C Fowler
email: emilie.bruand@univ-brest.fr

Mineral-whole rock isotope fidelity? A comparative study of Hf-Nd-O from high Ba-Sr granitoids

Keywords: Nd isotopes, Hf isotopes, O isotopes, titanite, apatite, zircon, high Ba-Sr granitoids, magma petrogenesis

It is well-established that lanthanide rare earth elements (REEs) have the potential to record the nature and source characteristics of their host magmas, in both whole-rock and their minerals.

Accessory minerals that concentrate REEs are especially useful in crustal evolution studies, both for their elemental and isotopic information; the classic and unrivalled example being zircon. Approaches using a single radiogenic isotopic system, or one radiogenic and one stable isotope system (e.g., Hf and O) in one REE-bearing mineral (usually zircon) are common, but those involving multiple isotopes in several minerals remain scarce despite offering many advantages. Importantly, the latter approaches also allow comparing different techniques and provide evidence on whether isotopic systems were disturbed by secondary processes. This contribution documents several isotopic systems within the abundant accessory mineral of Caledonian high Ba-Sr granitoids from Northwest Scotland. We present a multi-isotope study of titanite, zircon and apatite from two localities (Strontian and Rogart), which were selected for their contrasting whole-rock isotopic signatures -the former deriving from a depleted mantle source, whereas the latter derived from a strongly enriched mantle source. New in-situ Sm-Nd in titanite and apatite and Hf in zircon isotope data are discussed and compared with in-situ oxygen isotope data previously published for the same samples. An internal consistency is observed for Nd isotopes in apatite and titanite. Nd isotopes values for both minerals strongly correlate with Hf isotopes in zircon. Isotopic data at the mineral scale confirm the Strontian and Rogart source characteristics previously defined from whole-rock isotope data, with the Rogart having a more enriched signature than the Strontian source along the "Caledonian Parental Magma Array"(CPMA). In contrast, a significant discrepancy exists between whole-rock and REE-mineral oxygen isotope data as the latter can be affected by post emplacement alteration and hence can be misinterpreted. Importantly, the contribution of sediments in the CPMA source(s) can be estimated from a diagram combining Sm-Nd isotopic signatures and (La/Sm)N in apatite and titanite. Overall, we demonstrate that detailed petrogenetic records are not only available in zircons but also in magmatic titanite and apatite, and we suggest that integrated multi-mineral approaches have potential to maximise constraints from in-situ mineral isotope geochemistry.

Introduction

Advances in analysing various isotope systems in accessory minerals at (sub)-mineral scale have been critical in improving our understanding of the geological processes that shaped the continental crust. For example zircon (ZrSiO4), by way of U-Pb geochronology coupled with radiogenic Hf and stable O isotopes, has provided tight constraints on crust formation processes up to 4.4 billions years ago in the Hadean (e.g. Wilde et al. 2001a;[START_REF] Bell | Early Archean crustal evolution of the Jack Hills Zircon source terrane inferred from Lu -Hf , 207 Pb / 206 Pb , and d 18 O systematics of Jack Hills zircons[END_REF]. Isotopic data in zircon also greatly improved our knowledge of the mechanisms and rates of crustal growth, by linking sedimentary and igneous records (e.g. [START_REF] Kemp | Magmatic and Crustal Differentiation History of Granitic Rocks from Hf-O Isotopes in Zircon[END_REF][START_REF] Belousova | The growth of the continental crust: Constraints from zircon Hf-isotope data[END_REF][START_REF] Dhuime | A Change in the Geodynamics of Continental Growth 3 Billion Years Ago[END_REF]. However, there is increasing evidence that by studying zircon only, we are limiting our ability to fully understand a number of geological processes. This is mostly because (i) zircon crystallization is biased toward felsic compositions and (ii) when studying the complex history of ancient terrains, zircon is not very sensitive to important secondary processes, such as metamorphism or metasomatism ( Fisher et al. 2019;[START_REF] Hammerli | In situ trace element and Sm-Nd isotope analysis of accessory minerals in an Eoarchean tonalitic gneiss from Greenland : Implications for Hf and Nd isotope decoupling in Earth ' s ancient rocks[END_REF].

More recently, significant progress has been made with less studied REE-minerals (e.g. titanite, apatite, monazite, allanite), and it is now possible to interrogate multiple accessory minerals (including zircon) within a given rock. For example, trace elements in REE-minerals record petrogenetic information about granite petrogenesis (e.g., mixing, crystal fractionation; e.g. [START_REF] Miles | Evidence for distinct stages of magma history recorded by the compositions of accessory apatite and zircon[END_REF][START_REF] Bruand | Accessory mineral chemistry of high Ba-Sr granites from Northern Scotland: Constraints on petrogenesis and records of whole-rock Signature[END_REF][START_REF] Laurent | How do granitoid magmas mix with each other ? Insights from textures , trace element and Sr -Nd isotopic composition of apatite and titanite from the Matok pluton ( South Africa[END_REF]. In particular, trace elements in these minerals are sensitive to melt polymerisation (Prowatke andKlemme, 2006, 2005) and hence have potential to constrain the bulk mafic or felsic composition of their host rocks. Strontium concentration in apatite is a good proxy for the whole-rock Sr concentration (SrWR), and by extrapolation for the SiO2 content of the magma (e.g., [START_REF] Jennings | Characterization of magma from inclusions in zircon: Apatite and biotite work well, feldspar less so[END_REF][START_REF] Bruand | An apatite for progress: Inclusions in zircon and titanite constrain petrogenesis and provenance[END_REF].

Other trace elements and halogens can record metasomatic processes (e.g. [START_REF] Harlov | Apatite: A fingerprint for metasomatic processes[END_REF][START_REF] Zirner | Rare earth elements in apatite as a monitor of magmatic and metasomatic processes: The Il??maussaq complex, South Greenland[END_REF]. Recent advances with in-situ O isotope analysis have enabled the production of reliable data for a variety of REE-minerals [START_REF] Bonamici | Intragrain oxygen isotope zoning in titanite by SIMS: Cooling rates and fluid infiltration along the Carthage-Colton Mylonite Zone, Adirondack Mountains, NY, USA[END_REF][START_REF] Bruand | Oxygen isotopes in titanite and apatite , and their potential for crustal evolution research[END_REF][START_REF] Sun | Chemical and oxygen isotope composition of gem-quality apatites : Implications for oxygen isotope reference materials for secondary ion mass spectrometry ( SIMS )[END_REF][START_REF] Wudarska | SIMS-and IRMS-based study of apatite reference materials reveals new analytical challenges for oxygen isotope analysis[END_REF], which can be used to track potential alteration or sediment input to a magma source. Development of Sm-Nd in-situ analysis in various REE-minerals has been widely applied to igneous and metamorphic rocks (e.g. [START_REF] Foster | In situ Nd isotopic analysis of geological materials by laser ablation[END_REF]Fisher et al. 2011b;[START_REF] Yang | Sr and Nd isotopic compositions of apatite reference materials used in U-Th-Pb geochronology[END_REF][START_REF] Doucelance | In-situ determination of Nd isotope ratios in apatite by LA-MC-ICPMS : Challenges and limitations[END_REF]. Finally, other in-situ analytical procedures are currently being developed on REE-minerals: for instance Sr isotopes in apatite to trace the source of igneous rocks in the same fashion as Sm-Nd isotopes [START_REF] Emo | ScienceDirect Evidence for evolved Hadean crust from Sr isotopes in apatite within Eoarchean zircon from the Acasta Gneiss Complex[END_REF][START_REF] Gillespie | Strontium isotope analysis of apatite via SIMS[END_REF]. In the context of this burgeoning array of mineral-scale elemental and isotopic new approaches, attention has recently turned to the coherence between mineral and whole-rock data. For example, [START_REF] Gregory | Tracing the evolution of calc-alkaline magmas: In-situ Sm-Nd isotope studies of accessory minerals in the Bergell Igneous Complex, Italy[END_REF] showed that accessory minerals are a faithful proxy for the Sm-Nd isotopic composition of recent calc-alkaline magmas, while [START_REF] Hammerli | Neodymium isotope equilibration during crustal metamorphism revealed by in situ microanalysis of REE-rich accessory minerals[END_REF] quantified the equilibration of the Sm-Nd isotopic system in accessory minerals along a metamorphic gradient. However, a few recent studies have highlighted the decoupling of accessory mineral U-Pb and Sm-Nd isotopes in Archean granitoids. These studies, along with other studies on the decoupling of isotopic systems and/or trace elements in REE-minerals (e.g., Hf, Sr, U-Pb; [START_REF] Antoine | Understanding Preservation of Primary Signatures in Apatite by Comparing Matrix and Zircon -Hosted Crystals From the Eoarchean Acasta Gneiss Complex (Canada)[END_REF]Fisher et al., 2019;[START_REF] Gordon | Deformation-enhanced recrystallization of titanite drives decoupling between U-Pb and trace elements[END_REF][START_REF] Hammerli | In situ trace element and Sm-Nd isotope analysis of accessory minerals in an Eoarchean tonalitic gneiss from Greenland : Implications for Hf and Nd isotope decoupling in Earth ' s ancient rocks[END_REF], have important implications for our ability to reconstruct complex ancient terrains, with more work required to better understand the responsible parameters (P, T, fO2, fluid properties).

