Open Research Online The cadmium and zinc isotope compositions of the silicate Earth – implications for terrestrial volatile accretion

Zinc and Cd isotope compositions are presented for a comprehensive suite of terrestrial rocks to constrain the extent of Zn and Cd isotope fractionation during igneous processes and better deﬁne the d 66 Zn and d 114 Cd values of the silicate Earth (the d values denote per mille deviations of 66 Zn/ 64 Zn from JMC Lyon Zn and of 114 Cd/ 110 Cd from NIST SRM 3108 Cd). Analyses of spinel lherzolites


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Zinc and Cd isotope compositions are presented for a comprehensive suite of terrestrial rocks to constrain the extent of Zn and Cd isotope fractionation during igneous processes and better define the d 66 Zn and d 114 Cd values of the silicate Earth (the d values denote per mille deviations of 66 Zn/ 64 Zn from JMC Lyon Zn and of 114 Cd/ 110 Cd from NIST SRM 3108 Cd). Analyses of spinel lherzolites provide a bulk silicate Earth (BSE) d 114 Cd BSE value of -0.06 ± 0.03 ‰ (2SD). For Zn, the peridotite data of the current and previous studies define a mean d 66 Zn BSE = 0.20 ± 0.05 ‰ (2SD). Komatiite analyses of this and published investigations yield similar mean values, which suggests that the Zn and Cd isotope compositions of the mantle remained fairly constant since the Archean. Data for loess provide upper continental crust compositions of d 114 Cd = 0.03 ± 0.10 ‰ and d 66 Zn = 0.23 ± 0.07 ‰. The Zn isotope and abundance data for peridotites and oceanic basalts are in accord with the previous observation of a mantle array, with basalts having higher Zn concentrations and d 66 Zn values than the peridotites. To a first order, this reflects slightly incompatible behaviour of Zn during mantle melting and melt differentiation with associated enrichment of heavy Zn isotopes in the melt phase. Cadmium is marginally more incompatible than Zn during igneous processes and the oceanic basalts also display a minor enrichment of heavy Cd isotopes relative to peridotites. However, secondary processes produce significant Cd isotope variability in both mantle melts and peridotites, obscuring the primary igneous array. The d 66 Zn BSE estimates of this and previous studies resemble the Zn isotope compositions of CV and CO carbonaceous and some enstatite chondrites. In contrast, the BSE has a lower d 114 Cd BSE value than enstatite and carbonaceous chondrites. This implies that the Cd isotope composition of the BSE was either fractionated during accretion or that Earth's Cd inventory was not exclusively acquired from material related to carbonaceous and enstatite chondrites. Importantly, delivery of Zn and Cd to the BSE solely by CI and CM chondrites is not in accord with the meteorite and terrestrial stable isotope data of these elements.
Ó 2022 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Introduction
Despite decades of research, the source of Earth's volatiles, the timing of their accretion and whether the composition of the source materials matches any meteorites within collections are still topics of considerable debate. This uncertainty encompasses both moderately volatile elements, such as Na, Mn and Cu, with 50 % condensation temperatures (T C ) of between about 1300 K https://doi.org/10.1016/j.gca.2022.09.041 0016-7037/Ó 2022 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). and 700 K, and more volatile species, such as water and Cl, that condense at lower temperatures (Albarède, 2009;Wood et al., 2010). Notably, both the Earth and chondritic meteorites exhibit variable depletions in volatile constituents, which are generally correlated with an element's volatility, but display refractory element abundance ratios similar to those of the bulk Solar System, as approximated by the Sun and CI carbonaceous chondrites (Wasson and Chou, 1974;Wasson and Kallemeyn, 1988;McDonough and Sun, 1995;Palme and O'Neill, 2014).
Considering Earth's accretion history, many studies argue for volatile accretion during the main stages of accretion, whilst core formation was ongoing. Specifically, it was posited that oxidised, volatile-rich material was added during the later stages of accretion to an initially refractory and volatile-depleted proto-Earth (Wänke et al., 1984), with progressive oxidation of the mantle supported by continuous core formation models (Wade and Wood, 2005;Corgne et al., 2008;Siebert et al., 2011). Accretion of carbonaceous material equating to 15 % of Earth's mass during the later stages of accretion was thereby considered to satisfy both isotopic constraints  and terrestrial volatile element abundances (Marty, 2012;Albarède et al., 2013;Braukmüller et al., 2019). Alternatively, the close genetic relationship between Earth and enstatite chondrites in mass independent isotope compositions of O and various metals (including Ca, Ti, Cr, Ni, Mo, Ru, Nd), suggests that the latter may be the primary source of Earth's volatile inventory (Javoy et al., 2010;Warren, 2011;Burkhardt et al., 2011;Young et al., 2016;Dauphas, 2017;Fischer-Gödde and Kleine, 2017;Bermingham et al., 2018;Boyet et al., 2018;Gillmann et al., 2020). This is supported by data, which demonstrate that enstatite chondrites could have supplied Earth's water budget whilst also satisfying constraints from H and N isotopes (Piani et al., 2020). Finally, it was also argued that Earth's volatile budget was delivered by a volatile-rich late veneer following termination of accretion and core formation (Wang & Becker, 2013;Fischer-Gödde et al., 2020). Whilst the late veneer is typically estimated to have a mass of about 0.5 % of Earth's mass (M E ) from the abundances of highly siderophile elements (Holzheid et al., 2000, Walker, 2009) much larger masses exceeding 2 % M E have been suggested based on volatile element systematics (Albarède, 2009;Ballhaus et al., 2013).
Zinc and Cd are chemically similar group 12 elements that primarily occur as divalent cations in natural environments and which are both volatile in a cosmochemical sense. However, whilst Zn is moderately volatile with a 50 % condensation temperature of T C = 704 K, Cd is a highly volatile element with T C = 502 K (Wood et al., 2019). Given this, the mantle budgets and stable isotope signatures of the two elements record complementary information on Earth's volatile accretion history. Within Earth's upper mantle, Zn is a lithophile element as mantle sulphides hold less than 1 % of the Zn inventory due to a sulphide-silicate partition coefficient (D sul-sil Zn ) of less than about 3 (Li and Audétat, 2012;Kiseeva and Wood, 2013). In fertile spinel lherzolites, mineral Zn concentrations typically decrease in the order spinel ) olivine > orthopyroxene > clinopyroxene (Wang et al., 2017). The latter observation is in accord with experimental mineral melt partition coefficients, which indicate that Zn is significantly more compatible in spinel (D sp-melt Zn = 5.2) than in olivine, orthopyroxene, clinopyroxene and garnet, whereby the latter phases have D min-melt Zn melt values of about 1, 0.6, 0.4 and 0.2, respectively (Le Roux et al., 2011;Davis et al., 2013). As a consequence, Zn in spinel lherzolites is typically primarily hosted in olivine (>55 %), in intermediate proportions (of about 10-25 %) in orthopyroxene and spinel, with a smaller fraction present in clinopyroxene (<10 %). In accord with the partitioning data, Zn displays mildly incompatible behaviour during mantle melting (Le Roux et al., 2011;Davis et al., 2013;Wang et al., 2017;Sossi et al., 2018).
Even though Cd is regarded as more chalcophile than Zn, it is unlikely that sulphides are a sufficiently important host in the upper mantle to significantly impact Cd behaviour during melting, as previously suggested by Yi et al. (2000). With a D sul-sil Cd value of about 70 for an upper mantle with 8 % FeO (Kiseeva and Wood, 2013) and 120-250 lg/g S (McDonough and Sun, 1995;Salters and Stracke, 2004), less than 5 % of Cd will be hosted in sulphides, such that essentially lithophile behaviour is also expected for Cd. This conclusion is in accord with the observation of low Cd concentrations in sulphides of basaltic magmas and the finding that the Cd inventory of fertile, sulphide bearing mantle xenoliths is primarily hosted in the constituent silicate minerals rather than in grain boundaries or fluid inclusions (Norman et al., 2004;Witt-Eickschen et al., 2009). Within fertile lherzolites, mineral Cd concentrations decrease in the order clinopyroxene ($100 lg/g) > ort hopyroxene ($30 lg/g) > olivine ($15 lg/g). As a consequence, about half of the Cd budget of such rocks is present in clinopyroxene, with the remainder hosted to about equal proportions in orthopyroxene and olivine. In contrast to Zn, spinel is not an important upper mantle host of Cd, due to the low abundance of the mineral and relatively low Cd concentrations of typically less than 50 lg/g (Witt-Eickschen et al., 2009). Published data on the partitioning of Cd during igneous processes are significantly scarcer than for Zn, with experimental mineral-melt partition coefficient available only from a single study and which indicate that Cd is possibly compatible in clinopyroxene and garnet (with D min-melt Cd % 0.5-5) but mildly incompatible (D min-melt Cd % 0.2-0.5) in orthopyroxene and olivine (Adam and Green, 2006). This suggests that Cd should resemble Zn during upper mantle melting, with a mildly incompatible and primarily lithophile behaviour.
Whilst the Zn isotope composition of the bulk silicate Earth (BSE), its reservoirs, and Zn isotope fractionation during common igneous processes have been investigated by several studies (Chen et al., 2013;Doucet et al., 2016;Wang et al., 2017;Sossi et al., 2018;Beunon et al., 2020), very few such data are available for Cd and its isotopes, with no published results for mantle peridotites (Schmitt et al., 2009). This study fills this gap with Cd isotope analyses of a suite of mantle peridotites, mantle melts and other relevant rocks. Most samples were additionally analysed for Zn isotope compositions, to provide context for the Cd isotope data. As such, the current study provides the first comprehensive dataset for mantle rocks to evaluate the Cd isotope composition of the silicate Earth, whilst also enabling a re-evaluation of previous work on the Zn isotope systematics of the BSE. The Cd and Zn results are subsequently employed in the context of available data for chondritic meteorites to improve understanding of terrestrial volatile accretion.

