Iron and Carbon Isotope Constraints on the Formation Pathway of Iron-Rich Carbonates within the Dagushan Iron Formation, North China Craton

: Banded iron formations (BIFs) are enigmatic chemical sedimentary rocks that chronicle the geochemical and microbial cycling of iron and carbon in the Precambrian. However, the formation pathways of Fe carbonate, namely siderite, remain disputed. Here, we provide photomicrographs, Fe, C and O isotope of siderite, and organic C isotope of the whole rock from the ~2.52 Ga Dagushan BIF in the Anshan area, China, to discuss the origin of siderite. There are small magnetite grains that occur as inclusions within siderite, suggesting a diagenetic origin of the siderite. Moreover, the siderites have a wide range of iron isotope compositions ( δ 56 Fe Sd ) from − 0.180‰ to +0.463‰, and a relatively negative C isotope composition ( δ 13 C Sd = − 6.20‰ to − 1.57‰). These results are compatible with the reduction of an Fe(III)-oxyhydroxide precursor to dissolved Fe(II) through microbial dissimilatory iron reduction (DIR) during early diagenesis. Partial reduction of the precursor and possible mixing with seawater Fe(II) could explain the presence of siderite with negative δ 56 Fe, while sustained reaction of residual Fe(III)-oxyhydroxide could have produced siderite with positive δ 56 Fe values. Bicarbonate derived from both DIR and seawater may have provided a C source for siderite formation. Our results suggest that microbial respiration played an important role in the formation of siderite in the late Archean Dagushan BIF.


Introduction
Banded iron formations (BIFs) are chemical sedimentary rocks composed of iron-rich (total iron >15 wt.%) and silica-rich bands [1][2][3] that were commonly precipitated during the Archean and Paleoproterozoic. BIFs reflect not only the massive extent of iron (Fe) cycling and deposition during the Precambrian, but they also record critical information about ancient seawater geochemistry and the different (bio)chemical pathways through which the atmosphere-biosphere-hydrosphere systems have been linked throughout Earth's history [4][5][6][7]. Four mineralogical end-member facies of BIF have been described based on the characteristic Fe-bearing mineral assemblages, including (i) oxides (hematite, magnetite), (ii) carbonates (siderite, ankerite), (iii) silicates (e.g., greenalite, cummingtonite, grunerite), and (iv) sulfides (pyrite). Sulfide facies is not generally used to study sedimentary environments, as it is composed mainly of pyritic carbonaceous shale or slate and does not represent a chemical precipitate [2,3,8]. The abundance and distribution of these facies have been used to infer environmental conditions during deposition and subsequent sedimentary-diagenetic-metamorphic evolutionary processes [1][2][3]8].
Amongst these four facies, the carbonate facies provide the most valuable insights on the origin and coupled cycling of Fe and carbon (C) in BIFs [9]. Siderite is the major Fe-rich component in the carbonate facies of BIFs and its formation requires anoxic, ferruginous conditions, high alkalinity, and low sulfate concentrations [10][11][12]. Despite significant scientific interest and research, there is still no consensus on the origin of siderite, and two main formation pathways are proposed [13][14][15][16][17][18][19]. First, in Archean oceans where Fe(II) and HCO 3 − concentrations would have been high and the prevailing redox conditions were reducing [20][21][22][23], the direct precipitation of siderite from seawater may have been feasible [13,22,24,25]; however, Jiang and Tosca [26] have suggested that seawater siderite precipitation may have been kinetically unfavorable. Seawater-like carbon isotopes (δ 13 C~0‰) of siderite in some BIFs have been taken as evidence to support this direct precipitation pathway [25,27]. Second, microbial dissimilatory iron reduction (DIR) during early diagenesis has been shown to be a viable formation pathway for siderite formation based primarily on the relatively negative δ 13 C and highly variable δ 56 Fe values of many siderites, as well as experimental simulations [16,[28][29][30][31][32][33]. In particular, siderites in thẽ 2.5 Ga Brockman Iron Formation in Hamersley, Australia [30] and in the BIFs of thẽ 3.8 Ga Isua Supracrustal Belt, Greenland [31] are proposed to have been precipitated through DIR. Moreover, siderites have also been suggested to form through the ageing and transformation of green rust [34] and through the reaction of Fe(III) minerals and organic carbon (C org ) at elevated burial temperatures and pressures (e.g., ≥170 • C and ≥1.2 kbar) [17,19,35]. Interestingly, siderites are generally more common in Superior-type than Algomatype BIFs, which may reflect the commonly lower metamorphic grade in Superior-type BIFs. An exception to this is the Dagushan BIF (~2. 53-2.51 Ga) in the Anshan area, North China Craton (NCC), where siderites are widely distributed. The Dagushan BIF is the first Algoma-type BIF to be reported that has retained a series of relatively integrated depositional facies, including carbonate, oxide, and silicate facies [36]. The relatively mild metamorphic grade (greenschist-to lower amphibolite-facies) compared to typical Archean rocks (typically amphibolite-facies) also makes the Dagushan BIF a good target for examining the sources of C and Fe and the mechanisms that transformed them to siderite. Here, we report an integrated petrographic and C and Fe isotopic study on the siderites of the Dagushan BIF in order to constrain the formation pathway. We compare our results to other siderite-forming pathways proposed for different geological periods in order to provide new constraints on C and Fe cycling through time.
