# Determination of chromium isotopic composition in various geological material by thermal ionization mass spectrometry

Mélie Cornet, Caroline Fitoussi, Bernard Bourdon, Eric Pili

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Mélie Cornet, Caroline Fitoussi, Bernard Bourdon, Eric Pili. Determination of chromium isotopic composition in various geological material by thermal ionization mass spectrometry. International Journal of Mass Spectrometry, 2022, 480, pp.116897. 10.1016/j.ijms.2022.116897. hal-03788553

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# 1 Determination of chromium isotopic composition in various geological material by Thermal Ionization

## 2 Mass Spectrometry

4 Mélie Cornet¹, Caroline Fitoussi¹*, Bernard Bourdon¹, Eric Pili²

5 ¹Laboratoire de Géologie de Lyon (LGL-TPE), ENS de Lyon, CNRS, Université Claude Bernard de Lyon, 46 Allée d'Italie,

6 69364 Lyon Cedex 7, France

7 ²CEA, DAM, DIF, F-91297 Arpajon, France

8 *Corresponding author: caroline.fitoussi@ens-lyon.fr

10 Keywords: chromium isotopes, thermal ionization mass spectrometry, chemical separation

12 Abstract :

13 We present a new method for the chemical purification and the measurement of the isotopic composition of Cr by
14 Thermal-Ionization Mass Spectrometry in various geological materials. The separation and purification protocol was
15 adapted to match a wide range of geological and cosmochemical matrices and was tested with terrestrial reference
16 materials, uranium-rich samples and meteorites. The total Cr yield was at least 86% and the Cr/U ratio went from
17 7.84×10⁻⁵ to 5.72×10³ after purification for uranium-rich materials. It also permitted an efficient removal of matrix
18 elements such as Na and Mg and interfering elements such as Fe, Ti and V. Cr isotopic composition was measured
19 using multistatic and multidynamic modes. The multidynamic mode displayed no improvement of the external
20 reproducibility and internal precision compared with the multistatic mode, in contrast with what has been found
21 with other isotope systems. This method gave a reproducibility of 5 ppm and 13 ppm (2 s.d.) for the ⁵³Cr/⁵²Cr and
22 ⁵⁴Cr/⁵²Cr ratios respectively, over a period of several months, which represents an improvement of the long-term
23 reproducibility compared with the other published methods. The accuracy of the protocol was tested by measuring
24 terrestrial reference materials (AGV-1, AGV-2, BHVO-1 and BHVO-2) as well as extra-terrestrial samples (Bouvante,
25 Stannern and Waconda), displaying good agreement with published data. This method is thus suited to detect any
26 mass-independent fractionation or nucleosynthetic anomalies in geological materials.

29 **1. Introduction**

30 Chromium isotopes have become widely used geochemical tracers in the field of environmental geochemistry,
31 paleoclimate studies and high temperature geochemistry. Chromium (Cr) is a transition metal with four naturally
32 occurring stable isotopes: ⁵⁰Cr (4.35%), ⁵²Cr (83.79%), ⁵³Cr (9.50%), and ⁵⁴Cr (2.50%) [1]. It can exist in three
33 oxidation states in natural conditions (O, +III and +VI). The development of chromium isotopes as tracers in
34 geochemistry and cosmochemistry over the past decades is linked to the development of mass-spectrometry
35 techniques [2,3]. The Cr isotope mass-dependent variations have been used to study the oxidation state of the
36 Precambrian atmosphere and ocean [4,5] and to trace the fate of Cr as an environmental pollutant, notably in
37 relation with its redox states. Mass-independent variations have also played a key role not only in dating
38 meteorites using the ⁵³Mn-⁵³Cr radio-chronometer [6,7], but also in distinguishing different nucleosynthetic
39 provenances of extra-terrestrial samples [2,8]. However, mass-independent processes have never been used in
40 environmental investigations although redox changes are known to be linked to mass-independent fractionation
41 [9].
In contrast to mass-dependent fractionation, mass-independent processes can cause stable isotope fractionation driven by differences in the nuclear structure (i.e., nuclear size, shape and nuclear spin) rather than by differences in mass between the isotopes [10,11]. <sup>52</sup>Cr possesses a *magic* number of neutrons (N=28) and hence has a closed nuclear shell leading to a very stable and compact nucleus, as shown by spectroscopic studies [12,13]. Indeed, <sup>52</sup>Cr has a significantly smaller mean-square charge radius &lt;r<sup>2</sup>&gt; compared with other Cr isotopes [14]. A second possibility is that the behavior of <sup>53</sup>Cr could be affected by the odd-even effect leading to an anomalous &lt;r<sup>2</sup>&gt; value for this isotope. These characteristics implies that Cr isotopes might undergo mass-independent fractionation due to nuclear field shift effect, as observed by Fujii et al. in 2002 [15] and 2008 [16]. Moreover, among the four Cr isotopes, only <sup>53</sup>Cr possesses an odd number of neutrons. This isotope is thus the only one having a non-zero nuclear spin (I=3/2) and an associated magnetic field. For this reason, mass-independent fractionation of Cr isotopes can also originate from the magnetic isotope effect [17,18]. The study of mass-dependent fractionation (MDF) has shown that this type of isotopic fractionation. Mass-dependent Cr isotope fractionation has commonly been used to reconstruct past redox changes in the ocean, although it has been shown that this type of fractionation could be caused by other processes including reactions with organic acids [19-22]. The study of mass-independent fractionation (MIF) in natural samples, however, has never been explored as their amplitude appears to be below the instrumental error of MDF measurements [23]. MIF could thus be a tool worth investigating to better understand Cr geochemical pathways in the environment, provided the four Cr isotopes can be determined with sufficiently high precision.

The analysis of Cr isotope composition by thermal ionization mass spectrometry requires a very high degree of purity of Cr to avoid any isobaric interferences and any disturbances in the emission of Cr⁺ during the measurement. It allows reaching the required level of precision, as the magnitude of those fractionations are usually on the order of tens of ppm [16]. Therefore, several purification and measurement methods have already been established with robust results [24,25]. However, most of the existing techniques are dedicated to measuring extra-terrestrial material, and none has targeted terrestrial samples, precluding their use in the context of environmental or nuclear forensics (e.g. [26]). Regarding potential applications to nuclear forensics, solvent extraction was shown to be a source of mass-independent fractionation of chromium isotopes [16], and it is often used in the processing of uranium ores. One could thus argue that if such fractionation takes place during uranium purification then it could be used to trace the origin of these uranium rich materials which is one of the goals of the emerging field of nuclear forensics.

In this study, we developed a chemical purification method suitable for very diverse matrices such as uranium- bearing materials, organic-rich samples from water treatment plants, contaminated soils, waters, and chromium ore processing residues. Moreover, we developed a new normalization scheme suitable for directly investigating the variations in <sup>52</sup>Cr and <sup>53</sup>Cr abundances as they are the two Cr isotopes likely to undergo mass-independent fractionation by natural processes. One of our goals was to obtain an analytical method able to detect possibly small mass-independent fractionation, which requires the best possible precision. Finally, we tested both multidynamic and multistatic data acquisition techniques for Cr isotopic data reduction.

