P Chevreux

A Laplace

E Deloule

L Tissandier

N Massoni

Hafnium solubility determination in soda-lime aluminosilicate glass

Keywords: Hafnium oxide, solubility, aluminosilicate glass melt, reducing conditions, crystallization

The solubility of hafnium dioxide (HfO 2 ), used as an uranium surrogate, is measured in glass melts belonging to the CaO-Al 2 O 3 -SiO 2 and Na 2 O-CaO-Al 2 O 3 -SiO 2 systems, under oxidizing and reducing conditions. Two methods have been carried out to determine it and the kinetic factors controlling the HfO 2 dissolution in glass melt have been investigated in order to approach equilibrium. The solubility ranges from 3 to 6.5 mol% HfO 2 in aluminosilicate glasses at temperature between 1250°C and 1400°C, and is not affected by the redox conditions. Conversely, the solubility is modified by the melting temperature and the glass composition. The excess of alkalies or alkaline earths which are not involved in the charge balance of AlO 4 tetrahedrons in the silica network appears to play a significant role. Glass homogeneity is checked by scanning electron microscopy and X-ray diffraction. HfO 2 , HfSiO 4 , Ca 2 HfSi 4 O 12 , Na 4 Hf 2 (SiO 4 ) 3 and Na 2 HfSi 2 O 7 are metastable crystals observed in the glass melts. The stability of those crystalline phases mainly depends on the glass composition.

Introduction

1.1 Background Reprocessing of the spent nuclear fuel generates High Level Waste (HLW) which contains fission products and actinides. To be immobilized, these HLW are incorporated at about 1100°C in a borosilicate glass matrix. In the same way, Intermediate Level Waste (ILW) including both actinides and metals are planned to be confined by a vitrification process. The metallic fraction is melted with the glass melt at a higher temperature, between 1250°C and 1400°C, and the glass melt is expected to incorporate the actinides, uranium and plutonium mainly, in its silicate network. As boron is known to volatilize from borosilicate melts at high temperature [START_REF] Cable | Kinetics of volatilization of sodium borate melts[END_REF], aluminosilicate glasses appear as better candidates for that process. Besides, the molten metal phase imposes a strongly reducing environment to the glass melt and thus impacts actinides oxidation state and consequently their solubilities. In highly reducing conditions, U IV and Pu III are the main forms expected in the melt. Plutonium is more soluble in glass melted in reducing conditions (Pu III ) [START_REF] Cachia | Enhancing cerium and plutonium solubility by reduction in borosilicate glass[END_REF] while uranium is more soluble in oxidizing conditions (U VI ) [START_REF] Schreiber | The chemistry of uranium in borosilicate glasses .1. Simple base compositions relevant to the immobilization of nuclear waste[END_REF]. Moreover, only few data about uranium solubility in glasses melted in reducing conditions are given in the literature [START_REF] Schreiber | The chemistry of uranium in borosilicate glasses .1. Simple base compositions relevant to the immobilization of nuclear waste[END_REF][START_REF] Domine | Preliminary investigation of the processes governing the solubility of uranium in silicate melts[END_REF][START_REF] Lam | X-ray photoemission spectroscopy (xps) study of uranium, neptunium, and plutonium oxides in silicate-based glasses[END_REF][START_REF] Matyunin | Immobilization of U3O8 in borosilicate glass in an induction melter with a cold crucible[END_REF][START_REF] Schreiber | The chemistry of uranium in glass-forming aluminosilicate melts[END_REF] and fundamental data on uranium behavior in aluminosilicate glasses have to be investigated in such conditions. This study presents characteristics of aluminosilicate glasses containing hafnium (Hf IV ) which is taken as uranium surrogate [START_REF] Davis | Hafnium in peralkaline and peraluminous boro-aluminosilicate glass and glass sub-components: a solubility study[END_REF][START_REF] Fox | Plutonium feed impurity testing in lanthanide borosilicate (LaBS) glass[END_REF][START_REF] Lopez | Solubility of actinide surrogates in nuclear glasses[END_REF][START_REF] Zhang | Energetics of dissolution of Gd2O3 and HfO2 in sodium alumino-borosilicate glasses[END_REF]. Uranium and hafnium are both heavy elements and display quite similar ionic radii for a given coordination number. Preliminary results with hafnium are shown here, before a further study with uranium. The first objective of this work is to study hafnium incorporation into a glass-forming melt under reducing environment and to optimize the Hf-doped glasses elaboration conditions in order to approach equilibrium. The second objective is to determine hafnium solubility as a function of the melting temperature, the glass composition and the redox conditions. Hafnium crystallization is also investigated.

State of the art

The thermodynamic solubility of an element in the glass is the maximum concentration of this element that can be loaded in the glass network at a given temperature. To determine it, two methods are commonly used. The first one consists in gradually increasing the amount the element to incorporate in the glass until a heterogeneous phase appears in the system (crystallization or/and demixing) [START_REF] Deschanels | Plutonium solubility and self-irradiation effects in borosilicate glass[END_REF]. The second one is embodied in introducing the desired element in excess in the glass and measuring its concentration in the vitreous matrix [START_REF] Khedim | Solubility of chromium oxide in binary soda-silicate melts[END_REF][START_REF] Watson | Zircon saturation in felsic liquids -experimental results and applications to trace-element geochemistry[END_REF]. That means the saturated glass melt shows lots of heterogeneities. To make a difference between the gradation and the saturation methods, we named the last one the saturation solubility (S S ). The issue of reaching the equilibrium is raised in both cases. To approach equilibrium, the system has to verify several conditions [START_REF] Dickenson | Redox equilibria and the structural role of iron in alumino-silicate melts[END_REF], and if not, a conditional solubility (S C ) can be introduced notably for the gradation method [START_REF] Cachia | Enhancing cerium and plutonium solubility by reduction in borosilicate glass[END_REF][START_REF] Lopez | Solubility of actinide surrogates in nuclear glasses[END_REF]. This solubility depends on the experimental conditions used by the authors and it may be lower than the thermodynamic solubility for the gradation method or higher for the saturation technique [START_REF] Khedim | Kinetic and equilibrium factors affecting saturation of chromium oxide in soda-silicate melts[END_REF]. Most hafnium solubility studies are focused on borosilicate glasses. Lopez measured conditional solubilities in a borosilicate glass as function of the melting temperature [START_REF] Lopez | Solubility of actinide surrogates in nuclear glasses[END_REF]. At 1400°C, hafnium conditional solubility was between 1.2 and 1.5 mol% HfO 2 . Cachia [START_REF] Cachia | Solubilité d'éléments aux degrés d'oxydation III et IV dans les verres de borosilicate[END_REF] reported a higher conditional solubility at the same temperature, between 1.8 and 2.2 mol% HfO 2 in the same glass by modifying the experimental protocol. In the Na 2 O-B 2 O 3 system, Res [START_REF] Res | Transformation of Na2O-HfO2-B2O3 glass into a material having interconnected pores[END_REF] observed that increasing the Na 2 O concentration improved the HfO 2 solubility up to 12 mol% HfO 2 at 1400°C for a glass containing 18 mol% Na 2 O. Nevertheless, some dropletlike micro-heterogeneities were revealed by SEM in clear glasses. Feng [19] found that hafnium solubility in a sodium boro-aluminosilicate was positively related to the excess of Na 2 O relative to Al 2 O 3 . At 1450°C, the highest solubility measured in a Na-rich glass was 14.4 mol% HfO 2 . Unfortunately, few data are given about the way of determining that solubility limit. The relationship between the hafnium solubility and glass composition was also investigated by Davis [START_REF] Davis | Hafnium in peralkaline and peraluminous boro-aluminosilicate glass and glass sub-components: a solubility study[END_REF]. He demonstrated that the solubility limit of HfO 2 in peralkaline glasses (Na 2 O mol% > Al 2 O 3 mol%) in the system SiO 2 -Al 2 O 3 -B 2 O 3 -Na 2 O was linearly and positively correlated with the molar Na 2 O/(Na 2 O+Al 2 O 3 ) ratio. The solubility of HfO 2 in these glasses ranged from 2 to 16 mol% at 1450°C. This "peralkalinity effect" had been alike observed in B-free glass melts for +4 cations (such as Zr IV and Ti IV ) [START_REF] Watson | Zircon saturation in felsic liquids -experimental results and applications to trace-element geochemistry[END_REF][START_REF] Dickenson | Redox equilibria and the structural role of iron in alumino-silicate melts[END_REF][START_REF] Ellison | Solution behavior of +4 cations in high silica melts -petrologic and geochemical implications[END_REF]. In contrast, the mechanism for HfO 2 dissolution seems to be different in peraluminous glasses (Na 2 O mol% < Al 2 O 3 mol%). In the peraluminous meIts, the HfO 2 measured solubility by Davis [START_REF] Davis | Hafnium in peralkaline and peraluminous boro-aluminosilicate glass and glass sub-components: a solubility study[END_REF] is lower than 3 mol% and, B 2 O 3 and Al 2 O 3 may help to solubilize it. Ellison [START_REF] Ellison | Solution behavior of +4 cations in high silica melts -petrologic and geochemical implications[END_REF] showed that hafnium solubility decreased in B-free peraluminous melts in the system SiO 2 -Al 2 O 3 -Na 2 O-K 2 O with the SiO 2 content increasing and measured solubility limits lower than 1 mol% HfO 2 in equilibrated liquids at 1400°C. Above the solubility limit, the Hf-bearing crystallized phases were mainly monoclinic hafnia (HfO 2 ) [START_REF] Davis | Hafnium in peralkaline and peraluminous boro-aluminosilicate glass and glass sub-components: a solubility study[END_REF][START_REF] Fox | Plutonium feed impurity testing in lanthanide borosilicate (LaBS) glass[END_REF][START_REF] Res | Transformation of Na2O-HfO2-B2O3 glass into a material having interconnected pores[END_REF] and occasionally hafnon (HfSiO 4 ) [START_REF] Lopez | Solubility of actinide surrogates in nuclear glasses[END_REF][START_REF] Ellison | Solution behavior of +4 cations in high silica melts -petrologic and geochemical implications[END_REF]. All these authors had melted their glasses under oxidizing conditions, namely in air and in Pt-Rh, ZrO 2 or Al 2 O 3 crucibles.

Experimental and analytical procedures

2.1 General features Hf solubility was determined in two simplified aluminosilicate glasses based on the industrial glass formulation A and B, A glass containing 22.33 mol% Na 2 O while B being sodium free (Table 1) and for two bracketing temperatures (1250°C and 1400°C). Redox conditions during the Hf-doped glasses meting were changed using different types of crucibles and atmospheres. Platinum crucible (Pt-5%Au) and air atmosphere were used for oxidizing conditions, while pure graphite (C g ) or graphite and silicon carbide (C-SiC) crucibles and argon (Ar) atmosphere imposed reducing conditions. The C-SiC crucible (A5/0 Salamander Super, Morgan MMS) is a type of crucible frequently used in the metallurgy field. It is mainly composed of C g , SiC, a mullite binder (3Al 2 O 3 -2SiO 2 ) and some impurities such as Fe 3 Si. Ar atmosphere was used to prevent these crucibles from corrosion.

