German Montes-Hernandez
email: german.montes-hernandez@univ-grenoble-alpes.fr

Mamadou Bah

François Renard

Mechanism of the formation of engineered magnesite: A useful mineral to mitigate CO2 industrial emissions

Keywords: Engineered Magnesite Precipitation, Time-Resolved Raman Spectroscopy, Carbon Dioxide Mineralization, CO2 Mitigation, Mineral Nucleation and Growth

Magnesium carbonate production at the industrial scale is a realistic option to reduce the industrial emissions of CO2. Ultrabasic rocks and/or alkaline mine waste provide magnesium sources and are widely available in the Earth's crust. Here, we investigated the aqueous carbonation of magnesium hydroxide under moderate temperature (25-90°C) and pressure (initial pressure of CO2=50 bar) using NaOH as the CO2 sequestering agent. From time-resolved Raman measurements, we demonstrate that the aqueous carbonation of magnesium hydroxide can be an effective engineered method to trap CO2 into a solid material and produce large amounts of magnesite MgCO3 (6 kg/m 3 h), or hydromagnesite Mg5(CO3)4(OH)2.4H2O (120 kg/m 3 h) at 90°C or nesquehonite MgCO3.3H2O (40 kg/m 3 h) at 25°C. Higher production rates were measured for nesquehonite (at 25°C) and hydromagnesite (at 60 and 90°C). However, only the magnesite produced at 90°C ensures a permanent CO2 storage because this mineral is the most stable Mg carbonate under Earth surface conditions, and it could be co-used as construction material in roadbeds, bricks with fireretarding property and granular fill. The use of specific organic additives can reduce the reaction temperature to precipitate magnesite. For example, ferric EDTA (ethylenediaminetetraacetic acid) reduces the temperature from 90 to 60°C. However, more time is required to complete magnesite precipitation reaction at this lower temperature (15h at 90°C and 7 days at 60°C). These results suggests that functionalized organic groups can reduce the energetic barriers during mineral nucleation.

Table of Contents Graphic

Introduction

CO2 emissions have increased since the industrial revolution: about 36 Gt of CO2 that originate from fossil fuel are annually emitted into the atmosphere with 30% from industrial activities and 70% from transport, agriculture and other sources [START_REF] Peters | Towards real time verification of CO2 emissions[END_REF]. These non-regulated emissions have led to concerns about global warming as a progressive increase of CO2 concentration into atmosphere has been recorded in the last two centuries [START_REF] Peters | Towards real time verification of CO2 emissions[END_REF]. The energy transition (i.e., the use of carbon-free energy sources such as hydrogen, solar, wind, marine, hydraulic, geothermal) could significantly decrease CO2 emissions. Some limitations, such as the supply of rare Earth elements, large amounts of water requirements and natural risks, have raised some concerns about how fast this transition will occur [START_REF] Montes-Hernandez | Mineral sequestration of CO2 by aqueous carbonation of coal combustion fly-ash[END_REF][START_REF] Mediavilla | The transition towards renewable energies: Physical limits and temporal conditions[END_REF]. Moreover, conventional and unconventional fossil resources (gas, carbon and oil) are still available in geological formations [START_REF] Berg | Analysis of Ultimate Fossil Fuel Reserves and Associated CO2 Emissions in IPCC Scenarios[END_REF], and their exploitation and resulting CO2 emissions have been predicted to continue for 50-100 years [START_REF] Montes-Hernandez | Experimental assessment of CO2-mineral-toxic ion interactions in a simplified freshwater aquifer: Implications for CO2 leakage from deep geological storage[END_REF]. Therefore, CO2 capture from industrial sources and its transformation into re-usable products (e.g. ethanol, syngas, etc.) and/or non-energetic materials (e.g. calcite, magnesite, siderite, etc.) has been proposed to reduce CO2 emissions into the atmosphere [START_REF] Bai | Highly Active and Selective Hydrogenation of CO2 to Ethanol by Ordered Pd-Cu Nanoparticles[END_REF][START_REF] Ross | Tunable Cu Enrichment Enables Designer Syngas Electrosynthesis from CO2[END_REF][START_REF] Montes-Hernandez | Rapid precipitation of magnesite micro-crystals from Mg(OH)2-H2O-CO2 slurry enhanced by NaOH and a heat-ageing step (from 20 to 90°C)[END_REF][START_REF] Montes-Hernandez | Nanostructured calcite precipitated under hydrothermal conditions in the presence of organic and inorganic selenium[END_REF]. CO2 capture from industrial sources does not represent a technological or scientific obstacle, but the existing methods and technologies (including recovery of high-purity of CO2 and its liquefaction) remain highly expensive. In this way, the improvement and optimization on the CO2 capture units still represent important challenges. The goal of the present experimental study is to demonstrate that engineered magnesite (MgCO3) could be used as an effective option to store carbon dioxide within magnesite-rich solids. The obtained magnesiterich solids could then be used as civil construction materials (e.g. roadbed materials, bricks, granular fill) [START_REF]Gaseous Carbon Waste Streams Utilization: Status and Research Needs[END_REF]. Magnesite is the most stable carbonate mineral under typical Earth surface conditions, with the highest resistance to leaching and weathering [START_REF] Pokrovski | Calcite, dolomite and magnesite dissolution kinetics in aqueous solutions at acid to circumneutral pH, 25 to 150 C and 1 to 55 atm pCO2: New constraints on CO2 sequestration in sedimentary basins[END_REF]. The magnesite dissolution rate is 100-1000 times lower than that of calcite in a wide range of conditions, from ambient temperature to 150°C and pH from 1 to 14 [START_REF] Pokrovski | Calcite, dolomite and magnesite dissolution kinetics in aqueous solutions at acid to circumneutral pH, 25 to 150 C and 1 to 55 atm pCO2: New constraints on CO2 sequestration in sedimentary basins[END_REF]. For this reason, anhydrous magnesium carbonates (magnesite and dolomite) have been considered as relevant minerals to store permanently anthropogenic carbon dioxide. Magnesite and dolomite precipitation kinetics have been widely studied because their abiotic precipitation at ambient temperature (~25°C) is virtually impossible within typical experimental time scales [START_REF] Deelman | Breaking Ostwald's rule[END_REF][START_REF] Pimentel | The formation of the dolomite-analogue norsethite: Reaction pathway and cation ordering[END_REF]. The strong solvation shells of magnesium ions in aqueous media produces this limitation [START_REF] Deelman | Breaking Ostwald's rule[END_REF]. However, the sole effect of Mg hydration might not be the only factor of inhibition of magnesite and/or dolomite formation. Recent studies claim that a more intrinsic crystallization barrier and the influence of fluid chemistry (e.g., relative size of the constituting cations) prevent the formation of a long-range ordered crystallographic structures at ambient conditions [START_REF] Hänchen | Precipitation in the Mg-carbonate system-effects of temperature and CO2 pressure[END_REF][START_REF] Xu | Testing the cation-hydration effect on the crystallization of Ca-Mg-CO3 systems[END_REF]. Conversely, a recent study has reported magnesite precipitation in batch reactors at room temperature after 77 days of reaction with the aid of carboxylated polystyrene microspheres [START_REF] Power | Room temperature magnesite precipitation[END_REF]. Diluted ionic solutions (<0.1M) and microspheres coated with a high density of carboxyl groups at their surface allowed the binding and dehydration of Mg 2+ ions in solution, thereby minimizing the kinetic barrier and facilitating magnesite formation [START_REF] Power | Room temperature magnesite precipitation[END_REF].

However, the reaction mechanism and the nature of precipitating minerals between 1 and 77 days remain to be identified, and whether precipitation occurred via the formation of transient phases or by a direct nucleation event is unknown. Moreover, this method needs to be up-scaled to produce high-amounts of magnesite in reasonable time (24 hours). In order to overcome these limitations, the present study demonstrates magnesite precipitation at moderate temperature (60 and 90°C) by aqueous carbonation of magnesium hydroxide (Mg(OH)2) under anisobaric conditions (initial CO2 pressure = 50 bar). These conditions allow the production of high amounts of magnesite in only 15h at 90°C or 7 days at 60°C. Herein, NaOH was used as a CO2 sequestering agent and the ferric EDTA as a dehydration agent of Mg 2+ ions. Magnesium hydroxide was chosen because its engineered production from olivine and serpentine-rich materials was actively investigated for CO2 mineralization purpose [START_REF] Nduagu | Performance assessment of producing Mg(OH)2 for CO2 mineral sequestration[END_REF][START_REF] Madeddu | Extraction of Mg(OH)2 from Mg silicate minerals with NaOH assisted with H2O: implications for CO2 capture from exhaust flue gas[END_REF]. Magnesium oxide (MgO) and magnesium hydroxide (Mg(OH)2 may be produced from serpentine and other Mg-rich silicates. Both synthesized minerals have numerous industrial applications, and have been proposed as sinks to store anthropogenic carbon dioxide by transforming it into magnesium carbonate minerals [START_REF] Nduagu | Performance assessment of producing Mg(OH)2 for CO2 mineral sequestration[END_REF][START_REF] Madeddu | Extraction of Mg(OH)2 from Mg silicate minerals with NaOH assisted with H2O: implications for CO2 capture from exhaust flue gas[END_REF].

