A Aubin

R Ansart

M Hemati

T Lasuye

M Branly

MODELING AND SIMULATION OF DRYING OPERATION IN PVC POWDER PRODUCTION LINE: A PNEUMATIC DRYER MODEL

Keywords: pneumatic dryer, PVC, shrinking core, kinetic, model

A one-dimensional steady-state model is developed to simulate drying of PVC powder in a pneumatic dryer. In this model, a two-phase continuum model was used to describe the steady-state flow of a dilute dispersed phase (wet PVC powder) and a continuous phase (humid air) through dryer. The particle scale kinetics was obtained by immersion of a fixed mass of wet PVC's particles (cake) in a batch dense fluidized bed containing inert hot particles (glass bead). The drying kinetics was described by a shrinking core type model and integrated in pneumatic dryer model. The results show that the inlet temperature is the most important parameter in the operation. The drying rate is controlled by a two-stage process. The first stage corresponds to the surface water evaporation, and the second to the pore water evaporation.

INTRODUCTION

In PVC powder production line, after the polymerization step, a suspension, composed of water and PVC particles, is obtained. Most of this suspension's water is eliminated during a centrifugation step, leading to a wet porous powder, called "cake". The cake drying occurs essentially in a pneumatic dryer coupled with a fluidized bed dryer that role is to eliminate the residual humidity of PVC (less than 0,05 kg water/kg dry PVC). This operation consumes a lot of energy, between 125 and 375 J / kg dry PVC, in accordance to the operating conditions and the PVC's grade.

The pneumatic dryer is a technology commonly used in order to eliminate free or barely-bound water. A pneumatic dryer is a continuous, convective dryer with dilute solid transport. This technology presents numerous advantages [START_REF] Strumillo | Drying: principles, applications and design[END_REF][START_REF] Ouyang | Short contact time gas-solid systems[END_REF] such as:

• the short resident time of particles allows to dry thermosensible product, • in parallel flow, high temperature can be applied at the inlet giving high thermal efficiency, • the dryer can be used as a transport system.

With the purpose to optimize the drying process, i.e. reduces the energy consumption, this study focuses on: (i) the acquisition of the kinetics data in a batch dense fluidized bed, (ii) the modeling of the dehydration of PVC's particles in a pneumatic dryer.

DRYING KINETICS

Porous media drying is a complex problem, still not well-understand despite of the numerous studies that can be found in the literature, due to the coupled exchanges (mass, heat, and momentum transfers) between the gas and the particles [START_REF] Kowalski | Drying of porous materials[END_REF][START_REF] Prat | Recent advances in pore-scale model for drying of porous media[END_REF][START_REF] Segura | Pore-level modeling of isothermal drying of pore networks. Effect of gravity and pore shape and size distributions on saturation and transport parameters[END_REF].

As shown in figure 1, during the drying of a porous particle, two periods can be distinguished. The first period consists in the elimination of the free water located at its surface. In this case the evaporation is controlled by external transfers depending on the local relative velocity between the air and the particles, called slip velocity. These transfers depending on the drying technology have been widely studied, and the literature provides a lot of correlations, some times contradictory, for its estimation. In the second period, the water located in the particle's pore, is eliminated: the drying is controlled by a combination between external transfers.

In the case of porous particle, according to the of the solid, the internal transfers can be drive b or a combination of several elementary mechanisms such as:

• the capillarity effect, • the migration in adsorbed phase diffusion), • the vapor diffusion through the pores. The SEM pictures of PVC particles suspension polymerization process, particle can be represented by a " structure constituted of elementary diameter (see Fig. 2). The pore size distribution obtained by mercury porosimetry, families of pores (see Fig. 3):

• From 200 to 10 000 nm: the space between the primary particles. • From 50 to 200 nm: the primary particles porosity.

According to the Kelvin's law, the effect of the pore mean size diameter on water activity can be neglected for the values greater than 10 nm. According to the figure 3, the capillary effects can be neglected in the case of PVC's particle drying.

In the aim of characterizing the affinity of PVC toward the water vapor, some experiments between internal and ccording to the nature can be drive by one a combination of several elementary mechanisms migration in adsorbed phase (or liquid he vapor diffusion through the pores.

Particle drying PVC PROPERTIES les, produced by the , show that each can be represented by a "Pellet-grain" of elementary grains of 1 µm . The pore size distribution, obtained by mercury porosimetry, shows two he space between primary particles' According to the Kelvin's law, the effect of the pore mean size diameter on water activity can be glected for the values greater than 10 nm. , the capillary effects can be neglected in the case of PVC's particle drying.

the affinity of PVC , some experiments concerning the sorption equilibrium carried out. The results show that small affinity with water vapor containing 75% of relative humidity, the PVC's equilibrium humidity is about 2.4 g PVC). Moreover the PVC is the migration in adsorbed phase can be neglected. According to the nature of PVC's particles elementary mechanism can be transfer is the water vapor's diffusion through the pores.

In order to minimize the external effects, the kinetics study was performed by immersion of a fixed mass of wet PVC's particles (cake) fluidized bed containing inert bead). The complete description of the apparatus and that of the experimental procedure are presented elsewhere [START_REF] Aubin | Model and simulation of drying operation in PVC powder production line: Experimental and theoretical study of drying kinetics on particle scale[END_REF]2012t). The influence of the temperature, the water vapor pressure, the PVC grades and the fluidizing gas vel investigated. The evolution of the PVC humidity versus time is described correctly by a " core" type model.

KINETICS MODEL AT PARTICLE SCALE

In the shrinking core type model 4, particle's humidity is concentrate which will shrink during the drying and so form a dry crust at particle's surface [START_REF] Mezhericher | Heat and mass transfer of single droplet/wet particle drying[END_REF][START_REF] Mezhericher | Heat and mass transfer of single droplet/wet particle drying[END_REF][START_REF] Cheong | A receding interface model for the drying of slurry droplets[END_REF]. tion equilibrium have been ried out. The results show that the PVC has a vapor (e.g. in an atmosphere 75% of relative humidity, the PVC's equilibrium humidity is about 2.4 g of water / kg of insoluble in water, so the migration in adsorbed phase can be neglected. The complete description of the apparatus and that of the experimental procedure are presented elsewhere [START_REF] Aubin | Model and simulation of drying operation in PVC powder production line: Experimental and theoretical study of drying kinetics on particle scale[END_REF]2012t). The influence of the temperature, the water vapor pressure, the PVC grades and the fluidizing gas velocity are investigated. The evolution of the PVC humidity me is described correctly by a "shrinking AT PARTICLE SCALE shrinking core type model, as shown in figure , particle's humidity is concentrated in a moist core which will shrink during the drying and so form a dry [START_REF] Mezhericher | Heat and mass transfer of single droplet/wet particle drying[END_REF][START_REF] Mezhericher | Heat and mass transfer of single droplet/wet particle drying[END_REF] The evaporation takes place at the surface of the moist core, and the water vapor diffuses through the dry crust. To determine the drying kinetics the mass balance on a single particle is realized. The balance takes into account the water vapor diffusion through the crust and water vapor exchange at particle's surface. So, the rate of mass transfer can be expressed as:

ܰ ሶ ௪ ൌ ܭ ௬ . ሺܻ כ െ ܻ ஶ ሻ. (1)
Where Y * is the equilibrium humidity, Y ∞ the humidity of the air far from the particle, and K y is the global mass transfer coefficient expressed as:

ܭ ݕ ൌ ݇ ݕ ݅ܤ ܯ .ቀ ݀  ݀ ݄ ൗ െ1ቁ1
.

(

) 2
Where k y is the convective mass transfer coefficient, d p and d h the respective diameter of the particle and the humid core, and Bi M the dimensionless number called Biot number relative to mass transfer. This number represents the competition between external and internal transfer:

݅ܤ ெ ൌ .ோ ೌ .ఘ . ( 3
)
Where R is the particle's radius, ρ g the gas density, and D app the diffusion coefficient of water vapor in the air within a pore, calculated from the binary diffusion coefficient, D bin :

ܦ ൌ ܦ ఞ ఛ (4)
The porosity, χ, and the tortuosity, τ, values are indicated in the table 3.

Gas phase

ܨ . ܪ݀ ݖ݀ ൌ ܳ ՜ ܳ ௪՜ ܣ . Γ . ܪ ௪ (8)
Momentum balances Solid phase

߲ ݖ߲ ൫ߙ . ߩ . ܷ ଶ ൯ ൌ ߙ . ߲ܲ ݖ߲ െ ߙ . ߩ . ݃ ܫ ݃՜ (9)
Gas phase

߲ ݖ߲ ൫ߙ . ߩ . ܷ ଶ ൯ ൌ ߙ . ߲ܲ ݖ߲ െ ߙ . ߩ . ݃ ܫ ՜ ൣܷ െ ܷ ൧. Γ ܨ ,௪՜ (10)

Model's hypothesis

The aim of this study is to model a pneumatic dryer using the particle scale kinetics previously elaborated. In this model, a two-phase continuum model was used to describe the steady-state flow of a diluted dispersed phase (wet powder) and a continuous phase through a pneumatic dryer. The model is based on the following assumptions:

• Mass, energy and momentum balances occur between the two phases. • The frictions forces between the dispersed phase and the wall can be neglected.