## 2. Sample preparation

80

### a. Materials, reagents, and instruments

81

Samples were dissolved and stored in Teflon Savillex beakers. We used cation-exchange resin (BioRad AG50W-X12 200-400), anion-exchange resin (Eichrom AG1-X8 100-200 and AG1-X8 200-400), as well as polypropylene chromatography columns 2 mL bed volume (0.8x4cm). For each step of the chemical procedure, we used ultrapure water (milliQ water) and Optima nitric, hydrochloric and hydrofluoric acids. To minimise procedural blank, all chemical steps were performed in a clean lab (Laboratoire de Géologie de Lyon) under fume hood. Concentration measurements of samples and column calibration were done on an ICAP™ RQ ICP-MS (Thermo Scientific). A TIMS

87
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## b. Sample dissolution

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(Thermal Ionization Mass Spectrometer) Triton™ was used for isotope measurements at the Laboratoire de Géologie de Lyon, ENS de Lyon.

102

## c. Ion-exchange chromatography

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105

For organic-rich samples, such as water treatment plant samples, it is necessary to include a preliminary step of dissolution in nitric acid. The sample powder (in the case of solid samples) was dissolved in 5 mL of water with slow addition of 0.5 mL of concentrated $HNO_3$ and heated at 120°C for 24h. Samples were then dried down at 120°C and taken up in 5 mL of concentrated $HNO_3$ and 5 mL of HF and heated at 140°C for at least 48h. The use of HF allows the dissolution of silicates leading to the evaporation of gaseous $SiF_4$ but can also cause the formation of insoluble fluorides such as $MnF_2$, $CaF_2$, and $MgF_2$. Those fluorides are redissolved by adding aqua regia twice (HCl: $HNO_3$, 3:1), first without heating to prevent an excess of pressure inside the beaker, then at 120°C for 4h. Finally, the samples were dried down at 120°C and taken up in concentrated HCl, then several times in 5N HCl before ion-exchange chromatography. To ensure that fluoride dissolution was complete, the samples were centrifuged in 10 mL polypropylene vials for 5 minutes at 5000 rpm. Any remaining solid would then be visible at the bottom of the vial.

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111

After sample dissolution, Cr is separated and then purified from its matrix to generate a stable, interference-free signal during TIMS measurement. The purification was achieved through a multiple-step ion-exchange chromatography adapted from Trinquier et al., 2008 [27] and Liu et al., 2019 [25] and summarized in Table 1.

The first column contained 2 mL of AG1-X8 anion-exchange resin (100-200 mesh) and was used to separate the Mo fraction and part of the matrix. The column was washed with 10 mL of 5M HCl, deionized milliQ water, 10 mL of 6M HCl, and then rinsed again with deionized water. It was then conditioned with 6 mL of 5M HCl, and the sample was loaded in 2 mL of 5M HCl. The totality of Cr, along with most of the matrix, was eluted with 10 mL of 5M HCl. Mo and U were eluted with 30 mL of 0.6M HCl. The fraction containing Cr was then evaporated to dryness and taken up twice in 5M HF.

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At this step, fluoride flakes can still form, as most of the alkaline earth metals are eluted with Cr in the first column. The fluorides were centrifugated for 5 min at 5000 rpm in 5 mL of 5M HF. The precipitate was taken up and centrifuged once more following the same protocol to ensure a total removal of Cr from the fluorides. To ensure that no Cr was precipitated along with the fluorides, the Cr concentration of a reference material (BEN) was measured before and after precipitation. No Cr loss was observed. The supernatant was dried up and taken up in 2 mL of 5N HF for the second column.

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121

The second column contains 2 mL of AG1-X8 anion-exchange resin (100-200 mesh). The column was washed with 10 mL of 6M HCl, deionized water, 10 mL of a mix 6M $HNO_3$ and 3N HF, and then rinsed again with deionized water. It is conditioned with 10 mL of 5M HF with hydrogen peroxide (0.02 vol.%) and the sample was loaded in 2 mL of 5M HF and hydrogen peroxide (0.03 vol.%). Cr was eluted with 10 mL of 5M HF and hydrogen peroxide 0.03 vol.%.

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129

The next separation step was a two-stage Cr purification on a cation-exchange resin (AG50W-X12 200-400 mesh) as described in Liu et al., 2019 [28] with slight differences in the column diameter (0.8 cm instead of 0.4 cm used by Liu et al.). This third column was filled with 1 mL of resin, washed with 6 mL of 6M HCl and 10 mL of deionized water, and conditioned with 5 mL of 1M HCl. The sample was taken up in 200 µL of 6M HCl and diluted to 1.2 mL of 1M HCl with deionized water prior to its loading on the column. Cr was then eluted with 5 mL of 1M HCl. The sample was dried up and taken up in 2mL 8N $HNO_3$. Then, it is dried up again and taken up in 2 mL of 0.15M $HNO_3$ prior to its loading on the last column. This column contains 0.33 mL of resin, pre-washed with 4 mL of each of the following acids: 0.5M HF, deionized water, 1M HCl and 2M HCl. It was conditioned with 3 mL of 0.15M $HNO_3$ and
130 the matrix elements, Ti and V were eluted with 3 mL of 0.5M HF and 8 mL of 1M HCl. Cr was recovered with 7 mL of
131 2M HCl.

132

<table><caption>133 **Table 1 Protocol for Cr and Mo separation and Cr purification**</caption><thead><tr><th colspan="3">Step 1: Separation of Cr and Mo</th></tr><tr><th></th><th>Eluent</th><th>Volume</th></tr></thead><tbody><tr><td>AG1 X8 100-200 mesh</td><td></td><td>2 mL</td></tr><tr><td rowspan="4">Cleaning</td><td>5M HCl</td><td>10 mL</td></tr><tr><td>milliQ water</td><td>10 mL</td></tr><tr><td>0.6M HCl</td><td>10 mL</td></tr><tr><td>milliQ water</td><td>10 mL</td></tr><tr><td>Conditioning</td><td>5M HCl</td><td>10 mL</td></tr><tr><td>Loading</td><td>5M HCl</td><td>2 mL</td></tr><tr><td>Cr and matrix elution</td><td>5M HCl</td><td>10 mL</td></tr><tr><td>Mo and remaining matrix elution</td><td>0.6M HCl</td><td>30 mL</td></tr></tbody></table><table><thead><tr><th colspan="3">Step 2: Elimination of Ti and U</th></tr><tr><th></th><th>Eluent</th><th>Volume</th></tr></thead><tbody><tr><td>AG1 X8 100-200 mesh</td><td></td><td>2 mL</td></tr><tr><td rowspan="4">Cleaning</td><td>6M HCl</td><td>10 mL</td></tr><tr><td>milliQ water</td><td>10 mL</td></tr><tr><td>5M HF + 0.3% H<sub>2</sub>O<sub>2</sub></td><td>10 mL</td></tr><tr><td>5M HF + 0.3% H<sub>2</sub>O<sub>2</sub></td><td>10 mL</td></tr><tr><td>Conditioning</td><td>5M HF + 0.3% H<sub>2</sub>O<sub>2</sub></td><td>10 mL</td></tr><tr><td>Loading</td><td>5M HF + 0.3% H<sub>2</sub>O<sub>2</sub></td><td>2 mL</td></tr><tr><td>Cr collection</td><td>5M HF + 0.3% H<sub>2</sub>O<sub>2</sub></td><td>10 mL</td></tr></tbody></table><table><thead><tr><th colspan="3">Step 3: Elimination of Fe, V and matrix</th></tr><tr><th></th><th>Eluent</th><th>Volume</th></tr></thead><tbody><tr><td>AG 50W-X12 200-400 mesh</td><td></td><td>2 mL</td></tr><tr><td rowspan="2">Cleaning</td><td>6M HCl</td><td>10 mL</td></tr><tr><td>milliQ water</td><td>10 mL</td></tr><tr><td>Conditioning</td><td>1M HCl</td><td>5 mL</td></tr><tr><td rowspan="2">Loading</td><td>6M HCl</td><td>0.2 mL</td></tr><tr><td>milliQ water</td><td>1 mL</td></tr><tr><td>Cr collection</td><td>1 M HCl</td><td>7 mL</td></tr></tbody></table><table><thead><tr><th colspan="3">Step 4: Elimination of Ti, V and matrix</th></tr><tr><th></th><th>Eluent</th><th>Volume</th></tr></thead><tbody><tr><td>AG 50W-X12 200-400 mesh</td><td></td><td>0.33 mL</td></tr><tr><td rowspan="6">Cleaning</td><td>0.5M HF</td><td>3 mL</td></tr><tr><td>milliQ water</td><td>5 mL</td></tr><tr><td>1M HCl</td><td>3 mL</td></tr><tr><td>2M HCl</td><td>3 mL</td></tr><tr><td>milliQ water</td><td>5 mL</td></tr><tr><td>0.15M HNO<sub>3</sub></td><td>3 mL</td></tr><tr><td>Loading</td><td>0.15M HNO<sub>3</sub></td><td>2 mL</td></tr><tr><td>Al, Ti, and V elution</td><td>0.5M HF</td><td>3 mL</td></tr><tr><td>Mn, Cu and matrix elution</td><td>1M HCl</td><td>8 mL</td></tr></tbody></table>
<figure><img src="image_2.png" /><figcaption>Fig. 1. Relative fraction remaining after each step of purification of AGV-2 (y-axis in log-scale). For example, the remaining iron represents approximately 0.001% of its starting quantity.</figcaption></figure>

