Tu-Han Luu
email: tluu@ipgp.fr

Pamela Gutiérrez

Edward C Inglis

Daniel Roberts

Catherine Chauvel

HIGH-PRECISION SR AND ND ISOTOPE MEASUREMENTS USING A DYNAMIC ZOOM LENS-EQUIPPED THERMAL IONISATION MASS SPECTROMETER

Keywords:

Introduction

Isotope geochemistry has been widely used to probe the evolution and heterogeneity of the terrestrial mantle (e.g., [START_REF] White | Probing the Earth's Deep Interior through Geochemistry[END_REF]. Among the different tools available, radiogenic isotopes are of particular interest because (i) they are not directly fractionated by magmatic processes and thus are good source tracers, and (ii) they give information about the timing of processes via their parent-to-daughter decay ratios being time-integrated over the entire history of the Earth. A large number of isotope systems are available, but the most extensively used are the incompatible lithophile element systems: 87 Rb-87 Sr (half-life of 49.23 Ga), 147 Sm-143 Nd (halflife of 106 Ga), 176 Lu-176 Hf (half-life of 3.86 Ga), 138 La-138 Ce (half-life of 292.5 Ga), 238 U-206 Pb (half-life of 4.47 Ga), 235 U-207 Pb (half-life of 0.71 Ga), 232 Th-208 Pb (half-life of 14.05 Ga).

The 87 Rb-87 Sr and 147 Sm-143 Nd systems were the first used. A major advantage of these systems is that Rb is more incompatible than Sr while Sm is less incompatible than Nd during partial melting of the mantle. This results in a crust enriched in incompatible elements (high Rb/Sr and low Sm/Nd) and an upper mantle depleted in incompatible elements (low Rb/Sr and high Sm/Nd) after melt extraction. Pioneering work in the 1970s defined the 87 Sr/ 86 Sr and 143 Nd/ 144 Nd mantle array (De Paolo and Wasserburg, 1979), and since then traditional radiogenic (Sr-Nd-Pb) isotope compositions measured in oceanic island basalts (OIBs) around the world have refined the original mantle array to 5 end-member mantle components: DMM (for depleted MORB mantle), HIMU (corresponding to a reservoir with high 238 U/ 204 Pb and often associated with recycling of oceanic crust; [START_REF] Chauvel | HIMU-EM: the French Polynesian connection[END_REF]), EM1 and EM2 (for enriched mantle 1 and 2, which are reservoirs characterized by variable Rb/Sr and low Sm/Nd) and PREMA (for prevalent mantle) also called FOZO or C. Despite this, the exact number of end-member compositions and their nature are still highly debated. Indeed, establishing subtle differences depends on improved precision and accuracy of isotopic measurements.

Improvement in analytical techniques over the last years has led to better precisions for isotope measurements: differences of a few parts per million (ppm) can now be detected compared to precisions of the order of tens or hundreds of ppm in the late 1970s. This has allowed the definition of for example distinct parallel trends between EM1 and EM2 mantle end-members in the Ce-Nd isotope space or in the Hf-Nd isotope space (e.g., [START_REF] Doucelance | A Ce-Nd-Hf isotope perspective on the EMI-EMII endmember[END_REF][START_REF] Béguelin | Cerium isotope constraints on the nature of the Azores plume[END_REF]), leading to a better constraint on the nature and the age of the recycled material responsible for the extended mantle heterogeneity. Another example of the utility of high precision measurements for radiogenic isotope systems comes from [START_REF] Abouchami | Lead isotopes reveal bilateral asymmetry and vertical continuity in the Hawaiian mantle plume[END_REF] who used high precision Pb isotope data to report, for the first time, different trends between the two chains of Hawaiian volcanoes Loa and Kea, with only very little compositional overlap in their Pb isotope features. This has allowed to better constrain the structure and geometry of the plumes ascending to the surface. Similar fine structures could be found in the Sr-Nd isotopic space with the improvement in precision of Sr and Nd isotope data as reported in our study. Aside from mantle geochemistry, the improvements in analytical protocol have greatly advanced the field of geochronology. For example, the latest high-precision Sm-Nd geochronology data allow for the resolution of ages to a precision of ± 1.0 Ma on very small samples (1-10 ng of Nd; e.g., [START_REF] Starr | The subduction and exhumation history of the Voltri Ophiolite Italy: Evaluating exhumation mechanisms for high-pressure metamorphic massifs[END_REF].

In this paper, we demonstrate that the latest generation of thermal ionisation mass spectrometers (TIMS) from Nu Instruments allows precisions of a few ppm to be reached, by taking advantage of the presence of a large number of detectors accompanied by an efficient zoom lens system. As mentioned above, this will have important implications in the field of mantle geochemistry, but not only. Indeed, the Sr and Nd systematics are also powerful tools in fields such as cosmochemistry, archaeology, ocean chemistry or paleoclimatic studies, to only cite a few. Improving the precision on measurements should help establishing small differences in sources or in temporal variations, or it could be a key tool to distinguish minor changes in geological and environmental processes.

Chemical procedures a. Sample digestion

Complete digestion of between 50 mg and 100 mg of rock powder was accomplished using a 3:1 mixture of 28N HF and 16N HNO3 acids on a hotplate at ~ 120°C for at least two days. The samples were then dried down and redissolved two times with 5 ml of 6N HCl followed by 5ml of 2N HCl to decompose fluorides. The set of rock standards analysed in the course of this study comprises 5 basalts (BCR-2, BHVO-2, BIR-1, Be-N and BR-24), one rhyolite (RGM-1) and one andesite (AGV-2) to encompass a wide range of geological matrices.

b. Separation of strontium and neodymium

The Sr and Nd chemical separations were achieved in a two-step chromatographic procedure adapted from the one published in [START_REF] Chauvel | Comprehensive chemical and isotopic analyses of basalt and sediment reference materials[END_REF]. The first step, common to both elements, corresponds to a cation-exchange chromatography in HCl on a BioRad PolyPrep column filled with 2 ml of AG50W-X8 resin (200-400 mesh). This step allows the removal of major elements, while collecting the Sr fraction in 3.5N HCl and the LREE fraction in 6N HCl. From there, the Sr fraction was further purified using a small (~ 3 mm diameter) homemade shrink fit Teflon column filled with ~ 0.4 mL of Sr-spec resin (50-100 µm). Rubidium, and its interfering 87 Rb isotope, was removed using 3N HNO3 and Sr was collected in ultrapure Milli-Q® water (18.2 MΩ.cm). On the other hand, the LREE fraction was further purified using a plastic column (~ 7 mm diameter) filled with ~ 1 mL of Ln-spec resin (50-100 µm). During this step, the Nd fraction is collected in 0.25N HCl, allowing to separate it from Sm, the main interfering species when measuring 143 Nd/ 144 Nd. Our chemical procedures give a total procedural blank of ~ 100 pg for Sr and ~ 25 pg for Nd.

Following the Sr and Nd chemical separations, we systematically analysed an aliquot of 5% of each processed sample on an Agilent 8900 triple quadrupole ICP-MS at the Institut de Physique du Globe de Paris. This allows for the determination of the Sr and Nd recoveries, but also to ensure that no residual trace of Rb and Sm is present in the Sr and Nd fractions that will be loaded on filaments. Strontium and Nd recoveries were > 75% and > 85% respectively, giving on average more than 20 µg Sr and more than 1.5 µg Nd subsequently available for analysis, with typically Rb/Sr < 1´10 -5 and Sm/Nd < 6´10 -5 , for all the rock standards.

Strontium and neodymium isotope measurements by Nu TIMS

a. Generalities Strontium and neodymium isotopes are generally measured in static mode (on both TIMS and MC-ICPMS), with all the ion beams acquired simultaneously. This configuration is easier to set up on a mass spectrometer, does not necessitate a large number of detectors, and provide isotopic results precise enough when looking at variability between samples of the order of tens of ppm of more. However, when higher precision data is required, isotope measurements in a dynamic mode allow to better compensate for the relative deterioration of the Faraday detectors and their change in efficiency with time, and thus return more accurate isotopic results (e.g., [START_REF] Avanzinelli | High precision Sr, Nd and Pb isotopic analyses using the new generation Thermal Ionisation Mass Spectrometer ThermoFinnigan Triton-Ti ®[END_REF][START_REF] Henshall | High-precision strontium isotope analysis of geological samples by thermal ionization mass spectrometry[END_REF][START_REF] Fukai | Evaluation of the long-term fluctuation in isotope ratios measured by TIMS with the static, dynamic, and multistatic methods: A case study for Nd isotope measurements[END_REF].

