Getnet Kacha Deyu
email: getnet36@gmail.com

David Muñoz-Rojas

Laetitia Rapenne

Jean-Luc Deschanvres

Andreas Klein

Carmen Jiménez

Daniel Bellet
email: daniel.bellet@grenoble-inp.fr

Keywords: tin oxide, aluminum, spray pyrolysis, doping, transparent conductive oxide

), and then to (002) preferred cristallographic orientation upon Al doping. The lattice parameters (a and c) decreases with Al doping, following in a first approximation Vegard's law. The optical transmission does not change in the visible region with an average transmittance value of 72-81%. Conversely, in the near infrared (NIR) region, the plasmon frequency shifts towards the IR region upon increasing Al concentration in the grown films. Nominally undoped SnO 2 have a conductivity of ∼1120 S/cm, which is at least two orders of magnitude larger than what is reported in literature. This higher conductivity is attributed to the Cl -ions in the SnCl 4 •5(H 2 O) precursor, which would act as donor dopants. The introduction of Al into the SnO 2 lattice showed a decrease of the electrical conductivity of SnO 2 due to compensating hole generation. These findings will be useful for further studied tackling the tailoring of the properties of highly demanded fluorine doped tin oxide (FTO) films.

SnO 2 Films Deposited by Ultrasonic Spray Pyrolysis: Influence of Al Incorporation on the Properties 1. Introduction

Research in tin oxide (SnO 2 ) is gaining dramatic interest among the wide-band gap semiconductor community due to its unique photoelectric and outstanding electrical conduction properties. Furthermore, doping of SnO 2 with metal ions has been used to tailor the properties of the base material, which in turn has resulted in an enhancement of the device performance [START_REF] Batzill | The surface and materials science of tin oxide[END_REF][START_REF] Ginley | Transparent conducting oxides[END_REF][START_REF] Kılıç | Origins of coexistence of conductivity and transparency in SnO 2[END_REF][START_REF] Chopra | Transparent conductors-A status review[END_REF]. This makes SnO 2 thin films excellent candidates for large-scale applications in gas sensors [START_REF] Göpel | 2 sensors: Current status and future prospects[END_REF][START_REF] Kolmakov | Enhanced gas sensing by individual SnO 2 nanowires and nanobelts functionalized with Pd catalyst particles[END_REF], solar cells [START_REF] Snaith | 2 -based dye-sensitized hybrid solar cells exhibiting near unity absorbed photon-to-electron conversion efficiency[END_REF][START_REF] Hossain | Carrier generation and collection in CdS/CdSe-sensitized SnO 2 solar cells exhibiting unprecedented photocurrent densities[END_REF], lithium-ion batteries [START_REF] Alcántara | Preparation, sintering, and electrochemical properties of tin dioxide and Al-doped tin dioxides obtained from citrate precursors[END_REF][START_REF] Chen | 2 -based nanomaterials: Synthesis and application in lithium-ion batteries[END_REF], low emission window [START_REF] Batzill | The surface and materials science of tin oxide[END_REF], and UV photodetectors [START_REF] Hu | Ultrahigh external quantum efficiency from thin SnO 2 nanowire ultraviolet photodetectors[END_REF].

The material is n-type by nature due to an intrinsic doping mechanism [START_REF] Samson | Defect structure and electronic donor levels in stannic oxide crystals[END_REF] with a band gap of 3.6 eV and can be highly n-doped by addition of extrinsic dopant elements such as F, Sb, Ta, or Nb; p-doped by Li, or Cd doping; and isovalent by Ti doping among others [START_REF] Stjerna | Optical and electrical properties of radio frequency sputtered tin oxide films doped with oxygen vacancies, F, Sb[END_REF][START_REF] Wang | Ordered mesoporous Sb-, Nb-, and Ta-doped SnO 2 thin films with adjustable doping levels and high electrical conductivity[END_REF][START_REF] Zhang | Defect chemistry of the metal cation defects in the p-and n-doped SnO 2 nanocrystalline films[END_REF].

To comply with the specification imposed by the numerous applications, different SnO 2 properties are required. Undoped and surface doped SnO 2 thin films are very good candidates for semiconductor based gas sensing applications (Taguchi sensors) due to a naturally occurring high oxygen non-stoichiometry accommodated by the SnO 2 lattice [START_REF] Göpel | 2 sensors: Current status and future prospects[END_REF]. For this application, a variation of the electrical conductivity of a material as a function of the atmosphere is required. A well accepted model to explain such change of conductivity is based on the modification of band bending in the near-surface induced by adsorption/desorption of gas molecules on/from the oxide surface [START_REF] Yamazoe | Interactions of tin oxide surface with O 2 , H 2 O and H 2[END_REF][START_REF] Mcaleer | Tin oxide based gas sensors[END_REF]. Doped SnO 2 thin films are also used as front electrodes in optoelectronic devices such as thin film solar cells, displays and light emitting diodes [START_REF] Giusti | High performance ZnO-SnO 2 : F nanocomposite transparent electrodes for energy applications[END_REF]. In this field of application, tin oxide is an alternative to other transparent conductive oxide (TCO) materials such as Sn-doped In 2 O 3 (ITO) [START_REF] Deyu | Electrical Properties of Low-Temperature Processed Sn-Doped In 2 O 3 Thin Films: The Role of Microstructure and Oxygen Content and the Potential of Defect Modulation Doping[END_REF] and Al-doped ZnO [START_REF] Weidner | Comparative study of sputter-deposited SnO 2 films doped with antimony or tantalum[END_REF]. Although higher conductivity have been achieved with the two latter oxides, SnO 2 based TCO materials offer enhanced chemical, mechanical, and thermal stability, as well as the relative abundance of tin ores in the earth's crust [START_REF] Batzill | The surface and materials science of tin oxide[END_REF]. Another wide application area of SnO 2 is in low-emission window coatings, due to its high stability in various environmental conditions. The possibility to induce a high carrier concentration, typically by F-doping, results in the shifting of the plasma frequency in the near IR-region, thus resulting in an enhanced reflection of low energy heat radiation.

A wide variety of growth methods can typically be used for the deposition of undoped and differently doped tin oxide thin films, including magnetron sputtering [START_REF] Weidner | Comparative study of sputter-deposited SnO 2 films doped with antimony or tantalum[END_REF][START_REF] Weidner | Defect Modulation Doping[END_REF][START_REF] Körber | Surface and bulk properties of sputter deposited undoped and Sb-doped SnO 2 thin films[END_REF][START_REF] Kormunda | Preparation of pulsed DC magnetron deposited Fe-doped SnO 2 coatings[END_REF], molecular beam epitaxy [START_REF] White | Electron transport properties of antimony doped SnO 2 single crystalline thin films grown by plasma-assisted molecular beam epitaxy[END_REF], pulsed-laser deposition (PLD) [START_REF] Dai | Growth of highly oriented tin oxide thin films by laser evaporation deposition[END_REF], chemical vapor deposition (CVD) [START_REF] Kane | Chemical Vapor Deposition of Antimony-Doped Tin Oxide Films Formed from Dibutyl Tin Diacetate[END_REF], atomic layer deposition (ALD) [START_REF] Lee | A study on the thermoelectric properties of ALD-grown aluminum-doped tin oxide with respect to nanostructure modulations[END_REF], or spray pyrolysis [START_REF] Consonni | Preferential orientation of fluorine-doped SnO 2 thin films: The effects of growth temperature[END_REF][START_REF] Bruneaux | Correlation between structural and electrical properties of sprayed tin oxide films with and without fluorine doping[END_REF][START_REF] Zhang | High quality epitaxial fluorine-doped SnO 2 films by ultrasonic spray pyrolysis: Structural and physical property investigation[END_REF]. Spray pyrolysis has the advantages of being cost efficient and surface scalable [START_REF] Sears | Mechanics of film formation during the spray pyrolysis of tin oxide[END_REF].

To assist the design of SnO 2 -based nanomaterials for widespread use, it would be helpful to understand the role of dopants in the SnO 2 thin films. Thus far, a limited number of studies have been reported on Al-doped SnO 2 thin films deposited by various deposition methods including PLD [START_REF] Sinha | Effect of Al doping on structural, optical and electrical properties of SnO 2 thin films synthesized by pulsed laser deposition[END_REF], spray pyrolysis [START_REF] Bagheri-Mohagheghi | The influence of Al doping on the electrical, optical and structural properties of SnO 2 transparent conducting films deposited by the spray pyrolysis technique[END_REF][START_REF] Ravichandran | Type inversion and certain physical properties of spray pyrolysed SnO 2 : Al films for novel transparent electronics applications[END_REF], sol-gel [START_REF] Ahmed | Effect of Al doping on the conductivity type inversion and electro-optical properties of SnO 2 thin films synthesized by sol-gel technique[END_REF], powder sintering [START_REF] Xu | Promotion of tin oxide gas sensor by aluminum doping[END_REF], and ALD [START_REF] Lee | A study on the thermoelectric properties of ALD-grown aluminum-doped tin oxide with respect to nanostructure modulations[END_REF]. However, detailed studies on the effects of Al doping on the structural, optical, and electrical properties of tin oxide films are still lacking. In this contribution, aluminum (Al) doped SnO 2 thin films prepared by ultrasonic spray pyrolysis are investigated. The influence of Al incorporation with different concentration in tin oxide thin films on structural, optical, and electrical properties is examined.

Materials and Methods

Polycrystalline nominally undoped and Al-doped SnO 2 thin films were prepared by a homemade ultrasonic spray pyrolysis deposition system [START_REF] Consonni | Preferential orientation of fluorine-doped SnO 2 thin films: The effects of growth temperature[END_REF][START_REF] Zhang | High quality epitaxial fluorine-doped SnO 2 films by ultrasonic spray pyrolysis: Structural and physical property investigation[END_REF][START_REF] Rey | Electron scattering mechanisms in fluorine-doped SnO 2 thin films[END_REF] on different substrates, namely Si wafer, Corning C1737 borosilicate glass, fused silica glasses, and SiO 2 /Si wafer. The tin precursor was SnCl 4 •5(H 2 O) dissolved in methanol with a fixed concentration of 0.1 M. To incorporate aluminum in the SnO 2 thin films, aluminum acetylacetonate, Al(acac) 3 was added in different concentrations: 0.0005, 0.001, 0.0015, 0.002, 0.0025, 0.005, 0.01, and 0.015 M; corresponding to the Al/(Al+Sn) atomic ratio in a solution of 0%, 0.5%, 1%, 1.37%, 1.96%, 2.44%, 4.76%, 9.1%, and 13.04%. During deposition of the samples, the growth temperature was set at 500 • C, which resulted in a substrate surface temperature of 420 • C. This temperature setting was kept constant for all the substrates and depositions.