The Cr yield was always above 86% (see Figure 1 and Table 2) with a mean value of 95%, which is high enough to avoid any risk of poorly corrected MDF due to the purification [27]. The separation protocol was used handling materials so as not to overload the columns (calculated to be less than 10% of their nominal capacity). The total blank of the procedure was < 1 ng (measured with ICPMS (Inductively Coupled Mass Spectrometer), Icap Q™), which is negligible compared with the amount of Cr (1-30 µg) processed through the chemical purification. For U-bearing samples, the quasi-totality of uranium was eluted during step 2, allowing to reach a final Cr/U higher than 5×10³, starting from a Cr/U ratio as low as 8×10⁻⁵. Such a high enrichment factor in Cr relative to U would not be reached with published chemical separation. This is critical as the initial amount of U in these samples can exceed 80% (see Table 2). This was checked with two uranium ores and two uranium ore concentrates (see Table 2).

Overall, our chemical separation protocol gives high Cr yields while producing a high purity Cr fraction (all Cr fractions were checked for purity using an ICPMS and showed no interfering elements). This feature turned out critical for obtaining long run durations on the mass spectrometer, which is a critical element in reaching high precision Cr isotope data. This chemical separation method differs from previous studies, notably with the introduction of the first and second column that specifically aim at separating (U, Mo, Fe), and Ti, respectively. Furthermore, this protocol was designed to deal with a large variety of matrices (terrestrial rocks, meteorites or U-rich materials).
<table><caption>**Table 2** Uranium samples ratios Cr/U before and after chemical purification of Cr.</caption><thead><tr><th></th><th>Nature of sample</th><th>Cr (µg/g)</th><th>U (%)</th><th>Initial Cr/U</th><th>Final Cr/U*</th><th>Cr yield (%)</th></tr></thead><tbody><tr><td>Mongolia</td><td>Uranium ore, sandstone</td><td>6.45 ± 0.03</td><td>0.237 ± 0.001</td><td>2.72.10<sup>-3</sup></td><td>8.68.10<sup>3</sup></td><td>87</td></tr><tr><td>McClean Lake 1</td><td>Uranium ore feed**, McClean lake</td><td>153.3 ± 0.77</td><td>16 ± 0.08</td><td>9.58.10<sup>-4</sup></td><td>> 10<sup>4</sup></td><td>94</td></tr><tr><td>Morille</td><td>Uranium ore concentrate CETAMA</td><td>66.05 ± 0.33</td><td>84.3 ± 0.42</td><td>7.84.10<sup>-5</sup></td><td>5.72.10<sup>3</sup></td><td>99</td></tr><tr><td>McClean Lake 3</td><td>Uranium ore concentrate, McClean Lake mill</td><td>4.89 ± 0.02</td><td>2.7 ± 0.13</td><td>1.81.10<sup>-4</sup></td><td>> 10<sup>4</sup></td><td>86</td></tr></tbody></table>

### 3. Mass-spectrometry

#### a. Measurement protocol

Before any analysis, a mass scan using an ICPMS Icap Q™ was performed to ensure that no remaining element would disturb Cr⁺ emission during the analysis. The measurements of Cr isotope ratios were then performed on a Thermo Triton TIMS with nine Faraday cups equipped with 10¹¹ Ohms amplifiers. The chromium solution was loaded on a Re single filament preliminary outgassed under vacuum and the filament was gently heated with a current of 0.7 A. For each sample, 2 µg of Cr were loaded in 5% HCl at 1 µg of Cr/µL of solution, at the center of the filament. Once the sample solution was dried down, an activator solution composed of 1.4 µL of 4 wt.% silica gel, 1 µL of 5000 µg/mL H₃BO₃, and 0.7 µL of 1000 µg/mL Al was loaded on top of the sample. After drying down the activator, the current was increased until the filament was dull red, in order to form a glass at the surface of the filament. Cr analysis was performed with a single filament configuration. Each filament was heated to 1500 mA in 10 minutes, left at that intensity for 1 hour (to allow the evaporation of any residual alkali), then heated to 1800 mA in 6 minutes. Data acquisition started when the ⁵²Cr signal was at least 5x10⁻¹¹ A and the running temperature was kept between 1150°C and 1300°C in order to limit the emission of Cr oxides and avoid spurious effects in the isotope ratios after mass fractionation correction as described in Bourdon and Fitoussi, 2020 [29]. The acquisition was performed in dynamic multicollection with four magnet settings as presented in Table 3. For each measurement, at least 50 blocks of 16 cycles were obtained. For each beam configuration, Cr beam intensities were integrated over 8 seconds, and the idle time between each line was 2 seconds. The dynamic rotation of the amplifiers was used between each block, allowing all collectors to work with the same virtual amplifier as in [30]. Peak centering and auto-focus were applied before a group of four blocks. The baseline was measured between each block. The amplifier gains were measured before each analysis during the first step of heating. The total acquisition time was between 6 and 10 hours, including the heating routine and gain measurement.