A Nu TIMS was installed at the Institut de Physique du Globe de Paris early 2020 (Serial No. 010) to perform high-precision Sr and Nd isotope measurements, in addition to other isotope systems such as Ca and W isotopes for instance. The instrument is equipped with 16 fixed Faraday detectors, that can be dynamically connected to amplifiers with different feedback resistors (10 10 , 10 11 , 10 12 and 10 13 Ω). The fixed Faraday detectors system is compensated by the presence of a zoom-lens system located between the magnet and the detector array (Fig. 1a). This zoom-lens system is made of two lenses: quad 1 primarily focuses the individual beams, while quad 2 controls the dispersion of the beams relative to each other. The large number of detectors, in conjunction with an efficient zoom lens system, allows significant flexibility regarding the number of lines in a multidynamic acquisition routine whilst maintaining optimal peak alignment and peak shape for every measurement line despite the fact that the detectors are not movable. In practice, the natural dispersion of the Nu TIMS is such that the Re isotopes will align in adjacent collectors without the need for any quadratic field being applied to the zoom lens system. As we go lower in mass (as for Nd and Sr isotopes compared to Re), the distance between the isotopes increases (Fig. 1a-1), because lighter elements will be separated more as they pass through the magnetic sector. Applying the correct set of voltages to the zoom lens system (quad 1 and quad 2 values in Table 1, referring to the electrostatic field applied across each lens stack) will create a continuous electrostatic field which then effectively acts to demagnify the mass separation at the detectors by deflecting the isotopes increasingly when moving farther away from the central point of the lens stack (Fig. 1a-2 and1a-3). This allows for the alignment of the isotopes into the adjacent collectors whilst maintaining good peak shapes (Fig. 1b). Optimal alignment is now achieved electrostatically and not mechanically, allowing a robust and reproducible alignment within milliseconds and insuring robust conditions for multidynamic measurements. The benefit of a multidynamic acquisition routine is a better correction for cup efficiencies compared to static measurements, a better constraint on the oxide corrections when running in negative mode (for W isotopes for instance) and a better external reproducibility. Note that for Sr and Nd isotope analyses, all the Faraday cups used were connected to amplifiers with a 10 11 Ω feedback resistor, and a 30 min gain calibration was performed every morning.

Strontium isotopic measurements were performed using roughly 300 ng of Sr loaded on previously outgassed zone-refined Re single filaments. About 0.7 µl of TaF5 activator and 1 µl of sample in 0.5N HNO3 were loaded onto the filament, in between two Parafilm strips separated by ~ 3 mm, at ~ 0.75 A. The role of the Parafilm strips was to prevent the sample and the activator spreading on the filament during the loading, so that a small spot could be obtained. The activator and the sample were left to dry down between each step. The Parafilm strips were then burnt off at ~ 1.6 A and the filament glowed briefly to dull red at ~ 2.0 A. Rubidium interferences were monitored on the TIMS using 85 Rb, but even in the case of residual rubidium, it was burnt off from the filament before the strontium was properly emitted. The sample filament was slowly heated until a stable 88 Sr + beam of ~ 12-13 V was obtained and typically measured for 6-7 h (corresponding to ~ 200 cycles, with a total acquisition time of 80 s per cycle). The run length was variable and depended on when the sample was consumed. This translated into 'raw' 86 Sr/ 88 Sr typically close to 0.1204 at the start of an analysis and lower than 0.1185 (and sometimes even down to 0.1180) when the analysis stopped. Baselines were measured for 3 min every 20 cycles and peaks were recentred every 40 cycles.

Strontium isotopes were measured using a 5 lines acquisition routine (Table 1a). The 87 Sr/ 86 Sr and 84 Sr/ 86 Sr acquired in each line were corrected for instrumental mass fractionation with the exponential law using the 86 Sr/ 88 Sr acquired in the same line and assuming ( 86 Sr/ 88 Sr)ref = 0.1194. A multi-static 87 Sr/ 86 Sr (hereafter ( 87 Sr/ 86 Sr)multistat) and a multi-static 84 Sr/ 86 Sr (hereafter ( 84 Sr/ 86 Sr)multistat) can then be obtained by averaging the 5 static 87 Sr/ 86 Sr acquired in the 5 lines and the 4 static 84 Sr/ 86 Sr acquired in the first 4 lines, respectively. A dynamic 87 Sr/ 86 Sr is obtained by combining the measurements from two different magnetic field positions (e.g., lines 1 -2, Table 1a), following:

! !" !" !" !# " #$% = % ! !" !" $% !" !# $" " # × ! !" !" $" !" !! $% " % × ! !" !! !" !# " "&' (1)
We can note that a correction for time-drift is applied for dynamic ratios [START_REF] Garçon | Factors influencing the precision and accuracy of Nd isotope measurements by thermal ionization mass spectrometry[END_REF], and although the drift correction code may not be identical to [START_REF] Garçon | Factors influencing the precision and accuracy of Nd isotope measurements by thermal ionization mass spectrometry[END_REF], a similar effect can be seen. This time drift correction is utilized to minimize effects associated with a growing or changing signal emission between magnet positions. It does so by adding an extra measurement line at the start of each block and comparing this measurement to the following for a correction back to a set time and intensity. A multi-dynamic 87 Sr/ 86 Sr (hereafter ( 87 Sr/ 86 Sr)multidyn) can then be obtained by averaging the 4 dynamic 87 Sr/ 86 Sr. As mentioned earlier, we favoured dynamic measurements because they allow for the effective correction of potential differences in cup efficiencies and amplifier gains between Faraday detectors. Using the analytical conditions described above (very long and high intensity analysis), we obtained internal precision for an individual Sr analysis typically better than 2 x 10 -6 (2 se) on ( 87 Sr/ 86 Sr)multidyn (Fig. 2). In comparison, a 2 hours analysis (corresponding to more 'conventional' Sr isotope studies but with much higher intensities) gives an internal precision typically around 2.5 x 10 -6 (2 se) on ( 87 Sr/ 86 Sr)multidyn (Fig. 2). Finally, assuming that our analyses are made with a 88 Sr signal 4 to 10 times higher than 'conventional' Sr isotopes studies, we can estimate the internal precisions that would be obtained for 2 hours runs at low signal (1-3V on 88 Sr); these would be ~ 5-8 x 10 -6 (Fig. 2). Such values are comparable to the internal precisions obtained in similar conditions and using other TIMS (e.g., [START_REF] Carpentier | Fractionation of Sr and Hf isotopes by mineral sorting in Cascadia Basin terrigenous sediments[END_REF] or another Nu TIMS (e.g., [START_REF] Fourny | Comprehensive Pb-Sr-Nd-Hf isotopic, trace element and mineralogical characterization of mafic to ultramafic rock reference materials[END_REF][START_REF] Fourny | Isotopic and trace element geochemistry of the Kiglapait intrusion, Labrador: Deciphering the mantle source, crustal contributions and processes preserved in mafic layered intrusions[END_REF]. Neodymium isotopic measurements were performed using between 600 ng and 800 ng of Nd loaded on previously outgassed zone-refined Re double filaments. About 1 µl of sample in 0.5N HNO3 was loaded onto the sample filament, in between two Parafilm strips at ~ 0.75 A. Once dried, roughly 0.5 µl of 1N H3PO4 activator was loaded on top of the sample at ~ 1.2 A. Then, once the activator was dried and similarly to Sr, the Parafilm strips were burnt off at ~ 1.6 A and the filament glowed briefly to dull red at ~ 2.0 A. After having heated the ioniser filament to a temperature of ~ 1900°C in the source chamber, the sample filament was slowly heated until a stable 142 Nd + beam of ~ 6-8 V was obtained and typically measured for 7-8 h (corresponding to ~ 300 cycles, with a total acquisition time of 50 s per cycle). Unlike for Sr analyses, we did not systematically run until the Nd was totally consumed. However, if the sample was getting exhausted by the end of an analysis, it translated into 'raw' 146 Nd/ 144 Nd typically starting at 0.7200 to finish at 0.7250 when the analysis was stopped. Baselines were measured for 3 min every 20 cycles, and peaks were recentred every 60 cycles.

Similarly to the Sr method, Nd isotopes were measured using a 5 lines acquisition routine (Table 1b). The method and the equations described in this paper for Nd isotope measurements on the Nu TIMS are adapted from [START_REF] Thirlwall | Long-term reproducibility of multicollector Sr and Nd isotope ratio analysis[END_REF] 1b), following for instance:

! () &'( () &'' " #$%$* = %! () &'( $& () &'' $) " * × ! () &'( *+ () &'' $& " % × ' + &'( + &'' ( %, & (2)
With

𝐹 # = -. ⎝ ⎜ ⎜ ⎛ , -. &'# -. &'' / 012 3 -. &'# $) -. &'' *+ 4 & ⎠ ⎟ ⎟ ⎞ -.5 5 &'# 5 &'' 6 (3)
Dynamic 148 Nd/ 144 Nd and 150 Nd/ 144 Nd are obtained by combining the measurements from two different magnetic field positions (i.e. lines 1-3, 2-4 or 3-5, Table 1b), following for instance:

! () &'! () &'' " #$* = ! () &'! $' () &'# $) " # × ! () &'# () &'' " "&' × ' + &'! + &'# ( , ( (4)
With

𝐹 * = -. ⎝ ⎜ ⎜ ⎛ , -. &'# -. &'' / 012 3 -. &'# $' -. &'' $) 4 ( ⎠ ⎟ ⎟ ⎞ -.5 5 &'# 5 &'' 6 (5)
As in the Sr procedure, a correction for time-drift is applied for dynamic ratios. A multidynamic i Nd/ 144 Nd (hereafter ( i Nd/ 144 Nd)multidyn) can then be obtained by averaging the 3 dynamic i Nd/ 144 Nd. Using the analytical conditions described above (very long and high intensity analysis), we obtain internal precision for an individual Nd analysis typically better than 1 x 10 -6 (2 se) on ( 143 Nd/ 144 Nd)multidyn. We do not report values for 142 Nd/ 144 Nd in this paper because the chromatographic procedure used in the course of this study was not designed to remove Pr and Ce from Nd (Table 2b).

b. Reproducibility of pure standard solutions

We obtain ( 87 Sr/ 86 Sr)multidyn = 0.7102467 ± 0.0000043 (6.0 ppm, 2 s.d., n = 38) for NBS 987 (Fig. 3) and ( 143 Nd/ 144 Nd)multidyn = 0.5119537 ± 0.0000022 (4.2 ppm, 2 s.d., n = 31) for Rennes-Ames (Fig. 4). We can note here that if we consider only the sub data corresponding to the first 60 cycles (~ 2 hours) of each NBS 987 analysis, we obtain similar values, i.e. ( 87 Sr/ 86 Sr)multidyn = 0.7102456 ± 0.0000044 (6.2 ppm, 2 s.d., n = 38). These data are consistent with the data reported in the literature, however the external precisions reported here on pure standard solutions are two to three times better than the most precise published data for 87 Sr/ 86 Sr, and comparable to the most precise literature data for 143 Nd/ 144 Nd (Table 3 and Fig. 3a and4a).