A detailed characterization study was conducted using a wide range of standard analysis techniques. The surface morphology of different samples was analyzed by field emission gun-scanning electron microscopy (FEG-SEM Environmental FEI QUANTA 250). Top-view images were processed using digital ImageJ software in order to determine both the average and the biggest grain sizes in each film. The aluminum content in the prepared samples was estimated using an energy dispersive spectroscopy (EDS) analyzer equipped with a FEG-SEM system and Electron Probe Micro-Analyzer (EPMA, Cameca SX50 system equipped with wavelength dispersive spectrometers). EDS analyses were performed at low acceleration voltage (6 keV) to limit the signal obtained from the substrate so that a low atomic number element in a low concentration could be detected. EMPA measurements were performed at three different electron beam acceleration voltage values (11, 16, and 22 keV) and the data were analyzed using the Stratagem program dedicated to the analysis of thin films [START_REF] Sammelselg | Composition and thickness determination of thin oxide films: comparison of different programs and methods[END_REF]. Transmission electron microscopy (TEM) imaging was performed with a JEOL JEM 2010 microscope operating at 200 kV (0.19 nm resolution), equipped with energy-dispersive X-ray spectroscopy (EDX). Bragg-Brentano (θ-2θ) X-ray diffraction (XRD) patterns were collected with a Bruker D8 Advance Series II diffractometer (Billerica, MA, USA) using CuKα 1 radiation in the 2θ range of 10-70 • . Fourier-transform infrared (FTIR) measurements were performed in a Brucker Vertex 70 V spectrometer equipped with CsI beamsplitter and working under vacuum. Spectra were recorded with a resolution of 4 cm -1 by accumulating 64 scans in transmission mode. A UV-Vis-NIR spectrophotometer equipped with an integrating sphere (PerkinElmer Lambda 950, Waltham, MA, USA) was used to record the optical transmittance between 250 and 2500 nm. Hall effect measurements were performed at room temperature in the classical Van der Paw configuration using a homemade setup operating under a magnetic field of 0.5 T.

Results and Discussion

In order to evaluate the incorporation of aluminum in the SnO 2 thin films, EDS and EPMA measurements were performed on the films deposited on Si wafer substrates; the results are presented in Figure 1. EDS confirmed the presence of Al in the deposited tin oxide thin films. The aluminum peak at 1.486 keV intensifies as the amount of aluminum in the precursor solution increased, as shown in the magnified image of Figure 1a. The aluminum incorporation in each individual film was quantified from the EPMA analyses. The Al/(Al+Sn) atomic ratio obtained from EPMA is presented in Table 1 and the same results are plotted versus Al/(Al+Sn) atomic ratio in the starting solution as shown in Figure 1b. The aluminum content in the produced films is only about ∼1/3 of that in the precursor solution. This suggests that, under the current selected deposition conditions, tin oxide is more efficiently deposited than aluminum is incorporated.

For the sake of simplicity for presenting the results and further interpretation and discussion, sample identification is given here by using Al/(Al+Sn) results from EPMA, summarized in Table 1. Undoped tin oxide will be named as nominally undoped SnO 2 or Al doped tin oxide films (SnO 2 :Al) are differentiated as SnO 2 :Al-XX, with XX corresponding to the Al concentration.

The top view SEM images of nominally undoped SnO 2 and the different Al-doped SnO 2 films prepared on Si wafer substrates are shown in Figure 2. The thicknesses of these films were estimated from SEM cross-section measurements and are displayed in Table 1. The thickness variations among these films are mainly due to different deposition times [START_REF] Dai | Growth of highly oriented tin oxide thin films by laser evaporation deposition[END_REF][START_REF] Zhang | High quality epitaxial fluorine-doped SnO 2 films by ultrasonic spray pyrolysis: Structural and physical property investigation[END_REF], and 45 min) and a slight variation of average flow rate of the precursor solution (2-2.3 mL/min). The corresponding deposition rates are also given in Table 1. The produced films are all crystalline and significant morphological changes are observed upon Al incorporation. A similar trend has been observed for the films prepared on the other substrates. The SEM image of nominally undoped SnO 2 film clearly reveals the polycrystalline nature of the films as well as the presence of extended planar twin defects crossing the entire grains. Moreover, the density of these defects is high as several extended twin defects can be identified within individual grains. Similar observations have been reported by different researchers for SnO 2 films produced by spray pyrolysis and the density of twins increased with increasing the concencentration of tin precursor SnCl 4 •5(H 2 O) [START_REF] Consonni | Preferential orientation of fluorine-doped SnO 2 thin films: The effects of growth temperature[END_REF][START_REF] Bruneaux | Correlation between structural and electrical properties of sprayed tin oxide films with and without fluorine doping[END_REF][START_REF] Messad | Analysis of the effects of substrate temperature, concentration of tin chloride and nature of dopants on the structural and electrical properties of sprayed SnO 2 films[END_REF], along with an increase of deposition rate. It is important to note that these twin boundaries are not desirable since they are considered as an additional electron scattering sites, thus resulting as being detrimental for the electrical properties of SnO 2 [START_REF] Rey | Electron scattering mechanisms in fluorine-doped SnO 2 thin films[END_REF]. Although the density of planar defects decreased considerably upon doping, they can also be seen in the SnO 2 :Al-0.2 and 0.4 films; see (b) and (c) images of Figure 2, while, for higher Al content films (1.8-5.2), the lamellar twins are not present anymore.

Due to the presence of both grains and twin boundaries in nominally undoped SnO 2 and some of the Al-doped films, it is important to distinguish between the grain size (L g ) and crystallite size (L c ) of the studied films. The grain size (L g ) of the studied films was determined from top view SEM images shown in Figure 2, by using the digital image processing ImageJ software. The average and the biggest grain size of these films are plotted for different compositions of SnO 2 :Al thin films-see Figure 3a. The visual observation of SEM images of Figure 2 and the grain size plot of Figure 3a shows that the grain size decreased consistently with increasing alumina concentration in the precursor solution. This could result from a thermodynamically favored hetrogeneous nucleation of small grains induced by Al incorporation. Similar observations have been reported by Sinha et al. [START_REF] Sinha | Effect of Al doping on structural, optical and electrical properties of SnO 2 thin films synthesized by pulsed laser deposition[END_REF], Ahmed et al. [START_REF] Ahmed | Effect of Al doping on the conductivity type inversion and electro-optical properties of SnO 2 thin films synthesized by sol-gel technique[END_REF], and Moharrami et al. [START_REF] Moharrami | electrical, optical, thermoelectrical and photoconductivity properties of the SnO 2 -Al 2 O 3 binary transparent conducting films deposited by the spray pyrolysis method[END_REF]. Nominally undoped SnO 2 have an average grain size of 142 ± 27 nm with the biggest grain of the same film having a size of 710 nm, which indicates that the grain size range can span up to a factor of 6 within the same film. Similarly, for the highest Al content SnO 2 :Al-5.2 film, the average grain size is 67 ± 6 nm with the biggest grain being 300 nm, which also shows five times grain size variations within the film. These results are supported by the SEM images of the same films shown in the top and bottom images of Figure 3b. Figure 3a indicates that the Al composition within SnO 2 :Al films plays a key role in the final grain size, more than the film thickness for instance. Indeed, the dependency of the average or biggest grain size exhibit a monotonous dependency and is rather independent from film thickness, at least in the range of 200-800 nm, see Table 1. The physical origin of these observations is probably a favored heterogeneous nucleation induced by Al incorporation in the film.

TEM samples were prepared by scratching the surface using a diamond tip to scratch off particles on holey carbon copper grids. TEM analyses were performed to assess whether Al was completely incorporated into the tin oxide lattice structure or rather was incorporated as a secondary crystalline Al 2 O 3 phase. For this purpose, two different compositions of SnO 2 :Al-0.4 and -5.2 were selected and TEM electron diffraction and EDX analyses were performed, as shown in Figure 4. Al 2 O 3 can exist in different crystalline phases depending on its purity and different growth conditions. The polymorphs of alumina include γ, δ, κ, θ, and α, from which the α-phase is thermodynamically stable and is obtained at very high temperature ≥1000 • C [START_REF] Lee | Comparative study of electronic structures and dielectric properties of alumina polymorphs by first-principles methods[END_REF].

SnO 2 :Al-5.2 is the sample with the highest Al content in the studied composition series. The sample deposited on Si was studied by TEM analysis without further post annealing treatment. As can be seen in Figure 4a, the obtained diffraction rings are in good agreement with the indices of SnO 2 . As for Al 2 O 3 , there was no single diffraction ring matching the indices of crystalline alpha phase or any other alumina polymorphs.

Since as deposited SnO 2 :Al-5.2 film does not show any crystalline Al 2 O 3 phase, another composition of SnO 2 :Al-0.4 film deposited on SiO 2 /Si substrate was selected and further post annealed at 1000 • C for one hour in air before TEM analysis. This composition was selected due to its better electrical properties than that of SnO 2 :Al-5.2. Both the diffraction pattern and EDX results are presented in Figure 4b,c.

Similar to the as-deposited SnO 2 :Al-5.2 sample, the diffraction rings of this film are also in good agreement with indices of SnO 2 and there was no diffraction ring matching the indices of α-Al 2 O 3 or other alumina polymorphs. Thus, even though the sample was post annealed at 1000 • C, the TEM diffraction does not show a contribution associated with any polymorph of crystalline Al 2 O 3 . Actually, at this annealing temperature, theta or alpha phases would be present [START_REF] Lee | Comparative study of electronic structures and dielectric properties of alumina polymorphs by first-principles methods[END_REF][START_REF] Ponja | Synthesis and material characterization of amorphous and crystalline (α-) Al 2 O 3 via aerosol assisted chemical vapour deposition[END_REF], which we do not see in our case. The possible reason for the observed absence of the diffraction rings of Al 2 O 3 phases could be that the diffraction rings of SnO 2 and Al 2 O 3 are very close to each other. For example, the interreticular plane distance of SnO 2 (110) is 3.349 Å and that of Al 2 O 3 (012) 3.48 Å; this is also true for other peaks. In addition, Al 2 O 3 is in a very low quantity phase in the studied compositions. Hence, it is possible to have some spots of Al 2 O 3 in the diffraction images but also it is difficult to identify them. The EDX analysis of the same sample revealed the presence of a 2.1% of Al as cationic content. Therefore, it is reasonable to conclude that if not all, most of Al was incorporated into tin oxide lattice for the studied films. The XRD patterns of probed samples exhibit a systematic shift to higher degree and a broadening of the peaks upon increasing Al content in tin oxide films. To show this phenomenon, the (101) and (211) diffraction peaks were selected and plotted for all samples, in Figure 5b. For the (101) reflection, the peak position shifted from 33.84 • for nominally undoped tin oxide to 34.089 • for the SnO 2 -5.2 sample. Similarly, the (211) reflection exhibited a shift of 0.23 • to a higher angle for the SnO 2 -5.2 sample compared to nominally undoped SnO 2 . In both reflections, black dashed arrows were used for visual guidance of the peaks shifting to higher angle. In addition, broadening of the peaks can clearly be observed in both reflections as the Al content increased in the prepared samples. This shifting of the XRD peaks of tin oxide films upon increasing Al(acac) 3 concentration in the precursor solution is attributed to incorporation of Al into the SnO 2 lattice structure. In addition, the broadening of the peaks is related to the decrease of the grain size observed upon increasing the Al content. In six-fold coordination, the ionic radii of Al 3+ (0.051 nm) is about 30% smaller than that of Sn 4+ (0.071 nm), therefore it is compatible with the hypothesis that the Al dopant effectively substitutes the host atom effectively without forming any secondary phase in the system. The overall lattice parameter is thus expected to decrease as more Al ions occupy the Sn sites, as indeed observed experimentally, see Figure 5b. Similar observations have been reported by Lee et al. [START_REF] Lee | A study on the thermoelectric properties of ALD-grown aluminum-doped tin oxide with respect to nanostructure modulations[END_REF] for Al content in the film (atomic %) varing from 0 to 8.2%, Ravichandran et al. [START_REF] Ravichandran | Type inversion and certain physical properties of spray pyrolysed SnO 2 : Al films for novel transparent electronics applications[END_REF] with Al concentration in the starting solution increasing from 0-30 atomic %, and Thirumurugan et al. [START_REF] Thirumurugan | Effect of solvent volume on properties of SnO 2 :Al films[END_REF] for 3 atomic % doping. In addition, the broadening of the XRD peaks indicates a diminution of crystal sizes.