Approaches using a single isotopic system in one REE-mineral are common, but those involving multiple isotope analyses in several accessory minerals remain scarce (e.g. Fisher et al. 2019). The latter allow cross-calibration of different techniques and provide evidence on whether isotopic systems have been disturbed or not by secondary processes. Here we present a multi-isotopic study on selected REE-minerals from late Caledonian high-Ba-Sr granitoids sampled in Northern Scotland. Our data include new in-situ Sm-Nd isotopes in apatite and titanite, Hf isotopes in zircon, as well as O isotopes previously published by [START_REF] Bruand | Oxygen isotopes in titanite and apatite , and their potential for crustal evolution research[END_REF]. This represents the most comprehensive dataset of three isotope systems in three accessory minerals and their host rocks. Our approach allows us to rigorously test mineral versus whole-rock isotopic fidelity, and we show that in undeformed Phanerozoic granitoids selected for this study, radiogenic isotope ratios (Hf and Nd) give consistent values in all phases, while there is a notable discrepancy for O isotopes between whole rocks (OWR) and REEminerals (OREEml). We emphasise that titanite and apatite are, in the same way as zircon, powerful minerals to track magma sources, refine petrogenetic models and overcome late alteration of OWR data.

Geological and geochemical setting

All samples presented here are from high Ba-Sr granites intruded at the end of the Caledonian orogeny in Scotland. They have been interpreted as the result of a slab break off [START_REF] Atherton | Slab breakoff: A model for Caledonian, Late Granite syncollisional magmatism in the orthotectonic (metamorphic) zone of Scotland and Donegal, Ireland[END_REF][START_REF] Fowler | Petrogenesis of high Ba-Sr plutons from the Northern Highlands Terrane of the British Caledonian Province[END_REF][START_REF] Archibald | Testing petrogenetic models for contemporaneous mafic and felsic to intermediate magmatism within the "Newer Granite" suite of the Scottish and Irish Caledonides[END_REF] consequent upon continental collision between Laurentia and Baltica that followed closure of Iapetus during the Silurian and Devonian [START_REF] Atherton | Slab breakoff: A model for Caledonian, Late Granite syncollisional magmatism in the orthotectonic (metamorphic) zone of Scotland and Donegal, Ireland[END_REF][START_REF] Soper | The Iapetus suture zone in England, Scotland and eastern Ireland: a reconciliation of geological and deep seismic data[END_REF]. Geological features relevant to this study are described below but readers can refer to previous papers for the tectono-magmatic evolution of Scottish Highlands granites (e.g. [START_REF] Archibald | Testing petrogenetic models for contemporaneous mafic and felsic to intermediate magmatism within the "Newer Granite" suite of the Scottish and Irish Caledonides[END_REF][START_REF] Brown | The Newer Granite problem revisited: a transtensional origin for the Early Devonian trans-suture suite[END_REF][START_REF] Miles | Tectonic controls on post-subduction granite genesis and emplacement: The late Caledonian suite of Britain and Ireland[END_REF][START_REF] Soper | The Newer Granite problem: a geotectonic view[END_REF][START_REF] Stephens | Geochemical contrasts between late Caledonian granitoid plutons of northern, central and southern Scotland[END_REF].

The late Caledonian high Ba-Sr suite intrudes the Northern Highland terrane and can be divided petrographically into a western group of syenites and related rocks and a central-eastern group of granitic plutons and associated appinites (Fig. 1, Fowler et al., 2008 and references therein).

In this contribution, we present new isotopic data on REE-bearing minerals (titanite, apatite, zircon) from Rogart and Strontian plutons belonging to the central eastern granitic plutons. We chose these two localities for their contrasting origins from relatively enriched (Rogart) and relatively depleted sources (Strontian) along a "Caledonian Parental Magma Array" [START_REF] Fowler | Petrogenesis of high Ba-Sr plutons from the Northern Highlands Terrane of the British Caledonian Province[END_REF]. The Rogart and Strontian igneous complexes have a broadly concentric geometry and are dominated by biotite-hornblende granodiorite. Strontian has a biotite granodiorite central facies surrounded by hornblende-biotite granodiorite, which grades from porphyritic to non-porphyritic at its margin [START_REF] Sabine | The Strontian granite complex, Argyllshire[END_REF]. The hornblende-biotite granodiorite has been dated at 425 ± 3 Ma (U-Pb on zircon) and 423 ± 3 Ma (U-Pb on titanite; [START_REF] Rogers | Geochronology of appinitic and related granitic magmatism in the W Highlands of Scotland: constraints on the timing of transcurrent fault movement[END_REF]. The Rogart igneous complex is made up of an inner granodiorite and an outer tonalite, which are cross cut by a later granite. It is coeval with Strontian and has been dated around 420 Ma (K-Ar on biotite; [START_REF] Brown | Isotopic ages of late Caledonian granitic intrusions in the British Isles[END_REF]) and 425 ± 1.5 Ma (U-Pb on zircon; [START_REF] Kocks | Contrasting magma emplacement mechanisms within the Rogart igneous complex, NW Scotland, record the switch from regional contraction to strike-slip during the Caledonian orogeny. , 151(5)[END_REF].

Appinites [START_REF] Bailey | The geology of Ben Nevis and Glen Coe and the surrounding country (revised by EB Bailey)[END_REF] are mafic magma bodies (from centimetre to hundreds of metres scale) present in the main facies of both the Strontian and Rogart plutonic bodies. Scottish appinites are hydrous, mantle-derived rocks with shoshonitic affinities [START_REF] Fowler | Elemental evidence for crustal contamination of mantle-derived Caledonian syenite by metasediment anatexis and magma mixing[END_REF][START_REF] Fowler | Petrogenesis of high Ba-Sr plutons from the Northern Highlands Terrane of the British Caledonian Province[END_REF], and are widely believed to be the plutonic equivalents of calc-alkaline lamprophyres [START_REF] Murphy | Appinite suites: A record of the role of water in the genesis, transport, emplacement and crystallization of magma[END_REF][START_REF] Rock | Nature and origin of calc-alkaline lamprophyres: minettes, vogesites, kersantites and spessartites[END_REF]. Local mingling and mixing relationships can be observed between the main plutonic facies and the appinitic bodies in both plutons [START_REF] Stephenson | Caledonian igneous rocks of Great Britain[END_REF]. A mingling and intimate mixing event is recorded in the chemistry of apatite and titanite from the Strontian granite samples [START_REF] Bruand | Accessory mineral chemistry of high Ba-Sr granites from Northern Scotland: Constraints on petrogenesis and records of whole-rock Signature[END_REF]. On the basis of elemental, stable and radiogenic isotope evidence, both plutons are believed to have evolved by fractional crystallisation concurrent with variable assimilation of the surrounding Moine metasediments [START_REF] Fowler | Petrogenesis of high Ba-Sr granites: the Rogart pluton, Sutherland[END_REF][START_REF] Fowler | Petrogenesis of high Ba-Sr plutons from the Northern Highlands Terrane of the British Caledonian Province[END_REF]. 1968) and [START_REF] Kocks | Contrasting magma emplacement mechanisms within the Rogart igneous complex, NW Scotland, record the switch from regional contraction to strike-slip during the Caledonian orogeny. , 151(5)[END_REF]. RG (Rogart) and SR (Strontian) granites localities are the focus of this study.

Sample selection and preparation

Eight samples were selected for this study: three hornblende-biotite (hb-bi) granodiorites (SR1, SR3, SR4) and one appinite (SR2) from Strontian; as well as two tonalites (RT1, R2), one granite (RHG1) and one appinite (RA1) from Rogart. All samples from both plutons contain abundant accessory titanite, apatite and zircon [START_REF] Bruand | Apatite trace element and isotope applications to petrogenesis and provenance[END_REF][START_REF] Bruand | Accessory mineral chemistry of high Ba-Sr granites from Northern Scotland: Constraints on petrogenesis and records of whole-rock Signature[END_REF]. All hb-bi granodiorite samples from Strontian are chemically similar for major and trace element contents while granitoid compositions for major and trace elements contents from Rogart vary more widely. Details on whole rock major and trace elements contents and their interpretation can be found in [START_REF] Fowler | Petrogenesis of high Ba-Sr plutons from the Northern Highlands Terrane of the British Caledonian Province[END_REF] for Strontian and Fowler et al., (2001) for Rogart. Appinites in the central-eastern Northern Highlands carry the high Ba-Sr elemental signature, but are commonly even more enriched in LILEs (e.g. Sr, Ba), HFSEs (e.g. Nb, Th) and transition metals (e.g. Cr, Ni, V) than associated granodiorites and granites [START_REF] Fowler | Petrogenesis of high Ba-Sr plutons from the Northern Highlands Terrane of the British Caledonian Province[END_REF]. These characteristics can be observed in the two appinitic samples studied here (SR2 and RA1). The samples were crushed (jaw-crusher, ball mill or Selfrag™), sieved (<355 µm, 355-500 µm and 500-1000 µm fractions) and passed over a Wilfley table. A diamagnetic separator was then used to obtain fractions of different heavy minerals based on their diamagnetic properties. Titanite, apatite and zircon were handpicked, mounted in epoxy resin discs and polished for in-situ chemical analysis. All accessory minerals studied in the different samples have been imaged prior to analysis (Figs. 2) and characterised for their major and trace elements chemistries [START_REF] Bruand | Apatite trace element and isotope applications to petrogenesis and provenance[END_REF][START_REF] Bruand | Accessory mineral chemistry of high Ba-Sr granites from Northern Scotland: Constraints on petrogenesis and records of whole-rock Signature[END_REF]. Further details concerning the studied samples (Whole rock data, petrography and accessory mineral analyses) can be found in [START_REF] Fowler | Petrogenesis of high Ba-Sr plutons from the Northern Highlands Terrane of the British Caledonian Province[END_REF][START_REF] Fowler | Petrogenesis of high Ba-Sr granites: the Rogart pluton, Sutherland[END_REF] and [START_REF] Bruand | Oxygen isotopes in titanite and apatite , and their potential for crustal evolution research[END_REF][START_REF] Bruand | Accessory mineral chemistry of high Ba-Sr granites from Northern Scotland: Constraints on petrogenesis and records of whole-rock Signature[END_REF], and are not repeated here.