Glass fabrication

Starting glasses

The A and B glasses (Table 1) were prepared with the following commercial precursors: SiO 2 (Sifraco, 0.994); Na 2 CO 3 (Sigma-Aldrich, 1); CaO (Aldrich, 0.999); Al 2 O 3 (Sigma-Aldrich, 1). For the Na-rich A glass, a decarbonation step was previously performed at 850°C for 6h. Then, the mixed components (≈150 g) were melted at 1400°C for 3h in a platinum crucible (Pt-10%Rh), under air. Glass melts were then poured in stainless steel plate, milled and screened up to 400 μm particle size to be further used as starting glass materials for Hfdoped glasses. Milling was performed in a tungsten carbide (WC) vessel using WC balls (Planetary Ball Mill PM 200). Hafnium was added as HfO 2 powder (Alfa Aesar, 0.999) and mixed with the former glass powders. Three different types of hafnium particle size were used: 15, 70 and 158 μm. The particle size, expressed as the median value (d 50 ) and size distribution of powders were determined from the volume distribution measured by a laser granulometer (Malvern Mastersizer 3000) in ethanol. C glass was formed by adding 1.56 mol% HfO 2 to the Na-rich glass (Table 1). This value of 1.56 mol% HfO 2 is a relevant content for the industrial process. Moreover, the hafnium solubility in glass melt should be higher than this value as referenced in paragraph 1.2.

Optimized protocol definition for Hf-doped glasses

The influence of different experimental parameters (HfO 2 particle size, fusions number, melting time and temperature) has been checked for the C glass elaboration in order to optimize the process (Table 2). The powder mixture (≈3 g) was melted in a C-SiC crucible under Ar atmosphere. After melting, the molten glass was cooled by shutting off the heat source (cooling rate < 8°C/min). In case of several meltings, each remelting was preceded by a glass sample milling step (WC vessel and ball, Mixer Mill MM 200) to ensure its homogenization. Final glass samples were removed from the crucible and have roughly a 20 mm diameter and 6 mm height (Figure 2). An optimized protocol was then defined for Hf solubility measurements. To minimize hafnium sedimentation and its heterogeneities, fine HfO 2 powders were used (15 µm particle size). Remeltings enabled to homogenize the whole glass melt. The 3h run duration allowed to avoid bubbles and longer run duration did not really impact the HfO 2 dissolution and had the drawback of increasing the Na volatilization. Thus, the experimental procedure followed for solubility measurements comprised three meltings for 3h at 1250°C or 1400°C with two intermediate glass millings (Figure 1).

Glass characterizations

Homogeneity

Glass sample homogeneity was determined by scanning electron microscopy (SEM) and Xray diffraction (XRD). Secondary phases morphology and size were observed by SEM (Phillips XL30-WTMP and ZEISS Supra 55 FEG) coupled with energy dispersive X-ray spectroscopy (Brucker EDS analyser) allowing glass composition semi-quantitative analysis.

The conditions for electron microprobe analysis were an acceleration voltage 15 keV, a total of 5.10 5 counts and a Phirho(Z) method with standards. For SEM observations, crucibleshaped glass samples were cut in the middle and mounted in epoxy resin before being polished and carbon coated. Crystalline phases were identified by a PANalytical diffractometer (X'Pert MPD Pro, Bragg-Bretano geometry using a Ni-filtered the Cu Kα radiation, solid detector X'Celerator) using the EVA software from Bruker AXS company. The data acquisition was completed in the step scan mode (10-90° 2θ, step size 0,017° 2θ, total time counting of at least 5h). XRD measurements were carried out on glass powders. The modelization of the X-ray pattern was performed in two steps using the Fullprof_Suite program [START_REF] Frontera | FULLPROF as a new tool for flipping ratio analysis[END_REF]. Lattice parameters were first determined by the whole pattern decomposition then the structure was modeled by the Rietveld technique. Rietveld refinement was realized for highly crystallized glasses to assess the phases inventory previously done and obtain the relative mass fraction of each crystalline phase. For the latter, the amorphous phase is not considered.

Properties

The glass density was measured using a hydrostatic balance; the glass was weighed in air and then, in water according to Archimedes' principle. The reported density represents the mean value of three measurements. Viscosity measurements were performed by a stress imposed rheometer (Rheometrics Scientific SR 5000) [START_REF] Puig | High temperature rheological study of borosilicate glasses containing platinum group metal particles by means of a mixer-type rheometer[END_REF]. Basically, the rheometer was located above a vertical tubular furnace and a cylindrical crucible was placed in the furnace center. Rheological measurements were realized with a cylindrical rotor in the Couette geometry. Measurements Quenching in water were performed at several temperatures. For Newtonian melts, a model following a Vogel-Fulcher-Tammann (VFT) law was applied [START_REF] Ojovan | Viscosity and glass transition in amorphous oxides[END_REF].

Results

Hafnium incorporation

Sedimentation and heterogeneities

The C3 glass sample containing 1.56 mol% HfO 2 (158 μm particle size) and elaborated for 3 hours at 1250°C is firstly observed. The glass is transparent with a slightly yellowish tint, probably, due to minor contamination from the crucible or the grinding vessel (Figure 2) [START_REF] Davis | Hafnium in peralkaline and peraluminous boro-aluminosilicate glass and glass sub-components: a solubility study[END_REF]. Hafnia sedimentation is clearly observed at the bottom (Figure 2a) and the sample displays two distinct parts. In the top half, glass seems to be homogeneous without any crystalline phases, which is confirmed by SEM images (Figure 2b). Few bubbles are noticed. Heterogeneities, composed of crystal clusters, are only detected at the bottom (Figure 2b). According to XRD patterns, the crystalline phases are monoclinic HfO 2 , hexagonal Na 4 Hf 2 (SiO 4 ) 3 and triclinic Na 2 ZrSi 2 O 7 (more details in paragraph 3.2.2). Graphite C g is also detected by XRD. Hafnium being a heavy element, it is easily observable using back scattered electrons (BSE). In the analyzed section, Na 4 Hf 2 (SiO 4 ) 3 and HfO 2 crystals are identified by SEM (Figure 2c) contrary to the crystalline phase Na 2 ZrSi 2 O 7 . White halos surrounding theses crystals are also observed in BSE (Figure 2b), which demonstrates hafnium enrichment in the vitreous matrix. An hafnium concentration gradient in the glass matrix is observed in the whole sample, a lower concentration at the top and in the middle of sample (between 0.3 and 0.4 mol% HfO 2 ) than at the bottom (1.3 mol% HfO 2 ) (Figure 3a). To avoid these heterogeneities, several parameters were investigated such as hafnium precursor particle size, run duration, meltings number and temperature (Table 1). The glass sample microstructure was observed by SEM (Figure 4) and the HfO 2 concentration in glass network was determined by EDS analysis in three specific glass areas and compared to the targeted value, 1.56 mol% HfO 2 (Figure 3). The absence of HfO 2 compositional gradients in the glass was one of the features consistent with an approach to equilibrium.

Effect of precursor particle size

C0, C3 and C4 glass samples followed identical thermal treatment (1250°C, 3h) but were prepared with different hafnium powder particle sizes, namely and respectively 158, 70 and 15 μm. The decrease of the HfO 2 particle size widely limits the HfO 2 sedimentation by decreasing the amount and size of hafnium crystals in the glass (Figure 4a, b andc). The size of agglomerated crystals is from 200 to 400 μm sized in the C3 glass compared to 50-100 μm in the C0 glass. In the C4 glass, where hafnium particle size is very fine (15 μm), only a few of those crystals are noticed. Moreover, reactivity between glass and hafnium powders is enhanced using fine powders (increase of the reactive surface for a given volume). As a consequence, hafnium concentration in the glass melt is largely increased and almost reaches the targeted value (Figure 3a). However, a concentration gradient still remains in the whole sample. In the next parts, the intermediate 70 μm particle size (C0 glass) is selected to study the effect of the other parameters.

Effect of melting time

C0 and C1 glasses were elaborated at 1250°C for, respectively 3h and 12h. Increasing melting time does not change the samples general feature. White halos, hafnium concentration gradient and hafnium crystals at the bottom were still identified in the C1 glass (Figure 3b and Figure 4d). Nevertheless, hafnium concentration is higher at the bottom and the middle in the C1 glass than in the C0 one (about 40-50% more). On top of the sample, the hafnium concentration remains the same.

Effect of remelting

To achieve good homogenization, glasses are usually milled and melted several times [START_REF] Fox | Plutonium feed impurity testing in lanthanide borosilicate (LaBS) glass[END_REF][START_REF] Zhang | Energetics of dissolution of Gd2O3 and HfO2 in sodium alumino-borosilicate glasses[END_REF][START_REF] Ellison | Solution behavior of +4 cations in high silica melts -petrologic and geochemical implications[END_REF]. A standard remelting procedure was introduced with an intermediate milling step. Glass samples were melted once (C0 glass), twice (C5 glass) or three times (C6 glass) at 1250°C (Table 2). The hafnium concentration gradient has almost vanished after the second melting (Figure 3c). Hafnium concentration in the C5 glass is very close to the targeted value. Nevertheless, few hafnium crystals still stay at the bottom. After the third melting, C6 glass is homogeneous in concentration and only one hafnium crystal is found in the whole sample (Figure 4f). Bubbles are observed in both C5 and C6 glasses because of introduced air by the milling step. The milling step appears to be essential to homogenize the glass. This method (successive milling and remelting steps) is a convenient way of "stirring" the melt, and thus of improving dissolution kinetics, when thermal treatments can only be realized under static conditions [START_REF] Matyunin | Immobilization of U3O8 in borosilicate glass in an induction melter with a cold crucible[END_REF][START_REF] Vienna | Plutonium Dioxide Dissolution in Glass[END_REF].

Effect of melting temperature

The impact of the melting temperature was briefly studied. Indeed, some authors managed to get equilibrated melts by increasing the temperature up to 1560°C [START_REF] Davis | Hafnium in peralkaline and peraluminous boro-aluminosilicate glass and glass sub-components: a solubility study[END_REF]. In this study, the melting temperature was limited to 1400°C to minimize Na volatilization. A C2 glass sample was synthetized at 1400°C for 3h. Figure 3d shows that temperature increasing improves hafnium solubilization in the whole glass. Nonetheless, hafnium concentration gradient is also emphasized. At the bottom, a thick and whiter Hf-rich layer, about 0.65-1 mm (versus the 6 mm glass height) is observed (Figure 4e). This layer contains HfO 2 crystals and the surrounding Hf concentration is estimated up to 7.5 %mol HfO 2 in the melt. Above that layer, the Hf concentration is below 1.56 mol%. The crystalline phase Na 4 Hf 2 (SiO 4 ) 3 seems to be entirely dissolved in the glass at 1400°C as a reaction intermediate.

As expected, the C-SiC crucible provides a strong reducing environment and is able to reduce part of Na 2 O to the metallic form Na 0 at high temperature [START_REF] Walter | Vapor fractionation of silicate melts at high temperatures and atmospheric pressures[END_REF]. In these experiments, the glass lost, respectively, 14% and 28% of Na 2 O after 3h and 12h at 1250°C. The Na loss was around 37% after two meltings of 3h at 1250°C and 38% after 3h at 1400°C. These first experiments enabled to define an optimized Hf-doped glass elaboration procedure (Figure 1) allowing to approach the equilibrium and thus to measure solubility limits, while limiting the compositional changes due to alkali loss. 3.2 Solubility study

Hafnium solubility

The HfO 2 solubility in the aluminosilicate glass was determined in oxidizing (Pt-Au crucible) and reducing (C-SiC or C g crucibles) conditions at 1250°C and 1400°C for A glasses and only at 1400°C for B glasses, because below 1327°C, B melt starts to crystallize. Both conditional (S C ) and saturation (S S ) solubilities were measured and are indicated in Table 3.

