N Schmitt

S Colas

N Saurel

F Bassignot

B Vuillemin

J E Groetz

Detector-electrode for alpha spectrometry in water

Keywords: Alpha particle spectrometry, CVD diamond, Electrode, Monte-Carlo simulation, Thermocompression bonding, Silicon detector

Introduction

In the field of nuclear measurement, alpha particle spectrometry is used to identify radionuclides, mainly actinides, and to quantify them through their activity. It is carried out usually by using two different methods which require several chemical processes for the separation of radionuclides, in order to generate a radioactive source. A common method involves deposition of radionuclides of interest on a disc, whose the identification and quantification are measured in a vacuum chamber. The radioactive source should be as thin as possible in order to prevent energy loss and straggling by self-absorption and to identify alpha-emitting radionuclides by energy discrimination in the energy spectrum. This identification is performed through the centroid of peaks and the area beneath the peaks corresponds to the total activity of radionuclides. As a second method, alpha counting could be performed with organic liquid scintillators, with a high counting efficiency [START_REF] Knoll | Radiation Detection and Measurement[END_REF].

In the family of semiconductor detectors, the passivated planar detectors are the most used for alpha activity monitoring and radionuclides identification in the environment.

The PIPS ® detectors (Passivated Ion implant Planar Silicon) used in alpha spectrometry can not withstand an aggressive chemical and acid solution such as in nuclear effluents, making these detectors unappropriated for a direct measurement in situ [START_REF] Amoudry | Determination of the 239 Pu/ 240 Pu isotopic ratio by high resolution alpha spectrometry[END_REF], which would require to overlay the PIPS ® with a protective material [START_REF] Garcia | Alpha spectroscopy for in-situ liquid radioisotope measurements[END_REF]. As a potential candidate, diamond materials exhibit radiation hardness and chemical inertness properties. These properties made it possible for polycrystalline diamond to be successfully used as an immersed detector of alpha particles in a concentrated plutonium solution in nitric acid (2 mol l -1 ), with a 239 Pu concentration ranging from 10 to 100 mg l -1 [START_REF] Kozlov | Usage of diamond detectors as immersed alpha-counters[END_REF]. In this configuration, the path length of the alpha track before reaching the detector corresponds to the thickness of the liquid crossed by alpha particles, limited by their range in water, i.e. a few tens of micrometer. This technique can only measure active material close to the detector. In particular, it is suitable for real-time extremely high activity levels but not for monitoring low activities in water.

After this early success, diamond detector was improved by the use of synthetic diamond as an active alpha-detector [START_REF] Souw | Response of CVD diamond detectors to alpha radiation[END_REF][START_REF] Bergonzo | Corrosion hard CVD diamond alpha particle detectors for nuclear liquid source monitoring[END_REF][START_REF] Schirru | Thin single crystal diamond detectors for alpha particle detection[END_REF][START_REF] Dueñas | Diamond detector for alpha-particle spectrometry[END_REF][START_REF] Zhang | CVD diamond film detectors for alpha particles with a new electrode structure of reduced graphene oxide/Au[END_REF]. High quality diamond film can be produced by chemical vapor deposition (CVD) from a carbon precursor such as CH 4 or CO 2 and hydrogen. The carbon species and hydrogen must be activated since at low pressure, graphite is thermodynamically stable, and without activation, only graphite would be formed. Activation can be obtained at high temperature with a hot filament heated up to 2600 K, then atomic hydrogen is formed and the carbon species become activated in the vicinity of the hot metal. This method made possible the formation of polycrystalline CVD diamond on large areas. Nucleation is a critical phase in the diamond deposition process due to its strong influence on film roughness and pinhole formation.

The substrate surface must be treated before deposition to achieve a high nuclei density. As the temperature of the process is around 800-900 and high nuclei density is easier to achieve on carbide-forming material, diamond films are generally deposited on silicon-based material (Si, SiC, Si 3 N 4 ) or refractory metals and alloys [START_REF] Neocoat | Diamond coating and CVD technologies[END_REF].

In order to perform direct alpha spectrometry in a liquid sample, a preliminary work suggested combining the detection properties of a PIPS ® detector with the diamond shielding and electrode properties to develop an hybrid Si-diamond detector electrode. This type of detector has been manufactured by de Sanoit et al. with a process of boron doped diamond chemical vapor deposition on the surface of a commercial PIPS ® detector [START_REF] De Sanoit | Détecteur alpha électrochimique assité pour la mesure nucléaire en milieu liquide et procédé associé[END_REF][START_REF] De Sanoit | Design of an electrochemically assisted radiation sensor for alpha-spectrometry of actinides traces in water[END_REF]. The process consists in depositing actinides using an electrochemical technique directly onto the surface of the boron doped entrance window of the alpha detector, acting as a cathode [START_REF] Tran | Optimization of Actinides Trace Precipitation on Diamond/Si PIN Sensor for Alpha-Spectrometry in Aqueous Solution[END_REF][START_REF] De Sanoit | Detection method using an electrochemically-assisted alpha detector for nuclear measurement in liquid medium[END_REF]. Then, the alpha activity of the deposited actinides could be measured by the PIPS ® detector.

However, the high temperature required in the diamond CVD process on silicon substrates could significantly reduce the detection properties of the PIPS ® diode. The diffusion of implanted ions in silicon increases the dead zone of the diode, which could impact on the path of alpha particles before reaching the active part of the detector. In order to prevent this major drawback, it is imperative to avoid thermal processes and another method should be investigated.

The use of a metal layer such gold or indium as a bonding layer between two materials could be an attractive alternative [START_REF] Bassignot | Acoustic resonator based on periodically poled transducers: Fabrication and characterization[END_REF]. The application of such an innovative process will be a real breakthrough to the fabrication of a detector electrode. For this aim, the impact of the different layers and the feasibility of bonding a diamond electrode on a silicon detector has been studied. Monte-Carlo simulation has been used to design the new silicon detector by investigating the influence of the shielding, bonding, insulating and source layers on the detection properties over a range of alpha particle energies from 4 to 5.5 MeV. Afterwards, a preliminary feasibility study has been realised, followed by the development of the fabrication process using boron doped diamond electrode and silicon detector. In order to carry out in situ direct measurements in effluents, the surface of the detector should be in contact with the liquid sample containing the radionuclides. In this configuration, an actinide electroprecipitation can be realised to form a radioactive source on the detector surface. Such a method involves the use of a potential gradient between two electrodes to materialise an hydroxide layer on the cathode surface, which is the required condition for the actinide precipitation (Fig. 1).

Anode Cathode

ΔpH ΔV In aqueous solution, the range of potential is limited by the electrochemical water decomposition (through the system H 2 /H + on the reduction side and the system H 2 O/O 2 on the oxidation side). Performing the electrochemical reduction of dissolved oxygen in water (or water reduction) locally modifies the pH near the surface of the working electrode, that results in the formation of a base layer (pH 10-11 for the dissolved oxygen reduction, pH 12-13 for the water reduction). Increasing the pH of an aqueous solution containing actinide ions changes the structure of these ions: protons are expelled from the internal hydration sphere. In this way, the actinide ions accumulate hydroxyl ions (OH -) in the internal sphere and form monohydroxo or polynuclear complexes. As final products, solid hydroxides precipitate on the cathode surface if the solubility product is exceeded [START_REF] De Sanoit | Design of an electrochemically assisted radiation sensor for alpha-spectrometry of actinides traces in water[END_REF][START_REF] Tran | Optimization of Actinides Trace Precipitation on Diamond/Si PIN Sensor for Alpha-Spectrometry in Aqueous Solution[END_REF][START_REF] De Sanoit | Detection method using an electrochemically-assisted alpha detector for nuclear measurement in liquid medium[END_REF]. As a preliminary study, such a process on a diamond electrode has been performed in a sodium sulfate aqueous solution (0.3 mol l -1 , pH= 4) for a thorium concentration of 10 -3 mol l -1 . The experiment was carried out inside a laminar mixing cell of 300 ml, using chronoamperometry method with an applied voltage of -1 V during 20 hours. After drying, a yellow deposition was observed on the surface of the diamond It should be noted that this deposition was obtained after stopping the electroprecipitation and evaporating the solution. So, the exact composition of the actinide gel formed at the electrode surface in the solution is not very well known, together with its thickness and density. Therefore, the radioactive source was supposed homogeneous, with a density similar to that of water.

Hydroxide layer

Detector

The detector investigated has been approximated by a slab of pure silicon with a 2.54-cm diameter and 300-µm thickness with a density of 2.33 g cm -3 , on top of which a diamond electrode of the same area is bonded with a Ti-Au layer. This bonding layer is composed of: 100 nm of gold with a density of 19.30 g cm -3 , 50 nm of titanium with a density of 4.51 g cm -3 . The use of Ti in the bonding layer facilitates Au adhesion on Si and SiO 2 .

In the assembly process, this bonding layer is deposited on both parts, i.e. on the PIPS ® detector and on the diamond electrode.

As for the diamond electrode, it is made up of two different layers: the electrical insulating layer : silicon oxide SiO 2 with 500-nm thick with a density of 2.65 g cm -3 , and a silicon nitride Si 3 N 4 with 200-nm thick with a density of 3.44 g cm -3 , used in the diamond chemical vapor deposition process to strengthen the adhesion of the diamond layer on SiO 2 . the shielding layer is a polycrystalline diamond electrode with a density of 3.52 g cm -3 and doped with boron at around 8000 ppm, with an optimal thickness which was investigated by Monte-Carlo simulation.

