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The redox “filter” beneath magmatic orogens and the formation of continental crust

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Science Advances  16 May 2018:
Vol. 4, no. 5, eaar4444
DOI: 10.1126/sciadv.aar4444


The two most important magmatic differentiation series on Earth are the Fe-enriching tholeiitic series, which dominates the oceanic crust and island arcs, and the Fe-depleting calc-alkaline series, which dominates the continental crust and continental arcs. It is well known that calc-alkaline magmas are more oxidized when they erupt and are preferentially found in regions of thick crust, but why these quantities should be related remains unexplained. We use the redox-sensitive behavior of europium (Eu) in deep-seated, plagioclase-free arc cumulates to directly constrain the redox evolution of arc magmas at depth. Primitive arc cumulates have negative Eu anomalies, which, in the absence of plagioclase, can only be explained by Eu being partly reduced. We show that primitive arc magmas begin with low oxygen fugacities, similar to that of mid-ocean ridge basalts, but increase in oxygen fugacity by over two orders of magnitude during magmatic differentiation. This intracrustal oxidation is attended by Fe depletion coupled with fractionation of Fe-rich garnet. We conclude that garnet fractionation, owing to its preference for ferrous over ferric iron, results in simultaneous oxidation and Fe depletion of the magma. Favored at high pressure and water content, garnet fractionation explains the correlation between crustal thickness, oxygen fugacity, and the calc-alkaline character of arc magmas.


There is a long-standing debate on what controls the oxidized nature of arc magmas, particularly those formed in continental arcs (1, 2). This debate has profound implications for Earth’s evolution because oxidized arc magmas, manifested in the form of iron-depleted magmas, are the primary building blocks of the continental crust (3). The debate is centered on whether the oxidized signatures of arc magmas are inherited from the mantle source or developed during magmatic differentiation, crustal interaction, or degassing. Iron and sulfur oxidation states in melt inclusions have been used to suggest that fluids released from the subducted slab pervasively oxidize the sub-arc mantle, producing oxidized arc magmas from the onset (1, 4, 5), but redox-sensitive trace element ratios and Fe isotope signatures of basalts, which have been used to see through eruptive and differentiation processes, suggest that primitive arc magmas are not as oxidized as widely thought (68). None of the above studies, however, represent direct constraints on the oxidation state of primitive, pre-erupted magmas.

Here, we examine the Eu systematics of deep-seated (>45 to 80 km) garnet pyroxenite continental arc cumulates to provide the most direct constraint so far on arc magmas before they rise into the crust or erupt. Europium is a rare earth element (REE), but unlike most other REEs, which are exclusively trivalent under typical terrestrial conditions, Eu occurs in both divalent and trivalent states, so the ratio of Eu2+/Eu3+ is sensitive to variations in oxygen fugacity (fO2). Although Eu2+ strongly partitions into plagioclase, in all other magmatic minerals, Eu2+ is more incompatible than Eu3+ and neighboring REEs, making the total partitioning of Eu sensitive to fO2. Eu2+/Eu3+ may be a more robust redox-sensitive index than element pairs, such as V/Sc (9) and Zn/Fe (7), because the geochemical behavior of both Eu2+ and Eu3+ can be well constrained throughout magmatic differentiation. Eu systematics in plagioclase-free rocks can thus be used to constrain the Eu valence state, which in turn can be used to estimate oxygen fugacity using experimentally calibrated Eu oxybarometers (10).


We sampled garnet-bearing pyroxenite xenoliths from Miocene trachyandesitic volcanic centers on the margin of the Colorado Plateau in Arizona (11, 12). They have major element compositions complementary to typical continental arc plutonic rocks and are thus interpreted to represent arc cumulates (11). These deep cumulates do not contain any evidence of plagioclase. Titanite U/Pb systematics suggest crystallization in the Late Cretaceous or Early Paleogene (11). Their mineralogies and trace and major element signatures are identical to arc cumulates associated with the Cretaceous Sierra Nevada batholith toward the west (11, 13, 14). The Arizona garnet pyroxenites are thus interpreted to represent cumulates from hydrous arc magmas associated with Mesozoic to Early Cenozoic arc magmatism in western North America (11). They have Mg#s [atomic Mg/(Mg+Fe), where Fe represents total Fe] ranging from 0.5 to 0.82, the latter representing early formed cumulates from primitive arc magmas and the former representing cumulates from more evolved magmas (see the Supplementary Materials and Methods).