Samples
Zinc and Cd isotope analyses were carried out on samples from a variety of tectonic settings and locations to characterise Earth's main silicate reservoirs (Table 1). A total of 14 peridotite samples were analysed, including six spinel lherzolite xenoliths and one harzburgite xenolith from the continental portion of the Cameroon Line volcanic chain of west Africa, which represent melt depletion residues that have undergone variable degrees of metasomatism and partial melt interaction (Lee et al., 1996). Two lherzolites and one harzburgite from the Horoman Peridotite Massif of northern Japan, considered to be a melting residue of a mid-ocean ridge basalt (MORB) source, were also analysed (Takazawa et al., 1996;Yoshikawa and Nakamura, 2000). Isotope data are further presented for four serpentinized abyssal peridotites from Ocean Drilling Program (ODP) Sites  Separate rows for the same sample denote multiple digestions of a sample powder. * mass of individual sample digests. # number of mass spectrometer runs carried out for a given digest; $ samples were digested using a slightly modified procedure (see text for details). Reported uncertainties for sample digests that were analysed only once represent the between-run 2SD precision for replicate runs of the bracketing isotope standard in the same measurement session. For samples that were analysed more than once (using one or several disgests), the uncertainties represent the mean between-run 2SD of individual mass spectrometer runs.

(Hess Deep, Eastern Pacific Ocean) and 920 (Mid-Atlantic Ridge
Kane, or MARK, Fracture Zone). The MARK zone samples are harzburgites, which are thought to be residues formed by partial melting of fertile upper mantle (Casey, 1997;Niida, 1997), whilst the Hess Deep dunites were likely produced by interaction of refractory harzburgites with basaltic melts (Allan and Dick, 1996;Edwards and Malpas, 1996). Cadmium isotope data were also obtained for one xenolith from Kilbourne Hole, New Mexico (Irving, 1980), and a Twin Sisters dunite (Kruckenberg et al., 2013). Analyses were carried out on four Archean komatiites, two from Alexo, Canada, and one sample each from Munro Township in Canada and the Belingwe Greenstone Belt in Zimbabwe (Table 1). All four komatiites are spinifex-textured, whereby the Alexo komatiites are derived from the A2 (KAL-1) and A3 (M657) layers of the flow, whilst samples MT 20 and ZA-1 are from the A3 and A2 layers, respectively (Dupré et al., 1984;Arndt, 1986;Jochum et al., 1991;Chauvel et al., 1993;Lahaye and Arndt, 1996;Puchtel and Humayun, 2000). Owing to the high temperatures and associated high degrees of partial melting involved in komatiite formation, they are recorders for the Zn and Cd isotope signature of the Archean mantle, if isotopic effects from crustal contamination, fractional crystallisation and secondary alteration by metamorphism and weathering can be avoided or corrected for (McDonough and Sun, 1995;Dauphas et al., 2010;Sossi et al., 2018).
Also analysed were 10 mid-ocean ridge basalts (MORB) from dredges in the Atlantic, Indian, and Pacific Oceans, six ocean island basalts, from Iceland, Polynesia, Hawaii and Réunion, and olivine separates from the Réunion basalt (Table 1). The Zn and Cd isotope data for these samples reflect the combined effects of partial melting of the mantle, fractional crystallisation, contamination by oceanic crust (for OIB), and possible degassing during subaerial and shallow marine volcanism. Zinc and Cd isotope data are further presented for 13 loess deposits from Asia and Europe to characterise the upper continental crust (Table 1). Loess is suitable for this purpose, owing to the natural mechanical averaging involved in its formation (Taylor et al., 1983;Peucker-Ehrenbrink and Jahn, 2001). For quality control, further Zn and Cd isotope data were acquired for five USGS rock reference materials and these results are included in the characterisation of OIBs (BIR-1a, BHVO-2) and the upper continental crust (AGV-2, BCR-2, JB-2).

Laboratories and reagents
Sample preparation for the mass spectrometric analyses was carried out in ISO Class 4 laminar flow hoods within the ISO Class 6 clean room facilities of the MAGIC Laboratories at the Department of Earth Science and Engineering, Imperial College London. All water used was of !18.2 MX cm grade from a Millipore purification system. Distilled 6 M HCl, 12 M HCl, 16 M HNO 3 , 28 M HF and 8.5 M HBr as well as double-distilled ethanol (EtOH) were prepared from reagent grade starting materials by sub-boiling distillation in quartz or Teflon stills.

Sample leaching and digestion
The MORB samples were obtained as chips that were leached before digestion to remove superficial contamination. The chips were first cleaned with water, then EtOH, with agitation in an ultrasonic bath. Samples were then leached at room temperature for 15 min in an ultrasonic bath, first with 0.1 M HCl and then twice with 0.5 M HCl, with water rinsing between each step (Rehkämper et al., 1999b). Sample powders and chips were then weighed before undergoing acid digestion.
Silicate rock samples, weighing between 0.2 and 3.1 g, were first digested on a hotplate in 6-16 mL of a 1 + 2 to 1 + 3 mixture of 16 M HNO 3 and 28 M HF at 80 to 120°C for 4 to 10 days, and then dried down. The samples were next dissolved in 10-30 mL of a modified aqua regia mixture (1 + 1 of 6 M HCl and 16 M HNO 3 ) and refluxed at 90 to 130°C for 5 to 9 days, before being dried and dissolved in 10-30 mL of 6 M HCl and refluxed for 1 to 2 weeks at 100 to 140°C. Larger acid volumes of up to 60 mL were used for the digestion of the olivine separates. One batch of samples did not undergo a modified aqua regia stage after HF-HNO 3 digestion (see Table 1). Instead, these samples were digested in 10-30 mL of 16 M HNO 3 at 120°C, and then evaporated, before treatment with 6 M HCl. Spinel phases are known to host Zn in ultramafic rocks (O'Reilly et al., 1991;Wang et al., 2017). Therefore, any remaining mineral residues within the 6 M HCl sample solutions underwent further Parr bomb digestion in 12 M HCl at 130 to 150°C for 3 to 5 days, before being recombined with the main sample digest.