Balance equations

The mass, energy, and momentum balances developed in one-dimensional steady-state for both phases are presented in table 1. The transport equations for solid and gas humidity, deduced from the masse balances, are also included in this table.

Complementary equations

The volume rate of mass transfer Γ p , is expressed from the rate of mass-transfer ˙ܰሶ ௪ .

Γ ൌ െΓ ൌ െߙ . ݏ . ܰ ሶ ௪ . ( 13
)
Where α p is the local volume fraction of solid and s p the specific surface area of a particle.

As shown on figure 1, the particle's drying occurs in two periods [START_REF] Borde | Steady state one dimensional flow model for a pneumatic dryer[END_REF]. During the first period, the mass transfer is convective. Then the expression of the global mass transfer coefficient can be simplified as following:

ܭ ௬ ൌ ݇ ௬ . ቀ ఘ . ఘ ೢೌ 1 െ ߯ቁ. (14)
Where ρ p is the solid density, ρ water the liquid water density and χ the particle porosity.

During the second period, the mass transfer is convective and diffusive, and the global mass transfer is given by equation ( 2). This period starts when the surface humidity is totally eliminated, which means that the particle's humidity reaches a critical humidity, X c :

ܺ ൌ ఘ ೢೌ .ఞ ఘ . ( 15
)
The energy transfer between the two phases is expressed as followed:

ܳ ՜ ൌ െܳ ՜ ൌ ߙ . ܣ . ݏ . ݄. ൫ܶ െ ܶ ൯. ( 16
)
Where A c is the pipe cross section, h the heat-transfer coefficient, and Tp and Tg, the, respectively, solid and gas phase temperature.

Only the forces due to dragging are taken into account in the momentum transfer:

ܫ ՜ ൌ െܫ ՜ ൌ ଷ.ఈ .ఘ . మ . ସ.ௗ . ( 17
)
Where U r is the slip velocity.

The drag coefficient, Cd, is calculated by the Wen et Yu correlation (Schiller and Naumann, 1935):

ܥ ௗ ൌ ଶସ ோ ሺ1 0.15ܴ݁ .଼ ሻߙ ିଵ. (18)
The friction force between the pipe and the continuous phase is estimated by:

ܨ ,௪՜ ൌ .ఘ ଶ. . ܷ ଶ (19)
The friction factor, f, is calculated by the Blasius formula: Most of the correlations have been developed for a single particle, but in pneumatic dryers, collisions between particles occur. This has an important influence on the boundary layer surrounding the particle surface, and so on the transfers' rate. In order to model this phenomenon, Bandrowski (1977) expressed the Nusselt number as a function of the solid volume fraction, α p .

݂ ൌ ସ ோ ݂݅ ܴ݁ ൏ 2 100 (20) ݂ ൌ ,ଽଵ ோ భ/ర ݂݅

RESULTS AND DISCUSSION

The simulation data are resumed in table 3. The figures 5 and 6 represent the theoretical results obtained using the different correlations gathered in table 2 and the experimental founding of [START_REF] Baeyens | Pneumatic drying: the use of a large-scale experimental data in a design procedure[END_REF]. The results obtained with correlations of Ranz-Marshall (developed for a single particle), Gamson, and Kothari (developed for a fluidized bed) show important deviations with experimental results and so are not presented on these figures. The differences observed between experimental data and theoretical results can be explained by the worst dispersion of the wet cohesive PVC in the gas phase at the pipe's inlet zone. The theoretical results which fit the best the experimental data have been obtained using Bandrowski's correlation. This can be explained by the effect of the slip velocity on the Reynolds number, and so on the heat and mass transfer coefficients. As shown on Figure 7, this magnitude is really important at the inlet and progressively decreases along the dryer. This leads to very important variation of the transfer coefficients (see Fig. 8). In Bandrowski correlation, this effect is attenuated by the solid volume fraction of the dispersed phase. Indeed, as the solid go through the dryer, it is dispersed by the gas phase and its volume fraction decreases strongly at the dryer's inlet. where the solid velocity increases). Particle temperature increases until a constant value, which corresponds to the constant rate drying period. Due to the evaporation surface reduction, a small rise can be observed. When particle humidity reaches the critical humidity, the falling rate drying period starts, and as the drying rate decreases, the particle temperature increase will be stronger (figure 9).

Parameters study

The results of the following simulations have been obtained using the Bandrowski's correlation (see table 3).

The effect of dry air mass flowrate has been examined between 25 and 46.4 t/h. As shown on figure 9, this parameter has a small influence on the drying rate above 35 t/h. The air velocity influences the drying rate only in the acceleration zone, then the slip velocity is equal to the terminal settling velocity.

At the dryer's outlet the air is far to be saturated, so the decrease of the dry air flowrate does not affect the drying driving force significantly (e.g. a decrease of dry air flowrate from 46 t/h to 35 t/h increases the outlet solid humidity from 0.054 to 0.067 kg water / kg dry PVC, and a decrease of dry air flowrate from 35 t/h to 25 t/h increases the outlet solid humidity from 0.067 to 0.097 kg water / kg dry PVC). Concerning the inlet air temperature, the figure 10 shows a dominant effect (e.g. an increase of inlet air temperature from 96°C to 156°C decreases the outlet solid humidity from 0.097 to 0.014 kg water / kg dry PVC). Indeed, increasing the temperature lead to a more important heat-transfer driving force. But as the equilibrium humidity depends on the temperature, it will also increase the mass-transfer driving force.

The inlet air humidity effect has been investigated between 0 and 0.0105 kg water / kg dry air. The last value corresponds to an atmospheric air (15°C) almost saturated (98.4% of relative humidity). As shown on figure 11, such an increase of inlet air humidity increases the outlet solid humidity from 0.052 to 0.054 kg water / kg dry PVC. This increase shows that the inlet air humidity, which is a sustained parameter, slightly influences the drying driving force. It can be noticed that the solid temperature is influenced by: • the dry air flowrate during the falling drying rate period only, • the air humidity during the constant drying rate period only, • the air temperature influences it during both periods. In fact the temperature stage value of the constant drying period is controlled by the drying driving forces. As shown in equations ( 1) and ( 13), this force depends only on the air humidity, Y ∞ , and the equilibrium humidity, Y * , which is directly related to the solid temperature. In the falling drying rate period, the solid temperature increases until the thermal equilibrium with the air, which is controlled by the dry air flowrate and temperature.

CONCLUSIONS

A one-dimensional steady-state model for pneumatic dryer was established. This model is applied for the drying process of wet PVC powder. The drying rate is controlled by convective transfer in the first period and by convective and diffusive transfer in the second. The first period corresponds to the surface water drying; besides the second corresponds to the evaporation of the water in the pores, simulate by a shrinking core model. The model takes into account the convective heat, masse and momentum transfers. Parameters study shows that the inlet temperature is the most important parameter in the operation. But this model does not take into account the wet powder dispersion, which is certainly the limiting step of this process.

NOMENCLATURE

Fig

  Fig. 1: Particle drying PVC PROPERTIES

Fig 2 :

 2 Fig 2: SEM picture of a PVC particle

Fig 2 :

 2 Fig 2: SEM picture of a PVC particle

Fig. 4 :

 4 Fig.4: The shrinking core model This model has been validated in a previous study of the drying kinetics at particle's scale obtained in fluidized bed[START_REF] Aubin | Model and simulation of drying operation in PVC powder production line: Experimental and theoretical study of drying kinetics on particle scale[END_REF][START_REF] Aubin | Model and simulation of drying operation in PVC powder production line: Experimental and theoretical study of drying kinetics on particle scale[END_REF]. The results have shown that the resistance of internal transfers is about 1.5 times bigger than the external resistance (Bi M ≅

•

  Electrostatic forces and surface tension effects are neglected.• The wall heat loss is neglected.

Fig. 5 :

 5 Fig. 5: Comparison between experimental data and simulation results with different correlations: evolution of particle's humidity

Fig. 6 :

 6 Fig. 6: Comparison between experimental data and simulation results with different correlations: evolution of air temperature

Fig. 9 :

 9 Fig. 9: Evolution of solid humidity and temperature along the riser for different dry air flowrates: 46.4 t/h, 35 t/h, and 25 t/h.

Fig. 11 :

 11 Fig. 11: Evolution of solid humidity and temperature along the riser for different inlet air humidity: 0 ; 0.005 ; 0.0105 kg water / kg dry air

Table 1 :

 1 Main equations

		Mass balances
	Solid phase Gas phase	݀ ݖ݀	݀ ݖ݀ ൫ߙ . ߩ . ܷ ൯ ൌ Γ ൌ െΓ ൫ߙ . ߩ . ܷ ൯ ൌ Γ	(5) (6)
		Energy Balances
	Solid phase	ܨ	.	ܪ݀ ݖ݀	ൌ ܳ ՜ ܣ . Γ . ܪ ௪

•

  The continuous phase, composed by a mixture of water vapor and other gas, is considered as an ideal phase.• The particles are spherical and composed of a homogeneous porous matrix. • The particles size's distribution is considered as monodisperse • Liquid water and PVC density are constant.


