domain: chim chim.mate phys

text:
Florent Benzerga

A Marlec

François Sharaiha

Franck Cheviré

A Tessier

Moréac

L Le Gendre

C Le Paven

M Haydoura

R Benzerga

F Marlec

A Sharaiha

F Tessier

A Moréac

Thermal oxidation of oxynitride films as a strategy to achieve (Sr2Ta2O7)100-x(La2Ti2O7)x based oxide perovskite films with x = 1.65

come

Thermal oxidation of oxynitride films as a strategy to achieve (Sr2Ta2O7)100-x(La2Ti2O7)x based oxide perovskite films with x = 1.65

Introduction

ABO3-xNx (0 ≤ x ≤ 3) oxide and oxynitride perovskite compounds have been of interest to the scientific community for many years. Indeed, they possess remarkable and miscellaneous properties, allowing their use in many fields such as non-toxic pigments [START_REF] Jansen | Inorganic yellow-red pigments without toxic metals[END_REF][START_REF] Marchand | Typical features of nitrogen in nitride-type compounds[END_REF], high-K dielectrics [START_REF] Hosono | Additive sintering and post-ammonolysis of dielectric BaTaO2N oxynitride perovskite[END_REF][START_REF] Le Paven-Thivet | Oxynitride perovskite LaTiOxNy thin films deposited by reactive sputtering[END_REF], visible light active photocatalysts [START_REF] Wang | Nitrogen-doped simple and complex oxides for photocatalysis : A review[END_REF][START_REF] Nishimura | Effect of TiCl4 treatment on the photoelectrochemical properties of LaTiO2N electrodes for water splitting under visible light[END_REF] or colossal magnetoresistance materials [START_REF] Fuertes | Synthetic approaches in oxynitride chemistry[END_REF]. Depending on the applications, these materials can be prepared in the form of single crystals, powders, ceramics or thin films. The oxide materials targeted presented in this paper show a layered perovskite structure and belong to the (Sr2Ta2O7)100-x(La2Ti2O7)x solid solution recently developed by our research team [START_REF] Marlec | Ferroelectricity and high tunability in novel strontium and tantalum based layered perovskite materials[END_REF]. These original materials present interesting dielectric and ferroelectric properties, especially high tunabilities with potential applications in high frequencies tunable telecommunication devices.

The studied (Sr2Ta2O7)100-x(La2Ti2O7)x solid solution (hereinafter named as STLTO) combines two layered-type perovskites [START_REF] Lichtenberg | Synthesis of Perovskite-Related Layered AnBnO3n+2 = ABOX type niobates and titanates and study of their structural, electric and magnetic properties[END_REF] with dissimilar Curie temperatures (TC): Sr2Ta2O7 (STO), with TC = -107°C [START_REF] Hushur | The phase transitions of ferroelectric Sr2Ta2O7 crystals by MDSC, Brillouin and dielectric spectroscopy[END_REF] and La2Ti2O7 (LTO), with TC = 1461°C [START_REF] Yan | Piezoelectric Ceramics with Super-High Curie Points[END_REF]. We have demonstrated the ferroelectric behavior of this new family of compounds in the form of ceramics for compositions ranging from x = 0 to 5. Optimal performances were achieved for the composition x = 1.65: the permittivity value was ε' = 375 with tunability values T = 17.9 % at 4 kV/cm [START_REF] Marlec | Ferroelectricity and high tunability in novel strontium and tantalum based layered perovskite materials[END_REF] and T = 55 % at 30 kV/cm (10 kHz, room temperature) [START_REF] Haydoura | Dielectric characterization in low and high frequencies of new ferroelectric strontium and tantalum based perovskite ceramics[END_REF]. The purpose of the present work is to produce this STLTO specific composition as a thin film.

As discussed later in this paper, the combination of a stoichiometric STLTO oxide target with a dioxygen-rich reactive atmosphere during the radio-frequency (rf) magnetron sputtering deposition leads to Sr-deficient (Sr/Ta ≈ 0.55) thin films, shifting composition and structure from a perovskite to a Tetragonal Tungsten Bronze (TTB) type. An alternative synthesis pathway is to first deposit, under nitrogen-rich atmosphere, stoichiometric (Sr/Ta = 1) oxynitride perovskite thin films (hereinafter named as STLTON) and then produce, by thermal annealing under static air, a perovskite oxide-type material with the expected Sr/Ta = 1 ratio and so to avoid the TTB phase formation. As thin films, oxynitride materials present original properties compared to their oxide parents, such as an absorption in the visible domain, with potential application as photocatalysts for overall water-splitting [START_REF] Le Paven-Thivet | Photoelectrochemical properties of crystalline perovskite lanthanum titanium oxynitride films under visible light[END_REF][START_REF] Ziani | Photophysical properties of SrTaO2N thin films and influence of anion ordering : a joint theoretical and experimental investigation[END_REF]. As dielectrics, oxynitride thin films exhibit high permittivities with a potential ferroelectric behavior [START_REF] Oka | Possible ferroelectricity in perovskite oxynitride SrTaO2N epitaxial thin film[END_REF]. As an example, LaTiO2N and SrTaO2N films present higher permittivities than those of the corresponding oxide films, La2Ti2O7 and Sr2Ta2O7 respectively, but with higher dielectric losses [START_REF] Lu | Reactive sputtering deposition of perovskite oxide and oxynitride lanthanum titanium films : structural and dielectric characterization[END_REF][START_REF] Nguyen | Miniaturized notch antenna based on lanthanum titanium perovskite oxide thin films[END_REF][START_REF] Marlec | Deposition and dielectric study as function of thickness of perovskite oxynitride SrTaO2N thin films elaborated by reactive sputtering[END_REF][START_REF] Baristiran Kaynak | Enhanced leakage current behavior of Sr2Ta2O7-x/SrTiO3 bilayer dielectrics for metal-insulatormetal capacitors[END_REF].