Materials and Methods

Magnesite precipitation using NaOH as sequestering agent of CO2

As already demonstrated in our group (e.g. [START_REF] Montes-Hernandez | Rapid precipitation of magnesite micro-crystals from Mg(OH)2-H2O-CO2 slurry enhanced by NaOH and a heat-ageing step (from 20 to 90°C)[END_REF][START_REF] Montes-Hernandez | Time-resolved in situ Raman spectroscopy of the nucleation and growth of siderite, magnesite and calcite and their precursors[END_REF]), the NaOH enhances the magnesite precipitation at 90°C via aqueous carbonation process of magnesium hydroxide with compressed CO2. An initial CO2 pressure of 50bar ensures an excess of CO2 with respect to Mg(OH)2 in the reactor and ideal gas condition. In the present study, two new experiments were performed at 90 and 27°C, respectively, and monitored by time-resolved in situ Raman spectroscopy as described in Montes-Hernandez and Renard, 2016 [START_REF] Montes-Hernandez | Time-resolved in situ Raman spectroscopy of the nucleation and growth of siderite, magnesite and calcite and their precursors[END_REF]. Herein, carbonate speciation and precipitated particles were monitored for 24h with a 1-minute spectral acquisition time. The Raman spectra were treated in order to estimate the position, full wide half maximum (FWHM) and integrated surface area as a function of time for specific stronger peaks in order to explain the reaction mechanism and kinetics of Mg carbonates precipitation and particularly magnesite (MgCO3).

Magnesite precipitation using NaOH and organic additives

Magnesite precipitation was also investigated at 60°C in the presence of three organic molecules (Aspartame, ferric EDTA, and citric acid tri-sodium salt), expecting a dehydration effect of Mg 2+ ions or a chelation effect. In these experiments, 15 g of Mg(OH)2, provided by Sigma-Aldrich with chemical purity of 99%, 20g of NaOH, 1 g of organic additive, and 500 mL of high-purity water were mixed in the reactor (total internal volume of 960 mL). The slurry was immediately dispersed by mechanical agitation (400 rpm) and gaseous CO2, provided by Linde Gas S.A., was injected at 50 bar into the reactor. About 3 minutes at 25°C were required to reach the pre-defined pressure.

The agitation speed was kept to 400 rpm using a rotor with two blades (Parr reactor) that ensured homogeneous dispersion of reacting and precipitating solids and fast dispersion of the injected CO2 in the system. Following injection, the system was heated to 60°C, the pH of the solution and the CO2 consumption (pressure drop) were monitored in-situ during mineral formation for 24, 72 or 168 hours.

At the end of the experiment, the residual CO2 was degassed from the reactor by opening the gas line valve for five minutes. The solid product was recovered by centrifugation and washed twice with ultrapure water and then was dried directly in the centrifugation flasks at 60 °C for 48 h. The dry solid products were stored in plastic flasks for subsequent characterization by Raman spectroscopy, Field Emission Gun Scanning Electron Microscopy (FESEM) and powder X-ray diffraction (XRD). All ten performed experiments are summarized in Table 1.

Ex situ characterization of precipitates

XRD analyses were performed using a Siemens D5000 diffractometer in Bragg-Brentano geometry, equipped with a theta-theta goniometer with a rotating sample holder. Diffraction patterns were collected using Cu kα1 (kα1=1.5406 Ǻ) and kα2 (kα2=1.5444 Ǻ) radiation in the range 2 = 10 -70°, with a step size of 0.04° and a counting time of 6 seconds per step. For highresolution imaging, the solid products were dispersed by ultrasonic treatment in absolute ethanol for five to ten minutes. One or two droplets of the suspension were then deposited directly on an aluminum support and coated with platinum. The morphology of the crystals was imaged using a Zeiss Ultra 55 FESEM with a maximum spatial resolution of approximately 1 nm at 15kV.

Calculation of production rate

The production rate of a given magnesium carbonate was calculated as follows: Prate = (λ*MolMg(OH)2*MMgCarbonate)/(tmax*Vreactor) where λ is the chemical conversion factor for Mg carbonate phases determined from Raman spectroscopy when peaks intensity is constant for a given time-interval. The value λ=1 is reached when the peak intensity for a given Mg carbonate is constant and only a single mineral is detected. MolMg(OH)2 is the initial amount (in mol) of Mg(OH)2 (complete transformation was determined from ex-situ XRD measurements in recovered solid products); MMgCarbonate is the molar mass of a given Mg carbonate; tmax is the time where only one mineral phase exists and the peak intensity is constant; Vreactor is the effective volume of the reactor which is equal to0.6L (runs 1-2) or 1L (runs 3-10). This calculation using time-resolved experimental measurements could allow a realistic extrapolation to pilot and/or industrial scale assuming roughly proportional dimensions and equivalent precipitation times.

Results and discussion

Magnesite precipitation at 90°C: Reaction mechanism and kinetics

Carbonation of Mg(OH)2 at 25°C leads the precipitation of nesquehonite, with the following global reaction:

Mg(OH)2 + CO2 + 2H2O → MgCO3•3H2O (1)
The successive events involved during magnesium hydroxide carbonation are displayed in Fig. 1.

Dissolved NaOH enhanced the rate and amount of sequestration of injected CO2 (initial PCO2 =50 bar). The carbon dioxide dissolved into interacting alkaline solution (CO2(gas) ↔ CO2(aq)) was rapidly dissociated into CO3 2-(CO2(aq) + 2NaOH → CO3 -2 + H2O + 2Na + ). A fraction of the carbonate ions was protonated after about 60 minutes (CO3 -2 + H + →HCO3 -) producing a pH change in the interacting solution, and simultaneously enhancing the dissolution of magnesium hydroxide (Mg(OH)2 → Mg 2+ + 2OH -). All these combined reactions led to the precipitation of nesquehonite (Mg 2+ + HCO3 -+ 3H2O → MgCO3.3H2O + H + ) with a nucleation induction time of 105 minutes. This mineral grew by continuous dissolution of magnesium hydroxide until complete consumption in the reactor. Nesquehonite remained stable in the interacting solution until the end of experiment (72 h). Ex-situ FESEM images revealed micrometric crystals of prismatic elongated morphology (Fig. SI-1). Time-resolved Raman measurements and ex-situ characterization of solid confirm that magnesite precipitation was inhibited by nesquehonite precipitation at 25°C. Conversely, magnesite formation was rapidly obtained at 90°C and only 15 h were required to produce highpurity magnesite (~6 kg/m 3 h) as monitored by Raman spectroscopy (Fig. 2). The global reaction summarizes the process:

Mg(OH)2 + CO2 → MgCO3 + H2O (2)

A complete aqueous carbonation reaction was obtained at 90°C exclusively when NaOH was used as the CO2 sequestering agent, in agreement with previous results [START_REF] Montes-Hernandez | Rapid precipitation of magnesite micro-crystals from Mg(OH)2-H2O-CO2 slurry enhanced by NaOH and a heat-ageing step (from 20 to 90°C)[END_REF]. In the present study, a more detailed reaction mechanism and kinetics are demonstrated from the time-resolved in-situ Raman spectroscopy measurements and all temporal reaction events are shown in Fig. 2 and Fig. SI-2.

Similar to the nesquehonite case, the aqueous carbon dioxide (CO2(gas) ↔ CO2(aq)) was rapidly dissociated into CO3 2-(CO2(aq) + 2NaOH → CO3 -2 + H2O + 2Na + ), but this reaction remained active only during the first 100 minutes. Then, carbonate ions were rapidly protonated, forming bicarbonate ions (CO3 -2 + H + →HCO3 -) that may complex with Mg 2+ , leading to a shift of the maximum of the Raman peak of HCO3 -from 1020 cm -1 (Fig. 1) to 1011 cm -1 (Fig. 2). After 150 minutes, aqueous carbon dioxide and bicarbonate ions were the dominant species in the reactor, which induced a significant pH change in the interacting solution as suggested from carbonate speciation in relation with pH (inorganic carbonate fraction vs pH diagram). Under these conditions, the dissolution of magnesium hydroxide (Mg(OH)2 → Mg 2+ + 2OH -) was enhanced, and the release of magnesium ions generated oversaturation states with respect to several magnesium carbonates. Consequently, the nucleation of hydromagnesite was detected in-situ after 60 minutes of reaction (first nucleation-event).

