Pierre Florian

Alexey Novikov

James W E Drewitt

Louis Hennet

Vincent Sarou- Kanian

Dominique Massiot

Henry E Fischer

Daniel R Neuville

Structure and Dynamics of High-Temperature Strontium Aluminosilicate Melts

Keywords: High temperature, Melt, NMR, Neutron diffraction

We report the study of high-temperature melts (1600°C-2300°C) and related glasses in the SrO-Al2O3-SiO2 phase diagram considering three series: (i) depolymerized ([SrO]/[Al2O3] = 3); (ii) fully polymerized ([SrO]/[Al2O3] = 1); and (iii) per-aluminous ([SrO]/[Al2O3] < 1). By considering results from high-temperature 27 Al NMR and high temperature neutron diffraction, we demonstrate that the structure of the polymerized melts is controlled by a close-to-random distribution of Al and Si in the tetrahedral sites, while the depolymerized melts show smaller rings with a possible loss of Non-Bridging Oxygens on AlO4 units during cooling for high-silica compositions. Few five-fold coordinated V Al sites are present in all compositions except peraluminous ones where high amounts of high-coordinated aluminium are found in the glasses and melts with complex temperature dependence. In the high-temperature melts, Strontium has a coordination number of 8 or lower, i.e. lower than in the corresponding glasses.

The dynamics of the high-temperature melt were studied from 27 Al NMR relaxation and compared to macroscopic shear viscosity data. These methods provide correlation times in close agreement. At very high temperatures, the NMR correlation times can be related to oxygen selfdiffusion coefficient and we show a decrease of the latter with increasing Si/(Al+Si) ratio for polymerized melts with no compositional dependence for depolymerized ones. The dominant parameter controlling the temperature dependence of the aluminum environment of all melts is the distribution of Al-(OSi)p(OAl)(4-p) units.

Introduction

Aluminosilicates glass compositions are of widespread use in material science where they have found numerous industrial applications as e.g. cover glass for high-end display devices, holographic optical elements, high strength material with moderate expansion for radomes and zero expansion glass-ceramics. They are also central to Earth Sciences as melt models of magmas.

Our understanding of the atomic-scale structure of these materials in their glassy form has advanced substantially over the last decades owing to improvements in experimental methods [START_REF] Greaves | Inorganic glasses, glass-forming liquids and amorphizing solids[END_REF], and the interaction between alkaline, alkaline-earth or rare-earth cations and the aluminosilicate network is now grounded on solid rules [START_REF] Stebbins | Interactions between network cation coordination and non-bridging oxygen abundance in oxide glasses and melts: Insights from NMR spectroscopy[END_REF]. Those materials possess basic TO4 building blocks with T = Si or Al held together by covalent bonds when sharing corner(s) or electrostatic forces between Non-Bridging Oxygens (NBO) and counter cation(s) such as alkali or alkaline-earth elements. To understand and relate atomic arrangements to physical properties, some peculiar species have been outlined such as five-coordinated aluminum V Al [START_REF] Mcmillan | Al Coordination in Magneisum Aluminosilicate Glasses[END_REF][START_REF] Neuville | Al coordination and speciation in calcium aluminosilicate glasses: Effects of composition determined by Al-27 MQ-MAS NMR and Raman spectroscopy[END_REF]Neuville et al., 2008b), non-stoichiometric NBO [START_REF] Stebbins | NMR evidence for excess non-bridging oxygen in an aluminosilicate glass[END_REF], NBO on aluminum species [START_REF] Jaworski | Direct 17O NMR experimental evidence for Al-NBO bonds in Si-rich and highly polymerized aluminosilicate glasses[END_REF] or the putative tricluster oxygen which connects three tetrahedral species [START_REF] Lacy | Aluminum in Glasses and Melts[END_REF][START_REF] Toplis | Peraluminous viscosity maxima in Na2O-Al2O3-SiO2 liquids: The role of triclusters in tectosilicate melts[END_REF] all of those building blocks possibly organizing themselves at a larger scale into percolation channels (Le [START_REF] Losq | Percolation channels: a universal idea to describe the atomic structure and dynamics of glasses and melts[END_REF]. This picture, developed to describe glasses is used to provide a "snapshot" view of melt structure at high temperature [START_REF] Stebbins | Glass structure, melt structure, and dynamics: Some concepts for petrology[END_REF]. Nevertheless industrial high-temperature melt phase processes, like petrologic and geodynamic processes, cannot be understood without addressing their dynamics. Aluminosilicate melt's diffusivity, viscosity, electrical and thermal conductivity have receive much experimental and computational attention [START_REF] Ni | Transport properties of silicate melts[END_REF], yet only a few in-situ spectroscopic characterizations have been performed due to challengingly high melting temperatures [START_REF] Neuville | In situ High-Temperature Experiments[END_REF]. For pure aluminosilicate melt compositions, available X-ray scattering [START_REF] Krishnan | Structure of liquid Al6Si2O13 (3 : 2 mullite)[END_REF] and Nuclear Magnetic Resonance (NMR) [START_REF] Poe | SiO2-Al2O3 Liquids: In-Situ Study and High-Temperature Al-27 NMR-Spectroscopy and Molecular-Dynamics Simulation[END_REF] results reveal a short-range structure of the high-temperature liquid similar to that of the corresponding glasses, containing a significant proportion of V Al species and a viscosity microscopic mechanism driven by the atomic-scale fluctuations around aluminum at high alumina contents.

In the case of alkali aluminosilicates, sodium-based compositions are the most extensively studied in-situ at high temperature. Inelastic neutron scattering [START_REF] Kargl | Inelastic neutron scattering on sodium aluminosilicate melts: sodium diffusion and intermediate range order[END_REF]) and 23 Na NMR spectroscopy [START_REF] George | Dynamics of Na in sodium aluminosilicate glasses and liquids[END_REF][START_REF] Losq | The role of Al3+ on rheology and structural changes in sodium silicate and aluminosilicate glasses and melts[END_REF][START_REF] Liu | Relaxation Mechanisms and Effects of Motion in Albite (NaAlSi3O8) Liquid and Glass -A High-Temperature NMR-Study[END_REF][START_REF] Maekawa | Coordination of sodium ions in NaAlO2-SiO2 melts: A high temperature Na-23 NMR study[END_REF][START_REF] Stebbins | A High-Temperature High-Resolution NMR-Study of Na-23, Al-27 and Si-29 in Molten Silicates[END_REF] showed rapid sodium mobility above 300°C, mostly responsible for the relaxation and the conductivity. When Al/Na > 1 sodium charge-compensating A1O4 -units become dominant and the barrier against individual hops increases leading to a decrease in sodium mobility. The aluminosilicate network has been found by Raman spectroscopy [START_REF] Neuville | Role of aluminium in the silicate network: In situ, hightemperature study of glasses and melts on the join SiO2-NaAlO2[END_REF] to be formed by an Al/Si distribution on the corner-shared TO4 sites forming a fully polymerized three-dimensional network. In this case Si observed by 29 Si NMR [START_REF] Liu | Relaxation Mechanisms and Effects of Motion in Albite (NaAlSi3O8) Liquid and Glass -A High-Temperature NMR-Study[END_REF] as been seen to be rather immobile below the glass transition temperature. High-field 27 Al NMR data show also a clear increase of the V Al concentration (denoted hereafter as [ V Al]) with increasing temperature in the per-aluminous melts, whereas it is much more stable in the peralkaline ones [START_REF] Losq | The role of Al3+ on rheology and structural changes in sodium silicate and aluminosilicate glasses and melts[END_REF].

