Iron isotope fractionation and atom exchange during sorption of ferrous iron to mineral surfaces

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Geochimica et Cosmochimica Acta 73 (2009) 1795–1812

Iron isotope fractionation and atom exchange during sorptionof ferrous iron to mineral surfaces

Christian Mikutta a,b,*, Jan G. Wiederhold a,c, Olaf A. Cirpka b,Thomas B. Hofstetter a, Bernard Bourdon c, Urs Von Gunten a,b

a Institute of Biogeochemistry and Pollutant Dynamics, Department of Environmental Sciences, ETH Zurich,

Universitatstr. 16, CH-8092 Zurich, Switzerlandb Eawag, Swiss Federal Institute of Aquatic Science and Technology, Uberlandstr. 133, CH-8600 Dubendorf, Switzerland

c Institute of Isotope Geochemistry and Mineral Resources, ETH Zurich, Clausiusstr. 25, CH-8092 Zurich, Switzerland

Received 25 August 2008; accepted in revised form 12 January 2009; available online 27 February 2009

Abstract

The application of stable Fe isotopes as a tracer of the biogeochemical Fe cycle necessitates a mechanistic knowledge ofnatural fractionation processes. We studied the equilibrium Fe isotope fractionation upon sorption of Fe(II) to aluminumoxide (c-Al2O3), goethite (a-FeOOH), quartz (a-SiO2), and goethite-loaded quartz in batch experiments, and performed con-tinuous-flow column experiments to study the extent of equilibrium and kinetic Fe isotope fractionation during reactive trans-port of Fe(II) through pure and goethite-loaded quartz sand. In addition, batch and column experiments were used toquantify the coupled electron transfer-atom exchange between dissolved Fe(II) (Fe(II)aq) and structural Fe(III) of goethite.All experiments were conducted under strictly anoxic conditions at pH 7.2 in 20 mM MOPS (3-(N-morpholino)-propanesul-fonic acid) buffer and 23 �C. Iron isotope ratios were measured by high-resolution MC-ICP-MS. Isotope data were analyzedwith isotope fractionation models. In batch systems, we observed significant Fe isotope fractionation upon equilibrium sorp-tion of Fe(II) to all sorbents tested, except for aluminum oxide. The equilibrium enrichment factor, eeq

56=54, of the Fe(II)sorb–Fe(II)aq couple was 0.85 ± 0.10& (±2r) for quartz and 0.85 ± 0.08& (±2r) for goethite-loaded quartz. In the goethite sys-tem, the sorption-induced isotope fractionation was superimposed by atom exchange, leading to a d56/54Fe shift in solutiontowards the isotopic composition of the goethite. Without consideration of atom exchange, the equilibrium enrichment factorwas 2.01 ± 0.08& (±2r), but decreased to 0.73 ± 0.24& (±2r) when atom exchange was taken into account. The amount ofstructural Fe in goethite that equilibrated isotopically with Fe(II)aq via atom exchange was equivalent to one atomic Fe layerof the mineral surface (�3% of goethite-Fe). Column experiments showed significant Fe isotope fractionation withd56/54Fe(II)aq spanning a range of 1.00& and 1.65& for pure and goethite-loaded quartz, respectively. Reactive transportof Fe(II) under non-steady state conditions led to complex, non-monotonous Fe isotope trends that could be explained bya combination of kinetic and equilibrium isotope enrichment factors. Our results demonstrate that in abiotic anoxic systemswith near-neutral pH, sorption of Fe(II) to mineral surfaces, even to supposedly non-reactive minerals such as quartz, inducessignificant Fe isotope fractionation. Therefore we expect Fe isotope signatures in natural systems with changing concentrationgradients of Fe(II)aq to be affected by sorption.� 2009 Elsevier Ltd. All rights reserved.

0016-7037/$ - see front matter � 2009 Elsevier Ltd. All rights reserved.

doi:10.1016/j.gca.2009.01.014

* Corresponding author.E-mail address: [email protected] (C. Mikutta).

1. INTRODUCTION

The applicability of stable Fe isotopes as biogeochemicaltracers of the Fe cycle requires a detailed understanding ofprocesses leading to Fe isotope fractionation in natural sys-tems. In particular, sorption reactions involving dissolved

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1796 C. Mikutta et al. / Geochimica et Cosmochimica Acta 73 (2009) 1795–1812

Fe(II) (Fe(II)aq) and minerals are important processes gov-erning the fate of Fe in anoxic low-temperature aquatic andterrestrial environments. However, our knowledge aboutthe sorption-induced Fe isotope fractionation is still lim-ited. Here, we use the term ‘sorption’ to indicate the uptakeof Fe(II) by solids irrespective of the mechanism (Sposito,1984).

In natural systems, Fe(III)-(hydr)oxides are potent sor-bents for dissolved Fe(II). The equilibrium fractionationof Fe isotopes during sorption of Fe(II) to Fe(III)-(hydr)oxide phases has been addressed to some extent in studiesdealing with Fe isotope fractionation during microbial dis-similatory Fe reduction (Icopini et al., 2004; Crosby et al.,2005, 2007). Crosby et al. (2007), for example, found littleequilibrium Fe isotope fractionation between Fe(II) sorbedto hematite and dissolved Fe(II) (DFe(II)sorb–Fe(II)aq =0.30 ± 0.08& (±2r)), but reported a considerable fraction-ation effect for Fe(II) sorption to goethite (DFe(II)sorb–Fe(II)aq = 0.87 ± 0.09& (±2r)). For the goethite system,Icopini et al. (2004) estimated an equilibrium isotope frac-tionation between sorbed and dissolved Fe(II) of 2.05&

assuming that Fe(II)aq continuously equilibrates withsorbed Fe(II). While these studies suggest that meresorption of Fe(II) to Fe(III)-(hydr)oxides fractionates Feisotopes, the extent of fractionation in abiotic systems com-prising Fe(III)-(hydr)oxides and dissolved Fe(II) has notbeen studied in detail. In addition, no data are availableon the sorption-induced Fe isotope fractionation in thepresence of minerals which contain no or only smallamounts of Fe in their structure. Quartz, feldspars, andphyllosilicates may serve as important examples.

The extent of Fe isotope fractionation in natural systemswhere sorption is not in equilibrium may be governed by ki-netic rather than equilibrium isotope effects. There is ampleevidence in the literature that in predominantly abiotic lab-oratory and field systems with advective–dispersive trans-port through porous media, Fe isotopes can besignificantly fractionated (Anbar et al., 2000; Teutschet al., 2005; Matthews et al., 2008). In such ‘chromato-graphic’ systems, amplification of small equilibrium isotopefractionation can generate large variations in isotope ratiosof a solute at the invading front (Ellis et al., 2004). Teutschet al. (2005) performed an in situ chromatography experi-ment by injecting Fe-free oxygenated water into a reducedgroundwater aquifer. After repeated push–pull cycles theyobserved groundwater Fe components up to �3.3& ind56/54Fe lighter than the initial background Fe(II). Thisfinding was interpreted to result from the preferentialadsorption of heavy Fe isotopes to newly formed Fe(III)-(hydr)oxides upon pulling native groundwater into the pre-viously oxygenated zone. The relationship between d56/54Fevalues and Fe(II) concentrations was best described with anequilibrium enrichment factor, eeq

56=54, of 0.67& (Teutschet al., 2005). However, the interpretation of the push–pullexperiments provided by Teutsch et al. (2005) was laterquestioned by Johnson et al. (2008) who alternatively ar-gued that homogeneous precipitation of Fe(III)-(hydr)o-xides could have led to a groundwater Fe componentdepleted in heavy isotopes – an explanation ruled out byTeutsch et al. (2005). The controversial appraisal of sorp-

tion as a mechanism for Fe isotope fractionation in thestudy of Teutsch et al. (2005) warrants controlled labora-tory flow-through experiments in which homogeneous pre-cipitation reactions and biotic effects can be excluded. Insuch well-constrained systems, both kinetic and equilibriumFe isotope fractionation effects may be important but theirmagnitude is still unknown.

The investigation of equilibrium/kinetic Fe isotope frac-tionation effects for systems with Fe(II)aq and mineral sor-bents is not straightforward, especially for minerals thatcontain structural Fe(III). The first difficulty arises fromthe fact that the uptake of Fe(II) by mineral sorbentsmay occur simultaneously via different mechanisms, includ-ing adsorption, coprecipitation, surface precipitation, ormultinuclear clustering of metal ions at the mineral surface(Katz and Hayes, 1995; Ford et al., 2001). As a result, thesorption-induced Fe isotope fractionation may depend onthe surface loading of Fe(II) and reaction time. Anotherobstacle in the determination of equilibrium fractionationfactors for systems with Fe(III)-bearing phases is that theisotope mass balance may be biased by isotope exchangereactions between Fe(II)aq and structural Fe(III). RecentMossbauer spectroscopy studies have shown that 57Fe(II)sorbed onto 56Fe(III)-(hydr)oxides such as goethite, hema-tite, or ferrihydrite is oxidized at the surface, thus formingan Fe(III) layer on the mineral which is similar to the bulkoxide (Williams and Scherer, 2004; Larese-Casanova andScherer, 2007; Cwiertny et al., 2008). The reduction ofstructural Fe(III) due to electron transfer from sorbedFe(II) to an Fe(III) centre coupled with the subsequent re-lease of Fe(II) from the ferric phase may alter the isotopiccomposition of Fe(II)aq because the released Fe(II) bearsthe isotopic information of the ferric mineral phase. Thecoupled electron transfer-atom exchange (‘atom exchange’)at the Fe(III)-(hydr)oxide surface may be conceptually de-scribed by three consecutive steps (charges of surface com-plexes omitted):

1. Adsorption:

2 � iFeðIIIÞOHþ ½kFeðIIÞ�aq¡

� ðiFeðIIIÞOÞ2kFeðIIÞ þ 2½Hþ�aq ð1Þ

2. Electron transfer:

� ðiFeðIIIÞOÞ2kFeðIIÞþ � iFeðIIIÞOH¡

� ðiFeðIIIÞOÞ2kFeðIIIÞþ � iFeðIIÞOH ð2Þ

3. Desorption:

� iFeðIIÞOH¡½iFeðIIÞ�aq þ ½OH��aq: ð3Þ

In these equations, subscripts i and k denote different Feisotopes. Note that the adsorption of Fe(II) and reductionof structural Fe(III) may not necessarily happen at the samesite (Yanina and Rosso, 2008).