Nathan Brard

Johan Petit

Nicolas Emery

Nicolas Horezan

Stéphane Bach

Control of the nanostructure of MgO-Y 2 O 3 composite ceramics using two-step sintering for high temperature mid infrared window applications

Keywords: Y2O3-MgO nanocomposites, SPS, two-step sintering, sol-gel synthesis, IR transparent ceramic

Transparent Y2O3-MgO nanocomposite ceramic has been processed for mid-IR window applications. The powder was synthesized by a sol-gel route. The final temperature of this process has an impact on the crystallite size and crystallization ratio. A homogeneous powder with around 10 nm crystallite size was made with a final temperature of 600°C. The powder was then sintered by the SPS technique performing a two-step sintering process at 1200°C/50 MPa instead of a conventional bearing. A fully dense ceramic (>99%) with an average grain diameter of 150 nm (compared to 350 nm with one-stage sintering) was obtained. After HIP at 400 MPa and annealing in air for 100 h post-treatments, the IR transmittance in the 3-5 µm wavelength range exceeds 80% for a thickness of 1 mm. Transparency loss at 5 µm is less than 10% at 1000°C, which is more suitable for the IR's band II than materials such as sapphire, spinel or AlON.

1) Introduction

Transparent ceramics are materials of choice for high temperature infrared (IR) windows [START_REF] Goldstein | Transparent Ceramics at 50: Progress Made and Further Prospects[END_REF], [START_REF] Harris | Materials for Infrared Windows and Domes: Properties and Performance[END_REF]. Those windows are particularly used for aerospace applications. In this field, one of the challenges is to maintain sufficient IR transparency between 3 and 5 µm wavelength (band II) even at high temperature (1000°C) in atmospheric conditions. Indeed, these compounds show a degradation of their optical properties (transparency and emissivity) with the increase of temperature in the infrared because of the phonons' absorption [START_REF] Thomas | Infrared transmission properties of sapphire, spinel, yttria, and ALON as a function of temperature and frequency[END_REF], [START_REF] Harris | Durable 3-5 μm transmitting infrared window materials[END_REF]. Alumina, AlON and spinel-type ceramics have been developed for 3-5 µm band applications because of their transparency up to 6 µm [START_REF] Harris | Durable 3-5 μm transmitting infrared window materials[END_REF]. Nevertheless, at high temperature, strong absorptions occur below 5 µm and impact band II transparency limiting their use [START_REF] Thomas | Infrared transmission properties of sapphire, spinel, yttria, and ALON as a function of temperature and frequency[END_REF], [START_REF] Harris | Overview of progress in strengthening sapphire at elevated temperature[END_REF], [START_REF] Warner | Characterization of ALON optical ceramic[END_REF]. Thus, one way to go further is to find materials with a transparency beyond 6 µm to limit temperature impact on the 3-5 µm band transparency.

MgO and Y2O3 are transparent up to 9 µm but their thermomechanical resistances are quite weak when tested separately to be used in a harsh environment [START_REF] Harris | Durable 3-5 μm transmitting infrared window materials[END_REF]. However, many studies have combined these compounds into MgO-Y2O3 nanocomposite ceramics [START_REF] Kear | Submicron-grained transparent yttria composites[END_REF]- [START_REF] Jiang | Spark Plasma Sintering of an Infrared-Transparent Y2O3-MgO Nanocomposite[END_REF]. They proved that the nanostructure, assisted by the slowing down of granular growth due to their immiscibility [START_REF] Gleiter | Nanostructured materials: basic concepts and microstructure[END_REF], [START_REF] Xu | Hot Pressing of Infrared-Transparent Y2O3-MgO Nanocomposites Using Sol-Gel Combustion Synthesized Powders[END_REF], have permitted to keep a good IR transparency and increases its mechanical resistance. Thus, to reach such properties, the porosity ratio must be close to zero and the microstructure must be as homogeneous as possible. In addition, the average grain size must stay as small as possible (< 200 nm) due to the difference between MgO and Y2O3 refractive index values which leads to scattering at grain boundaries [START_REF] Apetz | Transparent Alumina: A Light-Scattering Model[END_REF]- [START_REF] Liu | Effect of volume ratio on optical and mechanical properties of Y2O3-MgO composites fabricated by spark-plasma-sintering process[END_REF] and to improve its mechanical properties [START_REF] Ryou | Below the Hall-Petch Limit in Nanocrystalline Ceramics[END_REF].

Several authors have developed dense MgO-Y2O3 nanocomposite ceramics with a homogeneous microstructure. Many powder synthesis routes have been reported: the mains are flame spray pyrolysis [START_REF] Jiang | Spark Plasma Sintering of an Infrared-Transparent Y2O3-MgO Nanocomposite[END_REF], colloidal dispersion of commercial powders [START_REF] Liu | Synthesis of highly-infrared transparent Y2O3-MgO nanocomposites by colloidal technique and SPS[END_REF], thermal decomposition [START_REF] Shen | Fabrication of infrared-transparent Y2O3-MgO composites using nanopowders synthesized via thermal decomposition[END_REF] and sol-gel method [START_REF] Chen | A Foaming Esterification Sol-Gel Route for the Synthesis of Magnesia-Yttria Nanocomposites[END_REF]. For sintering, natural sintering [START_REF] Wang | Infrared-Transparent Y2O3-MgO Nanocomposites Using Sol-Gel Combustion Synthesized Powder[END_REF], hot pressing [START_REF] Xu | Hot Pressing of Infrared-Transparent Y2O3-MgO Nanocomposites Using Sol-Gel Combustion Synthesized Powders[END_REF], [START_REF] Ma | Influence of microstructure control on optical and mechanical properties of infrared transparent Y2O3-MgO nanocomposite[END_REF] or Spark Plasma Sintering (SPS) [START_REF] Huang | Spark plasma sintering and mechanical behavior of magnesiayttria (50:50vol.%) nanocomposites[END_REF], [START_REF] Xie | Influence of moisture absorption on the synthesis and properties of Y2O3-MgO nanocomposites[END_REF] have been considered before an air annealing and/or a Hot Isostatic Pressing (HIP) post treatments. These materials exhibit very interesting optical properties (3-5 µm band transmission higher than 80% for a thickness of 1-2 mm) even up to 500°C (transparency higher than 76% and almost unchanged at 500°C for a thickness of 1mm) [START_REF] Shen | Preparation and study of the mechanical and optical properties of infrared transparent Y2O3-MgO composite ceramics[END_REF]. By reducing the grain size to less than 100 nm, transparency in the visible is even considered [START_REF] Liu | Evolution of microstructure, mechanical, and optical properties of Y2O3-MgO nanocomposites fabricated by high pressure spark plasma sintering[END_REF]. In addition, the composite has better mechanical properties (bending strength, thermal shock resistance) than pure MgO and Y2O3 [START_REF] Harris | Properties of an Infrared-Transparent MgO:Y2O3 Nanocomposite[END_REF]. Through this study, Pechini's esterification sol-gel route was chosen in order to process the nanocomposite powder [START_REF] Dimesso | Pechini Processes: An Alternate Approach of the Sol-Gel Method, Preparation, Properties, and Applications[END_REF], [START_REF] Ghorbani | Synthesis of MgO-Y2O3 composite nanopowder with a high specific surface area by the Pechini method[END_REF]. This route is based on the formation of chelate between magnesium and yttrium nitrate previously solubilized in deionized water with citric acid. The two cations are chelated and in a second step, with the presence of ethylene glycol, the chelates are cross-linked to create a gel through polyesterification. A powder is then obtained by oxidation when increasing the temperature. The sol-gel route was naturally chosen get a homogeneous nanometric powder dispersed in the polymeric network with an uniform distribution of cations. We have investigated the sol-gel synthesis by varying the final treatment temperature and the impact of the average crystallite size on the microstructure. We have carried out a novel two-step sintering by the SPS technique to densify our ceramics. The SPS has the advantage of being able to sinter quickly under pressure and a two-step sintering technique profile favors the densification over granular growth [START_REF] Chu | Precoarsening to Improve Microstructure and Sintering of Powder Compacts[END_REF]- [START_REF] Lóh | A review of two-step sintering for ceramics[END_REF]. Indeed, Ma et al. have successfully used a two-step hot pressing to improve density and transmission of a MgO-Y2O3 nanocomposite with limited grain growth [START_REF] Ma | Microstructural freezing of highly NIR transparent Y2O3-MgO nanocomposite via pressure-assisted two-step sintering[END_REF]. They reached a higher temperature before performing a decreasing to a long step of one hour at a lower temperature. In our work, a rapid cooling was performed after reaching the sintering temperature and just before an additional short 10 min step at the same temperature. To our knowledge, such a sintering profile has not been done yet on that compound. This whole process was followed by a post HIP treatment at 400 MPa. Finally, the optical transparency of these composite materials was determined up to 1000°C.