Without information on the energy resolution, the simulated detector is supposed ideal.

Monte-Carlo simulation

The MCNP6 (Monte-Carlo N-Particle) code [START_REF]Los Alamos National Laboratory[END_REF] was used to model the detector with the different added layers and a radioactive water source, with a density of 1 g cm -3 , in accordance with section 2. containing diluted 241 Am (5.49 MeV) for a mono energetic source, as well as 241 Am, 239 Pu (5.16 MeV) and 235 U (4.40 MeV) for a multi energetic source. Alpha particles were generated randomly throughout the volume of the simulated source, with an energy cut-off lowered to 1 keV. The observable or estimator, called tally in MCNP6, used for modelling the detector response is the F8 tally, which provides the pulse height created by alpha particles in the detector. Each run used 10 6 alpha particle as histories (one history is the complete description for one particle of its transport and interactions through matter) and the uncertainties on the number of counts were about 1.1%.

Energy loss for alpha particles is directly linked to the stopping power in every material (Fig. 4). Monte-Carlo simulation enables to take into account the energy and range straggling, behind the spread of energies after the monoenergetic alpha particles pass through a given thickness of material slab [START_REF] Knoll | Radiation Detection and Measurement[END_REF].

Simulation results

Influence of the diamond layer thickness

The constraints for the thickness of the diamond layer concern mainly the limitation of the particle energy attenuation, the modification of peak shape (width and height) and the conservation of the diamond properties as electrode. The thickness for the diamond layer investigated ranges from 0.1 to 1 µm, corresponding to the minimal deposited thickness achievable by the industrial partner, NeoCoat (La Chaux-de-Fonds, Switzerland), and an arbitrary maximum source thickness until total attenuation of alpha particles by the diamond layer. As Fig. 5 shows, the peak shape does not change from 0.1 to 1 µm, but the energy of the incident alpha particle shifts linearly to the lower energies and the height of the peak decreases. During its path in diamond, the energy of the incident alpha particle is attenuated. The thicker the diamond, the more the particle loses energy during its crossing. Increasing the thickness of the diamond layer broadens the peak. For such a thickness, the surface roughness, typically between 10 and 30 nm, could have a weak influence on the detection. Another parameter to take into account is the resistivity of the electrode: according to the boron doping level, a diamond electrode of 100 nm has approximately a resistivity of 20 mΩ cm, while a thicker diamond electrode of 1 µm could reach a resistivity of 5 mΩ cm, due to the effect of grain boundary. So our choice must be a compromise between the lower thickness and the best conductivity. In this way, optimal working electrode properties requires a thickness between 0.3 and 0.4 µm. For these thicknesses, decrease in full height was between 31.8% and 42.8%.

0.0¡10 0 5.0¡10 -3 1.0¡10 -2 1.5¡10 -2 2.0¡10 -2

Attenuation by insulating, shielding and bonding layers

Fig. 6 shows the initial alpha peak on the Si-diode, then with the presence of different slabs (insulating, bonding and diamond shielding, as shown in Fig. 3). Table 1 gives some parameter values characterizing the alpha peaks: the centroid, the full height (FH), the full width at half maximum (FWHM) and the area.

For an arbitrarily chosen source thickness of 100 nm, the identification of the most attenuating layer is possible. In this configuration, the insulating layer shifts the centroid 2.73% to lower energies and attenuates the intensity (FH) 82.45% from those values of the incident alpha particle in the Si-diode. The shielding and bonding layers provide respectively an attenuation of 5.85% and 2.21% of the initial FH peak (FH Si ). The insulating layer increases the FWHM from 0.02 MeV to 0.13 MeV, whereas the shielding layer increases it only from 0.13 to 0.18 MeV and the bonding layer from 0.18 to 0.22 MeV (Table 1). Attenuations due to the bonding and shielding layers are negligible compared to the attenuation due to the insulating layer.

Layer

2.21

Table 1: Characteristics for the simulated alpha peaks according to the different layers.

Source self absorption

Controlling the source thickness on the detector surface could be interesting to limit the self absorption of alpha particles in order to perform a real identification of radionuclides in the liquid solution. In this way, a limit of source thickness could be defined, 3. The source is 0.1 µm thick and it is composed of water containing 241 Am, with a density of 1 g cm -3 .

0.0¡10 0 2.0¡10 -2 4.0¡10 -2 6.0¡10 -2 8.0¡10 -2 1.0¡10 -1 1.2¡10 -1
beyond which the apparent activity remains constant (due to a source thickness greater than alpha particle path), but mainly because the radionuclide identification could not be performed in the absence of distinctive peaks.

In this configuration, the detector is composed of four different layers described in section 2.1.2 and Fig. 3, with the CVD diamond slab thickness set to 300 nm.

Mono-energetic source

For this aim, a mono energetic source, containing 241 Am (5.49 MeV), has been simulated. The investigated thickness for the source layer, from 0.1 µm to 10 µm, corresponds to an ideal source and a more realistic one. The source thickness depends on the time required by actinide electroprecipitation process as well as the hydrodynamics conditions inside the cell. The upper thickness corresponds to the alpha particle range at 5.49 MeV in water and is achievable by micro-fluidic cell or actinide electrodeposition.

Fig. 7 and Table 2 show the impact of the source thickness on the peak shape. As the thickness of the source increases, the height of the peak decreases, also with a growing broadening. With a thickness between 0.1 and 2 µm, the peak shape appears to be well defined. For thicker sources, beyond 2 µm, the widening of the peak prevents the identification of its centroid, which is a major concern for alpha spectrometry. However, the simulated activity decreases linearly as the thickness of the source increases. Such results suggest that the measurement of the global activity could be performed with this kind of detector without a complete source formation process.

0.0¡10 0 2.0¡10 -3 4.0¡10 -3 6.0¡10 -3 8.0¡10 -3 1.0¡10 -2 1.2¡10 -2 1.4¡10 -2 3 3.5 4 4.5 5 5.5 Normalized counts Energy (MeV)
0.1 µm 0.5 µm 1 µm 2 µm 5 µm 10 µm

Multi energetic source

In the following case, a multi energetic source, containing 241 Am (5.49 MeV) 239 Pu (5.16 MeV) and 235 U (4.40 MeV) with the same volumetric activity, has been simulated to investigate the limits for the energy discrimination in such an experimental setup.

Fig. 8 shows the influence of source thickness on the shape of peaks related to the three actinides. For a source thickness between 0.1 and 1 µm, the three peaks remain identifiable. The thicker the source, the wider the peaks and the centroids of the peaks shift to lower energies. At 2 µm thick, the peak height is truncated, the discrimination between the peaks of 239 Pu and 241 Am begins to be problematic due to the widening of the FWHM. For a higher source thickness, the distinction between 235 U, 239 Pu and 241 Am could not be performed, due to the strong self absorption of the source. This process involves a clean room technique developed by F. Bassignot et al [START_REF] Bassignot | Acoustic resonator based on periodically poled transducers: Fabrication and characterization[END_REF]: a thin layer of titanium/gold was first deposited by sputtering on the surface of both substrates. These substrates were then pre-bonded by mechanical compression of their metallized surfaces into a wafer bonding machine (EVG 501). Once the pre-bonding was done, the bonding process was completed by applying a strong pressure to the stack with an hy-draulic press. This last step should remove most of gluing defects due to surface flatness, total thickness variation and bow/wrap defects.

For this method, polished surfaces of optical quality were necessary to assure the bonding of the different substrates. A surface roughness of 30 nm and 1 nm were respectively measured for the diamond layer and the silicon detector. The measured surface roughness for both materials is lower than the limit of 80 nm required for a successful thermocompression bonding.

We remind that the electrode structure is composed of a boron doped diamond on a Si 3 N 4 /SiO 2 layer on a pure silicon wafer, with a total thickness around 1 µm. Due to the impossibility of handling such a thin material, the simplest way was to deposit on the free diamond surface an insulating layer, eroding the SiO 2 layer to have a surface roughness of 10 nm and then depositing the bonding layer of Ti/Au. Finally, the initial layers SiO 2 /Si 3 N 4 and Si wafer, on which the CVD diamond growth was made, had to be removed (section 4.3).

Bonding tests

Separate preliminary adhesion tests of the thermocompression bonding layer were performed, for a diamond electrode and a pure silicon wafer (electrode-Si wafer), for a PIPS ® detector and a pure silicon wafer (detector-Si wafer). The strength of the bonding was investigated by performing tearing test on the silicon layer with a tweezer and mechanical engraving. The electrode-Si wafer bonding was good enough to resist mechanical engraving. The detector-Si wafer bonding was not satisfying, due to the convexity of the detector surface. Removing the detector from its casing reduced the pressure applied on it and also its convexity, which enabled a satisfactory bonding on a silicon wafer (Fig. 9).

The final test was for the assembly of the electrode and the PIPS ® detector (electrode- detector). Sticking the BDD on the detector surface required the deposition of a Si 3 N 4 /SiO 2 layer on the BDD surface, then mechanically polished to clear surface defects of the electrode. After this intermediate step, the detector-electrode bonding was successfully achieved (Fig. 10).

