E K A K A Brett

J Prytulak

M Rehkämper

S J J Hammond

C Chauvel

A Stracke

M Willbold

Thallium elemental and isotopic systematics in ocean island lavas

Keywords: thallium, stable isotopes, mantle heterogeneity, ocean island basalts

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Introduction

The majority of intraplate oceanic volcanism is the surface expression of deep-rooted thermochemical upwellings, or 'mantle plumes' (e.g. [START_REF] Morgan | Convection plumes in the lower mantle[END_REF][START_REF] Hofmann | Mantle plumes from ancient oceanic crust[END_REF][START_REF] Montelli | A catalogue of deep mantle plumes: New results from finitefrequency tomography[END_REF]. Ocean island basalts (OIB) thus provide a window into geochemical heterogeneity of the otherwise inaccessible deep mantle (e.g. [START_REF] White | Probing the Earth's deep interior through geochemistry[END_REF]. [START_REF] Zindler | Chemical geodynamics[END_REF] first proposed a classification scheme for oceanic basalts based on the observation that their radiogenic Sr-Nd-Pb isotope ratios vary systematically between a restricted number of isotopic signatures, termed 'end-members' or 'components'. Decades of subsequent work has subdivided or refined the details and interpretations of the radiogenic Sr-Nd-Pb isotopic variability in oceanic basalts (e.g. [START_REF] Weaver | The origin of ocean island basalt end-member compositions: trace element and isotopic constraints[END_REF][START_REF] Chauvel | HIMU-EM: The French Polynesian connection[END_REF][START_REF] Hofmann | Mantle geochemistry: the message from oceanic volcanism[END_REF][START_REF] Workman | Major and trace element composition of the depleted MORB mantle (DMM)[END_REF][START_REF] Willbold | Trace element composition of mantle end-members: Implications for recycling of oceanic and upper and lower continental crust[END_REF]. In general, the chemical variations observed in OIB can be reproduced via mixing of ambient mantle with other components, commonly identified with various recycled crustal lithologies (e.g. [START_REF] Hofmann | Mantle plumes from ancient oceanic crust[END_REF][START_REF] Weaver | The origin of ocean island basalt end-member compositions: trace element and isotopic constraints[END_REF][START_REF] Chauvel | HIMU-EM: The French Polynesian connection[END_REF]. Within this framework, it is suggested that the so-called HIMU (high µ = 238 U/ 204 Pb) signature may represent ancient subducted oceanic crust, isolated for ~2 Ga, while enriched mantle (EM)-type signatures might represent incorporation of heterogeneous continental components in the form of clastic sediments or continental crust eroded at destructive plate margins (e.g. [START_REF] Hofmann | Mantle plumes from ancient oceanic crust[END_REF][START_REF] Zindler | Chemical geodynamics[END_REF][START_REF] Chauvel | HIMU-EM: The French Polynesian connection[END_REF][START_REF] Hofmann | Mantle geochemistry: the message from oceanic volcanism[END_REF][START_REF] Stracke | Recycling oceanic crust: Quantitative constraints[END_REF][START_REF] Stracke | FOZO, HIMU, and the rest of the mantle zoo[END_REF]Willbold andStracke 2006, 2010;[START_REF] Stracke | Earth's heterogeneous mantle: a product of convection-driven interaction between crust and mantle[END_REF].

Inferring mantle source compositions from the radiogenic isotope ratios observed in basalts is challenging, because sampling of the different source components via partial melting depends on a number of factors, such as initial concentrations, melting behaviour, partition coefficients, extent of melt mixing, and time elapsed between parent-daughter fractionation events. As a consequence, it is often difficult to reach unambiguous interpretations of the origins and history of mantle sources.

Resolving such ambiguities about the nature and origin of mantle composition and evolution on the basis of radiogenic isotopic variation observed in OIB is necessary to constrain global geochemical cycles and the Earth's thermal evolution. Stable isotope systematics may provide useful independent constraints, as lowtemperature surface environments have the potential to generate resolvable stable isotope fractionations, which might then be traced through subduction recycling into the mantle and subsequently sampled via OIB.

Analytical advances have enabled the development and application of a variety of stable isotope systems to igneous rocks, motivated in part by the potential for such systems to act as a tracer of recycled materials.

Many of these advances were recently reviewed in Teng et al. (eds), (2017), for stable isotope systems from Li to U. In general, larger isotope fractionations occur in surface environments than magmatic environments, and so a logical aim is to identify the incorporation of recycled surface material by determining whether magmatic rocks carry a stable isotopic signature that is distinguishable from the mantle.

Thallium: a potential tracer for recycled materials

Thallium is a highly incompatible element, conventionally grouped with the alkali elements due to the similar ionic radii of Tl + and the heavier alkali metals (e.g. [START_REF] Shaw | The geochemistry of thallium[END_REF][START_REF] Heinrichs | Terrestrial geochemistry of Cd, Bi, Tl, Pb, Zn and Rb[END_REF]. The relative abundance of the two stable isotopes, 205 Tl (~70%) and 203 Tl (~30%), is reported as ε 205 Tl relative to the NIST SRM 997 Tl isotope standard [START_REF] Rehkämper | The precise measurement of Tl isotopic compositions by MC-ICPMS: application to the analysis of geological materials and meteorites[END_REF]: Tl/ 203 Tlsample -205 Tl/ 203 TlSRM997)/( 205 Tl/ 203 TlSRM997)]

ε 205 TlSRM997 = 10000 • [( 205
Thallium does not appear to undergo isotope fractionation during the high-temperature igneous processes of partial melting, metasomatism, and anhydrous fractional crystallisation. A systematic study of two co-genetic igneous suites spanning a range of SiO2 contents from Iceland and the Mariana island arc found a restricted range in ε 205 Tl (Hekla: ε 205 Tl from -2.2 to -0.7; Anatahan: ε 205 Tl from -2.9 to 0.0), and indicates that no analytically resolvable Tl isotope fractionation occurs during anhydrous magmatic differentiation [START_REF] Prytulak | Thallium elemental behavior and stable isotope fractionation during magmatic processes[END_REF]. [START_REF] Fitzpayne | Thallium isotopic composition of phlogopite in kimberlitehosted MARID and PIC mantle xenoliths[END_REF] analysed phlogopite mineral separates from highly metasomatised mantle xenoliths, again finding a strikingly restricted range in isotopic composition (ε 205 Tl = -2.5 ± 1.3 2sd, n = 25). This implies that the Tl isotopic composition of magmatic products should correspond to that of their sources, allowing the use of Tl isotope ratios to disambiguate the history of even evolved igneous rocks.

Direct measurements of Tl isotope ratios in mantle peridotites are hindered by their low concentrations (e.g. primitive mantle <4 ng/g: [START_REF] Mcdonough | The composition of the earth[END_REF] 4.1 ng/g: [START_REF] Palme | Cosmochemical Estimates of Mantle Composition[END_REF]. However, a harzburgite analysed by [START_REF] Nielsen | Thallium as a tracer of fluid-rock interaction in the shallow Mariana forearc[END_REF] with ε 205 Tl = -2.0 ± 0.8 (2sd), is indistinguishable from the Tl isotopic composition of MORB (ε 205 Tl = -2.0 ± 1.0 2sd; Nielsen et al., 2006aNielsen et al., , 2017b)), thus suggesting that Tl isotopes are not fractionated by partial melting processes.

Thallium elemental systematics in MORB are constrained by several large self-consistent (i.e. samples measured by the same protocols in the same laboratory) datasets collected in recent years, including wellcalibrated high-precision Tl concentrations [START_REF] Jenner | Analysis of 60 elements in 616 ocean floor basaltic glasses[END_REF][START_REF] Nielsen | Chalcophile behaviour of thallium during MORB melting and implications for the sulfur content of the mantle[END_REF][START_REF] Yang | Elemental systematics in MORB glasses from the Mid-Atlantic Ridge[END_REF].

Thallium concentrations are generally 100s to 10,000s of ng/g with large isotopic fractionations at the Earth's surface. The continental crust is the main terrestrial host of Tl (~500 ng/g e.g. Rudnick and Gao, 2003;[START_REF] Jenner | Cumulate causes for the low contents of sulfide-loving elements in the continental crust[END_REF], with a Tl isotopic composition, inferred via loess, indistinguishable from MORB (Nielsen et al. 2006b). Relative to the mantle, modern altered upper oceanic crust (AOC) has elevated Tl concentrations (~200 ng/g) and light Tl isotopic compositions (ε 205 Tl ~ -20 to -5; Nielsen et al., 2006bNielsen et al., , 2017b)), whereas FeMn sediments have very high Tl contents (>10,000 ng/g) and preferentially incorporate the heavier Tl isotope (ε 205 Tl ~ +5 to +15; review of Nielsen et al., 2017b). The Tl concentration contrast spanning order of magnitude between the mantle and potential recycled components, coupled with the resolvable and opposite directions of isotope fractionation in surface materials relative to the mantle, theoretically makes Tl isotopic compositions extremely sensitive to contributions of recycled surface materials to the mantle. Indeed, previous work investigating subduction settings has shown that Tl isotope ratios of arc lavas can be directly linked to the isotopic composition of materials subducting outboard of the associated trenches [START_REF] Prytulak | Assessing the utility of thallium and thallium isotopes for tracing subduction zone inputs to the Mariana arc[END_REF][START_REF] Nielsen | Thallium as a tracer of fluid-rock interaction in the shallow Mariana forearc[END_REF][START_REF] Nielsen | Tracking along-arc sediment inputs to the Aleutian arc using thallium isotopes[END_REF]Nielsen et al., , 2017a;;[START_REF] Shu | Tracing subducted sediment inputs to the Ryukyu Arc-Okinawa Trough system: evidence from thallium isotopes[END_REF][START_REF] Shu | Closing the loop: subducted eclogites match thallium isotope compositions of ocean island basalts[END_REF]. By the same reasoning, Tl isotopic compositions may covary with traditional radiogenic isotope ratios in ocean island basalts, used to define mantle components. If some EM-type signatures reflect incorporation of recycled sediments, then isotopically heavy Tl is predicted. Likewise, if the HIMU OIB signature develops via input of AOC then HIMU lavas would be expected to exhibit isotopically light Tl.