<footnote>* For the samples with a final Cr/U ratio >10⁴, the final concentration of U was below the detection limit.</footnote>

<footnote>** unconformity-related</footnote>
<table><caption>Table 3 Configuration of the Faraday collectors for multistatic and multidynamic measurements</caption><thead><tr><th>Line/Faraday collector</th><th>L3</th><th>L2</th><th>L1</th><th>C</th><th>H1</th><th>H2</th><th>H3</th></tr></thead><tbody><tr><td>1</td><td><sup>51</sup>V</td><td><sup>52</sup>Cr</td><td><sup>53</sup>Cr</td><td><sup>54</sup>Cr</td><td></td><td><sup>56</sup>Fe</td><td></td></tr><tr><td>2</td><td><sup>50</sup>Cr</td><td><sup>51</sup>V</td><td><sup>52</sup>Cr</td><td><sup>53</sup>Cr</td><td><sup>54</sup>Cr</td><td><sup>55</sup>Mn</td><td><sup>56</sup>Fe</td></tr><tr><td>3</td><td><sup>49</sup>Ti</td><td><sup>50</sup>Cr</td><td><sup>51</sup>V</td><td><sup>52</sup>Cr</td><td><sup>53</sup>Cr</td><td><sup>54</sup>Cr</td><td><sup>55</sup>Mn</td></tr><tr><td>4</td><td><sup>48</sup>Ti</td><td><sup>49</sup>Ti</td><td><sup>50</sup>Cr</td><td><sup>51</sup>V</td><td><sup>52</sup>Cr</td><td><sup>53</sup>Cr</td><td><sup>54</sup>Cr</td></tr></tbody></table>

188

189

b. Isobaric interference correction

191 Ti, V and Fe produce direct isobaric interferences on Cr isotopes. Even though the purification process allowed an efficient separation of Cr from those elements, any possible residual emission must be monitored as it might bias the measurement of the two least abundant Cr isotopes: <sup>50</sup>Cr and <sup>54</sup>Cr. The interference correction for the <sup>50</sup>Ti and <sup>50</sup>V signal on the <sup>50</sup>Cr signal was calculated as follows:

$$^{50}\text{Cr}_{\text{corr}} = ^{50}\text{Cr}_{\text{meas}} - ^{51}\text{V}_{\text{meas}} * \frac{^{50}\text{V}}{^{51}\text{V}} - ^{48}\text{Ti}_{\text{meas}} * \frac{^{50}\text{Ti}}{^{48}\text{Ti}} \quad (1)$$

195

197 where <sup>i</sup>Cr, <sup>i</sup>V and <sup>i</sup>Ti refer to the ion intensities for the given isotopes, the corr and meas subscripts refer to the corrected and measured values, respectively. The isotopic ratios of interfering elements were fixed at 0.00250325 for <sup>50</sup>V/<sup>51</sup>V [31], 0.07033369 for <sup>48</sup>Ti/<sup>50</sup>Ti [32].

200

201 The correction of the <sup>54</sup>Fe interference on <sup>54</sup>Cr was calculated with the following equation:

$$^{54}\text{Cr}_{\text{corr}} = ^{54}\text{Cr}_{\text{meas}} - ^{56}\text{Fe}_{\text{meas}} * \frac{^{54}\text{Fe}}{^{56}\text{Fe}} \quad (2)$$

203 The isotopic ratio was fixed at 0.06370294 for the <sup>54</sup>Fe/<sup>56</sup>Fe ratio [30].

204

c. Data reduction

206 During the analysis, instrumental mass fractionation can be caused by the vaporization of the elements inside the source, leading to preferential release of light over heavy isotopes. This bias was corrected using the exponential law [34]. We chose to perform the data reduction using two distinct isotope ratios for the instrumental mass fractionation. Given that the expected mass-independent fractionation (MIF) is likely to impact <sup>52</sup>Cr and <sup>53</sup>Cr for the reasons described above, the first normalization ratio was <sup>50</sup>Cr/<sup>54</sup>Cr to identify MIF distinctly. However, as all the literature data is published using <sup>50</sup>Cr/<sup>52</sup>Cr as a normalization ratio [2,6-8,34-38], we also performed the data reduction using this ratio for the sake of inter-comparison.

213 The isotope ratios were displayed using the μ-notation as follows:

214

$$\mu \ ^{i}\text{Cr} = \left[ \frac{\left( \frac{^{i}\text{Cr}}{^{52}\text{Cr}} \right)_{\text{sample}} - 1}{\left( \frac{^{i}\text{Cr}}{^{52}\text{Cr}} \right)_{\text{standard}}} \right] \times 10^{6} \quad \text{with } i = 53 \text{ or } 54 \quad (3)$$
or for the ratios normalized with $^{54}$Cr: 215

$$
216 \quad \mu^{iCr} = \left[ \frac{\left( \frac{iCr}{^{54}Cr} \right)_{\text{sample}}}{\left( \frac{iCr}{^{54}Cr} \right)_{\text{standard}}} - 1 \right] \times 10^6 \quad \text{with } i = 52 \text{ or } 53 \quad (4)
$$

217

218 i. <u>⁵⁰Cr/⁵⁴Cr normalization</u>

219 For each Faraday cup configuration (Table 3), we calculated corrected isotope ratios following the equation:

220

221

$$
\frac{iCr}{^{54}Cr}_{corr} corr = \frac{iCr}{^{54}Cr}_{meas} \times \left(\frac{M_i}{M_{54}}\right)^{f1} \quad (5)
$$

222

223 where f1=ln[(^{54}Cr/^{50}Cr)true/(^{54}Cr/^{50}Cr)measured]/ln(M54/M50) with (^{54}Cr/^{50}Cr)true=0.5442097 [39], i = 52 or 53, and Mᵢ is
224 the absolute isotope mass of isotope i. ^52Cr/^54Cr and ^53Cr/^54Cr were corrected for mass fractionation using the
225 ^54Cr/^50Cr measured on the same line, to avoid uncertainty due to ion beam transmission differences between lines.
226 Multistatic ratios were calculated using the arithmetic mean of the three ratios calculated in beam configurations 2,
227 3, and 4 (See Table 3). The following equations can thus be written for the two Cr isotope ratios:

227 Multistatic ratios were calculated using the arithmetic mean of the three ratios calculated in beam configurations 2, 3, and 4 (See Table 3). The following equations can thus be written for the two Cr isotope ratios:

$$
228 \quad \frac{^{52}_{54}Cr}{Cr_{mstat}} = \frac{1}{3} \left[ \frac{^{52}_{54}Cr}{Cr_{l2}} \times \left(\frac{M_{52}}{M_{54}}\right)^{\frac{\ln\left(\frac{^{50}_{54}Cr\text{true}}{^{50}_{54}Cr\text{l2}}\right)}{\ln\left(\frac{M_{50}}{M_{54}}\right)}} + \frac{^{52}_{54}Cr}{Cr_{l3}} \times \left(\frac{M_{52}}{M_{54}}\right)^{\frac{\ln\left(\frac{^{50}_{54}Cr\text{true}}{^{50}_{54}Cr\text{l3}}\right)}{\ln\left(\frac{M_{50}}{M_{54}}\right)}} + \frac{^{52}_{54}Cr}{Cr_{l4}} \times \right. \\
\left. \frac{\frac{\ln\left(\frac{^{50}_{54}Cr\text{true}}{^{50}_{54}Cr\text{l4}}\right)}{\ln\left(\frac{M_{50}}{M_{54}}\right)}}{\frac{M_{52}}{M_{54}}} \right] \quad (6)
$$

229

231

$$
\frac{^{53}_{54}Cr}{Cr_{mstat}} = \frac{1}{3} \left[ \frac{^{53}_{54}Cr}{Cr_{l2}} \times \left(\frac{M_{53}}{M_{54}}\right)^{\frac{\ln\left(\frac{^{50}_{54}Cr\text{true}}{^{50}_{54}Cr\text{l2}}\right)}{\ln\left(\frac{M_{50}}{M_{54}}\right)}} + \frac{^{53}_{54}Cr}{Cr_{l3}} \times \left(\frac{M_{53}}{M_{54}}\right)^{\frac{\ln\left(\frac{^{50}_{54}Cr\text{true}}{^{50}_{54}Cr\text{l3}}\right)}{\ln\left(\frac{M_{50}}{M_{54}}\right)}} + \frac{^{53}_{54}Cr}{Cr_{l4}} \times \right. \\
\left. \frac{\ln\left(\frac{^{50}_{54}Cr\text{true}}{^{50}_{54}Cr\text{l4}}\right)}{\ln\left(\frac{M_{50}}{M_{54}}\right)} \right] \quad (7)
$$

232

230

233

234 The biases in amplifier gains were corrected for by using the dynamic rotation of the amplifiers over the course of
235 the analysis. However, the degradation of the Faraday collectors can also lead to a drift of measured isotope ratios,
236 as their efficiency may not decrease similarly. A dynamic acquisition of the isotope ratios, combining the ratios
237 measured on different lines over the same cycle can address this problem [40-45].