In the case of alkaline-earth aluminosilicates the investigations concentrated mostly on calciumbased compositions (CAS). X-ray absorption spectroscopy (Neuville et al., 2008a) demonstrated an increase of [ V Al] with temperature in the fully polymerized composition (anorthite), later confirmed by neutron diffraction (Jakse et al., 2012) which showed the presence of significant amounts of AlO5 units, oxygen triclusters and NBO, even in fully charge-compensated composition. 27 Al NMR [START_REF] Gruener | Bulk and local dynamics in glass-forming liquids: A viscosity, electrical conductivity, and NMR study of aluminosilicate melts[END_REF][START_REF] Kanehashi | In situ high temperature Al-27 NMR study of structure and dynamics in a calcium aluminosilicate glass and melt[END_REF] has given some insight on the dynamics taking place in calcium aluminosilicates, showing that NMR, viscosity and conductivity relaxation times coincide in the high-temperature regime whereas a decoupling occurs near the glass transition temperature due to the Ca motion. A similar result was obtained on magnesium aluminosilicate compositions [START_REF] George | Structure and dynamics of magnesium in silicate melts: A high-temperature Mg-25 NMR study[END_REF] with the diffusion of Mg shown to be strongly coupled to the network motion at temperatures above the glass transition temperature Tg. Higher concentrations of NBOs and of AlO5 species with increasing temperature were inferred by comparing quench-rate dependent and in-situ 27 Al NMR studies [START_REF] Stebbins | Temperature effects on nonbridging oxygen and aluminum coordination number in calcium aluminosilicate glasses and melts[END_REF]. Molecular Dynamic Simulations [START_REF] Benoit | Structural properties of molten silicates from ab initio molecular-dynamics simulations: Comparison between CaO-Al2O3-SiO2 and SiO2[END_REF] have also observed the excess of NBOs in the melt, along with the violation of the aluminum avoidance principle and the presence of "defects" such as five-fold coordinated silicon. Moreover, MD simulation using the isoconfigurational ensemble method suggested the presence in the melts of dynamical heterogeneities related to concentration fluctuations between Si-rich and (Ca,Al)-rich regions [START_REF] Vargheese | Origin of dynamical heterogeneities in calcium aluminosilicate liquids[END_REF].

All of the puzzle's pieces (NBO, high-coordinated Al, tri-bonded oxygens, cation mobility…) seem to be more or less accepted but the way they interact, or not, with each other is still an open question. Of particular importance is the dynamics of the aluminosilicate network in the melt at superliquidus and supercooled temperatures,and much remains to be done experimentally in this field. We hence used high-temperature 27 Al NMR and neutron diffraction techniques to explore alkaline-earth aluminosilicate compositions with various degrees of polymerization. Following our previous investigation [START_REF] Novikov | Al and Sr environment in tectosilicate glasses and melts: Viscosity, Raman and NMR investigation[END_REF] we chose strontium aluminosilicate compositions for which we already assessed structure and macroscopic properties of the glasses. Three different compositional regions were explored: along the "tectosilicate" or "charge balanced" join R =

[SrO]/[Al2O3] = 1, in the per-alkaline field with compositions on the join R = 3, and in the peraluminous R < 1 domain. If compositions along the join R = 1 are expected to be fully polymerized with only a small amount of V Al (we found [ V Al] < 4% in the glasses) and NBOs, compositions along the join R = 3 do contain a significant proportion of NBOs for charge balance reasons.

Besides, an important population of AlO5 and even AlO6 is expected in the R < 1 field. Such marked changes are bound to impact the melt' structure and dynamics and, to the best of our knowledge, have not yet been explored in such a systematic way in-situ.

Experimental

Figure 1: ternary diagram showing all investigated compositions. Per-alkaline compositions are represented as red squares, compensated ones as blue triangles and per-aluminous ones as green circles.

All samples were taken from the batches studied previously [START_REF] Charpentier | Structure of strontium aluminosilicate glasses from molecular dynamics simulations, neutron diffraction and nuclear magnetic resonance studies[END_REF][START_REF] Novikov | Al and Sr environment in tectosilicate glasses and melts: Viscosity, Raman and NMR investigation[END_REF]. Droplets of glasses suitable for the NMR levitation experiments were obtained using an "external" levitation device. Sample compositions (figure 1) are named according to their SiO2 and Al2O3 molar composition: SASiO2%.Al2O3%, the molar fraction of SrO being (100-SiO2%-Al2O3%). The sample (a sphere of 2.6 mm ± 0.5 mm diameter) is in aerodynamically levitated on a gas stream (air) and heated and heated at top and bottom by two CO2 lasers as previously described [START_REF] Florian | A time-resolved Al-27 NMRstudy of the cooling process of liquid alumina from 2450°C to crystallization[END_REF]. The sample is heated and stabilized (a few seconds) above its melting point and the 27 Al NMR signal is recorded every 10 ms during the free cooling of the sample when the laser is turned off. The temperature of the sample during the experiments was monitored with an IMPAC IN 140/5-H pyrometer (λ = 5.14 μm) allowing measurements from 500 to 2500 °C.

However, the area monitored by the pyrometer was greater than the sample' size. A temperature calibration was made against the observed recalescence of compounds with known crystallization temperature (Al2O3, SrSiO3, CaMgSi2O6, Li2SiO3). Spheres of different diameters were used for each compound and several crystallization events were registered and averaged for each sphere.

Therefore, all presented temperatures are reliable within ± 50 °C. Typical spectra obtained this way are shown in Figure 2.

The relaxation time of 27 880 µs ± 30 µs, T2 ~ 800 µs ± 30 µs, 1/1/2 ~ 740 µs ± 20 µs, with T1 the spin-lattice relaxation time, T2 spin-spin relaxation time, and 1/2 the full width at half maximum. These relaxation times are short enough to allow repetition of acquisition down to 10 ms (>5 times T1) and thus to obtain a time resolved signature of the melt during its cooling. This also minimizes the experimental time, reducing possible vaporization that has been checked to be negligible by measuring weight loss after the high-temperature experiment. The drawback of this procedure is that it does not allow signal averaging, limiting the sensitivity of the experiment and the increasingly broadened signal is progressively lost with increasing linewidth upon cooling. This is particularly true for the compositions containing the lowest amount of Al2O3.

The evolution of the NMR parameters with temperature and compositions have been fitted to adequate functions (detailed below) using the "NonLinearModelFit" build-in function of Mathematica 10.1 [START_REF] Research | Mathematica[END_REF] including statistical analysis.

High-temperature neutron diffraction (ND) measurements have been carried out on 5 samples [START_REF] Hennet | Structural study of strontium aluminosilicate glasses and melts[END_REF] using the aerodynamic levitation and laser heating system installed on the D4C diffractometer [START_REF] Fischer | D4c: A very high precision diffractometer for disordered materials[END_REF] at the Institut Laue-Langevin in Grenoble (France), as described in [START_REF] Hennet | Levitation apparatus for neutron diffraction investigations on high temperature liquids[END_REF]. Diffraction measurements were taken for the molten samples at temperatures above the melting point for all studied compositions, for the empty levitation device inside the diffraction chamber, and for vanadium samples for making an absolute normalization of the scattered intensity. The neutron wavelength used during the experiment was 0.4985 Å, giving a scattering vector Q-range of about 0.3-23.6 Å -1 . The data processing was performed using the program CORRECT [START_REF] Howe | Interplay between non-bridging oxygen, triclusters, and fivefold Al coordination in low silica content calcium aluminosilicate melts[END_REF], which corrects the data for attenuation, background, multiple scattering and inelasticity effects. The derived structure factors for all the measured samples are presented in figure 3.

