J B Vaney

A Piarristeguy

A Pradel

E Alleno

B Lenoir

C Candolfi

A Dauscher

A P Gonçalves

E B Lopes

G Delaizir

J Monnier

M Ribes

C Godart

Thermal stability and thermoelectric properties of CuxAs40-xTe60-ySey semiconducting glasses

We report on the thermal behavior and thermoelectric properties of bulk chalcogenide glasses in the systems CuxAs40-xTe60 (20 ≤ x ≤ 32.5) and CuxAs40-xTe60-ySey, (0 ≤ y ≤ 9) synthesized by conventional melt-quenching techniques. The thermal stability of these glasses was probed by differential scanning calorimetry to determine the characteristic Tg and ΔT temperatures, both of which increasing noticeably with y. Thermoelectric properties were found to be mainly influenced by the Cu concentration with respect to the Se content. The thermal conductivity is practically composition-independent throughout the compositional range covered. A maximum ZT value of 0.02 at 300 K increasing to 0.06 at 375 K was achieved for the composition Cu30As10Te54Se6.

1.Introduction

The efficiency of thermoelectric materials, which enable to convert a temperature gradient into electrical energy through Seebeck effect, and conversely electrical energy into thermal energy by the Peltier effect, is governed by the dimensionless thermoelectric figure of merit ZT defined as . This formula relates three physical properties intrinsic to the material: the electrical resistivity r, the thermopower or Seebeck coefficient S, and the thermal conductivity λ, all given at the absolute temperature T. The conventional strategy to enhance the ZT values consists in modifying the crystalline structure of materials that possess inherently good electrical properties by alloying and/or inserting foreign species to decrease the thermal conductivity. Alternatively, designing novel materials with inherently low thermal conductivity values would leave the power factor S 2 /r the only relevant parameter to be optimized. Glasses naturally belong to this class of materials since they show extremely low thermal conductivities due to strong phonon scattering induced by their non-periodic

structure. Yet, their high electrical resistivity remains an obstacle to push their ZT values closer to those observed in crystalline semiconductors and semimetals.

Te-containing chalcogenide glasses [START_REF] Borisova | Glassy Semiconductors[END_REF] were recently studied to determine their thermoelectric properties near room temperature. Studies focusing on the influence of a partial substitution by transition metals demonstrated that introducing Cu in glassy matrix, such as Ge-Te or As-Te, leads to a sharp drop in electrical resistivity by several orders of magnitude. The concomitant less-pronounced decrease in the thermopower values then

ZT = S 2 T / ρλ
resulted in a drastic increase in the power factor up to up to 0.1 mW.K -2 .m -1 at 300K

(measured on CuxAs45-xTe55 ribbons), bringing ZT values to encouraging levels [START_REF] Goncalves | [END_REF]3].

However, the amorphous state of these glasses should be thermodynamically stable i.e. the glass-transition temperature Tg should be high enough to prevent crystallization to occur.

Investigations on the thermal behavior of Cu-As-Te glasses have shown that transition-metal doping noticeably modifies both Tg and the glass-stability criterion ΔT [START_REF] Borisova | Glassy Semiconductors[END_REF][START_REF] Tanaka | Amorphous Semiconductors and related materials[END_REF] (defined as the difference between the onset temperature of the crystallization Tx and Tg). This last parameter, that embodies the crystallization ability of the material, was found to be substantially affected by the Cu concentration.

Glasses in the Cu-As-Te system show a rather low Tg (slightly above 130°C) and ΔT parameters [3,[START_REF] Vazquez | [END_REF], both of which limiting their potential use as thermoelectric materials. Their poor thermal stability may be also a major hurdle to the glass-ceramization process that constitutes an alternative way to enhance the thermoelectric properties.

In this study, efforts were devoted to enlarge the stability domain of Cu-As-Te glasses by systematically varying the Cu and Se contents in CuxAs40-xTe60-ySey, while trying to maintain or enhance the thermoelectric properties of the system. The influence of this substitution on the thermoelectric properties was investigated by means of electrical resistivity, thermopower and thermal conductivity measurements between 300 and 375 K.

2.Experimental

Samples preparation and characterization

CuxAs40-xTe60-ySey samples with x = 20, 22.5, 25, 27.5, 30 and 32.5 at% and y = 0, 3, 6 and 9 at% were prepared from high-purity copper pellets (99.9995%, Sigma-Aldrich), tellurium (99.995%, 5NPlus), arsenic (99.99%, Goodfellow) and selenium powders (99.99%, Sigma-Aldrich). Regardless of the starting composition, a total stoichiometric weight of 4 g was placed into a quartz ampoule (6mm inner diameter) and sealed under secondary vacuum (10 -5 mbar). The ampoules were then heated at 850°C with a 9°C.h -1 heating rate and kept at this temperature for one hour. The tubes were regularly rocked in the furnace to ensure a better chemical homogenization. The ampoules were then cooled down to 600°C and further quenched in a "salt + ice + water" bath. To improve the mechanical properties of the glasses by releasing stresses, the obtained ingot was further annealed at Tg -10°C for 20 minutes.

Powder x-ray diffraction (PXRD) was carried out using a Philips X-PERT PRO II to confirm the amorphous state of the samples (see Figure 1 for a typical XRPD pattern). The thermal behavior of the bulk glasses was investigated on powdered samples (about 7mg) by differential scanning calorimetry (DSC) using a DSC1 (Mettler Toledo) at a rate of 10°C.min - 1 in sealed Al crucibles.

Thermoelectric properties measurements

To determine the thermoelectric potential of these materials, the three relevant transport properties were measured separately for each composition. The thermal conductivity λ was obtained by measuring the thermal diffusivity and specific heat of the samples. The thermal conductivity was then calculated following the formula , where is the density calculated from the weight and geometrical dimensions of the samples. Thermal diffusivity was determined using the laser flash technique with a LFA 427 (Netzsch) on 6×6×1 mm 3 square-shaped samples. was measured using a DSC 404 F3 Pegasus (Netszch).

Electrical resistivity measurements were performed on disk-shaped samples (Ø ≈ 8mm) using the Van der Pauw method. The disks were further cut into bar-shaped samples (≈ 1×1×8mm 3 ) for thermopower measurements carried out between 300K and 375K at fixed temperature using a homemade apparatus based on the differential method. Stabilized positive and negative thermal gradients (ΔT ≈ 2 K) were obtained by heating alternatively each end of the sample: the thermopower values then stands for an average of the forward and reverse values. The temperature gradient and thermoelectric voltage were measured by two N-type thermocouples pressed by mulite rods against one side of the sample. A test of the accuracy of this system was obtained by measuring elemental Ni and comparing it to a standard measurement performed in the temperature range 300 -400 K by Laubitz et al. [6]. The absolute average difference between this test and literature is 0.4 µV.K -1 i.e. 1.6% as a relative average difference.

a C p λ = aC p ρ V ρ V C p

Thermal Stability properties

The glass transition temperature Tg and the glass stability ΔT of CuxAs40-xTe60-ySey samples were determined from DSC measurements and are shown in Figure 2. It is worth noticing that the Se substitution enlarges the vitreous domain relatively to Cu, i.e. the higher the concentration of Se, the higher the concentration of Cu in the vitreous state (Fig. 2). These results evidence two main trends of these thermal parameters with the Cu and Se concentrations. First, increasing the Se content results in a higher Tg. Secondly, at a given Cu content, Se substitution increases ΔT. Further, samples of composition nearer to the vitreous domain limit tend to exhibit lower stability towards crystallization regardless of Se ratio.

The fact that crystallization occurs in several steps -each leading to visible peaks on DSC scans as shown in Figure 3 -suggests that their evolution with Se or Cu concentration plays a major role in determining glass stability. A main characteristic is that, depending on the proximity to the amorphous border, additional peaks associated to crystallization of phases drastically lower ΔT. To confirm this feature, additional data were collected for glasses of compositions CuxAs40-xTe60 with x > 25 at%. Because these compositions cannot be obtained by conventional melt-quenching technique, they were synthetized by twin-roll meltspinning as described in detail by Piarristeguy et al. [7]. The results show that an additional crystallization peak shows up for compositions with x > 30 at % (see Figure 3).