Analytical techniques

The following text describes the analytical methods for new data presented herein. Associated O isotope procedures are described in [START_REF] Bruand | Oxygen isotopes in titanite and apatite , and their potential for crustal evolution research[END_REF].

In-situ Sm-Nd isotope measurements in apatite and titanite

Neodymium isotope measurements were performed using a Thermo Fisher Scientific™ Neptune Plus™ mass spectrometer coupled with a 193-nm wavelength Resonetics™ M-50E laser system at the Laboratoire Magmas et Volcans (LMV, Clermont-Ferrand, France).

Analyses were realised with a combination of X-Skimmer and Jet-interface cones and followed the procedure described in [START_REF] Doucelance | In-situ determination of Nd isotope ratios in apatite by LA-MC-ICPMS : Challenges and limitations[END_REF]. For titanite, typical measurements consisted of 70 or 90 cycles with a laser ablation spots of 73 μm in diameter. For apatite, raster analyses were performed (53 μm spot size, 85 μm length) with 130 cycles and an integration time of 1s. The same spot/raster settings were applied on the standards. The first 15 cycles being of every measurement were used to evaluate the baseline level of each Faraday Cup. Oxides were monitored and maintained at <5% (ThO/Th). Baseline and gain reductions were operated online; all other calculations were performed off-line using an in-house Microsoft Excel™ spreadsheet. Gain calibration was done at the beginning of each analytical session. Analyses were performed over 5 different analytical sessions. Doped-Jndi glass was analysed regularly during the different sessions to monitor potential 147 Sm/ 144 Nd drift that has been reported previously [START_REF] Doucelance | In-situ determination of Nd isotope ratios in apatite by LA-MC-ICPMS : Challenges and limitations[END_REF] [START_REF] Foster | In situ Nd isotopic analysis of geological materials by laser ablation[END_REF][START_REF] Spandler | MKED1: A new titanite standard for in situ analysis of Sm-Nd isotopes and U-Pb geochronology[END_REF] have been used for normalization and to correct for instrumental drift when necessary. Laser fluence was set to 3.8-4.1 J/cm 2 , frequency 6 Hz, He flow rate was 700-875 ml/min and N2 1.8-2.6 ml/min depending on the session. All unknowns and standards data acquired can be found in Supplementary data_Table 1. Initial εNd values were calculated using the decay constant of 6.54*10 -12 [START_REF] Lugmair | Lunar initial 143Nd/144Nd: Differential evolution of the lunar crust and mantle[END_REF], the CHUR parameters of 143 Nd/ 144 Nd =0.512630 and 147 Sm/ 144 Nd =0.1960 [START_REF] Bouvier | The Lu-Hf and Sm-Nd isotopic composition of CHUR: Constraints from unequilibrated chondrites and implications for the bulk composition of terrestrial planets[END_REF] and an age of 425 Ma for the samples from both localities.

In-situ Lu-Hf isotope measurements in zircon

The Lu-Hf analyses were performed at the University of Bristol (Bristol Isotope Group) using a ThermoFinnigan Neptune plus multicollector inductively-coupled plasma mass spectrometer (MC-ICP-MS) coupled with a Photon-Machine Analyte G2 Excimer laser (193 nm wavelength). Ablation was performed using 50 µm and 40 µm spot sizes, a laser frequency of 4 Hz, and the energy density of the laser beam was c. 6 J/cm 2 . A typical analysis was 90 seconds, including a 30 seconds background measurement and a 60 seconds ablation period.

Correction for the interferences and mass bias followed the Bristol routine procedure [START_REF] Hawkesworth | Using hafnium and oxygen isotopes in zircons to unravel the record of crustal evolution[END_REF][START_REF] Kemp | Concurrent Pb-Hf isotope analysis of zircon by laser ablation multi-collector ICP-MS, with implications for the crustal evolution of Greenland and the Himalayas[END_REF]. The correction for the isobaric interference of Yb and Lu on 176 Hf was made following a method detailed in Fisher et al. (2011a). For Yb, the interference-free 171 Yb was corrected for mass bias effects using an exponential law and 173 Yb/ 171 Yb = 1.132685 [START_REF] Chu | Hf isotope ratio analysis using multi-collector inductively coupled plasma mass spectrometry: An evaluation of isobaric interference corrections[END_REF]. The mass bias-corrected 171 Yb was monitored during the run and the magnitude of the 176 Yb interference on 176 Hf was calculated using 176 Yb/ 171 Yb = 0.901864 [START_REF] Chu | Hf isotope ratio analysis using multi-collector inductively coupled plasma mass spectrometry: An evaluation of isobaric interference corrections[END_REF]. For Lu, the interference-free 175 Lu was corrected for mass bias effects assuming βLu = βYb and using an exponential law. The mass bias-corrected 176 Lu was monitored during the run and the magnitude of the 176 Lu interference on 176 Hf was calculated using 176 Lu/ 175 Lu = 0.02655 [START_REF] Vervoort | Isotopic composition of Yb and the determination of Lu concentrations and Lu/Hf ratios by isotope dilution using MC-ICPMS[END_REF]. Interference-corrected 176 Hf/ 177 Hf were corrected for mass bias using an exponential law and 179 Hf/ 177 Hf = 0.7325 [START_REF] Patchett | A routine high-precision method for Lu-Hf isotope geochemistry and chronology[END_REF], and were finally normalized to JMC-475 = 0.282160. The accuracy and long-term reproducibility of the measurements were gauged by analysing repeatedly three zircon reference standards (Plesovice, Mud Tank and TEMORA 2; Supplementary data_Table 2). 176 Lu/ 177 Hf vs 176 Yb/ 177 Hf values of our unknowns plot within the range of standards analysed during analytical session attesting to efficient isobaric correction. Initial εHf values for this study were calculated using the decay constant of 1.867*10 -11 [START_REF] Söderlund | The 176Lu decay constant determined by Lu-Hf and U-Pb isotope systematics of Precambrian mafic intrusions[END_REF], the CHUR parameters 176 Hf/ 177 Hf=0.282785 and 176 Lu/ 177 Hf = 0.0336 [START_REF] Bouvier | The Lu-Hf and Sm-Nd isotopic composition of CHUR: Constraints from unequilibrated chondrites and implications for the bulk composition of terrestrial planets[END_REF] and an age of 425 Ma.

Results

Full data are available in Appendix A, and a summary that also includes published O isotope data is presented in Table 1 below. Overall, Nd isotope data for the high Ba-Sr samples can be split into two groups. The first group includes Rogart samples RT1, R2 and RGH-1 with similar average 143 Nd /144 Ndi values ranging between 0.511866 (±0.000038; 2SD) and 0.511889 (±0.000036) for titanite, and between 0.511870 (±0.000109) and 0.511896 (±0.000087) for apatite (Fig. 3 and Appendix_A). The second group includes all Strontian samples + Rogart appinite RA1, with similar average 143 Nd /144 Ndi values ranging between 0.512032 (±0.000039) and 0.512129 (2SD 0.000032) for titanite, and 0.512083 (±0.000083) and 0.512119 (±0.000109) for apatite (Fig. 3 and Appendix_A). Most data are within uncertainty of the whole-rock associated (Fig. 3). Average εNdi values for group 1 samples are reported in Table 1. They are between -3.8 ± 0.8 (2SD) and -4.3 ± 0.8 (2SD) for titanite and between -3. 7 ± 1.8 (2SD) and -4.20 ± 2.1 (2SD) for apatite.

For group 2 Strontian samples and RA1, average εNdi values are between -1.0 ± 0.8 (2SD) and 0.9 ± 0.6 (2SD) for titanite and -0.4 ± 1.0 (2SD) and 1.2 ± 2.0 (2SD) for apatite.

Rogart apatite and titanite 143 Nd /144 Ndinitial values are identical within uncertainty (Fig. 3).

Overall, due to their lower concentration in LREE and the smaller spot required for analyses, errors on apatite analyses are greater than for titanite. For example, Nd concentrations in titanite from RA1 vary between 5300 and 11900 ppm, but between 762 and 1700 ppm for apatite [START_REF] Bruand | Accessory mineral chemistry of high Ba-Sr granites from Northern Scotland: Constraints on petrogenesis and records of whole-rock Signature[END_REF]. Such differences are present in all samples studied here [START_REF] Bruand | Accessory mineral chemistry of high Ba-Sr granites from Northern Scotland: Constraints on petrogenesis and records of whole-rock Signature[END_REF]. Consequently, reproducibility on RA1 titanite 143/144 Ndi is 76 ppm and 102 ppm on apatite (Appendix_A). For the same reasons, greater errors for apatite measurements are also observed in Strontian samples. For example, uncertainty on SR3 titanite is 120 ppm, but 200 ppm on apatite (Appendix_A). Hf isotopes have been measured in all samples except RA1 which is an appinite with very few zircons. Those separated were analysed for trace elements and oxygen isotopes but attempts with Hf led to unacceptable signal due to the presence of inclusions during ablation. The remaining data define the same two analytical groups (Fig. 4A). Rogart granitoids (R2, RGH-1, RT1) have average eHf ranging between -5.9 ± 0.6 (1SD) and -5.7 ± 0.6 (1SD), whilst a more radiogenic group defined by Strontian samples vary between -2.3 ± 0.6 (1SD) and -0.3 ± 0.7 (1SD; Table 1 and Appendix_B). Two data points from RT1 are not included in the average calculations. They have very negative eHf (-23.8, -14.2) measured in xenocrystic cores (Fig. 4, Appendix_B). These xenocrysts have not been dated and reported eHf values have been calculated at 425 Ma for the sake of comparison.