The isotopic equilibration between Fe in solution andFe(III)-(hydr)oxides has been studied for both Fe(III)(Rea et al., 1994; Skulan et al., 2002; Poulson et al., 2005)and Fe(II) (Pedersen et al., 2005). While Fe(III)-studieswith ferrihydrite (Rea et al., 1994; Poulson et al., 2005) indi-cated that isotope exchange is limited to Fe atoms in avail-able sorption sites, Pedersen et al. (2005) showed that more

Sorption-induced Fe isotope fractionation sorption-induced Fe isotope fractionation 1797

than one atomic Fe layer of ferrihydrite, goethite, and lep-idocrocite was involved in the Fe isotope exchange reaction.This finding has been explained in terms of the catalytic ac-tion of sorbed Fe(II) which destabilizes the crystal structureupon reduction of structural Fe(III) (Pedersen et al., 2005).

The main objective of this study was to explore the Feisotope fractionation during sorption of Fe(II) to mineralsurfaces under strictly anoxic conditions at near-neutralpH. Specific objectives were:

(1) to determine the extent of equilibrium Fe isotopefractionation between dissolved and sorbed Fe(II) forminerals with and without structural Fe(III),(2) to test whether the fractionation of Fe isotopes dur-ing reactive transport of Fe(II) through synthetic aquifermaterials is amplified with respect to the fractionationobserved in closed equilibrium systems (‘chromato-graphic fractionation’),(3) to investigate the relative contribution of kinetic andequilibrium isotope effects to the apparent Fe isotopefractionation in flow-through systems,(4) to quantify the extent of atom exchange between dis-solved Fe(II) and structurally bound Fe(III) in equilib-rium and flow-through systems.

Objective 1 was assessed by batch experiments using alu-minum oxide, goethite, quartz, and goethite-loaded quartzas mineral sorbents. The Fe isotope fractionation duringreactive transport of Fe(II) was studied with column exper-iments using pure and goethite-loaded quartz sand as arti-ficial aquifer materials (objective 2). The relativecontribution of equilibrium and kinetic isotope effects tothe apparent Fe isotope fractionation in flow-through sys-tems was tested by isotope fractionation modeling of batchand column experiments with quartz (objective 3). In orderto determine the extent of atom exchange between Fe(II)aq

and structurally bound Fe(III) (objective 4), we conductedbatch experiments with goethite and modeled isotope datawith an equilibrium isotope fractionation model accountingfor atom exchange. In addition, a column experiment withgoethite-loaded quartz allowed us to quantify directly theatom exchange at the goethite surface. Complementaryexperiments were carried out with pure quartz for whichatom exchange reactions are impossible.

2. MATERIALS AND METHODS

2.1. Sorbents

We used three different mineral sorbents differing instructure and reactivity: aluminum oxide (c-Al2O3), goe-thite (a-FeOOH), and quartz (a-SiO2) sieved to a particlesize >200 lm. In addition, we synthesized goethite-loadedquartz sand. The minerals had a specific BET surfacearea of 145 m2/g (c-Al2O3), 30 m2/g (a-FeOOH), and0.28 m2/g (a-SiO2). The goethite-loaded quartz sand con-tained 0.97 ± 0.01 (±1r) g Fe/kg. Specific information onthe origin, synthesis, purification, and characterization ofthe mineral sorbents can be found in the electronicannex.

2.2. Isotope fractionation experiments

Experiments were conducted in a glove box (Unilab, M.Braun Inertgas-Systeme, Garching, Germany) equippedwith a MB-OX-EC oxygen probe, an MB-LMF-II solventfilter, and a MB 20G gas purification system. The atmo-sphere consisted of 100% N2(g) and the partial pressure ofO2(g) was maintained below 0.1 ppm. The laboratory tem-perature was regulated during all these experiments at23 ± 1 �C.

All glassware used was acid-washed and extensivelyrinsed with ultrapure water (18.2 MX cm) before use. Anyplastic ware used in glove box experiments, e.g., vials, pip-ette tips, or disposable syringes, was equilibrated with theglove box atmosphere for at least several days before beingused in order to remove oxygen traces.

In all experiments, 20 mM MOPS buffer (3-(N-morpho-lino)-propanesulfonic acid, Sigma–Aldrich, >99%) pre-pared with ultrapure water was used to maintain thesolution pH at 7.2 ± 0.1. The complexation of heavy metalsby MOPS has been tested to be negligible (Yu et al., 1997;Mash et al., 2003). Also, the interaction of MOPS with min-eral surfaces does reportedly not affect surface-related reac-tions (Kraemer et al., 1999).

Anoxic MOPS solutions pre-adjusted to pH 7.2 and an-oxic ultrapure water used for cleaning (e.g., pH electrode)and the preparation of anoxic HCl and NaOH solutionsfor pH adjustments were prepared by purging solutionswith Ar gas for 3 h at �80 �C. Concentrated HCl andNaOH (Sigma–Aldrich, puriss p.a.) solutions, which werefurther diluted with anoxic water in the glove box, werepurged with Ar gas for 1 h at room temperature. Stocksolutions of FeCl2 (�0.6 M) were prepared by heating Fepowder (Fe0

ðsÞ, Merck) at 100–150 �C in 1 M HCl underAr atmosphere until the H2(g) production nearly stopped(1–2 h). The solution was then transferred into the glovebox, filtered (0.2 lm), and stored in the dark to inhibitthe photochemical oxidation of Fe(II). Because we alwaysprepared fresh Fe(II) stock solutions, d56/54Fe values ofthe initial Fe(II) varied from experiment to experiment(1.16–1.74&). These variations are presumably due to theincomplete oxidation of zero valent iron and/or isotopefractionation during oxidation.

2.2.1. Batch experiments

Sorption of Fe(II) to aluminum oxide, goethite, purequartz, and goethite-loaded quartz was studied in 20 mMMOPS at pH 7.2 ± 0.1. All experiments were performedin triplicates. The solids were allowed to pre-equilibratewith MOPS solution for 24 h and the pH was readjustedto pH 7.20 ± 0.05 with dilute anoxic NaOH or HCl if nec-essary. Then, FeCl2 solution with known isotopic composi-tion was added to the mineral suspensions contained in 25-mL serum bottles to obtain initial Fe(II) concentrationsspanning at least two orders of magnitude. The initialFe(II) concentrations, Fe(II)ini, used in the experimentsare listed in Table 1 along with the solid concentrationsand equilibration times.

Reactors were shaken outside the glove box in the darkon a rotary shaker at �60 rpm (aluminum oxide and


goethite experiments) or �25 rpm (pure and goethite-loaded quartz experiments). A lower rotation speed waschosen for the quartz sands to reduce abrasion of quartzgrains (and/or goethite), thus avoiding the creation ofnew sorption sites for Fe(II). For every manual pH adjust-ment, the reactors were re-transferred into the glove boxwhere, after final equilibration, samples were filteredthrough 0.2-lm 25-mm disposable syringe filters made ofregenerated cellulose. Sorption of Fe(II) to these filterswas tested and found to be negligible. The pH of thefiltrates was then recorded and the filtrates were stabilizedby addition of 200 lL of distilled 6 M HCl. The resultingpH was <1. Total Fe concentrations in the filtrates weredetermined with inductively coupled plasma – optical emis-sion spectrometry (ICP-OES, Vista-MPX, Varian). Ironstandards for ICP-OES analyses were prepared in 20 mMMOPS solution acidified with 2.5 vol.% of suprapureTM

30% HCl (Merck). Ferrous Fe was measured colorimetri-cally with an UVIKON 860 UV/Vis spectrophotometer(Tegimenta AG, Switzerland) at 562 nm after complexationwith ferrozine (Stookey, 1970). The difference between ini-tial and final Fe(II) concentrations was ascribed to sorbedFe(II). The dilution of the samples due to pH adjustmentsduring equilibration was accounted for in the calculationof the amount of sorbed Fe(II).

2.2.2. Column experiments

Iron isotope fractionation during reactive transport ofFe(II) was studied with quartz and goethite-loaded quartzas sorbents. The experimental setup is depicted in Fig. 1.The setup consisted of two HPLC pumps (PU-2080, Jasco)operated in constant flow mode, a degasser (Gastorr BG-14), a two-position switching valve (Rheodyne 7000), a25-cm glass chromatography column with an inner diame-ter of 1 cm (Omnifit), and a fraction collector (Gilson, FC203B). Tubing material was exclusively made of FEP Tef-lon� (Upchurch Scientific). The column was equipped with25-lm polypropylene frits.