Surface etching

Once the bonding completed, the etching process of the electrode surface layer was necessary to release the detector active aperture from the original silicon substrate of the BDD. The first step used a mechanical etching to lower the high purity silicon substrate of the BDD electrode to 50 µm thick. Then the detector has been immersed in a KOH solution, to remove the silicon substrate without damage on the silica layer. This etching step has been followed by a mixed solution of hydrofluoric acid (HF) and nitric acid (HNO 3 ) to remove the silica and silicone nitride layers above the electrode. Fig. 10 shows that the KOH did not remove successfully the silicon substrate and that the hydrofluoric acid was too aggressive and strongly altered the detector surface, the bonding area and the diamond electrode. Hydrofluoric acid behaves like a gas, the presence of defects at the interface gold-material or Au-Au promotes its diffusion through the material, thus resulting in these unwanted damages (Fig. 10).

Discussion

A 0.3 to 0.4 µm thin shielding layer of diamond material on top of a standard PIPS ® detector would have a limited impact with regard to the alpha spectrometry properties of the device (Fig. 5). However, the insulating layer, required to perform both actinide electro-chemically assisted precipitation and alpha spectrometry, reduces the detection properties of the detector-electrode (Fig. 6). In those cases, a 0.1 µm thick source has been simulated, that corresponds to an ideal source. The thickness of the source could impact significantly the quality of the alpha spectra, since a 241 Am source emits alpha particles that are detected at energies below 4 MeV (Fig. 7). Below a source thickness of 2 µm, the peaks from 235 U, 239 Pu and 241 Am could be identifiable for an alpha multienergetic source. Above 2 µm, signals from 235 U and 239 Pu are completely hidden by the signal from 241 Am (Fig. 8).

The feasibility study revealed that the detector and the electrode surfaces are not perfectly flat. The thermal process used to produce CVD diamond and silicon detector was responsible of this significant drawback. On the other hand, the pressure applied in its case was causing the convexity of the detector. Opening the case of the PIPS ® detector allowed to reduce this problem and successfully perform thermocompression bonding with a Ti-Au layer between diamond electrode and silicon detector (Fig. 9).

The surface etching with hydrofluoric acid was too aggressive for the detector (Fig. 10).

To prevent this, a dry etching process was chosen and a plasma etching process is thus under study. It allowed to reach a remaining thickness of 1.6 µm on the surface of the diamond electrode.

Conclusion

The feasibility of a new alpha detector-electrode, combining Si diode and CVD diamond assembled by thermocompression, and its impact on detection properties were investigated. To preserve the boron doped diamond shielding and electrode properties with a low attenuation of the incident alpha particle energy, the diamond thickness should be kept between 300 nm and 400 nm. The insulating layer is responsible for most of the attenuation in the energy of alpha particles. On the other hand, the contribution of the bonding layer on attenuation could be neglected. For an ideal detector in terms of resolution and an homogeneous source thinner than 2 µm, the identification of alpha emitters with similar volumetric activities could be performed. Such conditions could be achieved by performing actinides electrodeposition in a well-mixed aqueous solution.

1 .

 1 Electroprecipitation and source deposition

Figure 1 :

 1 Figure 1: Diagram of the actinide electroprecipitation between two working electrodes.

  electrode (Fig 2, left) and the thorium was identified by gamma spectrometry through its progenies, 228 Ac, 212 Pb and 208 Tl (Fig. 2, right).

Figure 2 :

 2 Figure 2: Left: Thorium deposited on the surface of a boron doped diamond electrode. Right: Gamma spectrum of thorium deposited on the boron doped diamond electrode.

Fig. 3

 3 Fig. 3 shows the stacking of all different layers, corresponding to the different configurations of the detector: bare Si diode, corresponding to the PIPS ® detector, PIPS ® detector with the electrical insulating layer (SiO 2 /Si 3 N 4 ) PIPS ® detector with the insulating layer and the shielding layer in CVD diamond. This configuration would correspond to the growth of CVD diamond on the PIPS ® detector, which was the first process investigated by de Sanoit et al. PIPS ® detector with the bonding layer of Ti/Au for the assembly with the insu- lating layer and the CVD diamond. The last diagram corresponds to this project with a gold layer for the bonding of the diamond electrode on the Si diode. The use of Ti in the bonding layer facilitates Au adhesion on Si and SiO 2 .

  1.1. The considered case uses an aqueous solution

Figure 3 :

 3 Figure 3: Diagram (not to scale) of the different slabs used to study the impact of the coating layers on alpha particle measurement.

Figure 4 :

 4 Figure4: Stopping power of water, gold, silicon and silicon dioxide normalized to their densities[START_REF] Berger | Stopping-Power & Range Tables for Electrons, Protons, and Helium Ions[END_REF].

Figure 5 :

 5 Figure 5: Plot of the simulated alpha spectra as a function of CVD diamond thickness.

Figure 6 :

 6 Figure6: MCNP6 simulation of the alpha spectra for the different detector configurations shown in Fig.3. The source is 0.1 µm thick and it is composed of water containing 241 Am, with a density of 1 g cm -3 .

Figure 7 :

 7 Figure 7: MCNP6 simulation of the impact of the source thickness on alpha measurement.

Figure 8 :

 8 Figure 8: MCNP6 alpha particle spectra for a detector-electrode with different source thicknesses containing 241 Am, 239 Pu and 235 U.

4 .

 4 Feasibility study for assembly4.1. Assembly processThermocompression bonding at room temperature (15 -25) was studied to assemble a boron doped diamond (BDD) electrode on the surface of the silicon detector.

Figure 9 :Figure 10 :

 910 Figure 9: BDD electrode bonded on top of a silicon wafer (left) and silicon wafer bonded on top of the detector (right)

Table 2 :

 2 Characteristics of the simulated spectra according to the source thickness.

Preprint submitted to ElsevierDecember 2, 2019

Concerning the assembly process, thermocompression of diamond electrode on the silicon detector surface was successfully achieved without visible damage on both substrates.

However, this process requires a roughness under 10 nm and can only be performed in clean room conditions. As releasing the active window is still under development, other experiments are focused on the dry attack of the diamond substrates.

Aknowledgement

The authors would like to thank Christophe Provent and David Rats from NeoCoat, La Chaux-de-Fonds -Switzerland (http://www.neocoat.ch), for the valuable discussions and supplying the diamond electrodes.


A New PWM Control based on an Optimized Zero Sequence

Component injection: Application in a Two-Level Inverter

Bourgeade Adrien 1 , Malek Ghanes 1 , Fadel Maurice 2 , Bouarfa Abdelkader 3 , Barbot Jean-Pierre 4

Abstract-In this paper, a new optimization problem is proposed for improvement of PWM control of an inverter that supplies a generic RLE load. Two objectives functions are studied separately: Weighted Total Harmonic Distortion (WTHD) of load voltages and total losses. The gap contribution is related to optimize the zero sequence component waveform by defining special decision variables. By doing so, the proposed PWM strategy allows to improve the WTHD and efficiency of converters by keeping a classical PWM implementation scheme. Moreover this approach has the same way of thinking than the two main different classes of PWM strategies that are Space-Vector-based PWM (SVM) methods and classic carrierbased PWM methods (CBPWM). It is well known that there is an equivalence between SVM and CBPWM through the zero sequence component injection. So, optimized zero sequences are proposed for the two objectives functions considered, and the simulation results show a significant improvement compared to classical CBPWM strategies. Moreover the proposed strategy allows an implementation on existing hardware by modifying only the modulation component software.

Index Terms-Optimized PWM, optimal SVM, PWM, SVM, Zero Sequence Component

I. INTRODUCTION

Carrier-based PWM (CBPWM) exists since almost one century [START_REF] Prince | The inverter[END_REF] to control power electronic devices such as inverters. Many works tried to improve the PWM by injecting harmonics in the modulated signal [START_REF] Holtz | Pulsewidth modulation for electronic power conversion[END_REF]- [START_REF] Capitaneanu | General and algebraic synthesis for pwm methods[END_REF], or on searching vector modulation methods [START_REF] Bozorgi | Optimum switching pattern of matrix converter space vector modulation[END_REF], [START_REF] Zhou | Relationship between space-vector modulation and three-phase carrier-based pwm: a comprehensive analysis [three-phase inverters[END_REF].

More recently it also appeared Optimal Pulse Patterns (OPP) strategies as [START_REF] Birda | Synchronous optimal pulse-width modulation with differently modulated waveform symmetry properties for feeding synchronous motor with high magnetic anisotropy[END_REF]- [START_REF] Fei | A generalized formulation of quarterwave symmetry she-pwm problems for multilevel inverters[END_REF]. Most of the papers are concerned about minimisation of Total Harmonic Distortion (THD) or Weighted Total Harmonic Distortion (WTHD). Different algorithms uses WTHD because it is a good way to evaluate current behaviour in an electric motor. Indeed motors behaves as a low pass filter, and WTHD allows to take into account this dynamic without considering a specific electrical motor.

Moreover, the control loop is considered as a black box, control loop is supposed to give a correct information about sinusoidal signal frequency (f 1 ), phase reference and desired voltage (m.E DC , here m is called modulation index and E DC the bus voltage).

