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Calculated aqueous-solution-solid-solution relations in the low-temperature CaO-MgO-FeO-CO*-Hz0

system

TERRI L. WOODS’ and ROBERTM. GARRELS Department of Marine Science, University of South Florida, St. Petersbug, FL 33701 USA (Received April 27, 1990; accepted in revised form July 30, 199 1)

Abstract-A method of estimating an aqueous-solution composition from that of solid-solutions believed to be in equilibrium with it is derived. The low-temperature ternary Ca-Fe-Mg phase relations of the rhombohedral carbonates are investigated using this method, and their phase diagrams at 25 and 150°C are calculated. Algebraic manipulations of equilibrium constant equations representing dissolution of the carbonates yield equations for the phase boundaries separating calcite from an ankerite-dolomite solid-solution and an ankerite-dolomite solid-solution from a siderite-magnesite solid-solution. A value for the free energy of formation of ankerite is estimated (- 18 18.0 f 0.8 kJ/mol, 25’C) from compositions of natural coexisting carbonates. Necessary compositional information for the carbonates was derived from the relatively unmetamorphosed Early Proterozoic Marra Mamba Banded Iron-Formation of the Hamersley Basin of Western Australia. The method yielded information on the uFg+/uc8z+ and uMgz+/ucaz+ratios of the solutions that deposited the carbonates of the Marra Mamba. The method suggests a depositing solution for the carbonates of the Lower Marra Mamba Iron-Formation significantly richer in iron than was likely to have been the case for Early Proterozoic seawater. INTRODUCTION

previously developed involved only binary systems or were based on experiments done at temperatures above 250°C at pressures higher than those at the Earth’s surface. Data on the phase relations of other divalent metal carbonates arc much more limited. The most extensive experimental work has been done on the CaCOs-MgCO3, MgC03-FeC03, CaCOs-FeCOs , CaC03-MnCOs , and most recently, C&OSSrC03 joins, as these are the most commonly occurring natural systems. High-temperature work included the studies of HARKER and TUTTLE ( 1955), GRAFTER GOLDSMITH( 1955), GOLDSMITH and GRAF (1957, 1958), GOLDSMITH and HEARD (1961), GOLDSMITHet al. ( 1962), ROSENBERG( 1963), DECAPITANI and PETERS( 1981), FANELLIet al. ( 1983), GOLDSMITH (1983), and CAFQBIANCOand NAVROTSKY(1987). Complete miscibility at high temperatures is seen on the joins MgC03-FeC03 (295-500°C) and MnCOJ-FeC03 (45O’C) (ROSENBERG, 1963), and MnC03-MgCO, (450-5OO’C; GOLDSMITHand GRAF, 1960). Of all ternary systems, phases in the CaC03-MgC03-FeCO, system are the most extensively investigated and the only ones to be studied experimentally by more than one laboratory (GOLDSMITH et al. 1962; RoSENBERG,1967; GOLDSMITH,1983; REEDER, 1983; ANOVITZ and ESSENE,1987). ANOVITZand ESSENE( 1987) combined a careful evaluation of earlier experimental work with data on the compositions of naturally occurring carbonates to derive approximate ternary phase diagrams at 250, 400, 550, and 7OO“C. Recent studies of carbonate solid-solutions at low temperatures have been conducted by BUSENBERG and PLUMMER (1989), MUCCI ( 1986,1987), BISCHOFF~~al. ( 1987), HowSON et al. (1987), and ROSENBERG(1987) on the Ca-Mgcarbonates; by FUBINI and STONE ( 1983), MIDDLEBURGet al. (1987), PINGITORE et al. (1988), MUCCI (1988), and JAKOBSENand POSTMA ( 1989) on the Ca-Mn-carbonates; and by PLUMMER and BUSENBERG (1987) on the