The S C is determined by progressively increasing the amount of added HfO 2 in the glass until the formation of Hf-bearing crystals (Figure 5a andb). The lower limit corresponds to the maximal quantity of Hf that could be incorporated in the homogeneous glass matrix. And the upper limit refers to the quantity of Hf where the first heterogeneities are observed. The S S is characterized by HfO 2 concentration measurements in a HfO 2 -saturated glass with Hf-bearing crystals (Figure 5c andd). The main glasses compositions are shown in Table 4. Each Hf concentration value represents an average of several measurements (from 6 to 12 points of EDS analyses).

Glass containing crystals

The measured conditional solubility is either lower or close to the saturation solubility. The S S limit is higher than the upper S C limit only for two Hf-bearing glasses: A and B glasses melted in a Pt-Au crucible at 1250°C and 1400°C respectively. This suggests that the glass elaboration conditions were well-optimized to reach equilibrium for most glasses. However, the saturation solubility is independent of hafnium dissolution kinetics contrary to the conditional solubility. In the nuclear field, the conditional solubility has been used to compare actinides and surrogates [START_REF] Lopez | Solubility of actinide surrogates in nuclear glasses[END_REF][START_REF] Deschanels | Plutonium solubility and self-irradiation effects in borosilicate glass[END_REF]. This solubility ensures that the glass sample is totally homogeneous for a given glass-making protocol but does not necessarily correspond to the maximum amount that can be incorporated in the glass. In the following, we will essentially consider the saturation solubility. Indeed, we can consider that saturation experiments provide us hafnium concentrations close to the equilibrium concentration, as no hafnium concentration gradient is observed. Only the A glass with 10 mol% HfO 2 melted in C-SiC crucible at 1250°C (AS8 sample) showed a concentration gradient, and consequently, the HfO 2 saturation solubility limit was not determined for it. Furthermore, an excess of hafnium above the saturation solubility should not significantly change the saturation concentration of HfO 2.

The redox conditions (oxidizing or reducing conditions) do not affect the hafnium solubility. Saturation experiments in C g and Pt-Au crucibles for the B-series show that BS4 and BS5 glasses exhibit the same saturation concentration about 5.5-6 mol% HfO 2 at 1400°C. The hafnium concentration of HfO 2 -saturated melts increases with the melting temperature, from 3 mol% HfO 2 at 1250°C to 6-6.5 mol% HfO 2 at 1400°C for the As-series melted in a Pt-Au crucible.

The hafnium solubility also depends on the glass composition. At 1400°C in oxidizing conditions, the Bs-serie glasses exhibit a solubility of 5.5-6 mol% and the As-series, a slightly higher of 6-6.5 mol% HfO 2 . Furthermore, glasses melted in C-SiC crucibles (AS7 and BS2 glasses) exhibit lower solubilities than glasses elaborated in Pt-Au or C g crucibles (AS5, BS4 and BS5 glasses): 4.5 mol% HfO 2 for A melts and 3.5-4 mol% HfO 2 for B melts. This can be explained by the use of C-SiC crucible that interacts with the glasses and modifies their compositions. Indeed, at high temperature, the mullite binder (3Al 2 O 3 -2SiO 2 ) diffuses in the glass as proven by the enrichment of Al 2 O 3 and SiO 2 in AS7 and BS2 samples (Table 4).

Hafnium crystallization

The mineralogy of the different crystals-bearing glasses above the HfO 2 solubility limit changes with the glass composition and the redox conditions (Table 4). For the A-series glasses elaborated in oxidizing conditions (1250°C or 1400°C), the main crystallized phase is hexagonal Na 4 Hf 2 (SiO 3 ) 4 as shown in Figure 6 and Figure 7b. The Rietveld refinement attests that those crystals represent 79 wt% of the whole crystalline phases attended (Table 5). Monoclinic HfO 2 crystals (21 wt%) are also identified by both XRD and SEM/EDS. In the A-series melted in C-SiC crucible at 1400°C, the only Hf-bearing crystallized phase is HfO 2 . Some cristobalite (SiO 2 ) is also detected (around 30 wt%). At lower temperature, the other crystalline phase (40 wt%) seems to correspond to the triclinic parakeldyshite Na 2 ZrSi 2 O 7 phase [START_REF] Ferreira | Synthesis and structural characterization of zirconium silicates[END_REF]. Because of the possible cross-substitution of Zr and Hf, the formula of the observed crystalline phase in Figure 7a might correspond to Na 2 HfSi 2 O 7 . This stoichiometry is confirmed by EDS analysis of the crystal (Table 6). Na migration under electron beam may explain the slight drop between the analysis and the pure phase stoichiometry. EDS analysis also suggests that a substitution of Na 2 O by CaO is also likely to occur in that crystal. Since no XRD pattern of Na 2 HfSi 2 O 7 is referenced in the literature to our knowledge, we have first considered the same space group for Na 2 Hf 2 SiO 7 than for parakeldyshite. The atomic positions of parakeldyshite were used with a complete substitution of Zr by Hf. The Rietveld refinement of the XRD pattern is consistent with this result, as shown by the χ2 equal to 4.9 (Figure 8). The cell parameters of the Na 2 HfSi 2 O 7 crystalline phase are extracted from the refinement and given in Table 7. In order to validate the refinement, the sodium hafnium disilicate Na 2 HfSi 2 O 7 was synthetized and its structure was refined. The triclinic space group was confirmed and the atomic positions were determined [START_REF] Massoni | Crystal structure of Na2HfSi2O7[END_REF].

For the B-series glasses (Na-free) elaborated in oxidizing conditions, monoclinic Ca 2 HfSi 4 O 12 , tetragonal HfSiO 4 and HfO 2 crystals are observed by SEM (Figure 7d) and detected by XRD (Figure 6). The main phase is Ca 2 HfSi 4 O 12 (89 wt%) and other phases are HfO 2 (6 wt%) and HfSiO 4 (5 wt%). In reducing conditions, the crystallized phases are HfSiO 4 and HfO 2 according to XRD results (Figure 6). For glasses melted in C-SiC crucibles, HfO 2 crystals are not detected by XRD (certainly below the device detection limit) but some tiny ones (few hundred of nanometers) are shown up in SEM images (Figure 7c). However, XRD patterns often show the presence of graphite carbon and silicon carbide. These impurities come from the reaction between glass and C-SiC crucible at the glass/crucible interface. A thin layer belonging to the C-SiC crucible was systematically observed on the sample surface after heating. So a variable part of this layer could be introduced in the sample during the XRD preparation. The C and SiC content are not taken into account in the crystalline phase percentage calculation.

Table 5

Relative percentage in mass of some crystals in glass, data obtained after the Rietveld refinement of crystallized glass samples. Error for each crystal is ± 2 wt%. * Reduced chi square is an indicator of the fit goodness as determined in [START_REF] Frontera | FULLPROF as a new tool for flipping ratio analysis[END_REF].

Glass

Table 7

Cell parameters (a, b, c, α, β, γ and cell volumes) of the Na2HfSi2O7 crystals present in the studied sample, extracted from the whole pattern decomposition, and of the triclinic Na2ZrSi2O7 crystals. Hf-bearing crystals display different forms (Figure 7). HfO 2 gets two types of crystal sizes, several hundred nanometers and several microns. Micrometric crystals are located in the glass and have an isometric shape while nanometric HfO 2 are often observed inside the Hf silicate crystals. These silicate crystals have an isometric shape and range in size from 10 μm to 50 μm. Other crystal morphologies are also observed in the A-series fused in C-SiC at 1400°C (Figure 9). These hafnium crystals are located at the interface between the glass and the crucible and display several forms such as needle (Figure 10a), dendrite (Figure 10b andc) and crown (Figure 10d) shapes. Surrounding these crystals, a depletion of HfO 2 and CaO and an enrichment of other oxides (SiO 2 and Al 2 O 3 ) are noticed (Table 8). Those crystals are not observed using Pt-Au crucibles. viscosity but not enough to avoid HfO 2 sedimentation. In a laminar flow, the sedimentation velocity (m.s -1 ) of spherical particles in a melt can be described by the Stokes' law:

Crystalline

phase a (Å) b (Å) c (Å) α (°) β (°) γ (°) V (Å 3 ) Ref
(1) with r, the particle radius (m) g, the standard acceleration (m.s -2 ) ρ, the density (kg.cm -3 ) η, the fluid viscosity (Pa.s)

Considering these hypotheses (laminar flow and spherical particles) and equation ( 1), 158 μm diameter HfO 2 particles in A melt fall in about 15 min from the top to the bottom of the glass sample (around 6 mm) at 1250°C and more rapidly in 5 min at 1400°C. HfO 2 sedimentation is accelerated at 1400°C, while hafnium diffusion into the glass melt is enhanced. Equation ( 1) also shows that decreasing HfO 2 particle size drastically slows down the sedimentation velocity. At 1250°C, 70 μm diameter HfO 2 particles fall in 75 min and 15 μm diameter HfO 2 particles in more than one day. This effect has to be coupled with the increase in Hf precursors dissolution kinetics for smaller initial particle sizes [START_REF] Lopez | Solubilité des actinides et de leurs simulants dans les verres nucléaires : limites d'incorporation et compréhension des mécanismes[END_REF], both leading to a better HfO 2 incorporation. When equilibrium is not established, HfO 2 sedimentation widely limits its incorporation into the glass matrix. At the bottom of the crucible, the glass melt surrounding crystals is supersaturated in hafnium which largely slows down HfO 2 crystals dissolution into the whole glass sample. Furthermore, increasing duration could make the sedimentation layer denser [START_REF] Matyunin | Immobilization of U3O8 in borosilicate glass in an induction melter with a cold crucible[END_REF] and thus makes it harder to dissolve crystals. In that case, crystallization is due to the presence of undissolved particles, relicts of hafnium oxide particles introduced into the initial powder mixture or to new formed crystals. 4.2 Hafnium solubility Our hafnium solubility results may now be compared to other studies. In this work, we show that the redox conditions do not affect the HfO 2 solubility which is consistent with the fact that Hf displays only one oxidation state in the glass, namely Hf IV . Therefore the HfO 2 solubilization mechanism must be the same for reduced or oxidized glass melts. A higher melting temperature improves the HfO 2 solubility limits as commonly observed by authors [START_REF] Lopez | Solubility of actinide surrogates in nuclear glasses[END_REF][START_REF] Ellison | Solution behavior of +4 cations in high silica melts -petrologic and geochemical implications[END_REF][START_REF] Vienna | Plutonium Dioxide Dissolution in Glass[END_REF]. Since the oxidation state is fixed (Hf IV ), the enhancing of the solubility is only controlled by the temperature. The interpretation of the HfO 2 solubility in aluminosilicate glass as a function of the glass composition is based on previous studies. For peralkaline glass, Davis [START_REF] Davis | Hafnium in peralkaline and peraluminous boro-aluminosilicate glass and glass sub-components: a solubility study[END_REF] has demonstrated that the hafnium solubility is strongly and positively related to the excess of alkalis which are not used for charge compensation. We can define the following M* ratio (with the oxide content in mol%):

(

) 2
where M' and M'' are respectively metal divalent and monovalent cations. According to Davis, for peralkaline glasses (M* ≥ 0.5), the hafnium solubility increases with M*. Applied to our case M* is written:

(3)

All our glass samples have M* > 0.5 (Table 4) and belong to the peralkaline field. Glass samples melted in C-SiC crucibles present a lower M* (0.71 and 0.74 for AS7 and BS2 samples) than glasses fused in other crucibles (0.84 and 0.83 for AS5, BS4 and BS5 samples). For AS7 glass sample, the lessening of M* is accentuated by Na volatilization. A decrease in HfO 2 solubility is observed as M* decreases (Table 3). Indeed, for AS7 and BS2 glasses, the melt compositions are enriched in Al 2 O 3 and SiO 2 because of the mullite binder from the crucible, hence show a lower excess of alkalis or alkaline earths. Nevertheless, a slight solubility difference is observed between AS5 and BS4 glasses although their respective M* are comparable. Therefore, it seems that the nature of cations may play a small role. Some authors [START_REF] Watson | Zircon saturation in felsic liquids -experimental results and applications to trace-element geochemistry[END_REF][START_REF] Dickenson | Redox equilibria and the structural role of iron in alumino-silicate melts[END_REF] have shown that, in peralkaline melts, the increase of the M'O/M'' 2 O ratio smoothly enhances the solubilities of +4 cations (for instance, Ti and Zr). Thus, the substitution of Na 2 O by CaO should slightly decrease the hafnium solubility as observed. When M* is higher than 0.5, these cations act both as network modifiers and charge compensators in the aluminosilcate network. Classically, Ca 2+ serves as a charge balancing for two AlO 4 tetrahedrons or two non-bridging oxygens and Na + charge balancing for one AlO 4 tetrahedron or one non-bridging oxygen. Ca might cause a steric hindrance more significant than Na. This assumption to explain the low HfO 2 solubility difference between AS5 and BS4 melts needs further experiments to confirm it.