According to the literature, this paper is dedicated to improve the performances of existing strategies (SVM, THIPWM 1 6 ,...). In order to achieve this goal, a new PWM control consisting on using an optimized Zero Sequence Component (ZSC) that generalizes the CBPWM is proposed. By doing so, the following issues are improved in terms of two objectives functions: the WTHD and efficiency. Furthermore with the proposed strategy only the modulation component software is changed without modifying the existing hardwares. The well known robustness of classical CBPWM and the phase symmetry are preserved. The strategy is applied to a two-level inverter and developed within an EV manufacturer to feed a synchronous motor.

In simulation the proposed strategy is tested and compared to SVM and THIPWM 1 6 by using a two level inverter feeding an RLE load. The comparison is realised by taking in account two objectives functions, WTHD and the efficiency RLE load. and proposed strategy is done in simulation according to WTHD and efficiency on an RLE motor. SVM and THIPWM are selected to be compared to the proposed strategy because SVM is a gold standard PWM and THIPWM one is the gold standard of CBPWM strategies [START_REF] Holtz | Advanced pwm and predictive control -an overview[END_REF], [START_REF] Holmes | Pulse Width Modulation for Power Converters: Principles and Practice[END_REF]. SVM is a good starting point because it has been demonstrated that it is equivalent to CBPWM with a specific zero sequence injection [START_REF] Zhou | Relationship between space-vector modulation and three-phase carrier-based pwm: a comprehensive analysis [three-phase inverters[END_REF], [START_REF] Bowes | The relationship between spacevector modulation and regular-sampled pwm[END_REF], [START_REF] Holmes | The general relationship between regular-sampled pulse-width-modulation and space vector modulation for hard switched converters[END_REF].

Next, section II describes the objective functions for the considered case. Then, a description of the proposed method is developed in section III. Section IV provides a resolution way. Simulation results and discussion are given in section V. The paper ends with a conclusion in section VI.

II. OBJECTIVE FUNCTION DESCRIPTION

In order to test and compare strategies, an ideal inverter is considered. It is represented by eq. ( 1) where S x , is the command of the leg x. E DC The bus voltage and finally V, is the vector of the simple voltages.

V = E DC 3   2 -1 -1 -1 2 -1 -1 -1 2     S a S b S c   (1)
To achieve the comparison, two main objectives functions (WTHD and efficiency of RLE load) are used. Even if these objective functions are approximating, they afford a good indication on solution quality. The commutation and conduction losses of RLE model (Fig. 1) are computed. The

A. WTHD

The WTHD does not depend on a load and allows to evaluate solution quality quite faster and easier. The WTHD equation is represented in eq. ( 2).

V WTHD,% = 100 V 1 n≥2 V n n 2 (2)
Where V 1 is the desired voltage (expressed as mE DC ), which is also the fundamental voltage and V n is the voltage of the harmonic number n [START_REF] Holmes | Pulse Width Modulation for Power Converters: Principles and Practice[END_REF].

In order to implement it in a solver, a modified WTHD is considered in eq. ( 3). This equation does not have any physic meaning but is useful to analyse the solutions.

V WTHDm = n≥2 a 2 n,V + b 2 n,V n 2 (3)
Where a n,V and b n,V are the Fourier coefficients of the single phase of the load.

B. Efficiency of the RLE load

The considered case, is the RLE load connected to a to level inverter, see Fig. 1.

The efficiency is defined as follows

η RLE = P u P tot + P u (4)
Where P u represents the useful power and P tot the total losses.

To compute efficiency, evaluation of the losses in the inverter is given in the next.

1) Losses in the inverter: The main losses in the inverter are due to IGBT and Diode losses. For such components, there are two kind of losses, the conduction losses and the switching losses. The first one is due to the internal resistance of the semiconductor. The second one, is due to the on/off transition delay.

P cond = 1 2π 2π 0 S(α)V ce |i(α)|dα (5)
P sw = 1 2 f 1 N dec i=1 (E on (α i ) + E of f (α i )) + 1 2 f 1 N dec i=1 (-1) i (E on (α i ) -E of f (α i )) (6)
Equations ( 5) and eq. ( 6) [START_REF] Capitaneanu | General and algebraic synthesis for pwm methods[END_REF] are quite simple. Indeed they depend on few parameters and on the angle position. The functions V ce , E on ans E of f are given by the data sheets of the chosen semiconductors under a polynomial form. Moreover, S is equal to one when the switch is on and zero otherwise. This switching function S depends of the comparison between the carrier and the modulating signal, the current i depends of S and switching losses E on and E of f depend on i. With this knowledge a strong link between inverter losses and command can be done.

P tot = 3P cond + 3P sw + 3 n≥2 (V n I n cos(φ n )) (7)
In eq. ( 7) V n , I n designate voltage and current for the harmonic n respectively for the load phase voltage and load phase current. P cond , P sw are the conduction and switching losses, and φ n is the angle between harmonic voltage and harmonic current.

For this evaluation, the Fourier decomposition of the current is given here after.

2) Fourier decomposition of load currents: From Fig. 1, the analytical solution of the phase load current is given by:

i(α) =   i 0 - n≥1 Ra n,V -nLωb n,V (nLω) 2 + R 2   e -Rα Lω + n≥1 (Ra n,V -nLωb n,V ) cos(nα) (nLω) 2 + R 2 + n≥1 (Rb n,V + nLωa n,V ) sin(nα) (nLω) 2 + R 2 + Ra 1,E -Lωb 1,E R 2 + (Lω) 2 e -Rα Lω - (Ra 1,V -Lωb 1,V ) (Lω) 2 + R 2 cos(α) - (Rb 1,E + Lωa 1,E ) (Lω) 2 + R 2 sin(α) (8)
where R represents a resistor, L an inductance and ω = 2πf 1 . Moreover a n,V and b n,V are the Fourier coefficients of the considered single phase voltage of the load, and E(ω) = E sin(ωt + φ), with φ depending on the considered phase. It can be then decomposed as Fourier coefficients, a 1,E and b 1,E . This equation conduce to

E(ω) = a 1,E cos(ωt) + b 1,E sin(ωt)
The steady state solutions of eq. ( 8) is defined as follow:

i(α) = n≥1 (Ra n,V -nLωb n,V ) (nLω) 2 + R 2 cos(nα) + n≥1 (Rb n,V + nLωa n,V ) (nLω) 2 + R 2 sin(nα) - (Ra 1,V -Lωb 1,V ) (Lω) 2 + R 2 cos(α) - (Rb 1,E + Lωa 1,E ) (Lω) 2 + R 2 sin(α) (9)
From eq. ( 9), a current Fourier decomposition appears, and the fundamental of the current is:

a 1,I = R(a 1,V -a 1,E )-Lω(b 1,V -b 1,E ) (Lω) 2 +R 2 b 1,I = R(b 1,V -b 1,E )+Lω(a 1,V -a 1,E ) (Lω) 2 +R 2 (10)
In the same way from eq. ( 9), harmonics are obtained with:

a n,I = Ra n,V -nLωb n,V (nLω) 2 +R 2 ∀n ∈ N * \{1} b n,I = Rb n,V +nLωa n,V (nLω) 2 +R 2 ∀n ∈ N * \{1} (11)
In order to decompose the losses are decomposed in two parts

P K = 3P cond + 3P sw (12)
and

P H = 3 n≥2 (V n I n cos(φ n )) (13)
P H is similar to WTHD, consequently the WTHD is indirectly included in [START_REF] Bozorgi | Optimum switching pattern of matrix converter space vector modulation[END_REF]. The P K losses is useful to determine the impact of harmonic minimisation on the optimal solutions.

III. MULTIPLE HARMONIC INJECTION DESCRIPTION

A. Multiple harmonic injection

The zero sequence component modulation consist to find the optimal harmonics to inject in the modulating signal. Because it is impossible to compute a complete Fourier decomposition, it is necessary to set the maximal harmonic considered in computation, it has been fixed arbitrary to n h = 20, corresponding to 60 harmonics over the electrical frequency. This number is sufficiently large to generate precisely classical zero sequence components, to inject in the modulating signal. Consequently, this technique can reproduce SVM, THIPWM, DPWMmin and DPWMmax. Nevertheless this harmonic regeneration does not work with some DPWM strategies,due to discontinuities which generate a strong Gibbs effect. This Gibbs effect generate unexpected extra switching. Then in the proposed zero sequence harmonic the generation of strong discontinuities (extra switching) is avoided. v 0 (t) ∈ -1 2 ; 1 2 (14) Fig. 2 shows the principle scheme of the proposed method. The idea is to compute Fourier coefficients (a 0,v0 , a n,v0 , b n,v0 ) with an optimisation algorithm in order to generate the ideal zero sequence component. This optimisation problem is computed for a specific modulation index (m), frequency (f 1 ) and number of switches per period (4N ) with respect of the Fourier description of v 0 found in eq. ( 14). More precisely this equation is used to compute the modulated signal depending on time and not on frequency as before.

Intersection with a triangular function leads to generate commutation angles Fig. 2. The number of switching angles by period is equal to 4N , where N is the number of switching per quarter period. The switches found are then enumerated as

0 < α 1 < α 2 • • • < α 4N < 2π.
With this angles determination, eq. ( 15), eq. ( 16) and eq. ( 17) [START_REF] Birth | Generalized three-level oprimal pulse patterns with lower harmonic distortion[END_REF] allow to compute switching sequence (S), and then phase voltage of the inverter is accessible thanks to eq. ( 1).

a 0,S = 1 2π   2π - 4N j=1 (-1) j α j   ( 15
)
a n,S = -

1 nπ   4N j=1 (-1) j sin(nα j )   (16) b n,S = 1 nπ   4N j=1 (-1) j cos(nα j )   (17)
Therefore, optimisation of eq. ( 3), eq. ( 7) and eq. ( 12) according to some constraints can be done in next section.