Our measurement of JNdi-1 gives ( 143 Nd/ 144 Nd)multidyn = 0.5120941 ± 0.0000022 (4.4 ppm, 2 s.d., n = 9), which is slightly lower than the reference value of 0.512115 ± 0.000007 reported in [START_REF] Tanaka | JNdi-1: a neodymium isotopic reference in consistency with LaJolla neodymium[END_REF]. However, our ( 143 Nd/ 144 Nd)multidyn is in agreement with the highprecision data of 0.512099 ± 0.000005 (9.2 ppm, 2 s.d., n = 54) reported in [START_REF] Garçon | Factors influencing the precision and accuracy of Nd isotope measurements by thermal ionization mass spectrometry[END_REF]. It is also very close to the latest high-precision data reported by Pin and Gannoun (2019 a,b) of 0.512101 ± 0.000003 (5.9 ppm, 2 s.d., n = 12) and 0.512104 ± 0.000003 (5.9 ppm, 2 s.d., n = 15). We note that despite plotting within error of each other, the two values reported by Pin and Gannoun indicate that small variations can occur for analyses run on the same instrument in the same laboratory, even in the course of high precision isotope work.

Also, as seen in Figure 3b, there is no resolvable difference between ( 87 Sr/ 86 Sr)multidyn and ( 87 Sr/ 86 Sr)multistat, which is expected when the drift in the mass bias is corrected properly and the Faraday cups show little evidence for deterioration (the detectors have been used for less than a year in the course of this study). Similarly to 87 Sr/ 86 Sr, there seems to be no significant offset between ( 143 Nd/ 144 Nd)multidyn and ( 143 Nd/ 144 Nd)multistat, the difference between the two ratios being on average ~ 2 ppm , i.e. within error (Fig. 4b). It is also important to note that for the Nd systematics, the multidynamic method yields more reproducible data than the multistatic method, translating into a smaller error on the mean ratio (± 0.0000022 versus ± 0.0000040 on the 143 Nd/ 144 Nd, 2 s.d., n = 31). For the Sr systematics, both methods seem to give comparable reproducibility at the moment (± 0.0000043 versus ± 0.0000041 on the 87 Sr/ 86 Sr, 2 s.d., n=38). One thing worth to note here is that, as shown in Figure 4b, the 143 Nd/ 144 Nd seems to decrease with time (for both ( 143 Nd/ 144 Nd)multidyn and ( 143 Nd/ 144 Nd)multistat). The origin of this drift is not clear to us yet, but we believe it could be several things, from how the beam behaves (growing or dying), how it fractionates (i.e. reverse fractionation occurring; e.g., [START_REF] Garçon | Factors influencing the precision and accuracy of Nd isotope measurements by thermal ionization mass spectrometry[END_REF]) to the gain or the bucket efficiency. Thus, if we can see a 4 ppm change between running the analysis using a standard or reverse cup configuration (see below), maybe the same could be seen between a growing and dying signal. Alternatively, a good indication of bucket efficiency would be to monitor how the 143 Nd/ 144 Nd static ratios behave individually when the gain is stable over a time period. However, we could not see one ( 143 Nd/ 144 Nd)stat being systematically and significantly lower than the others. Overall, it is difficult to say what causes this change given it is a very small change.

Furthermore, we have compared two reverse methods (Table 1b and1c) for Nd isotope measurements on the pure standard solution Rennes-Ames and have noticed the ( 143 Nd/ 144 Nd)multidyn obtained with each method were within errors of each other. Thus, in February 2021, we obtained a ( 143 Nd/ 144 Nd)multidyn of 0.5119535 ± 0.0000013 (2.5 ppm, 2 s.d., n = 7) with the cup configuration reported in table 1b, which is within error of ( 143 Nd/ 144 Nd)multidyn = 0.5119514 ± 0.0000018 (3.5 ppm, 2 s.d., n = 5) obtained with the reverse method reported in table 1c. The relative difference between those two values is of ~ 4 ppm. Similarly, we obtained the same relative difference of ~ 4 ppm for ( 143 Nd/ 144 Nd)multidyn between the two Nd reverse methods in June 2021, with the cup configuration reported in table 1b giving 0.5119500 ± 0.0000004 and the set-up reported in Table 1c giving 0.5119481 ± 0.0000007. Overall, although the method reported in Table 1b seems to give a slightly higher ( 143 Nd/ 144 Nd)multidyn, this is not significant compared to the external reproducibility (2 s.d.) of 4-5 ppm reported in this study for ( 143 Nd/ 144 Nd)multidyn. The cup configuration reported in Table 1b was the one finally used during this study.

Finally, the data obtained in this study for stable isotopes, i.e. 84 Sr/ 86 Sr = 0.0564902 ± 0.0000018 (31.9 ppm, 2 s.d., n = 38) for NBS 987, and 145 Nd/ 144 Nd = 0.3484004 ± 0.0000013 (3.7 ppm, 2 s.d., n = 31), 148 Nd/ 144 Nd = 0.2415798 ± 0.0000019 (8.0 ppm, 2 s.d., n = 31) and 150 Nd/ 144 Nd = 0.2364508 ± 0.0000056 (23.5 ppm, 2 s.d., n = 31) for Rennes-Ames, are consistent with previous studies (Table 3). The precisions reported here on those ratios are comparable to the latest high-precision isotope data reported in [START_REF] Burkhardt | Elemental and isotopic variability in solar system materials by mixing and processing of primordial disk reservoirs[END_REF] for the Sr standard solution NBS 987 and Pin and Gannoun (2019) for the Nd standard solution Rennes-Ames (Fig. 5).

c. Precision

In this section, we compare the actual errors of our analyses on the Nu TIMS with the theoretical uncertainties expected from Johnson-Nyquist noise and counting statistics, these processes being considered as the two main contributors to the observed internal uncertainty for a given analysis. The reader is referred to the supplementary section of [START_REF] Luu | Bulk chondrite variability in mass independent magnesium isotope compositions -Implications for initial solar system 26 Al/ 27 Al and the timing of terrestrial accretion[END_REF] for more details about the theoretical uncertainty model and the calculations, but the important details are summarized below.

Johnson-Nyquist noise (sJohnson), the phenomenon of thermally-generated voltage noise in the feedback resistor, has a standard deviation given by 𝜎 789:;8: = + <=>?

@

, where R is the feedback resistor of the amplifier connected to the Faraday cup (here 10 11 Ω for all cups measuring Sr and Nd isotopes), k is the Boltzmann constant (= 1.38×10 -23 J/K), T is the amplifier housing temperature (= 307 K) and t is the total integration time (= integration time per static measurement × total number of cycles). Note that we include this noise in our uncertainty model for completeness, but it is insignificant compared to the shot noise. Counting statistics (scounting), or shot noise, describes the statistics of the arrival of ions at the detector as a Poisson distribution. It is given by 𝜎 A8B:@C:D = + E 5 =& @ , where Vm is the mean amplifier output voltage over the total integration time t, and e is the elementary charge (= 1.60 × 10 -19 C). Combining these errors by adding in quadrature the total absolute error on each isotope gives

𝜎 FG; H =
2𝑠𝑒 "&I +BI@C)K: = 2 × # %: + 𝑛 × (𝜎 "&I H ) % + 𝑛 × (𝜎 "&I L ) % + (4𝑛 -2) × 5𝜎 "&I K 6
% , where n correspond to the number of static measurements -1 (so n = 4 in our case). Finally, the 2 s.e. absolute error on the ( 87 Sr/ 86 Sr)multidyn is calculated as:

2𝑠𝑒 FG; +BI@C)K: = 2𝑠𝑒 "&I +BI@C)K: × M !" M !#
, where A87 and A86 correspond to the relative abundances of 87 Sr (7.00%) and 86 Sr (9.86%) isotopes, respectively. The reader is referred to the supplementary information of this paper for more details about these equations and the error propagation calculations.