238

239 The Cr dynamic ratios were calculated according to the following equation:

240

$$
\left(\frac{^{52}\text{Cr}}{^{54}\text{Cr}}\right)_{\text{Dyn}} = \left(\frac{I^{52}\text{Cr}_1}{I^{54}\text{Cr}_1}\right)^{\frac{1}{1-\beta}} \times \left(\frac{I^{52}\text{Cr}_3}{I^{50}\text{Cr}_3}\right)^{\frac{\beta}{\beta-1}} \times \left(\frac{I^{54}\text{Cr}}{I^{50}\text{Cr}}\right)^{\frac{\beta}{1-\beta}} \times \left(\frac{G_{L2}}{G_C}\right)^{\frac{1+\beta}{1-\beta}} \quad (8)
$$

241 with

242

$$
\beta = \frac{\ln\left(\frac{M_{52}}{M_{54}}\right)}{\ln\left(\frac{M_{52}}{M_{50}}\right)} \quad (9)
$$

243

244

245

246

$$
\left(\frac{^{53}\text{Cr}}{^{54}\text{Cr}}\right)_{\text{Dyn}} = \left[ \left(\frac{I^{53}\text{Cr}_1}{I^{54}\text{Cr}_1}\right) \times \left(\frac{I^{53}\text{Cr}_2}{I^{54}\text{Cr}_2}\right) \times \left(\frac{I^{53}\text{Cr}_3}{I^{54}\text{Cr}_3}\right) \right]^{\frac{1}{3(1-\varphi)}} \times \left(\frac{I^{53}\text{Cr}_4}{I^{50}\text{Cr}_4}\right)^{\frac{\varphi}{\varphi-1}} \times \left(\frac{I^{54}\text{Cr}}{I^{50}\text{Cr}}\right)^{\frac{\varphi}{1-\varphi}} \\
\times \left(\frac{G_{H2}}{G_{L1}}\right)^{\frac{1+3\varphi}{3(\varphi-1)}} \qquad (10)
$$

247 with

248

$$
\varphi = \frac{\ln\left(\frac{M_{53}}{M_{54}}\right)}{\ln\left(\frac{M_{53}}{M_{50}}\right)} \quad (11)
$$

249

250 I⁵⁰Crᵢ, I⁵²Crᵢ, I⁵³Crᵢ, I⁵⁴Crᵢ are the true intensities of the ion beams in acquisition line j, and G₉₂, G₉₁, Gₑ and G₉₂ are the
gains of the Faraday collectors for the given beam configurations.

252 The combination of isotope ratios measured with different lines minimizes the influence of collector efficiencies.

253 Indeed, due to the small value of their exponent ($\frac{1+\beta}{1-\beta} = 0.01813871$ in eq (4) and $\frac{1+3\varphi}{3(\varphi-1)} = 0,0094$ in eq (5)) the
254 ratio of collector efficiencies is very close to 1. Considering a typical gain fluctuation in the Faraday amplifiers
255 obtained during gain calibration procedure of 20 ppm (2 s.d.) for the efficiencies, it will affect only by 0.4 ppm the

254
255
256
257
258
259
260
261
The same data reduction was performed using ⁵⁰Cr/⁵²Cr as the normalization ratio to correct the instrumental mass
fractionation. For each line, we calculated corrected isotope ratios following the relation:

$$
\left(\frac{^{52}\text{Cr}}{^{54}\text{Cr}}\right)_{\text{Dyn}} \text{ ratio and by } 0.2 \text{ ppm the } \left(\frac{^{53}\text{Cr}}{^{54}\text{Cr}}\right)_{\text{Dyn}} \text{ ratio (2 s.d.). These values are small compared to the other sources}
$$

of uncertainty.

258

259 ii. <sup>50</sup>Cr/<sup>52</sup>Cr normalization

260 The same data reduction was performed using ⁵⁰Cr/⁵²Cr as the normalization ratio to correct the instrumental mass

261 fractionation. For each line, we calculated corrected isotope ratios following the relation:
$$ \frac{iCr}{^{52}Cr_{corr}} = \frac{iCr}{^{52}Cr_{meas}} \times \left(\frac{M_i}{M_{52}}\right)^{f^2} \quad (12) $$

where $f^2=\ln[(^{52}Cr/^{50}Cr)_{true}/(^{52}Cr/^{50}Cr)_{measured}]/\ln(M_{52}/M_{50})$ with $(^{52}Cr/^{50}Cr)_{true}=19.283232$ [39] and $i = 53$ or $54$. Multistatic ratios were calculated using the geometrical mean of the three ratios calculated for beam configurations 2, 3, and 4 (see Table 3). The following equations can then be used for Cr isotope ratios:

$$ \frac{^{53}Cr}{^{52}Cr_{mstat}} = \frac{1}{3} \left[ \frac{^{53}Cr}{^{52}Cr_{l2}} \times \left(\frac{M_{53}}{M_{52}}\right)^{\frac{\ln\left(\frac{^{50}Cr}{^{52}Cr_{true}}\right)}{\ln\left(\frac{^{50}Cr}{^{52}Cr_{l2}}\right)}} + \frac{^{53}Cr}{^{52}Cr_{l3}} \times \left(\frac{M_{53}}{M_{52}}\right)^{\frac{\ln\left(\frac{^{50}Cr}{^{52}Cr_{true}}\right)}{\ln\left(\frac{^{50}Cr}{^{52}Cr_{l3}}\right)}} + \frac{^{53}Cr}{^{52}Cr_{l4}} \times \left(\frac{M_{53}}{M_{52}}\right)^{\frac{\ln\left(\frac{^{50}Cr_{true}}{^{52}Cr_{l4}}\right)}{\ln\left(\frac{^{50}Cr_{true}}{^{52}Cr_{l4}}\right)}} \right] \quad (13) $$

$$ \frac{^{54}Cr}{^{52}Cr_{mstat}} = \frac{1}{3} \left[ \frac{^{54}Cr}{^{52}Cr_{l2}} \times \left(\frac{M_{54}}{M_{52}}\right)^{\frac{\ln\left(\frac{^{50}Cr}{^{52}Cr_{true}}\right)}{\ln\left(\frac{^{50}Cr}{^{52}Cr_{l2}}\right)}} + \frac{^{54}Cr}{^{52}Cr_{l3}} \times \left(\frac{M_{54}}{M_{52}}\right)^{\frac{\ln\left(\frac{^{50}Cr}{^{52}Cr_{true}}\right)}{\ln\left(\frac{^{50}Cr}{^{52}Cr_{l3}}\right)}} + \frac{^{54}Cr}{^{52}Cr_{l4}} \times \left(\frac{M_{54}}{M_{52}}\right)^{\frac{\ln\left(\frac{^{50}Cr_{true}}{^{52}Cr_{l4}}\right)}{\ln\left(\frac{^{50}Cr_{true}}{^{52}Cr_{l4}}\right)}} \right] \quad (14) $$