Three distinctive sedimentary facies are recognized in the Dagushan BIF: (1) an oxide facies, mainly composed of magnetite; (2) a silicate facies, composed of cummingtonite, stilpnomelane, and chlorite (silicate > 20%); (3) a carbonate facies, with siderite as the dominant Fe-bearing phase. As the major constituent (~50% vol.%) of the Dagushan BIF, the silicate facies BIF is distributed mainly in the south of the formation (Figure 2), and the oxide-facies BIF occurs primarily in the middle of the formation, making up to ca. 30 vol.% of the total BIF. The carbonate facies accounts for the remaining 20 vol.% of the Dagushan BIF and is spread predominantly over the northern region. The Dagushan BIF is associated with well-bedded chlorite-quartz schist, biotite gneiss, and minor mica-quartz schist ( Figure 2) [43]. The beds strike north-west and dip 40-70 • to north-east, and some of these supracrustal rocks are cross-cut by quartz and calcite veins that indicate later-stage hydrothermal alteration. Igneous rocks extend widely in the study area, consisting predominantly of Mesoarchean granite, Cretaceous granite, granite porphyry, diorite porphyrite, and diabase dikes (Figure 3a). The~3.0 Ga Mesoarchean granite (Donganshan granite, [51]), is on the footwall of the Neoarchean supracrustal rocks (Figures 2 and 3b). All field observations indicate a fault contact between it and the BIF. The Cretaceous granite (Qianshan granite, [52]), as well as granite porphyry, shows evident unconformable contact relationships with the Dagushan supracrustal rocks.

Analytical Methods
Samples were obtained from open pit outcrops in the northern part of the Dagushan iron mine (41 • 03 10" N, 123 • 03 27" E). Detailed petrographic examinations using transmitted and reflected light were carried out to determine the mineralogy and paragenetic history of all BIF samples. Scanning electron microscopy equipped with energy dispersive spectrometry (SEM-EDS) was used to examine small-scale relationships between textures and measure elemental abundances at the Institute of Geology and Geophysics, Chinese Academy of Sciences in Beijing (IGGCAS). Major element compositions of siderite were determined by wavelength dispersive spectrometry using a JEOL JXA8100 electron probe microanalyzer (EPMA) at the IGGCAS, Beijing. The analyses were carried out at an accelerating voltage of 15 kV and a beam spot diameter of 5 µm with a 20 nA beam current and a 10-30 s counting time on peak. The analytical precision for most elements is estimated to be better than 1.5%.
Ten representative carbonate facies samples were chipped with a hammer to remove weathered surfaces and cleaned with ultrapure water (1.82 MΩ cm). Pure siderite mineral separates were obtained using standard density and magnetic techniques, and then powered to~200 µm fineness in an agate mill in order to avoid any metal contact before further geochemical analysis. The agate mill was cleaned with deionized water and alcohol between each sample.