Sample selection and aims

Previous Tl isotope studies of OIB have used the interpretive framework of isotopically heavy thallium indicating FeMn sediments and/or pelagic clays, and isotopically light thallium indicating AOC. Previous work has examined Hawai'i (Nielsen et al., 2006a), the Azores [START_REF] Nielsen | Thallium isotopes in Iceland and Azores lavasimplications for the role of altered crust and mantle geochemistry[END_REF], Iceland [START_REF] Nielsen | Thallium isotopes in Iceland and Azores lavasimplications for the role of altered crust and mantle geochemistry[END_REF][START_REF] Prytulak | Thallium elemental behavior and stable isotope fractionation during magmatic processes[END_REF], and St. Helena [START_REF] Blusztajn | Thallium isotope systematics in volcanic rocks from St Helena -constraints on the origin of the HIMU reservoir[END_REF], documenting a range of ε 205 Tl = -10 to +3.9. This large range is mostly due to variations in rocks from Hawai'i, ascribed to the addition of FeMn sediments, and St Helena, ascribed to the addition of AOC. Thus far, no published studies have examined EM-type lavas, or HIMU lavas from localities other than St Helena. Here, we investigate EM-type lavas and expand the number of HIMU localities, to better characterize the full range of known OIB sources. All selected samples have radiogenic isotope data and show limited evidence of alteration (e.g. low loss on ignition, freshness on inspection of thin section). The 48 new analyses comprise 32 [START_REF]Non-traditional stable isotopes[END_REF] other EM) and 16 HIMU lavas (Table 1). We aim to evaluate, on a global scale, the potential relationships between Tl elemental abundances, Tl stable isotopes, and radiogenic isotopic compositions in OIB to investigate the nature of mantle components and the efficiency of Tl cycling between crust and mantle.

Methods

Sample digestions and chemical separations were carried out in the MAGIC Laboratories, Imperial College London, as described in [START_REF] Brett | Thallium concentration and stable isotope compositions of sixteen international reference materials[END_REF]. Purified water (resistivity 18.2 MΩ cm from a Milli-Q system) and acids purified via sub-boiling distillation in quartz or PTFE stills were used throughout.

Trace element determination

While Tl concentrations can be determined during isotope ratio measurements, early studies report uncertainties of 25% (e.g. [START_REF] Rehkämper | Thallium isotope variations in seawater and hydrogenetic, diagenetic, and hydrothermal ferromanganese deposits[END_REF], improved to ~10% by later work (e.g. [START_REF] Prytulak | Assessing the utility of thallium and thallium isotopes for tracing subduction zone inputs to the Mariana arc[END_REF] for relatively high concentration samples >20 ng/g. In contrast, the precision of Tl measurements via ICP-QQQ ('triple-quad' inductively coupled plasma mass spectrometer) is generally <4% RSD, though the uncertainty is higher for samples with lower Tl concentrations. Concentrations for 39 trace elements, including Tl, were obtained at the Open University, UK, using an Agilent 8800 ICP-QQQ following the procedure detailed in [START_REF] Brett | Thallium concentration and stable isotope compositions of sixteen international reference materials[END_REF].

In brief, for most samples approximately 50 mg of powder was weighed into a screw-top Savillex ® PFA vial.

To ensure precise and accurate determination of low Tl concentrations, ~75-100 mg of powder was weighed out for samples G6, FH-01, TH39, HV64, 74-386, and 108B. A 3:1 mixture of concentrated HF and HNO3 was added to the vials, which were then heated to 140 °C for at least 24 hours. Samples were subsequently evaporated to near dryness, and dried down from 0.5-1 ml concentrated HNO3 at 180 °C at least three times in order to destroy insoluble fluorides formed during the initial digestion. Samples were next taken up in 2 ml 6M HCl, and refluxed at 120 °C for at least 24 hours, during which time they were ultrasonicated twice for 20 minutes, before being evaporated to complete dryness at 120 °C. 2 ml concentrated HNO3 and 1 ml water were then added to each sample, followed by refluxing at 140 °C for at least 24 hours. Samples were again evaporated to dryness at 140 °C, before finally being made up to 1000-fold dilution in 2% HNO3. Sample solutions were aspirated using a quartz microflow nebuliser with an uptake rate of 0.5 ml min -1 , with sensitivity on the order of 1-5 x 10 7 cps per µg/ml, depending on the element. Two collision/reaction gas configurations were used: no gas, for Tl and most other elements, and O2, for most Rare Earth Elements (see [START_REF] Brett | Thallium concentration and stable isotope compositions of sixteen international reference materials[END_REF]. In the no gas configuration, oxide levels, measured as CeO + /Ce + , were kept below 1%; double-charged species, measured as Ce 2+ /Ce + , were kept at 1.6%.

All elements except Tl were calibrated using the values provided in [START_REF] Eggins | A simple method for the precise determination of ≥40 trace elements in geological samples by ICPMS using enriched isotope internal standardisation[END_REF] for USGS reference materials (RMs) W-2 and DNC-1. For Tl, USGS RMs BIR-1, BHVO-2 and AGV-1 were used as calibrators, employing the values of [START_REF] Brett | Thallium concentration and stable isotope compositions of sixteen international reference materials[END_REF]. Calibrator materials were run at the beginning of each measurement session. An internal solution standard (with Be, Rh, In, Tm, Re, Bi) was added online to monitor and correct instrumental drift. Drift was further monitored after every five measurements of unknown solutions with a measurement block comprising GSJ RM JB-2, 2% HNO3, and a repeated unknown sample (G-6).

Thallium isotope ratio determination

Procedures for Tl separation and subsequent measurement of Tl isotopic compositions followed established protocols. Briefly, all procedures were carried out at the MAGIC Laboratories, Imperial College London.

Samples were digested via standard HF-HNO3 techniques, and Tl isolated from the matrix using a 2-stage ion exchange chromatography procedure detailed in [START_REF] Rehkämper | The precise measurement of Tl isotopic compositions by MC-ICPMS: application to the analysis of geological materials and meteorites[END_REF] and [START_REF] Nielsen | The precise and accurate determination of thallium isotope compositions and concentrations for water samples by MC-ICPMS[END_REF], with modifications as described in [START_REF] Brett | Thallium concentration and stable isotope compositions of sixteen international reference materials[END_REF]. The majority of isotope ratio measurements were performed using a Nu HR MC-ICP-MS equipped with 10 11 Ω resistors, as low resolution measurements using a ~100 µl/min flow rate nebuliser connected to an Aridus, Aridus II or Nu DSN desolvating system, with Tl solutions ranging in concentration from 2-5 ng ml -1 and a sensitivity of ~800 V/ppm Tl.

The limited availability of powder for some OIB samples, coupled with low Tl concentrations, required measurement of solutions with Tl concentrations of <1 ng/ml. Measurements of these low-concentration analytes on the Nu HR MC-ICP-MS are less precise than those of solutions with 2-5 ng/ml Tl. Measurements on a Nu Plasma II MC-ICP-MS during the later phase of the project have significantly increased sensitivity compared to the Nu HR MC-ICP-MS. For Tl, sensitivity on the Nu Plasma II was routinely well in excess of 1000 V/ppm at the same measurement conditions. Otherwise, the method for isotope ratio determination on the Nu Plasma II was identical to the Nu HR, as described in [START_REF] Brett | Thallium concentration and stable isotope compositions of sixteen international reference materials[END_REF].

A secondary Tl isotope reference solution from Aldrich ('Aldrich Tl solution'), first characterised by [START_REF] Rehkämper | The precise measurement of Tl isotopic compositions by MC-ICPMS: application to the analysis of geological materials and meteorites[END_REF], is routinely used (>2000 measurements across at least seven laboratories; Nielsen et al., 2017b) to monitor machine performance. At least two measurements of the Aldrich Tl solution were performed at the beginning and end of each session, with additional measurements performed throughout, typically after every 6 unknown samples. Additionally, a well-characterised USGS reference material (typically BCR-2, though AGV-2 and BHVO-2 were also used) was processed through the complete sample preparation procedure with every batch of 10 samples prepared for MC-ICP-MS analysis.

Powder leaching tests. Thallium can be concentrated in secondary clays and ferromanganese coatings. To assess possible effects of secondary, low-temperature alteration processes on Tl isotopic composition, powder leaching experiments were performed. Samples with isotopic compositions that differed from average MORB by more than 3 ε units, as determined on unleached powders, were chosen for these leaching experiments.

The leaching protocol followed the cold acid leaching of [START_REF] Weis | Isotope geochemistry of Ninetyeast Ridge basement basalts: Sr, Nd, and Pb evidence for involvement of the Kerguelen hot spot[END_REF]. Approximately 10 ml 6M HCl was added to 100-300 mg of a sample powder, and the suspension was ultrasonicated for 30 minutes.

