Molina Boisseau

Sonochemical activity in ultrasonic reactors under heterogeneous conditions

Keywords: Ultrasound, Sonochemistry, Calorimetry, Acoustic radiation power, Heterogeneous media, Suspension

Due to its physical and chemical effects, ultrasound is widely used for industrial purposes, especially in heterogeneous medium. Nevertheless, this heterogeneity can influence the ultrasonic activity. In this study, the effect of the addition of inert glass beads on the sonochemical activity inside an ultrasonic reactor is investigated by monitoring the formation rate of triiodide, and the ultrasonic power is measured by calorimetry and by acoustic radiation. It was found that the sonochemical activity strongly depends on the surface area of the surface developed by the glass beads in the medium: it decreases above a critical area value (around 10 -2 m 2 ), partly due to wave scattering and attenuation. This result is confirmed for a large range of frequencies (from 20 to 1135 kHz) and glass beads diameters glass beads (from 8-12 µm to 6 mm). It was also demonstrated that above a given threshold of the developed surface area, only part of the supplied ultrasonic power is devoted to chemical effects of ultrasound. Finally, the acoustic radiation power appears to describe the influence of solids on sonochemical activity, contrary to the calorimetric power.

Highlights

• Ultrasonic power measured by calorimetry is not affected by glass beads addition • Glass beads surface area is a relevant criterion to describe sonochemical activity • Sonochemical activity decreases above a critical surface area for all frequencies

• Acoustic radiation power is relevant to describe glass beads effect on sonoactivity

Introduction

Many applications are reported about low and high frequency ultrasound, applied in various sonochemical processes involving heterogeneous media. For example, nanostructured materials can be synthesized at ambient temperature and pressure, in a short reaction time, with the use of power ultrasound. It is even possible to control the size of powder and/or modify the material surface [START_REF] Muthoosamy | State of the art and recent advances in the ultrasoundassisted synthesis, exfoliation and functionalization of graphene derivatives[END_REF][START_REF] Harifi | A review on textile sonoprocessing: A special focus on sonosynthesis of nanomaterials on textile substrates[END_REF]. Ultrasound can also be used to enhance solid-liquid extraction: this ultrasound-assisted extraction allows to recover heat-sensitive bioactive 2 compounds at low temperature and promote the use of GRAS (generally recognized as safe) solvent [START_REF] Vilkhu | Applications and opportunities for ultrasound assisted extraction in the food industry -A review[END_REF]. Also in adsorption process, the regeneration of the adsorbent and the mass transfer were proven to be improved by means of ultrasonic waves [START_REF] Breitbach | Influence of ultrasound on adsorption processes[END_REF]. Another example is sonocrystallisation, where ultrasound is used to decrease the induction time and the metastable zone, and to increase the nucleation rate. Crystals with controlled size and distribution are likely to be obtained [START_REF] Kim | The Effects of Ultrasound on Crystals: Sonocrystallization and Sonofragmentation[END_REF].

Even if ultrasound in heterogeneous medium is widely used in such different domains, only few articles are dedicated to the study on the influence of heterogeneity on the sonochemical activity. Main studies previously reported are summarized in Table 1, where the surface area of the particles is calculated according to the data available in these papers. In 2002, Keck et al. investigated the influence of quartz particles (2 -25 µm) on the chemical effects induced by ultrasound from 68 to 1028 kHz, under Ar/O2 or N2/O2 conditions. The authors noticed the activity increases at 206 kHz due to a bubbles shape modification, which enables more radicals release in the bulk by increasing bubble interface [START_REF] Keck | Influence of particles on sonochemical reactions in aqueous solutions[END_REF]. They also reported that the ultrasonic activity was reduced for all the other frequencies, due to ultrasound attenuation. [START_REF] Tuziuti | Correlation between Acoustic Cavitation Noise and Yield Enhancement of Sonochemical Reaction by Particle Addition[END_REF] studied the enhancement of sonochemical reaction by adding different amounts (0 -100 mg) of alumina particles (1 -80 µm). They observed that with an appropriate amount (20 mg) and size (20 µm) of particles, the sonochemical activity increases by increasing the population of cavitating bubbles [START_REF] Tuziuti | Correlation between Acoustic Cavitation Noise and Yield Enhancement of Sonochemical Reaction by Particle Addition[END_REF]. [START_REF] Her | Sonochemical enhancement of hydrogen peroxide production by inert glass beads and TiO2-coated glass beads in water[END_REF] investigated the role of inert or TiO2 coated glass beads (from 50 to 5000 µm diameters) on the H2O2 production.

Their conclusion was that the inert glass addition increases the sonochemical activity at low frequency (28 kHz) by increasing the formation rate of cavitation bubbles. At higher frequencies (580 and 1000 kHz) this activity decreases, except for 100 µm (10-50 g.L -1 ), due to wave-particle interference [START_REF] Her | Sonochemical enhancement of hydrogen peroxide production by inert glass beads and TiO2-coated glass beads in water[END_REF]. [START_REF] Stoian | Intensification of sonochemical reactions in solid-liquid systems under fully suspended condition[END_REF] studied the influence of particle addition (ion exchange resin, sand, and glass beads) with different diameters (207 -1290 µm) and concentrations on the sonochemical activity in a full stirred reactor at 20 kHz. The authors found that the sonochemical activity of ultrasound is changed according to the particle concentration. They reported a first decrease due to wave attenuation, for volumetric solid concentrations (Cv) from 0 to 0.01. Then they reported an increase of the sonochemical activity for Cv from 0.01 to 0.4, due to the enhancement of cavitation bubbles. However, above Cv = 0.4, this activity decreased due to change of the medium viscosity [START_REF] Stoian | Intensification of sonochemical reactions in solid-liquid systems under fully suspended condition[END_REF]. More recently, [START_REF] Son | Cavitational activity in heterogeneous systems containing fine particles[END_REF] have investigated the cavitational activity in heterogeneous systems containing fine particles in a 28 kHz double-bath sonoreactor. Their results clearly suggested that there were no significant differences in calorimetric energies for both with and without particles conditions. Furthermore, the chemical activity was evaluated using sonochemiluminescence (SCL) and different trends were observed depending on the presence and size of beads [START_REF] Son | Cavitational activity in heterogeneous systems containing fine particles[END_REF].

In order to obtain complementary understanding on the effect of heterogeneity on ultrasound activity, this research aims to investigate the influence of the presence of divided solids on sonochemical activity within a low or high frequency ultrasonic reactor. Inert glass beads are used in order to simulate solid heterogeneity, with different diameter and concentration.

Diameters were chosen considering the characteristic parameters of an ultrasonic system: its wavelength and the diameter of its acoustic cavitation bubbles. The global ultrasonic activity and the chemical ultrasonic activity were quantified by different methods and they were systematically compared in homogeneous and heterogeneous conditions. The ultrasonic power was measured by calorimetry while the chemical activity was monitored by iodide dosimetry. For both devices, the same 500 mL reactor vessel is used, with a double jacket in order to maintain a constant temperature at 20 ± 1 °C, thanks to a cryothermostat bath (Thermo Fisher Scientific Arctic A25). Each experiment last 30 minutes, and triplicates are carried on. As the used vessels are very similar, the reactor shape is not likely to influence the obtained results [START_REF] Lim | The effects of liquid height/volume, initial concentration of reactant and acoustic power on sonochemical oxidation[END_REF][START_REF] Gogate | Sonochemical reactors: Important design and scale up considerations with a special emphasis on heterogeneous systems[END_REF].

Glass beads

In order to simulate the heterogeneity in the medium, glass beads are used. They were chosen because they are easy to characterize through their diameter and chemically inert. Preliminary tests have shown triiodide adsorption is negligible (less than 1%) and SEM photographs have proven sonication has no effect on beads structure. These beads were used at different mass concentrations, ranging from 3.2 10 -3 to 80 g.L -1 .

A wide range of glass beads diameters (between 8-12 and 6000 µm) was tested. The objective was to be in the same order of magnitude as the wavelength (from 1400 to 4000 µm for high frequency) and the cavitation bubbles diameter. From 213 to 1136 kHz, the cavitation bubbles diameter was estimated to be from 4 to 8 µm thanks to the work of Brotchie et al. [START_REF] Brotchie | Effect of Power and Frequency on Bubble-Size Distributions in Acoustic Cavitation[END_REF], and it was also calculated from 2.8 (at 1174 kHz) to 164.5 µm (at 20 kHz) with Minnaert equation [START_REF] Minnaert | On musical air-bubbles and the sounds of running water[END_REF].

Calorimetry

The ultrasonic power (PUS) supplied to the medium was measured by calorimetry [START_REF] Boldo | New Operating Method Improves Calorimetric Measurement of Ultrasonic Power[END_REF]. This method is classically used to thermally characterize an ultrasound device by monitoring the temperature change of the irradiated medium. Carefully The reactor is thermally insulated carefully by glass wool, and two temperature probes are placed within the reactor to confirm the temperature homogeneity inside the irradiated medium. Before calorimetry, the temperature of the liquid inside the vessel is reduced by 5°C under the ambient temperature, and the monitoring stops when the temperature of the irradiated liquid is 5°C above the ambient temperature.

Assuming that the reactor is thermally insulated, the ultrasonic power is obtained by the following energy balance:

P = m C , (1)
where mwater is the mass of water contained in the reactor (0.5 kg), Cp,water is the heat capacity of water (4.18 kJ.kg -1 .K -1 ) and is the slope of the experimental curve at the point where the temperature of the sonicated water equals the ambient temperature.

Nevertheless, the obtained value gives the net ultrasonic power present dissipated in the medium. The ultrasonic power absorbed by the reactor vessel must be estimated. So a calibrated resistance (11.5 Ohm) is used with a power supply (Française d'Instrumentation FI 3610) at 2.97 A and 34 V in order to measure the energy absorbed by the vessel. This energy is turned into an equivalent mass of water to be added at the energy balance as follows:

P = (m + m ) C (2)
where meq-water is the energy absorbed by the reactor vessel converted into an equivalent mass of water. Finally, the total ultrasonic power generated transferred by the transducer is calculated by equation (2).

KI dosimetry

Considered as reproductive, easy to set up and reliable [START_REF] Iida | Sonochemistry and its dosimetry[END_REF], this technique is based on the irradiation of an aqueous solution of potassium iodide (KI) by ultrasound [START_REF] Koda | A standard method to calibrate sonochemical efficiency of an individual reaction system[END_REF]. A fraction of iodide (I -) is oxidized into diiodine (I2) by radicals produced by cavitation bubbles implosion.

Then the rest of iodine reacts with diiodine. So the final product triiodide (I3 -) is generated according to the following reaction:

2 HO • +3 I - 2 OH -+ I3 - (3)
From an initial solution of potassium iodide (10 g.L -1 ), the absorbance of the yellow triiodide is measured at 355 nm (spectrophotometer Shimadzu UVmini 1240). Finally, its concentration is obtained thanks to its molar attenuation coefficient (ε = 26300 L.mol -1 .cm -1 ).

For heterogeneous medium, addition of glass beads was considered since the obtained solution is homogenized even for the highest concentration. Therefore, hydrodynamic conditions are thereby nearly the same than under homogeneous conditions and the ultrasonic reactor can be considered as a batch reactor. So, the following equation is obtained thanks to the mass-balance based on triiodide production and provides the triiodine formation rate r(I3 -):

r(I ) = • = !" # (4)
Moreover the concentration of triiodide increases linearly with sonication time (Fig. 2).