PAIRSOF RELATEDMINERALSone or both of which can show extensive solid-solution with respect to the same two elements are often found together in nature (e.g., the rhombohedral carbonates of the calcite and dolomite structures). Equations describing the relationship between an aqueous solution and these. mineral pairs have the potential to yield valuable information about depositional and diagenetic conditions in such systems. This paper describes the development of these equations and their application to an assemblage of chemically diverse carbonates from the Early Proterozoic Marra Mamba Banded Iron-Formation. The Marra Mar&a Iron-Formation presents a rare opportunity to investigate a low-temperature, relatively unmetamorphosed, equilibrium assemblage of carbonates. In this paper, the terms ankerite (CaFe( CO,),), dolomite (CaMg( CO&), siderite (FeCOs), and magnesite ( MgC03) will be used to refer to the pure iron and magnesium endmembers of the ankerite-dolomite and siderite-magnesite solid-solutions. The pure iron endmember, ankerite, has never been found naturally nor has it been produced in the laboratory (REEDER, 1983); it is a hypothetical endmember use&l in thermodynamic modelling. No structural reason for the limited solubility of iron in this solid-solution has been discovered ( REEDER and DOLLASE, 1989). PREVIOUS WORK Experimental

and Theoretical Investigations

Ca-Mg-Fe carbonates arc common minerals at the Earth’s surface, but data on their low-temperature (~250°C) ternary phase relationships are rare. Most thermodynamic models

’ Present address: East Carolina University, Dept. of Geology, Greenville, NC 27858-4353 USA. 3031

3032

T. L. Woods and R. M. GarreIs

Ca-S-carbonates. Investigations and discussions of solid-solution /aqueous-solution theory have been published by THORSTENSONand PLUMMER (1977), LIPPMANN (1977, 1980, 1982), LAFON (1978), GARRXZLSand WOLLAST (1978), MACKENZIE et al. (1983), Muccl and MORSE ( 1983), WALTERand MORSEf 1984), GLYNN and F&ARDoN (1990), GLYNN (1990), and GLYNN et al. (1990). There is only a small amount of experimental data available for CaMg-Fe carbonates at low temperatures ( VEGARD, 1947; GOLDSMITHand GRAF, 1957; RICKETTS, 1980). Compositional Data for Natural Low-temperature Assemblages ESSENE (1983) compiled compositional data for carbonates in the Ca-Fe-Mg-Mn system. The data were taken from hydrothermal, sedimentary, and metamorphic occurrences. These data showed the complete solution between MgC03 and FeCOs, and MnCOZ and FeC03. Compositional joins (such as rn~n~i~-rhod~hrosite) for which carbonate compositions are missing were taken as permissive evidence of a solvus gap. ESSENE( 1983) pointed out,, however, that there may be geochemical or petrological reasons for the lack of intermediates. The solid-solution between dolomite and ankerite does not extend through the entire range of iron-rich compositions, although it appears to be continuous up to about 70 mol% of the CaFe(C031Z component. This is consistent with the experimental work of ~LDSMITH et al. ( 1962) and ROSENBERG( 1960, 1963). Com~sition~ descriptions of low-temperature naturally Occurring carbonates in the ternary Ca-Fe-Mg or quaternary Ca-Fe-Mg-Mn systems are also found in BEUKESet al. ( 1990), KLEIN and BEUKES (1989), CURTIS et al. (1986), PEARSON(1974), and MATSUMOTOand IIJIMA ( 198 1).

GEOLOGY Geologic Setting The Marra Mamba Iron-Formation has been extensively studied. The general geology, stratigraphy, sedimentology, and diagenesis of the Marra Mamba were investigated by MACLEOD (1966) and TRENDALLand BLOCKLEY(1970). Carbon and oxygen isotopic com@tions were determined by BECKERand CLAYTON(1976) and BAUR et al. (1985). KLEIN and GOLE ( 198 I ) and EWERS and MORRIS ( 1980) have thoroughly investigated the chemistry and mineralogy of the deposit. The Marra Mamba Iron-Formation is of Early Proterozoic age. It is found in outcrop over about 90,OOOkm* in Western Australia (TRENDALLand BLOCKLEY,1970) and is the iowermost unit of the Hamersley Group. The Hamersley Group overlies a thick, mainly volcanic and pyroclastic sequence and is overlain by a sequence of elastic sediments, dolomites, and basalts (TRENDALL, 1968). According to TRENDALL ( 1968), the Hamersley Basin was probably closed and had the general dimensions of the outcrop area. The iron formations of the Hamersley are relatively unme~mo~ho~d and were subjected to a maximum temperature of 300eC after deposition (AYERS, 1972; BECKERand CLAYTON, 1976; KLEIN and GOLE, 198 1) . Maximum pressure is estimated at 1.2 kbars (KLEIN and GOLE, 198 I). TRENDALLand BLOCK-