After settling for at least 30 minutes, the leachate was drawn off and discarded, and a further ~10 ml 6M HCl was added to samples, which were then ultrasonicated again for 20-30 minutes. This process was repeated until the leachate ran clear (a minimum of 3 cycles), and was then repeated a further 2 times with purified water in place of HCl. Leached powders were then evaporated, digested, separated and measured in the same manner as unleached powders.

Results

Trace element concentrations

Table 2 lists key major and trace element concentrations for the 48 OIB samples. Thallium concentrations range from 7 to 235 ng/g. The full dataset of 39 elements is provided in Electronic Annex 1 along with results for the reference materials measured contemporaneously with the OIB samples. Trace element concentrations obtained for repeated measurement of BCR-2 and JB-2 are in good agreement with accepted values (Electronic Annex 2). For most elements, RSDs are generally <3%; for Tl, RSDs are <7% for 34 samples, and >10% for 5 samples (Electronic Annex 2).

Many samples have existing trace element data published on the same powders (Electronic Annex 2, 3), and there is generally good agreement with previous work. We emphasize that the new data pays particular attention to the calibration of Tl concentration measurements, and is therefore be used throughout the remainder of this work.

Thallium isotope ratios

Table 2 presents the Tl isotopic composition of the 48 global OIB measured in this study, highlighting samples with isotopic compositions determined for both leached and unleached powders. Thallium isotopic compositions range from -6.4 to +6.6 and do not co-vary with Tl concentrations (Fig. 1). The quoted uncertainties take into account the measurement instrument and signal intensity, and are reported as the highest of (1) the uncertainty for repeat analyses of BCR-2 on the Nu HR, (2) the uncertainty for repeated measurements of the Aldrich Tl solution on the Nu Plasma II, or (3) the uncertainty for repeat analyses of a given sample.

The long-term intermediate precision of the Aldrich Tl solution measured on the Nu HR contemporaneously with OIB samples was ε 205 Tl = -0.8 ± 0.4 (2sd; n = 211, 14 sessions, 4 years), calculated using the average ε 205 Tl values obtained during each measurement session due to the large number of analyses. Unleached digestions of USGS reference materials AGV-2 (1), BCR-2 (10) and BHVO-2 (2) yielded ε 205 Tl values of -2.9 ± 0.5 (2sd; n = 3, 1 session), -2.6 ± 0.5 (2sd; n = 21, 4 sessions), and -1.2 ± 0.8 (2sd; n = 3, 1 session) for measurements with signal intensity on mass 205 > 1 V. For measurements of BCR-2 (4 digestions) with signal intensity < 1 V, ε 205 Tl = -2.5 ± 1.3 (2sd; n = 21, 3 sessions). For both Aldrich solution and USGS RMs, many of these determinations were first reported in [START_REF] Brett | Thallium concentration and stable isotope compositions of sixteen international reference materials[END_REF] and the values obtained are in good agreement with previous compilations (Nielsen et al., 2017b;[START_REF] Prytulak | Thallium elemental behavior and stable isotope fractionation during magmatic processes[END_REF].

The average obtained for the Aldrich Tl solution on the Nu Plasma II was ε 205 Tl = -0.8 ± 0.8 (2sd; n = 28, 2 sessions, 2 months), with the higher uncertainty reflecting both the smaller number of analyses and the lower concentration of solutions. One unleached dissolution of BCR-2 yielded ε 205 Tl = -3.1 ± 0.8 (2sd; n = 1), while one leached dissolution yielded ε 205 Tl = -2.1 ± 0.8 (2sd, n = 1), demonstrating that our leaching procedure does not introduce resolvable ε 205 Tl fractionations.

Assessing secondary effects on Tl isotope ratios

Melt evolution. Many stable isotope systems display isotope fractionation during fractional crystallisation (e.g. Teng et al., 2017). Thallium behaviour has been previously been investigated using two cogenetic suites with invariant radiogenic isotopic compositions from different tectonic settings: Hekla, Iceland, and Anatahan, Marianas [START_REF] Prytulak | Thallium elemental behavior and stable isotope fractionation during magmatic processes[END_REF]. Neither suite fractionates hydrous phases, nor do they exhibit resolvable Tl isotope fractionation during differentiation. [START_REF] Rader | Mineralogical thallium geochemistry and isotope variations from igneous, metamorphic, and metasomatic systems[END_REF] show that hydrous K-rich phases such as micas can exhibit distinct Tl isotopic compositions (ε 205 Tl from -12.1 to +5.3) coupled with significant Tl enrichments (>5 µg/g). As such, while it is not possible to completely rule out crystallisationinduced fractionation, it is highly unlikely for the OIB studied here. With the caveat that our samples are not genetically related, there is no systematic variation of ε 205 Tl with inferred or observed phenocryst phases or with MgO content in the current dataset (Fig. S1). We thus do not exclude any samples on this basis.

Degassing. Magmatic degassing can induce kinetic Tl isotope fractionation [START_REF] Baker | Investigation of thallium fluxes from subaerial volcanism-Implications for the present and past mass balance of thallium in the oceans[END_REF], theoretically producing residues with heavy Tl isotopic compositions and low Tl concentrations relative to incompatible refractory elements in contrast with condensates with isotopically light Tl, though these have yet to be reliably identified in nature. Various ratios have been employed to assess sample degassing, including Th/Tl [START_REF] Nielsen | Thallium isotopes in Iceland and Azores lavasimplications for the role of altered crust and mantle geochemistry[END_REF], Pb/Tl [START_REF] Rehkämper | The mass balance of dissolved thallium in the oceans[END_REF][START_REF] Baker | Investigation of thallium fluxes from subaerial volcanism-Implications for the present and past mass balance of thallium in the oceans[END_REF], Cs/Tl [START_REF] Prytulak | Assessing the utility of thallium and thallium isotopes for tracing subduction zone inputs to the Mariana arc[END_REF] and Ce/Tl (Nielsen et al., 2017a). The use of such ratios is challenging: Nielsen et al. (2017a) note that in arc settings, high Ce/Tl ratios potentially indicative of kinetic processes are still lower than the average value for the upper mantle. In the current dataset, there is no co-variation indicative of degassing between ε 205 Tl and relevant trace element concentrations or ratios for samples from individual volcanoes (not shown). This lack of chemical evidence is coupled with a lack of textural evidence for significant degassing, in that samples are thought to have been emplaced during effusive eruptions and show no significant vesicularity. Therefore, no data are rejected on this basis.

Post-depositional effects. In submarine lavas, both contamination (increasing the Tl contents of the rocks) and alteration (decreasing the Tl contents, via weathering) potentially cause resolvable differences in ε 205 Tl.

As little as 1 µg of FeMn oxyhydroxide coating per gram of sample can cause an analytically resolvable shift to heavier isotope signatures, while submarine alteration may efficiently strip Tl (at high temperatures) or add isotopically light Tl (at low temperatures) (Nielsen et al., 2006a). Samples exhibiting very low Tl concentration and ε 205 Tl therefore require scrutiny for other evidence of alteration, whereas samples with very high Tl concentration and extreme ε 205 Tl require scrutiny for contamination. A good example of the effects of alteration on Tl concentrations and isotopic compositions is provided by the study of Bluzstajn et al. (2018) on St. Helena lavas. In this case, a sample (SH-75) was excluded due to its high Tl concentration (339 ng/g) combined with an isotopic composition of ε 205 Tl = -4.06 and visual evidence of alteration. The authors consider surficial contamination by secondary clay minerals to be the most likely explanation for these features.

All OIB lavas analysed in this study were collected subaerially, although ambiguous records mean that it is unclear if the oldest Rurutu lavas were erupted in a subaerial or submarine environment [START_REF] Chauvel | Contrasting old and young volcanism in Rurutu Island, Austral chain[END_REF]. One Rurutu lava (RRT-037) shows the highest ε 205 Tl value (6.6 ± 0.5 2sd) reported for oceanic basalts thus far, warranting further assessment. However, rather than relying solely on chemical variation to identify such effects, five samples with ε 205 Tl signatures significantly different from the mantle value were leached and reanalysed alongside USGS reference material BCR-2. The residues from the cold HCl leach retained 1% to 50% of the original Tl, resulting in 0.05 to 1.9 ng/g total Tl available for analysis (~6 ng/g for BCR-2), thus resulting in larger analytical errors for ε 205 Tl (typically about ± 1 ε). Notably, there is no systematic offset in ε 205 Tl for the leached relative to the unleached sample powders (Table 2). This provides strong evidence that the positive and negative ε 205 Tl end-members in our dataset are not due to surficial contamination. Therefore, we do not exclude any samples on this basis.

Assessment of subaerial post-depositional alteration is more challenging. These processes may remove Tl from the sample without significant Tl isotope fractionation. While large fractionations do arise in lowtemperature environments, strong mineralogical control is exerted by secondary sulphides in low-T hydrothermally altered oceanic crust [START_REF] Coggon | Controls on thallium uptake during hydrothermal alteration of the upper ocean crust[END_REF] and by birnessite in FeMn sediments [START_REF] Peacock | Oxidative scavenging of thallium by birnessite: explanation for thallium enrichment and stable isotope fractionation in marine ferromanganese precipitates[END_REF][START_REF] Nielsen | Towards an understanding of thallium isotope fractionation during adsorption to manganese oxides[END_REF]. Suspended riverine particulate matter, created through weathering, exhibits ε 205 Tl very similar to that of loess, with the oxyhydroxide fraction generally containing only minor Tl that is not isotopically distinct [START_REF] Nielsen | Thallium isotope composition of the upper continental crust and riversan investigation of the continental sources of dissolved marine thallium[END_REF]. However, loss on ignition (LOI) is a traditional qualitative indicator of such alteration. All 48 analysed samples have LOI < 4%, and 41 have LOI < 2%. The seven samples with LOI > 2% were described as showing no identifiable petrological evidence of alteration (see Table 1 and references therein). Therefore, no data are excluded on this basis.