The variation of lattice constants (a and c) of tin oxide films versus Al atomic (%) in the film is presented in Figure 5c. The lattice parameters' values a and c were determined from the Equation ( 1) using ( 110), ( 101), (200), and (211) diffraction lines:

1 d hkl = h 2 + k 2 a 2 + l 2 c 2 , ( 1
)
where d hkl is the lattice parameter and h, k, and l are the Miller indices. The errors both in determining the lattice parameters from different diffraction lines and the Al atomic (%) from EPMA measurements are included in the plot. Without doping, the lattice constants of SnO 2 are: a = 4.74769 ± 0.0026 Å and c = 3.19093 ± 0.00164 Å, which are close to the standard SnO 2 powder (a = 4.73820 Å and c = 3.18710 Å). As the dopant concentration increases, both lattice constants decrease considerably and the relative decrease in c is almost double that for a. To confirm whether the evolution of the lattice parameters upon doping follows Vegard's law [START_REF] Denton | s law[END_REF][START_REF] Vegard | Untersuchungen über Mischkristalle und Legierungen[END_REF], which predicts a linear decrease of alloy lattice as the concentration of smaller size dopant increases, a linear fit has been plotted in Figure 5c. With a consideration of both the error bars of lattice parameters and Al atomic % of EPMA measurements, a and c follow Vegard's law rather well.

It has been stated that the electrical and optical properties of SnO 2 thin films depend on their preferential crystallographic orientations (i.e., texture) [START_REF] Chopra | Transparent conductors-A status review[END_REF]. Thus, a deeper understanding and control of the structural ordering is important to adjust these properties. The film texture strongly influences the grain boundary nature, which can affect the electrical mobility by scattering the free charge carriers. Additionally, the film texture governs the crystallographic orientation of the top facets and interface properties in heterojunctions. Interestingly, the preferred orientations are in turn governed by different physical mechanisms and this includes the following parameters by growth conditions, film thickness, type of substrate, nature of chemical precursors, and doping [START_REF] Consonni | Preferential orientation of fluorine-doped SnO 2 thin films: The effects of growth temperature[END_REF][START_REF] Agashe | Structural properties of SnO 2 :F films deposited by spray pyrolysis[END_REF][START_REF] Gordillo | Preparation and characterization of SnO 2 thin films deposited by spray pyrolysis from SnCl 2 and SnCl 4 precursors[END_REF][START_REF] Fantini | Influence of the substrate on the crystalline properties of sprayed tin dioxide thin films[END_REF].

As dopant ions substitute the host ions, the film growth orientation is altered as a result of mechanical strain induced in the lattice [START_REF] Gilardi | Effect of dopant-host ionic radii mismatch on acceptor-doped barium zirconate microstructure and proton conductivity[END_REF][START_REF] Thirumoorthi | Effect of F doping on physical properties of (211) oriented SnO 2 thin films prepared by jet nebulizer spray pyrolysis technique[END_REF][START_REF] Harrington | The effects of lattice strain, dislocations, and microstructure on the transport properties of YSZ films[END_REF]. Here, the XRD patterns also show significant preferential orientations with Al incorporation into the tin oxide films. The change of texture coefficient C hkl for SnO 2 films upon different percentage of Al doping has been calculated based on θ-2θ XRD measurements of Figure 5a. Only seven main peaks were taken into account: (110), ( 101), ( 200), ( 211), (002), (112), and (301). The texture analysis was quantitatively carried out from the Kα 1 component of each diffraction peak in the framework of the Harris method [START_REF] Harris | Quantitative measurement of preferred orientation in rolled uranium bars[END_REF]. The texture coefficients C hkl for each (hkl) crystallographic directions and degree of preferred orientation σ were respectively defined as the following in Equation (2):

C hkl = I hkl I o,hkl 1 N Σ N I hkl I o,hkl and σ = Σ N (C hkl -1) 2 √ N , (2)
where I hkl is the intensity of (hkl) reflection of studied samples; I o,hkl is the intensity of the corresponding plane in the reference of powder (PDF 00-041-1445) from the International Center for Diffraction Data (ICDD), and N represents the number of reflections, in our case N = 7. Basically, for randomly oriented samples, the texture coefficient and degree of preferred orientation equal 1 and 0, respectively. In contrast, for perfectly oriented grain samples along the (hkl) direction, the texture coefficient equals N for (hkl) planes (N = 7 in our case) and 0 for other crystallographic planes and consequently the degree of preferred orientation is √ N -1. The pronounced structural reordering correlated with the evolution of texture coefficients for each (hkl) crystallographic direction and the degree of preferred orientation of the studied films are shown in Figure 5d. For nominally undoped SnO 2 , the (301) crystallographic orientation is dominant with a texture coefficient of 4.57 and the (211) crystallographic orientation also has a C hkl of 1.45. In the case of SnO 2 :Al-0.2 sample, (301) is still the dominant orientation. In contrast, a texture change is observed for the SnO 2 :Al-1.64 film. Here, the (101) crystallographic orientation became the dominant orientation with a C hkl of 2.56. For the SnO 2 :Al-1.8 sample, the texture changed again and (002) becomes the dominant orientation with a C hkl of 2.27. Finally, it became the only dominant orientation for SnO 2 :Al-3.8 and -5.2 films. As a result, polycrstalline SnO 2 thin films undergo a texture transition from (301) to (101), and then (002) preferred cristallographic orientation upon increasing Al content in the grown films [START_REF] Thompson | Structure evolution during processing of polycrystalline films[END_REF].

It is further shown that the relative intensity between different (hkl) Bragg reflections is strongly dependent on the amount of Al incorporated into the growing film. The degree of preferred orientation is drastically reduced from 1.53 in undoped SnO 2 to ≈0.88 for SnO 2 :Al-0.2 film. It remained almost unchanged between 0.2 and 1.8 films, and then suddenly increased to 2.2 for the SnO 2 :Al-3.8 film. Finally, for the highest Al content SnO 2 :Al-5.2 film, the degree of preferred orientation reduced to 1.4 as can be seen in the insert of Figure 5d.

Films deposited on silicon wafer substrates were further examined by FTIR and the results are presented in Figure 6a. For better visual guidance, all the spectra were normalized with the same intensity for the Si-O v band at 612.5 cm -1 . The spectra peaks present at 245, 282.5, and 612.5 cm -1 are assigned to the Sn-O vibration [START_REF] Ahmed | Effect of Al doping on the conductivity type inversion and electro-optical properties of SnO 2 thin films synthesized by sol-gel technique[END_REF][START_REF] Zhang | The FTIR studies of SnO 2 :Sb (ATO) films deposited by spray pyrolysis[END_REF], while a peak at 468.92 cm -1 is assigned to Sn-O-Sn stretching. Even though there was no independent peak observed which could be assigned to aluminum, Al incorporation has an influence on the broadening of Sn-O-Sn peaks and leads to a decrease of the relative intensity of the Sn-O-Sn stretching mode. This could be attributed to the formation of Sn-O-Al bonds. Actually, Kumar and coworkers [START_REF] Kumar | Structural investigation of nanomixed xSnO 2 -Al 2 O 3 synthesized by sol-gel route[END_REF] reported similar broadening and attenuation of the Sn-O-Sn band as a function of increasing Al content in the SnO 2 thin films. Nevertheless, the exact position of Sn-O-Al band is not yet reported in literature or on FTIR handbooks to our knowledge.

The total transmittance spectra of nominally undoped and Al-doped SnO 2 thin films on Corning glass substrates measured between 250 and 2500 nm range are shown in Figure 6b. Virtually no shifting of the leading edge at short wavelengths, representing the onset of the leading optical band-to-band absorption (absorption edge), is observed upon Al doping. Thus, there was no blue-shift of the absorption edge. The average total transmittance in the visible (VIS) region of 380-780 nm is high for all films, 72-81%, which is important for TCO applications. Meanwhile, in the near infrared (NIR) region above 1200 nm, a difference in plasma absorption between the samples is observed. Since aluminum is acting as an acceptor doping in SnO 2 , a plasmon frequency shift towards the IR region is observed with increasing Al doping into the tin oxide films. In the spectral range of relevant electromagnetic wavelengths for the applications in which TCOs are used (i.e., flat screens, solar cells, etc.), free electrons dominate the electrical and optical properties. These properties can be described in a first approximation by the Drude free electron theory [START_REF] Coutts | Characterization of transparent conducting oxides[END_REF]. This theory often accounts for the measurable properties of TCOs, such as transmittance and reflectance, and their relationship to extrinsically controllable parameters (such as carrier concentration) and intrinsically uncontrollable properties (such as crystal lattice and effective mass). The plasmon frequency shift towards higher wavelength observed upon Al doping is in a good agreement with the determined free carrier concentrations, see Figure 7c. Due to the fact that SnO 2 is naturally n-type TCO, the transmittance drop in NIR region was ascribed to plasmonic absorption. Doping with aluminum favors the creation of holes as low valence Al 3+ cations substitute Sn 4+ ones. For this reason, Al 3+ cations play the role of charge compensators and the transmittance in the INR region increases consequently, as shown by Figure 6b. The free carrier concentrations influence the resonant frequency of the plasma absorption according to the following relation within the framework of Drude theory [START_REF] Coutts | Characterization of transparent conducting oxides[END_REF]:

ω p = ne 2 m * ε 0 ε ∞ , (3)
where ω p is plasma frequency, n is charge carrier density, e is elementary charge, m * is carrier effective mass, ε 0 is vacuum permittivity, and ε ∞ is the value for the film dielectric constant at high frequencies.

For highly doped TCOs, the plasmon energies are up to 1 eV, which is in the near infrared region of the electromagnetic spectrum. Due to the high number of free electrons, the incident infrared radiation is not transmitted but is rather reflected; this is a key feature for application of differently doped tin oxide thin films as low-emissivity window coatings.