The Cr dynamic ratios were calculated according to the following equation:

$$ \left(\frac{^{53}Cr}{^{52}Cr}\right)_{Dyn} = \left[ \left(\frac{I^{53}Cr_1}{I^{52}Cr_1}\right) \times \left(\frac{I^{53}Cr_2}{I^{52}Cr_2}\right) \right]^{1/2} \times \left(\frac{I^{50}Cr_3}{I^{52}Cr_3}\right)^{-\Omega} \times \left(\frac{^{50}Cr}{^{52}Cr}\right)_{true}^{\Omega} \times \left(\frac{G_c}{G_{L1}}\right)^{\frac{1+2\Omega}{2}} \quad (15) $$

with

$$ \Omega = \frac{\ln\left(\frac{M_{53}}{M_{52}}\right)}{n\left(\frac{M_{50}}{M_{52}}\right)} \quad (16) $$

and

$$ \left(\frac{^{54}Cr}{^{52}Cr}\right)_{Dyn} = \left(\frac{I^{54}Cr_1}{I^{52}Cr_1}\right) \times \left(\frac{I^{50}Cr_3}{I^{52}Cr_3}\right)^{-\beta} \times \left(\frac{^{50}Cr}{^{52}Cr}\right)_{true}^{\beta} \times \left(\frac{G_c}{G_{L2}}\right)^{\beta+1} \quad (17) $$

with $\beta$ being the same parameter as that defined for the dynamic calculation of $^{52}Cr/^{54}Cr$ (see equation (9)). Considering once again an efficiency difference of 10 ppm between the two collectors involved in the calculation of the isotopic ratio, the relative shift would be of 0.1 ppm for $(\frac{^{53}Cr}{^{52}Cr})_{Dyn}$ $(\frac{1+2\Omega}{2} = 0.0128051$ in equation (15)) and of 0.4 ppm for $(\frac{^{54}Cr}{^{52}Cr})_{Dyn}$ $(\beta+1 = 0.0356311$ in equation (17)). These values are negligible relative to the other sources of uncertainty.
286 **4. Results and discussion**

287 **a. Cr isotope measurements of monoelemental standards**

288
289 i. <sup>50</sup>Cr/<sup>54</sup>Cr normalization

290 Over a period of five months, repeated measurements of Cr mono-elemental standard solution (Alfa Aesar™) in
291 multistatic mode yielded ⁵²Cr/⁵⁴Cr = 35.4404921±0.0002326 (2 s.d., n=24) and ⁵³Cr/⁵⁴Cr = 4.0212937±0.0000256 (2
292 s.d., n=24). The corresponding external reproducibility on the µ'Cr values (2 s.d.) is of 6.6 ppm for the ⁵²Cr/⁵⁴Cr ratio
293 and 6.3 ppm for the ⁵³Cr/⁵⁴Cr ratio. A slight drift was observed during this 5-month period, but its value is well
294 below the external reproducibility (See Figure 2a).

295 The same measurements in dynamic mode yielded ⁵²Cr/⁵⁴Cr = 35.4407131±0.0000387 (2 s.d., n=24) and ⁵³Cr/⁵⁴Cr =
296 4.0213189±0,0000277 (2 s.d., n=24). The external reproducibility on the µ'Cr values (2 s.d.) is thus 10.8 ppm for the
297 ⁵²Cr/⁵⁴Cr ratio and 7 ppm for the ⁵³Cr/⁵⁴Cr ratio (Figure 2b).

298 The dynamic mode did not seem to provide any improvement to the external reproducibility compared with the
299 multistatic acquisition mode. Indeed, the external reproducibility was better using the multistatic data reduction
300 for both isotopic ratios. The additional source of errors in the dynamic reduction mode might have resulted from
301 the fact that the normalization ratio was not acquired on the same line (i.e. at the same time and with the same
302 optical zooms) as the measured isotope ratios (see Roth et al., 2014 [42] for a discussion of the potential effects),
303 possibly leading to a drift of the ratio along time and to a difference of transmission between the ion beams.

304

<figure><img src="image_3.png" /></figure>

305

306 **Fig. 2.** Repeated multistatic (a) and dynamic (b) measurements of the ⁵²Cr/⁵⁴Cr and ⁵³Cr/⁵⁴Cr over a 5-months period on Cr Alfa Aesar™
307 standard. The same scale is used for the two data reduction modes of the same ratios. Darker grey bands represent the external
308 reproducibility (2 s.d.) centered around the mean value (blue line). The error bars represent the internal reproducibility of each analysis (2
309 s.e.).

310

311 ii. <sup>50</sup>Cr/<sup>52</sup>Cr normalization
Over five months, repeated measurements of Cr mono-element standard solution (Alfa Aesar™) in multistatic mode yielded ⁵³Cr/⁵²Cr = 0.11345516±0.00000059 (2 s.d., n=24) and ⁵⁴Cr/⁵²Cr = 0.02821094±0.00000036 (2 s.d., n=24). The external reproducibility (2 s.d.) was of 5.2 ppm for ⁵³Cr/⁵²Cr and 12.9 ppm for ⁵⁴Cr/⁵²Cr. As for the isotope ratios calculated with the other normalization ratio, a slight drift was observed during this 5-month period. Once again, its value cannot be resolved from the external reproducibility (see Figure 3a). The same measurements in dynamic mode yielded ⁵³Cr/⁵²Cr = 0.11345444±0.00000083 (2 s.d., n=24) and ⁵⁴Cr/⁵²Cr = 0.02821039±0.00000052 (2 s.d., n=24). The external reproducibility (2 s.d.) was of 9.2 ppm for the ⁵³Cr/⁵²Cr ratio and 14.0 ppm for the ⁵⁴Cr/⁵²Cr ratio (Figure 3b). As observed for the isotopic ratios normalized with ⁵⁰Cr/⁵⁴Cr, the dynamic acquisition did not improve the external reproducibility.

321

<figure><img src="image_4.png" /><figcaption>Fig. 3. Repeated multistatic (a) and dynamic (b) measurements of the ⁵³Cr/⁵²Cr and ⁵⁴Cr/⁵²Cr over a 5-months period on Cr Alfa Aesar™ standard. The same scale is used for the two data reduction modes of the same ratio. Darker grey bands represent the external reproducibility (2 s.d.) centred on the mean value (blue line). The error bars represent the internal reproducibility of each analysis (2 s.e.).</figcaption></figure>

322

323

324

325

326

327

328

329

330

331

332

333

334

335

336

337

338

339

340

341

As shown in Figure 4, the overall external reproducibilities, over a single period of measurement and over several months, were better than the best published reproducibilities in the literature. As shown in Table S1 compiling available data used in Figure 4, the Cr load used for our standard runs were higher than those used in literature studies (except for the study of Kadlag et al. 2021 [46]). One could note that our ⁵²Cr signal was typically a factor of ~2.4 smaller than those used in previous studies (except for Kadlag et al. 2021 [46]). Similarly, the run durations were greater than those reported in Figure 4. These factors may account partly for the better reproducibilities we obtained and one could speculate that similar results would have been obtained if previous studies had also used longer run durations. However, we must highlight here several differences in our methodology that may explain the observed difference. First, our chemical separation while maintaining a high yield gave a high purity Cr fraction with no matrix or interfering element (at least at the level of our ICPMS measurement used to check purity). In particular, Ti and V were specifically purified with an additional column in the chemical protocol. This created the conditions to obtain very stable and long Cr emissions. Second, our control of filament temperature to avoid oxide species prevent spurious mass fractionation effect that can lead to a dispersion of the data. Third, the calibration of each amplifier decay to avoid any residual signals (as described in Yobregat et al. 2017 [44]) sometimes observed with multiple cup configurations (e.g. Qin et al. 2010 [47]) were avoided.
<figure><img src="image_5.png" /><figcaption>Fig. 4. A comparison of the external reproducibility (2 s.d.) of existing methods for Cr mass-independent isotopic variations [8,25,27,46,47,48] (ref. [8] procedure used the total evaporation method). The diamonds correspond to short-term reproducibility (one to two weeks), the circles to long-term reproducibility (several months).</figcaption></figure>

**b. Application to reference materials**

The chemical purification and mass spectrometry method were applied to terrestrial samples and meteorites in order to validate our analytical method.