LEY ( 1970) informally divided the formation into the following three parts: ( 1) lower banded iron formation (about 137 m thick), (2) middle “‘shaly” member (about 37 m thick), and (3) upper banded iron formation (about 61 m thick). We accept most of the physical conditions of deposition described by BAUR et al. (1985), including deposition in a large, quiescent water body, below wave base (to preserve intricate banding), below the photic zone (to explain the absence of stromatolites), and under atmospheric oxygen pressures less than 10m2 of present atmospheric levels (to permit transportation of iron as the ferrous ion). We don’t accept all the conditions they describe because their chemical model applies to banded iron formations in which the carbonate ion is of biological origin. We do not believe this to be the case for the Marra Mamba.

Detailed, well-documented chemical analyses (e.g., Table 1) ,petrographic studies (textural analyses), and electron microprobe analyses (mineral compositions) were conducted on unaltered drill core from the deposit by KLEIN and GOLE ( 198 1). The following brief mineralogical and chemical description of the deposit is taken from their work. The uppermost and lowermost parts of the Marra Mamba Iron-Formation show significant differences in mineralogy. The uproot part includes quartz, magnetite, minn~~te, riebeckite, stilpnomelane, dolomit~anke~te, calcite, and minor pyrite. The lowermost part contains significantly more pyrite than the upper, plus pyrrhotite, quartz, magnesite-siderite, dolomite-ankerite, stilpnomelane, minnesotaite, and minor carbon (up to 2 wt%). These differences in mineralogy are reflected in the differences of bulk composition shown in Table I. The Upper Marra Mamba is richer in oxidized iron and calcium, while the Lower Marra Mamba is richer in reduced iron, m~~iurn, sulfur, and carbon. The carbonates of the Marra Mamba exhibit a wide range in iron-to-magnesium ratios, extensive solid-solution among the carbonate mine&, and the highest iron content found in dolomiteankerites. The upper and lower parts of the Marra Mamba are sometimes stratigraphically separated by the middle “‘shaly” member. This suggested to GARRELS (1987) that, following a hiatus in Lower Marra Mamba deposition, a new Table 1. Average composition of the Upper and Lower Marra Ha&a Ironformation (Klein and Gale, 1981)

Component Si02

Fe203 Fe0

ng0 Ca0 Al203

Hn0 NazO x20 P205

TiO2 S C

Weight percent upper Lower 42.4 45.9 22.5 3.4 16.9 21.2 3.8 4.0 5.8 1.5 .4 .1 .4 .2 .l