The deep petrogenetic origins of the garnet pyroxenites and the lack of any visible evidence for plagioclase make these pyroxenites ideal for applying Eu systematics as an oxybarometer of arc magmas before eruption. To avoid potential contamination of the whole-rock xenolith by recent injection of Miocene host lavas onto grain boundaries, we performed in situ laser ablation ICP-MS (inductively coupled plasma mass spectrometry) analyses of garnets and clinopyroxenes in thin sections (see the Supplementary Materials and Methods). Longer dwell times on Sm, Gd, and Eu were applied to increase the precision and accuracy of the analyses.

Oxygen fugacity of primitive arc magmas constrained by mineral Eu anomalies

Europium valence can be quantified from the relative difference (the Eu anomaly) in geochemical behavior between Eu2+ and neighboring REEs. Eu anomalies are expressed as Eu/Eu*, where Eu* represents the hypothetical concentration of Eu if it behaved solely like a trivalent REE and is calculated by polynomial interpolation of REE systematics in the order of their ionic radii (see the Supplementary Materials and Methods). We find that both clinopyroxene and garnet show increasing Eu/Eu* with decreasing Mg# (Fig. 1), a measure of the extent of differentiation. This negative correlation is consistent with Eu2+ being more incompatible than Eu3+ and is also consistent with plagioclase being absent during the entire crystallization history of these cumulates because plagioclase fractionation would decrease Eu/Eu* with differentiation. Because of the lack of plagioclase, the fact that the most primitive cumulates have Eu/Eu* <1 is interesting. Global compilations of arc magmas show that primitive arc magmas have Eu/Eu* of unity (see the Supplementary Materials and Methods); only after MgO contents decrease to levels below 6 weight % (wt %) does Eu/Eu* deviate from unity due to the onset of plagioclase fractionation (15). In conclusion, the negative Eu anomalies of the primitive arc cumulates can only be explained if Eu is of mixed valence.

Fig. 1 Eu/Eu* in clinopyroxene and garnet in deep arc cumulates as a function of whole-rock Mg#.

(A and B) Individual spot data measured by laser ablation ICP-MS. The error bars denoted in (A) and (B) are the long-term (~8 months) reproducibilities (2 SD) of measuring Eu/Eu* in basaltic glass standards BIR-1G and BCR-2G. (C) The mean Eu/Eu* in clinopyroxene and garnet for each rock sample. Error bars are 2 standard error of mean (2 SEM).

We now use the Eu/Eu* of the most primitive arc cumulates (CC-ME1, whole-rock Mg# = 0.77; SB1-ME9, Mg# = 0.82) to calculate the Eu valence state, which in turn allows us to place an upper bound on the fO2 of primitive arc magmas (Fig. 2A). The Eu/Eu* of a mineral is controlled by the composition of the melt (including the melt’s Eu/Eu* and Eu2+/Eu3+) and the ratio of the mineral/melt partitioning of Eu2+ (Embedded Image) to Eu3+ (Embedded Image). From mass balance, Eu valence in the melt (Eu3+/ΣEu) can be calculated using the following equation (derivation in the Supplemental Materials)Embedded Image(1)

Fig. 2 Magma redox conditions calculated from garnet and clinopyroxene Eu anomalies.

(A) Estimating fO2 of primitive magma. Garnet and clinopyroxene Eu/Eu*-fO2 plotted on the contours of Embedded Image. The probability distribution is for sample CC-ME1, the second most primitive garnet-bearing pyroxenite in this work. (B) Evolution of the bulk Eu partition coefficient relative to DEu* (bulk partition coefficient of Eu3+) during crystal fractionation, calculated using the observed Eu/Eu* of garnets and an incremental crystal fractionation model (see the Supplementary Materials and Methods). Dots with error bars (95% confidence interval) represent DEu/DEu* values estimated from Eu/Eu* of garnets in cumulates. Residual melt fraction estimated by converting whole-rock cumulate Mg# to the Mg# of a melt in equilibrium with the cumulate and inferring melt fraction from empirical relationships between melt Mg# and indices of melt fraction, such as K2O (see the Supplementary Materials and Methods). The uncertainties are from the measured garnet Eu/Eu* and cumulate-melt Mg# coupling and are propagated into the calculated DEu/DEu* and fO2 by a Monte Carlo resampling method (see the Supplementary Materials and Methods). Thick red line demarcates median values, and thin red line displays 95% confidence interval envelope. The total Eu partition coefficients in (B) were converted to fO2 in (C). Clinopyroxenes show the same Eu/Eu*-Mg# trend as garnet (Fig. 1), but we use garnet data to calculate the redox paths because the perfect incompatibility of Eu2+ in garnet simplifies Eq. 1 and reduces uncertainty.