Assuming the triiodide formation reaction follows a zero-order kinetics, triiodide formation rate is likely to be directly estimated by the value of the slope of the obtained straight line, as

proposed by [START_REF] Merouani | Influence of experimental parameters on sonochemistry dosimetries: KI oxidation, Fricke reaction and H2O2 production[END_REF]. In this study, two types of triiodide formation rate are defined. In this study, we defined two different notations for triiodide formation rate: in the case of homogeneous media (without particles) the formation rate is represented by r(I3 -)0 whereas in the case of heterogeneous media (presence of glass beads) the formation rate is denoted r(I3 -).

Acoustic radiation power

When a solid target is immersed in a liquid irradiated by ultrasound, it undergoes a radiation force providing some information about the acoustic radiation power [START_REF] Zieniuk | Measurement of ultrasonic exposure with radiation force and thermal methods[END_REF], denoted PUS-rad.

This power is measured according to the International Electrotechnical Commission (IEC)

61161 norm [START_REF]IEC 61161 norm Ultrasonics -Power measurement -Radiation force balances and performance requirements[END_REF]: a silicon target (diameter 6.5 cm) is set at the liquid surface and hooked to a precision balance (Kern-PCB 2500-2) in order to record its weight. Then the acoustic radiation power is calculated by the following equation

PUS-rad = ∆m g c ( 5
)
where g is the gravitational acceleration (9.81 m.s -2 ), ∆m is the difference of weight with and without ultrasound (kg), and c is the sound velocity in water (1500 m.s -1 ).

The acoustic radiation power depends on several parameters of the target (material, size, distance from the transducer …) [START_REF] Hekkenberg | Validated ultrasonic power measurements up to 20 W[END_REF][START_REF] Zeqiri | A radiation force balance target material for applications below 0.5 MHz[END_REF] but the obtained values are in the same range as the power obtained by calorimetry, according to the literature [START_REF] Kikuchi | Calorimetric method for measuring high ultrasonic power using water as a heating material[END_REF][START_REF] Uchida | Effect of Heat Generation of Ultrasound Transducer on Ultrasonic Power Measured by Calorimetric Method[END_REF][START_REF] Morgado | Measurement of ultrasound power using a calorimeter[END_REF]. In our case, experiments were only performed at 575 kHz, because target is damaged for higher frequencies.

Gas experiments

Most of experiments are achieved with an atmospheric open vessel, under air conditions, but sonochemical activity is influenced by dissolved gases. As a consequence, some experiments are carried on under argon. For these trials, water is preliminary deaerated and saturated by argon bubbling for 20 minutes. Then the sonication is performed with a slight argon current maintained just above the liquid surface, to avoid any oxygen and nitrogen dissolution.

Results and discussion

Ultrasonic power measured by calorimetry: effect of particles

In order to investigate the effect of heterogeneous media on PUS, calorimetric experiments were carried out first without heterogeneity (ultra-pure water), then in the presence of glass beads, with different diameters and different concentrations.

In a homogeneous medium (0 g.L -1 ), the electrical input power was adjusted to obtain a similar ultrasonic power (around 50 W) for all the studied frequencies as shown in All these observations put in evidence that the ultrasonic power measured by calorimetry is not influenced by the presence of glass beads. The same result was observed by Stoian et al.

in terms of volumetric power [START_REF] Stoian | Intensification of sonochemical reactions in solid-liquid systems under fully suspended condition[END_REF]. The dissipated power global energy available in the system remains unchanged for all our experimental operating conditions. While such an observation is in good agreement with recent work by Son et al. [START_REF] Son | Cavitational activity in heterogeneous systems containing fine particles[END_REF], it is expected that complementary data dealing with the sonochemical activity should give more information.

3.2.Ultrasonic chemical activity measured by iodometry: effect of particles addition

The sonochemical activity was monitored by potassium iodide dosimetry and the formation rate r(I3 -) is a relevant indicator of the amount of radical species produced by sonolysis of water [START_REF] Price | The use of dosimeters to measure radical production in aqueous sonochemical systems[END_REF].

Sonochemical activity in homogenous media

For all the experiments, the reactors have the same shape and volume, and the same ultrasonic power is adjusted. So the frequency is assumed to be the single parameter likely to influence the sonochemical activity. The triiodide formation rates (r(I3 -)0) are plotted according to the frequencies (Fig 4). As it can be seen, results show a maximal rate at 575 kHz with a value of 2.3 ± 0.1 µM.min -1 , and a minimal rate at low frequency with a value of 0.28 ± 0.01 µM.min - 1 . So, the optimal sonochemical activity is obtained at 575 kHz and the sonochemical activity is divided by a factor of 10 ten-fold lower at 20 kHz. This result is in accordance with the literature: the same decreasing factor ratio between high and low frequencies was reported by Koda [START_REF] Koda | A standard method to calibrate sonochemical efficiency of an individual reaction system[END_REF]. The maximal sonochemical activity between 300 and 600 kHz was previously reported by different authors [START_REF] Koda | A standard method to calibrate sonochemical efficiency of an individual reaction system[END_REF][START_REF] Petrier | Unexpected frequency effects on the rate of oxidative processes induced by ultrasound[END_REF][START_REF] Kanthale | Sonoluminescence, sonochemistry (H2O2 yield) and bubble dynamics: Frequency and power effects[END_REF][START_REF] Wood | A parametric review of sonochemistry: Control and augmentation of sonochemical activity in aqueous solutions[END_REF] and was explained by a larger population of active cavitation bubbles when the frequency increases. But this beneficial effect of the frequency is reduced for higher frequencies by the reduction of the growth time of cavitation bubbles, which leads to a reduction of sonochemical activity [START_REF] Merouani | A method for predicting the number of active bubbles in sonochemical reactors[END_REF]. Therefore, our study mainly focused on the sonochemical activity at high frequency, and most of the results reported in this paper were obtained at 575 kHz.

Sonochemical activity in heterogeneous media

In order to investigate if the sonochemical activity is affected by solid heterogeneity, the rates of triiodide formation (r(I3 -)) in the presence of glass beads were measured as previously detailed in this paper (Fig. 2). Experimental formation rates observed with 8-12 µm diameter glass beads are given in Fig 5 . First of all, results exhibit that 575 kHz is the most efficient frequency for all the glass beads concentrations, as in homogeneous media. Secondly whatever the frequency is, it can be noticed that r(I3 -) decreases when the particles concentration increases. In the literature, this result is controversial because on the one hand the particle addition may promote the acoustic cavitation by reducing the cavitation threshold and may increase the number of nucleation sites or even modify the shape of imploding bubbles releasing more radicals [START_REF] Keck | Influence of particles on sonochemical reactions in aqueous solutions[END_REF][START_REF] Lim | The effects of liquid height/volume, initial concentration of reactant and acoustic power on sonochemical oxidation[END_REF]. On the other hand, at more concentrated media, the acoustic cavitation may decrease because of the wave attenuation [START_REF] Keck | Influence of particles on sonochemical reactions in aqueous solutions[END_REF][START_REF] Tuziuti | Correlation between Acoustic Cavitation Noise and Yield Enhancement of Sonochemical Reaction by Particle Addition[END_REF][START_REF] Her | Sonochemical enhancement of hydrogen peroxide production by inert glass beads and TiO2-coated glass beads in water[END_REF]. Similar experiments were then performed with other glass beads diameters. To highlight the influence of these glass beads, results are presented using a ratio defined as the rate of triiodide formation in heterogeneous medium (r(I3 -)) divided by the formation rate in homogeneous medium (r(I3 -)0). As shown in Fig. 6 at low glass beads concentration, I3 - formation rates ratio remains constant and close to 1, illustrating the sonochemical activity is not affected by the presence of particles, whatever the glass beads diameter. To our knowledge, this phenomenon has never been reported in the literature [START_REF] Keck | Influence of particles on sonochemical reactions in aqueous solutions[END_REF][START_REF] Tuziuti | Correlation between Acoustic Cavitation Noise and Yield Enhancement of Sonochemical Reaction by Particle Addition[END_REF][START_REF] Her | Sonochemical enhancement of hydrogen peroxide production by inert glass beads and TiO2-coated glass beads in water[END_REF][START_REF] Stoian | Intensification of sonochemical reactions in solid-liquid systems under fully suspended condition[END_REF]. According to experimental results exhibited in Fig. 6, it seems that for each glass beads diameter, the I3 - formation rates ratio decreases above a certain particle concentration, partially due to wave attenuation. According to the literature, the effect of inert particles on sonochemical activity is considered to result from two types of interaction. The first interaction takes place between the waves and the particles, and it provokes an attenuation and a scattering of the ultrasonic waves for concentrated suspensions [START_REF] Keck | Influence of particles on sonochemical reactions in aqueous solutions[END_REF][START_REF] Tuziuti | Correlation between Acoustic Cavitation Noise and Yield Enhancement of Sonochemical Reaction by Particle Addition[END_REF][START_REF] Her | Sonochemical enhancement of hydrogen peroxide production by inert glass beads and TiO2-coated glass beads in water[END_REF][START_REF] Stoian | Intensification of sonochemical reactions in solid-liquid systems under fully suspended condition[END_REF] (Table 1). The second interaction takes place between the particles and the cavitation bubbles: the particles can interfere at the different stages of the cavitation bubble lifetime. (i) At the initial nucleation step, the solid particles can be supposed to act as additional nucleation sites [START_REF] Suslick | On the origin of sonoluminescence and sonochemistry[END_REF], so their presence will improve the sonochemical activity by increasing the number of bubbles. (ii) At the growing stage, it was reported that small and low-density particles can be located at the ultrasonic wave antinodes where the tiny bubbles grow and become active resulting in a detrimental competition [START_REF] Mitome | Action of Ultrasound on Particles and Cavitation Bubbles[END_REF]. (iii) At the last phase of the cavitation bubble lifetime, the presence of particles is generally supposed to promote asymmetric implosions enhancing thereby the sonochemical activity [START_REF] Keck | Influence of particles on sonochemical reactions in aqueous solutions[END_REF][START_REF] Tuziuti | Correlation between Acoustic Cavitation Noise and Yield Enhancement of Sonochemical Reaction by Particle Addition[END_REF][START_REF] Her | Sonochemical enhancement of hydrogen peroxide production by inert glass beads and TiO2-coated glass beads in water[END_REF].

In our case, below the critical area, the sonochemical activity remains unchanged. On the one hand, this is due to the fact that the particles did not play the role of nucleation site, because the used glass beads are smooth and not small enough, which can reduce the probability of the cavitation occurrence according to the work of Zhang et al. [START_REF] Zhang | Controlled Cavitation at Nano/Microparticle Surfaces[END_REF]. On the other hand, there is no wave scattering and attenuation due to the low particle concentration. Furthermore, no second interaction can be expected at this level because the glass beads are too dense to be trapped at the wave antinodes. Nevertheless, as they can be dragged away by the acoustic streaming, the particles did not play the role of solid wall, which enhance radical release by modifying the shape of imploding bubbles as described by Keck [6] or Tuziuti [START_REF] Tuziuti | Correlation between Acoustic Cavitation Noise and Yield Enhancement of Sonochemical Reaction by Particle Addition[END_REF].