Iron isotope analyses for siderite were conducted at the Laboratory of Isotope Geology, Institute of Geology, Chinese Academy of Geological Sciences. A detailed description of the sample dissolution, chemical separation, and Fe isotope analysis is given in [53]. The procedure for chromatographic separation of Fe using an AG MP-1 anion exchange resin (100-200 mesh) followed that previously used by [54]. Following chromatographic separation, Fe isotope ratios were measured in high mass resolution mode on a Nu Plasma HR MC-ICP-MS using a standard-sample bracketing (SSB) approach. The Fe isotope results are expressed as deviations of the sample Fe isotope ratio from that of the reference material IRMM-14 in per mil: The long-term external reproducibility is estimated to be better than 0.05‰ for δ 56 Fe at the SD level, based on repeated measurements of in-house CAGS Fe solutions and national basaltic standard reference material CAGSR-1 (GBW-07105) against IRMM-014 [53].
Total inorganic carbon (TIC), total organic carbon (TOC), and the isotopic composition of organic carbon (δ 13 C org ) were measured on 10 selected samples at ALS Chemex, China. Abundances of TIC were analyzed with an Ethanolamine Color Coulomb Instrument after being treated with HClO 4 . The precision of the analyses (1σ) was better than 0.2%. Aliquots (200 mg) for TOC analysis were first treated with 10 vol.% HCl at 60 • C to remove carbonate [9], and then washed with distilled water to remove HCl. Afterward, the samples were dried overnight (50 • C) and then analyzed using an LECO CS-400 analyzer. Sample splits (300 mg to 1.5 g) for δ 13 C org analysis were acidified with 6 N HCl in a centrifuge beaker to remove any carbonates. The decalcified samples (30-100 mg) + CuO wire (1 g) were added to quartz tubes, and combusted at 500 • C for 1 h and at 850 • C for another 3 h. Isotopic ratios were analyzed using cryogenically purified CO 2 on a Finnigan MAT-253 mass spectrometer and are reported in standard δ-notation relative to the Vienna Peedee Belemnite (VPDB) standard: Analytical precision for the values is better than ±0.06‰ (1σ) based on measurements of geostandards GBW04407 (−22.43‰) and IAEA-600 (−27.5‰).

Bulk Carbon Content and Isotopes and Siderite Iron Isotopes
The TOC and TIC of the BIF samples, and carbon isotope ratios of C org , are presented along with previously published siderite C isotope data (δ 13 C Sid ) in Table 2. The TOC contents in BIF samples are less than 0.11 wt.%, consistent with the minor amount of C org (graphite) observed microscopically, while the TIC contents of the samples are higher and range widely from 0.92 to 3.36 wt.%. Carbon isotope ratios of δ 13 C org are relatively consistent, varying from −26.8‰ to −23.2‰, with an average of −25.4‰. There is no obvious correlation between TOC and δ 13 C org in the dataset. Neither is any obvious correlation observed between δ 13 C sid and δ 18 O Sid values ( Figure S1), suggesting that samples have only undergone low-grade alteration [55]. In addition, the contents of primary organic carbon precipitated on the seafloor are relatively low, varying from 0.73 to 1.25 wt.%, and the calculation process is shown in Table 3.  The iron isotope compositions (δ 56 Fe) of siderite from the Dagushan BIF are predominantly positive and range from −0.180 to +0.463‰, with a mean value of +0.187‰, and show an entirely mass-dependent relationship with δ 57 Fe (R 2 = 0.99) (Table 4, Figure  S2). Only three samples have slightly negative δ 56 Fe values between -0.18 and −0.06‰. Analytical error on the sample measurements (1 standard deviation) varies from 0.011 to 0.052.

Mineral Paragenesis
Siderite, typically occurring as microcrystalline, single rhomb-shaped crystals or massive layers, is the most common carbonate mineral in BIFs, and it may form penecontemporaneously with early ferric oxyhydroxide precipitates or during later diagenesis [13,16,17,57,58]. Siderite and magnetite are the main Fe-bearing minerals in the Dagushan carbonate facies BIF.