5Mg 2+ + 4HCO3 -+ 6H2O → Mg5(CO3)4(OH)2.4H2O + 6H + (3)
Hydromagnesite formed as a transient mineral phase that reached a maximum spectral intensity after 120 minutes. Then, this mineral dissolved in a destabilization processes through a decrease of spectral peak surface area (i.e., Fig. 3) progressively before the nucleation of magnesite that was detected after 240 minutes of reaction (second nucleation-event).

Mg 2+ + HCO3 -→ MgCO3 + H + (Nucleation) [START_REF] Berg | Analysis of Ultimate Fossil Fuel Reserves and Associated CO2 Emissions in IPCC Scenarios[END_REF] After this magnesite nucleation event, the growth of magnesite was mainly nourished by progressive dissolution of hydromagnesite. The temporal evolution of peak surface areas and Full Width Half Maximum (FWHM) for hydromagnesite and magnesite minerals (Figs. 3 and4)

suggest that this reaction included coupled dissolution-reprecipitation. Hydromagnesite was completely consumed after 13 h. An Ostwald repining process could explain the growth in the following two hours. Equilibrium was reached after 15 h of reaction, as demonstrated by the constant FWHM of magnesite after this time (Fig. 4). FESEM images revealed rhombohedral single crystals with sizes <5 µm (Fig. SI-3), in agreement with previous work [START_REF] Montes-Hernandez | Rapid precipitation of magnesite micro-crystals from Mg(OH)2-H2O-CO2 slurry enhanced by NaOH and a heat-ageing step (from 20 to 90°C)[END_REF].

Role of temperature and organic additives

Several complementary experiments were performed in order to assess the evolution of pH in-situ, the dehydration effect of organic additives around Mg ions, and the role of reaction temperature (Table 1, Fig. 5). For all of these experiments, the pH decreased from 12.4 to 9 in the first 10 minutes and then continued to decrease at a slower rate until stabilization to a value in the range 5.5-6 after 1 h of reaction. This result indicates that the pH was mainly controlled by inorganic carbonate speciation and CO2 pressure (Figs. SI-4 and 5), and that organic additives had a little or undetected influence. This result is in agreement with time-lapse Raman measurements where a protonation process of carbonate ions was also detected, indicating a pH change in the interacting solution (Figs. 1,2). Conversely, organic additive has significant effect on the texture (crystal size)

and structural water content of the mineral produced, as identified in recovered suspensions by Raman ex-situ measurements (Fig. 5). Hydromagnesite was the main mineral phase precipitated at 60°C for 24 h in the absence or presence of organic additive. However, both the mineral texture, measured by the Full Width Half Maximum (FWHM) of the largest Raman peak, and the structural water content, measured by the position of largest Raman peak, were slightly different with respect to the reference of the hydromagnesite precipitated in a solution free of additive. In addition, some traces of magnesite were detected after 24 h of reaction when ferric EDTA or citric acid tri-sodium salt were used. For the EDTA additive, slow hydromagnesite-to-magnesite transformation was detected and about 7 days were required to obtain high-purity magnesite at 60°C. Only nesquehonite was detected at 25°C in the presence of EDTA (Fig. 5). This result confirms that magnesite precipitation from the aqueous carbonation of magnesium hydroxide at room temperature was inhibited, or strongly retarded, by the precipitation of nesquehonite.

Environmental implications

Magnesite formation at room temperature (<30°C) from the aqueous carbonation of magnesium hydroxide remains a scientific challenge. This formation could make the magnesite precipitation an economical issue to store permanently the CO2 with important environmental advantages:

(1) reduce CO2 emissions from the industrial sector (e.g. steel and cement industry, coal-fired power),

(2) obtain magnesite-rich or high-purity magnesite materials with an aggregate value (e.g. fabrication of roadbed materials, bricks, granular fill, fire-retardant building material) at low or moderate temperature and reduced time (<24 h) and,

(3) use of mine solid wastes (e.g., mines in ultrabasic rocks) or widely available Mg-silicates as a magnesium source to capture CO2.

In practice, the residual alkaline-solution used during magnesite production could be recycled for future carbonation experiments or re-used in other chemical processes, but these options were not assessed in the present study.

In this context, the production of magnesite material as an effective solution to reduce the industrial CO2 emission may be a serious option at industrial scale as now proposed by Cambridge Carbon Capture (http://www.cacaca.co.uk/#news).

Conclusion

In the present study, we demonstrated that high-purity magnesite can be produced from the carbonation of magnesium hydroxide at a rate of about 6 kg/m 3 h, and thus a mineralization rate of CO2 into magnesite of about 3kg/m 3 h. Higher productions were estimated for hydromagnesite (120 kg/m 3 h) and nesquehonite (40 kg/m 3 h), but these minerals are thermodynamically less stable at Earth surface conditions than magnesite.

Our time-resolved Raman measurements allowed a detailed description of reaction mechanism and kinetics of carbonation of magnesium hydroxide in batch reactor conditions. This experimental setup offers new possibilities for investigating mineral condensation from ionic solutions and slurries, and for investigating other chemical reactions at the solid-fluid interfaces.

Figure 1 .

 1 Figure 1. Time-lapse Raman spectroscopy monitoring of the aqueous carbonation of magnesium

Figure 2 .

 2 Figure 2. Time-lapse Raman spectroscopy monitoring of the aqueous carbonation of magnesium

Figure 3 .

 3 Figure 3. Kinetics of nucleation and growth of hydromagnesite and magnesite during aqueous

Figure 4 .

 4 Figure 4. Crystal growth mechanism of magnesite (blue) at 90°C, nourished by hydromagnesite

Figure 5 .

 5 Figure 5. pH measured in-situ during aqueous carbonation of magnesium hydroxide in eight

Table 1 .

 1 Experiments of magnesium carbonates precipitation from Mg(OH)2-NaOH-H2O-CO2354 slurry under anisobaric conditions (initial CO2 pressure of 50bar).

	355
	Run Temperature	Additive	Real-time	Exp.	Mineral	Final mineral
			monitoring	Duration	transient	phase(s)
	(°C)	(1g)
				(h)	phase(s)
	1	-	Raman	72	none	nesquehonite
			spectroscopy
	2	-	Raman	24	hydromagnesite	magnesite
			spectroscopy
	3	-	pH probe	24	N/A	Magnesite and
						residual
						hydromagnesite
	4	-	pH probe	24	N/A	hydromagnesite
	5	citric acid	pH probe	24	N/A	hydromagnesite
	6	aspartame	pH probe	24	N/A	hydromagnesite
	7	EDTA	pH probe	24	N/A	hydrogmagnesite
	8	EDTA	pH probe	72	N/A	magnesite and
						hydromagnesite
	9	EDTA	pH probe	168	N/A	magnesite
	10	EDTA	pH probe	168	N/A	nesquehonite
	356

Acknowledgements

The authors acknowledge funding from the French National Centre for Scientific Research (CNRS). We thank Nathaniel Findling for technical assistance.


German Montes-Hernandez
email: german.montes-hernandez@univ-grenoble-alpes.fr

Synthesis of Magnetite, Ceria and Magnetite-Ceria Materials by Calcination of Nanostructured Precursor-Minerals

Keywords: Magnetic materials, Composites, Crystallization, Electron microscopy

The present short communication reports an original experimental calcination method to synthesize magnetic materials with high thermal stability such as magnetite (Fe3O4) with typical spinel and atypical crystal shape, sub-micrometric rounded crystals of ceria (CeO2) and magnetiteceria composites with varied shape and size of crystals; these latter depending on the nature of mineral precursors (goethite, siderite or ferrihydrite). Herein, it was demonstrated that cooperative redox reactions and simple vacuum can be used to synthesize magnetic composite materials by calcination of nanostructured mineral precursors. In this way, bastnäsite mineral (CeCO3F) is a powerful reducing agent to synthesize magnetite from reductive dehydration of ferric oxyhydroxides.