.2 .l .l

2.2 .l -3 -5 .05 .l .5 .7

3033

Geochemistry of Ca-Mg-Fe carbonates

siders deposition of the carbonates to have been an isolated process. This can be justified on the grounds that KLEIN and GALE (198 1) often observed carbonates of the Marra Mamba forming relatively continuous, thin bands between bands of magnetite and silicates. Also, GARREL~( 1987) showed that the precipitation of siderite-magnesite and the silica phase can be separated in time due to differing solubilities. A consideration of the Fe-Mg partitioning between carbonates and silicates is beyond the scope of this paper. FRENCH ( 1973), DIMROTHand CHAUVEL( 1973), PERRY et al. (1973), MAYNARD (1983), and KLEIN and BEUKES ( 1989) all concluded that the siderite-magnesites observed in banded iron formations were either a part of the original precipitate or equilibrated with it during early diagenesis. Siderite-magnesite is believed to have precipitated in microcrystalline form. Many siderite-magnesite occurrences show indications of significant recrystallization ( FLORAN and PAPIKE,1975). Calcite and the dolomite-ankerite minerals occur most commonly as replacements of other carbonates or as r~~st~li~tion products (LABERGE, 1964, AYERS, 1972; DIMROTH and CHAUVEL, 1973; RORAN and PAPIKE, 1975; KLEIN and GOLE, 198 1). As FLORAN and PAPIKE ( 1975 ) point out, “It should be emphasized that many of the carbonate replacement textures are of local origin and due, in part, to ~c~s~ll~tion.” FRENCH ( 1973) concluded that the primary minerals of banded iron formations formed from the original precipitate, near the sediment-water interface, at pressures of less than a few hundred ban and temperatures less than lOO-150°C. Based on isotopic and experimental data for the observed assemblages of minerals, KLEIN ( 1983) considers diagenetic reactions such as those indicated for the Marra Mamba to have occurred below 180°C. DIMROTH and CHAUVEL( 1973) and EWERSand MORRIS ( 198 1) both

set of chemical and possibly physical conditions prevailed in some portions of the basin during the later phase of deposition.

Carbonates are often major constituents in the uppermost section, and pairs of coexisting calcite and dolomite-ankerite are abundant. Compositions of the carbonates in this portion of the Marra Mamba are shown in Fig. 1. The tie lines in this diagram (and in Fig. 2) connect pairs of coexisting carbonate minerals observed by KLEIN and GOLE ( I98 1) to be in physical contact. The crossing tie lines probably indicate disequilibrium between some pairs of carbonates, but KLEIN and GOLE ( 198 1) did not report textural evidence of disequilibrium. The calcites are nearly pure CaCO, (usually with less than 2 wt% Fe0 and/or MnO and less than 1 wt% MgO). The members of the dolomite-anke~te series contain about 25-64 mol% of the CaFe( C03)* component and usually less than 1 wt% MnO. Members of the dolomite-ankerite series occur throughout the Marra Mamba, but m~~ite-~de~te/dolo~~-skews pairs occur only in the lower part. Compositions of carbonates in this portion of the Marra Mamba are shown in Fig. 2. Here members of the dolomite-ankerite series contain about 26-7 1 mol% of the CaFe(C03)z component, which appears to be the maximum possible iron content for any temperature (ANOVITZand ESSENE,1987). They usually contain less than 0.5 wt% MnO. (Because of the low (and similar) MnO contents of all the Marra Mamba carbonates, the effect of MnO on the phase relations was judged to be negligible.) The compositions of the magnesite-siderites range from FQ.sMg,,,COs to nearly pure iron siderite (97 mol%). A complex assemblage of carbonates and silicates is currently observed in many places in the Marra Mamba. HOWever, a simplified treatment is adopted in this paper that con-

Molecular

MSCOS

50

%

FeCO;MnCO

3

f%G. 1. Carbonate compositions determined for the upper portion of the Marra Mamba Iron-Formation. The apices of the triangle represent 100 mol% of the indicated component. ~lomite-anke~t~ ranging from 25-64 mol% of the CaFe(CO& component and containing minor amounts of excess CaCO3 and M&03-FecO, are shown in the stippled region. These dolomite-ankerites were found to be in physical contact with calcite compositions in the hatched region. From KLEIN and GOLE (198 I, Fig. 3).

3034

T. L. Woods and R. M. Carrels

CaCO

3

A Molecular % \

50

Siderite; 159 analyses

FeC03+MnC0

3

FIG, 2. Carbonate compositions determined for the lower portion of the Marra Mamha Iron-Formation. The apices of the triangle represent 100 mol% of the indicated component. Dolomite-ankerites ranging From 26-7 1 mol% of the CaFe( CO& component and containing minor amounts of excess CaCOr and MgCO~FeCO~ are shown in the stippled region. These dolomite-skeets were found to he in physical contact with matte-ideate ~rn~~tions ranging from 50-97 mol% of the FeC03 component (shown in the irregular stippled region at the base of the triangle). The tie lines connect coexisting (i.e., physically touching) pairs of carbonates, and are separated into the following three approximately parallel sets: I, II, and III. These correspond to the most gently dipping, those of intermediate slopes, and the most steeply dipping, respectively. From KLEIN and GOLE (1981, Fig. 3).

believe that crystahization and rectystaHization precipitates

occurred

of the original very early in the diagenetic process.