So, the original concept presented here is to deposit stoichiometric oxynitride films and anneal them under air in order to keep Sr/Ta equal to 1 and therefore produce stoichiometric oxide films that cannot be achieved by the sputtering of an oxide target even under an oxygencontaining plasma. Long term annealing (4 hours) of oxynitride films were performed at temperatures in the range [450 -1000°C]. As detailed further, the resulting samples display an oxide character (Band gap Eg ≈ 4.5) but still contain a significant amount of nitrogen ; they could be described as intermediate phases as previously shown by L. Le Gendre et al. [START_REF] Gendre | A new class of inorganic compounds containing dinitrogenmetal bounds[END_REF][START_REF] Gendre | Raman scattering investigations of dinitrogen entities in oxidized LaTiO2N perovskite[END_REF] and A. Rachel et al. [START_REF] Rachel | Tantalum and niobium perovskite oxynitrides : Synthesis and analysis of the thermal behavior[END_REF] on powder materials. The present article is divided as follows. The deposition of the oxide STLTO and oxynitride STLTON thin films is first presented ; then, the annealing of oxynitride samples is studied, including their chemical, optical, structural and Raman characterization. Dielectric measurements are finally presented which emphasize very interesting dielectric properties of the original intermediate produced phases.

Experimental

1. Oxide target for the sputtering deposition STLTO and STLTON layers were deposited by sputtering from a home-made oxide target, prepared by solid state reaction and cold uniaxial compaction. The (Sr2Ta2O7)100x(La2Ti2O7)x STLTO powder with composition x = 1.65 was synthesized according to the following process: stoichiometric amounts of high purity powders of SrCO3, Ta2O5, La2O3 and TiO2 were homogenized in isopropanol for 1 h in an agate mortar and dried at 110°C. The obtained powder was pressed into a pellet using an uniaxial press (5 MPa), then calcined in air for 15 h at 1000°C, milled and calcined again at 1400°C for 15 h. In order to obtain the sputtering target, 74 grams of the synthesized (Sr2Ta2O7)98.35(La2Ti2O7)1.65 powder were mixed with an organic binder (Rhodoviol 5% wt.) facilitating the shaping and subsequently the manipulability of the target; afterwards, the powder was compacted under static uniaxial pressure of approximately 35 MPa. The target was then slightly treated at 600°C under air to remove the organic binder and obtain some grain cohesion and avoid a collapse of the target during handling. The θ-2θ XRD diagram of the target is presented in Figure 1 : all diffracted peaks can be indexed in a unit cell isostructural to that Sr2Ta2O7 compound (JCPDF 70-0248).

EDS analysis of a dedicated sample gives a strontium to tantalum ratio Sr/Ta = 0.98, which confirms the targeted stoichiometry of the STLTO oxide material.

Thin films deposition and characterization methods

STLTO and STLTON films were deposited by reactive rf magnetron sputtering (Plassys MP450S) using the home made STLTO target located at 5 cm from the substrate holder. The deposition chamber was pumped down to a base pressure of 10 -5 Pa ; during deposition, the dynamic pressure was maintained at 2.5 Pa (30 mTorr). Depositions were performed under a reactive atmosphere consisting in (Ar + O2) or (Ar + N2) gas for the deposition of STLTO oxide and STLTON films respectively. The percentage (vol.%) of the reactive gas (O2, N2) in the sputtering atmosphere was varied from 5 to 75. At each change of this percentage, the target was pre-sputtered before deposition during 4 hours under the same dioxygen/dinitrogen percentage than the one used during the deposition, in order to oxidize/nitride the target surface and reach a stable state. The rf power was adjusted at PRF = 90 W and the substrate temperature (TS) was fixed at TS = 800°C. Thickness of films was changed by the duration of the deposition.

At each run, films were deposited on two single-crystalline substrates obtained from Crystal GmbH (Berlin, Germany): MgO(001) and conductive niobium-doped (1.4 at.%) SrTiO3(001) (Nb-STO). The latter was used to serve both as substrate and bottom electrode for the dielectric characterization, while MgO serves for the determination of the band-gap by UVVisible transmittance and for the determination of the crystallization. X-ray diffraction patterns of films (and powders) were obtained using a Rigaku SmartLab diffractometer (Cu Kα1 radiation). Conventional θ-2θ diagrams were recorded at 0.01° intervals with a 2 s count time at each step.

UV-visible transmittance spectra were recorded using a Perkin-Elmer Lambda 20 spectrometer in the 200 -1100 nm wavelengths range. For each sample, the absorption coefficient α is calculated from the transmittance (T) using the relation α = (1/t)(ln(1/T)), where t is the thickness of the film. The bandgap of the material (Eg) is calculated assuming a direct allowed transition and using the relation (αhν)² = hν -Eg, where hν is the photon energy. In the plot of (αhν)² as a function of h , the extrapolation of the linear region of the plot at zero gives the value of Eg [START_REF] Kubelka | Ein beitrag zur optik der farbanstriche[END_REF].

A Horiba/Jobin-Y micro-raman spectrometer was used to collect unpolarized Raman spectra of the thin films in backscattering geometry at ambient temperature. These Raman measurements have been performed with a laser diode at 532 nm. Optical density filters were used to decrease the laser power to avoid heating at the focus point of the laser on the sample.

The spectral dispersion was around 1.5cm -1 /pixel. Energy Dispersive Spectrometry (EDS) was used to investigate the cations and nitrogen relative compositions of samples ; analyses were performed using the Aztek OXFORD software through a Jeol JSM IT100 Scanning Electronic Microscope (SEM) operating at 10 kV. Surface of films and cross-section morphologies for the measurement of the thickness of the films were characterized by the above SEM ; the error on the thickness values from the cross-section observations is estimated as being ± 10 nm.

Low frequency dielectric properties (permittivity ε' and dielectric losses tanδ) were measured by a LCR meter (LCR-819 GWInstek). Experiments were conducted on films deposited on 1.4 at.% Nb-doped SrTiO3 (Nb-STO) substrates deposited in the same run than those on MgO substrates. Measurements were performed on capacitance structures in which the bottom electrode is the conducting Nb:STO substrate whereas 200 nm sputtered silver serves as the top electrode. Measurements were done at 10 kHz and room temperature ; external DC electric fields (0-310 kV) were applied to point out a possible variation of the permittivity, i.e. tunability (T) defined as T(%) = | ε'Eε'E=0 | / ε'E=0.

Results

1.

Oxide STLTO and oxynitride STLTON thin film deposition at x = 1.65 First, in order to obtain directly the oxide composition, a series of film samples was achieved by sputtering the STLTO target under the reactive (Ar + O2) gas, varying the percentage of O2 from 5 to 75 %O2. Thin film samples are presented in Table 1 along with their composition in cations (ratio Sr/Ta), band gaps (Eg) values and thicknesses which are higher than 870 nm.