**i. Terrestrial materials**

The measurement of Cr isotopes for several terrestrial materials was performed on one chromite (Merensky Reef chromite), two basalts (BCR-2 and BHVO-2) and two andesites (AGV-1 and AGV-2). The calculation of the µ⁵³Cr and µ⁵⁴Cr relatively to the Alfa Aesar™ mono-elemental standard solution displayed a systematic shift towards positive values between 5 and 13 ppm for µ⁵³Cr and 11 and 25 ppm for µ⁵⁴Cr. This shift could have originated either from a mass-independent fractionation induced by the purification procedure or from the fact that the mono-elemental standard was itself fractionated. The Alfa Aesar™ standard was thus processed through the chemical purification. Its isotopic composition proved to be identical, within uncertainty, to that of the same standard directly measured without chemical purification. We concluded that it was not the chemical purification process that induced the shift of the isotopic values of the terrestrial material but rather the use of an already mass-independent fractionated mono-elemental standard for the calculation of µ¹Cr. Therefore, the material used for the calculation of µ¹Cr is hereafter taken as the Merensky Reef (MR) chromite, similarly to the study of Trinquier et al. [2].

According to Trinquier et al, 2007 [2], Trinquier et al., 2008 [27], Göpel et al., 2015 [24], Mougel et al., 2019 [25], Qin et al., 2020 [47], terrestrial materials do not display any mass-independent fractionation, which lends further confidence in our approach. The calculation of µ⁵³Cr and µ⁵⁴Cr (N = ⁵⁰Cr/⁵²Cr) relative to the Merensky Reef chromite (Table 4) yielded the same lack of mass-independent fractionation (Table 5).

<table><caption>**Table 4** ⁵³Cr/⁵²Cr and ⁵⁴Cr/⁵²Cr data for the Merensky Reef (MR) chromite calculated with the two data acquisition modes. For each measurement the internal reproducibility is given as 2 s.e.=2 s.d./n¹/² with n the number of cycles.</caption><thead><tr><th></th><th>⁵³Cr/⁵²Cr mstat<br>± 2 s.e.<br>(N=⁵⁰Cr/⁵²Cr)</th><th>⁵³Cr/⁵²Cr dyn<br>± 2 s.e.<br>(N=⁵⁰Cr/⁵²Cr)</th><th>⁵⁴Cr/⁵²Cr mstat<br>± 2 s.e.<br>(N=⁵⁰Cr/⁵²Cr)</th><th>⁵⁴Cr/⁵²Cr dyn<br>± 2 s.e.<br>(N=⁵⁰Cr/⁵²Cr)</th></tr></thead><tbody><tr><td>MR chromite</td><td>0.11345652<br>± 0.0000002</td><td>0.11345549<br>± 0.00000027</td><td>0.02821178<br>± 0.00000010</td><td>0.02821101<br>± 0.00000016</td></tr><tr><td>MR chromite</td><td>0.1134561</td><td>0.11345537</td><td>0.0282116</td><td>0.02821112</td></tr></tbody></table>
<table><caption>Table 5 $\mu^{53}$Cr and $\mu^{54}$Cr deviations from the mean of Merensky Reef chromite of terrestrial materials.</caption><tbody><tr><td></td><td>± 0.0000002</td><td>± 0.00000026</td><td>± 0.00000011</td><td>± 0.00000018</td></tr><tr><td>MR chromite</td><td>0.11345631</td><td>0.11345621</td><td>0.02821167</td><td>0.02821144</td></tr><tr><td></td><td>± 0.0000002</td><td>± 0.00000023</td><td>± 0.00000009</td><td>± 0.00000015</td></tr><tr><td>MR chromite</td><td>0.11345588</td><td>0.11345481</td><td>0.02821142</td><td>0.02821063</td></tr><tr><td></td><td>± 0.0000002</td><td>± 0.00000029</td><td>± 0.00000010</td><td>± 0.00000018</td></tr><tr><td>MR chromite</td><td>0.11345611</td><td>0.11345557</td><td>0.02821155</td><td>0.02821119</td></tr><tr><td></td><td>± 0.0000002</td><td>± 0.00000023</td><td>± 0.00000008</td><td>± 0.00000015</td></tr><tr><td>MR chromite</td><td>0.11345593</td><td>0.11345544</td><td>0.02821138</td><td>0.0282112</td></tr><tr><td></td><td>± 0.0000002</td><td>± 0.00000024</td><td>± 0.00000010</td><td>± 0.00000016</td></tr><tr><td>MR chromite</td><td>0.11345606</td><td>0.11345547</td><td>0.02821164</td><td>0.02821087</td></tr><tr><td></td><td>± 0.0000002</td><td>± 0.00000032</td><td>± 0.00000012</td><td>± 0.00000020</td></tr><tr><td>Mean</td><td>0.11345613</td><td>0.11345548</td><td>0.02821157</td><td>0.02821107</td></tr><tr><td>MR chromite ±2 s.d.</td><td>± 0.0000004</td><td>± 0.0000008</td><td>± 0.0000003</td><td>± 0.0000005</td></tr></tbody></table>

<table><thead><tr><th></th><th>μ<sup>53</sup>Cr mstat ±2 s.e.<br>(N=50Cr/52Cr)</th><th>μ<sup>53</sup>Cr dyn ±2 s.e.<br>(N=50Cr/52Cr)</th><th>μ<sup>54</sup>Cr mstat ±2 s.e.<br>(N=50Cr/52Cr)</th><th>μ<sup>54</sup>Cr dyn ±2 s.e.<br>(N=50Cr/52Cr)</th></tr></thead><tbody><tr><td>AGV-1</td><td>-1.1 ± 2.6</td><td>7.6 ± 3.6</td><td>-7.2 ± 5.8</td><td>11.8 ± 9.6</td></tr><tr><td>AGV-2</td><td>-1.4 ± 2.2</td><td>0.2 ± 3.0</td><td>-1.6 ± 4.5</td><td>-3.6 ± 8.1</td></tr><tr><td>BCR-2</td><td>-0.9 ± 2.5</td><td>-4.6 ± 3.4</td><td>1.0 ± 5.1</td><td>5.3 ± 8.6</td></tr><tr><td>BHVO-2</td><td>0.6 ± 1.9</td><td>3.2 ± 2.5</td><td>2.5 ± 4.1</td><td>2.9 ± 6.9</td></tr><tr><td>Mean terrestrial samples ±2 s.d.</td><td>-0.7 ± 0.9</td><td>1.6 ± 5.1</td><td>-1.3 ± 4.3</td><td>4.1 ± 6.4</td></tr></tbody></table>

Similarly, the normalization involving the $^{50}$Cr/$^{54}$Cr ratio yielded no mass-independent fractionation on these terrestrial samples (Table 6).