Introduction

Synthetic ceria (CeO2) and magnetite (Fe3O4) are crucial oxides in many industrial and/or medical applications related to their extraordinary chemical properties (acid-base and oxidation-reduction behavior), thermal stability and oxygen mobility [START_REF] Bumajdad | Cerium oxide nanoparticles prepared in self-assembled systems[END_REF][START_REF] Leino | The influence of various synthesis methods on the catalytic activity of cerium oxide in one-pot synthesis of diethyl carbonate starting from CO2, ethanol and butylene oxide[END_REF][START_REF] Gokon | Comparative study of activity of cerium oxide at thermal reduction temperatures of 1300-1550 °C for solar thermochemical two-step water-splitting cycle[END_REF][START_REF] Mosayebi | Synthesis, functionalization, and design of magnetic nanoparticles for theranostic applications[END_REF][START_REF] Usman | Magnetite and green Rust: synthesis, properties, and environmental applications of mixed-valent iron minerals[END_REF][START_REF] Jolivet | Iron oxide chemistry. From molecular clusters to extended solid networks[END_REF]. They have found their applications in catalysis (photo-), luminescent materials, fuel cell, free radical scavenger, gas sensor, cosmetic material, optical additives, polishing materials, water splitting, ceramic pigments, biomedicine, magnetic storage media, etc. [START_REF] Bumajdad | Cerium oxide nanoparticles prepared in self-assembled systems[END_REF][START_REF] Leino | The influence of various synthesis methods on the catalytic activity of cerium oxide in one-pot synthesis of diethyl carbonate starting from CO2, ethanol and butylene oxide[END_REF][START_REF] Gokon | Comparative study of activity of cerium oxide at thermal reduction temperatures of 1300-1550 °C for solar thermochemical two-step water-splitting cycle[END_REF][START_REF] Mosayebi | Synthesis, functionalization, and design of magnetic nanoparticles for theranostic applications[END_REF][START_REF] Usman | Magnetite and green Rust: synthesis, properties, and environmental applications of mixed-valent iron minerals[END_REF][START_REF] Jolivet | Iron oxide chemistry. From molecular clusters to extended solid networks[END_REF]. In general, magnetite or ceria are independently used; however, recently their association as magnetite-ceria composites have been also explored in catalytic reactions, for example, in the degradation of organic molecules [START_REF] Gan | Degradation of Pantoprazole in aqueous solution using magnetic nanoscaled Fe3O4/CeO2 composite: Effect of system parameters and degradation pathway[END_REF], in Fenton reactions [START_REF] Xu | Magnetic Nanoscaled Fe3O4/CeO2 Composite as an Efficient Fenton-Like Heterogeneous Catalyst for Degradation of 4-Chlorophenol[END_REF], in multicomponent redox reactions [START_REF] Gawande | Magnetically recyclable magnetite-ceria (Nanocat-Fe-Ce) nanocatalystapplications in multicomponent reactions under benign conditions[END_REF] and in the dephosphorylation of phosphopeptides [START_REF] Min | Magnetite/ceria-codecorated titanoniobate nanosheet: A 2D catalytic nanoprobe for efficient enrichment and programmed dephosphorylation of phosphopeptides[END_REF]. In this way, the improving of existing methods and/or developing innovative routes to obtain wellcontrolled crystal shapes and sizes remain important challenges in materials science. The present short communication reports an original calcination method to synthesize magnetite, ceria and magnetite-ceria composites with high thermal stability and probably with relevant catalytic properties by using dynamic vacuum (≈5x10 -6 mbar) and bastnäsite (CeCO3F) nanostructured mineral as reducing agents. In fact, four nanostructured minerals goethite (FeO(OH)), siderite (FeCO3), ferrihydrite 6-lines and bastnäsite (CeCO3F) were synthesized at low T (<95°C), methods already published by my group [START_REF] Hajji | Arsenite and chromate sequestration onto ferrihydrite, siderite and goethite nanostructured minerals: Isotherms from flow-through reactor experiments and XAS measurements[END_REF][START_REF] Montes-Hernandez | Synthesis of Ceria (CeO2 and CeO2-x) Nanoparticles via Decarbonation and Ce(III) Oxydation of Synthetic Bastnäsite (CeCO3F[END_REF][START_REF] Montes-Hernandez | Fast precipitation of acicular goethite from ferric hydroxide gel under moderate temperature (30 and 70 C degrees)[END_REF][START_REF] Montes-Hernandez | Time-resolved in situ Raman spectroscopy of the nucleation and growth of siderite, magnesite and calcite and their precursors[END_REF]. Then the obtained nanostructured minerals are used as powdered precursors in order to synthesize magnetite from reductive dehydration of goethite or from oxidative decarbonation of siderite, ceria from oxidative decarbonation of bastnäsite and magnetite-ceria composites from cooperative and/or competitive redox reactions. Mineral composition and crystal shape and size were mainly determined by XRD and FESEM.

Materials and Methods

Synthesis of mineral precursors and nano-magnetite reference

Goethite, siderite, ferrihydrite and bastnäsite minerals were synthesized by using already published methods [START_REF] Hajji | Arsenite and chromate sequestration onto ferrihydrite, siderite and goethite nanostructured minerals: Isotherms from flow-through reactor experiments and XAS measurements[END_REF][START_REF] Montes-Hernandez | Synthesis of Ceria (CeO2 and CeO2-x) Nanoparticles via Decarbonation and Ce(III) Oxydation of Synthetic Bastnäsite (CeCO3F[END_REF][START_REF] Montes-Hernandez | Fast precipitation of acicular goethite from ferric hydroxide gel under moderate temperature (30 and 70 C degrees)[END_REF][START_REF] Montes-Hernandez | Time-resolved in situ Raman spectroscopy of the nucleation and growth of siderite, magnesite and calcite and their precursors[END_REF]. In supplementary information, only the overall reaction of synthesis of precursor and magnetite reference, including a basic characterization by XRD and FESEM are provided

(Figure SI-1).

Synthesis of magnetite, ceria and magnetite-ceria composites

Magnetite from oxidative decarbonation of siderite 2g of dry siderite placed in an alumina ceramic crucible were calcinated at 500°C under secondary vacuum (≈5x10 -6 mbar) for 5h by using a quartz tubular reactor. A heating rate of 30°C/min was performed in all experiments. At the end of experiment, the calcinated product were cooled under dynamic vacuum at room temperature (~19°C).

Magnetite from reductive dehydration of goethite

1g of dry goethite and 1g of dry bastnäsite placed independently in an alumina ceramic crucible (e.i. without solid-solid contact) were calcinated at the same above conditions. In this case, the bastnäsite transformation into ceria (CeO2) improves the reducing conditions in the reactor allowing complete goethite transformation into magnetite.

Ceria from oxidative decarbonation of bastnäsite

2g of dry bastnäsite placed in an alumina ceramic crucible were calcinated at the same above conditions.

Synthesis Fe3O4-CeO2 composites

Three different binary mineral-precursor mixtures (ferrihydrite-bastnäsite, goethite-bastnäsite and siderite-bastnäsite) were manually prepared by using equivalent weighs in an agate mortar and mixed by a pestle. Then, 2g of each mineral mixture were placed in an alumina ceramic crucible and calcinated at the same above conditions.

All calcinated solid products were manually recovered and stored in plastic flasks for subsequent characterization by XRD and FESEM (see supplementary information).

Results and Discussion

All main results are summarized in Figures 1 to 3

The formation of magnetite is improved when bastnäsite mineral is used as supplementary reducing agent in the reactor (see Figure SI-2). In such case, the Ce(III) oxidation to Ce(IV) initially contained in cerium carbonate creates a most reducing atmosphere into the reactor during calcination process. FESEM images have revealed two crystals shapes of magnetite, typical spinel shape and acicular crystals; letter shape was probably inherited from original goethite shape (Figure 1).

Magnetite formation from siderite decarbonation

3FeCO3 + 0.5O2  Fe3O4 + 3CO2 (2)
The constrained dynamic vacuum was enough to favor the magnetite formation rather than hematite (Fe2O3). Assuming that water is also present in the system (residual water in vacuum atmosphere), the following oxidative reaction (3FeCO3 + H2O  Fe3O4 + 3CO2 + H2) could also contribute to magnetite formation. Surprisingly, synthesize magnetite have conserved the initial shape of siderite spherical aggregates as revealed by FESEM, however, the magnetite micrometric (<3µm) spherical agglomerates constituted by magnetite nanoparticles are now observed (Figure 1).

Ceria formation from bastnäsite decarbonation

2CeCO3F + O2  2CeO2 + 2CO2 + F2 (3)
This reaction can be auto-enhanced by in situ produced flour than can react with residual water in the system to form additional oxidants (e.g. F2 + H2O  0.5O2 + 2HF). However, the XRD has also revealed cerium oxide fluoride (CeOF) that is generally a transient phase during ceria formation from oxidative decarbonation of bastnäsite (CeCO3F  CeOF + CO2) with a short lifetime under air atmosphere as already demonstrated [START_REF] Montes-Hernandez | Synthesis of Ceria (CeO2 and CeO2-x) Nanoparticles via Decarbonation and Ce(III) Oxydation of Synthetic Bastnäsite (CeCO3F[END_REF]. Finally, FESEM images have revealed rounded ceria nanoparticles with high agglomeration degree with respect to ceria formed under air atmosphere (see Figure 2).