Eq. 1 assumes that the mineral is in equilibrium with the melt (subsolidus reequilibration in garnet-pyroxenites has minimal effect on mineral Eu/Eu* because Eu2+ is highly incompatible in garnet). Embedded Image is estimated from the behavior of trivalent REEs, whereas Embedded Image can be estimated from the behavior of geochemically similar Sr2+. In clinopyroxene, Embedded Image can be equated to DSr/Embedded Image, which ranges between 0.03 and 1.53 with a median value of 0.22 (n = 89, excluding kimberlites and carbonatites) based on published partition coefficients (16). Additional constraints come from clinopyroxenes in ureilite meteorites, wherein most of the Eu is divalent due to the highly reducing conditions of ureilites (17). Ureilite clinopyroxenes have Eu/Eu* ranging from 0.18 to 0.63 with a median value of 0.29 (n = 49), and assuming that parental magmas begin with Embedded Image = 1, the measured Eu/Eu* values in ureilites provide an upper bound of ~0.2 on Embedded Image. In garnet, Sr is highly incompatible, which is consistent with the pyroxenite garnets having Sr barely above detection limits (0.1 to 1 parts per million); Embedded Image is thus effectively zero in garnet, simplifying Eq. 1. In the extreme case, in which Embedded Image = 0 for all minerals, Eq. 1 simplifies such that the ratio of the Eu anomaly in the pyroxenite versus that in the melt provides a maximum bound on the Eu3+/ΣEu ratio.

We use both clinopyroxene and garnet in the most primitive cumulates to estimate the Eu valence state of the primitive magma. As noted above, the primitive magma is assumed to have Embedded Image= 1. We can use experimentally calibrated Eu2+/Eu3+fO2 relationships in silicate melts (10) to obtain fO2. Details of the calculation are provided in the Supplementary Materials. Garnets and clinopyroxenes in CC-ME1 give similar magma fO2 values of −1.0 (±1.0, 2 SD) and −1.0 (±0.5, 2 SD) log10 units relative to the fayalite-magnetite-quartz (FMQ) buffer (Fig. 2A), identical to within error that inferred from mid-ocean ridge basalts (FMQ−1 to FMQ) (1820). If garnet and clinopyroxene Embedded Image ratios are higher than those used here, which seems unlikely, even lower fO2 values would be estimated (Fig. 2A). Sample SB1-ME9 has too few garnets to investigate while clinopyroxenes show significant scatter in Eu/Eu* (Fig. 1A) due to uncertainties associated with extremely low REE concentrations (tens of parts per billion Eu). Nevertheless, the mean Eu/Eu* of SB1-ME9 clinopyroxenes is identical to those of CC-ME1 (Fig. 1C). We thus use CC-ME1 to constrain the maximum fO2 in primitive arc magmas.

Redox evolution of arc magmas during differentiation

We now turn to the increase of Eu/Eu* with decreasing Mg#. This trend reflects the enrichment of more incompatible Eu2+ in the melt and/or rising fO2 with differentiation. Progressive crystal fractionation leads to a predictable decrease in the Mg# of the melt and cumulate (see the Supplementary Materials and Methods). Using a semiempirical relationship between Mg# of the cumulate and residual melt fraction relative to a primitive mantle-derived magma to estimate the residual melt fraction corresponding to each cumulate, we can estimate the mineral/melt partition coefficient at any given Mg# by incrementally crystallizing cumulates. This inverse approach allows us to identify how the cumulate/melt bulk Eu partition coefficient, calculated as DEu relative to DEu* (DEu/DEu*; Fig. 2B), varies with crystallization in the cumulates. The DEu/DEu* ratio, which reflects the Eu2+/Eu3+ ratio in the melt, is then converted to fO2 (Fig. 2C) using experimental constraints (10).

