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Aquatic Geochemistry6: 147–199, 2000.© 2000Kluwer Academic Publishers. Printed in the Netherlands.

147

Application of Gibbs Energy Minimization toModel Early-Diagenetic Solid-SolutionAqueous-Solution Equilibria Involving AuthigenicRhodochrosites in Anoxic Baltic Sea Sediments

DMITRII A. KULIK 1,2, MICHAEL KERSTEN3,∗, UWE HEISER4 andTHOMAS NEUMANN4

1Baltic Sea Research Institute (IOW), Seestr. 15, D-18119 Rostock, Germany;2Permanent address:Environmental Radiogeochemistry Centre NAS Ukraine, Palladin Prosp. 34a, 252180 Kyiv,Ukraine; 3Geoscience Institute, Johannes-Gutenberg University, Becherweg 21, D-55099 Mainz,Germany;4Institute for Petrography and Geochemistry, TH Karlsruhe, Kaiserstr.12, D-76128Karlsruhe, Germany (∗Author for correspondence: E-mail: [email protected])

(Received in final form 29 September 1999)

Abstract. The natural early-diagenetic environment “anoxic porewater – authigenic mineral phases”has been characterized in sediment of the Gotland Deep, Baltic Sea, by a closed-system model.Occurrence of carbonate precipitates as thin almost pure white laminae was considered as a naturalexperiment for long-term equilibration between these phases and porewater. Plots of distributioncoefficients indicate that metastable equilibrium exists between porewater and the authigenic Ca-richrhodochrosite phases below 7 cm depth. A thermodynamic model of porewater geochemistry atinsituP = 25 bar andT = 5 ◦C was developed using the Gibbs energy minimization (GEM) approach.The values of isobaric-isothermal potentials of Mn, Ca, Fe, Mg, Sr, Ba, C, and O, calculated from theporewater composition, were used in a new “dual thermodynamic” calculation approach to estimatesolid activity coefficients of the end-members in the non-ideal solid solution (Mn, Ca, Mg, Sr, Ba,Fe)CO3, i.e., at full major and minor multi-component complexity. The regular Margules interactionparameters for the composing binaries estimated by this model wereαMn-Ca = 1.9± 0.5,αMn-Mg =0.6,αCa-Mg = 3.7,αMn-Fe = 0.2,αCa-Fe = 2.8,αMn-Sr = 9.7,αCa-Sr = 2.15,αMn-Ba = 4.0,αCa-Ba= 1.4, validating the theoretical predictions given by Lippmann in his pioneering 1980’s paper. Thestrictly thermodynamic equilibrium model is not only able to match both the measured porewaterand carbonate solid-solution composition, but also to predict that the porewater pH, pe, alkalinity, anddissolved Mn, Fe, and S concentrations are controlled by the authigenic mineral buffering assemblagemackinawite-greigite-rhodochrosite. Our model is only compatible with the idea of ACR formationwith typical composition (XMn between 70–75%) in the topmost sediment layer which, however,needs a major source of MnII

aq. This is provided by reduction of particulate Mn oxides precipitatedin significant amounts in the water column upon major inflow events in the Baltic Sea. The modelenables also to set up scenarios of changing environmental conditions, e.g., to predict the non-linearresponse of the carbonate solid-solution composition to changes in Mn loading, alkalinity and salin-ity of the sediment-water system. The results suggest that the major and especially minor elementcontents (Sr, Mg, Ba) in authigenic carbonates can be applied as an environmental paleoproxy.

Key words: solid-solution, Gibbs energy minimization, manganese, carbonates, Baltic sea

148 DMITRII A. KULIK ET AL.

1. Glossary of Symbols and Abbreviations

ACR authigenic Ca-rich rhodochrosite, formed in the sediments of Gotland Deep

A, B, C coefficients in the three-term temperature approximation Equation(19)aj thermodynamic activity ofj th species

å,Aγ ,Bγ ,bγ parameters of the extended Debye–Hückel Equation (18)

A stoichiometry matrix

aij stoichiometry coefficient ofith independent component inj th species

α dimensionless Margules interaction parameter

b vector of bulk chemical composition (in moles of elements)

Cp0 standard heat capacity at constant pressure

γj practical (molal) activity coefficient ofj th aqueous species

8 set of phases in GEM system formulation

cj molarity of j th species (mol L−1)

EDH extended Debye–Hückel Equation (18) to calculate aqueous activity coeffi-cients

D empirical (concentration-scale) distribution (partitioning) coefficient

DT dual thermodynamic formulation to estimate concentrations (DTC Equation(8)), activity coefficients (DTA Equation (9)), and Gibbs energies (DTG Equa-tion (10)) of trace elements in multi-component solid-solutions as a specialfeature of the GEM model applied

δX uncertainty related to variable mole fractionX

fO2, fCO2 fugacity of oxygen or carbon dioxide gas

G(x) total Gibbs energy of the system at compositionx (dimensionless)

g0j,T P

standard state Gibbs energy of formation ofj th gas or mineral from elements;or standard partial molal Gibbs energy of aqueous species (J mol−1)

GEM Gibbs energy minimization

H0j enthalpy of formation from elements (J mol−1)

HKF Helgeson–Kirkham–Flowers (1981) equation of state for aqueous species

I effective molal ionic strength of aqueous electrolyte

Kd theoretical (free ion activity-scale) partition coefficient

Kj,k equilibrium constants of reaction

KSP solubility product

LMA Law-of-mass-action, which most aquatic ion association models are based on

λj rational (mole fraction) activity coefficient ofj th solid solution end-member

M Madelung factor (kJ mol−1)

mj molality of j th species in the aqueous phase (mol kg−1 of H2O solvent)

Mj molality of j th species in the solid phase (mol kg−1 of solid solvent)

µ chemical potential (theoretical isobaric-isothermal potential)

µj , µ′j

element of vector of “dual” chemical potentials of species calculated fromchemical potentials of independent components (GEM, dimensionless)

N set of independent components (stoichiometry units) in GEM formulation

L set of dependent components, or species in GEM formulation

� saturation index (dimensionless)

P pressure, bar

EARLY-DIAGENETIC SOLID-SOLUTION AQUEOUS-SOLUTION EQUILIBRIA 149

R universal gas constant (8.3144 J K−1 mol−1)

r cation-anion distance in rhombohedral carbonates

R set of kinetic restrictions (KarpovEquations (7) and (8))

ρTr ratio of two binary interaction parameters

S0 (partial molal) third-law entropy

SB salinity of the Baltic Sea water, per mil

SSAS solid-solution aqueous-solution thermodynamic equilibrium model

T temperature (K)

ui element of the “dual solution” vector of chemical potentials of independentcomponents in GEM (dimensionless)

u vector of dual solution of the equilibrium problem in GEM formulation (dimen-sionless)

vj element of “prime” vectorv of chemical potentials calculated from activity ofspecies (GEM, dimensionless)

V0 standard molal volume (m3 mol−1)

W Margules interaction parameter (J mol−1)

V 0j

(partial molal) volume ofj th species (cm3 mol−1)

Xjj,aq mole fraction ofith element orj th species in aqueous solution

Xjj,s mole fraction ofith element orj th species in solid sediment

Xjj,SS mole fraction of ofith element orj th species in solid solution

xj number of moles ofj th species (an element of prime solutionx̂ vector in GEMapproach)

zj formal charge ofj th aqueous species; empirical parameter of the extendedDebye–Hückel Equation (24)

65 Lippmann’s total solubility product

ςi ratio of free ion activity to total aqueous molality ofith element

2. Introduction

From its onset some 40 years ago (Sillen, 1961), geochemical modeling has de-veloped into a well-recognized tool for the interpretation of geochemical data interms of aqueous speciation and solid phase composition. It helps in elucidatingfactors and processes which control evolution of groundwater, marine or hydro-thermal geochemical environments (Langmuir, 1997). Activity products calculatedfrom measured total concentrations of dissolved metals in sediment-water systemsoften deviate from those calculated from the solubility products of the respectivepure solid phases. One of the reasons is that natural minerals are usually im-pure, and often can be considered as solid solutions. These solid solution-aqueoussolution (SSAS) equilibria cannot be described by a simple solubility product.Moreover, such solid solutions are often non-ideal producing complex non-linearrelationships between measurable bulk compositions of the co-existing aqueoussolution and solid phases, together with differences in aqueous speciation andactivity coefficients of the participating metals. This results in a large scatter of dis-


tribution coefficients (see below, Equation (1)). Further complications are inducedby the influence of precipitation kinetics on trace metal incorporation into naturalmineral phases, especially pronounced for carbonates (Morse and Bender, 1990)which imply that metal partitioning may be strongly affected by kinetic factors(Mucci, 1988) and may even lead to complex zoning in the solids (Prieto et al.,1997). All this makes retrieving thermodynamic properties of solid solutions fromcompositional data a non-trivial task even for simple laboratory conditions. Thequestion at hand is whether modern geochemical modeling techniques can still behelpful in interpretation of partitioning of elements in such complex natural SSASsystems. In fact, it is, as we will show in this contribution based on thermodynamicmodeling of multi-component aqueous and solid solutions which advances beyondthe results given by the pioneering Lippmann (1980) paper.

The natural anoxic sediment-porewater system of the Gotland deep in the cent-ral Baltic Sea is characterized by abundant formation of authigenic Fe sulfidesand Mn-rich carbonates which has been extensively investigated (Manheim, 1961,1982; Suess, 1979; Emelyanov, 1986; Boesen and Postma, 1988; Jakobsen andPostma, 1989; Huckriede and Meischner, 1996; Neumann et al., 1997; Sternbeckand Sohlenius, 1997; Carman and Rahm, 1997). Occurrences of similar Mn-richcarbonates have been described in many other periodically stagnant marine orbrackish basins (Calvert and Price, 1970; Pedersen and Price, 1982; Morad and Al–Aasm, 1997; Lepland and Stevens, 1998), and were probably inherent in formationof ancient manganiferous black shales (Calvert and Pedersen, 1996; Huckriede andMeischner, 1996). Quick transformation of Mn oxides to Mn-rich carbonates ontop of organic-rich marine sediment was demonstrated experimentally (e.g., Allerand Rude, 1988). We try to consider the sediment-porewater system of the Gotlanddeep, with the embedded Ca-rich rhodochrosite laminae precipitated up to thou-sands of years B.P., as a kind of natural SSAS precipitation experiment alternativeto laboratory experiments on carbonates, which mostly suffer from the influence ofreaction kinetics (Lorens, 1981; Böttcher, 1995, 1997a, 1997b; Sternbeck, 1997;Rimstidt et al., 1998).

There are several contradictory interpretations on how composition of authi-genic rhodochrosites is related to porewater composition, changes in salinity andredox variations in the near-bottom water. For instance, there is no consensus withrespect to what causes precipitation of Ca-rhodochrosites and where does it occur:(i) within the sediment due to the increase in carbonate alkalinity following sulfatereduction and buildup of ammonia (Neumann et al., 1997); (ii) due to diffusion ofCa+2 ions from underlying sediments (Suess, 1979; Jakobsen and Postma, 1989);or (iii) at or above the sediment surface by reduction of large amounts of Mn-oxides in a high-alkalinity environment (Sternbeck and Sohlenius, 1997; Leplandand Stevens, 1998). Carman and Rahm (1997) conclude that interstitial waters insediments of the Baltic Sea deeps were saturated or oversaturated with both pureand mixed manganese carbonates. Jakobsen and Postma (1989) have found thatthese porewaters are greatly oversaturated with respect to both rhodochrosite and


calcite, and proposed a regular solid solution model with CaCO3 and MnCO3 endmembers and a negative Margules interaction parameter. However, it is well knownthat the high-temperature calcite-rhodochrosite system is asymmetric and has pos-itive excess free energy which causes a large miscibility gap (De Capitani andPeters, 1981; Capobianco and Navrotsky, 1987). Theoretical predicitions for lowtemperature carbonates (Lippmann, 1980) also result in positive excess free energyof mixing. Middelburg et al. (1987) applied this positive excess free energy ofmixing and Lippmann diagrams to investigate compositions of mixed carbonates,which control Mn concentrations measured in pore water profiles. Their model pre-dicted a metastable miscibility gap betweenXMn = 0.192 andXMn = 0.808, whichlead these authors to postulate three mixed Mn–Ca carbonate phases: Mn-calcite,Ca-rhodochrosite, and kutnahorite (CaMn[CO3]2) as the thermodynamically stableordered solid-solution phase of intermediate composition, i.e., quite analogous tothe dolomite system. They noted also a large difference between Mn concentrationin pore water of carbonate-rich sediments (10–65µmol/kg) and carbonate-poorsediments (100–180µmol/kg), and attributed this to Mn co-precipitation with cal-cite surfaces. Although the conclusion of these authors, namely that solubility ofMn-bearing carbonates cannot be adequately described by a single thermodynamicequilibrium constant, is in principle true, the real problem with their model isthat most of the recently measured compositions of authigenic rhodochrosites fallwithin the range ofXMn between 0.48 and 0.82, with an average around 0.7, i.e.,just inside the proposed miscibility gap. There is no indication of any existence ofauthigenic carbonate phases other than Ca-rhodochrosite in natural anoxic Mn-richsediments (cf., e.g., Sternbeck and Sohlenius, 1997; Lepland and Stevens, 1998). Infact, complete miscibility between both calcite and rhodochrosite end-members hasbeen found with precipitation experiments conducted recently by Böttcher (1998).

In view of this debate and intriguing disagreements on interpretation of bothnatural mechanisms and thermodynamics controlling mixed Mn-carbonate pre-cipitation, and backed up by available data on composition of porewater andco-existing authigenic Ca-rich rhodochrosite (ACR) in Gotland deep sediments,this study had the following objectives: (i) to assess how close are the ACR tothermodynamic equilibrium with porewater in the natural environment, (ii) to de-termine consistent thermodynamic data including Margules interaction parametersof the multiple-component ACR solid solution ([Mn, Ca, Sr, Ba, Mg, Fe]CO3)from compositional data, and (iii) to evaluate whether the impact of metastabilityon ACR composition is potentially responsible for the above mentioned contra-dictions (and whether this metastability can be accounted for in thermodynamicequilibrium models). The major challenge for our approach, however, was todevelop a thermodynamic equilibrium model capable to predict a natural anoxic-sulphidic sediment-porewater system at full complexity in order to deconvolute themulti-component carbonate SSAS model out of the field data.