However, above the critical area value, the sonochemical activity is dramatically decreased, that cannot be only due to the wave scattering and attenuation like it was as reported in the literature [START_REF] Keck | Influence of particles on sonochemical reactions in aqueous solutions[END_REF][START_REF] Tuziuti | Correlation between Acoustic Cavitation Noise and Yield Enhancement of Sonochemical Reaction by Particle Addition[END_REF][START_REF] Her | Sonochemical enhancement of hydrogen peroxide production by inert glass beads and TiO2-coated glass beads in water[END_REF][START_REF] Stoian | Intensification of sonochemical reactions in solid-liquid systems under fully suspended condition[END_REF][START_REF] Lu | Sonolysis of synthetic sediment particles: particle characteristics affecting particle dissolution and size reduction[END_REF], because our highest particle concentration (80 g.L -1 ) is lower than the concentrations used by these researchers (Table 1). For example, Stoian [START_REF] Stoian | Intensification of sonochemical reactions in solid-liquid systems under fully suspended condition[END_REF] worked with a concentration between 12.2 g.L -1 and 610 g.L -1 and Tuziuti [START_REF] Tuziuti | Correlation between Acoustic Cavitation Noise and Yield Enhancement of Sonochemical Reaction by Particle Addition[END_REF] used a concentration from 10 to 100 g.L -1 . Finally, it can be thought that the particles may induce an asymmetric implosion, likely to decrease sonochemical activity, according to different studies [START_REF] Lu | Sonolysis of synthetic sediment particles: particle characteristics affecting particle dissolution and size reduction[END_REF][START_REF] Huang | Effects of Solid Particle Properties on Cavitation Erosion in Solid-Water Mixtures[END_REF]. As surprisingly shown in Fig. 8, the same trend was observed for all the ultrasonic frequencies used in this work: the sonochemical activity first remains unchanged and then sharply decreases above the same critical surface area inside the reactor. So, for these studied frequencies, the addition of inert glass particles reduces the sonochemical activity above a critical area, estimated to be 3.10 -2 m².

Effect of gas on sonochemical activity in heterogeneous media

As for a homogeneous medium, sonochemical activity in a heterogeneous medium is influenced by dissolved gases. According to the gases, oxidant species are not the same, so chemical reactions pathways are modified. For instance, sonication of water under air leads to the formation of different species, among which nitrites and nitrates whereas sonication under argon is known to be • OH specific [START_REF] Ouerhani | Spectroscopy of Sonoluminescence and Sonochemistry in Water Saturated with N2-Ar Mixtures[END_REF]. So experiments were carried on under argon conditions (section 2.6) with and without 8-12 µm glass beads, with a 51.5 ± 0.5 W calorimetric power at 575 kHz. literature [START_REF] Mark | OH-radical formation by ultrasound in aqueous solution -Part II: Terephthalate and Fricke dosimetry and the influence of various conditions on the sonolytic yield[END_REF][START_REF] Mead | The effect of ultrasound on water in the presence of dissolved gases[END_REF][START_REF] Beckett | Impact of Ultrasonic Frequency on Aqueous Sonoluminescence and Sonochemistry[END_REF][START_REF] Kidak | Effects of operating parameters on sonochemical decomposition of phenol[END_REF][START_REF] Kitajima | Mechanism of O2-accelerated sonolysis of bisphenol A[END_REF][START_REF] Torres | Ultrasonic cavitation applied to the treatment of bisphenol A. Effect of sonochemical parameters and analysis of BPA by-products[END_REF], so the triiodine formation rate declines.

In the presence of glass beads, results obtained under air and argon conditions were compared (Fig. 9). Both curves exhibit the same trend: a first plateau where the sonochemical activity remains constant followed by a drastic decrease above a critical value of the developed surface area. As previously explained, this reduction of activity is probably due to wave attenuation and to less energetic bubbles implosions [START_REF] Huang | Effects of Solid Particle Properties on Cavitation Erosion in Solid-Water Mixtures[END_REF][START_REF] Supponen | Luminescence from cavitation bubbles deformed in uniform pressure gradients[END_REF][START_REF] Allegra | Attenuation of Sound in Suspensions and Emulsions: Theory and Experiments[END_REF][START_REF] Su | Particle size characterization by ultrasonic attenuation spectra[END_REF]. Under argon conditions, the value of the critical developed surface area (close to 3.10 -1 m²) is higher than the value observed for air conditions (close to 3.10 -2 m²). For argon, even if the sonochemical activity is initially lower, its decrease appears to be less important. It can be explained by the higher temperature reached when cavitation bubbles implode, due to this mono-atomic gas presence inside these bubbles [START_REF] Morgado | Measurement of ultrasound power using a calorimeter[END_REF][START_REF] Hua | Optimization of ultrasonic irradiation as an advanced oxidation technology[END_REF][START_REF] Wayment | Frequency effect on the sonochemical remediation of alachlor[END_REF][START_REF] Guzman-Duque | Effects of sonochemical parameters and inorganic ions during the sonochemical degradation of crystal violet in water[END_REF][START_REF] Gao | Factors affecting sonolytic degradation of sulfamethazine in water[END_REF] that counteracts the detrimental effect of glass beads.

Even if iodometry under argon condition is much more • OH specific compared to air condition, the same trend is obtained for both conditions. So air iodometry is likely to be used to describe the effect of glass beads addition within an ultrasound reactor.

The real ultrasonic power devoted to sonochemistry

Whatever the frequency is, for all the beads diameters and concentrations, the calorimetric ultrasonic power (PUS) released inside the reactor in heterogeneous medium was constant (section 3.1) while the sonochemical activity decreased above a critical value of developed surface area (section 3.2) in the same conditions. From a chemical engineer viewpoint, it could be helpful to estimate the proportion of the ultrasonic power supplied to the reactor that is assumed to be devoted to chemical effect. So, calibration experiments were made without glass beads: the ultrasonic power and the triiodide formation rate were both measured for several electrical power inputs. The obtained data enables to link r(I3 -)0 and PUS for the different ultrasound frequencies Fig. 10. For all the frequencies, it can be noted the triiodine formation rate increases with the ultrasonic power once the cavitation threshold is overpassed [START_REF] Connolly | Ultrasonic Cavitation Thresholds in Water[END_REF]. Above this threshold, the observed increase of the sonochemical activity can be attributed to the growing of acoustic bubbles population [START_REF] Gogate | Intensification of cavitational activity in the sonochemical reactors using gaseous additives[END_REF]. It was therefore assumed that without particles the ultrasonic power measured by calorimetry is partly turned into sonochemical activity due to the relationship between these both parameters variables as suggested by results in Fig. 10. Then the linear approximations of these curves were used as calibration curves (Fig. 11) to estimate the proportion of the equivalent ultrasonic power devoted to chemical activity under heterogeneous conditions, denoted PUS-chemical. Even if such an assessment tool may be criticisable questionable, it can be regarded as a useful tool for preliminary diagnosis tests for ultrasonic reactors performances. This procedure was then extended to all our experimental results under heterogeneous conditions. It was thereby possible to estimate a power fraction defined as the equivalent ultrasonic power devoted to cavitation sonochemical activity divided by the total ultrasonic power estimated by calorimetry. This methodology leads to curves given in Fig. 12 where the power fraction is given as a function of the developed surface area by solid particles within the reactor. Finally, as exhibited in Fig. 12, the power fraction remains constant at first, but decreases sharply after a critical developed surface area. Therefore, the ultrasonic power distribution changes: mainly devoted to sonochemistry for low developed surface areas (below 10 -2 m 2 ) it is dissipated into mechanical effects for higher areas. So, using this type of diagram can be helpful to determine the predominant effect of ultrasound in an heterogeneous medium simulated by glass beads and thereby to determine the efficiency of our sonochemical reactor.

Acoustic radiation power

In order to estimate directly the sonochemical activity from physical tests, special attention has been given to the radiation power, because the calorimetric ultrasonic power seems not to be adapted for the entire range of studied developed surface areas (sections 3.1 and 3.2).

At 575 kHz, acoustic radiation power and calorimetric power were compared for homogeneous medium. The obtained values (PUS = 51.5 ± 0.5 W and PUS-rad = 51.0 ± 1.0 W) proves our analytical method is efficient. Then the acoustic radiation power was measured at 575 kHz in the presence of 8-12 µm glass beads, at different concentrations, for the same calorimetric power (PUS = 51.5 ± 0.5 W). Normalized results of triiodine formation rate, calorimetric power and radiation power were compared (Fig. 13). The calorimetric power remains constant as mentioned previously (section 3.1), but the acoustic radiation power appears to follow the same trend as the sonochemical activity measured via the triiodine formation rate. At low developed surface area, the radiation power remains constant (ratio close to 1), so the presence of particles does not perturb ultrasound waves propagation. Nevertheless, above a critical value of developed surface area (around 10 - 1 m 2 ), radiation power decreases drastically. This is due to wave-matter interactions, mainly scattering and attenuation, induced by glass beads [START_REF] Allegra | Attenuation of Sound in Suspensions and Emulsions: Theory and Experiments[END_REF][START_REF] Su | Particle size characterization by ultrasonic attenuation spectra[END_REF][START_REF] Challis | Ultrasonic wave propagation in concentrated slurries -The modelling problem[END_REF]. Hence glass beads, whose acoustic impedance is different than water acoustic impedance, disturb wave propagation towards the target. As a conclusion, at the studied frequency, contrary to the calorimetric power, the acoustic radiation power is a relevant parameter to describe the influence of solids on sonochemical activity.

Conclusions

The aim of this paper was to acquire a better knowledge on to study the sonochemical activity in heterogeneous medium, according to the varying concentration (0-80 g.L -1 ) and diameter Whatever the concentration and diameter of glass beads are, the ultrasonic power measured by calorimetry was not affected by particles glass beads addition, even when the power supply was reduced. One might here consider that such a result could be expected since the ultrasonic power measured by calorimetry only gives general information on the overall energy available in the system without any distinction on its nature. However, the results from the chemical characterization have shown dependence between the area of the surface developed by the particles and the chemical activity of ultrasound. On the contrary, the chemical characterization has shown dependence between the surface area of the surface developed by the particles and the chemical activity of ultrasound. Indeed, the sonochemical activity remains constant below a surface area threshold critical area value and it sharply decreases above it. In our case, it seems the addition of particles did not increase bubbles population by playing the role of nucleation sites. Above the critical surface area, the activity decrease is due to wave scattering and attenuation on the one hand, and bubble stabilization on the other hand, which reduced the energy release.

Glass beads addition has the same effect on the sonochemical activity and on the acoustic radiation power, while the measured calorimetry is unchanged. As a consequence, the acoustic radiation power is a relevant parameter to describe the influence of solids on sonochemical activity.

The criterion suggested by our results is the surface area developed by of the particles within the reactor, whose advantage is to take into account both size and concentration of the heterogeneous media. Once a threshold of the developed surface area is overpassed, a switch in the proportion of mechanical and chemical energy leads to a decrease of the sonochemical activity.

Fig. 1 .

 1 Fig. 1. Ultrasonic reactors (1.a: high frequency reactor, 1.b: low frequency reactor)

Fig. 2 .

 2 Fig. 2. Examples of chemical characterization by iodometry of an ultrasonic system at 575 kHz (dp = 8-12 µm, V = 500 mL, PUS = 51.5 ± 0,5 W, T = 20 ± 1 °C)

  Fig 3.a.

Fig. 3 .