The effect of Se and Cu on the thermal properties of Cu-As-Te glasses may be a direct consequence of modifications of the local environment of the As and Te atoms i.e. of their coordination number. The Cu-As-Te glasses are believed to be structured with Cu located at the center of tetrahedral units linked together by As atoms or Te chains [8,9]. We surmise that, at low substitution levels, Se atoms directly replaces Te atoms in the matrix thereby diminishing the number of Te-Te bonds in favor of Te-Se and, to a lesser extent, Se-Se bonds.

Since both types of bonds exhibit higher binding energies with respect to Te-Te bonds (184.2 kJ•mol -1 for Se-Se compared to 138.2 kJ•mol -1 for Te-Te [10]), the resulting network should be then more tightly bound and thus, less susceptible to crystallization.

In addition, the introduction of Cu in quantities over 3 at% strongly affects the glass structure [11]. Glassy As2Te3, similarly to As2Se3 glasses, is supposed to be structurally made of distorted layers bound together by van der Waals interactions [START_REF] Tanaka | Amorphous Semiconductors and related materials[END_REF], though the more metallic nature of Te compared to Se may lead to a higher degree of interactions between the different layers. The substitution of trigonally-coordinated As atoms by tetrahedrally-coordinated Cu atoms develops stronger binding between the layers, resulting in a more rigid network i.e. in a higher average coordination number [12]. In principle, an increase in Tg should be then observed with increasing the Cu content [START_REF] Popov | Semiconducting Chalcogenide Glass I[END_REF]. Our data, however, follows this trend only up to 27.5 at%. Above this concentration, Tg decreases suggesting that the structural assumptions described above are no longer valid. Xin et al. [START_REF] Xin | [END_REF] have shown that homopolar Cu-Cu bonds dominate in Cu-As-Se glasses at large Cu concentrations (> 20%) while the coordination of Cu and As (respectively tetrahedral and trigonal) remains unaffected. Given the lower energy of Cu-Cu bonds (488.7 kJ.mol -1 , calculated from [15]) compared to Cu-Te, Cu-Se and Cu-As bonds (536.8, 666.9 and 533.5 kJ.mol -1 , respectively, calculated from Pauling's relation [START_REF] Pauling | The Nature of Chemical Bond[END_REF]), the presence of homopolar bonds might give rise to a balance between the rigidity of the network and the bonding energies. Yet, because of the different nature of the Te and Se bonds, the possibility that Cu could be trigonally-coordinated at high Cu concentrations cannot be strictly excluded in the present case. Another possible origin of the observed dependence could be related to the presence of nano-sized crystals undetectable by PXRD that might grow due to the proximity of the glass-domain border in the Cu-As-Te phase diagram. Further work is in progress to better understand the overall dependence of Tg with the Cu and Se contents.

Thermoelectric properties at 300K

Figure 4 shows the electrical resistivity and thermopower measured at 300 K on the different CuxAs40-xTe60-ySey samples. Increasing the Cu concentration leads to a decrease in ρ (Figure 4a) while substituting Se for Te has the opposite effect. Assuming that the network structure remains unchanged upon alloying with Se, this last feature may be related to the less metallic character of Se compared to Te [START_REF] Borisova | Glassy Semiconductors[END_REF][START_REF] Tanaka | Amorphous Semiconductors and related materials[END_REF]. For compositions falling near the glass-domain limit (i.e. at the lowest Se content for a given Cu concentration), the beneficial influence of Cu on ρ overwhelms the detrimental effect of Se. This property enables to substantially lower ρ by one order of magnitude while maintaining the glass stability in this system. Noteworthy, ionic conductivity associated with mobile Cu atoms seems unlikely to play a significant role on the decrease in the ρ values observed in the present case. A decrease in the band gap width, as demonstrated by Goncalves et al. in Cu-Ge-Te glasses [START_REF] Goncalves | [END_REF], appears more reasonable due to the less ionic nature of Te compared to Se. This conclusion seems further corroborated by the results obtained by Bychov et al. [START_REF] Bychkov | [END_REF]18] in the Cu-As-Se system indicating a negligible ionic contribution to the electrical conductivity.

Figure 4b depicts the evolution of the thermopower values with the Cu content. A clear trend towards a decrease in S with x can be easily noticed. The influence of Se is more pronounced on S since the measured values range between 400 and 700μV.K -1 as typically observed in Se-containing glasses. Such high values originate from a large density of states at the Fermi level due to charged and neutral coordination defects (dangling bonds) [START_REF] Tanaka | Amorphous Semiconductors and related materials[END_REF][START_REF]Mott and Davis in Electronic processes in Non-crystalline Materials[END_REF]. The composition Cu25As15Te51Se9 does not seem to follow the trend observed i.e. a decrease in the thermopower values with y. This behavior might be related to the proximity of this composition to the crystalline border, possibly leading to differences in the glass structure and/or to the presence of nano-sized crystals in the glassy matrix that might affect S.

The power factor at 300K for each composition is shown in Figure 4c. These results

show that the power factor faithfully reflect the trend observed for the electrical resistivity, whose evolution is mainly driven by the Cu content. A maximum value of 22 μW.m -1 .K -2 was measured, showing that a sensible increase can be achieved near the vitreous domain limit as in Cu30As10Te54Se6 for instance. These power factors are of the same order of magnitude as those obtained by Goncalves et al. [3], yet, with a high concentration of Se.

The thermal conductivity values measured at 300 K are shown in

Thermoelectric properties up to 375 K for the compositional line CuxAs40-xTe54Se6

The temperature dependence of the thermoelectric properties for the glasses lying on the compositional line CuxAs40-xTe54Se6 (x = 25, 27.5 and 30) is depicted in Figure 7. Due to the low Tg (around 400 K) and the narrow domain of stability of these glasses, these measurements were limited to 375 K. The data decreases with increasing temperature indicating that charge carriers are thermally excited across the band gap (Figure 7a). This semiconducting behavior can be modeled by an Arrhenius law where is the activation energy and is the Boltzmann constant. Fitting the data with and as

ρ(T ) ρ(T ) = ρ 0 e E a k B T E a k B ρ(T ) E a ρ 0
free parameters (Figure 8) led to activation energies of 455 meV, 444 meV and 348 meV for the x = 25, 27.5 and 30 samples, respectively. According to Mott and Davis [START_REF]Mott and Davis in Electronic processes in Non-crystalline Materials[END_REF], when the conduction occurs through extended states rather than through hopping between localized states, the activation energy equals to the width of the band gap . The values inferred decreases with the Cu content and are therefore consistent with the idea that the decrease in is mainly due to gap narrowing.

The thermal conductivity data (Figure 7b) show only weak temperature dependence as expected from the amorphous nature of these materials. The slight decrease observed is likely due to increasing phonon-phonon scattering events as the temperature increases. As a consequence, the evolution of ZT (Figure 7c) is mainly driven by electrical properties, especially by the decrease in resistivity that overwhelms the decrease in thermopower. We finally obtain a noticeable threefold increase in ZT on going from 300K to 375K for each composition of the system CuxAs40-xTe54Se6, reaching a peak ZT of 0.06 at 375K for x = 30.

Conclusion

The thermal behavior together with the thermoelectric properties of CuxAs40-xTe60-ySey chalcogenide glasses was investigated by means of DSC, electrical resistivity, thermopower and thermal conductivity measurements. Our results show that substituting Se for Te in small quantities help to broaden the stability domain by increasing both Tg and ΔT. The electrical resistivity values decrease with increasing the Cu content and shows a metallic-like behavior.

