Rachel Pflieger
email: rachel.pflieger@cea.fr

Manuel Lejeune

Cédric Noel

Thierry Belmonte

Sergey I Nikitenko

Micheline Draye

Diagnosing the plasma formed during acoustic cavitation in [BEPip][NTf2] ionic liquid

Sonoluminescence (SL) spectra of a very dry [BEPip][NTf2] ionic liquid were measured in the first minutes of sonication under Ar. The intense sonoluminescence allowed us to monitor the timeevolution of the SL spectra. Several molecular emissions were observed. Rovibronic temperatures of C2 and CN were determined giving vibrational temperatures of 5800 ± 500 K and 6000 ± 500 K and rotational temperatures (i.e. translational or gas temperatures) of 4000 ± 500 K. These temperatures stay remarkably constant during the sonolysis, while SL spectra undergo strong changes that illustrate the very fast evolution of the plasma during the first minutes of sonication. The expected strong decrease in the plasma electron energy also reflects in the evolution of the populations of CH electronically excited states. The physical meaning of temperatures derived from molecular emissions in SL spectra is discussed.

Introduction

Sonochemistry is the chemical activity observed under ultrasonic irradiation of a liquid. Its origin is acoustic cavitation, i.e. nucleation, growth and implosive collapse of microbubbles of gas and vapor. Though its formation mechanism is still a subject of debate, it is widely admitted that a plasma forms in acoustic cavitation bubbles at collapse. [START_REF] Bruggeman | Plasma-liquid interactions: a review and roadmap[END_REF] This plasma emits light, the so-called sonoluminescence, whose emission spectra are the signature of the formed plasma.

Ionic liquids (IL) are solvents with very interesting properties (they have a very low vapor pressure, are non-flammable, nonexplosive, liquid over a wide range of temperature, possess a high thermal stability and high ionic and thermal conductivities) that explain their use in many applications in organic synthesis, separation technology, energy, materials, analytical applications, biotechnology etc. [START_REF] Claus | Ionic liquids in biotechnology and beyond[END_REF][START_REF] Kore | Group IIIA Halometallate Ionic Liquids: Speciation and Applications in Catalysis[END_REF][START_REF] Macfarlane | Energy applications of ionic liquids[END_REF][START_REF] Turgis | Ketone functionalized task specific ionic liquids for selective tantalum extraction[END_REF] These properties and in particular their essentially zero vapor pressure make them ideal solvents for sonochemistry [START_REF] Flannigan | Sonochemistry and sonoluminescence in ionic liquids, molten salts, and concentrated electrolyte solutions[END_REF] since they a priori do not interfere in chemical reactions inside bubbles. Indeed, a significant increase in the rate of several sonochemical reactions was reported, [START_REF] Srinivasan | Ultrasound promoted para-selective nitration of phenols in ionic liquid[END_REF][START_REF] Rajagopal | Ultrasound promoted Suzuki cross-coupling reactions in ionic liquid at ambient conditions[END_REF] as well as some selectivity in the reaction products. [START_REF] Chatel | H2O2/NaHCO3-mediated enantioselective epoxidation of olefins in NTf2-based ionic liquids and under ultrasound[END_REF][START_REF] Letort | New insights into the catalytic reduction of aliphatic nitro compounds with hypophosphites under ultrasonic irradiation[END_REF] The same properties also make ionic liquids potentially an ideal medium as far as reaching extreme conditions is concerned since the bubble content would consist purely of the dissolved gas, which optimizes the concentration of energy at collapse, limits any loss of energy by vibrational excitation and chemical reactions, and hence allows more extreme conditions (e.g. higher temperatures) in the collapsing bubbles. [START_REF] Merouani | Acoustic cavitation in 1-butyl-3-methylimidazolium bis(triflluoromethyl-sulfonyl)imide based ionic liquid[END_REF] Despite the growing interest in the combined use of IL and ultrasound, acoustic cavitation in these media has been poorly characterized. Oxley et al. [START_REF] Oxley | Sonochemistry and sonoluminescence of roomtemperature ionic liquids[END_REF] studied sonochemistry and sonoluminescence of N,N'-dialkylimidazolium IL at 20 kHz under Ar. They observed some degradation of the IL resulting in its coloration, in the presence of several decomposition products in the head gas and in molecular emissions in the SL spectra. The degradation mechanism by pyrolysis, either at the bubble-liquid interface or more probably inside the intra-bubble plasma (after droplet injection or maybe vaporization of the IL in the overheated zone surrounding the bubble,where the temperature would be high enough to increase the IL volatility [START_REF] Earle | The distillation and volatility of ionic liquids[END_REF] ), was later confirmed on methyloctylpyrrolidinium bis(trifluoromethylsulfonyl)-imide sonicated at 20 kHz under Ar. [START_REF] Chatel | Hydrophobic Bis(trifluoromethylsulfonyl)imide-Based Ionic Liquids Pyrolysis: Through the Window of the Ultrasonic Reactor[END_REF] It is to be underlined that though the effects (coloration of the IL, absorption of light in SL spectra) were obvious, degradation remained at the trace level. The formation of degradation products however opened a way for an experimental determination of the reached temperatures in sonicated IL. To the best of our knowledge, only one single experimental temperature [START_REF] Kanthale | Sonoluminescence quenching and cavitation bubble temperature measurements in an ionic liquid[END_REF] was reported in the literature, in a study on the sonication of 1ethyl-3-methylimidazolium-ethyl sulfate at 213 kHz under Ar. This temperature was determined by the methyl radical recombination method, which relies upon the kinetics of recombination reactions of methyl radicals. As acknowledged by the authors, the obtained temperature (3500 K) was surprisingly low and similar to that obtained in water, though it was expected to be much higher.11 This apparent discrepancy can be ascribed to the biases of the method: thermal equilibrium is assumed, parallel reaction pathways are neglected and a ''mean chemical temperature'' is obtained, whose spatial and temporal resolutions are not well defined. [START_REF] Ciawi | Limitations of the methyl radical recombination method for acoustic cavitation bubble temperature measurements in aqueous solutions[END_REF][START_REF] Pflieger | Influence of Ultrasonic Frequency on Swan Band Sonoluminescence and Sonochemical Activity in Aqueous tert-Butyl Alcohol Solutions[END_REF] For these reasons, other experimental determinations of the reached temperatures in IL are needed. Thanks to the presence of several molecular emission bands, [START_REF] Flannigan | Sonochemistry and sonoluminescence in ionic liquids, molten salts, and concentrated electrolyte solutions[END_REF][START_REF] Chatel | Hydrophobic Bis(trifluoromethylsulfonyl)imide-Based Ionic Liquids Pyrolysis: Through the Window of the Ultrasonic Reactor[END_REF] SL spectra offer an insight into the sonochemical plasma and the temperatures reached during the bubble collapse. The present work reports SL spectra obtained during the sonication of N,Nbutyl-ethyl-piperidinium bis(trifluoromethylsulfonyl) imide ([BEPip][NTf2]) at 20 kHz under Ar and the rovibronic temperatures obtained from spectroscopic fitting of the observed molecular emissions. Their physical meaning and link to the plasma electron temperature are questioned. Furthermore, SL spectra were monitored over time of sonication to follow the impact on the plasma of the degradation of the IL. The latter was made possible by an optimization of experimental conditions, and in particular by the use of a very dry IL -indeed, previous works [START_REF] Chatel | Hydrophobic Bis(trifluoromethylsulfonyl)imide-Based Ionic Liquids Pyrolysis: Through the Window of the Ultrasonic Reactor[END_REF][START_REF] Kanthale | Sonoluminescence quenching and cavitation bubble temperature measurements in an ionic liquid[END_REF] showed that a decrease in the water concentration in the IL strongly increased the SL intensity but also the degradation of the IL.

Materials and methods

N-Ethylpiperidine and 1-bromobutane were purchased from Aldrich and distillated immediately prior to use. Lithium bis-(trifluoromethyl)imide salt was purchased by abcr GmbH and used as received. Acetonitrile was dried from conventional method and stored under argon over molecular sieves 3 Å. [START_REF] Perrin | Purification of laboratory chemicals[END_REF] The Room Temperature Ionic Liquid (RTIL) was prepared in two steps (Scheme 1) according to a previously published procedure: [START_REF] Traore | New insight into indium electrochemistry in a Tf2N-based room-temperature ionic liquid[END_REF] (i) piperidinium bromide salt was synthetized by Mentschukin's reaction between n-ethylpiperidine (1 eq.) and 1-bromobutane (1 eq.) in acetonitrile at 80°C for 16 h under argon; (ii) BEPipBr salt was then dissolved in deionized water and reacted with LiNTf2 (1 eq.) overnight at room temperature, to give [BEPip][NTf2] as a viscous colorless liquid. [BEPip][NTf2] was dried at 80°C for 24 h under vacuum and stored under dry argon (yield: 80%, two steps). The water content was determined by Karl Fischer titration and was found less than 10 ppm. Synthesized ionic liquids were then characterized by nuclear magnetic resonance 1 H NMR. [START_REF] Bruggeman | Plasma-liquid interactions: a review and roadmap[END_REF] H NMR (400.13 MHz, CDCl3, 298 K): δ 0.99 (t, 3H, 3 J = 7.2 Hz), 1.40 (sex, 2H, 3 J = 7.2 Hz), 1.57-1.65 (m, 2H), 1.72 (quin, 2H, 3 J = 6.0 Hz), 1.86 (bs, 4H), 3.16-3.20 (m, 2H), 3.31 (t, 4H, 3 J = 6.0 Hz), 3.36 (q, 2H, 3 J = 7.2 Hz) ppm. Note that no brominated impurities were detected by Headspace Gas Chromatography Mass Spectrometry (Perkin Elmer) by thermal desorption experiment, performed by PerkinElmer.

Sonication was performed in a stainless steel reactor specifically designed for the SL measurements of small volumes of ionic liquids, and described in detail elsewhere. [START_REF] Chatel | Hydrophobic Bis(trifluoromethylsulfonyl)imide-Based Ionic Liquids Pyrolysis: Through the Window of the Ultrasonic Reactor[END_REF] The 20 kHz horn (1 cm 2 , 750 W Sonics generator) was set to work at 35% of its maximum amplitude. The specific heat capacity of [BEPip][NTf2] is not known, but the absorbed acoustic power can be estimated to be around 15 W by analogy with similar ionic liquids. [START_REF] Chatel | Hydrophobic Bis(trifluoromethylsulfonyl)imide-Based Ionic Liquids Pyrolysis: Through the Window of the Ultrasonic Reactor[END_REF] For all experiments, 30 mL of [BEPip][NTf2] were submitted to continuous Ar (99.999% purity, Air Liquide) gas flow about 30 minutes before sonication and during the ultrasonic treatment, at a controlled rate of 14 mL min -1 . The reactor was continuously cooled using a Huber Unistat Tango thermo-cryostat set at 1°C. The temperature of the IL was thus initially 1°C and reached 33°C after 12 min of sonolysis.