Aliquoting and double spiking of samples
Small ( 5%) aliquots of the 6 M HCl sample solutions were utilised for the Zn isotope analyses, with most of the remaining sample solutions used for the Cd isotope measurements. To enable optimal double spiking of the aliquots, the concentrations of Zn and Cd must be known. For samples where the elemental concentrations were not previously determined, appropriate analyses were carried out on a further small (generally 5 %) aliquot. For spiking, the respective sample aliquots were mixed with appropriate volumes of a 64 Zn-67 Zn double spike with 64 Zn/ 67 Zn % 2.5 (Arnold et al., 2010) and a 111 Cd-113 Cd double spike with 111 Cd/ 113 Cd % 1.7 (Xue et al., 2012). The spiking was dosed to obtain near-optimal molar ratios of spike-derived Zn or Cd to natural Zn or Cd of S/N % 1.0 to 1.2, but higher S/N ratios of up to 1.8 were employed for samples where only limited Cd was available for analysis. The spike-sample mixtures were refluxed for 24 h on a hotplate to ensure full equilibration, evaporated to dryness, and dried down twice with a few drops of 6 M HCl.

Separation of Zn and Cd by anion exchange chromatography
For the separation of Zn, the Zn sample aliquots were taken up in 1 mL of 1 M HCl, refluxed at about 100°C for 30 min and cooled to room temperature prior to loading onto the previously prepared anion exchange columns. The separation of Zn from the sample matrix employed a single-stage procedure as outlined by Bridgestock et al. (2014) (Table S1, Supplementary Material). This chemical separation produced Zn yields of between about 80 and 100 %, calculated based on the ion beam intensities that were obtained in the isotope analyses. Similarly, the Cd sample aliquots were re-dissolved in 15-30 mL of 3 M HCl prior to loading onto the anion exchange columns. The three-stage Cd column chemistry follows published procedures (Ripperger and Rehkämper, 2007;Xue et al., 2012). After column chemistry, the Cd fractions were extracted twice with heptane, to remove residual organics (Murphy et al., 2016). The Cd yield of the chemical separation was typically between 65 and 100 %, with the exception of five samples, which had yields of about 30 to 50 % (also calculated from the ion beam intensities of the isotope measurements). Most likely, the low yields reflect Cd loss during the chemical separation and purification procedure.

Zn and Cd stable isotope measurements and data reduction
The Zn and Cd isotope measurements were carried out in the MAGIC Laboratories at Imperial College London. Most analyses were done using a Nu Plasma HR MC-ICP-MS but a Nu Plasma II instrument was applied for isotopic analysis of Cd-depleted samples where higher sensitivities were desirable. Samples were introduced with a Cetac autosampler and either a Nu instruments DSN-100 or a Cetac Aridus desolvation system using glass nebulizers with nominal uptake rates of 100 ll/min. The Zn isotope analyses involved monitoring of the 64 Zn, 66 Zn, 67 Zn, and 68 Zn ion beams with Faraday collectors equipped with 10 11 X resistors at instrumental sensitivities of > 100 V/(lg/ml). The ion beams at mass numbers 62 ( 62 Ni + ) and 68.5 ( 137 Ba 2+ ) were also measured to correct for isobaric interferences. The presence of Ti was examined, via regular mass scans of sample solutions and the ion beam monitor at mass number 62 (as this also encompasses 46 TiO + ). Based on these measurements, the contribution of polyatomic 48 TiO + to the ion beam at mass number 64 ( 64 Zn + ) is 5 ppm at most and hence negligible.
The isotopic analyses of samples were carried out relative to bracketing measurements of standard solutions that were prepared as mixtures of the AA-ETH Zn isotope reference material (Archer et al., 2017) In the following, all d 66 Zn data are reported relative to the JMC Lyon Zn reference material. To this end, the d 66 Zn AA-ETH values were converted with the standard conversion identity, which can be approximated as: where the isotopic offset between AA-ETH and JMC Lyon Zn, D 66 Zn AA-ETH -JMC Lyon , is 0.28 ± 0.02 ‰ (Archer et al., 2017). The uncertainty of D 66 Zn AA-ETH -JMC Lyon is not propagated in the calculation of d 66 Zn because a common offset correction is applied in the community (Archer et al., 2017). All samples and standards were prepared using 0.1 M HNO 3 to give solutions with S/N ratios and total Zn concentrations (of 50 to 100 ng/ml) that matched to within better than 10 % and 15 % respectively. The isotope measurements were carried out using established protocols (Bridgestock et al., 2014) which feature runs that start with a peak centring routine, three blocks of data acquisition each encompassing 20 five second integration cycles and a preceding 15 s determination of the electronic baselines whilst the ion beam is deflected in the electrostatic analyser. Between runs, the sample introduction system was washed with 0.1 M HNO 3 for 120 s.
The Cd isotope analyses were carried out using established methods (Ripperger and Rehkämper, 2007;Xue et al., 2012) that are similar to those used for Zn. In brief, the ion beams of 111 Cd, 112 Cd, 113 Cd, and 114 Cd were monitored for data acquisition, whilst 115 In and 117 Sn ion beams were measured for interference corrections using Faraday collectors with 10 11 X resistors. Instrumental sensitivity for Cd was typically 200-300 and 600-700 V/(lg/ml) for the Nu Plasma HR-ICP-MS and the Nu Plasma II, respectively. The sample analyses were carried out with Cd solutions of 70 ng/mL (with lower levels employed for a few samples with limited Cd) in 0.1 M HNO 3 relative to matching standards that were prepared as mixtures of NIST SRM 3108 Cd (Abouchami et al., 2013) with the Cd double spike. The Cd stable isotope compositions of the samples are expressed as d 114 Cd values relative to the NIST SRM 3108 Cd isotope reference material (Abouchami et al., 2013): Following the mass spectrometric measurements, the reduction of the double spike data was carried out offline using an iterative approach, which corrects for both the monitored isobaric interferences and any laboratory-or instrument-induced mass discrimination (Arnold et al., 2010;Xue et al., 2012). If a sample was only analysed once, the quoted uncertainties of the Zn and Cd isotope data (Table 1) represent the (external or between-run) 2SD precision obtained for multiple analyses of the bracketing isotope standards (AA-ETH Zn or NIST SRM 3108 Cd) in the same measurement session. For samples that were analysed more than once (Table 1), the quoted uncertainties are the average between-run 2SD precision of the individual isotopic runs. The 2SD between-run uncertainties for both repeated sample and standard runs in a measurement session were ±0.01 to ± 0.09 ‰ for d 66 Zn, and ±0.02 to ±0.13 ‰ for d 114 Cd. These values are similar to the within-run (internal) 2SE uncertainties of individual measurements, which were between ±0.03 and ±0.07 ‰ for d 66 Zn, and ±0.03 and ±0.13 ‰ for d 114 Cd. In the following, all quoted errors for isotope data represent 2SD uncertainties, unless otherwise stated.
The Zn and Cd concentrations were determined using the isotope dilution technique, which utilised the measured and massbias corrected 67 Zn/ 68 Zn and 111 Cd/ 114 Cd ratios of the spiked sample solutions. Total blanks of the analytical procedures were 0.7 to 1.3 ng for Zn and 0.2 to 20 pg for Cd. Higher blanks of 1.2 to 5.3 ng Zn and of 46 to 123 pg Cd were encountered when Parr bombs were employed in the acid digestion of samples. However, in no case did the blanks reach levels exceeding 1.8 % and 0.3 % of the indigenous Zn and Cd present in samples, respectively, and typical blank contributions were much lower at <0.1 %. The measured concentrations were adjusted for the minor blanks but no blank corrections were applied to the isotopic data, as the Zn and Cd isotope compositions of the blanks were not well-defined and the blank corrections were insignificant given the other analytical uncertainties of the data.

Results for quality control and reference material samples
The secondary London Zn isotope reference material was routinely analysed alongside samples throughout this study, yielding d 66 Zn = 0.09 ± 0.05 ‰ (n = 45), consistent with previous measurements (Arnold et al., 2010;Larner and Rehkämper, 2012;Moore et al., 2017). Similarly, repeated analyses of the BAM-I012 Cd isotope reference material yielded a mean of d 114 Cd = -1.33 ± 0.07 ‰ (n = 59), in excellent agreement with earlier measurements (Abouchami et al., 2013;Murphy et al., 2016). Furthermore, multiple analyses of the USGS reference materials AGV-2, BCR-2, BHVO-2 and BIR-1a yielded precise Zn and Cd isotope composition and concentration data that are consistently in good agreement with previously published results (Table 1; Tables S3,  S4, Supplementary Material). Notably, the Zn and Cd isotope data compiled for BHVO-2 show more scatter than the results obtained for the other rock reference materials, and this may be indicative of minor sample heterogeneity in the BHVO-2 powder.