The introduction of Se in these glasses drives the system towards a semiconducting regime of conduction. These trends are reflected by the composition and temperature dependences of the thermopower. The thermal conductivity is practically unperturbed by the chemical substitutions and remains typical of chalcogenide-based amorphous compounds. Taken as a

E a = (E c -E v ) / 2
ρ whole, these measurements highlighted the opposite effect of Cu and Se on the ZT values: an increase in the Cu content results in an increase in ZT, while an increase in the Se content is detrimental to the thermoelectric properties. Nevertheless, the beneficial influence of Cu overweights that of Se, leading to an overall increase in ZT that reaches 0.02 at 300K and increases to 0.06 at 375K in Cu30As10Te54Se6. In addition, the thermal stability of glassy samples can be of significant importance in the case of glass-ceramization process that requires large ΔT in order to control precisely the crystalline fraction in the glassy matrix.

This technique may possibly give rise to enhanced thermoelectric performance in chalcogenide glasses and will be the subject of forthcoming studies dedicated to Cu-As-Te-Se glasses.

Figure captions

Figure 5 .

 5 Because of the experimental inaccuracy that inevitably accompanies the measurement of λ via the density, specific heat and thermal diffusivity, no clear trend with the Cu and/or Se concentration is observed The λ values only slightly vary with the composition since no drastic structural changes were unveiled. All the samples are amorphous, synonymous to intrinsically low λ values that amount to 0.3 W.m -1 .K -1 . The calculated ZT values are displayed in Figure 6. Due to the apparent lack of influence of Cu and Se contents on thermal conductivity, the ZT values follow the variations in the power factor. The maximum ZT value obtained in the present series of samples reaches 0.02 in the Cu30As10Te51Se6 glass.

Figure 1 :

 1 Figure 1: PXRD pattern of Cu25As15Te60.

Figure 2 :

 2 Figure 2: Thermal parameters of the CuxAs40-xTe60-ySey glasses within the vitreous domain for

Figure 3 :

 3 Figure 3: DSC patterns measured in the system CuxAs40-xTe51Se9 for x = 25, 27.5, 30 and

Figure 4 :

 4 Figure 4: Room temperature electrical resistivity (a), thermopower (b) and power factor (c) of

Figure 5 :

 5 Figure 5: Room temperature thermal conductivity values for CuxAs40-xTe60-ySey.

Figure 6 :

 6 Figure 6: ZT values at room temperature for the system CuxAs40-xTe60-ySey.

Figure 7 :

 7 Figure 7: Temperature dependence of the electrical resistivity (a, dashed lines), thermopower

Figure 8 :

 8 Figure 8: Arrhenius fitting of resistivity data between 300 and 375 K for the compositional

Figure 1 Figure 2 Figure 3

 123 Figure 1

Figure 4

 4 Figure 4

Figure 5

 5 Figure 5

Figure 6

 6 Figure 6

Figure 7

 7 Figure 7

Figure 8

 8 Figure 8

Acknowledgments

This work was carried out in the framework of the project ANR-PROGELEC-VTG (Verre Thermo-Générateur) and therefore financially supported by the French National Agency ANR to which we are very grateful. In addition, we would like to thank Olivier Rouleau, Joël Couve and Viktoriia Ohorodniichuk for their helpful contribution to the characterization of the samples.


Vincent Cornu

Philippe Baran

Damien Calluaud

Laurent David

EFFECTS OF VARIOUS CONFIGURATIONS OF VERTICAL SLOT FISHWAYS ON FISH BEHAVIOUR IN AN EXPERIMENTAL FLUME

The knowledge of fish behaviour within vertical slot fishways is limited. This paper describes fish progression through five pools of the 1:4 scale vertical slot fishway of the University of Poitiers (France). Fish behaviour is studied by video monitoring in the third pool of the model. The results are analyzed comparing the number of fish passages between the pools, the stabling zones used by fish in the monitoring pool during their progression and fish trajectories. Comparison of four different pool configurations is performed to estimate the effect of geometric variations on the upstream migration efficiency.

1

INTRODUCTION

In an attempt to restore the connectivity of fragmented river habitat which is very important to achieve ecological status in relation to the EU Water Framework Directive, a variety of passage facilities have been installed at river barriers. Vertical slot fishways (VSFs) is one of this device used to facilitate fish passage through dams particularly diadromous species. However, the small cyprinids are rarely considered like target species and the efficiency of fish pass are rarely documented to produce improvement of fishways. A detailed knowledge of flows within these hydraulic structures and the interactions between fishes and turbulence characteristics are vital for successful passage through a fishway ( [START_REF] Hotchkiss | Turbulence investigation and reproduction for assisting downstream migrating juvenile salmonids[END_REF], [START_REF] Odeh | Evaluation of the effects of turbulence on the behavior of migratory fish[END_REF] and [START_REF] Silva | Effects of water velocity and turbulence on the behaviour of Iberian barbel (Luciobarbus bocagei, Steindachner 1864) in an experimental pool-type fishway[END_REF]).

Flows in VSF are turbulent and present unsteady vortex dynamics in relation to the geometric parameters of the pools (slope and pool geometry) ( [START_REF] Puertas | An experimental approach to the hydraulics of vertical slot fishways[END_REF], [START_REF] Rajaratnam | New designs for vertical slot fishways[END_REF], [START_REF] Tarrade | Detailed experimental study of hydrodynamic turbulent flows generated in vertical slot fishways[END_REF] and [START_REF] Wang | Contribution of experimental fluid mechanics to the design of vertical slot fish passes[END_REF]). Two typical flow patterns can be observed. In the first flow pattern (FP1), generally observed with large pool widths and low slopes, the principal flow leaving the slot entered the pools as a curved jet which opened out before converging again towards the next slot. The jet created a large recirculation zone occupying roughly half of the pool between the cross-walls and had an unsteady beating movement around the large baffle. In the second flow pattern (FP2), generally observed with small pool widths and high slopes, the jet had a high curve form and hit the opposite side wall. Two large contra-rotating swirls were then generated in the upstream corner of the pool and in the convex part of the jet and a smaller one occurred near the large baffle ( [START_REF] Calluaud | Scale effects of turbulence flows in vertical slot fishways: field and laboratory measurement investigation[END_REF] and [START_REF] Wang | Contribution of experimental fluid mechanics to the design of vertical slot fish passes[END_REF]).

Experimental investigations were carried out in the Institut Pprime of the University of Poitiers (France) to characterize turbulence levels and unsteady behaviours of the flow developed in different VSF. In particular, Calluaud et al. [START_REF] Calluaud | Proper-orthogonal basis decomposition of spatio-temporal flow evolutions modified by cylinder in a vertical slot fishway[END_REF] and Calluaud et al. [START_REF] Calluaud | Experimental study of 2D instationary flow in vertical slot fishways with and without cylinders[END_REF] determine how the design of existing fishways might be affected by minor modification, like cylinders addition within the pool. The aim of those adaptations is to manage the flow and to modify the turbulence levels in order to facilitate the passage of small species and juveniles. To improve the cylinder effect and to emphasize the ecological efficiency, biological experiments had been done on the 1:4 VSF model since 2004. Biological experiments were mainly conducted for FP1. In this flow pattern, fish behaviour was described [START_REF] Wang | Contribution of experimental fluid mechanics to the design of vertical slot fish passes[END_REF], fishes did not have major difficulties to cross the device. The effect of the cylinder introduction was mostly felt on the residence times of fishes, they were spent less time in the pool with the presence of a cylinder [START_REF] Chambon | Comparaison d'efficacité de montaison pour différentes configurations dans une passé à poissons à fentes verticales[END_REF]. For FP2 fishes had difficulties to cross the model but the weakness of the data set collected did not reveal a possible effect of the introduction of cylinders on fish behaviour in pools. In this study, the behaviour of chub is analysed in the third pool of the model for FP2. Four configurations of pools are tested to highlight the effect of the introduction of cylinders on fish behaviour.