Magnetite-Ceria composite from ferrihydrite-bastnäsite mixture 3Fe2O3.2(FeO(OH)).nH2O  4Fe3O4 + O2 + (n+3)H2O (4a)

2CeCO3F + O2  2CeO2 + 2CO2 + F2 (4b)
A complete transformation of ferrihydrite into magnetite was particularly possible by means of cerium oxidation contained in bastnaesite. This means that a cooperative double-redox reaction exists: Fe 3+ /Fe 2+ and O 2-/O2 for magnetite formation and Ce 3+ /Ce 4+ , O2/O 2-and F -/F2 for ceria formation. In terms of mineral composition, the XRD has revealed magnetite and ceria as major phases and a minor proportion of cerium oxide fluoride (CeOF) and sodium fluoride (NaF) were also detected in final products, indicating an incomplete oxidation of cerium initially contained in bastnäsite mesocrystals (see XRD patterns in Figure 3). FESEM images have revealed homogeneous mixture of micrometer magnetite crystal (<2µm) with spinel shape and submicrometric ceria crystals with rounded shape. Ceria particles adhered onto magnetite crystals or forming aggregates.

Magnetite-Ceria composite from goethite-bastnäsite mixture

3FeOOH  Fe3O4 + 0.25O2 + 1.5H2O (5a) 2CeCO3F + O2  2CeO2 + 2CO2 + F2 (5b)
This cooperative double redox reaction is identical to ferrihydrite-bastnäsite system, however, different crystal shape and size and different water content exist between goethite and ferrihydrite (see Figure SI-1). As expected, magnetite-ceria composite was synthesized as revealed from XRD patterns. In this case, sub-micrometric magnetite crystals with spinel shape are homogeneously mixed with nanometric ceria rounded-crystals having high agglomeration and/or aggregation degree as observed in the FESEM image (Figure 3).

Magnetite-Ceria composite from siderite-bastnäsite mixture

3FeCO3 + 0.5O2  Fe3O4 + 3CO2 (6a) 2CeCO3F + O2  2CeO2 + 2CO2 + F2 (6b)
Contrary to two above cooperative redox systems, here, an oxidative-decarbonation competition exists as illustrated in reactions 6a and 6b. Despite this competition, the magnetite-ceria composite was successfully synthesized as revealed by XRD (Figure 3). However, a more reducing environment in the reactor was created because a higher proportion of cerium oxide fluoride (CeOF) and also iron oxide (FeO) were detected; both mineral phases implying only decarbonation process without oxidation, possible only in high reducing systems. FESEM images have revealed sub-micrometric magnetite and ceria crystals with rounded shape and with high agglomeration degree (see Figure 3 and Figure SI-3).

Conclusion

Magnetite with typical spinel and atypical crystal shape, sub-micrometric rounded crystals of ceria and magnetite-ceria composites with varied shape and size of crystals were synthesized by calcination under dynamic secondary vacuum and using bastnäsite as complementary solid reducing agent.

  concerning particularly FESEM images and DRX patterns of calcinated products. Based on this conventional solid characterization for precursors (Figure SI-1) and calcinated products, an overall redox reaction for each investigated scenario is suggested as follows: Magnetite formation from goethite 3FeOOH  Fe3O4 + 0.25O2 + 1.5H2O

Figure 1 .

 1 Figure 1. XRD patterns for three magnetite synthesized for three different reaction pathways and

Figure 2 .

 2 Figure 2. XRD patterns for two ceria synthesized under air atmosphere (reference) and under

Figure 3 .

 3 Figure 3. XRD patterns for three magnetite-ceria composite materials synthesized by calcination

Acknowledgements

The authors are grateful to CNRS and UGA for providing funding support. IPAG is grateful for allowing the access to calcination experiments. We thank Nathaniel Findling, Olivier Brissaud, Pierre Beck and Eric Quirico for their technical assistance.


S Chinnayya

D A Xu

Lacoste

K P Chatelain
email: karl.chatelain@kaust.edu.sa

R Mével
email: mevel@mail.tsinghua.edu.cn

J Melguizo-Gavilanes
email: josue.melguizo-gavilanes@cnrs.pprime.fr

A Chinnayya

S Xu
email: slxu@tsinghua.edu.cn

D A Lacoste
email: deanna.lacoste@kaust.edu.sa

King Abdullah

Effect of Incident Laser Sheet

Keywords: detonation front visualization, OH-planar laser induced fluorescence (OH-PLIF), spectroscopic modeling, LIF model

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Introduction

Planar Laser-Induced Fluorescence of OH radical (OH-PLIF) is a powerful technique used to characterize the structure of the reaction zone during the propagation of weakly [START_REF] Austin | The role of instability in gaseous detonation[END_REF][START_REF] Pintgen | Laser-optical visualization of detonation structures[END_REF] and highly unstable detonations [START_REF] Pintgen | Direct observations of reaction zone structure in propagating detonations[END_REF][START_REF] Austin | Reaction zones in highly unstable detonations[END_REF]. This technique has also been employed to characterize the reinitiation mechanism of a highly unstable detonation in a bifurcation channel [START_REF] Li | A study of detonation re-initiation through multiple reflections in a 90-degree bifurcation channel[END_REF][START_REF] Li | Reflected re-initiation of gaseous detonation[END_REF]. In weakly unstable detonations, the regular and smooth shock front and the related gas dynamics result in a well defined and regular keystone-like structure of the reaction zone. The combustion is essentially driven by the shock-induced autoignition mechanism. In highly unstable detonations, the keystone shape of the reaction zone, although still visible, appears much less sharp. The reaction front is wrinkled and demonstrates small-scale variations in intensity. Pockets of low fluorescence intensity are visible behind the detonation front. The combustion is then driven by both shock-induced ignition and diffusioncontrolled burning [START_REF] Radulescu | A detonation paradox: Why inviscid detonation simulations predict the incorrect trend for the role of instability in gaseous cellular detonations? Combust[END_REF]. To enable direct comparison between the experimental PLIF images and 2D numerical simulations, Mével et al. [START_REF] Mével | Application of a laser induced fluorescence model to the numerical simulation of detonation waves in hydrogen-oxygen-diluent mixtures[END_REF][START_REF] Mével | Detonation in hydrogen-nitrous oxide-diluent mixtures: An experimental and numerical study[END_REF] developed a LIF model to obtain numerical PLIF images. They showed that the PLIF images become increasingly less representative of the OH field further behind the shock front. Under most detonation conditions, the LIF process is within the optically-thick regime due to the high OH concentrations. In other words, this optically-thick regime corresponds to the strong absorption of the incident laser light by the high OH concentration at the beginning of the reaction zone, which makes the zones of high OH concentration (away from the front) less visible due to the attenuation of the laser light as it travels through the medium. Such an effect was also highlighted by Mével under shock tube/pulsed laser-induced fluorescence conditions [START_REF] Mével | Optical regime diagram of the shock tube/pulsed laser-induced fluorescence imaging technique[END_REF]. In [START_REF] Mével | Optical regime diagram of the shock tube/pulsed laser-induced fluorescence imaging technique[END_REF], three regimes were identified depending on the characteristics of the optical path: (i) optically thin; (ii) optically thick; and (iii) non-physical. Although the study of Mével et al. [START_REF] Mével | Application of a laser induced fluorescence model to the numerical simulation of detonation waves in hydrogen-oxygen-diluent mixtures[END_REF] examined in detail the effect of various parameters on the PLIF intensity, they have focused on a single laser orientation, the frontal, for which the laser sheet propagation is opposed to the detonation wave propagation. However, other studies [START_REF] Eder | Brennverhalten schallnaher und überschallschneller wasserstoff-luft flammen[END_REF][START_REF] Lee | Deflagration to detonation transition processes by turbulence-generating obstacles in pulse detonation engines[END_REF][START_REF] Wang | Study on reaction zone structure of gaseous detonation wave by planar laser induced fluorescence technique[END_REF] employed a different experimental configuration, the transverse, for which the laser sheet propagation is perpendicular to the detonation wave propagation. This orientation might enable observation of regions of high OHconcentration far downstream of the detonation front. The goal of the present study is to investigate the effect of the incident laser light sheet orientation on the OH-PLIF imaging of a detonation wave reaction zone. For the purpose of this contribution, we limited our investigation to a weakly unstable detonation wave in hydrogen-oxygen mixtures highly diluted with argon to enable direct comparison with the experimental OH-PLIF images available in the literature. An updated LIF model was developed and validated using steady one-dimensional (1D) and unsteady two-dimensional (2D) numerical simulations. A comparison of two numerical OH-PLIF images obtained with the aforementioned laser orientations is performed to highlight the benefits and drawbacks of the two laser orientations.