Figure 12 presents our results compared to previous studies, with the HfO 2 solubility plotted as a function of the M* ratio. The HfO 2 solubility is higher in peralkaline glasses than in peraluminous ones and borosilicate glasses tend to exhibit higher hafnium solubilities than aluminosilicate glasses. For the borosilicate glasses, the melting temperature is 50°C higher than in aluminosilicate glasses. Boron appears to improve the HfO 2 solubility but its role still remains unclear [START_REF] Davis | Hafnium in peralkaline and peraluminous boro-aluminosilicate glass and glass sub-components: a solubility study[END_REF].

Hafnium crystallization

The morphology of hafnium silicate crystals suggests that these crystals are quickly formed and quite stable in the melt. The HfO 2 crystals seem to grow following an Oswald ripening process [START_REF] Voorhees | The theory of Ostwald ripening[END_REF][START_REF] Yao | Theory and simulation of Ostwald ripening[END_REF]. Nanometric HfO 2 are not observed in the melt but as inclusions in the hafnium silicate crystals indicating that they might have been poikilitically enclosed in the silicates before their growth. Dendritic or needle crystals could be quench crystals [START_REF] Chen | Olivine dissolution in basaltic melt[END_REF]. As the temperature decreases during quenching, the glass melt becomes supersaturated with hafnium leading to a quick overgrowth of hafnium crystal along one or two preferential axes. However, those crystals are concentrated at the glass/crucible interface which is not logical for quench crystals. These crystals should also be observed in the core of the glass sample where the cooling rate is ordinarily the lowest. Moreover, the crown-shaped crystals do not really look like quench crystals. All this suggests that these crystals result from a reaction between the glass and the C-SiC crucible. The mullite binder might react with the glass melt in this area as shown by the glass enrichment in Al 2 O 3 and SiO 2 and depletion in other elements (CaO and HfO 2 ). All these crystallization mechanisms are not fully understood in this work and need to be deepened. The Na 2 HfSi 2 O 7 crystalline phase has been detected for the first time. The existence of this phase is confirmed by its synthesis and its crystal structure determination. The Rietveld refinement of the XRD pattern containing this crystalline phase allows us to quantify it. The isomorphic character between the Na 2 HfSi 2 O 7 and the parakeldyshite Na 2 ZrSi 2 O 7 can be explained by close ionic radii for Hf and Zr for the same coordination number [START_REF] Shannon | Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides[END_REF]. All detail [8] [START_REF] Davis | Hafnium in peralkaline and peraluminous boro-aluminosilicate glass and glass sub-components: a solubility study[END_REF][START_REF] Feng | Distribution and solubility of radionuclides in waste forms for disposition of plutonium and spent nuclear fuels: Preliminary results[END_REF] [8] [START_REF] Res | Transformation of Na2O-HfO2-B2O3 glass into a material having interconnected pores[END_REF] about the structure of Na 2 HfSi 2 O 7 are currently submitted and reviewed for a formal data deposition into XRD databases.

Conclusion

In this study, an experimental protocol has been developed in order to measure the hafnium solubility in aluminosilicate glass melted in both oxidizing and reducing conditions. Hf-doped glass elaboration conditions have been optimized to limit the HfO 2 sedimentation and to approach equilibrium. Contrary to the conditional solubility, the saturation solubility readily allows to determine a thermodynamic solubility. As hafnium speciation remains the same in the glass matrix (Hf IV ), its solubility is not affected by the redox conditions. In peralkaline glasses (with molar content (Na 2 O+CaO)>Al 2 O 3 ), the HfO 2 solubility limit is positively correlated with the melting temperature and the excess of network modifier cation (Na 2 O and CaO) relatively to Al 2 O 3 . The hafnium solubility also seems to be slightly impacted by the nature of these cations. These results are in agreement with previous studies of +4 cations in borosilicate or aluminosilicate glasses. The hafnium solubility appears to be higher in borosilicate glasses than in aluminosilicate glasses for a similar excess of alkalis or alkaline earths. Above the hafnium solubility limit, formations of HfO 2 , HfSiO 4 , Ca 2 HfSi 4 O 12 , Na 4 Hf 2 (SiO 4 ) 3 and Na 2 HfSi 2 O 7 crystals have been observed in those glasses. The glass composition and potentially the redox conditions change the nature of the Hf-bearing crystals. The existence of the Na 2 HfSi 2 O 7 crystalline phase has been evidenced in Na-rich aluminosilicate melts and for temperatures close to 1250°C. The Rietveld refinement of Na 2 HfSi 2 O 7 has been successfully performed. The Na 2 HfSi 2 O 7 phase structure appears to be very similar than the parakeldyshite Na 2 ZrSi 2 O 7 phase structure. The optimization of Hf-doped glass elaboration conditions will be further used for the preparation of U-doped glasses. Indeed, the uranium incorporation in the glass melt faces to the same sedimentation issues [START_REF] Matyunin | Immobilization of U3O8 in borosilicate glass in an induction melter with a cold crucible[END_REF]. Besides, UO 2 solubility is also likely to be related to the excess of alkalis [START_REF] Domine | Preliminary investigation of the processes governing the solubility of uranium in silicate melts[END_REF]. The uranium behavior however remains more complex than the hafnium one. The chemistry of uranium in glass melt is ruled by the equilibria of U VI -U V -U IV [START_REF] Schreiber | The chemistry of uranium in glass-forming aluminosilicate melts[END_REF]. The UO 2 solubility in glass melt as the function of the oxygen fugacity (fO 2 ) is the subject of ongoing studies and those data will be compared to the HfO 2 solubility.

Figure 1 .

 1 Figure 1. The general procedure of glass elaboration for Hf solubility measurements.

Figure 2 .

 2 Figure 2. Picture (a) and scanning electron microscopy images (b) and (c) of heterogeneities observed in Hfdoped glass (C3 sample).

Figure 3 .Figure 4 .

 34 Figure 3. Variation in HfO2 concentration as a function of glass area for several glasses elaborated in different conditions. Impact of (a) HfO2 particle size, (b) melting time, (c) remelting, (d) melting temperature. HfO2 concentration as related to mole percent. Error bars represent the random standard uncertainty calculated by multiplying the standard deviation of the mean and the student t-factor at the 95% level of confidence.

Figure 5 .

 5 Figure 5. SEM images of Hf-doped A glasses, elaborated in Pt-Au crucible at 1250°C, containing (a) 1.5 mol%, (b) 2 mol% and (c,d) 5 mol% HfO2, showing the two methods for the solubility measurements (gradation and saturation).

Figure 6 .Figure 7 .

 67 Figure 6. XRD patterns of Hf-doped glasses elaborated in oxidizing and reducing conditions at 1250°C or 1400°C. The glass sample without adding HfO2 was melted in C-SiC crucible at 1400°C for 3h. Note that the enlarge part of patterns between 2θ = 18-50° is shown to get better insight of the diffraction peaks due to the crystallization.

Figure 8 .

 8 Figure 8. Rietveld refinement of XRD pattern containing the detected Na2HfSi2O7 crystalline phase in the A glass with 10 mol% HfO2 melted in C-SiC at 1250°C (AS8).

Figure 9 .

 9 Figure 9. SEM image of the interface between the C-SiC crucible and the glass in the AS6 sample, showing (1) and (2) different areas.

Figure 10 . 4 Discussion 4 . 1

 10441 Figure 10. SEM images of Hf-bearing crystals observed in Hf-doped A glasses melted in C-SiC crucible at 1400°C with several morphologies (a) needle shaped, (b,c) dendritic shaped and (d) crown shaped .

Figure 11 .

 11 Figure 11. Steady state viscosity of glass melts for different compositions as a function of the temperature. The dash lines represent the VFT model and the symbols are the measured data. Note that all glasses are totally homogeneous within the measuring range.

Figure 12 .

 12 Figure 12. Comparison of hafnium solubility in A and B glasses to hafnium solubility in several types of glasses from the literature. HfO2 concentration in mole percent is plotted as the function of the M* ratio (CaO+Na2O)/(CaO+Na2O+Al2O3) in molar content.

Table 1

 1 Targeted chemical compositions of main glasses.

	Glass composition (mol%)

Table 2

 2 Glass elaboration parameters of 1.56 mol% HfO2-doped glasses melted in C-SiC crucible.

			Glass elaboration parameters
	Sample name
		Melting time	Melting temperature	HfO 2 particle size	Fusions number
	C0	3h	1250°C	70 μm	1
	C1	12h	1250°C	70 μm	1
	C2	3h	1400°C	70 μm	1
	C3	3h	1250°C	158 μm	1
	C4	3h	1250°C	15 μm	1
	C5	3h + 3h	1250°C	70 μm	2
	C6	3h + 3h +1h	1250°C	70 μm	3
	A and B glass powders were respectively mixed with different amounts of HfO 2 , ranging from
	1.56 mol% to 10 mol% HfO 2 in the final glass. The powder mixture was fused either in a Pt-
	Au crucible and air atmosphere (oxidizing conditions) or in a C-SiC (or C g ) crucible under Ar
	atmosphere (reducing conditions). Glasses were directly quenched in air (cooling rate about
	100°C/min) and then milled. The milling and remelting steps were done twice. Finally, the
	crucible was removed from the hot furnace and quenched immediately by immersing the
	bottom of the crucible into a cold water bath to prevent crystallization during cooling (cooling
	rate about 100°C/s). Glasses were not annealed.

Table 3

 3 Solubility limits of hafnium determined in A and B aluminosilicate glasses elaborated in oxidizing and reducing conditions at 1250°C and 1400°C.