Conductivity of nominally undoped and the different Al-doped SnO 2 thin films is provided in Figure 7a. Hall effect results of the same films are also displayed in Figure 7b for the carrier mobility and (c) for the carrier concentration. Due to the experimental limitations of the Hall effect setup used, no Hall effect could be measured for the doped films above SnO 2 :Al-1.64. Our nominally undoped tin oxide films prepared on different substrates have a conductivity of ≈1.1 × 10 3 S/cm. Surprisingly, this value is at least two orders of magnitude higher than the conductivity of undoped SnO 2 films reported in literature. For magnetron sputtered films, the reported conductivity varies from 10 -5 to 10 0 S/cm depending on the different deposition conditions [START_REF] Weidner | Defect Modulation Doping[END_REF][START_REF] Körber | Surface and bulk properties of sputter deposited undoped and Sb-doped SnO 2 thin films[END_REF]. Similarly, SnO 2 films prepared by PLD have conductivity values of ≤4.5 ×10 1 S/cm [START_REF] Kim | Transparent conducting Sb-doped SnO 2 thin films grown by pulsed-laser deposition[END_REF], and that of sol-gel exhibit values ≤10 0 S/cm [START_REF] Maddalena | Electrical conductivity of tin oxide films prepared by the sol-gel method[END_REF]. The higher conductivity obtained for the thin films studied here (deposited by spray pyrolysis) is probably related to the tin precursor used, namely, SnCl 4 •5(H 2 O). Since chlorine has one less 2p orbital to fill than oxygen, substitution of O 2-ions by Cl -ions leads to an increase of free electrons per SnO 2 unit formula. For every chlorine substitution, a tin atom retains an extra 5 s electron which enters the conduction band of the lattice [START_REF] Messad | Analysis of the effects of substrate temperature, concentration of tin chloride and nature of dopants on the structural and electrical properties of sprayed SnO 2 films[END_REF][START_REF] Vincent | The nature of semiconductivity in polycrystalline tin oxide[END_REF]. In addition, oxygen vacancies are deep donors in SnO 2 [START_REF] Ágoston | Intrinsic n-type behavior in transparent conducting oxides: A comparative hybrid-functional study of In 2 O 3 , SnO 2 , and ZnO[END_REF][START_REF] Swallow | Self-compensation in transparent conducting F-doped SnO 2[END_REF], which can not be easily ionized and contribute to the electrical conduction. Eventually, we were not able to detect chlorine on our samples using different physicochemical analysis techniques.

In order to address the actual role of the incorporated chlorine atoms with respect to the electrical properties, Messad et al. [START_REF] Messad | Analysis of the effects of substrate temperature, concentration of tin chloride and nature of dopants on the structural and electrical properties of sprayed SnO 2 films[END_REF] performed Rutherford back scattering (RBS) analyses on spray deposited SnO 2 films from SnCl 4 precursor to determine the bulk chloride concentration (n Cl -) and compared it with the Hall carrier concentration (n) of the same films. Their results showed that for unintentionally doped SnO 2 films deposited with precursor concentration of 0.1 M and substrate temperature between 400 and 550 • C, the chlorine ion concentration (n Cl -) and Hall concentration (n) have the same values. Thus, they concluded that, within these experimental conditions, the carrier density can be even identified with chlorine content. Meanwhile, at a deposition temperature higher than 550 • C, the n Cl - decreased with increasing substrate temperature. This is due to the breakage of Sn-Cl bonds with increasing temperature, as it was evident with Auger electron spectroscopy (AES) [START_REF] Kim | Electrical properties and gas-sensing behavior of SnO 2 films prepared by chemical vapor deposition[END_REF] and Secondary ion mass spectroscopy (SIMS) [START_REF] Ferron | Anomalous incorporation of fluorine in tin oxide films produced with the pyrosol method[END_REF] observations. Even though they [START_REF] Messad | Analysis of the effects of substrate temperature, concentration of tin chloride and nature of dopants on the structural and electrical properties of sprayed SnO 2 films[END_REF] successfully demonstrated the incorporation of chlorine ions, under the same deposition conditions, they measured a conductivity of 6 × 10 1 S/cm. This is in fact two orders of magnitude lower that the conductivity reported in the present article for nominally undoped films.

For Al doped films, the scenario is different. Since Al 3+ ions substitute Sn 4+ , a hole is generated per SnO 2 molecule and compensates an existing carrier electron. Thus, the conductivity of tin oxide films does not improve upon Al incorporation. The conductivity of SnO 2 :Al decreases consistently with increasing Al content due to the presence of compensating holes and, for the highest Al content (1.8, 3.8, and 5.2) films, the conductivity drops to ∼10 -4 S/cm.

Hall effect measurements were possible only for the films with composition up to SnO 2 :Al-1.64, the last three films in the series being too resistive and thus impossible to be measured with our system. Hall mobility exhibits a pronounced reduction with small Al incorporation. It decreased from ≈23 cm 2 /Vs for undoped films to ≈5 cm 2 /Vs for SnO 2 :Al-0.15 samples. With further increasing Al concentration up to SnO 2 :Al-1.64, the mobility stayed in the following range: 1-5 cm 2 /Vs. This reduction in mobility could be attributed to the change in micro-structure of the films upon Al incorporation due to the grain size reduction for instance. Conversely, the carrier concentration was not affected in low Al content films with value of ≈ 1 × 10 20 cm -3 , being obtained for doping values up to 0.3. Then, it decreased for the SnO 2 :Al-0.4 film and finally dropped by three orders of magnitude ≈ 1 × 10 17 cm -3 for SnO 2 :Al-1.64 samples.

The relation between the charge carrier concentration and mobility is rather complicated in polycrystalline semiconducting materials [START_REF] Ellmer | Past achievements and future challenges in the development of optically transparent electrodes[END_REF]. In general, these materials exhibit a vast amount of grain barriers depending on their mean grain size, which constitute crystallographically disturbed regions, leading to electronic defects in the band gap of semiconductors. These defects are charged by carriers from the grains. Charge balance causes a depletion zone on both sides of a grain barrier accompanied by an energetic barrier for the carriers [START_REF] Ellmer | Carrier transport in polycrystalline transparent conductive oxides: A comparative study of zinc oxide and indium oxide[END_REF]. The carriers therefore need to cross these energetic barriers and this is mostly a thermally activated process. Frischbier and coworkers [START_REF] Frischbier | Influence of dopant species and concentration on grain boundary scattering in degenerately doped In 2 O 3 thin films[END_REF] reported that grain boundaries may influence the carrier mobility even up to the carrier concentrations of 10 21 cm -3 . Usually, such a high carrier density is achieved by degenerately doping the semiconductor and ionized impurities should be the main scattering mechanism for the reduction of charge carrier mobility [START_REF] Ellmer | Carrier transport in polycrystalline transparent conductive oxides: A comparative study of zinc oxide and indium oxide[END_REF]. As we have seen in the morphological study, aluminum incorporation resulted in a heterogeneous nucleation of smaller grains which leads to the formation of more grain boundaries, which act as a potential barrier and reduce carrier mobility. Therefore, the observed reduction in mobility is reasonable. At the same time, Al doping favors the creation of holes as low valence Al 3+ cations substitute Sn 4+ ones. The created holes then compensate the existing carrier electrons and charge carrier density decreases. This is supported by the results of Hall effect measurements as carrier concentration decreased by up to three orders of magnitude only by incorporation of 1.64% of Al. Some reports claim [START_REF] Ravichandran | Type inversion and certain physical properties of spray pyrolysed SnO 2 : Al films for novel transparent electronics applications[END_REF][START_REF] Ahmed | Effect of Al doping on the conductivity type inversion and electro-optical properties of SnO 2 thin films synthesized by sol-gel technique[END_REF] that, for a high enough Al doping of tin oxide, the type inversion of conductivity could have been observed. This would mean having a tin oxide thin film with p-type conductivity. Mohagheghi et al. reported this transition can take place close to 8% of Al incorporated into their films [START_REF] Bagheri-Mohagheghi | The influence of Al doping on the electrical, optical and structural properties of SnO 2 transparent conducting films deposited by the spray pyrolysis technique[END_REF]. Meanwhile, in our Hall effect results, we did not see such a type inversion behavior, probably because our SnO 2 :Al thin films did not have high enough Al content.

Conclusions

In summary, we have presented a comprehensive study describing the change in structural, optical, and electrical properties of tin oxide thin films prepared by ultrasonic spray pyrolysis upon Al incorporation. The doping was possible by Al 3+ cations substituting Sn 4+ sites in the SnO 2 lattice, as deducted from TEM and XRD analyses.

SEM images showed a decreasing grain size with increasing Al content in the prepared tin oxide thin films. In addition, Al doping drastically decreased the number of planar twin defects present in tin oxide films. EPMA analyses revealed that only ∼1/3 of Al present in the precursor solution is actually transferred into the grown films.

Al doping also resulted in structural reordering of tin oxide by texture transition from (301) to (101), and then to (002) upon increasing Al content in the grown films. The optical transmittance of tin oxide was not changed in the visible region with an average transmittance of 72-81% being obtained. Meanwhile, a difference in plasmon absorption is observed in the near infrared region for all samples: the plasmon frequency shifted towards the IR region as a function of Al doping concentration.

Nominally undoped tin oxide films exhibit a conductivity of ≈1.1 × 10 3 S/cm, which is at least two orders of magnitude higher than the conductivity reported for undoped tin oxide films. This higher conductivity stems from the SnCl 4 •5(H 2 O) precursor used during sample preparation, in which Cl - ions act as an additional donor doping. Since aluminum is a low valence cation doping for SnO 2 , the conductivity of tin oxide films decreased with incorporation of Al.

These findings help to improve the understanding of the effect of Al doping on the properties of tin oxide thin films, including structural, optical, and electrical properties. In addition, the gained knowledge can be transferred to modify the properties of highly demanded florine doped tin oxide (FTO) thin films.

Figure 1 .

 1 Figure 1. (a) EDS spectra at 6 keV of different SnO 2 :Al thin films prepared on Si wafer substrates. In the right, magnified spectra of the same films around 1.5 keV is shown to see the evolution of Al peak; (b) relative Al content as obtained from EPMA compared to the amount in the precursor solution. A dashed line represents the linear relationship.

Figure 2 .

 2 Figure 2. Top-view FEG-SEM images of nominally undoped SnO 2 and different Al-doped SnO 2 thin films deposited on silicon wafer. (a) represent the pure SnO 2 , while (b)-(f) corresponding to Al-doped films with the number associated with each image is the measured atomic ratio (Al/Al+Sn) in the films. All images have the same scale of 1 µm and the green scale bar presented in image (a) will be used for all images.

Figure 3 .

 3 Figure 3. (a) the change of average grain size in tin oxide thin films versus Al cationic ratio in the film: the biggest grain within the same films are also represented; (b) visual illustration of the size dispersion in the studied samples: SEM images of nominally undoped SnO 2 and SnO 2 :Al-5.2 films are shown.In both cases, the biggest grains are colored in violet, while some smaller grains are colored in sky blue for comparison.

Figure 4 .

 4 Figure 4. TEM electron diffraction patterns of different as deposited and post annealed SnO 2 :Al films. (a) diffraction patterns of as deposited SnO 2 :Al-5.2 film prepared on Si wafer substrate with indices of SnO 2 (ICDD-00-041-1445) and α-Al 2 O 3 (ICDD-00-046-1212); (b) diffraction pattern of SnO 2 :Al-0.4 film prepared on SiO 2 /Si substrate, which was further post annealed at 1000 • C for one hour in air, with indices of both SnO 2 and α-Al 2 O 3 ; and (c) EDX of the same SnO 2 :Al-0.4 sample which reveals the presence of Al 2.1% as cationic content. The θ-2θ XRD diffraction patterns of undoped SnO 2 and different Al-doped SnO 2 thin films collected between 10 • and 70 • (in 2θ scale) are shown in Figure 5a. The XRD spectra match with high tetragonal SnO 2 with PDF card (00-041-1445), with no Al 2 O 3 polymorph being detected. This is another indication that Al was successfully incorporated into the tin oxide films without forming secondary crystalline Al 2 O 3 phases.The XRD patterns of probed samples exhibit a systematic shift to higher degree and a broadening of the peaks upon increasing Al content in tin oxide films. To show this phenomenon, the (101) and (211) diffraction peaks were selected and plotted for all samples, in Figure5b. For the (101) reflection, the peak position shifted from 33.84 • for nominally undoped tin oxide to 34.089 • for the SnO 2 -5.2 sample. Similarly, the (211) reflection exhibited a shift of 0.23 • to a higher angle for the SnO 2 -5.2 sample compared to nominally undoped SnO 2 . In both reflections, black dashed arrows were used for visual guidance of the peaks shifting to higher angle. In addition, broadening of the peaks can clearly be observed in both reflections as the Al content increased in the prepared samples.