MATERIALS AND METHODS

Experimental device

The experiment was conducted in the 1:4 VSF model at the Institut Pprime of the University of Poitiers (Figure 1). The model consists of five pools, L = 0.75 m long and H = 0.55 m deep installed in a plexiglass flume. The model is described in details by Tarrade et al. [START_REF] Tarrade | Detailed experimental study of hydrodynamic turbulent flows generated in vertical slot fishways[END_REF]. The width of the slot is b = 0.075 m and the width of the pools is fixed at B= 0.5 m (B/b =6 .67). The flume slope is 7.5 %, within the range of those commonly used in this type of fishway [START_REF] Wang | Contribution of experimental fluid mechanics to the design of vertical slot fish passes[END_REF]. The flow discharge in the fishway is Q = 23 L.s -1 . In these conditions, the jet from the slot has a high curve form and hits the opposite side wall and generates two large contra-rotating swirls in the upstream corner of the pool and in the convex part of the jet (FP2). Water for the experiments was drawn from the domestic water supply and recirculated through the system for at least one week prior to the experiment to ensure dechlorination, and checked for temperature, dissolved oxygen and nitrites daily. A water temperature regulation system was installed in the lower tank. Fish-tanks and filter pump were set up in the redistribution tank.

Fish capture and holding

Chubs were collected from "Petite Blourde" stream, one tributary of the River Vienne, central France. Sampling was conducted using electrofishing (DREAM electronic model HERON ® ). Sixty chubs (total length: 9,7-15,9 cm) were brought to the laboratory facilities and randomly introduced into two fish-tanks, at 30 individuals per tank. Fish sizes among fish-tanks were close [mean total length (TL) ± SD: Batch A = 12,5 ± 1,9 cm, Batch B = 13,6 ± 1,1 cm], which allowed for valid comparisons between experiments. TL was chosen in relation to fish swimming abilities particularly their critical and maximum swimming speeds to place them in difficult flow conditions in pools of the flume.

Fish-tanks set up in the redistribution tank of the flume allowed fish stabling in conditions similar to experimental conditions. Difference in water temperature between experiments (mean temperature = 16°C) was <0.3°C. Fishes were kept in fish-tanks two days before the beginning of experiments, without foods. Hall test was illuminated with projectors with a constant brightness between 08.00-18.00 hours. Tests were performed after a first passage in the model to minimize a possible learning effect.

Experiments

Four different configurations were tested (Figure 2): basic pools, pools with 1 cylinder, pools with 3 cylinders allocated in line and pools with 3 cylinders allocated in triangle. The introduction of cylinders is based on the principle of dividing the jet from the slot into two parts (1 cylinder) and then dividing again the secondary jet into two parts (3 cylinders in triangle) or aligning cylinders with the large baffle (3 cylinders in line). The optimization of the cylinders positioning was performed by calculating [START_REF] Bourtal | Design optimization of existing vertical slot fishways by cylinders adjunction[END_REF]. After starting the model and waiting for the balancing of pools, 25 individuals randomly selected from a batch were transferred into the downstream pool separated using a screen (pool No.5). Fishes were held in the pool No.5 for 15 min before each test to allow them to adapt to the flow. Then, the screen was removed and the experiment began for a duration of 90 min. The volume of the pool No.5 was reduced by half for 5 minutes after 60 min and 90 min to encourage migration attempts. At the end of 90 min the device was stopped and fishes were transferred to the fish-tank.

One test per batch and per day occurred during the experimental period (13-27 November 2010). Each configuration was tested at least three times to obtain enough data to perform statistical analysis.

Video monitoring

A 45° mirror positioned under the pool No.3 allows observation of fish movements inside this pool. The fish behaviour was continually recorded by video camera (Sony, HDR-HC9E model) during each trial.The flume walls were papered with black paper, except the bottom of the pool No.3, to place fishes in conditions close to reality. Each test represents a sequence of 90 minutes. Each sequence was analyzed to track fish movements between pools No.2, No.3 and No.4 and their movements between three significant zones of the monitoring pool (Figure 3). Figure 3. Stabling zones (zone 1, 2 and 3), observed positions of fish in the different zones, basic movements of fish between pools (A: entry through the downstream slot, B: exit through the upstream slot, C: entry through the upstream slot, D: exit through the downstream slot, E: stay in the pool) and scenarios (AB: pass through the pool, AD: enter the pool but wash back later, AE: enter the pool and stay till end of the experiment, CB: wash back from the upstream pool and enter again, CD: wash back through the pool, CE: Wash back from the upstream pool and stay in the pool till end of experiment).

Data analyses

At first, all the fish movements between pools videotaped during the experiments were recorded as the 5 basic movements and the 6 scenarios, from which were defined three indices of behaviour as: Efficiency (Eff):

Efficiency, expressed in percentage (%), was defined as the ratio of ascent subtract wash back into and through the pool No.3 to the number of fish used in the experiment,

( ) 100 fish of number CE CD AB (%) Eff × + - = (1)
Activity Index (AI): Activity Index, expressed in movements per individual (mov/ind), was defined as the ratio of the number of slots crossings to the number of fish used in the experiment, Data were analysed using analysis of variance (parametric tests) to compare (i) efficiency, (ii) activity index and (iii) downstream index between the four pools configurations. Fisher's Exact Tests for Count Data was used to investigate the distribution dependency of access to different zones of the pool No.3 or another pool between the four configurations.

RESULTS

Fish behaviour in the fish pass

The movement of fishes within the model is a complex process strongly affected by the flow and the vortex structures. We observed upstream and downstream movements, interrupted with stops in three significant pool zones. In these three "stabling zones", velocity and turbulent kinetic energy are sparsely unfavorable for fish stabling. Streams organization in stabling zones determines the fish position inside: head directed towards the slot in zone 1, and tail toward the slot in zones 2 and 3 (Table 1). 706 basic movements were recorded during the 18 trials. Upstream movements (A and B) are the most encountered, those represent more than 73 % of fish movements (n= 522) all configurations combined (Table 1). Upstream scenario (AB) represents more than 66 % of the sampling but downstream scenario (CD, 18.1 %) and pool crossing failure scenario (AD, 14.4 %) are not negligible.

Table 1. Number of fish basic movements and scenarios in the VSF where chubs were placed in the downstream pool No.5 and videotaped their movements across the pool No.3, where n is the number of fish observations and Eff is define by Eq. ( 1), AI by Eq. ( 2) and DI by Eq. (

Fish efficiency between the different configurations

The average efficiency is only 30,6 % for the experimental conditions in the configuration of pools without cylinders (Table 1). The introduction of cylinders in pools significantly improves the efficiency (ANOVA, F = 6.09, P < 0.05). The increase of efficiency is 11,7 % with the introduction of a cylinder, 16,5 % with 3 cylinders in line and 16,8 % with 3 cylinders in triangle.

The positioning of cylinders in pools has no effects on the Activity Index (ANOVA, F = 2.52, P = 0.10). Fish activity tends to be higher with the presence of three cylinders in pools. Fish activity passes from 1,28 to 1,95 movements per individu (mov/ind) with the introduction of 3 cylinders in triangle and to 2,29 mov/ind. with the introduction of three cylinders in line.

There are no significant differences of the Downstream Index between configurations (ANOVA, F = 0.71, P = 0.56). The Downstream Index has varied between 27,4 % and 41,5 % depending on the considered configuration. The downstream movement is an inhering phenomenon in fish progression within the model, the introduction of cylinders in pools has no effect on it.

Fish trajectory

When fish enter the pool No.3 through the downstream slot (n=285), most of them seek to leave the jet swimming toward zone 1 (Table 2). The presence of cylinders does not alter the first zone crossed by fish (Fisher, P = 0.55). This trajectory represents more than 98 % of fish movements (n = 281) for all combined configurations. Most of fish leave the pool No.3 from zone 1 (more than 92 % of individuals for all combined configurations). The introduction of cylinders in pools significantly affects the last zone occupied by fish before leaving the pool (Fisher, P < 0.05). There is an increase of access the upstream pool from zone 1: +12,9 % with a cylinder, +14,1 % with 3 cylinders in triangle and +16,1 % with 3 cylinders in line.