Zinc isotope and concentration data
The lherzolites display a narrow range in d 66 Zn values, from 0.22 to 0.25 ‰, with Zn concentrations between 44 and 51 lg/g, whilst the harzburgites display an even smaller d 66 Zn range from 0.12 to 0.16 ‰, with 40 to 43 lg/g of Zn (Fig. 1a, Table 1). The ODP Hole 895D and 895E Hess Deep dunites are characterised by Zn contents of 66 and 46 lg/g, respectively, and d 66 Zn of 0.10 and 0.11 ‰.
The MORBs and OIBs also display significant Zn isotope variability, with d 66 Zn values of 0.21 to 0.44 ‰ and 0.20 to 0.40 ‰, respectively. Both the MORBs and OIBs are characterised by similar Zn concentrations of 43 to 166 lg/g for the former and 67 to 152 lg/g for the latter. The loess samples, which characterise the continental crust, display d 66 Zn values ranging from 0.18 to 0.28 ‰, with Zn concentrations between 40 and 80 lg/g (Fig. 1a, Table 1).

Cadmium isotope and concentration data
The d 114 Cd values of the peridotites, except for Cameroon Line spinel lherzolites P13 and C273Q, fall between -0.16 and 0.10 ‰, with the harzburgites and dunites displaying lower Cd concentrations, of 11 to 16 ng/g and 5 to 14 ng/g, respectively, than the lherzolites, which have 15 to 36 ng/g Cd (Fig. 1b, Table 1). Lherzolite xenoliths P13 and C273Q display more fractionated d 114 Cd values of 0.87 ± 0.03 ‰ and -0.29 ± 0.05 ‰, respectively, that are coupled with higher Cd concentrations of about 42 ng/g. The d 114 Cd values of the komatiites vary from -0.33 to 0.12 ‰, with Cd contents of 47 to 77 ng/g. Compared to the komatiites, both MORBs (with 71 to 162 ng/g Cd, except SO157 63 DS-1 with 302 ng/g Cd) and OIBs (76 to 182 ng/g Cd) have higher Cd concentrations. The data acquired for the MORB and OIB samples (except for Réunion basalt RE 114) also display similar d 114 Cd ranges, of about 0.00 to 0.24 ‰ and -0.04 to 0.26 ‰, respectively, (Fig. 1b,  Table 1). Together, the MORBs and OIBs define an average oceanic basalt d 114 Cd of 0.13 ± 0.12 ‰ (n = 21), broadly consistent with previous analyses of basalts (Schmitt et al., 2009;Liu et al., 2019). The Réunion basalt RE 114 is strongly enriched in heavy Cd isotopes relative to the other basalts of this study, with a mean d 114 Cd = 0.50 ± 0.05 ‰. In comparison, the RE 114 olivine separate is depleted in Cd relative to the bulk sample (22 ng/g versus 80 ng/ g) and features a lower d 114 Cd of 0.18 ± 0.04 ‰ (Fig. 1b, Table 1). Most of the loess sediments have d 114 Cd values between -0.05 and 0.23 ‰, with the exception of Lingtai sample B0020 (L9), which is characterised by d 114 Cd = -0.30 ± 0.10 ‰ (2SD). The Cd concentrations of the loess range from 95 to 262 ng/g.

The Zn and Cd isotope composition of the upper continental crust
Previous work has shown that analyses of loess can provide useful constraints on the average elemental and isotope composition of the upper continental crust. Whilst many loess samples reveal signs of chemical weathering it was also shown that even soluble elements, such as Rb and Cs, are typically not depleted in loess due to alteration (Taylor and McLennan, 1985;Gallet et al., 1998;Rudnick and Gao, 2014). Loss of Zn and Cd from loess by weathering is, furthermore, not expected to be associated with severe isotopic effects. In detail, soil formation was found to be associated either with no significant Zn isotope fractionation or, in strongly weathered soils, loss of isotopically heavy Zn (Bigalke et al., 2010;Opfergelt et al., 2017;Little et al., 2019). For Cd, soil profiles revealed preferential removal of isotopically heavy Cd from the soils to fluids (Imseng et al., 2018;Barraza et al., 2019). In the following, the data acquired in this study for European and Asian loess (Fig. 1, Table 1) are evaluated to characterise the Zn and Cd isotope compositions of the upper continental crust.
The loess samples of this study give a mean d 66 Zn of 0.23 ± 0.07 ‰ (2SD, n = 9). The observation that the 2SD of the average is only slightly larger than the typical analytical error (of ±0.05 ‰), suggests that isotopic effects from secondary alteration are either absent or minimal. Notably, the loess average overlaps with the d 66 Zn data obtained for the igneous crustal rocks AGV-2 (0.28 ± 0.03 ‰) and BCR-2 (0.28 ± 0.06) and is identical, within error, to the published 'lithogenic' Zn isotope value of d 66 Zn = 0.2 7 ± 0.14 ‰, which Little et al. (2016) calculated from data for 50 crustal igneous rocks, sediments and aerosols. The loess data are, furthermore, indistinguishable from a recent lower continental crust d 66 Zn estimate of 0.28 ± 0.04 ‰ (95 % SE), as defined by lower crustal xenoliths and granulite terrains from the North China Craton . Together, these observations suggest that the Zn isotope composition of the continental crust is relatively homogeneous, on both a global basis and with depth, and similar to that of mantle-derived basalts (Fig. 1).
For Cd, 11 of the 13 analysed loess samples have a limited range of Cd isotope compositions, with d 114 Cd of between -0.05 ± 0.03 ‰ and 0.10 ± 0.09 ‰ (Table 1). In contrast, Lingtai loess B0020 (L9) from the Chinese Loess Plateau (CLP) and Moldovian loess sample 2-8.10 are characterized by d 114 Cd values of -0.30 ± 0.10 ‰ and 0.23 ± 0.11 ‰, respectively. Notably, some loess sequences from the central CLP experienced particularly extensive pedogenic processing (Chen et al., 1997;Ding et al., 1999), which may be associated with preferential loss of heavy Cd isotopes (Imseng et al., 2018;Barraza et al., 2019). The origin of the heavy Cd isotope composition of loess 2-8.10 is unclear but could reflect an unusual d 114 Cd value for the precursor rocks and/or preferential loss of sulphides enriched in isotopically light Cd. Excluding samples B0020 (L9) and 2-8.10, the Asian and European loess samples define an average d 114 Cd = 0.04 ± 0.09 ‰ (2SD, n = 11), in good agreement with three loess analyses of Schmitt et al. (2009). Combining the loess data of this study (Table 1) and Schmitt et al. (2009) gives a mean d 114 Cd of 0.03 ± 0.10 ‰ (2SD, n = 14) for the upper continental crust, in excellent agreement with a previous upper continental crust estimate of 0.05 ± 0.10 ‰ that was based on continental sulphides (Schmitt et al., 2009;Rehkämper et al., 2011).