Lu-Hf isotopes in zircon

Discussion

First we discuss the results for minerals, which are less commonly analysed for their available isotope systems -apatite and titanite. We then add data for zircon and consider the potential for enhanced understanding of geological processes with a combined, multi-mineral approach.

6.1 Apatite and titanite versus whole-rock data. Detailed pioneer work was carried out by [START_REF] Paterson | Evidence for inherited S m -Nd isotopes in granitoid zircons[END_REF] on different granitoid samples from Strontian. They presented Sm-Nd isotopic analyses for both whole-rocks and fractions of multiple grains (apatite, titanite, +/-monazite and zircon). They obtained an eNdWR of 0.4 (±1.2, 2SD), eNdap -0.1 (±1.2, 2SD), eNdtitanite 0.1 (±0.8, 2SD) for Strontian granodiorite (BPSRT1), and they reported eNd values for one sample in the center of the pluton with an eNdWR value of -4.4 (±0.8, 2SD) (cf. Table 1). These results are in line with our new data (Figure 5).

Interestingly, [START_REF] Paterson | Evidence for inherited S m -Nd isotopes in granitoid zircons[END_REF] also reported Sm-Nd analyses in zircon in disequilibrium with the other accessory phases (titanite, monazite) and the whole-rocks, and they concluded to a potential inherited contribution from some zircons. Over the last three decades, the development of in-situ techniques has allowed to analyse smaller zones of single minerals with better uncertainties, to refine (i) our understanding of chemical and isotopic behaviour of accessory minerals and (ii) petrogenetic processes affecting magmas. Our new data reveal a close consistency between eNd in apatite and titanite within the same sample and, importantly, with previous whole-rock determinations (Table 1). As highlighted in Section 5, eNd values obtained in Rogart granites (RT1, R2 and RGH-1) are similar and range between -3.8 and -4.3

for titanites, and between -3.7 and -4.2 for apatite (Table 1), while the appinitic sample from the same locality (RA1) give higher eNd values for titanite (about -1.0) and for apatite (about -0.4). Overall, this last sample is comparable with eNd from Strontian (Fig. 5). Appinitic samples from both localities tend to have slightly lower titanite average eNd (-0.2 for SR2 and -1.0 for RA1, Table 1) than for Strontian granitoids (eNd=0.4-0.9, Fig. 5A). This is however not fully resolvable considering uncertainties on the data. While more scattered, apatites show exactly the same tendency (Fig. 5B). When disaggregated by locality, some familiar differences emerge (Fig. 5). On the basis of whole-rock data isotopes only, [START_REF] Fowler | Petrogenesis of high Ba-Sr plutons from the Northern Highlands Terrane of the British Caledonian Province[END_REF] argued that the parent magmas of the high Ba-Sr granitoids derived from a Caledonian Parental Magma Array (CPMA, Fig. 6b) that extended from isotopically depleted to isotopically enriched compositions, broadly from the southwest toward the northeast of the Northern Highland Terrane (Fig. 1). A number of high Ba-Sr granites, including Strontian and Rogart, fall on welldefined eNd vs 87 Sr/ 86 Sri trajectories suggesting assimilation of host rock Moine metasediments, from either end of the CPMA (Fig. 6b). For Rogart, [START_REF] Fowler | Petrogenesis of high Ba-Sr granites: the Rogart pluton, Sutherland[END_REF] proposed that AFC was the controlling process and that the isotopic values limited Moine input to ca. 25%. Later, [START_REF] Fowler | Petrogenesis of high Ba-Sr plutons from the Northern Highlands Terrane of the British Caledonian Province[END_REF] suggested that Strontian evolved via similar processes but originated from less-enriched mantle-derived parent magmas. One key observation that the most mafic samples were often the most "contaminated" is confirmed by our RA1 appinite insitu data (Fig. 5). This was interpreted as the consequence of a complex building of the plutonic body involving several batches of magma with different routes within the crust. In contrast to the fidelity with which radiogenic isotopes in accessory minerals record the primary composition of the source magma from which they crystallised, the oxygen signature is not so clear cut. [START_REF] Fowler | Petrogenesis of high Ba-Sr plutons from the Northern Highlands Terrane of the British Caledonian Province[END_REF] observed higher whole-rock O isotope values for Rogart (d 18 O =8.5-10.6‰) than for Strontian (d 18 O=6.7-8‰, Fig. 7), apparently correlated with increasing 86 Sr/ 87 Sri and decreasing eNd (Fig. 6b) and unrelated to LOI (Fowler et al., 2008, their Fig. 10). These were originally interpreted as the consequence of higher pelagic sediment input to the Rogart mantle source [START_REF] Fowler | Petrogenesis of high Ba-Sr plutons from the Northern Highlands Terrane of the British Caledonian Province[END_REF]. A subsequent study of the same samples using in-situ O isotopes in accessory minerals [START_REF] Bruand | Oxygen isotopes in titanite and apatite , and their potential for crustal evolution research[END_REF]the source of the O data considered here) recorded homogeneous oxygen isotopes across all minerals (apatite, titanite and zircon) from both localities (Fig. 7). This decoupling between whole rock and in-situ oxygen data was interpreted as the consequence of feldspar alteration (visible in thin section), being stronger in Rogart and in the most differentiated samples [START_REF] Bruand | Oxygen isotopes in titanite and apatite , and their potential for crustal evolution research[END_REF]. The petrogenetic consequence is that required pelagic sediments input previously estimated at about 10% for these samples is not a preferred model anymore [START_REF] Fowler | Petrogenesis of high Ba-Sr plutons from the Northern Highlands Terrane of the British Caledonian Province[END_REF]. 6.2 Hf in zircon vs Sm-Nd in apatite and titanite.

The Hf and Nd isotope systems are very closely related, an obvious result of their parentage.

Plotting average eHf in zircon versus eNd in titanite and apatite for both localities plot close to the terrestrial array (Fig. 6a). The datasets reveal two groups of samples -Rogart and Strontian, relatively "enriched" and "depleted" respectively in both isotope systems, directly comparable with the traditional whole-rock treatment of Nd and Sr isotopes (Fig. 6b). Both diagrams illustrate that the juvenile component increase from Rogart to Strontian. Strontian samples are plotting slightly lower than the terrestrial array line itself but is still within the original field defined by the data in Vervoort et al. (2011, grey field on figure 6a). These slightly lower values, could also be interpreted as the consequence of residual xenocrysts preventing the full homogeneisation of the magma source during the incorporation of rocks rich in zircons. Both localities present xenocrysts but dissolution of zircon in the magma source might have been less efficient than in Rogart.

Tracking sediment/crustal assimilation by combining isotopes and elements in apatite and titanite