Discussion

We combine our new dataset with published studies to explore Tl behaviour at constructive plate margins and in intraplate settings. We first revisit the relative compatibility of Tl during mantle melting, then present models of Tl behaviour during MORB and OIB melting. Finally, we examine Tl isotope systematics alongside Sr-Nd-Pb radiogenic isotopic compositions in the global OIB dataset to explore implications for cycling of Tl through the solid Earth.

Tl elemental systematics

Thallium is highly incompatible during magmatic processes. Absolute Tl concentrations in OIB are thus principally determined by the extent of partial melting and fractional crystallisation. To compare the geochemistry of samples representing different degrees of melting, normalised incompatible element diagrams and ratios of trace elements with similar chemical partitioning are often employed. Quantitative assessment of how similarly two elements partition is theoretically straightforward: in a log-log plot of element concentrations, pairs of elements that partition identically produce a linear trend with a slope of unity (e.g. [START_REF] Sims | Inferences about mantle magma sources from incompatible element concentration ratios in oceanic basalts[END_REF]. Such assessments are improved by taking into account the uncertainties in concentration for both elements (e.g. by using York regressions: [START_REF] York | Unified equations for the slope, intercept, and standard errors of the best straight line[END_REF][START_REF] Reed | A spreadsheet for linear least-squares fitting with errors in both coordinates[END_REF]. In reality, however, analytical and statistical errors potentially obscure small deviations from linearity, especially between highly incompatible elements. It is therefore important to keep in mind that such relationships are at best indicative of relative compatibility contrasts. For MORB data, [START_REF] Nielsen | Chalcophile behaviour of thallium during MORB melting and implications for the sulfur content of the mantle[END_REF] calculated that La, Ce, and Pb had partitioning most similar to Tl, with log[Tl] -log[Ce] yielding a slope of 0.999 ± 0.034 (2sd, n = 594). Results for the expanded dataset incorporating [START_REF] Yang | Elemental systematics in MORB glasses from the Mid-Atlantic Ridge[END_REF] are very similar (Table 3).

OIB clearly derive from heterogeneous sources. As such there is no expectation that log-log plots would provide anything other than a very approximate indication of relative partitioning. Indeed, even for samples from a single location there is a marked lack of coherence in log-log diagrams of Tl versus any trace element (not shown). Of all analysed elements, the closest approach to a slope of unity with log[Tl] is achieved for log[Rb], as found by [START_REF] Dupuy | Partition coefficient of thallium compared with rubidium[END_REF] for acidic volcanic rocks (Table 3). However, the uncertainty is so high that this is not a robust result. While lower uncertainties are achieved for log[Ce] and log[La], the slope does not approximate unity. Attempting to identify elements with similar bulk partition coefficients to Tl during OIB generation via log-log plots is therefore problematic.

Normalised incompatible element diagrams. Thallium has been placed both between La and Ce, for lowpressure fractionation of MORB [START_REF] Jenner | Cumulate causes for the low contents of sulfide-loving elements in the continental crust[END_REF], and between Cs and Rb [START_REF] Prytulak | Thallium elemental behavior and stable isotope fractionation during magmatic processes[END_REF], following Dupuy et al., 1973). Given the ambiguity regarding placement and the lack of compelling indications from log-log plots, we consider both compatibility orderings for the presentation of OIB data. Incompatible elements normalised to PM abundances are shown in Figure 2 (with normalisation to DM shown in Fig. S2).

Notable is the marked negative Tl anomaly compared to other large-ion lithophile elements (47 of 48 samples) and REE (all samples). The La-Tl-Ce ordering produces visually similar Tl depletions to elements that are fluid-mobile during subduction processing, particularly Pb. The co-variation is less striking for the Cs-Tl-Rb ordering, which might reflect the larger uncertainties of Cs abundances and/or the inferred greater similarity in fluid-mobile behaviour. Interestingly, the magnitude of the negative Tl anomaly co-varies with absolute Tl abundance, regardless of ordering (Fig. S3). Such co-variation would be anticipated if the ambient mantle contains negligible Tl, such that increasing Tl abundances from exotic source(s) correlate directly with less negative Tl anomalies. In this scenario, the normalising PM (and DM) Tl concentration would be overestimated.

'Invariant' trace element ratios. Ratios of trace elements with similar partitioning are commonly used to 'see through' the effects of magmatic evolution: where partitioning is identical, ratios should be identical in source and product. However, selecting a suitable ratio for Tl in OIB is challenging. The Cs/Tl ratio has been used, as partitioning of these two elements and their fluid mobility was assumed to be similar (e.g., Nielsen et al., 2006a;[START_REF] Prytulak | Assessing the utility of thallium and thallium isotopes for tracing subduction zone inputs to the Mariana arc[END_REF][START_REF] Jenner | Cumulate causes for the low contents of sulfide-loving elements in the continental crust[END_REF]. However, Cs/Tl can be affected by both degassing and possible sequestration of Tl in accessory minerals during subduction (e.g., [START_REF] Prytulak | Assessing the utility of thallium and thallium isotopes for tracing subduction zone inputs to the Mariana arc[END_REF] and although Cs concentration determinations are routinely performed during ICP-MS analyses they often have relatively large errors due to the low abundance of Cs in igneous systems. The Ce/Tl ratio has also been used to assess Tl systematics in igneous settings, and has the advantage of a limited range in MORB (e.g. [START_REF] Nielsen | Chalcophile behaviour of thallium during MORB melting and implications for the sulfur content of the mantle[END_REF]Nielsen et al., , 2017b)). As Tl partitioning is likely different between MORB and OIB regimes, no single ratio will be invariant for both tectonic settings.

In the new OIB dataset, Ce/Tl varies over an order of magnitude at a similar degree of magmatic differentiation. While absolute Tl concentrations in OIB vary with MgO content, taken as a measure of the extent of differentiation, Ce/Tl ratios do not (Fig. 3). Therefore, the range of Ce/Tl in OIB likely arises from some combination of source heterogeneity and melting processes. For example, [START_REF] Shu | Closing the loop: subducted eclogites match thallium isotope compositions of ocean island basalts[END_REF] observed a wide range of Ce/Tl in subducted eclogites, which are geochemically similar to altered subducted oceanic crust that is thought to be a common component in OIB sources. Some authors have noted generally higher Ce/Tl ratios in OIB compared to MORB [START_REF] Nielsen | Chalcophile behaviour of thallium during MORB melting and implications for the sulfur content of the mantle[END_REF][START_REF] Blusztajn | Thallium isotope systematics in volcanic rocks from St Helena -constraints on the origin of the HIMU reservoir[END_REF]. When examining all available data, a clear tectonic distinction between MORB, arc and OIB lavas is apparent (Fig. 4): (1) arc lavas generally exhibit the lowest Ce/Tl and highest Tl concentrations, alongside the most scattered distribution, even when filtered to exclude non-basaltic samples; (2) MORB Ce/Tl clusters around 1140, as previously discussed in [START_REF] Nielsen | Chalcophile behaviour of thallium during MORB melting and implications for the sulfur content of the mantle[END_REF], and (3) global OIB form a remarkably coherent array that is clearly distinct from MORB, with overlap between the different mantle components defined by radiogenic isotopes. Similar patterns are observed for ratios of Tl with Rb, Cs, La and Pb, though with these latter ratios the different tectonic settings are less clearly distinguished (Fig. S4), motivating the further focus on Ce/Tl systematics.

Modelling Tl variations in MORB and OIB

The systematic variation of Tl versus Ce/Tl in global MORB and OIB can be explored with simple melting and mixing models (Fig. 5,6). Fractional, non-modal melting models help explore the contrasting Ce/Tl patterns of MORB and OIB, though simplifying assumptions must be made for several parameters (Tables 456). [START_REF] Nielsen | Chalcophile behaviour of thallium during MORB melting and implications for the sulfur content of the mantle[END_REF] identified constraints for the majority of these parameters for MORB generation, and modelled production of the "near-uniform" Ce/Tl ratio for MORB through variation of S concentrations and associated D Tl sulf/sil values. However, subsequent findings warrant some re-evaluation of parameters.

While it is clear that Tl is hosted in sulphides to some extent, recent investigations into the partitioning of Tl indicates that it is less strongly chalcophile than previously assumed (e.g. [START_REF] Kiseeva | The effects of composition and temperature on chalcophile and lithophile element partitioning into magmatic sulphides[END_REF][START_REF] Wood | Trace element partitioning into sulfide: how lithophile elements become chalcophile and vice versa[END_REF][START_REF] Jenner | Cumulate causes for the low contents of sulfide-loving elements in the continental crust[END_REF] and see Appendix for detailed discussion). We therefore explored D Tl sulf/sil values between 1 and 25 and present results for D Tl sulf/sil = 10 (e.g. Kiseeva andWood, 2013, 2015; see Appendix for detailed discussion). We also consider the effects of variation in D Ce cpx/melt between 0.01 and 0.8, which encompasses the wide range attributed to differences in mineral chemistry (Table 5; Appendix). We also present the effects of variation in initial Tl and Ce concentration on our melting model (Fig. 5c,5d;

MORB. The MORB dataset in

Appendix), with D Ce cpx/melt = 0.1 (equivalent to bulk D Ce = 0.015, i.e. the average value for peridotite melting calculated by [START_REF] Stracke | The importance of melt extraction for tracing mantle heterogeneity[END_REF]. Again, variation in either of these parameters can account for both the average Ce/Tl ratio in MORB and the sense of the observed variation.