Light emission spectra were collected through a flat quartz window using parabolic Al-coated mirrors and recorded with a SP 2356i Roper Scientific spectrometer coupled with a CCD camera with UV coating (SPEC10-100BR Roper Scientific) cooled by liquid-nitrogen. A low-resolution grating (150blz500; spectral resolution 1.6 nm) was used to enable the measurement of the whole spectrum (from 230 nm up to 750 nm) at once. Spectral calibration was performed using a Hg(Ar) pen-ray lamp (model LSP035, LOT-Oriel) and correction for background noise and for the quantum efficiencies of grating and CCD was performed. Each spectrum corresponds to 60 s of acquisition time.

Emissions from the C2 Swan system (A 3 Πg-X' 3 Πu) and CN violet system (B 2 Σ-X 2 Σ) were simulated by the spectroscopy code Specair, [START_REF] Laux | Optical diagnostics of atmospheric pressure air plasmas[END_REF] after subtraction of a baseline and normalization. The simulation input parameters vibrational temperature Tv, rotational temperature Tr and ''effective pressure'' p (combining pressure and Stark effects [START_REF] Pflieger | Use of NH (A(3)Pi-X-3 Sigma(-)) sonoluminescence for diagnostics of nonequilibrium plasma produced by multibubble cavitation[END_REF] ) were manually varied and optimized to fit experimental spectra as well as possible.

Quadrupole mass spectrometry (PROLAB 300, Thermo Fischer) was used to monitor the composition of the gas phase during sonication. 1a) and the corresponding SL spectrum presents emission bands that can be assigned [START_REF] Pearse | The Identification of Molecular Spectra[END_REF] to C2, CN, CH, and possibly to SO2, species that may arise from the degradation of [BEPip][NTf2]. The strongest transitions of SO2 (at 300.1 and 296.1 nm) cannot be observed due to light absorption by the IL. [START_REF] Chatel | Hydrophobic Bis(trifluoromethylsulfonyl)imide-Based Ionic Liquids Pyrolysis: Through the Window of the Ultrasonic Reactor[END_REF] This sign of degradation is quite surprising since it is expected that the initial bubble content will be pure Ar, due to the essentially zero vapor pressure of IL. This presence of emission bands in the SL spectrum thus clearly points out that some degradation of [BEPip][NTf2] occurs from the very beginning of the sonolysis, possibly by a mechanism of droplet injection of the IL into the bubble core.

Results and discussion

Time-evolution of the SL spectra

During the first two minutes of sonication (Fig. 1a), the intensities of the SL continuum and of the molecular emission bands strongly increase, which can be traced back to the evolution of the IL's temperature: it shows a very fast increase in the first minute of sonication and temperature reaches its steady-state value after 2 minutes. As an IL, [BEPip][NTf2] is very viscous at room temperature and below, but in general the viscosity of RTIL decreases exponentially with temperature. [START_REF] Liu | Temperature Dependence on Density, Viscosity, and Electrical Conductivity of Ionic Liquid 1-Ethyl-3-Methylimidazolium Fluoride[END_REF] A high viscosity hinders nucleation and therefore limits the number of cavitation bubbles. [START_REF] Young | Sonoluminescence[END_REF] As the bulk temperature increases, the rates of nucleation and coalescence increase, leading to the formation of more (light emitting) cavitation bubbles, hence the higher SL intensity. After 2 minutes of sonication, the steadystate bulk temperature being reached, the number of cavitation bubbles is expected to be constant, reflecting in a much slower evolution of the SL continuum intensity. Fig. 1b also shows that absorption of the SL light by the formed degradation products becomes intense. However, emission bands can still be observed.

Fig. 2 provides a closer look at the time evolution of the intensities of the SL continuum, taken at 600 nm, and of the main molecular emissions (whose intensities were corrected for absorption). During the first two minutes, all intensities strongly increase due to the increase in number of cavitation bubbles induced by the lowering of viscosity. Up to t = 5 min, the SL continuum intensity then stays constant while molecular emissions decrease. The following decrease in the continuum intensity (t ≥ 5 min) indicates progressive poisoning of the plasma by gaseous by-products. Interestingly, the intensities of the various emission bands follow different trends: CN shows a strong decrease after 2 min sonolysis, while the intensities of C2 and CH continue to increase or slowly decrease. This observation can be explained by considering that the various excited species can be formed from different sources: directly from the ionic liquid, but also from secondary (volatile) degradation products of [BEPip][NTf2], e.g. methane or acetylene, the presence of which was confirmed by MS analysis. The study of the degradation mechanism of this IL and the formed degradation products will be the object of a separate paper.

Determination of rovibronic temperatures

Rovibronic temperatures were determined on two spectroscopic probes (C2 Swan bands and CN violet) using Specair 20 software. Fig. 3 presents the measured Swan band emission for the second minute of sonication, together with its simulation. Derived vibrational and rotational temperatures are Tv = 5800 ± 500 K and Tr = 4000 ± 500 K. The inequality Tv > Tr is the usual case in a non-equilibrium plasma. Interestingly, simulated vibrational and rotational temperatures remain constant during the sonolysis, at least in the first 6 minutes, before absorption prevents computational fitting of the emission. Fig. 4 presents the measured CN violet emission for the second minute of sonication, together with its Specair simulation. Due to absorption, only the first two minutes of sonolysis are usable. Both can be fitted by the same vibrational temperature: Tv = 6000 ± 500 K, in good agreement with C2 vibrational temperature. In the particular case of CN and with the present spectral resolution, Tr cannot be derived accurately because its influence on the spectral shape (at the used spectral resolution) cannot be easily separated from that of the effective pressure.

It is remarkable that CN and C2 vibrational temperatures stay constant in the first minutes of sonolysis, while the plasma characteristics obviously change: the viscosity of the IL decreases (impacting the bubbles' dynamics and thus the violence of their collapse), and the intensities of molecular emissions vary with time, indicating changes in the bubble content. Due to the almost zero vapor pressure of the IL, the initial bubble content is pure Ar, a monoatomic gas very favorable for cavitation. [START_REF] Young | Sonoluminescence[END_REF] The IL then starts to be degraded after being introduced into the plasma by droplet injection. Among its degradation products many are volatile, such as sulfur dioxide, carbon dioxide, acetylene, ethylene, methane etc. (that were detected by MS of the produced gases). They diffuse into the bubbles where they consume part of the collapse energy by chemical reactions and electronic, vibrational and rotational excitations. The electron temperature is expected to strongly decrease concurrently with the poisoning of the plasma. The fact that CN and C2 vibrational temperatures stay constant indicates that here they cannot be used to estimate the electron temperature. In other words, these excited states were not formed directly from the ground state by electron impact but by chemical reactions induced by impacts with energy transfer, like those involving metastable Ar for instance, and therefore they cannot be used as probes of the characteristics of the electrons.

Use of CH electronic transitions

Two different electronic systems of CH are clearly visible on the SL spectra: CH (A-X) and CH (C-X). The third one, CH (B-X), is hidden by the very strong CN emission. The formation of excited states of CH is often reported in the literature in hydrocarbon combustion [START_REF] Devriendt | Direct identification of the C2H(X(2)Sigma(+))+O(P-3)-4CH(A(2)Delta)+CO reaction as the source of the CH(A(2)Delta-4X(2)Pi) chemiluminescence in C2H2/O/H atomic flames[END_REF] and attributed to oxidation of a fuel derived radical by O, O2, OH or even SO2 [START_REF] Swinnen | Theoretical and experimental investigation of the C2H + SO2 reaction over the range T = 295-800 K[END_REF] -the formation of SO2 in the sonolysis of [BEPip][NTf2] was confirmed by mass spectrometry analysis of the produced gases. Determination of the exact processes leading to the formation of the observed excited species is beyond the scope of this paper, considering the complexity of the present system. However, several known precursors of CH excited states were observed by mass spectrometry of the produced gases: e.g. acetylene, 25 methane 27 and ethylene. [START_REF] Cai | Spark-enhanced ignition and flame stabilization in an ethylene-fueled scramjet combustor with a rear-wall-expansion geometry[END_REF] Thus it is highly probable that several concomitant reaction pathways do produce CH, each pathway populating in a different manner CH electronically excited states. [START_REF] Gueye | Interaction of (3-Aminopropyl)-triethoxysilane With Late ArN2 Afterglow: Application to Nanoparticles Synthesis[END_REF] Therefore, no equilibrium is expected between these excited states and care should be taken in using the relative intensities of their emissions for a temperature determination. To illustrate this remark, let us consider on the contrary equilibrium, and that electronic excitation of CH occurs by electron impact. In this case, one can consider that the populations of the electronic levels follow Boltzmann law, and derive CH electronic temperature Te from the populations (nA, nC) of the emitting levels:

where gi is the degeneracy of the electronic level i and Ei is its energy. These relative populations of the emitting levels (Fig. 4) can be derived from the measured emission intensities (IA-X, IC-X): and with AA-X the radiative transition probability from level A to level X, hνA-X the photon energy, Ω the solid angle of observation and V the observed plasma volume.

It follows from the previous equations, with K a constant:

The electronic temperature of CH can thus be derived from the slope of Boltzmann plot vs. Ei (insert in Fig. 4). Obtained CH electronic temperatures are of 3.9 eV ≈ 46 000 K (± 27 000 K) for the first minute of sonication, 0.75 eV ≈ 8700 K (± 2000 K) for the second minute and 0.72 eV ≈ 8400 K (± 3600 K) for the third minute of sonication.

Although the observed trend is in agreement with the expected decrease in electron temperature in the first minute(s) of sonication and as long as degradation products accumulate in the bubbles, the very high value calculated for the first minute of sonication clearly casts doubt on the made hypothesis. Indeed, such a high experimentally determined temperature has never been reported for acoustic cavitation. Moreover, it strongly disagrees with the electronic temperature previously estimated in a similar SL-favorable medium (another liquid with very low vapor pressure): Eddingsaas et al. [START_REF] Eddingsaas | Evidence for a plasma core during multibubble sonoluminescence in sulfuric acid[END_REF] derived an electronic temperature of 8000 K from the Ar (4p-4s) emission in concentrated sulfuric acid sonicated at 20 kHz under Ar. The discrepancy is to be attributed to the made assumptions: CH excited states are not produced by electron impact but by different chemical reactions, and their relative populations cannot be used to estimate an electronic temperature.

That being said, it is remarkable that a very high relative population of CH (C 2 Σ + ) state, 0.38 31% (Fig. 5), is reached at the very beginning of sonication, when the bubble content is almost only Ar, indicating that enough energy is present to produce it. As soon as degradation products are formed and poison the bubble interior, i.e. from the second minute of sonication, CH (C 2 Σ + ) population relatively to CH (A 1 Π) one strongly decreases to 0.12. This huge change that happens in the first two minutes of sonication underlines the strong and fast change in bubble content and in sonochemical plasma characteristics during sonication, due to the degradation of the solvent.