Figure 5 .

 5 Figure 5. (a) X-ray diffraction (XRD) θ-2θ patterns of nominally undoped SnO 2 and different Al-doped SnO 2 thin films with increasing Al content in the prepared samples using Si wafer substrate. In the same plot, the diffraction peaks corresponding to SnO 2 are marked with dashed lines (PDF-00-041-1445) and labeled with individual crystallographic orientation on the top; (b) demonstration for broadening and shifting to higher angles of XRD patterns of tin oxide films upon Al incorporation. Here, two dashed black arrows are used to indicate that the Bragg peak position is continuously increased with increasing Al content in the grown films; (c) lattice constants a and c vs. Al cationic (%) in the film. The lattice constants of standard SnO 2 JCPDS powder are also included for comparison. The linear interpolations (red lines) between SnO 2 and SnO 2 :Al-5.2 films are plotted to show the linear relationship between lattice constant and Al concentration in the films following Vegard's law; (d) the change of texture coefficients C hkl calculated for tin oxide and different Al-doped SnO 2 films plotted for different SnO 2 :Al compositions. The color code of different crystallographic orientations (hkl) which are used to calculate C hkl are represented in the legend.The plot for the degree of preferred orientation σ of the same films also shown in the insert. Note that, for a better visual, the x-axis of (d) is not in a linear scale.

Figure 6 .

 6 Figure 6. (a) normalized FTIR spectra of nominally undoped and different Al-doped tin oxide thin films, (b) optical transmittance of nominally undoped SnO 2 and different Al-doped SnO 2 thin films as a function of wavelength.The transmittance of bare glass is included for comparison.

Figure 7 .

 7 Figure 7. Conductivity (a), carrier mobility (b), and carrier concentration (c) of nominally undoped SnO 2 and Al-doped SnO 2 thin films with different compositions prepared on different substrates. Hall measurements were possible only for samples with composition up to SnO 2 :Al-1.64.

Table 1 .

 1 Al/(Al+Sn) ratio in solution and in the different Al-doped SnO 2 thin films (from EPMA data): Film thickness from SEM cross-section and deposition time and rate of studied films. The deposition rates are given with uncertainty of ±0.5 nm/min.

Al/(Al+Sn) Solution Al/(Al+Sn) Film Film Thickness Deposition Time Deposition Rate

	(%)	(%)	(nm)	(min)	(nm/min)
	0	-	670	45	15
	0.5	0.15	260	25	10.4
	1	0.2	340	30	11.3
	1.37	0.3	260	25	10.4
	1.96	0.4	290	25	11.6
	2.44	1.64 ± 0.08	200	30	6.7
	4.76	1.8 ± 0.08	660	45	14.66
	9.1	3.8 ± 0.2	800	45	17.7
	13.04	5.2 ± 0.5	580	45	13

Acknowledgments:

The authors would like to thank Hervé Roussel for performing the XRD measurements. The authors would like also to acknowledge Agence Nationale de la Recherche (ANR) via the project ANR-15-CE05-0019 (INDEED). In addition, this work benefited from the facilities and expertise of the OPE)N(RA characterization platform of FMNT (FR 2542, fmnt.fr) supported by CNRS, Grenoble INP and UGA. We acknowledge support by the German Research Foundation and the Open Access Publishing Fund of Technische Universität Darmstadt.

Author Contributions: Thin film depositions and main characterizations were performed by G.K.D. TEM characterization was performed by L.R. Discussion and interpretation of results was conducted by all authors. Manuscript was written by G.K.D. and revised by all authors. Funding has been acquired by D.B. and A.K.

Funding: This work was carried out in the framework of EJD-FunMat (European Joint Doctorate for Multifunctional Materials) and has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant No. 641640.

Conflicts of Interest:

The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analysis, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.

Abbreviations

The following abbreviations are used in this manuscript:


Alessandra Sabina Lanotte

Alain Noullez

Massimo Vergassola

Achim Wirth

A Lanottea

A Noulleza

Large-scale dynamo produced by negative magnetic eddy diffusivities

Keywords: Dynamo processes, stability, turbulent diffusion

INTRODUCTION

The generation of large-scale magnetic fi elds is one of the key issues in magnetohydrodynamics (e.g., [START_REF] Moffatt | Magnetic field generation in electrically conducting fluids[END_REF]. The nature and the properties of self-inductive mechanisms capable of maintaining a per sistent magnetization are of particular importance for cosmical ob jects, such as stars or galaxies [START_REF] Parker | Cosmical Magnetic Fields[END_REF][START_REF] Zeldovich | Magnetic Fields in Astro physics[END_REF]. For the investigation of magnetic fields growth, the Lorentz reaction of the magnetic field B on the velocity v can be neglected (at least initially) and the resulting dynamics is commonly known as the *Corresponding author. e-mail: lanotte@obs-nice.fr kinematic dynamo problem. The velocity field v is indeed prescribed a priori as a function (deterministic or random) of the space-time vari ables x and t. The issue is to determine the characteristics of the pos sible growth of the large-scale components of B(x, t) (large-scale dynamo) in terms ofv properties. The major effect of the incompressible flow v on the mean magnetic field B is to generate a mean electro motive force (e.m.f.) £, infl uencing the evolution of B according to the induction equation ( 1)

In a mean-fi eld framework [START_REF] Moffatt | Magnetic field generation in electrically conducting fluids[END_REF], the e.m.f. is expanded in a gradient series as (2) where the coefficients aij and f3ijt are functionals of the velocity fi eld v. Higher-order terms involve more than one spatial gradient of B . The gradient expansion has a fully systematic status in scale-separated situations, i.e., when the velocity v has finite typical space-time scales and the scales of interest for B are much larger than all of them. The first term in the expansion (2) is responsible for the well-known a-effect [START_REF] Steenbeck | A calculation of the mean electromotive force in an electrically conducting fluid in turbulent motion, under the influence of Coriolis forces[END_REF]. If the a tensor does not identically vanish, the term associated to it in (1) (first-order in space variables) will indeed become dominant with respect to the second-order molecular diffusivity term at sufficiently large scales. In three dimensions, this leads to an ex ponential growth of B with a growth rate proportional to the wave number k. Lack of parity-invariance is the central ingredient for a-type instabilities. By parity-invariant flow we mean those fi elds v admit ting a center of symmetry relative to which the simultaneous reversal xi--+ -x and vi--+ -v leaves the flow invariant (deterministically or statis tically, depending on the case considered). When no such center can be found, parity invariance is broken. Since the e.m.f. £ is a vector and B is a pseudo-vector, such breaking is a necessary condition for aij not to vanish identically. By the same argument, the average value of the magnetic helicity A(x, t) • B(x, t) is guaranteed to vanish in parity invariant situations. 1 When the fl.ow does not admit any center of symmetry, the mean value of (kinetic) helicity can vanish or not. The latter case generally leads to stronger dynamos at large scales, with growth rates proportional to the wavenumber k (and not k? as in the former case). It is therefore commonly accepted that helicity plays an important role for o:-type instabilities [START_REF] Gilbert | Helicity is unnecessary for alpha effect dynamos, but it helps[END_REF]. Note also that o: instabilities have a vanishing threshold in the magnetic Rey nolds number, as the molecular diffusivity is subdominant at sufficiently large scales.

For parity-invariant fl ow, a possible large-scale dynamo cannot take place via the a-effect and second-order terms in (2) become relevant. Inserting them into (1), a formally diffusive equation is obtained, where "formally" is meant to stress that the second-order operator on the right-hand side is not guaranteed to be (semi) negative-defi nite. It is certainly negative definite when the molecular diffusivity is large enough to dominate turbulent effects. But when the magnetic Reynolds number is increased, it is conceivable that the turbulent term associ ated to the f3 tensor could destabilize the large scales and quanti tatively overwhelm the stabilizing molecular contribution, thus leading to dynamo, i.e., the growth of B. This circumstance would corre spond to a negative magnetic eddy diffusivity and would provide for a dynamo mechanism not requiring any breaking of parity invariance and/or mean helicity. The purpose of the present paper is to address the question formulated in Section 7.4 of [START_REF] Moffatt | Magnetic field generation in electrically conducting fluids[END_REF] whether this dynamo mechanism is physically realizable.

The answer to the equivalent question for other physical situations is known. For the transport of passive scalars, the effect of an incom pressible velocity v is always stabilizing, i.e., the eddy diffusivity is larger than the molecular diffusivity [START_REF] Mc Laughlin | Convection of rnicro structures and related problems[END_REF]. For time-independent potential flow, the eddy diffusivity is smaller than the molecular diffusivity, but it cannot become negative (Vergassola and Avellaneda, 1997). Another relevant situation is momentum trans port in the Navier-Stokes equations. The effect analogous to the a effect is the so-called AKA effect [START_REF] Frisch | Large-scale flow driven by the anisotropic kinetic alpha effect[END_REF], which also disappears in the presence of parity-invariance. The existence of negative eddy viscosities is now well established, in two and in three dimensions, both for isotropic and anisotropic flow [START_REF] Meshalkin | Investigation of the stability of a stationary solution of a system of equations for the plane movement of an incompressible viscous fluid[END_REF]Nepomnyashchy, 1976;[START_REF] Sivashinsky | Weak turbulence in periodic flows[END_REF][START_REF] Gama | Negative eddy viscosity in isotropically fo rced two-dimensional flow: linear and nonlinear dynamics[END_REF][START_REF] Wirth | Eddy viscosity of three-dimensional flow[END_REF]. The existence of negative eddy viscosities points in favor of negative magnetic eddy diff usivities, but this indication should be taken with caution. Indeed, for simple parallel flows (depending on a single coordinate), the eddy viscosity is for example known to be negative, but the origin of the instability (at least in this case) comes entirely from the non-local pressure term (e.g., [START_REF] Meshalkin | Investigation of the stability of a stationary solution of a system of equations for the plane movement of an incompressible viscous fluid[END_REF][START_REF] Dubrulle | Eddy viscosity of parity-invariant flow[END_REF], which is absent in the kinematic dynamo problem. This important difference is confi rmed in the Appendix, where the same problem of parallel flow is solved for magnetic fi elds and no dynamo is indeed present.

