) at high magnification.

Figure 3 :

 3 Figure 3: PXRD of Cu 15 As 30 Te 55 powder after (a) continuously ball-milled at t BM = 20, 45 and 130 min (Continuous BM), compared to the non-ball-milled glass (t BM = 0min) and (b) incrementally ball-milled at t BM = 20, 45, 90, 180 and 360 min (Interrupted BM). The vertical dashed lines show the shift between non ball-milled and ball-milled glass and the black arrows show the diffraction line appearance. The baselines are different in panels (a) and (b) because of the different sample holders. The hump observed at 38° for continuous ball-milled samples is an artifact of the sample holder.

Figure 4 :

 4 Figure 4: DSC thermograms of the Cu 15 As 30 Te 55 powders for various ball milling times. Black dots correspond to different annealing temperatures (438, 459 and 478 K, see text).

Figure 5 :

 5 Figure 5: PXRD of 90 min ball-milled Cu 15 As 30 Te 55 powder after heat-treatments at 438, 459 and 478 K (β-As 2 Te 3 , -AsTe, -Cu 1.4 Te (rickardite) phases andα-As 2 Te 3 ).

Figure 6 :

 6 Figure 6: Glass transformation degree f as a function of ball-milling time t BM . Squares are related to the incrementally ball-milled batch. Triangles are related to three other batches ballmilled without interruption during t BM = 20, 45, 130 min. The continuous line is a spline through the entire dataset.

Figure 7 :

 7 Figure 7: SEM micrographs of SPS glass-ceramics at two magnifications (× 1k and × 10k) ; a & b: the hand-ground reference (t BM = 0 min) ; c & d : t BM = 20 min ball-milled sample; e & f : t BM = 360 min. SPS was performed at 423 K with 10 min dwell time, under a pressure of 50 MPa (reference and t BM = 360 min) or 80 MPa (t BM = 20 min). Elemental EDX maps of these last two samples: t BM = 0 min (g) and t BM =20 min (h).

Figure 8 :

 8 Figure 8: PXRD patterns of a SPS sample (t BM =130 min, dwell 0 min, 80MPa, 423 K) between 10 and 60°. The main characteristic diffraction lines of Cu 1.4 Te, AsTe, α-As 2 Te 3 and β-As 2 Te 3 and the contribution of glass to the background (gray zone) are shown.

Figure 9 :

 9 Figure9: a-c. Crystallized phase fractions extracted from Rietveld refinements and d. normalized glass rate extracted from the SPSed glass-ceramics patterns, plotted as a function of t BM . The solid lines represents the mean of phase fractions for each t BM . The grey area is plotted to recall that the corresponding samples were partially crystallized after ball-milling.

Figure 10 :

 10 Figure 10: a. Seebeck coefficient, b. electrical resistivity, c. thermal conductivity,and d. figure of merit ZT at 400 K for the SPS (See Table1for the SPS conditions) glass-ceramics as a function of t BM . The solid lines represent the mean of transport properties for each t BM. The grey area is plotted to recall that the corresponding samples were partially crystallized after ball-milling.

Figure 1 :Figure 2 :Figure 3 :Figure 4 :Figure 5 :

 12345 Figure 1: (a) SPS cycle of the reference sample (423 K, 80 MPa, dwell time = 30 min). Open squares are related to the temperature T inside the die and closed squares to load applied to the sample. (b) Corresponding shrinkage (mm) as a function of time during the same SPS cycle. 115x169mm (150 x 150 DPI)

Figure 6 :Figure 7 :Figure 8 :

 678 Figure 6: Glass transformation degree f as a function of ball-milling time tBM. Squares are related to the incrementally ball-milled batch. Triangles are related to three other batches ball-milled without interruption during tBM = 20, 45, 130 min. The continuous line is a spline through the entire dataset. 287x200mm (300 x 300 DPI)

Figure 9 :