Discussion on the temperatures

All spectroscopically determined temperatures here are, as expected, higher than the ''chemical'' one (3500 K [START_REF] Kanthale | Sonoluminescence quenching and cavitation bubble temperature measurements in an ionic liquid[END_REF] ). They also illustrate the non-equilibrium state of the plasma, with Te > Tv > Tr. Even if comparison of spectroscopic temperatures is not straightforward, valued information can be derived from them. First of all, it is usually considered that rotational temperatures are equal to the gas (or translational) temperature since only a few collisions are needed for equilibration (the high pressure of the sonochemical plasma makes this condition easily fulfilled). Thus an estimate of the gas temperature at the time of C2 emission is given by C2 rotational temperature Tgas = Tr = 4000 ± 500 K. Also vibrational temperatures could be derived from CN and C2 emissions: fitting with Specair is possible because populations of excited vibrational levels follow Boltzmann law. Excited species undergo enough collisions to reach a vibrational equilibrium, which illustrates in the good agreement obtained between C2 and CN vibrational temperatures (Tv (C2) = 5800 ± 500 K and Tv (CN) = 6000 ± 500 K). In this view, it is interesting to compare C2 and CN rovibronic temperatures during the sonication of [BEPip][NTf2] at 20 kHz under Ar with literature values derived from multibubble SL spectra (considering the same ultrasonic frequency and gas) of aqueous solutions or concentrated acids. Fitting of C2 Swan bands in a 10 -3 M aqueous benzene solution gave Tv = 4300 ± 200 K, 31 and in aqueous tertbutanol solutions (0.05-0.4 M) Tv = 6300 ± 1000 K. [START_REF] Pflieger | Influence of Ultrasonic Frequency on Swan Band Sonoluminescence and Sonochemical Activity in Aqueous tert-Butyl Alcohol Solutions[END_REF] It was also shown, though at high ultrasonic frequency, that decreasing the tert-butanol concentration led to an increase in C2 vibrational temperature,17 so that higher temperatures would be expected at lower concentration. In a 0.1 M ammonia solution, vibrational temperatures of 9000 ± 1000 K for OH (A 2 Σ+-X 2 Π) and 7000 ± 1000 K for NH (A 3 Π-X 2 Σ -) were estimated. [START_REF] Pflieger | Use of NH (A(3)Pi-X-3 Sigma(-)) sonoluminescence for diagnostics of nonequilibrium plasma produced by multibubble cavitation[END_REF] Concerning concentrated acids, Ar (4p-4s) emission in sulfuric acid corresponded to an electronic temperature of 8000 K, while in phosphoric acid OH (A 2 Σ + -X 2 Π) and PO (B 2 Σ + -X 2 Π) indicated vibrational temperatures of 9500 K and 4000 K, respectively. All these temperatures show a strong similarity, although more extreme conditions would be expected for IL (and concentrated acids, that share with IL a very low vapor pressure) than for aqueous solutions. Thus, the comparison of rovibronic temperatures leads to the same paradox (shifted to somewhat higher temperatures) as previously observed with chemical temperatures: [START_REF] Kanthale | Sonoluminescence quenching and cavitation bubble temperature measurements in an ionic liquid[END_REF] temperatures estimated for ionic liquids (and in concentrated acids) are of the same order of magnitude as in aqueous solutions, although more extreme conditions are expected from the quasi adiabatic heating model. This is not necessarily discordant, considering that the plasma is non-equilibrium, so that vibrational temperatures are smaller than electronic temperatures. In this view, they are only an order of magnitude estimate of the electron temperature Tel.

Moreover, as discussed above, CN and C2 vibrational temperatures staying constant while the electron temperature is expected to strongly decrease concurrently with the poisoning of the plasma indicates that they are disconnected from the electron temperature. These excited states and their emissions are probes of the chemical reactions that formed them, which explains why different temperatures were obtained in the literature from OH, C2, PO or NH emissions.

In a similar way, the emissions from two electronic systems of CH observed in the SL spectra of [BEPip][NTf2] unfortunately cannot be directly used to determine the plasma electron energy, although they reflect its evolution and that of the bubble content. The ratio of populations of CH (C 2 Σ + ) and CH (A 1 Π) states measured in the first minute of sonication is 0.38 (31%), i.e. very high (under the assumption that CH electronically excited states would be populated by electron impact and that their populations would follow Boltzmann law it would correspond to an electronic temperature of 3.9 eV). It shows a very fast and strong decrease and equals 0.12 in the second minute of sonication. Present SL spectra measurements are integrated over one minute, and it is expected that the relative population of CH (C 2 Σ + ) vs. CH (A 1 Π) be even higher in the first seconds of sonication, betraying a very energetic initial plasma.

Conclusion

Sonication of a very dry [BEPip][NTf2] ionic liquid under Ar produces an intense sonoluminescence, which allowed us to monitor the time-evolution of the SL spectra. Several molecular emissions were observed, the origin of which is the direct degradation of the ionic liquid and that of its degradation products. Rovibronic temperatures of C2 and CN were determined, giving vibrational temperatures of the order of 5800 K and rotational temperatures (i.e. gas temperatures) of 4000 ± 500 K. These temperatures stay constant during the first minutes of sonolysis, as long as absorption of SL light by the sonolysis degradation products does not prevent from simulating the emissions. This stability of rovibronic temperatures is contradictory to the observed changes in SL continuum intensity and in excited states emission intensities that reflect the changes in the plasma state induced by the changing bubbles' contents. This apparent discrepancy indicates that these rovibronic temperatures cannot be used as estimates of the plasma electron properties.

Two electronic systems of CH are observed in the SL spectra of [BEPip][NTf2]. Their relative intensities strongly decrease in the first two minutes of sonication, reflecting the uptake of volatile degradation products inside the bubbles. The ratio of populations of CH (C 2 Σ + ) and CH (A 1 Π) states measured in the first minute of sonication is very high, but strongly decreases in the second minute of sonication due to the change in the bubble content, from pure Ar to a mixture of Ar and volatile degradation products, that leads to poisoning of the plasma and to a much lower ability to produce highly excited states (e.g. CH (C 2 Σ + )). Future work will follow two directions. First it will focus on measuring SL spectra in the very early stages of sonication (i.e. in the first seconds), to characterize the formed plasma when the degradation of [BEPip][NTf2] is still negligible. This aim requires further technical developments of the experimental set-up and in particular an amplification of the SL light that is very dim, even in the optimized conditions of a very dry IL. These experimental data will help reconsidering the model of formation of the sonochemical plasma, and its comparison with ''more conventional'' plasmas. Second, it should study and compare more molecular emissions in SL, to try and shed some more light on the mechanisms of formation of the excited species and determine which useful information can be derived from them. Am. Chem. Soc., 1999, 121, 5817-5818.

Fig. 1

 1 Fig.1presents the SL spectra measured during the first 10 minutes of sonolysis of [BEPip][NTf2]. Light emission is observed from the first minute of sonication (Fig.1a) and the corresponding SL spectrum presents emission bands that can be assigned[START_REF] Pearse | The Identification of Molecular Spectra[END_REF] to C2, CN, CH, and possibly to SO2, species that may arise from the degradation of [BEPip][NTf2]. The strongest transitions of SO2 (at 300.1 and 296.1 nm) cannot be observed due to light absorption by the IL.[START_REF] Chatel | Hydrophobic Bis(trifluoromethylsulfonyl)imide-Based Ionic Liquids Pyrolysis: Through the Window of the Ultrasonic Reactor[END_REF] This sign of degradation is quite surprising since it is expected that the initial bubble content will be pure Ar, due to the essentially zero vapor pressure of IL. This presence of emission bands in the SL spectrum thus clearly points out that some degradation

Scheme 1 :Fig. 1 :

 11 Scheme 1: Synthesis of [BEPip][NTf2] ionic liquid

Fig. 2 :Fig. 3 :

 23 Fig. 2: Time-evolution of the intensities of molecular emission bands and of the SL continuum during the sonolysis of [BEPip][NTf2] at 20 kHz under Ar. The symbol size was adjusted to represent the uncertainty

Fig. 4

 4 Fig. 4 Measured CN violet emission in SL (second minute of sonication of [BEPip][NTf2] at 20 kHz under Ar) after subtraction of a baseline and normalization, and Specair simulation (Tv = 6000 ± 500 K, Tr = 5500 ± 2000 K, ''p'' = 4000 bar).

Fig. 5 :

 5 Fig. 5: Time-evolution of the relative population of C electronic level of CH, relatively to A electronic level. Insert: Boltzmann plot of CH for the first minutes of sonolysis of [BEPip][NTf2] at 20 kHz under Ar.

Acknowledgements

The Réseau Plasmas Froids from French CNRS is acknowledged for providing some of us with an IPMC. The Agence Nationale de la Recherche is acknowledged for financial support through the SILEXE project (ANR-13-CDII-0010). C. Meillat and PerkinElmer are acknowledged for GC-MS experiments.


Gaëlle Delaizir

Andrea Piarristeguy

Annie Pradel

Olivier Masson

Assil Bouzid

Short range order and network connectivity in amorphous AsTe3 : a first principles, machine learning, and XRD study

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

Introduction

Chalcogenide glasses are attractive materials for a wide range of technologically relevant applications including chemical sensors, medical and environmental devices, optical lenses, optical fibers, optoelectronic devices, Li-ion solid-state batteries and phase change memories. [1][2][3][4][5][6][7][8][START_REF] Musgraves | Springer Handbook of Glass[END_REF][START_REF] Zhang | [END_REF] Most of chalcogenide glasses exhibit a semi-conducting behavior owing to their peculiar electronic band-structure where spatially localized electronic states contribute to the electrical transport. While this feature is a main drawback for practical applications in semiconductor and optoelectronic areas, it is of interest for applications in the thermoelectric domain where a high thermopower and a very low thermal conductivity are highly required.

Among thermoelectric chalcogenide materials, Te-based compounds show outstanding performances. Within this family, crystalline Bi 2 Te 3 is the best thermoelectric material operating at room temperature. [START_REF] Goldsmid | Thermoelectric refrigeration[END_REF][START_REF] Rowe | Thermoelectrics and its energy harvesting. 2. Modules, systems, and applications in thermoelectrics[END_REF] In addition, its isostructural β -As 2 Te 3 compound shows remarkable thermoelectric properties. [START_REF] Vaney | [END_REF] The search for high performing thermoelectric materials led recently to the development of a new crystalline compound with composition AsTe 3 , that exhibits a very low thermal conductivity and an interesting figure of merit (ZT) peak value of 0.3 at 405 K, indicative of its thermoelectric performance. 14 An interesting feature of this compound is that it was exclusively synthesized from a Institut de Recherche sur les Céramiques (IRCER), UMR CNRS 7315-Université de Limoges, France. b Address, ICGM, Univ Montpellier, CNRS, ENSCM, Montpellier, France. ‡ assil.bouzid@unilim.fr † gaelle.delaizir@unilim.fr the full and congruent crystallization of the parent glass. 14 Thus, while only the crystalline phase is of interest for thermoelectric applications, a better control of the synthesis and stability of the cristalline phase require a fundamental understanding of the parent glassy AsTe 3 . In this work, we focus on the structural properties of the amorphous phase of AsTe 3 . Within the As-Te family, several glassy As x Te 1-x (0.2 ≤ x ≤ 0.8) compositions were synthesized and their properties investigated. [15][16][17][18][19][20][21][22][23][24][25][26][27] However, all the studied compositions were found to be thermally unstable and require either fast quenching rates 14 or conventional quenching of very small quantities to retain their vitreous state. 15 The atomic scale picture of As-Te systems remains elusive and various descriptions of the network connectivity and the short range order are provided in the literature. [15][16][17][18][19][20]28 In particular, Mössbauer spectroscopy revealed the presence of three fold Te environments in Te-rich compounds. 28 This result was extended by Raman measurements which proposed that a large fraction of three fold Te occurs in the entire compositional range of As atoms. 15 On the opposite side, recent X-ray diffraction experiments combined with X-ray absorption fine structure (EX-AFS) spectroscopy and reverse Monte Carlo simulation, 17 in addition to high-resolution two-dimensional projection magic-angleturning 125 Te nuclear magnetic resonance (NMR) spectroscopy revealed that coordination number of As and Te obey the 8-N rule over the entire compositional range. 16 Moreover, most of these studies reported the presence of a significant chemical disorder irrespective of the Te concentration in the material.