The Zn isotope compositions of peridotites
The lherzolites from the Cameroon Line and the Horoman peridotite massif define a mean d 66 Zn of 0.23 ± 0.03 ‰ (2SD, n = 6) and the data resemble results obtained for lherzolites from the North China Craton (Wang et al., 2017) and the Italian Alps (Huang et al., 2018a) (Fig. 1a, Tables 1, 2). In comparison, slightly lighter Zn isotope compositions were determined for lherzolites from the Balmuccia lherzolite massif (Sossi et al., 2018). The lherzolites analysed here have Zn concentrations of about 44 to 51 lg/g and are thus slightly depleted in Zn relative to BSE estimates of about 54 lg/g Zn (McDonough and Sun, 1995;Wang et al., 2018), likely attesting to minor melt depletion during their formation (Lee et al., 1996;Takazawa et al., 1996;Yoshikawa and Nakamura, 2000). Previous studies furthermore indicate that Cameroon Line and Horoman peridotites were subject to variable, but generally light to moderate, metasomatism (Takazawa et al., 1992;Lee et al., 1996;Takazawa et al., 1996;Anguelova et al., 2022), and in the case of the latter, re-enrichment by sulphides (Rehkämper et al., 1999a). The limited variability of our lherzolite Zn isotope compositions and the lack of significant Zn isotope effects relative to many previously analysed lherzolites suggests that such processes, as well as surficial weathering, had little impact on the d 66 Zn values of the Cameroon Line and Horoman samples.
Compared to the lherzolites, the harzburgites from the Cameroon Line (N12) and Horoman (BZ 116) as well as the MARK Zone abyssal harzburgites are more depleted in Zn, with concentrations of 40 to 43 lg/g, and they display lower d 66 Zn values of between 0. 12 ± 0.06 ‰ and 0.16 ± 0.07 ‰ (Table 1). Similar results were obtained for other previously analysed harzburgites (Doucet et al., 2016;Wang et al., 2017) and possibly reflect extraction of an isotopically heavy melt. The Hess Deep dunites also display light Zn isotope compositions, but these samples are not true melt depletion residues, instead forming from the interaction of basaltic melts with refractory harzburgites (Allan and Dick, 1996;Edwards and Malpas, 1996). Notably, the dunites and harzburgites together define a mean d 66 Zn = 0.13 ± 0.05 ‰ (2SD, n = 6) that is significantly lower compared to the lherzolite average.

The Zn isotope compositions of komatiites
Komatiites form by extensive partial melting of the mantle at high temperatures and often record only minor fractional crystallisation and contamination by continental crust. As such, they are, in principle, suitable archives to determine the isotope compositions of Zn and other elements in the Archean mantle (McDonough and Sun, 1995;Dauphas et al., 2010;Sossi et al., 2018). The two komatiites analysed here have different d 66 Zn values, with results of 0.14 ± 0.05 ‰ for M657 from Alexo and 0.00 ± 0.05 ‰ for MT20 from Munro Township (Fig. 1, Table 1). The origin of this isotopic difference is uncertain because both samples are derived from the spinifex-textured A3 zones of their flows and both have similar Zn/Fe ratios (of $9), which are indicative of limited Zn loss or addition by secondary alteration (Sossi et al, 2018). Notably, the Alexo komatiite of this study and 12 of 13 spinifex and olivine cumulate komatiites analysed by Sossi et al.(2018) from six different localities have d 66 Zn values of between 0.14 and 0.20 ‰ (Fig. 1a, Table S5). This suggests that these samples most likely record a relatively homogeneous Archean mantle composition, with a mean of 0.18 ± 0.04 ‰ (2SD, n = 13). In contrast, a Barberton olivine cumulate komatiite of Sossi et al (2018) and sample MT 20, which was sampled from the lower (A3) part of the spinifex zone and features relatively high MgO and Ni concentrations coupled with low Cr, have much lower d 66 Zn values of or close to 0 ‰. Whilst it is conceivable the light Zn isotope signatures of the latter two komatiites reflect accumulation of olivine characterised by low d 66 Zn, such an origin is not readily reconciled with the limited Zn isotope fractionation that was inferred for magmatic systems (Sossi et al., 2018).

The Zn isotope compositions of oceanic basalts
Extending from the peridotites, the komatiites and oceanic basalts define an igneous 'mantle array' in a plot of d 66 Zn versus Zn concentration, whereby the melts feature higher Zn abundances coupled with slightly heavier Zn isotope compositions (Fig. 2a, b). The MORB and OIB samples display similar Zn isotope compositions, with a combined average d 66 Zn of 0.30 ± 0.14 ‰ (2SD, n = 17), generally consistent with previously analysed basalts (Herzog et al., 2009;Chen et al., 2013;Wang et al., 2017;Huang et al., 2018b;Beunon et al., 2020). The observed variability of basalt compositions clearly exceeds the analytical uncertainty (of about ±0.05 ‰; Table 1), presumably reflecting Zn isotope variations from both primary igneous and subsequent secondary processes.
The higher d 66 Zn values and Zn concentrations of mantle melts relative to lherzolites is mirrored by the lower d 66 Zn values and Zn concentrations of refractory harzburgites and dunites. These systematic differences most likely reflect, to a first order, isotope fractionation and incompatible behaviour of Zn during partial melting of the mantle and melt differentiation. During melting, isotopically heavy Zn preferentially partitions into the melt phase, leaving behind a more refractory and isotopically light peridotite residue that is depleted in Zn (Fig. 2a, b). Previous studies have come to similar conclusions (Doucet et al., 2016;Wang et al., 2017;Sossi et al., 2018), but the driver for isotope fractionation during partial melting remains a topic of debate. Wang et al. (2017) measured elevated d 66 Zn in spinel separates from multiple peridotites but found no significant differences in the d 66 Zn values of olivine, clinopyroxene and orthopyroxene or any significant correlation between peridotite d 66 Zn and extracted melt fraction or pressure of equilibration. Based on non-modal fractional melting models, Wang et al. (2017) showed that the observed isotope fractionations could result from consumption of isotopically heavy spinel during the melting process. Sossi et al. (2018) argued, however, that spinel abundances in lherzolites are too low to act as a significant control on peridotite d 66 Zn. In contrast, they suggested that Zn isotope fractionation is controlled by differences in the coordination number of Zn in olivine (octahedral coordination) and melt (tetrahedral coordination), whereby the latter is enriched in isotopically heavy Zn due to the stronger Zn-O bonding. Fig. 2a confirms that Zn is incompatible during mantle melting. This is in accord with previous studies, which inferred bulk solidliquid distribution coefficients, D Zn , of between about 0.6 and 1.0 for the partitioning of Zn during melting of peridotites (Le Roux et al., 2011;Davis et al., 2013;Wang et al., 2017;Sossi et al., 2018;Beunon et al., 2020). Based on the inter-mineral fractionations observed by Wang et al. (2017), Sossi et al. (2018) inferred a mantle-melt Zn isotope fractionation of D 66 Zn mantle-melt = -0.07 ‰ , whilst Chen et al. (2013) concluded that Zn isotope fractionation during high-temperature magmatic differentiation is unlikely to exceed ± 0.10 ‰, based on analyses of volcanic rocks from Kilauea Iki lava lake and Hekla volcano. Notably, similar estimates of D Zn = 0.75 and D 66 Zn mantle-melt = -0.03 ± 0.09 ‰. were obtained in this study, based on the assumption that the partitioning of Zn between mantle and continental crust is governed by magmatic processes (Hofmann, 2014;see Supplementary Materials).
The results of simple, illustrative batch melting and (subsequent) fractional crystallisation calculations (see Supplementary Materials) are superimposed onto the global peridotite and mantle melt data of Fig. 2b. The modelling assumes an initial mantle source with 54 lg/g Zn (McDonough and Sun, 1995;Wang et al., 2018) and d 66 Zn = 0.20 ‰ and employs parameters of D Zn = 0.7 and D 66 Zn mantle-melt = -0.07 ‰, in accord with available constraints. Notably, the calculated igneous trends demonstrate that, to a first order, the variable Zn isotope compositions and concentrations of the global mantle array seen in Fig. 2a, b can be explained by partitioning of mildly incompatible Zn into the melt phase during igneous processes and associated enrichment of isotopically light Zn in the melt.
The significant scatter of data within and about the trend of Fig. 2a, b is readily explained by additional primary and secondary processes. The variable Zn concentrations and isotope compositions exhibited by OIBs may reflect melting of more fertile mantle reservoirs that were enriched by admixing of eclogitic oceanic crust (Beunon et al., 2020) or possibly fluids expelled from dehydrating ocean crust in subduction zone settings. Similarly, mantle heterogeneities associated with contamination by subducted carbonate sediments can cause large shifts in the Zn isotope compositions of mantle melts (Liu et al., 2016;Liao et al., 2020), whilst some degree of Zn isotope heterogeneity may also have developed in the mantle by millions of years of melt depletion (Wang et al., 2017;Zhu et al., 2021). Depth dependant changes in mineralogy may further impact D Zn and D 66 Zn mantle-melt values, causing further scatter in Fig. 2a, b. In particular, previous studies hint at a possible decrease in the D Zn of olivine, pyroxenes, and garnet, and an increase for spinel, at higher temperatures (Horn et al., 1994;Adam and Green, 2006;Le Roux et al., 2011;Davis et al., 2013). Secondary processes, including fluid exsolution, serpentinization, as well as metasomatism and melt percolation with associated Zn transfer (Telus et al., 2012;Wang et al., 2017;Huang et al., 2018a;Huang et al., 2019) can also generate Zn isotope fractionations that may be equal to or greater than those resulting from magmatic processes. Notably, despite these many potential avenues for generating Zn isotope variability, the generated variations are relatively small such that the igneous array remains fairly well defined.