3. Experimental

3.1. SAMPLING SITE

The Baltic Sea is one of the largest brackish sea areas in the world located in thehumid climatic zone of the northern temperate latitudes. It is well structured intoa series of basins and deeps separated by sills which separate inflowing saline,oxygen-rich North Sea waters with a salinitySB of 32 to 34 from outflowingbrackish waters with salinities ranging from 7 to 10 (Figure 1). Water balance isaffected by freshwater surplus (475 km3/a) which causes an outflow of brackishwater. This large-scale estuarine circulation system maintains stable stratificationwhich prevents oxygenation of the deep water in the central Baltic by local convec-tive mixing. Episodic major inflow events of saline water through the Danish Straitsand the Belt Sea is able to displace the stagnant and thus anoxic bottom water inthe central deeps (up to 250 m). This bottom water renewal process, known as theBaltic inflow event, depends on favourable climatic conditions (Matthäus, 1995).Major inflows occur only during the winter season, interrupted by intervals fromone to many years. At least during the first three quarters of the present century,major inflows were observed more or less regularly. Since the mid-seventies, theirfrequency and intensity has changed. Only a few major events have occurred sincethen, and no inflow event at all was recorded from the beginning of 1983 to the endof 1992. Conditions in the central deeps have changed drastically and led to themost significant and serious stagnation period with the highest hydrogen sulfideconcentrations (0.2 mmol/kg6H2S) ever observed in bottom waters of the BalticSea (Matthäus and Lass, 1995).

A series of relatively small inflow events started with beginning of 1993 andled to the consecutive filling of the western basins. The last major event led ul-timately to a re-oxygenation, and for the first time since 1977, the whole watercolumn became oxic during summer 1994 (Matthäus, 1995). Following the inflow-mediated redox changes, precipitation of the dissolved Fe and Mn pool producedabout 150,000 tons of particulate oxyhydroxide precipitates within a few weeksforming a thin layer (some mm) onto the sediment surface (Brügmann et al.,1997). However, this oxide layer becomes unstable under re-establishment of an-oxic conditions a few years later upon exhaustion of the stagnant oxygen pool. Bycomparing thin rhodochrosite layers in dated sediment cores with the historicalrecord of inflow events, Huckriede and Meischner (1996) and Neumann et al.(1997) have hypothesized an early diagenetic transformation of the Mn/Fe oxideinto rhodochosite/Fe-sulphide layers. Rhodochrosite laminates in sediments whichmay be traced back up to the formation of the Baltic Sea some 8000 years B.P. mayhence represent paleoproxies for such inflow events.


Figure 1. Sampling station in the Gotland Deep, both in its lateral and vertical location withinthe Baltic Sea system.


3.2. SAMPLING PROCEDURES

Sediment cores were taken during the cruise of R/VPetr Kottsovin the centralGotland Basin at IOW station # 211650 (57◦18.35′N, 20◦02.99′E, water depth245.5 m, Figure 1) in July 1997. A gravity multi-coring device was used to takefour parallel cores of 55 cm length, 10 cm diameter, allowing for retrieval of an un-disturbed sediment/water interface. Immediately after retrieval the sediment coreswere displaced into a cold-storage room at 6◦C onboard ship. pH was measuredat 1-cm depth intervals within the liner of the first core using a portable pH probeand meter. Distinct light laminae were separated from a parallel core immediatelyfrozen by dry ice by scraping them off with a stainless-steel scalpel at depthsbetween 6.9–7.6 cm, and between 52.8–53.2 cm, respectively. Another core wassub-sampled for bulk analyses and radionuclide dating (Heiser et al., 2000). Porewater sampling was performed on a third core immediately after retrieval. Thissediment core was extruded through the bottom of an argon-flushed glove box toprevent oxidation. After centrifugation of the sediment subsamples in capped vials,the supernatant water was separated using 0.45µm membrane filters. Porewatersubsamples were analyzed immediately inside the box for total alkalinity accordingto the two-point titration method of van den Berg and Rogers (1989). Others werefrozen after addition of the anti-fouling agent sodium azide to determine later majoranion concentrations, or acidified and frozen to determine trace metals.

3.3. ANALYTICAL METHODS

Leaching of sediment sub-samples was carried out by treating 500 mg of the bulksamples or about 50 mg of the separated laminae with 25 ml or 2.5 ml 1 M HCl,respectively. After addition of the acid, samples were treated for 20 min in anultrasonic bath at room temperature and subsequently heated for 1 h at 90◦C.Some samples were leached in 1 M HCl at room temperature for 24 h, and sub-sequently the mixture was heated at 90◦C for 1 h treated as described by Sohleniuset al. (1996). Both methods yielded the same results within the analytical error.Total Ca, Mn, and Fe contents in the solid sample digestions, as well as Ca andMn contents in pore water, were determined using multi-element total reflectanceX-ray fluorescence spectroscopy (TXRF Extra II, Atomika). Measurements wereconducted for 2000–2500 s using a Mo-Kα X-ray beam at 50 kV and 5–38 mAcurrent. The element Ga was used as an internal standard. Mg, Ba, and Fe contentswere measured using the conventional atomic absorption spectroscopy technique(AAS 1100 B, Perkin Elmer). Chloride and sulfate contents in the pore watersamples were determined by ion chromatography (DX 100, Dionex). Total carbonand total sulfur in the sediment bulk samples were measured with a conventionalCS-analyzer (CSA 302, Leybold Heraeus).


4. Results

4.1. POREWATER AND AUTHIGENIC CA-RICH RHODOCHROSITE(ACR)SOLID-SOLUTION COMPOSITION

Porewater in top sediments of the Gotland deep is enriched in Mn, Ca, Na, K, P,N, but depleted in Mg, Sr, and S compared to the overlying near-bottom water(Table I). Comparison of our data with that of Carman and Rahm (1997) showssignificant deviations in Fe and Cl concentrations as well as in pH for the top-most 9 cm sediment, which may be explained by the different sampling timesand hydrodynamic conditions. The higher pH found by these authors in 1990 mayresult from more than ten years of anaerobic degradation of organic matter understagnant conditions. Our core 211650-2 was taken 7 years later upon a series ofsalt-water inflows into the Gotland Deep (Matthäus and Lass, 1995), which prob-ably caused resuspension of the surficial 5 cm of sediment with less alkaline wateras evidenced by radionuclide profiles (Heiser et al., 2000). This event, followed byaerobic degradation of organic matter, may have lowered pH close to the sedimentsurface. Chlorinity in the surface sediment could also be influenced by an intrusionof relatively saline water into the Gotland Deep. Our determined Cl concentrationsof about 185 mM are consistent with the bottom waterSB of 12, while Carmanand Rahm (1997) measured contents up to 239 mmol/kg at 9 cm corresponding toanSB of about 15 which may be a relict from the previous major 1975/76 inflowevents.

Table II contains data which characterize the composition of the carbonate insediments of Gotland and Landsort deeps, both from literature and our study forcomparison. These data were obtained using two different analytical techniques:microprobe determinations on carbonate grains (Jakobsen and Postma, 1989; Le-pland and Stevens, 1998) and leaching by acetate or HCl solution of separatelaminae samples (Jakobsen and Postma, 1989; Sternbeck and Sohlenius, 1997;Huckriede and Meischner, 1996; this work). Samples from core 211650 wereleached with 1 M HCl, to dissolve primarily the carbonates. However, some contri-bution from co-digested acid volatile sulphide (AVS) phases, or cations adsorbedon clay mineral surfaces, cannot be excluded. Both microprobe and leaching tech-niques provided more or less consistent data at least for the major element molefractions (Ca, Mn, Mg, and Fe) in ACR, but some trace elements were determinedfrom leaching procedures only (Sr, Ba, Zn, Cu, and Ni, cf. Table II). The problemwith such measurements was that Fe, Mg, Zn, and Cu contents obtained from thedarker laminae samples were systematically higher than those measured in whiteor light-gray laminae. This probably reflects contamination with sulfides (or clayminerals), therefore trace metal contents measured in light laminae should be takenas maximum estimates for metal contents in carbonate phase. No significant zo-nation was found in the carbonate laminae by cathodoluminescence measurements.Based on these considerations, we have compiled the ACR model composition withassociated uncertainties (Table II).


Table I. Representative chemistry of the Gotland Deep porewater

Element or BMSa BY15 Core 211650 Porewater Model BSWa

parameter, units (sampled 1990 (sampled 1997, model atin-situ

by CR97b), this work) (molal units, SB = 12, 4.5◦C5–9 cm depth 24–26 cm depth this work) (KKL98)b

Ca, mM 4.34± 0.15 3.9± 0.1 4.002 3.9016

Mn, µM 186± 30 200± 20 190.26 17.221

Sr,µM 23± 2 28± 3 27.935 32.935

Fe,µM 1.23± 0.5 4.0± 2 2.528 0.0019

Mg, mM 14.6± 1 14.4± 0.4 14.408 18.548

Na, mM 167± 5 169.58 162.66

K, mM 4.65± 0.1 4.6724 3.559

Ba,µM 13.3± 0.7 13.20

B, µM 151.17 151.17

F,µM 28.78 28.78

Cl, mM 233± 5 185± 6 192.58 189.47

Br, µM 250± 10 291.54 291.53

S, mM 8.15± 0.06 7.3522 9.8487

SO2−4 , mM 6.0± 0.2 9.8487

HS-,µM 465± 10 0

C, mM 5.313 1.9073

N, mM 1.204 (NH3) 1.2234 0.013 (NO3)

Ar, mM 1.3713 1.3712

P,µM 146± 40 152.32 2.280

Si,µM 0.9978 0.9978

H, mM 10.778 2.1532

O, mM 45.2456 45.42046

pH 7.89± 0.05 7.6± 0.02 7.611 7.225

pe −4.032 12.79

Eh, mV −0.188 −0.222 0.703

AlkT, mM 7.5± 0.3 1.691

AlkC, mM 3.93± 0.7 1.689

Solid phases at ACRa, MnOxa,

equilibrium greigite, HFOa

mackinawite

a Abbreviations: ACR – authigenic Ca-rich rhodochrosite; BMS – Baltic monitoring station;BSW – Baltic Sea water; HFO – hydrous ferric oxide; MnOx – non-stoichiometric Mn oxide.b References: CR97 – Carman and Rahm (1997); KKL98 – Kersten et al. (1998).


Table II. Composition of authigenic rhodochrosites (ACR) in the Baltic Sea sediments,recalculated to mole fractions of the carbonate end-members (in mol%)

End-member JP89a SS97a LS98a HM96a This work, This work,

sampled in core ACR model

211650-2

MnCO3 51–83 63 77 +7−8 74± 10 70± 4b 71± 4

CaCO3 13–41 35 22 +9−5 24± 4 26± 4b 26± 4

MgCO3 2–5 n.d. 1.0 +3−1 2.7± 0.3 4.7± 0.5c 3.0± 1

FeCO3 0–2 n.d. n.d. 0.06± 0.03 0.01c 0.1 +0.9−0.09

SrCO3 n.d. 0.09 n.d. n.d. 0.072± 0.01b 0.072± 0.01

BaCO3 n.d. n.d. n.d. 0.026± 0.04 0.16d 0.03± 0.01

ZnCO3 n.d. n.d. n.d. 0.007± 0.004 0.05c 0.01± 0.005

Method of Microprobe Leaching SEM EDS Acetate leaching HCl leaching SSAS model

determination (ACR laminae)

a References: JP89 – Jakobsen and Postma (1989); SS97 – Sternbeck and Sohlenius (1997);LS98 – Lepland and Stevens (1998); HM96 – Huckriede and Meischner (1996). Other data:Mn 85%, Ca 10%, Mg 5% (Suess, 1979); Mn 60–70%, Ca 30–32%, Mg 0–8% (Manheim,1982).b Mixed laminae and bulk sediment from depth 24–27 cm.c Separated white laminae only, but from various depths.d Bulk sediment from 9 cm depth.n.d. = not determined.

Examination of the vertical porewater and sediment profiles reveals high pos-itive correlation between Ca, Mn, and Sr both in sediment and in porewater. Theobvious interpretation of this characteristic pattern is that these elements are alltogether controlled by the ACR phase dissolution. This correlation can be demon-strated using plots of particular element mole fractionsXi,s in sediment (Xi,s =Mi,s/(MCa,s +MMn,s+MSr,s), which display quite uniform distribution below 7 cmdepth (Figure 2 a,b,c), with medianXCa,s = 0.27± 0.08,XMn,s = 0.71± 0.08,andXSr,s = 0.0007± 0.0003. Plots of mole fractions of total dissolved elementsXi,aq = [i]/([Ca] + [Mn] + [Sr]) also demonstrate uniform trends below 7 cm depthsuggesting solubility control (Figure 2 d,e,f).XMn,aq steadily increases between 7and 17 cm depth, then remains constant below 20 cm depth, indicating steady-stateconditions achieved with progressing diagenetic sulphate reduction. That is whywe assumed the porewater composition at 24–26 cm depth to be representative forlocal equilibrium, and used it for thermodynamic calculations and derivation ofMargules parameters for the SSAS model.