In the present work, we resort to first-principles molecular dynamics (FPMD) combined with, machine learning (ML) and Xray diffraction (XRD) to investigate the atomic scale structural organization of glassy Te-rich AsTe 3 compound. FPMD techniques have shown a high record of reliability in investigating a wide class of chalcogenides including S, Se and Te-based materials. [29][30][31][32][33][34][35] We focus our efforts solely on the amorphous AsTe 3 compound, as a good understanding of its structure provides direct insights into that of the metastable undoped crystalline AsTe 3 thermoelectric material.

The paper is organized as follows. Synthesis and sample characterisation are given in Section 2. In Sec. 3, we provide a description of the FPMD methodology (Sec. 3.1) and machine learning approach (Sec. 3.2) employed in this work. Results, including real and reciprocal space properties, atomic local environment and network connectivity, are presented in Sec. 4. The conclusions of our work are drawn in Sec. 5.

Sample preparation and caracterisation

AsTe 3 Synthesis

AsTe 3 was synthesized from high-purity elemental As (Goodfellow, 99.99%) and Te (5N+, 99.99%). Approximately 3 g of stoichiometric powders were placed in a cylindrical silica ampule (6 mm inner diameter and 1 mm thick) sealed under secondary vacuum (10 -5 mbar). The tube was subsequently heated in a vertical furnace up to 1123 K, with a low heating rate of 9 Kh -1 , held at this temperature for 2 h, and finally quenched in a salt-ice-water mixture. The obtained ingot was crushed into small pieces, remelted then quenched using the twin roller quenching technique. To this end, the resulting pieces were placed in a quartz tube with a drilled hole at the bottom of the tube. These pieces were heated using a radio frequency induction furnace, which allowed their temperature to rise very rapidly. An over pressure using an Ar gas jet was introduced forcing small droplets of the melt to flow through the hole in between the rotating twin rollers. Amorphous quenched flakes (typically ∼ 40 µm in thickness and ∼ 1 cm2 in surface area) were released by the rollers and dropped into an Al collector. The entire process was carried out inside a glove box kept under Ar atmosphere (for more details on the experimental procedure see Pradel et al. [ 36]).

Physico-chemical caracterisations

The chemical composition of the amorphous flakes after twin roller quenching was checked by SEM-EDS using a ZEISS EVO HD15 equipment. Different flakes and zones were analyzed in order to obtain information on their chemical homogeneity. We find mean atomic percentages of 24.3±1.0 and 75.7±1.0 for As and Te in the amorphous flakes, respectively. This result is in agreement with the target stoichiometric composition AsTe 3 . Glass transition and crystallization temperatures were recorded using Differential Scanning Calorimetry (DSC) AQ20 (TA Instruments) with a heating rate of 10 K/min as displayed in Figure 1. The DSC thermogram shows that AsTe 3 glass exhibits a glass transition temperature (T g ) and a temperature of the onset of the crystallization (T c ) at 367 K and 413 K, respectively. These temperatures are quite similar to the values obtained by J. Cornet et al. 19 on similar As-Te glasses. We note that the difference between T c and T g is about 46 K, which indicates a rather limited thermal stability of this glass 37 Furthermore, the density (ρ 0 ) of AsTe 3 powder was determined using an helium pycnometer (Micromeritics) and was found to be 5.639 gcm -3 , close to the value reported by J. Cornet et al. 19 Insights into the structure of amorphous AsTe 3 sample was obtained throught X-ray total scattering. Measurements of the total X-ray structure factor S T (k) were performed with a dedicated laboratory setup based on a Bruker D8 advance diffractometer (λ =0.559422 Å) equipped with a silver sealed tube and rapid LynxEye XE-T detector. This setup was modified in order to maximize collected intensities, to minimize spurious signal from empty environment and to get good counting statistics up to a large scattering vector length of 21.8 Å -1 . Raw S T (k) data were corrected, normalized and Fourier transformed using a homemade software [START_REF] Masson | pyTSRedX, a data reduction program to obtain the atomic pair distribution function[END_REF] in order to get the atomic Pair Distribution Function (PDF) of the sample (g T (r)). The corrections included capillary, empty environment and Compton scatterings, fluorescence, absorption and polarization. The obtained S T (k) and g T (r) are plotted in Figures 3 and4, respectively and will be discussed in section 4.1.

Computational details

First-principles molecular dynamics simulations

In this work, the electronic structure is described in the framework of density functional theory. We resort to the Becke Lee, Yang and Parr (BLYP) [START_REF] Becke | [END_REF]40 functional to describe the exchange and correlation parts of the total energy. The choice of BLYP is motivated by its high record of reliability when applied for chalcogenide materials. [29][30][31][32][33][34][35] In particular, BLYP demonstrated a superior performances compared to Perdew, Burke, and Ernzerhof 41 (PBE) functional when modelling Te-based, GeTe 4 , binary chalcogenide system, 42 and led to very good structural models for ternary systems including Ge 2 Sb 2 Te 5 , 43 Ga 4 Sb 6 Te 3 44 and, Ga 10 Ge 15 Te 75 . 45 The core-valence interactions are described by normconserving Troullier and Martins pseudopotentials. 46 The wave functions of the valence electrons were expanded in a plane-wave basis set defined by a kinetic energy cutoff of 40 Ry. The Brillouin zone was sampled at the Γ point. In the case of Tebased chalcogenides, it has been shown that van der Waals (vdW) corrections play an essential role in reproducing structural models featuring a good agreement with experiments. 42,45 Therefore, we account for long-range dispersion forces through the DFT-D2 correction term due to Grimme. 47 We resort to the Car-Parrinello molecular dynamics as implemented in the CPMD code. 48 A fictitious electron mass of 500 a.u. and a time step of ∆t = 0.12 fs are used to integrate the equations of motion, ensuring a good control of the conserved quantity. A Nosé-Hoover thermostat chain [49][50][51][52] is implemented to ensure the temperature control of the ionic degrees of freedom and a similar thermostat due to Blöchl and Parrinello 53 ensures the control of the temperature of the fictitious electronic degrees of freedom. We model AsTe 3 using a periodic cubic cell containing 240 atoms (60 As and 180 Te) at the experimental density of 5.639 gcm -3 (cell side length 20.07 Å). The initial configuration was built by selecting 240 atomic positions from an old binary chalcogenide (GeSe 4 54 ) and performing an atom substitution. The system was then subject to a thermal annealing cycle as follows: 10 ps at T = 300K, 10 ps at T = 500K, 50 ps at T = 650K, 50 ps at T = 500K and 25 ps at 300K. We note that both atomic species reached high mobility during the run at the melting temperature (T = 650 K) characterised by a liquid-like diffusion coefficients (D As = 3.5 10 -5 cm 2 /s and D Te = 4.2 10 -5 cm 2 /s). As such As and Te have undergone displacements several times larger than interatomic distances which ensures that no memory remains from the used initial configuration. The residual stress is calculated for the final structure obtained at T = 300K and was found to be equal to ∼ 0.8 GPa. Such a residual stress has been shown to alter the equilibrium structural properties of chalcogenide systems 55 and was eliminated by relaxing the cell following the procedure described in Ref. 55 yielding a slightly lower glass density of 5.45 gcm -3 (cell side length 20.3 Å). The obtained stress-free structure was then further annealed at T = 300K during 43 ps at an internal stress lower than 0.05 GPa. The final 20 ps of this trajectory were used to compute statistical averages of the structural properties of glassy AsTe 3 presented in this work.

In order to achieve an accurate and unbiased description of the network connectivity, we rely on the formalism of the maximally localized Wannier functions (MLWF). 56,57 Within this method, a Wannier function (w n (r)) corresponds to the localization of two electrons and its center (W) gives its average position. As such, MLWF leads to an accurate and compact real-space representation of the electronic structure, which we can use to define chemical bonds and lone pairs. In practice, w n (r) and their corresponding centers W are obtained by an on the fly unitary transformation of the Kohn-Sham orbitals ψ i (r) under the constraint of minimizing the spatial extension (spread, Ω) of the resulting w n (r) as follows:

Ω = ∑ n w n |r 2 |w n -w n |r|w n 2 (1)
Wannier functions were computed on top of 30 to 100 configurations selected along the last 20ps at T = 300K and their centers were used to investigate the network connectivity (occurrence of

Machine learning modelling

Despite the predictive power of FPMD methodology, its extension to large time-and size scales is inherently associated to the explicit treatment of the electrons and of their interactions. This limitation can be overcome by resorting to machine learning (ML) to generate interatomic potentials that allows a costeffective simulations of large systems. In particular, we resort to the Gaussian Approximation Potential (ML-GAP) approach that allows to learn and reproduce smooth highly dimensional potential energy surface by interpolating DFT data. [58][59][60] In this technique, each point of the potential energy surface is written as a sum of a universal local atomic energy function ε i that depends on the geometry of neighbors atoms structure around atom i and within a sphere of radius r cut . Then, Gaussian regression process [START_REF] Mackay | Information theory, inference and learning algorithms[END_REF][START_REF] Rasmussen | [END_REF] is used to define a model for ε i as a linear combination of nonlinear Kernel functions. An extensive review of this technique is provided in Ref. 60 . This technique has been successfully applied to model glasses, liquids, and crystals. [63][64][65][66] In this work, we apply ML-GAP technique as implemented in QUIP (http://www.libatoms.org). We combine two descriptors for the representation of the atomic structure where the Smooth Overlap of Atomic Positions (SOAP) 67 is complemented by a nonparametric two-body distance descriptor in order to prevent nonphysical clustering of atoms. We train the ML-GAP potential on a data base build by extracting representative configurations from the FPMD trajectories as follows: 216, 240, and 243 configurations at T = 650 K, 500 K, and 300 K, respectively, and 240 stressfree configurations at T = 300 K. This amounts to 225360 local environment to be fitted. In order to achieve a good accuracy of the data base, we recomputed DFT energies, forces, and stresses for all the configurations at an energy cutoff of 140 Ry. Table 1 shows the details of the GAP model and the hyper-parameters of the used descriptors.

The obtained ML-GAP potential is then used to compute ener- gies and forces on the training configurations. The results presented in Figure 2 show a very good match between all the quantities within a root mean square errors of 1.25 meV/atom for energy and 0.16 eV/Å for the force. Similar errors were also obtained on a validation data base made of configurations unknown to the trained potential, thereby validating the accuracy of the obtained ML-GAP interatomic potential.