The results of that model are plotted in Figure 6, for the case of Sr systematics. We chose to plot the typical internal precisions (2 s.e.) for ( 87 Sr/ 86 Sr)multidyn against 1/sqrt(number of ions detected) because this latter parameter reflects the total integration time, while accounting for the different average total intensities of the dataset. On figure 6a, we can clearly see that the data fall below the model, for both the geostandards and the pure standard solution NBS 987. This is unexpected and may not look correct at first glance. However, we used a Monte Carlo simulation for the quintuple-jump uncertainty on the ratio and it agrees well with the error propagation model described above, so we are confident that the discrepancy between the actual and the theoretical errors is not due to a mistake in the algebra of propagating the errors. We then investigated the effect of the time-drift correction. As mentioned earlier, a correction for time-drift is applied for dynamic ratios. This is because the use of a time-drift correction in a dynamic routine helps reducing possible fractionation changes between measurement lines, which could cause a bias on the final ratio as suggested in [START_REF] Garçon | Factors influencing the precision and accuracy of Nd isotope measurements by thermal ionization mass spectrometry[END_REF] and observed by [START_REF] Roth | Revisiting the 142 Nd deficits in the 1[END_REF]. We note that although the drift correction code may not be identical to [START_REF] Garçon | Factors influencing the precision and accuracy of Nd isotope measurements by thermal ionization mass spectrometry[END_REF], a similar effect can be seen. If the time-drift correction is ignored, it appears that the data are now consistent with the model (Fig. 6b): the typical uncertainties reported in Table 3 for both pure standard solution NBS987 and terrestrial rock standards are now very close to the modelled errors, showing that (i) there is no effect of the matrix on the precision of an analysis, and that (ii) the Nu TIMS is performing at the best of its capabilities. We can note that the ( 87 Sr/ 86 Sr)multidyn with and without time drift correction are differing by less than 4 ppm (Table 4), which is not significant compared to the 6 ppm external reproducibility we report. Thus, all the data reported in this paper have been processed using a time drift correction.

Results for terrestrial rock standards

The ( 87 Sr/ 86 Sr)multidyn and ( 143 Nd/ 144 Nd)multidyn obtained for rock standards in this study are reported in Table 3. All the results obtained by our method are in agreement with published data (Fig. 7 and8). For instance, we obtained ( 87 Sr/ 86 Sr)multidyn = 0.7034750 ± 0.0000023 (3.3 ppm, 2 s.d., n = 4) and ( 143 Nd/ 144 Nd)multidyn = 0.5129662 ± 0.0000025 (4.8 ppm, 2 s.d., n = 4) for BHVO-2, and ( 87 Sr/ 86 Sr)multidyn = 0.7039814 ± 0.0000059 (8.3 ppm, 2 s.d., n = 4) and ( 143 Nd/ 144 Nd)multidyn = 0.5127702 ± 0.0000033 (6.4 ppm, 2 s.d., n = 3) for AGV-2. We should note that the variability in 143 Nd/ 144 Nd for JNdi-1 between different studies (see section 3.b) has to be taken into account when comparing the 143 Nd/ 144 Nd in the literature for terrestrial standards. The important thing to note here is that, for both systems, the precisions reported in this study are much better than most previous studies (Fig. 7 and8), with an external reproducibility of typically 5-6 ppm (2 s.d.) for 87 Sr/ 86 Sr and 4-5 ppm (2 s.d.) for 143 Nd/ 144 Nd. We can also note that, although our chemistry protocol does not remove 141 Pr nor 140 Ce (with typically 2 < 141 Pr + / 146 Nd + < 4 and 140 Ce + / 146 Nd + < 1 for rock standards at the start of an analysis), this does not seem to affect the accuracy of the 143 Nd/ 144 Nd.

Implications

The level of precision reached for Sr and Nd systematics in this study opens new perspectives in the field of Earth Sciences, but not only.

Indeed, the extent of the application of radiogenic isotopes is not restricted to Earth Sciences. In archaeology, 87 Sr/ 86 Sr and 143 Nd/ 144 Nd represent a powerful tool as source tracers. For instance, small differences in isotope ratios can be decisive in discriminating sources at the origin of raw materials that have been used for making prehistoric artefacts, and this information can be precious to understand patterns of migrations and/or interactions between prehistoric societies. However, few data have been produced with good precision (e.g., [START_REF] Weisler | Cook Island artifact geochemistry demonstrates spatial and temporal extent of pre-European interarchipelago voyaging in East Polynesia[END_REF][START_REF] Hermann | Combined geochemical and geochronological analyses of stone artefacts provide unambiguous evidence of intra-and inter-island interactions in Polynesia[END_REF]) and thereby most studies have limited conclusions given the geochemical similarity of sources and some unclear geological complications regarding the source of Sr (e.g., Thomsen and Andreasen, 2019).

In cosmochemistry, small isotopic anomalies, commonly down to the ppm level, are present among solar system materials at a planetary scale, and so, being able to detect them provide important constraints on planetary bodies relationships and the dynamical evolution of the solar system. Considering Sr isotopes, the level of analytical precision of most studies (~ 8-10 ppm, 2 s.e.; e.g., [START_REF] Hans | Rb-Sr chronology of volatile depletion in differentiated protoplanets: BABI, ADOR and ALL revisited[END_REF][START_REF] Henshall | High-precision strontium isotope analysis of geological samples by thermal ionization mass spectrometry[END_REF]) did not allow identification of massindependent variations in 84 Sr/ 86 Sr between enstatite chondrites, ordinary chondrites, eucrites, Moon, Mars and the Earth; only carbonaceous chondrites showed small resolvable positive anomalies in 84 Sr, between 40 and 60 ppm relative to NBS 987 (e.g., [START_REF] Moynier | Planetary-scale strontium isotopic heterogeneity and the age of volatile depletion of early solar system materials[END_REF]). The latest study of bulk planetary materials by [START_REF] Burkhardt | Elemental and isotopic variability in solar system materials by mixing and processing of primordial disk reservoirs[END_REF] has modified this picture, reporting ordinary and enstatite chondrites, as well as Moon, with small resolvable negative anomalies in 84 Sr, on the order of -10 to -20 ppm relative to NBS 987. This demonstrates that improving analytical precision is key to better resolve small isotopic variability, and thus why the level of precision reached for 84 Sr/ 86 Sr in this study (2 s.e. of ~ 5 ppm, Fig. 5a) is useful. The same reasoning could be true for other systematics, e.g. mass-independent variations in 40 Ca.

High precision data such as those reported in this study also opens new chronology perspectives. Even if most of the uncertainty on ages comes from the poor determination of the parent/daughter ratio, enhanced precision on the isotopic ratio translates into a smaller propagated uncertainty on the age determined from Rb-Sr or Sm-Nd isochrons (Fig. 9). We should be able to obtain Rb-Sr or Sm-Nd isochrons for much younger rocks, with greater resolution between previously indistinguishable suites. We should also be able to obtain isochrons for phases with lower Rb/Sr or Sm/Nd, for which the excesses in the decay products of 87 Rb and 143 Sm will be small but now detectable with our improved analytical precisions on 87 Sr/ 86 Sr and 143 Nd/ 144 Nd. For example, recently, Baxter et al. ( 2017) reported high-precision Sm-Nd dating of individual growth zones within single garnet crystals in eclogites and other metamorphic rocks, and highlighted multistage processes occurring in subduction.

In mantle geochemistry, small scale mantle heterogeneities, such as those discovered when Pb isotopes started being measured with high precision (e.g., [START_REF] Abouchami | Lead isotopes reveal bilateral asymmetry and vertical continuity in the Hawaiian mantle plume[END_REF], might be discovered for volcanic rocks in both Sr and Nd isotopic spaces. Indeed, before the study by [START_REF] Abouchami | Lead isotopes reveal bilateral asymmetry and vertical continuity in the Hawaiian mantle plume[END_REF], the two chains of Hawaiian volcanoes Loa and Kea were thought to have overlapping radiogenic isotope features (for Pb, Sr and Nd systematics). However, the high precision Pb isotope data reported for the first time in [START_REF] Abouchami | Lead isotopes reveal bilateral asymmetry and vertical continuity in the Hawaiian mantle plume[END_REF] thanks to a Pb triple-spike technique have allowed to differentiate the Loa and Kea trends, with only a very little compositional overlap. Similar discoveries could be expected with the improvement in precision of Sr and Nd isotope data as reported in our study.

Finally, the preservation in the Earth's deep interior of early-formed material, either recycled from the surface reservoirs or residual from the early mantle differentiation, has recently been evidenced by the detection of small variability in 182 W (Mundl et [START_REF] Peters | Hadean silicate differentiation preserved by anomalous 142 Nd/ 144 Nd ratios in the Réunion hotspot source[END_REF]). These recent discoveries are very exciting and we are currently developing analytical methods for high precision 182 W and 142 Nd isotope measurements on our Nu TIMS at IPGP, in order to expand the currently limited dataset available.

Conclusions

We report high-precision Sr and Nd isotope data, with an external reproducibility on the order of 5-6 ppm (2 s.d.) for 87 Sr/ 86 Sr and 4-5 ppm (2 s.d.) for 143 Nd/ 144 Nd. This is the first time such a level of precision is reported with a TIMS from Nu Instruments. Such precisions are of key importance in the field of Earth Sciences because Sr and Nd systematics are powerful tools to trace sources of materials and to date them, but they also open new opportunities in fields such as cosmochemistry, paleoclimatic studies, archaeology, tracing of food origin or forensics.

Acknowledgements

This work was supported by grant from European Research Council (ERC grant SHRED, Grant Agreement no. [833632] -Survival of Hadean REmnants in a Dynamic mantle). THL would like to thank Christopher Coath from the Bristol Isotope Group for his expertise regarding the statistics and error propagation section and acknowledge authorship of the derivation of the theoretical uncertainty provided in the supplementary information. We thank Tod Waight and an anonymous reviewer for their constructive reviews that allowed for a muchimproved manuscript. We also thank Balz Kamber for editorial handling.