Fine-grained subhedral siderite crystallites (<50 µm) and fine-grained magnetite (<50 µm) are evenly distributed amongst the quartz (Figure 4a). These are likely to have formed relatively rapidly during the early stage of diagenesis due to their small sizes. Moreover, fine-grained magnetite occurs as inclusions within some medium to largegrained subhedral-euhedral siderites (50-150 µm) (Figure 4c), whereas siderite is not found within magnetite grains, suggesting that large-grained siderite post-dates the finegrained magnetite and probably formed later during diagenesis. Additionally, the irregular siderite aggregates in the iron-rich microbands, intergrown with green platy chamosite ( Figure 4e) and medium to large coarse-grained magnetite (50-150 µm), are formed from preferentially concentrated siderite grains where several Fe oxide layers coalesce due to burial compaction, and may distort the primary microlamination (Figures 3c and 4d), providing further evidence for siderite formation during later diagenesis. In addition, medium to large-grained siderite grains are occasionally replaced by magnetite on the edges (Figure 4b), likely through metamorphic alteration and oxidation.
In sum, fine-grained magnetite and siderite are likely to have formed during the early diagenesis, while medium to large-grained magnetite, siderite aggregates possibly formed during later diagenesis. Finally, siderite may have been oxidized to magnetite during subsequent metamorphism.

Direct Precipitation from Seawater
Siderite is typically formed in anoxic and Fe-rich (but S-poor) conditions under high alkalinity [10][11][12]59]. Accordingly, some previous publications have argued that, similar to other marine carbonates, ancient siderite in BIF formed through the combination of dis-solved Fe(II) with dissolved carbon dioxide, in the form of HCO 3 -, and directly precipitated from seawater via the following reaction [13,[20][21][22]24,25,60]: Although it has recently been argued that the kinetics of Fe(II)-carbonate precipitation in Precambrian seawater would have limited its direct precipitation [26]. When considering the direct precipitation from seawater, the δ 13 C Sid composition can be used to evaluate whether siderite precipitated directly in equilibrium with seawater. The dissolved inorganic carbon (DIC) pool in Precambrian seawater is expected to have had δ 13 C values close to 0‰, expect for some anomalous periods in the early Paleoproterozoic and the late Neoproterozoic [61]. Thus, carbonate minerals comprising limestones and dolomite precipitated directly from the seawater, and typically have δ 13 C carb values of~0‰ [61,62]. For example, Ca-Mg carbonates associated with the 2.52 Ga Gamohaan Formation BIFs [63][64][65][66] and stratigraphically equivalent Campbellrand platform rocks [67] have δ 13 C carb values from −1.0 to 0‰. Given that C isotope fractionation between calcite and siderite in equilibrium with the same fluid at 25 • C is about −0.5‰ [68], estimated values of δ 13 C Sid formed in equilibrium with Archean seawater should range from −1.5 to −0.5‰. However, the distinctly negative δ 13 C Sid values, ranging from −6.20 to −1.57‰, in the Dagushan BIF ( Table 2) fall below the expected values for seawater-derived siderite, suggesting that the more negative δ 13 C Sid values indicate that an additional negative C isotope reservoir, such as organic matter, must have contributed to siderite formation (see next section).
The Fe isotopic signatures in Dagushan siderites corroborate the C isotopes. The main Fe(II) source of the Archean ocean are hydrothermal fluids [4] which are expected to have a δ 56 Fe composition of around −0.2‰ or less [29,31]. In addition, the equilibrium Fe(II)aq-siderite fractionation factor is estimated to be −0.5 ± 0.2‰ from experimental observations [69], or −2.1 to −1.6‰ based on theoretical calculations [70][71][72]. Accordingly, siderites precipitated in equilibrium with seawater are predicted to have negative Fe isotopic ratios from −2 to −0.5‰. Similar light δ 56 Fe values are observed in Fe-poor carbonates from the Wittenoom Dolomite in the Hamersley basin [31]. By contrast, siderites in the Dagushan BIF have δ 56 Fe values that range from −0.180 to +0.463‰, uniformly higher than values predicted for seawater-precipitated siderite. In sum, siderites from our study area do not carry typical isotopic signatures reflective of formation in equilibrium with seawater. Therefore, we posit that siderite in the Dagushan BIF could not have precipitated directly in the water column.

