Stability of Mg-Ca carbonates

Stability of Mg-Ca carbonates

Geochimxa et Cosmochinuca Acta, 1977, Vol. 41. pp. 265 lo 270. Pergamon Press. Printed 1” Great Britain Stability of Mg-Ca carbonates* BOER Ko...

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Geochimxa

et Cosmochinuca

Acta,

1977, Vol. 41. pp. 265 lo 270. Pergamon

Press.

Printed

1” Great

Britain

Stability of Mg-Ca carbonates* BOER Koninklijke/Shell, Exploratie en Produktie Laboratorium, Rijswijk, The Netherlands R. B.

(Received

2 December

DE

1975; accepted

in revised form 9 September

1976)

Abstract-In this article a diagram is constructed in which the stability of Mg-Ca-carbonates can be represented as a function of only two parameters. By means of this diagram the relative stability of the various carbonates can be easily compared. INTRODUCTION

CARBONATES have for a long time been an inexhaustible source of frustrations to geochemists who desperately tried to cling to the rules of thermodynamics. For these investigators, natural carbonates are not even a straw to catch at. Firstly, the carbonates most frequently formed in nature are aragonite and high-Mg calcite-unstable forms which subsequently recrystallize very slowly into calcite. Secondly, all ocean surfaces are supersaturated with respect to calcite, aragonite and dolomite (CLOUD, 1965; LIPPMANN,1973; MILLIMAN,1974). However, no dolomite forms in oceans, nor do dolomite crystals show any tendency to grow when immersed in sea-water. Also, the growth of calcite and aragonite crystals is extremely slow or absent under these circumstances. DE GROUTand DUYVIS(1966) suggested that a kinetic factor inhibits carbonate growth. Inhibition is caused by the adsorption of Mg2+ (H,O), ions on the surfaces. Growth of carbonates requires either desorption of the Mg’+ (H20)6 or their dehydration and subsequent incorporation of Mg in the lattice. Both processes are apparently very difficult and slow. Inhibition of carbonate-crystal growth by adsorbed Mg’+-ions is advocated by Miiller and PAREKH (1975), while other authors, e.g. CHAVEet al. (1962), PLUMMERand MACKENZIE(1974) and BERNER(1975) have found that Mg ‘+-ions incorporated in the bulk crystal-forming a mixed crystal called ‘magnesium calcite’-increases the solubility of the calcite. Experiments with the inhibition of Mgzf on calcite growth have been published by BISCHOFFand FYFE (1968). Reviews of the subject have been prepared by LIPPMANN(1973) and MILLIMAN(1974). In studies on natural Mg-calcites, CHAVE et al.

homogeneous but contain inclusions of very-high-Mg calcites and possibly even brucite. As the solubilities of high-Mg calcites are higher than those of low-Mg calcites, the measured solubilities could well refer to those of the high-Mg calcites. Thus the solubilities measured by CHAVEet al. (1962) may be either too high or too low, while, in spite of all precautions taken by PLUMMERand MACKENZIE(1974), their measured solubilities may be too high. In this paper a description is given of the thermodynamic stability of the various Mg-Ca carbonates and a diagram is constructed in which these stabilities can readily be compared at different Mg/Ca ratios in the solution. KATZ (1973) has shown experimentally which Mg-calcite precipitates from a solution with a specific Mg’+/Ca’+ ratio up to 3% Mg-calcite. His findings, combined with CHAVE’S(1962) data and our description of the thermodynamic solubility of the various Mg-calcites, produces a ‘kinetic saturation curve’ in the diagram (Fig. 1). At any Mg/Ca ratio (mdll)’ 165 . \ \ \ \

(1962) found much higher stabilities and lower solubilities than PLUMMERand Mackenzie (1974). Plummer

and Mackenzie attributed this to the fact that Mg-calcites tend to dissolve incongruently, precipitating low-Mg calcite, which would yield too low solubilities. MILLIMANet al. (1971) and PLUMMERand MACKENZIE(1974) showed that natural Mg-calcites are not .,

2

5

1

l&tama.lalrdedfmChowct.l.

* Publication No. 466 of the Koninklijke/Shell, Explorative en Produktie Laboratorium.