Numerical simulation methods

Laser induced fluorescence model

Similar to Mével et al. [START_REF] Mével | Application of a laser induced fluorescence model to the numerical simulation of detonation waves in hydrogen-oxygen-diluent mixtures[END_REF], we employed the 3-level LIF model of Bessler et al. [START_REF] Bessler | A versatile modeling tool for nitric oxide lif spectra[END_REF]. In the linear regime and at steady-state, the fluorescence intensity for one pumped electronic transition is given by Eq. 1,

F ∝ f B Γ I 0 ν I b N OH B 1 Q � A i , (1)
where f B is the Boltzmann fraction, Γ is the dimensionless overlap integral, I 0 ν is the normalized spectral laser irradiance, I b is a dimensionless factor accounting for the light sheet absorption, N OH is the OH radical number density, B is the Einstein B coefficient, Q is the quenching rate, and A i are the Einstein A coefficients.

The parameters in Eq. 1 are calculated as described in Mével et al. [START_REF] Mével | Application of a laser induced fluorescence model to the numerical simulation of detonation waves in hydrogen-oxygen-diluent mixtures[END_REF] with five main changes: (i) different laser sheet orientations with respect to the detonation front can now be considered; (ii) the collisional broadening (Δν c ) is calculated (more accurately) using Eq. 2,

Δν c = P � A X A σ 2 AB � 8 πµ AB kT � 1/2 ( 2
)
where P is the pressure, T is the temperature, k is the Boltzmann's constant, X A is the mole fraction of species A, and σ AB and µ AB correspond, respectively, to the optical collision diameter and the reduced mass between species A with the fluorescent species (B = OH); (iii) the absorption lineshape function is calculated using a Voigt profile as described in [START_REF] Hanson | Spectroscopy and optical diagnostics for gases[END_REF]; (iv) when the shifts apply (see section 3.2), the linecenter shift of the absorption lines is calculated considering both the pressure (δ P ) and the Doppler shift (δ D ), as described in [START_REF] Hanson | Spectroscopy and optical diagnostics for gases[END_REF][START_REF] Gordon | The HI-TRAN2016 molecular spectroscopic database[END_REF]. For any absorption line i, the pressure shifted absorption line is calculated using Eq. 3 and the pressure shift is obtained δ Pi = ν i,shiftedν i,0 ,

ν i,shifted = ν i,0 + P � A X A δ A,T ref � T ref T � M (3)
where ν i,0 and ν i,shifted correspond to the initial and the shifted absorption linecenter, respectively, for a specific mixture in given temperature and pressure conditions; δ A,T ref and M are the pressure shift parameters associated to a given species A (at a given mole fraction X A ) at a reference temperature (T ref ). The Doppler shift δ D is calculated using Eq. 4,

δ D ν 0 = u c (4)
where δ D and ν 0 are respectively the shift value and the initial absorption linecenter, u and c are respectively the gas mean velocity in the laser direction and the speed of light. The updated LIF model also (v) dynamically considers the contribution of the absorption lines spectrally close to the laser linecenter (± 0.25 nm). The importance of these adjacent lines is strongly dependent on the experimental conditions and the position of the laser linecenter. Here, five transitions are considered P 1 (5), Q 21 (9), Q 2 (8), Q 1 (9), Q 12 (8) (shown in dashed lines in Fig. 1) whereas Mével et al. [START_REF] Mével | Application of a laser induced fluorescence model to the numerical simulation of detonation waves in hydrogen-oxygen-diluent mixtures[END_REF] used only Q 2 (8), Q 1 (9). This more complex approach is justified by the higher initial pressure used by Wang et al. [START_REF] Wang | Study on reaction zone structure of gaseous detonation wave by planar laser induced fluorescence technique[END_REF] than that of Austin et al. [START_REF] Austin | Reaction zones in highly unstable detonations[END_REF]. The contribution of the adjacent absorption lines is illustrated in Fig. 1 for conditions corresponding to the von Neumann (vN) and the Chapman-Jouguet (CJ) states. At the von Neumann state, the calculated absorption lineshape is 16% higher, at the laser linecenter, when five lines are considered instead of two. This difference reduces to 4% at the CJ state. A more detailed evolution of the Voigt profile along the detonation front is presented in Appendix 1.

The dimensions of the laser sheet and the Gaussian spatial distribution of the laser energy [START_REF] Thiery | Theoretical and experimental intensity analysis of laser light sheets for flow visualization[END_REF] are taken into account to accurately compare the experimental and simulated LIF signals for each validation case. Additionally, the curvature of the detonation front is corrected to consider the non-homogeneous optical path in the 1D simulations (ZND). This correction reconstructs the (vertical) optical path, considering a pile of ZND calculations that have the same (vertical) thickness as observed experimentally, to obtain the correct laser absorption. For each ZND calculation, the detonation front is shifted from each other by the offset observed in the experimental image. This correction cannot be applied on the 2D validation, as the curvature is determined by the simulation.

Reaction Model

The reaction model employed for all the simulations is the reaction model of Mével et al. [START_REF] Mével | Hydrogen-nitrous oxide delay times: Shock tube experimental study and kinetic modelling[END_REF]. It is composed of 9 chemical species (including Ar) and 29 reversible reactions. It has been extensively validated for different hydrogen-oxidizer mixtures and has demonstrated good predictive capabilities for a wide range of experimental conditions including detonation relevant conditions [START_REF] Mével | Fundamental combustion properties of oxygen enriched hydrogen/air mixtures relevant to safety analysis: Experimental and simulation study[END_REF][START_REF] Davidenko | Numerical study of the detonation structure in rich H 2 -NO 2 /N 2 O 4 and very lean H 2 -N 2 O mixtures[END_REF][START_REF] Gallier | Detonation wave diffraction in H 2 -O 2 -Ar mixtures[END_REF].

Detonation models

The steady 1D detonation simulations are performed using a ZND code implemented in CHEMKIN-II. It is based on the work of Shepherd [START_REF] Shepherd | Chemical kinetics of hydrogen-air-diluent detonations[END_REF] and is equivalent to the ZND code available within the Shock and Detonation Toolbox implemented with Cantera [START_REF] Browne | Numerical solution methods for shock and detonation jump conditions[END_REF] of application of this ZND code can be found in [START_REF] Davidenko | Numerical study of the detonation structure in rich H 2 -NO 2 /N 2 O 4 and very lean H 2 -N 2 O mixtures[END_REF][START_REF] Mével | Etude de mécanismes cinétiques et des propriétés explosives des systèmes hydrogène-protoxyde d'azote et silane-protoxyde d'azote : application à la sécurité industrielle[END_REF][START_REF] Mével | Structure of detonation propagating in lean and rich dimethyl ether-oxygen mixtures[END_REF].

The unsteady 2D simulations are performed using an inviscid formulation with detailed chemistry with an in-house code RESIDENT (REcycling mesh Simulation of DEtonations). Particulars about the numerical methods used, spatial and temporal discretizations as well as the parallelization methodology can be found in [START_REF] Reynaud | A computational study of the interaction of gaseous detonations with a compressible layer[END_REF][START_REF] Taileb | Chemistry Modeling Effects on the Interaction of a Gaseous Detonation with an Inert Layer. 27th International Colloquium on the Dynamics of Explosions and Reactive Systems[END_REF]. Briefly, we use operator splitting to couple the hydrodynamics to the chemistry together with directional splitting, along with a ninth-order monotonicity preserving interpolation in space, and a third order explicit Runge-Kutta in time. The integration of the chemical source terms follows the methodology described in [START_REF] Savard | A computationally-efficient, semi-implicit, iterative method for the time-integration of reacting flows with stiff chemistry[END_REF] to avoid being limited by the smallest time scales dictated by the chemistry. Although this method was proposed in the context of turbulent simulations, it seems to perform efficiently for detonations as well. Simulations are conducted in the laboratory frame using 400 processors and a fixed squared domain of 40 mm. A sliding window technique [START_REF] Sow | On the viscous boundary layer of weakly unstable detonations in narrow channels[END_REF] is used to keep the propagating detonation within the computational domain at all times. A uniform mesh resolution of Δ x = Δ y = 10 µm is used in the 2D simulations, which corresponds to a ratio of Δ i /Δ x ∼ 20 [START_REF] Sharpe | Transverse waves in numerical simulations of cellular detonations[END_REF], where Δ i is the induction zone length, defined as the distance from the leading shock to maximum thermicity. Increasing the resolution did not result in changes in the numerically predicted cell size.

Validation methodology

To compare the experimental results with the steady 1D simulations, 1D LIF intensity profiles are extracted from the experimental PLIF images. The post-processing sequence is illustrated in Fig. 2 and comprises: (i) defining subdomains of interest based on the detonation front structure; (ii) normalizing the profile in this subdomain; (iii) performing a vertical averaging of the signal to get the 1D profile. These experimental 1D fluorescence profiles are compared with the ZND OH profile and the simulated fluorescence intensity profile.

The 2D validation of the model relies on a comparison of the experimental images and a 2D synthetic PLIF image following the methodology described in Mével et al. [START_REF] Mével | Application of a laser induced fluorescence model to the numerical simulation of detonation waves in hydrogen-oxygen-diluent mixtures[END_REF]. As performed with the 1D validation, this synthetic PLIF image is calculated from the 2D field of OH using the LIF model.