The models thus highlight two main points.

1. As previously noted, MORB Ce/Tl exhibits some variation with Tl concentration that exceeds measurement uncertainties [START_REF] Nielsen | Chalcophile behaviour of thallium during MORB melting and implications for the sulfur content of the mantle[END_REF]. We suggest that Ce/Tl variations in MORB can be explained through a combination of melting effects, a range of D Ce cpx/melt associated with variations in the mineral composition of clinopyroxene, and variations in source concentrations of Tl and Ce.

Notably, this model does not require that bulk partition coefficients for Ce and Tl be approximately equal, and is nonetheless able to satisfy the constraint that a log-log concentration plot should exhibit a slope close to unity given the observed maximum concentration of Tl in MORB.

Regardless of the chosen value of D

OIB.

Fractional melting models assuming either a PM or a DM source (Table 4) with up to 15% melting are shown in Fig. 6a. It is immediately apparent that partial melting alone cannot produce the observed OIB Ce/Tl array from a PM or DM source, even for extreme values of D Ce cpx/melt. The systematics in a plot of Tl/Ce versus Tl [START_REF] Minster | Systematic use of trace elements in igneous processes[END_REF]; Fig. S5) emphasise that the observed range exceeds that which can be explained by partial melting and fractional crystallisation alone, consistent with longstanding radiogenic isotopic evidence for the heterogeneous and mixed nature of OIB sources. Notably, variations in S concentration or D Tl sulf/sil have no significant effect on model fit, but do affect the required degree of partial melting.

To explain the variation in the OIB array we first establish constraints on the mixed source compositions. In this context, solid state mixing is assumed, rather than mixing of partial melts of distinct components.

Parameters including partition coefficients and initial elemental concentrations were varied until approximate matches between model output and the observed data array for up to 15% melting were achieved (Fig. 6b).

We then incorporate the assumption that OIB lavas are typically the product of ~3-5% melting. In this scenario, the required source materials vary over an order of magnitude in terms of Tl concentration even within a single island (Fig. 6c,6d). A striking feature of the model is that the majority of the array requires a source that is significantly more enriched in Ce than PM estimates, without similar enrichment in Tl. Indeed, most lavas require Tl source concentrations lower than PM estimates, and in some instances more depleted than DM. Of all the OIB samples analysed to date (n = 93) only 10 (~11%) require a source Tl concentration >3.5 ng/g, i.e. more enriched in Tl than PM. Notably, although lavas from individual islands require source heterogeneity in terms of Tl concentration, lavas representing distinct radiogenic isotopic compositions have overlapping Ce/Tl ranges.

The mixed source concentrations required by the OIB Ce/Tl array can be interpreted as a mantle 'background' that is extremely depleted in Tl, with addition of a material characterised by high Ce and heterogeneous Tl concentrations, broadly consistent with models of widespread addition of subducted materials to the mixed OIB source. However, prior to subduction surface materials with high Ce concentrations (e.g. FeMn sediments) also exhibit elevated Tl concentrations that greatly exceed values that can be accommodated by the mixing-melting model. If subducted materials are the exotic addition controlling Ce/Tl systematics in OIB, it is necessary that the majority of Tl must be removed or otherwise lost during subduction processing, rather than being recycled into the deep mantle. A ~20% addition of such 'subduction-processed oceanic crust' (Table 6) to mantle strongly depleted in Tl would produce an appropriate mixed OIB source.

Recently, [START_REF] Shu | Closing the loop: subducted eclogites match thallium isotope compositions of ocean island basalts[END_REF] analysed the trace element and Tl isotopic composition of a number of eclogites subducted to a maximum depth of ~90 km before being exhumed, which might represent such 'subductionprocessed' oceanic crust. This sample suite has an average Ce concentration of 20 µg/g with an average Tl concentration of 55 ng/g (Table 6). While the Ce concentration is consistent with the requirements for our proposed subduction-processed oceanic crust, the Tl concentration is an order of magnitude more than the maximum we invoke to satisfy our constraints on OIB source concentrations. However, as the eclogite samples remained within the stability field of Tl-rich phengite, it is likely that further Tl loss would occur during deeper subduction beyond the phengite stability field.

We agree with the findings of Shu et al. ( 2019) that OIB Ce/Tl systematics indicate widespread incorporation of subduction-processed oceanic crust into the OIB source, which may consist of (ancient, relatively enriched) oceanic crust with variable addition of a continental crust component. The Ce/Tl systematics of OIB thus highlight similarities, not differences, between mantle components distinguished by their radiogenic isotopic compositions. The complete overlap between different lavas representing distinct (enriched) mantle end-members strongly implies that a high-Ce, low-Tl material such as subductionprocessed oceanic crust is common to OIB sources, and that Tl is near quantitatively removed during subduction.

Thallium isotopic composition of OIB

The Tl isotopic composition of the mantle is strikingly homogeneous, and no resolvable Tl isotopic fractionation is observed during partial melting or fractional crystallisation. Therefore, the significant Tl isotopic variability observed in global OIB (ε 205 Tl -10.0 to +6.6) requires the addition of isotopically distinct material to the lavas. The addition of such material can happen in the source, en route to the surface, and/or via subaerial/submarine alteration. We have already argued that alteration does not play a significant role in the new data, and previous work has similarly screened and discounted altered samples.

Thallium isotopic compositions were predicted to covary with the Sr-Nd-Pb radiogenic isotopes used to classify mantle components, depending on whether AOC or recycled sediments were the primary contributor of exotic material. However, the elemental systematics of Tl in OIB appear to require highly efficient removal of Tl during subduction, which potentially weakens the link between deep mantle recycling and OIB sources in terms of Tl isotopes. Indeed, the first order observation for our global dataset is that primary Tl isotopic compositions do not co-vary with radiogenic Pb, Sr, Nd, or Hf isotopes (Fig. 7), even within the chemically diverse Marquesas island group. Although the range is large, the average ε 205 Tl for HIMU and EM-type lavas overlap within error. For HIMU ε 205 Tl = -2.6 ± 6.6 (2s, n = 37), and for EM ε 205 Tl = -1.3 ± 4.4 (2s, n = 32). The overlap remains even if the comparison is restricted to main-phase St Helena lavas and EMI-type lavas, for which ε 205 Tl = -3.2 ± 3.1 (2s, n = 10) and ε 205 Tl = -1.1 ± 4.0 (2s, n = 13), respectively.

The absence of correlation between Tl isotopic compositions and Sr-Nd-Pb-Hf radiogenic isotope systems is consistent with trace element modelling that requires the mantle sources to be ubiquitously depleted in Tl, likely due to near-quantitative removal of Tl during the subduction process. Elemental parent-daughter pairs for radiogenic isotopes do not show this same level of depletion in OIB sources, and thus Tl and radiogenic Sr-Nd-Pb-Hf isotopic compositions can be easily decoupled, as noted by the first study of Tl isotopic composition in OIB (Nielsen et al. 2006a).

However, our finding that Tl isotope systematics may not be a straightforward "fingerprint" of recycled AOC or FeMn sediment to OIB source regions is at odds with previous work. While no variation in Tl isotopic composition was found in lavas from the Azores or Iceland [START_REF] Nielsen | Thallium isotopes in Iceland and Azores lavasimplications for the role of altered crust and mantle geochemistry[END_REF], incorporation of deeply subducted FeMn sediment was invoked to explain variations observed in Hawai'ian picrites (Nielsen et al., 2006a), and HIMU-type St Helena basalts have been argued to show evidence for incorporation of subducted AOC [START_REF] Blusztajn | Thallium isotope systematics in volcanic rocks from St Helena -constraints on the origin of the HIMU reservoir[END_REF]. In the case of Hawai'i, the absence of correlation between Tl stable and Os radiogenic isotopes was noted, despite the potential for FeMn sediment contributions to control both systems, and ascribed to the very high Tl/Os ratio such sediments exhibit.

Our new data provide a basis for re-evaluating the systematics of Tl isotopes in the HIMU mantle endmember. The isotopic criterion most commonly used to distinguish HIMU lavas is their radiogenic Pb isotopic compositions (i.e. 206 Pb/ 204 Pb > 19.5), which is commonly interpreted to arise from the subduction of AOC with high 238 U/ 204 Pb ratios ('high µ'), that was isolated in the mantle for 1-2 Ga (e.g. [START_REF] Hofmann | Mantle plumes from ancient oceanic crust[END_REF][START_REF] Zindler | Chemical geodynamics[END_REF][START_REF] Chauvel | HIMU-EM: The French Polynesian connection[END_REF][START_REF] Stracke | FOZO, HIMU, and the rest of the mantle zoo[END_REF]. While acknowledging decoupling of Tl and Sr-Nd-Hf-Pb isotopes, [START_REF] Blusztajn | Thallium isotope systematics in volcanic rocks from St Helena -constraints on the origin of the HIMU reservoir[END_REF] argue that Tl isotopic compositions that are generally lighter than those found for MORB combined with Ce/Tl variations provide evidence for the presence of a recycled upper AOC component in the St Helena source, from which up to 90% of Tl (relative to Ce) was stripped during subduction processing. Subsequent work investigated eclogites from Cabe

Ortegal and the Raspas Complex, thought to represent the metamorphic equivalents of altered oceanic crust [START_REF] Shu | Closing the loop: subducted eclogites match thallium isotope compositions of ocean island basalts[END_REF]. The eclogites have a similar range in Tl isotopic compositions as the main phase St.