IV. OPTIMISATION PROBLEM SETTING

The fmincon function of the optimisation toolbox of MatLab is used to perform the optimisation problem. As fmincon propose only local minimum solutions. It is necessary to randomly chose many v 0 Fourier description to chose sufficiently large number of v 0 . Then a quality evaluation for each Fourier description is performed with eq. ( 18). This equation consider the chosen objective function, f , its description is given by eq. ( 3), eq. ( 7) or eq. ( 12). In the objective function f (WTHD, P tot or P K ), no constraints are considered. In order to find solutions with constraints respect, two penalty terms is added in eq. ( 18).

f v = f (x) + K 1 9 i=1 (max(c i , 0)) + K 2 9 i=1 g(c i ) (18)
Where x = (a 0,v0 , a n,v0 , b n,v0 ) is the decision vector, K 1 and K 2 are two penalty coefficients (In this paper setting equal to

K 1 = K 2 = 10 6 ). Moreover c = (c 1 , c 2 • • • , c 9 )
is the vector of constraints, these constraints are the same then for the problem eq. ( 20) . In eq. ( 18), g is defined as follow:

g(c i ) = 1 if c i > 0 otherwise (19)
Remark, eq. ( 18), was inspired by the work of Sierra et al. [START_REF] Sierra | Improving pso-based multi-objective optimization using crowding, mutation and -dominance[END_REF].

The first penalty of eq. ( 18) indicates how far away the current solution is from the feasible domain and the second penalty evaluates how many constraints are violated.

After selection of the best first v 0 (starting point) according to eq. ( 18). Fmincon find a local minimum around the starting point with respect to the problem defined by [START_REF] Takahashi | Optimum pwm waveforms of an inverter for decreasing acoustic noise of an induction motor[END_REF]. This problem try to minimise objective function (eq. ( 3), eq. ( 7) or eq. ( 12)), which means decreasing WTHD and increasing efficiency. Those objectives are constrained by nine constraints, those constraints force the solutions to respect the desired voltage.

       f.o min(f (x)) s.c a 0,Va = 0, a 1,Va = 0, b 1,Va = mE DC a 0,V b = 0, a 1,V b = - √ 3 2 mE DC , b 1,V b = -1 2 mE DC a 0,Vc = 0, a 1,Vc = + √ 3 2 mE DC , b 1,Vc = -1 2 mE DC (20)
In order to preserve at least this local minimum, the solution from the previous modulation index is chosen as a reference starting point with respect to the new random starting points. For example, the solutions found for m = Relative margin, ( r eq.( 21)) for optimal harmonic injection compared with SVM and THIPWM 1 6 applied to WTHD (eq.( 2)) for N=5 Fig. 5.

Relative margin, ( r eq.( 21)) for optimal harmonic injection compared with SVM and THIPWM 1 6 applied to Total losses (Ptot eq.( 7)) for N = 5 0.5, will be one of the starting point of the computation for the next discretisation step m = 0.501, this step is equal to 0.001. In addition, and to ensure that harmonic injection increase the solution quality, the solutions obtained (v 0 ) from Fourier decomposition of SVM, DPWMMin, DPWMMax, THIPWM1/6 and THIPWM1/4 are also considered as starting points for (20).

V. RESULTS AND DISCUSSION

A. Results

The Fig. 4, represent a WTHD comparison between SVM, THIPWM 1 6 and optimal harmonic injection. The idea here is to represent the relative margin (defined in eq. ( 21)) between our strategy and two classical ones. Fig. 5 does the same comparison for the RLE load total losses and Fig. 6 for the switching losses only.

In eq. ( 21) y c represent the objective function cost of the classical symmetry (SVM or THIPWM 1 6 in this paper) and y o the proposed objective function value of harmonic injection one.

For the proposed method the WTHD is improved in front of SVM for any modulation index and reach almost 2% for high modulation index (Fig. 4). On another hand, our optimal Relative margin, ( r eq.( 21)) for optimal harmonic injection compared with SVM and THIPWM 1 6 applied to switches losses only (P K eq.( 12)) for N = 5 Fig. 7. Normalised and centred v 0 comparison between harmonic injection and SVM for WTHD (eq.( 2)) considering N = 5 and m = 0.5 computation afford a small gain in comparison to THIPWM 1 6 (according to WTHD objective function), the improvement never overcome 0.5% of improvement. Furthermore, for THIPWM 1 6 the WTHD improvement is only for low and high modulation index. This observation is a confirmation of the literature, where THIPWM 1 6 is considered as the best manner to reduce current harmonics.

Considering total losses objective function (Fig. 5, eq. ( 7)) and switching losses objective function (Fig. 6, eq. ( 12)), the harmonics losses (eq. ( 13)), seems to have a negligible impact on relative margin improvement. Furthermore, improvement appears to fit the same curve for both objective functions. But for these figures the improvement is more quantifiable than for WTHD one (Fig. 4), and is around 1% of increasing for every modulation index.

In Fig. 7 and Fig. 8 is represented the zero sequence component for WTHD objective function and total losses. For the WTHD (Figs. 7 and4), as expected the optimal harmonic signal is near THIPWM 1 6 wave form for m = 0.5, which is not surprising according to the corresponding improvement of harmonic injection seen on Fig. 4.

About total losses and switching losses (Figs.8, 5 and 6), the optimal curve for low modulation index (m = 0.1) is quite surprising because it does not looks like any classical carrier based strategy. The curve looks like a sawtooth function, and a small Gibbs effect appears near the Fig. 8. Normalised and centred v 0 comparison between harmonic injection and SVM for Total losses (eq.( 7)) and considering switches losses (eq.( 12)) for N = 5 and m = 0.1 discontinuities.

Furthermore the optimal injection for total losses and for switching losses only, seems to be the same, except a different mean value (a 0 in eq. ( 14)). Consequently the optimal curve for switch losses is similar to the one obtained by a DPWM strategy. This observation leads to consider eq. ( 13) imposes that v 0 signal to have a mean value equal to zero in an optimal case.

Let's notice on Figs. 4, 5 and 6, SVM and THIPWM 1 6 solutions has a negative relative margins. This implies that classical solutions are better than optimal zero sequence component. Nevertheless, for these modulation index, SVM and THIPWM 1 6 do not respect the specified constraints. So, both classical strategies are unfeasible according to constraints definition (see eq. ( 20)) and especially inside tolerance.

B. Discussion

The carrier based property of the proposed strategy will ensure a fast implementation. The main problem seems to be the synchronism, because one of our main assumptions is to set invariant the number of commutations per period.

In this paper, the idea beyond this method is really simple, because it is just a particular case of harmonic injection. Because of the carrier based property of the method, this strategy will be easier to implement in comparison to OPPs. Off-lines solutions affording better solutions but are way more complicated to implement on a a real engine.

Furthermore, ElectroMagnetic Compatibility (EMC) [START_REF] Lezynski | Random modulation in inverters with respect to electromagnetic compatibility and power quality[END_REF], or noise and harshness [START_REF] Takahashi | Optimum pwm waveforms of an inverter for decreasing acoustic noise of an induction motor[END_REF]- [START_REF] Gieras | Noise of Polyphase Electric Motors[END_REF] problems are ignored but should be considered in future works. Moreover, results has been obtained in simulations. And in the next months an implementation will be done.

VI. CONCLUSION

The results in this paper highlight the benefits of the proposed method with respect to SVM and THIPWM 1 6 (more generally in front of every classical carrier based zero sequence component). About WTHD, results support the well known observation that THIPWM 1 6 is the better injection to increase current harmonic quality. For the RLE load 1% of improvement could seems negligible, nevertheless considering, for example, the particular case of electric vehicles the range is one of the most important criterion to consider. Consequently each percent of power saved is a real improvement.

As the optimisation strategy can be easily generalized to more voltage levels, in a future work the proposed method will be applied to a multilevel converter.

Fig. 1 .

 1 Fig. 1. Scheme of the RLE model

Fig. 2 .

 2 Fig.2. Principle of ZSCM, a zero sequence component is generated from the computed optimal Fourier specter (here is represented as an example the SVM one).

Fig. 3 .

 3 Fig.3. Following the arrows, is represented the zero sequence component and the reference. On the second picture it is the modulated signal (sum of the two last ones). The comparison between the modulated signal and the carrier signal. Finally here is the command generated.

v 0

 0 (t) = a 0 + n h n=1 a n,v0 cos(3nωt) + b n,v0 sin(3nωt)

Fig. 4 .

 4 Fig. 4.Relative margin, ( r eq.(21)) for optimal harmonic injection compared with SVM and THIPWM1 6 applied to WTHD (eq.(2)) for N=5

Fig. 6 .

 6 Fig. 6.

Authorized licensed use limited to: INP TOULOUSE. Downloaded on January 14,2022 at 22:06:37 UTC from IEEE Xplore. Restrictions apply.

This work was supported by the project Chair between Renault and Centrale Nantes about performances of electric vehicles propulsion.