Films deposited with %O2 ≥ 10 are transparent with band-gap values close to 4.4 eV (Figure 2a for the film deposited with %O2 = 25 named hereafter as "STLTO as-deposited").

Fringes observed in the transmittance spectrum at high wavelength values arise from interferences at the air/film and film/substrate interfaces and their spacing depend on the thickness of film, as well as its roughness and density. The film deposited with %O2 = 5 has a band gap value Eg = 3.2 eV and is grey ; this can denote an oxygen deficiency in the sample due to the low percentage of dioxygen used during its deposition.

All oxide films present Sr/Ta ratios in the range 0.53 to 0.55 as can be seen in blue in Figure 3, denoting a systematic major strontium deficiency in films compared to the sputtering target, and so to the expected composition (the quantification of La was not made here because of its very small amount in STLTO with x =1.65 ; we assume the same La-deficiency as Sr in our films). Therefore, the XRD diagrams (Figure 4 for the "STLTO as-deposited" film and Figure S1 for all samples) cannot be indexed based on the Sr2Ta2O7 perovskite compound for which the ratio Sr/Ta = 1. Considering Sr/Ta ratio values close to 0.55, we propose to identify the phase in films to the strontium-deficient Sr2.83Ta5O15 compound (PDF 9012069) belonging to the tetragonal tungsten bronze (TTB) family. Sr2.83Ta5O15 is an isotype to the β'-SrTa2O6 TTB material studied by Kim et al. [START_REF] Lee | Crystal structure analysis of tungsten bronzes β-SrTa2O6 and β'-SrTa2O6 by synchrotron X-ray and neutron powder diffraction[END_REF]. The indexation of peaks reveals of an orientation of films along their c-axis. Moreover, no amorphous contribution, such as a large bump between 15 and 35°, can be detected in the XRD patterns which would have been the signature of a compound gathering a Ta and Ti over-stoechiometry consequence of the Sr and La deficiency in films.

The film deposited with %O2 = 5 exhibits the less intense peaks thus evidencing the lowest crystallization. The films deposited with % O2 = 50 and 75 show an asymmetry of the (00l) peaks ; we can consider the existence of a (620) contribution for these samples. We also note that the position of the (00l) peaks moves to lower angular values when %O2 increases, which corresponds to an increasing out-of-plane c parameter, as can be seen in Figure 5. This c parameter increase is not linear, a plateau at c ≈ 3.93 Å is reached when % O2 ≥ 50. The tabulated c lattice parameter of Sr2.83Ta5O15 is c = 3.864 Å (PDF 9012069) which denotes a discrepancy with the above experimental value ; this can be due to the crystalline influence of the substrate inducing tensile or compressive strains in thin films.

As a conclusion on this series of samples, the sputtering of the STLTO target by the reactive dioxygen gas has not led to the expected result ; strontium deficient TTB oxide films have been obtained instead of stoichiometric perovskite oxide compounds.

The deposition of films using a reactive dinitrogen gas, producing oxynitride STLTON films, was thus performed by sputtering the same STLTO oxide target and using identical deposition parameters than for the above oxide films but under reactive (Ar + N2) gas with %N2 ranging from 5 to 75 (Table 2).

The deposited films are orange-brown in agreement with an absorption in the visible range and band gap values close to 2.3 eV (Table 2 and Figure 2b for the film deposited with %N2 = 25 named hereafter as "STLTON as-deposited"). Nitrogen is detected by EDS analysis, as expected, but the important feature is that Sr/Ta ratios are close to 1 (Table 2), with a significant evolution as seen in Figure 3 : Sr/Ta increases with %N2 and the value of 1 is attained for %N2 ≈ 25.

XRD diagrams (Figure 4 for the "STLTON as-deposited" film and Figure S2 for all samples) can be indexed according to the isostructural SrTaO2N compound (JCPDF 79-1311), with clear (00l) texturation of films. No evolution of the angular peak positions can be noticed as a function of %N2, contrary to what was observed for the oxide films (as a function of %O2)

; for the STLTON "as-deposited" film c parameter equals 4.083 Å. Comparison of the diagrams of the STLTON and STLTO "as-deposited" samples (Figure 4) shows that the two sets of peaks (oxynitride vs. oxide) are easily differentiated by XRD analysis.

Annealings of STLTON films

Giving the proper cation stoichiometry of the STLTON oxynitride films, annealing of these films was performed as a way to produce stoichiometric oxide films. Annealings were done at various temperatures (TA = 450, 550, 600, 650 and 1000°C) for 4 h in ambient air ; ramp temperature was 2°C/min for heating and cooling. Annealed samples features, with the "as-deposited" oxide / oxynitride films and the STLTO pristine powder used for the sputtering target, are presented in Table 3.

EDS analysis of the films before and after annealing (Table 3) underlines that the Sr/Ta ratios remain close to 1 for the different annealing temperatures, with no proven trend. Moreover, nitrogen is detected in all annealed films and is in the range 8.5 -9.5 at.%, except for the film treated at the highest temperature (TA = 1000°C) which does not contain nitrogen.

Discrepancies in the atomic contents from one annealed film to another are due to the uncertainty of the quantification by the EDS method.

As regards the optical transmittance (Figure S3), the starting oxynitride film shows absorption in the visible range with a band gap Eg = 2.3 eV. Visible absorption persists for the film annealed at TA = 450°C ; band gap of 2.5 eV is determined. The situation changes radically for TA higher than 550°C : absorption is observed below 400 nm, band gap values are then all greater than 4.1 eV with a rather large spread of values. Due to extreme degradation of the film after the heat treatment at TA = 1000°C, transmittance measurement was not performed on it. XRD analysis (Figure 6) shows that the annealing at TA = 450°C does not affect the XRD signature of the sample which remains that of an oxynitride and, so, is similar to that of the "STLTON as-deposited" film.