FIGURE 2:

Comparison between the internal errors typically obtained when running the Sr isotope analyses (i) with more than 10V of signal on 88 Sr + for 6-7 hours (i.e. our standard conditions, blue dots) and (ii) with more than 10V of signal on 88 Sr + for 2 hours only (orange crosses). An estimation of the internal errors obtained when running with less than 3V of signal for 2 hours is also shown for comparison (black arrow).

0.0E+00

(f) (e) (d) (c) (o) (a) (l) (l) (j) (i) (h) (g)
a. a. Improvement on the uncertainty of the age determined from a Rb-Sr isochron with improvement of the precision on the 87 Sr/ 86 Sr for extraterrestrial materials (here for ~ 4.55 Ga old eucrites, [START_REF] Birck | Chronology and chemical history of the parent body of basaltic achondrites studied by the 87 Rb-87 Sr method[END_REF]). We assumed an error of 1% on 87 Rb/ 86 Sr as stated in [START_REF] Birck | Chronology and chemical history of the parent body of basaltic achondrites studied by the 87 Rb-87 Sr method[END_REF]. b. Improvement on the uncertainty of the age determined from a Sm-Nd isochron with improvement of the precision on the 143 Nd/ 144 Nd for terrestrial materials (here for 2.76 Ga old samples from Kambalda, [START_REF] Chauvel | The Sm-Nd age of Kambalda volcanics is 500 Ma too old! Earth Planet[END_REF]. We assumed an error of 0.2% on the 147 Sm/ 144 Nd as estimated in [START_REF] Chauvel | The Sm-Nd age of Kambalda volcanics is 500 Ma too old! Earth Planet[END_REF].

(n) (m) (l) (k) (k) (j) (i) (h) (g) (f) (e) (e) (d) (c) (b) (a) (o) (k) (k) (t) (s) (b) a. (r) (q) (p)
A.

B. 788

  and Garçon et al. (2018). The 143 Nd/ 144 Nd, 145 Nd/ 144 Nd, 148 Nd/ 144 Nd and 150 Nd/ 144 Nd acquired in each line were corrected for instrumental mass fractionation with the exponential law using the 146 Nd/ 144 Nd acquired in the same line and assuming ( 146 Nd/ 144 Nd)ref = 0.7219. A multi-static i Nd/ 144 Nd (hereafter ( i Nd/ 144 Nd)multistat, with i = 143, 145, 148 or 150) can then be obtained by averaging the 5 static i Nd/ 144 Nd acquired in the 5 lines. Dynamic 143 Nd/ 144 Nd and 145 Nd/ 144 Nd are obtained by combining the measurements from three different magnetic field positions (i.e. lines 1-2-3, 2-3-4 or 3-4-5, Table

FIGURE 1 :

 1 FIGURE 1: a. Schematic showing where the zoom lens system allowing peak alignment while having fixed Faraday detectors sits on the Nu TIMS, and what happens to the ion beams when using or not the zoom lens system. a-1: No voltage is applied on quads 1 and 2, resulting in two ion beams diverging and being unfocused at the collector array. a-2: A voltage is applied on quad 1 only, resulting in two ion beams being focused but the natural dispersion of these ion beams does not align with the collector array. a-3: Voltages are now applied on both quads 1 and 2, resulting in two ion beams being now focused at the correct collectors. b. Peak alignment achieved with fixed Faraday detectors for Sr and Nd isotopes when applying adequate voltages on the zoom lens system. The isotopes 84 Sr, 86 Sr, 87 Sr and 88 Sr are collected in H1, H5, H7 and H9 detectors, respectively (C-1). The isotopes 142 Nd, 143 Nd, 144 Nd, 145 Nd, 146 Nd, 148 Nd and 150 Nd are collected in L2, L1, Ax, H1, H2, H4 and H6, respectively (C-2).

  87 Sr/ S6 Sr = 0.7102467 ± 0.0000043 (6.0 ppm, 2sd, n= 38) Average Multistatic: 87 Sr/ S6 Sr = 0.7102465 ± 0.0000041(5.7 ppm, 2sd, n= 38) b.Time Time

FIGURE 4 :

 4 FIGURE 4: a. Comparison of our mean ( 143 Nd/ 144 Nd)multidyn measured for the pure Nd standard solutions JNDi-1 and Rennes-Ames (blue circles) with literature data (grey circles). Note that we added the reference Fourny et al. (2016) for comparison, given the few data available in the literature for the Nd standard solution Rennes-Ames. Note that the yellow circle corresponds to the recommended value reported by Zhang and Hu (2020) after a compilation of the data available in Georem. Error bars correspond to 2 s.d. Literature: (a) Tanaka et al. 2000, (b) Le Fèvre and Pin 2005, (c) Li et al. 2007, (d) Aciego et al. 2009, (e) Chu et al. 2009, (f) Li et al 2011a, (g) Li et al 2011b, (h) Ali and Srinivasan 2011, (i) Li et al. 2014, (j) Pin et al. 2014, (k) Fourny et al. 2016, (l) Garçon et al. 2018, (m) Pin and Gannoun 2019a, (n) Pin and Gannoun 2019b, (o) Zhang and Hu 2020, (p) Chauvel and Blichert-Toft 2001, (q) Caro et al. 2003, (r) Caro et al. 2006, (s) Weis et al. 2006, (t) Chauvel et al. 2011. b. Comparison between ( 143 Nd/ 144 Nd)multidyn and ( 143 Nd/ 144 Nd)multistat measured in Rennes-Ames over a period of ~ 8 months on the Nu TIMS. Error bars on individual data correspond to internal 2 se.

Sr

FIGURE 8 :

 8 FIGURE 8: Multidynamic 143 Nd/ 144 Nd measured for different geostandards in the course of this study (blue symbols) and comparison with the literature. BCR-1, BHVO-1, BIR-1 and AGV-1 are represented as circles, while BCR-2, BHVO-2 and AGV-2 are represented as diamonds. Recommended values from Zhang and Hu (2020) are also shown for comparison (yellow symbols). Literature: (a-t) same as in Figure 4a, (u) Raczek et al. 2003, (v) Mahlen et al. 2008, (w) Yang et al. 2010, (x) Li et al. 2012, (y) Klaver et al. 2015, (z) Li et al. 2015, (aa) Carpentier et al. 2014, (ab) Koornneef et al. 2015.

FIGURE 9 :

 9 FIGURE 9:a. Improvement on the uncertainty of the age determined from a Rb-Sr isochron with improvement of the precision on the 87 Sr/ 86 Sr for extraterrestrial materials (here for ~ 4.55 Ga old eucrites,[START_REF] Birck | Chronology and chemical history of the parent body of basaltic achondrites studied by the 87 Rb-87 Sr method[END_REF]). We assumed an error of 1% on 87 Rb/ 86 Sr as stated in[START_REF] Birck | Chronology and chemical history of the parent body of basaltic achondrites studied by the 87 Rb-87 Sr method[END_REF]. b. Improvement on the uncertainty of the age determined from a Sm-Nd isochron with improvement of the precision on the 143 Nd/ 144 Nd for terrestrial materials (here for 2.76 Ga old samples from Kambalda,[START_REF] Chauvel | The Sm-Nd age of Kambalda volcanics is 500 Ma too old! Earth Planet[END_REF]. We assumed an error of 0.2% on the 147 Sm/ 144 Nd as estimated in[START_REF] Chauvel | The Sm-Nd age of Kambalda volcanics is 500 Ma too old! Earth Planet[END_REF].

  Age uncertainty (Ma)Relative error on 87 Sr/ 86 Sr ( ppm)Whole rock eucrites (from[START_REF] Birck | Chronology and chemical history of the parent body of basaltic achondrites studied by the 87 Rb-87 Sr method[END_REF] a.

  Age uncertainty (Ma)Relative error on 143 Nd/ 144 Nd ( ppm) Kambalda samples (from[START_REF] Chauvel | The Sm-Nd age of Kambalda volcanics is 500 Ma too old! Earth Planet[END_REF] b.

  , 87 or 88 for Sr isotopes for instance. From there, the 2 s.e. relative error on the ( 87 Sr/ 86 Sr)multidyn is derived by the quintuple jump type error propagation calculation as:

	+𝜎 789:;8: %	+ 𝜎 A8B:@C:D %	, and the total relative error can be written as 𝜎 "&I H =	+ J 678 E 5 + , with
	x = 86

  al. 2017, Rizo et al. 2016) and 142 Nd (Peters et al. 2018), the decay products of the short-lived 182 Hf (half-life of 8.9 Myr) and 146 Sm (half-life of 103 Myr), respectively. The total range of variations among modern ocean island basalts does not exceed 15 ppm in 142 Nd/ 144 Nd and 25 ppm for 182 W/ 184 W. These small variabilities have become detectable thanks to the high analytical precisions recently reached with dynamic measurements on the TIMS, i.e. ± 4 ppm on 182 W/ 184 W (2 s.d.; Mundl et al. 2017) and ± 4.4 ppm on 142 Nd/ 144 Nd (2 s.d., in

TABLE 1 :

 1 Collector configuration used for Sr (a) and Nd (b) isotope measurements on the Nu TIMS during the course of this study. Note that the numbers in bold purple correspond to the mass used for the peak centering for each line. (c) Reverse configuration for Nd used to test if there is any difference between methods b and c.