2

5 (1962)

I

1

10

20

50

b.4q.-v(w)ra

Fig. 1. Stability diagram for Mg-Ca-carbonates. 265

R. B. DE BOER

266

of the solution, the points of this curve represent the solubility of the specific Mg-calcite that, according to KATZ (1973) would be formed from such a solution.

coordinates are plotted on a logarithmic scale so that the lines representing the saturations of the different Mg-Ca carbonates are straight. This is clear from the equation log K = log(Ca2+)1i2(Mg2+)112(CO:-)

CALCULATION OF Mg-CALCITE SOLUBILITIES

(3)

Solubilities of Mg-calcites have been measured by et al. (1962), who arrived at the following properties of the solution: 1. (H+) 2. pco, = (1 - pHIo) = 0.97 atm 3. 2[Ca*‘] + 2[Mg*+] = [HCO;] + Z[COi-1 + [OH-] - [H+] 4. [Mg2+]/[Ca2+] = equal to that of the dissolving carbonates. With knowledge of the activity coefficients at specified ionic strength (GARRELSand CHRIST, 1965), the complex formation (GARRELSand THOMSON, 1962}, the first and second dissociation constants of carbonic acid and finally of the solubility of CO, (ELLIS,1959), all concentrations and activities of the ions participating in the equilibrium can be calculated (see Table 1). Similar calculations have been published by Plummer and MACKENZIE(1974). Now that the activities (Mg2+), (Ca*‘) and (CO:-) have been obtained, the solubility product of the Mgcalcites can be calculated. This solubility product is defined as

CHAVE

KMg--_caiciie = (Ca’+)’ _ X(Mg2‘)“(CO:-),

(1)

where x is the cationic fraction of Mg2’- substituted for Caz+. THE STABILITY DIAGRAM FOR MeCa-CARBONATES

If we indicate log ~(Ca2+)‘~*(Mg2~)“~(CO~-)~ by

Yand

by X, equation (3) represents a straight line according

to Y = (f - x)X + 1ogK.

(4)

In principle, one could also choose for the Y-axis the value of the expression log {(Ca2’)(CO<-)~, log ((Mg’+) (CO:-)] or in general the expression log {(Ca2’)‘-‘(Mg~ (CO:-)] with any value from 0 to 1 for a. The relative positions of the stabifity lines will not change. However, instead of Y = (f - x) X + log K the equation would change into Y = (a - x) X + log K.

As follows from equation (4), the slopes of the lines are exactly determined by the compositions of the carbonates. Thus, the curve of each carbonate is determined by its solubility in a solution with a known Mg/Ca-ratio and by its composition. It can be shown that any point in the diagram that lies below the solubility line of a specific carbonate is undersaturated with respect to this particular carbonate. At the Mg2’/Ca2+ ratio of such a point, the following relation applies

(Ca2’),‘d:(Mg2*)~~:(CO:-),,, Using the solubility products as calculated from CHAVEet al.‘s (1962) or PLUMMERand MACKENZIE’S <: (Ca2+)~~~(Mg2+)~~:(CO:-)ca,r (5) (1974) data, it is possible to represent the relative stawhere sol refers to the solution, and sat to the bilities of the Mg-calcites in a diagram. It should be saturated condition. remembered that the different Mg-calcites have differThis can be re-arranged to ent compositions, so that their relative stabilities cannot be represented by a single value (as is, for in(Ca’ %,;“(Mg2 ‘)&r(CO,2%,I stance, the case with the relative stabilities of calcite ~Ca”)~~,(Mg~ ‘),,, ~-l’~) and aragonite). The‘relative stabilities also depend on ’ i (Mg2+),,t(CaZ+),, > the Mg/Ca ratio in the solution. Solubilities of these carbonates should therefore be represented by lines in a two-dimensional diagram, of which one coordinate is the Mg/Ca-ratio in the solution. For the other coordinate, we choose the expression (Ca’+)“* (Mg’+)“’ (CO:-), as explained below (see also Fig. 1). Equation (1) for the solubility product of an MgCa carbonate (Mg,Ca, _$ZO,) can be re-arranged to K = (Mg2~)‘i2(Ca2~)“Z(CO~~)

The solub~lity product is thus expressed as a function of the two parameters of Fig. 1. In Fig. 1 both

<

(Ca2+)~~~x(Mg”‘)~~~B,(CO~-),, (6)

and thus to (Ca2+)~~,;X(Mg*‘);Tbl(C05-)so, < (ca2’)~,;“(Mg2’)~~,(cO~-),,,.