CONCLUSION

Fish behaviour within vertical slot fishways is now better understood. Crossing the device is a complex process strongly affected by the flow and the structure. It is a mixture of upstream movements, downstream movements and stops. Significant zones of the pool are used by fish during their displacements. Fish stops in these zones because hydrodynamic conditions (velocity and turbulent kinetic energy) are favorable for stationary swimming. Streams organization in stabling zones determines the fish position inside. Upon entry of fish in the pool through the downstream slot, most of them seek to leave the jet and swim to a zone behind the small baffle, called zone 1 in this study. This zone is a key zone for fish progression through the device, the most of fish leaves the pool from zone 1. Cylinder introduction within pools affects the upstream efficiency. The increase of efficiency is 16,8 % with the introduction of three cylinders in triangle in pools of the model. The introduction of cylinders does not change the first passage zone but changes the use of stabling zones, increasing the use of zone 1 by fish.

Figure 1 .

 1 Figure 1. Experimental device. a) pump, b) flowmeter, c) upper tank, d) vertical slot fishway model, e) lower tank, f) redistribution tank, g) fish-tanks, h) system of temperature regulation, i) circulation pump, j) filter pump, k) 45° mirror.

Figure 2 .

 2 Figure 2. Pools configurations with flow streamlines: a) no cylinder, b) 1 cylinder, c) 3 cylinders in line, d) 3 cylinders in triangle.

3 )

 3 DI): Downstream Index, expressed in percentage (%), was defined as the ratio of the number of downstream slot crossings to the number of upstream slot crossings, In a second step, all the fish movements between pools and particular zones of the pool No.3 videotaped during the experiments were coded and recorded. The proportions of access to different zones of the monitoring pool or another pool were analyzed for fishes entering in the pool No.3 through the downstream slot and for fishes leaving the pool No.3 through the upstream slot.

  .

			Configuration of pools of the vertical slot fish pass
	Variables		no cylinder 1 cylinder	3 cylinders in line	3 cylinders in triangle
	Number of fish		170	71	70	114
		A (n)	89	44	62	89
	Basic movements	B (n) C (n) D (n)	72 20 37	39 9 14	51 18 29	76 22 35
		E (n)	0	0	0	0
		AB (n)	70	38	50	75
	Scenarios	AD (n) CB (n)	19 2	6 1	12 1	14 1
		CD (n)	18	8	17	21
	Indices of behaviour	Eff (%) AI (mov/ind.) DI (%)	30,59 1,28 35,4	42,25 1,49 27,71	47,14 2,29 41,59	47,37 1,95 34,55

Table 2 :

 2 Chub trajectory between pools and stabling zones for fishes entered in pool No.3 through the downstream slot and for fishes leaving the pool No.3 to the upstream pool, where n is the number of fish observations.

	Configuration of pools of the vertical slot fish pass

Acknowledgements

This work was supported by the "Office National de l'Eau et des Milieux Aquatiques" (ONEMA), "Voies Navigables de France" (VNF) and the "European Regional Development Fund" (ERDF / FEDER).


Jean-Baptiste B Vaney

Gaëlle Delaizir

Eric Alleno

Olivier Rouleau

Andrea Piarristeguy

Judith Monnier

Claude Godart

Michel Ribes

Raphael Escalier

Annie Pradel
email: annie.pradel@univ-montp2.fr

A P Gonçalves

E B Lopes

G J Cuello

P Ziolkowski

E Müller

C Candolfi

A Dauscher

B Lenoir

A comprehensive study of the crystallization of Cu-As-Te glasses: microstructure and thermoelectric properties

Keywords: glass-ceramics, chalcogenide, thermoelectric properties

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

Introduction

Thermoelectric materials offer an effective way to convert thermal energy into electrical energy (Seebeck effect) and, reciprocally, electrical energy into thermal energy (Peltier effect). The performance of thermoelectric devices is directly related to the materials' dimensionless thermoelectric figure of merit ZT defined by where T is the absolute temperature, α is the Seebeck coefficient (or thermopower), is the power factor, 𝜌 is the electrical resistivity and λ is the total thermal conductivity. [START_REF] Ioffe | Semiconductor Thermoelements and Thermoelectric Cooling[END_REF] A good thermoelectric material should display simultaneously a large thermopower, a low electrical resistivity and a low thermal conductivity. However, these three transport properties are mutually interdependent via the carrier concentration, making the optimization of the thermoelectric properties a complex task. In most thermoelectric materials, optimum power factors are obtained when the carrier concentration ranges between 10 18 and 10 21 cm -3 at room temperature i.e. in heavily doped crystalline semiconductors or semimetals. [START_REF] Snyder | [END_REF][START_REF] Rowe | Thermoelectrics Handbook: Macro to Nano[END_REF] Another key ingredient leading to high thermoelectric materials is their complex crystalline structure that enables to lower the thermal conductivity values. Several strategies are usually employed to disrupt more efficiently the heat-carrying acoustic phonons either on an atomic or a microscopic scale. The former possibilities include mass fluctuations upon alloying or the presence of loosely-bounded atoms in oversized atomic cages. [START_REF] Rowe | Thermoelectrics Handbook: Macro to Nano[END_REF] Nanostructuring is at the heart of the latter approach through a combination of a micron-sized matrix embedding nanoscale precipitates across multiple length scales. [START_REF] Biswas | [END_REF][5][6][7] A radically different strategy may be adopted by focusing on materials exhibiting intrinsically very low thermal conductivity values leaving 𝑃 the only relevant parameter to be optimized. Organic amorphous materials like conducting polymers have been attracting great l rl

a PT T ZT = = 2 r a / 2 = P
attentions in recent years for their promising thermoelectric properties around room temperature. [8][9][10] Inorganic glassy materials offer also this possibility since their ability to conduct heat is hampered by their inherent disorder. In addition, the plethora of chemical compositions achievable allows tuning their electronic properties from metallic-like to semiconducting-like, for instance, in glasses based on chalcogenides (S, Se, Te) and/or pnictides (As, Sb, Bi, etc). 11 However, one of the main obstacles to consider them for thermoelectric applications is their high electrical resistivity, which has prevented so far to achieve large ZT values.

A fine control of the electrical resistivity therefore appears as the most challenging problem to be overcome before further considering these materials as potential thermoelectric materials. Though a first possibility would consist in varying the compositions to control the carrier concentration as in their crystalline analogues, a precise knowledge of the exact coordination number of the atoms is difficult to achieve. Another strategy relies on a controlled partial crystallization of the glassy matrix to lower the electrical resistivity.

Provided a precise control of the fraction of crystalline phase can be obtained, this innovative approach might help to improve the thermoelectric properties and hence, warrants further attention.

Here, we report detailed investigations on semiconducting chalcogenide glasses and glass-ceramics based on the Cu-As-Te system. More precisely, we focused on the glass composition Cu15As30Te55 and studied the influence of the crystalline nature and fraction on its thermoelectric properties. The choice of this particular composition is based on two main characteristics suitable for the purpose of the present study. First, the synthesis of a pure amorphous form of this compound can be easily done by a conventional quenching method and thus, does not need ultrafast-quenching techniques such as melt-spinning. Second, this glass composition has a very high electrical resistivity with respect to glasses containing higher Cu contents so that the influence of a crystallized fraction on ρ is expected to be exacerbated.

Experimental

The glassy samples were synthesized in silica tubes under secondary vacuum. Starting elements, As (Goodfellow, 99.99%), Te (5N+, 99.99%) and Cu (Sigma-Aldrich, 99.999%), were first weighed in stoichiometric quantities (to obtain a total batch of ~ 5g) and introduced in a silica tube. The tube was subsequently evacuated, sealed and heated in a furnace with the low heating rate of 9K.h -1 up to 1123K, held at this temperature for 2h and eventually quenched in a salt-ice-water mixture. The resulting ingots were hand-ground to micron-sized powders.

The thermal behavior of the as-quenched samples were studied by Differential Scanning Calorimetry (DSC) performed using TA instrument Q100 equipment from room temperature up to 573K using different heating rates ranging from 5 up to 40K.min -1 . Spark Plasma Sintering (SPS) of the powders was realized with the Dr. Sinter 505 Syntex, the set-up belonging to the "Plate-forme de Frittage Ile de France" (Thiais, France). This technique allowed us to obtain both amorphous bulk samples as well as glass-ceramic composites. The amorphous powders were introduced in a 8mm diameter graphite die. To gain further insights into the influence of this process on the crystalline fraction, we varied the dwell time parameter from 0 to 30 minutes at a temperature of 423K or 433K and under a pressure of either 50MPa or 100MPa.