Diagenesis and metamorphism of the iron formations is widely believed to have been virtually isochemical (except for Hz0 and CO,) on a district-wide scale, although minor exchange of elements may have occurred between bands (EWERS and MORRIS, 1981; KLEIN, 1983; PERRY et al., 1973). AYERS (1972) made this statement about the Dales Gorge Member of the Hamersley Iron-Formation: “There is no petrographic evidence to suggest that large volumes of any of these constituents f i.e., silicon, iron, aluminum, calcium, magnesium or oxygen] have been added since deposition.” (The Dales Gorge Member is stratigraphically separated from the Marra Mamba by less than 300 m.) JAMES and TRENDALL (1982, p. 2 IO ) commented, “The sheer bulk of banded iron-fo~ations laid down in the basin [ Hamersley] makes it unlikely that gross chemical modification has taken place.” BAUR et al. ( 1985, p. 279) stated, “On balance, we reject the hypothesis that the carbon isotope alternation over millimeter distances in the Marra Mamba and Bruno’s Band cores found here is primarily a metamorphic effect, and favor the view that it resulted from processes involved in, or closely related to, the banded iron-formation depositional mechanism.” In summary, siderite-magnesite is believed to have precip itated initially from the solution as a microcrystalline phase. In most cases, the dolomite-anke~te/side~te-ma~~ite assemblages originated by reptacement or recrystallization of an initially precipitated phase. Candidates for such a phase include a calcium-rich siderite-magnesite, a met&table calcium-magnesium-iron carbonate, a two-carbonate assem-

blage of calcite and siderite-magnesite, an iron-rich dolomite, etc. During recrystallization, the initial assemblages are believed to have had ample time to equilibrate with the water in which they were trapped at temperatures less than 180°C. Subsequent low-grade me~rno~h~srn is not believed to have altered the iron-magnesium ratios of the, by then, completely recrystallized solid carbonates. In view of this information and the vastness of geological time available for this lowtemperature assemblage to equilibrate, we believe equilibrium was closely approached in this system. EQUILIBRIUM

RELATIONS

Previous Work The criterion for thermodynamic equilibrium in systems involving slid-~lutions is that the chemical potentiafs of the components of interest be equal in all the phases in which they occur. With this as a starting point, the equilibrium constant equations for the minerals of interest can be derived. Such an approach has been applied in fields as distinct as high-temperature metamorphic petrology and low-temperature aqueous geochemistry to yield info~ation about the temperature, pressure, and chemical compositions of coexisting solid- and liquid-solutions. Some early applications and discussions of these concepts in high-temperature processes include the work of RAMBERG and DEVORE ( 195 I), KRETZ (1959,

1961),

MUELLER (1960,

196t),

and MCINTIRE

(

1963). This approach is well-established for high-temperature systems where equilibrium can be assumed. Such an approach may also yield valuable insight into conditions of formation for low-temperature systems that react on geolog-

Geochemistry of Ca-Mg-Fe carbonates

KZ = KA =

ical time scales, whose minerals show few signs of disequilibrium, and which show only minor alterations due to metamorphism (for example, the Marra Mamba) . The derivation of the equations that describe equilibrium between solid-solutions and an aqueous solution was first developed by GIBBS ( 1876, 1878). Applications of these equations to solid-solution/aqueous-solution systems have been described by LERMAN( 1965), LIPPMANN ( 1977, 1980),

Following GIBBS( 1876, 1878 ), the following mass action equations can be written for the carbonates: (1)

Ks

=

aF&eO:-/asy

(2)

Km

=

aMg2+eO;-/am,

(3)

K. =

&a2+aFe2+(&O;-)2/aaT

(4)

& =

~~Z+h4g2+(kO-)2/ad~

(5)

aFd

(6)

Kt = K,X, = aF$+&O;-/Xs,

(7)

1 -X,),

Table 2. Thermodynamic Phase

(8) data

used

for

calculations

AG"f

So

k;r/mol 25°C CaCOj

(c)

calcite’

MgC03 (c) magnesite' FeCOg (c) siderite" CaMg(C03)z (c) dolomite' CaFe(co3)z (c) ankerite Mg*+ (aq)d Ca'+ (aq)d Fe*+ (aq)d C03*- (aq)d

xs) .