Mineral chemical data gathered from the same accessory minerals [START_REF] Bruand | Accessory mineral chemistry of high Ba-Sr granites from Northern Scotland: Constraints on petrogenesis and records of whole-rock Signature[END_REF][START_REF] Bruand | Accessory mineral constraints on crustal evolution: elemental fingerprints for magma discrimination[END_REF] provide the opportunity to investigate variations in elemental ratios that are key for petrogenetic studies. Earlier studies have demonstrated the potential of using REE-bearing minerals and the Sm-Nd systems in crustal evolution studies [START_REF] Fisher | Combining Nd isotopes in monazite and Hf isotopes in zircon to understand complex open-system processes in granitic magmas[END_REF][START_REF] Gregory | Tracing the evolution of calc-alkaline magmas: In-situ Sm-Nd isotope studies of accessory minerals in the Bergell Igneous Complex, Italy[END_REF][START_REF] Hammerli | Combined Hf and Nd isotope microanalysis of co-existing zircon and REE-rich accessory minerals: High resolution insights into crustal processes[END_REF]. In particular, [START_REF] Gregory | Tracing the evolution of calc-alkaline magmas: In-situ Sm-Nd isotope studies of accessory minerals in the Bergell Igneous Complex, Italy[END_REF] have shown that in-situ Nd isotopes in REE-minerals could faithfully record the source characteristics of a suite of plutons in the Bergell pluton (Italy). Later, [START_REF] Hammerli | Generation of I-type granitic rocks by melting of heterogeneous lower crust[END_REF] used a combination of Nd-Hf-O isotopes in accessory minerals and whole rock to trace melt source in the crust. Although the Nd signature of the magma source was very successfully recovered, they failed to find trace elements systematics tracking crustal assimilation. From the present dataset, we provide an index of crustal assimilation, which is given by the (La/Sm)N ratio. The (La/Sm)N ratio in apatite has been shown sensitive to the Aluminium Saturation Index (ASI) of igneous rocks (e.g. [START_REF] Belousova | Trace-element signatures of apatites in granitoids from the Mt Isa Inlier, Northwestern Queensland[END_REF][START_REF] Bruand | Accessory mineral constraints on crustal evolution: elemental fingerprints for magma discrimination[END_REF][START_REF] Miles | Evidence for distinct stages of magma history recorded by the compositions of accessory apatite and zircon[END_REF], with apatite from peraluminous magmas (ASI>1) having lower (La/Sm)N ratios than apatite from metaluminous magmas (ASI<1). In the present sample suite, all studied samples are metaluminous, but (La/Sm)N variations reveal interesting features seemingly related to the source of the studied granitoids. In figure 8, the (La/Sm)N versus eNd for apatite and titanite shows consistent differences between the plutons -positive eNd (ca. 0.5) with relatively high (La/Sm)N (up to 7.8 in titanite and 20 in apatite) at Strontian versus negative eNd (ca. -4) with relatively low (La/Sm)N (between 0.5 and 2.3 in titanite and <5 in apatite) at Rogart. Part of the (La/Sm)N variation observed within accessories in a given sample has been attributed to in-situ crystal fractionation [START_REF] Bruand | Accessory mineral chemistry of high Ba-Sr granites from Northern Scotland: Constraints on petrogenesis and records of whole-rock Signature[END_REF]. Additionally, part of this scatter within a given sample can also occasionally reflect competition with other accessory phases and/or delay of crystallization of certain phases. For example, titanite (interstitial in texture) is crystallising late in the appinites while apatite is crystallising early. Even if the scatter of data is relatively pronounced in each sample, there is a clear difference between the 2 granitoid localities that cannot account for in-situ crystal fractionation. This interpretation is confirmed by whole rock data as both localities have similar whole rock SiO2-MgO ranges and have been shown to have encountered similar crystallization fractionation process [START_REF] Fowler | Petrogenesis of high Ba-Sr granites: the Rogart pluton, Sutherland[END_REF][START_REF] Fowler | Petrogenesis of high Ba-Sr plutons from the Northern Highlands Terrane of the British Caledonian Province[END_REF]. Whole rock (La/Sm)N for both granitoids localities have a similar range and show no correlations with eNd.

In their whole-rock study, [START_REF] Fowler | Petrogenesis of high Ba-Sr plutons from the Northern Highlands Terrane of the British Caledonian Province[END_REF] defined a "Caledonian Parental Mantle Array" as a variable source for Scottish Caledonian granitoids (Fig. 6b), defined by variable sediment input in the source. In this study, we show that the variations of up to 5 eNd recorded between both localities in both phases are clearly recording the influence in sediments along the Caledonian Parental Magma Array previously defined as the main reservoir of Caledonian granitoids in Northwest Scotland (Fig 8b). On the other hand, d 18 Ozr in the same samples show limited variations (5.6-6.3 ‰, Table 1) close to a mantle-like source (d 18 Ozrmantle=5.3±0.6 2SD, [START_REF] Valley | In-situ oxygen isotope geochemistry by Ion Microprobe[END_REF]. The maximum estimated AFC contamination (based on radiogenic isotopes) is of the order of 25% [START_REF] Fowler | Petrogenesis of high Ba-Sr granites: the Rogart pluton, Sutherland[END_REF]. On the other hand, the maximum [START_REF] Fowler | Petrogenesis of high Ba-Sr plutons from the Northern Highlands Terrane of the British Caledonian Province[END_REF]. 2014) and can be found in Appendix_C. [START_REF] Gregory | Tracing the evolution of calc-alkaline magmas: In-situ Sm-Nd isotope studies of accessory minerals in the Bergell Igneous Complex, Italy[END_REF] and [START_REF] Sun | Apatite geochemical and SrNd isotopic insights into granitoid petrogenesis[END_REF] reported internal variation of eNd within apatite, interpreted as evidence of local crustal assimilation preserved at the grain scale. To our knowledge, there are no such reports using titanite. In our case, confirmation of at least some crustal assimilation is provided by the presence of xenocrysts in zircons. Thus, while trace element chemistry in zircon from granitoids is less amenable to petrogenetic interpretation, its well-known capacity to preserve xenocrysts can add important additional constraints. In both locations reported here, xenocrysts in zircon have been described [START_REF] Bruand | Accessory mineral chemistry of high Ba-Sr granites from Northern Scotland: Constraints on petrogenesis and records of whole-rock Signature[END_REF].

Unfortunately, Hf measurements could be performed only in one sample (from Rogart). eHf results for two xenocrysts are strongly negative and may suggest contamination with a strongly enriched component (Fig. 4b). As the xenocryst could not be dated, the eHf values are minimum values. Oxygen isotope measurements (d 18 O up to 8.5‰) are consistent with this interpretation.

Other xenocrysts have been analysed for O but not Hf isotopes, due to their small size. They range between 5.9‰ and 8.7‰, which is a slightly larger variation than that observed in the granites (5.5-6.5‰; [START_REF] Bruand | Oxygen isotopes in titanite and apatite , and their potential for crustal evolution research[END_REF]. Very few literature data combining O and Hf measurements exist for the local Moine metasediments, but two samples in the Morar formation analysed by [START_REF] Lancaster | Understanding the roles of crustal growth and preservation in the detrital zircon record[END_REF] show similar values to the xenocrysts of this study.

Implication for ancient terranes

Earlier studies (e.g. [START_REF] Iizuka | Tracing the provenance and recrystallization processes of the Earth's oldest detritus at Mt. Narryer and Jack Hills, Western Australia: An in situ Sm-Nd isotopic study of monazite[END_REF] have proved that Sm-Nd isotopes in accessory minerals constitute the only robust record of the evolution of the Sm-Nd system in eroded or disturbed ancient terranes. However, accessory minerals in granitoids can also be reactive to metamorphism. They may record past metamorphic events under certain conditions: (i) a temperature above the closure temperature of the accessory mineral has to be attained; (ii) whole-rock characteristics and/or fluid-assisted metamorphic event can promote their dissolution and reprecipitation (e.g. [START_REF] Rapp | Monazite solubility and dissolution kinetics : implications for the thorium and light rare earth chemistry of felsic magmas[END_REF][START_REF] Watson | Dissolution, growth and survival of zircons during crustal fusion: kinetic principals, geological models and implications for isotopic inheritance[END_REF][START_REF] Wolf | Apatite dissolution into peraluminous haplogranitic melts : An experimental study of solubilities and mechanisms[END_REF].

As a consequence, metamorphic events affecting ancient terranes have potential to reopen isotopic systems in accessory minerals, and to erase their primary igneous history leading to anomalous whole-rock isotopic signatures. This has been recently discussed in two studies on accessory minerals within Archean grey gneisses [START_REF] Hammerli | In situ trace element and Sm-Nd isotope analysis of accessory minerals in an Eoarchean tonalitic gneiss from Greenland : Implications for Hf and Nd isotope decoupling in Earth ' s ancient rocks[END_REF][START_REF] Fisher | Disturbances in the Sm -Nd isotope system of the Acasta Gneiss Complex -Implications for the Nd isotope record of the early Earth[END_REF], and this may explain apparent contradictory findings in the recent literature. Indeed, contradictory radiogenic signatures for Hf isotopes in zircon and Nd isotopes in bulk-rock have been at the core of major speculations about early Earth's evolution. The discovery of superchondritic Nd isotope ratios was used to infer the presence of a highly depleted mantle early in Earth history, and which could reflect the extraction of large volumes of crust [START_REF] Bennett | Nd isotopic evidence for transient , highly depleted mantle reservoirs in the early history of the Earth[END_REF]. However, chondritic Hf isotope ratios in zircon point towards no/little mantle depletion over the same period of time [START_REF] Vervoort | Clarifying the zircon Hf isotope record of crust -mantle evolution[END_REF]. Recent measurements [START_REF] Hammerli | In situ trace element and Sm-Nd isotope analysis of accessory minerals in an Eoarchean tonalitic gneiss from Greenland : Implications for Hf and Nd isotope decoupling in Earth ' s ancient rocks[END_REF] on accessory minerals from Eoarchean gneisses suggest that these minerals can record LREE mobility during HT metamorphic events that can shift whole-rock Nd radiogenic value.