The density of the different glass and glass-ceramics bulk was determined through the Archimedean principle using a Kern balance. This balance enables weighing solids in air (mair) as well as in a solvent (in our case, water mwater). If the density of the buoyancy medium is known (ρ0) the density of the solid (ρ) is calculated as follows:

𝜌 = ! !"# ! !"# "! $!%&# 𝜌 # (1)
The microstructure of both the amorphous and glass-ceramics bulk samples was investigated on fresh fracture along the cross section using a LEO SEM-FEG microscope.

Composition of crystalline and glassy phases was estimated using Energy Dispersive X-ray Spectroscopy (EDXS) on a polished cross-section surface.

To identify the crystalline phases, powder x-ray diffraction (PXRD) measurements on the surface of the SPS bulk samples were carried out at room temperature using a D8 Bruker diffractometer equipped with a Vantec 1D-detector. To derive the integral breadth of the x-ray line of the crystalline phase, a pattern was recorded in the 2q range 10-90° with another D8

diffractometer equipped with a 1D-detector and a primary monochromator filtering the Cu-Kα2 emission line. A good signal-to-noise ratio at large 2q was obtained for a total recording time of 96 hours. The integral breadths of several lines were determined by fitting a

Lorentzian profile on a background-subtracted pattern. The instrumental contribution to the integral breadth ( ) was determined by a preliminary experiment on LaB6 and subtracted from the observed integral breadth ( ) to provide an estimated intrinsic sample broadening ( ).

Neutron thermodiffraction was used to study the crystallization process occurring in the glasses upon heating. The neutron diffraction experiments were performed using the D1B instrument at the Institut Laue-Langevin in Grenoble (France) with a nominal wavelength of 2.52Å. Two samples of compositions Cu15As30Te55 and Cu20As20Te60 were placed in nonsealed cylindrical vanadium containers in vacuum (outer diameter of 8mm and inner diameter of 7.6mm). Using a standard ILL furnace (vertical top loading furnace), neutron diffraction spectra were continuously collected on samples subjected to the following heating ramps: from room temperature to 363K at a rate of 5K/min and then from 363K to 473K at a lower

β i β 0
β e rate of 0.1K/min. For the cooling process, the furnace was simply switched off to allow the samples to reach room temperature in 'free fall'.

Electrical resistivity measurements were performed on disk-shaped samples (Ø ~ 8mm) using the van der Pauw technique. 12 The disks were then cut in bar-shaped samples (~ 1×1×8mm 3 ) for thermopower measurements performed under argon atmosphere between 300K and 360K. The measurements were done at fixed temperatures using a homemade apparatus based on the differential method. 13 Stabilized positive and negative thermal gradients (∆T ~ 2K) were applied by heating alternatively each end of the sample: the thermopower values were then obtained as an average of the forward and reverse values. The temperature gradient and thermoelectric voltage were measured by two n-type thermocouples pressed by mulite rods against one side of the sample.

Thermopower mapping was conducted under vacuum using a potential Seebeck microprobe (PSM) on a sample surface of 4×0.5mm 2 with a resolution of 10×10µm 2 . 14 This measurement was performed on a glass-ceramic sample obtained at 423K, 50MPa, 30min.

dwell time. The scan direction of the measurements was in rising x-direction (type writer style), beginning from zero for every new line. The contact detection was established by a load cell and a microcontroller giving a trigger signal to the transient recorder. The applied force at each measurement point was about 1.65 mN/µm². The elapsed time between contact and desired force-trigger was about 3 ms. For each point, two thermopower values were saved from different time domains. The measurement temperature is estimated to be 5 to 10 K above room temperature. Black fragments visible in the resulting maps along the measurement direction or as a single point are due to contact problems.

The thermal conductivity was determined at room temperature via thermal diffusivity measurements performed under argon atmosphere on cylinder-shaped samples using a LFA 427 (Netzsch) equipment. Both properties are related by the formula where is

V p aC r l = a the thermal diffusivity,
is the specific heat and is the density measured by the Archimedean principle as previously mentioned. Specific heat measurements (DSC 403 F3, Netzsch) were performed by the continuous scanning method under argon atmosphere.

Results and discussion

Glass-ceramics formation and microstructure

The crystallization behavior of the Cu15As30Te55 glass was investigated using DSC experiments. The thermograms presented in Figure 1a show the evolution of thermodynamic properties up to 573K using different heating rates (ν = 5, 10, 20 and 40K.min -1 ). Two characteristic temperatures are clearly observed on the DSC curves: the glass transition temperature Tg and the crystallization temperature Tp. Both temperatures increase with the heating rate. Increasing the heating rate from 5K.min -1 to 40K.min -1 , Tg and the first crystallization temperature Tp1 shift from 394K to 408K and from 423K to 441K, respectively.

According to Hruby, 15 the difference between these two temperatures (Tp1 -Tg) can be used as a criterion to determine the thermal stability of a glass which is considered as stable when this difference exceeds 100K. In the present case, a difference of ~30K is obtained indicating that this glass is rather thermally unstable. The presence of two distinct exothermic peaks suggests that the crystallization of two different phases occurs. The peaks are better resolved at low heating rates i.e. at 5 or 10K.min -1 . The crystallization activation energy Ec can be inferred using the method introduced by Ozawa and specifically designed for non-isothermal study. 16 As shown in Figure 1b, the value of Ec is deduced from the slope of plotted as a function of following the relation

(2) p C V r n ln 1 / 1000 p T ( ) R E T d d c p - = ÷ ÷ ø ö ç ç è ae 1 1 lnn
where R is the gas constant. The crystallization energy Ec of the first peak Tp1 is equal to 189 kJ.mol -1 . This low value suggests that the glass composition requires few amount of energy to jump to crystalline state hence, making the sample poorly stable and quite prone to crystallization.

The SPS parameters (pressure, temperature, vertical displacement of punches) during the sintering process are shown in Figure 2. The sintering process starts around 373K to become maximal at 413K before ending at 423K. It is generally assumed that the sintering of amorphous powders by SPS proceeds through a viscous flow mechanism. [START_REF] Rahaman | Sintering of ceramics[END_REF] For the synthesis of glass-ceramics, two mechanisms have been assumed. The first one associates the densification of glassy powder through viscous sintering to a subsequent devitrification of the matrix. [START_REF] Rahaman | Sintering of ceramics[END_REF] The second possible mechanism implies densification and concomitantly a gradual crystallization of the matrix through the growth of neck between glassy particles. [START_REF] Rahaman | Sintering of ceramics[END_REF] For a given glass composition, the amorphous phase has a considerably lower viscosity than the corresponding crystalline phase, so that the sintering of polycrystalline material is inevitably more difficult than its amorphous counterpart. This suggests that the first mechanism described above, i.e. achieving full density prior to any significant crystallization, is likely at play. Moreover, it is well known that the current distribution in the SPS die and through the sample is different in the case of a conductor and an insulating material. [START_REF] Anselmi-Tamburini | [END_REF] In the case of a non-electrically conducting sample such as alumina or silica based glass, no Joule heating is expected through the sample so that the die ensures sample's heating. This contrasts with the case of conducting materials such as metals or metallic glasses, for which Joule heating starts immediately through the sample at the beginning of the process. Due to the semiconducting properties of the Cu15As30Te55 glass composition, 19 we surmise that heating occurs through both the carbon die and the powder.

Based on the above considerations, a series of SPS experiments was carried out in order to obtain either a glass bulk material or glass-ceramics with different crystalline fractions.

From the DSC data collected at the rate of 40K.min -1 , the sintering temperatures were chosen accordingly to lie between the glass transition and the first crystallization temperature i.e. 423K or 433K. Applied pressures of 50 and 100MPa were selected and different dwell times were tested (0, 2, 5, 10 and 30 min.) with the aim of varying the crystalline fraction.