Dr Pierre Gibot
email: pierre.gibot@isl.eu

Julien Parmentier
email: julien.parmentier@uha.fr

Loic Vidal
email: loic.vidal@uha.fr

Fabien Schnell
email: fabien.schnell@isl.eu

Habiba Nouali
email: habiba.nouali@uha.fr

Denis Spitzer
email: denis.spitzer@isl.eu

Porous WS 2 and W 2 N powders by hard templating with colloidal silica

Keywords: Tungsten disulfide, Tungsten nitride, Surface properties, Colloidal silica, Hard-Template Tungsten disulfide, Tungsten nitride, Surface properties, Colloidal silica, Hard-Template

Meso-and macroporous tungsten disulfide (WS2) and tungsten nitride (W2N) powders materials were successfully synthesized by reduction of [WO3/colloidal silica] composites under hydrogen sulfide and ammonia gases respectively. The colloidal silica, marketed as Ludox®, was used as a hard template and its removal from the composite led to a porosity release. The products were characterized by X-ray diffraction, nitrogen adsorption, mercury porosimetry and electron microscopy. Wellcrystallized samples with specific surfaces areas close to ~ 40 m2.g-1 were thus synthesized. The present approach might be easily extended to the synthesis of other nitrides and sulfides materials.

Introduction

Transition metal-based materials exhibit vast and interesting physico-chemical properties (mechanical, electrical, optical, electrochemical, magnetic) covering a large number of proved or suggested applications in diverse domains [START_REF] Oyama | The Chemistry of Transition metal Carbides and Nitrides[END_REF]. Among these compounds, the tungsten-based materials have attracted much attention nowadays in particular when tungsten atoms are associated to non-metallic species such as the pnictogenides (group 15) or the chalcogenides (group 16) of the periodic table of the elements. Among these compounds, the most known and investigated ones are tungsten nitride and tungsten disulfide noted W 2 N and WS 2 , respectively. These compounds have common unique properties as for instance a chemical inertia toward alkali and acid environments, a high thermal stability (high melting and boiling points) and interesting electronic properties (semi-conductor for WS 2 and conductor for W 2 N) [START_REF]Handbook of Chemistry and Physics[END_REF]. The tungsten nitride offers a high strength and hardness whereas the tungsten disulfide shows lubricating properties related to its layered structure [START_REF]Handbook of Chemistry and Physics[END_REF][START_REF] Rapoport | Modification of contact surfaces by fullerene-like solid lubricant nanoparticles[END_REF]. Their competitive electrical and ionic conductivities compared to some current electrode materials make them serious candidates for the development of advanced energy storage systems and fuel cells [START_REF] Dong | Nanostructured transition metal nitrides for energy storage and fuel cells[END_REF][START_REF] Zhong | A novel non-noble electrocatalyst for oxygen reduction in proton exchange membrane fuel cells[END_REF][START_REF] Liu | An ordered mesoporous WS 2 anode material with superior electrochemical performance for lithium ion batteries[END_REF]. It has also been mentioned that these two tungsten-based inorganic materials would be attractive solutions in catalysis, in substitution of noble metal catalysts (e.g. Pt), for instance in hydrogenation and dehydrogenation reactions, hydrodesulphurization of crude oil and NO dissociation [START_REF] Mcgee | Basic properties of molybdenum and tungsten nitride catalysts?[END_REF][START_REF] Chen | Synthesis of open-ended MoS 2 nanotubes and the application as the catalyst of methanation[END_REF][START_REF] Shi | Catalytic activities of tungsten nitride for NO dissociation and reduction with hydrogen[END_REF]. The performance of the materials used or considered for such applications are greatly dependant of wellspecific criteria such as morphology (0 -3D), nanostructuring and surface properties. From these considerations, authors have conducted works for attempting to reach the synthesis of nanostructured tungsten nitride and tungsten disulfide developing specific design such as high specific surfaces areas with controlled porosities for optimized performances toward the above-mentioned applications.

From the literature, syntheses of W 2 N and WS 2 materials were early focussed on thin films preparation. For that, authors implemented different methods such as chemical vapour deposition (CVD) [START_REF] Kafizas | CVD and precursor chemistry of transition metal nitrides[END_REF][START_REF] Zhu | Morphology, structure and growth of WS 2 nanotubes[END_REF] for both tungsten-based materials, atomic layer deposition (ALD) and plasmaenhanced chemical vapour deposition (PECVD) for the tungsten nitride films [START_REF] Kafizas | CVD and precursor chemistry of transition metal nitrides[END_REF] and laser ablation for the tungsten disulfide preparation [START_REF] Sen | Encapsulated and hollow closed-cage structures of WS 2 and MoS 2 prepared by laser ablation at 450-1050[END_REF]. Regarding bulk W 2 N and WS 2 , two approaches were developed in the literature based (or not) on the use of a template. The absence of a template, oxide-to-nitride (nitridation) and oxide-to-sulfide (sulfidation) processes can be operated from nitrogen-and sulphur-containing reagents (e.g.: carbamide ((NH 2 ) 2 CO), thiocarbamide ((NH 2 ) 2 CS) and pure sulphur) mixed with various tungsten precursors (WO 3 , WO 2.72 , H 2 WO 4 , WCl 4 , (NH 4 ) 6 W 7 O 24 .4H 2 O) to produce nanostructured W 2 N [START_REF] Giordano | Synthesis of crystalline metal nitride and metal carbide nanostructures by solgel chemistry[END_REF] and WS 2 [START_REF] Wu | WS 2 nanosheets as a highly efficient electrocatalyst for hydrogen evolution reaction[END_REF][START_REF] Wu | Synthesis of WS 2 nanosheets by a novel mechanical activation method[END_REF][START_REF] Shiva | Employing synergistic interactions between few-layer WS 2 and reduced graphene oxide to improve lithium storage, cyclability and rate capability of Li-ion batteries[END_REF][17] materials, respectively. Others authors substituted solid reactants containing nitrogen and sulfur by gaseous reagents such as ammonia (NH 3 ) and hydrogen sulfide (H 2 S), respectively, for an enhancement of the interfacial reactivity between the components [START_REF] Bai | Synthesis and characterization of mesostructured tungsten nitride by using tungstic acid as the precursor[END_REF][START_REF] Villaseca | Synthesis and characterization of tungsten nitride (W 2 N) from WO 3 and H 2 WO 4 to be used in the electrode of electrochemical devices[END_REF][START_REF] Ko | Template-free synthesis and characterization of mesoporous tungsten nitride nanoplates[END_REF][START_REF] Chakrapani | WO 3 and W 2 N nanowire arrays for photoelectrochemical hydrogen production[END_REF][START_REF] Kim | A study of preparation of tungsten nitride catalysts with high surface area[END_REF][START_REF] Sun | Synthesis of tungsten disulfide nanotubes from different precursor[END_REF][START_REF] Sun | Synthesis and structural characterization of tungsten disulfide nanomaterials[END_REF]. With the use of a hard-template that is supposed to control the size and shape of the porosity, the fabrication of tailored tungsten-based inorganic compounds were performed by means of silica mesoporous templates (SBA- [START_REF] Liu | An ordered mesoporous WS 2 anode material with superior electrochemical performance for lithium ion batteries[END_REF][START_REF] Shi | Synthesis of Highly Ordered Mesoporous Crystalline WS 2 and MoS 2 via a High-Temperature Reductive Sulfuration Route[END_REF] and W 2 N [START_REF] Meyer | Space-confined preparation of high surface area tungsten oxide and tungsten nitride inside the pores of mesoporous silica SBA-15[END_REF] materials (after template removal), respectively. As expected, this last approach leads to the fabrication of promising highly ordered mesoporous tungsten nitride and suphide materials, with among the highest specific surfaces areas and best controlled pore sizes ever reported. Nevertheless, this multi-steps synthesis (silica template synthesis, impregnation/calcination stages with the metal precursor repeated at least twice, template leaching…) is time-consuming (> week) and generally yields to limited amount of materials. To limit these drawbacks, cheap and marketed silica hard template obtained from an evaporated colloidal silica solution is an alternative route for synthesizing tailored ceramics as recently demonstrated in the literature [START_REF] Gibot | Original synthesis of chromium (III) oxide nanoparticles[END_REF][START_REF] Gibot | Synthesis of WO 3 nanoparticles for superthermites by the template method from silica spheres[END_REF][START_REF] Goettmann | Chemical synthesis of mesoporous carbon nitrides using hard templates and their use as a metal-free catalyst for Friedel-Crafts reaction of benzene[END_REF][START_REF] An | Direct synthesis of porous molybdenum disulfide materials using silica sol as the template[END_REF].

Here we describe a simple method for synthesizing significant surface areas W 2 N and WS 2 materials involving the use of hydrated phosphotungstic acid and commercial colloidal silica (amorphous SiO 2 beads) as tungsten and template sources, respectively. The as-synthesized tungsten nitride and disulfide ceramics were characterized with conventional laboratory techniques. [START_REF] Gibot | Synthesis of WO 3 nanoparticles for superthermites by the template method from silica spheres[END_REF]. The mixture was stirred for 1h, dried in an oven at 80°C (Heraeus, VT6025 model, Germany) to evaporate the solvent and then calcined in air at 600°C (2°C.min -1 -2h) (Nabertherm GmbH, LT9/12/P320 model, Germany).