Helena lavas (ε 205 Tl ≈ -5.5 to -1.0), and thus [START_REF] Shu | Closing the loop: subducted eclogites match thallium isotope compositions of ocean island basalts[END_REF] proposed a genetic link between the two.

This interpretation is complicated by the observation that, for the full OIB dataset (Fig. 8), the majority of HIMU samples have ε 205 Tl values that overlap with the range of results obtained for EM-type samples (ε 205 Tl ⩾ -6.5; Fig. 8b,8d). In addition, there is no convincing co-variation of ε 205 Tl with Ce/Tl and Ce/Pb for either St Helena lavas (Fig. 8a,8c) or the complete OIB dataset, with EM-type samples again overlapping the whole range of HIMU-type lavas. While one HIMU-type lava does exhibit the lightest reported Tl isotopic composition of any OIB sampled to date (ε 205 Tl ≈ -10), the broad overlap in ε 205 Tl for HIMU-and EM-type OIB does not provide a clear distinction between different mantle end-members based on Tl isotopic compositions alone. It therefore appears that Tl isotopic compositions are decoupled not just from radiogenic isotopes and Tl concentrations, as suggested by [START_REF] Shu | Closing the loop: subducted eclogites match thallium isotope compositions of ocean island basalts[END_REF], but alsoat least on a global scalefrom incompatible trace element ratios held to be indicative of AOC contributions.

We concur with the conclusion of [START_REF] Blusztajn | Thallium isotope systematics in volcanic rocks from St Helena -constraints on the origin of the HIMU reservoir[END_REF] that the Ce/Tl ratios of OIB appear to be broadly complementary to those found in island arc lavas. It is therefore necessary to explain how Tl isotopic systematics become (apparently) decoupled from Tl elemental systematics. Fitting our model to elemental systematics data requires highly efficient (~99%, relative to Ce) removal of Tl from heterogeneous subducting materials, with only a small proportion of subducted Tl returned to OIB source regions in the deep mantle. Therefore, the low Tl concentrations of the OIB sources produce magmas with Tl signatures that can be readily overprinted by addition of isotopically distinct material.

The notion that Tl isotopic compositions distinct from mantle values are due to the input of Tl-rich, isotopically distinct materials can be further examined via the magnitude of the negative Tl concentration anomaly observed for OIB relative to geochemically similar elements. When the magnitude of the Tl anomaly Tl/Tl* (see caption to Figure 9) is plotted against Tl isotopic composition, samples with Tl/Tl* > ~0.5 (calculated relative to Cs and Rb) generally have Tl isotopic compositions that differ from the mantle (Fig. 9a,9b). As would be expected given the decoupling of Tl and radiogenic isotopic compositions, this pattern is not restricted to or consistent within any one radiogenic isotope end-member, and some samples with Tl/Tl* < ~0.5 also display non-mantle values. Ruling out post-depositional isotopic effects, the question that arises is where does the addition of material with non-mantle Tl isotopic compositions take place? The mantle source or en route to eruption?

Addition of isotopically distinct Tl to the OIB source via residual Tl from a subduction-processed slab and/or addition during ascent through the crust via assimilation of country rock, including sediments and previously-erupted and subsequently altered lavas are both reasonable processes. For example, variation in the extent and type of material assimilated during different stages of magmatism might account for the distinct average Tl isotopic compositions observed by [START_REF] Blusztajn | Thallium isotope systematics in volcanic rocks from St Helena -constraints on the origin of the HIMU reservoir[END_REF] for St Helena early-, main-, and late-stage lavas. Given the Tl concentration contrast between magma and potential inputs, neither origin for Tl isotope variationssource heterogeneity or assimilationwould necessarily cause resolvable changes to other geochemical markers (e.g. model of Nielsen et al., 2006a; Fig. S6). Caution is therefore advisable when interpreting Tl isotopic compositions of OIB as a direct reflection of the mantle source. However, there is the potential that variable crustal assimilation of isotopically distinct Tl might be identifiable in high resolution studies of lavas from individual volcanic edifices, yielding insight into their magmatic plumbing architecture.

Conclusions

Fresh lavas from divergent, convergent and intraplate settings can be distinguished by their distinct systematics in plots of Ce/Tl versus Tl concentrations. The observed patterns can be reproduced by models of fractional, non-modal melting, providing insights into the cycling of Tl through the mantle. The Ce/Tl systematics of MORB can be reproduced by the combined effects of different extents of partial melting and variations in D Ce cpx/melt and initial Tl and Ce concentrations, without a significant role for sulfides. In contrast, the Ce/Tl systematics of OIB cannot be generated from a primitive mantle source, but instead require a source that is markedly depleted in Tl (<1 ng/g) prior to addition of exotic thallium. The requirement for Tldepleted OIB source regions is consistent with mounting evidence that the extent of present day mantle depletion may be underestimated (e.g. [START_REF] Stracke | Earth's heterogeneous mantle: a product of convection-driven interaction between crust and mantle[END_REF][START_REF] Stracke | Abyssal peridotite Hf isotopes identify extreme mantle depletion[END_REF][START_REF] Stracke | Ubiquitous ultra-depleted domains in Earth's mantle[END_REF][START_REF] Salters | Domains of depleted mantle: new evidence from hafnium and neodymium isotopes[END_REF][START_REF] Salters | Mineralogy of the mid-ocean-ridge basalt source from neodymium isotopic composition of abyssal peridotites[END_REF][START_REF] Cipriani | Oceanic crust generated by elusive parents: Sr and Nd isotopes in basalt-peridotite pairs from the Mid-Atlantic Ridge[END_REF][START_REF] Sanfillippo | Role of ancient, ultra-depleted mantle in mid-ocean-ridge magmatism[END_REF]. The OIB array can be generated from a depleted mantle source with addition of up to 20% subducted material from which >99% of Tl has been stripped during subduction processing. This suggests that Tl constitutes an extreme example of the behaviour of fluid-mobile elements in subduction zone settings, such that co-variations of Tl with other elements may further constrain elemental subduction zone cycling.

Thallium and radiogenic isotopic compositions are decoupled, and Tl isotopic compositions cannot be used in isolation to distinguish between continental and oceanic crust contribution to OIB source regions. The observed decoupling of Tl and radiogenic isotopic compositions most likely reflects ( 1) the sensitivity of Tl to small variations in the isotopic composition of residual Tl, and/or (2) the extreme Tl concentration contrast between mantle and surface materials. Despite the lack of co-variation with radiogenic isotopes, global OIB display a significant range in primary Tl isotopic compositions which must reflect addition of isotopically distinct material. However, where this Tl addition takes places remains ambiguous. The potential incorporation of Tl-rich materials at crustal levels during magma ascent is a feasible alternative interpretation to the generation of Tl isotopic variability due to incorporation of residual slab-derived Tl at mantle depths following subduction processing.

OIB. We used the values of [START_REF] Mcdonough | The composition of the earth[END_REF] as our initial values for PM, then varied concentrations as required to fit our model to the data.

II. Thallium partitioning

Chalcophilia. [START_REF] Nielsen | Chalcophile behaviour of thallium during MORB melting and implications for the sulfur content of the mantle[END_REF] based their values of D Tl sulf/sil during MORB melting on data from [START_REF] Kiseeva | A simple model for chalcophile element partitioning between sulphide and silicate liquids with geochemical applications[END_REF], who reported D Tl sulf/sil = 4-24. However, a growing body of evidence supports the concept that "mixed affinity" behaviour is exhibited by Tl, i.e. elemental behaviour cannot be described as either predominantly chalcophile or predominantly lithophile. [START_REF] Kiseeva | The effects of composition and temperature on chalcophile and lithophile element partitioning into magmatic sulphides[END_REF] report D Tl sulf/sil of 4-33, and note that "partitioning of most elements is a strong function of the oxygen (or FeO) content of the sulphide", which "increases linearly with the FeO content of the silicate melt and decreases with the Ni content of the sulphide." [START_REF] Wood | Trace element partitioning into sulfide: how lithophile elements become chalcophile and vice versa[END_REF] go on to state that Tl partitioning does not obey this simple model, nor one extended through consideration of additional parameters: "Despite simple and predictable partitioning behavior for many elements, several important elements (Ni, Cu, Ag, Mn, Tl) show strongly non-linear dependences of logD i on log[FeO] and we were unable to assign them to any one particular category in terms of affinity for sulfide."

Jenner (2017) calculated that for typical MORB melting D Tl sulf/sil = 7; [START_REF] Greaney | The behavior of chalcophile elements during magmatic differentiation as observed in Kilauea Iki lava lake, Hawaii[END_REF] observe mixed affinity behaviour during magmatic differentiation at Kilauea Iki. [START_REF] Wang | The distribution of lead and thallium in mantle rocks: Insights from the Balmuccia peridotite massif (Italian Alps)[END_REF] suggested that a significant proportion of the Tl contents of peridotites are hosted in interstitial late-crystallising silicate phases, finding that sulphides typically contribute <30% of the bulk rock Tl budget. These observations are consistent with poor correlation of Tl concentrations with chalcophile element concentrations in most igneous contexts (e.g. [START_REF] Prytulak | Thallium elemental behavior and stable isotope fractionation during magmatic processes[END_REF].