It is important to note that although these studies rely only on few heavily disturbed samples, they highlight several limitations in our current knowledge of the effect of metamorphism on LREE behaviour in accessory phases, which needs to be better addressed in the future. For example in [START_REF] Fisher | Disturbances in the Sm -Nd isotope system of the Acasta Gneiss Complex -Implications for the Nd isotope record of the early Earth[END_REF], while the U-Pb system in apatite dates a younger event from the Slave craton (1.8-1.9 Ga, Wopmay orogeny), its Sm-Nd signature preserves a much older event (at about 2.65 Ga). This observation highlights that the reopening of the U-Pb system could be much more sensible than the Sm-Nd isotopic system. Another key observation in [START_REF] Fisher | Disturbances in the Sm -Nd isotope system of the Acasta Gneiss Complex -Implications for the Nd isotope record of the early Earth[END_REF] is that different accessory minerals can record different timing of the reopening of the Sm-Nd system. Indeed, in Acasta while the apatite Sm-Nd isochron records a 2.65 Ga event, titanite records a much older Sm-Nd signature (3.3 Ga) consistent with zircon U-Pb age. This study [START_REF] Fisher | Disturbances in the Sm -Nd isotope system of the Acasta Gneiss Complex -Implications for the Nd isotope record of the early Earth[END_REF] is consistent with recent trace elements data collected on apatite and titanite in Archean TTG affected by greenschist to amphibolite facies, which reveal that trace elements in titanite are less prone to be disturbed by metamorphism than in apatite [START_REF] Bruand | Accessory mineral constraints on crustal evolution: elemental fingerprints for magma discrimination[END_REF]. Indeed, [START_REF] Bruand | Accessory mineral constraints on crustal evolution: elemental fingerprints for magma discrimination[END_REF] have demonstrated that trace elements in accessory minerals from Archean granitoids affected by later greenschist to amphibolite facies from different cratons (Kaapvaal, Slave, Karelia) could preserve under certain conditions original/igneous trace elements concentrations. The major impact of metamorphism on titanite and apatite chemistry was demonstrated to induce a decrease of LREE concentration. They could clearly show that in the Slave craton, secondary apatite were depleted in LREE when compared to primary apatite (e.g. apatite inclusions armoured in zircon). Under greenschist to amphibolite facies, the same chemical systematic on apatite chemistry has also been convincingly demonstrated on other lithologies (e.g. metapelite: [START_REF] Henrichs | The trace element and U-Pb systematics of metamorphic apatite[END_REF][START_REF] O'sullivan | The trace element composition of apatite and its application to detrital provenance studies[END_REF]. Combining the ability of the Sm-Nd system to date the geological process recorded, its source tracer potential and trace element signatures within the accessory phases, give new opportunities to refine geological event affecting igneous rocks (e.g. later metamorphic event, mixing event with another magma, etc.). Once the igneous origin of the accessory minerals have been confirmed using recent trace elements discriminators (e.g. [START_REF] O'sullivan | The trace element composition of apatite and its application to detrital provenance studies[END_REF][START_REF] Bruand | Accessory mineral constraints on crustal evolution: elemental fingerprints for magma discrimination[END_REF], the eNd associated to element ratios such as (La/Sm)N in apatite or titanite could help to refine the source characteristics of a given magma (Fig. 8). Ultimately this will allow to observe the crustal/sediment component in its source at the grain scale.

Conclusion

In this contribution we document several isotope systems within zircon, apatite and titanite. We

Figure 1 :

 1 Figure 1: Map from the Northern Highland region (Scotland), modified after Fowler et al. (2008) and showing samples localities and ages from Rogers and Dunning (1991), Brown et al. (1968) and(Kocks et

Figure 2 :

 2 Figure 2 : Representative back-scattered electron images of titanite (a-b). RA1 and SR2 are appinites, other samples are granitoids. (a-d) Numbers represent Nd isotope analyses done by LA-MC-ICPMS and correspond to the data reported in appendix A. (e-f) Numbers represent Hf isotope analyses (Appendix B)

Figure 3 :

 3 Figure 3 : 143 Nd /144 Ndinitial for apatite and titanite from both localities (R = Rogart and S = Strontian), along with whole rock (WR) data from the same samples (Fowler et al. , 2001 and 2008). Error bars on single minerals and whole rock are 2 sigma and are smaller than symbols if not visible. Dashed horizontal lines represents whole rock value.

Figure 4 :

 4 Figure 4 : eHf (A; this study) and d 18 O (B; from Bruand et al. (2019)) in zircon for both localities. Error bars are 2 sigma and are smaller than symbols if not visible.

Figure 5 :

 5 Figure 5 : eNdinitial values for titanite (left) and apatite (right) for both localities. Error bars are 2 sigma or within the symbol if not visible. app.= appinite, gr.= granitoid. Black (WR) and dotted lines (a-titanite and b-apatite) are data from Paterson et al. (1992). BPSRT1, BPSRA1 and BPSRG1 are samples from Paterson et al. (1992).

Figure 6 :

 6 Figure 6: A-eNdinitial for titanite, apatite and WR versus eHfinitial in zircon for Rogart and Strontian localities. d 18 Ozr ranges are also reported on the figure. Appinite RA1 sample is not reported on this figure due to the lack of Hf data. Error bars are 1 SD. B-from Fowler et al. (2001): eNd versus 87 Sr/ 86 Sri for Caledonian high Ba-Sr granitoids from the NHT including Strontian and Rogart (black stars), annotated with d 18 OWR. CPMA= Caledonian Parental Magma Array.

Figure 7 :

 7 Figure 7: δ 18 O versus SiO2WR for high Ba-Sr samples modified after Brand et al. (2019). ). RHG1 has a higher δ 18 O whole-rock value (10.6 ‰), which is interpreted to be the result of late feldspar alteration (Fowler et al., 2001; Bruand et al., 2014). No variations of oxygen isotopic values are resolvable between the less and the most differentiated samples for apatite and titanite. zr: zircon, ap: apatite, ttn: titanite.

estimated

  Moine metasediment input into the source, using an average Moine d 18 O value of about 8‰ to attain the maximum d 18 O of our sample, is about 15%. This interesting discrepancy is currently unresolved, but could perhaps relate to fractionation from incongruent dynamic melting reactions during assimilation, a sample spot bias towards early-crystallising zones in the accessory phases or be related to the analytical uncertaintie. Using Sr isotopes,[START_REF] Fowler | Petrogenesis of high Ba-Sr plutons from the Northern Highlands Terrane of the British Caledonian Province[END_REF] could distinguish two clear sources of subsequent crustal contamination moving the granitoids signatures away from the CPMA: (i) Moine metasediment contamination affecting the granites (e.g., Rogart, Strontian) and (ii) Lewisian basement contamination affecting the syenites (Fig.6b). Based on whole rock isotope data, both localities sampled here have been affected by Moine metasediments assimilation, which created small eNd variations (< 3 eNd;

Figure 8 :

 8 Figure 8: eNdinitial versus log (La/Sm)N in apatite (A) and titanite (B) for both localities. eNdinitial values are averages values per samples (Table 1) and (La/Sm)N are from Bruand et al. (2014, 2020). Ra1 and Sr2 are appinites while Rogart Gr. and Strontian Gr. are granitoids. CPMA= Caledonian Parental Magma Array. Both minerals record the influence of the CPMA source in their elemental and isotopic signatures. Trace elements data are from Bruand et al. (2014) and can be found in Appendix_C.

  show close agreement between radiogenic isotopes (Hf and Nd) within the accessory minerals and with previous whole rock data(Nd) to confirm an unbiased radiogenic isotope record in the accessory phases. A main point of this study being that while Nd isotopes and associated (La/Sm)N in apatite and titanite are powerful indicator of the CPMA source variabilities present in the northwest Scotland Caledonian granites, the assimilation of the host Moine sediments is only clearly visible by the presence of xenocrysts in zircons.

  . Primary standards for apatite (Durango from Doucelance et al., 2020; 143 Nd/ 144 Nd= 0.512483 and 147 Sm/ 144 Nd= 0.076096) and titanite (SPREN; 143 Nd/ 144 Nd= 0.512252 and 147 Sm/ 144 Nd= 0.1319 or MKED-1; 143 Nd/ 144 Nd= 0.51163 and 147 Sm/ 144 Nd= 0.127 ;

Table 1 : Summary of isotopic data for the studied samples. *Whole rock isotopic analyses are from Fowler et al. (2001, 2008). Reported whole rock uncertainties are based on uncertainties of the standards analysed during the analytical session. The values reported are averages and associated standard deviations for each sample. β Oxygen data are from Bruand et al. (2019). εHf , 87 Sr/ 86 Sri and εNd are calculated at 425 Ma.

 1

		Sample	RA1	RT1	R2	RGH1	SR1	SR2	SR3	SR4
			appinite tonalite tonalite granite granodiorite appinite granodiorite granodiorite
		εNd	-0.3	-4.1	-3.9	-	0.7	0.1	0.3	1.4
		2SD	0.5	0.5	0.5	-	0.5	0.5	0.5	0.5
	Whole	87 Sr/ 86 Sri 0.70630 0.70633 0.70673	-	0.70527	0.70577	0.70559	0.70559
	rock*	2SD 0.00002 0.00002 0.00002	-	0.00002	0.00002	0.00002	0.00002
		δ 18 O	-	8.5	8.7	-	8	6.7	7.8	6.7
		2SD	-	0.2	0.2	-	0.2	0.2	0.2	0.2
		Av. εHf	-	-5.6	-5.9	-5.7	-0.8	-1.7	-0.3	-2.3
		2SD	-	1.2	1.1	0.8	1.2	1.4	1.4	1.2
	Zircon	Av.
		δ 18 O𝛃	5.6	6.2	5.9	6.0	6.0	5.9	5.7	6.3
		2SD	0.3	0.5	0.7	0.3	0.3	0.4	0.4	0.2
		Av.
		δ 18 O𝛃	4.3	4.8	4.7	5.2	4.8	5.4	5.3	4.3
	Titanite	2SD	0.7	0.4	0.2	0.4	0.8	0.3	0.3	0.3
		Av. εNd	-1.0	-3.8	-4.2	-4.3	0.9	-0.2	0.8	0.4
		2SD	0.8	0.7	0.7	0.7	0.6	1.0	1.2	0.8
		Av.
		δ 18 O𝛃	5.1	5.3	5.3	5.8	-	6.1	5.8	4.6
	Apatite	2SD	0.4	0.4	0.3	0.4	-	0.6	0.5	0.7
		Av. εNd	-0.4	-3.7	-3.7	-4.2	-	0.0	1.2	0.7
		2SD	1.0	0.9	1.7	2.1	-	1.9	2.0	2.1
	5.1 Sm-Nd isotopes in apatite and titanite.