Results

NMR

The evolutions of the 27 Al chemical shift (line's position) as a function of temperature are given in figure 4, for the full temperature range of this study. For both R = 1 and R = 3, the 27 Al chemical shift increases with decreasing silica molar ratio . In the per-aluminous region, substituting SrO by Al2O3 at fixed SiO2 content decreases significantly the 27 Al chemical shift (figure 4c). As seen in figure 4 there is a linear evolution of the chemical shift with respect to temperature in this very superliquidus regime (T > 2xTg), in agreement with our previous observations on alkaline-earth aluminate [START_REF] Capron | Local structure and dynamics of high temperature SrO-Al2O3 liquids studied by Al-27 NMR and SrK-edge XAS spectroscopy[END_REF] and rare-earth aluminosilicate [START_REF] Florian | Al-27 NMR study of the structure of lanthanum-and yttrium-based aluminosilicate glasses and melts[END_REF] compositions.

Significant scattering is observed when the signal broadens at low temperature or at low Al2O3 content due to diminishing signal to noise ratio as described above. For each cooling experiment the evolution of the 27 Al chemical shift versus temperature has been fitted with a linear function,

where the slopes and intercepts are given in table 1.

R < 1

Reports of the evolution of 27 Al chemical shifts with temperature in the high-temperature melts are scarce. The 27 Al peak maximum has been observed to decrease with increasing temperature (from 65.1 ppm at 1300 °C to 63.3 ppm ± 1 ppm at 1400 °C) for a per-calcic aluminosilicate melt [START_REF] Kanehashi | In situ high temperature Al-27 NMR study of structure and dynamics in a calcium aluminosilicate glass and melt[END_REF]. Our previous study of sodium aluminosilicate glasses [START_REF] Losq | The role of Al3+ on rheology and structural changes in sodium silicate and aluminosilicate glasses and melts[END_REF] have also shown a decrease of iso with increasing temperature (d/dT = -3.0 ppm/1000 °C) up to Tm where it drops, followed by a slower decrease thereafter with d/dT ~ -1.6 ppm/1000 °C, consistent with our current measurement found in the range -3.6 to 1.5 ppm/1000 °C. This slope range fits also within the one observed for lanthanum and yttrium melts using a levitationtype experiment [START_REF] Florian | Al-27 NMR study of the structure of lanthanum-and yttrium-based aluminosilicate glasses and melts[END_REF]. As discussed above the linewidth 1/2 of the 27 Al spectra (ranging from 0.4 to more than 2.5 kHz) is a measure of the spin-spin or spin-lattice relaxation time and thus of the dynamics of the molten sample at the atomic level and depends upon composition and temperature (figure S1).

For R = 1 and R < 1 we observe an increasing linewidth with increasing SiO2 content, in contrast with the R = 3 join where all 1/2 vs T curves are superimposed with the noise. Always well-defined at high temperatures, the precision of this measurement diminishes at low temperature and/or low alumina content.

In all cases, 1/2 can be related to the aluminum correlation times of movement through the following set of hypotheses. We first checked on a couple of samples not prawned to vaporization that the 27 Al NMR spin-lattice relaxation time T1 is obtained from the line width (see experimental section) according to:

𝑇 1 = 1 𝜋Δ𝜈 1/2 (1)
which means that we have reached the fully averaged motional regime. The evolution of 1/2 as a function of temperature is hence an evolution of NMR relaxation times, known to be caused by the time-fluctuation of the NMR interactions. Under the assumption that the dominant interaction in our case is the quadrupolar interaction, T1 can in turn be expressed as a function of the correlation time of the fluctuation of the quadrupolar interaction c and the time-averaged dynamic quadrupolar product 𝐶 ̃𝑄𝜂 = 𝐶 ̃𝑄√1 + 𝜂 ̃𝑄 2 3 ⁄ of the aluminum sites [START_REF] Abragam | The Principles of Nuclear Magnetism[END_REF][START_REF] Petit | Fictitious Spin-1/2 Operators and Multitransition Nuclear-Relaxation in Solids -General Theory[END_REF] :

1 𝑇 1 = 3 10 𝜋 2 2𝐼+3 𝐼 2 (2𝐼-1) 𝐶 ̃𝑄𝜂 2 𝜏 𝑐 ( 2
)
where This compositional dependence of the correlation time is evidenced by a plot of c at 2000 °C as a function of the Al/(Al+Si) ratio (figure 6). For this plot we used experimental temperature closest to 2000 °C and derived their predicted c value using an exponential fit of the c = f(1/T) evolution along with the related confidence interval for this selected point. The presence of NBOs (along the R = 3 join) seems to render c,2000°C independent on both Si/(Al+Si) and NBO/T ratios, which are in the range 0.50-0.80 and 0.99-2.44 respectively. In the absence of NBOs, the 27 Al NMR correlation time increases linearly with increasing Si/(Al+Si). c,2000°C is slightly lower in peraluminous compositions than at R = 1 but this is almost within the error bars of our measurement.

I

Neutron Diffraction

Due to the susceptibility of SiO2 to volatilise during the long counting times required for hightemperature neutron diffraction measurements, we studied only compositions containing up to 42 %mol and 33 %mol of silica along the joins R = 1 and 3 respectively.

The total structure factors S(Q) of all studied samples are presented in figure 2. As reported in table 2 for the compositions along both the composition lines R = 1 and 3, increasing the SiO2 content leads to a shift in the position Q1 of the first peak (FSDP) in S(Q) towards lower Q values with a corresponding increase in peak height. This indicates that the degree of intermediate-range order is improved by incorporating silica into the structure. As observed with calcium aluminosilicate compositions, this shift, which is expected with the increase of the silica concentration, could be also a signature of the increase of the ring size [START_REF] Hennet | Neutron diffraction of calcium aluminosilicate glasses and melts[END_REF]. As seen in table 2, for the same silica content the Q1 values are higher for R = 3 than for R = 1. Hence, this seems to show that the ring size becomes smaller when the SrO content is increased, consistent with a higher fraction of NBO.