	a.
			Sr configuration H11 H9 H7 H5 H3 H1 L1 L3 Integration time (s) Quad 1 (V) Quad 2 (V)
			Line 1			88 87 86 85 84 83 82 81		16			27	-27
			Line 2			89 88 87 86 85 84 83 82		16			28	-42
			Line 3			90 89 88 87 86 85 84 83		16			33	-61
			Line 4			91 90 89 88 87 86 85 84		16			34	-77
			Line 5			92 91 90 89 88 87 86 85		16			36	-91
	b.
	Nd configuration H11 H10	H9	H8	H7	H6	H5	H4	H3	H2	H1	Ax	L1	L2	L3	L4	Integration time (s) Quad 1 (V) Quad 2 (V)
	Line 1	155 154 153 152 151 150 149 148 147 146 145 144 143 142 141 137	10	-15	127
	Line 2	154 153 152 151 150 149 148 147 146 145 144 143 142 141 140 136	10	-15	134
	Line 3	153 152 151 150 149 148 147 146 145 144 143 142 141 140 139 135	10	-17	139
	Line 4	152 151 150 149 148 147 146 145 144 143 142 141 140 139 138 134	10	-17	145
	Line 5	151 150 149 148 147 146 145 144 143 142 141 140 139 138 137 133	10	-17	148
	c.
	Nd Reverse	H11 H10 H9 H8 H7 H6 H5 H4 H3 H2 H1 Ax L1 L2 L3 L4	Integration time (s)	Quad 1 (V)	Quad 2 (V)
	Line 1	151	150 149 148 147 146 145 144 143 142 141 140 139 138 137 133	10	-18	149
	Line 2	152	151 150 149 148 147 146 145 144 143 142 141 140 139 138 134	10	-18	146
	Line 3	153	152 151 150 149 148 147 146 145 144 143 142 141 140 139 135	10	-18	140
	Line 4	154	153 152 151 150 149 148 147 146 145 144 143 142 141 140 136	10	-17	137
	Line 5	155	154 153 152 151 150 149 148 147 146 145 144 143 142 141 137	10	-17	131

TABLE 2 :

 2 a. Potential interferences (a) in the mass region 84-88 affecting the Sr isotope results 645 and (b) in the mass region 142-150 affecting the Nd isotope results. In practice, Kr, oxides and 646 doubly charged ions constitute a major issue when using plasma source mass spectrometers, 647 but they are very rare when using a TIMS. Only interferences coming from Rb and Ce-Sm (bold 648 purple) are considered when measuring Sr and Nd isotopes on a TIMS. A good Sr and Nd 649 chemical separation prior to isotope analyses on the TIMS is mandatory. Fe 16 O2 + 54 Fe 16 O 17 O + 54 Fe 16 O 18 O + 54 Fe 17 O2 + 56 Fe 16 O2 + Zn oxides 68 Zn 16 O + 68 Zn 18 O + 70 Zn 16 O + 70 Zn 17 O + 70 Zn 18 O + Ga oxides 69 Ga 17 O + 69 Ga 18 O + 71 Ga 16 O + 71 Ga 17 O + Ca dimers 40 Ca 44 Ca + 40 Ca 46 Ca + 40 Ca 48 Ca + 42 Ca2 + 42 Ca 44 Ca + 42 Ca 46 Ca + 43 Ca2 + 43 Ca 44 Ca + 44 Ca2 +

	650
	651
	652	a.
		Sr	84 Sr +	86 Sr +	87 Sr +	88 Sr +
		Kr	84 Kr +	86 Kr +
		Rb			87 Rb +
		REE	168 Yb 2+	172 Yb 2+	174 Yb 2+	176 Yb 2+
			168 Er 2+
						176 Lu 2+
					174 Hf 2+	176 Hf 2+
	Fe oxides 54 653
	654	b.
		Nd	142 Nd 143 Nd	144 Nd	145 Nd	146 Nd	148 Nd	150 Nd
		Ce

142 Ce + Sm 144 Sm + 148 Sm + 150 Sm+ Ba

  oxides 130 Ba 16 O 132 Ba 16 O 134 Ba 16 O 132 Ba 18 O Ru oxides 96 Ru 16 O3 + 98 Ru 16 O3 + 100 Ru 16 O3 + 102 Ru 16 O3 +

	655
	656

TABLE 3 :

 3 Strontium and neodymium isotope compositions for pure standard solutions and terrestrial rocks measured in the course of this study.657All the ratios are multidynamic except the 84 Sr/ 86 Sr which are multistatic. Rep = the solution was loaded a second time on a different filament. 658

	87 Sr/ 86 Sr	2se/2sd	84 Sr/ 86 Sr	2se/2sd	Yield
					(%)

143 Nd/ 144 Nd 2se/2sd 145 Nd/ 144 Nd 2se/2sd 148 Nd/ 144 Nd 2se/2sd 150 Nd/ 144 Nd 2se

									/2sd	Yield
									(%)
	Pure standard	NBS 987	0.7102467	4.3´10 -6 0.0564902 1.8´10 -6
	Solutions			(n = 38)	(n=38)
		Rennes-Ames				0.5119537	2.2´10 -6 0.3484004	1.3´10 -6 0.2415798	1.9´10 -6 0.2364508	5.6´10 -6
							(n=31)	(n=31)	(n=31)	(n=31)
	Terrestrial rocks
	BHVO-2 BHVO-2 a				0.5129680	7.3´10 -7 0.3484000	2.2´10 -7 0.2415805	3.3´10 -7 0.2364501	5.3´10 -7 34
		BHVO-2 Pam	0.7034753	1.9´10 -6 0.0564891 5.1´10 -7 29	0.5129658	6.2´10 -7 0.3483998	1.8´10 -7 0.2415793	2.6´10 -7 0.2364491	4.5´10 -7 40
		BHVO-2 b	0.7034737	1.2´10 -6 0.0564890 4.5´10 -7 86	0.5129653	6.5´10 -7 0.3483992	2.1´10 -7 0.2415791	2.7´10 -7 0.2364487	4.0´10 -7 84
		BHVO-2 c	0.7034765	1.4´10 -6 0.0564899 5.3´10 -7 75	0.5129656	6.0´10 -7 0.3483997	1.7´10 -7 0.2415802	2.5´10 -7 0.2364502	3.6´10 -7 89
		BHVO-2 c rep	0.7034746	1.4´10 -6 0.0564883 4.4´10 -7
		mean 0.7034750	2.3´10 -6 0.0564891 1.3´10 -6	0.5129662	2.5´10 -6 0.3483996	7.2´10 -7 0.2415798	1.4´10 -6 0.2364495	1.5´10 -6
	BCR-2 BCR-2 a	0.7050090	1.5´10 -6 0.0564898 5.1´10 -7 27	0.5126183	8.5´10 -7 0.3484002	2.9´10 -7 0.2415858	3.7´10 -7 0.2364560	5.8´10 -7 18
		BCR-2 b	0.7050103	9.9´10 -7 0.0564873 4.5´10 -7 78
		BCR-2 c	0.7050093	1.3´10 -6 0.0564893 4.3´10 -7 93	0.5126142	5.1´10 -7 0.3483987	1.4´10 -7 0.2415789	1.9´10 -7 0.2364471	2.9´10 -7 90
		BCR-2 c rep	0.7050077	1.1´10 -6 0.0564889 4.3´10 -7
		mean 0.7050091	2.2´10 -6 0.0564893 8.4´10 -7	0.5126162	5.7´10 -6 0.3483994	2.1´10 -6 0.2415824	9.7´10 -6 0.2364515	1.3´10 -5
	BR-24 BR-24 a	0.7050381	1.2´10 -6 0.0564882 4.2´10 -7 87	0.5127711	5.5´10 -7 0.3483991	1.5´10 -7 0.2415791	2.3´10 -7 0.2364482	3.9´10 -7 92
		BR-24 b	0.7050380	1.6´10 -6 0.0564881 5.9´10 -7 87	0.5127711	5.3´10 -7 0.3483988	1.7´10 -7 0.2415796	2.3´10 -7 0.2364496	3.5´10 -7 89
		BR-24 b rep	0.7050379	1.2´10 -6 0.0564878 4.1´10 -7
		mean 0.7050380	1.8´10 -7 0.0564880 4.2´10 -7	0.5127711	2.8´10 -8 0.3483989	4.7´10 -7 0.2415793	7.9´10 -7 0.2364489	2.1´10 -6
	BIR-1 BIR-1 a	0.7031000	1.5´10 -6 0.0564888 4.7´10 -7 74	0.5130710	9.2´10 -7 0.3483992	2.7´10 -7 0.2415824	4.1´10 -7 0.2364516	5.5´10 -7 87
		BIR-1 b	0.7030985	1.6´10 -6 0.0564892 5.6´10 -7 71	0.5130734	9.5´10 -7 0.3483992	2.6´10 -7 0.2415795	3.6´10 -7 0.2364482	5.9´10 -7 86
		BIR-1 b rep	0.7030959	1.3´10 -6 0.0564898 4.2´10 -7

mean 0.7030981 4.1´10 -6 0.0564893 1.1´10 -6 0.5130722 3.5´10 -6 0.3483992 5.7´10 -8 0.2415810 4.0´10 -6 0.2364499 4.8´10 -6