Arguments in favor of negative magnetic eddy diffusivities were previously given in [START_REF] Roberts | Dynamo action of fluid motions with two-dimensional periodicity[END_REF] and [START_REF] Kraichnan | Diffusion of weak magnetic fields by isotropic turbulence[END_REF]. The atten tion in [START_REF] Roberts | Dynamo action of fluid motions with two-dimensional periodicity[END_REF] was mainly concentrated on a-type dynamo, but some evidence was also given that magnetic fields could grow when orders higher than the first in (2) are relevant. A three-scale argu ment was considered in [START_REF] Kraichnan | Diffusion of weak magnetic fields by isotropic turbulence[END_REF] to show that fluctuations of the a-coefficient at intermediate scales could give a negative contri bution to the eddy diffusivity on large scales, but no defi nite con clusion could be drawn. Here, we shall analyze the problem using multiscale techniques, presented in Section 2. The advantage is that the nature and the order of the large-scale dynamics can be systematically identifi ed and the calculation of the eddy-diffusivity tensor is reduced to the solution of auxiliary equations on the elementary periodicity cell. In Section 3, numerical simulations of the auxiliary equations are used to investigate a steady variant of the Taylor-Green vortex, which is found to produce a negative magnetic eddy diffusivity above a critical Reynolds number.

MULTISCALE FORMALISM

The aim of this section is to present the multiscale formalism that will be later exploited for the calculation of magnetic eddy diffusivities.

The incompressible velocity fi eld v(x, t) in the kinematic dynamo equation

(3)
is supposed to have a finite typical length scale £ 0 , e.g., to be £ 0 - periodic, and we shall be interested in the dynamics of the magnetic field B at scales L » l0. The ratio l0/ L = c «: I provides a small parameter that can be exploited for a perturbative solution. The per turbation being singular (e.g., [START_REF] Bender | Advanced Mathematical Methods for Scientists and Engineers[END_REF], it is neces sary to treat the problem by singular perturbation methods (see [START_REF] Nayfeh | Perturbation Methods[END_REF][START_REF] Van Dyke | Perturbation Methods in Fluid Mechanics[END_REF]. The most convenient method for the case at stake is the multiscale technique, also known as homogeniza tion [START_REF] Bensoussan | Asymptotic Analysis for Periodic Structures[END_REF]. In addition to the original variables (x, t) ("fast" variables) characterizing the basic flow v, a new set of space-time variables X, T ("slow" variables) is introduced. The ration ale in their choice is that the large-scale dynamics should be 0(1) in the new variables, e.g., X = ex. The prescription that resolves the singularity is to treat the two sets of variables, fast and slow, as inde pendent throughout the perturbative expansion. The enlargement of degrees of freedom is compensated by the presence of non-trivial solvability conditions in the resulting equations, giving the large-scale evolution equations.

Let us implement the previous procedure for the kinematic dynamo equation (3). Since we are interested in eddy diffusivities we shall impose the velocity field v to be parity-invariant. This ensures the ab sence of the o: effect and makes the dynamics at large scales expected to be second-order in the space variables. The appropriate rescalings for the slow variables 2 are then ( 4)

Treating fast and slow variables as independent implies the following chain rule for the derivatives

(5)
Here, we denote by the symbol {) the derivatives with respect to fast variables and by (V, or) those with respect to slow variables. The solution is then sought in the form of a perturbative series in c:

(6)

where the B (n) functions depend on both fast and slow variables.

Inserting the expansion (6) and the rule for derivatives (5) into the original equation (3), we derive the following hierarchy of equations:

I (!) (0 ) -(0) -(0 ) O(c) AB = -v•VB + 2178•VB + (V•B )v (8) O(c 2 ) AB< 2 l = -v•VB<'l + 2178•VB< l l + (V•B ( ll)v -O, . B ( O) + 1 7 V' 2 B ( O) . ( 9
)
The operator A is simply the induction operator acting on fast variables: Note that these conditions mix different orders of B (n), implying, for example, that ox (v x u<l)) ;.b v • au<I) _ B0)•8v.

A• =a,• -ax (vx •) -11&•, (10
The operator A having derivatives at the left of all terms, the average (A f) vanishes for any f having the same periodicities as v.

A necessary solvability condition for the auxiliary equations of the hierarchy is thus

A f = gsol�lity(g) = O , (14)
where(•) denotes the average over the periodicities of the basic flow v.

In more general terms, by the Fredholm alternative theorem, the right hand side g should be orthogonal to constant functions, that constitute the null-space of the operator A t , adjoint of A. with the eddy diffusivity expressed in terms of averages of the r field:

(23)

The large-scale dynamics is formally diffusive, as expected. Note that, according to the definition ( 23), the eddy diffusivity T/ E is the sum of the molecular contribution T/ and those due to the presence of the small-scale velocity field v. Since the transported quantity is a vector, the eddy diffusivity is a fourth-order tensor, whose entries are averages of functions depending only on fast variables. For a generic velocity field, the tensor rfutm will not be isotropic, i.e., the eddy diffusivity will depend on the direction. To single out this dependence, it is useful to decompose a generic field Bon the Fourier basis and note that we can look for eigenfunctions of ( 22) in the form of plane waves:

(24 )

Plugging (24) into ( 22), for each unit vector k we obtain the following eigenvalue problem:

Mim(k)bm = ef (k)bi, (25)
(26)

The non-trivial part of this (d x d) matrix lives in fact on the (d-1) dimensional sub-space perpendicular to the vector k, the latter having zero eigenvalue. In three dimensions, once the entries of the T/ E tensor are known, the calculation of the eddy diffusivity in a given direction reduces therefore to the simple diagonalization of a 2 x 2 matrix.

TAYLOR-GREEN FLOWS

In this section we shall discuss the behavior of magnetic eddy diffusivities for the Taylor-Green flow, and a slight variant of it that will be shown to produce a negative magnetic eddy diffusivity.

The Taylor-Green flow v T 0 : v;-0 = sinxcosycosz, v;0 = -cosxsinycosz, v;0 = 0, ( 27)

was thoroughly investigated in the study of vorticity enhancement by vortex-line stretching and the consequent production of small-scale eddies [START_REF] Brachet | Small-scale structure of the Taylor-Green vortex[END_REF]. The planes x, y or z = mr (with n integer) are of mirror symmetry and they constitute the faces of the so-called impermeable box since no fluid crosses these boundaries. The overall geometry of the flow resembles that of a now classical experimental con fi guration consisting of a shear layer between two counter-rotating disks. The many symmetries of the Taylor-Green flow (see [START_REF] Brachet | Small-scale structure of the Taylor-Green vortex[END_REF] ensure that when v T0 is used as initial condition in a Na vier-Stokes simulation, the resulting fl ow admits the following Fourier expansion (when bifurcations breaking these symmetries are neglected): where the vector u vanishes unless the integers (m, n,p) are all even or all odd. The full MHD nonlinear problem with a Taylor-Green forcing on the velocity was recently numerically investigated in for example [START_REF] Nore | Dynamo action in the Taylor Green vortex near threshold[END_REF]. For very high viscosities only the basic mode of the forcing is active, while more and more modes other than the basic one are excited in the expansion (28) when the Reynolds number is increased (the non-basic modes will be referred to, in the sequel, as recirculation modes). The important observation made in Nore et al.

(1997) is that the magnetic fi eld grows for sufficiently large Reynolds numbers when the forcing is not on the smallest wavenumber of the box. Furthermore, the fastest growing mode of the magnetic field has a component on the smallest wavenumber, suggesting a sort of scale separation. These were our motivations in considering the following generalization (with the two most energetic recirculation modes) of the Taylor-Green flow Vx = sinxcosycosz+Asin2xcos 2z + B(sinxcos 3ycos z + (5/13) sin 3xcosycosz] vy = -cos x sin y cos z +A sin 2y cos 2z

-B[cos 3x sinycosz + (5/13) cosxsin 3ycos z]

Vz = -Asin2z(cos2x+cos2y) + B[(2/ 13 ) cosxcos 3ysin z -(2/13' ) cos 3xcosy sin z] , (29)
where A and B are free parameters. The other constants, multiples of 1/ 13 , could also have in principle been left free. For simplicity, we decided to set them to the value they take when the solution of the Navier-Stokes equations with a Taylor-Green forcing is expanded in powers of the Reynolds number. Note that both the original Taylor Green flow ( 27) and its variant (29) are parity-invariant (with respect to the origin). The vanishing of the mean helicity (h(x)) = (v•w) and the absence of a effect are therefore guaranteed. An important quali tative difference between the two fl ows is that, for (27), h(x) itself van ishes everywhere and not just its average value. This is not the case for the fl ow (29) where helicity fluctuations, although globally vanish ing, are locally quite strong. The magnetic eddy diffusivities for the flows ( 27) and ( 29) are calculated using the formalism of Section 2 and numerically solving the resulting auxiliary equations (1 6) and (20). The numerical code is a standard pseudo-spectral one, with the classical 2/3 truncation procedure for dealiasing [START_REF] Gottlieb | Numerical Analysis of Spectral Methods: Theory and Applications[END_REF]. Since magnetic Reynolds numbers (defined here as Rm= 1/ry ) turn out to be of order ten, only moderate resolutions 32 3 and 64 3 are needed. We checked by the energy spectra that truncation or finite size errors are negligible for the range of magnetic ?iffusivities consid e red; it was verified that the results for the two resolutions coincide within relative errors of few per cent.

To solve the auxiliary equations, the most convenient way is to apply repeatedly the evolution operatorA with a sufficiently small timestep until the field settles down to a stationary state. Note that this requires all small-scale modes to be damped (which is certainly guaranteed if the Reynolds numbers is small enough). This very same assumption is indeed also implicitly assumed in the multiscale pro cedure itself: for the dynamo instability to be at large scales, and for multiscale techniques to be applicable, it is necessary for small scales to be stable. The validity of such an assumption can be checked a posteriori.

Let us now tum to the discussion of the results. In Figure 1, to better highlight the effects of the small-scale velocity field on large scale transport, we have plotted the minimum, over the unit wave numbers k, of the difference between the eddy diffusivity 7f (k), defined in ( 23), and the molecular diffusivity T/• For both the Taylor-Green flow ( 27) and the flow ( 29) with only the first recirculating mode excited (A = 1, B = 0), such difference always remains positive, and a fortiori so does the whole eddy diffusivity TJE. In particular, in the former case, the eddy diffusivity has a tendency to saturate to a fi nite value, while in the latter case, the tendency is to decrease. However, when the magnetic Reynolds number is increased above Rm � 11, the kinematic dynamo equation becomes unstable at small scales, comparable to those of the velocity field, indicating that the primary dynamo mechanism is not acting at large scales. The evidence of negative magnetic eddy diffusivities is finally obtained for the flow (29) with A = B = l. As shown in Figure 2, for Rm � K;,, rit � 7.9, there is at least one mode k having a negative eddy diffusivity 7f (k). As follows from (24), the corresponding eigencomponent of the magnetic field is exponentially amplifi ed, with a growth-rate proportional to k 2 . The modes lying in the xy plane are the most unstable for any Rm > �,:jt (and, of course, they are the first to become unstable), with the corre sponding eigencomponent of the magnetic field of the form B = (0, 0, Bz exp ik •x). For Rm > �,:jt, there is in fact a whole basin of un stable directions k around the most unstable one. At Rm= 10.52, the angular amplitude of the basin is roughly rr/6::; ()::; 5rr/6 (Fig. 3), where ()is the polar angle in spherical coordinates (r, (), ¢). In conclusion, the possibility of a dynamo action by negative magnetic eddy diffusivities has been demonstrated. Helicity fluctua tions, although globally vanishing, appear to play an important role in producing the negative eddy diffusivity, confirming the intuition of [START_REF] Kraichnan | Diffusion of weak magnetic fields by isotropic turbulence[END_REF]. The negative eddy diffusivity mechanism does not require any breaking of parity invariance and offers therefore an alternative to a-type effects.