After the columns had been slowly saturated with20 mM MOPS solution (pH 7.2) at a flow rate of 0.05–0.1 mL/min for at least 24 h, the column materials were re-acted with 20 mM MOPS solution (pH 7.2) containingeither 0.60 mM FeCl2(aq) (quartz experiment) or 0.57 mMFeCl2(aq) (goethite-loaded quartz experiment). The flowrate was set to 0.2 mL/min. Once the concentration ofFe(II) in the effluent reached >90% of the initial Fe(II) con-centration, desorption was initiated by rinsing the columnswith 20 mM MOPS solution (pH 7.2). The pH of the efflu-ent never deviated from the target pH by more than

Table 1Experimental conditions of the batch experiments (pH 7.2 ± 0.1, 20 mM

Sorbent Solid concentration [g/L] Initial Fe(II) [

Aluminum oxide 10 0.54–53.7Goethite 10 0.11–48.9Quartz 500 0.021–2.1Goethite-loaded quartz 500 0.21–15.6

a SSA = specific BET surface area determined with N2 gas adsorption.b Equilibrium pH deviated by up to 1.0 unit from the target pH of 7.2c Not analyzed.

0.1 unit. Finally, after Fe(II)aq reached concentration levels<10 lM, the columns were flushed with dilute anoxic HClto desorb any remaining Fe(II). The recovery of Fe(II) inthe effluent was 95% in the quartz experiment and 100%in the experiment with goethite-loaded quartz. Samplingtime varied from 3 to 50 min/tube. Ferrous Fe concentra-tions were generally determined immediately after samplingusing the Ferrozine method. In the case of the goethite-loaded quartz, samples were also analyzed for total Fe byICP-OES since the detachment of goethite particles fromthe quartz grains might have contributed to the isotopiccomposition of dissolved Fe. For the measurement of Feisotopes, samples were partially pooled to yield a total Femass of about 5–50 lg Fe per sample. Subsequently, thepooled samples were acidified with distilled 6 M HCl to apH < 1, and transferred into the clean chemistry laboratoryfor further processing.

2.2.3. Iron isotope analysis

For Fe isotope analysis, samples were purified accordingto a slightly revised procedure of the methods previouslydescribed by Teutsch et al. (2005) and Wiederhold et al.(2007). All acids used during sample processing (6 MHCl, 14.3 M HNO3) were previously distilled using aquartz–glass still. All diluted acid solutions used were pre-pared with ultra-high purity water (P18.3 MX cm). Samplevolumes containing 5–50 lg Fe were placed in pre-cleanedTeflon beakers and the solvent was evaporated at approxi-mately 180 �C after addition of 3 � 0.5 mL of 30% H2O2

(suprapureTM, Merck) and 1 mL of 14.3 M HNO3 in orderto oxidize the MOPS buffer and Fe(II). Before the sampleswere evaporated to complete dryness, the Fe was taken upin 0.5–1 mL of 6 M HCl. The samples were subsequentlypurified on Teflon columns filled with approximately1 mL anion exchange resin (Bio-Rad, AG1 X4, 200–400mesh). In 6 M HCl medium, Fe(III) is present as FeCl�4 an-ion which is effectively adsorbed onto the resin while thematrix elements are eluted by rinsing the column with6 M HCl. Prior to sample addition, the anion exchange re-sin was cleaned with 2 � 1 mL of 1:5 (v/v) diluted 14.3 MHNO3 and conditioned with 4 � 0.5 mL of 6 M HCl. Afterloading the sample onto the column, the sample matrix waseluted by addition of 7 � 0.5 mL 6 M HCl. The Fe was thenquantitatively eluted from the column with 0.05 M HCl.The samples were again evaporated to almost complete dry-ness and taken up in 5 mL 0.05 M HCl as solution matrixfor the Fe isotope measurements. Tests revealed (i) thatMOPS and its potential degradation products had no influ-ence on the accuracy of our Fe isotope measurements be-

MOPS, 23 ± 1 �C).

mM] Initial Fe(II)/SSAa [lmol/m2] Equilibration time [h]

0.37–37 72b/2400.37–163 720.15–15 48n.a.c 72

(see electronic annex).

Fig. 1. Experimental setup of the column experiments performed in an anoxic glove box (O2 < 0.1 ppm). Not to scale.


cause the d56/54Fe value of the IRMM-014 standard mixedwith MOPS solution and processed according our samplepurification procedure was not significantly affected(D < 0.1&), and (ii) that during sample purification andelution steps no Fe was lost (<1%).

The Fe isotope ratios of our samples were determinedon a large-geometry Nu 1700 multiple collector induc-tively coupled plasma mass spectrometer (MC-ICP-MS,Nu Instruments, UK) operated at a resolution of 2500(m/Dm) which allowed us to fully resolve argide (ArN+,ArO+, ArOH+) and chloride (37Cl16OH) interferencesfrom the Fe mass spectrum. The instrument was coupledwith an ASX-100 autosampler (Cetac, USA) and a DSN-100 desolvation nebulizer system (Nu instruments). Weused the sample-standard bracketing approach to correctfor instrumental mass bias (Schoenberg and von Blanck-enburg, 2005) with IRMM-014 as standard referencematerial. Prior to mass spectrometry analysis, standardand sample solutions were diluted to 150 lg/L Fe with0.05 M HCl. The typical sensitivity of the total Fe signalwas about 6–7 V (150 lg/L Fe, uptake rate = 80–100 lL/min). All four Fe isotopes were simultaneously collectedin Faraday cups equipped with 1011X resistors. The po-tential contribution of 54Cr to the 54Fe signal was moni-tored using the mass 52 (52Cr). However, the presence ofCr in our samples was negligible because the 54Cr beamwas typically less than about 0.1% of the 54Fe beam.The isotopic composition was expressed in delta notation,where

d56=54Fe ¼ð56Fe=54FeÞsample

ð56Fe=54FeÞIRMM-014

� 1

!� 1000&; and ð4Þ

d57=54Fe ¼ð57Fe=54 FeÞsample

ð57Fe=54FeÞ IRMM-014

� 1

!� 1000&: ð5Þ

Here, (56Fe/54Fe)sample or (57Fe/54Fe)sample and(56Fe/54Fe)IRMM-014 or (57Fe/54Fe)IRMM-014 refer to themeasured isotope ratios of the sample and the mean isotoperatios of the standards placed before and after all samplesin the run sequence, respectively. Because the fractionationof Fe isotopes is mass-dependent, both values can be inter-converted in the absence of isobaric interferences by theapproximation d57/54Fe = 1.5 � d56/54Fe. Here, we only re-port d56/54Fe values and errors are always given as 2r. Aplot of 56Fe/54Fe versus 57Fe/54Fe ratios showed that thedata followed the theoretical mass-dependent fractionationline, demonstrating the absence of isobaric interferences.Samples were only analyzed after repeated measurementsof our internal house standard (ETH Fe salt) againstIRMM-014 yielding results consistent with our long-termvalues (d56/54Fe = �0.72 ± 0.13& (±2r), n = 210). Stan-dard solutions were prepared at 150 lg/L Fe in identicalsolution matrix as our samples and the IRMM-014 refer-ence. The ETH Fe salt standard was repeatedly analyzedafter every eighth sample measurement and at the end ofthe analytical session. Every sample was measured in tripli-cate or quadruplicate and the precision of these measure-ments was better than or similar to the long-termprecision of our internal house standard.

We also investigated the potential isotopic zoning of thegoethite and the fractionation of Fe in the goethite duringthe preparation of the goethite-loaded quartz. In the firstcase, goethite was dissolved in 6 M HCl in a water bathat 45 �C for 1, 4, and 8 h. The fractions of Fe dissolved were0.7%, 6.2%, and 18.5%, respectively. The samples were fil-tered (0.2 lm) and analyzed for total Fe with ICP-OESand for Fe isotopic ratios with MC-ICP-MS. Goethite at-tached to the quartz grains and pure goethite were alsocompletely dissolved in 6 M HCl and the isotope ratios ana-lyzed with MC-ICP-MS. The d56/54Fe of pure goethite was0.10 ± 0.13& and neither the Fe isotope composition in the


three dissolved fractions nor that of goethite associatedwith quartz differed significantly from this value (D56/54Fewithin ±0.13&).