2) Material and methods

2.1) Synthesis of MgO-Y2O3 nanocomposite powder

MgO-Y2O3 nanocomposite powders were synthetized using the Pechini's process, with a composition leading to a volume ratio between the two oxides of 50:50 in the final sintered samples. An aqueous solution was prepared using magnesium nitrate hexahydrate (Mg(NO3)2•6H2O, 99.5%), yttrium nitrate hexahydrate (Y(NO3)3•6H2O, 99.5%), citric acid monohydrate (C6H8O7•H2O, 99.5%) and ethylene glycol (C2H6O2, 99%). The molar ratio of citric acid on ethylene glycol was settled to 3.39 and the molar ratio of citric acid on metal nitrates to 0.45, according to the proportions used by Xu et al. [START_REF] Xu | Spark plasma sintering of Y2O3-MgO composite nanopowder synthesized by the esterification sol-gel route[END_REF]. Both magnesium and yttrium nitrates were previously solubilized in deionized water. As a second step, an alumina crucible was filled with the solution. Batches of 10 g, for the first tests at different temperature, and then 50 g of powders were synthesized and heat treated in 0.5 L and 2.5 L alumina crucibles respectively. Crucibles were placed in an oven at 200°C for 3 h to evaporate the water of the solution. Once the gel was formed, crucibles were put in a muffle furnace preheated at 200°C. Afterwards, the furnace was heated at a rate of 100°C/h from 200°C to a temperature included between 600°C and 1200°C, and kept 2 h at the chosen temperature to obtain the powder (FIG 1). After this thermal treatment, the powder was crushed in a glass mortar and sieved at 50 µm. The MgO-Y2O3 nanocomposite powders were finally dried in an oven at 150°C and stored into a desiccator.

FIG 1. MgO-Y2O3 nanocomposite powder (10g) obtained after the 600-1200°C heat treatment (thermal sol-gel process). Inner diameter of the crucible = 90mm. (1-column fitting image)

2.2) Sintering

These powders were sintered using our SPS facility with unpulsed direct current. ONERA's SPS can deliver currents up to 40 kA and a force up to 250 t, allowing samples of 20 to 300 mm in diameter to be sintered. A graphite die was filled in with powder to make pellets with a 30 mm diameter and a 3 mm thickness (after sintering). Electric and thermal contacts between rams, powder and mold were provided by two layers of 0.25 mm thick graphite paper. For the sintering treatments, two thermal profiles were used with a maximum temperature of 1200°C. In both of them, ramps of 200°C/min under 50 MPa were applied to reach 1200°C with a presintering dwell of 5 min at 850°C during which the pressure is increased from 10 MPa to 50 MPa (FIG 2). The first thermal profile was composed of a simple step of 10 min at 1200°C. The second thermal profile was composed of two steps: first, the temperature was raised up to the sintering temperature (1200°C) and at this temperature the power was stopped and the pressure was suddenly released to let the sample cool down naturally to room temperature. This step is a kind of "quenching". A second step is then added with a classical dwell of 10 min at 1200°C (FIG 2). For the rest of this study, the two profiles will be referred as "one-step" or "twostep" process. In order to better interpret the difference of the profile, a sample was analyzed just after the first heating of the two step profile. Furthermore, temperatures were both measured by an optical pyrometer focusing on a hole in the side of the die and a thermocouple measuring the temperature through one of the two pistons at 4 mm from the center of the sample. The temperature process was controlled by the thermocouple temperature.

FIG 2. Thermal profiles for the SPS process: a) with "one step" b) with "two step". (1-column fitting image)

Sintered samples were then Hot Isostatically Pressed (HIP) at 1200°C under 400 MPa for 2 h. Then, samples were air annealed in a muffle furnace for 20 to 100 h at 1000°C. Finally, a polishing down to 1/4 µm was carried out prior to their characterizations.

2.3) Characterization

Thermogravimetric analysis of the sol-gel synthesis and pure magnesium and yttrium nitrates hexahydrated oxidation were performed from distinct analyses under air using alumina crucibles. The MgO-Y2O3 nanocomposite powder was observed by transmission electron microscope (TEM) and analyzed by X-ray diffraction (XRD) using a diffractometer with a Co K𝛼 source. GSAS-EXPGUI package [START_REF] Larson | General structure analysis system (GSAS)[END_REF], [START_REF] Toby | EXPGUI, a graphical user interface for GSAS[END_REF] was employed to analyze the diffraction patterns with the Rietveld method to determine the ratio of crystallized MgO and Y2O3 of the total crystalline phases and the average crystallites sizes using the Scherrer formula. For sintered samples, their microstructure was observed using a scanning electron microscope (SEM). Images were collected on polished slices of sintered samples and the average grain size was measured using the intercept method on the SEM pictures with a coefficient of 1.56 [START_REF] Mendelson | Average Grain Size in Polycrystalline Ceramics[END_REF]. Moreover, the porosity ratio was measured using the Archimedes method, assuming a density of 4.293 g/cm 3 for the 50:50 vol% composite. The accuracy of that method is around 1%. Optical transmission in the near and the mid infrared of the MgO-Y2O3 nanocomposite samples were performed using a Fourier Transform IR spectrophotometer. Transmission curves were measured on samples of a given thickness and then recalculated to correspond to a thickness of 1 mm to facilitate the comparison between samples. For this purpose, the attenuation coefficient, as a function of wavelength, 𝛼(𝜆) (cm -1 ), is calculated from equation ( 1) with taking into account multiple reflections on the surfaces [START_REF] Apetz | Transparent Alumina: A Light-Scattering Model[END_REF], [START_REF] Krell | Transmission physics and consequences for materials selection, manufacturing, and applications[END_REF]:

𝛼(𝜆) = 1 𝑙 ln [ 2𝑛(𝜆) 𝑅𝐼𝑇(1 + 𝑛(𝜆) 2 ) ] (1)
Where 𝑅𝐼𝑇 is the Real In line Transmission, 𝑙 (cm) the thickness of the sample and 𝑛(𝜆) is the refractive index of the sample at the wavelength . The average index between the two indices of MgO and Y2O3 at 4.85 µm, 𝑛 𝑀𝑔𝑂-𝑌 2 𝑂 3 = 1.7321, have been chosen from Harris et al. [START_REF] Harris | Properties of an Infrared-Transparent MgO:Y2O3 Nanocomposite[END_REF]. This results in 86 % for the theoretical transmittance limit, taking into account perfect diopter reflections. A special care should be taken when analyzing the graphs because this calculation can significantly amplify error below 15 % of transmission.

At last, the high-temperature transmission measurements were carried out using a specific IR scanning spectrophotometer assembled at ONERA. The sample is heated in a chamber at temperatures ranging from 20 to 1000°C. Measurements are made using a monochromator, a lock in amplifier, anti-reflected ZnSe optics, an IR lamp, a long-pass filter at 4.5 µm and a 77K cooled MCT detector.

3) Results and discussion

3.1) Powder synthesis, crystallite size and quality

The different steps of the sol-gel process were investigated by thermogravimetric analysis shown in the The synthesis seems to be completed at 800°C. Increasing the temperature of the thermal treatment will affect the crystallinity of the powders. We tested treatments with a temperature between 600°C and 1200°C. XRD analyses confirm that for all the temperatures, both MgO and Y2O3 are present without any additional phase (FIG 5). The higher the temperature, the lower the full half maximum width of the diffraction peaks is, meaning an increasing average grain size. Then, Rietveld refinements were performed using the GSAS-EXPGUI software suite with a good correlation to the experimental curves (FIG Relevant refined parameters are given in Table 1. It can be noted that lattice constants decreases with the increase of the synthesis temperature. According with the nanoparticles behaviors, the lattice parameter decreases as the crystallite size increases for nanometric sizes [START_REF] Deshpande | Size dependency variation in lattice parameter and valency states in nanocrystalline cerium oxide[END_REF]. Results from the treatment of the diffractograms by Rietveld refinement were undertaken to determine the mean grain size of crystallites inside the powders. They are presented in the FIG 6. First, the mean crystallite diameter of the powder increases logically with the temperature (FIG 6a). The average crystallite diameter goes from 10 nm at 600°C to about 70-80 nm for a temperature of 1200°C. Moreover, the FIG 6b shows the evolution of the crystalline phase ratio of MgO in the total crystalline phase (MgO + Y2O3) as a function of the final temperature treatment of the powder. It suggests that magnesia crystallizes at a lower temperature than yttria and the expected theoretical volume ratio (50/50) appears beyond 800/900°C. Below this temperature, a higher fraction of Y2O3 than MgO remains amorphous. However, it is expected that the yttria amorphous fraction will crystallize during the sintering process (around 1200°C), leading to a sintered sample without amorphous domains. In addition, keeping a small crystallite size by heating the powder at a lower temperature will have a positive impact on the final grain size after SPS treatments.