 3 Fig. 3. Ultrasonic power measured by calorimetry. a: with 8-12 µm glass beads, b: with 90-150 µm glass beads For the studied frequencies and Then, at the same electrical power level, for all the studied frequencies and in presence of 8-12 µm diameter glass beads, the ultrasonic power was measured by calorimetry. in heterogeneous medium was represented in The result is displayed in Fig. 3.a. It can be observed that the addition of particles has no effect on PUS whatever the concentration is in the range from 0.1 to 5 g.L -1 , because the obtained calorimetric power is close to 50 W for all the concentrations. This result was corroborated by other glass bead diameters (Fig 3.b). Moreover, some complementary experiments were carried out for the 5 frequencies with an ultrasonic power of 22 W and the addition of particles has also no effect on PUS.

Fig. 4 .

 4 Fig. 4. Sonochemical activity measured by iodometry in homogeneous medium (V = 500 mL, PUS = 51.5 ± 0.5 W)

Fig. 5 .

 5 Fig. 5. Effect of glass bead concentration on triiodine formation rate, for different frequencies (dp = 8-12 µm, V = 500 mL, PUS = 51.5 ± 0,5 W, T = 20 ± 1 °C)

Fig. 6 . 7 .

 67 Fig. 6. Effect of the glass bead concentration on the triiodine formation rate, for different diameters (f = 575 kHz, V = 500 mL, PUS = 51.5 ± 0.5 W, T = 20 ± 1 °C)For all these experiments, both diameter and concentration of particles are likely to be different. So, in order to take into account these two parameters simultaneously, the area of the developed surface due to the presence of beads inside the reactor was considered as a new criterion to express the results. It is defined as the area of the surface induced by the amount

Fig. 7 .

 7 Fig. 7. Normalized I3 -formation rates, for different surface areas and diameters. (f = 575 kHz, V = 500 mL, PUS = 51.5 ± 0.5 W, T = 20 ± 1 °C)

Fig. 8 .

 8 Fig. 8. I3 -formation rates ratio at different frequencies for different surface areas and diameters. (V = 500 mL, PUS = 51.5 ± 0.5 W, T = 20 ± 1 °C, dp from 8-12 µm to 6 mm)

Fig. 9 .

 9 Fig. 9. Combined effect of gas and glass beads presence on triiodine formation rate (dp = 8-12 µm, f = 575 kHz, V = 500 mL, PUS = 51.5 ± 0.5 W, T = 20 ± 1 °C) Without any beads, triiodine formation rate decreases from 2.3 ± 0.1 µmol.min -1 under air condition to 0.65 ± 0.04 µmol.min -1 under argon condition. Under argon condition, there is no contribution of the oxidant reagents generated by oxygen ( • OOH, • OH et O) as reported in the

Fig. 10 .

 10 Fig. 10. I3 -formation rate as a function of calorimetric ultrasonic power for the same electric power in homogeneous medium (0 g.L -1 , V = 500 mL, T = 20 ± 1 °C)

Fig. 11 .

 11 Fig. 11. Instance of calibration (f = 575 kHz, 0 g.L -1 , V = 500 mL, T = 20 ± 1 °C) to estimate the equivalent ultrasonic power devoted to chemical activity under heterogeneous conditions.

Fig. 12 .

 12 Fig. 12. Dependence of the ultrasonic power devoted to the sonochemical activity on the developed surface area.

Fig. 13 .

 13 Fig. 13. Comparison of triiodine formation rate, calorimetric power and radiation power in heterogeneous medium (dp = 8-12 µm, f = 575 kHz, V = 500 mL, T = 20 ± 1 °C)

( 8 -

 8 [START_REF] Lim | The effects of liquid height/volume, initial concentration of reactant and acoustic power on sonochemical oxidation[END_REF] to 6000 µm) of chemically inert glass beads. A wide range of ultrasonic frequency (20 to 1135 kHz) was used. The ultrasonic power was measured by calorimetry or by radiation, and the sonochemical activity was monitored by iodide oxidation following the formation rate of triiodide.

Table 1 . Summary of main publications about ultrasound in heterogeneous media

 1

	Authors	Particles	Diameter (µm)	Concentration (g.L -1 )	Calculated area (m²)	Frequency (kHz)	Gas condition	Reported effects
	Keck et al. [6]	Quartz	2-25	1-25	0.15-10 4	68-206-353-620-1028	N2/O2 Ar/O2	The particle addition reduces the sonochemical activity except at 206 kHz
	Lu et al. [11]	Silica Alumina	2-130 130	2-200	0.92-6 10 3	20	Air	The sonoactivity is reduced, for all diameters and concentrations
								The sonoactivity is
	Tuziuti et al. [7]	Alumina	1-80	10-100	0.38-15.2	42	Air	increased with an appropriate particle
								size and concentration
	Her et al. [8]	Glass with and without TiO2 coating	50-5000	10-200	48-4800	28-580-1000	Air	The sonoactivity is decreased with particle addition except at 28 kHz
		Resin	625					The sonoactivity is
	Stoian et al. [9]	Sand	309	12.2-610	12.2-30.2	20	Air	maximal for a 0.4 solid volumetric
		Glass	207-1290					concentration
	Son et al. [10]	Clay Glass	75 75-2000	100-333	0.12-3.2	28	Air	No difference in calorimetric energies. SCL depends on the presence and the size
	This research	Glass beads	8-6000	0.003-80	1.5 10 -4 -0.95	20-376-575 -858-1135	Air Ar

2. Materials and methods 2.1 . Ultrasonic reactors

	Two different devices are used to generate ultrasound. The high frequency generator MFG
	and the corresponding transducers are provided by Meinhardt Ultrasonics (Fig 1.a). Two
	transducers are used in order to vary frequency: 376, 575, 858 and 1135 kHz are studied.
	These interchangeable flat transducers (50 mm diameter) are placed at the bottom of the
	vessel. The low frequency equipment is a homemade cup horn based on a 20 kHz Sonics
	Vibracell 75115 generator (Fig 1.b) with a 25 mm probe.


Ke Zhu
email: zhu@ipgp.fr

Frederic Moynier

Martin Schiller

Conel M O'

D Alexander

Jean-Alix J-A Barrat

Addi Bischoff

Martin Bizzarro

Frédéric Moynier

Mass-independent and mass-dependent Cr isotopic composition of the Rumuruti (R) chondrites: Implications for their origin and planet formation

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Chondrites which contain chondrules, matrix, Fe-Ni metal and refractory inclusions, are the most primitive rocks in the Solar System available to us (e.g., [START_REF] Krot | 1.1 -Classification of Meteorites and Their Genetic Relationships A2 -Holland[END_REF]. Because they did not melt and differentiate, they may record the information of evolution of early Solar System. Chondrites also have a bulk chemical composition that is thought to be representative of their parent bodies, and are often used to approximate the compositions of the building blocks of the terrestrial planets such as the Earth (e.g., [START_REF] Allègre | The chemical composition of the Earth[END_REF]. Amongst the chondrites, the Rumuruti (R) chondrites are only recognized as a new group and class in 1994 [START_REF] Bischoff | Acfer 217-A new member of the Rumuruti chondrite group (R)[END_REF][START_REF] Kallemeyn | The compositional classification of chondrites: VII. The R chondrite group[END_REF][START_REF] Rubin | Pecora Escarpment 91002: A member of the new Rumuruti (R) chondrite group[END_REF][START_REF] Schulze | Mineralogy and chemistry of Rumuruti: The first meteorite fall of the new R chondrite group[END_REF]. The physical and chemical features of the R chondrites are reviewed in detail by [START_REF] Bischoff | The Rumuruti chondrite group[END_REF].

Unlike other chondrites, including carbonaceous (CC), ordinary (OC) and enstatite chondrites (EC), the R chondrites have some unusual or characteristic features : 1) most of the R chondrites are breccias that contain clasts with various degree of metamorphism; 2) they have high abundances of olivine (70 vol.%); 3) matrix and chondruls have similar abundances; 4) they formed under high oxygen fugacity conditions as demonstrated by the absence of Fe-Ni metal; 5) the size of chondrules are on average ~400 μm; 6) they have element (except for Zn and Se) abundances that are similar to those in ordinary chondrites (~0.95 times of CI chondrites); 7) they have high TiO2 contents in the Cr-spinels; 8) Ca-Al-rich inclusions (CAIs) are rare (Rout and Bischoff, 2008;Rout et al., 2009Rout et al., , 2010)); 9) they have higher Δ 17 O (mass-independent 17 O/ 16 O isotope ratios; 2.72 ± 0.31) compositions than all the other chondrite groups; 10) very primitive type 3 lithologies only exist as clasts in R chondrite breccias (Bischoff, 2008); 11) within the most primitive type 3 lithologies the chondrule-matrix complementary is well defined (Friend et al., 2017).

Combining Δ 17 O with ε 54 Cr (the parts per 10,000 deviation of the mass fractionation corrected 54 Cr/ 52 Cr ratio from a terrestrial standard) is a powerful tool for establishing relationships between Solar System materials [START_REF] Clayton | Oxygen isotope studies of carbonaceous chondrites[END_REF][START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF][START_REF] Warren | Stable-isotopic anomalies and the accretionary assemblage of the Earth and Mars: A subordinate role for carbonaceous chondrites[END_REF]. All known bulk Solar System materials belong to one of two reservoirs: carbonaceous-chondrite (CC) with ε 54 Cr value > 0.3 and non-carbonaceous-chondrite (NC) with ε 54 Cr value < 0.3 [START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF][START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF]. However, the ε 54 Cr values for R chondrites are still poorly known. One of only two R chondrites with previously reported ε 54 Cr values [0.43 ± 0.09, Elephant Moraine [EET] 96026 [START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF]] has since been re-classified as a CV3 or an ungrouped C4/5 chondrite (Meteoritical Bulletin Database;

https://www.lpi.usra.edu/meteor). The only other measured R chondrite, Northwest Africa [NWA] 753 (R3.9), -0.11 ± 0.25 [START_REF] Larsen | Evidence for magnesium isotope heterogeneity in the solar protoplanetary disk[END_REF], has a large uncertainty that spans the ε 54 Cr values of both OCs and ECs. Furthermore, just one measured sample cannot safely be taken to represent the R chondrite parent body, since there could be some degree of ε 54 Cr variability within a chondrite parent body as already observed for CV, CO, and CM chondrites [START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF][START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF]. Apart from the one relatively imprecise ε 54 Cr measurement, no other iron-group neutron-rich nucleosynthetic isotope data has been reported for the R chondrites (e.g., Ca, Ti and Ni isotope anomalies). Since the R chondrites are non-carbonaceous chondrites (NCs), studying their ε 54 Cr composition can also be used to further test, whether the NCs all have different Cr isotopic composition than the carbonaceous chondrites (e.g., [START_REF] Göpel | Mn-Cr systematics in primitive meteorites: Insights from mineral separation and partial dissolution[END_REF][START_REF] Sanborn | Carbonaceous Achondrites Northwest Africa 6704/6693: Milestones for Early Solar System Chronology and Genealogy[END_REF][START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF][START_REF] Warren | Stable-isotopic anomalies and the accretionary assemblage of the Earth and Mars: A subordinate role for carbonaceous chondrites[END_REF].

The variations in the abundance of 53 Cr (expressed as ε 53 Cr) mostly result from the decay of 53 Mn, with a half-life of 3.7 Ma [START_REF] Holden | Total half-lives for selected nuclides[END_REF][START_REF] Honda | Half-life of Mn 53[END_REF].