2.3. Modeling data from batch experiments

2.3.1. Sorption

We described equilibrium sorption of Fe(II) by a two-site Langmuir isotherm:

seqFe ¼

sImax � KI

Fe

1þ KIFe � cFe

þ sIImax � KII

Fe

1þ KIIFe � cFe

� �� cFe; ð6Þ

where seqFe is the equilibrium concentration of sorbed Fe(II)

[mol/kg], sImax and sII

max are the sorption capacities of sites Iand II [mol/kg], KI

Fe and KIIFe are the equilibrium coefficients

of sorption at sites I and II [m3/mol], and cFe is the aque-ous-phase concentration of Fe(II) [mol/m3]. We used thetwo-site Langmuir model because (i) other models, includ-ing the Freundlich or the single-site Langmuir model, didnot fit the data in most instances, and (ii) equilibrium coef-ficients KI

Fe and KIIFe were needed for transport modeling of

the column experiments.For the estimation of the sorption parameters, we con-

sidered the mass balance in batch experiments:

ctotFe¼ h� cini

Fe¼ h� cFeþð1�hÞ�qs� seqFe

¼ cFe hþð1�hÞ�qs� sImax�KI

Fe

1þKIFe� cFe

þð1�hÞ�qs� sIImax�KII

Fe

1þKIIFe� cFe

� �ð7Þ

in which ctotFe is the total Fe concentration [mol/m3], that is,

the number of moles of Fe(II) in both the aqueous andsorbing phases divided by the total volume, h is the volu-metric water content [�], and qs denotes the mass densityof the solids [kg/m3]. Prior to contact with minerals, allFe(II) participating in sorption reactions is in the aqueousphase. At this stage, the aqueous-phase concentration iscini

Fe. Thus ctotFe can easily be computed for all individual

experiments. For a given set of parameters sImax, sII

max, KIFe,

and KIIFe, the equilibrium concentration cFe was computed

by Picard iteration: the concentration in the denominatorsof Eq. (7) were fixed to the current estimate, which was up-dated by dividing ctot

Fe by the term in the bracket on theright-hand side of Eq. (7). The parameters sI

max, sIImax, KI

Fe,and KII

Fe were determined by fitting the simulated relation-ship cFeðcini

FeÞ to the experimental data. As objective functionwe used the sum of squared residuals weighted by theuncertainty of the individual measurements. As optimiza-tion scheme, we applied the Gauss–Newton method. To en-sure that the estimated parameters were positive, weestimated their logarithm. Then, the best estimates andthe standard deviations rlnp of estimation of the log-param-eters were delogarithmized, resulting in an estimatedparameter and a factor of variation FV:

FV p ¼ expðrln pÞ: ð8Þ

2.3.2. Equilibrium fractionation of Fe isotopes without atom

exchange

The equilibrium fractionation factor aeqi=k [�] can be de-

fined as:

aeqi=k ¼

seqi

seqk

� ck

ci¼ Ki

Kk; ð9Þ

where the subscripts denote different isotopes with i > k

(e.g., i = 56Fe, k = 54Fe), K is the equilibrium sorption coef-ficient for a specific sorption site [m3/mol]. For conve-nience, aeq

i=k can also be expressed as an equilibriumenrichment factor according to:

eeqi=k ¼ ða

eqi=k � 1Þ � 1000&: ð10Þ

Values eeqi=k > 0 imply that the heavier isotope i sorbs

more strongly than the lighter isotope k.A method of describing equilibrium isotope fraction-

ation without considering a particular sorption model canbe achieved by mass balance calculations. The mass balanceapproach yields a weighted average isotope fractionationfactor in terms of all reactive surface sites of a specific sor-bent. The equilibrium fractionation factor aeq

i=k or the asso-ciated enrichment factor eeq

i=k can be determined from theisotope mass balance:

di=kFeðIIÞini ¼ di=kFeðIIÞsorb � F sorb þ di=kFeðIIÞaq

� ð1� F sorbÞ; ð11Þ

where di/kFe(II)ini is the isotope ratio in delta notation inthe initial solution prior to contact with the solid phase,di/kFe(II)sorb relates to the sorbed Fe(II) after equilibration,and di/kFe(II)aq to the aqueous phase after equilibration.Fsorb denotes the number of kFe atoms in the sorbing phase,N sorb

k Fe , divided by the total number of kFe atoms in both theaqueous and sorbing phase, N ini

k Fe ¼ N sorbk Fe þ N aq

k Fe. For small

Fe isotope fractionations, this ratio is assumed to beidentical to the molar fraction of total Fe:

F sorb ¼N sorb

k Fe

N sorbk Fe þ N aq

k Fe

� N sorbFe

N sorbFe þ N aq

Fe

: ð12Þ

The definition of the equilibrium fractionation factor,Eq. (10), may be reformulated as:

di=kFeðIIÞsorb ¼ aeqi=k � di=kFeðIIÞaq þ ða

eqi=k � 1Þ � 1000&

¼eeq

i=k

1000&þ 1

!� di=kFeðIIÞaq þ eeq

i=k ð13Þ

which can be combined with Eq. (11) to obtain:

di=kFeðIIÞaq ¼di=kFeðIIÞini � eeq

i=k � F sorb

eeqi=k

1000&� F sorb þ 1

: ð14Þ

For small values of eeqi=k , Eq. (14) can be approximated

as:

di=kFeðIIÞaq � di=kFeðIIÞini � eeqi=k � F sorb: ð15Þ

Eq. (15) can be used to estimate the equilibrium enrich-ment factor eeq

i=k by linear regression, regardless of the actualshape of the sorption isotherm. For eeq

i=k values in the orderof 1&, the error introduced by the approximation made inEq. (15) is in the third digit of the estimated eeq

i=k value. For

the estimation of the slope eeqi=k and intercept di/kFe(II)ini in

Eq. (15), we used a Bayesian regression scheme because bothdi/kFe(II)aq and Fsorb are prone to measurement error (Press


et al., 1992). In this scheme, we estimated not only eeqi=k and

di/kFe(II)ini, but also the true values of Fsorb. The objectivefunction includes the sum of squared residuals in di/kFe(II)aq,weighted by their measurement error, and the sum of squareddeviations between measured and estimated Fsorb values, alsoweighted by their measurement errors. As optimizationscheme, we used the Gauss–Newton method.

Eqs. (14) and (15) were formulated for a closed system,where all Fe(II) participating in sorption originates fromthe initial solution with isotopic composition according todi/kFe(II)ini.

2.3.3. Equilibrium fractionation of Fe isotopes with atom

exchange

In this model we assume that a certain number N exFe of Fe

atoms participate in atom exchange at the goethite surfaceafter interfacial electron transfer from adsorbed Fe(II) tolattice-bound Fe(III). In the following, we use the ratio M

of the number N inik Fe of kFe atoms introduced with the initial

aqueous solution to the sum of kFe atoms in both the solu-tion and the exchangeable pool of goethite-Fe. Again, weassume that the following approximation is valid:

M ¼N sorb

k Fe þ N aqk Fe

N sorbk Fe þ N aq

k Feþ N ex

k Fe

� N sorbFe þ N aq

Fe

N sorbFe þ N aq

Fe þ N exFe

¼ N iniFe

N iniFe þ N ex

Fe

: ð16Þ

Here, N aqk Fe

and N sorbk Fe are the number of kFe atoms in the

aqueous solution and sorbed onto the mineral surface,respectively. The number with subscript ‘Fe’ refers to totalFe rather than kFe.

Prior to the sorption experiment, Fe atoms in theexchangeable Fe pool have the same isotopic composi-tion as the goethite, which is denoted as di/kFegoethite

(d56/54 Fegoethite = 0.10&). After equilibration, we assumethat the isotopic composition in the exchangeable Fepool is identical to that of the sorbed Fe, di/kFe(II)sorb.This results in the following isotope mass balance:

di=kFeðIIÞini �M þ di=kFegoethite � ð1�MÞ¼ di=kFeðIIÞsorb � ðF sorb �M þ 1�MÞþ di=kFeðIIÞaq � ð1� F sorbÞ �M ð17Þ

Substituting Eq. (13) into Eq. (17) and solving for di/k

Fe(II)aq leads to:

di=k FeðIIÞaq ¼di=k Fegoethite�ð1�MÞþdi=k FeðIIÞini�M� eeq

i=k �ð1þðF sorb�1Þ�MÞeeqi=k

1000&�ððF sorb�1Þ�Mþ1Þþ1

;

ð18Þ

which simplifies to Eq. (14) in the limiting case of M = 1,corresponding to the situation where no atom exchangetakes place. It is important to note that M depends onthe Fe concentration in the initial solution (Eq. (16)). Thatis, in a series of batch experiments with varying initial con-centrations of Fe(II), the ratio M differs from experiment toexperiment. The fixed property in such a series of experi-ments is the number N ex

Fe of Fe atoms participating in atomexchange. We normalized N ex

Fe to the mass of goethite, lead-ing to a mass-related concentration sex

Fe of exchangeableFe(III) [mol/kg].

2.4. Modeling of Fe(II) transport and Fe isotopes in column

experiments

Because each isotope i can be treated as individualchemical component competing with j other isotopes forsorption sites, we use the multi-component two-site Lang-muir isotherm to describe sorption of Fe isotopes:

seqi ¼

sImax � KI

i

1þP

jKIj � cj

þ sIImax � KII

i

1þP

jKIIj � cj

!� ci; ð19Þ

where index i denotes an isotope-specific quantity, and in-dex j refers to Fe isotopes competing with isotope i for sorp-tion sites I and II. All other parameters have their usualmeaning (see Eq. (6)).