Results and discussion

Validation using steady 1D simulation

Frontal laser orientation Figure 3 presents two validation cases of the present LIF model with the experimental results from Austin [START_REF] Austin | The role of instability in gaseous detonation[END_REF] that uses a frontal laser orientation. The present LIF model reproduces the experimental 1D profiles for all the areas investigated. From this comparison and the results obtained with other areas not presented here, it can be concluded that the modifications made to the LIF model does not degrade the overall agreement between the experimental and calculated profiles for the frontal orientation, obtained previously [START_REF] Mével | Application of a laser induced fluorescence model to the numerical simulation of detonation waves in hydrogen-oxygen-diluent mixtures[END_REF].

Transverse laser orientation

Figure 4 presents two validation cases of the present LIF model with the experimental results from Wang [START_REF] Wang | Study on reaction zone structure of gaseous detonation wave by planar laser induced fluorescence technique[END_REF], which used a transverse laser orientation. The two areas selected aim to represent conditions for short and long optical path (vertically), respectively.

The experimental 1D LIF signal obtained with the transverse laser orientation is not representative of the X OH profile and the LIF signal decreases rapidly after the detonation front, similar to the frontal orientation. This decrease seems induced by the experimental setup, that uses a relatively narrow laser sheet (24 mm) for which only half of the sheet illuminates the reaction front. The other half of the sheet travels through the fresh gases located ahead of the detonation front.

The base numerical LIF signal (referred to as Model with a solid red line in Figs. 4b and4c) does not seem to be able to reproduce the overall experimental shape. Eventhough these results include the following effects: (i) the non-homogeneous optical path, (ii) the spatial distribution of the laser energy, and (iii) the curvature of the detonation front (by shifting the position of the detonation front), the saturation of the experimental images has been neglected. To mimic experimental observations, this saturation is simulated (referred to as Model sat. with a green solid line) by amplifying the LIF signal and clipping the maximum value to 1. The agreement between the experimental and the modeled LIF signals (Figs. 4b and4c) is significantly improved by accounting for the saturation, notably the double peak is well reproduced in c). Additional validation cases present similar features and are presented in Appendix 2. Observed in most of the area with long (vertical) optical paths, the presence of this double peak is mainly due to the curvature of the detonation and the vertical laser orientation, which produces a non-monotonic energy profile distribution along the detonation front axis (horizontal). The 1D fluorescence profile for area 2 in Fig. 4c can be characterized by three regions: (i) for a short distance behind the leading shock (≤ 1 mm), the fluorescence signal is at its maximum value, which is due to the high laser intensity reaching this location, as the laser sheet travels through fresh gases only (located vertically above area 2); (ii) the second fluorescence peak (near 5 mm) is smaller than the first one, due to the attenuated laser energy received by the OH molecules at this specific (horizontal) distance behind the leading shock. The double peak shape seems more pronounced in the present conditions due to the narrow laser sheet, which induces a strong fluorescence decay beyond 6 mm behind the leading shock. (iii) the local fluorescence minimum (near 2 mm), located between the two fluorescence peaks, is due to a lower laser energy at this specific location, compared to both (i) and (ii). This lower laser energy is due to the high OH density pockets in the previous areas located above vertically (or for shorter optical paths). It is noted that part of the difference of width between the experimental and the simulated signals for area 1 is due to the edge of the optical windows (which is noticeable with the rounded shape at the top of Fig. 4a), which obscures the experimental signal at this location.

Many aspects of the imaging system had to be included in the modeling to obtain qualitative agreement with the experimental data. To the best of our knowledge, all the images currently available in the literature [START_REF] Eder | Brennverhalten schallnaher und überschallschneller wasserstoff-luft flammen[END_REF][START_REF] Lee | Deflagration to detonation transition processes by turbulence-generating obstacles in pulse detonation engines[END_REF] obtained with the transverse laser orientation show some degree of saturation, hence no further validation can be performed. Since some of these aspects are difficult to quantify in the present validation data, additional experimental data are required to better validate the model. New experimental data must be obtained with OH-PLIF images free of saturation and with a known spatial distribution of the incident laser energy.

Effect of the absorption line shift

Due to the high pressure and the high flow velocity involved in detonations, both the pressure and the Doppler line shifts, denoted δ P and δ D , are expected to be nonnegligible. This section aims to quantify these values along the detonation front and to identify their relevance to reproduce the LIF signals. Only Austin's conditions can be used to investigate these effects, as δ D = 0 for the transverse laser orientation.

Figure 5a presents the evolution of both shifts and the total linecenter shift δ Tot. along the detonation for a single absorption line (Q 12 [START_REF] Mével | Application of a laser induced fluorescence model to the numerical simulation of detonation waves in hydrogen-oxygen-diluent mixtures[END_REF]). Similar trends are obtained with the other absorption lines. Although the Doppler line shift δ D is important in such high speed flow, with a relative contribution from 80 to 85% along the detonation, the δ Tot. remains low at this condition (δ Tot. < 1.5 pm), as presented in Fig. 5a. In Fig. 5b, the experimental 1D LIF profile is compared with three different simulated LIF profiles. In the first one (Model no shift) none of the absorption line shifts are considered; in the second one (Model + δ P ), only the pressure shift is included; while in the third one (Model + δ P+D ) both (the Doppler and the pressure shifts) are included. For this condition, the pressure and the Doppler shift have a negligible and limited (a 3.5 % increase of the fluorescence signal in average) effect on the overall fluorescence signal, respectively. As observed in Fig. 5a, the low δ Tot. is mainly due to the low pressure conditions used in the validation cases from Austin [START_REF] Austin | The role of instability in gaseous detonation[END_REF]. However, similar conclusions (δ Tot. < 1 pm) can be drawn for the conditions from Wang [START_REF] Wang | Study on reaction zone structure of gaseous detonation wave by planar laser induced fluorescence technique[END_REF], obtained at higher initial pressure (P 1 = 45 kPa) but with a transverse laser orientation, for which δ D = 0 and δ P < 1 pm. Further discussions on the absorption line changes as a function of the experimental conditions are presented in Appendix 3.

As presented in Eq. 4, the δ D must be calculated with care as it can be either zero (transverse laser orientation), have the same sign as the δ P (frontal orientation, meaning laser light propagating opposite to the flow), have the opposite sign as that of δ P which can induce a shift to the UV in specific conditions (dorsal laser orientation, meaning laser light propagating in the same direction as the flow).

Unsteady 2D simulation

Experimental-numerical comparison of the 2D PLIF signals Figure 6 compares the curved and saturated experimental OH-PLIF field (in a)) with the ideal, essentially flat numerical ones obtained with (in b)) and without corrections (in c)) to consider saturation of the camera. The level of saturation is the same as the one used in the 1D validation in Fig. 4. As seen in Fig. 6b, the corrected fluorescence signal reproduces qualitatively the experimental OH-PLIF images, notably the width of the front illuminated with the laser sheet and the relative fluorescence intensity between the top and the bottom of the image. As observed in the 1D validation of the trans-verse orientation, the shape of the front is different on the top left of the images (short optical path). This difference is due to the edge of the visualization window, which is displayed in dashed black lines in Fig. 6b but not considered in the LIF intensity calculation. The numerical OH-PLIF image, in Fig. 6b, qualitatively reproduces the experimental OH-PLIF image from Wang, when both the saturation of the camera and the edge of the visualisation window are accounted for.

Based on the different validation of the LIF model, Fig. 6c aims to represent the hypothetical experimental OH-PLIF image without saturation of the camera. This synthetic OH-PLIF image demonstrates a strong absorption of the laser energy along the vertical axis, which is barely noticeable in the experimental images due to the saturation of the camera. The numerical LIF signal rapidly drops close to 0 after only 20 mm (from the top of the image). The double peaks observed experimentally, which were reproduced with the 1D simulations (Fig. 4, are also observed on the 2D numerical PLIF (see line at 3.3 mm in Fig. 7. In addition, even more complex profiles can be observed for different vertical positions (see line at 9.9 mm in Fig. 7. These more complex profiles are due to the combination of the OH concentration nonuniformity and the spatial distribution of the laser energy inside the reaction front. These very complex LIF intensity profiles emphasize the need for new experimental data with precise measurements of the laser energy profile to fully validate the transverse orientation of the LIF model.