The density of the glass bulk material was measured to be 5.9 g.cm -3 when the conditions 100MPa-423K-no-dwell-time were applied (Table 1). This value compares well with that obtained on the initial glass synthesized by the conventional melt-quenching technique. The PXRD pattern of the obtained pellet was indeed that of an amorphous material (Figure 3b) demonstrating that fully-densified amorphous samples were successfully obtained by SPS treatment. Upon partial crystallization, the density increases to 6.30 ± 0.10 g.cm -3 at the maximum crystalline fraction (433K, 50MPa, 2' dwell time). As we shall see below, this result can be attributed to the crystallization of the β-As2Te3 compound that has a theoretical density of 6.29 g.cm -3 . 20 PXRD measurements were carried out to determine the nature of the phases crystallizing in the glassy matrix (Figures 3c to 3h). The well-defined peaks showing up correspond to the crystallization of the β-As2Te3 phase (see Figure 3a for its PXRD pattern).

An additional small peak appearing at longer dwell time (marked by *) could not be unambiguously identified and might correspond to either α-As2Te3, AsTe or CuTe.

Figures 4a to 4c show the EDXS measurements performed to obtain further information on the microstructure and its evolution with the SPS parameters. In the present case, a precise determination of the crystalline fraction is challenging given the different phases coexisting at the micron and sub-micron scales i.e. an amorphous phase containing well-crystallized nanosized precipitates surrounded by biphasic regions composed of dendritic crystalline domains embedded in a glassy matrix. Thus, as a first estimation, only the relative part of each domain (amorphous and biphasic) was determined using image-analysis software on EDXS-SEM pictures. The percentage obtained should therefore be regarded as an upper bound of the actual crystalline fraction. Within this rough approximation, the results indicate an increase in the crystalline fraction as the dwell time increases up to 30 min. under the same temperature and pressure conditions (Table I). EDXS reveals that Te and As elements are homogeneously distributed in the material which is not the case for the Cu (Figure 5). Quantitative analyses of these crystals suggest that the chemical composition corresponds to As2Te3 without any detectable traces of Cu, further corroborating the indexation of the PXRD pattern. As a consequence, the remaining glassy domains are enriched in Cu compared to the composition of the initial amorphous phase. Based on these images, the crystallized nano-sized domains are estimated to be less than 100 nm.

More intriguing is the fact that the β-form of As2Te3 crystallizes in the present case.

While α-As2Te3 (monoclinic structure, space group ) 20 is stable in ambient conditions and can be easily synthesized by conventional solid-state synthesis routes, the β-As2Te3 allotropic structure (rhombohedral structure of Bi2Te3 structure type, space group ) [20][21][22] is metastable and could be so far only synthesized under high-pressure or by rapid quenching. 20- 23 The fact that the metastable high-pressure β-As2Te3 phase is favored in the glass may be due to the constraint of the material through an applied pressure during the SPS process. It's well known that the β variety is denser than the stable α form. 23 Thus a phase transition β®α at room temperature would imply an increase in volume ∆Vβ®α>0. 23 Since the β-As2Te3 crystals are embedded in the glassy matrix, this volume change is prevented in the present case.

This conclusion seems to be further corroborated by neutron thermodiffraction experiments carried out to determine not only the nature of the phase crystallizing in the m C / 2 m R3 glassy matrix but also their evolution upon heating. Figures 6a and6b show 3D plots of the entire set of data collected up to 473K on the Cu15As30Te55 and Cu20As20Te60 glasses, respectively. Up to 405K, both samples remain in an amorphous state without any discernable changes. Above this temperature, three distinct peaks are visible at 48.1°, 65.5° and 75.5° (Figures 7a to 7c show that, at temperatures at which the SPS treatment is performed (423 and 433K), the a-As2Te3 phase should be predominant in the crystalline fraction of the composite sample. The applied pressure during the SPS process together with internal stresses thus likely plays an important role in the stabilization of the b phase. 23 Upon closer inspection of Figure 3 (patterns h and g), it can be noticed that, even in the most crystallized sample, the reflections corresponding to b-As2Te3 in the PXRD pattern are broad likely due to the size of the precipitates and/or microstrains. To determine which mechanism is at play here, the integral breadth of the reflections was evaluated based on PXRD data at higher resolution collected on the most-crystallized sample (Figure 8). The socalled Williamson-Hall relation then allows separating the size (Dv, volume-weighted column length) from the microstrain (e, maximum strain) broadening. 24 These two quantities are related to the intrinsic integral breadth by: (3) where λ is the wavelength of the CuKα radiation. As shown in Figure 9, clearly varies linearly with the scattering vector . A linear fit against the experimental data with Dv and e as fitting parameters yield Dv = 80 ± 30 nm and e = 0.29% ± 0.06%. A better estimation of both Dv and e was derived from Rietveld refinements of the pattern using the Fullprof software. 25 This method enables a more reliable analysis of the microstructural effects by fitting each reflection to a pseudo-Voigt function, unlike the Williamson-Hall plot where a Lorentzian profile is assumed. In the literature, two Bi2Te3-type structures were reported for b-As2Te3 by Shu et al. 21,22 . These two models differ by slightly different positions of the As and Te atoms. We initially refined the experimental data considering both structures. In each case, the positions of the atoms and the lattice parameters were kept constant and the size and strain parameters were solely allowed to vary. Since a better agreement was found with the structure reported by Shu et al. 22 in 1986 (R-factors of RB = 21.5% and RB = 31.3%, respectively), refinements were pursued with this structure. In a second step, the positions of the atoms were released. The best refinement (Figure 8) led to Dv = 73 nm and e = 0.28% (R-factors of Rp = 0.9% and RB = 13.7%). As a consistency check, the same analysis was repeated in another part of the sample and yielded very similar values (Dv = 82 nm and e = 0.39%). While the size of the crystalline domain of metastable b-As2Te3found to be small -is consistent with EDXS analyses, the value of the strain parameter is more surprising. Such high value, similar to that found in ball-milled molybdenum (0.4%) for instance, 26 may be considered as evidence of the presence of strong internal stresses stabilizing the β form of the As2Te3 compound.

Thermoelectric properties

Figure 10 shows the temperature dependence of the electrical resistivity of the glass and glass-ceramic samples. The ρ values of the amorphous parent compound reach about 1 Ω.m at 300K, in line with previous results. 19 The electrical resistivity decreases by 4 orders of magnitude when crystals of β-As2Te3 are present in the glassy matrix. This decrease mainly originates from the presence of crystalline phase rather than an enhancement of the copper enriched amorphous phase since the decrease is almost doubled to that observed in pure As-Te-Cu glasses with different Cu contents. 27 As mentioned above, As2Te3 crystallizes in two allotropic forms consisting of either a rhombohedral structure (β-As2Te3) or a monoclinic structure (α-As2Te3). α-As2Te3 exhibits at 300K high thermoelectric power (ranging between -230 and -260 µV/K), low thermal conductivity (estimated to 4.0 W.m -1 .K -1 ) and an electrical resistivity value of 40 µΩ.m. 20,28 Though the thermopower values of β-As2Te3 remains so far unknown, it might show similar α values due to the strong similarities in the crystal and electronic structures of both compounds. 29 Regardless of the crystalline fraction, α slowly increases with temperature up to 365K and shows positive values indicating that all the samples are p-type materials (Figure 11). The Cu15As30Te55 parent glass exhibits the highest α value reaching 900µV.K -1 at 315K. The presence of crystalline β-As2Te3 in the glassy matrix markedly influences the values of α that drop to 70µV.K -1 at the maximum crystalline fraction. While the strong decrease in the ρ values may be the main ingredient lowering α as usually observed in crystalline semiconductors, the type of charge carriers dominating the electronic transport in β-As2Te3 may also play a significant role. When both electrons and holes contribute to the electrical conduction, α decreases due to the opposite sign of the contribution to the thermopower of both carriers. In the present case, if β-As2Te3 indeed behaves as an n-type semiconductor as suggested by Scheidemantel et al. 20 , its contribution to α would then partially cancel that of the amorphous phase thereby decreasing the overall α values.