In the column experiments, sorption is not at equilib-rium. We describe advective–dispersive transport of isotopei subject to kinetic adsorption and desorption by the advec-tion–dispersion equation coupled to a multi-rate masstransfer model (Haggerty and Gorelick, 1995; Carreraet al., 1998; Cvetkovic and Haggerty, 2002):

h @ci@t þ q @ci

@x � hD @2ci@x2 ¼ ð1� hÞqs

R smax

0pðsÞs ðsiðsÞ � seq

i Þds@siðsÞ@t ¼ 1

s ðseqi � siðsÞÞ

;

ð20Þ

where q is the specific discharge or Darcy velocity [m/s] andD is the dispersion coefficient [m2/s]. The ratio hD/q isknown as dispersivity [m]. s is a mass-transfer time [s],p(s) is the probability density function of s [1/s], smax isthe maximum mass-transfer time [s], si(s) is the sorbed-phase concentration [mol/kg] of isotope i in the sorbingphase characterized by the mass-transfer time s. The trans-port equation of isotope i depends on the concentrations ofall isotopes because seq

i does (Eq. (19)).The multi-rate mass transfer model implies a distribu-

tion of mass-transfer times in contrast to a single mass-transfer coefficient used in simple linear-driving-forcemodels of sorption (Haggerty and Gorelick, 1995). We havealso tried to fit the measured breakthrough curve of Fe(II)with a single mass-transfer time and with a distinct mass-transfer time for each sorption site. These models couldnot reproduce the shape of the breakthrough curve.

For the distribution p(s) of the mass-transfer time s, weassume a truncated power-law distribution:

pðsÞ ¼ 1� ns1�n

max

s�n ð21Þ

with the exponent n [�] ranging between zero and unity. Inthe numerical implementation the range [0, smax] was subdi-vided into 10 sub-ranges with increasing bin size. For eachsub-range, the integral of p(s) and the mean mass-transfertime within that sub-range was computed, leading to a setof ten effective mass-transfer times and associatedprobabilities.

The transport coefficients h, q, and D of Eq. (20) werefitted from conservative-tracer tests using NaNO3 as a tra-cer. The breakthrough curves were monitored with a con-ductometer (Metrohm, L712 with LF1100 measuring cell).The mass-density of the solids qs was set to the value ofquartz. The equilibrium-sorption coefficients sI

max, sIImax, KI

i ,


and KIIi , as well as the equilibrium enrichment factor, eeq

i=k ,were determined from the batch experiments. The coeffi-cients smax and n, describing the distribution of mass-trans-fer times s, were fitted from the breakthrough curve ofFe(II) using the Nelder-Mead simplex algorithm (Lagariaset al., 1998). We simulated the breakthrough curve of Feisotopes using kinetic enrichment factors ekin

i=k (i > k) rangingbetween 0& and 5&. The kinetic isotope enrichment factoris defined as

ekini=k ¼ ðakin

i=k � 1Þ � 1000&; ð22Þ

where akini=k [�] is the kinetic isotope fractionation factor gi-

ven by the ratio of mass-transfer times for two isotopes:

akini=k ¼

si

sk: ð23Þ

That is, ekini=k > 0 implies that isotope i sorbs more slowly

than isotope k.For both equilibrium and kinetic fractionation, we as-

sumed that the enrichment factors of isotope 57Fe can bescaled to that of 56Fe by eeq

57=54 ¼ 1:5� eeq56=54 and

ekin57=54 ¼ 1:5� ekin

56=54.

3. RESULTS AND DISCUSSION

3.1. Microscopy

Scanning and transmission electron micrographs of thesorbents used are displayed in Fig. 2.

Images of the goethite-loaded quartz demonstrate thatacicular goethite crystals did not form a homogeneous sin-gle-layer coating but instead accumulated in cracks and fis-sures of quartz grains with no preferred orientation (Fig. 2eand f). The extensive twinning of goethite crystals was vis-ible at larger magnification (Fig. 2g, h). Fig. 2g and h alsoillustrate that the dominating (110) faces and the (021)faces terminating the goethite crystals were well developedin our sample.

3.2. Equilibrium Fe isotope fractionation in batch

experiments

Sorption isotherms of Fe(II) are depicted in Fig. 3 andthe corresponding sorption parameters are compiled in Ta-ble 2. Our sorption data imply that for the highest Fe(II)aq

equilibrium concentrations, the amount of Fe(II) sorbed toaluminum oxide and goethite was beyond the monolayercapacity. These data points were not considered in the mod-eling of Fe isotope fractionations. A detailed discussion ontheoretical and observed Fe(II) sorption capacities for eachsorbent can be found in the electronic annex.

Fig. 4 shows the d56/54Fe values of dissolved Fe(II) as afunction of the fraction of sorbed Fe(II), Fsorb. For alumi-num oxide, we plotted two experiments in which we variedthe equilibration time and Fsorb. Both experimental datasets imply that an equilibrium isotope fractionation effectis nearly absent, that is eeq

56=54 � 0& (Fig. 4A, Table 3). Sim-ilar results have been obtained for Zn(II) sorption to a-Al2O3 (Pokrovsky et al., 2005) and for Cr(VI) sorption toc-Al2O3 (Ellis et al., 2004).

There is evidence that metal-(hydr)oxides can enhancethe precipitation of divalent metal cations at solution con-centrations much lower than predicted for homogeneousmetal precipitation. Surface precipitate formation of diva-lent transition metals on alumina phases has been invokedin a number of studies (Tewari and Lee, 1975; Towle et al.,1997; Nano and Strathmann, 2006). As already mentioned,the maximum amount of Fe(II) sorbed to aluminum oxidefar exceeded the monolayer coverage, implying that a sig-nificant fraction of Fe(II) was removed from solution byprecipitation. The simultaneous occurrence of adsorptionand precipitation may conceal an observable equilibriumisotope effect. It is conceivable that, for example, light Feisotopes are preferentially sequestered in a surface precipi-tate while heavy isotopes are favored in an adsorption reac-tion. However, it would seem fortuitous that the two effectsbalance each other.

In contrast to aluminum oxide, we observed strong equi-librium fractionation effects for all other sorbents tested(Fig. 4, Table 3). The equilibrium enrichment factor eeq

56=54

for Fe(II) sorption to pure quartz was 0.85 ± 0.04& (±1r)as determined from the fit of Eq. (15) to data in Fig. 4B.The magnitude of Fe isotope fractionation upon equilibriumsorption of Fe(II) to quartz (Table 3) documents that quartz,an ubiquitous mineral in soils and sediments, has an intrinsicability to fractionate Fe isotopes during sorption of Fe(II).To the best of our knowledge, no data on the sorption-in-duced Fe isotope fractionation of quartz are yet availablein the literature. Note that the equilibrium enrichment factorcalculated for pure quartz is similar in magnitude to or evenlarger than those observed in anaerobic abiotic and bioticsystems where Fe(II) participated in sorption reactions withFe(III) phases (Table 4).

The fractionation of Fe isotopes due to equilibriumsorption of Fe(II) onto goethite was computed either withor without atom exchange. For these calculations, we omit-ted data that were presumably influenced by the precipita-tion of Fe(OH)2(s) (see open symbols in Fig. 4C). Withoutconsideration of atom exchange between dissolved Fe(II)and structural goethite-Fe, the calculated enrichment factoreeq

56=54 was 2.01 ± 0.04& (±1r). This equilibrium enrichmentfactor is – though likely by coincidence – in agreement withthe value reported by Icopini et al. (2004) (Tables 3 and 4).However, eeq

56=54 in our goethite experiments is biased by iso-topically light goethite-Fe which was reduced by sorbedFe(II) and subsequently released into solution. Conse-quently, no satisfying fit could be produced when goethitedata were modeled without atom exchange by constrainingM in Eq. (18) to be equal to unity (Fig. 4C). In contrast,when atom exchange was taken into account, a reasonablefit of the goethite data could be achieved with an enrich-ment factor eeq

56=54 of 0.73 ± 0.12& (±1r) and a sexFe value

of 0.384 ± 0.136 mol/kg goethite (±1r) (Fig. 4C, Table 3).Our results show that when atom exchange at the goe-

thite surface was accounted for, eeq56=54 decreased notably

and is comparable in magnitude with the enrichment fac-tors of pure quartz (this study) and goethite used in exper-iments investigating the microbial reductive dissolution ofFe(III)-(hydr)oxides (Crosby et al., 2005, 2007) (Table 4).Our data indicate that the isotopic composition of dissolved

Fig. 2. Scanning electron microscopy images of aluminum oxide (a and b), quartz (c and d), and goethite-loaded quartz (e and f).Transmission electron microscopy images of the goethite are shown in panels g and h.


Fe(II) in our goethite system was controlled both by atomexchange between dissolved Fe(II) and structurally-boundFe(III) and the sorption-induced Fe isotope fractionation.We also fitted the Rayleigh equation (Criss, 1999) to thegoethite data by adjusting the fractionation factor a56/54

to 1.0008 and plotted the result in Fig. 4C. Clearly, the frac-tionation of Fe isotopes in our goethite experiment cannotbe explained by a Rayleigh-type process as the sorbed Fe isstill in equilibrium with dissolved Fe over the course of theexperiment.

Fig. 3. Sorption isotherms of Fe(II) for aluminum oxide, goethite, goethite-loaded quartz, and pure quartz (pH 7.2 ± 0.1, 20 mM MOPS,23 ± 1 �C). Lines indicate model fits (see text for details); aluminum oxide: single Langmuir model; goethite, goethite-loaded quartz, andquartz: two-site Langmuir model.

Table 2Fitted sorption parameters of batch experiments. Aluminum oxide: single Langmuir model; goethite, quartz, and goethite-loaded quartz:two-site Langmuir model. sI

max, sIImax: sorption capacities of sites I and II; KI

Fe, KIIFe: associated equilibrium coefficients of sorption; FV: factor of

variation, that is, exponent of the standard deviation of the estimated log parameter; n.a.: not applicable.