For TA ≥ 550°C, an important decrease in the intensity of peaks is observed along with an offset of the positions towards higher 2θ angular values (Figure 6b). These positions correspond neither to that of the STLTO pristine stoichiometric powder, nor to that of the "STLTO asdeposited" film with a strontium deficiency. Angular positions of the annealed films are at intermediate positions. Thus, three sets of the out-of-plane c parameter are highlighted in Figure 7 : cPC ≈ 4.08 Å for oxynitride compounds ("as-deposited" and annealed at TA = 450°C), cPC ≈ 3.99 Å for the other annealed films and cPC ≈ 3.945 Å for the oxide pristine powder. Moreover, it is observed in XRD that the peak intensities of the annealed films decrease as TA increases, while maintaining a textured crystallization with the presence of (00l) peaks. An amorphization of annealed oxynitride films while keeping a perovskite structure is thus observed, as already reported on partially annealed oxynitride powders [START_REF] Gendre | A new class of inorganic compounds containing dinitrogenmetal bounds[END_REF].

Surface morphologies of annealed samples are visible in Figure S4. At high magnification, the initial "as-deposited" oxynitride film is finely granular with grain sizes below 100 nm. The granularity increases with the annealing temperature. At TA = 1000°C, the film is very smooth. At low magnifications, we can see that films undergo increasing damage as the annealing temperature increases. At TA = 550°C and 600°C, we observe the formation of craters where the film begins to peel off the substrate. This phenomenon is accentuated at TA = 650°C with the presence of holes where the film has completely taken off from the substrate and, finally at TA = 1000°C, the film remains only in the state of fragments on the substrate. Figure 8 presents the Raman spectra, in the [2300 -2350 cm-1] range, of the MgO substrate on which films are deposited, the "STLTON-as-deposited" film and the STLTON-25 film annealed at 600°C. This sample was chosen for the Raman characterization (and for the dielectric measurements as seen below) because it remains as a quasi-continuous film, maintains a textured growth and a Sr/Ta ratio close to 1.

First of all, we find that no peak is visible in the explored range for the as-deposited oxynitride film. The signal at 2331cm -1 detected on MgO corresponds to the presence of N2 adsorbed molecules [START_REF] Gendre | Raman scattering investigations of dinitrogen entities in oxidized LaTiO2N perovskite[END_REF] on the surface of the substrate. Two signals are observed for the STLTON-25 annealed film : a weakly intense shoulder at 2331 cm -1 and an intense signal at 2328 cm -1 . The first one corresponds to adsorbed N2 on the surface of the film, while the second corresponds to N2 molecules trapped in an oxide matrix as previously reported [START_REF] Gendre | Raman scattering investigations of dinitrogen entities in oxidized LaTiO2N perovskite[END_REF][START_REF] Rachel | Tantalum and niobium perovskite oxynitrides : Synthesis and analysis of the thermal behavior[END_REF][START_REF] Ebbinghaus | Perovskiterelated oxynitrides : recent developments in synthesis, characterisation and investigations of physical properties[END_REF][START_REF] Clarke | Structure of Zr2ON2 by Neutron Powder Diffraction : The Absence of Nitride-Oxide Ordering[END_REF][START_REF] Kumar | ): Synthesis, structure and properties[END_REF] on partially oxidized oxynitride powders. Indeed, there is a variety of studies which have examined the thermal stability of oxynitride powders, mainly by thermogravimetric analysis (TGA). Many oxynitrides with a large range of compositions and structures lead to such a dinitrogen-containing phase during the first stage of their oxidation. Specific examples, with their related structure type, are : perovskites (SrTaO2N [START_REF] Rachel | Tantalum and niobium perovskite oxynitrides : Synthesis and analysis of the thermal behavior[END_REF][START_REF] Aguiar | The vast colour spectrum of ternary metal oxynitride pigments[END_REF], LaTiO2N [START_REF] Gendre | Raman scattering investigations of dinitrogen entities in oxidized LaTiO2N perovskite[END_REF], BaTaO2N [START_REF] Gendre | A new class of inorganic compounds containing dinitrogenmetal bounds[END_REF][START_REF] Aguiar | The vast colour spectrum of ternary metal oxynitride pigments[END_REF], SrNbO2N [START_REF] Rachel | Tantalum and niobium perovskite oxynitrides : Synthesis and analysis of the thermal behavior[END_REF][START_REF] Ebbinghaus | Perovskiterelated oxynitrides : recent developments in synthesis, characterisation and investigations of physical properties[END_REF][START_REF] Aguiar | The vast colour spectrum of ternary metal oxynitride pigments[END_REF], LaFeO3-xNx [START_REF] Sierra Gallego | A novel LaFeO3-xNx oxynitride : Synthesis and characterization[END_REF], LaNbON2 [START_REF] Kumar | ): Synthesis, structure and properties[END_REF], SrTi1-xNbx(O,N)3 [START_REF] Maegli | Perovskite-type SrTi1-xNbx(O,N)3 compounds: Synthesis, crystal structure and optical properties[END_REF]), rock salt type (NbOxNy [START_REF] Gendre | A new class of inorganic compounds containing dinitrogenmetal bounds[END_REF], TiOxNy [START_REF] Gendre | A new class of inorganic compounds containing dinitrogenmetal bounds[END_REF], CrOxNy [START_REF] Gendre | A new class of inorganic compounds containing dinitrogenmetal bounds[END_REF]), cuspidine-type (Y4Si2O7N2 [START_REF] Van Krevel | Oxidation resistance of Ln-Si-O-N powders[END_REF]), Ruddlesden-Popper type (Sr2NbO3N [START_REF] Tobias | Synthesis and crystal structure of novel Ruddlesden-Popper strontium niobium oxynitrides[END_REF]), Fluorite type (bixbyite Zr2ON2 [START_REF] Clarke | Structure of Zr2ON2 by Neutron Powder Diffraction : The Absence of Nitride-Oxide Ordering[END_REF]) or Spinel (AlOxNy [START_REF] Goursat | Contribution à l'étude du système Al/0/N II: rétention d'azote dans les produits d'oxydation de l'oxynitrure d'aluminium γ[END_REF]). While monitoring by TGA the mass variation related to the oxidation of the starting oxynitride (under air or oxygencontaining atmosphere), one can observe, between the oxynitride and the oxide mass levels a so-called intermediate phase [START_REF] Gendre | Raman scattering investigations of dinitrogen entities in oxidized LaTiO2N perovskite[END_REF][START_REF] Rachel | Tantalum and niobium perovskite oxynitrides : Synthesis and analysis of the thermal behavior[END_REF]. This phase is related to important dinitrogen retention since, depending on the oxynitride chemical composition involved, the N2 amount, trapped in the oxide lattice, can reach as much as 70% of the initial nitrogen. The Raman signature of this dinitrogen molecule in weak interaction with the oxide lattice has been systematically detected close to 2328 cm -1 [START_REF] Gendre | Raman scattering investigations of dinitrogen entities in oxidized LaTiO2N perovskite[END_REF][START_REF] Rachel | Tantalum and niobium perovskite oxynitrides : Synthesis and analysis of the thermal behavior[END_REF][START_REF] Ebbinghaus | Perovskiterelated oxynitrides : recent developments in synthesis, characterisation and investigations of physical properties[END_REF][START_REF] Clarke | Structure of Zr2ON2 by Neutron Powder Diffraction : The Absence of Nitride-Oxide Ordering[END_REF][START_REF] Kumar | ): Synthesis, structure and properties[END_REF][START_REF] Aguiar | The vast colour spectrum of ternary metal oxynitride pigments[END_REF][START_REF] Tessier | Thermochemistry of a New Class of Materials Containing Dinitrogen Pairs in an Oxide Matrix[END_REF]. The presence of N2 molecules in large quantities leads to a strong amorphization of the original structure (see [START_REF] Gendre | A new class of inorganic compounds containing dinitrogenmetal bounds[END_REF] for example). Furthermore, several XPS studies of the controlled oxidation of large range of oxynitrides have confirmed the conversion of the nitride ions (N1s BE = 397 eV) to nitrogen species with a higher oxidation state (N1s BE = 403 eV) consistent with the presence of dinitrogen molecules weakly bound to the oxide lattice [START_REF] Gendre | A new class of inorganic compounds containing dinitrogenmetal bounds[END_REF][START_REF] Kumar | ): Synthesis, structure and properties[END_REF].