4.2. PARTITIONING COEFFICIENTS

Two distinct approaches are commonly used to quantify coprecipitation processes:(i) solid solution models and (ii) distribution models based on empirical (condi-tional) partition coefficients. The latter approach involving carbonates has been


Figure 2. Profiles of Ca, Sr, and Mn molar fractions in bulk sediment (plots A, B, C) andporewater (plots D, E, F) of the core 211650-2 sampled in 1997.

recently reviewed by Rimstidt et al. (1998) and Curti (1999). Partitioning of a traceelement (Tr) between a mineral of a major element (M) and aqueous solution isusually described by the empirical partitioning coefficient,D:

D = XTr

XM× mMmTr

, (1)

whereX denotes the mole fraction in solid phase (assuming that the bulk solidhas the same composition as it’s surface in contact with the aqueous phase) andm


stands for molality in the aqueous phase. Values of logD of Ca and Sr, calculatedfrom the bulk sediment and porewater data for the core 211650, are relativelyconstant at depths below 7 cm (Figure 3a), with a median logDCa = −1.7± 0.2and logDSr = −2.4 ± 0.5. Above that depth, current-induced sediment mixingand resuspension leads to severe distortion of the equilibria (Heiser et al., 2000).Between 15 and 21 cm, several points peak at higher logD values which correlateswith enhanced dissolved Mn, Ca, and Fe concentrations. This may indicate thatrapid deposition of ACR on these levels resulted in more dispersed carbonates,relatively enriched in Ca and Sr, and that the diagenetic re-crystallization processstill continues in these layers. Plots of logD of Ca and Sr vs.XMn of the separateACR laminae show negative slopes (Figure 3b). Very similar negative slopes arefound on such plots for bulk sediment data with porewater compositions taken forthe respective depth, but with relatively large scatter. This type of dependence ofD on solid phase composition may suggest that either reaction kinetics or a non-ideal solid solution behavior is involved, especially because the slope for logDSr

is significantly larger than that for logDCa.The dissolved Fe concentrations in the porewater below 7 cm depth vary

between 2 and 11µM, with median values at about 4± 2 µM. AbundantFe sulphides are present in the bulk sediment, including monosulphide (FeS),greigite (Fe3S4), and pyrite (FeS2), as has been reported already by others (Suess,1979; Boesen and Postma, 1988; Huckriede and Meischner, 1996; Sternbeck andSohlenius, 1997; Carman and Rahm, 1997). Concentrations of dissolved Fe inporewater are most probably controlled by metastable solubility of some of theseFe sulphides. In the gray carbonate laminae of the surficial sediment, extractableconcentrations of solid phase Fe are 2–3 times higher than in the light ACR laminaeof deeper sediment layers, obviously reflecting some Fe sulphide contamination inthe former. The same conclusion can be deduced for Ba (cf. Table II), where ourdata are systematically higher than those measured by Huckriede and Meischner(1996) probably due to different extraction techniques used.

5. The Thermodynamic Model

5.1. CALCULATION OF THERMODYNAMIC SSAS EQUILIBRIA IN

EARLY-DIAGENETIC ENVIRONMENTS

The early-diagenetic system “sulfidic porewater–authigenic minerals” in anoxicmarine sediments is not yet well understood due to a severe lack of sufficientlyvalidated models capable to provide a comprehensive mathematical description ofthe diagenetic behavior of a large number of dissolved and solid-sediment speciesthat are related through interconversion reactions and/or by their production orconsumption during organic matter decay. There are, in general, two groups ofnumerical algorithms which can be applied for modeling such open systems:(A) Explicit kinetic mass transport numerical schemes such as STEADYSED

(Wang and Van Cappellen, 1996) based on a carefully chosen set of forward-


Figure 3. Profile of the empirical partitioning coefficient logD for Ca (block dots) and Sr(open dots) in bulk sediment (above) and logD of the same elements vs.XMn relationship forseparate carbonate laminae (below, regression for Ca:y = −4.6− 1.9x, r2 = 0.91; regressionfor Sr:y = −0.44− 2.70x, r2 = 0.92; both with 95% prediction intervals).

and backward rates of diagenetic reactions, especially on explicit considera-tion of (microbial) degradation of organic matter and coupled redox reactionsinvolving the major elements C, N, Fe, Mn, and S, together with (one-dimensional) diffusive/advective vertical transport of aqueous species in theporewater profile.

(B) Steady-state approaches involve speciation codes based on the Law-of-MassAction (LMA) formulation of the equilibrium system and solve the (one-dimensional) mass-transport problem by a two-step multi-box approach. Ex-


amples of such an approach include the STEADYQL algorithm (Furrer andWehrli, 1996) and the CoTAM code (Hensen et al., 1997).

The above mentioned state-of-the-art models provide an open-system approachin that they couple thermodynamic with kinetic or mass transport models to re-produce porewater profiles. One of the major disadvantages of using LMA-basedmodels, however, is that they cannot treat pH as a dependent variable. Moreover,different redox states of the same element (e.g., Fe2+, Fe3+) must be assigned toseparate mass-balance constraints, with input-defined and therefore prefixed Eh orpe values. For SSAS systems, the most severe limitation is that one must alreadyknow the equilibrium composition of the solid solution and its solubility product,which, however, is a function of the aqueous speciation, solid-solution compositionand end-member activity coefficients. One way to overcome this complication (atleast for binary SSAS systems) is the application of Lippmann equations or atleast the concept of “stoichiometric solubility”, e.g., by using the MBSSAS codeas a subroutine to PHREEQC (Glynn, 1991). Since our primary goal for this firstattempt to approach the problem was not to model the mass transfer in a porewaterprofile, but rather to explore the possible local-equilibrium solid-solution behaviourof Mn-rich carbonates, we will not consider the above true open-system diageneticmodels but use a closed-system GEM approach.

The GEM approach is to a large extent complementary to LMA, albeit notfrequently used in low temperature geochemistry. In GEM formulation,all speciesare taken with their formal elemental stoichiometry into the mass balance (totalmoles of chemical elements and zero charge), albeit an alternative choice of stoi-chiometric units, e.g., aqueous ions or metal oxides, is always possible (Karpov etal., 1997). Species belong to either single- or multi-component aqueous, gaseous,liquid or solid phases which may (or may not) appear at the equilibrium state.A non-linear minimization algorithm based upon linear algebraic vector-matrixnotation of a convex programming approach (Karpov et al., 1997) iteratively findssuch quantities of all relevant species that minimize the total Gibbs energy of thesystem, subject to the elemental mass balance constraints. In brief, letxj denotequantity of aj th species;vj an approximation ofprimechemical potential of thisspecies (expressed via the standard state chemical potential and concentration), andG(x) the total Gibbs energy function of the system given by:

G(x) =∑j

xj vj , j ∈ L. (2)

In vector-matrix algebraic notation, the problem of finding the equilibrium phaseassemblage and speciation of the system (vectorx, numbers of moles of species)is defined by:

G(x)⇒ min, subject toAx = b, x ∈ R, (3)

whereR is a set of kinetic upper-lower restrictions tox (trivially, x ≥ 0). Thevector x̂ will be an optimal solution of the problem (Equation (3)) if and only if


such a vectoru exists that the following conditions of optimality are satisfied (cf.Karpov et al., 1997):

v − AT u ≥ 0,

Ax̂ = b,

x̂ ≥ 0,

x̂T (v − AT u) = 0, (4)

(T is a transpose operation). These four “Karpov” criteria are fulfilled upon conver-gence of the “Interior Points Method” (IPM) – a powerful non-linear minimizationalgorithm used as the numerical basis of the SELEKTOR computer codes (Karpovet al., 1997) designed for finding a stable phase assemblage and an equilibriumspeciation in complex heterogeneous solid-aqueous multi-phase systems. We per-formed our modeling calculations with the version 3.2β of the SELEKTOR-A code(Kulik et al., 1997). The above briefing readily suggest that GEM programs areclearly more demanding in their numerical implementation and also for consistentthermodynamic input data than the LMA codes. But once established, their clearbenefit is that they provide at least two facilities which are not available with theLMA approach. First, the GEM code can calculate equilibrium redox and pH (pe)state with the speciation of any (non-ideal) aqueous and multiple-component solidsolutions in one run, thus obviating the need for any supplementary assumptionsand iterations. Second, the IPM algorithm principally calculates the dualu vector(Equation (4)) containing equilibrium values of chemical (partial molar) potentialsfor stoichiometric units, usually chemical elements and charge. This provides asound basis of an innovative “Dual-Thermodynamic” (DT) technique for retrievalof thermodynamic data, such as activity coefficients or values of standard-stateGibbs energy of formation of solid-solution end-members, from experimentallyknown bulk compositions of equilibrated aqueous and solid phases (Kulik et al.,1998). This technique is described below as it has been used for retrieval ofMargules interaction parameters for multiple-component ACR solid solutions.

5.2. ESTIMATION OF SOLID-SOLUTION PARAMETERS BY THE“ DUAL

THERMODYNAMIC” APPROACH

5.2.1. The Dual Thermodynamic Formulation

Let us rewrite the first Karpov criterium (first inequality in Equation (4)) for aj thspecies in a multi-component phase, e.g., an aqueous species or an end-member ina multiple solid solution:

vj − µj ≤ 0, whereµj =∑i

aij ui, i ∈ N, j ∈ L. (5)


aij is a formula stoichiometry coefficient (e.g.,a = 1 for Mn, C anda = 3 for O inMnCO3). When the phase is stable, this inequality transforms to equality for eachof its species:

vj = µj =∑i

aij ui . (5a)

This is just an alternative mathematical expression of the fundamental definition ofequilibrium by Gibbs: the (isobaric-isothermal) chemical potential of a (independ-ent) component must be the same in all phases present in an equilibrium state. TheGEM-IPM speciation algorithm directly exploits this classic idea. Numerically, onemust writevj ≈ µj because of possible small round-off errors and mass-balancedeviations. For aj th solid-solution end-member, the “prime” approximation ofchemical potential takes the usual form (cf. Nordstrom and Munoz, 1994; Karpovet al., 1997):

vj =g0j,T P

RT+ lnXj + ln λj , (6)

whereg0j,T P is a standard molar Gibbs energy of formation from elements recalcu-

lated at temperatureT and pressureP of interest;R is universal gas constant;Xjis a mole fraction andλj is a rational activity coefficient. Symbolv is used here fortheprimechemical potential (Equation (6)) calculated via the standard state and theactivity terms, while theµ symbol is reserved for the alternative, dual expression ofchemical potential, calculated only via the formula stoichiometry and the chemicalpotentials of stoichiometric units (Equation (5a). At equilibrium, we can combineEquations (5a) and (6) to obtain:

∑i

aij ui ≈g0j,T P

RT+ lnXj + lnλj , (7)

and call it abasic Dual-Thermodynamic (DT) equation for solid-solution species.If no other information except theT , P and bulk composition vectorb of the

system is provided before calculation of an equilibrium state then the basic DTEquation (7) can be immediately used for estimation of equilibrium concentrationsof trace solid-solution end-members even if they are not included into the massbalance, but theirg0

j,T P andλj values are known:

lnX∗j =∑i

aij ui −g0j,T P

RT− ln λj . (8)

This equation will be referred to as adual-thermodynamic concentration (DTC)equation. It provides a general way to estimate thermodynamic partition coeffi-cients for trace elements in a SSAS equilibrium.


If the g0j,T P value for a solid-solution species is known and experimental in-

formation about its equilibrium concentration available, then Equation (7) can bere-arranged into aDual Thermodynamic Activity coefficient (DTA) equation:

ln λ∗j =∑i

aij ui −g0j,T P

RT− lnXj, (9)

which provides data for obtaining values of interaction parameters for the solidsolution models of choice (see below). However, if theg0

j,T P value for a solid-solution species is uncertain, but experimental information about its equilibriumconcentration is available and the activity coefficient is fixed (e.g., assuming idealbehavior or theoretically predicted non-ideal interaction parameters), Equation (7)converts into aDual Thermodynamic standard Gibbs energy (DTG) equation:

g∗j,T P = RT(∑

i

aij ui − ln λj − lnXj

), (10)

which permits to obtain consistent values of Gibbs energy of formationg0j,T P (and

hence, solubility productsKSP ) for minerals based on experimental or naturalcompositions of co-existing aqueous and solid phases.

Clearly, absolute or “true” values of chemical potentials of elements in anysystems cannot be determined, so the relative values of theu vector calculated bythe IPM refer to the same standard states of elements and species as the respectiveg0j,T P values. However, Equations (7)–(9) remain valid at any consistent choice

of standard states or units of measurement because they all include thedifferencebetween stoichiometric chemical potential and standard-state Gibbs energyg0

j,T P .The above three equations (DTC, DTA, and DTG) are quite general and remain thesame regardless of the number of other species involved into a solid solution, aswell as of the complexity of the whole SSAS chemical system (which may containother solid solutions, gas mixture, sorption phases, single-component minerals etc).The only prerequisite is that the (local/partial) equilibrium state is achieved, andthus, chemical potentials of elements are equalized in all stable phases, which oftenmay not be easy to be proven, especially for low-temperature experimental andnatural systems.

Application of DTA or DTG equations requires first to subdivide an SSASsystem into two parts: (i)a representative sub-systemN ′ representing the aqueousphase plus other equilibrated phases with known thermodynamic properties forall species and given bulk chemical composition, and (ii) anon-representativesubsystemN∗ ⊆ N ′ of solid-solution end-member(s) with partially unknownthermodynamic properties, but of known (i.e., experimentally measured) concen-trations. For the second step, the GEM-IPM algorithm is used for calculation ofthe equilibrium state in the representative subsystem only (at selected orin situ TandP conditions). The dualu′ vector of chemical potentials of elements obtained


from this calculation is then used at the third step for computing the “dual” (stoi-chiometric) chemical potentials for species included into the non-representativesubsystem:

µ′j =∑j

aij u′i . (11)

The fourth step consists in substitutingµ∗j values into DTA (Equation (7)) orDTG (Equation (10)) relations to obtain the sought-for estimates ofλ∗j or g0

j,T P ,respectively. From estimates of activity coefficientsλ∗j , at the fifth step, the valuesof interaction parameters can be obtained for the mixing model of choice, as de-scribed in more detail below. Ultimately, the whole solid solution model can thenbe assembled and included (in part) into the representative subsystem for obtain-ing the best possible fit of parameters. Alternatively, the whole sequence can berepeated from the second step with less species remaining in a non-representativesub-system for sensitivity studies.