Acknowledgements

We are grateful to M. Gannoun for the help provided with the LA-MC-ICPMS analyses. This work was partly supported by the Natural Environment Research Council (grant NE/I025573/1), by the French Government Laboratory of Excellence initiative n° ANR-10-LABX-0006, and by the French National Research Agency (grant ANR-21-CE49-0001-01, AMNESIA, PI EB). This is Laboratory of Excellence ClerVolc contribution number 586. This manuscript benefited from constructive reviews by two anonymous reviewers. We thank Balz Kamber for his editorial handling.


Ivonne Rodriguez-Donis

Vincent Gerbaud

Alien Arias-Barreto

Xavier Joulia

Heterogeneous batch distillation processes for waste solvent recovery in pharmaceutical industry

Keywords: heterogeneous entrainer, batch column, azeotropic and extractive distillation

A su mmary a bout ou r exp eriences in th e introduction of h eterogeneous en trainers in azeotropic and extractive batch distillati on is present ed in this work. Esse ntial advantages of th e app lication of h eterogeneous en trainers ar e showed b y rigorous simulation and exp erimental v erification in a b ench batch d istillation co lumn for separating several azeot ropic mixtures suc h as acetonitrile -water, n hexane -ethy l acetate and chloroform -methanol, commonly found in pharmaceutical industry.

Introduction

Batch distillation is widely used in pharm aceutical and s pecialty chem ical industry to recover valuable components from waste of solvent mixtures. The regular presence of azeotropes re stricts seve rely the number of feasible separations . Azeotropic and extractive disti llations are the most co mmon alternatives encounte red i n the indust ry, requiring the addition of a third component to enhance the volatility of the components. Synthesis and d esign o f a new batch distillation p rocess is d one in two step s: (1 ) selection of an adequ ate en trainer along w ith th e column co nfiguration an d t he corresponding pr oduct c ut sequence. It c an be d one using a rece nt computer t ool RegSolExpert® (P roSim SA) i ncluding a n ex haustive s et of r ules for sel ecting b oth, homogeneous and heterogeneous entrainers and (2) the process design for determining the main operating parameters by using a batch process simulator such as ProSim Batch (ProSim SA). In general, heterogeneous entrainers have a more privileged position than homogeneous because a higher num ber of tern ary diagrams are suitable. Indeed, m ore than 70% of the feasibility rules included in RegSolExpert® match up to heterogeneous entrainers. In this paper, we present a general procedure to systematize the search for an appropriate azeotropic or extractive distillation process enabling th e separation of nonideal binary mixtures by introducing heterogeneous entrainers. Primary criter ia for selecti ng feasible heterogeneous entrainer com prise t he non pollutant component and the m arket availability. For the s eparation of aqueous -organic mixtures, many feasible entrainers could be found among those inducing a liquid-liquid phase sp lit with water and v ice v ersa, water see ms to b e a p romising can didate fo r organic wast es. Esse ntial fea tures of t he a pplication of heterogeneous ent rainers are showed by ri gorous simulation an d e xperimental veri fication i n a benc h batch distillation column for separating three commonly found mixtures: acetonitrile -wate r, n hexane -ethyl acetate and chloroform -methanol.

Heterogeneous entrainers in batch azeotropic distillation (HABD)

Azeotropic distillation in a batch rectifying column is based on the complete addition of an adequate amount of entrainer together with the azeotropic mixture as initial charge in the boiler. One unstable node given by a c omponent or mixture can be drawn as a t op product. The general feasibility criterion for selecting a heterogeneous entrainer can be summarized as fo llows: choose a low , intermediate or high boiling entrainer (E) giving rise to a ternary system in which the heterogeneous azeotrope is an unstable node of the residue curve map. The sepa ration of all components is better if: (a) t he heterogeneous azeotrope is binary instea d of terna ry, (b ) t he hete roazeotrope com position defines a n approx. equ al liq uid phase sp lit in th e d ecanter and (c) t he immiscib ility g ap is larg e leading to a high purity of the distillate and the entrainer-rich phase. These features will be analyzed c onsidering t wo azeotropic m ixtures: acetoni trile -water and n he xaneethyl acetate in a batch rectifier and a quaternary mixture in a middle vessel column.

Rectifying column configuration

The mixture acetonitrile -water displays a minimum boiling azeotrope with x acetonitrile = 0.676 at 76 .8°C. Th e i nitial entrainer can didate list in cluded 91 en trainers spann ing a wide spectrum of c hemical fa milies. Acc ording t o RegSolEx pert®, on ly 21 en trainers matched with so me feasib ility criterio n (Gerb aud et al ., 2006). Fo ur ho mogeneous entrainers were rejected because the separation was possible due to the curvature of the distillation bou ndaries and led to co mplex se quences of operating tasks. Fro m th e 17 remains het erogeneous com pounds only three l ight ent rainers di d n ot form t ernary azeotrope: dic hloromethane (39. 4°C), c hloroform (61°C) and acrylonitrile (77.3°C ). Only ch loroform an d acrylonitrile were test ed. Acrylonitrile has been found earlier by manual searc h (R odriguez e t al . 200 2) i n an ex perimental dat abase [START_REF] Gmehling | Azeotropic Data[END_REF]. Figure 1a Simulation results for both heterogeneous entrainers are reported in Table 1 considering only the reflux of the entrai ner-rich phase and showing the superiority of chloroform in recovery and purity of all components. However, the operating times were very similar (about 6 .5 hours) b ecause bo th en trainers lead to a si milar p hase sp lit ratio in to th e decanter from the condensed top vapour (about 0.16 in water-rich phase). Experimental validation of HABD with acrylonitrile were carried out in a SHOTT batch distillation colu mn av ailable in a bench scale (R odriguez et al., 200 2; 200 5) considering two reflux policies: case (1) only the reflux of acrylonitrile-rich phase from the decanter for the mixture a cetonitrile -water and case (2 ) an additional reflux given by a portion of t he c ondensed vapour by m anipulating t he open/close t ime of t he solenoid val ve for t he se paration of n hexane -ethyl acetate using acetonitrile. Experimental val ues are sh own i n Figure 1b an d Table 1 for case ( 1) an d Fi gure 2 displays th e si mulation and experimental r esults for th e case (2) d emonstrating th e acceptable performance of the HABD process. In HABD, the still path moves in a bi gger region wherein it is connecte d to the binary heterogeneous va pour at t he col umn t op a nd t he boiler can reac h t he stable n ode o f acetonitrile at the end of the process (see still path in Figure 1 and 2 starting in x S0 ). In the case of the sole reflux of the decanted entrainer-rich phase, the boundary of HABD is given by a hypothetical line joi ning the homogeneous azeotrope t o be separated and the composition of th e product-rich phase (dotted line in Figure 1b and 2). Although in both cases good agreement was obt ained between simulation and experimental results, the refl ux policy est ablished in case (2 ) p rovided a m ore st able am ount proportion of both l iquid phases i nside t he deca nter d uring the whole process . Theoretically as computed by simulation in Figure 1b and Figure 2, the composition of t he top vapour stayed closer t o the binary heteroazeotrope composition for case (2). As in continuous heterogeneous azeotropic distillation, liqui d -li quid spli tting occ urred inside the t op section in the SCHOTT column and experimental validations went well.

Middle vessel column configuration (MVC) with light or intermediate entrainer

Analysis of the h eterogeneous azeo tropic distillation in th is co lumn co nfiguration has been made only by using rigorous simulation with ProSim Batch. MVC enable to split quaternary m ixtures by a si ngle t ask l ike the ternary m ixtures using a b atch rectifier.

The sepa ration of acrylonit rile (light en trainer) -acetonitrile -water -acetic acid mixture was studied elsewh ere i nvolving a sin gle basic d istillation reg ion i n the quaternary co mposition spa ce (R odriguez et al ., 2 001). The binary h eteroazeotrope reaches the column top and a suitable reflux policy keep acetonitrile and acetic acid stay into th e middle v essel an d the bo iler at th e end of the proces s, respectively. Now, the use of a n intermediate boiling hete rogeneous entrainer (i sobutyl acetate) is viable for separating a methanol -water -propanoic acid mixture (residue curve map in figure 3). The homogeneous m ixture methanol -water -p ropanoic aci d ex hibits a sa ddle azeotropic point and it can not be separated by conventi onal distill ation process.

However, separation is feasible in a MVC by HABD with isobutyl acetate. Two binary azeotropes occur but in this case, both ar e saddle points and t he composition space is divided by an unstable distillation boundary in two basic distillation regions. Methanol is the sole unstable node while water and propanoic acid are the stable nodes of their respective regions. The still initial charge into the still and the middle vessel (x 0 ) has to be located inside the region wherein propanoic acid is the stable node. Figure 3 displays the composition into the boiler (x S ) and the reflux drum (x top ) after the heat and liqui d filling op eration of th e whole co lumn. An ad equate definition of th e liq uid ho ldup inside the reflux drum and t he middle vessel allows the separation of four components by one single operating step under infinite reflux ratio. Methanol goes to the top reflux drum ( x 1 ), propanoic acid concentrates in to t he boiler ( x 4 ) an d the saddle bi nary heteroazeotrope water (x 2 ) -isobutyl acetate ( x 3 ) is kept into the m iddle v essel at th e end of t he process. Figure 3 sh ows th e final co mposition and t he com position p ath inside t he still, th e cond enser and t he mid dle v essel alo ng with th e co lumn specifications operated under reflux total c onditions until steady stat e is reached (after about 2 hours). Distillate removal or closed operation can start afterwards.