In the foregoing calculations, we assume a bulk cumulate-melt partition coefficient of 0.5 for Eu3+ (DEu*), which is likely a maximum bound based on published mineral-melt partition coefficients of Eu3+ for clinopyroxene (21) and garnet (22). In the Supplementary Materials, we vary the value of DEu* (0.2 to 0.8) to test the sensitivity of our model to DEu*. If the value of DEu* is lower than that used here, calculated magma fO2 rises more rapidly with differentiation, so our estimates of fO2 during differentiation are minimum bounds. On the basis of this analysis, we find that fO2 increased from FMQ−1 to at least FMQ+1 with crystal fractionation of these garnet pyroxenite cumulates (Fig. 2C). Our observations suggest that the fO2 of the sub-arc mantle may not be significantly different from that beneath mid-ocean ridges and that the oxidized signature of arc magmas may be acquired during ascent and differentiation.


The initially low fO2 inferred for primitive arc magmas raises the question of what drives the Fe depletion characterizing calc-alkaline series differentiation. Iron depletion, which distinguishes the calc-alkaline series from the tholeiitic series, is generally attributed to early magnetite fractionation in oxidized magmas. However, if primitive arc magmas are reduced, magnetite saturation will be suppressed initially (23) and magmatic differentiation should follow the Fe-enriching tholeiitic series unless the magma becomes oxidized during differentiation. Resolving this calc-alkaline paradox thus requires an intracrustal process that simultaneously depletes Fe and oxidizes the residual melt.

There are several ways to oxidize magmas in the crust. Assimilation of oxidized crustal materials is one possibility, but the origin and abundance of oxidized materials in deep arc crust are enigmatic if primitive arc magmas—the building blocks of arc crust—are reduced. Coupled fractional crystallization and recharge in magma chambers has also been invoked to explain Fe3+ enrichment in arc magma differentiation (24), but whether such a process can explain early Fe depletion is unclear.

Some hints come from the well-known, but incompletely understood, observation that immature island arcs are predominantly tholeiitic, whereas continental arcs mostly generate calc-alkaline magmas (2530). These compositional relationships with crustal thickness are also reflected by the magma FeOT-MgO correlations in global arcs (Fig. 3). If these different differentiation trends are controlled by crustal thickness, it seems worthwhile to explore whether the average pressure of differentiation, by controlling the crystallizing assemblage (27, 3133), may influence magma redox evolution.

Fig. 3 FeOT-MgO systematics in arc and mid ocean ridge (MOR) magmas.

Data are presented as MgO binned (0.5 wt %) average and 2 SEM. Tholeiitic differentiation is represented by the mid-ocean ridge series (MOR). We divide arc igneous samples (mostly of Cenozoic ages) into three groups based on their modern arc crustal thickness: <25, 25 to 50, and >50 km. Arc magma compositions transition from tholeiitic to calc-alkaline as crust thickness increases. MOR data are from Keller et al. (58); arc data are from GeoRoc compilation and provided in data file S2.

Magma redox conditions are largely controlled by the Fe3+/Fe2+ ratio because Fe is generally the most abundant source of electron transfer in most magmas. Therefore, melt redox will be dictated by the bulk solid/liquid partition coefficient ratio DFe (III)/DFe (II). We use pMELTS (34), a thermodynamic melting model, to simulate crystal fractionation of a hydrous basaltic melt (see the Supplementary Materials and Methods) at pressures between 0.2 and 2.0 GPa, corresponding to the range of crustal thickness from tholeiitic island arcs (~20 km) to calc-alkaline continental arcs (50 to 80 km).

At low pressure, Fe is moderately incompatible in olivine and clinopyroxene and strongly incompatible in plagioclase, so crystallization leads to Fe enrichment. Although Fe3+ is generally incompatible in Fe-bearing silicates, the low-pressure silicate fractionating phases incorporate limited Fe (Fig. 4A). Furthermore, the combination of crystallizing low Fe3+/ΣFe silicate phases with high Fe3+/ΣFe iron oxide phases limits the extent to which crystal fractionation at low pressure can increase magma redox state.

Fig. 4 Garnet control on Fe depletion.