Silicate minerals.

Although Tl is known to be highly incompatible, partitioning of Tl between silicate minerals and melt remains poorly constrained. [START_REF] Nielsen | Chalcophile behaviour of thallium during MORB melting and implications for the sulfur content of the mantle[END_REF] therefore assumed D Tl min/melt identical to D Rb min/melt due to the similarity in ionic charge and radius. Tl + is well-known to substitute for K + in silicate minerals (e.g. [START_REF] Shaw | The geochemistry of thallium[END_REF], as documented by e.g. [START_REF] Rader | Mineralogical thallium geochemistry and isotope variations from igneous, metamorphic, and metasomatic systems[END_REF], and we also assume similar partitioning behaviour of Rb and Tl in silicate contexts.

III. Cerium partitioning

Although variation in mineral-melt partitioning of Ce between clinopyroxene and basaltic melt (herein D Ce cpx/melt) is not required to model the MORB Ce/Tl array, it is likely that such variation does exist and does contribute to the observed pattern. The GERM database (as of June 2020) documents a total range in D Ce cpx/melt from 0.017 [START_REF] Frey | Rare earth abundances in a high-temperature peridotite intrusion[END_REF] to 0.82 [START_REF] Vannucci | Partitioning of REE, Y, Sr, Zr and Ti between clinopyroxene and silicate melts in the mantle under La Palma (Canary Islands): implications for the nature of the metasomatic agents[END_REF], excluding the values of [START_REF] Nagasawa | Rare-Earth distribution in alkali rocks from Oki-Dogo Island, Japan[END_REF], which were determined on natural samples showing signs of significant alteration [START_REF] Uchimizu | Geology and petrology of alkali rocks from Dogo, Oki Islands[END_REF].

D Ce cpx/melt is generally observed to increase with increasing Wollastonite and tetrahedrally-coordinated Al content of clinopyroxene. The data compilation of [START_REF] Sun | Distribution of REE between clinopyroxene and basaltic melt along a mantle adiabat: effects of major elemnet composition, water, and temperature[END_REF] features a range of D Ce cpx/melt from 0.019 [START_REF] Salters | Trace element partitioning during the initial stages of melting beneath mid-ocean ridges[END_REF] to 0.27 [START_REF] Gaetani | Partitioning of rare earth elements between clinopyroxene and silicate melt: crystal-chemical controls[END_REF], excluding the data of [START_REF] Wood | Experimental determination of aluminous clinopyroxene-melt partition coefficients for potassic liquids, with application to the evolution of the Roman province potassic magmas[END_REF] determined for highly potassic melts (D Ce cpx/melt from 0.48 to 1.31). This information is presented graphically in Figure A1. [START_REF] Johnston | Constraints on clinopyroxene/melt partitioning of REE, Rb, Sr, Ti, Cr, Zr, and Nb during mantle melting: first insights from direct peridotite melting experiments at 1.0 GPa[END_REF] additionally determined a D Ce cpx/melt value of 0.47 during experiments on the partial melting of peridotite (not shown). Further data for partitioning of REE in the presence of high-Ca clinopyroxenes was compiled by Bédard (2014), though the dataset for terrestrial basalts is limited.

While [START_REF] Sun | Distribution of REE between clinopyroxene and basaltic melt along a mantle adiabat: effects of major elemnet composition, water, and temperature[END_REF] provided recommended values for D Ce cpx/melt during MORB melting, they note that these values are based on highly simplified thermodynamic models of clinopyroxene that may represent unrealistically restricted mineral composition ranges. We therefore explore a range of D Ce cpx/melt from 0.01 to 0.8 in our modelling. We do not consider 0.8 a value that is likely to be achieved in natural rocks, but it is informative as an end-member scenario. positioned both between Cs and Rb [START_REF] Prytulak | Thallium elemental behavior and stable isotope fractionation during magmatic processes[END_REF] and between La and Ce [START_REF] Jenner | Cumulate causes for the low contents of sulfide-loving elements in the continental crust[END_REF]. The ordering otherwise follows that of [START_REF] Willbold | Trace element composition of mantle end-members: Implications for recycling of oceanic and upper and lower continental crust[END_REF]. For almost all samples there is a clear negative Tl anomaly regardless of position, as emphasised by the averages for each end-member. [START_REF] Workman | Major and trace element composition of the depleted MORB mantle (DMM)[END_REF], and other values as for subfigure (c). Symbols and data sources as in Figure 4. Helena lavas indicated a role for subduction-processed AOC in generating the HIMU array. However, this trend is not replicated in HIMU lavas from other localities, and is not unique to HIMU-type lavas. Symbols and data sources as in Figure 4. Relative to Cs and Rb, Tl/Tl* values > 0.5 (for both PM and DM normalisations) are associated with Tl isotopic compositions that are distinct from the mantle range (green band). Relative to La and Ce, it is less clear whether there is any association. Symbols and data sources as in Figure 4. Table 3. Slopes obtained for York regressions [START_REF] York | Unified equations for the slope, intercept, and standard errors of the best straight line[END_REF] between log[Tl] and log [Element] * Sulphur concentration at sulphide saturation for basaltic melts [START_REF] Liu | Sulfur concentration at sulfide saturation (SCSS) in magmatic silicate melts[END_REF][START_REF] Mavrogenes | The relative effects of pressure, temperature and oxygen fugacity on the solubility of sulfide in mafic magmas[END_REF][START_REF] O'neill | The sulfide capacity and the sulfur content at sulfide saturation of silicate melts at 1400°C and 1 bar[END_REF].

Figure captions

  Figure5combines the studies of[START_REF] Jenner | Analysis of 60 elements in 616 ocean floor basaltic glasses[END_REF],[START_REF] Nielsen | Chalcophile behaviour of thallium during MORB melting and implications for the sulfur content of the mantle[END_REF] and[START_REF] Yang | Elemental systematics in MORB glasses from the Mid-Atlantic Ridge[END_REF], excluding samples with MgO < 6wt%, seamounts, back-arc basins and aseismic ridges. These studies yield a combined mean MORB Ce/Tl of 1220 ± 570 (2sd, n = 909).Fractional melting models assuming a spinel lherzolite source with variations in D Ce cpx/melt and initial elemental concentration are shown in Figure5, with the fractional melting model of[START_REF] Nielsen | Chalcophile behaviour of thallium during MORB melting and implications for the sulfur content of the mantle[END_REF] reproduced in Figure5a. We explore a range of D Ce cpx/melt in Figure5b, reproducing not only the average Ce/Tl value observed for MORB but also the sense of variation in the data. Compared to the model of[START_REF] Nielsen | Chalcophile behaviour of thallium during MORB melting and implications for the sulfur content of the mantle[END_REF], the reduced compatibility of Tl in sulphides means that the model is less sensitive to the S concentration of the upper mantle. Considering only variations in the bulk partitioning of Ce, over 80% of MORB samples can be explained with a range of D Ce cpx/melt up to ~0.35. Furthermore, about 50% of MORB samples are explained by D Ce cpx/melt ≤ 0.2, while fewer than 2% of MORB samples require D Ce cpx/melt ≥ 0.8.

Figure 1 :

 1 Figure 1: Plot of ε 205 Tl against Tl concentration. There is no covariation. Large symbols: this study. Other

Figure 2 :

 2 Figure 2: Primitive Mantle-normalised trace element plots. Note that Tl appears twice (highlighted),

Figure 3 :

 3 Figure 3: (a) Ce/Tl and (b) Tl concentrations plotted against MgO contents. Thallium is a highly

Figure 4 :

 4 Figure 4: Plot of Ce/Tl ratios versus Tl concentrations in oceanic basalts and subduction zone volcanics.

Figure 5 :

 5 Figure 5: (a) MORB melting model of Nielsen et al. (2014), with TlDM = 0.48 ng/g, SDM = 195 µg/g and D Tlsulf/sil = 36 (for other parameters see Table5). (b) Modified MORB melting model assuming SDM = 100

Figure 6 :

 6 Figure 6: (a) Melting of PM (grey) and DM (black) sources (Table 6) with varying D Ce cpx/melt. (b) Melting of (i) a hypothetical mixed source with Tl = 1 ng/g, Ce = 15 µg/g, and D Ce cpx/melt = 0.8; and (ii) a hypothetical mixed source with Tl = 0.5 ng/g, Ce = 5 µg/g, and D Ce cpx/melt = 0.15. (c) 3-5% melting of a hypothetical source with Ce = 5 µg/g and D Ce cpx/melt = 0.1. Source Tl concentration varies as indicated on figure. (d) As subfigure (c), but instead Ce = 15 µg/g and D Ce cpx/melt = 0.5. Symbols and data sources as in Figure 4. All displayed models assume 100 µg/g S (Ding and Dasgupta, 2018) and D Tl sulf/sil = 10. All melting percentages

Figure 7 :

 7 Figure 7: Plots of ε 205 Tl against (a) 87 Sr/ 86 Sr, (b) 143 Nd/ 144 Nd, (c) 176 Hf/ 177 Hf, (d) 206 Pb/ 204 Pb, (e) 207 Pb/ 204 Pb, (f) 208 Pb/ 204 Pb. For OIB samples, there is no co-variation of ε 205 Tl and the radiogenic isotope systems commonly used to define mantle components, with the possible exception of 143 Nd/ 144 Nd in Icelandic

Figure 8 :

 8 Figure 8: Plots of ratios employed to track AOC contributions to OIB source against ε 205 Tl. (a) Ce/Tl against ε 205 Tl, showing literature main-phase St Helena lavas and St Helena samples from this study, (b) Ce/Tl against ε 205 Tl for all OIB samples, (c) Ce/Pb against ε 205 Tl with the same samples as subfigure (a), (d) Ce/Pb against ε 205 Tl for all OIB samples. Blusztajn et al. (2018) argued that a sense of correlation for main-phase St

Figure 9 :

 9 Figure 9: Plot of ε 205 Tl against Tl/Tl* ratios. Tl* = Brett_etal_GCA_Eqn1.pdf or

Figure A1 :

 A1 Figure A1: D Ce cpx/melt values versus CaO in clinopyroxene. This illustrative plot has not been corrected for

  9532sd is quoted as the highest of (1) the uncertainty for repeat analyses of BCR-2 on the Nu HR, (2) the 954 uncertainty for repeated measurements of the Aldrich Tl solution on the Nu Plasma II, or (3) the uncertainty 955 for repeat analyses of a given sample.