The Zn isotope composition of the bulk silicate Earth
The average d 66 Zn values of the Horoman and Cameroon Line lherzolites and results for previously studied lherzolite localities are combined in the following to obtain a new estimate for the d 66 Zn of the BSE (Table 2). This estimate does not include results for harzburgites and dunites, as their d 66 Zn values may be impacted by melt depletion even though current melting models do not predict significant Zn isotope fractionation in peridotite residues for up to 30 % melt extraction (Sossi et al., 2018). Our preferred d 66 Zn BSE estimate is obtained by averaging the mean Zn isotope data determined for lherzolites from five distinct localities, with each characterised by at least two samples. In addition, the compilation includes the d 66 Zn value of 0.20 ± 0.03 ‰ determined for the Baffin Island parental mantle reservoir by McCoy-West et al. (2018). However, the fertile Vitim and Tariat off-craton lherzolites of Doucet et al. (2016) are excluded from our preferred d 66 Zn BSE estimate, as these rocks display unusually high d 66 Zn values of about 0.3 ‰ and the origin of this heavy Zn isotope signature is unclear. Together, the selected localities define a d 66 Zn BSE of 0.20 ± 0.05 ‰ (2SD; Table 2), consistent with previous BSE estimates (Wang et al., 2017;Sossi et al., 2018). However, inclusion of the Doucet et al. (2016) data produces only a marginally higher d 66 Zn BSE value of 0.22 ± 0.08 ‰ (2SD; Table 2).
Notably, our new d 66 Zn BSE value overlaps with the mean d 66 Zn = 0.18 ± 0.04 ‰ (2SD, n = 13) determined for komatiites. This latter average, which is based on the data for spinifex-textured and olivine cumulate komatiites of Sossi et al. (2018) and the Alexo komatiite M657 of this study, should approximate the Zn isotope composition of the Archean mantle. The close overlap of the komatiite mean with the peridotite-based d 66 Zn BSE estimate suggests that the Zn isotope composition of the mantle remained relatively constant since the Archean, as previously inferred by Sossi et al. (2018).

The Cd isotope compositions of peridotites
The Cd isotope compositions of the peridotites are more variable than those of Zn, both overall and for individual localities (Fig. 1a, b, Table 1). In particular, the Cameroon Line spinel lherzolites P13 and C273Q exhibit strongly fractionated Cd isotope compositions of 0.87 ± 0.03 ‰ and -0.29 ± 0.05 ‰, respectively. In contrast, the remaining spinel lherzolites from the Cameroon Line, the Horoman Massif and Kilbourne Hole (termed 'undisturbed' in the following) display a narrow range of d 114 Cd values with a mean of -0.06 ± 0.03 ‰ (2SD, n = 4), whereas the Horoman plagioclase lherzolite has a much higher d 114 Cd of 0.10 ± 0.05 ‰. Furthermore, a single harzburgite has a d 114 Cd, of -0.08 ± 0.05 ‰, which resembles the undisturbed spinel lherzolites, whereas three others have significantly heavier isotope compositions, with d 114 Cd values of between 0.05 ± 0.05 ‰ and 0.10 ± 0.04 ‰. Finally, the three dunites from the Hess Deep and Twin Sisters have negative d 114 Cd values of -0.14 ± 0.05 ‰ to -0.02 ± 0.05 ‰, similar to the spinel lherzolites (Fig. 1, Table 1).
Whilst the variable d 114 Cd values observed for peridotites are difficult to understand in detail, the Cd concentrations show more straightforward systematics. In particular, the lherzolite Cd concentrations are on average (31 ± 10 ng/g; 1SD, n = 9) about 3x higher than those of the harzburgites and dunites (11 ± 4 ng/g; 1SD, n = 7), and slightly lower than, but still within uncertainty of, previous BSE estimates of about 38 ng/g (McDonough and Sun, 1995;Witt-Eickschen et al., 2009;Wang et al., 2018). This difference is, at least in part, most likely a consequence of melt extraction with associated depletion of Cd in the residue. Given that oceanic basalts have Cd isotope compositions that are typically either similar to or heavier compared to the 'undisturbed' spinel lherzolites of this study, melt extraction should produce mantle residues with d 114 Cd values that are similar to or lower than those of the lherzolites. In contrast, three of the four analysed harzburgites have much heavier Cd isotope compositions, which must therefore be of secondary origin (Figs. 1, 2c, d).
The Cd isotope systematics of many, if not most, peridotites studied here are hence most likely a consequence of melt extraction, with either limited or no resolvable isotope fractionation in the residue, and subsequent overprinting by one or several secondary processes. Notably, there is no clear correlation between changes in Cd isotope compositions and petrographic indicators of metasomatism and melt-rock reaction. For example, the two strongly fractionated Cameroon Line samples C273Q and P13 have the highest Cd concentrations of the peridotites analysed here, and this may indicate that the unusual Cd isotope signatures are a consequence of secondary processes that enriched the Cd abundances of the rocks. However, both samples show less petrographic and geochemical evidence of secondary alteration than peridotite P3 (Lee et al., 1996), which appears to have an unperturbed Cd isotope composition. Furthermore, samples from both the Hess Deep and MARK ODP sites were affected by melt depletion and multiple secondary processes, including melt percolation and reaction and serpentinization (Allan and Dick, 1996;Edwards and Malpas, 1996;Casey, 1997;Niida, 1997;Rehkämper et al., 1999a). Whilst the Hess Deep dunites display Cd isotope compositions generally in line with most of the Cameroon Line peridotites, the MARK harzburgites display heavy Cd isotope enrichments. This may imply that some combination of the aforementioned processes can lead to enrichments of heavy Cd isotopes in residual mantle rocks.
Of further interest is the previous conclusion that the Zn isotope compositions that were determined for a subset of the peridotites primarily record igneous processes, with little or no significant isotope effects from subsequent secondary processes and weathering. As the Cd isotope compositions of peridotites appear to be more susceptible to alteration, this indicates that secondary reactions more readily affect the ng/g-level abundances of Cd than the lg/ g concentrations of Zn. Such an explanation is viable if alteration impacts minor phases that are important hosts for Cd but not Zn or involves reactions with fluids or melts that have high Cd/Zn ratios. Notably, Zn is primarily hosted in olivine, volumetrically the most abundant mineral in peridotites, whilst Cd is concentrated in clinopyroxene, which is typically a modally minor phase. Cadmium is, furthermore, more volatile in high temperature environments than Zn (Hinkley et al., 1994;Rubin, 1997), and such mobility may also generate stable isotope effects for Cd in peridotites.

The Cd isotope compositions of komatiites
The four analysed komatiites show significant Cd isotope variability, whereby Munro Township sample MT 20 has an unusually low d 114 Cd of -0.33 ± 0.04 ‰ relative to the other rocks (Table 1). Notably, MT20 also has an atypically light Zn isotope composition that diverges from published Zn isotope data for other komatiites from Munro and other localities ( Fig. 1; Table S5). Whilst the unusual Zn isotope signature of this sample may have an igneous origin, it is unclear whether this can account for the light Cd isotope composition, for example by accumulation of olivine or possibly sulphides with low d 114 Cd. Given that the Cd isotope compositions of two peridotites were altered by >0.25 ‰ by secondary processes to both higher and lower d 114 Cd values, such an origin is also probable in this case. Weathering processes alone are an unlikely cause, however, as even strongly weathered soils typically show Cd isotope shifts of less than 0.3 ‰ (Imseng et al., 2018;Barraza et al., 2019).
The d 114 Cd values of the three remaining spinifex-textured komatiites from Alexo and Belingwe range from -0.12 ± 0.03 ‰ to 0.12 ± 0.03 ‰ (Table 1, Fig. 1b). With an isotopic variability that exceeds the analytical uncertainty by about a factor of x2 to x3, the Cd isotope compositions of these samples were likely also affected by secondary alteration. Despite this, the mean d 114 Cd value defined by the komatiites, of 0.01 ± 0.19 ‰ (2SD, n = 3), overlaps with the Cd isotope compositions of the 'undisturbed' spinel lherzolites (Fig. 1b). Notably, sample ZA-1, which is derived from the particularly fresh Belingwe komatiite flow (Nisbet et al., 1987;Chauvel et al., 1993), is characterised by an intermediate d 114 Cd value of 0.03 ± 0.05 ‰.