5.2.2. Estimation of Margules Interaction Parameters

The data reported in the literature suggest that rhodochrosite solid-solutions en-countered in marine sediments consist mainly of the Mn- and Ca-carbonateend-members, with some admixture of Mg-carbonate end-member of up to 2–5%.Other elements (Fe, Sr, Ba, trace metals) are present in mole fractions of less than1% and can thus be considered as trace end-members. MgCO3 can be taken eitheras major or trace end-member, depending on the precision required. In the formercase, one has to deal with a ternary solid solution, but for the first approxima-tion, we will consider a symmetrical Margules mixing model with only two majorend-members: MnCO3 and CaCO3. To derive equations for Margules interactionparametersWij of major and trace end-members, let us investigate first the activity-coefficient expression for a ternary system. It can be obtained, for instance, fromthe full theoretical subregular expression of Helffrich and Wood (1989, Equation(6)) by settingWij =Wji :

RT ln λ1 = W12X2(1−X1)+W13X3(1−X1)−W23X2X3

+W123X2X3(1− 2X1). (12)

Equations for the two other activity coefficients can be obtained by cyclic permuta-tion of the indices. Let the third end-member be a trace one (X3� 1), and the othertwo be major end-members. Then Equation (12) can be expanded to:

RT ln λ1 ≈ W12X2−W12X2X1+W13X3−W13X3X1

−W23X2X3−W123X2X3− 2W123X1X2X3. (13)


If the ternary interaction parameters are negligible then all terms involvingX3 canbe omitted:

RT ln λ1 ≈ W12X2−W12X2X1 = W12X2(1−X1) ≈ W0(1−X1)2, (13a)

which is approximately equal to the expression for the binary system (W0 denotesa symmetric binary parameter). The same reasoning applied to the second majorend-member results in

RT ln λ2 ≈ W0X21, (14)

or, for a dimensionless interaction parameterα0 = W0/RT ,

α0 = ln λ2(1−X2)−2, or α0 = ln λ1(1−X1)

−2. (14a)

If both numbers obtained in this way coincide (within reasonable uncertaintylimits) then this is a good indication that the symmetric binary approximationis applicable. The resulting Margules interaction parameters for both the majorend-members in the binary symmetric approximation are given in Table III.

Now, let us consider the trace end member, assuming index 1 for trace, 2 and 3for major end-members for compatibility with Equations (12) and (13), respect-ively. All terms involving X1 now can be skipped from Equation (13a), whichyields:

RT ln λ1 ≈ W12X2+W13X3−W23X2X3+W123X2X3

≈ W12X2+W13X3−X2X3(W0−W123). (15)

Permutation of indices back to 3 for the trace, and 1 or 2 for the major end-membersleads to:

RT ln λ3 ≈ W31X1+W32X2−X1X2(W0−W123). (15a)

A remarkable feature of Equation (15a) is that the activity coefficient for the traceend-member depends on mole fractions of major end-members only. The rightmostterm shows also that, ifX1� X2, the value ofλ3 becomes less affected byW0 andW123 interaction parameters. For this study, we assumeW123 = 0 (as well as all thehigher-order parameters), although, in general, its value should be regressed fromthe data for multiple experimental composition points. Equation (15a) simplifiesthen to:

RT ln λ3 ≈ W31X1+W32X2−W0X1X2. (15b)

The remaining problem is how to calculate the two different binary interactionparametersW31 andW32, or dimensionlessαTr,1 andαTr,2, from a single value ofln λ3 (if only one experimental composition is available). One way to do this is to


Table III. Thermodynamic data for some diagenetic sulfide phases and end-member carbon-ates.A, B, C are coefficients of the 3-term equation logK = AB/T + C lnT obtained usingthermochemical data from Robie and Hemingway (1995) and Shock et al. (1997)

Phase LogKSP , Ref. A B C LogKSP , 1G0298, 1G0

278,

1 bar, 25 bar, J/mole J/mole

25 ◦C 5 ◦C

Amorphous −2.95 [1, 2] 56.7542−2108.16 −9.23783 −2.85 −96376 −95170

FeS ± 0.09

Mackinawite −3.55 [1, 2] 56.7542−2287.05 −9.23783 −3.46 −99801 −98614

FeS ± 0.09

Troilite −5.25 [1, 2] 56.7546−2794.02 −9.23783 −5.28 −109505 −108317

FeS ± 0.15

Greigite −4.4 [1, 2] 165.5005−7052.36 −27.1512 −4.22 −311960 −307385

Fe3S4 ± 0.15

Marcasite −16.05 [3] 55.0154−6444.03 −8.67944 −17.0 −171150 −169980

FeS2

Pyrite −16.4 [1, 2] 55.0154−6548.38 −8.67944 −17.35 −173150 −171981

FeS2 ± 0.1

Alabandite 0.4 [4, 2] 51.9702−1135.95 −8.38251 0.71 −216289 −214702

MnS ± 0.2

Calcite −8.31 [3, 5] 130.8884−5678.66 −21.0882 −8.215 −1128206 −1126400

CaCO3 +0.1−0.17

Rhodochrosite−10.31 [3, 5] 123.6056−5717.63 −20.1381 −10.29 −817370 −815432

MnCO3 +0.23−0.9

Siderite −10.54 [3, 5] 128.4520−5530.65 −21.1391 −10.406 −679649 −677761

FeCO3 +0.1−0.3

Magnesite −5.1 [3, 5] 122.1981−3606.24 −20.2195 −4.57 −1011080 −1009793

MgCO3 +0.2−2.9

Strontianite −9.28 [3, 5] 134.9439−6407.78 −21.5410 −9.33 −1144790 −1142868

SrCO3 ± 0.1

Witherite −8.31 [3, 5] 132.2919−6346.76 −20.9412 −8.39 −1136200 −1133966

BaCO3 −0.3

Smithsonite −10.28 [3, 5] 124.6236−5422.26 −20.4854 −10.165 −733940 −732333

ZnCO3 ± 0.4

Reactions: MS + H+ = M2+ + HS−; 13(Fe3S4) + H+ = Fe2+ + HS− + 1

3S0; FeS2 + H+ = Fe2++ HS− + S0; MCO3 = M2+ + CO2−

3 .References: [1] Morse et al., 1987; [2] Huerta-Diaz et al., 1998; [3] Langmuir, 1997; [4] Smithand Martell, 1976; [5] Rimstidt et al., 1998.

assume that the ratio of interaction parameters likeρTr = αTr2/αTr1 does not dependon metastability and is independently known. In case of rhombohedral carbonatesolid solutions, such ratios can be obtained from the values of symmetric inter-action parametersα for the binary carbonate systems given by Lippmann (1980).Theseα values were predicted from excess enthalpy of mixing using cation-anion(metal – CO2−

3 ) distancesrj−An in pure carbonate end-members and the theoryof isomorphous miscibility in ionic crystals (cf. also Urusov, 1977). However, for


Figure 4. Correlation between interionic distance and cation radii in rhombohedral carbonates(MgCO3 excluded from regression; squares: values ofrCat−An for Ba and Zn predicted fromthis correlation).

Sr and Ba forming orthorhombic pure carbonates, this approach is not directlyapplicable (cf. Böttcher, 1997c). Lippmann (1980) has found a value ofα = 2.5 forthe aragonite-strontianite solid-solution from empirical data. Casey et al. (1996)estimatedα = 3.1 for the aragonite-strontianite binary from experimental data.Böttcher (1997c) obtainedα = 2.6 for a hypothetical calcite-rhombohedral SrCO3

system following the Madelung–Vegard approach of Lippmann (1980). Thus, wecan assume the same non-ideality for Ca–Sr binary in authigenic rhombohedralMn–Ca carbonates (α = 2.5), which then permits to calculaterSr−An = 3.366 usingeffective cationic radiirSr = 1.16 Å andrCa = 1.00 Å, both in six-fold coordination(values ofrCat from Rimstidt et al., 1998, originally from Shannon, 1976). With theexception of Mg, the values ofrCa−An, rMn−An, rFe−An now form a good correlationagainst effective cationic radiirCat (Figure 4), permitting further interpolation torBa−An and, for instance,rZn−An values to represent heavy metal incorporation.From these cation-anion distances, we have estimated theα values forX = 0.5 inTr–Ca and Tr–Mn binary sub-systems (Tr = Sr, Ba, Zn) using the same Madelung–Vegard approach as Lippmann (1980). With thus obtainedρTr = αTr−Ca/αTr−Mn,both regular binary Margules parameters for a trace carbonate end-member can bepredicted:

αTr,1 = ln λTr + α0X1X2

X1+ ρTrX2; αTr,2 = ρTrαTr,1. (16)


Table IV. Composition of aqueous solution and chemical potentials of elementsui in therepresentative porewater model atin-situP = 25 bar,T = 5 ◦C. Calculated parameters ofaqueous phase:I = 0.225m; pH = 7.611 (molal activity scale); pe =− 4.032; Eh =−0.222 V

Element LogmT Mg/(kg soln) Logς = ui/RT ui , J/mole

logaf i − logmT

Ar −2.86287 54.100 1.011 2338

B −3.82055 1.6140 −1.8401 −145.146 −335672

Ba −4.87932 1.7907 −0.5865 −236.415 −546746

Br −3.53530 23.006 −0.1477 −61.9670 −143308

C −2.27465 63.025 −3.1508 (CO−23 ) −3.21317 −7431

−0.2210 (HCO−3 )

Ca −2.39775 158.40 −0.5238 −227.684 −526553

Cl −0.71539 6742.7 −0.1537 −67.4982 −156100

F −4.54090 0.5400 −0.2933 −142.314 −329122

Fe −5.59731 0.1394 −1.2327 (Fe+2) −37.6499 −87071

H −1.96745 10.729 −5.6432 (H+) −8.23560 −19046

K −2.33046 180.42 −0.1501 −117.681 −272154

Mg −1.84138 345.85 −0.4652 −184.253 −426114

Mn −3.72065 10.323 −1.0175 (Mn+2) −92.6228 −214204

N −2.91242 16.924 −0.1591 (NH+4 ) 1.76167 4074

Na −0.77063 3850.2 −0.1364 −105.546 −244090

O −1.34442 714.92 −5.7719 (OH−) −85.4932 −197716

P −3.81726 4.6592 −5.9975 (PO−34 ) −150.776 −348692

S −2.13358 232.78 −0.8039 (SO−24 ) −4.99124 −11543

−2.1084 (HS−)

Si −6.00093 0.0277 −202.476 −468257

Sr −4.55386 2.4170 −0.5596 −237.285 −548758

Charge −9.28129 −21464

This equation can be simplified by an assumption thatαTr2 = αTr1 (or ρTr = 1),and also that one of the two binary interactions is ideal (for example, FeCO3 inMnCO3). In the latter case (αTr,1 = 0), Equation (16) can be replaced by:

αTr,2 = ln λTr

X2+ α0X1; αTr,1 = 0. (17)

Note that only predicted ratiosρTr, but not separateαTr-Ca or αTr−Mn values, wereused in the DT calculations discussed below.


5.3. UNCERTAINTIES ASSOCIATED WITHESTIMATION OF SOLID-SOLUTION

PARAMETERS

In reality, both thermodynamic data and bulk experimental compositions can bedetermined only with a limited precision. Equation (7) suggests that at least foursources of uncertainty are to be considered in the Dual Thermodynamic calcula-tions: (i) errors in the bulk composition of the chosen sub-system (in our case,the aqueous solution, Table I); (ii) standard molar free energy of formation ofrelevant aqueous complexes (e.g., sulphide complexes in our anoxic sediment sys-tem,Table A-1); (iii) determination of solid-solution composition (uncertainty inmole fractionsXj , Table II); and (iv)g0

j,T P values of solid-solution end-members(uncertainty in logKSP , Table III). In the GEM-IPM algorithm, the first and secondsources actually translate into uncertainty of values in the dualu vector, and henceinto uncertainty of stoichiometric chemical potentialsµ of the non-representativespecies. This kind of uncertainty can be minimized by choosing the appropriateaqueous electrolyte model with a consistent set of thermodynamic data for theaqueous species, including correct temperature and pressure dependencies (cf.Section 5.4). The data on the composition of the aqueous phase should also beconstrained as much as possible (cf. Section 4.1). In order to assess the impact ofuncertainty,δX, in mole fractions (source (iii)) and solubility products of carbonateend-members (source (iv)) onto estimates of Margules parameters, we performedDTA calculations (Equations (14) and (15)) not only for the accepted “median”Xj andg0

j,T P values, but also forXj − δ(Xj), Xj + δ(Xj), and for a number ofreported logKSP values for each end-member. Upon analyzing the results, it waspossible to construct a consistent set of symmetric Margules parameters and solu-bility products for the ACR solid-solution model, and estimate the uncertainties ofα values thus obtained (bold numbers in Table VI).

5.4. THERMODYNAMIC DATA FOR THE AQUEOUS ELECTROLYTE MODEL

A GEM approach has not yet been widely used to model speciation in sea-water. We therefore developed first a thermodynamic model of Baltic Sea water(Kersten et al., 1998). This model considers the main interactions of all solidphases with porewater solutions, which can affect chemical potentials of the mainSSAS system-bearing elements C, O, Mn, Ca, Fe, Mg, Sr, and Ba. All majorcations and anions were included, as well as strong and weak aqueous complexesbetween these cations and ligands, and dissolved gases, which form the extendedstoichiometry matrix for the whole elemental system B–Ca–N–C–S–Cl–Br–F–K–Mg–Na–Sr–P–Si–Fe–Mn–O–H–Ar–Ba and charge. The thermodynamic databaseof partial molal properties for use in the GEM code SELEKTOR-A (Kulik et al.,1997) is based on the most recent SUPCRT data set for aqueous species (Shock etal., 1997). Extensions for some yet undefined trace metal aqueous complexes weremade using PRONSPREP97/PARCOR algorithms (Sverjensky et al., 1997) andone-, two- and three-term extrapolations of cation or ligand exchange reactions


(e.g., Gu et al., 1994). The thus obtained data file provides also for temperatureand pressure change corrections in partial molal properties of aqueous species bymeans of the HKF equation-of-state (Helgeson et al., 1981). This dataset formsthe basis of an ion-association model of seawater which includes weak Cl− com-plexes of major cations. Activity coefficients of individual aqueous species,γj , arecalculated using the extended Debye–Hückel (EDH) equation:

logγj =−Aγ z2

j

√I

1+ Bγa0γ

√I+ bγ I, (18)

where zj stands for species charge,I – for the effective molal ionic strength,Aγ andBγ are coeficients depending onT andP , the common EDH parameterbγ = 0.064 (at 25◦C) represents NaCl as the major electrolyte, anda0

γ denotesthe individual Kielland ion-size parameter. The whole seawater model has beenfine-tuned against measured parameters of the carbonate system (Millero, 1995)by calculating equilibria at 1 bar, 25◦C in normative seawater bulk composition(Kulik et al., in prep.). The GEM model correctly reproduced the measured pHNBS,pHTRIS, f (CO2), and saturation index�CaCO3 over a wide range ofT , P andSBconditions. At givenSB and T , contents of dissolved gases in water like CO2

can be found by computing equilibrium in the system “aqueous solution-excessmodel air”. In the model air composition necessary to accomplish the GEM model,N2 was replaced by argon, andN2,gas, N2,aq were excluded from calculations toavoid problems related to the biologically mediated strong disequilibrium betweenatmosphericN2 gas and nitrogen species in the euphotic zone (cf. Stumm andMorgan, 1996). The model composition of the near-bottom water has ultimatelybeen obtained from a conservative mixing model of the Gotland Deep brackishwater column. It has been assumed that bulk composition of a parcel of brackishwater is made of the “Baltic winter surface water” (BWSW) and the “Belt Seanormative inflow water” (BNIW) salt end-members, with the appropriate amountof water according to thein situ salinity. Chemical changes in the water columnwere modeled on assumption that they are coupled to aerobic oxidation of organicmatter. Bulk composition of the last, suboxic point of the model profile (240 mdepth,SB = 12,T = 4.5 ◦C; cf. Table I) has been taken to provide concentrationsof conservative elements in a “model porewater” composition, modified accordingto the results of our investigations and literature data (Boesen and Postma, 1988;Jakobsen and Postma, 1989; Huckriede and Meischner, 1996; Carman and Rahm,1997; Kersten et al., 1998).