The 53 Cr is a sensitive tracer of the timing of formation of the chondrites and their components, and the differentiation of planetesimals and planets [START_REF] Lugmair | Early solar system timescales according to 53 Mn-53 Cr systematics[END_REF][START_REF] Shukolyukov | Manganese-chromium isotope systematics of carbonaceous chondrites[END_REF]. For example, the 53 Mn-53 Cr short-lived chronometry has been successfully used to date the accretion of chondrite parent bodies [START_REF] Trinquier | 53Mn-53Cr systematics of the early Solar System revisited[END_REF] and formation of chondrules [START_REF] Nyquist | Manganese-chromium formation intervals for chondrules from the Bishunpur and Chainpur meteorites[END_REF][START_REF] Yamashita | 53Mn-53Cr chronometry of CB chondrite: Evidence for uniform distribution of 53Mn in the early solar system[END_REF][START_REF] Yin | Toward consistent chronology in the early solar system: high-resolution 53Mn-53Cr chronometry for chondrules[END_REF][START_REF] Yin | Mn-53Cr Systematics of Allende Chondrules and epsilon 54Cr--Cap Delta17O Correlation in Bulk Carbonaceous Chondrites[END_REF]Zhu et al., 2019a;Zhu et al., 2020a) of which ages potentially represent the earliest accretion ages of their host chondrites. Therefore, the ε 53 Cr values of the R chondrites may also provide significant information about the origin of their parent body(ies), as well as its possible relationship to differentiated achondrite parent bodies.

The Cr stable isotopes (expressed as δ 53 Cr, the per mil variation of the 53 Cr/ 52 Cr ratio relative to a terrestrial standard, NIST SRM 979) is a tracer of planetary evolution, including volatile depletion [START_REF] Sossi | Volatile loss following cooling and accretion of the Moon revealed by chromium isotopes[END_REF]Zhu et al., 2019c), magmatic processes [START_REF] Bonnand | The influence of igneous processes on the chromium isotopic compositions of Ocean Island basalts[END_REF]Bonnand et al., 2016a;[START_REF] Shen | Stable chromium isotope fractionation during magmatic differentiation: Insights from Hawaiian basalts and implications for planetary redox conditions[END_REF][START_REF] Sossi | Volatile loss following cooling and accretion of the Moon revealed by chromium isotopes[END_REF]Zhu et al., 2019c), and possibly core formation [START_REF] Moynier | Isotopic evidence of Cr partitioning into Earth's core[END_REF]. However, an unknown is the starting isotope composition of the material before fractionation, i.e., those of the planetary precursors. It is therefore important to investigate the presently unknown Cr stable isotopic composition of the R chondrites, including the various petrologic types (from R3 to R6).

Here, we report high-precision mass-independent and mass-dependent Cr isotope data for 12 bulk R chondrites that sample the full range of petrologic types (3-6) and one R chondrite-like clast from a polymict ureilite, Almahata Sitta. We use the radiogenic and nucleosynthetic Cr isotope anomalies and Cr stable isotope compositions of the R chondrites to discuss their possible relationship with other chondrites and achondrites. The Cr isotope composition of the R chondrite-like clast within the polymict ureilite Almahata Sitta [START_REF] Bischoff | Asteroid 2008 TC3-Almahata Sitta: A spectacular breccia containing many different ureilitic and chondritic lithologies[END_REF]Horstmann and Bischoff 2014) is used to test whether this clast is indeed related to R-chondrites, and further track the potential transport processes and dynamics (from a chondrite parent body to an achondrite parent body) in the early Solar System.

Samples and analytical methods

Sample information and dissolution

The sample suite analyzed in this study includes 12 bulk R chondrites: Rumuruti R chondrite samples with no fusion crusts weighing 0.5 to 1 g were crushed to a fine powder using a boron carbide mortar and pestle. A fraction of the powders (ca.

100 mg) were digested by sequential mixtures of concentrated HF+HNO3 (2:1) and HNO3 + HCl (1:3) in Parr Bombs under pressurized steel jackets for 3-4 days at 180 ℃ respectively, and no visible residues were observed. Then, ~1%, ~5% and ~5% aliquots were extracted for measurements of 55 Mn/ 52 Cr ratios, mass-independent and mass-dependent Cr isotope fractionation, respectively. The rest of the solution is kept for other chemical and isotopic analysis.

Mass-independent Cr isotope (ε 53 Cr and ε 54 Cr) measurements

A four-step column chemistry was used to purify the sample for mass-independent Cr isotope measurements in a clean laboratory at Earth and Planetary Laboratory, Carnegie Institute for Science. Firstly, we used an anion chromatographic purification column to efficiently remove Fe and Ni in 6M HCl. Prior to sample loading on cation exchange columns, we used a Cr pre-treatment procedure involving dissolution in 10M HCl at >120 °C to efficiently promote the formation of Cr 3+ -Cl species, which have a low affinity for the cation exchanger and thus elute early.

This was followed by elution of Cr on a 1 ml cation exchange column in 20 ml of 0.5M HNO3 to remove the major elements, including Mg, Ca, Al, and Ni, and to collect all the Cr species (major Cr 0 and minor Cr 2+ and Cr 3+ ) to reach a >99% recovery. The samples were then exposed to 0.5M HNO3 + 0.6% H2O2 at room temperature for >1 day to promote the formation of Cr 3+ [START_REF] Larsen | Chromatographic speciation of Cr(III)-species, inter-species equilibrium isotope fractionation and improved chemical purification strategies for high-precision isotope analysis[END_REF]. However, it is difficult to transform all Cr to Cr 3+ , so the Cr 0 -bearing material is collected in 0.5 ml of the loading solution and 0.5 ml of 0.5N HNO3 elution to increase the recovery to >95% in the next column. The third clean-up column involved Cr purification from Al, Ti, V, and Fe (and other high-field-strength elements), as well as Na and K, on a small (0.33ml) cation exchange column using 0.5M HNO3, 1M HF, and 6M HCl. Finally, for the fourth column, 0.7 ml of TODGA resin was used in 8N HCl to remove the residual Fe, V, and Ti (which remained on the column) that have isobaric isotopes with 54 Cr ( 54 Fe) and 50 Cr ( 50 V and 50 Ti) [START_REF] Pedersen | Testing accretion mechanisms of the H chondrite parent body utilizing nucleosynthetic anomalies[END_REF]. The full procedure reaches a total yield of between 95% and 99%, and effectively removes any matrix, especially Fe, V, and Ti, that might influence analysis by Multiple Collector-Inductively Coupled Plasma-Mass Spectrometry (MC-ICP-MS). The total blank of the isolation procedure is 10-12 ng for Cr and can be neglected given the typical sample size, ~10 μg of Cr.

The 55 Mn/ 52 Cr ratios were measured on a MC-ICP-MS Neptune Plus. We initially prepared three Mn-Cr doped artificial standard solutions gravitationally, with

Mn-Cr contents of 10-100 ppb, 50-100 ppb and 100-100 ppb and Mn/Cr ratios of 0.1, 0.5 and 1.0. The unpurified sample solutions were diluted to a Cr content of ~100 ppb.

The intensities for 55 Mn and 52 Cr on faraday detectors obtained when analyzing the standard and sample solutions ranged from 0.5 V to 5 V, and 10 cycles of 4 seconds each were measured in each analysis to obtain a target precision for the 55 Mn/ 52 Cr ratios better than 1%. After establishing a calibration curve (R 2 > 0.999) based on the true and measured 55 Mn/ 52 Cr ratios of the three artificial standards, the 55 Mn/ 52 Cr ratios of the chondrite samples could be calculated. The final estimated precision is <5% (Zhu et al., 2020a;Zhu et al., 2020b).

Compared to Thermal Ionization Mass Spectrometry (TIMS), chromium isotope analysis by MC-ICP-MS has the advantage that the high ionization efficiency of the plasma results in relative constant mass fractionation, which by use of the sample-standard-bracketing approach can be well corrected for and essentially eliminates the need for consideration of the instrumental mass fractionation. Thermal ionization, on the other hand, inherently does not produce stable mass fractionation through time, which may cause a residual, apparent mass-dependent effect after mass fractionation correction by exponential law (assuming kinetic fractionation), which is demonstrated by the correlation between ε 53 Cr and ε 54 Cr with slope of ~2.6 of Cr isotope standards [START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF][START_REF] Trinquier | The nature of the KT impactor. A 54 Cr reappraisal[END_REF]. This effect ultimately limits both the obtainable accuracy and precision of mass fractionation corrected isotope data obtained by TIMS. Therefore, Cr isotope analysis by MC-ICP-MS can achieve higher data precision than by TIMS for comparable measurement signal and time but typically requires larger amount of sample due to the lower transmission efficiency of the MC-ICP-MS (e.g., [START_REF] Pedersen | Testing accretion mechanisms of the H chondrite parent body utilizing nucleosynthetic anomalies[END_REF][START_REF] Schiller | Precise measurement of chromium isotopes by MC-ICPMS[END_REF]Zhu et al., 2020b).

The Cr isotopic compositions of all the samples were determined using one of

Mass-dependent Cr isotope (δ 53 Cr) measurements

The whole procedure of mass-dependent Cr isotope analysis was performed at the Institut de Physique du Globe de Paris (IPGP) on aliquots of the same dissolutions used for mass-independent isotope measurements. This measurement techniques followed the same procedure as described in [START_REF] Sossi | Volatile loss following cooling and accretion of the Moon revealed by chromium isotopes[END_REF] and Zhu et al. (2019c).

First, the appropriate amount of 50 Cr-54 Cr double spike (28% of the Cr content endemic to the sample) was added to the aliquot, which was then refluxed in a closed beaker at 120 °C overnight to homogenize the sample and spikes (e.g., [START_REF] Wu | High-Sensitivity Measurement of Cr Isotopes by Double Spike MC-ICP-MS at the 10 ng Level[END_REF]. Then, samples were chemically purified for Cr via a two-step cation exchange chromatography followed by previous works [START_REF] Sossi | Volatile loss following cooling and accretion of the Moon revealed by chromium isotopes[END_REF]Zhu et al., 2019c).

This method has a total procedural yield of 60-90% and a blank of ~5 ng of Cr.

Compared to the total ~10 μg of Cr, the blank can be neglected. The final Cr cut was evaporated in concentrated HNO3 drops 3 to 5 times to convert the HCl medium to HNO3 and to remove leftover organics (i.e., the resin) following which the samples were diluted to a concentration of 1 ppm Cr, in 2% (0.317 M) HNO3 for isotope analysis.

The Cr stable isotope compositions of these purified samples were measured on a Thermo Scientific Neptune Plus MC-ICP-MS housed at the IPGP. Analytical details are described in [START_REF] Sossi | Volatile loss following cooling and accretion of the Moon revealed by chromium isotopes[END_REF] and Zhu et al. (2019c). The final Cr stable isotope data (δ 53 Cr) for R chondrites were corrected taking their respective mass-independent Cr isotope compositions analyzed on the same aliquots. The isotopic ratio for samples is reported in delta notation relative to NIST SRM 979:

δ $‰& = '( / ) / ) -1 × 1000. (2)
The uncertainties quoted for individual samples are 2SD of single sample measurements (100 cycles for at least two times) or 2SD reproducibility of several NIST SRM 979 measurements in the same analytical session (~0.02 ‰), whichever is the largest.