(A) Percentage of total initial Fe content removed by various fractionating phases after 60% crystal fractionation. Results are from pMELTS simulation of hydrous basalt crystal fractionation (fractional crystallization) under 0.2 to 2.0 GPa, 4 wt % starting water content, and a constant fO2 of FMQ. (B) The extent of Fe depletion in arc magmas, as quantified by FeOT/MgO in moderately differentiated samples of 4 ± 1 wt % MgO, correlates with garnet fractionation index [Dy/Yb]N, where the subscript T denotes total Fe and N means C1 chondrite-normalized. Data are presented as FeOT/MgO binned (0.1) average values and 2 SEM.

On the other hand, as pressure increases, the Fe-bearing crystallizing assemblage transitions from olivine + clinopyroxene + spinel/magnetite to garnet + clinopyroxene (Fig. 4A). At high pressure, garnet is the major Fe-bearing phase and removes up to ~50% of the total initial Fe in the melt, consistent with experimental observations (35). The connection between calc-alkaline differentiation and garnet fractionation was first proposed by Green and Ringwood (3638). Here, we show that the effect of garnet fractionation is borne out in global compilations of arc magma data, where Fe depletion clearly correlates with Dy/Yb (Fig. 4B), the latter being a strong tracer of garnet fractionation (39, 40). Garnets in pyroxenites have been shown to have extremely low ferric Fe contents (Fe3+/ΣFe < 0.01) (41). Eclogite garnets have also been found to contain low ferric Fe (Fe3+/ΣFe < 0.08) (42, 43). We note that although Fe3+ is more compatible in clinopyroxene than in garnet (44), clinopyroxene takes much less Fe than garnet. Collectively, fractionation of garnet-bearing cumulates at high pressure can simultaneously drive Fe depletion and increase Fe3+/ΣFe in the derivative melt with differentiation.

To quantify the garnet fractionation effect on Fe valence in the derivative melt, we use a simplified crystal fractionation model in which the crystallizing assemblage is represented by garnet, whereas all other phases are treated as a separate nongarnet assemblage. As a minimum bound on the degree of Fe depletion, we designate the nongarnet assemblage to have bulk partition coefficients of 1 and 0.8 for Fe2+ and Fe3+, respectively. We assume that garnet takes only Fe2+ and has a bulk Fe partition coefficient significantly >1. For various differentiation pressures, we explore a range of garnet mode from 0 to 30% in the fractionation assemblage, and a range from 0 to 60% Fe removal via garnet fractionation. When the garnet mode is zero, as would be the case for low-pressure differentiation, magma fO2 remains nearly constant (Fig. 5B). When garnet mode increases and its fractionation removes over 40% of the total Fe, the magma can be progressively oxidized to at least FMQ+1, consistent with the terminal magma redox conditions constrained by observed cumulate Eu/Eu* values. Our forward-modeled Eu/Eu* trend during garnet fractionation agrees well with the observed cumulate Eu/Eu* data (Fig. 5C).

Fig. 5 Modeled garnet effect on magma redox evolution with differentiation.

(A) Fe depletion curves assuming 0 to 60% Fe removal by garnet fractionation. (B) Magma fO2 evolution curves as a function of the amount of Fe removed by garnet fractionation. Magma fO2 paths calculated from cumulate Eu/Eu* data (shaded area) are also shown for comparison. (C) Calculated Eu/Eu* in cumulate garnet based on the magma fO2 evolution curves in (B). Superimposed are the cumulate garnet Eu/Eu* data from this work.

We recognize that magma oxidation and Fe depletion paths will also be influenced by Fe oxides and changing Fe partition coefficients with differentiation, which are not accounted for in our simplified model. Nevertheless, we show that garnet fractionation leads to simultaneous Fe depletion (35) and oxidation of the derivative melt, both of which characterize calc-alkaline differentiation. Because the mode of garnet, and thus the amount of Fe removed by garnet, increases with pressure and water content in the melt during crystal fractionation (45), this model explains why calc-alkaline differentiation is associated with thickened crust. Magnetite saturation should only occur after the magma is significantly oxidized by garnet fractionation, and is unlikely to be the main driver of Fe depletion in calc-alkaline series because magnetite removes ferric Fe, which reduces the fO2 of the derivative melt and prevents the magma from remaining oxidized. Fe-oxide fractionation is a consequence of increasing fO2. Consistent with this conclusion is that Fe oxides only appear in the differentiated cumulates, not the primitive ones. With progressive differentiation, eventual coprecipitation of magnetite and garnet may then buffer the differentiated arc magmas at a certain fO2 above FMQ.