Thermodynamic data for solid phases (authigenic sulphides, carbonates) werecollected from literature (Table III). Considerable care was taken in recalculationsof properties of these solids to thein situT (5 ◦C) andP (25 bar), consistent to suchchanges predicted by the HKF equations for aqueous ions and complexes. Wherepossible, standard values of molar entropyS0, heat capacity,Cp0, and volume,V 0,were taken from the compilation of Robie and Hemingway (1995), or were estim-ated on the basis of the additivity principle, and used together with the reported


logKSP,298 to calculate coefficients of the three-term temperature approximation(Table III):

g0j,T P = A+

B

T+ C ln T ,

where

A = 1S0T0−1Cp0

T0(1+ ln T0)

2.303R,B = −1H

0T0+1Cp0

T0· T0

2.303R,C = 1Cp0

T0

2.303R,

(19)

andT0, T , 1S, and1Cp stand for the reference temperature (298.15 K), temper-ature of interest, changes in entropy, and heat capacity of the reaction, respectively(Nordstrom and Munoz, 1994). This three-term approximation of logK requiresnon-zeroA, B, andC coefficients in Equation (19). The two-term approximation(i.e., the commonVan’t Hoff equation) implies non-zeroA, B, but with C = 0,whereas the one-term approximation requiresB= 0,C = 0, and non-zeroA coef-ficient. If thermodynamic properties are known for the reaction and all but one ofits components, the partial molal/molar properties of thisj th component can becalculated for any temperature of interest:

4j(T ) =−14(T )+ L∑

j−1

µj4j(T )

/νij , (20)

where4 stands for one of standard partial molar (molal) properties: Gibbs energyg0, enthalpyH 0, third-law entropyS0, heat capacityCp0, volumeV 0 for indi-vidual species.14 represents their respective changes in the reaction involvingL

components with stoichiometric coefficientsνij .For dissolution reactions of carbonates and sulfides, the three-term extrapol-

ation produces practically the same values ofg0 as the direct calculation basedon Cp = f (T ) equation and thermochemical data. The two-term extrapolationyields a correct trend, but produces a positive deviation of about 0.5 kJ/mole at 5◦C. The one-term extrapolation yields an inverse temperature trend, except for iso-coloumbic reactions (e.g., of the type CaCO3 + Mn+2 = MnCO3 + Ca+2), where itresults in about the same relatively small deviation as theVan’t Hoffequation.

5.5. EARLY DIAGENETIC MODELING OF ALKALINITY AND PH -BUFFERING

REACTIONS

While variation of major ion concentrations is significant (0.1 to 5 mmol/kg,depending on the element: Table I), pH, Eh, carbonate alkalinity, dissolved Feconcentration and sulphide/sulphate ratio appear to be well-defined, suggesting that

EA

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GE

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SO

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OLU

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NA

QU

EO

US

-SO

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ION

EQ

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173

Table V. Results of DTA calculations of a Margules interaction parameter for major ACR end-members in binary symmetricapproximation

End- g0278, pKSP log� X, µ∗, 1/RT ln λ∗ δx(ln λ∗) α∗ = W∗/RT δx− (α∗) δx+ (α∗) α, recom.

member J/mole ± X J/mole

MnCO3 −813902 10.00 −0.164 0.71 −814782 −0.3805 −0.0380 ± 0.06 −0.4521 0.63 1.04

−815492 10.29 0.127± 0.04 0.3070 0.6495 7.7229 −1.22 1.80

−817092 11.19 1.027 2.3825 2.7250 32.4020 −7.60 10.32

CaCO3 −1125933 8.12 −0.232 0.26 −1127131 −0.5180 0.8291 ± 0.16 1.5140 0.13 0.18

−1126463 8.22 −0.132 ± 0.04 −0.2888 1.0582 1.9325 0.08 −0.13 1.90

−1127528 8.39 0.053 0.1717 1.5187 2.7734 0.00−0.02 ± 0.50

MnCO3, −814362 10.08 −0.084 0.71 −814782 −0.1816 0.1609 ± 0.06 1.9130 0.10 −0.19 1.90

adjusted

� is a saturation index for the end-members;δx is the uncertainty (deviation) introduced by uncertainty in the mole fraction (±X).

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Table VI. Results of DTA calculations of Margules interaction parameters for Fe, Mg, Sr, and Ba end-members in “trace” approximation(Equation (15b))

End- g0278, pKSP log� X, % µ∗, 1/RT ln λ∗ δx(lnλ∗) αTr-Mn δX(αTr-Mn) αTr-Ca δX(αTr-Ca)

member J/mole ± X J/mole

SrCO3 −1142399 9.23 −1.309 0.072 −1149336 −3.0000 4.2368 0.13 5.983 0.20 1.304 0.04

(ρ = 0.218) −1142929 9.33 −1.209 ± 0.01 −2.7704 4.4658 6.282 1.370

−1143459 9.43 −1.109 −2.5412 4.6950 6.581 1.435

6.3± 0.3 1.4± 0.1BaCO3 −1133966 8.39 −2.501 0.03 −1147324 −5.7761 2.3357 0.4 3.355 0.40 1.171 0.2

(ρ = 0.349) −1135300 8.65 −2.251 ±0.01 −5.2005 2.9112 4.074 1.422

3.4± 0.4 1.2± 0.3FeCO3 −677303 10.31 −1.945 0.1 −687649 −4.4737 2.4341 0.6 0.640 0.6 8.963 8.0

(ρ = 14.0) −677833 10.41 −1.845 −0.09 −4.2445 2.6633 0.693 9.700

−679433 10.71 −1.545 +0.9 −3.5526 3.3551 0.852 11.927

0.7± 0.4 9.7± 5.0MgCO3 −1009863 5.10 −2.632 3.0 −1026692 −7.2769 −3.7704 0.7 −1.423 0.3 −9.266 1.0

(ρ = 6.51) −1020963 7.10 −0.632 ± 1.0 −2.4772 1.0293 0.574 3.739

−1025800 8.10 0.368 −0.3857 3.1209 1.445 9.407

−1027500 8.42 0.688 0.3494 3.8559 1.751 11.40

1.45± 0.3 9.4± 2.0

The most appropriate values of symmetric Margules parameters determined from different runs to derive the uncertainty limits are given inboldface (cf. Section 5.6).


certain metastable solid phases are probably buffering both redox and alkalinityconditions. Therefore, the first trial-and-error runs were performed at a large excessof solid phase stoichiometries (10 moles per 100 kg of model porewater, cf. Table I)in various combinations, but always atin situ T andP (5 ◦C and 25 bar). Sinceunderstanding of the iron geochemistry is most important in any early diageneticmodel (Boudreau and Canfield, 1988), relevant Fe oxides (hydromagnetite, ferri-hydrite), Fe sulphides (mackinawite, greigite, marcasite), Fe phosphate (vivianite),together with various carbonates (rhodochrosite, calcite, dolomite, siderite) wereallowed to participate in the system setup. However, the calculated equilibriumporewater compositions did not conform to the measured ones when using anyone single iron-source mineral. Concentrations of dissolved Fe and S were alwaysorders of magnitude too low in presence of stable FeS2 (marcasite, pyrite), in turnmuch too high in presence of hydromagnetite or other ferric oxyhydroxides. Excessvivianite resulted in too high dissolved P and Fe concentrations, while calcite yiel-ded higher Ca concentrations than measured in porewater of core 211650 (but thesame as reported by Carman and Rahm, 1997). Ultimately, addition of a compositeFe source using both FeS + Fe3S4 in excess resulted in an equilibrium porewatercomposition quite close to the measured one. Only in presence of this unique solidmackinawite/greigite buffering couple, the calculated pH, Eh, and alkalinity of thewater, as well as total [Fe]aq and [S]aq, could be readily adjusted close to measuredvalues by simply adding free C and/or CO2 to the bulk composition of the GEMsystem. At [Mn]aq close to 190µM, as measured at 25 cm depth in sediment core211650, the model yielded a slight undersaturation with respect to pure rhodo-chrosite and calcite. Further reducing the system by adding C or H always resultedin a decrease of both [S]aq and [Fe]aq, an oversaturation with respect to calcite andrhodochrosite, and an increase of pH, alkalinity and the sulphide/sulphate ratio,i.e., just the same trend as seen deeper in the sediment (cf. Jakobsen and Postma,1989). It is noteworthy that pH modeling of early diagenetic reactions to providea quantitative answer to the old enigma of the enhanced buffering capacity ofanoxic sediments is much facilitated by using the thermodynamic GEM approach,while attempts to predict pH in sulphidic sediments using LMA modeling (coupledwith transport) have yet failed mostly due to the inherent mass balance problems(e.g., Boudreau and Canfield, 1988; Wang and Van Cappellen, 1996). However,our closed-system model cannot produce a profile of any of the geochemical para-meters and provide thus a first but preliminary step in early diagenesis model-ing using the GEM approach. Efforts to add a mass transport capability are underway.

Based on these trial-and-error calculations, we finally selected a bulk compos-ition for the model porewater, best matching the measured field data (cf. Table I).The obviously irrelevant FeS2 phase was switched off from subsequent calculationsfor convenience, though abundant framboidal pyrite is present throughout thesesediments (e.g., Boesen and Postma, 1988; Sternbeck and Sohlenius, 1997; Carmanand Rahm, 1997). Obviously pyrite formation is kinetically limited and probably


requires certain high oversaturation set up by the solubility of mackinawite and/orgreigite. This bulk composition has alone been used for calculation of an equilib-rium speciation and chemical potentials of elements,ui, for the porewater model at25 cm depth andin situP , T . Variations of the bulk composition, causing changesin pH of less than± 0.2 units, or± 1 mM in total alkalinity (in presence of themackinawite-greigite assemblage), resulted in chemical potential variations ofuC,uO, uCa, uMn of less than 0.8 kJ/mole. Thus obtained speciation (Table A-1) showsimportant differences in complexation behavior of divalent metals, which can beconveniently expressed by calculating the ratioςi of freeith ion activity to its totaldissolved concentration (in log molality scale, Table IV):

logςi = logafree,i − logmi (21)

The rather high concentrations of dissolved Fe measured in porewater (1–4µM,Table I), or obtained in thein situ bell-jar experiments by Bågander and Carman(1994), are reproduced with the same solubility products of both the mackinawite-greigite sulphides as reported by others (e.g., Morse et al., 1987; Huerta-Diaz etal., 1997) and that are generally accepted (Morel and Hering, 1993; Stumm andMorgan, 1996). However, this was possible in our model because we assumed thata major fraction of the dissolved Fe and Mn is strongly complexed by bisulfideas reported earlier by Luther et al. (1996) and recently approved by Al-Farawatiand van den Berg (1999). In order to achieve the excellent model match with theporewater data, we made in fact no correction at all to the pKa of the MnHS+complex, and made the FeHS+ complex pKa only 0.3 units weaker than that usedby Luther et al. (1996). Another implication of using these complexation constantsis that solubility of Fe and Mn should now strongly depend on both pH and totalS in the system (at fixedfO2), and because Ca, Mg, and Sr are not affected bystrong HS− complexes, one cannot expect that the molality ratios like [Ca]/[Mn]or [Sr]/[Mn] are equal to their activity ratios {Ca+2}/{Mn +2} or {Sr+2}/{Mn +2},respectively. This deviating behavior must be considered when empirical distri-bution coefficients are compared to thermodynamicKd values, or porewater dataare plotted over the Lippmann diagrams. Based on the aqueous speciation cal-culations, we have suggested a convenient way to solve this problem using theς -ratio (Equation (21)). The results (Tables IV, A-1) show that Mn+2 and Fe+2

are strongly affected by sulphide complexation (up to 70% as hydrogen sulphidecomplex), yielding logς values around−1.0 (Table IV), while Ca+2, Mg+2, Sr+2

and Ba+2 are not affected by any sulphide complexation. The latter elements existpredominantly in free ionic forms, with logς values around−0.5. Alkali metalcations (Na+, K+) and halogen anions (Cl−, Br−) are the least complexed and havehigher activity coefficients than the divalent ions, which is reflected in their logς

values between−0.12 and−0.15. Such differences in activity-to-molality ratiosmay explain some peculiarities in porewater composition, saturation and empiricalD values discussed below.