	Hf-doped glasses		Melting conditions			Hafnium solubility limits
	Glass series	T (°C)	Crucible	Atmosphere	Conditional solubility (HfO 2 mol%)	Saturation solubility (HfO 2 mol%)
		1250	Pt-Au	Air	1.5	a	< S c < 2
	A-series

Table 4

 4 Glass compositions (mol%) determined by microprobe (EDS) and crystalline phases observed for different elaboration conditions. The M* ratio is expressed as molar (CaO+Na2O)/(CaO+Na2O+Al2O3) ratio. The random standard uncertainty is calculated by multiplying the standard deviation of the mean and the student t-factor at the 95% level of confidence.

	Glass Name	Starting glass	Temperature (°C)	Redox conditions	Added HfO 2 , (mol%)	SiO (mol%) 2	Al (mol%) 2 O 3	CaO (mol%)	Na (mol%) 2 O	HfO (mol%) 2	Fe (mol%) 2 O 3	Crystalline phases	M*
						57.30	6.30	13.91	20.82	1.66
	AS1	A	1250	Pt-Au	1.5	+/-	+/-	+/-	+/-	+/-	0	None	0.85
						0.10	0.03	0.05	0.08	0.05
	AS2	A	1250	Pt-Au	4.0	57.54 +/-0.30	6.34 +/-0.07	13.78 +/-0.09	19.25 +/-0.24	3.09 +/-0.08	0	Na 4 Hf 2 (SiO 4 ) 3 , HfO 2	0.84
						62.44	7.72	13.41	13.90	2.53	0.31
	AS3	A	1250	C-SiC	2.5	+/-	+/-	+/-	+/-	+/-	+/-	None	0.78
						0.49	0.12	0.49	0.39	0.07	0.03
						55.60	6.02	13.20	20.01	5.17
	AS4	A	1400	Pt-Au	5.0	+/-	+/-	+/-	+/-	+/-	0	None	0.85
						0.12	0.04	0.06	0.08	0.09
	AS5	A	1400	Pt-Au	7.0	55.19 +/-0.09	6.13 +/-0.03	13.28 +/-0.12	19.36 +/-0.16	6.04 +/-0.07	0	Na 4 Hf 2 (SiO 4 ) 3 , HfO 2	0.84
						65.02	7.95	13.17	10.59	3.02	0.26
	AS6	A	1400	C-SiC	3.0	+/-	+/-	+/-	+/-	+/-	+/-	Dendrites	0.75
						0.91	0.30	0.92	0.53	0.15	0.04
						65.77	8.60	11.98	8.93	4.52	0.21
	AS7	A	1400	C-SiC	7.0	+/-	+/-	+/-	+/-	+/-	+/-	HfO 2	0.71
						0.17	0.09	0.46	0.17	0.08	0.17
						61.16	7.50	28.27		3.07
	BS1	B	1400	C-SiC	3.5	+/-	+/-	+/-	0	+/-	0	None	0.79
						0.24	0.05	0.22		0.07
						61.77	8.49	24.60	1.07	3.56	0.51
	BS2	B	1400	C-SiC	7.0	+/-	+/-	+/-	+/-	+/-	+/-	HfSiO 4 , HfO 2	0.75
						0.37	0.23	0.78	0.21	0.14	0.21
						56.65	6.23	34.11		3.02
	BS3	B	1400	Pt-Au	3.0	+/-	+/-	+/-	0	+/-	0	None	0.85
						0.07	0.02	0.11		0.06
	BS4	B	1400	Pt-Au	7.0	54.92 +/-0.05	6.55 +/-0.03	32.91 +/-0.09	0	5.61 +/-0.06	0	Ca 2 HfSi 4 O 12 , HfSiO 4 ,	0.83

Table 6

 6 Composition of the observed Na2HfSi2O7 crystalline phase determined by microprobe (EDS) in the studied sample (AS8) and compared to the stoichiometric one.

	Chemical elements	O (at%)	Si (at%)	Na (at%)	Hf (at%)	Ca (at%)
	Theoretical formula of Na 2 HfSi 2 O 7	58.3	16.7	16.7	8.3	0
	Measured composition of the Na 2 HfSi 2 O 7 crystal	60.1	17.6	11.6	8.4	2.4

Table 8

 8 Glass compositions of two areas;[START_REF] Cable | Kinetics of volatilization of sodium borate melts[END_REF] close to the interface between the C-SiC crucible and the glass and (2) far from this interface; determined by microprobe (EDS) in the AS6 sample.

	Point of	SiO 2	Al 2 O 3	CaO	Na 2 O	HfO 2	Fe 2 O 3
	analysis	(mol%)	(mol%)	(mol%)	(mol%)	(mol%)	(mol%)
	1	77.63	9.44	2.71	7.81	2.30	0.11
	2	67.85	8.42	10.75	8.39	4.31	0.29

Acknowlegdments

The authors gratefully acknowledge B. Pénélon for performing viscosity measurements. This work was financially supported by CEA, AREVA and ANDRA.


Othmane Bouchenafa
email: obouchenafa@estp-paris.eu

Rabah Hamzaoui
email: rhamzaoui@estp-paris.eu

Louiza Azem

Abdelkrim Bennabi

Johan Colin

Manufacturing equivalent Clinker by indirect mechanosynthesis process

Keywords: Equivalent Clinker, mechanosynthesis, cement, low CO2 emission

This study is focused to the proposition of new cement manufacturing process. It is widely known that the cement production is responsible for a significant CO2 release each year (approximatively 4 billon ton). So, it is became necessary to find another cement manufacturing process with a minimum CO2 emission. The aim of this work is to manufacture equivalent clinker by indirect mechanosynthesis process. It consists to combine between mechanical activation of the raw materials (mixture of limestone and clay) and heat treatment less than 900 °C. The equivalent clinker obtained by this method shows the presence of the alite (tricalcim silicate) C3S and belite (dicalcium silicate) C2S and Tricalcium aluminate C3A. CO2 emission by this technique is estimated by 0.3 Ton for 1 Ton of equivalent clinker.

1| INTRODUCTION

The demand for cement is growing steadily. Significant growth is occurring in countries such as China and India, as well as in areas such as the Middle East and North Africa. [START_REF] Schneider | Sustainable cement production-present and future[END_REF] The global cement production will keep rising due to the demographic expansion and the infrastructure demand related this expansion. Global cement production is set to grow by 12-23% by 2050 from the current level. [START_REF]Carbon Emissions Reductions up to[END_REF] Some estimates put the cement industry total as high as 5% of total global anthropogenic CO2 emissions. [START_REF] Gartner | Industrially interesting approaches to 'low-CO2' cements[END_REF] Many solutions have been studied and used to reduce these CO2 emissions, as the clinker substitution, Carbone capitation and storage (CCS), use of alternative fuels [START_REF] Schneider | Sustainable cement production-present and future[END_REF].

The cement manufacturing process has been known since the beginning of the 19th century. [START_REF] Hewlett | Lea's Chemistry of Cement and Concrete[END_REF] The Portland cement is produced by milling a mixture of calcareous materials (limestone) and argillaceous materials (clay), and materials containing silica and iron oxide, burning them at a temperature between 1300 and 1500°C, and a fine milling to produce clinker. In order to obtain cement, only gypsum, water and grinding aids are allowed to add. [START_REF] Afnor | Cement -Part 1: composition, specifications and conformity criteria for common cements[END_REF] The objective of this study is to improve the process of the clinkerisation by introducing the mechanosynthesis (indirect mechanosynthesis) and thus reducing CO2 emissions. The indirect mechanosynthesis is consisting on coupling a mechanical activation with short duration and adding another process for obtaining the final product. In our case, we have used a heat treatment. The combination between a shot milling duration and a heat treatment is also called "Mechanically Activated Annealing process" [START_REF] Suryanarayana | Mechanical alloying and milling[END_REF] The mechanosynthesis is a high-energy ball milling technique wherein the powder particles are subjected to mechanical energy transfer inducing plastic deformation both equilibrium and metastable phases can be synthesized by this process; in addition, there is a reduction of the particle sizes with modification of the shape and reduction of the grain sizes. During the process, the powder particles are regularly flattened, cold-welded, fractured and rewelded. [START_REF] Suryanarayana | Mechanical alloying and milling[END_REF]7] Mechanosynthesis provides a way to mix and combine solids ranging from the scale of a powder particle to the micrometric scale, while the crystallite (grains) will shrink to a nanoscale size and will provide nanostructured materials. [7,[START_REF]Novel Synthesis and Characterization of Nanostructured Materials[END_REF] In the case of the mixing of different powders and elements, it is possible to produce during the milling process amorphous alloys, nanocrystalline, nanocomposites, solid solutions, intermetallic and materials with non-equilibrium structures at room temperature [START_REF] Suryanarayana | Mechanical alloying and milling[END_REF][7][START_REF]Novel Synthesis and Characterization of Nanostructured Materials[END_REF] Hamzaoui et al. [START_REF] Hamzaoui | The sequel of modified fly ashes using high energy ball milling on mechanical performance of substituted past cement[END_REF] used a planetary ball mill to activate fly ash at different milling times 1h, 6h, and 9h. They observed that the fly ash particle size reduction was optimal at 1h where, for 50% CEMI substitution by milled fly ashes, the compressive strength gain of cement-fly ashes pastes increased after 28 curing days. In addition, they found that the maximum compressive strength gain reached an improvement of +23.9% with fly ashes milled for 3 h after 90 curing days. Bouaziz et al. [START_REF] Bouaziz | Efficiency of high energy over conventional milling of granulated blast furnace slag powder to improve mechanical performance of slag cement paste[END_REF] used also the mechanosynthesis for the slag activation for 1h to 9h of milling. The particle size reduction was optimal for 3h of milling. For 45% of CEM-I replacement, the authors shown that the optimal compressive strength gain corresponds to 3 h of milling and reached +8.8% for 120 curing days.

In order to obtain an equivalent clinker, we have used a mix of limestone and clay and used an indirect mechanosynthesis.

2| Materi als and methods

Raw materials, clinker and cement (OPC)

Limestone

The limestone used for this study was provides from OMYA. It is constituted of >97% of calcium carbonate (CaCO3) in calcite structure.

Clay

The clay used in this work is Proclay kaolinite provided from Beaujard-Poigny site (France). It contains Kaolinite and quartz.

Conventional clinker.

In our study, for comparison to the equivalent clinker, we have used clinker provided from Vicat Company.

The chemical compositions of the raw materials, clinker and ordinary Portland cement are conducted by X-ray fluorescence; the results are summarized in table 1.

Equivalent clinker process

For the production of clinker two processes are used: mechanosynthesis (mechanical activation) and heat treatment

Mechanical activation (mechanosynthesis)

Mechanical activation is carried out by planetary ball miller (RETSCH PM 400). This device is composed of four vials mounted on a planar disc. With the rotation of the disc, the vials move in a circular and in opposite direction compared to the disc rotation. The ball-to-powder weight ratio is 4. For the preparation of the equivalent clinker, we put in the vial 80% of limestone (160 g) and 20% of clay (40g).

To avoid the contamination, the vials are sealed. The rotation speeds of the disc and the vials are Ω = 400 rpm and ω = 800 rpm, respectively. Different milling durations are used from 15 minutes to 60min. Thirty-millimeter diameter steel balls and 500 ml volume steel vials are used.

Heat treatment

Different temperatures are used from 400° to 900°C for 1 hour using an Electric industrial oven (Kaesermann & Sperisen).

Characterization of powders

The chemical composition of all the products is obtained by an elemental analysis conducted with X-ray fluorescence spectroscopy and carried out using S2 RANGER instrument from Bruker.