In our case, SLTTON thin films annealed in the range [550-650°C] under air present an optical oxide signature (Eg > 4.1 eV), clearly showing that the 2p states of nitrogen are no longer occupying the top of the valence band as regularly observed when N 3-substitutes for O 2- within the anionic network of the crystal structure of (oxy)nitrides. This is in agreement with molecular N2 trapped and weakly bonded within an oxide perovskite-type matrix as suggested by a nitrogen retention detected by EDS, a strong structural amorphization seen in XRD analysis and an intense Raman signal at 2328 cm -1 . Moreover, the c-axis cell parameter value of the annealed films, extracted from the XRD patterns, is also intermediate to those of the "asdeposited" oxynitride films and of the pristine powder.

Thermally oxidized at a low temperature ranging from 550°C to 650°C, SLTTON film can thus be described as perovskite-type intermediate phases with a nitrogen amount (≈ 9 at.%) compatible with a SrTaO3.5(N2)0.25 typical composition (at.%N = 8.3) consistent with the TGA analysis previously conducted on SrTaO2N powder [START_REF] Rachel | Tantalum and niobium perovskite oxynitrides : Synthesis and analysis of the thermal behavior[END_REF][START_REF] Aguiar | The vast colour spectrum of ternary metal oxynitride pigments[END_REF].

Dielectric characterization

The purpose of the present study was to achieve a stoichiometric composition for STLTO oxide films and to characterize the dielectric properties of samples with the aim to emphasize high tunabilities of their permittivity as what was pointed out for STLTO dense ceramics [START_REF] Marlec | Ferroelectricity and high tunability in novel strontium and tantalum based layered perovskite materials[END_REF][START_REF] Haydoura | Dielectric characterization in low and high frequencies of new ferroelectric strontium and tantalum based perovskite ceramics[END_REF].

Annealings under air of stoichiometric oxynitride films has led to original film samples corresponding to intermediate phases between pure oxide and pure oxynitride, which still contain nitrogen in the form of N≡N pairs in an oxide matrix. It is then of interest to characterize their dielectric properties.

First of all, let's present in Figure 9 the evolution of the permittivity as a function of a DC electric field of the "STLTO as-deposited" film. At E = 0 and 10 kHz, this TTB-oxide film presents a permittivity value ε' = 139 with dielectric loss tanθ = 3.10-3. Moreover, these characteristics vary with the DC bias, with a tunability equal to T = 9 % at 310 kV/cm, 10 kHz and room temperature. Our TTB-STLTO-film is tunable but the present tunability value is far lower from the one measured on the perovskite-STLTO-ceramic with the composition x = 1.65 (T ≈ 55 % at 30 kV/cm [START_REF] Haydoura | Dielectric characterization in low and high frequencies of new ferroelectric strontium and tantalum based perovskite ceramics[END_REF]). Nevertheless, we note that the dielectric losses of this TTB oxide film are very low (tanθ = 3 10-3 at 310 kV/cm) which may be interesting in order to reduce the loss of insertion of a tunable antenna [START_REF] Nguyen | Miniaturized and reconfigurable notch antenna based on a BST ferroelectric thin film[END_REF] based on this TTB material, for instance.

The oxynitride "STLTON as-deposited" sample has the following dielectric characteristics : at E = 0 and 10 kHz, ε '~ 2350 with very high losses tanθ ~ 3.5. These high values may be explained by the slight nitrogen over-stoechiometry evidenced by the EDS measurement (Nat% = 24.5, Table 3) which would cause the formation of polarizable defects in the structure of the materials leading to a high permittivity and high losses. Moreover, no electric field can be applied to this film as a high leakage current is observed as soon as the field is applied. Its permittivity meets those previously reported on other oxynitride films, SrTaO2N [START_REF] Oka | Possible ferroelectricity in perovskite oxynitride SrTaO2N epitaxial thin films[END_REF] and LaTiO2N [START_REF] Ziani | Structural and dielectric properties of oxynitride perovskite LaTiOxNy thin films[END_REF] films for example. For the STLTON annealed films, dielectric measurements were performed on the STLTON-25 film annealed at TA = 600°C. Figure 10 presents the evolution as a function of a static electric field of its permittivity and dielectric loss tangent. Compared to the "as-deposited" STLTON sample, we noticed a notable evolution of its dielectric characteristics : at E = 0 and 10 kHz, the permittivity remains high (ε '~ 2200) but the losses have fallen sharply to tanθ ~ 0.07. Moreover, we observe a variation of its permittivity with the DC bias, from ε '= 2200 to ε' = 1620, which corresponds to a tunability T = 26 % at 30 kV/cm. The associated dielectric loss tangent remain relatively constant, from tanθ ~ 0.07 to tanθ ~ 0.18 at 30 kV/cm. Beyond, the film no longer holds tension and losses rise away. In other words, the dielectric properties of the annealed STLTON films are intermediate as well between those of the TTB as-deposited oxide films (tunability and low losses) and those of the oxynitride films (high permittivity, no stability upon electric field). Looking for stoichiometric STLTO oxide films, we have obtained original intermediate phases which present very interesting dielectric characteristics with a high tunability (26 %) at a low bias (30 kV/cm). This tunability is much more higher than that obtained on the TTB STLTO film at the same bias (T = 0.01%). It is almost comparable to the tunability (T = 55 % at 30 kV/cm) obtained on a x = 1.65 STLTO ceramic [START_REF] Haydoura | Dielectric characterization in low and high frequencies of new ferroelectric strontium and tantalum based perovskite ceramics[END_REF] and so can be interesting from the moment the dielectric losses of the intermediate phase are lowered, for example by a second annealing during long times (several ten hours) at moderate temperatures (350 -450°C).