5.6. ESTIMATION OF ACTIVITY COEFFICIENTS AND MARGULES INTERACTION

PARAMETERS FROM THE FIELD DATA BY THE MULTI-COMPONENT ACR

SOLID-SOLUTION MODEL

As the first step, chemical potentialsµ for MnCO3 and CaCO3 stoichiometrieswere calculated from theui values using Equation (5a) (Table V). They were thenused in DTA calculations of regular Margules interaction parameters for the majorMnCO3–CaCO3 binary according to Equation (14a) for different values of pKSP ,within the uncertainty intervals ofXMn andXCa in the ACR solid-solution phase(Table VI). For the pure CaCO3 end member, all calculated values of the Margulesparameterα0 were positive and fall within a small range. At the recommendedpKSP = 8.22, a value ofα0 = 1.9± 0.5 results for calcite, with the uncertaintytracing back mainly to pKSP uncertainty. For the MnCO3 end-member, however,the DTA calculations revealed a very small uncertainty of lnλ, but with a quite bigrange inα0 estimates (from−0.45 to +7.7, and even up to +32.4). This intriguingresult reflects rather high sensitivity to pKSP or g0

278 values of the predominantMnCO3 end-member. The uncertainty ofα0 induced by variations inXMn wasminimal (the same as for the CaCO3 end-member) atα0 = 2.1 for pKSP = 10.1,but drastically increased both at smaller and larger pKSP values. Based on thepresumption that the ACR solid-solution behavior can be approximated by theregular model, we have to select and fix such a pKSP value for the MnCO3 end-member that yields the sameα0 = 1.9 as the one obtained for CaCO3 end-member.The DTG calculation (Equation (11)) then yields a pKSP,MnCO3 = 10.08, i.e., higherthan pKSP = 9.46 used recently by McBeath et al. (1998), albeit pKSP for both end-members are in general within the range of constants for calcite and rhodochrositereported elsewhere in the literature (accounting for the slight correction toin situT , P conditions, see Table III). The recommended value ofα0 = 1.9 is positive butsmaller than the value ofα = 3.25 predicted by Lippmann (1980). In particular, itwould not produce a miscibility gap, in accordance with the recent experimentalfindings by Böttcher (1998) and our own field observations.

Once the value ofα0 is determined for the major end-member binary, DTAcalculations for trace carbonate end-members can be performed using Equation(15b). Values ofρTr = αTr2/αTr1 ratios listed in Table VI have been estimated fromα values for Mg and Fe (Lippmann, 1980), or predicted as described above for Sr,Ba, and Zn. For the FeCO3 end member, the uncertainty ofαFe−Mn is greater, butDTA estimates are the same as predicted by Lippmann (1980). For the MgCO3 end-member, a quite large uncertainty in DTA calculations is induced by the big scatterin published pKSP,MgCO3 at 25 ◦C, with more than 3 pK units difference in therange from 5.1 to 8.4. The smallest pKSP = 5.1 selected by Rimstidt et al. (1998)results in large negative values ofαMg−Mn ≈ −1.4 andαMg−Ca≈ −9.3, which is incontradiction with the positive interaction parameters found for all other carbonatebinaries, and in particular also inconsistent to theoretical reasoning (Lippmann,1980; Urusov, 1977). However, for the pKSP = 8.1 (at 5◦C) derived from the


SUPCRT92 database, positive values ofαMg−Mn andαMg−Ca were calculated, infairly good agreement with Lippmann’s values (Table VII). It has been pointed out(Gamsjäger, 1989; Königsberger et al., 1992) that the large scatter of publishedpKSP values most probably reflects the difference in solubilities of magnesiteand hydrous Mg carbonates such as nesquehonite, with magnesite under variousconditions even less soluble than calcite. We can therefore conclude that the lowerpKSP ≈ 5.1 of the MgCO3 end-member is less reliable, and rather accept a valueof pKSP = 8.1 for magnesite.

For Sr, DTA calculations result in small uncertainty, withαSr−Mn andαSr−Ca

values twice lower than predicted. For the Ba end member, DTA calculation resultsin positive Margules parameters of about the same magnitude as for SrCO3, i.e.,about 5.5 times lower than predicted (Table VII), although we must admit that theunderlying dataset on both Ba concentrations in porewater and in the carbonatelaminae is relatively weak. In both cases, solubility products of the end-memberswere taken for the orthorhombic minerals strontianite and barite in agreement withTesoriero and Pankow (1996) and Rimstidt et al. (1998). Böttcher (1997c) poin-ted out that such solubility products are not strictly applicable to incorporationof Sr and Ba into the calcite lattice, and must be replaced with the pKSP valuesfor hypothetical rhombohedral end-members. Solubility products of the latter canonly be theoretically predicted. Böttcher (1997c) suggests pKSP = 7.62 for SrCO3

(orthorhombic), 1.65 pK units more soluble than pKSP of strontianite. Comparisonof this large difference with the experimentally measured1pKSP = 0.14 betweencalcite and aragonite, at the similar differences1rCat = rCat,IX − rCat,VI betweensix- and nine-fold cationic radii (1rCa = 0.18 Å and1rSr = 0.13 Å, cf. Shannon,1976), points out that such predictions may still be uncertain up to 1–1.5 pK units.Moreover, the SSAS model predictions will remain correct as long as the estimatedMargules interaction parameters are consistent with the solubility products of theend-members, especially if these end-members are present in trace mole fraction(as in the case of Sr and Ba in ACR phase). In conclusion, we consider appropriatefor practical reasons to use pKSP values for strontianite and witherite as the Sr andBa end-members of our SSAS model in agreement with Pankov (1997).

Now we can compare the interaction parameters as derived for the ACR SSASmodel from the Gotland Deep field data with that predicted from theory of iso-morphous miscibility (Table VII). However, the ultimate test for consistence of theMargules interaction parameters obtained so far is a GEM calculation of (meta-stable) equilibria in the complete SSAS system “porewater – ACR solid-solution– excess mackinawite + greigite”. The symmetric solid-solution model for themulti-component (Mn, Ca, Mg, Sr, Fe, Ba)-carbonate has been implemented inthe database of the SELEKTOR-A code with theα values found by DTA cal-culations (Tables VI and V), and then inserted into the system together with thethermodynamic data for the rhombohedral carbonate end-members. 0.01 moles ofa carbonate phase with the measured mean composition ofXMn = 0.71,XCa =0.26,XMg = 0.03,XFe = 0.001,XSr = 0.0007, andXBa = 0.0003 were added to the


bulk composition of 100 kg of model porewater (Table I), together with FeS andFe3S4 (10 moles each, i.e., both in excess). In such a GEM calculation, all chemicalpotentials in the system would be dominated by equilibrium in the porewater/Fe-sulphide sub-system, and a low quantity of carbonate solid solution will adjust itscomposition to the overall equilibrium. In a number of subsequent model runs,the values of interaction parametersαTr−Mn andαTr−Ca were adjusted keeping therespectiveρ ratios of the interaction parameters constant. In that case,g0

278 for theCaCO3 end-member had to be made 250 J/mole (0.045 pK units) more positive tokeep up with an unchangedαMn−Ca = 1.9. Such “fine-tuning” of the SSAS modelresulted in a perfect reproduction of measured porewater and carbonate metal con-centrations in calculated equilibrium states, with adjusted interaction parametersfor the ACR solid-solution trace end-member pseudo-binaries (Table VII). Theoverall quality of this fitting was checked by increasing the initial addition of theabove ACR phase composition by 10, 100, and 1000 times, respectively. In allcalculations, pH kept stable within 7.6± 0.01 units, and chemical potentials ofall elements differed by less than 80 J/mole. The adjusted Margules parametersdisplay the same trend as in Table VI, but are a bit smaller for Fe and Mn, andhigher for Sr and Ba. Metastability of the ACR solid-solution affects theα valuesthe stronger, the larger are their values obtained from Lippmann predictions. This“retardation” effect can be conveniently expressed by dividing the “tuned” by thepredicted Margules parameters (αtuned/αpred in Table VII), which are in the range0.4–0.6 for the Mn–Ca, Fe–Mn, Fe–Ca, Mg–Mn, and Mg–Ca binary. We would gothat far to postulate the same ratio (0.4) for the Zn–Ca binary for prediction pur-poses. Rather low value for Ba joins (0.2) can be explained by some insufficiencyof the input data.

5.7. LIPPMANN DIAGRAMS FOR THE AUTHIGENIC (MN, CA, SR)CO3 AND (TR,MN)CO3 PSEUDO-BINARIES

Lippmann phase diagrams can now readily be constructed from the total solubilityproduct (65) functions versus the appropriate mole and activity fractions (Xjor Xj,aq) as coordinates (Lippmann, 1980; Glynn and Reardon, 1990) using theMBSSAS code (Glynn, 1991) and based on the symmetric Margules parametersandς -parameters for conversion from molal concentrations to free ion activity re-quired for the Lippmann approach. The benefit of the activity-fraction scale is thatthere is no necessity to consider the extent of ion pairing and/or complexation withother ions in the aqueous solution. The effect of speciation can be quite important insulphidic marine porewaters, as discussed above. Consequently, a speciation modelof ion complexation in the aqueous solution with total ion activity coefficients willalways be required in the construction of Lippmann diagrams from experimentalconcentration data. The solidus and solutus curves can be easily plotted and used topredict the solubility of any ideal solid solution at thermodynamic equilibrium (i.e.,ataj = Xj ). The description of the thermodynamic properties of a non-ideal solid

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Table VII. Comparison of symmetric binary interaction parameters predicted from isomorphous miscibility theory and those estimatedwith DTA and GEM calculations from Gotland Deep porewater-sediment data

Cation r(VI), ri-An, Binary Gex (X = 0.5) α Ref. ρ α (DTA α (GEM αtuned/αpred αaccepted

Å Å J/mole (predicted) (predicted) equation) tuning)

Mn2+ 0.67 3.051

Ca2+ 1.00 3.213 Ca–Mn 2013.8 3.249 L, T 1.9± 0.5 1.9b 0.6 1.9

Mg2+ 0.72 2.953 Mg–Mn 836.6 1.350 L, T 6.510 1.45± 0.3 0.6 0.4 0.6

Mg–Ca 5444.5 8.785 9.4± 2.0 3.7 3.7

Fe2+ 0.61 2.995 Fe–Mn 267.4 0.432 L, T 14.00 0.7± 0.4 0.2 0.46 0.2

Fe–Ca 3748.4 6.048a 9.7± 5.0 2.8 2.8

Sr2+ 1.16 3.366 Sr–Mn 4176.8 11.45 L, T 0.218 6.3± 0.3 9.7 0.85 9.7

Sr–Ca 1550.2 2.500 1.4± 0.1 2.15 2.15

Ba2+ 1.36 3.471 Ba–Mn 11982 19.33 T 0.349 3.4± 0.4 4.0 0.2 4.0

Ba–Ca 7094.5 6.739 1.2± 0.3 1.4 1.4

Zn2+ 0.74 3.076 Zn–Mn 51.21 0.083 T 27.66 0.4c 0.0

Zn–Ca 1422.8 2.296 0.9

References: Cationic radii: Rimstidt et al. (1998), Table III. L: Lippmann, 1980; T: this work.a Misprintedα = 6.4357 is given in (Table II in Lippmann, 1980).b Consistent withg0

278= −1126213 J/mole for CaCO3, andg0278= −814360 J/mole for MnCO3.

c Assumed the same as for the Mg and Fe end-members.


solution, and hence of the solid-phase activity coefficients vs. solid compositionrelations, requires knowledge of the respectiveλj = f (Xj) equations for solidend-member activity coefficients. The values of interaction parameters in theseequations for (pseudo)binary systems can be predicted theoretically, as done above,or simply adjusted in graphical fitting of thesolidusandsolutuscurves against theempirical65 points on the Lippmann diagram plots (Glynn and Reardon, 1990).This is, however, difficult for ternary and higher-order solid solutions, and we willthus limit our discussion to some of pseudo-binary systems.

A Lippmann diagram based on an ideal mixing model (α = 0) derived for theACR solid-solution system with end-member pKSP,MnCO3 = 10.08 and pKSP,CaCO3

= 8.21 is shown in Figure 5. Log∑5 values for porewater data were estimated us-

ing ςMn = −1.0175 andςCa= −0.5238 (Equation (21), Table IV). A mixing curvefor our non-ideal model with the same end-member pKSP values, but with theproposed interaction parameterα0 = 1.9, was added to the Lippmann diagram. An-other, hypothetical one was added, based on a strongly non-linear system involvingeven a mixing gap due to the higher interaction parameterα = 3.25 (Lippmann,1980). Comparison of these curves with the field data demonstrates that our mod-erately non-ideal SSAS model is quite consistent to the natural porewater andsediment chemistry, while both the ideal and strongly non-ideal SSAS models fitnot that well. The theoretical distribution constants logKd were also calculated forboth the ideal and non-ideal cases of the (Mn, Ca)CO3 binary using theς -valuesof Table IV, and plotted together with empirical logD values based on the totaldissolved concentration data (Figure 5). The logD points display a slope consistentto the one predicted by the non-ideal symmetric model line, but are shifted upfrom that line by about 0.5 log units. This shift can be attributed to the differencein aqueous complexation between Mn (strongly affected by HS− complexes) andCa (not affected), expressed in the differenceςMn − ςCa ≈ −0.5. Addition ofthis difference to logD values results in a perfect match of thus obtained “activ-ity” Kd with the theoretical distribution constants for the non-ideal SSAS model(Figure 5). Though much less used, thermodynamic partition coefficientsKd maydiffer considerably from the more commonly used empirial partition coefficientsD. This is due to non-ideality of either the aqueous solution (ionic strength andcomplexation effects) or of the solid solution (related, e.g., to large differences inthe ionic radii of the major and trace element). The latter case is exemplified bya Lippmann diagram for the (Mn, Sr)CO3 binary (Figure 6). It shows a minimumon the solidus curve due to quite high positive interaction parameterαSr−Mn = 9.7(Table VII), suggesting a miscibility gap betweenXSr > 0.06 andXSr < 0.95.The porewater and sediment points for Sr fit with the solutus and solidus curves forthe Mn–Sr binary, but not for the Ca–Sr binary (Figure 6). One should be awareof the fact, however, that both are just projections of a 3-D space to one of thecoordinate planes, which points to a principal limitation of the Lippmann approachwhen applied to non-ideal ternary or higher order solid-solutions.