The total pair distribution function is calculated from the structure factor by the Fourier transform:

𝑔(𝑟) -1 = 1 2𝜋 2 𝑟𝜌 0 ∫ [𝑆(𝑄) -1] ∞ 0 𝑄 𝑠𝑖𝑛(𝑄𝑟)𝑑𝑄 (3)
where ρ0 denotes the atomic number density, estimated as ~95% of the glass densities reported in our previous works [START_REF] Charpentier | Structure of strontium aluminosilicate glasses from molecular dynamics simulations, neutron diffraction and nuclear magnetic resonance studies[END_REF]. As there is no experimental data available at this time, this estimation is based on our work on CAS glasses and liquids [START_REF] Hennet | Neutron diffraction of calcium aluminosilicate glasses and melts[END_REF] Coordination numbers and bond distances were determined by making Gaussian fit to the correlation function 𝑇(𝑟) = 4𝜋𝑟𝜌 0 𝑔(𝑟) as described by [START_REF] Hennet | Neutron diffraction of calcium aluminosilicate glasses and melts[END_REF] samples, the average Al coordination number is found to be close to 4. Despite the relatively large error value of ± 0.5, a fraction of 5-6% AlO5 units is estimated in the liquid state for all compositions, in agreement with AlO5 fractions found in the related glasses [START_REF] Novikov | Al and Sr environment in tectosilicate glasses and melts: Viscosity, Raman and NMR investigation[END_REF]. has been estimated between 8.5 and 9.0 [START_REF] Charpentier | Structure of strontium aluminosilicate glasses from molecular dynamics simulations, neutron diffraction and nuclear magnetic resonance studies[END_REF][START_REF] Novikov | Al and Sr environment in tectosilicate glasses and melts: Viscosity, Raman and NMR investigation[END_REF], in the liquid state the coordination number is expected to be around 8 for the join R = 3 and somewhat means the average between iso( IV Al) and iso( V Al) weighted by the IV Al and V Al populations respectively, as derived from the simulations of the MAS spectra of the glasses [START_REF] Charpentier | Structure of strontium aluminosilicate glasses from molecular dynamics simulations, neutron diffraction and nuclear magnetic resonance studies[END_REF][START_REF] Novikov | Al and Sr environment in tectosilicate glasses and melts: Viscosity, Raman and NMR investigation[END_REF]. For the R = 1 compositions we observe a linear evolution of the 27 Al chemical shift at 2000 °C (2000°C) versus Si/(Si+Al), with a slope of -27.4 ± 0.8 ppm/mol%. This is comparable to the value of -30.6 ± 1.2 ppm/ mol% observed for the evolution of <iso>glass and -28.0 ppm/ mol% [START_REF] Charpentier | Structure of strontium aluminosilicate glasses from molecular dynamics simulations, neutron diffraction and nuclear magnetic resonance studies[END_REF] for iso( IV Al)glass. The evolution in the melt can therefore be ascribed, like in the glass [START_REF] Charpentier | Structure of strontium aluminosilicate glasses from molecular dynamics simulations, neutron diffraction and nuclear magnetic resonance studies[END_REF], to the progressive substitution of Al by Si in the second aluminum coordination sphere upon increasing Si/(Si+Al), favoring the Al-O-Si linkages. It leads to an average of -7.1 ppm/substitution for the melt and -7.8 ppm for the glass. Our Neutron diffraction results confirm that the amount of V Al is only a few percent, like in the glass, and will hence not significantly influence the melt's aluminum chemical shifts for the R = 1 and 3 joins.

For the join R = 3 compositions, the <iso>glass is a combination of two linear function of Si/(Si+Al) with: a slope of -49.3 ± 1.2 ppm/mol% below Si/(Al+Si) ~ 0.7 and -25.2 ± 2.5 ppm/ mol% above. If the slope at high silica content matches the slope found for R = 1 and hence points to a progressive substitution of Si by Al, the more negative slope at low silica content shows the existence of an additional mechanism. Since depolymerization of the aluminum units has been shown to produce an increase of iso(Al IV ) in calcium aluminosilicate glasses [START_REF] Neuville | Al coordination and speciation in calcium aluminosilicate glasses: Effects of composition determined by Al-27 MQ-MAS NMR and Raman spectroscopy[END_REF] and that gehlenite Ca2Al2SiO7 shows a iso difference of +11 ppm between an AlO4-(Al2Si2) and an AlO4-(Al2Si) configuration [START_REF] Florian | Elucidation of the Al/Si Ordering in Gehlenite Ca2Al2SiO7 by Combined 29Si and 27Al NMR Spectroscopy/Quantum Chemical Calculations[END_REF], the two compositional behavior of <iso>glass can be understood as the formation of NBOs on the AlO4 units below Si/(Al+Si) ~ 0.7. This finding in the glassy state is in excellent agreement with 17 O NMR measurements on CAS glasses [START_REF] Allwardt | Bonding preferences of non-bridging O atoms: Evidence from O-17 MAS and 3QMAS NMR on calcium aluminate and low-silica Caaluminosilicate glasses[END_REF] predicting a disappearance of Al-NBO for compositions richer in SiO2 than CAS33, i.e. above Si/(Al+Si) = 0.67. A striking difference with the evolution in the melt is that the entire compositional range explored is characterized by a single slope of -49.6 ± 2.2 ppm/ mol% consistent with the presence of NBOs on AlO4 over the full compositional range, a behavior also seen in our Molecular Dynamics simulations [START_REF] Charpentier | Structure of strontium aluminosilicate glasses from molecular dynamics simulations, neutron diffraction and nuclear magnetic resonance studies[END_REF]. Keeping in mind that at high silica content a low 27 Al NMR signal-to-noise ratio (low alumina content) produces an increased uncertainty on the in-situ measurements, this suggests that NBOs on AlO4 present in the high temperature per-alkaline melts can be fully lost in the glass for high-silica compositions while they are kept at lower silica content. Our finding suggests that, near Tg, high concentration of silica favors the polymerization of the melt around Al[O(Al,Si)]4 species for which iso is solely controlled by the Si/(Al+Si) ratio, similarly to the join R = 1.

For both joins the chemical shifts obtained in the melts are lower than the ones derived from the glasses, a consequence of both thermal (decrease of Al-O distances) and structural (increase in average Al coordination) effects. Thermal effects are difficult to evaluate as they are a combination of thermal expansion and quantum quasiharmonic vibrations [START_REF] Nemausat | Phonon effects on x-ray absorption and nuclear magnetic resonance spectroscopies[END_REF] difficult to disentangle and producing counter-intuitive, coordination-dependent, evolutions with temperature.

But since our Neutron diffraction measurements points to [ V Al] in the melts close to the one in the glasses, the dominant mechanisms at the origin of this downward shift from glass to melt is thermal expansion.