Conclusion

The objective of the present work was to produce as thin films the x = 1.65 composition of the perovskite (Sr2Ta2O7)100-x(La2Ti2O7)x (STLTO) solid solution, exhibiting, as ceramics, optimum dielectric and ferroelectric properties. Deposition of thin films by rf magnetron sputtering of the oxide STLTO (x = 1.65) target under dioxygen reactive gas produces systematically tetragonal tungsten bronze (TTB) films with Sr/Ta close to 0.55, thus denoting a high strontium deficiency in samples. The stoichiometric ratio can be achieved but in oxynitride STLTON films deposited using the same target under dinitrogen reactive gas. The post-annealing under air of the oxynitride films in the temperature range [450-1000°C] lead to transparent films still containing a certain amount of nitrogen. Raman experiments highlight the presence of nitrogen-nitrogen pairs embedded in a perovskite oxide matrix, thus identifying these annealed oxynitride films as intermediate phases already evidenced in powders. Dielectric measurements on a STLTON film annealed at 600°C during 4 h show a significant reduction of the dielectric losses to some 10-2, with a permittivity still at a high level close to 2000 (RT, 10 kHz). The tunability of this original compound is at a high level with a tunability value of 26 % at 30 kV/cm much more higher than that obtained on the TTB film at the same bias (T = 0.01%). Table 1: List of STLTO films deposited by rf magnetron sputtering with different percentages of reactive dioxygen gas, along with the cationic composition (ratio Sr/Ta), the band gap (Eg) and the thickness of samples.

Table 2: List of STLTON films deposited by rf magnetron sputtering with different percentages of reactive dinitrogen gas, along with the cationic composition (ratio Sr/Ta) and the band gap (Eg).

Figure 1 .

 1 Figure 1. θ-2θ XRD diagram of the (Sr2Ta2O7)98.35(La2Ti2O7)1.65 target (hereafter named as "Pristine STLTO powder") used for the deposition of thin films by reactive radio-frequency magnetron sputtering (indexation according to Sr2Ta2O7).

Figure 2 .

 2 Figure 2. (a) UV-visible transmittance spectra and (b) curves for the determination of the band gap values of the "STLTO as-deposited" and "STLTON as-deposited" films deposited by reactive rf magnetron sputtering with, respectively, %O2 = 25 and %N2 = 25.

Figure 3 .

 3 Figure 3. Evolution as a function of the reactive gas (O2 or N2) percentage in the sputtering plasma of the Sr/Ta ratio of STLTO and STLTON films deposited by reactive rf magnetron sputtering.

Figure 4 .Figure 5 .

 45 Figure 4. θ-2θ XRD diagrams of the STLTO and STLTON "as-deposited" films on MgO substrates by reactive rf magnetron sputtering (indexation according to Sr2,83Ta5O15 for STLTO and to SrTaO2N for STLTON)

Figure 6 :

 6 Figure 6: (a) Complete θ-2θ XRD diagrams of STLTON thin films annealed under air during 4 h at different annealing temperatures. Comparison is made to that of STLTON and STLTO as-deposited films and pristine STLTO powder (b) details between 40 and 50° (the orange and blue dotted lines are a visual cue for the oxynitride and oxide positions, respectively, while the annealed films are marked by a grey line ; * sample holder).

Figure 7 .

 7 Figure 7. Evolution as a function of the annealing temperature (TA) of the cell parameter c of annealed-STLTON thin films. Their characteristics are compared to that of STLTON asdeposited film and STLTO pristine powder.

Figure 8 .

 8 Figure 8. Raman spectra in the [2300-2350]cm -1 range of the bare MgO substrate, the asdeposited STLTON-25 oxynitride film and the STLTON-25 film annealed under air at 600°C during 4 h.

Figure 9 .

 9 Figure 9. Evolution as a function of a static electric field of the permittivity (ε') and the dielectric loss tangent (tanθ) of: (a) the oxide STLTO "as-deposited".

Figure 10 .

 10 Figure 10. Evolution as a function of a static electric field of the permittivity (ε') and the dielectric loss tangent (tanθ) of the STLTON film annealed at TA = 600°C.

Table 3 :

 3 List of samples of interest for the annealing of STLTON film, along with the cationic composition (ratio Sr/Ta), the nitrogen content and the anionic composition (O/N), determined by EDS, and the band-gap Eg measured by UV-Visible Transmittance.

Acknowledgements

This work was supported by the European Union through the European Regional Development Fund (ERDF) and by the Ministry of Higher Education and Research, Brittany Région and Côtes d'Armor Département through the CPER Projects MATECOM and SOPHIE-STICC. This publication work was also supported by the Conseil Départemental des Côtes d'Armor, Saint Brieuc Armor Agglomération and the Syndicat de Gestion du Pole Universitaire de Saint Brieuc (France). Authors also thank the SIR platform of ScanMAT at University of Rennes 1 for technical assistance for the Raman measurements.