The Cd isotope composition of oceanic basalts
Similar to Zn, the Cd data of mantle melts define an igneous array that extends from the peridotites in a diagram of d 114 Cd versus Cd concentration (Fig. 2c, d). As for Zn, the Cd concentrations also increase from the peridotites through the komatiites to the oceanic basalts, most likely as a consequence of incompatible behaviour of Cd (Yi et al., 2000;Witt-Eickschen et al., 2009). However, the isotopic effects are less clearly defined than for Zn (Fig. 2a,  b), which at least in part reflects the greater degree of scatter in the Cd isotope data, particularly for the peridotites and komatiites. In detail, the MORB and OIB samples show a mean d 114 Cd of 0.13 ± 0. 12 ‰ (2SD, n = 16) that is slightly enriched in heavy Cd isotopes relative to the peridotites. This marginal enrichment and the isotopic variability, which clearly exceeds the analytical errors, further argue for some degree of Cd isotope fractionation during partial melting of the mantle and melt differentiation. Given that the Zn and Cd data of Fig. 2a, b and c, d, respectively, define similar trends, it is reasonable to conclude that the Cd mantle array of Fig. 2c, d is also primarily the result of incompatible behaviour and associated isotope fractionation of Cd during partial melting and fractional crystallisation.
Published constraints on the partitioning and isotope fractionation of Cd during igneous processes are significantly scarcer than for Zn. Based on analyses of MORB and OIB, Yi et al. (2000) inferred that Cd is moderately or slightly incompatible during mantle melting with a bulk mineral-melt D Cd of > 0.01. The only experimental partitioning data available constrain the distribution of Cd between mica-and amphibole-bearing garnet lherzolite and hydrous basanitic melt (Adam and Green, 2006). For clinopyroxene, garnet, orthopyroxene and spinel, the latter study determined , with the reasonable assumption that spinel has no bearing on the partitioning of Cd (Witt-Eickschen et al., 2009). Notably, a similar D Cd value of about 0.48 can be inferred for mantle melting from the Cd concentration ratio of the BSE versus the continental crust (Hofmann, 2014; see Supplementary Materials for details). Furthermore, Fig. 3a shows that the BSE-normalised concentrations of Cd and Zn are positively correlated across mantle melts and peridotites, indicating that the two elements behave similarly during igneous processes. The more rapid increase of Cd versus Zn concentrations in mantle melts (with a slope of about 2) thereby suggests that the former element is more incompatible than the latter, with D Cd /D Zn % 0.5. Assuming D Zn = 0.7 (Sossi et al., 2018;Beunon et al., 2020) this yields D Cd = 0.35, in accord with our estimate derived from mineral-melt D values.
As of yet, there are no published constraints on Cd isotope fractionation during partial melting of the mantle and subsequent melt differentiation. Fig. 3b shows that whilst there is a small but well-resolved difference in d 66 Zn between peridotites and mantle melts, such a difference is not clearly resolved for Cd isotopes. Using the inferred compositions of the continental crust (d 114 Cd = 0.03 ± 0.10 ‰) and the BSE (d 114 Cd = -0.06 ± 0.03 ‰; see below), a D 114 Cd mantle-melt of -0.09 ± 0.10 ‰ can be estimated for partial melting of the mantle, in accord with the previous conclusion that isotope fractionation during igneous processes generates either a small or negligible enrichment of heavy Cd isotopes in mantle melts (Hofmann, 2014; see Supplementary Materials for details). Unfortunately, the large range of d 114 Cd values exhibited by peridotites and basalts limits any further inferences about the extent and origin of Cd isotope fractionation during igneous processes.
Importantly, the results of the batch melting and fractional crystallisation calculations confirm that the global Cd isotope systematics observed for peridotites and mantle basalts most likely primarily reflect melting and melt differentiation of mantle material. The modelling presented in Fig. 2c, d uses a mantle source composition with 38n/g Cd and d 114 Cd = -0.06 and employs reasonable parameters of D Cd = 0.35, such that Cd is marginally more incompatible than Zn, and D 114 Cd mantle-melt of -0.09 ‰. It is noted, however, that the modelling results of Fig. 2 are only presented for illustration, particularly because the simple calculations do not consider differences in melt source compositions and the dynamics of partial melting and melt differentiation, all factors that will invariably generate significant scatter about and beyond the petrogenic trends shown in Fig. 2.
Additional scatter is furthermore expected for the Cd data of mantle melts as a result of secondary processes, particularly given the significantly lower Cd concentration of igneous rocks compared to Zn. Of particular relevance is magmatic outgassing of volatile Cd and associated isotope fractionation in oceanic basalts. Prytulak et al. (2013) found a Mariana arc lava that was anomalously enriched in heavy Tl isotopes, which they attributed to volcanic degassing. A number of studies have furthermore shown that Cd is amongst the elements that are most efficiently lost from silicate melts during magmatic outgassing and most strongly enriched in volcanic gases (Hinkley et al., 1994;Rubin;MacKenzie and Canil, 2008;Norris and Wood, 2017;Sossi et al., 2019;Zelenski et al., 2021). Such outgassing and associated isotope fractionation may hence be responsible for the unusually high d 114 Cd value of Réunion Island basalt RE 114 (Table 1). Notably, the large Cd isotope difference of >0.3 ‰ between the RE 114 whole rock (d 114 Cd = 0.50 ± 0.05 ‰) and olivine phenocrysts from this sample (d 114 Cd = 0.18 ± 0.04 ‰) is unlikely to record equilibrium isotope fractionation during differentiation, given the limited extent of Cd isotope fractionation that was inferred for igneous processes (with D 114 Cd mantle-melt < 0.2 ‰). Rather, the heavy Cd isotope composition of RE 114 is most likely due to loss of volatile Cd and with preferential loss of light Cd isotopes during open system degassing of the magma. In contrast, the lighter Cd isotope composition of the RE 114 olivine separate reflects olivine fractionation prior to Cd degassing and associated isotope fractionation. The RE 114 olivine is also depleted in Cd relative to the whole rock (22 versus 80 ng/g), confirming that Cd is moderately incompatible in olivine relative to melt.

The Cd isotope composition of the bulk silicate Earth
The data obtained for peridotites and mantle melts indicate that igneous processes generate at most minor Cd isotope fractionations. As such, a straightforward estimate for the d 114 Cd value of the BSE can be determined from the overall mean determined for all peridotites, including the harzburgites and dunites, but excluding the most anomalous samples C273Q and P13. This approach gives a d 114 Cd BSE of -0.02 ± 0.15 ‰ (2SD, n = 12), A more precise and robust BSE estimate can be obtained, however, from the results obtained for four 'undisturbed' spinel lherzolites from three localities, which define a mean d 114 Cd BSE value of -0.06 ± 0.03 ‰ (2SD). This d 114 Cd BSE estimate is preferred because it is based on data that was at most marginally effected by Cd mobilisation and isotope fractionation during secondary alteration of the rocks.
Our result is in good agreement with a previous BSE estimate of -0.03 ± 0.10 ‰ (Schmitt et al., 2009;Rehkämper et al., 2011) but is more robust because it does not rely on data for oceanic basalts or samples from the continental crust, which may be biased by any isotope fractionation that occurs during partial melting and melt differentiation. Notably, our d 114 Cd BSE estimate is also within error of the komatiite d 114 Cd mean of 0.01 ± 0.19 ‰ (2SD, n = 3), which excludes anomalous sample MT20. Assuming that the komatiite average is representative of the Archean mantle, this would indicate that the Cd isotope composition of the silicate Earth remained nearly constant through time. However, the komatiite mean has a large error, such that the conclusion is subject to significant uncertainty.