The R < 1 compositions explore two constant [SiO2] ranges (horizontal lines in figure 1) with varying Sr/Al ratio and their iso do not show linear correlations with composition. At fixed [SiO2] we observe a marked decrease of both <iso>glass and 2000°C upon crossing the R = 1 join that correlates with the presence of significant amounts of higher coordination states of aluminum ( V Al and even VI Al) in the corresponding glasses (evidenced by 27 Al MAS NMR experiments, see figure S4). The chemical shift difference between <iso>glass and 2000°C is now down to an average of -0.6 ppm which suggests that the structure of those compositions are less prone to temperature effects than the one on the joins R = 3 and R = 1. Yet there seems to be a cross-over between glass and melt evolutions (see crossing dashed lines in figure 9) pointing to the presence of various competing mechanisms affecting 2000°C at low silica content: thermal expansion, aluminum average coordination, NBOs on AlO4 units as seen before, but also the possible presence of tricoordinated oxygen involving AlO5 units. where  is the viscosity [START_REF] Angell | Perspective on the glass transition[END_REF] measures the thermal dependence of the structure at Tg, our ∂/∂T results provide similar insights at temperature larger than 2 Tg. A link between ∂/∂T and glass forming ability has been formerly observed in calcium aluminates [START_REF] Massiot | Structure and dynamics of oxide melts and glasses: A view from multinuclear and high temperature NMR[END_REF][START_REF] Neuville | The structure of crystals, glasses, and melts along the CaO-Al2O3 join: Results from Raman, Al L-and K-edge Xray absorption, and Al-27 NMR spectroscopy[END_REF]. In this case all compositions forming glasses showed values of ∂/∂T below -2 ppm/1000°C whereas non-glass forming ones where found above this threshold. Here we observe an increase of ∂/∂T with increasing Si/(Al+Si) with a close-to-linear and common behavior for all compositions. This shows that Si/(Al+Si), i.e. the distribution of Al-(OSi)p(OAl)(4-p) units, is the dominant parameter that controls the temperature dependence of the aluminum environment. This can be related to the temperature dependence of the melt viscosity seen in fully polymerized systems by Molecular Dynamic simulations [START_REF] Scamehorn | Viscosity-Temperature Relations and Structure in Fully Polymerized Aluminosilicate Melts from Ion Dynamics Simulations[END_REF] and for which the fragility increases with increasing Al/Si ratio. Interestingly, neither the presence of high-coordinated aluminum species (R < 1) nor that of Si-NBOs or Al-NBOs (R = 3) seems to have a dramatic effect on ∂/∂T. It shows that the ability of aluminum to adjust its local structure to temperature changes is controlled by the network connectivity. The behavior of the intercept, i.e. the extrapolation of <iso> evolution at 0 °C, mimics the evolution seen for 2000°C

(figure 9), showing a structural continuity between the high-temperature melt and the glassy state.

The Tg by 29 Si NMR [START_REF] Farnan | High-temperature Si-29 NMR investigation of solid and molten silicates[END_REF] but much lower than the values of 215 kJ/mol and 258 kJ/mol obtained by high-temperature shear viscosity measurements in SA26.37 and SA50.25 melts respectively [START_REF] Urbain | Viscosity of Liquid Silica, Silicates and Alumino-Silicates[END_REF]. We can also note that our measurement fall below the 257 kJ/mol -985 kJ/mol range of activation energies for shear viscosity found in calciumaluminosilicate melts [START_REF] Toplis | Shear viscosities of CaO-AL(2)O(3)-SiO2, and MgO-Al2O3-SiO2 liquids: Implications for the structural role of aluminium and the degree of polymerisation of synthetic and natural aluminosilicate melts[END_REF]. The correlation time for shear viscosity can be obtained using Maxwell equation

𝜏 𝑠 = 𝜂 𝐺 ∞ ⁄ ,
where  is the shear viscosity and 𝐺 ∞ = 10 10±0.5 Pa the infinite frequency shear modulus [START_REF] Dingwell | Relaxation in silicate melts[END_REF]. We previously compared those with the NMR-derived c and have found in the case of aluminosilicate compositions agreements for calcium-aluminosilicates [START_REF] Gruener | Bulk and local dynamics in glass-forming liquids: A viscosity, electrical conductivity, and NMR study of aluminosilicate melts[END_REF] but strong mismatch for yttrium-aluminosilicates [START_REF] Florian | Al-27 NMR study of the structure of lanthanum-and yttrium-based aluminosilicate glasses and melts[END_REF]. We performed low-temperature viscosity measurements on all compositions [START_REF] Novikov | Al and Sr environment in tectosilicate glasses and melts: Viscosity, Raman and NMR investigation[END_REF] but the only high-temperature viscosity measurements available to us for strontium-aluminosilicates are those of Urbain [START_REF] Urbain | Viscosity of Liquid Silica, Silicates and Alumino-Silicates[END_REF] obtained on only two compositions. They are compared to the NMR correlation times in figure 12. The correlation times derived by the two techniques are in very good agreement considering the error on 𝐺 ∞ which leads to an uncertainty of ± 0.5 on 𝑙𝑜𝑔 10 (𝜏 𝑠 ). It is highly improbable that AlOn units exist in melts for a long enough period of time to consider their translational and rotational diffusion [START_REF] Liu | Diffusive motion in alkali silicate meltsan NMR-study at high temperature[END_REF][START_REF] Stebbins | Glass structure, melt structure, and dynamics: Some concepts for petrology[END_REF]. As a consequence, the 27 Al NMR relaxation from which we derived c and Ea happens through vibrations of the Al-O bonds and probes dynamics close to the Larmor frequency. Since the melt' shear viscosity is expected to be controlled by the oxygen diffusion [START_REF] Dingwell | Relaxation in silicate melts[END_REF], the correspondence between c and s shows a coupling between the Al-O vibrations at the origin of the NMR relaxation and the oxygen self-diffusion coefficient D linked to the shear viscosity through the Eyring equation 𝐷 = 𝑘 𝐵 𝑇 𝜂𝜆 ⁄ .

The origin of the coupling can be found in random walk theory of activated diffusion where the diffusion coefficient is related to the average square jump length 〈𝜆 2 〉, the average jump frequency  and a geometric factor  (1/6 for unrestricted motion in three dimensions) through the equation an "aluminum-centered" point of view that can be extended to the entire aluminosilicate network, in the limit that it is observed at temperature significantly higher than Tg. The correlation times derived by NMR and those obtained by fitting the shear viscosity at low and high temperature are in reasonably good agreement, showing that both mechanisms share at least some common features. The discrepancy lies in the activation energies, which are lower for NMR relaxation than for shear viscosity, showing that the temperature dependence of both processes at 𝑇 𝑇 𝑔 ⁄ ≥ 2 is not strictly the same. Yet their correlation time being comparable one can convert the NMR ones in term of oxygen self-diffusion coefficient and show a decrease of oxygen diffusivity D with increasing Si/(Al+Si) ratio for polymerized melts along with an absence of compositional dependence for depolymerized ones.

Overall this study shows that if the structure of the strontium alumino-silicate glasses studied here are a good approximation of the structure of the high-temperature melts, some compositionaldependent discrepancies appear as well. Although technically challenging, a combined in-situ/exsitu study proves to be a very powerful approach to the description of the actual melt structure. This is even more true if one combines techniques providing information about the aluminosilicate network and the cation environement, as 27 Al NMR and diffraction techniques do. For the high temperatures explored here 27 Al NMR turns out also to give insights into the oxygen selfdiffusion and its variation with composition, a parameter which is otherwise very difficult to obtain. Future plans are to develop an experimental approach which would allow us to perform NMR close to the glass transition, a very challenging task considering the lack of sensitivity of this technique.

Figure 2 .

 2 Figure 2. One-scan High-Temperature 27 Al NMR spectra (blue lines) of SA10.45 melt at different temperatures during the melt's cooling. The red lines are fits of the NMR signal with Lorentzian function. The very high-temperature NMR experiments were performed on a 9.4 T Bruker Avance I spectrometer operating at 104.3 MHz. 27 Al chemical shift are referenced to 1M solution of Al(NO3)3. The setup is based on an aerodynamic levitation device located inside the NMR probe.

Figure 3 .

 3 Figure 3. Total structure factors S(Q) of the liquid SAS samples for R = 1 (a) and 3 (b).

Figure 4 .

 4 Figure 4. Evolution of the 27 Al NMR line's position during free cooling of all compositions studied: (a) on the chargecompensation line (R = 1), (b) in the per-alkaline field (R = 3) and (c) in the per-aluminous region (R < 1).