J Léchelle

S Martin

K Saikouk

R Boyer

K Saleh

M Guessasma

J Fortin

Densification rate in a granular mechanical sintering model based on flux balance

Keywords: sintering, model, powder, morphology, chemical potential I

Properties of a solid state sintering model developed for the study of nuclear fuel sintering are studied (chemical potential at surfaces expression and along a grain boundary). They generalize classical sintering laws in symmetrical cases with a constant grain boundary mean curvature (rounded or plane grain boundary). The shrinkage rate is discussed for classical analytical models with their geometrical assumptions, and their tacit assumptions are emphasized. With our model, morphology of grains resulting from their fabrication route can be taken into account.

Flux balance along the triple line gives an insight to sinterability of powders due to their morphology.

Introduction

Sinterability of powders for nuclear fuel pellets is of major importance for fuel fabrication. This property does not only depend on the chemical composition of the material (Pu or Am contents of the MOX material) and on the thermodynamic conditions of sintering but also on the morphology of the powder -both on the crystallite scale and on that of aggregates [START_REF] Guillet | Nuclear Fuels[END_REF][START_REF] Mihaila | MSC-DFEM Model for the sintering of ceramic nuclear Fuels[END_REF]. Models have shown attempts to tackle the influence of morphology on sintering [START_REF] Eggersdorfer | Aggregate morphology evolution by sintering: Number and diameter of primary particles[END_REF][START_REF] Wakai | Tensor virial equation of evolving surfaces in sintering of aggregates of particles by diffusion[END_REF].

The study presented hereafter deals with the effect of crystallite morphology upon the shrinkage rate of two crystallites in contact. Such a law can be used for instance in macroscopic models based on the discrete element method [START_REF] Yan | Effect of size and homogeneity of rigid inclusions on the sintering of composites[END_REF] or based on non-smooth contact dynamics (Martin, Contribution à la modélisation du frittage à l'état solide, 2014; Martin, Guessasma, Léchelle, Fortin, Saleh, & Adenot, 2014) to get an insight upon its macroscopic consequences on the macroscopic shrinkage rate. In any case this study gives a hint on the way shrinkage may be influenced by the morphology of crystallites [START_REF] Nkou Bouala | Preparation and characterisation of uranium oxides with spherical shapes and hierarchical structures[END_REF].

Literature [START_REF] Coblenz | Initial stage solid state sintering models. A critical analysis and assessment[END_REF][START_REF] Parhami | A model for the sintering and coarsening of rows of spherical particles[END_REF][START_REF] Delannay | Experimental validation of a new model for the initial stage of sintering of single phase systems[END_REF][START_REF] Bouvard | Deformation of Interparticle Necks by Diffusion-Controlled Creep[END_REF] gives analytical laws or numerical treatment of models to account for the shrinkage rate. These models are generally based on the assumption that particles (crystallites) are spherical and that the initial grain boundary is a plane. In that case two symmetry elements make the problem simpler, they are the rotation axis and the symmetry plane perpendicular to this axis. In order for the model to make it possible to predict the evolution of curved grain boundaries, for instance in the third stage of sintering, where neighboring grains may coalesce and lead to a non-regularly curved grain boundary, a more general approach is required.

A model on a sub-granular scale was proposed. Its main specific feature is the way chemical potential of atoms is computed within this framework. The chemical potential definition is valid both at interfaces of crystallites and in the bulk of grains and makes it possible to take into account both bulk, surface and grain boundary diffusion. The chemical potential term can include other contributions such as the electric field contribution [START_REF] Munir | The effect of electric field and pressure on the synthesis and consolidation of materials: A review of the spark plasma sintering method[END_REF][START_REF] Olevsky | Constitutive modeling of spark-plasma sintering of conductive materials[END_REF] and mechanical boundary conditions may match those of Spark Plasma Sintering (SPS) in which sintering is pressure assisted [START_REF] Mourad | Advances in the numerical treatment of grain-boundary migration: Coupling with mass transport and mechanics[END_REF].

In the framework of the modelling of sintering on a sub-granular scale, a local densification law has been derived in the case of two grains. Predictions of the shrinkage rate can be obtained with the classical Herring and Gibbs-Thomson chemical potentials (i.e. with an interface defined chemical potential), or with the chemical potential we have proposed which is defined everywhere both in the bulk of grains or at inerfaces. Tacit assumptions of classical models are emphasized. Consequences upon morphological effects on the shrinkage rate are analyzed on the crystallite scale.

II. Model description

Two crystallites in contact are considered as schemed in Figure 1. Each possesses a free surface Γ 1 (resp. Γ 2 ) and they share a grain boundary (GB) denoted Γ 1/2 the thickness of which is δ GB .

If σ is the stress tensor, boundary conditions used to compute the displacement field are of von Neumann type at free surfaces Γ 1 and Γ 2 due to Laplace law. In the framework of Herring approximation [START_REF] Herring | The physics of powder metallurgy : A symposium held at Bayside[END_REF] they read:

. = - -2 + + (1)
with p gas the pressure of the outer gas, n 1 (resp. n 2 ) the outer normal, γ SV the solid/vapor surface energy, κ m the local mean solid/vapor curvature defined as ! + " and R 1 and R 2 are the local principal curvature radii. When surface energy does not vary with outer surface local direction the latter expression simplifies into Gibbs-Thomson's law:

. = - -#2 $ (2)
For Γ 1/2 grain boundary the boundary condition reads:

. = . -2 %& %& (3)
corresponding to a finite jump in stress across the interface (i.e. over a δ GB wide area).

For materials with a surface energy varying with orientation, the chemical potential of atoms and vacancies in the vicinity of an interface, μ is given by [START_REF] Philibert | Diffusion et transport de matière dans les solides[END_REF]:

( = ( ) -( = ( *+,- . + / 0 + 1 + + (4)
where A denotes an atom and V a vacancy, and Ω the atomic (resp. molar) volume, which reads more simply in the isotropic case :

Ω 1 Ω 2 Γ 2 Γ 1 Γ 1/2 n 1 GB n 1 n 2 ( = ( ) -( = ( *+,- . + / 0 + 1 (5)
Shrinkage rate is linked to the normal velocity of interfaces, hence to flows of matter. These latter depend on the chemical potential accordingly to Onsager law [START_REF] Philibert | Diffusion et transport de matière dans les solides[END_REF]:

2 ) = -L )) ∇ ! 5 6 " (6)
with T temperature and L AA Onsager's coefficient. In our solid state sintering model [START_REF] Ajdour | Développement d'un code de calcul pour la simulation du frittage en phase solide[END_REF][START_REF] Martin | Modélisation phénoménologique granulaire du frittage à une échelle représentative de la pastille de matériau[END_REF] the chemical potential is defined at any place in the grains (bulk or interfaces) by: ( = ( *+,- .