	Be-N Be-N a	0.7038004	1.6´10 -6 0.0564873 6.0´10 -7 75	0.5128642	6.0´10 -7 0.3483994	1.8´10 -7 0.2415804	2.3´10 -7 0.2364517	3.9´10 -7 91
	Be-N a rep	0.7037995	1.1´10 -6 0.0564875 4.4´10 -7
	Be-N b	0.7037999	1.5´10 -6 0.0564883 5.1´10 -7 89	0.5128617	6.1´10 -7 0.3483991	1.8´10 -7 0.2415815	2.3´10 -7 0.2364530	3.6´10 -7 86
	mean 0.7037999	8.6´10 -7 0.0564877 1.1´10 -6	0.5128629	3.5´10 -6 0.3483993	4.5´10 -7 0.2415809	1.6´10 -6 0.2364524	1.8´10 -6
	RGM-1 RGM1-a		12					9
	RGM-1 b	0.7042043	1.4´10 -6 0.0564873 4.4´10 -7 71	0.5127778	6.9´10 -7 0.3483999	2.1´10 -7 0.2415802	2.6´10 -7 0.2364489	4.1´10 -7 91
	RGM-1 b rep	0.7041943	1.1´10 -6 0.0564886 4.1´10 -7
	RGM-1 c		85
	mean 0.7041993	1.4´10 -5 0.0564880 1.9´10 -6
	AGV-2 AGV-2 a	0.7039781	1.8´10 -6 0.0564908 6.1´10 -7 14	0.5127720	9.0´10 -7 0.3484012	3.3´10 -7 0.2415795	3.5´10 -7 0.2364480	6.7´10 -7 15
	AGV-2 b	0.7039843	9.5´10 -7 0.0564875 3.9´10 -7 85	0.5127688	6.2´10 -7 0.3483987	2.0´10 -7 0.2415780	2.6´10 -7 0.2364465	4.1´10 -7 79
	AGV-2 c	0.7039800	1.2´10 -6 0.0564896 4.5´10 -7 93	0.5127698	5.4´10 -7 0.3483988	1.5´10 -7 0.2415810	2.3´10 -7 0.2364508	3.6´10 -7 91
	AGV-2 c rep	0.7039835	1.3´10 -6 0.0564877 4.4´10 -7
	mean 0.7039814	5.9´10 -6 0.0564889 3.2´10 -6	0.5127702	3.3´10 -6 0.3483996	2.8´10 -6 0.2415795	3.0´10 -6 0.2364485	4.4´10 -6
	659

  Comparison of our mean ( 87 Sr/ 86 Sr)multidyn (blue circle) with literature data (grey circles) for the pure Sr standard solution NBS 987. Note that the yellow circle corresponds to the recommended value reported by Zhang and Hu (2020) after a compilation of the data available in Georem. Error bars correspond to 2 sd. Literature: (a) Raczek et al. 2003, (b) Weis et al. Comparison between ( 87 Sr/ 86 Sr)multidyn and ( 87 Sr/ 86 Sr)multistat measured in the NBS 987 standard solution over a period of ~ 10 months on the Nu TIMS. Error bars on individual data correspond to internal 2 se.

	FIGURE 3:
	a. 2006, (c) Makishima et al. 2008, (d) Aciego et al. 2009, (e) Yang et al. 2010, (f) Chauvel et al.
	7.0E-06 2011, (g) Yang et al. 2012, (h) Carpentier et al. 2014, (i) Li et al. 2014, (j) Pin et al. 2014, (k)
	High signal and very long analysis Mokadem et al. 2015, (l) Fourny et al. 2016, (m) Yobregat et al. 2017, (n) Di et al. 2021, (o)
	1.0E-06 2.0E-06 3.0E-06 4.0E-06 5.0E-06 6.0E-06 Zhang and Hu 2020. 0 2se internal on ( 87 Sr/ 86 Sr) multidyn 0.710180 0.710200 0.710220 0.710240 0.710260 0.710280 0.710300 87 Sr/ 86 Sr b. 0.710160	(b)	50	100 Number of cycles of measurement 150 200 250 High signal and 2h analysis Estimated errors at low signal and 300 2h analysis

  Stable Sr and Nd isotope compositions of the pure standard solutions NBS 987 (a) and Rennes-Ames (b-c) obtained in the course of this study. Error bars correspond to 2 s.e. For comparison are also plotted the latest high precision data (mean ± 2 s.d.) from Burckhardt et al. (2019) andPin and Gannoun (2019). Comparison between the theoretical precision modelled on multidynamic 87 Sr/ 86 Sr (blue line) and the actual uncertainties obtained for our analyses of NBS 987 (purple diamonds) and geostandards (green dots), with time drift correction (a) and without time drift correction (b). Multidynamic 87 Sr/ 86 Sr measured for different geostandards in the course of this study (blue symbols) and comparison with literature data (grey symbols). BCR-1, BHVO-1, BIR-1 and AGV-1 are represented as circles, while BCR-2, BHVO-2 and AGV-2 are represented as diamonds. Note that the data from[START_REF] Raczek | Neodymium and strontium isotope data for USGS reference materials BCR-1, BCR-2, BHVO-1, BHVO-2, AGV-1, AGV-2, GSP-1, GSP-2 and eight MPI-DING reference glasses[END_REF] have been renormalized to 0.710248 given the different 87 Sr/ 86 Sr they reported for NBS 987 compared to other studies (see Figure3a). Recommended values from[START_REF] Zhang | Estimation of isotopic reference values for pure materials and geological reference materials[END_REF] are also shown for comparison (yellow symbols). Literature: (a-o) same as in figure 3a. (p) Li et al. 2012, (q) Neymark et al. 2014, (r) Klaver et al. 2015, (s) Jweda et al. 2016, (t) Fourny et al. 2019, (u) Koornneef et. 2015.

		FIGURE 5: FIGURE 6: FIGURE 7:
				8.0E-06
				0.056496 7.0E-06	With time drift correction	Burckhart et al. (2019)
	753	87 Sr/ 86	0.704960 0.704980 0.705000 0.705040 0.705060 0.705080 0.705020	0.056484 0.056486 0.056488 0.056490 0.056492 0.056494 0.0E+00 ( 84 Sr/ 86 Sr) multistatic 1.0E-06 2.0E-06 3.0E-06 4.0E-06 5.0E-06 6.0E-06 Sr Sr/ 86 2se internal on 87	Average Multistatic: 84 Sr/ S6 Sr = 0.0564902 ± 0.0000018 (32 ppm, 2sd, n= 38) 755	a. geostandards modeled error NBS 987
	754 757		143 Nd/ 144 Nd A. B.	0.511946 0.511948 0.511950 0.511952 0.511954 0.511956 0.511958 0.511960 0.511962 0.241576 Average Multidynamic: 143 Nd/ 144 Nd = 0.5119537 ± 0.0000022 (4.2 ppm, 2sd, n= 31) ( 148 0.241578 0.241580 Nd/ 144 1/sqrt(total ions) Average Multistatic: (7.9 ppm, 2sd, n= 31) 143 Nd/ 144 Nd = 0.5119526 ± 0.0000040 (2019) Pin and Gannoun Time Time b. 0.348396 0.348398 0.348400 0.348402 0.348404 0.348406 ( 145 Pin and Gannoun (2019) 0.0E+00 5.0E-07 1.0E-06 1.5E-06 1/sqrt(total ions) mutidynamic 8.0E-06 Nd) No time drift correction 7.0E-06 Nd/ 144 ( 145 Nd/ 144 Nd) multidyn = 0.3484004 ± 0.0000013 (3.7 ppm, 2sd, n= 31) 0.241582 0.241584 0.241586 0.0E+00 5.0E-07 1.0E-06 1.5E-06 Nd) 0.0E+00 mutidynamic ( 148 Nd/ 144 Nd) multidyn = 0.2415798 ± 0.0000019 (8.0 ppm, 2sd, n= 31) geostandards 1.0E-06 2.0E-06 3.0E-06 4.0E-06 5.0E-06 6.0E-06 modeled error NBS 987 2se internal on 87 Sr 756 Sr/ 86
				0.511944

b.

c.


ITAP, James Taylor

Rhiann Jakubowski

Terence Bates

Robert Bates

Assessing the value of cover crops in vineyards using proximal sensing approaches

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

Introduction:

In 2012, a National Grape and Wine Initative (NGWI) project brought investment in vineyard sensing to the Lake Erie viticulture region via a Crop Load project at Cornell's Lake Erie Research and Extension Laboratory (CLEREL). Financial support was made available to growers interested in installing yield monitoring technology (ATV grape yield monitor (GYM), Roslin, South Australia, Australia) on their harvesters. One commercial contract operator and one family-run enterprise in the region took advantage of this offer. In addition to the yield monitoring technology, terrestrialmounted canopy sensors (N-Tech Greenseeker RT100 (N-Tech Industries Inc, Ukiah, CA, USA) and an apparent soil electrical conductivity (EC a ) surveying service DualEM,Milton,Ontario,Canada) were also made available to the growers free of charge through Cornell's Cooperative Extension (CCE) service. Therefore, these two growers very rapidly gained access to information from on-the-go sensors providing high-resolution information on yield, vine size (canopy) and soil variability within their vineyard blocks (while all local growers had access to the vine size and soil data if they wanted to engage with the extension service).