Figure 5. Lippmann diagram (above) together with logD and logKd plots (below) for themajor (Mn, Ca)CO3 binary of the multi-component SSAS system.


Figure 6. Lippmann diagrams for the (Mn, Sr)CO3 (above) and (Ca, Sr)CO3 (below)pseudo-binaries of the multi-component SSAS system.


6. Discussion

6.1. POSSIBLE CONTROLS ON COMPOSITION OF AUTHIGENIC

RHODOCHROSITES

The buffering properties of the metastable early diagenetic equilibrium system“porewater-authigenic phases” are further enhanced by participation of the car-bonate solid-solution phase. Typical for SSAS behavior, this ACR phase wouldadjust its equilibrium composition not only relative to any changes in Mn loador alkalinity, but also even to changes in the effective solid/water ratio. In real-ity, authigenic phases like ACR may undergo complex ripening-recrystallizationprocesses according to the Ostwald step rule (Morse and Casey, 1988), with su-perimposed redistribution of components between the ACR and aqueous phase.Such diagenetic redistribution would enrich the Mn-carbonate content in certainlaminae and thereby bring it closer to equilibrium due to decreasing precipitationrates (as found experimentally by Sternbeck, 1997). The detailed thermodynamicSSAS equilibrium model (see Section 5) can now readily be used for interpretationof how composition of such authigenic rhodochrosites is related to porewater com-position, salinity, and alkalinity variations in the near-bottom water. We performedsome model runs for assessing the influence of three main factors invoked forprecipitation of rhodochrosites in the marine environment: (i) input of dissolvedMnII from a reduced Mn oxide pool at the sediment-water interface, (ii) increasingalkalinity due to sulfate reduction, and (iii) salinity changes in the near-bottomwater. Any of these three factors can influence the amount and composition of theACR precipitates at the apparently metastable thermodynamic equilibrium. Thiswould allow us to justify (or reject) various currently debated hypotheses.

6.1.1. Mn Loading Variations

To assess the impact of the first factor (MnII load), we have computed a seriesof GEM runs atin situ P = 25 bar andT = 5 ◦C with a full-complexity modelsystem (190µmol/kg of dissolved MnII at equilibrium with small excess of thesix-component non-ideal ACR solid-solution composition (columns 5 and 7 ofTable II), 10 moles of FeS and 10 moles of Fe3S4 per 100 kg of model pore-water), but at different additions of MnII with MnO or MnCO3 stoichiometry.For the model calculation, pH was maintained close to the natural level of 7.61by adding small amounts of CO2. The ACR phase disappeared at equilibrium if≥ 30 µmol/(kg H2O) of MnII were subtracted from the PW model bulk com-position. Conversely, ca. 180–200µmol/kg of MnII had to be added (i.e., anapproximately two-fold initial oversaturation resulted in practically the samecalculated ACR composition and Mnaq as used before for parameterization ofthe solid-solution model) in order to obtain typical composition of authigenicrhodochrosite (XMn = 70%). This “Mn-titration” at constant pH shows a lineardependence of precipitated ACR mass vs. MnII addition, but with non-linearchange in ACR solid-solution composition and total dissolved Mn (Figure 7). This


behavior is quite typical for the non-ideal SSAS systems (although very differ-ent from what we expect for the fixed-composition minerals). Figure 7 illustratesthis point and also shows how addition of excess MnII will shift the compositionof carbonate solid-solution in case when the whole equilibrium is dominated bythe aqueous phase (composition of which changes insignificantly). At low MnII

additions, the whole system gets into another equilibrium state in which a littlebit of carbonate solid-solution of different composition precipitates.XMn rapidlydecreases to below 0.55, with the respective parallel increase inXCa andXMg.At MnII additions above 200µmol/kg H2O, the model predicts only a sluggishincrease inXMn of up to 0.81.XSr displays a nearly linear trend with respect toMn loading. We can conclude that a low amount of MnII supply to porewater(e.g., from reductive dissolution of small amounts of Mn oxides settled on topof the sediment) would be sufficient to cause large variations in the Ca/Mn ratioof the rhodochrosite precipitates. Conversely, large loadings (e.g., subsequent tomajor oxidation events in the water column) would produce more or less uniformcompositions with relatively highXMn varying between 0.7 and 0.8, as observedbelow the topmost mixed sediment layer (Figures 2 and 3). The occurrence of theACR precipitates of persistent composition as found in the Baltic Sea sediment mayhence be taken as a paleoproxy for major oxidation events caused in the overlyingwater, albeit composition variations of the major cations in rhodochrosite are lessindicative for the extent of such events.

6.1.2. Alkalinity Variations

For the second “alkalinity” factor, another series of GEM runs was performed inthe same system at constant MnII addition of 180µmol/kg H2O, but now allowingfor pH variation between 7.4 and 7.6 (adjusted by simply adding/subtracting HClor CO2, which would correspond to the impact of changing alkalinity). From theresults plotted on Figure 8 it follows that at pH≤ 7.55, there is only a small changeof XMn from 0.86 to 0.80, while by an increase of the pH value above 7.6, theACR composition changes drastically down toXMn = 0.2, with an increase ofXCa

= 0.6 balanced by a concommittant increase inXMg. The last two points in thisprofile, however, are not certain because Mg becomes already a major end-member,while the solid-solution interaction parameters were retrieved assuming that it is atrace end-member. Nevertheless, we believe that the curves are qualitatively correctand can therefore explain the large variation in measured Mg contents in ACR.They also evidence that early diagenetic variations in alkalinity (e.g., reflectingthe extent of sulfate reduction) can seriously influence the equilibrated carbonatesolid-solution composition.

Our model suggests that at porewater pH values above 7.6, as reported byCarman and Rahm (1997) for their sampling campaign in 1990, Mn-rich ACRshould be no more stable. Theoretically, a high carbonate and/or sulphide alkalinitycan not be expected to induce precipitation of “mixed manganese carbonates”, asclaimed by these authors. Moreover, our models predict that authigenic Ca-rich


Figure 7. Variation of the equilibrium composition of the ACR solid-solution precipitate withincreasing MnII addition at pH = 7.61 (SSAS model atin-situ25 bar, 5◦C).


Figure 8. Variation of the equilibrium composition of the ACR solid-solution precipitate withincrease in alkalinity (pH) at constant MnII input (180µM, SSAS model atin-situ 25 bar, 5◦C).


rhodochrosites of commonly described compositional range (XMn around 70%) aremetastable under ambient seawater pH = 8.0± 0.3 and would tend to change toapproximately equal mole fractions of Ca and Mn end-members. This may explainoccurrence of such “pseudo-kutnahorite” compositions described earlier for theauthigenic carbonates of Panama Basin with normal salinity seawater (Pedersenand Price, 1982).

6.1.3. Salinity Variations

For the impact of the third factor (salinity), a series of model runs has beenperformed in the same system to follow salinity change, again at constant MnII

addition of 180µmol/kg H2O, but at this time with varying composition of theconservative part of the porewater according to the following equations:

y = (SB − 0.171)/35.029

MNSW = 34.2y

MBRW = 0.17(1− y)

MH2O = 1000− SB, (22)

whereSB is salinity,MH2O is total mass of water,MNSW is mass of the “normativesea salt” end-member composition, andMBRW is mass of the “Baltic river watersalt” end-member composition (in grams; Kersten et al., 1998). The differencesbetween the near-bottom and the pore water composition were retained the sameas in Table III for a salinity of 12h, except the point withSB = 1h (where nodeficit in mg and Sr concentration was assumed). The resulting curves (Figure 9)reveal an intriguing non-linear shape, which is albeit again characteristic for thenon-ideal solid-solution behavior. Significant changes in both the major (Mn/Caratio) and trace element composition of the multi-component solid-solution fallbetween aSB of 5 and 15, i.e., the typical range for the brackish water in the centralBaltic Sea. Sr shows a quite peculiar trend. Opposite to the increase of dissolvedSr with salinity in brackish water, the Sr content in the solid-solution decreases.The model thus predicts that the amount of this element in ACR could be taken asa salinity paleoproxy for the Baltic Sea.

6.2. IMPLICATIONS OF GEM SSAS MODELING FOR MECHANISMS OF ACR

FORMATION IN THE GOTLAND DEEP

Based on the thermodynamic SSAS model scenarios described in Section 6.1, wemay now discuss various hypotheses on mechanisms of Ca-rhodochrosite precip-itation. Of the three viewpoints mentioned in the introduction, neither seems tobe completely true with respect to our equilibrium model. Our modeling results


Figure 9. Non-linear variation of the equilibrium composition of the ACR solid-solution pre-cipitate with increase in salinity at constant pH 7.5± 0.1 and MnII input (180µM, SSASmodel atin-situ25 bar, 5◦C).


strongly support the idea (iii) that precipitation of significant quantities of ACRwith typical composition (XMn between 70–75%) can be triggered only by a rapidaddition of at least 0.2 mmoles MnII

aq per 1 kg of suboxic/anoxic porewater. Thisis only possible due to massive reduction of particular Mn oxides following ma-jor inflow events in the Baltic Sea. High-alkalinity environment, as supposed bySternbeck and Sohlenius (1997), is not required. Moreover, increase in alkalinitywould shift the system towards precipitation of Ca/Mg-rich carbonates (Section5.1.2), and thus can not cause precipitation of Mn-rich carbonate phases at theambient bulk composition of the porewater-sediment system. It is unlikely thatMn-rich ACR precipitates above the sediment-water interface because of rapidmixing in the near-bottom water layer, dropping MnII

aq concentrations far below thesaturation level. Indirect evidence for that is provided by Heiser et al. (2000) whodescribe the absence of ACR in top 6 cm as a result of recent resuspension events.These authors have in fact found, that Mn carbonate previously present in the topsediment was completely dissolved before re-settling of sediment, in the time scalefrom days to weeks. We conclude therefore that the most probable location wherethe initial ACR precipitation occurs is within the first few centimeters below thesediment-water interface. Quick raise of MnII

aq concentration due to diffusion fromthe top sediment may reach these depths where other parameters of the porewaterare already more or less fixed by the equilibration with the metastable mackinaw-ite/greigite buffer assemblage. The classic idea that ACR precipitation is caused orenhanced due to diffusion of Ca2+ ions from underlying sediments (Suess, 1979;Jakobsen and Postma, 1989) is not compatible with our model results, becauseany addition of CaIIaq (or increase of salinity at constant MnII load) should shiftACR composition towards “pseudo-kutnahorite” (XMn < 0.5). On-going early-diagenetic sulfate reduction and production of ammonia by degradation of organicmatter, together or alone, can only lead to a decrease ofXMn in certain ACRlaminae.

7. Conclusions

1. The natural early-diagenetic environment “anoxic porewater – authigenic min-eral phases” has been characterized in sediment of the Gotland Deep, BalticSea, by a closed-system model. Occurrence of carbonate precipitates as al-most pure white laminae was considered as a natural experiment for long-termequilibration between these phases and porewater. Plots of distribution coef-ficients indicate that metastable equilibrium exists between porewater and theauthigenic Ca-rich rhodochrosite phases below 7 cm depth.

2. A thermodynamic model of porewater geochemistry atin situ P = 25 barand T = 5 ◦C was developed using the Gibbs energy minimization (GEM)approach. The values of isobaric-isothermal potentials of Mn, Ca, Fe, Mg, Sr,Ba, C, and O, calculated from the porewater composition, were used in a new“dual thermodynamic” approach to estimate solid activity coefficients of the


end-members in the non-ideal solid solution. With respect to the SSAS equi-librium modeling of the carbonate system, we were able not only to supportthe hypothesis of complete mixing between the prime end-members MnCO3

and CaCO3, but also to represent for the first time a multi-component solid-solution including minor element contribution: (Mn, Ca, Mg, Sr, Fe, Ba)CO3.The regular Margules interaction parameters for the composing binaries estim-ated by this model wereαMn−Ca = 1.9 ± 0.5, αMn−Mg = 0.6,αCa−Mg = 3.7,αMn−Fe = 0.2,αCa−Fe = 2.8,αMn−Sr = 9.7,αCa−Sr = 2.15,αMn−Ba = 4.0,αCa−Ba =1.4, validating the theoretical predictions of the positive interaction parametersgiven by Lippmann (1980) based on theory of isomorphous miscibility. TheseMargules parameters are consistent with pKSP values of 10.08 (MnCO3), 8.18(CaCO3), 8.10 (MgCO3), 10.41 (FeCO3), 9.33 (SrCO3) and 8.39 (BaCO3).A frequently applied pKSP ≈ 5.0 of the MgCO3 end-member (cf. Rimstidtet al., 1998) fails to provide consistent predictions of Margules interactionparameters and distribution coefficients.

3. Lippmann diagrams andKd plots for Mn–Ca, Mn–Sr, and Mn–Fe bi-naries show good agreement with porewater and carbonate composition data.However, the difference between the Lippmann approach and our GEM-DTAcalculations is that estimations by the former are limited to (pseudo)binarysystems, while the latter approach can easily handle complex SSAS systemsfar beyond the binary. In using the GEM approach, we were thus able to ad-vance beyond this present limitation in modeling thermodynamic equilibria inaqueous environments.

4. Our strictly thermodynamic equilibrium model is not only able to matchboth the measured porewater and carbonate solid-solution composition, butalso to predict that the porewater pH, pe, alkalinity, and dissolved Mn,Fe, and S concentrations are controlled by the authigenic mineral bufferingassemblage mackinawite-greigite-rhodochrosite. It was found that the differ-ences in aqueous speciation can strongly influence empiricalD values inanoxic systems. In case of sulphidic porewater, one can expect that Ca, Sr, andMg would not be significantly affected by HS− complexes, while Mn, Fe, Znwould be mainly bound to such complexes at relatively high dissolved sulfurconcentrations. The association constants suggested by Luther et al. (1996)were used in this study and resulted in quite consistent porewater model andsolubilities of authigenic sulfides and carbonates.