Let us finally recall that in the case when the velocity field is random and has a short-correlation time, an exact equation for the mean magnetic field exists (Katsantzev, 1968). The stretching term B•iJv does not give any contribution and the resulting magnetic eddy diffusivity tensor is simply % i m = 'f/ O; mOj / + O; m fo° (vj( x, t) v1 (x, O) ) dt, which is positive-definite (and position-independent for a homoge neous flow).

  8,B= (Vx£) + 17V' 2 B .

  ) and B ( O) = (B< 0 l) + B ( O) has been decomposed in its mean and fluctuating parts. For the divergence-free conditions, we obtain at the various orders of c O(c1 ) o•B{l ) + V•B ( o ) = 0,

  The first solvability condition at O(c 0 ) is automatically satisfied since (8v) = 0. Using the linearity of the equation, its solution can be generally written in the form Sij ( x, t)(B1 ) , with the field Sij having zero mean and satisfying the equation At the next order O(c1), the solvability condition or equivalently using (15) (v ;(x ) S1 1( x )) -( vJ(x ) S u( x )) = 0, be non trivial, corresponding to the a effect. However, if the velocity is parity invariant v(-x) = -v(x), from (16) it follows that Sij(-x) = Sij(x) and the average in (18) therefore vanishes. Using again the linearity of the equation, we can write its solution in the form(19) where the fi eld rij1(x) is the zero-mean solution of Arij1(x, t ) = -8av1 -v1Sa + viSJt + 2ry81Sa.(20)Finally, from the solvability condition at O(t:2) we obtain the evolution equation for the large-scale magnetic field (B (O))(X, T):Substituting in (2 1) the expression (19), we obtain(22)

FIGURE 1

 1 FIGURE 1 The difference (7fmin -11) between the minimum (over the wavevector k directions) of the eddy diffusivity 7f (k) and the molecular diffusivity 11 vs. the magnetic Reynolds number. According to the defi nition in (23), the difference (1-,£-11) gives the contribution to the eddy diffusivity arising from the presence of the small-scale velocity fi eld v. Circles refer to the fl ow (27); squares to the fl ow (29) with (A = 1, B = 0).

FIGURE 2

 2 FIGURE 2 'fhe minimum rfnn n (over the wavevector k directions) of the magnetic eddy diffusivity rf (k) vs. the magnetic Reynolds number, for the flow (29) with A = B = I. As the magnetic eddy diffusivity r/ def i ned in (23) already includes the molecular contribution, the change of sign of the curve at Rm = R";1 � 7.874 corresponds to the threshold for the magnetic field growth.

FIGURE 3

 3 FIGURE 3The variation of the eddy diffusivity !f (k) with respect to the angle (} between the wavevector k and the i axis, for Rm = 10.52.

In the relation above, A is the vector potential satisfying 8 = V x A.

In the presence of the a effect, two slow times should be introduced: T1 = ct, to capture the a dynamics and T 2 = e 2 t for the eddy diffusivity contributions.

Acknowledgements

We are most grateful to M. E. Brachet, U. Frisch, H. Politano and A. Pouquet for useful discussions. The work was supported by CNRS GdR "Mecanique des Fluides Geophysiques et Astrophysiques". Numerical simulations were performed at the Observatoire de la Cote d'Azur in the framework of the SIVAM project. AL was supported by the EEC under contract No. ERB-FMBI-CT96-0974. AW was supported by NASA grant NAG5-713.

APPENDIX A. SIMPLE ANALYTICALLY SOLVABLE CASES

We shall briefl y discuss here some simple cases where the calculation of the magnetic eddy diffusivity can be carried out analytically. For none of them does the eddy diffusivity turn out to be negative.

Let us start from the case when the magnetic Reynolds number R m is small enough to permit a perturbative expansion of the mag netic eddy diffusivity. The operator A in (10) then reduces to the heat operator 1{ = 8 1 -T/& whose inversion on periodic functions having zero mean and a spectrum decaying sufficiently fast is well defined and easy to perform, e.g., in Fourier space. The solutions at the dominant order of the auxiliary equations ( 8) and ( 9) are thus:

The expression of the eddy diffusivity tensor immediately follows from (23). For time-independent velocity fields, the turbulent contribu tion turns out to be positive definite. Indeed, the combination I= -r/J1 m k/<.1b;b m [which is the one involved in (26)] reduces to .2) which is clearly positive. For a generic fl ow, the previous formulae are just the first term of the expansion in the magnetic Reynolds number. There is however the special class of parallel flow where they hold in general. These fl ows are defi ned as:

where the simplifying feature is that they depend on a single coordinate (here arbitrarily chosen to be x) . It follows that, in solving (8) and ( 9), the term iJ x (v x •) in A identically vanishes and the solution of the equations reduces again to inverting the heat operator.

The previous perturbative formulae can therefore be simply carried over and the eddy diffusivity tensor is guaranteed to be positive defi nite by the general result (A.2).


Somia Haouache

Ayman Karam

Tony Chave

Prince Jonathan Clarhaut

Nana Amaniampong

José M García Fernández

Karine De Oliveira Vigier

Isabelle Capron

François Jerome

Nana Prince

Amaniampong

José M Garcia Fernandez

François Jérôme

Selective radical depolymerization of cellulose to glucose induced by high frequency ultrasound

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

Introduction

The depolymerisation of cellulose 1 to glucose has become an important reaction paving the way to various biobased chemicals such as ethanol, furandicarboxylic acid, caprolactame, sorbitol, levulinic acid, -valerolactone, among many others. 2 The hydrolysis of cellulose to glucose is however difficult to achieve and often constitutes an obstacle in the synthesis of downstream products. 3 Indeed, this reaction requires overcoming high energy barriers of about 30-40 kcal/mol, 3a, 4 essentially because cellulose exhibits a highly cohesive hydrogen bond network, 1,5 strong Van der Waals interactions, 6 and electronic effects. 7 To date, the selective hydrolysis of cellulose to glucose is performed by enzymatic routes. 8 Although this route is deployed on a large scale for the production of ethanol, the price of enzymes as well as low space time yield and costly downstream purification processes hamper the large development of this route in the chemical industry. Alternatively, acid catalysts can also depolymerize cellulose, but they require harsh conditions and thus unfortunately afford glucose in low yield due to the formation of tar-like materials. 2,3 The exploration of alternative technologies capable of selectively depolymerizing cellulose to glucose with a high efficiency is still an open scientific question. 9 Supercritical water has emerged as a promising route for releasing glucose from cellulose 10 and this process was even scaled-up by Renmatix. 11 Solvent free technologies, aiming at producing concentrated feed of glucose, were also explored and one may cite the depolymerisation of cellulose by mechanocatalysis 12 or by nonthermal atmospheric plasma (NTAP). 13 With these solvent-free technologies, depolymerisation and repolymerization reactions occur simultaneously and processable water soluble oligosaccharides are obtained instead of monomeric glucose. Here we report an alternative technology based on the use of high frequency ultrasound (HFUS). The ultrasonic irradiation of cellulose at a high frequency leads to a complete depolymerisation of cellulose to glucose, without any catalyst. In addition, the depolymerisation of cellulose induced by HFUS does not need any external source of heating or pressure, the energy being brought by the implosion of cavitation bubbles. 14 When applied within a liquid, ultrasonic irradiation induce the nucleation, growth and collapse of gas and vapour filled bubbles. In contrast to the very popular low frequency ultrasound (< 80 kHz) which mostly induces physical effects (shock waves, micro-jets, turbulences, etc.), irradiation of water at high frequencies (> 150 kHz) mainly leads to the in situ formation of H• and •OH radicals resulting from the dissociation of water molecule. 15 Once these cavitation bubbles implode, in situ formed radicals can recombine or react with solutes inducing chemical effects. Inspired by our previous works on NTAP, 13 we conceived that these in situ produced radicals should theoretically induce the cleavage of the glycosidic bonds of cellulose. 16 Being able to selectively depolymerize cellulose When solid particles are present in an ultrasonic reactor, they act as nuclei for the formation and growth of cavitation bubbles. Close to a surface, the implosion of cavitation bubbles is very asymmetric and generates high-speed jets of liquid towards the surface, a good mean to concentrate radicals on a particle. 17 Applied to cellulose, this physical principle should be an efficient mean to control the reaction selectivity by concentrating radicals on the cellulose particle surfaces, thus preventing side reactions of released glucose into the bulk solution.

Result and discussion

To demonstrate the potential of the above concept, we first subjected microcrystalline cellulose (MCC, Avicel PH 200) to an ultrasonic irradiation at 525 kHz (acoustic power density of 0.36 W.mL -1 ) in water, at 60 °C, and under atmospheric pressure of air. Analysis of the products formed was performed by HPLC and the conversion of cellulose was monitored by size exclusion chromatography (SEC) and difference of weight. To our delight, after 3 h of irradiation, glucose was formed in 30 % mass yield (Scheme 1). The reaction was fully selective to glucose, no other product was detected either by HPLC or mass spectrometry (Fig. S1). 1 H and 13 C NMR confirmed the selectivity of the reaction and recorded NMR spectra of the crude product were rigorously similar to that of standard glucose (Fig. S2,S3). The absence of water-soluble low molecular weight oligosaccharides also suggests that the depolymerization occurs at the terminal position of the cellulosic chain. The yield of glucose also perfectly fits with the conversion of cellulose (30 %), determined by measuring the difference of weight before and after HFUS treatment. Interestingly, the reaction also proceeded well at 40 °C and even 25 °C, without affecting the yield and the selectivity into glucose.

To rationalize the high selectivity into glucose, the remaining MCC was removed by filtration after 3 h and the as-obtained aqueous solution of glucose was subjected again to ultrasonic irradiations. Pleasingly, in the absence of cellulose particles, ultrasonic irradiation of the homogeneous solution of glucose led to quick degradation, through uncontrolled oxidation reactions, with gluconic acid being formed as a primary product, Scheme 1. Depolymerisation of cellulose to glucose induced by HFUS.

as observed earlier. 18 This counter experiment is in agreement with the advanced hypothesis that, in the presence of MCC, radicals preferentially react with the cellulose particles rather than with released glucose in the bulk solution, thus optimizing the selectivity to glucose. Analysis of the recovered cellulose by SEC confirmed its depolymerisation with a reduction in the weight-average molecular weight (Mw) and the numberaverage molecular weight (Mn) from 49.10 3 to 43.10 3 g.mol -1 and 38.10 3 to 30.10 3 g.mol -1 , respectively, after 3 h of reaction (Fig. S4). Furthermore, analysis of the linking pattern of the recovered cellulosic material showed the exclusive occurrence of -(14)-linked glucose units, as expected for cellulose. These results rule out the possible occurrence of repolymerization reactions, which would have led to the formation of 1,6 glycosidic linkages, as previously observed by the mechanocatalytic 12g or the NTAP technologies. 13c FT-IR and XPS analyses confirmed that no oxidation or C-C bond cleavage of the recovered cellulose occurred in our conditions, at least it is below the detection limit of our apparatus (Fig. S5,S6). In addition, XRD analysis did not show any change in the crystallinity index before and after HFUS, which strongly suggest that the in situ produced H• and •OH radicals selectively cleave the glycosidic bonds of cellulose (Fig. S7).