Finally, we exploit the ML-GAP potential to produce a large amorphous model of AsTe 3 containing 1920 atoms (480 As and 1440 Te). MD is carried out using the ML-GAP potential in the NVT ensemble (cell side length 40.6 Å) and with an integration time step of 0.5 fs as implemented in the LAMMPS code 68 . As in the case of the FPMD model, the glass is obtained after a thermal annealing cycle featuring: 5 ps at T = 300K, 5 ps at T = 500 K, 70 ps at T = 650 K, 70 ps at T = 500 K, and 70 ps at T = 300 K. The obtained glassy model will allow us to consolidate the FPMD structural model of AsTe 3 by relaying on a large size system obtained at the DFT accuracy. When useful, results of the ML-GAP AsTe 3 model are presented and discussed throughout the paper.

Results

Total structure factor and total pair correlation function: Experiments vs Modelling

In X-ray diffraction experiments the total X-ray structure factor S T (k) is defined by:

S T (k) -1 = 2 ∑ α=1 2 ∑ β =1 c α c β f α (k) f β (k) | f (k) 2 | S FZ αβ (k) -1 , (2)
where α and β denote one of the two chemical species As and/or Te. c α and f α (k) are the atomic concentrations of species α (As, or Te) and its corresponding scattering factor. S FZ αβ (k) is the Faber-Ziman (FZ) partial structure factor and k is the magnitude of the scattering vector. 69 S FZ αβ (k) partial structure factors can be directly calculated on the equilibrium trajectory by solving the Debye equation in the reciprocal space. Consequently, one can have a direct access to the S T (k). Alternatively, S FZ αβ (k) can be obtained by Fourier transform (FFT) of the real space pair correlation functions g αβ (r) as follows:

S FZ αβ (k) -1 = 4πρ 0 k ∞ 0 r g αβ (r) -1 sin(kr)dr. ( 3
)
Similarly to S T (k) the total pair distribution function g T (r) is often calculated using g αβ (r):

g T (r) -1 ≈ 2 ∑ α=1 2 ∑ β =1 c α c β f α (k 0 ) f β (k 0 ) | f (k 0 ) 2 | g αβ (r) -1 . (4)
Where the scattering factors are evaluated at some arbitrary value k 0 , generally zero. While this approximation often leads to a fair representation of g T (r), the magnitude of the first peaks can be altered, in particular for samples combining both heavy and light elements. We here resort to the method developed by Masson and Thomas 70 where an exact and explicit g T (r) expression was derived. In their formalism, g T (r) can be obtained through a weighted linear combination of modified partial pair correlation functions where the weights are defined as the mean values of the Faber-Ziman factors over the considered reciprocal space range. In practice, the modified partial pair correlation functions are obtained by superposing on the original partial PDFs their weighted and symmetrically shifted ghost PDF functions. A full description of this method is provided in Ref. [ 70].

The measured X-ray structure factor of glassy AsTe 3 is provided in figure 3. We remark that S T (k) features a narrow first peak at about 1.8 Å -1 , followed by a much broader peaks (∼ 3.35 and 5.25 Å -1 ) and rapidly damped oscillations corresponding to a structural correlation length of about 12 Å -1 . Figure 3 shows also the AsTe 3 total structure factor directly calculated in the reciprocal space and that obtained by Fourier transform of the pair correlation functions of the FPMD model in addition to the FFT S T (k) of the ML-GAP model. Furthermore, we provide the measured X-ray structure factor of glassy As 20 Te 80 from Ref. [ 17]. Our results show a good agreement between FPMD/ML-GAP models and the measured data over the entire range of reciprocal space within typical statistical fluctuations. In particular, the positions and intensities of the first three peaks (k < 6 Å -1 ) are very well reproduced. Small discrepancies occur for large k values. Despite the slightly different composition, we find that AsTe 3 data are in a very good agreement with those of As 20 Te 80 . 17 Amorphous chalcogenide systems feature an intermediate range order (IRO) that manifests through the appearance of the first sharp diffraction peak (FSDP) at around k ∼ 1 Å -1 in the total structure factor. 71,72 In the particular case of Ge-based chalcogenides, the IRO was correlated to the occurrence of a particular connectivity between Ge-centered tetrahedra through edge-and corner-sharing connections. 29 In the case of As 2 Te 3 , diffraction data showed the presence of a FSDP in the amorphous phase. 73 However, it appears from our results that while a small shoulder for k ranging from 1 to 1.4 Å -1 is present in the case of the FPMD model of AsTe 3 (see panel in Figure 3), the ML-GAP model does not show any distinguishable feature around 1 Å -1 . The absence of a relevant FSDP reveals that the IRO is very limited in amorphous AsTe 3 . We note that the small peak at k < 1 Å -1 cannot be ascribed to any structural feature as it is a Fourier transform artifact due to the finite system size. Overall, we remark that the S T (k) obtained through FFT allows to capture all the features of the structure factor calculated directly in the reciprocal space.

Figure 4 shows the experimental g T (r) obtained by Fourier transforming the measured S T (k) and compared to that obtained from FPMD and ML-GAP models. The measured g T (r) shows an overall pattern typical of amorphous materials. We distinguish a first sharp peak at 2.71 Å, followed by a second broader peak at 4.02 Å reflecting the first and second coordination shells, respectively. Few other peaks occur at larger r values, however, their intensities are rapidly damped due to the abscence of long range correlations in the amorphous phase.

Compared to experiments, the g T (r) as obtained from the FPMD and ML-GAP models shows an excellent agreement over the entire real space range. For r < 5.4 Å, the measured first peak shows a slightly higher intensity compared to the modelled one, while the opposite case occurs when looking at the second peak. We also remark that the experimental g T (r) show a small shoulder at around 3.5 Å that is not reproduced in the modelled ones. These small discrepancies are typical of statistical errors and are expected to have a very limited influence on the short range order of AsTe 3 . This rational is substantiated by the fact that the integral of the first peak up to the first minimum, which directly correlates to the average atomic coordination number, gives the same result for FPMD and XRD pattern. The same rational applies also to the second peak. For r > 5.4 Å, the FPMD and ML-GAP models reproduce the positions and intensities of the peaks occurring at medium range distances. Overall, these results provide evidences that our models allow for a very good description of the topology of glassy AsTe 3 in comparison to experiments.

Faber-Ziman partial structure factors

In order to disentangle the various contributions of each chemical species into the network topology we consider the partial FZ structure factors as displayed in Fig. 5.

Focusing on S FZ TeTe (k), one can immediately remark that it follows closely the pattern of the total structure factor S T (k) (see Fig. 3). This result is not surprising and is a direct consequence of the large concentration of Te atoms in the system, as well as their large atomic scattering factor, that leads to a dominant contribution of S FZ TeTe (k) into the total structure factor as evidenced by Eq. 2. We remark that the small discrepancies between the measured and calculated S T (k) at k larger than 6 Å -1 observed in Figure 3 are mainly due to the Te-Te correlations. In this respect, a more accurate description of these correlation would require a higher level of theory for the description of vdW interactions within the DFT setup. Nevertheless, such discrepancies occurring at high k values are expected to have a very limited impact on the local structure around Te. In the case of S FZ AsTe (k) and S FZ AsAs (k), we remark the occurrence of an FSDP-like peaks in between 1 Å -1 and 1.5 Å -1 , which might be correlated with the occurrence of an intermediate range order around As atoms. Nevertheless, due to the small concentration of As atoms, these peaks are barely visible in the S T (k). In addition, while the ML-GAP model shows a reduction of the fluctuations of S FZ AsAs (k) for k < 4 Å -1 it does not promote any clear peak around 1 Å -1 . Taken together, FZ partial structure factors provide evidences of the dominance of Te-Te correlations as well as a very limited IRO in amorphous AsTe 3 .

Partial pair correlation functions

As-As

As-Te Te-Te Fig. 6 The partial pair correlation functions g TeTe (r), g AsTe (r), and g AsAs (r) for amorphous AsTe 3 at T = 300 K obtained from FPMD (red lines) and ML-GAP (green lines). The curves are shifted vertically for clarity.

The atomic-scale picture of AsTe 3 as described in the reciprocal space can be substantiated by investigating the real space properties of this glass. Figure 6 shows the FPMD and ML-GAP calculated partial pair correlation functions of glassy AsTe 3 .

g AsAs (r) feature a narrow first peak around 2.51 Å indicative of the presence of As-As homopolar bonds in glassy AsTe 3 . The high intensity of this peak reflects that As homopolar bonds occurs in a relatively large fraction. For larger r values, we remark that the FPMD model suffers from some statistical fluctuations due to the relatively small number of As atoms in the cell. This leads to a wide first minimum gap between the first and the second peaks in addition to the absence of a clear trend for r > 5 Å. Interestingly, the ML-GAP model provides a better description of the As-As correlations in real space where peaks representative of second (around 4 Å) and third (around 6.2 Å) coordination shells are well distinguished in comparison to the FPMD model. We note also a small reduction of the intensity of the first peak in the ML-GAP model.

Focusing on g TeTe (r), we find a first peak centered around 2.81 Å indicative of homopolar Te-Te bonds and a second peak around 4.06 Å originating from the Te belonging to the second coordination shell. These two peaks feature a similar intensities due to the high concentration of Te atoms and their ability to form -Te-Te-Telinkages. In addition, one can distinguish three peaks at medium range distances (r > 5.5 Å) that might be indicative of the presence of long Te n chains with n > 3. Finally, g AsTe (r) shows a first sharp peak around 2.65 Å. For r larger than 3 Å we remark some similarities between g AsTe (r) and g TeTe (r), which can be attributed to a preference of As and Te to have Te atoms on their third and forth coordination shells. Hence, the picture of glassy AsTe 3 could be rationalized in terms of highly chemically disordered structure (occurrence of As-As and Te-Te bonds) where As-centered motifs are linked through relatively long Te chains.

Let us now compare atomic bond lengths found in amorphous AsTe 74 The β -As 2 Te 3 compound is isostructural to the well-known Bi 2 Te 3based thermoelectric materials used in solid-state cooling applications. [START_REF] Goldsmid | Thermoelectric refrigeration[END_REF][START_REF] Rowe | Thermoelectrics and its energy harvesting. 2. Modules, systems, and applications in thermoelectrics[END_REF] In this structure, As atoms exhibit a more homogeneous environment since all As atoms are octahedrally coordinated (three short As-Te bonds with d=2.735 Å and three long As-Te bonds with d=3.132 Å). Overall, we remark that the As-Te bonds in both α-and β -As 2 Te 3 crystalline compounds are longer than those found in As 2 Te 3 or AsTe 3 glasses (d As-Te =2.65 Å). [74][75][76]

Coordination numbers and atomic local environments

More insights into the AsTe 3 network can be obtained by looking at the atomic coordination numbers. Partial coordination numbers can be obtained by two different methods. The first method relies on the partial pair correlation functions and consists on estimating n αβ by integrating the first peak of g αβ (r) up to a given cutoff distance corresponding to the position of the first mini-mum. The total As and Te coordination numbers are then obtained as follows: n As = n AsAs + n AsTe , and n Te = n TeTe + n TeAs , respectively. We here note that n AsTe = 3n TeAs . Finally, the average coordination number can be defined irrespective of the chemical species and is given by n = c As n As + c Te n Te . While this method is commonly used to estimate coordination numbers from molecular dynamics trajectories, its accuracy depends on the adopted distance cutoffs. In particular, in the case where first minimums of the g αβ (r) cannot be defined accurately, any small variation of the used cutoffs could lead to a significant change in the coordination numbers.