5. The model permits also to set up scenarios of changing environmental condi-tions, e.g., to predict the non-linear response of the carbonate solid-solutioncomposition to changes in three main factors: Mn loading, alkalinity and sa-linity of the sediment-water system. The results suggest that the major andespecially minor element contents (Sr, Mg, Ba) in authigenic carbonates canbe applied as an environmental paleoproxy, e.g., Ba for the typical estuarinesalinity range between 1 and 5, Sr for the brackish range of 5–15, and Mgor Fe for 20–35. Our modeling results are only compatible with the idea that


initial precipitation of ACR with typical composition (XMn between 70–75%)occurred in top sediment and was triggered by diffusion of MnII

aq in porewa-ter due to massive reduction of particulate Mn oxides following major inflowevents in the Baltic Sea.

Acknowledgements

This research was supported by the German Science Foundation (DFG grants Ne687/1-1 and in part Ha 1834/3-2). Discussions with Hermann Huckriede, who in-troduced us to the enigmatic sediment mineralogy of the Baltic Sea basins, areappreciated. Jan Harff from the Institute for Baltic Sea Research at Warnemündeinvited two of us (T.N. & U.H.) to join the cruise of R/VPetr Kottsovto the centralBaltic Sea in Summer 1997. The authors wish to thank the captain and crew fortheir cooperation during that sampling campaign. The manuscript was significantlyimproved by helpful comments of Michael Böttcher, Enzo Curti, Frank Manheim,and two anonymous reviewers.


Appendix

Table A-1. GEM Model of Equilibrium Speciation for Porewater of the Gotland Deep Sediment

Species Molality, Activity Activity Dual chem. Input (25 Ion-size

calculated coefficient (molal) potential bar, 5◦C) parameter

mj γj log aj µ∗j, J/mol g0

f, J/mol a0, Å

B(OH)03 1.46567e-04 1.0236 −3.8238 −985957 −965611 0.045

BF(OH)−3 2.33024e-09 0.72725 −8.7709 −1293615 −1246925 3.5

BO−2 3.00480e-06 0.72725 −5.6605 −709639 −679513 3.5

Ba(BO2)+ 3.20498e-10 0.75095 −9.6186 −1299313 −1248110 4.5

Ba(CO3)0 4.40605e-09 0.8384 −8.4325 −1147324 −1102436 −0.34

Ba(HCO3)+ 1.20722e-07 0.75095 −7.0426 −1187834 −1150348 4.5

Ba(S2O3)0 1.16526e-11 1.0337 −10.9192 −1151436 −1093307 0

Ba(SO4)0 1.69545e-06 1 −5.7707 −1349152 −1318439 −1

Ba+2 1.12393e-05 0.30439 −5.4658 −589674 −560585 5.0

BaCl+ 1.42858e-07 0.75095 −6.9695 −724310 −687213 4.5

BaF+ 3.60150e-11 0.75095 −10.5679 −897332 −841073 4.5

Ca(BO2)+ 2.30149e-07 0.75095 −6.7624 −1279121 −1243127 4.5

Ca(CO3)0 6.42170e-06 0.8384 −5.2689 −1127131 −1099090 −0.34

Ca(H2PO4)+ 2.82898e-07 0.75095 −6.6728 −1725664 −1690147 4.5

Ca(HCO3)+ 6.02003e-05 0.75095 −4.3448 −1167642 −1144522 4.5

Ca(HPO4)0 8.63908e-06 1 −5.0635 −1685154 −1658206 −1

Ca(HSO4)+ 3.60764e-11 0.75095 −10.5672 −1369469 −1313215 4.5

Ca(HSiO3)+ 1.06819e-10 0.75095 −10.0957 −1628468 −1574723 4.5

Ca(OH)+ 9.74213e-10 0.75095 −9.1357 −764779 −716147 4.5

Ca(PO4)− 1.53837e-06 0.72725 −5.9513 −1644643 −1612969 3.5

Ca(S2O3)0 2.22305e-09 1.0337 −8.6386 −1131243 −1085258 0

Ca(SO4)0 2.52709e-04 1 −3.5974 −1328959 −1309819 −1

Ca(SiO3)0 1.76481e-12 1.0337 −11.7389 −1587957 −1525463 0

Ca+2 3.56886e-03 0.33575 −2.9215 −569482 −553941 6.0

CaCl+ 9.58774e-05 0.75095 −4.1427 −704117 −682073 4.5

CaCl02 6.47345e-06 1.0337 −5.1745 −838752 −811214 0

CaF+ 4.72138e-07 0.75095 −6.4503 −877139 −842807 4.5

Fe(CO3)0 7.09763e-08 0.8384 −7.2254 −687649 −647600 −0.34

Fe(H2PO4)+ 1.02069e-09 0.75095 −9.1155 −1286182 −1237658 4.5

Fe(HCO3)+ 1.51631e-07 0.75095 −6.9436 −728160 −691201 4.5

Fe(HPO4)0 8.59680e-09 1.0337 −8.0513 −1245672 −1202815 0

Fe(NH3)+2 4.69960e-11 0.33575 −10.8019 −183064 −125559 5.0

Fe(OH)+ 8.82312e-10 0.75095 −9.1788 −325297 −276436 4.5


Table A1.Continued.



mj γj log aj µ∗j , J/mol g0f , J/mol a0, Å

Fe(SO4)0 2.55452e-08 1 −7.5927 −889477 −849062 −1

Fe+2 4.40499e-07 0.33575 −6.8300 −130000 −93646 6.0

FeCl+ 1.82558e-08 0.75095 −7.8630 −264635 −222781 4.5

FeF+ 8.04377e-11 0.75095 −10.2189 −437657 −383257 4.5

FeSH+ 1.80998e-06 0.75095 −5.8667 −139124 −109490 4.5

Ar0 1.37129e-03 1.0647 −2.8356 2338 17422 0.121

CH04 2.68081e-10 1.0692 −9.5427 −83615 −32816 0.129

CO02 2.41192e-04 1.0505 −3.5962 −402863 −383726 0.095

H02 1.94796e-11 1.0499 −10.6893 −38092 18813 0.094

H2S0 2.80485e-05 1.0104 −4.5476 −49635 −25435 0.02

K(HPO4)− 6.55597e-07 0.72725 −6.3217 −1409291 −1375643 3.5

K(OH)0 7.07913e-11 1.0337 −10.1356 −488916 −434959 0

K(S2O3)- 3.56763e-10 0.72725 −9.5859 −855380 −804350 3.5

K(SO4)− 3.92321e-05 0.72725 −4.5447 −1053096 −1028911 3.5

K+ 4.63182e-03 0.71387 −2.4806 −293618 −280425 3.0

KBr0 8.19424e-09 1.0337 −8.0721 −415462 −372494 0

KCl0 7.16922e-07 1.0337 −6.1301 −428254 −395627 0

Mg(BO2)+ 5.83258e-07 0.75095 −6.3585 −1178681 −1144838 4.5

Mg(CO3)0 1.34551e-05 0.8384 −4.9477 −1026692 −1000361 −0.34

Mg(H2PO4)+ 1.97633e-06 0.75095 −5.8285 −1625224 −1594204 4.5

Mg(HCO3)+ 2.81313e-04 0.75095 −3.6752 −1067202 −1047648 4.5

Mg(HPO4)0 5.18463e-05 1.0337 −4.2709 −1584714 −1561988 −1

Mg(HSiO3)+ 8.91888e-10 0.75095 −9.1741 −1528028 −1479192 4.5

Mg(OH)+ 8.99211e-08 0.75095 −7.1705 −664340 −626172 4.5

Mg(PO4)− 8.55824e-08 0.72725 −7.2059 −1544204 −1505848 3.5

Mg(S2O3)0 5.39865e-09 1.0337 −8.2533 −1030804 −986871 0

Mg(SO4)0 7.85499e-04 1 −3.1049 −1228520 −1212002 −1

Mg(SiO3)0 1.06049e-10 1.0337 −9.9601 −1487518 −1434496 0

Mg+2 1.25842e-02 0.39223 −2.3066 −469042 −456776 8.0

MgCl+ 6.81394e-04 0.75095 −3.2910 −603678 −586169 4.5

MgF+ 8.01192e-06 0.75095 −5.2207 −776700 −748916 4.5

Mn(CO3)0 1.72811e-06 0.8384 −5.8390 −814782 −782116 −0.34

Mn(HCO3)+ 9.39648e-06 0.75095 −5.1514 −855293 −827877 4.5

Mn(NH3)+2 2.76967e-09 0.33575 −9.0316 −310197 −262120 5.0

Mn(OH)+ 4.11559e-09 0.75095 −8.5100 −452430 −407130 4.5

Mn(S2O3)0 3.09023e-11 1.0337 −10.4956 −818894 −763021 0

Mn(SO4)0 1.38257e-06 1 −5.8593 −1016610 −985425 −1


Table A1.Continued.




Mn+2 5.44356e-05 0.33575 −4.7381 −257133 −231918 6.0

MnCl+ 1.49036e-06 0.75095 −5.9511 −391768 −360094 4.5

MnF+ 2.73608e-09 0.75095 −8.6873 −564790 −518546 4.5

MnSH+ 1.21820e-04 0.75095 −4.0387 −266258 −244768 4.5

NH4(SO4)− 6.23572e-06 0.72725 −5.3434 −853052 −821614 3.5

NH4+ 1.21290e-03 0.69928 −3.0715 −93575 −77235 2.5

Na(BO2)0 7.77524e-07 1.0337 −6.0949 −975194 −942754 0

Na(CO3)− 8.39264e-06 0.72725 −5.2144 −823204 −795453 3.5

Na(H2PO4)0 6.96948e-07 1.0337 −6.1424 −1421737 −1389045 0

Na(HCO3)0 3.57579e-04 1.0337 −3.4322 −863715 −845454 0

Na(HPO4)− 3.18434e-05 0.72725 −4.6353 −1381227 −1356560 3.5

Na(HSiO3)0 1.02665e-07 1.0337 −6.9742 −1324541 −1287419 0

Na(OH)0 5.75187e-09 1.0337 −8.2258 −460852 −417066 0

Na(S2O3)− 1.34426e-08 0.6012 −8.0925 −827316 −784240 3.5

Na(SO4)− 1.76957e-03 0.72725 −2.8904 −1025032 −1009657 3.5

Na+ 1.64980e-01 0.75095 −0.9070 −265555 −260742 4.5

NaBr0 8.96192e-07 1.0337 −6.0332 −387398 −355288 0

NaCl0 2.42970e-03 1.0337 −2.6000 −400190 −386361 0

NaF0 1.49017e-07 1.0337 −6.8124 −573212 −536952 0

H2PO−4 7.89047e-06 0.75095 −5.2273 −1156183 −1128363 4.5

H3PO04 1.70644e-11 1.0273 −10.7562 −1196693 −1139342 0.052

HPO4−2 4.68363e-05 0.27083 −4.8967 −1115672 −1089613 4.0

P2O7−4 2.10306e-12 0.00487 −13.9896 −1995536 −1921057 4.0

PO4−3 3.01746e-09 0.05076 −9.8148 −1075162 −1022913 4.0

H2S02 1.06640e-11 1.0337 −10.9577 −61178 −2844 0

HS− 7.87570e-05 0.72725 −4.2420 −9125 13448 3.5

HS2- 4.88496e-09 0.72725 −8.4495 −20668 24310 3.5

HS−3 1.42756e-12 0.72725 −11.9837 −32211 34748 3.5

S−22 1.43544e-11 0.30439 −11.3596 19843 80317 5.0

S2O−23 5.52651e-10 0.27083 −9.8249 −573305 −521003 5.0

HSO−4 2.21401e-09 0.72725 −8.7931 −799988 −753180 3.5

SO−24 4.26394e-03 0.27083 −2.9375 −759477 −743851 4.0

HSiO−3 8.84909e-09 0.72725 −8.1914 −1058986 −1015382 3.5

SiO02 8.85235e-07 1.0423 −6.0349 −863688 −831568 0.08

Sr(BO2)+ 8.13613e-10 0.75095 −9.2140 −1301325 −1252277 4.5

Sr(CO3)0 1.57129e-08 0.8384 −7.8803 −1149336 −1107389 −0.34

Sr(HCO3)+ 5.14938e-07 0.75095 −6.4126 −1189847 −1155715 4.5


Table A1.Continued.




Sr(HPO4)0 1.10388e-08 1 −7.9571 −1707359 −1665003 −1

Sr(OH)+ 1.82028e-12 0.75095 −11.8643 −786984 −723822 4.5

Sr(PO4)− 7.14555e-10 0.72725 −9.2843 −1666848 −1617425 3.5

Sr(S2O3)0 1.24895e-11 1.0337 −10.8890 −1153448 −1095479 0

Sr(SO4)0 1.41977e-06 1 −5.8478 −1351164 −1320040 −1

Sr+2 2.52991e-05 0.30439 −5.1135 −591687 −564473 5.0

SrCl+ 6.72225e-07 0.75095 −6.2969 −726322 −692807 4.5

SrF+ 1.93837e-10 0.75095 −9.8370 −899344 −846978 4.5

Br− 2.90638e-04 0.71387 −3.6830 −121844 −102248 3.0

CO−23 1.30419e-05 0.28788 −5.4254 −557650 −528775 4.5

HCO−3 4.31954e-03 0.73957 −2.4956 −598160 −584887 4.0

Cl− 1.89355e-01 0.71387 −0.8691 −134635 −130024 3.0

F− 2.01421e-05 0.72725 −4.8342 −307658 −281931 3.5

HF0 3.58635e-10 1.0337 −9.4309 −348168 −297964 0

OH− 1.07172e-07 0.71387 −7.1163 −195298 −157419 3.5

H+ 2.83943e-08 0.86341 −7.6106 −40510 0 13

H2O0 5.48294e+03 1 −0.0031 −235808 −235791 −1

(i) number of moles of water-solvent is shown asmj ; (ii) excess greigite and mackinawite arepresent at equilibrium state; (iii) all solid single-component carbonates, troilite, pyrite, marcasiteand goethite were excluded from calculation; (iv) parameters in the last column: for chargedspecies effective ionic radiia0, in Å; for neutral species: if not−1 or 0, then third parameter ofthe extended Debye-Hueckel equation, i.e., salting-out coefficient; if 0, then assumed the same asthe common third EDH parameter (bγ = 0.064); if−1, then the activity is set simply to 1.

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