<table><caption>Table 6 $\mu^{52}$Cr and $\mu^{53}$Cr deviations from the mean of Merensky Reef chromite of terrestrial materials.</caption><thead><tr><th></th><th>μ<sup>52</sup>Cr mstat ±2 s.e.<br>(N=50Cr/54Cr)</th><th>μ<sup>52</sup>Cr dyn ±2 s.e.<br>(N=50Cr/54Cr)</th><th>μ<sup>53</sup>Cr mstat ±2 s.e.<br>(N=50Cr/54Cr)</th><th>μ<sup>53</sup>Cr dyn ±2 s.e.<br>(N=50Cr/54Cr)</th></tr></thead><tbody><tr><td>AGV-1</td><td>3.8 ± 3.0</td><td>-5.8 ± 5.0</td><td>3.6 ± 3.9</td><td>-2.0 ± 3.7</td></tr><tr><td>AGV-2</td><td>1.0 ± 2.3</td><td>3.0 ± 4.1</td><td>1.5 ± 3.4</td><td>-0.2 ± 3.3</td></tr><tr><td>BCR-2</td><td>-0.7 ± 2.6</td><td>-2.9 ± 4.4</td><td>-1.5 ± 3.5</td><td>1.1 ± 3.5</td></tr><tr><td>BHVO-2</td><td>-0.2 ± 2.3</td><td>-0.8 ± 3.9</td><td>0.5 ± 3.4</td><td>-4.6 ± 3.4</td></tr><tr><td>Mean terrestrial samples ±2 s.d.</td><td>1.0 ± 2.0</td><td>-1.6 ± 3.7</td><td>1.1 ± 2.1</td><td>-1.4 ± 2.7</td></tr></tbody></table>

## ii. Uranium ore concentrates

A Cr-doped uranium ore concentrate standard from CETAMA, Morille, was analyzed to ensure that the application of our method to uranium-rich samples were not affected by any matrix effect causing spurious mass-independent fractionation. The calculation of the isotopic composition of this standard compared to a terrestrial standard displayed no mass-independent fractionation in the sample (Table 7).

<table><caption>Table 7 $\mu^{52}$Cr and $\mu^{53}$Cr deviations from the mean of Merensky Reef chromite for the uranium ore concentrate standard Morille.</caption><thead><tr><th></th><th>μ<sup>52</sup>Cr mstat ±2 s.e.<br>(N=50Cr/54Cr)</th><th>μ<sup>52</sup>Cr dyn ±2 s.e.<br>(N=50Cr/54Cr)</th><th>μ<sup>53</sup>Cr mstat ±2 s.e.<br>(N=50Cr/54Cr)</th><th>μ<sup>53</sup>Cr dyn ±2 s.e.<br>(N=50Cr/54Cr)</th></tr></thead><tbody><tr><td>Morille</td><td>-1.8 ± 3.3</td><td>-2.2 ± 4.5</td><td>-2.0 ± 3.7</td><td>-3.4 ± 3.6</td></tr></tbody></table>

## iii. Meteorites
The Cr isotope compositions of two eucrites (Bouvante and Stannern) and one ordinary chondrite (Waconda) have been measured and are reported in Table 8. The isotope composition of the Waconda ordinary chondrite was compared with the mean of ordinary chondrites published by Trinquier et al., 2007 [2] as it is assumed that, due to their common origin, ordinary chondrites should have a similar isotopic composition for $^{54}$Cr/$^{52}$Cr [2,24,47].

<table><caption>**Table 8** Measurements for $^{53}$Cr/$^{52}$Cr and $^{54}$Cr/$^{52}$Cr on various meteorites and comparison with literature data</caption><thead><tr><th></th><th>Reference</th><th>μ<sup>53</sup>Cr mstat ±2 s.d.<br>(N=50Cr/52Cr)</th><th>μ<sup>53</sup>Cr dyn ±2 s.d.<br>(N=50Cr/52Cr)</th><th>μ<sup>54</sup>Cr mstat ±2 s.d.<br>(N=50Cr/52Cr)</th><th>μ<sup>54</sup>Cr dyn ±2 s.d.<br>(N=50Cr/52Cr)</th><th>n</th></tr></thead><tbody><tr><td>Waconda<br>Mean ordinary chondrite</td><td>This study<br>Literature</td><td></td><td></td><td>-45.2 ± 6.3<br>-42 ± 3 [2]</td><td>-42.4 ± 7.0</td><td>4</td></tr><tr><td>Bouvante</td><td>This study<br>Literature</td><td>50.5 ± 3.6<br>65 ± 12 [7]</td><td>48.3 ± 2.5</td><td>-78.5 ± 8.4<br>-78 ± 6 [2]</td><td>-81.1 ± 7.0</td><td>6</td></tr><tr><td>Stannern</td><td>This study<br>Literature</td><td>55.6 ± 4.3<br>63 ± 7 [7]</td><td>55.3 ± 3.3</td><td>-72.3 ± 11.1<br>-71 ± 7 [2]</td><td>-74.8 ± 8.3</td><td>5</td></tr></tbody></table>

The isotope compositions of Waconda, Bouvante and Stannern were identical within uncertainties to the Cr isotope compositions published by Trinquier et al. in 2007 [2] and 2008 [27] (Table 8). These results, along with the results on terrestrial samples, validated our chemical purification as well as the Cr isotope measurement method as a means for detecting mass-independent Cr isotope anomalies. Even if the dynamic data reduction did not provide any improvement on external uncertainties over a long period of time, the data comparison of terrestrial and meteoric samples showed the accuracy of measured values using the dynamic mode.

## 5. Conclusions

We have developed a new analytical method for Cr separation and for the measurement of mass-independent fractionation of Cr isotopes by TIMS that is applicable to a wide range of geological and environmental matrices. The method was tested with meteorites and terrestrial rocks, including also uranium-rich samples. For uranium-rich samples the chemical separation was modified to ensure proper removal of uranium in the final Cr fractions and the method was tested with various uranium ores. The total Cr recovery after the purification process was above 87% with a mean value of 95%, avoiding any risk of chemistry-induced mass-dependent or mass-independent fractionation. An Alfa Aesar Cr standard solution was shown to carry small but resolvable mass-independent signature and could not be used for reference. In contrast, terrestrial rocks did not show any μCr value resolvable from zero.

A full multi-dynamic data reduction scheme was developed and tested. It yielded no improvement in Cr isotope reproducibility compared with the multistatic data reduction, in contrast with other isotope systems. This may be due to residual corrections originating from difference in transmission between the different magnet settings or from rapid temporal drift in the ratio used for mass fractionation.

Using the multistatic mode, the external reproducibility (2 s.d.) was of 5.2 ppm for μCr corresponding to $^{53}$Cr/$^{52}$Cr ratios and 12.9 ppm for μCr corresponding to $^{54}$Cr/$^{52}$Cr ratios, determined by the analysis of a Cr mono-elemental standard over a period of several months. The analysis of the same standard in multistatic mode showed an external reproducibility of 6.6 ppm for $^{52}$Cr/$^{54}$Cr and 6.3 ppm for $^{53}$Cr/$^{54}$Cr ratios. This method produces Cr isotope data for meteorites that are consistent with previously published work indicating the presence of nucleosynthetic
420 anomalies. This analytical method is also suitable for the determination of Cr mass-independent fractionation in
421 environmental and nuclear forensic studies.

422

423 Acknowledgments

424 We thank one anonymous reviewer and Anne Trinquier for their constructive comments that helped improve the
425 manuscript. This study was funded partly by the Labex LIO ANR-10-LABX-0066, by the CEFIPRA project #6109-1, and
426 by a CEA- ENS Lyon-CNRS-UCBL collaboration.

427

428

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<figure><img src="image_6.png" /></figure>

A comparison of the external reproducibility (2 s.d.) of existing methods for Cr mass-independent isotopic variations. The diamonds correspond to short-term reproducibility, the circles to long-term reproducibility.