 9 Figure 9: a-c. Crystallized phase fractions extracted from Rietveld refinements and d. normalized glass rate extracted from the SPSed glass-ceramics patterns, plotted as a function of tBM. The solid lines represents the mean of phase fractions for each tBM. The grey area is plotted to recall that the corresponding samples were partially crystallized after ball-milling. 108x237mm (150 x 150 DPI)

Figure 10 :

 10 Figure 10: a. Seebeck coefficient, b. electrical resistivity, c. thermal conductivity, and d. figure of merit ZT at 400 K for the SPS (See Table1for the SPS conditions) glass-ceramics as a function of tBM. The solid lines represent the mean of transport properties for each tBM. The grey area is plotted to recall that the corresponding samples were partially crystallized after ball-milling.119x194mm (150 x 150 DPI)

Table captions Table 1 :

 captions1 Ball-milling times t BM , experimental SPS conditions (T = 423K, dwell time, pressure and maximal temperature in SPS T max ), density, crystallized phase fractions (extracted from Rietveld refinement), normalized glass rate, and thermoelectric properties measured at 400K.

Table 2 :

 2 Glass transition T g and first crystallization T c temperatures of the Cu 15 As 30 Te 55 sample as a function of the ball milling time t BM .

	F o r
	P e
	e r
	R e
	v
	i e
	w
	19

Table 1 :

 1 Ball-milling times t BM , experimental SPS conditions (T = 423K, dwell time, pressure and maximal temperature in SPS T max ), density, crystallized phase fractions (extracted from Rietveld refinement), normalized glass rate, and thermoelectric properties measured at 400K.

Table 2 :

 2 Glass transition T g and first crystallization T c temperatures of the Cu 15 As 30 Te 55 sample as a function of the ball milling time t BM .

			.4	6.17	32	66	2	0	0.24	80	2.0	0.9	0.14
	0	10 min / 80 MPa	427.4	6.29	69	0	22	9	0.14	76	1.7	1.8	0.08
	0	20 min / 80 MPa	428.3	6.32	69	12	15	5	0.13	77	1.2	1.5	0.13
	0	30 min / 80 MPa	426.9	6.24	55	10	18	16	0.19	76	1.4	1.6	0.10
	0	0 min / 50 MPa	427.9	6.31	64	0	19	17	0.08	81	-	-	-
	0	10 min / 50 MPa	425.4	6.22	34	64	2	0	0.28	77	1.3	1.2	0.15
	0	20 min / 50 MPa	430.3	6.31	64	13	20	4	0.11	76	1.3	1.6	0.11
	20	0 min / 80 MPa	425.9	6.28	0	95	5	0	0.18	94	1.4	0.9	0.29
	20	10 min / 80 MPa	428.4	6.34	54	10	18	18	0.09	101	2.3	-	-
	20	20 min / 80 MPa	426.9	6.34	10	56	16	18	0.16	87	-	-	-
	45	0min/80MPa	423.0	6.29	0	90	8	2	0.25	91	1.4	-	-
	45	10min/80MPa	423.5	6.33	0	91	9	0	0.25	89	1.4	1.0	0.24
	45	20min/80MPa	423.5	6.26	0	88	10	2	0.28	93	1.5	0.9	0.26
	130	0 min / 50 MPa	426.9	6.34	38	44	5	13	0.21	91	1.4	1.0	0.22
	130	10 min / 50 MPa	426.9	6.29	25	59	4	12	0.20	86	1.6	1.0	0.19
	130	20 min / 50 MPa	425.9	6.25	24	43	15	18	0.22	86	1.7	1.0	0.17
	360	0 min / 50 MPa	423.0	6.24	43	16	22	19	0.33	91	1.3	1.1	0.23
	360	10 min / 50 MPa	423.0	6.27	45	14	22	19	0.34	92	-	-	-
	360	20 min / 50 MPa	425.0	6.30	0	62	38	0	0.20	91	1.2	1.2	0.24

Acknowledgements

The authors would like to thank financial support from the French National Agency (ANR) in the frame of its program "PROGELEC" (Verre Thermo-Générateur "VTG"). The authors warmly thank Olivier Rouleau for thermoelectric measurements.