In order to go beyond this limitation, we resort to a second method based on the MLWF formalism. We recall that a Wannier function corresponds to the localization of two electrons and its center gives its average position. Hence, a chemical bond between two atoms α and β is defined when a Wannier center W is shared between the two considered atoms such as r αβr αWr βW ≤ 0.1 Å. Here r is a distance, α and β refers to As and/or Te atoms, and a 0.1 Å tolerance is considered to account for small deviations that occurs on the spacial localization of the W center. Consequently, one can accurately estimate the coordination number of each element by counting the number of chemical bonds. In addition, proportion of atoms α (As or Te) that are l-fold coordinated to other atoms (As or/and Te), nα (l), can be obtained. An illustration of the Wannier centers occurring in AsTe 3 is provided in Fig. 7. Table 2 summarizes the obtained coordination numbers of AsTe 3 . We find that As and Te coordination numbers obtained by integration of g αβ (r) are slightly larger than those obtained from the MLFW analysis. In particular, n TeTe shows the largest difference between the two methods, which can be ascribed to the ill defined first minimum in the g TeTe (r). We now focus on the MLWF coordination numbers and compare the results of the FPMD and ML-GAP models. We find a slight dependence of the partial coordination numbers on the cell size. In particular, n AsAs decreases from 0.75 (FPMD) to 0.66 (ML-GAP) at the expanses of n AsTe that increases from 2.25 (FPMD) to 2.32 (ML-GAP). Nevertheless, the overall n As remains constant (3.00) with increasing the cell size. Looking at n TeAs , we find that both models lead to a very similar values. In contrast, a larger n TeTe is obtained from ML-GAP compared to FPMD. This leads to an n Te of 2.08 in the case of the ML-GAP model and to 2.00 in the case of the FPMD model. Overall, the picture of the amorphous AsTe 3 network as obtained from the MLWF formalism is in good agreement with the "8-N" rule which predicts coordination numbers of 3 and 2 for As and Te, respectively. These results are in good agreement with previous RMC data on As 20 Te 80 17 and experiments. 15,16 We deepen the description of the AsTe 3 glassy network by looking at the details of the atomic local environments of As and Te atoms obtained through the MLWF decomposition on the FPMD and ML-GAP models (see Table 3). First we focus on the FPMD model. We find that 97% of As atoms are three-fold coordinated with a minor fraction of two-and four-fold As configurations (see table 3). Such a distribution of configurations is inline with the As coordination number n As =3. Looking at the breakdown of the 3-fold As environment, we find that configurations containing at least one homopolar As-As bond (As-AsTe 2 and As-As 2 Te) are as numerous as 59% compared to the chemically ordered As-Te 3 configurations (38 %). Interestingly, despite the low concentration of As atoms in AsTe 3 , 61% of them belong to homopolar bonds (see Table 3). While this result agrees with previous modelling 17,18 it is in a strike contrast with NMR and Raman spectroscopy results 15,16 where As-As homopolar bonds appear only for As concentration x > 0.3 in amorphous As x Te 1-x . This absence of As homopolar bonds in glassy AsTe 3 might be ascribed to the way their fractions are estimated from NMR and Raman spectroscopy. Actually, both experiments 15,16 rely on molecular dissociation models in order to estimate the fractions of As-Te, As-As, and Te-Te bonds. On the one hand, this procedure employs empirical parameters and, on the other hand, it replies on the dissociation of either As 2 Te 3 or AsTe. As such, the fraction of As-As bonds cannot be accessed in a straight forward manner and might be subject to large error bars due to the non inclusion of a more J o u r n a l N a me , [ y e a r ] , [ v o l . ] ,

Table 3 Percentage nα (l) of the different coordination units in the FPMD model of glassy AsTe 3 , error bars are typically of ∼ 1%. We note that the n α (l) is given with respect to the number of atoms α in the system. We also provide the fractions of As and Te atoms involved in homopolar bonds N AsAs and N AsAs , respectively. Values between parenthesis correspond to ML-GAP model. general model. Moreover, the occurence of large fractions of homopolar bonds in As-Te systems might also be ascribed to the very similar bond energies of As-As, As-Te, and Te-Te bonds. 77 Compared to As, Te shows a larger distribution of local environments. In particular, Te occurs mainly in 2-fold structural motifs (87.9 %) together with small fractions of under coordinated (1-fold Te, 5.8%) and over coordinated (3-fold Te, 5.9 %) units, in agreement with the Te coordination number n Te =2. Interestingly, while these three Te environments are present in crystalline As 2 Te 3 , 16 the occurrence of three fold coordinated Te in glassy As x Te 1-x has been longly discussed in literature. Recent EXAFS and NMR spectroscopy proved that Te atom is mainly two fold over the entire range of compositions as predicted by the 8-N rule. 16,17 In the contrary, Mössbauer and Raman spectroscopy, 15,28 suggests the occurrence of a non negligible fraction of 3-fold Te. The picture of Te-rich amorphous As x Te 1-x as stems out from our FPMD model shows that a small fraction of 3-fold Te occurs in AsTe 3 . In particular, we find that 3-fold Te occurs in Te-AsTe 2 (2.96 %), Te-As 2 Te (1.7 %), and, Te-Te 3 (1.23 %) units which differs from that found in the stoichiometric As 2 Te 3 system where Te-As 3 is the main building block.

Coming to the ML-GAP model, we remark that it reproduces the overall population of the atomic local environments found in the FPMD model. Nevertheless, few differences are noticeable and might be due to the enhanced description of the As-As correlations in the ML-GAP model. In particular, the fraction of As-As 2 Te in the ML-GAP model is found to decrease by about 5% compared to the FPMD model. This result is in line with the decrease of the n AsAs (see Table 2) discussed previously. More interestingly, we find that the fraction of 3-fold Te increases by about 8% at the expanses of 2-fold Te in the ML-GAP model with respect to the FPMD results. This finding consolidates our results on the presence of 3-fold Te in amorphous AsTe 3 and shows that it occurs not only as a chemically ordered As-Te 3 configuration, but also as As-AsTe 2 , and As-As 2 Te configurations. Such a picture might explain the difficulty of detecting Te(III) structural units from experiments. Furthermore, we find that the ML-GAP model features a sizeable fraction of homopolar bonds, 57% and 81% for As and Te, respectively. Overall, our results show that while As and Te fairly obey the 8-N rule, over and under coordinated atoms are present in glassy AsTe 3 . In the particular case of Te, we find that the occurrence of Te(III) is not necessarily in contrast with an average coordination number close to n Te = 2. Moreover, the 3-fold Te environment is found to be altered by the presence of homopolar bonds.

Network connectivity

It is of interest to focus on the network topology and connectivity. Figure 8 shows the bond angle distributions around As and Te atoms. ML-GAP model shows smoother bond angle distributions than the FPMD system thanks to a larger number of As atoms. Therefore, we only comment the results of the ML-GAP model. As features a broad angular distribution centred around ∼ 95 • and ∼ 97 • in the case of As-As-Te and Te-As-Te environments, respectively, consistent with a pyramidal 3-fold structure of As. In the case of As-As-As units we distinguish a main peak around ∼ 97 • and an extended tail up to ∼ 120 • . Coming to Te, we find that As-Te-As bond angle distribution shows a broad peak centered at around 95 • . In the case of Te-Te-As, the angular distribution becomes less broad and centers around 95 • . Finally, for the Te-Te-Te chains we distinguish a main peak centered around 97 • and a second less intense peak around 167 • . In order to access the structural origins of these peaks we report in Tab. 3 the chains analysis of glassy AsTe 3 . We note that a chain of atoms belonging to species α is defined as a linear sequence of atoms connected through chemical bonds where the two end atoms are singly coordinated, and the intermediate atoms are two fold coordinated to α atoms. In this definition, a chain of length n is quantized by the number of atoms forming the chain normalized to the total number of atoms of species α. We note that chains statistics obtained from the FPMD and the ML-GAP models cannot be directly compared as they contain substantially different fractions of Te-Te 3 configurations, which lead to the exclusion of a sizeable number of Te atoms when searching for chains. Hereafter we solely focus on the results obtained from the large cell with ML-GAP.

Focusing on As, we remark that it forms mainly dimer and trimer chains, and to a less extent 4-membered As chains (∼ 3%). These chains are reflected in the As bond angle distribution. The first peak around 95-97 • is attributed to As pyramids irrespective of the chemical order and the tail observed in the As-As-As bond angle distribution in the vicinity of ∼ 118 • is attributed to As chains with n = 4. The intensity of this peak is consistent with the small fraction of such chains. The As pyramids are predominantly linked to each other through three types of Te linkages. One can distinguish Te connecting two As pyramids is a "corner-sharing" fashion (As-Te-As), short Te chains involving Te dimers (As-Te-Te-As), and long Te chains (As-Te..Te..Te-As). As shown in Tab. 3, long linear Te chains up to n = 7 occurs in relevant proportions and are responsible of the peak at ∼ 167 • in the Te-Te-Te bond angular distribution. 42 Aiming at a complete picture of glassy AsTe 3 topology we in-vestigate the network connectivity through the rings analysis. We employ the RINGS method 78,79 to calculate the connectivity profile following the King/Franzblau shortest paths criterion. 80,81 In this method, all atoms are considered as initial points to begin the search for a given ring, and homopolar bonds are allowed during the searching procedure. We use the first minimum of the partial pair correlation functions as cutoff distances and search for rings with a maximum of 30 atoms. The distribution of rings in AsTe 3 can be quantified by two quantities: R c (n) which represents the number of rings containing n atoms (As or Te), and P n (n) represents the number of atoms that can be used as the origin of search for at least one ring containing n atoms. Both R c (n) and P n (n) are normalized to the total number of atoms in our model. Due to size effects, rings in the FPMD model show a large statistical fluctuations, therefore only results of the ML-GAP model are presented in Fig. 9. Our results reveal that only 4 and 5 membered rings show a meaningful concentration with about 13% and 18% atoms that could be at the origin of these rings, respectively.

In summary, the AsTe 3 shows a particular connectivity where As belongs to pyramidal structures with a high level of chemical disorder. The pyramids are rather connected through Te chains than rings and no significant IRO can be identified in the amorphous phase of AsTe 3 . A representative snapshot of the AsTe 3 structure is provided in Fig. 10.