To further investigate this last possibility, thermopower mapping of the surface of glassceramic compounds was carried out. Figure 12a shows a map realized on a 4×0.5 mm 2 surface area on the glass-ceramics obtained with the SPS parameters 423K, 100MPa and 30 min. for which, both amorphous and biphasic phases coexist (Figure 12b). The distribution of the thermopower values, depicted in Figure 12c, clearly indicates contributions from two distinct phases: one coming from a phase with high positive α values and a second with lower α values. The observed two-peak structure of the recorded signal may thus correspond to the amorphous and crystalline domains, respectively. Considering the average effect of the thermopower mapping due to the presence of dendritic domains of size below the resolution of the instrument, the tendency of the low α values towards negative values might indicate an intrinsic n-type behavior of the β-As2Te3 crystals.

The presence of a substantial crystalline fraction in the glassy matrix does not lead to drastic changes in specific heat that amounts to 0.25 J.g -1 .K -1 at 300K regardless of the crystalline fraction. The thermal conductivity values, listed in Table I, clearly increase concomitantly with the crystalline fraction: on going from the pure amorphous phase to the most crystallized sample, increases from 0.2 to 1.1 W.m -1 .K -1 at 300K. This change towards higher values cast doubt on the validity of the assumption made in Ref. 30 where a value measured in the Ge20Te80 glassy material has been used to estimate the ZT value of the Cu-containing samples (glass and glass-ceramics samples). The actual ZT value is likely to be significantly lower than the estimation given (0.2 at 300K). Note that such a trend with the crystalline fraction is not confined to the present glass-ceramics and has been already observed in oxide glass-ceramics. 21 These results provide an alternative way to estimate the crystalline fraction in the glassceramic samples. Within the effective-medium approach developed by Landauer 31 to model the thermal conductivity of composite materials, the thermal conductivity of the glass-ceramic samples composed of crystallized and amorphous phases can be expressed as The values obtained by this model, and listed in Table I, indicate a rather non-linear increase in the crystalline fraction when the dwell time increases. At the longest dwell time used here corresponds the maximum crystalline fraction that amounts to ~ 43%.

The highest power factor ( 260 µW.K -2 .m -1 at 300K) was achieved in the glassceramics exhibiting the highest crystalline fraction. Combined with the thermal conductivity values, this leads to a ZT value of ~ 0.08 at 300K that increases to 0.14 at 365K. This value remains low compared to that of Bi2Te3-based materials considered as reference materials for room temperature applications. This limitation in the ZT enhancement may result from the balance between the positive influence of crystallized β-As2Te3 on the electrical resistivity and its detrimental effect on the thermopower. Further optimization of the thermoelectric performance might be achieved provided p-type crystals in an intrinsically p-type glassy matrix could be grown.

Conclusion

The microstructure and thermal stability of the Cu15As30Te55 glass and its corresponding glass-ceramics analogues were investigated by means of DSC, x-ray diffraction and temperature-dependent neutron diffraction experiments. Transport properties measurements were further carried out to determine the influence of a partial crystallization on the thermoelectric properties. SPS-controlled process was demonstrated to be an efficient tool to

λ crys λ glass glass f glass crys 1 f f - = λ crys = λ crys/glass λ glass crys f » P = T
crystallize a substantial fraction of the glassy matrix. The metastable β-As2Te3 phase was found to crystallize first through the glassy matrix as the dwell time or the temperature of the SPS treatment increases. While this phase should undergo a transition to the stable a-As2Te3 above 409K i.e. at temperatures below that of the SPS treatment, the metastable β phase is found to be solely present in the glass-ceramics samples regardless of the SPS parameters used. The applied pressure and/or internal stresses during crystal growth likely play a role in the stabilization of this phase. The presence of crystallized domains has a strong and beneficial influence on the electrical resistivity that decreases by four orders of magnitude.

This result provides a proof-of-principle showing the potential of this approach in tuning the electrical conduction in chalcogenide-based glasses. Yet, our study also suggests that the nature of the crystalline phase is essential in optimizing the thermoelectric efficiency. In the present case, the crystallization of β-As2Te3 lowers the thermopower values possibly due to an intrinsic n-type behavior suggested by thermopower mapping. The ZT values are nevertheless enhanced in the glass-ceramic samples reaching 0.14 at 365K. The control of the type of conduction of the crystalline phase appears crucial to improve the thermoelectric efficiency of glass-ceramic compounds. This may be realized via changing and/or doping the initial glass composition and will be at the core of forthcoming studies.

Figure 12

  ) and correspond to the three main reflections of the b-As2Te3 phase. Within a very narrow temperature window of ~2K, the b-As2Te3 phase undergoes a structural transition to the a-type structure that does not show further evolution with temperature up to 473K. These results clearly indicate a narrow domain of existence of the b-As2Te3 phase and

  conductivity of the β-As2Te3 phase, is the thermal conductivity of the pure amorphous compound, is the volume fraction of the amorphous phase and is the volume fraction of the crystallized phase. Assuming that the thermal conductivity of β-As2Te3 is 4.0 W.m -1 .K -1 and using the experimental values of and , the volume fraction of the crystallized phase may be inferred.29

Figure 1 :

 1 Figure 1: (a) DSC curve of the Cu15As30Te55 glass, (b) calculation of crystallization energy Ec

Figure 2 :

 2 Figure 2: Graph showing the pressure applied and shrinkage (in mm) as a function of

Figure 3 :

 3 Figure 3: XRD patterns of (a) β-As2Te3, glass and glass-ceramics sintered with the SPS

Figure 4 :

 4 Figure 4: SEM images of SPS glass and glass-ceramics showing the presence of dendritic

Figure 5 :

 5 Figure 5: Composition measured by EDXS revealing the presence of β-As2Te3 surrounded by

Figure 6 :

 6 Figure 6: 3D plots of the powder thermodiffraction data collected between 10° and 120° as a

Figure 7 :

 7 Figure 7: (a) 2D mapping of the diffraction data of the Cu20As20Te60 sample as a function of

Figure 8 :

 8 Figure 8: Rietveld refinement of the high-resolution x-ray powder pattern (see text for

Figure 9 :

 9 Figure 9: Williamson -Hall plot of the sample integral breadth (βe) as a function of the

Figure 10 :

 10 Figure 10: Electrical resistivity as a function of temperature for different SPS glass and glass-

Figure 11 :

 11 Figure 11: Thermopower as a function of temperature for different glass and glass-ceramic

Figure 12 :

 12 Figure 12: (a) Mapping of the Seebeck coefficient (4×0.5mm 2 ) of the glass-ceramics (423K,

Figure 4 200nmFigure 5 Figure 6

 456 Figure 4

Table I .

 I Density, volume fraction of the biphasic domains, room temperature thermoelectric properties and crystalline fraction inferred from Eq.(4) of the different SPS glasses and glassceramics.

	SPS parameters	0'-423K-100MPa	5'-423K-100MPa	10'-423K-100MPa	30'-423K-100MPa	2'-433K-50MPa
	Density (g.cm -3 )	5.90 ± 0.1	6.03 ± 0.1	6.13 ± 0.1	6.23 ± 0.1	6.30 ± 0.1
	Biphasic fraction (vol %)	0	53	67	80	89
	r (mW.cm)	7.9.10 4	8.2	7.2	4.3	1.2
	a (µV.K -1 )	870	70	72	69	55
	Power factor (µW.m -1 .K -2 )	1	60	72	111	257
	l (W.m -1 .K -1 )	0.22	0.40	0.43	0.50	1.07
	(vol %)	0	18	21	25	43
	ZT (300K)	0.001	0.004	0.050	0.060	0.072

crys f

Acknowledgements

The authors would like to thank financial support from the French National Agency (ANR) in the frame of its programme "PROGELEC" (Verre Thermo-Générateur "VTG"). G. D. also acknowledges the support from the Limousin Region for its financial support through FEDER program. E. B. L. and A. P. G. acknowledge the support of FCT, Portugal under the contract nr. PTDC/CTM/102766/2008.