Figure 5 .

 5 Figure 5. Evolution of the 27 Al NMR correlation times during free cooling of all compositions studied: (a) on the charge-compensation line (R = 1), (b) in the per-alkaline field (R = 3) and (c) in the per-aluminous region (R < 1).

Figure 5

 5 Figure5presents the evolution of log10(c) for aluminum correlation times versus inverse temperature. There is a clear linear behavior for all compositions in our temperature range, pointing to an Arrhenius behavior of the latter. As directly seen from the linewidth, composition has a strong impact on the aluminum correlation times along the join R = 1, does separate the two [SiO2] (33.3 and 50.0 %mol) in the per-aluminous field but has no clear impact for compositions belonging to the join R = 3. Correlation times c are found to vary typically in the range 10 ps to 250 ps. They increase with increasing [SiO2] along the join R = 1 as well as in the per-aluminous field. They with increasing temperature in all cases.

Figure 6 .

 6 Figure 6. Evolution of the 27 Al NMR correlation time at 2000 °C for compositions R = 1 (blue, triangles), R = 3 (red, rectangles) and R < 1 (green, circles). Error bars show the confidence intervals derived from the linear fit (figure 5) and lines are linear regressions.

Figure 7

 7 Figure7shows the total pair distribution functions g(r) for all the compositions studied along the joins R = 1 and R = 3. In all cases, the first peak corresponds to an overlapped contribution from both the Si-O and the Al-O nearest neighbor pairs. Its position shifts gradually toward the Si-O bond distance with increasing SiO2 concentration. As shown in figure8(a), for compositions containing 33% of silica taken as an example, the Si-O and Al-O local environment in the liquid and the corresponding glass are very similar. However, an increase in the fraction of AlO5 units is found in the melts, as indicated by a more pronounced shoulder on the high r part of the first peak in g(r).

Figure 7 .

 7 Figure 7. Total pair distribution functions g(r) for the liquid SAS along the composition lines R = 1 (a) and R = 3 (b). The positions of the various correlations are shown as a guide. O-O correlations are calculated assuming SiO4, AlO4, SrO6 and SrO8 polyhedra.

  in the case of liquid calcium aluminosilicates. The Gaussian fit was performed by fixing the coordination number of the Si-O bond to 4 leading to a bond length of 1.65 Å similar to what has been found with CAS compositions[START_REF] Hennet | Neutron diffraction of calcium aluminosilicate glasses and melts[END_REF]. The fits are shown in figure8(b) for all compositions studied by neutron diffraction and the results for the Al-O correlations are summarized in table 2. For all

Figure 8 .

 8 Figure 8. (a) Total pair distribution functions g(r) in the liquid and glassy states for the two samples SA33.33 and SA33.17. (b) Total correlation function T(r) for all studied compositions along the joins R=1 and 3. The partial and total are shown in comparison to the experimental data. The short-range order around Sr is more difficult to study as Sr-O correlations are completely overlapped by the contributions of the O-O pairs arising from Si-O and Al-O tetrahedra and highly coordinated Sr-O polyhedra (CN ≥ 7). Considering the g(r) functions in figure8a, it seems that the Sr environment is more complex in the liquid than in the glass. On the one hand, a first Sr-O contribution is present at distances shorter than 2.53 Å (typical for SrO6), meaning that Sr-O with coordination less than 6 should be present. On the other hand, all pair distribution functions also exhibit also a peak at ~3.0 Å corresponding to O-O distances in SrO8 polyhedra. For the join R = 1, some correlations observed between 3.0 Å and 3.6 Å could be attributed to O-O bonds for 7-fold coordinated Sr. Then compared to the glass compositions in which the Sr-O coordination number

DiscussionFigure 9

 9 Figure 9 presents an overview of the 27 Al chemical shifts observed in molten droplets at 2000 °C 2000°C and centers of gravity <iso>glass of the 27 Al MAS NMR spectra obtained on related glasses versus Si/(Al+Si). Both R = 1 and R = 3 joins show a linear evolution (figure S2 and S3 report versus [SiO2] and [Al2O3] respectively). Here "center of gravity of the MAS NMR spectra"

Figure 9 .

 9 Figure 9. 27 Al chemical shifts at 2000°C 2000°C (red) and "barycenter" of the glass spectra <iso>glass see text for details) (blue) for R = 1 (rectangles), R = 3 (triangles) and R < 1 (circles) compositions. Continuous lines are linear fit, dashed ones are guides for the eyes for [SiO2] = 33% (top) and [SiO2] = 50% (bottom).

Figure 10 .

 10 Figure 10. Evolution of the slope (bottom) and intercept (top) of the iso = f(T) of the linear regressions for compositions R = 1 (triangles), R = 3 (rectangles) and R < 1 (circles). Error bars show 95% confidence intervals (within symbol when not shown) and lines are linear regressions.The time-resolved acquisition of 27 Al during free cooling also provides measurements of 𝛿 = 𝑓(𝑇) (figure4) that traces the evolution with temperature of the average structure of the melt viewed by aluminum. Slopes ∂/∂T and intercepts (0) of the 𝛿 = 𝑓(𝑇) extracted from the linear regression on the data points (figure4) are given in table 1 and displayed in figure10as a function of the Si/(Al+Si) ratio.This ∂/∂T slope represents the temperature dependence of the average local aluminum

  Arrhenian behavior of the 27 Al NMR correlation times as a function of temperature allows deriving an activation energy Ea and pre-exponential factor 0 which are shown as a function of composition in figure 11. As already inferred from the evolutions of c itself (figure 5) the NBOcontaining compositions (R = 3) depart from the others. When R ≤ 1 compositions show a constant activation energy around 140 kJ/mol and a frequency factor in the range 0.01 ps to 0.04 ps, R = 3 ones display Ea ~ 100 kJ/mol and 0 ~ 0.03 ps to 0.23 ps. Those values of activation energies are fully consistent with the ~ 135 kJ/mol obtained on a glass of albite composition (NaAlSi3O8) above

Figure 11 .

 11 Figure11. Evolution of the activation energy Ea (bottom) and pre-exponential ('frequency') factor 0 of the 27 Al NMR relaxation for compositions R = 1 (triangles), R = 3 (rectangles) and R < 1 (circles). Error bars show 95% confidence intervals (within symbol when not shown).

Figure 12 .

 12 Figure12. Correlation times derived from NMR (triangles and diamonds) and shear viscosity (squares and circles) as a function of temperature and for the compositions SA50.25 (blue) and SA26.37 (red). Only one in two NMR data points are drawn for clarity purposes. Lines are fits using the VTF equation with HT NMR and LT viscosity data (see text for details).

Table 1 .

 1 Results of the linear fit of the melt's 27 Al positions vs temperature, observed position at 2000°C, activation energies and pre-exponential factor (standard errors in parenthesis) and average positions <iso>glass obtained from the studies of the glasses[START_REF] Novikov | Al and Sr environment in tectosilicate glasses and melts: Viscosity, Raman and NMR investigation[END_REF]. High silica containing compositions SA75.12 and SA75.06 have too high vaporization tendency to perform high temperature experiments.