[ 1 ]

 1 [START_REF] Workman | Major and trace element composition of the depleted MORB mantle (DMM)[END_REF]; [2][START_REF] Baker | Determining the composition of high-pressure mantle melts using diamond aggregates[END_REF] and[START_REF] Wasylenki | Near-solidus melting of the shallow upper mantle: partial melting experiments on depleted peridotite[END_REF], as modified by[START_REF] Nielsen | Chalcophile behaviour of thallium during MORB melting and implications for the sulfur content of the mantle[END_REF]; [3][START_REF] Elliott | The origin of enriched mantle beneath São Miguel, Azores[END_REF].

  Figure3

  Figure S2

  Figure S3

  Figure S4

  Figure S5

  Ce cpx/melt, a model incorporating lower compatibility of Tl in sulphides than previously assumed yields a best fit for a TlDM abundance of 0.27 ng/g. This value is calculated assuming that (i) samples with the lowest Tl concentrations on average represent the highest degree of melting, i.e. the closest approach to the DM Ce/Tl ratio, and (ii) an average CeDM

	of 0.55 µg/g (Workman and Hart, 2005). Our proposed TlDM is considerably lower than the estimate
	of Salters and Stracke (2004) of 0.38 ng/g, and much lower than that of Nielsen et al. (2014) of 0.48
	ng/g.

Table 5

 5

	). (b) Modified MORB melting model assuming SDM = 100

Table 1 .

 1 This illustrative plot has not been corrected for pressure and temperature, or for other compositional variables including degree of hydration. With the notable exception of[START_REF] Green | SIMS determination of trace element partition coefficients between garnet, clinopyroxene, and hydrous basaltic liquids at 2-7.5 GPa and 1080-1200[END_REF] and the two McDade studies, which examine melting under strongly hydrous conditions, there is a general sense of increasing Ce compatibility as CaO in cpx increases both Summary of OIB localities with published Tl concentration and isotopic composition data.

	934
	within and between studies.

Table 2 .

 2 Key geochemical data for OIB samples analysed in this study. MgO values per Table1and references therein (see Electronic Annex 2b for full details) 949 † Marquesas lavas exhibit variable composition: at a given 87 Sr/ 86 Sr value, lavas from the 'Ua Huka' group 950 (Ua Huka, young Hiva Oa) have higher Nd isotopic compositions, and lavas from the 'Fatu Hiva' group 951 (Fatu Hiva, old Hiva Oa, Montane, Tahuata) have higher 206 Pb/ 204 Pb (see[START_REF] Chauvel | The size of plume heterogeneities constrained by Marquesas isotopic stripes[END_REF] Electronic

	946
	947
	Sample	MgO* (wt%) Ce (µg/g) Tl (ng/g) Ce/Tl ε 205 Tl 2sd Dissolutions Measurements (n)
	Gough (EMI)
	G6	7.94	101	26	3915	0.5	2.2	3 (1 NU + 2 NUII)
	G102	5.28	107	76	1402	-2.5	0.6	3
	G117	4.52	113	39	2921	3.8	0.6	4
	G118	12.97	73.9	49	1495	-0.6	0.5	2
	G132	5.04	87.1	95	919	-4.6	0.5	3
	G135	5.85	112	53	2104	-0.6	0.5	2
	B167	3.39	107	74	1437	-3.2	0.5	1
	Tristan da Cunha
	(EMI)
	T16	4.74	134	101	1321	-2.3	0.5	2
	T60	12.2	60.9	38	1600	-0.3	0.5	2
	T64	8.91	115	64	1796	-1.1	0.5	1
	T122	7.28	104	55	1888	-1.2	0.5	2
	T497	7.61	136	87	1559	-1.2	0.8	9
	T557	8	112	56	2006	-1.2	1.5	7
	T557 (leached)					-1.6	0.9	1 (NUII)
	Fatu Hiva,
	Marquesas (EM † )
	FH01	10.6	110	7 16740	0.0	1.3	1
	FH11	6.8	99.0	26	3837	-3.6	0.8	3
	FH18	12.2	81.5	32	2554	-1.8	0.5	1
	Hiva Oa,
	Marquesas (EM † )
	HV64	8	81.1	17	4649	0.7	0.5	1
	HV76	5.14	72.7	63	1162	-0.3	0.7	2
	Montane,
	Marquesas (EM † )
	MT04	5.63	71.6	18	3996	-3.9	1.0	3 (2 NU + 1 NUII)
	MT08	5.53	82.0	25	3224	0.6	0.5	2
	Tahuata,
	Marquesas (EM † )
	TH4	6.37	108	77	1415	-2.9	0.5	1
	TH5	7.44	137	66	2064	-0.5	0.5	2
	TH8	4.67	96.3	24	4045	1.0	0.5	1
	TH8 (leached)					2.2	0.9	1 (NUII)
	TH13	6.09	80.7	15	5482	-3.5	0.6	4
	TH14	8.37	109	177	614	-6.4	0.5	4
	TH18	6.4	87.6	43	2014	0.4	1.2	3 (2 NU + 1 NUII)
	TH18 (leached)					-0.2	0.8	1 (Nu II)
	TH31	5.6	82.1	18	4574	-1.9	1.1	2 (1 NU + 1 NUII)
	TH39	9.2	81.5	18	4533	4.4	0.9	1
	Ua Huka,
	Marquesas (EM † )
	UH53	0.38	155	235	663	-1.8	0.5	4
	UH81	7.75	90.4	121	748	-1.9	0.5	5
	UH89	7.2	89.8	39	2278	-3.5	0.5	3
	UH93	9.85	72.8	97	753	-1.2	0.5	3
	St Helena (HIMU)

* 952 Annex 2).

Table 4 .

 4 (see text). For MORB, n = 909 except Cs, for which n = 702. For OIB, n = 48. Modal mineralogy and reaction coefficients used in melting models.

		MORB		OIB
	Element	slope	2sd	slope	2sd
	Ce	0.994	0.030	0.102	0.122
	Cs	2.608		2.033	0.571
	La	1.285	0.047	0.116	0.136
	Pb	0.875	0.021	1.131	0.488
	Rb	3.114	0.218	1.091	0.504

Acknowledgements

AB was funded by an Imperial College London Earth Science and Engineering Janet Watson departmental

PhD scholarship with all analytical costs covered by start-up funds to JP. We thank Barry Coles and Katharina Kreissig for keeping the MAGIC instruments and clean labs running smoothly. CC was supported in part by ERC project SHRED (project 833632), and this is contribution 4149 of the IPGP. We appreciate the comments of Folkmar Hauff, Kevin Konrad, four anonymous reviewers, and the editorial handling of James Day, all of which helped improve the manuscript.

Appendix

I. Elemental concentrations MORB. For Ce concentration, we use the values of [START_REF] Workman | Major and trace element composition of the depleted MORB mantle (DMM)[END_REF] for Depleted MORB Mantle (DMM), Enriched MORB Mantle (EMM), and the average MORB source. For Tl concentration, we consider previous DMM estimates along with values that provide the best fit for our model. with scatter leaving room for some fractional crystallisation, the observed range significantly exceeds that which can be explained simply through a combination of melting and fractional crystallisation. The OIB trend therefore requires mixing melts from different sources, one of which cannot contain more than negligible Tl (note y-intercept of trend). Symbols and data sources as in Figure 5.

Supplementary Figures

Figure S6:

Mixing between St Helena HIMU average composition [START_REF] Blusztajn | Thallium isotope systematics in volcanic rocks from St Helena -constraints on the origin of the HIMU reservoir[END_REF] and three "AOC" values (see Table S1). Ticks correspond to admixture of 10%, 20% and 30% of AOC as labelled for ODP 504B. Table S1. For DM, values are taken from [START_REF] Salters | Composition of the depleted mantle[END_REF], except ε 205 Tl (Nielsen et al., 2006a).

For DSDP 417/418, supercomposite values are taken from [START_REF] Blusztajn | Thallium isotope systematics in volcanic rocks from St Helena -constraints on the origin of the HIMU reservoir[END_REF]Staudigel et al. (1995).

ODP 504B values are taken from Nielsen et al. (2006b) and Bach et al. (2003). "Modern AOC" values are taken from [START_REF] Blusztajn | Thallium isotope systematics in volcanic rocks from St Helena -constraints on the origin of the HIMU reservoir[END_REF] or inferred (underlined). St Helena average values are as reported by