Conclusions

We used X-ray diffraction, first-principles molecular dynamics, and machine learning interatomic potentials to study the glassy phase of AsTe 3 compound. X-ray diffraction experiments confirmed the nature of the amorphous phase AsTe 3 elaborated by twin roller quenching technique. The differential scanning calorimetry showed that glassy AsTe 3 exhibits a glass transition temperature T g and a temperature of the onset of the crystal- lization T c at 367 K and 413 K, respectively. Measured X-ray total structure factor and total pair correlation function were compared to those obtained from the FPMD model yielding a very good agreement. We then exploit the FPMD date to generate a machine learned interatomic potential through the Gaussian approximation potential framework, and use it to produce a large size AsTe 3 amorphous model. Then, the atomic scale structure of glassy AsTe 3 was investigated based on the obtained FPMD and ML-GAP models. We found that As and Te obey the 8-N rule with an average coordination numbers of 3 and 2, respectively, in the case of the FPMD model, and 2.99 and 2.08, respectively, in the case of the ML-GAP model. In addition, we find that significant fractions of under and over coordinated atoms exist in the amorphous phase with about 6% (FPMD) and 13% (ML-GAP) of 3-fold Te. Despite the low As concentration in AsTe 3 , its local environment features a very high chemical disorder that manifests through the occurrence of homopolar bonds including 57 % of As atoms (ML-GAP model). The overall picture of AsTe 3 glass is mainly made by As centered pyramidal structures linked through Te n chains. Our results provides a comprehensive picture of the chemistry and network connectivity of amorphous AsTe 3 .

Fig. 1

 1 Fig. 1 Differential scanning calorimetry thermogram of amorphous AsTe 3 . The glass transition temperature T g and the crystallization temperature T c are provided.

  bonding between neighboring atoms).

Fig. 2

 2 Fig. 2 Comparison between total energies (top panel) and force components (bottom panel) as obtained from ML-GAP potential and DFT calculations on the training data base.

Fig. 3

 3 Fig.3Total X-ray structure factor for amorphous AsTe 3 at T = 300 K. The experimental results (blue lines) are compared to the calculated FPMD S T (k) in the reciprocal space (gray lines) or obtained through Fourier transform of the pair correlation functions with a cutoff value k max = 21.8 Å (red lines), and to the ML-GAP S T (k) (green lines). These results are also compared to the measured S T (k) for amorphous As 20 Te 80 from Ref.[ 17] (black lines). The inset represents a zoom on the FSDP region.

Fig. 4

 4 Fig. 4 Total pair correlation function for amorphous AsTe 3 at T = 300 K. The experimental results (blue lines) are compared to the FPMD calculated S T (k) (red lines) and to ML-GAP S T (k) (green lines).

Fig. 5

 5 Fig.5The Faber-Ziman partial structure factors S FZ TeTe (k), S FZ AsTe (k), and S FZ AsAs (k) for amorphous AsTe 3 at T = 300 K obtained from FPMD (red lines) and ML-GAP (green lines). The curves are shifted vertically for clarity.

3

 3 to those found in stable α-As 2 Te 3 and metastable β -As 2 Te 3 crystalline counterparts. α-As 2 Te 3 and β -As 2 Te 3 crystallize in monoclinic and rhombohedral phases, respectively. The crystal structure of α-As 2 Te 3 consists of zig-zag chains where As atoms are either trigonally (As(I) site) or octahedrally (As(II) site) coordinated to the Te atoms yielding three various Te (Te(I), Te(II), and Te(III)) sites. More precisely, Te(I) type atoms are bonded to two As(I) atoms (typical bond length d Te(I)-As(I) =2.77 Å) and one As(II) atom (d Te(I)-As(II) =2.93 Å). Te(II) atoms are bonded to two As(II) atoms (d Te(II)-As(II) =2.90 Å) and one As(I) atom (d Te(II)-As(I) =2.68 Å) and finally, the Te(III) atoms are bonded to three As(II) atoms (d Te(III)-As(II) =2.76 or =2.85 Å).

Fig. 7

 7 Fig. 7 Details of the bonding environment for glassy AsTe 3 . For the color code: As (purple), Te (light orange), and Wannier centers (labeled as W) (light brown). Only a few As and Te atoms are presented along with representative Wannier centers. We distinguish three different Wannier centers: W B centers occurring along As-Te bonds, W H centers occurring along homopolar Te-Te or As-As bonds, and W LP , indicates the lone pair (LP) valence electrons not participating in chemical bonds.

Fig. 8

 8 Fig. 8 Bond angle distribution around As atom (top) and around Te atom (bottom).

Fig. 9

 9 Fig.9Connectivity profiles for amorphous AsTe 3 ML-GAP model obtained using the RINGS method. (top panel) R c (n), number of rings of size n normalized to the total number of atoms in the model, (bottom panel) P n (n), number of atoms at the origin of at least one ring of size n normalized to the total number of atoms in the model. Vertical lines represnts the standard deviation.

Fig. 10

 10 Fig. 10 Snapshot of amorphous AsTe 3 FPMD model at T = 300 K. For the color code: As (purple), and Te (light green). As centered pyramids are also highlighted and periodic clones are shown for clarity.

Table 1

 1 GAP model and hyper-parameters of the SOAP and 2_body kernels.

	Atomic environment kernel	SOAP	2_body
	r cut	6	6
	r ∆	1	1
	σ ω	1.0	0.0995
	θ	-	1
	σ atom	0.5	-
	ξ	4	-
	n max	8	-
	l max	8	-
	Represenative environments 1600	50

Table 2

 2 Coordination numbers as obtained from the FPMD and ML-GAP models. Results computed either by integrating the PDFs up to the first minimum or based on the MLWF analysis. Typical standard deviation of the MLWF results is of ∼ 0.02.

		FPMD	ML-GAP
		PDF MLWF PDF MLWF
	n AsAs 0.78	0.75	0.67	0.66
	n AsTe 2.26	2.25	2.36	2.32
	n TeAs 0.75	0.75	0.78	0.77
	n TeTe 1.33	1.25	1.45	1.31
	n As	3.04	3.00	2.98	2.99
	n Te	2.08	2.00	2.23	2.08

| 1-12

[1][2][3][4][5][6][7][8][START_REF] Musgraves | Springer Handbook of Glass[END_REF][START_REF] Zhang | [END_REF][START_REF] Goldsmid | Thermoelectric refrigeration[END_REF][START_REF] Rowe | Thermoelectrics and its energy harvesting. 2. Modules, systems, and applications in thermoelectrics[END_REF]

| 1-12

J o u r n a l N a me , [ y e a r ] , [ v o l . ] ,

Acknowledgments

The authors thank Mickaël Bigot for his help in sample preparation and Sébastien Le Roux for his courtesy on providing Atomes software (https://www.conectus.fr/atomes) that was used for part of the analysis and for making Figs. 7 and 10. We used computational resources provided by the computing facilities MCIA (Mésocentre de Calcul Intensif Aquitain) of the Université de Bordeaux and of the Université de Pau et des Pays l'Adour. 1-12 J o u r n a l N a me , [ y e a r ] , [ v o l . ] ,

Notes and references


domain: spi.other spi stat

text:
Dmitry Kucharavy
email: dkucharavy@unistra.fr

David Damand
email: damand@unistra.fr

Samia Gamoura
email: samia.gamoura@em-strasbourg.eu

Marc Barth
email: marc.barth@unistra.fr

Morocco "New advances and challenges for sustainable and smart industries" SUPPORTING STRATEGIC DECISION-MAKING IN MANUFACTURING 4.0 WITH MIX OF QUALITATIVE AND QUANTITATIVE DATA ANALYTICS

Keywords: data analytics, technology forecast, strategic decision making; Researching Future methodology

How to strengthen strategic decision-making with reliable forecast about manufacturing 4.0? As it was observed, the long-range forecasts are biased by competences and experiences of analysts. For improving reliability of strategic forecasting, it is proposed to use a combination of logistic function and problem mapping approach unified by paradigm of available-limiting resources. This paper provides an introduction how results of Researching Future methodology (RFm) can be applied for decision making. Some results, limitations, and perspectives of the current version of RFm are discussed.

INTRODUCTION

The concept of Industry 4.0 needs a lot of emerging technologies to be realized. To support strategic decision-making about emerging technologies a set of principal questions must be answered consistently. A technology can be defined as a threefold synergy of artefacts, knowledge & skills (to use, produce, and maintain that artefact), and regulations & limitations for exploiting the artefacts [START_REF] Grübler | Technology and Global Change[END_REF].

Forecasting the distant changes is serving the goalsetting, decision-making, strategic planning, policymaking, consensus building and organization of education [START_REF] Armstrong | Long-Range Forecasting: From Crystal Ball to Computer[END_REF][START_REF] Preez | Technological Threat and Opportunity Assessment[END_REF]Porter and Group 2004). It is widely recognized that reliable forecasting of technological changes is required in the 21th century more than in the 20th century due to a larger scale and a higher impact of technologies on society, economies and environment (e.g. new energy sources, synthetic biology, artificial general intelligence).

Uncertainty is a distinctive feature of technological evolution among with dynamic, systemic, and cumulative characteristics [START_REF] Grübler | Technology and Global Change[END_REF]. The mission of forecast is to reduce uncertainties of transitions to next technologies. The basic cause of technological uncertainty originates from the fact that from distance it seems there are a variety of solutions to perform a specific task-function. Meanwhile, the limited resources from economic, social, environmental and technical contexts shape a certain solution for implementation.

Since strategic decisions affect a distant future, decisionmakers confront with uncertainties about appropriate criteria and its weights.

Why does an applied technology change and is replaced? In general, the application of a technical solution leads to arising new socio-economic and market demands. That is why the today concept of Industry supposed be substituted by Industry 4.0 and the industrial economies are shifting towards circular economy.

To shift towards new paradigm of industry the numerous strategic decisions must be taken. Meanwhile, the reliability of predictions, supporting critical decisions are far from required. Internet of Things (IoT) is a core technology for Industry 4.0 and for revitalizing Big Data application in practice. However, the predictions about IoT have been changed several times during last years: in 2012 IBM predicted 1 trillion IoT devices by 2015, in 2017 CISCO predicted 50 billion IoT by 2020, in 2018 GSMA predicted 25 billion IoT devices by 2025 [START_REF] Dusmikeev | Inventive Problems in IoT[END_REF]. In that situation, companies need to update their strategic decision quite often which is a costly practice and it does not improve competitiveness of companies involved in industry.

Managers and stakeholders need reliable forecasts to prioritize their investments into new technologies. For improving trustworthiness, technological forecasts have to apply quantifiable metrics [START_REF] Armstrong | Priniciples of Forecasting: A Handbook for Researchers and Practitioner[END_REF].

The needs about forecasting in context of effective strategic decision-making can be formulated into two questions: Q1: How to know the future criteria and its weights for long-range strategic decisions about technologies? Q2: How to define an operational method for exploring the future technical criteria in accordance with socioeconomic and environmental changes?

MOSIM '20 -November 12-14, 2020 -Agadir -Morocco In presented paper we introduce a method for systematic research about emerging and future technologies for supporting strategic decision-making.