	Sample <iso>glass	Slope	Intercept	2000°C (T°C)	Ea	0
		(ppm)	(ppm/1000°C)	(ppm)	(ppm)	(kJ/mol)	(ps)
	SA75.12	59.7
	SA63.18	62.0	1.00 (0.89)	56.6 (1.82) 58.6 (2001) 132.5 (9.8) 0.468 (0.240)
	SA57.21	63.4	-1.11 (0.82)	62.7 (1.65) 61.0 (2000) 127.8 (5.9) 0.171 (0.336)
	SA50.25	65.0	-0.68 (0.67)	63.4 (1.32) 61.9 (2005) 136.1 (3.9) 0.201 (0.043)
	SA42.29	67.0	-1.32 (0.27)	66.9 (0.54) 64.1 (1997) 137.4 (3.3) 0.206 (0.036)
	SA33.33	70.3	-2.85 (0.27)	72.4 (0.52) 66.6 (1996) 137.1 (2.5) 0.153 (0.021)
	SA26.37	73.4	-2.43 (0.17)	73.8 (0.33) 69.0 (1998) 141.1 (1.6) 0.109 (0.010)
	SA20.40	75.2	-2.76 (0.13)	76.2 (0.23) 70.7 (1999) 140.1 (1.9) 0.065 (0.007)
	SA10.45	77.3	-3.64 (0.10)	80.5 (0.19) 73.2 (2004) 137.4 (1.7) 0.077 (0.008)
	SA75.06	59.3
	SA66.09	60.7	0.10 (1.28)	57.2 (2.57) 55.7 (2002) 86.5 (13.4) 1.990 (1.407)
	SA60.10	62.1	-0.89 (0.84)	61.1 (1.65) 59.3 (1994)	94.7 (9.2) 1.782 (0.897)
	SA50.12	65.0	0.92 (0.46)	60.4 (0.91) 62.4 (2000)	98.2 (5.7) 1.238 (0.382)
	SA42.14	68.3	-3.13 (0.65)	73.1 (1.23) 66.3 (1995)	90.4 (5.1) 1.700 (0.486)
	SA38.16	70.5	-0.41 (0.49)	69.0 (0.91) 68.0 (1994) 106.0 (4.1) 0.761 (0.177)
	SA33.17	73.5	-0.87 (0.68)	72.8 (1.27) 71.2 (2005) 110.7 (4.1) 0.774 (0.179)
	SA50.30	62.3	-0.42 (0.66)	61.6 (1.22) 60.5 (2005) 131.1 (3.9) 0.188 (0.042)
	SA50.35	59.1	-1.17 (0.47)	61.8 (0.88) 59.3 (2003) 141.5 (3.1) 0.147 (0.026)
	SA50.40	55.7	0.82 (0.45)	55.8 (0.84) 57.4 (2003) 137.2 (2.1) 0.161 (0.019)
	SA33.38	67.3	-2.09 (0.35)	69.4 (0.65) 65.1 (2002) 142.8 (1.7) 0.141 (0.014)
	SA33.43	64.7	-1.49 (0.27)	66.5 (0.51) 63.3 (2004) 139.7 (1.3) 0.155 (0.012)

Table 2 ,

 2 , which is a similar system. All values are listed in table 2. Summary of the structural parameters obtained from neutron diffraction for all measured samples.

	Sample ρ0 (Å -3 ) T (°C) Q1 (Å -1 ) rAl-O (Å) CNAl-O
	SA20.40 0.0682 1750	2.03	1.756	4.06
	SA33.33 0.0691 1750	2.00	1.761	4.05
	SA42.29 0.0696 1850	1.95	1.766	4.06
	SA20.20 0.0633 2050	2.13	1.758	4.06
	SA33.17 0.0663 1750	2.08	1.763	4.05

Acknowledgments

We thank Alain Bertoni for help with the neutron diffraction experiments and the Institut Laue-Langevin for the beamtime allocation. This research was conducted under funding from the ANR DyStrAS project (ANR-13-BS08-0012).

𝐷 = 𝛾〈𝜆 2 〉Γ.

(5)

In the case of random motion of a diffusing atom over a potential barrier,  has been expressed

as:

where  is the frequency of vibration of the atom around its equilibrium position and G is the "free energy of activation" [START_REF] Perkins | Diffusion and Permeation of He, Ne, Ar, Kr, and D2 through Silicon Oxide Thin Films[END_REF][START_REF] Wert | Diffusion Coefficient of C in $\ensuremath{\alpha}$-Iron[END_REF][START_REF] Zener | Theory of Do for Atomic Diffusion in Metals[END_REF]. The (Debye) frequency  is on the order of 10 12 -10 13 Hz and is at the origin of the time-modulation of the NMR interaction responsible for NMR relaxation. In the derivation of Zener [START_REF] Zener | Theory of Do for Atomic Diffusion in Metals[END_REF], G is the work required to produce a lattice's distortion allowing the jump and then H is the measured activation energy of diffusion (retrieved by plotting ln(D) as a function of 1/T) which in transition state theory is often equated with the sum of the energy required to launch a species for a diffusive jump and the energy needed to form a landing site for the species.

At high enough temperature 𝑒 -Δ𝐺 𝑘 𝐵 𝑇 ⁄ goes to unity and the oxygen vibrations  becomes the jump frequency  (equation ( 6)) leading to a coupling of oxygen diffusivity and NMR relaxation through equation ( 5). Practically this is seen at 𝑇 𝑇 𝑔 ⁄ ≥ 2 but only for the most fragile liquids.

Using  =  = 1/c,2000°C,  = 2.8 Å (twice the oxygen ionic radius) and  = 1/6 equation ( 5) leads to D in the range 130 to 750 10 -12 m 2 /s. This range is difficult to compare with tracer diffusion measurements in aluminosilicate melts as a wide scattering in the measurements is found in the literature, spanning several orders of magnitude. For anorthite CaAl2Si2O8 melt (CA40.20 in our notation) at 2000°C and 1 atm, "reliable" values of 15 10 -12 m 2 /s, 264 10 -12 m 2 /s and 823 10 -12 m 2 /s have been reported [START_REF] Dunn | Oxygen diffusion in three silicate melts along the join diopside-anorthite[END_REF]. With this in mind, the compositional evolution of the aluminum NMR c at 2000 °C displayed in figure 6 can be viewed as a decrease of oxygen diffusivity D with increasing Si/(Al+Si) ratio for polymerized melts from 748 10 -12 m 2 /s (SA20.40) down to 131 10 - 12 m 2 /s (SA57.21), whereas depolymerized melts (R = 3) have oxygen diffusivity of approximately 310 ± 100 10 -12 m 2 /s and no clear compositional dependence. This can also be viewed as evolution of the viscosity of those melts since D is inversely proportional to  according to the Eyring equation. Note that for Si/(Al+Si) > 0.5 the higher values of c at 2000°C obtained on the polymerized compositions (SA57.21 and SA63.18) with respect to the depolymerized ones (figure 6) translate into lower oxygen self-diffusion coefficient and higher viscosity, as expected.

Conclusions

We have been investigating the SrO-Al2O3-SiO2 ternary system in the high temperature melt In terms of structure, we found that the high-temperature melt structure follows that of related glasses to a reasonable extent. Low amounts of V Al species are found in the polymerized melts, in agreement with our finding in the glasses. The structure of the polymerized melts is controlled by the close-to-random distribution of Al and Si in the tetrahedral sites of the aluminosilicate network.