X-ray investigation is performed using Bruker D2 phaser diffractometer with a continuous scanning mode and Cu Kα radiation (λ = 0.1541 nm). The lines are measured in the 2θ range (5-70) ° by an increment of 0.02° for 0.15 s. The software used for building the X-ray diffraction diagrams is DIFFRAC.EVA with ICDD PDF2. In order to improve the relevance of the time evolutions of X-ray diffraction diagrams, X-ray investigation is conduced according to different milling durations from the same vial sampling.

IR spectroscopy is performed by a Thermo Scientific Nicolet IS10 instrument equipped with Smart iTR (with Diamond Plate) accessory. With this ATR (Attenuated Total Reflectance) accessory, the IR spectroscopy is able to analyze solids, liquids, pastes and gels. The results are analyzed with Omnic Software.

In order to have an idea about the fineness of the equivalent clinker, the specific surface area was determined by two methods, Blaine method (Air permeability) and the BET method (nitrogen adsorption).

Blain method is done by Blaine permeabilimeter with automatic time measurement according to EN 196-6 and ASTM C204 from Controlab.

The BET method is performed with the use of a Gemini VII 2390 instrument from Micrometrics. The Analyses is performed using a static volumetric technique in which the adsorptive flows into a tube containing the sample and into a balance tube simultaneously. The internal volume and the temperature surrounding both tubes is maintained in identical conditions. Helium gas is used to determine samples density.

3| Results and discussion

X-ray diffraction analysis

In this study, we have given the name Equi. Clinker A for the product of the indirect mechanosynthesis process after 15min of milling and 1hour of heat treatment. For the name of Equi. Clinker B concerning the product of 1 hour of milling and 1 hour of heat treatment.

The X-ray diffractions analysis of the conventional clinker and the two types of equivalent clinker produced are shown in Figure 1. The patterns give information about the impact of our process on the clinkerization of the mixture of limestone and the clay.

The X-ray pattern of the conventional clinker shows various structures as the di-calcium silicate (β-C2S) Ca2SiO4 PDF# 00-001-1012, tri-calcium silicate (C3S) Ca3SiO5 PDF# 00-055-0738, Calcium Aluminium oxide (C3A) Ca3Al2O6 PDF# 00-014-0693, Calcium Aluminum iron oxide PDF# 00-010-0032 Ca4 Al2 Fe2 +3 O10 and Lime CaO.

We observe the presence of the Alite and belite the compounds that supposed to be in the clinker and responsible of the C-S-H and C-H production after cement hydration reactions. In addtion, there are few peaks of CaO (lime) which show that all lime has reacted for the Alite and the belite production.

Comparing to the pattern of the conventional clinker, we have found the same structures: the di-calcium silicate (β-C2S The presence of CaO may be due to the fact that this lime has not reacted with other elements such as silica or iron oxide.

From the two observations, we can say that the new clinkerization process is not as efficient as the classical process and this proposed process should be more improved.

Some additional peaks of C3A are found in the equi. clinker A and B at 17.236°, 19.161°. We observe also the peak C3A at 26.675° is more intense in the two new clinkers that in the conventional one.

. Results are summarized in Table 2. It is observed the presence of compounds as the ß-C2S or C3S by the absorption band Si-O at 992, 912 and 846 cm -1 for the two equivalent clinker A and B. The absorption band Si-O is identified at 1025 cm -1 for the conventional clinker [START_REF] Hughes | Determining cement composition by Fourier transform infrared spectroscopy[END_REF][START_REF] Benosman | Valorisation de la spectrométrie infrarouge (FTIR) pour l'analyse qualitative de composes des ciments, argiles, et des mélanges ciment/argile[END_REF]. FTIR data confirm the X-ray diffraction results.

The width band between 1360 and 1568 can be related to calcium carbonate (C-O). In addition, calcium carbonate (C-O) band is identified at 876 cm -1 (observed only in the 2 patterns of the two equivalent clinkers A and B) and 712 cm - 1 (observed in the 3 patterns). For adsorption band (Al-O) observed at 861 cm -1 found in the two patterns of the equivalents clinker A and B can be related to C3A.

In conventional clinker, we have identified band (Fe-O) at 700 cm -1 related to C3AF [START_REF] Hughes | Determining cement composition by Fourier transform infrared spectroscopy[END_REF][START_REF] Benosman | Valorisation de la spectrométrie infrarouge (FTIR) pour l'analyse qualitative de composes des ciments, argiles, et des mélanges ciment/argile[END_REF].

Specific surface area measurement by Blaine permeability and BET method.

In table 3, we give the results of the specific surface analysis done by the use of two different methods Blaine permeability and BET method Generally, the specific surface of the commercially available cement is between 0.25 m² / g and 0.45 m² / g measured by Blaine method. We observe from the results that the finesses of the two equivalent clinker A and B are higher than SSA of commercial cement. This high specific surface is due to the milling process. Mechanosynthesis provides a way of mixing and combining solids from the scale of a powder particle down to the micrometric scale, while the crystallite (grains) will scale down to a nanometric size and obtaining nanostructured materials [START_REF] Suryanarayana | Mechanical alloying and milling[END_REF][START_REF] Hamzaoui | The sequel of modified fly ashes using high energy ball milling on mechanical performance of substituted past cement[END_REF][START_REF] Bouaziz | Efficiency of high energy over conventional milling of granulated blast furnace slag powder to improve mechanical performance of slag cement paste[END_REF].

In addition, we remark that the SSA of the equi. clinker A is high than that of equi. clinker B.

This difference between equi. clinker A and B can be explained by the agglomeration of particles due to the coldwelding during the milling process [START_REF] Hamzaoui | The sequel of modified fly ashes using high energy ball milling on mechanical performance of substituted past cement[END_REF][START_REF] Bouaziz | Efficiency of high energy over conventional milling of granulated blast furnace slag powder to improve mechanical performance of slag cement paste[END_REF].

Fig. 1 |Fig. 2 |

 12 Fig.1 | XDR patterns of the conventional clinker and equivalent clinker A and B

Conclusion I t i

  s k n o wn t h a t t h e e n vi r o n m e n t a l i m p a c t o f c e m e n t p r o d u c t i o n m u s t b e r e d u c e d . O u r r e s e a r c h wo r k a i m s t o r e d u c e t h i s i m p a c t a n d p r o d u c e a c e m e n t wi t h t h e s a m e p e r f o r m a n c e . W e o b s e r ve f r o m t h e s t r u c t u r a l s t u d y t h a t t h e p r o c e s s o f t h e i n d i r e c t m e c h a n o s yn t h e s i s h a ve b e e n a b l e t o p r o d u c e t h e c r ys t a l l i n e p h a s e s w a n t e d i n t h e c e m e n t a s t h e A l i t e C 3 S a n d B e l i t e C 2 S . Th e e xt r a a m o u n t o f l i m e o b s e r ve d i n t h e t wo e q u i va l e n t c l i n k e r s i s a n i s s u e t h a t we m u s t k e e p wo r k o n , a n d i m p r o ve o u r p r o c e s s t o i n c r e a s e s t h e p r o d u c t i o n o f t h e C 3 S a n d C 2 S . F u r t h e r i n ve s t i g a t i o n o n t h e m i c r o s t r u c t u r e a n d t h e m e c h a n i c a l p e r f o r m a n c e s o f t h e e q u i va l e n t c l i n k e r a r e i n p r o g r e s s . Mo r e o ve r , c o n c e r n i n g t h e e n e r g y c o n s u m p t i o n a n d t h e C O 2 e m i s s i o n s o f t h e i n d i r e c t m e c h a n o s yn t h e s i s p r o c e s s a r e u n d e r i n ve s t i g a t i o n .

Table 1 |

 1 Chemical composition of the raw materials

	Oxide	Limestone	Kaolinite	Clinker
	CaO	97.78	0.72	71.85
	SiO2	0.97	67.70	14.66
	Al2O3		23.62	3.02
	FeO3	0.22	2.04	3.97
	Na2O
	SO3	0.14	0.59	2.26
	MnO	0.08
	SrO	0.21		0.28
	TiO2		3.52	0.27
	P2O5		0.72	0.24
	MgO			1.8
	K2O	0.18		1.3
	Others	0.42	1.09	0.35
	2.2 Methods

Table 2 | Assignment of FTIR peaks of clinkers using the Thermo-Scientific Omnic series software

 2

	C r ys t a l l i n e	W a ve l e n g t h ( c m -1 )
	p h a s e s
	ß -C 2 S o r C 3 S	8 4 6 9 1 2 , 9 9 2 , 1 0 2 5
	(Si-O)
	C a C O 3 (C-O)	7 1 2 , 8 7 6 ,
	C 3 A (Al-O)	861
	C 3 AF( F e -O)	700

Table 3 | Specific surface by Blaine permeability and BET method of the equivalents clinker

 3

ACKNOWLEDGEMENT

We want to thank Margareta Walferdein from IRC/ ESTP Cachan for here assistance in the XRD. We thank ESTP foundation organism for financing the Phd thesis.


Etienne Herth

Maciej Baranski

Djaffar Berlharet

David Bouville

Laurie E Calvet

Christophe Gorecki

Djaar Berlharet

Fast ultra-deep silicon cavities: Toward isotropically etched spherical silicon molds using an ICP-DRIE

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INTRODUCTION

Microsystem technologies are widely used in manufacturing and laboratory research. Today, mainstream microelectronics and microtechnology predominantly use silicon as substrate material. The Inductive Coupled Plasma (ICP) reactor has been thus widely used for anisotropic silicon etching because it is able to obtain a high aspect ratio, while maintaining a vertical side wall [1][2][3][4][5] . Indeed, by Deep Reactive Ion Etching (DRIE) technology, the silicon substrate and III-V compound semiconductors can be etched fairly quickly and manufactured at low cost for mass production 6,7 . This plasma technology is becoming increasingly attractive in a very wide set of applications [8][9][10][11] as well as for microfluidic devices [12][13][14] , microprobes 15 , microlens molds [16][17][18] , roll bearing components 19 and micro-optic structures 20 .

The development of advanced MOEMS and Microfluidic devices demands different shapes with plane, spherical, aspheric and free form surfaces of high profile and excellent surface finish. The design of aspheric surfaces is extremely important in optical systems (eg microlenses) and has been applied in various applications. For instance, in miniaturized systems aspheric surfaces can correct aberrations, improve the image quality and reduce the size and weight of optical systems. Further investigation has been carried out in our laboratory to manufacture microlense molds by wet etching 16 . Isotropic etching of silicon can be obtained by wet chemistry or by plasma etching 21 , however the latter has not gained a) Electronic mail: etienne.herth@c2n.upsaclay.fr much attention compared with wet etching the isotropic in both glass 22,23 and silicon materials. Likewise, silicon wet etching is always used in MEMS during the final stage of the micromachining process, such as the release of the cantilever beam from the substrate [24][START_REF] Herth | Symposium on Design, Test, Integration and Packaging of MEMS/MOEMS (DTIP)[END_REF][START_REF] Herth | Symposium on Design, Test, Integration and Packaging of MEMS/MOEMS (DTIP)[END_REF] . Belen et al. have developed a semiempirical feature scale model of Si etching in SF 6 plasma, as well as the effect ion incidence angle [START_REF] Belen | [END_REF][28][29] . The authors have been numerically investigated the relationship between microscale patterns on a Si wafer, the interfacial structure of the plasma and the feature profile of deep-Si etching under plasma. Although the ICP-DRIE technology has been actively studied and published in several articles explaining the effect of etching parameters on the profile, the deep anisotropic etching was generaly limited above 500 µm etching depth and hilights the need and demand to preserve the straigth sidewall 5,30 . In micro-optical systems, the elimination of optical aberration can be achieved by using aspherical silicon molds characterized by negative conic constant, however not many micro-fabrication technologies allow arbitrary control of generated geometries of microlenses. To address this issue, our strategy is based on cheaper and improved etching methods. The purpose of this paper is to discuss and to give the details of fast etching and ultra deep silicon (>1 mm) trenches and as well as its curvated cavities and their properties. In this respect our motivation is to combine anisotropic and isotropic etch in one DRIE tool. In this article we will present results for various silicon size features as a function of ICP etch processes. This paper is organised as follows: the second section describes the process used to fabricate, characterize and compare various apertures sizes. The third sec-tion describes the ICP process for silicon cavities of millimeter range depths. In the fourth section, we investigate the isotropic effect by exploring how the shape of the silicon aperture evolves during the ICP processes. We conclude with a discussion of these investigations and its application to microfluidic, microlense molds, and microsystems through MOEMS and BIOMEMS applications.