Zinc and Cd stable isotopes in comparison to chondritic meteorites
Whilst there is considerable debate about the timing and nature of Earth's volatile delivery, the majority of investigations concur that volatile species were most likely added in the later stages of accretion by material that was akin in composition to carbonaceous or enstatite chondrites or a mixture of both (Albarède, 2009;Wood et al., 2010;Fischer-Gödde et al, 2020). To further assess the provenance of terrestrial volatiles, it is of interest to compare the BSE Zn and Cd isotope compositions with data for chondritic meteorites from published investigations (Fig. 4). In a plot of d 66 Zn versus Zn concentrations, the majority of carbonaceous chondrites define a clear trend that extends from volatile rich CI chondrites with d 66 Zn % 0.45 ‰, through CM and CV to more volatile depleted CO and CR chondrites with lower d 66 Zn (Fig. 4a). Although many enstatite and ordinary chondrites are in accord with this trend, some samples display significant deviations to both higher and lower d 66 Zn values. The latter deviations are thought to relate to parent body rather than nebular processes, particularly volatile mobility induced by thermal or shock metamorphism (Luck et al., 2005;Moynier et al., 2011). As such, the trend defined by the majority of the carbonaceous chondrites has been interpreted to reflect processes in the protosolar disk, such as variable mixing of meteoritic components (Luck et al., 2005;Pringle et al., 2017).
Published results for Zn (Bridgestock et al., 2014;Mahan et al., 2017) demonstrate that isotope fractionation during metal-silicate partitioning, and hence core formation, is either negligible or nearly so. As such, the d 66 Zn BSE value of 0.20 ± 0.05 ‰ is also directly relevant for the bulk Earth (BE). Using a BE Zn concentration of 70 ± 18 lg/g (Mahan et al. (2018), the BE plots along the volatile depleted end of the nebular Zn trend defined by carbonaceous chondrites (Fig. 4a), as previously shown by Sossi et al. (2018). This suggests that Earth's volatile inventory may well have been provided by material resembling carbonaceous and/or enstatite chondrites as well as bulk material from ordinary chondrite parent bodies. However, assuming that no further Zn isotope fractionation took place during accretion, the d 66 Zn value of the BSE and BE is not in accord with models which posit that volatiles were delivered to Earth solely by CI-or CM-like material, as there is a small but significant difference in the Zn isotope compositions of these chondrite groups compared to the BSE. Instead, Earth's Zn isotope signature closely resembles more volatile depleted CV and CO chondrites.
For Cd, the BE estimate uses a concentration of 80 ± 21 ng/g, which implies that the majority of the BE Cd inventory ($70 %) is concentrated in the core (Wang et al. (2018). It furthermore assumes that the Cd isotope compositions of the BE and BSE are identical, with d 114 Cd = -0.06 ± 0.03 ‰, due to lack of metalsilicate isotope fractionation during core formation (Fig. 4b).
Whilst experimental evidence for the latter inference is currently lacking, the assumption is reasonable, given the absence of Zn isotope fractionation during metal-silicate partitioning. A 'nebular' trend, as defined for Zn by the data of carbonaceous chondrites in Fig. 4a is not clearly apparent in the Cd plot of Fig. 4b, due to the paucity of published high precision Cd isotope data for meteorites and the scatter in the available results. Furthermore, the Cd isotope compositions of meteorites are more readily altered by volatilisation than Zn isotopes and chondritic d 114 Cd values that fall outside the range of about 0.2 to 0.5 ‰ are thought to reflect isotope fractionation during parent body processing (Wombacher et al., 2003;Wombacher et al., 2008;Palk et al., 2018).
The data shown in Fig. 4b hence suggest that d 114 Cd BSE , and therefore the inferred d 114 Cd BE value, are about 0.2 ‰ lower compared to the lightest Cd isotope compositions recorded for carbonaceous and enstatite chondrites. There are a number of reasonable explanations for this discrepancy. First, the limited currently available Cd isotope data for chondrites may be biased toward d 114 Cd values that are too high on average. Second, it is possible that Earth acquired its Cd inventory from chondritic meteorites but that subsequent processes fractionated the Cd isotope composition of the BE or BSE during accretion. Loss of Cd by volatilisation from an early terrestrial magma ocean or partial recondensation of volatilised Cd following the giant impact are, however, expected to generate an Earth with a heavy Cd isotope composition relative to chondrites. Volatility-related Cd isotope fractionations are hence unlikely to be responsible for the low d 114 Cd of the BSE. Fractionation of Cd isotopes during core formation provides a reasonable alternative mechanism, especially as a smaller fraction of the BE Cd inventory is inferred to be present in the BSE than for Zn, possibly due to late segregation of a sulphide melt to the core (O'Neill, 1991;Savage et al., 2015;Wang et al., 2018). Experimental evidence for Cd isotope fractionation during core formation, which confirms or rebuts this conclusion is not available at present, however. Finally, as suggested previously for Zn (Sossi et al., 2018), it is conceivable that the terrestrial budget of Cd was partly provided by material which had a lower d 114 Cd compared to the known compositions of carbonaceous and enstatite chondrites that are unaffected by metamorphic alteration. If correct, this may imply that a significant portion of Earth's Cd and other volatile elements may have been sourced from a reservoir that is not related to known carbonaceous and enstatite chondrites. However, considering the current uncertainties, the origin and significance of the observed offset in d 114 Cd between the BSE and carbonaceous and enstatite chondrites remains to be resolved by further investigations.

Conclusions
The Zn and Cd isotope compositions of a comprehensive suite of diverse terrestrial rocks were determined to constrain the extent of Zn and Cd isotope fractionation during magmatic processes and to better define the d 66 Zn and d 114 Cd values of the silicate Earth.
Results obtained for spinel lherzolites provide a d 114 Cd BSE value of -0.06 ± 0.03 ‰ (2SD). For Zn, the lherzolite data of this study are combined with literature results to define a d 66 Zn BSE value of +0.20 ± 0.05 ‰ (2SD), in accord with previous BSE estimates (Wang et al., 2017;Sossi et al., 2018). Data obtained for komatiites are in accord with the d 114 Cd BSE and d 66 Zn BSE estimates, which suggests that both mantle isotope compositions are broadly unchanged since the Archean. Analyses of loess as well as continental igneous rocks furthermore yield upper continental crust compositions of d 114 Cd = 0.03 ± 0.10 ‰ and d 66 Zn = 0.23 ± 0.07 ‰.
The Zn data available for peridotites and oceanic basalts define a mantle array, with basalts having higher Zn concentrations and higher d 66 Zn than the peridotites. These systematics imply that Zn is slightly incompatible during mantle melting and melt differentiation, with associated enrichment of heavy Zn isotopes in the melt phase. Cadmium is marginally more incompatible than Zn during partial mantle melting and MORB and OIB samples generally display minor enrichments of heavy Cd isotopes relative to peridotites. However, secondary processes including magmatic volatilisation, metasomatism and weathering can generate Cd isotope variability in both mantle melts and peridotites, obscuring the primary array produced by mantle melting.
The d 66 Zn BSE estimates of this and previous studies resemble the Zn isotope compositions of CV and CO carbonaceous and some enstatite chondrites. Given the negligible Zn isotope fractionation during core formation, this overlap is consistent with delivery of Zn and other similarly volatile elements to Earth solely by material related to carbonaceous, enstatite and/or ordinary chondrites. Conversely, the BSE has a lower d 114 Cd value compared to known enstatite and carbonaceous chondrites. This implies that either the Cd isotope signature of the BSE was altered during accretion and/or core formation or that Earth accreted material with a Cd isotope composition that is not recorded in hitherto analysed carbonaceous and enstatite chondrites. Importantly, delivery of Zn and Cd solely by CI and CM chondrites is not in accord with the terrestrial stable isotope compositions of both elements.

Data availability
Data will be made available on request.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Supplementary Text: Extended Methods -Modelling trace element concentrations and stable isotope compositions for batch melting and fractional crystallisation. Estimation of D Zn , D Cd and D 66 Zn mantle-melt , D 114 Cd mantle-melt values based on the Zn, Cd concentrations and isotope compositions of the BSE and continental crust. Supplementary Tables. Table S1 Column chemistry for the separation of Zn from silicate rock and meteorite samples.