Sorbent sImax [mol/kg] FV sII

max [mol/kg] FV KIFe [m3/mol] FV KII

Fe [m3/mol] FV

Aluminum oxidea 4.40 1.62 n.a. 0.189 2.26 n.a.Goethite 0.0524 1.04 0.150 1.20 801 1.52 0.738 1.41Quartz 2.66 � 10�4 1.09 7.86 � 10�4 1.06 264 1.24 3.01 1.23Goethite-loaded quartz 6.98 � 10�4 1.07 2.45 � 10�3 1.17 146 1.57 0.236 1.36

a Two hundred and forty-hours equilibration.


The equilibrium enrichment factor of goethite-loadedquartz was identical within error to pure quartz (Fig. 4D,Table 3). We predicted d56/54Fe(II)aq in the experiment withgoethite-loaded quartz by a linear mixing model using thesorption and isotope fractionation parameters of purequartz and goethite (Tables 2 and 3). Here we assumed thatboth sorbents are independent of each other. The isotopicmass balance in the context of this model can be written as:

di=kFeðIIÞini �M þ di=kFegoethite � ð1�MÞ¼ di=kFeðIIÞgoethite

sorb � ðF goethitesorb �M þ 1�MÞ

þ di=kFeðIIÞquartzsorb � F quartz

sorb �M þ di=kFeðIIÞaq

�ð1� F goethitesorb � F quartz

sorb Þ �M ;

ð24Þ

where

F goethitesorb ¼

N sorb;goethitek Fe

N inik Fe

� N sorb;goethiteFe

N iniFe

;

F quartzsorb ¼

N sorb;quartzk Fe

N inik Fe

� N sorb;quartzFe

N iniFe

;

N iniFe ¼ N sorb;goethite

Fe þ N sorb;quartzFe þ N aq

Fe; and

M ¼N ini

k Fe

N inik FeþN ex

k Fe

� N iniFe

N iniFeþN ex

Fe

Substitution of the enrichment factor (Eq. (13)) into Eq.(24) and solving for di/kFe(II)aq leads to:

di=kFeðIIÞaq ¼di=kFeðIIÞini �M þ di=kFegoethite � ð1�MÞ

egoethite

i=k

1000&� ðF goethite

sorb �M þ 1�MÞ þ 1þequartz

i=k

1000&� F quartz

sorb �M:

ð25Þ

The prediction of Eq. (25) is shown as a dashed line inFig. 4D. Obviously, the model prediction corresponds rea-sonably well with the observations when the long-term pre-cision of our internal house standard (2r = 0.13&) and theerror of the exchangeable Fe(III) pool of goethite (Table 3)are considered.

We note that in the experiments with goethite-loadedquartz, goethite provided 2/3 of sorption sites for sorbedFe(II) (Table 2). Because the apparent enrichment factorof goethite (eeq

56=54 without atom exchange) was much largerthan that of pure quartz, one would expect goethite to havea significant influence on the equilibrium enrichment factorof goethite-loaded quartz (Table 3). However, Fig. 4B andD show the contrary. Thus, the question arises why the iso-topic composition of Fe(II)aq in sorption equilibrium withgoethite-loaded quartz can equally well be described withor without atom exchange (Eq. (15) vs. Eq. (25)). Thisobservation most likely results from the small pool size ofexchangeable Fe(III), sex

Fe, in the ‘quartz + goethite’ systemand hence from a value of M in Eq. (25) close to unity(>0.8 for Fe(II)aq > 1 mM). In addition, d56/54Fe(II)aq ismuch more sensitive to parameter M (implicitly to sex

FeÞ inEq. (25) than to d56/54Fegoethite. It follows that without con-

Fig. 4. Plots of d56/54Fe of dissolved Fe(II) as a function of the fractional Fe(II) sorption (cf. Eq. (12)). A: aluminum oxide; B: quartz, blackline = fit of Eq. (15), gray line = calculated isotopic composition of sorbed Fe(II); C: goethite, black lines = fit of (i) Eq. (18) with/withoutatom exchange (AE), and (ii) the Rayleigh equation (Criss, 1999) with an adjusted fractionation factor of 1.0008, gray line = calculatedisotopic composition of sorbed Fe(II) with AE, open symbols indicate samples that were presumably oversaturated with respect to Fe(OH)2(s)

and thus not considered in the fits; D: goethite-loaded quartz, solid black line = fit of Eq. (15), dashed line = prediction of d56/54Fe(II)aq

assuming that the extent of AE and the equilibrium enrichment factor of goethite in the mineral mixture is identical to pure goethite (Eq. (25)),gray line = calculated isotopic composition of sorbed Fe(II). eeq

56=54 is the equilibrium enrichment factor of the Fe(II)sorb-Fe(II)aq couple and sexFe

is the amount of goethite-Fe that can be exchanged for Fe(II) in solution. Parameter estimates are given with their standard deviationobtained from regression analysis. Error bars denote ±2r of replicate measurements (n = 3–4). The long-term precision (±2r) of our internalhouse standard was 0.13&. Note (i) that the scale of the y-axis in the panel C differs from all others, and (ii) that the measured d56/54Fe of theinitial Fe(II) solution is always given at Fsorb = 0.

Table 3Parameters of Fe isotope fractionation fitted from batch experiments by Bayesian linear regression. Numbers following ‘‘±” indicate standarddeviation of estimation.

Sorbent eeq56=54 [&] d 56/54Fe(II)ini [&] Correlation coeff. [�]

Aluminum oxidea �0.11 ± 0.02b 1.19 ± 0.01 �0.83Goethite (no atom exchange) 2.01 ± 0.04 1.32 ± 0.03 �0.85Quartz 0.85 ± 0.05 1.22 ± 0.02 �0.88Goethite-loaded quartz 0.85 ± 0.04 1.24 ± 0.02 �0.82Goethite (atom exchange) 0.73 ± 0.12 1.60 ± 0.16 sex

Fe � eeq56=54 : �0:79

sexFe � d56=54FeðIIÞini : 0:71

eeq56=54 � d56=54FeðIIÞini : �0:31

sexFe ¼ 0:384 � 0:136 mol/kg goethite

a Two hundred and forty-hours equilibration.b Effect is within analytical error.


sideration of sexFe in the ‘quartz + goethite’ system, one

would erroneously conclude that less atom exchange takesplace at the goethite surface in the goethite-loaded quartzsystem than in the goethite system. In other words, the ratio

between the pool size of isotopically exchangeable Fe(III)and the initial Fe(II) concentration significantly influencesthe Fe isotope composition of the aqueous solution inequilibrated closed systems.

Table 4Equilibrium Fe isotope enrichment factors (56/54) for the interaction of Fe(II)aq with mineral surfaces in abiotic and biotic systems. Errors aregiven as twice the standard deviation.

Couple A–B, mineral, process, pHa Enrichment factor for A–B Reference

Abiotic experiments

Fe(II)sorb–Fe(II)aq, quartz, sorption, pH 7.2 0.85 ± 0.10& This studyFe(II)sorb–Fe(II)aq, goethite-loaded quartz, sorption, pH 7.2 0.85 ± 0.08& This studyFe(II)sorb–Fe(II)aq, goethite, sorption, pH 7.2 0.73 ± 0.24&b This studyFe(II)sorb–Fe(II)aq, aluminum oxide, sorption, pH 7.2 �0&

c This studyFe(II)sorb–Fe(II)aq, goethite, sorption, pH 7.5 2.05&d Icopini et al. (2004)Siderite-Fe(II)aq, precipitation + adsorption, pHini = 4 �0.48 ± 0.22& Wiesli et al. (2004)

Biotic experiments

Siderite–Fe(II)aq, DIRe, Geobacter sulfurreducens �0& Johnson et al. (2005)Fe(II)sorb–Fe(II)aq, hematite or goethite, DIR, pH 6.8,

Geobacter sulfurreducens + Shewanella putrefaciens (pooled)0.30 ± 0.08& (hematite)0.87 ± 0.09& (goethite)

Crosby et al. (2007)

Fe(II)sorb–Fe(II)aq, hematite or goethite, DIR, pH 6.8,Geobacter sulfurreducens

0.38 ± 0.20& (hematite)0.86 ± 0.34& (goethite)

Crosby et al. (2005)

Magnetite–Fe(II)aq, DIR, Geobacter sulfurreducens 1.34 ± 0.22& Johnson et al. (2005)

a pH given when stated.b Calculated with atom exchange.c Effect is within analytical error.d Calculated without atom exchange.e DIR: microbial dissimilatory Fe reduction.


We wish to stress that fractionation of Fe isotopes uponinteraction with a solid phase may also depend on the coor-dination chemistry of dissolved Fe (Anbar et al., 2000; Bul-len et al., 2001). Because we employed differentconcentration ranges of Fe(II)ini as FeCl2(aq) in our experi-ments (Table 1), changes in Fe(II) coordination may haveaffected the extent of fractionation not only between differ-ent sorbents but also within a single batch experiment. Spe-ciation calculations indicated that the activity ratio Fe2+/FeOH+ in our experiments remained constant with decreas-ing Fe(II)ini whereas the activity ratio between Fe2+ (orFeOH+) and FeCl+ increased exponentially. The contribu-tion of FeCl+complexes to Fe(II)ini was less than 1% for thedata used in the computation of enrichment factors (Fig. 4).Because the relationship between d56/54Fe(II)aq and Fsorb inFig. 4B–D could be well modeled with constant enrichmentfactors, a significant effect of FeCl+ complexes on the Feisotope fractionation during sorption seems unlikely.