In contrast to this, the depolymerized glasses exhibit NBOs on the AlO4 units only below Si/(Al+Si) ~ 0.7 whereas the evolution of the melts is consistent with the presence of NBOs on AlO4 over the full compositional range. Within our measurements uncertainties, this suggests that NBOs on AlO4 present in the high temperature per-alkaline melts can be fully lost during cooling for high-silica compositions while they are kept at lower silica content. Addition of SrO at a given silica content decreases medium range order (e.g. smaller ring sizes than the one found for polymerized melts), in line with the presence of NBOs on aluminum units breaking the aluminosilicate network.

High amounts of high-coordinated aluminium are seen in per-aluminous compositions in the glasses and the melts. Competing mechanisms are at play during cooling, which are not observed along the joins R = 3 and R = 1, especially at low silica content. This could point towards the presence of tri-coordinated oxygen which would not be kept in significant amounts in the glasses.

On the modifier side, the strontium environment is seen to be more complex in the melt than in the glass, with a broader distribution of coordination number than that in the glass. We estimated it to be around 8 for the join R = 3 and somewhat less for R = 1, compared to values ranging between 8.5 and 9.0 obtained for the glassas shown byMD simulations [START_REF] Charpentier | Structure of strontium aluminosilicate glasses from molecular dynamics simulations, neutron diffraction and nuclear magnetic resonance studies[END_REF][START_REF] Novikov | Al and Sr environment in tectosilicate glasses and melts: Viscosity, Raman and NMR investigation[END_REF].

The evolution of the 27 Al NMR line position as a function of temperature and compositions

shows that the distribution of Al-(OSi)p(OAl)(4-p) units is the dominant parameter controlling the temperature dependence of the aluminum environment, a behavior related to increased fragility with increasing Al/Si ratio as seen by Molecular Dynamic simulations [START_REF] Scamehorn | Viscosity-Temperature Relations and Structure in Fully Polymerized Aluminosilicate Melts from Ion Dynamics Simulations[END_REF]. We also probed the dynamics of those melts through the 27 Al NMR relaxation. This gives


Airborne transmission of respiratory diseases involves a number of disciplines such as virology, or fluid mechanics. The outbreak of COVID-19 has triggered a number of numerical studies to better understand the fate and transport of respiratory droplets in the air. This research aims at developing a methodology to evaluate the variability in numerical simulations of airborne dispersion that can provide astimations of social distancing precautions. For that purpose, we rely on standard techniques available in computational fluid dynamics (CFD) software to run numerical simulations of airborne dispersion. We then used variance-based methods [2], such as the "Sobol indices" or "variance-based sensitivity indices", to analyse the variability of a number of parameters that were demonstrated to affect droplet dispersion.

For illustrative purposes, this paper details the results from the simple scenario of droplet emission in quiescent air. In this scenario, two observables are considered: the number of particles remaining above a given height after a period of time (here 1.5 m after 20 s) and the mean distance from the source after a given time period (here 20 s).

We performed numerical simulations with the Lagrangian tracking module of Code_Saturne CFD software [L1]. Prior to injection, the fluid was at rest and at a temperature of 25 °C. Droplets were injected into a box with dimensions of 4 x 3 x 2 m. Droplets are injected in the domain at a given location, with a height representative of an average adult's height (here 1 x 2 x 1.7 m) and approximating the shape of a mouth (an ellipsoid with a width of 0.03 m and height of 0.015 m). In accordance with previous studies [1,2], we assumed droplets to be expelled from the mouth within a fixed cone, i.e. with a vertical injection angle in the range of 15 to 40° and with a horizontal injection angle in the range of -5 to 5°. Droplets were all injected with the same size and velocity. Simulations were run for a physical time of 20 s (with a time step of 0.01 s). To complete the simulation set-up, five additional input parameters were used as uncertainty sources modelled with the help of standard random distributions. A simulation is realised with a random trial of the input parameters according to the following distributions:  The droplet diameter (uniform distribution between 1 and 10 µm);  The number of injected droplets (uniform distribution between 700 and 1,300);  The cough velocity (Gaussian distribution, mean of 10 m/s and variance of 2 m/s);  The cough duration (Gaussian distribution, mean of 75 ms and variance of 6 ms);  The head angle in relation to the vertical direction (uniform distribution from -15 to 50°).

Results

Figure 1 shows a typical set of results from our simulations: the droplets are dispersed in the flow at rest. Once injected in the simulation, these droplets undergo only Brownian motion and settling due to gravity. Due to their size and the fact that no evaporation is accounted for, gravity is the predominant force, which leads to their sedimentation on the ground within a finite time.

Using OpenTurns scientific library and API [2, L2], 6.000 simulations were performed with various values of the five uncertainty sources (i.e. droplet diameter, number of droplets, head angle, cough velocity and cough duration). The results obtained with the first order Sobol index are summarised in Table 1.

Observable

Number of droplets

Droplet diameter

Cough velocity

Cough duration

Head angle

Np (z>1.5 m) 0,252435 -0,0593705 0,0942603 -0,0427005 0,434486 <Xp-X0> 0,0838429 0,084791 0,346216 0,123051 0,765763 Table 1. First-order Sobol indices obtained from 6,000 simulations, with a column for each uncertainty source and two lines corresponding to the two observables (number of droplets remaining above a height of 1.5 m and the mean distance from the point source along the x-direction) .

As expected, it appears that the number of droplets remaining above a certain height (here 1.5 m) varies mostly with the angle at which the head is tilted. The second parameter that affects the results is actually the number of droplets emitted during coughing, while the injection velocity is only the third most influential parameter (with a much lower importance).

Yet, if the observable of interest is taken to be the mean distance travelled by droplets along the horizontal direction, then the analysis changes. The results are again mostly affected by the angle at which the head is tilted, but the second input affecting the results is the velocity of injection of the droplets. The cough duration, the number of particles and the diameter of particles are less influential on the result.

This study illustrates the application of sensitivity analysis techniques to investigate the variability of numerical simulations of airborne dispersion. The first results show the robustness of such techniques as well as their limitations. In particular, in the simple case considered, the head angle during the cough is the key parameter driving the particles towards the ground. However, these results are expected to change significantly if another observable is used. Moreover, this study shows that, as prerequisite of the sensitivity analysis, a clear definition of an observable is needed.

Simulations in more complex cases are still underway due to the high numerical costs and size of data generated by such numerical experiments. In the near future, our analysis will move towards more realistic descriptions, including models for droplet evaporation/condensation as well as new models related to viral and biological properties (lifetime, contagiousness, etc.) that appear to be key in designing more efficient public health recommendations [1].

  Social Distancing: The Sensitivity of Numerical Simulations by Christophe Henry, Kerlyns Martinez-Rodriguez, Mireille Bossy (Université Côte d'Azur, Inria, CNRS, Cemef, France), Hervé Guillard (Université Côte D'Azur, Inria, CNRS, LJAD, France), Nicolas Rutard and Angelo Murrone (DMPE, ONERA, France) Researchers from Inria and the French Aerospace Lab ONERA are collaborating on a joint project. The goal is to assess the variability in the advice for social distancing precautions that can be drawn from numerical simulations of airborne dispersion. This variability depends on a number of factors, including: physical variables (e.g. droplet size, ejection velocity), modelling methods used (e.g. turbulence model) and numerical aspects (mesh). We use sensitivity analysis tools to quantify and order the role these factors play in influencing the numerical results.