(7)

A similar reasoning holds for points in the diagram that lie above the solubility line of a specific carbonate (supersaturated solutions). Consequently, the ordinate value of Fig. 1 can be used as an indication of the ~lub~lity of a carbonate in a solution with a specific MgiCa-ratio. Hence, a

267

Stability of Mg-Ca carbonates carbonate of which the solubility line at this particular Mg/Ca-ratio shown in Fig. 1, is higher than that of another carbonate will have a tendency to dissolve in favour of the other carbonate, even when their solubility products suggest the opposite. As shown in equation (2), at Mg/Ca = 1 the value of the Y-axis is equal to the solubility product of the carbonates. The values of this product is equal to exp (AGIRT), where AG is the free energy of formation of the carbonate from its ions. When the K-values obtained from Chave’s work are plotted on the line Mg/Ca = 1, and the lines with pertaining slopes drawn, we obtain a picture as shown in Fig. 1 indicating the relative stabilities of the Mg-Ca carbonates in solutions containing Mg and Ca. As can be seen from the lines, the 5% Mg-calcite is stable with respect to 10% Mg-calcite as well as magnesium-free calcite, over the entire range of Mg/ Ca-values considered, except for the very low Mg’+/ Ca”-ratios where magnesium-free calcite is most stable. Although similar lines drawn on the basis of PLUMMERand MACKENZIE’S (1974) work differ somewhat from those given in Fig. 1, the conclusion remains the same: the most stable calcites are those with very low Mg-contents.

COMPARISON OF PUBLISHED STABILITIES A check on the consistency of the published values of carbonate stability can be made as follows. Assume that the unordered Mg-calcites are an ideal mixture of calcite and magnesite. The AG of the Mg-calcite would then be equal to AGr,,g_ca,cite = (1 - x) AG, + xAG, + RT [x In x + (1 - x) In (1 - x)],

(8)

where AG, = the (Gibbs) free energy of calcite, AG, = the (Gibbs) free energy of magnesite. The third term is the usual term for entropy of mixing [HILL (1960) equation 2&20] ; it corrects for the fact that there are far more possibilities for realisation for mixed crystal than for a pure equivalent. If the mixed crystal is not ideal, a fourth term appears where the difference between ideal and non-ideal behaviour can be expressed. This term mainly contains the difference in energy between two MggCa interactions minus on Ca-Ca and one Mg-Mg interaction because all other interactions have been taken into account in equation (8). In a crystal with n cations, there are fn (n - 1) cationic interactions, but only cations close to each other will influence the energy situation considerably. Let there be N interactions of the cations in closest juxtaposition. Using probabilistic considerations, one can see that there are .y2 N Mg-Mg interactions (1 - x)’ N Ca-Ca interactions, and 2x(1 - x) N Ca-Mg interactions.

However, in equation (8) x N Mg-Mg interactions, and (1 - x) N Ca-Ca interactions have been taken into account. This gives a difference in energy of .x(1 - x) NAE, where AE is the energy of two Mg-Ca minus one Mg-Mg minus one Ca-Ca interaction. The same applies to the interaction between cations farther away from each other. Thus, the total effect is x(1 - x) xi Ni AEi, where i indicates all sorts of cationic interactions. Hence, for non-ideal behaviour equation (8) becomes ~~~~~~~~~~~~ = xAG, + (1 - x) AG, + RTCx ln x + (1 - ~)ln(l +

~(1

-

X)

- x)]

Ci Ni AEi.

The last two terms of (9) represent the mixing effect of calcite and magnesite crystals. This result is analogous to HILL’S(1960) for mixing in concentrated solutions (his equations 20-19/21). From equation (9) the value of 1 NiAEi can be calculated when values of AG, and AG, are known. An approximate value of AG, can be abstracted from CHAVE’S(1962) work. From the abundance of data for AG, (LANGMUIR,1965; MOREY,1962; HALLAand VAN TASSEL,1966) we adopted the value given by LANCMUIR(1965). This value seemed very high, but Langmuir’s arguments for its adoption are strong. Using these data for AG, and AG,, xNiAEi can be calculated as a function of X. The values obtained are shown in Table 1. In Table 1 the values from the experiments by CHAVEet al. (1962) and those carried out by PLUMMER and MACKENZIE(1974) have been elaborated, together with HOSTETLER’S(1963) estimated protodolomite value and LANGMUIR’S (1965) magnesite value. In this table and in Fig. 2 it can be seen that the values for CiNiAEi are low for the Mg-calcite values obtained by CHAVE et al. (1962). However, the xiNiAEi data obtained by PLUMMERand MACKENZIE (1974) seem fairly high. PLUMMERand MACKENZIE’S (1974) data for calcites with around 20% Mg replacing Ca give a value of around -800 cal/mol for x(1 - x) &NiAEi. This value would indicate that the excess energy of two Mg-Ca interactions, minus that of one Ca-Ca and one Mg-Mg interaction, is around 5000 cal/mol. This seems unlikely, because the difference begween AG, and AG, is only 4000 cal/mol and the xiNiAEi is only a second-order correction. So unless the Mg-calcites are mixed crystals that are far from ideal-an assumption not supported by any published evidence -the data of Chave et al. are probably closer to the real values than PLUMMERand MACKENZIE’S(1974).