II. FABRICATION AND CHARACTERIZATION METHODS

The experiments were performed in a Surface Process Technology Systems (SPTS) Rapier tool. It was used with up to 3 kW of 13.56 MHz power. The temperature of the wafer is controlled using an electro-static chuck. Gases employed in this study were perfluorocyclobutane (C 4 F 8 ), sulfur hexafluoride (SF 6 ), and oxygen (O 2 ) (in sccm, denoting cubic centimeters per minute). An oxygen cleaning was performed between each experiment to remove polymer from the sidewalls of the reactor, minimizing contamination and preserving repeatability. There are numerous important etchant properties, such as etch rate, masking materials, selectivity, surface roughness. Kovacs and al. [START_REF] Kovacs | Proc. IEEE[END_REF] have provided a generalized comparison of the various etchants in terms of many of these important properties and the availability of suitable masking films. In this work, different etch processes were studied and their general characteristics were compared. Typical parameters for these processes are presented in Fig. 1 and tabulated in Table I. Standard microfabrication steps followed to obtain test samples are described in Fig. 1.

III. RESULTS

A. Anisotropic etch

In deep silicon etching for microelectromechanical system(MEMS) typical etch depths are generally 10-500 µm [START_REF] Galayko | [END_REF] . Using the Bosch process, very high aspect ratio trenches of up to 107:1 were reported for 374 nm widths by Marty et al. 33 . More recently, aspect ratios of 160:1 were reported by Parasuraman et al. for trenches of 250 nm widths 34 . However, for differents MEMS and MOEMS applications, etch depth greater than 500 µm are needed. We have targeted 1.4 mm depths using a mask photoresist (AZ9260) which is suitable and can be deposited with thickness of more than 20 µm. The DRIE conditions are summarized in Table I. In these experiments, the duty cycle was fixed at 10 % (see Fig. 2), its effect is important on the etching process and profile , while varying the other parameters . This pre-test shown in Table I, is focused on the coupling effect of the gas mixture, the source power and the pressure on the etching rate and profile (see Fig. 2b).

As expected, it becomes evident that the etch rates are monotonically decreased with decreasing aperture size as seen in Fig. 2a. This is the so-called "Aspect Ratio Dependent Etching" (ARDE) effect. The results of the etch profiles are carefully analyzed by the isotropic ratio 35 , A F defined as:

A F = 1 - r lat r vert (1)
where r lat is either the horizontal dimension of the foot edge from the mask edge or the undercut rate and r vert is either the vertical etched depth or the etch rate as illustrated in Fig. 3.

Fig. 4 shows a selection of the sidewall profiles that have been obtained in our experiments. These SEMs clearly demonstrate that it is difficult to obtain a straightforward definition of the anisotropy. Indeed, depending on the process parameters, the profiles may vary from ideal isotropy. No significant amount of undercut was observed using the recipe 1a, which results in an anisotropy value of 1 indicating a perfect vertical sidewall with no mask undercut. Previously, good results of ultra-deep silicon cavities with smooth sidewalls, using an Alcatel DRIE reactor tool, have been reported 36 with etch rate around to 5 µm/min. However, based on the recipe 1 results, the relative etch rate with the same design rule, the rate process is higher and close to 11 µm/min with a scalloping of around 250 nm. A consequence of the pulsed DRIE process with this high etch rate is improved cost, efficiency and yield of the microfabrication devices. Mastering deep etching technologies has enabled manufacturing and to miniaturization of the atomic-clock and magnetometer as highlighted in Fig. 4. Nevertheless, to completely etch through a 1.4 mm thick silicon wafer suffers the intrinsic disadvantage of scalloped sidewalls and high sidewall surface roughness. For instance, the process needs to be one tuned for every aperture size during the same step. Recipe 1a consists of alternating isotropic etching under SF 6 plasma and passivation using the C 4 F 8 plasma. When silicon is being etched using this Bosch process, silicon grass, due to the residual passivation layer, is formed at the bottom of the holes as etching by-products. If the passivation layer, after C 4 F 8 deposition, is not completely removed, it makes a micromask. Silicon grasses are thus undesirable by-products in micro-devices. To overcome these drawbacks, optimized recipe processes are presented in more detail in Table II. Besides three recipes presented in Table I, gradual increase of process ecthing time on several etch steps using presented SF 6 /C 4 F 8 as well as other parameter (pressures, power) presented in Table II, proves that this approach has many special advantages e.g., smooth trench sidewall, high etch rate and selectivity. Table II and Fig. 5 present the results for these trenches. No mask undercut was observed using recipe 1a and 1b, the surface scalloping inherent to the bosch process were around to 200 nm. The chamber pressure principally affects the mean free path (MFP) of an ion in the plasma, with lower pressures providing longer paths and thus higher energy ions. Finally, we observed in Fig. 5 that the etch rates were nonlinear. One of the significant issues in this etch is the ARDE (Aspect Ratio Dependent Etch). The silicon etch rate depends on the mask opening size. In particular, the smallest mask opening was etched the slowest.

The etch profile appears straight and with smooth sidewall. With revised recipe 1b, we have successfully etched trenches as narrow as 10 µm for 55 µm depth and as wide as 1100 µm for 117 µm depth. The performance shows for this method a good application potential for the production of microelectronic and MOEMS, and MEMS in particular, to completely etch through a thicker silicon wafer (more than 500 µm). The reported process was employed to fabricate cells for miniature atomic clocks [START_REF] Maurice | Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)[END_REF] .

Moving on towards less vertical (anisotropic)etch processes, the continuous process using a SF 6 /O 2 plasma seems to be the best compromise between straigth sidewall and complete curvated shaped. Nevertheless, SF 6 /O 2 gas chemistry tends to generate bowing in silicon [START_REF] Dixit | [END_REF] . Although the fabrication of the tapered through silicon vias by SF 6 /O 2 and SF 6 /O 2 /Ar plasma has been reported [START_REF] Dixit | [END_REF]39 , the effect of SF 6 /O 2 /C 4 F 8 chemistry on both the slope angle and roughness has not been provided. Recipe 2 resulted in an anistropy close to 0.7 @70 mTorr. In fact, at high O 2 pressures, the value of the anisotropy, as defined before, may be lower because of outward by sloping etch profiles. This gas chemistry provided an overall etching rate about 7µm/min, a roughness lower than 200 nm @70 mTorr and a tapered profile with sidewall angles between 55-70 • .

A similar technology using a continuous process with a pure SF 6 plasma to create a spherical cavity has been reported, but the geometrical parameters of the etched cavities has not been provided in detail. The study of the undercut and the curvature profile, in the case of an anisotropy factor close to 0 (recipe 3) is considered in more depth in the next section.

B. Isotropic etch

Even though wet silicon etch can have an aspect ratio as high as 600, this deep anistropic etch technique by aqueous solutions is inherently limited to the fabrication of structures such as microlenses mold (see Fig. 6) where the isotropic effect is desired. In recent years, much effort has been placed on further improving isotropic wet etching 16,40 and in isotropic dry etching [17][18][19] . Consequently, the spherical cavity size was found to depend mostly on the size of the etch-mask opening, and be independent of the etching time. A variety of mask materials and etching conditions were investigated to obtain a large spherical cavity (2.5 mm in radius) with good circularity and smoothness. Early works focused on microlenses, which were specifically developed for different MOEMS applications 16,20,41 . Previous reports on isotropic dry etching technology have been documented 17,19 showing that the anisotropic plasma can be optimized, when the mask opening and the process parameter are matched, to produce a sphere shape (Fig. 6). Here, we considered different size of circular mask openings ( ranging from 20 µm to 600 µm). The SF 6 flow rate was increased at 500 sccm and pressure from 40 mTorr to 150 mTorr. The isotropic chemical etching of F * radicals caused the lateral etching, which resulted in the sideways undercut. Fig. 7 shows mask undercut and etch depth as a function of mask opening diameter. The results show that for all the test structures analyzed, the etch rate increased quite significantly with increasing pressure. The undercut and the etch depth are found to increase with mask opening, but tends to saturate between 350 µm to 600 µm diameters, which indicates that the silicon etch rate is principally limited by the availability of fluorine radicals at the silicon substrate.

At high pressure, the non-uniformity of etch depth was observed. This could be attributed in large part to the limitations of the pumping system of the ICP reactor, which plays an increasingly important role in the uniformity of species diffusion inside the reactor. Fig. 8 shows that for different mask openings, the degree of anisotropic etching given in equation 1 is between 0.2 to 0.4 whatever the pressure. Increasing the pressure should increase the atomic fluorine concentration and decrease the ion bombardment. Both effects lead to a reduction of the anisotropy, in agreement with our results at high pressures (100 mTorr and 150 mTorr). However, at 500 sccm SF 6 flow rate, the etch rate and undercut rate were saturated because of (a)the recombination of radicals before reaching the sample surface and /or (b) insufficient source power (2000 W) to promote the dissociation of SF 6 and produce fluorine radicals.

These results show that the physical etching rate in the vertical direction increased faster than in horizontal direction when the pressure was higher than 40 mTorr. SEM of cleaved samples was utilized to confirm the degree and the profile of this anisotropic measurements.

Fig. 9 shows SEM micrographs of the etched surface taken with a 45 • tilt for wafers etched at 40 mTorr, 100 mTorr and 150 mTorr pressure. These results show that surface roughness decreases significantly at lower pressure. Clearly, as presented in Fig. 10, the curvature of the cavity is variable and depends on the mask opening and the fabrication process. For larger opening masks, the profiles show a very flat center region. As a consequence, the degree of anisotropic etching is a good indicator and must be completed by SEM view or by interferometry measurement.

Nevertheless, spherical profile measurements are more difficult than flat surfaces. The more complex geometries are often described as conic sections that can be expressed by the following equation :

Z (r) = cr 2 1 + 1 -(k + 1) c 2 r 2 + N ∑ i=n 0 α i r i ( 2
)
where r is the radial coordinate, c is vertex curvature, α i are the polynomials coefficients. This formulation is used in geometric optics to specify oblate elliptical k > 0, spherical k = 0, prolate elliptical 0 < k < -1, parabolic k = -1, and hyperbolic k < -1. When the paraxial approximation is valid, the optical surface can be treated as a spherical surface with the same radius.

The normalized conic constant k and the radius of curvature (ROC) of the profiles 42 were analyzed by fitting a sphere to the bottom part of the silicon cavities.