3.3. Column experiments

3.3.1. General aspects

Fig. 5 shows the breakthrough curves of Fe(II) and thecorresponding D56/54Feaq-ini values defined as difference ind56/54Fe between Fe(II) of the injected solution and thatmeasured in the outflow of the quartz column (Fig. 5A)and goethite-loaded quartz column (Fig. 5B).

Note that the horizontal bars associated with D56/54Feaq-ini

values indicate the range of samples pooled for isotopemeasurements. For the goethite-loaded quartz, cout/c0 oftotal Fe as determined from ICP-OES measurements coin-cides well with that of Fe(II)aq; hence the detachment ofgoethite crystals from quartz grains was negligible. TheD56/54Fe values observed in experiments with pure and goe-thite-loaded quartz deviated up to 0.88& and 1.63& fromthe respective input solution (Fig. 5). Thus, Fe isotope frac-

tionation in the ‘chromatographic’ flow-through systemswas hardly amplified in comparison with the batch systems(Fig. 5). A similar magnitude of effects was recently ob-served by Matthews et al. (2008) who studied Fe isotopefractionation during sorption of Fe(III) in a quartz columnat pH 0–2.

3.3.2. Simulation of Fe(II) breakthrough curves and Fe

isotope trends

Table 5 lists all parameters used in the simulations of thecolumn experiment with quartz and their origin. Fig. 6shows the simulated breakthrough curve of Fe(II) in theoutflow of the quartz column and the associated isotopesignature using various kinetic enrichment factors. The fitof the simulated Fe(II) breakthrough curve to the measureddata was satisfactory although slight systematic differencesremain (Fig. 6A). These differences indicate that the power-law model of Eq. (21) used for the distribution p(s) of mass-transfer times may not be fully appropriate. However, thefit is significantly better than that obtained with a singlemass-transfer time or a single mass-transfer time per sorp-tion site (both not shown).

The breakthrough of the invading front is retarded by afactor of �3 in comparison with a conservative tracer as ex-pected for a sorbing compound (Fig. 6A). At the recedingfront, however, the concentration of Fe(II) synchronouslystarts decreasing with decreasing tracer concentrations.This asymmetry is caused by the nonlinearity of Langmuirsorption, in which retardation is the strongest at the small-est concentrations.

In a system with sorption in local equilibrium, the invad-ing front would be much steeper than in the experimentalcolumn. The corresponding breakthrough curve is shownas a dotted line in Fig. 6A. Without sorption kinetics, theinflow concentration would be reached almost immediatelyafter the beginning of the breakthrough. In the experiment,

Fig. 5. Breakthrough curves of Fe and isotopic composition of Fe(II)aq (pH 7.2, 20 mM MOPS, 23 �C). c0 is the initial Fe concentration inour Fe(II) reservoir (cf. Fig. 1). Light gray area: rinsing of columns with 20 mM MOPS (pH 7.2); dark gray area: rinsing of columns with0.25 M HCl (A) and 0.01 M HCl (B). The isotopic composition is reported as D56/54Feaq-ini = d 56/54Fe(II)aq–d56/54Fe(II)ini. The solid blacklines in each graph indicate no isotope fractionation with respect to the initial Fe(II) solution. The dashed black line in (B) shows the isotopiccomposition of goethite on the D56/54Fe scale. Asterisks on D56/54Feaq-ini values mark samples for which the isotopic composition has beenestimated by linear interpolation between adjacent samples. Horizontal ‘error’ bars of D56/54Feaq-ini denote the range of samples contributingto the isotope measurements in equal volume shares; vertical error bars indicate the 2r-uncertainty of a sample’s d56/54Fe value. In addition,the 2r-precision of our internal house standard is given in the upper left corner of each panel. For the goethite-loaded quartz cout/c0 of [Fe]total

as determined from ICP-OES measurements is also provided. Note that the scales of the x- and y-axis are not the same for both sorbents.Data used for Fig. 5 are compiled in the electronic annex (Tables EA6–EA9).

Table 5Parameters used in the simulations of the quartz column experiments.

Parameter Estimated value ± standard deviationa Factor of uncertaintyb

From conservative tracer experiments

h 0.40 ± 2.67 � 10�4�

q 4.24 � 10�5 m/s (direct measurement)hD/q 3.42 � 10�4 ± 1.29 � 10�5 m�

qs 2650 kg/m3 (literature value)

From batch studies with quartz

sImax 2.66 � 10�4 mol/kg* 1.09

sIImax 7.86 � 10�4 mol/kg* 1.06

KIFe 264 m3/mol* 1.24

KIIFe 3.01 m3/mol* 1.23

eeq56=54 0.85 ± 0.05&�

From total Fe(II) in the outflow of the quartz column

n 0.720* 1.013smax 15.3 � 105 s* 1.111c

Parameter variation

ekin56=54 0–5& in steps of 0.5&

a Estimation based on the parameter (�) or its logarithm (*).b Exp(rlnp), where rlnp is the standard deviation of estimation of the log parameter.c Correlation coefficient of estimation between ln(n) and ln(smax): 0.93.


Fig. 6. Simulated breakthrough curves of the column experiment with pure quartz. A: Total Fe(II); dashed line: conservative tracer, dottedline: simulated Fe(II) assuming local equilibrium, solid line: simulated Fe(II) assuming multi-rate mass transfer (MRMT), symbols: measuredFe(II). B: Simulated d56/54Fe in the outflow using different kinetic enrichment factors ekin

56=54 and a constant equilibrium enrichment factor eeq56=54;

thick solid line: trend in d56/54Fe when local equilibrium is assumed, dashed line: d56/54Fe of the input solution.


by contrast, a fast concentration increase is followed bygradual further increase. The inflow concentration wasnever attained, a clear indication of slow sorption kinetics.The shape of the receding front is influenced by both non-linearity of Langmuir sorption and sorption kinetics.

Fig. 6B shows simulated isotope ratios d56/54Fe(II)aq inthe outflow. Without kinetic fractionation, ekin

56=54 ¼ 0&,the sorbed Fe(II) is enriched in heavy Fe isotopes becauseof the equilibrium fractionation effect. This results in a rel-ative accumulation of light Fe in the aqueous-phase solu-tion at the invading front. When desorption of Fe(II) isthen initiated, the aqueous-phase Fe(II) becomes isotopi-cally heavier in the receding front.

Kinetic isotope fractionation alters this picture. Sincelight Fe(II) is sorbing faster, the remaining aqueous-phaseFe(II) becomes heavier at the invading front. Only at laterstages does the equilibrium fractionation, which favors hea-vy isotopes in the sorbing phase, determine the observedisotope fractionation. Depending on the degree of kineticisotope fractionation, that is, the value of ekin

56=54, we maysimulate a start of Fe(II) breakthrough with high values

of d56/54Fe(II)aq, followed by a time period with enrichedlight isotopes. The distribution p(s) of mass-transfer timesmay lead to a non-monotonous variation of d56/54Fe(II)aq

in the invading front. If Fe(II) had reached the inflow con-centration, d56/54Fe(II)aq would have been identical to thevalue of the injected solution. Incomplete breakthrough,however, can cause d56/54Fe(II)aq values differing from theinjected solution. The stronger the kinetic fractionation,the lighter is the simulated Fe(II) in the receding front. Thisphenomenon is caused by the faster desorption of the lightFe isotopes.

Although simulated trends in d56/54Fe(II)aq measured inthe outflow of the quartz column only roughly correspondto observed data, all the models we tested failed to repro-duce the isotope trends correctly (Fig. 6B). Obviously, theinterplay between equilibrium and kinetic sorption of Feisotopes can lead to an intricate time-dependence of isotopefractionation in the outflow of the column. The complexitymay be further increased by differentiating between the twosorption sites in fractionation, or by making ekin

56=54 depen-dent on the mass-transfer time s. Nevertheless, our results


show that sorption of Fe isotopes during reactive transportof Fe in anoxic, pH-neutral and quartz-rich aquifers undernon steady-state conditions can produce significant Fe iso-tope fractionation in solution, which is consistent with thestudy of Teutsch et al. (2005). In our column experimentwith goethite-loaded quartz sand, sorption reactions pro-duced dissolved Fe(II) up to 1.63& lighter compared toFe(II) in the initial stock solution. This value comparesfavorably in direction and magnitude to the fractionationsof up to �3.3& observed by Teutsch et al. (2005). Likewise,our equilibrium enrichment factor for goethite-loadedquartz of 0.85& (Fe(II)sorb–Fe(II)aq) is close to the enrich-ment factor of 0.67& calculated from the Teutsch et al.experiment. However, a direct comparison of Fe isotopefractionations observed in the Teutsch et al. (2005) studyand our experiments is hardly possible because the systemsdiffer in terms of composition and scale.

Under our experimental conditions, sorption kinetics ofFe isotopes seem to exert a major control on Fe isotopefractionation (Fig. 6). As in all chromatographic systems,strong effects occur only at concentration fronts travelingthrough the system. In suboxic and anoxic environmentssuch as aquifers or soils, changes in Fe(II) concentrationsmay be caused by (i) changes in hydrologic boundary con-ditions, e.g., at the onset of groundwater recharge or due tovarying infiltration rates, or by (ii) changing productionrates of Fe(II)aq during microbial dissimilatory Fereduction.