R. B. DE BOER

268

Table 1. Calculated solubility products and free energy of Mg-calcites*

%Mg

AS

PH

** AH_

x(1-x)

zNtA L

0

6.02

3.34

-10584 -10584

0

2

6.02

3.09

-10636 -10584

+ 67

3

6.00

2.62

-10725 -10635

+170

7.5

6.06

3.38

-10587 -10451

+118

12.5

6.10

3.92

-10507 -10320

+154

12.5

6.20

7.3E

-10165 - 3378

-188

13.0

6.205

7.52

-10152 - 3362

-187

13.5

6.14

4.95

-10380 -10185

+ 52

16.5

6.22

7.8C

-10133 - 3916

-115

20.0

6.25

8.37

-10057 - 9620

- 94

23.0

6.35

- 3737 - 9487

-327

16.U

0.0

-11520 -11520

0

6.9

-11380 -11230

+ 10

10.4

-10300 -10700

-370

12.7

-10730 -10500

-480

17.3

-10210 - 9930

-820

19.2

-10060 - 9770

-930

23.6

- 9830 - 3570

-940

24.4

- 9890 - 3560

-920

26.7

- 9393 - 3650

-730

50.0

100

-223

100.0

8000

0

3

i -

4

* AG, AH and AE values in cal/mol. **AH = AC - RT[x In x + (1 - x) In (1 - x)]. *** 1 = CHAVEet al. (1962). 2 = PLUMMERand MACKENZIE(1974). 3 = HosTETLER(1963). 4 = LANGMUIR(1965).

0.05 -

5

0.1

0.15

x(1 ‘4)

0.2

1

l?ecalculotsddato

from:

z

CONSTRUCTION

I.25

OF ‘KINETIC-SATURATION CURVE

In 1973, KATZ recrystallized aragonite into calcite in Mg-bearing solutions and found that the Mg/Ca ratio in the calcite is a function of the Mg’+/Ca’+ ratio in the solution, as expressed by the DOERNERHOSKINS (1925) distribution law.

2 .:._

z

g-1000= x

(Mg/Ca)cryatal = 1 (MgZ+/Ca2+)sa~ution. I

-5CO-

-

X

Mgin

colclte

Fig. 2. Excess energy of Mg-calcites with respect to calcite and magnesite.

At 25°C he found a value for i of 0.0573 f 0.017. Katz’ data were obtained at rather low Mg/Ca ratios. Experiments carried out by Fiichtbauer and Hardie (personal communication) suggest that these data can be extrapolated to higher Mg/Ca-ratios with reasonable accuracy. At an Mg’+/Ca’+ ratio of 5.15, they obtained a value for 1 of 0.32. Let us consider a supersaturated solution with a specific Mg2+/Ca2+ ratio. This solution tends to precipitate a calcite with a specific Mg-content at or near the value predicted by KATZ (1973) and Fiichtbauer and Hardie. After precipitation of a given amount of Mg-calcite, the supersaturation with respect to this particular Mgcalcite is zero. At this point, the composition of the solution can only reach a still lower level of saturation after all precipitated Mg-calcite has recrystallized into a more stable carbonate. Depending on the