In addition to the interest in agri-tech and precision viticulture at this time, there was a growing interest in the role of cover crops within cool-climate vineyards in North America [START_REF] Messiga | Soil quality response to cover crops and amendments in a vineyard in Nova Scotia[END_REF]. Interrow cover crops planted mid-summer were being advocated to improve soil quality, particularly by breaking up compaction layers, and to improve trafficability during harvest (September/October) when the soil may be saturated. However, this is offset by a concern among growers that the interow cover crop may compete with the vines to the detriment of production (yield). By chance, the same family-run vineyard enterprise that had invested in the yield-monitoring technology was also interested in using cover crops. In this case, the younger generation was interested in possibilities of the agri-tech innovation, whilst it was the older generation who was interested in the cover crop innovation. These two innovations are complementary in nature, there is no trade-off between them, and the agri-tech sensors provided a potential way of assessing the local site-specific effect of the cover crop on production. To this end an on-farm experiment was designed using precision viticulture technologies to establish and monitor cover crop effects.

Materials and Methods:

The experiment was performed from 2013 to 2017 in a 2.2 ha Concord (Vitis Labrusca) vineyard near Westfield, NY. The vineyard is a single high-wire cordon managed by machine pruning with hand follow up. Vineyard layout is 2.74 m between rows and 2.44 m between vines within rows. Management was done using best management practices as recommended by CCE [START_REF] Jordan | Cultural practices for commercial vineyards[END_REF] 2.1 Sensing Grape yield monitoring was performed at harvest with a load-cell sensor embedded in a false weighbridge on the discharge conveyor belt, that has been shown to be accurate and reliable with regular calibration in these vineyards [START_REF] Taylor | Evaluation of a grape yield monitor for use mid-season and at harvest[END_REF]). However, the system was not perfect and yield data in 2015 were not able to be retrieved. Canopy sensing in mid to late July was done to map vine size using a side-on approach where cane length in the canopy side wall relates well to vine size in these vineyards [START_REF] Taylor | A protocol to map vine size in commercial single high-wire trellis vineyards using 'off-the-shelf' proximal canopy sensing systems[END_REF]. Soil surveys were performed in late spring (full soil moisture profile) by CLEREL with a DualEM-1s mounted on a PVC sled and dragged along the inter-rows behind an all terrain vehicle. The Dual-EM recorded the EC a , which is indicative of soil texture differences when performed at field capacity soil moisture. The between row distance (2.74 m) meant that there was little interference from the trellis wires on the EC a response if the sled was kept central in the inter-row. All these production data layers (canopy and yield)were collected automatically and routinely by the grower during routine vineyard operations. It did not require specialised surveys or additional time. Figure 1: Vineyard maps of soil apparent electrical conductivity (EC a ; mS/m) and NDVI (Normalised Differences Vegetation Index) values derived from terrestrial-mounted soil and canopy sensors respectively. These have been fused and classed into two potential management zones (right) using k-means clustering. Cluster 1 (red) is a zone of lower vigour associated with a heavier soil texture (higher EC a ) while Cluster 2 has higher vigour on a lighter texture soil.

All sensor data were cleaned and interpolated using local block kriging onto a common 2.74 m grid and collated into a spreadsheet for analysis using the general protocol of [START_REF] Taylor | Establishing management classes for broadacre grain production[END_REF].

Experimental Design.

The interpolated 2013 canopy and ECa data were clustered by staff at CLEREL to form two management classes using k-means clustering (see [START_REF] Taylor | Establishing management classes for broadacre grain production[END_REF]). This separated the vineyard block into an area of relatively large vine size on a medium texture soil type and an area of smaller vine size associated with a heavier soil texture (higher EC a ).

The vineyard managers were convinced that the cover crop would be beneficial to soil quality in the long-term, even if there was a short-term effect on production, so the default position in the vineyard was to plant the cover crop. Several possible experimental designs were discussed with the two vineyard managers (owners), including a simple half and half split and a complex chequerboard arrangement over the entire field, as well as strip trials and subplots stratified on the mangement classes. The managers were asked to propose alternative designs as well, but did not feel comfortable doing this at this time (i.e. at their first experience with this form of digially-enabled experimentation). Based on their desire to have as much as the vineyard as possible under a cover crop and to understand the response in the lighter and heavier soil texture classes, the managers opted for the sub-plot approach of [START_REF] Whelan | A 'small strip' approach to empirically determining management class yield response functions and calculating the potential financial 'net wastage' associated with whole-field uniform-rate fertiliser application[END_REF] that mininises the treatment area relative to a full strip approach.

Figure 2: Left: The as-applied prescription map indicating the subplots where the cover crop was not sown each year and; Right: the centre pixels within each subplot (circles) and the paired pseudo subplot cover crop treatment pixels (squares) used for the analysis.

To implement this design, seven sub-plots were identified in each management class where the cover crop was omitted (see [START_REF] Whelan | A 'small strip' approach to empirically determining management class yield response functions and calculating the potential financial 'net wastage' associated with whole-field uniform-rate fertiliser application[END_REF] for full details of the design). These subplots were three panel lengths long (~21 m) and incorporated two interrows, such that the central vine trellis had no cover crop on either side. Three panels was considered long enough to have the sensors pick up any treatment efects. A prescription map was developed and applied that simply omitted sowing the cover crop in the absent treatments (Fig. 2). The remaining area of vineyard inter-row was planted to a predominantly radish cover crop mix (forage and tillage radish; Brassica sp.), to help break up the subsoil. Consequently, there was no predefined cover crop treatment area in the design. Instead, seven additional 'pseudo' subplots were randomly selected and the data extracted at these sites to complement the absent cover crop treatments. Having paired treatments like this a) ensured a balanced design for subsequent analysis using classical statistical techniques, and b) made it simple for the grower to understand the comparison. The treatment design was extracted to the spreadsheet containing all the interpolated sensor data. In total there were 35 'pixels' of interpolated data associated with each treatment (Fig 2). Treatment subplot location were kept constant each year to avoid inter-annual effects.

Experimental Analysis

The design above was a balanced stratified block design. Treatment means were calculated and plotted for the period 2013-17 (note that the yield data for 2015 was not available) using JMP (v13, SAS Inc, CA, USA). ANOVA was not performed at this point as the intent was to illustrate trends to the grower for their satisfaction, rather than apply a rigorous scientific analysis.

Results and Discussion

Experiment implementation and data collection

The growers had a generally positive experience with the agri-tech innovations. As noted, yield data were lost in one of the four years; however the canopy data was routinely collected by the grower during general vineyard operations with little issue (only once runnning the sensor by accident into a fence post, which it survived). This is not to say that the technology was perfect or that it did not require care in acquisition. However, the younger manager was engaged with the technology, which made acquisition reliable. The sowing of the cover crops was also a positive experience using the prescription map and a variable rate actuator on the planter. It is noted that this was fairly simple, as it was just a binary cut-off system, and more complex rate changes may introduce more problems.

Data Analysis

The preprocessing and mapping (interpolation) of the data was performed by a trained research associate at CLEREL. Data processing tools are not yet at the stage where the growers themselves could easily engage with the analysis itself. However, simply plotting the trends and response curves was accessible to the grower and useful to their decision process. These plots are shown in Fig. 3.

Firstly, the difference between the high (blue) and low (red) vigour areas was clear in both the yield response and the NDVI response. It was also clear that the difference between subplots, with or without cover crop, was very consistent over the four years . The high vigour subplots with cover crop had ~0.5 tn/ac (~1.1 Mg/ha) higher yield than the absent cover crop subplots at the start of the experiment. Conversely, in the low vigour area, the absent cover crop area started with ~0.5 ton/ac (~1.1 Mg/ha) advantage. In both cases, this advantage was maintained regardless of the treatment type. This indicated, based on the sensor data, that the cover crop was having very little impact on production potential. The same conclusion can be drawn from the canopy vigour (NDVI) plots.

So, the experiment clearly indicated that the cover crop was not adversely competing with the vines. There did not appear to be a negative effect on vine size or on yield from adding the cover crop to the vineyard management. However, anecdotally, the cover crop was providing an ecosystem service by improving soil structure (less compaction noted), both through the action of the roots and by reducing the impact of farm machinery trafficking in the vineyards. In the latter case, there were also other benefits reported by the grower associated with improved vehicular access and trafficability. This reassured the growers that extending cover cropping to all their vineyards (i.e. upscaling from 2.2 ha to ~90 ha) would not result in any major financial setback to production. A grower's interest in the effect of inter-row cover crops on the bottom-line of the vineyard's production was assessed using an experimental design that was monitored using embedded routine sensing systems. The design allowed the grower to define the question and test their belief (i.e. the default was a presence of cover crop, not an absence). Monitoring using sensors showed that vine size and yield did not appear to be affected by the presence of the cover crop. Implementing the experiment and collecting data was relatively straightforward; however the analysis and the design still requires expert intervention. The skills needed for this would be a limitation to wider application of this approach. The agri-tech required is not a limitation provided care is taken with the use of the agri-tech.

Figure 1 :

 1 Figure 1: Plot of treatment means over time for the real (absent cover crop) and pseudo (present) treatment pixels in Figure 2. Line colour follows the zone delineation in Fig. 1 -red = low vigour and blue = high vigour. Dashed lines indicate where the cover crop was absent and the solid line indicates that the coer crop was present (pseudo treatments) (Note imperial units as provided to a US grower.) Conclusion:

Acknowledgement : This work was supported by the National Grape Research Alliance (NGRA) (formerly NGWI). We would like to express our gratitude to NGRA and its supporting viticulture organizations. Additional financial support was also provided by the New York Grape and Wine Foundation and the USDA-NIFA Specialty Crop Research Initiative Award No. 2015-51181-24393. T