(11)

Therefore, the composition of each solid-solution is fixed by the ratio of &$+/a&@+ in the aqueous solution. Studies by TALANTSEV and SAZONOV ( 1979) and ANOVITZand ESSENE ( 1987) on the partitioning of iron and magnesium between these carbonates do, in fact, suggest that the iron/magnesium ratios observed in these minerals are more a function of the composition of the precipitating solution than of the temperature and pressure. This equilibrium constant also represents the distribution coefficient for the siderite-magnesite exchange reaction of iron and magnesium by way of an aqueous solution. If such a system is ever to reach true equilibrium, a complete recrystallization of the initial solid is required. Evidence presented previously suggests that the carbonates of the Marra Mamba were extensively recrystallized. Solid-state diffusion at low temperatures is not likely to modify the compositions of minerals formed in such an environment. BR~~TTERet al. ( 1970) tried to estimate the Ca2+ self-diffusion coefficient in calcite at low temperatures. The extrapolated diffusion coefficient at 20°C from a measurement made at high temperatures is so small that the mass transport of calcium ions by

where K& KS, K,,,, K,, and Kd are the dissolution equilibrium constants for pure calcite, siderite, magnesite, ankerite, and dolomite, respectively, for 25°C and 1 atm. The activities of calcite, siderite, magnesite, ankerite, and dolomite are represented by &, a,, a,,,, a,, and Q, respectively. The values of these equilibrium constants were calculated from the free energies of formation given in Table 2. The values involving ankerite were calculated during the course of this research. Incorporating activity coefficients for the solids into the equilibrium constant term, Eqns. ( 1-5) can be rewritten as fo11ows:

Kg = K,,,X, = aM,z+ko:-/(

1 aMgz+&

Kr = K,X, = ~az+aco:-/Xc,

(10)

recognizing that in a binary solid-solution consisting of endmembers A and B, X, = 1 - X,. The two binary solidsolutions considered here are siderite-magnesite and ankeritedolomite. For all but an ideal solid-solution, K* will depend on the composition of the solid. Simple algebraic manipulations of these five equations make it possible to derive relationships between the composition of a mineral solid-solution and the composition of the aqueous solution that deposited it. The mineral containing the endmembers (e.g., the magnesite-siderite solid-solution) is in equilibrium with the aqueous solution. Therefore, the dissolution constants for both these endmembers must be satisfied, and the following equilibrium constant can be defined by combining Eqns. (7) and (8), as follows:

Derivation of the Genera1 Model

ac,2+e0:-lac,

(9)

~a2+aFd&O~-)2/Xa,

Kd* = &X, = ac,z+aMBz+(aco:-)2/( 1 - XJ,

THORSTENSON and PLUMMER(1977), GARREL~and WOLLAST( 1978), MILLERand RAJAGOPALAN ( 1976), MILLER et al. (1976,1981), BIJSENBERG and PLUMMER ( 1989), and GLYNN and REARD~N( 1990).