Results

All the Mn/Cr ratios, mass-independent and mass-dependent Cr isotope data for the 12 bulk R chondrites and the clast MS-CH from the meteorite/asteroid Almahata Sitta are reported in Table 1. The ε 54 Cr values for all R chondrites are homogeneous, with an average value of -0.06 ± 0.08 (2SD, N = 12) (Figures 1 and2). All the R chondrites have a restricted range of 55 Mn/ 52 Cr ratios of 0.68 ± 0.04 (2SD, except NWA 2446 which has a 55 Mn/ 52 Cr of 0.60), but have different ε 53 Cr values ranging from 0.19 ± 0.02 to 0.27 ± 0.02 (Figure 3a,b), averaging at 0.23 ± 0.05 (2SD, N = 12). There is no correlation between the 55 Mn/ 52 Cr ratios and the ε 53 Cr values (Figure 3b). The R-chondrite-like clast, MS-CH, possesses ε 53 Cr = 0.18 ± 0.04 and ε 54 Cr = -0.16 ± 0.07 that are indistinguishable within uncertainties to those of the R chondrites. Also, all the R chondrites possess homogeneous stable Cr isotope compositions (Figure 4), with an average δ 53 Cr = -0.12 ± 0.03 ‰ (2SD, N = 12) that is indistinguishable to that of MS-CH with δ 53 Cr of -0.11 ± 0.05 ‰.

The mass-independent Cr isotope data for PCC-1 and DTS-2b in this study are consistent with literature data [START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF][START_REF] Schiller | Precise measurement of chromium isotopes by MC-ICPMS[END_REF][START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF][START_REF] Trinquier | 53Mn-53Cr systematics of the early Solar System revisited[END_REF]Zhu et al., 2019b;Zhu et al., 2020b).

The mass-dependent δ 53 Cr data (measured by double spike technique) for BHVO-2 and PCC-1 are also consistent with the literature data (Bonnand et al., 2016b;[START_REF] Liu | High-Precision Measurement of Stable Cr Isotopes in Geological Reference Materials by a Double-Spike TIMS Method[END_REF][START_REF] Schoenberg | The stable Cr isotopic compositions of chondrites and silicate planetary reservoirs[END_REF][START_REF] Sossi | Volatile loss following cooling and accretion of the Moon revealed by chromium isotopes[END_REF][START_REF] Wu | High-Sensitivity Measurement of Cr Isotopes by Double Spike MC-ICP-MS at the 10 ng Level[END_REF]Zhu et al., 2019c).

Discussion

Homogeneous ε 54 Cr in R chondrites

Cosmogenic effects, especially in samples with high Fe/Cr ratios and cosmic ray exposure ages (CREA), can modify the Cr isotope composition (e.g., [START_REF] Shima | Distribution of spallation produced chromium between alloys in iron meteorites[END_REF]. The R chondrites have lower Fe/Cr ratios of ~105 [START_REF] Kallemeyn | The compositional classification of chondrites: VII. The R chondrite group[END_REF][START_REF] Schulze | Mineralogy and chemistry of Rumuruti: The first meteorite fall of the new R chondrite group[END_REF] and similar CREA of 0.1~74 Ma [START_REF] Schultz | Rumuruti chondrites: Noble gases, exposure ages, pairing, and parent body history[END_REF] relative to angrites (Fe/Cr = 70-700; CREA = 6-70 Ma) that do not show any cosmogenic effects (Zhu et al., 2019b). Moreover, the ε 54 Cr for all the R chondrites irrespective of their exposure age are indistinguishable from each other, such that the Cr isotope alteration from cosmogenic effects, if present, are currently not detectable and, thus, can be ignored.

As a group/class of NCs, the homogeneous ε 54 Cr value of the R chondrites of -0.06 ± 0.08 (2SD, N = 12; Figures 1 and2) confirms the observation that there is a Cr isotopic difference between the NCs (ε 54 Cr < 0.3) and the CCs (ε 54 Cr > 0.3) [START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF][START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF]. The ε 54 Cr values for R chondrites are similar within error to those of the ECs [ε 54 Cr = 0.01 ± 0.11; 2SD, N = 12; [START_REF] Mougel | Chromium isotopic homogeneity between the Moon, the Earth, and enstatite chondrites[END_REF][START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF][START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF]Zhu et al., 2020a)]. We can use this new value to update the ε 54 Cr sequence between the different groups of chondrites (Figure 1) to be:

CC > EC = RC > OC [START_REF] Göpel | Mn-Cr systematics in primitive meteorites: Insights from mineral separation and partial dissolution[END_REF][START_REF] Mougel | Chromium isotopic homogeneity between the Moon, the Earth, and enstatite chondrites[END_REF][START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF][START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF]. It should be noted that the average ε 54 Cr value for R chondrites also overlaps within error with those of the Earth [ε 54 Cr = 0.09 ± 0.12; 2SD, N=14, [START_REF] Mougel | Chromium isotopic homogeneity between the Moon, the Earth, and enstatite chondrites[END_REF][START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF] [START_REF] Righter | Compositional relationships between meteorites and terrestrial planets[END_REF]] that are more commonly proposed as major building blocks of the Earth [START_REF] Javoy | The chemical composition of the Earth: Enstatite chondrite models[END_REF].

However, the R chondrites have much higher Δ 17 O values [~2.7 [START_REF] Bischoff | The Rumuruti chondrite group[END_REF][START_REF] Schulze | Mineralogy and chemistry of Rumuruti: The first meteorite fall of the new R chondrite group[END_REF][START_REF] Weisberg | The Carlisle Lakes-type chondrites: A new grouplet with high Δ17O and evidence for nebular oxidation[END_REF]] than the Earth-Moon system [~0; [START_REF] Cano | Distinct oxygen isotope compositions of the Earth and Moon[END_REF][START_REF] Clayton | Oxygen isotope studies of achondrites[END_REF][START_REF] Greenwood | Oxygen isotopic evidence for accretion of Earth's water before a high-energy Moon-forming giant impact[END_REF][START_REF] Pack | The triple oxygen isotope composition of the Earth mantle and understanding ΔO17 variations in terrestrial rocks and minerals[END_REF][START_REF] Wiechert | Oxygen isotopes and the Moon-forming giant impact[END_REF][START_REF] Young | Oxygen isotopic evidence for vigorous mixing during the Moon-forming giant impact[END_REF]; Figure 2] and the Mg/Si and Al/Si of the R chondrites do not match those of the bulk Earth (Alexander, 2019b). Therefore, while their Cr isotopic composition and oxidation state match the Earth, the R chondrites or their precursors cannot totally represent the building materials for the Earth-Moon system. Nevertheless, in ε 54 Cr-Δ 17 O space (Figure 2) the R chondrites define an end member and should, therefore, be considered in mixing models for planetary precursors (e.g., Alexander, 2019a;Alexander, 2019b;[START_REF] Dauphas | The isotopic nature of the Earth's accreting material through time[END_REF]. It is also clear that the R chondrites have distinct ε 54 Cr values from those of the OCs [ε 54 Cr = -0.39 ± 0.09; (2SD, N = 18; [START_REF] Pedersen | Testing accretion mechanisms of the H chondrite parent body utilizing nucleosynthetic anomalies[END_REF][START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF][START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF]], suggesting that there is no genetic relationship between them, even though they have some affinities in terms of their bulk compositions (Alexander, 2019b;[START_REF] Kallemeyn | The compositional classification of chondrites: VII. The R chondrite group[END_REF][START_REF] Palme | The composition of a new R-chondrite and the classification of chondritic meteorites[END_REF].

The CB, CO, and CK chondrites all exhibit ε 54 Cr variability within each group (Figure 1) and even between several specimens of the same meteorite, e.g., Allende with ε 54 Cr values ranging from 0.86 ± 0.09 [START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF] to 1.10 ± 0.08 (Zhu et al., 2020b). These heterogeneities probably reflect heterogeneities in the abundances of isotopically extreme CAIs, amoeboid olivine aggregates (AOAs) [with high ε 54 Cr values, up to ~10 [START_REF] Trinquier | Origin of Nucleosynthetic Isotope Heterogeneity in the Solar Protoplanetary Disk[END_REF]] and chondrules [START_REF] Bollard | Combined U-corrected Pb-Pb dating and 26Al-26Mg systematics of individual chondrules -Evidence for a reduced initial abundance of 26Al amongst inner Solar System chondrules[END_REF][START_REF] Olsen | Magnesium and 54Cr isotope compositions of carbonaceous chondrite chondrules -Insights into early disk processes[END_REF][START_REF] Qin | Extreme 54Cr-rich nano-oxides in the CI chondrite Orgueil -Implication for a late supernova injection into the solar system[END_REF]Zhu et al., 2019a;Zhu et al., 2020a) at the scale of the samples analyzed. All measured R chondrites have similar ε 54 Cr values, which is consistent with the very low CAI abundances in R chondrites [START_REF] Russell | A Survey of Calcium-Aluminum-rich Inclusions from R Chondrites: Implications for Relationships Between Meteorite Groups[END_REF].

Similar to the CK chondrites, OCs, and ECs that also experienced various degrees of metamorphism, with petrological types of 3~6 [START_REF] Pedersen | Testing accretion mechanisms of the H chondrite parent body utilizing nucleosynthetic anomalies[END_REF][START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF][START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF], the ε 54 Cr values of the RCs are independent of petrologic types.

This confirms that metamorphism on chondrite parent bodies did not cause the loss of 54 Cr-rich carrying phases (e.g., [START_REF] Dauphas | Neutron-rich chromium isotope anomalies in supernova nanoparticles[END_REF][START_REF] Nittler | Extremely 54Cr-and 50Ti-rich Presolar Oxide Grains in a Primitive Meteorite: Formation in Rare Types of Supernovae and Implications for the Astrophysical Context of Solar System Birth[END_REF][START_REF] Qin | Extreme 54Cr-rich nano-oxides in the CI chondrite Orgueil -Implication for a late supernova injection into the solar system[END_REF].

4.2

The 53 Mn-53 Cr systematics in R chondrites.

It can be seen in Figure 3 that the R chondrites have almost uniform 55 Mn/ 52 Cr ratios (averagely ~0.68) but variable ε 53 Cr values. The ε 53 Cr variation within the R chondrite parent body should result from the mixing of their chondritic components.

Chondrites are complex assemblages, including CAIs, AOAs, chondrules, metals, sulfides, and matrix, and these different components formed at different times and under varying physical conditions [START_REF] Krot | 1.1 -Classification of Meteorites and Their Genetic Relationships A2 -Holland[END_REF]. Refractory inclusions are scarce in R chondrites, i.e., CAIs + AOAs that are < 0.1 vol.% [START_REF] Bischoff | The Rumuruti chondrite group[END_REF][START_REF] Krot | 1.1 -Classification of Meteorites and Their Genetic Relationships A2 -Holland[END_REF], so the mixing of different proportion for chondrules and matrix may contribute to the ε 53 Cr variations. Chondrules are high-temperature magmatic objects and they or their precursors experienced volatile element fractionation [START_REF] Mahan | Volatile element evolution of chondrules through time[END_REF][START_REF] Palme | 2.2 -Solar System Abundances of the Elements[END_REF][START_REF] Pringle | The origin of volatile element depletion in early solar system material: Clues from Zn isotopes in chondrules[END_REF]) that caused Mn/Cr variability.