RELATED WORKS

The consideration about technological future grew up rapidly in the beginning of 1950s. This attention was fueled by need for decisions about next defense systems and space programs. Harold Linstone (he was founding editor-in-chief of the international journal Technological Forecasting and Social Change) distinguishes three eras of technological forecast [START_REF] Linstone | Three Eras of Technology Foresight[END_REF]): industrial society era, information technology era, and biotechnology era. Since the beginning [START_REF] Ayres | Technological Forecasting and Long-Range Planning[END_REF]) the approaches applied for technological forecasting were described by three categories: (1) quantitative (hard, statistical, objective) methods, (2) qualitative (soft, judgmental, subjective) methods, and (3) combined methods (combination of quantitative methods to improve accuracy, combination of qualitative methods to decrease biases, and combination of quantitative and qualitative methods to improve completeness of study). Those three categories were arranged about two dimensions: normative forecasting and exploratory forecasting [START_REF] Martino | Technological Forecasting for Decision Making[END_REF][START_REF] Armstrong | Long-Range Forecasting: From Crystal Ball to Computer[END_REF].

The subject of long-range strategic forecasting might be considered at least from three perspectives: from strategic planning, from decision-making and from forecasting methodology [START_REF] Martino | Technological Forecasting for Decision Making[END_REF][START_REF] Armstrong | Priniciples of Forecasting: A Handbook for Researchers and Practitioner[END_REF][START_REF] Roper | Forecasting and Management of Technology. 2nd Revise[END_REF]. In other words, the corporate strategy, business strategy, and functional strategy have to be consistent with future internal, external and technological contexts [START_REF] Nakano | Supply Chain Management : Strategy and Organization[END_REF]. The selected list of publications relevant to technological forecasting (partially presented in Table 9) considers more than 260 titles [START_REF] Slupinski | Technology Forecasting -State of the Art Update / Deliverable 2.3 FORMAT Project[END_REF][START_REF] Cascini | FORMAT -Building an Original Methodology for Technology Forecasting through Researchers Exchanges between Industry and Academia[END_REF] of forecasting approaches.

The growing number of reviews on Technology Forecasting (TF) during last two decades [START_REF] Firat | Technological Forecasting -A Review[END_REF][START_REF] Miles | Development of Technology Foresight: A Review[END_REF][START_REF] Kang | A Review on Technology Forecasting Methods and Their Application Area[END_REF]) confirm a steady interest for consistent prediction of technological future. Nevertheless, the rapid growth of publications, institutions and companies involved in technological forecasting for last decades generated multiple approaches. The current situation might be described as "methodological chaos", which is not likely to vanish rapidly.

Different TF review articles developed from disparate perspectives propose various classifications and barely compatible conclusions. For instance, one group of publications emphasize on TF methods [START_REF] Makridakis | FORECASTING: Methods and Applications[END_REF][START_REF] Martino | Technological Forecasting for Decision Making[END_REF]; when second group is focused on development of approaches to select appropriate techniques [START_REF] Armstrong | Priniciples of Forecasting: A Handbook for Researchers and Practitioner[END_REF][START_REF] Glenn | [END_REF]; third one is centered on various fields of TF, its purposes, evolution and application [START_REF] Firat | Technological Forecasting -A Review[END_REF]; fourth one is focused on trend in TF research and application areas of TF methods [START_REF] Kang | A Review on Technology Forecasting Methods and Their Application Area[END_REF]. It is not a completed list since different objectives cause various classifications. There are many overlapping activities to study future of technologies (Porter and Group 2004):

• technology monitoring (analyzing relevant information and data, e.g. patent analysis) • technology intelligence (using collected data and information for decision-making) • forecasting ("describing the emergence, performance, features, or impacts of a technology at some time in the future") • roadmapping (connected predicted technological changes and products into strategic plans) • assessment ("…concerned with the impacts of technology") • foresight ("…to identify future technology developments and their interactions with socie-ty…") • "la prospective" ("…focuses more on proactivity and building the future…") [START_REF] Godet | To Predict or to Build the Future[END_REF]. Some latest books about forecasting principles and practice suggests a rich toolbox of methods [START_REF] Hyndman | Forecasting: Principles and Practice[END_REF].

Numerous quantitative are useful for forecasting and supporting operational and tactical decisionmaking, but they are limited to support strategic decision making. Explorative qualitative methods are widely applied to forecast changes, but they are limited for answering questions When and Where. The effective strategic decisions are limited by information-processing capabilities, cognitive biases and believes of decisionmakers.

In addition to reliable knowledge about future criteria for assessment of new technologies, it is critical to have solutions for dealing with limited capacity of processing information, cognitive biases and believes of decisionmakers.

CONTRIBUTION

Problems are more important than solutions. Solutions can become obsolete when problems remain.

-Niels Bohr A method for long-range technological forecasting faces conflicting requirements for being qualitative and quantitative at the same time. A long-range forecast must be qualitative to be explorative for predicting qualitative changes (e.g. emerging of Internet because of high number of personal computers in use) and for exploring unobvious features. Meanwhile, the forecasting method must be quantitative for providing reproducible results, testing the relationship among variables in dynamic way and to minimize biases and cognitive limitations of experts.

MOSIM'20 -November 12-14, 2020 -Agadir -Morocco

In order to answer suggested contradictions a mixed method [START_REF] Creswell | Research Design : Qualitative, Quantitative, and Mixed Method Approaches[END_REF] for strategic forecasting was suggested. The Researching Future method (RFm) was designed as a synergy of qualitative and quantitative approaches. RFm facilitates mainly bounded rationality model for strategic decision-making and provides incentives for intuitive decision-making. For clarifying the basic paradigm of limiting resources of mixed method approach applied for designing RFm the working hypotheses are presented below and illustrated by Figure 2.

Hypothesis 1: natural growth of a system under competition might be modelled by logistic S-curve.

Hypothesis 2: pace of growth and upper limit of growth depends on available and limiting resource (e.g. niche capacity for market, available energy sources). Hypothesis 3: knowledge about available and limiting resources allows a list of distinctive features of next system(s). years Population / growing variable limit of system's resources (midpoint of growth) limit of available resources (end of exponential growth) physical limit of resources (asymptotic limit of growth)

Figure 2: Main working hypothesis of the Researching Future methodology that allowing connection of qualitative and quantitative parts of study.

Applied paradigm of limiting resources was inspired by two books 'The limits to growth' [START_REF] Meadows | The Limits to Growth[END_REF] and 'Creativity as an Exact science' [START_REF] Altshuller | Creativity as an Exact Science[END_REF]. This paradigm is applied to interconnect qualitative and quantitative studies and to satisfy most of the conflicting requirements about cognitive limitation. At the same time, the concept of limiting resources allows cross verification of forecasts performed with S-curve studies and with mapping the contradictions.

According to certain practical evidence RFm will give useful forecasts when (1) the causal relationship cannot be estimated precisely, (2) the limiting resources change considerably over time, and (3) the change in limiting resources is not evident for decision makers. The RFm was introduced mostly for satisfying needs of organizations about consistent knowledge for supporting strategic decision-making.

PRELIMINARY RESULTS

The earliest results of the project about future of logistics warehouse system was presented during the MOSIM'18 conference in Toulouse [START_REF] Kucharavy | Entrepôt Du Futur : Formalisation Des Caractéristiques Clefs[END_REF]) and in recent publication in Logistique & Management journal [START_REF] Kucharavy | Entrepôt Du Futur : Le Concept de Cartographie de Contradictions[END_REF]. In this section we are discussing the application of produced map of contradiction for strategic decision making.

When mapping problem-contradictions, the set of problems is transformed into a system of problems, when missed problems is identified and excessive contradictions are aggregated. A system of contradictions provides a synergetic effect when key problems can be identified. Knowledge about key problems facilitate the assessment of necessary and available resources. Those knowledges provide criteria MOSIM'20 -November 12-14, 2020 -Agadir -Morocco for assessment of new technologies and they are useful for strategic decision making. The map of contradictions can be applied for evaluation of a potential for emerging technologies and for construction of a roadmap of development for examined technical system.

How does it work? When decision is taken the different options can be evaluated using multi-criteria method [START_REF] Roy | Méthodologie Multicritère d'Aide à La Décision[END_REF] when criteria and their weights are applied to compare the alternatives. When using map of contradictions, the alternatives are compared to number and importance of problems on the map that can be answered using a certain alternative technology.

The developed map of contradictions for logistics warehousing [START_REF] Kucharavy | Entrepôt Du Futur : Le Concept de Cartographie de Contradictions[END_REF]

AND PROSPECTS

This paper has introduced a methodology for learning about long-range technological changes. From a decision-making viewpoint, the suggested approach provides a systematic comprehension of stakes and links between technological advances and the business opportunities.

The timed map of contradictions suggests a transparent description of challenges vs. time required. Resulting maps for various emerging technologies are comparable and allow learning about future when minimizing personal and professional biases of experts.

When answering the first question about criteria and weights for strategic decisions, the hypothesis that knowing problems is more useful than information about emerging technologies has been tested. The results of several projects were appreciated by partners and clients. Meanwhile, it is still required to find a quantifiable way to validate obtained results.

To address the second question about operational method, the suggested case study illustrates the recognized advantages and weak points of applied RFm methodology. The mixed methods approach allows compensating disadvantages of quantitative studies and reinforcing the explorative features of qualitative studies. Nevertheless, the process of mapping contradictions needs significant improvements.

The following limitations of present version of Researching Future methodology have to be noticed: (1) application of RFm requires a high level of expertise and quickly goes to the limits of known; (2) the forecasting study takes a considerable time and human resources; (3) contradiction models are difficult to apply without sufficient practice; (4) quantitative study using S-curves and logistic substitution models require practical skills in regression analysis; (5) the completeness of study about technical, economic, environmental and social contexts depends seriously the competences of the core team; (6) definition of the aims of and the scope of study before starting the project is vital for project success.

What are prospects for RFm? The methodology is currently under development, application and testing with industrial partners, research, and academic institutions. The next steps of our research about RFm for decisionmaking include:

• testing approaches from system dynamics [START_REF] Sterman | System Dynamics: Systems Thinking and Modeling for a Complex World[END_REF]), • testing some concepts from cognitive mapping [START_REF] Gray | Using Fuzzy Cognitive Mapping as a Participatory Approach to Analyze Change, Preferred States, and Perceived Resilience of Social-Ecological Systems[END_REF]), • evaluating and testing certain techniques for modelling complex adaptive systems using Big Data and AI technologies.

For improving the operational level of the methodology, it is planned to examine some visual analytics tools, business intelligence approaches, and recent ideas from data science and machine learning for enhancing forecasting capacity of RFm when reducing forecasting expenses and project time.

Figure 1 :

 1 Figure 1: Flow chart of RFm for strategic forecasting Within RFm the quantitative study with logistic S-curves answers for questions about timing (when?) and location (where?) of pivotal changes, when the qualitative study using mapping contradictions answers about principal characteristics (what?) of next technology. The entire forecasting method applies qualitative and quantitative data simultaneously and interactively (Pascal, Aldebert, and Rouziès 2018) for answering the forecast questions. For clarifying the basic paradigm of limiting resources of mixed method approach applied for designing RFm the working hypotheses are presented below and illustrated by Figure 2.

ACKNOWLEDGMENTS

The research about RFm during last three years was funded by FM Logistic Corporate SAS and by University of Strasbourg.