K, =

3035

-1130.1 -1027.8 -679.4 -2167.2 -1818.0b -454.8 -552.9 -92.2 -528.0

J/mol/deg

15O'C

-1143.5 -1038. -694.5 -2190.7 -1845.8b -440.7 -548.2 -81.4 -524.0

92.7 65.7 105.0 155.2 189.6= -138.1 -56.5 -104.6 -50.0

"Helgeson et al. (1978) bCalculated in the text. 'Calculated by the method of Helgeson et al, (1978, pp.44-51). dShock & Helgeson (1988)

T. L. Woods and R. M. Garrels

3036

volume diffusion is insignificant even over the age of the Earth. TALANTSEVand SAZONOV( 1979) also point out that the dolomite-ankerite and magnesite-siderite lattices are very stable and do not transform easily during post-crystallization alteration. In order to calculate the ratios of aFez+l&=z+and aMgz+/k+ in the aqueous solution in equilibtium with solids in the upper half of the carbonate compositional triangle (Fig. 1 ), two equations are necessary. The first describes equilibrium between calcite and either endmember of the ankeritedolomite solid-solution. The other describes the Fe-Mg exchange ~uilib~um between dolomite and ankerite f a&ogous to Eqn. ( 11 )] . Dolomite/calcite equilibrium is described by the following reaction:

dolomite were use& but the mineral represented is the ordered carbonate with the dolomite structure (Rj) and not the disordered mineral with the calcite structure ( R~c) . Whenever the activities of these half-formula carbonates are included in an equation, the numeric value is calculated as the square root of the full-formula value. The algebra for developing the equation representing equilibrium between the two solidsolutions is given in the Appendix. The equation that results is as follows:

CaMg(C0,)2(c)

This quadratic equation can be solved for UF$+/&=Z+for various values of aMg2+/aCaz+ and the equilibrium constants.

+ Ca’+(aq) = 2 CaCO,(c)

+ Mg*+( aq).

( I2)

Writing the ~uilib~um constant for this reaction and solving it for the mole fraction of dolomite yields xd

=

tr$)2aM,z+ ,

(13)

where K& = K&d. The other equation necessary is that representing equilibrium between ankerite and dolomite: Ca~(~~)~(c)

+ Fe*+(aq) = CaFe(C03)2(c)

+ Mg’+(aq).

(14)

Now substituting the expression for the mole fraction of dolomite from Eqn. ( 13) into the equilibrium constant expression for Eqn. ( 14) yields the following:

Rearranging and simplifying gives the following:

(15) Using Eqn. ( 15), the boundary representing equilibrium between calcite and ankerite-dolomite in an aqueous solution can be calculated and plotted on an activity-activity diagram when numerical values for K$,,, K&, and (a,)* are substituted. To calculate the ion ratios in equilibrium with particular members of the solid-solution, equations such as ( 13) are solved for the appropriate ion ratio. The coexistence of the ankerite-dolomite solid-solution with the siderite-magnesite solid-solution can be described in a similar way. The analogous calculation is similar to, but slightly more complicated, than that for the coexistence of calcite with the ankerite-dolomite solid-solution. It is necessary to combine three equations, two of which represent exchange reactions between the endmembers of the solidsolutions. The third represents equi~ib~um between the two solid-solutions (either an ankerite f siderite equation or a dolomite/magnesite equation). To simplify some of the algebra involved in this calculation, half-formulas for ankerite and

Appli~tion of the Ekpmtionsto the Mama Mamba Application of these equations to determine the composition of the original aqueous solution that deposited an assemblage of carbonates requires ( 1) that the physical conditions and effects of deposition and diagenesis can be assessed, (2) that significant evidence for total recrystallization of the solids exists, and (3) that equilibrium was achieved. Evidence from the Marra Mamba and other iron formations presented above suggests that these are reasonable assumptions for this deposit. Assumptions and estimations A number of estimations and assumptions were made in order to apply Eqns. ( 15) and ( 16) to the Marra Mamba. The first involves the nearly pure chemical ~m~sition of the calcite phase, which permitted us to regard it as a pure phase for which a = X = I. Secondly, the activity coefficients for the siderite-magnesite and ankerite-dolomite solid-solutions were estimated using a regular activity-composition model and the MBSSAS program of GLYNN ( 1991). Thirdly, a free energy value for ankerite was estimated from the chemical composition of coexisting pairs of side~te-rn~~te and ~ke~t~otorn~~ using this regular mixing model. These assumptions and estimations are discussed below. Figure 1 [and Table 2 from KLEIN and GOLE ( 198 1)] shows the range in calcite compositions observed in the Marra Mamba. The calcites usually have