Authigenic Precipitation from Porewater by DIR
Another proposed formation pathway for siderite in BIFs is authigenic precipitation from sediment porewater, facilitated by dissimilatory iron reduction (DIR). DIR is a widespread microbial metabolic pathway through which Fe(III)-reducing bacteria oxidize organic carbon for energy and tie electron transport to the reduction of an Fe(III)oxyhydroxide, such as ferrihydrite (Fe(OH)3). This anaerobic metabolism produces dissolved Fe(II), depending on the porewater composition, can facilitate the precipitation secondary Fe(II)-bearing minerals such as siderite (R.2). This biologically induced form of biomineralization has been demonstrated to be a viable pathway capable of accounting for siderite in both modern sediments [73,74] and the rock record [28,29,32,33,75,76].

Fe(OH) 3 + CH 2 O + 3 HCO 3 -→FeCO 3 + 3 OH -+ 7 H 2 O (2)
A flux of reactive ferrihydrite and C org to the seafloor in Neoarchean oceans, where dissimilatory sulfate reduction was suppressed by low sulfate levels, would support high levels of DIR [29]. Such a pathway could have converted ferrihydrite to siderite in the Dagushan BIF, as is supported by several lines of evidence including petrographic observations, negative δ 13 C Sid values, and varying δ 56 Fe values in siderites, while the presence of graphite supports the previous presence of organic biomass that could have acted as the electron donor to facilitate DIR. In this regard, the fine-grained graphite (~20 µm, Figure 4g,h) is likely to be the final product of remnant organic carbon after being metamorphosed.
From a petrographic perspective, there is no siderite found in magnetite grains, whereas small magnetite grains occur as inclusions within siderite (Figure 4c). This is important because not only does it confirm a diagenetic pathway rather than precipitation from seawater, but it also implies that magnetite formed even earlier. Furthermore, some siderite and quartz grains appear as irregular aggregates that have distorted the primary microlamination and several Fe-rich microbands (Figure 3c), suggesting that these were preferentially concentrated during burial compaction.
The negative δ 13 C Sid values,~−6.20 to −1.57‰, of the Dagushan BIFs, which are significantly lower than those expected via precipitation from seawater, require a source of C with a lighter isotopic composition. The best candidate for this is the organic matter present in the Dagushan BIFs which displays a narrow range of very low δ 13 C org between −26.8 and −23.2‰. The oxidation of C org delivers isotopically light dissolved inorganic carbon (DIC) to porewaters, where it mixes with seawater-derived DIC with δ 13 C around 0‰ ([DIC] sw ). Theoretically, siderites with δ 13 C ratios nearing −25‰ could be formed entirely from a pool of carbonate derived through DIR, while siderites possessing δ 13 C ratios around 0‰ could have formed entirely from an inorganic reservoir derived from seawater. Accordingly, the wide range of negative δ 13 C Sid values in the Dagushan BIF may reflect varying proportions of both end member sources (i.e., seawater/diagenetic HCO 3 anions) during siderite formation within sediments.
Mixing of bicarbonate pools is further implied by a positive correlation (R = 0.86, Figure 6) between TOC and δ 13 C Sid . If the TOC contents of primary sediments were initially similar, this positive correlation would indicate that in samples where the residual organic matter content is lower, a relatively larger fraction of the organic matter was oxidized through DIR and a higher proportion of DIR-derived C participated in the forming of siderite, leading to a lower carbon isotope value. Through a simple mass-balance model (R.3) presented in [3], the proportions of HCO 3 -(δ 13 C sw = 0‰) from seawater and organic carbon (δ 13 C org = −25‰) may be calculated as follows: [DIC] Sid δ 13 C Sid = [DIC] org δ 13 C org + [DIC] sw δ 13 C sw where [DIC] Sid and [DIC] sw are the mass fractions of inorganic C in siderite and seawater, respectively, while [DIC] org represents inorganic carbon content that is derived from organic carbon though DIR. The δ 13 C Sid , δ 13 C org , and δ 13 C sw are the carbon isotope compositions of siderite (~−6.20 to −1.57‰), organic carbon (~−26.80 to −23.2‰), and seawater (~0‰), respectively. Accordingly, the proportion of the organic carbon that contributed to siderite formation ([DIC] org /TIC) depends on the value of δ 13 C org /δ 13 C Sid , and corresponds to about 6.78-24.90% of DIR-derived C in Dagushan BIF siderites (Table 2).