Experimental section

Synthesis of the tungsten nitride and suphide ceramics

The composites were heat-treated at 750°C (3h) (Carbolite Gero, GHA 12/300 model, United Kingdom) while exposed to a flow of H 2 S or NH 3 gas depending of the nature of the desired ceramic;

i.e the tungsten disulfide (WS 2 ) or the tungsten nitride (W 2 N), respectively. The gas flow was fixed at a rate of 1.2 L.h -1 . The resulting [WS 2 /SiO 2 ] and [W 2 N/SiO 2 ] composites were then treated with a 10% hydrofluoric acid solution to remove the silica spheres. The powders were recovered by centrifugation, washed several times with distilled water and acetone and finally placed in an oven at 80°C for 3h hours (Heraeus, VT6025 model, Germany). The grey-black tungsten-based products were denoted WS 2 or W 2 N. Sulfidation and nitridation were also performed in the same experimental conditions on nanostructured WO 3 material (after silica template removal) in order to assess the need of maintaining or not the hard template during the reduction processes. These data are reported in the supporting information part.

Characterizations techniques

The X-Ray powder Diffraction (XRD) was conducted on a D8 Advance diffractometer (Bruker, Germany) using a Cu K radiation (=1.54056 Å) with a Lynxeye detector and operating at 40 kV -40 mA. X-ray diffraction patterns were recorded between 2 = 10-80° with a step size of 0.02° and a step time of 0.1 sec. Nitrogen adsorption isotherms were performed at -196°C by means of an Accelerated Surface Area and Porosimetry system (ASAP 2020, Micromeritics, USA). Prior to the analyses, the samples were outgassed at 150°C under vacuum for 10 h. The specific surface areas (S BET ) were calculated according to the Brunauer-Emmett-Teller (BET) method within the 0.05-0.25 relative pressure range. The error on the measurement including the weighting mass is more or less 2%. The pore size distributions were obtained by following the Barret-Joyner-Halenda (BJH) approach applied to the desorption branches. To determine the macroporosity of samples the mercury intrusion porosimetry technique (Autopore IV, Micromeritics, USA) was selected. It is based on the progressive mercury intrusion into the material pores under controlled pressure. The morphologies and structures of the tungsten-based ceramics were investigated from a scanning and transmission electron microscopes such as the Nova NanoSEM 450 and the ARM-200F of the FEI (USA) and JEOL (Japan) companies, respectively. The [SiO 2 /WO 3 ] composite prepared following the experimental conditions as-above described was analysed by using the nitrogen adsorption technique and the X-ray powder diffraction (Figure 1). The composite exhibits a type IV isotherm characteristic of the presence of mesopores. Owing to the large relative pressure value where capillary condensations take place, mesopores size could not be determined accurately. Their sizes are centred on 15 nm. The specific surface area and the pore volume were equal to 21 m 2 .g -1 and 0.07 cm 3 .g -1 , respectively. The corresponding diffractogram (Figure 1, insert) shows reflexions of WO 3 tungsten (VI) oxide phase (JCPDS No 43-1035, P2 1 /n space group). No other crystalline phases were detected confirming the amorphous character of SiO 2 silica particle template. The [SiO 2 /WO 3 ] composite was then exposed to a H 2 S or NH 3 atmosphere before the removal of the silica template for the preparation of the targeted tungsten disulfide and ditungsten nitride materials, respectively.

Results and Discussion

3.2. Characterizations of the WS 2 and W 2 N materials.

Figure 2 shows the XRD patterns of the samples synthesized from the sulfidation (Figure 1A) and nitridation (Figure 1B) of the hard templated tungsten (VI) oxide, respectively. About the first pattern, the most intense diffraction peaks can be assigned to (002), (004), (100), (103) (006), ( 105), ( 110 For the sample obtained after nitridation of the tungsten trioxide (Figure 1B), four well-resolved diffraction peaks are observed and can be indexed to the (111), (200), ( 220) and (311) crystal planes of a cubic structure (space group P-3m1) corresponding to the W 2 N material (JCPDS card No. 25-1257).

The lattice parameter values of each material were calculated according to the well-known Bragg's law and the metric equations. For the tungsten nitride sample, the lattice parameter a was equal to 4.129 Å and for the tungsten disulfide a and c were equal to 3.137 Å and 12.575 Å, respectively. The crystallographic data are similar to the tabulated values given by the corresponding cards (a W2N = 4.126 Å, a WS2 = 3.154 Å, c WS2 = 12.362 Å).

The global reaction mechanisms of the tungsten oxide-to-sulfide and the tungsten oxide-to-nitride conversions, from sulphur-and nitrogen-rich gaseous sources, are expressed as follows:

WO 3(s) + 3H 2 S (g) → WS 2(s) + 3H 2 O (g) + S (g) (1)
4WO 3(s) + 8NH 3(g) → 2W 2 N (s) + 12H 2 O (g) + 3N 2(g) (2)
A release of gaseous species such as water molecules and sulphur or nitrogen gas occurs. The experimental weight changes of the [WO 3 /Ludox  TM40] composites (48.2 wt% in WO 3 ) recorded before and after heat treatments under H 2 S or NH 3 were compared to the theoretical ones based on the chemical reactions ( 1) and (2) given previously. Experimentally, weight variations of +6.6% and -15.8% were noted for the sulfidation and nitridation stages, respectively. According to the reactions (1) and ( 2), the theoretical weights changes (gain or loss) were calculated as equal to +7.0% and -17.7 %, respectively, suggesting a partial conversion of the oxide to the sulfide (95% yield) and to the nitride (90% yield). This discrepancy could also be related to the experimental uncertainty coupled to a surface oxidation of the non-oxide phases by air (after the synthesis) and in the case of the nitridation to the formation of an amorphous phase, that is not detected by XRD [START_REF] Giordano | Synthesis of crystalline metal nitride and metal carbide nanostructures by solgel chemistry[END_REF][START_REF] Meyer | Space-confined preparation of high surface area tungsten oxide and tungsten nitride inside the pores of mesoporous silica SBA-15[END_REF].

The nitrogen adsorption-desorption isotherms of the tungsten disulfide and nitride samples, prepared with Ludox  TM40 as hard template, are shown in Figure 3A and3B. Both curves exhibit type-IV profiles with hysteresis loops characteristic of large mesopores, according to the IUPAC classification.

The surface properties data; i.e. the specific surfaces areas and cumulated pore volumes, for both prepared materials have been gathered in Table 1. The specific surface areas are high for such type of materials with a value close to 40 m 2 /g. For both non-oxides tungsten-based samples, a broad pore-size distribution was observed in the large mesoporesmall macropore range (insert of Figures 3A and3B) but caution should be taken regarding the given values since nitrogen physisorption is not accurate for such large pore sizes. This type of porosity corresponds to an interparticular porosity, with an average size around 30 -50 nm, that could be related to the templating process. Calculated pore volumes (BJH method) for pores below 100 nm (insert Figures 3) display values around 0.26 and 0.20 cm 3 /g for WS 2 and W 2 N samples respectively. Since spherical silica nanoparticles template removal is supposed to lead to spherical pores shape that does not fit with the cylindrical pore shape considered for pore size calculation by BJH model, direct comparison between pore size and silica particle diameter could not be done.

Nevertheless, these values should be in the same order of magnitude [START_REF] Rocha | Improvement in the pore size distribution for ordered mesoporous materials with cylindrical and spherical pores using the Kelvin equation[END_REF]. Owing to the large mesopore size observed, complementary analysis was performed by Hg porosimetry. Mercury porosimetry performed on both samples displayed similar features: a broad pore size distribution in the whole pore size range explored (5 nm -10 μm). Two main contributions of pores can nevertheless be observed for both samples: the first one is centered on 10 μm and could be attributed to inter-agglomerate porosity whereas the second is in the mesopore -small macropore range and was ascribed in the interparticular porosity probably templated by the silica spheres. This second porosity is well defined for W 2 N samples (upward swing around 50 nm in Figure 4B) whereas it is broadly distributed for WS 2 sample (with may be a small maximum around 10 nm). Even if nitrogen physisorption is not adapted to accurately measure large mesopores and small macropores, Hg porosimetry data are in good agreement with N 2 adsorption regarding pore volumes measured in their common pore size range (pore size below around 100 nm). Indeed, Hg-cumulative pore volume values are 0.24 and 0.21 cm 3 /g to be compared to N 2 -cumulative pore volume of 0.26 and 0.20 cm 3 /g for WS 2 and W 2 N samples, respectively. The mesoporosity detected by both techniques evidences the templating effect of silica nanospheres. The low magnifications pictures of both materials exhibit powders constituted of agglomerated particles with nanosized dimensions. For the tungsten disulfide (Figure 5A), the particles exhibit a typical layered morphology as reported in the literature [17,[START_REF] Sun | Synthesis and structural characterization of tungsten disulfide nanomaterials[END_REF][START_REF] Shi | Synthesis of Highly Ordered Mesoporous Crystalline WS 2 and MoS 2 via a High-Temperature Reductive Sulfuration Route[END_REF] while particles with a coalesced sphere-shape morphology, are observed for the tungsten heminitride material having a cubic structure (Figure 5B). These different aspect ratios related to isotropic and anisotropic crystal growths could explained why only the W 2 N sample succeed to maintain the templated pore size in the mesoporous range (population of pores around 50 nm, evidenced by Hg porosimetry in Figure 4B)while a broader pore size distribution is encountered in the case of WS 2 (Figure 4A). The high-resolution TEM images (insert of each low magnification picture) clearly show that the particles are well-crystallized since crystallographic planes are noticed. Moreover, from these images, an approximate particle size may be determined; ranging from 20 to 30 nm for the tungsten nitride and 5 -10 nm and 40 -50 nm (thickness and length), for the tungsten sulfide material.