-7 8

9:

-/ : <

with ε the strain tensor. Our materials show an elastic limit thrice higher than the stress due to surface curvature at any temperature along the thermal cycle [START_REF] Fossati | Contribution à l'étude des propriétés mécaniques du combustible nucléaire : modélisation atomistique de la déformation du dioxyde d'uranium[END_REF]) so that free sintering can be modeled with an elastic constitutive law:

< = s: σ (8)
with s the compliance matrix. Its terms are small enough so that the density of elastic energy can be regarded as a small second order term in σ. If stress is hydrostatic at boundaries σ is close to ? = -p -0 + 1 (A ∈ #1,2,3$ with Voïgt notations) and meets the expression of Gibbs-Thomson of the chemical potential. The approach differs from Wakai's [START_REF] Wakai | Tensor virial equation of evolving surfaces in sintering of aggregates of particles by diffusion[END_REF] by the fact that the stress field is computed by solving Navier-Lamé equations with Laplace boundary conditions and non-translation and non-rotation as algebraic conditions.

III. Resultst and Discussion : shrinkage rate

The advantage of our expression also compared with other mechanical models [START_REF] Bruchon | Finite element simulation of mass transport during sintering of a granular packing. part I. surface and lattice diffusions[END_REF] is the differentiability of the chemical potential within a grain (between the bulk and the interfaces) so that both bulk, surface and grain boundary diffusion phenomena can be described with the same chemical potential.

For any surface S belonging to a free interface Γ i , Ficks's second law gives the movements of the interfaces [START_REF] Léchelle | A sub-granular scale model for solid state free sintering: results on the evolution of two grains[END_REF] :

∬ G ? H . ? IJ = Ω ∬ !L . ? + IAM NL O" IJ (9)
With V int the interface velocity, div S the surface divergence operator and J s the surface flow. The mass of quasiincompressible matter produced along the grain boundary by grain 1 per time unit and transferred towards direction of grain 2 through a unit surface of the grain boundary is [START_REF] Martin | Modélisation phénoménologique granulaire du frittage à une échelle représentative de la pastille de matériau[END_REF]: The expression of the velocity of the interface in the case of Gibbs-Thomson's law can be written as follows:

G P = -/ !L %& ⊥ . %& " -/ IAM NL %& Q O (10) L %& ⊥ ,
M = / !L %& ⊥ + L %& ⊥ " . %& - R ST ST U ST V -6 ∆ (11)
with δ GB the grain boundary thickness. In the case of our model bulk diffusion also depends on stress, so that:

L %& X ⊥ = U ST V -6 7 ! 8 ∑ ? 8 ?Q + ∑ ∑ ∇ -, Z ,Q Z -Q " (12)
Figure 2 : definition of volume (or bulk) and grain boundary fluxes Relation ( 11) is valid even if grain boundary curvature is not constant and gives a local value of the interface velocity along the grain boundary.

n 1 GB J = GB J bulk J GB J ⊥

GB

For a plane grain boundary ∆ = ∆ (classical Laplace's operator). If in addition grains are symmetrical with respect to the grain boundary, the symmetry of the problem leads to v n =0 so that: ∆ μ = 0, and µ is a second order polynomial of the distance from the grain boundary center. In that case the flux is nul in the center on symmetry grounds and linear with the distance from the grain boundary, its divergence is a constant and can be estimated from its difference between the triple line and the center of the grain boundary. Thus classical results are found back.

If S is taken as the whole grain boundary, Kirchhoff analogue for matter flow at triple point T reads:

L . H = -L %& . H ST (13)
with H (resp. H , H ST ) the outer normal of the triple line for a surface element belonging to surface Γ 1 (resp. Γ 2 , Γ GB ) which is tangent to Γ 1 (resp. Γ 2 , Γ GB ) (see Figure 3). So that: curvature grain boundary with an absence of diffusion perpendicular to the grain boundary (L %& ⊥ =0) the shrinkage rate would be zero: ℎ P = 0. The latter conclusions are changed when grains are no more considered as rigid, but for instance elastic at a given (quasi-static time step) during the sintering process since in that case the chemical potential in the bulk of grains is no more constant (μ *+,-= b ≠ μ . ).

G P = -/ ∬ L %& ⊥ IJ ] -/ ∮ L %& Q I_ `= -/ ∬ L %& ⊥ IJ ] + / ∮ L Q I_ ` (14

IV. Conclusion

The compatibility of a solid state sintering model under development presented in Ajdour's and Martin's works [START_REF] Ajdour | Développement d'un code de calcul pour la simulation du frittage en phase solide[END_REF][START_REF] Martin | Modélisation phénoménologique granulaire du frittage à une échelle représentative de la pastille de matériau[END_REF], with other models with assumptions on geometry was shown. Its compatibility with Gibbs-Thomson's law was also shown.

Predictions of the shrinkage rate in the symmetrical case show that this rate only depends on the geometry of crystallites at their surface in the vicinity of the triple line, i.e. to the morphology of crystallites resulting from their fabrication route [START_REF] Nkou Bouala | Preparation and characterisation of uranium oxides with spherical shapes and hierarchical structures[END_REF]. In a more general case (absence of symmetry of the grain boundary)

our model can be used to predict shrinkage rates.

Figure 1 :

 1 Figure 1: schematics of a contact between two sintering grains -notations

  Figure 2 . Their respective diffusion coefficients are those obtained by the study of grain growth and by tracer

)

  And the shrinkage rate averaged on the grain boundary is: ℎ = N G P + G P O. If diffusion perpendicular to the grain boundary can be neglected the shrinkage rate only depends on the change in mean curvature at the surface of crystallites in the vicinity of the triple line, i.e. on the morphology of crystallites, or indirectly on the fabrication route of the powder. The higher the changes in curvature radii are, the fastest the shrinkage should begin.

Figure 3 :

 3 Figure 3: Kirchhoff's analogue of current law: geometry of discretized surfaces in the vicinity of a triple point

Acknowledgments

Authors are grateful to the Gen IV project "Atelier de Fabrication des Coeurs (AFCOE)" for its support.