Chondrules' redox history evolved with time, but globally they are reduced and probably formed at fO2 of iron-wüstite buffer (IW) -1 to -2 [START_REF] Mahan | Volatile element evolution of chondrules through time[END_REF], under which conditions Mn is more volatile than Cr [START_REF] Sossi | Evaporation of moderately volatile elements from silicate melts: experiments and theory[END_REF]. This explains why chondrules have on average lower Mn/Cr ratios [e.g., CO chondrules with 55 Mn/ 52 Cr ranging from 0.2-0.7; (Zhu et al., 2019a)] than unfractionated matrix that can be represented by CI chondrites with 55 Mn/ 52 Cr of ~0.8 [START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF][START_REF] Trinquier | 53Mn-53Cr systematics of the early Solar System revisited[END_REF] and on average lower ε 53 Cr [e.g., CO chondrules with ε 53 Cr ranging from 0.0 to 0.2; (Zhu et al., 2019a)] than matrix representing by CI chondrites with ε 53 Cr of 0.20-0.25 [START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF][START_REF] Trinquier | 53Mn-53Cr systematics of the early Solar System revisited[END_REF]. The bulk R chondrites, OCs and ECs all have similar Mn/Cr ratios, but the ε 53 Cr values of OCs and ECs are systematically lower than those of the R chondrite (Figure 3). This ε 53 Cr difference between different chondrite groups may simply reflect the different ε 53 Cr reservoirs in different chondrite accretion regions.

Homogeneous δ 53 Cr in R chondrites.

Previous studies have shown that all the CCs, OCs, and ECs have homogeneous Cr stable isotope compositions, δ 53 Cr = -0.11 ± 0.05 ‰ [2SD, N = 30; NCC = 11, NOC = 17, NEC = 2; (Bonnand et al., 2016b;[START_REF] Schoenberg | The stable Cr isotopic compositions of chondrites and silicate planetary reservoirs[END_REF]]. The δ 53 Cr values for all chondrites are similar to that of the bulk silicate Earth [δ 53 Cr = -0.11 ± 0.06 ‰;

2SD, N = 36; [START_REF] Schoenberg | The stable Cr isotope inventory of solid Earth reservoirs determined by double spike MC-ICP-MS[END_REF][START_REF] Sossi | Volatile loss following cooling and accretion of the Moon revealed by chromium isotopes[END_REF]], suggesting that core formation or volatile processes cause little Cr stable isotope fractionation, which is further supported by high-pressure metal-silicate experiments (Bonnand et al., 2016b).

In this study, we found that the δ 53 Cr values for the R chondrites, -0.12 ± 0.03 ‰ (2SD, N = 12), also fall in the chondrite-Earth δ 53 Cr range. This supports the view that, when corrected for their different nucleosynthetic signatures, the chondrite reservoirs have a homogeneous Cr stable isotope with δ 53 Cr = -0.12 ± 0.04 ‰ (2SD, N =42).

Different chondrites groups record different redox conditions [START_REF] Rubin | Oxidation state in chondrites[END_REF]. In detail, the oxidized R and CVoxi chondrites record oxygen fugacities (fO2) of fayalite-magnetite-quartz buffer (FMQ) ~-2, OCs have fO2 of FMQ ~-6, and ECs are the most reduced, with fO2 of FMQ -8 to -10 ( [START_REF] Righter | Compositional relationships between meteorites and terrestrial planets[END_REF][START_REF] Righter | Temperature and oxygen fugacity constraints on CK and R chondrites and implications for water and oxidation in the early solar system[END_REF]. The varied redox conditions for different chondrite groups correlate with their hydrogen isotope ratios (Alexander, 2019b), suggesting that the addition of water plays an important role in oxidation. The Cr stable isotope compositions of all these chondrites are homogeneous and, therefore, were not affected by parent body fO2 conditions. This is perhaps surprising given the resolvable isotopic fractionation observed during Cr 2+ /Cr 3+ exchange in magmatic processes on the Earth (Bonnand et al., 2020;[START_REF] Shen | Stable chromium isotope fractionation during magmatic differentiation: Insights from Hawaiian basalts and implications for planetary redox conditions[END_REF], the Moon (Bonnand et al., 2016a;[START_REF] Sossi | Volatile loss following cooling and accretion of the Moon revealed by chromium isotopes[END_REF] and HEDs [(perhaps Vesta; (Zhu et al., 2019c)). However, it is firstly consistent with that water contained little Cr, which would not change the Cr species in chondrite parent body. Then, although it is possible that the presence of water oxidized Cr from Cr 2+ to Cr 3+ , which may result in Cr stable isotope fractionation (Cr 3+ would be isotopically heavier than Cr 2+ ). However, in absence of loss of Cr via volatilization from the chondrite parent body, this effect would not lead to Cr isotope fractionation between chondrite groups. In any case, the homogeneous δ 53 Cr values between all chondrite groups strongly suggests that differentiated planets also had initial δ 53 Cr similar to chondrites, since chondrites are believed as their precursors (e.g., [START_REF] Allègre | The chemical composition of the Earth[END_REF].

The Cr stable isotopic difference between planetary mantles with different oxygen fugacities, e.g., Earth [δ 53 Cr = -0.11 ± 0.06 [START_REF] Schoenberg | The stable Cr isotope inventory of solid Earth reservoirs determined by double spike MC-ICP-MS[END_REF][START_REF] Sossi | Volatile loss following cooling and accretion of the Moon revealed by chromium isotopes[END_REF]], Moon [δ 53 Cr = -0.21 ± 0.03 (Bonnand et al., 2016a;[START_REF] Sossi | Volatile loss following cooling and accretion of the Moon revealed by chromium isotopes[END_REF]] and HEDs (Vesta) [δ 53 Cr = -0.22 ± 0.03 (Zhu et al., 2019c)], is not due to variability in the initial composition but to planetary differentiation processes, e.g., volatile depletion and/or partial melting [START_REF] Sossi | Volatile loss following cooling and accretion of the Moon revealed by chromium isotopes[END_REF]Zhu et al., 2019c).

The R chondrites with petrologic types ranging from 3 to 6 have homogeneous δ 53 Cr values, suggesting that metamorphism does not affect the Cr isotopic composition of the bulk samples. In detail, metamorphism would not redistribute the Cr species inside chondrite parent bodies, which mimics the water effect as discussed above. Thus, in consequence, no differences were observed studying the Cr isotopic compositions of the brecciated rocks among the R chondrites. This is also consistent with the lack of resolvable Cr stable isotopic variability among metamorphic rocks [START_REF] Shen | Chromium isotope signature during continental crust subduction recorded in metamorphic rocks[END_REF][START_REF] Wang | Chromium isotope fractionation during subduction-related metamorphism, black shale weathering, and hydrothermal alteration[END_REF], the δ 53 Cr value of every R chondrite can represent its bulk parent body.

Chromium isotope composition of the R chondrite-like clast of

Almahata Sitta

Almahata Sitta (debris from asteroid 2008 TC3) is a polymict ureilite that contains not only ureilitic clasts but also some chondritic clasts from OCs and ECs [START_REF] Bischoff | Asteroid 2008 TC3-Almahata Sitta: A spectacular breccia containing many different ureilitic and chondritic lithologies[END_REF]. One of the chondritic clasts, MS-CH, is unusual. It is a petrologic type ~3.8 chondrite with a chondrule/matrix ratio of about 1.5. This clast has a Δ 17 O = ~1.76 and contains chondrules with an average size of roughly 450 μm [START_REF] Horstmann | Almahata Sitta-Fragment MS-CH: Characterization of a new chondrite type[END_REF]. All these characteristics are similar to those of the R chondrites. The 55 Mn/ 52 Cr, ε 53 Cr and ε 54 Cr values for this clast determined here are 0.70 ± 0.04, 0.18 ± 0.04, and -0.16 ± 0.07, respectively, and also resemble those of R chondrites [ 55 Mn/ 52 Cr = 0.68 ± 0.04, ε 53 Cr = 0.23 ± 0.05, and ε 54 Cr = -0.06 ± 0.08 (2SD, N = 12)]. These compositions also support the classification of this clast as R chondrite-like. It should be noted that this clast cannot have any genetic relationship to CK chondrites, which have higher ε 54 Cr ranging from 0.33 ± 0.12 [START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF] to 0.63 ± 0.09 [START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF], although the clast contains equilibrated and metamorphosed olivine, similar to CK chondrites [START_REF] Horstmann | Almahata Sitta-Fragment MS-CH: Characterization of a new chondrite type[END_REF]. The δ 53 Cr value of this clast (-0.11 ± 0.15) is also consistent with that of R chondrites, but since all chondrites have similar stable isotopic composition, this is not surprising. However, it should be noted that both the Δ 17 O and ε 54 Cr values for this clast are slightly lower than those of the R chondrite group. More importantly, the clast contains some metals (unknown from R chondrites) and chromites in this clast have much lower TiO2 (~1.35 wt.%) contents [START_REF] Horstmann | Almahata Sitta-Fragment MS-CH: Characterization of a new chondrite type[END_REF] than those of R chondrites (typically >5 wt.%; [START_REF] Bischoff | The Rumuruti chondrite group[END_REF]. There are also no magnetites and platinum-group-element-rich phases in this clast, while this is usually the case for R chondrites [START_REF] Horstmann | Almahata Sitta-Fragment MS-CH: Characterization of a new chondrite type[END_REF]. Therefore, the chemical, petrological and isotopic features of this clast do not match any currently known chondrite groups and it should remain an ungrouped non-carbonaceous chondrite. The similar Δ 17 O and ε 54 Cr signatures between this clast and the R chondrites may suggest they accreted at a similar locations or in a similar environments in the Solar System (e.g., [START_REF] Desch | The effect of Jupiter's formation on the distribution of refractory elements and inclusions in meteorites[END_REF]. Furthermore, the observation of chondritic clasts in achondrites (e.g., Zolensky et al., 1996;Goodrich et al., Bischoff et al., 2006;2010;Patzek et al., 2018) is consistent with the extensive transportation processes in early Solar System (Weidenschilling, 1977), which is also supported by the transportation of chondrule precursors [START_REF] Olsen | Magnesium and 54Cr isotope compositions of carbonaceous chondrite chondrules -Insights into early disk processes[END_REF]Zhu et al., 2019a;Zhu et al., 2020a) and the observation of an angrite-like clast in a CH chondrite [START_REF] Zhang | Unique angrite-like fragments in a CH3 chondrite reveal a new basaltic planetesimal[END_REF].