3.2) SPS Sintering and grain size

Several samples have been processed to study the impact of the crystallite size but also of the thermal treatment on the post-sintering microstructure. Table 2 summarizes the process parameters corresponding to the samples and gives the average grain diameters of each ceramic as well as their porosity ratio. Samples' microstructure by SEM micrographs are presented in FIG 7. On the one hand, a classical one-step sintering as presented in the experimental part was performed on the synthesized powders prepared at 600 to 1000°C by the sol-gel process. After a same sintering procedure, a finer microstructure is obtained for ceramic prepared from finer powder. An increase of about 100 nm of the average grain diameter is observed between the nanocomposite sintered from a powder prepared at 600°C (1A) and the ceramic obtained from powder prepared at 1000°C (1D). Nevertheless, the one-step sintering thermal profile is not efficient enough in terms of control of the grain size and improvement of the density. Indeed, in all these samples, the density remains around 90%, which is too low to expect a good IR transmission. The origin of this quite low density could be explained by the characteristics of the powder such as the morphology and distribution of aggregates. Xie et al. have highlighted the possible creation of porosity if a rapid moisture release occurs during sintering because the hydrophilicity of MgO-Y2O3 nanopowders [START_REF] Xie | Influence of moisture absorption on the synthesis and properties of Y2O3-MgO nanocomposites[END_REF]. In the present study, even with a powder treated above 1000°C (1D), the density is still quite low.

On the other hand, as presented in the experimental part, our novel two-step SPS sintering profile has been tested in order to improve the quality of the ceramic. The Table 2 sums up the characteristics of the two-step sintered samples from the powder treated at 800°C (2A). Post treated ceramics by air annealing at 1000°C for 20 h (2C), by HIP at 1200°C under 400 MPa for 2 h (2D) and by HIP (same conditions) followed by air annealing 20 h (2E) or 100 h (2F) are also shown. The sintering of the sample 2B was stopped in the intermediate stage, after the first rapid cooling and before the 10 min stage. As seen in the Table 2 the two-step SPS treatment allows to keep the grain size twice as small as with the one-step profile and also to keep the porosity ratio below 1%. Adding post treatments makes the grain size grow but it stays below 250 nm.

So, the two-step sintering method as proposed in the present work is clearly an effective process to prepare MgO-Y2O3 nanocomposites with a high densification and a reduced grain size. The two-step profiles proposed by Chu et al. [START_REF] Chu | Precoarsening to Improve Microstructure and Sintering of Powder Compacts[END_REF] or from Chen and Wang [START_REF] Chen | Sintering dense nanocrystalline ceramics without final-stage grain growth[END_REF] are slightly different than ours and have also yielded good results in grain growth inhibition. They explain that the reduction of the driving force for grain growth could be obtained with the modification of the grain size distribution and the creation of a network of grain boundaries anchored by the relatively immobile three-grain junction lines, the four-grain junction points and so on. The energy required for the migration of these junctions is quite high and, at the second step, favours the diffusion along the grain boundaries limiting the grain growth. If a critical density is initially achieved in the first step, there are enough of those junctions throughout the sample to inhibit the migration of grain boundaries in the following phase [START_REF] Lóh | A review of two-step sintering for ceramics[END_REF], [START_REF] Wang | Two-Step Sintering of Ceramics with Constant Grain-Size, I. Y2O3[END_REF]. In this study, the intermediate sample (2B) has a porosity ratio of 10% which seems to be enough to avoid the grain growth during the second step. As the temperature in the second step is similar to the first one, the thermal history of this material (i.e., the sudden cooling at the beginning of the step) plays a significant role. The formation of a microstructure favouring diffusion at grain boundaries as described above could be promoted by the rapid cooling and the pressure release.

In addition, the two post-treatments are very important to improve the quality of our material. In the case of air annealing, the objective is to reduce mechanical stresses within the ceramic and to fill the oxygen vacancies formed during SPS sintering, which is a reducing environment. Otherwise, the HIP treatment increases the sample density as much as possible. As shown in the FIG 7 and Table 2, both processes (2C and 2D) slightly increase the grain size which still stays fine. Optimization of the annealing and HIP parameters will be done in further work.

3.3) Optical properties

The FT-IR spectrometer transmittance of the samples are given in the FIG 8. These curves are calculated from experimental curves to correspond to a 1 mm thick sample. Firstly, near and mid-infrared transmittance of 1C and 2A samples, sintered with the same powder, are compared. The transmittance of the two-step sintered sample, which has a finer and denser microstructure, is clearly higher than the one obtained with the onestep profile, which has a porosity ratio of almost 10%. Indeed, the transparency of the former reaches about 55% between 4 and 6 µm for a thickness of 1 mm whereas, for the latter, it stays below 20%. Nevertheless, two absorption bands can be observed: one around 3 μm is related to the remaining hydroxyled compounds. This band is particularly annoying because it affects the 3-5 µm band.

The second absorption band around 7 μm would be caused by the stretching vibration of a carboxylate group because of carbon contamination from the SPS or from the sol-gel process [START_REF] Yong | Study on carbon contamination and carboxylate group formation in Y2O3-MgO nanocomposites fabricated by spark plasma sintering[END_REF]. To improve the transparency, the results of several post-treatments are then presented in the FIG 8. The HIP at 400 MPa (1200°C, 2 h), which reduces the size and quantity of the pores, greatly improves the overall transparency of the sample 2D. In this case, the transparency for 1 mm thickness reached 70% at 5 µm. However, this process does not have an impact on the different absorption peaks. Subsequently, air annealing further improves the overall transparency of the samples 2E and 2F. It goes up to around 75% at 5 µm for a 20 hours treatment and exceeds 80% for a 100 hours treatment. Annealing also reduces significantly the absorption band around 3 µm. Unfortunately, the peak around 7 µm is not affected. Some authors showed that it is possible to make it disappear by using additives such as LiF in the powder [START_REF] Ma | Insight into the scavenger effect of LiF on extinction of a carboxylate group for mid-infrared transparent Y2O3-MgO nanocomposite[END_REF]. However, this peak is not located between 3 and 5 µm wavelength and so does not really affects the potential applications in that range. However, we needed to check that the band does not move to the 3-5 µm range when the temperature increases. ). This is due to the 2 mm thickness and also because the detector in the high temperature transmission bench is located at a much longer distance from the sample than in the FTIR spectrometer (FIG 8). Nevertheless, when the temperature increases, the sample transmittance decreases gradually from the longer wavelength to the shorter wavelengths. This behaviour is related to multiphoton absorption. When the temperature increases, there is more energy and a higher probability for multiples phonon to absorb a photon, decreasing the transmittance [START_REF] Harrington | Temperature Dependence of Multiphonon Absorption[END_REF]. Consequently, the material's emissivity also increases, which may have a strong impact on the signal to noise ratio measured by an IR detector according to the application [START_REF] Thomas | Infrared transmission properties of sapphire, spinel, yttria, and ALON as a function of temperature and frequency[END_REF], [START_REF] Harris | Durable 3-5 μm transmitting infrared window materials[END_REF]. This is a well-known limit of the infrared windows at high temperatures. In the MgO-Y2O3 nanocomposite material, at 5µm, there is almost no effect up to 500°C and then it decreases very slowly. At 1000°C, the loss of transparency remains below 10%. After measurement at high temperature, another measurement was carried out à 20°C to verify that there is no irreversible modification of the sample quality. This measurement, presented in the FIG 9 too, shows a very slight loss of the transparency, surely due to partial reduction of the sample during the measurement in the graphite furnace. To conclude, compared to the other well-known materials whose optical properties at 5 µm temperature are summarized in the Table 3, those measurement confirm that losses in 3-5 µm band are less significant in MgO-Y2O3 that in sapphire for example. Furthermore, the absorption peak at 7 µm due to carbon pollution during the production process does not change in temperature and does not seem to be a problem.

4) Conclusion

Nanocomposite powders of magnesia and yttria with a volume ratio of 50:50 have been synthetized by a sol-gel route. By varying the temperature treatment in this process, it was possible to obtain grains of varying sizes and we observe different amorphous/crystalline phase ratio. With a synthesis at 1200°C, crystallites between 70 and 80 nm were obtained. By lowering the synthesis temperature to 600°C, the crystallite size is reduced to about 10 nm. Using powders produced at lower temperatures resulted in sintered materials with finer microstructures.

Next, a novel two-step profile was proposed for SPS sintering. The rapid cooling and the pressure release, seem to have to be taken into consideration in the formation of the intermediate microstructure in two-step sintering. Compared to a conventional one-step sintering profile, it significantly improved the sample quality by reducing the grain size and the porosity ratio. At 1200°C (200°C/min) and under 50 MPa, the two-step sintering resulted in Y2O3-MgO nanocomposite ceramics with an average grain diameter of about 150 nm (compared to 350 nm with one-step sintering) and a density over 99% (compared to 90% with a one-step sintering). Finally, after post treating the material with HIP at 400 MPa and annealing in air for 100 h, the IR transmission for a thickness of 1 mm exceeds 80% in the IR band II between 3 and 5 µm wavelength. Due to the process, parasitic absorption bands appeared at 3 µm and 7 µm. The first one is in the 3-5 µm range but can be removed by air annealing. The second one is not the the IR band II so for application in that range, it is not a real issue. Moreover, there is almost no opacification at 5 µm up to 500°C and very few up to 1000°C.