Additional characterizations of the WS 2 and the W 2 N were provided by scanning electron microscopy.

Representative micrographs are shown within Figure 6A and 6B. The disulfide and nitride samples are featured by highly agglomerated nanoparticles exhibiting a quasi-spherical morphology. From a meticulous observation, the particle size ranges from 20 to 30 nm which is consistent with the size of the WO 3 precursor material [START_REF] Gibot | Synthesis of WO 3 nanoparticles for superthermites by the template method from silica spheres[END_REF] implying that no significant structural modification occurred during the oxide-to-sulfide and oxide-to-nitride conversions. This observation can be largely attributed to the presence of the siliceous hard template during the reductive treatment under hydrogen sulfide or ammonia environments of the [WO 3 /SiO 2 ] nanocomposite. Indeed, sulfidation or nitridation of WO 3 material (obtained after the template removal of the [WO 3 /SiO 2 ] nanocomposite) led to bigger particles (> 50 nm) which appeared more sintered (Figure 7). The specific surfaces areas of the WS 2 and W 2 N samples were calculated as close to 16 and 18 m 2 .g -1 , respectively, which are nearly 2-2.5

times lower than the values obtained for the sulfide-and nitrogen-based samples synthesized from the sulfidation and nitridation of the [WO 3 /SiO 2 ] nanocomposites. The silica template causes a confinement effect of the oxide matter during the treatment under hydrogen sulfide or ammonia thus limiting the growth or the sintering of the resulting particles. By comparison with the literature, our WS 2 and W 2 N samples may be ranked as interesting materials regarding their specific surface areas (around 40 m 2 /g) and their process based on an economic and commercially available hard-template. For instance, tungsten disulfide was elaborated by heat treatment under reductive atmosphere either after a mechanical ball-milling step or by impregnation method (under vacuum or not) of three-dimensional ordered mesoporous silicas (hard templates) of SBA-15 or KIT-6 mesostructures. If in the first case, large scale fabrication can be considered, the specific surface appears limited (10.5 m 2 /g [START_REF] Wu | WS 2 nanosheets as a highly efficient electrocatalyst for hydrogen evolution reaction[END_REF]) whereas it is no more the case regarding the second process that offers surface areas up to 110-120 m 2 /g [START_REF] Liu | An ordered mesoporous WS 2 anode material with superior electrochemical performance for lithium ion batteries[END_REF][START_REF] Shi | Synthesis of Highly Ordered Mesoporous Crystalline WS 2 and MoS 2 via a High-Temperature Reductive Sulfuration Route[END_REF] with limited amount of material.

Moreover, these two approaches are more energy-and time-consuming (ball-milling of 24h, silica template synthesis) than our investigated route. Regarding the tungsten nitride material, the amplitude of variation of the specific surface area value is narrower since values of 17 m 2 /g to 79 m 2 /g were reported [START_REF] Shi | Catalytic activities of tungsten nitride for NO dissociation and reduction with hydrogen[END_REF][START_REF] Villaseca | Synthesis and characterization of tungsten nitride (W 2 N) from WO 3 and H 2 WO 4 to be used in the electrode of electrochemical devices[END_REF][START_REF] Meyer | Space-confined preparation of high surface area tungsten oxide and tungsten nitride inside the pores of mesoporous silica SBA-15[END_REF][START_REF] Mcgee | Basic properties of molybdenum and tungsten nitride catalysts?[END_REF][START_REF] Ko | Template-free synthesis and characterization of mesoporous tungsten nitride nanoplates[END_REF][START_REF] Giordano | Synthesis of crystalline metal nitride and metal carbide nanostructures by solgel chemistry[END_REF][START_REF] Bai | Synthesis and characterization of mesostructured tungsten nitride by using tungstic acid as the precursor[END_REF][START_REF] Kim | A study of preparation of tungsten nitride catalysts with high surface area[END_REF]. The nitrogen-based ceramic materials with the highest surface properties are essentially prepared from tungstic acid (WO 3 .xH 2 O) as tungsten precursor. This molecule is non soluble in aqueous medium that may be a potential drawback for the preparation of nitrides materials with well-defined morphologies (2D-, 3D-structures) by the hard-template route whereas for our process, the phosphotungstic acid is highly soluble in water (2 kg/L).

Conclusions

Meso-and macroporous tungsten disulfide (WS 2 ) and hemitungsten nitride (W 2 N) powders were successfully synthesized by means of tungsten (VI) oxide as tungsten source and colloidal silica acting as hard template. The surface properties of the WS 2 and W 2 N materials (specific surfaces areas ~ 40 m 2 .g -1 , pore volume of around 0.2 cm 3 .g -1 for pores below 100 nm) are comparable to the values given in the literature where non commercial templates have been used. To sum up, colloidal silicas may be a competitive solution for the development of mesoporous sulfides and nitrides ceramics since the template is easily available in large amounts, marketed in different particle sizes and more economic than the classical ordered mesoporous silica matrices (M41S, SBA, FSU…), conventionally used for similar research.

3. 1 .

 1 Characterizations of the [SiO 2 /WO 3 ] composite.

Figure 1 :

 1 Figure 1: Nitrogen adsorption-desorption isotherm (77K) and XRD pattern (insert) of the SiO 2 /WO 3 composite.

  ), (112) and (201) Miller planes which features a hexagonal structure (space group P6 3 /mmc) as related to the WS 2 material (JCPDS card No. 08-0237).

Figure 2 :

 2 Figure 2: XRD patterns of the tungsten disulfide WS 2 (A) and nitride W 2 N (B) synthesized from colloidal silica as hard template.

Figure 3 :

 3 Figure 3: Nitrogen adsorption-desorption isotherms and cumulative pore distribution curves (insert) of tungsten disulfide (A) and tungsten nitride (B) synthesized from colloidal silica as hard template.

Figure 4 :

 4 Figure 4: Cumulative pore volume and differential intrusion versus mean diameter pore size obtained by mercury intrusion porosimetry for WS 2 (A) and W 2 N (B) samples.

Figure 5

 5 Figure 5 displays the transmission electron microscope views of the WS 2 (Figure 5A) and W 2 N (Figure 5B) materials.

Figure 5 :

 5 Figure 5: TEM micrographs of the WS 2 (A) and W 2 N (B) prepared from colloidal silica template.

Figure 6 :

 6 Figure 6: SEM views of the WS 2 (A) and W 2 N (B) prepared from colloidal silica template.

Figure 7 :

 7 Figure 7: TEM views of the WS 2 (A) and W 2 N (B) materials prepared from sulfidation and nitridation of WO 3 material free of LudoxTM40 template.

Figure 1 :

 1 Figure 1: Nitrogen adsorption-desorption isotherm (77K) and XRD pattern (in insert) of the [SiO 2 /WO 3 ] composite.

Figure 2 :

 2 Figure 2: XRD patterns of the tungsten disulfide WS 2 (A) and nitride W 2 N (B) synthesized from colloidal silica as hard template.

Figure 3 :

 3 Figure 3: Nitrogen adsorption-desorption isotherms and cumulative pore size distribution curves (insert) of tungsten disulfide (A) and tungsten nitride (B) synthesized from colloidal silica as hard template.

Figure 4 :

 4 Figure 4: Cumulative pore volume and differential intrusion versus mean diameter pore size obtained by mercury intrusion porosimetry for WS 2 (A) and W 2 N (B) samples.

Figure 5 :

 5 Figure 5: TEM views of the WS 2 (A) and W 2 N (B) prepared from colloidal silica template.

Figure 6 :

 6 Figure 6: SEM views of the WS 2 (A) and W 2 N (B) prepared from colloidal silica template.

Figure 7 :

 7 Figure 7: TEM views of the WS 2 (A) and W 2 N (B) materials prepared from sulfidation and nitridation of WO 3 material free of LudoxTM40 template.

  Figure 1 Click here to download high resolution image

  15, KIT-6), as nanostructurated host materials, infiltrated by diverse tungsten precursors such as phosphotungstic acid (PTA, H 3 PW 12 O 40 .xH 2 O) and ammonium metatungstate (AMT, (NH 4 ) 6 (H 2 W 12 O 40 ).xH 2 O) and then exposed to H 2 S and NH 3 gaseous environments for the preparation of 3D-mesoporous WS 2

Table 1 : Surface properties, determined by N 2 physisorption (77K), of the nanocomposites [W-based ceramic/silica hard template] (1) and the W-based ceramics after the silica template removal (2). * determined from the BJH method for pores below 100 nm.

 1

Table caption Table 1 : Surface properties, determined by N 2 physisorption (77K), of the nanocomposites [W-based ceramic/silica hard template] (1) and the W-based ceramics after the silica template removal (2). * determined from the BJH method for pores below 100 nm.

 caption1

Table

	Table caption
	Ceramic	Specific surface area (m 2 /g)	Pore volume* (cm 3 /g)
	W 2 N_TM40 (1)	19	0.05
	W 2 N (2)	37	0.20
	WS 2 _TM40 (1)	20	0.06
	WS 2	(2)	38	0.26