3.4. Quantification of atom exchange at the goethite surface

3.4.1. Batch experiments

Previous studies have shown (i) that Fe(II) sorbed toFe(III)-(hydr)oxides can be oxidized and subsequentlyincorporated into a Fe(III) layer similar in structure tothe bulk oxide (Williams and Scherer, 2004; Silvesteret al., 2005; Cwiertny et al., 2008), and (ii) that in the pres-

Fig. 7. Calculated influence of atom exchange on the isotopic compositioof Fe(II). Atom exchange is given as percentage of total goethite-Feencompasses the range of possible d56/54Fe(II)aq values which fall in betwereads as follows: at a fixed Fe(II)aq concentration of 15 mM, 5% atom excerror bar represents the long-term precision (±2r) of our internal house

ence of Fe(II)aq there is an isotopic exchange between struc-turally bound Fe in the Fe(III)-(hydr)oxides and Fe(II)aq

(Pedersen et al., 2005). Likewise, our data indicate thatsorbed Fe(II) is oxidized at the surface of goethite but alsothat the Fe(II) synchronously formed from structuralFe(III) at the goethite surface is partially released into solu-tion. One of the key questions refers to the pool size of iso-topically exchangeable Fe(III) in the goethite structure. Toaddress this question, we assumed that the dominatingfaces in our goethite sample are (110) and (021) with afractional contribution of 0.9 and 0.1, respectively. We cal-culated the number of Fe atoms present at the (110) facewith 7.8 nm�2 and that of the (021) face with 6.1 nm�2 byevaluating a block of 100unit cells using the program Crys-talMaker� (v. 1.4.4). Lattice parameters of goethite weretaken from Gualtieri and Venturelli (1999). Weighing theFe occupancies of each face by its fractional contributionto the total surface area, we obtained an average Fe densityof 7.6 nm�2 and this value translates into an atomic Femonolayer comprising 3.4% of the goethite’s Fe. Basedon the fitted sex

Fe value of 0.384 ± 0.136 mol/kg goethite(�3.4% of the goethite-Fe), we conclude that the exchange-able Fe(III) is equivalent to a single surface atom layer ofFe. This result deviates from findings of Pedersen et al.(2005) who inferred that up to four monolayers of goe-thite-Fe exchanged with Fe(II)aq during equilibration atpH �6.5 for up to 16 days. We speculate that this differencecould be explained by the lower pH and longer equilibra-tion time but also by a lower intrinsic stability towardsFe(II)-induced crystal transformation of the 55Fe-labeledgoethite of Pedersen et al. (2005) compared with ourgoethite.

In Fig. 7 we examined the effect of atom exchange be-tween dissolved Fe(II) and goethite-Fe on the isotopic com-position of Fe(II)aq as a function of (i) the Fe(II)aq

concentration and (ii) the extent of atom exchange ex-pressed as percentage of goethite-Fe present in our batch

n of Fe(II)aq in equilibrium with goethite assuming no net sorptionpresent in our batch experiments (112.5 mM). The white area

en the limits set by d56/54Fe(II)ini and d56/54Fe(III)goethite. The Figurehange will lower the initial d56/54Fe(II)aq from 1.54& to �1&. Thestandard.


experiment. In this calculation we constrained the aqueous-phase concentration of Fe(II) to be constant, that is, onlyatom exchange was allowed (zero net sorption of ferrousFe). In this case, the isotope mass balance simplifies to:

d56=54FeðIIÞaq ¼N Fe;goethite

N aqFe

� d56=54Fegoethite

þ 1� N Fe;goethite

N aqFe

� �� d56=54FeðIIÞini; ð26Þ

where d56/54Fe(II)ini refers to the isotopic composition ofdissolved Fe(II) prior to atom exchange. According toEq. (26), the isotopic composition of the solution must fallin the range given by the d56/54Fe of the initial Fe(II) solu-tion and goethite. (When all Fe(II)aq exchanges with goe-thite-Fe, the d56/54Fe of Fe(II)aq essentially becomes thatof goethite.) Being as hypothetical as illuminating, Fig. 7demonstrates that (i) atom exchange will have the largest ef-fect on the isotopic Fe composition in solution at low Fe(II)concentrations, and (ii) for the lowest Fe(II) concentrationsin our batch experiments, the isotopic solution compositioncannot be solely explained in terms of atom exchange, thatis, a sorption-related Fe isotope fractionation must also beinvoked. In addition, since only one atomic Fe layer of goe-thite exchanged with Fe(II) in our experiments, experimen-tal data falling below the 5%-line in Fig. 7 must beinfluenced by an isotope fractionation processes other thanatom exchange, such as adsorption and/or precipitation.

3.4.2. Column experiments

In order to quantify the atom exchange at the goethitesurface, we calculated the isotopic composition of Fe(II)recovered after complete desorption, Fe(II)recov, andcompared this value with the d56/54Fe value of the initialsolution (1.74 ± 0.06&). For this we weighed the d56/54Fevalue of each of the j sample groups in Fig. 5B by their frac-tional Fe content and then summed all products accordingto:

d56=54FeðIIÞrecov ¼Xj

d56=54FeðIIÞjaq � FeðIIÞjaq=FeðIIÞrecov:

ð27Þ

Note that d56/54Fe(II)aq values covered the whole break-through curve, except for two data points which were line-arly interpolated (Fig. 5B); the influence of these datapoints on the calculated d56/54Fe(II)recov, however, wasinsignificant. We then obtained a d56/54Fe(II)recov value of1.46&, which is 0.28& lighter than the initial Fe(II)solution. Thus one can state that light goethite-Fe(d56/54Fe = 0.1&) contributed to the d56/54Fe of Fe(II)recov

in our experiment, confirming an atom exchange betweendissolved Fe(II) and the goethite on the quartz grains.Based on (i) the 0.28& difference between d56/54Fe(II)ini

and d56/54Fe (II)recov, (ii) the isotopic composition of goe-thite, (iii) the goethite loading on the quartz, and (iv) thequartz content in the column, we calculated by mass bal-ance that approximately 2.9% of the total goethite-Fe(III)had participated in atom exchange. This value is in verygood agreement with the 3.4% (�1 atomic Fe monolayer)determined from the goethite batch data. Considering theduration of the batch and column experiments (72 h vs.

�40 h), a similar value obtained for sexFe suggests that the

pool-size of isotopically exchangeable goethite-Fe did notchange much with increasing equilibration time. Our find-ings, however, do not preclude the possibility of an increas-ing sex

Fe upon long-term equilibration of Fe(II) with goethite.Using Eq. (27) in the case of the pure quartz column exper-iment, where 95% of the initial Fe(II) was recovered, we ob-tained a d56/54Fe(II)recov of 1.26&, which is identical withinexperimental error to the d56/54Fe of the initial Fe solution(1.28 ± 0.06 &). Our finding is therefore consistent with theabsence of an atom exchange between Fe(II)aq and a pureSiO2 surface.

4. CONCLUSIONS

Based on our anoxic and abiotic experiments at pH 7.2we can draw the following conclusions:

1. When sorption equilibrium is attained between dissolvedFe(II) and Fe(II) sorbed to goethite, quartz, or goethite-loaded quartz, heavy Fe isotopes partition preferentiallyin the sorbing phase. In contrast, the equilibrium Fe iso-tope fractionation induced by sorption of Fe(II) to alu-minum oxide is negligible.

2. Equilibrium sorption of Fe(II) to quartz fractionatesFe isotopes to the same extent as sorption of Fe(II)to goethite in anoxic biotic and abiotic laboratorysystems.

3. The Fe(III)-pool of goethite, sexFe, which isotopically

equilibrates with dissolved Fe(II) via atom exchangewithin up to 72 h is equivalent to one atomic Fe layer.

4. Atom exchange between aqueous-phase Fe(II) andstructural Fe of Fe(III)-(hydr)oxides can control the iso-topic composition of dissolved Fe(II) in equilibratedclosed systems when (i) d56/54Fe of Fe(III)-(hydr)oxidesand Fe(II)aq differ, and (ii) the solute concentration islow relative to the pool size of isotopically exchangeableFe(III).

5. Reactive transport of Fe(II) under non-steady state con-ditions can lead to significant Fe isotope fractionation(>1.5&) and complex non-monotonous Fe isotopetrends. Model results suggest that kinetic isotope effectsstrongly influence the sorption-induced Fe isotope frac-tionation in flow-through systems.

6. The accurate prediction of Fe isotope trends in allegedlysimple flow-through systems warrants furtherinvestigation.

ACKNOWLEDGEMENTS

We are indebted to Andrea Herre, Jakob Frommer, andRobert Mikutta who measured the BET surface area of our sor-bents. Ralf Kaegi is gratefully acknowledged for providing theSEM/TEM images and Kurt Barmettler for his support in thelaboratory. Nadya Teutsch is kindly acknowledged for herengagement initiating this project. We thank Felix Oberli, BenReynolds and the staff of the ETH isotope lab for excellentmaintenance and support. This work was financially supportedby the Swiss National Science Foundation (grant no. 200020-108098).


APPENDIX A. SUPPLEMENTARY DATA

Supplementary data associated with this article can befound, in the online version, at doi:10.1016/j.gca.2009.01.014.

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Iron isotope fractionation and atom exchange during sorption of ferrous iron to mineral surfaces