The SPS and HIP parameters still need to be optimized, and the processing of bigger parts (up to 100 mm diameter) is under progress.

FIG 3 .

 3 FIG 3. Thermogravimetric analysis (rise in 3°C per min). a: mass loss as a function of the temperature during sol-gel synthesis of a MgO-Y2O3 nanocomposite powder after a pre-treatment at 200°C during 2h. b: Derivatives from the mass loss as a function of the temperature of pure magnesium and yttrium nitrates hexahydrated obtained from distinct analyses. (1.5-column fitting image)The FIG4shows an aggregate of the sol-gel powder after a thermal treatment at 800°C. The crystallite size appears to be well below 100 nm.

FIG 4 .

 4 FIG 4. TEM images of the sol-gel powder synthetized at 800°C. (1-column fitting image)

FIG 5 .

 5 FIG 5. X-ray Diffraction on sol-gel powders synthesized with different final temperatures (λcobalt=1.7889 Å) in black cross. The peaks corresponding to the plane families of MgO (Mg) and Y2O3 (Y) are indicated by green and orange vertical lines below. The red solid lines represent the curves calculated by Rietveld refinement. The blue solid lines show the difference between the experimental curves and the calculated curves. (2-column fitting image)

FIG 6 .

 6 FIG 6. a: Crystallite size as a function of sol-gel final temperature treatment. b: Volume fraction of the MgO crystalline phase as a function of sol-gel final temperature treatment (calculated from the mass fraction obtained with Rietveld analysis). (2-column fitting image)

FIG 7 .

 7 FIG 7. SEM pictures (BSE) showing the microstructures (light: yttria; dark: magnesia) of MgO-Y2O3 nanocomposite samples. On the first row, the samples were all one-step sintered with powders synthetized by sol-gel process at different temperatures. 1A: 600°C, 1B: 700°C, 1C: 800°C, 1D: 1000°C. On the second row, the samples were two-step sintered with the same powder synthetized at 800°C and then post treated. Sintering of the sample 2B was stopped after the rapid cooling. 2A and 2B: no post treatment, 2C: 20 h air annealing at 1000°C, 2D: HIP at 1200°C under 400 MPa during 2 h. (2-column fitting image)

FIG 8 .

 8 FIG 8. FT-IR transmittance of MgO-Y2O3 nanocomposite samples sintered in different ways (resumed inTable 2). These curves are calculated to correspond to a 1mm thick sample. (1-column fitting image)

FIG 9 .

 9 FIG 9. Infrared transmittance of a 2 mm thick MgO-Y2O3 nanocomposite sample from 20°C to 1000°C. The sample was sintered by SPS with a twostep sintering (1200°C, 50MPa, 200°C/min) followed byHIP (1200°C, 2h, 400MPa) and air annealing (1200°C, 100h). (1-column fitting image)The FIG 9 presents the transparency of the MgO-Y2O3 nanocomposite sample 2F sintered by the two-step SPS profile followed by a HIP post-treatment (400 MPa, 1200°C, 2 h) and then air annealing (1000°C, 100 h) at temperatures up to 1000°C. In this figure, one can see that the overall transmittance is lower at room temperature than in FIG 8 (about 60% versus 80%). This is due to the 2 mm thickness and also because the detector in the high temperature transmission bench is located at a much longer distance from the sample than in the FTIR spectrometer (FIG8). Nevertheless, when the temperature increases, the sample transmittance decreases gradually from the longer wavelength to the shorter wavelengths. This behaviour is related to multiphoton absorption. When the temperature increases, there is more energy and a higher probability for multiples phonon to absorb a photon, decreasing the transmittance[START_REF] Harrington | Temperature Dependence of Multiphonon Absorption[END_REF]. Consequently, the material's emissivity also increases, which may have a strong impact on the signal to noise ratio measured by an IR detector according to the application[START_REF] Thomas | Infrared transmission properties of sapphire, spinel, yttria, and ALON as a function of temperature and frequency[END_REF],[START_REF] Harris | Durable 3-5 μm transmitting infrared window materials[END_REF]. This is a well-known limit of the infrared windows at high temperatures. In the MgO-Y2O3 nanocomposite material, at 5µm, there is almost no effect up to 500°C and then it decreases very slowly. At 1000°C, the loss of transparency remains below 10%. After measurement at high temperature, another measurement was carried out à 20°C to verify that there is no irreversible modification of the sample quality. This measurement, presented in the FIG9too, shows a very slight loss of the transparency, surely due to partial reduction of the sample during the measurement in the graphite furnace. To conclude, compared to the other well-known materials whose optical properties at 5 µm temperature are summarized in the Table3, those measurement confirm that losses in 3-5 µm band are less significant in MgO-Y2O3 that in sapphire for example. Furthermore, the absorption peak at 7 µm due to carbon pollution during the production process does not change in temperature and does not seem to be a problem.

Table 1 .

 1 Relevant refined parameters and statistical index (chi², Rp and Rwp) from Rietveld refinement of MgO-Y2O3 nanocomposite powders synthesised at different temperatures. Standard deviation is given in brackets.MgO has a cubic crystal system (space group: Fm-3m) with a lattice constant of 4.217 Å[START_REF] Sasaki | X-Ray Determination of Electron-Density Distributions in Oxides, MgO, MnO, CoO, and NiO, and Atomic Scattering Factors of their Constituent Atoms[END_REF]. Y2O3 has a cubic crystal system (space group: Ia-3) with a lattice constant of 10.604 Å[START_REF] Paton | A refinement of the crystal structure of yttria[END_REF].

	Powder synthesis temperature (°C)	Lattice constant (Å)	Mass fraction of MgO (%)	Estimated crystallite sizes (nm)	Chi²	Rp (%)	Rwp (%)
		MgO	Y2O3		MgO	Y2O3
	600	4.238 (5)	10.64 (1)	55 (0.4)	7	5	1.799	1.19	1.49
	700	4.225 (2)	10.617 (5)	46 (0.3)	18	12	1.632	1.12	1.41
	800	4.220 (2)	10.607 (4)	45 (0.3)	24	18	1.522	1.11	1.40
	900	4.217 (1)	10.605 (2)	44 (0.3)	32	29	1.841	1.11	1.40
	1000	4.215 (1)	10.603 (2)	44 (0.3)	44	40	2.021	1.14	1.47
	1200	4.214 (1)	10.600 (1)	42 (0.3)	77	71	2.677	1.27	1.69

Table 2 .

 2 Summary of the different MgO-Y2O3 nanocomposite samples processed in the present work. Mean grain size (intercept method with 1.56 ratio) and porosity ratio (Archimedes method) are given depending on the process parameters. Air annealing was processed at 1000°C and HIP at 1200°C under 400MPa.

	Sample	Powder synthesis temperature (°C)	Sintering conditions	Post treatments	Mean grain size (nm)	Porosity ratio (%) ± 1%
	1A	600	One step	-	280	12
	1B	700	One step	-	300	13
	1C	800	One step	-	350	10
	1D	1000	One step	-	410	9
	2A	800	Two-step	-	150	< 1
	2B	800	Intermediate two-step	-	100	10
	2C	800	Two-step	Air annealing (20h)	180	< 1
	2D	800	Two-step	HIP (2h)	220	< 1
	2E	800	Two-step	HIP (2h) + Air annealing (20h)	230	< 1
	2F	800	Two-step	HIP (2h) + Air annealing (100h)	240	< 1

Table 3 .

 3 Transmittance at 5µm at low and high temperature for transparent ceramics.

	Materials	Thickness	Transmittance at low temperature	Transmittance at High temperature	Refs
	Sapphire (c-axis)	2 mm	75% (25°C)	61% (427°C) 43% (827°C)	[5]
	AlON	2 mm	63% (25°C)	44% (500°C)	Calculated from [6]
	Spinel	2 mm	78% (25°C)	66% (500°C)	Calculated from [6]
	MgO-Y2O3 nanocomposite	1mm	86% (25°C)	83% (500°C)	[23]
	MgO-Y2O3 nanocomposite	2 mm	61% (20°C)	60% (500°C) 53% (1000°C)	This work

Acknowledgments

The authors would like to thank Frédéric Fossard (ONERA) for the TEM images, Cédric Lopes (ONERA) for HIP post-treatments, as well as Catherine Rio (ONERA), Marie-Hélène Ritti (ONERA) and Katia Dennis (ONERA) for their help during powder processing and characterization of the samples.

Funding

This work was supported by the AID (French Innovation Defence Agency) and ONERA (The French Aerospace Lab).