In addition to C isotopes, the Fe isotope composition of Fe-rich carbonates can be used to probe their formation processes. As mentioned above, siderites in the Dagushan BIF have δ 56 Fe values from −0.180 to +0.463‰, which is best explained through inheritance from a ferrihydrite precursor formed through the partial oxidization of dissolved Fe(II) that typically produces δ 56 Fe fractionations of~+1.2‰ [77]. This was then followed by DIR (pathway 2, Figure 7), rather than direct precipitation from seawater, or conversion from green rust [34], as these would result in negative fractionations (pathway 1, Figure 7). The DIR in the Dagushan BIF was likely not quantitative, since magnetite formed during diagenesis is commonly present in the carbonate facies. If so, significant δ 56 Fe fractionations would have accompanied DIR, since equilibrium fractionation between produced Fe(II) and the ferrihydrite surface is around −3.0 to −0.5‰ [16,29,[78][79][80]. Assuming ∆Fe Fe(II)-Fe(OH)3 = −2‰ and a 50% degree of reduction under equilibrium conditions, then the microbially reduced Fe(II) and the remaining ferrihydrite would have had a δ 56 Fe value of~−0.5‰ and +1.5‰, respectively, if calculated from simple mass balance with δ 56 Fe Fe(OH)3~+ 0.5‰. Furthermore, as is suggested to be the case with DIC, Fe(II) with low-δ 56 Fe could have been mobilized in the sediment pores, and mixed with Fe(II) from the seawater which had a δ 56 Fe value of around 0‰, or higher in the Neoarchean [81,82]. The precise iron isotope value is dependent on the proportions of Fe(II) from the DIR and seawater inputs. For example, if the ratio is 1:1, siderite would be expected to have a δ 56 Fe composition of −0.25‰ (pathway 2, partial reaction, Figure 7). By contrast, siderite formed from the remnant substrate by near-complete reduction of residual ferrihydrite would inherit a positive δ 56 Fe signature, and is expected to have δ 56 Fe values around +1.5‰ (pathway 2, residual reaction), but this greatly depends upon the initial value of ferrihydrite, the amount of Fe(II) that was converted into magnetite, and the prior loss of low-δ 56 Fe Fe(II) into the water column. The Fe isotope values of siderites in the Dagushan BIF are consistent with those predicted above. These features are also similar to the siderites in the Brockman Iron Formation (Hamersley Basin, Western Australia), the Kuruman Iron Formation (Transvaal Supergroup, South Africa), and the Cauê Formation BIF (Brazil) [16,29,31,76], which is a strong indicator that DIR played a significant role in the origin of siderite in many Neoarchean to Paleoproterozoic BIFs.

Calculation for the Contents of Organic Carbon Precipitated on the Seafloor
Combining the content of residual TOC with the total iron content of the samples in the Dagushan BIF, the total primary organic carbon content precipitated on the seafloor with the BIF (TOC*) may be approximated, ranging from 0.73 to 1.25 wt.‰ ( Table 3). Assuming that all the total inorganic carbon (TIC) is from siderite, we can then estimate the molar abundance of carbon (m c ) in siderite: mc = TIC/12 g/mol, which would equal the mole number of the iron atom (m Fe ) in siderite based on the stoichiometric formula for siderite, FeCO 3 . Accordingly, the mass fraction of Fe in siderite (M Sid ) is: M Sid = m Fe * 56 g/mol = m c * 56 g/mol = TIC/12 g/mol * 56 g/mol. If we consider that the total Fe (TFe) represents the contribution from siderite and magnetite and ignore the Fe contributed from chamosite, due to its low modal content, we then calculate the  [28], and thus, the required organic carbon content is: M oc = m TFe(II) /4 * 12 g/mol.
Therefore, the minimum total organic carbon that precipitated on the seafloor during BIF deposition may be estimated by combining M oc and tested residual TOC in samples. It is noted here that graphite is sparsely distributed within our samples, and that overall the TOC preserved in our samples remains low (down to 0.04 wt.%). This is much lower than those of other BIFs such as the Mozaan Group, South Africa, which have TOC contents ranging from 0.4 to 2.5 wt.‰ [83].