The kinetic profile of the reaction was next monitored at 60°C and revealed an induction period of about 3 h. At the moment, we have no rational explanation for this induction period. It seems it corresponds to the time for the HFUS reactor to reach its optimal efficiency (see ESI for additional information). For instance, when ultrasonic irradiation of neat water was performed for 3 h prior to addition of cellulose, the induction period was reduced to only 10 min. After this period, cellulose was quasi instantaneously depolymerized to glucose, indicating that the depolymerisation rate of cellulose was very high. Subjecting cellulose to HFUS for a reaction time higher than 3 h did not result in a further improvement of the glucose yield, meaning that the depolymerisation of cellulose has stopped.

Scheme 2. Kinetic profile of the reaction recorded at 60°C under air (525 kHz, acoustic power: 0.36 W.mL -1 ). Cellulose was introduced before (blue) or after (orange) warm-up of the reactor

To get more insight on this phenomenon, the amount of cellulose suspended in water was varied from 0.5 wt% to 5 wt%. Independently of the cellulose loading, the depolymerisation reaction always stopped when the concentration of glucose Please do not adjust margins Please do not adjust margins reached 16.7 mmol.L -1 (i.e. 0.3 g.L -1 ), suggesting that released glucose inhibits the depolymerisation of cellulose induced by HFUS. We speculated that, at a certain concentration of glucose, this latter can trap the radicals on the cellulose particle surface. More information on this aspect is provided hereinafter. Complete depolymerisation of cellulose by HFUS should be theoretically feasible by switching from batch to continuous or semi-continuous processes. In this context, the cellulose recovered by filtration after the first batch was resuspended in pure water and subjected again to HFUS. Interestingly, the depolymerisation occurred but stopped again at a concentration of glucose of 16.7 mmol.L -1 , leading to a cumulative yield of glucose of 60% after two runs (2 x 0.3 g of glucose, Scheme 1). These experiments could be reproduced four consecutive times leading to a quantitative depolymerisation of cellulose to glucose (Scheme 1). To explore the possibilities for further improving the glucose yield, we next investigated the reaction mechanism. It is widely accepted that irradiation of water at a high frequency leads to its homolytic dissociation to H• and •OH radicals. 15 The H• radicals being difficult to observe due to fast recombination reactions, we first focused our investigations on the in situ produced •OH radicals. To this end, the formation of •OH radicals was monitored by fluorimetry using terephthalic acid (TPA) as an •OH radical scavenger (Scheme 3, Fig. S8). 19 It is noteworthy that curves presented on scheme 3 reach a maximum, and even decrease in some cases, which does not reflect the reality; it is actually due to the over-oxidation of the as-formed hydroxyterephthalic acid. Under air, the formation of •OH radicals was clearly evidenced by fluorimetry analysis.

Ratio of specific heat, thermal conductivity and water solubility of gases impact the temperature of cavitation bubbles and thus the generation of radicals. In this context, the gaseous atmosphere was varied and changed from air to O2, Ar, H2 and mixtures of Ar/H2 and Ar/O2 (Scheme 3). In line with the state of the art on HFUS, the initial formation rate of •OH radicals was the highest in an Ar/O2 atmosphere. 20 Conversely, addition of H2 to Ar dramatically inhibited the formation rate of •OH radicals, which was even inhibited when using neat H2 as a Scheme 3. Titration of •OH radical using TPA (2 mM) as a function of the gaseous atmosphere. *The decrease in the •OH radical amount with time under Ar/O2 is due to the large production of •OH radicals which degrade TPA-OH used as a probe.

gaseous atmosphere, in line with previous report (Scheme 3). 21 We noticed that the efficiency of HFUS-mediated cellulose depolymerisation was inversely proportional to the formation of •OH radicals, i.e the higher the initial formation rate of •OH radicals, the lower the glucose yield (Scheme 4). For instance, cellulose was depolymerized to glucose with 63% yield under an H2 atmosphere (vs 30% under air) while no •OH radical was formed in this case, suggesting that H• radicals are more likely to be involved in the reaction mechanism. To independently assess the role of H• and •OH radicals in the reaction mechanism, control experiments were performed by adding two different radical scavengers during the ultrasonication of cellulose (Table 1). First, the ultrasonic irradiation of cellulose was performed under an Ar/H2 atmosphere in an aqueous solution of TPA (2.0 mM), with the aim of in situ trapping the •OH radicals. Consistent with our expectations, the glucose yield remained similar in the presence of 2.0 mM of TPA, supporting that •OH radicals have no major role in our case on the cellulose depolymerisation mechanism (Table 1, entry 2). This conclusion is also supported by FT-IR and XPS analyses which did not show oxidation, C-C bond cleavage or rearrangement of remaining cellulose. Next, the same reaction was performed by replacing TPA by carbon tetrachloride (CCl4). CCl4 is known to trap the H• radicals inside the cavitation bubbles. 16 Despite the poor miscibility of CCl4 in water, addition of CCl4 completely inhibited the reaction, highlighting the important role of H• radicals in the Please do not adjust margins Please do not adjust margins depolymerisation of cellulose (Table 1, entry 3). This result is also consistent with our experiments under air, O2 and Ar/O2 for which the lowest yields in glucose were observed (Scheme 4). Indeed, H• radicals are known to be recombined with O2 to form•OH and •OOH radicals, as Niwano and Sivakumar previously observed by ESR spin trapping 21 and dosimetry experiments, 19 respectively. Hence, it is anticipated that the amount of free H• radicals is rather low under O2 and Ar/O2 atmosphere, explaining the low glucose yields obtained in these cases.

Altogether, these results show that the depolymerisation of cellulose observed under HFUS is enhanced under an H2 atmosphere, suggesting that H• radicals propelled onto the surface of cellulose particles can cleave the glycosidic bond of cellulose, presumably in a similar way as acid catalyst (protonation of the anomeric or the endocyclic oxygen of the terminal non-reducing glucopyranose unit). [START_REF] Bhaumik | Chapter 1:Conversion of Biomass into Sugars[END_REF] Depending on the nature of the gaseous atmosphere, the amount of H• radicals, and their recombination rate, can significantly differ. Although deeper investigations are needed at this stage to fully clarify the reaction mechanism, co-feeding the reactor with H2 seems to be an option to enhance the contact/reactivity of H• radicals with the cellulose surface and to ensure its extensive depolymerisation.

As above mentioned, at a certain concentration, glucose may interact with cellulose particle surfaces where it could locally trap radicals. Under oxygen free conditions, no change in pH (~ 6.5) was observed, even at extended reaction times, ruling out a possible oxidation of glucose in this case. This was further supported by 13 C NMR and mass spectrometry investigations, which did not show the formation of any C=O group. Furthermore, unlike TPA, when 16 mM of glucose was initially added to cellulose, the depolymerisation was completely inhibited, suggesting that glucose similarly behaves as CCl4 and scavenge H• radicals on the cellulose surface. As an evidence to it, we observed that, at extended ultrasonic irradiation time under H2 or Ar/H2 atmospheres, the glucose yield gradually decreased and fructose was concomitantly formed (Fig. S9). This observation was supported by HPLC analysis and by 1 H/ 13 C NMR investigations, which clearly evidenced the selective formation of glucose and fructose in a 83/17 (glucose/fructose) ratio (Fig. S9, S10, S11). Although additional experiments are needed to fully rationalize the reaction mechanism, the absence of pH change and the partial isomerization of glucose to fructose under oxygen free atmosphere are strong arguments in favour of the involvement of H• radicals. This claim is also in agreement with our previous report which show, by density functional theory calculations, that H• radicals promote the ring opening of glucose, 17a a known key step in its isomerization to fructose. Interestingly, previously reported technologies involving radical of cellulose such as photolysis, UV excitation, radiolysis by X-ray, -ray irradiation, electron beam, etc., [START_REF] Wencka | [END_REF] led also to glycosidic bond cleavage but with uncontrolled side dehydration, recombination or rearrangement of the glucosyl unit. Hence, in situ produced radicals alone cannot explain the very high selectivity into glucose observed using HFUS. One may suspect that, as in the case of supercritical water or the mechanocatalytic process, the implosion of cavitation bubbles on the surface of cellulose locally provides enough physical forces (pressure, shock waves, etc.) capable of inducing a conformational change of the glycosidic bond, 7a which then become much more reactive.

Conclusions

We show here that HFUS is an alternative technology capable of selectively depolymerizing cellulose to glucose. The possible transfer of radicals produced inside the cavitation bubbles onto the cellulose particle surfaces was an efficient mean to prevent the concomitant side-degradation of glucose into the bulk solution. In contrast to previously reported technologies, this work is distinguished in that (i) no catalyst was needed, (ii) the depolymerization of cellulose occurs in water at atmospheric pressure and temperatures below 60°C, including room temperature, and (iii) it proceeds in a very selective fashion. A deeper understanding of the reaction mechanism suggest that H• radicals are more likely to be responsible for the depolymerisation of cellulose. By recirculating unreacted cellulose into the HFUS reactor, it was possible to selectively and quantitatively depolymerize cellulose to glucose, which constitute one of the rare cases reported so far. A combined experimental-theoretical approach is now the topic of current investigations in our groups in order to get more insight on the reaction mechanism, including the observed induction period in Scheme 2.

Scheme 4 .

 4 Scheme 4. Maximum yield of glucose as a function of the gaseous atmosphere (60°C, 525 kHz)

Additive

  This journal is © The Royal Society of Chemistry 20xx

Table 1 .

 1 Influence of H• and •OH radical scavengers in the HFUS-induced depolymerisation of cellulose

	Entry	Radical scavenger	Glucose yield (%)
	1	-	52%
	2	TPA	51%
	3	CCl4	0

Acknowledgements

Authors are grateful to the CNRS, the University of Poitiers and INRA for their financial supports. FJ and IC also strongly acknowledge the Agence Nationale de la Recherche for the funding of this work (project CELLOPLASM N° ANR-16-CE07-0003), including the PhD grant of SH. The GDR CNRS-INRA SYMBIOSE is also acknowledged for funding. JMGF acknowledges financial support from MCIU-AEI-FEDER (contract number RTI2018-097609-B-C21). Authors are also grateful to the region Nouvelle Aquitaine for the CPER and EU-FEDER support. We also gratefully acknowledge Karine Cahier, the BIBS (INRA, Nantes, France) and PLATINA (IC2MP, Poitiers, France) platforms for their technical assistance.

Notes and references

1 a) D. Klemm, B. Heublein, h.-P. Fink, A. Bohn, Angew. Chem. Int. Ed. 2005, 44, 3358-3393; b) D. Klemm, F. Kramer, S. Moritz, T. Lindström, M. Ankerfors, D. Gray, A. Dorris, Angew. Chem. Int. Ed. 2011, 50, 5438-5466; c) I. Siro, D. Plackett, Cellulose 2010, 17 (3), 459-494; d) R. J. Moon, A. Martini, J.

Conflicts of interest

There are no conflicts to declare