Élise Vareilles
email: elise.vareilles@mines-albi.fr

Thierry Coudert
email: thierry.coudert@enit.fr

Michel Aldanondo
email: michel.aldanondo@mines-albi.fr

Laurent Geneste
email: laurent.geneste@enit.fr

Joël Abeille
email: joel.abeille@pulsar-innovations.fr

Coupling system design

Keywords: System Design, Project Planning, Aiding Decision, Knowledge based System

come

INTRODUCTION

Because of the increasing complexity of products, the distributed nature of designers' skills, and the need to integrate management systems and tools, today's product or system design processes interact more and more closely with all other business processes in a company, such as supplier selection, purchasing, marketing, production planning, maintenance, etc. In such a context, the interactions between the building of a system design project and the design of the system itself have not been sufficiently investigated. There is a particular lack of integrated models and decision support systems. The building of design activities, from requirements definition to solution definition, and the planning and control of these activities are important tasks, see PMBOK 2004 . However, there are few works which propose integrated models and tools that can assist engineers in the task of building design projects

The authors wish like to thank their partners in the ATLAS project, the French National Research Agency (ANR) and the 7 th Strategic Activity Domain (Architecture and Integration) of Aerospace Valley for their involvement in this project.

in accordance with the design of systems, in planning the design activities and finally, in controlling their execution. Design of a system and planning of a design project are usually considered as separate fields of study. Standard processes exist for each, and many studies have been carried out on these topics leading to adapted models and methodologies. However, few studies have focused on the interactions between these two processes. A decision made within the domain of system design can have important effects on project planning (e.g. choosing to explore one or more solutions can cause significant delay while these solutions are developed, or may affect particular -and not necessarily available -design resources). Reciprocally, a decision made within the project domain may have a strong influence on system design (e.g. a short delay or a lack of resources means that an existing component cannot be adapted in order to satisfy the requirements). Therefore, the coupling between these two processes requires the ability to propagate decisions from one environment to the other and to check that the modification of the tasks within both domains is consistent. In Abeille et al. 2010, the coupling and the meta-model describing coupled entities have been presented. Basic processes of coupling have been described. The present article is more a discussion about how to link systems and projects in order to formalize the synchronization between both domains and to avoid inconsistent information. The article is organized as follow: in section 2, the context of the study is described. In section 3, the background is defined and in section 4, proposals are discussed with regard to existing approaches.

CONTEXT OF THE STUDY

The research parameters were formalized by interviewing fifteen companies belonging to the world competitiveness cluster, Aerospace Valley. This task is a part of the ATLAS project that involves five academic institutions and two companies, funded by the French Government (ANR project).

The most important results of this benchmarking exercise can be summarized as follows: all the companies interviewed are confronted with this coupling problem but they have not implemented specific tools to support this coupling process. Most of the time, the coupling is performed by means of non-formalized human interactions. Even if some companies use procedures, their decisions are based on human experience. Only 18% of companies use software or collaborative tools. The majority of companies (50%) makes integrated decisions during meetings involving the different stakeholders. The use of standards or reference scenarios is also used by the most advanced companies. This concerns the use of generic models for designing different categories of systems, or the conversion of capitalized design solutions into databases. Meanwhile, the complexity of systems and projects is increasing. In a distributed multi-national context, the design of a system is often carried out in several sites involving several partners. Clearly, the use of adapted and integrated tools to manage these complex design projects is becoming a requirement in such contexts. These tools also need to be adapted to multi-responsibility projects.

To illustrate the global context of this study, it is considered that a project (associated with a system that needs to be designed) is under the responsibility of a program manager. The program manager interacts with (i) a design manager who works within a design system environment and (ii) a planning manager who works within a project planning environment. The difficulty involved in designing the system, as well as the complexity of the associated project, leads to them being hierarchically decomposed according to the axiomatic design approach, Yoshikawa (1989), [START_REF] Suh | Axiomatic Design: Advances and Applications[END_REF] and [START_REF] Albano | Axiomatic approach to structural design[END_REF] . The different design approaches are discussed in section 3.1.1. In such cases, systems can be decomposed into subsystems, leading to the decomposition of associated development projects into associated (more exactly coupled) sub-projects. The corollary is that complex design projects can be decomposed into sub-projects leading to the decomposition of the coupled system in the same manner. In this context, the program manager, at his level, can be seen as a "coupling manager" who fixes orientations and objectives, makes decisions and defines decision parameters for the two other parts. (S)he is also in charge of resolving conflicts. Within this framework, considering two hierarchical levels, either the design manager of the upper level becomes the program manager of the lower level, or it is the planning manager who takes on this role. This outcome varies from company to company. It is also possible, in some cases at the lowest levels, to have only one person in charge of the three responsibilities.

BACKGROUND AND DISCUSSIONS

Definition of System Design and Project Planning

System Design Definition H. A. [START_REF] Simon | The science of the artificial[END_REF] first characterized design as a search process. Design can be seen as a project that aims at creating a new object or transforming an existing one [START_REF] Huysentruyt | Contribution to the development of a general theory of design[END_REF]). Design is also considered as a knowledge discovery process in which information and knowledge of diverse sources are shared and processed simultaneously by a team of designers involved in the life phases of a product [START_REF] Tang | A knowledge-based architecture for Intelligent Design Support[END_REF] and [START_REF] Wang | An Agent-Based System Supporting Collaborative Product Design[END_REF]) . Therefore, knowledge in design processes is a key factor. [START_REF] Brown | Expert system for a class of mecanical design activity[END_REF] gives a taxonomy of design processes depending on three domains of knowledge: the domain of the object to design, the domain of the design process and the domain of requirements about the objects to design. This classification leads the authors to define three domains of design: routine, innovative and creative. In routine design, the three domains are well known and can be used. For innovative design, even if the structure of the objects to design is familiar, some new characteristics are required in order, for instance, to provide the market with innovations on existing products, leading design activity to investigate new technologies (better performance, new functionalities, etc.). On the other hand, when new technologies appear, innovation can lead the design activity to propose new applications. Creative design refers to the act of producing new ideas or concepts with a minimum of knowledge.

There are a lot of existing design methodologies described in the literature (see, for instance, the methodologies described in [START_REF] Suh | The principles of Design[END_REF], [START_REF] Pahl | Engineering Design: a Systematic Approach[END_REF], [START_REF] Dieter | Engineering design -A materials and processing approach[END_REF] and [START_REF] Ullman | The mechanical design process[END_REF], or for a wide panorama, [START_REF] Blessing | Comparison of Design Models Proposed in Prescriptive Literature[END_REF] . Among the widely used methodologies, Axiomatic Design (AD) proposed by [START_REF] Suh | The principles of Design[END_REF] is a top down and iterative approach that makes links between requirements or functions (functional requirements) to be fulfilled and technical solutions (design parameters and process variables). The design process zigzags between the four following domains: needs, solutions, tasks and resources. Pahl and Beitz [START_REF] Pahl | Engineering Design: a Systematic Approach[END_REF])describe a systematic approach for all design and development tasks. The design process is composed of the following four sequential stages guiding the design of a product from scratch to full specification: requirements clarification, conceptual design, embodiment design and detailed design. Requirements clarification defines customer or stakeholders requirements. Conceptual, embodiment and detailed design are activities that serve to develop products or systems gradually.

From a system engineering viewpoint, the works of the International Council on Systems Engineering (INCOSE) have been considered in detail. Among them, the EIA-632 standard [START_REF] Martin | Evolution of EIA-632 from an interim standard to a full standard[END_REF], EIA (1990))provides some structuring processes for system design widely used by companies in the electronics domain. It defines a global engineering process that makes it possible to transform customer requirements into technical solutions. The AT-LAS project proposals are based on this standard, which provides an integrated set of fundamental processes to aid a designer in the engineering or re-engineering of a system. The approach is based on the following premises:

• a system consists of one or more products to be delivered, as well as sets of related enabling products (products that sustain the end products during their life cycle, e.g. a specific tool required to build a product); • products are an integrated composite of hierarchical elements which need to meet the defined stakeholder requirements; • the engineering of a system and its related products is accomplished by applying a set of processes to each element of the system hierarchy .

This approach is incrementally applied in an engineering life cycle framework that can be implemented during phases of an enterprise-based life cycle (for example, during production, operations, support, or disposal).

Therefore, the design process proposed in this article is structured as follows:

i) the definition and/or the specification of the requirements, ii) the identification of the technological solutions which can fulfill these requirements, iii) the associations requirements / solution, iv) and according to the complexity, the decomposition of the design process up to a certain level of abstraction.

According to the level of detail of these activities, the proposed design process is compliant with the typology of Pahl and Beitz [START_REF] Pahl | Engineering Design: a Systematic Approach[END_REF] , in a "Conceptual / Embodiment / Detailed" design context as well as the EIA-632 standard requirements. The recursive decomposition of the design process also complies with a top-down cycle that zigzags between requirements and solutions in accordance with the recommendations of "axiomatic design" proposed by [START_REF] Suh | Axiomatic Design: Advances and Applications[END_REF] . The result of the design process is then considered as a set of associations (i.e. specified requirements coupled with technological solutions) structured in a hierarchical way. Indeed, the specifications of requirements lead to some technological solutions and, when a system is decomposed into many sub-systems, a technological solution for a system leads to the specification of requirements for its sub-systems.

Project Planning Definition

The project planning domain concerns the Project Time Management (PTM) process as defined by the Project Management Institute (PMBOK (2004)) . The PTM process is one of the nine processes proposed by the PMI that cover the six following activities: identification and sequencing of activities, estimation of resources and durations, scheduling of activities, and control of the execution of the schedule.