Effects of the laser orientation the detonation front visualization

The effect of the two laser orientations is investigated using the results from the unsteady 2D simulation, in Fig. 8. These results consider an ideal laser sheet (without a Gaussian spatial energy distribution) to preclude the effect of the laser energy profile. For a frontal orientation, the present results are similar to those obtained by Mével et al. [START_REF] Mével | Application of a laser induced fluorescence model to the numerical simulation of detonation waves in hydrogen-oxygen-diluent mixtures[END_REF] with a high fluorescence intensity confined to the detonation front. The use of a transverse laser orientation enables to visualize regions of high LIF intensity (in Fig. 8c) far behind the detonation front but limited to 1 cm vertically. In the case of the transverse laser orientation, the LIF intensity (at least for short optical paths) better represents the OH profile along the detonation front compared to the frontal laser orientation. In addition, the LIF signal obtained from the transverse laser orientation enables to observe, to some extent, the complex patterns associated with the OH concentration in Fig. 8a but with different intensities. These observations are not possible from the

Conclusions

An improved version of the LIF model presented in Mével et al. [START_REF] Mével | Application of a laser induced fluorescence model to the numerical simulation of detonation waves in hydrogen-oxygen-diluent mixtures[END_REF] has been developed and validated against 1D and 2D simulations using OH-PLIF images from the literature. Although detonation involves both high speed flow and high pressure variations, the absorption linecenter shifts have a negligible effect on the overall fluorescence signal for the present experimental conditions. The effect of the laser sheet orientation on the OH-PLIF imaging is investigated numerically by using the validated LIF model on 2D OH concentration distributions obtained from numerical simulations. Based on the present results, the transverse orientation of the incident laser sheet could enable to observe regions of high OH-concentration behind the detonation front. While the visualization of domains with relatively short optical paths enables such observation, domains far from it are significantly affected by laser absorption because a detonation is an optically-thick reactive flow, at least in the experimental configuration we studied. In addition, the curvature of the detonation front can create a non-homogeneous optical path which complicates the interpretation of the PLIF images and LIF profiles extracted from them. Such an effect is not observed for the PLIF imaging with the frontal laser light orientation. This work demonstrates that the use of the transverse laser orientation with a wide laser sheet and a known and appropriate spatial distribution of the laser energy allows to visualize reactive areas behind the detonation front. While these results show a qualitative agreement with experimental data, new experimental data are required to quantitatively validate this promising transverse laser orientation and to confirm whether this laser orientation provides useful additional information during visualization of the detonation front.

Fig. 1

 1 Fig. 1 Effect of the number of absorption lines considered to calculate the absorption lineshapes at two positions (X) behind the detonation leading shock. The normalization is performed considering the maximum of the two Voigt profiles (i.e. the 2-line and the 5-line profiles) over the entire ZND profile. The five absorption lines, represented by black-dashed lines, use the same normalization value. Conditions: 2H 2 -O 2 -10Ar at P 1 = 45.3 kPa and T 1 = 295 K

Fig. 2

 2 Fig. 2 Post-processing methodology: extraction of 1D LIF intensity profiles from the experimental PLIF images. Conditions: 2H 2 -O 2 -10Ar at P 1 = 45.3 kPa and T 1 = 295 K

Fig. 3 Fig. 4

 34 Fig. 3 1D validation of the frontal laser orientation (from the right) using an OH-PLIF image from Austin [1] in a). 1D experimental (black dots) and ZND (red lines) LIF profiles, obtained for areas 1 and 2, are respectively presented in b) and c). ZND OH mole fractions (blue lines) are represented for comparison. Conditions: 2H 2 -O 2 -12Ar at P 1 = 20 kPa and T 1 = 295 K

Fig. 5

 5 Fig. 5 Quantification of the absorption line shift on a single transition (Q 12 (8)), in a). Effect of the absorption line shifts on the fluorescence signal, in b). The area 2 used previously in the 1D validation (Fig. 3c) is shown for comparison. Conditions use a frontal laser orientation and a 2H 2 -O 2 -12Ar mixture at P 1 = 20 kPa and T 1 = 295 K

Fig. 6 Fig. 7

 67 Fig. 6 Comparison between experimental and numerical OH-PLIF images. a) experimental OH-PLIF from Wang [13]; b) numerical OH-PLIF including corrections for camera saturation; c) numerical OH-PLIF without corrections for camera saturation. Color scale is identical between b) and c). In b), the dashed line represents the edge of the observation window, based on the experimental dimensions. In c), the blue and red dotted lines represent the location of the two profiles represented in Fig. 7. Conditions: 2H 2 -O 2 -10Ar at P 1 = 45.3 kPa and T 1 = 295 K

  a) Normalized 2D field of OH b) PLIF image with frontal laser orientation c) PLIF image with transverse laser orientation

Fig. 8 Fig. 9 Fig. 10 Fig. 11

 891011 Fig. 8 Effect of the laser sheet orientation on OH-PLIF imaging of detonation. The initial 2D field of OH is given in a) for comparison. Conditions similar to Wang [13]: 2H 2 -O 2 -10Ar at P 1 = 45.3 kPa and T 1 = 295 K

  . Examples

	(Voigt) [-]	0.8 1	X=20 m T=1971 K P=1.2 MPa		5 lines 2 lines Norm. laser profile
	lineshapes	0.4 0.6
	Normalized	0 0.2
			283.98	284	284.02	284.04
					[nm]
			a) von Neumann state
	[-] (Voigt)	0.8 1	X=1 m T=2814 K P=0.7MPa		5 lines 2 lines Norm. laser profile
	lineshapes	0.4 0.6
	Normalized	0.2
		0
			283.98	284	284.02	284.04
					[nm]
				b) CJ state

Acknowledgements Research reported in this publication was supported by the King Abdullah University of Science and Technology (KAUST). RM was supported by the 1000 Young Talent of China program, a start-up fund of the Center for Combustion Energy of Tsinghua University, and the 1000 Young Talent Matching Fund from Tsinghua University. The computations were performed using HPC resources from the cluster of Pprime, the Mésocentre de Calcul Poitevin and from GENCI-CINES (Grant 2018-A0052B07735). This work was supported by the CPER FEDER Project of Région Nouvelle Aquitaine. The authors are grateful to Joanna M. Austin for allowing the use of her experimental OH-PLIF image in Fig. 3.

Conflict of interest

The authors declare that they have no conflict of interest.

Appendix 1: Sequence of images of the Voigt profile evolution along the detonation front

This appendix presents a more detailed evolution of the Voigt profiles presented in Fig. 1, with a higher spatial resolution to better illustrate the absorption lineshape evolution along the distance behind the leading shock (X). Similarly to the results presented in Fig. 1, the absorption lines are simulated based on Wang's experimental conditions with a transverse laser orientation (δ D = 0 and δ Tot. = δ P ). A movie presenting this sequence of images with intermediate positions is available in the Supplementary material.

Appendix 2: Additional 1D validation cases with the transverse laser orientation.

Figure 10 presents two additional 1D validation cases extracted from Wang's OH-PLIF image [START_REF] Wang | Study on reaction zone structure of gaseous detonation wave by planar laser induced fluorescence technique[END_REF]. As presented for areas 1 and 2, the LIF model reproduces qualitatively the overall intensity profile for both areas 3 and 4 when the correction accounting for the saturation of the camera is included. In area 3, the fluorescence decay has an overall offset of 2 mm, which is relatively small considering the non-ideality in the experimental image (the tilted detonation front). In area 4, the double peak structure is reproduced in the simulation with a local fluorescence intensity minimum located near 2 mm as observed experimentally. The double peak intensity is underestimated by 25% in area 4, this might indicate that the fluorescence signal attenuation is overestimated in the current model or this might be due to an overestimated laser intensity attenuation. As discussed in Sec.3.1 and emphasized in the conclusions, new experimental data are required to fully validate the LIF model for the transverse laser orientation.

Appendix 3: Relevance of the new LIF model

This appendix demonstrates the need to develop the new LIF model and to consider the improvements presented in this work, notably the absorption line shifts and the Voigt profile calculation. As explained in Sec.3.2, the two laser orientations (the transverse and the frontal) must be considered independently as the Doppler shift is significantly different for these two orientations. Only three characteristic distances from the detonation front are presented in Figs. 11 and12: von Neumann state (X vN ), induction length (Δ i ), CJ state (X CJ ).

Figure 11 emphasizes the contribution of the Doppler shift (δ D ) for Wang's conditions, for both the two and the five line calculations of the Voigt profile. As the laser linecenter is constant, the δ D contribution is observed by comparing the shift of the Voigt profile maximum with the laser linecenter between Figs. 11a and11b for the three positions. As the δ D decreases with the distance behind the leading shock and is mainly contributing to the δ Tot. , it must be noted that the shift is the strongest for X vN .

Figure 12 presents the evolution of both the two and the five line calculation of the Voigt profile at two different pressure conditions using a frontal laser orientation and for the three distances from the detonation front, defined previously: X vN , Δ i , and X CJ .

These figures show the need to consider the contribution of additional absorption lines for higher initial pressure in this specific spectral range.