Constant organic material inputs to oceans are usually in the form of allochthonous and/or autochthonous particulates that sink from the surface down onto the seafloor. The water depth and the distance from the shore are the predominant factors that govern the flux of organic material to the seafloor [84]. According to Chester [85], less than 0.1% of organic material makes its way through deeper waters without being remineralized and ends up buried into pelagic sediments, compared to 5% in nearshore sediments. This relationship may help to explain the relatively low C org abundance in the study materials, as the Dagushan BIFs were likely deposited in bathyal-abysmal basin.

Comparison with Siderites in Other BIFs through Time
Iron and C isotope data of siderite samples from a selection of BIFs of different ages (from 3.8 to 1.3 Ga) are summarized in Table 5 and plotted in Figure 8. These include thẽ 3.  (Figure 8), which implies that siderites in BIF are generally not formed in equilibrium with seawater, but instead are products of early diagenetic mineral formation in the soft sediment prior to lithification [16,76]. One exception is the Jingtieshan BIF, which has a narrower Fe isotope range between −0.71‰ and −0.41‰ (apart from a single sample with δ 56 Fe = −1.62‰), suggesting the possibility of isotope equilibrium with submarine hydrothermal fluids and seawater [81]; however, even there the δ 13 C values imply a significant contribution from remineralized C org . The δ 56 Fe and δ 13 C signatures of siderite in the~3.8 Ga Isua and 2.65 Ga Cauê BIFs-similarly an Algoma-type BIF-are the most similar to those of the Dagushan BIF. The most significant difference is that all δ 56 Fe values of siderite in the Isua BIF samples are positive, which have been interpreted as a result of complete DIR [31]. Thus, despite the large age difference between different siderites at different locations, microbial DIR seems to have persisted as a dominant influence on sediment geochemistry from~3.8 to~2. 45 Ga in BIF depositional settings [31,39,76].  [68,69] and theoretical estimates [70][71][72] of equilibrium isotope fractionation between Fe(II) aq -siderite and HCO 3 --siderite.

Conclusions
Based on the Fe and C isotopic analyses presented here, the formation pathways for siderite in the carbonate facies of the~2.52 Ga Dagushan BIF (Anshan area, China) are well constrained. The relatively negative δ 13 C and highly variable δ 56 Fe values are inconsistent with the siderites forming in equilibrium with Archean seawater and negate the potential for the direct precipitation from the water column in our study area. Thus, our siderite samples cannot be used as a direct proxy of paleomarine conditions, but instead they represent a valuable record of early diagenetic processes.
The significant pathway for siderite formation was likely DIR, where organic matter was oxidized with ferrihydrite acting as the terminal electron acceptor, and siderite being produced as a passive by-product. The positive and negative δ 56 Fe values of siderites measured in this study may be explained, respectively, by partial to quantitative reduction of the precursor ferrihydrite, which was originally the product of partial oxidation which generated the positive δ 56 Fe values. However, quantitative reduction would require that all ferrihydrite was reduced by DIR and all ferrihydrite was transformed to siderite. This is contradicted by abundant magnetite grains within the samples studied here. Consequently, a multiple-stage DIR process may offer the best explanation for siderite formation in the study area. Here, Fe(II) produced by partial reduction of the precursor ferrihydrite through DIR could have mixed with seawater-sourced Fe(II) in sediment porewater to produce a range of δ 56 Fe values. By contrast, sustained reaction of residual ferrihydrite would have produced positive δ 56 Fe values up to +1.5‰. The δ 56 Fe of the precursor ferrihydrite, the degree of DIR, and the proportion of DIR-derived and seawater-sourced Fe(II) that contributed to siderite formation are the most significant factors influencing the δ 56 Fe of siderites. In addition, the negative δ 13 C values in the Dagushan BIF require both DIR-derived and seawater-sourced HCO 3 -, with less than 25% being derived though DIR, consistent with the overall low C org content of the Dagushan BIF. Similarities in the C and Fe isotope systematics between the Dagushan BIF and a series of other Archean-Paleoproterozoic are a testament to the pervasive nature of DIR in Precambrian marine sediments.