In the proposed approach, the project planning definition is a top-down approach, where some kind of global planning is achieved at a high level and is progressively detailed at lower levels by means of sub-projects. This multi-level and multi-project approach makes it possible

Interaction between Design and Planning Processes

The axiomatic design and the above-mentioned standards allow four interacting domains to be identified: (i) the requirements or specifications, (ii) the solutions, (iii) the tasks or activities and, (iv) the resources. The first two domains relates to the system design process and the last two domains to the project planning process. Although there are few studies that address this coupling problem, one can mention: (i) the studies initialized at M.I.T [START_REF] Eppinger | Organizing the tasks in complex design projects[END_REF]) on the use of methods and techniques used on product design in order to facilitate project design. These studies are the source of scientific developments around DSM (Design Structure Matrix), such as those of Lindemann (2007) . The interactions between the four identified domains are defined; (ii) in the same way, axiomatic design identifies various domains (Customer Needs, Functional Requirements, Design Parameters and Process Variables) and sees them as interacting [START_REF] Suh | Axiomatic Design: Advances and Applications[END_REF]) . An example of implementation is presented in Goncalves-Coelho (2004) . The interactions between domains are clearly defined: design towards planning but also planning towards design;

(iii) another approach, introduced by Gero (1990), proposes models based on three domains: Function, Behavior and Structure (FBS). The aim of this study is to take into account the product behavior (expected and effective) and to inventory in a formal way eight sub-processes of design. However, tools for interactions between processes are not considered explicitly; (iv) a study that is very close to the problem addressed was undertaken by Stewart Requirements collection task

Task of design of solution1

Task of design of solution2

Fig. 1. System and Project Entities

All these studies indeed confirm the four reserved domains (requirements, solutions, tasks and resources) and the existence of causal links that involve interactions between these four domains. However, except in Steward et al. (2000)and [START_REF] Lu | Integration of Product Design Process and Task Management for Product Data Management Systems[END_REF], no tools are provided to support or aid interactions between both design and planning processes.

DISCUSSIONS AND PROPOSALS

The integrated (meta-)model proposed in this article is inspired by the EIA-632 engineering standard. It is proposed with the objective of formalizing the methodological coupling between project planning and design. EIA-632 meta-model is, moreover, a high level model describing processes and entities with a low level of detail, and coupling is not clearly formalized. However, before describing the proposed integrated model, the different possible ways of coupling both domains are discussed. Two coupled entities are then considered: system entities and project entities (the corresponding meta-model is described in detail in section 5). A system entity is composed of one set of requirements, noted SR, and one or more solutions (or system alternatives), noted SA i , as shown in the left part of Fig. 1. A project entity is composed of one task of requirements collection, noted T R, and one or more tasks of solution design (or alternative development task), noted T D i , as shown in the right part of Fig. 1.

As mentioned in section 3.1.1, the proposed model is based on a structural and hierarchical decomposition of systems into sub-systems and/or projects into sub-projects (guided by their intrinsic complexity). Observing system entities and project entities, three kinds of coupling have been defined :

• one system entity is coupled with one project entity,

• one project entity is coupled with several system entities and, • one system entity is coupled with several project entities.

These three kinds of coupling are discussed below.

• One system entity is coupled with one project entity (Fig. 2): in this situation, the design of a system entity is controlled by a single project and each subsystem design is controlled by a single coupled sub-project. The risk of conflicting system requirements can be controlled because only one project task is in charge of collecting requirements for a particular system, taking into account required resources. The decision to decompose into sub-systems can be taken during the design of a solution (or during the definition of a project). The sub-projects involved will be created at this time, necessarily adapted to plan and control required resources. Low project levels receive clear objectives from higher levels with a facilitated control of the former by the latter. However, for very Fig. 4. Further Projects Entities coupled with one Design Entity ning managers for one system to be designed).

It is then nearly impossible to formalize the relationships between different (non-formalized) parts of the system and the different sub-projects. • one sub-system is controlled by several subprojects (Fig. 4(b)): in such a case, the system and the project are decomposed, but there are several sub-projects managing the design of only one sub-system. The drawbacks of the above situation are the same.

Of these three kinds of coupling, the first one, based on a bijection between system and project entities, has been chosen for this study. This coupling is called structural coupling in the following parts of the article. It is very well suited to defining coupling relationships, because it keeps the same structure on both domains. This characteristic is very important in order to define and carry out consistent coupled planning and design processes by means of well suited decision aided tools. It is fully compliant with the Axiomatic Design of [START_REF] Suh | The principles of Design[END_REF] and its zigzagging methodology (see section 3.2). It is also important to preserve the semantic of entities on both domains without mixing information. Furthermore, in this article we favor a progressive top-down design approach where sub-projects and sub-systems are defined only when required and when their context is well known. For instance, the decision to subcontract the design of a particular sub-system can be taken only after a suitable requirements analysis and when these requirements have been confronted with available resources. At this time, the choice of a subcontractor and the definition of the required sub-project, as well as its characteristics and constraints, can be established. More classical methodologies in this field consider that both hierarchies are first constructed independently and that links are drawn later on. Such an approach can lead to incompatibilities, because projects are defined outside of their real design context without taking into account the required resources, skills and distributed partners. Therefore, our proposal is based on the assumption of bijection between project and design entities.

PROPOSAL FOR AN INTEGRATED MODEL

In this section, we focus only on the integrated model supporting the bijective link coupling. Firstly, we present the structural coupling that ensures a bijection between systems and projects. This coupling corresponds to a kind of systematic mapping between system BOM1 and projects WBS 2 and is the basis of all of our proposals.

CONCLUSION

The aim of this article was to discuss the architecture capable of supporting a coupling between the design process and the planning process. The context and the background of the study have been presented in section 2. The multilevel design process and planning process have been described in accordance with academic standards and with the EIA-632 standard used in companies. The different possibilities of coupling both domains have been proposed and discussed in section 3. Finally, the choice to preserve bijective relationships between system entities and project entities has been made and justified.

Firstly, perspectives of this work concern the integration of local decoupling mechanisms between both domains when required at lower levels of decomposition. Within section 3, we discussed the assumption about bijective relationships between both domains and this assumption has been maintained for all of our proposals. However, it can be difficult to maintain this kind of strict coupling for systems having many levels of decomposition. It requires systematically drawing links between entities, even when they are simple. A methodological problem can arise if a very simple system must necessarily be linked to its project. Therefore, an exception to this rule is possible, enabling managers to define a hierarchical decomposition of very simple systems with only one associated project when a certain level of decomposition is reached (this exception is not detailed in the proposals). In this case, the coupling could be carried out manually (the project manager explicitly constructs the links between entities) and could continue to work. Alternatively, no coupling is performed and is thus no longer supported by the integrated model. Clearly, this method of operation needs to be controlled and reserved to specific situations where designers of low levels want to decompose a very simple system to develop it without a framework given by the planning environment. It can not be generalized to a whole system.

Secondly, perspectives of this work concern the formalization of the coupling based on field knowledge. Another part of the ATLAS project concerns the use (or reuse) of contextualized knowledge stored in a data base and usable via a Case-Base Reasoning methodology and of formalized knowledge stored as a Constraint Based model [START_REF] Aldanondo | Towards an association of product configuration with production planning[END_REF]). This kind of knowledge is called field knowledge and is very important in order to reduce the time required to develop new systems from requirements. This time gain can be achieved by reusing and adapting past solutions to fulfill new requirements. The reuse can be applied to systems and their alternatives as well as to the different development tasks, adapting them to the new context and to the new requirements (coupling by reuse).

It can be also achieved by applying filtering methods to Constraints Satisfaction Problems limiting the authorized domains of combinations of design variables. The solution space is then reduced in order to guide the decision makers.

A software mockup illustrating all couplings identified in the ATLAS project, and based on the bijective assumption, can be consulted at http://193.51.2.246:5500/. This mockup matches industrialists' expectations.

Bill Of Materials

Fig. 3. One Project Entity coupled with further Design Entities complex systems with a great number of systems and subsystems, this systematic approach can lead to a large number of projects within one project, even for a very simple system. • One project entity is coupled with several system entities. In this case, two situations have been identified:

• one project controls a system and its sub-system design simultaneously (Fig. 3(a)): the main advantage here is to factorize the project management for all the involved systems with only one planning manager. However, the development planning information about different systems is mixed: only single requirements collection task performed early for all the systems and subsystems. This can lead to problems since the requirements characterization of a sub-system can require a high level of expertise (and consequently, particular resources). Furthermore, the choice of decomposition into sub-systems can be difficult to anticipate before starting the design work. • one project controls several sub-systems at the same hierarchical level (Fig. 3(b)): in this case, the planning manager can encounter difficulties in planning multiple interventions from (potentially distributed) designers for the different subsystems. Furthermore, information regarding the requirements of each sub-system is identified when performing a single task within the project, which could potentially lead to inconsistencies. • One system entity is coupled with several project entities: two situations have been identified:

• one system is controlled by one project and its sub-projects (Fig. 4(a)): in such a case, the system to be designed is not considered complex enough to be decomposed, but the management of its design can not be done by only one level of project. The risk is to create duplicated tasks as well as conflicting responsibilities (several plan-