In summary, the Fe-depleting calc-alkaline differentiation series, which dominates the composition of the continental crust, may not be determined by initial magma redox conditions, but may instead be controlled by the effective pressure of magmatic differentiation in the crust. Our conclusions do not exclude other scenarios for generating calc-alkaline signatures, such as partial melting of eclogitic slabs, crustal contamination, and metasomatic oxidation of the sub-arc mantle (1, 4, 5), and no doubt, calc-alkaline magmas occasionally do occur in island arcs. However, the overall relationship between crustal thickness and degree of calc alkalinity appears to be a general global phenomenon and points to the dominance of upper plate thickening, or orogenic processes, in the formation of calc-alkaline magmas and Earth’s continental crust (4648). Our study provides an internally consistent mechanism for explaining this connection between oxidation and magmatic differentiation in thick crust.

Important implications follow. Iron depletion driven by garnet fractionation under reduced conditions will lead to sulfide saturation in the magma because sulfide solubility decreases with FeO content in the melt, thereby driving extensive sulfide coprecipitation with the cumulates (47, 49, 50). Deep continental arc cumulates may be an important reservoir for chalcophile elements and unradiogenic Pb isotopes (47, 51, 52). If these cumulates were to founder back into the mantle, owing to their high densities (14, 5255), then the progressive growth of the continental crust would lead to a flux of reduced materials to the mantle, leaving behind a more oxidized continental crust. We thus envision that the formation of continental crust results in a gravity-driven redox filter, which may have influenced Earth’s surface redox evolution by limiting the magmatic output of ferrous Fe and sulfides (56, 57).


Details about the samples, analytical techniques, and modeling are provided in the Supplementary Materials. Data are provided in data files S1 to S3.


Supplementary material for this article is available at

Supplementary Materials and Methods

Supplementary Text

fig. S1. Comparison between our measured Eu/Eu* in glass standards BCR-2G, BIR-1G, KL2-G, ML3B-G, and StHs6/80-G.

fig. S2. Long-term (8 months) reproducibility in the analysis of glass standards BIR-1G and BCR-2G.

fig. S3. Chondrite-normalized REE/FeO values for clinopyroxene.

fig. S4. Chondrite-normalized REE/FeO values for garnet.

fig. S5. Mean Eu/Eu* versus MgO in global arc lavas.

fig. S6. Calculated logfO2 as a function of optical basicity assuming Eu/Eu* = 0.8 in garnet.

fig. S7. Mineral Mg# versus whole-rock Mg# in the cumulates documented in this work.

fig. S8. Melt-cumulate Mg# correlation simulated by pMELTS at 2 GPa, 4 wt % H2O, and various oxygen fugacities.

fig. S9. Observed K2O-Mg# correlation in arc magmas, parameterized by an exponential function shown in the figure.

fig. S10. Error propagation by Monte Carlo resampling.

fig. S11. Sensitivity test of calculated DEu/DEu* and redox paths to the value of DEu* used in the crystal fractionation model.

fig. S12. Calculated optical basicity (Λ) as a function of Mg# in arc magmas.

data file S1. In-situ mineral composition data and cumulate whole-rock data.

data file S2. Primitive arc magma compositions.

data file S3. Global arc igneous rock compilation.

References (5963)

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Acknowledgments: We thank J. Gao for helping us with coding in the pMELTS simulations. We also thank X. Chu, A. Burnham, and G. Costin for the discussions. We thank G. Gaetani for handling the manuscript, and D. Canil and two other anonymous reviewers for their constructive comments. Funding: This project was supported by Frontiers of Earth Systems and Dynamics (NSF OCE-1338842). Author contributions: G.E. made the first discovery of the Eu/Eu*-Mg# correlation in preliminary whole-rock data. M.E. did petrographic and whole-rock characterization to study the petrogenesis of the cumulates. M.T. designed the in situ analytical method, collected the data, and built the models. C.-T.A.L. and M.T interpreted the data and wrote the manuscript. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors.
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