Conclusion

This work reports the first high-precision nucleosynthetic signatures of the Rumuruti (R) chondrites. All the R chondrites possess homogeneous ε 54 Cr: -0.06 ± 0.08 (2SD, N = 12), which is independent on their petrological types (R3-R6). The Rumuruti chondrites are from this study, and the others come from the literature data [START_REF] Göpel | Mn-Cr systematics in primitive meteorites: Insights from mineral separation and partial dissolution[END_REF][START_REF] Mougel | Chromium isotopic homogeneity between the Moon, the Earth, and enstatite chondrites[END_REF][START_REF] Pedersen | Testing accretion mechanisms of the H chondrite parent body utilizing nucleosynthetic anomalies[END_REF][START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF][START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF][START_REF] Trinquier | 53Mn-53Cr systematics of the early Solar System revisited[END_REF][START_REF] Yamashita | 53Mn-53Cr chronometry of CB chondrite: Evidence for uniform distribution of 53Mn in the early solar system[END_REF]. The ε 54 Cr = 0.09 ± 0.12 (2SD, N = 14) for Earth is from data in this study and literature [START_REF] Mougel | Chromium isotopic homogeneity between the Moon, the Earth, and enstatite chondrites[END_REF][START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF], while the ε 54 Cr = 0.09 ± 0.08 for the Moon is from [START_REF] Mougel | Chromium isotopic homogeneity between the Moon, the Earth, and enstatite chondrites[END_REF]. [START_REF] Clayton | Oxygen isotope studies of carbonaceous chondrites[END_REF][START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF]. The R chondrites (described as average values with 2SD uncertainty) are located at the top of this diagram. CC: Carbonaceous chondrite; NC: non-CCs; APB: angrite parent body; UPB: ureilite parent body. The colored circles represent the same samples in Fig. 1. The detailed data source for Cr isotopes are: chondrites [START_REF] Göpel | Mn-Cr systematics in primitive meteorites: Insights from mineral separation and partial dissolution[END_REF][START_REF] Mougel | Chromium isotopic homogeneity between the Moon, the Earth, and enstatite chondrites[END_REF][START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF][START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF], Earth [START_REF] Qin | Contributors to chromium isotope variation of meteorites[END_REF][START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF], Moon [START_REF] Mougel | Chromium isotopic homogeneity between the Moon, the Earth, and enstatite chondrites[END_REF], one aubrite [START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF], SNC-Mars [START_REF] Kruijer | Onset of magma ocean solidification on Mars inferred from Mn-Cr chronometry[END_REF], angrite APB (Zhu et al., 2019b), HED-Vesta [START_REF] Trinquier | Widespread 54Cr heterogeneity in the inner solar system[END_REF], Acapulcoite-Lodranite clan [START_REF] Li | Evidence for a multilayered internal structure of the chondritic acapulcoite-lodranite parent asteroid[END_REF], Winonaites [START_REF] Li | Evidence for a multilayered internal structure of the chondritic acapulcoite-lodranite parent asteroid[END_REF], UPB [START_REF] Yamakawa | Chromium isotope systematics of achondrites: Chronology and isotopic heterogeneity of the inner solar system bodies[END_REF]Zhu et al., 2020b). The O isotope data sources are from two review papers [START_REF] Greenwood | Melting and differentiation of early-formed asteroids: The perspective from high precision oxygen isotope studies[END_REF][START_REF] Ireland | Oxygen Isotopes and Sampling of the Solar System[END_REF]. chondrites (Bonnand et al., 2016b;[START_REF] Schoenberg | The stable Cr isotopic compositions of chondrites and silicate planetary reservoirs[END_REF], Earth [START_REF] Jerram | The δ53Cr isotope composition of komatiite flows and implications for the composition of the bulk silicate Earth[END_REF][START_REF] Schoenberg | The stable Cr isotope inventory of solid Earth reservoirs determined by double spike MC-ICP-MS[END_REF][START_REF] Sossi | Volatile loss following cooling and accretion of the Moon revealed by chromium isotopes[END_REF], Moon (Bonnand et al., 2016a;[START_REF] Sossi | Volatile loss following cooling and accretion of the Moon revealed by chromium isotopes[END_REF] and HEDs-Vesta (Zhu et al., 2019c).

  ], Moon [ε 54 Cr = 0.09 ± 0.08;[START_REF] Mougel | Chromium isotopic homogeneity between the Moon, the Earth, and enstatite chondrites[END_REF]] and one aubrite meteorite [ε 54Cr = -0.16 ± 0.19; {Trinquier, 2007 #139}]. Other than the ε 54 Cr features, the R chondrites also formed with oxygen fugacities [FMQ -4 ~ FMQ 0 oxygen buffer;[START_REF] Righter | Temperature and oxygen fugacity constraints on CK and R chondrites and implications for water and oxidation in the early solar system[END_REF]] that were much closer to the Earth's upper mantle value [fO2 = FMQ -4 ~ FMQ +2;[START_REF] Mccammon | The paradox of mantle redox[END_REF]] compared to the much more reduced ECs

ε

  54 Cr values for R chondrites are similar to those of enstatite chondrites, the Earth-Moon system, and aubrites. R chondrites have 55 Mn/ 52 Cr of ~0.68 and ε 53 Cr of 0.23 ± 0.05 (2SD, N = 12), which are higher than those of most of other chondrite groups. The variable 55 Mn/ 52 Cr and ε 53 Cr may be caused by the different abundance of chondrules that experienced volatile-loss and are, on average, depleted in Mn.All the R chondrites with types of 3-6 (as well as brecciated R chondrites) possess homogeneous δ 53 Cr values, -0.12 ± 0.03 (2SD, N = 12). This clearly indicates that metamorphism on chondrite parent bodies does not fractionate Cr stable isotopes.Combined with other chondrites, all the chondrites define a homogeneous δ 53 Cr = -0.12 ± 0.04 (2SD, N = 40). The δ 53 Cr homogeneity between chondrites and Earth confirms that terrestrial core formation and/or any volatilization did not cause Cr stable isotope fractionation. Finally, the chondritic clast, MS-CH, within the Almahata Sitta polymict ureilite has ε 53 Cr = 0.18 ± 0.04, ε 54 Cr = -0.16 ± 0.07, and δ 53 Cr = -0.11 ± 0.05 reinforcing its close affinity to R-chondrites, although other chemical and petrological evidence does not support it to be a clast from the R chondrite parent body. 453 454 fellowship (#201706340161) and IPGP for the funding support of traveling, "Aide à la MOBILITE INTERNATIONALE des doctorants de l'IPGP (2019)", to visit Carnegie Science. Timothy Mock and Mary Horan are appreciated for their assistance in ICP-MS analysis and clean labs respectively.

Figure 1

 1 Figure 1 The ε 54 Cr variation for different groups of chondrites. The warm-color circles are the carbonaceous chondrites that all possess ε 54 Cr > 0.3, while the blue diamonds, black circles, and green squares indicate the enstatite (EH, EL), Rumuruti, and ordinary (H, L, LL) chondrites, respectively. The gray bar indicates the ε 54 Cr values for the Earth-Moon system. The data for the

Figure 2 .

 2 Figure 2. The ε 54 Cr and ∆ 17 O values of CCs (warm-color shade), OCs (green shade), ECs (blue shade), and RCs (black shade), as well as achondrites, terrestrial and lunar samples (gray ellipses). The ε 54 Cr and ∆ 17 O values are positively correlated in CCs, e.g., CK chondrites have the lowest ε 54 Cr and ∆ 17 O values, while CI chondrites have the highest ε 54 Cr and ∆ 17 O values[START_REF] Clayton | Oxygen isotope studies of carbonaceous chondrites[END_REF]

Figure 3

 3 Figure 3 The 53 Mn-53 Cr data of R chondrites. Most of R chondrite have similar 55 Mn/ 52 Cr ratios (~0.68) but distinguishable ε 53 Cr values, which may be caused by the variable abundance of chondrules and matrix.

Figure 4 .

 4 Figure 4. Comparison of the δ 53 Cr variations amongst chondrites, achondrites and the Earth-Moon system. The circles are chondrites of which color corresponds to Figure 1, 2 and 3, while the real pictures of planets represent the Earth, Moon and Vesta themselves. The gray bar defines the average δ 53 Cr values (-0.12 ± 0.04; 2SD, N =42) of all the chondrites. Literature data sources:

  the MC-ICP-MS Neptune Plus located at the Centre for Star and Planet Formation, The 53 Cr/ 52 Cr and 54 Cr/ 52 Cr ratios were normalized to a constant 50 Cr/ 52 Cr ratio of 0.051859 using the exponential law(Lugmair and

	Shukolyukov, 1998). All the measured isotopic ratios are expressed relative to NIST
	SRM 979 in the epsilon notations:
	ε	=	/	/	-1 × 10000 (1),
	with x = 53 or 54.

Globe Institute, University of Copenhagen. Detailed analytical and data reduction methods are described elsewhere

[START_REF] Pedersen | Testing accretion mechanisms of the H chondrite parent body utilizing nucleosynthetic anomalies[END_REF][START_REF] Schiller | Precise measurement of chromium isotopes by MC-ICPMS[END_REF] Zhu et al., 2020b)

. The Cr isotopic composition of each sample was measured by sample-standard bracketing using the NIST SRM 979 Cr standard. Sample solutions with ~0.5 ppm Cr were introduced to the plasma via an ESI Apex IR resulting in 52 Cr signals of 20-40 V at an uptake rate of ~0.06 mL/min. Each sample was measured five times and the resulting average 2 standard error (2se) uncertainty for ε 53 Cr and ε 54 Cr are ~0.02 and ~0.06, respectively.

Table 1

 1 The 53 Mn-53 Cr and Cr stable isotope data for Rumuruti (R) chondrites, one R chondrite-like clast in a polymict ureilite (Almahata Sitta) 479 and other data quality-control standards. 480

	Name	Type	55 Mn/ 52 Cr	ε 53 Cr	2SE	ε 54 Cr	2SE	N	δ 53 Cr	2SD	N
	Rumuruti	R3.8-6	0.71	0.27	0.03	-0.03	0.04	5	-0.11	0.02
	PCA 91002	R3.8-6	0.68	0.25	0.01	-0.05	0.07	5	-0.12	0.04
	LAP 03645	R	0.69	0.20	0.02	-0.01	0.04	5	-0.14	0.02
	NWA 1476	R3	0.73	0.23	0.02	-0.10	0.06	5	-0.11	0.02
	NWA 2446	R3	0.60	0.20	0.04	-0.12	0.05	5	-0.11	0.03
	NWA 753	R3.9	0.66	0.22	0.02	-0.06	0.06	5	-0.09	0.03
	MIL 07440	R4	0.69	0.25	0.03	-0.06	0.07	5	-0.13	0.04
	LAP 03639	R4	0.68	0.24	0.01	-0.01	0.06	5	-0.13	0.03
	NWA 053	R4	0.66	0.27	0.02	-0.13	0.03	5	-0.11	0.03
	NWA 6145	R5	0.67	0.22	0.02	-0.07	0.10	5	-0.12	0.02
	MIL 11207	R6	0.69	0.19	0.02	-0.04	0.07	5	-0.12	0.03
	LAP 04840	R6	0.68	0.22	0.02	-0.03	0.03	5	-0.12	0.02
	MS-CH	Clast in Ureilite	0.70	0.18	0.04	-0.16	0.07	5	-0.11	0.05
	BHVO-2	Basalt							-0.11	0.03
	PCC-1	Peridotite		-0.02	0.03	0.01	0.07	5	-0.08	0.05
	DTS-2b	Dunite		0.06	0.02	0.12	0.06	5
	481

Acknowledgements

Three reviewers, Associate Editor Yuri Amelin and Executive Editor Jeffrey G.

Catalano are deeply thanked for constructive comments which greatly improved the quality of this paper. We thank the Meteorite Working Group (NASA), and the Museum für Naturkunde (Berlin; A. Greshake) for providing additional samples of Rumuruti chondrites. US Antarctic meteorite samples are recovered by the Antarctic search for Meteorites (ANSMET) program which has been funded by NSF and NASA, and characterized and curated in the Department of Mineral Sciences of the Smithsonian Institution and Astromaterials Curation Office at NASA Johnson Space Center. F. M. acknowledges funding from the European Research Council under the H2020 framework program/ERC grant agreement (ERC starting grant, #637503-PRISTINE) and financial support of the UnivEarthS Labex program at Sorbonne Paris Cité (#ANR-10-LABX-0023 and #ANR-11-IDEX-0005-02), and the ANR through a chaire d'excellence Sorbonne Paris Cité. M. S. acknowledges funding from the Villum Fonden (#00025333). M. B. acknowledges funding from the Carlsberg Foundation (#CF18-1105), the Danish National Research Foundation (#DNRF97) and the European Research Council (ERC Advanced Grant Agreement, #833275-DEEPTIME). A. B. thanks the support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation, #263649064) -TRR 170 (subproject B05). This is TRR170 Publication No. xx. K. Z. thanks the China Scholarship Council (CSC) for the PhD