As expected, the mask opening data (see Fig. 11 and Fig. 12) and the conic constant k suggest that a mask opening of 10 µm to 210 µm allows a semi-circular cross-section and was therefore selected as the opening for future isotropic etching experiments for microlense molds. For larger openings masks, the ROC is higher due to the flat profile. The surface roughness increased with change in chamber pressure and was affected significantly for the largest opening masks. Furthermore, in the literature, the roughness, the size aperture and the cavity depth are spread over a wide range according to the mask opening, the process parameters and the etching time. One example of these results is summarized in Table III.

Compared with the microlenses molds 17 and microballbearing mold 19 as is shown in Table III, the smallest opening masks showed much low roughness. The RMS is higher than the respective values reported in 19 due to the higher pressure and larger mask openings used in this work. Larsen et al. 17 highlighted the role of platen temperature ranging from 0 • C to 40 • C, in making the radius of curvature of the profile, also showing the effect of the coil and platen power and pressure, however the mask opening was < 65 µm. The general trends observed can be summarized as: increased plate power reduces the roughness. Low coil power improves sphericity, but reduces the cavity depth and uniformity. Hanrahan et al. 19 reported a methodology to obtain the circular bearing crosssections by SF 6 plasma-based etching; Herein, the strategy was based on a two step isotropic etch. The bulk of the material is removed in the first etch and the depth and curvature are almost fully realized. The second etching step is used to remove the reentrant silicon from beneath the masking material, ultimately widening the raceway and slightly affecting the curvature with lower roughness. However they did not elaborate on the effect of any process parameters on the geometrical characteristics of the spherical profile (k).

Compared with other common isotropic etching using ICP, our data suggests that an opening up to 200 µm would be able to give a semi-circular mold. As the cavity gets smaller, ROC decreases rapidly until a minimum is reached. The profile obtained by SEM imaging (Fig. 9b), with a diameter of 100 µm reveals that the structure can be described by conic section k = 0.18, and ROC = 55.5 µm at 100 mTorr. With such negative conic constants are highly desirable for the fabrication, for instances, of micro-optical scanners 20 .

IV. DISCUSSION

During this DRIE study , we have investigated both anisotropic and isotropic etching processes: anisotropic etching to achieve depth, and isotropic etching in order to obtain the desired spherical shape. There are many parameters in the processing: pressure, coil power/ platen power, etch/passivation time ratio, flow rate of etch/passivation gas, temperature. The effect of process parameters is already well known.

The reason behind choosing chuck temperature as 0 • C was for improving the mask selectivity of the UV photoresist. When the temperature increases, the rate of C x F y species desorption increases, leading an overall decrease in polymer deposition rate during the passivation cycle and reducing the risk of the silicon-grass formation. Thus, at 0 • C, the pressure was lower (30 up to 40 mTorr) to reduce the rate depositon of the passivation layer, with the adapted times of the deposition cycle (to preserve a good sidewall and slope angle) and the ion bombardement cycle (to remove all passivation on the silicon surface). Low process pressure (Recipe 1a, SF 6 @ 30 mTorr) is beneficial for high-aspect ratio etching as presented in Fig. 2.a, as exchange of species in narrow deep trenches is accelerated by the higher mean-free path of the gas molecules and radicals. Recipe 1b is a trade-off with higher etch rate (15 µm/min) requirements, where the etch rate increases with higher pressure levels (SF 6 @ 70 mTorr). For a deeper etching (up to 1.4 mm), both proposed anisotropic processes (slope angle close to 90 • ) are suitable in order to prevent undesirable etching side effects, such as undercut or bowing and Si grasses. However, Equation 1does not give information whether the anisotropy is due to mask undercut, to the Bosch process above-mentioned parameters or the sloped profiles. The SF 6 /O 2 chemistry (recipe 2, Table I) has an ioninhibitor process where SF 6 breaks into SF + 5 , e -and F * radicals. The oxygen reacts with silicon and SF + 5 and forms protecting Si x O y and Si x O y F z layers on the via sidewalls. While, the F * radicals etch the silicon by isotropic chemical etching, resulting in tapered slope (see Fig. 4). The sideways undercut increases with the SF 6 flow rate (@ 500sccm). With a careful optimized ratio of SF 6 /O 2 , vias with a continuous tapering profile are formed. The addition of C 4 F 8 (100sccm) is very effective inducing also a sidewall protection, increase the selectivity when using photoresist masks, and promotes a smooth surface morphology (@ 40 mTorr).

The recipe 2 is a promise to manufacture tapered vias (with a slope angle of 55-70 • ) for 3D interconnections and/or MEMS packaging 43 as seen in Table I and Fig. 4, using a continuous SF 6 /C 4 F 8 /0 2 plasma chemistry (@ 70 mTorr) with a selectivity of 82:1. For microfluidic applications vias with tapered sidewall can be used as diffuser or nozzle. Moreover, the ICP isotropic etching technology provides an excellent alternative to release microcantilever beams and other suspended design from silicon substrate with low cost and one tool. But, in pure SF 6 plasma chemistry (up to 150 mTorr), the manufacturing of microchannels with spherical cavity has obvious advantages such as simple geometry for calculation of the flow rate and the volume of aquaeuous solution injected 44 . However, spherical profile measurements are more difficult than flat surfaces.

Herein, we show that the proposed investigation, in conjunction with other characterizations tools, is therefore able to predict the curvature according to the mask aperture designed and paramater process. This in turn allows using the semi-analytical solution as a very fast solver in analyzes of results. Thus, this approach plays an essential role for the particular design for replication of microfluidic systems. Further research will be forthcoming for the manufacturing of microlenses where the lower roughness and spherical curvature are essential for optimal functioning.

For the past few years, many efforts have been made to study the structures in the Bosch. We demonstrate here :

• Various demands on mask selectivity, etch rate and profile can be met in the fabrication of the silicon based on this starting point recipes.

• Fast and ultra deep etching realised at reasonably high etch rates.

• A baseline for controlling the profile of anisotropic silicon manufacturing and / or isotropic processes open a wide area of applications with one tool.

Silicon dioxide, metal masks, or even photoresist (eg AZnLOF 2020, SPR220, AZ9260) are commonly used. We propose to use a photoresist mask that is low cost approach and uses equipment, widespread in the microelectronics laboratories and industry. Nevertheless, the microfabrication route is time consuming. Alternative methods have been commercialized using a dry laminated film photoresists, which are cheaper than spin-on liquid photoresists. Latter can be easly using in our proposed dry etching process.

In this work, the performed experiments were based on the anisotropic plasma toward isotropic plasma etching in order to investigate the fast ultra-deep silicon cavities of the plasma process using an ICP-DRIE but also to determine the range of structures that could be also fabricated toward isotropical plasma. Through the isotropic plasma, we demonstrated a clear potential of this technique for the generation of more complex shapes than the ones that can be produced by wetetching based techniques. In particular, we presented the possibility of creating aspherical shapes with desirable negative conic constant and high aspect ratio (and consequently high Numerical aperture NA of corresponding optical elements).

V. CONCLUSIONS

A commercially available modern plasma etch system in high frequency (13.5 MHz) has been investigated for best performance, with respect to the design goal. It demonstrated stable and good reliability of isotropic etching by ICP-DRIE for MEMS and MOEMS applications. A cycling and a continuous plasma etching process using respectively SF 6 /C 4 F 8 , SF 6 /C 4 F 8 /O 2 and pure SF 6 gases for manufacturing vertical trenches, tapered vias, and spherical shapes, were analyzed. A trade-off between profile and feature size can usually be found quite easily. The anisotropic silicon etch rates in ICP-DRIE reactor can reach 15 µm/min. Empirical models, which fit very well with the experimental data, were proposed. These can serve for design rules in microelectronics, optoelectronics laboratories and industry. This study opens large scale applications which require high etch rate and stable process, controllable profile, surface properties and low costs. We investigated the possibility to generate larger spherical shapes or structures characterized by negative conic constants that are difficult to make by use of wet etching techniques. A combination of different plasma parameters have been studied and the related ICP recipes can prove useful for optoelectronic, microelectronic and microsystem applications.

FIG. 1 .FIG. 2 .FIG. 3 .FIG. 4 .FIG. 5 .FIG. 6 .FIG. 7 .FIG. 8 .

 12345678 FIG. 1. Flow chart of the fabrication process for the silicon microlens mold : silicon wafer, b) spin coating photoresist, c) photolithography and d) dry ecthing.

FIG. 9 .FIG. 10 .FIG. 11 .FIG. 12 .

 9101112 FIG. 9. Cross sectional SEM micrograph of bulk-etched cavities in a 100 Si substrate for different chamber pressure. The parameters of the etching process were : Temperature = 0 • C, coil power = 2000 W, platen power = 20 W, SF 6 = 500 sccm standard cubic centimeters per minute (sccm) at pressure : a) 40 mtorr, b) 100 mtorr and c) 150 mtorr as indicated.

TABLE I .

 I Different etch processes.

	Parameters		Recipe 1a Recipe 2 Recipe 3
	Pressure	(mTorr)	30	40	40
	Coil Power	(Watts)	2500	2200	2000
	Platen Power	(Watts)	20	20	20
	Flow rate SF 6	(sccm)	400	500	500
	Flow rate O 2	(sccm)	-	80	-
	Flow rate C 4 F 8	(sccm)	300	100	-
	Chuck temperature (C)	0	0	0
	Mask Opening	(µm)	300	480	95
	Undercut	(µm)	1	100	52.4
	Etch rate	(µm/min)	11	7	8
	Selectivity Si:Resist (µm)	158:1	82:1	37:1
	Anisotropy		1	0.7	-
	Etch Profile		Vertical Directional Isotropic
	TABLE II. Optimized Bosch process parameters for etching silicon by ICP-DRIE.
	Recipe	Parameters		Passivation Ion Bombardement Etch
		Process Time (s)	1.2-1.5	1.3-1.5	2.5
		Pressure (mTorr)	40	30	30
	Recipe 1a	Coil Power (Watts) Platen Power (Watts)	2500 20	2500 50	2500 20
		Flow rate SF 6 (sccm)	-	400	400
		Flow rate C 4 F 8 (sccm)	330	-	-
		Process Time (s)	1.5-1.8	1.5-2	3
		Pressure (mTorr)	30	50	70
	Recipe 1b	Coil Power (Watts) Platen Power (Watts)	2500 20	2500 150	2500 25
		Flow rate SF 6 (sccm)	-	450	450
		Flow rate C 4 F 8 (sccm)	300	-	-

TABLE III .

 III Discussion and comparison between our work and previous research to manufacture the mold silicon by using a ICP-DRIE reactor.

	Reference		Our work	[ 17 ]	[ 19 ]
	Photoresist mask		AZ9260	NC	AZ9260
	Mask Opening	(µm)	20-600	7-62	100-200
	Chamber pressure (mTorr) 40-150	10-70	17-27
	Coil Power	(Watts)	2000 1000-3000	850
	Platen Power	(Watts)	20	0-16	6-16
	Flow rate SF 6	(sccm)	500	200-300	100
	Flow rate Ar	(sccm)	-	-	40
	Flow rate O 2	(sccm)	-	0-30	-
	Chuck temperature (C)	0	0-40	30
	Etch time	(s)	900	300-750 120-300
	Cavity depth	(µm)	27-290 28.6-100 75-260
	ROC	(µm)	0.12-4 0.41-1.15 0.02-0.14

ACKNOWLEDGMENTS

This work was partly supported by the French RENATECH network with FEMTO-ST and C2N technological facilities.