Heterogeneous entrainers in batch extractive distillation (HBED)

Extractive distillation is th e most u sed process in t he in dustry due t o its op erating simplicity. Bu t, th e selectio n o f th e en trainer is b ased mainly o n a c riterion: Hi gh boiling homogeneous entrainer forming no additional azeotropes. Despite the criterion simplicity, designing a n ew extractive distillation process is o ften complicated. Indeed, many suitable entraine rs enhanci ng si gnificantly the relative vol atility of azeot ropic components usually give rise to new binary and even ternary heterogeneous azeotropes, that are often saddles. Therefore, these entrainers were always considered as unfeasible although it is not the case usi ng HEBD process (Rodriguez et al., 2003) because a more general criterion rules extractive distillation process feasibility (Rodriguez- Donis et al., 2009aDonis et al., , 2009b)). Un like t o azeo tropic distillation, t he en trainer is fed co ntinuously at some column position, leading to different column sections. Our precedent works concerned three ternary mixtures: acetonitrile -wa ter with butyl acetate, ethanol -water wi th ethyl acetate and c hloroform -m ethanol with water (Rodriguez et al., 2003, Van Kaam et al. 2008). HEBD brings a few more advantages:

(1) HEBD i n a b atch recti fier is sim pler th an ex tractive batch distillation using a homogeneous entrainer fe d at som e i ntermediate t ray, as i s usual . Indeed, t he heterogeneous entrainer can be fed at the column top leading only to an extractive column section and allowing the withdrawal of the saddle binary heteroazeotrope as top va por. Th e furt her c ondensation of t he t op va por ge nerates t wo l iquid p hases similar to the heteroazeotropic distillation process, (2) Water i s often a sui table non p ollutant het erogeneous e ntrainer for organic wast es treatment. And, organic compounds are suited for aqueous-organic wastes split. (3) HEBD offers more ternary diagrams alternatives than the numerous HABD ones.

Experimental validation in the SCHOTT distillation column was recently performed for the sepa ration of chl oroform -methanol -wat er waste usi ng t he i nner c omponent, water, as het erogeneous entrainer. Figure 4 displays the simulation results (x S ) and the experimental verification (x exp ) of the process. Even if the performance of t he process was good a nd ade quate agreem ent between e xperiments an d p rediction was al so obtained, extreme care m ust be taken with the regulation of the heat duty in the boiler. Accumulation of water in to th e boiler r equired a co ntinuous incr easing of the oil b ath temperature wherei n the boil er was imm ersed. Howev er, pollution of meth anol in th e chloroform-rich phase occurs rapidly if the correct ratio of the water flow rate an d the vapor o verflow i nside t he col umn i s sur passed. Indeed, a si gnificant am ount o f heterogeneous entrainer was required for the separation of all studied ternary system by HEBD given by th e interception of the univolatility line  12 in the heterogeneous edge close to the entrainer vertex. A better column configuration must be considered such as middle vessel column or those having two boilers as proposed by [START_REF] Hua | [END_REF].

Conclusions

Application o f heterogeneous e ntrainer for se parating n on-ideal m ixtures using azeotropic and extractive batch distillation demonstrated important advantages having a straight effect over the economy of t he process: more potential candidates reducing the time of t he preliminary process synthesis, less amount of entrainer is usually required, heterogeneous en trainer neutralizes th e ef fect of th e d istillation b oundaries of the residue c urve map gi ving a bigger feasi ble re gion a nd al lowing t he se paration of al l components i n o ne si ngle ope rating t ask. F or t he se paration o f a queous-organic mixtures, many feasible entrainers could be found among those inducing a liquid-liquid phase sp lit with water and v ice v ersa, water see ms to b e a p romising can didate fo r separating organic wastes. Possibility of the use of non pollutant entrainers is increased.

Figure 1 .

 1 Figure 1. Residue curve map and simulation results of HABD.

  Figure 2. Simulation and experimental results for n hexane -ethyl acetate -acetonitrile. Those two examples bring important insights on HABD: (a) less entrainer amount is require d in the initial charge, compared to azeotropic distillation with a homogeneous entrainer. (b) the liquid -liqu id splitting of the top condensed vapour allows the straightforward withdrawal of one component (water or n hexane) as distillate, (c) reflux policy can be versatile given by only the reflux of th e entrainer-rich phase or by a com bined re flux of both decanted phases (R odriguez-Donis et al ., 2 002, Skouras et al., 2005), (d) the adequate reflux policy displaces th e typical distillation boundary of the residue curve map close to the binary side of azeotropic components. Therefore, the feasible region is not l imited b y t he typical d istillation boundary of th e residue curve m ap anymore (Lang, 2006).

Figure 3 .

 3 Figure 3. Separation of a quaternary mixture for HABD in a middle vessel column.

Figure 4 .

 4 Figure 4. Simulation results and experimental validation of HEBD.

Table 1 .

 1 Simulation results chloroform vs acrylonitrile

		Chloroform	Acrylonitrile (* experimental values)
	Aqueous	x Water =0.9996	x Water =0.947	*x Water =0.946
	Phase	R ecovery =97.8%	R ecovery =92.6%	*R ecovery =89.0%
	Entrainer	x E =0.9990	x E =0.712	*x E =0.6916
	Phase	R ecovery =81.0%	R ecovery =72.0%	*R ecovery =69.0%
	Final	x acetonitrile = 0.9945	x acetonitrile = 0.992	*x acetonitrile = 0.995
	Still	R ecovery = 99.2%	R ecovery = 95.6%	*R ecovery = 91.8%


Objective: General procedure to systematize the search of several alternatives enabling the separation of non-ideal binary mixtures such as pressure-swing distillation, azeotropic and extractive distillation.

Objective: General procedure to systematize the search of several alternatives enabling the separation of non-ideal binary mixtures such as pressure-swing distillation, azeotropic and extractive distillation.

REGSOLexpert

 A wizard computer tool including 224 feasibility rules, and 326 batch azeotropic and extractive distillation processes.

 Systematic checking for each entrainer candidate for determining its feasibility to be used in rectifying or stripping batch column.

 A list of potential homogeneous and heterogeneous entrainers E in an optimal time for separating A and B as any industrial mixture.

  Extraction of bioactive substances from biological sources TMIN Azeotrope: T = 53.5 °C, XA= 0.65 4 -Simulation vs Experiments : heat up 12 min : R  F E = 0 120 min : R  F E = 20 100 min : R = 1.4 (-D) F E = 20 60 min R = 10 (-D) F E = 20 20 min : E-B separation FE = 0 R = 1.Liquid chromatography separation in pharmaceutical Industry TMIN Azeotrope: T = 77 °C, XA= 0.67 1 -Selecting Heterogeneous Entrainer with RegSolExpert® Initial List: 55 candidates from several chemical families (DIPPR database) Heterogeneous E: Acrylonitrile and Chloroform form unstable heteroazeotrope with H20 entrainer candidates Ei for d e f Computation azeotropes: AEi, BEi, ABEi 2-Residue curve map of ABE i Topological stability: A, B, Ei, AB, AEi, BEi, ABEi 3-Feasibility rule cheking Not match match 4 -Batch distillation sequences 5-Simulation + Economic evaluation CONCLUSIONS Heterogeneous entrainers have a more privileged position than homogeneous. Higher number of ternary diagram match with feasible rules Pressure swing distillation is a privileged option. It doesn't involve additional entrainer. Simple performance in one or two batch distillation column operating at different pressures. Heterogeneous entrainers in HABD: little amount of entrainer, separatrix can be crossed by the still path, simplest batch distillation sequence, more flexible reflux policy (entrainer-rich phase or both decanted phases) Heterogeneous entrainers in HEBD: Complex ternary residue curves are feasibles, withdrawal of saddle binary heterazeotrope at the column top by feeding E at the top of the column , more flexible reflux policy as HABD Water seems a promising candidate for treatment organic wastes by HEBD and HABD. cheap, non toxic, non pollutant

Chloroform (A) 61.1°C + Methanol (B) 64.5°C + Water (E) 100°C REGSOLexpert : Entrainer Selection Tool for Waste Solvent Recovery by Batch Distillation Processes RODRIGUEZ DONIS Ivonne, GERBAUD Vincent, BAUDOUIN Olivier, JOULIA Xavier ivonne.rdguez@infomed.sld.cu ; Vincent.Gerbaud@ensiacet.fr

	Entrainer	TB (°C)		Process Rejection
	Acetic acid	118	1.87	BED	1, 3
	Allyl alcohol	97	1.23	BED	1, 2, 3
	Aliphatic Alcohols	96 -118	1.50	BED	3
	Water	100	398	HBED	-
	n-Butyl acetate	126 .5	0.11	BED	3
	Furfural	161. 4	0.42	BED	1, 2, 3
	Pyridine	115.2	0.52	BED	1, 2, 3
	Nitrobenzene	210.6	0.05	BED	1, 2, 3
	4-methyl-2-pentanone	116.7	0.18	BED	2, 3
	Methyl cyclohexane	101	0.02	HBED	2, 3
					.9	0.8	0.7	0.6	0.5	0.4	0.3	0.2	0.1	0