269

Stability of Mg-Ca carbonates

Mg2+/Ca’+ ratio in the solution, this can be either low-Mg calcite or dolomite, or both minerals. This last stage of equilibration requires complete recrystallization at low supersaturations to a phase with an Mg-content lower than that which occurs upon direct precipitation. Very probably this second stage is much slower than the first, and in many precipitation reactions this stage will not be completed. The degree of saturation of the solution will then be determined by the solubility of the Mg-calcite that was precipitated first. Using KATZ’S(1973) data, we can predict which Mgcalcite will precipitate from water of a specific Mg/Ca ratio. Elaboration of CHAVE’S(1962) work shows how soluble this Mg-calcite will be. The curve through the points obtained, referred to as the ‘kinetic-saturation curve’, is also given in Fig. 1. It should be remembered that this curve does not represent the solubilities of the most stable calcites but of calcites whose Mg-contents are governed by a non-equilibrium process. As shown in equations (5H7), the most stable calcite at a specific Mg/Ca ratio is that represented by the lowest line in Figs. 1 and 3. If the precipitation rate of Mg-carbonates in nature were high enough, the kinetic saturation curve could be found back in nature. Lakes in which evaporation is so fast that carbonates are precipitated, would then show compositions coinciding with this saturation curve. A summary of data on such compositions has been made by HOSTETLER(1963). His data are replotted in Fig. 3. It can be seen that at both low and high Mg2+/Ca2+ ratios of the solutions the points come near the line, but in between there is a discrepancy. Sea-water, which is much less saturated than lake water of the same Mg/Ca ratio, coincides with the line. [Composition after GARRELS and THOMPSON (1962)J Adoption of Fiichtbauer and Hardie’s value would cause the ‘kinetic saturation curve’ to move to the right in Fig. 1, whereas adoption of PLUMMER and MACKENZIE’S(1974) data would cause it to move upwards. The coincidence of the line with the seawater point may therefore be coincidental. The graph shows clearly that neither aragonite nor calcite, nor dolomite are in equilibrium with the lake water. Evidently, the net influx of dissolved HCO;, Ca2+ and Mg 2+ ions is so rapid, compared with the precipitation rate of the carbonates, that no equilibrium is reached. Even with sea-water with a very low average evaporation rate, no saturation is reached with respect to dolomite or aragonite. The precipitation rate of Mg-calcites, on the other hand, is so fast that the partial equilibrium, indicated by the kinetic saturation curve, is reached.

DOLOMITE

FORMATION

Apart from the inhibition by hydrated Mg2+ ions, the growth of dolomite is also hampered by a decrease in crystal ordering during growth. Mg2 + and

‘0 1 Fig. 3. Water

composition

of evaporative

lakes

and

sea-water.

Ca*’ ions that arrive at the dolomite surface have a certain preference for the Mg2+ and Ca2+ sites, respectively. However, this preference is not such that all Mg2+ and Ca 2+ ions occupy their own sites. Some Ca2+ ions occupy the Mg2+ sites and the reverse. Consequently, the crystal rim becomes less ordered and the preference of the cations for their own places diminishes. At last the crystal rim is an Mg-calcite or a protodolomite and has the inherent higher solubility. Thus, growth of dolomite directly from the solution seems impossible as long as the supersaturation is high enough to establish and maintain such an unordered rim; at best a protodolomite is formed when the supersaturation is high enough. Figure 3 shows that (protoklolomite is reported only from lakes where the ionic product of (Ca)“’ (Mg’+)i!’ (CO,) is higher than 10m7. This mineral can later on, by solid-state diffusion of the Ca2’ and Mg2 + ions to their own sites, slowly transform into dolomite. Alternatively, transformation may take place via a recrystallization stage. A completely distinct model for dolomite formation has been proposed by HANSHAW et al. (1971). Here dolomitization proceeds at low supersaturation and Mg/Ca ratios lower than those in sea-water. Although little is known about this mechanism, an explanation might be that supersaturation is so low that the unordered rim cannot be formed because it is unstable in the diluted solution. The dolomite might then form very slowly because of low supersaturation, but it is unhampered by any surface layer.

R. B.

270 CONCLUSIONS

1. Calcite with a low Mg-content (O-5%) is the most stable Mg-calcite at Mg/Ca ratios ranging from 0 to 100, or even more, thus over the whole range of Mg/Ca ratios occurring in nature. This conclusion is reached irrespective of the adoption of data found by either CHAVEet ai. (1962) or PLUMMERand MACKENZIE(1974). 2. In evaporative lakes and in sea-water, the Mgcalcite formed is at most in partial equilibrium with the lake (sea-)water, indicated by the ‘kinetic saturation curve’, but never in true equilibrium. 3. In such lakes, higher supersaturations with respect to calcite, are normally accompanied by a higher Mg/Ca ratio. 4. Figure 3 indicates that in lakes with an Mg/Ca ratio higher than 11 the ionic product of (Mgz+)l/z (Ca2 t)1’2 (CO:-) is normally higher than lo-‘; only in these lakes (but not in all of them) has (proto)dolo-’ mite been reported to form (HOSTETL~R.1963). 5. At moderate tem~ratures, sea-water is in equilibrium with respect to 25% Mg-calcite; its composition coincides with the ‘kinetic saturation curve’ for Mg-calcites, which may be coincidental. Acknowledgements-The

work presented here was sponsored by ‘Shell Internationale Petroleum Maatschappij B. V.‘, The Hague. Many thanks are due to Dr F. TH. HESSELINK and Dr C. BEZEMER (Shell’s Rijswijk laboratory), and Prof. Dr P. HARTMAN(University of Leiden) for critically reading the manuscript and for their valuable advice. I would like to thank Prof. Dr H. F&ZHTRAUER for making available some unpubiish~ data on the distribution coefficient of Mg and Ca between carbonate crystal and solution. The manuscript was reviewed by Prof. Dr R. WOLLASTand gained much from his critical remarks,

DE BOER

CHAVEK. E., DEFFEYE~ K. S., WEYLP. K., GARRELSR. M. and THOMPSON M. E. (1962) Observations of the solubility of skeletal carbonates in aqueous solutions. Science 137, 33-34. CLQUDP. E. (1965) Carbonate precipitation and dissolution in the marine environment. In: Chemical oceunography. (editors J. P. Riley and G. Skirrow), Vol. 2, Chapter 17, pp. 127-158. Academic Press. D~ERNERH. A. and HOXINS W. M. (1925) Coprecipitation of radium and barium sulfates. J. Amer. Chem. Sot. 47, 662-675.

ELLISA. J. (1959) The solubility of calcite in carbon dioxide solutions. Amer. J. Sci. 2571 354-365. GARRELSR. M. and CHRISTC. L. (1965) Solutions Minerals md Equilibria, 1st edition, 450 pp. Harper & Row. GARRELSR. M. and THOMPSONM. E. (1962) A chemical model for sea water at 25°C and one atmospheric total pressure. Amer. J. Sci. 260, 57-66. GREAT K. DE and DUYVISE. M. (1966) Crystal form of precipitated calcium carbonate as influenced by _ adsorbed magnesium ions. Nature 212, 183-184. HALLA F. and TASSELR. VAN (1966) AuflGsunaserscheinungen bei Erdalkalicarbonaten 111 (Magnesia? MgCOs). Radex Rundschau 6, 356-362.

HANSHAWB. B., BACK W. and DEIKER. G. (1971) A geochemical hypothesis for dolomit~ation by ground water. Econ. Geol. 66, 710-724. HILL T. L. (1960) An ~nt$aductjQn to Statistical Thermo&ramics, 508 pp. Addison-Wesley. HOSTETLER P. B. (1963) The degree of saturation of maene. sium and calcium carbonate minerals in natural waters. I.A.S.H. Commission of Subterranean Waters, Publ. 64, 3449. KATZ A. (1973) The interaction of magnesium with calcite during crystal growth at 2590°C and one atmosphere. Geochim. Cosmochim. Acta 37, 156331586. LANGMUIRD. (1965) Stability of carbonates in the system MgO-CO,-H,O. J. Geo2. 73, 730-754. LIPPMANNF. (1973) Sedimentary Carbonate Minerals, 1st edition, 229 pp. Springer-Verlag. MILLION J. D. (1974) Marine Car~~~fes, 1st edition, 379 pp. Springer-Verlag. MILLION J. D., GASINERM. and MILLER J. (1971) Utilization of magnesium in coralline algae. Buli. Geol. Sot. I

Amer. 82, 573-579.

REFERENCES BERNERR. A. (1975) The role of magnesium in the crystal growth of calcite and aragonite from sea water. Geochim. Cosmochim. Acta 39, 489-504.

BISCHOFFJ. L. and FYFE W. S. (1968) Catalysis, inhibition and the aragonite-calcite problem I: The aragonitecalcite transformation. Amer. J. Sci. 266, 65-79.

MUELLER P. and PAREKHP. P. (1975) Influence of magnesium on the ion-activity product of calcium and carbonate dissolved in sea water: a new approach. Marine Chem. 3, 63-11.

MOREYG. W. (1962) The action of water on calcite, magnesite and dolomite. Amer. Mineral. 47, 14561460. PLUMMERL. N. and MACKENZIEF. T. (1974) Predicting mineral solubility from rate data: application to the dissolution of magnesium calcites. Amer. J. Sci. 274, 61-83.