an ideal solid solution model for calculating solubility of clay...

Clay Minerals (1981) 16, 361-373.

A N I D E A L S O L I D S O L U T I O N M O D E L

F O R C A L C U L A T I N G S O L U B I L I T Y

O F C L A Y M I N E R A L S

Y. T A R D Y AND B. F R I T Z *

Laboratorie de Pddologie et de Gdochimie, 38, rue des Trente Six Ponts, 31078 Toulouse, and *Centre de S~dimentologie et de G~ochimie de la Surface, 1, rue Blessig, 67084 Strasbourg, France

(Received 24 April 1981; revised 20 May 1981)

ABSTRACT: A method for estimating Gibbs free energies and stabilities of clay minerals is proposed for use with computer programs aimed at calculating the chemical evolution of natural water-rock systems. This is based on (i) a model for ideal solid solutions of a large number of end-member compositions and (ii) a data set of estimated solubility products from 36 end-members. The application of the method to the production of experimental or natural clay stabilities is discussed.

In the evolution of natural water-rock systems, clay minerals appear as omnipresent reactants or products of chemical reactions. In an at tempt to model such reactions by the use of computer programs, clay mineral compositions have to be considered essentially as variable. It is possible to take into account such chemical composition variations by considering clays (i) as a set of separate mineral phases and including in the models a large number of minerals of discrete compositions and their solubilities, or (ii) as solid solutions whose compositions change continuously during the chemical processes.

The first method was followed by Fritz & Tardy (1974, 1976) and Fritz (1975). The results obtained were roughly in agreement with natural observations. Nevertheless, this method is limited in practice as it requires too large a data set to cover the whole range of chemical composition of natural clays. The second approach was used by Helgeson & Mackenzie (1970) for illite-montmorillonite solid solutions. This appears the most suitable for modelling and understanding the chemical evolution of natural systems, although the type of solid solution model has to be chosen, as well as the different end-members and their relative solubility products.

S O L U B I L I T Y P R O D U C T O F T H E D I F F E R E N T E N D - M E M B E R S

Several methods for estimating the thermodynamic properties of clay minerals or phyllosilicates have been presented in the literature (Karpov & Kashik, 1968; Eugster & Chou, 1973; Tardy & Garrels, 1974; Nriagu, 1975; Mattigod & Sposito, 1978). These methods are of different value, and the estimated Gibbs free energies in a given mineral differ considerably from one method to another. The method of Tardy & Garrels (1974) was used successfully by Fritz & Tardy (1974) and Fritz (1975) for calculating mineral sequences in weathering conditions. This method, based on the assumption that the Gibbs free energy contribution of a given oxide constituent to the free energy of formation of a phyllosilicate is constant from one mineral to another, was performed to evaluate the

0009-8558/81/1200-0361502.00 �9 1981 The Mineralogical Society

362 Y. Tardy and B. Fritz

stability of clay minerals considered as discrete phases, and to create the data set mentioned above. This approach has now been abandoned and replaced here by a method of direct estimation of log Ksp (solubility products) of the end-members, which are combined to calculate the solubility of the solid solutions.

As a first approximation, it is possible to start from solubility products of well-crystallized phyllosilicates for which thermodynamic data are available: muscovite, annite, phlogopite, pyrophyllite, minnesotaite and talc (Table 1, column 4) (Helgeson et al., 1978). By applying these data to experimental, natural or simulated cases, it has been found that such solubility products are generally too low and that such well-crystallized phyllosilicates are too stable for explaining clay stability fields.

By a method of trial and error, Fritz (unpublished data) obtained a set of empirically determined values which seem to satisfy the different natural or experimental situations. These data (which are given in column 5 of Table 1) fit the linear relationships of log Ksp a s

a function of the parameter AO 2- of Tardy & Garrels (1976, 1977) as well as the initial ones. Not surprisingly, a solubility correction appears necessary to transform well-crystallized micas or uncharged layer-silicates into clay minerals of low crystallinity and small size. Fig. 1 shows that this correction is more important for the magnesian phyllosilicates than for the aluminous ones in both series.

Furthermore, exchange constants are required for deriving log Ksp of potassium clays into cation exchanged clays. In spite of the tremendous amount of existing data, it is still difficult to figure out how the chemical composition and the charge on the layers influence the cation exchange constants. In these conditions, the difference between two solubility products of layers of the same composition, exchanged with two different cations

FE3+ ~L3+ FE2+ ~B2+

+20 L ~ " TALC

+i0 ~ ,

-10

-20 I 250 -200 -150 -1O0 ~0 2- CATION (KJ MOL -I)

FIG. 1. Log Ksp (solubility product) of poorly-crystallized clays and well-crystallized phyllosilicates as functions of the parameter AO 2- cation.

J

> -

2 +30

Solid solution model for clays 3 6 3

0

P~

0 0

e~

0

<

m

0

ooooooooo ~ ~ ~ ' -

0 0 0 0 0 ~ 0 0 0 0 0 0

+ + + ~ + + + + + + + +

~ + + + ~ ~ ~ ~ ~

~ ~ ~ + + ~ ~ ~ ~

• ~ ~ ~ ~ ~ + ~ + + + ~ ~ + + +

~ o ~ ~ 2 2 ~ 2 ~ o o 0 o

+ + + + + + + + + + + + + + + + + + + +

+ + + + + + + +

0 0 0 0 0 0 0 0

~oo22=oo ~

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. . J

o

~0 , ~

oo

~ o o ~

�9 ~ o

o o


(commonly called exchange constants), will be considered as independent of the kind of clay on which cations are adsorbed. The different values chosen are those of Tardy & Garrels (1974) and are calculated from the selected values of 'AG exchangeable oxide'. Then, the log K exchanges chosen are:

log Ksp (clay-Na)-- log Ksp (clay-K) = + 0.806 log K~p (clay-Ca0.5)- log K~p (clay-K)= + 0.733 log Ksp (clay-Mg0.5) -- tog Ksp (clay-K)= + 0.733.

Similar considerations are followed when estimating solubility products of octahedrally charged minerals. In fact, natural mineral formulae (Weaver & Pollard, 1973) do not show any clear correlation between the octahedral charge and the nature of the octahedral cations. Provisionally, then, it may be assumed that the differences in solubility products between uncharged and octahedrally charged minerals are independent of the octahedral composition. Furthermore, the octahedral charge will not be greater than 1.0 for 12 oxygens in the formula unit, which corresponds to the celadonite layer. The solubility products obtained are such that an uncharged stevensite (talc formula) would be more stable than an octahedrally charged stevensite. A difference of one log K unit was found good enough to permit the octahedral charge distribution of clays considered in Table 2:

log Ksp Mg3Si4Ol0(OH)2-log Ksp (Mg0.s)Mg2.sSi4010(OH)2 = - 1.

According to the previous relationship:

log Ksp (clay-Mg0.5)-log Ksp (clay-K) = 0-733

and because

we have

and

log Ksp Mg3Si4Om(OH)2-clay = 25.162

log Ksp (Mg0.5)Mg2.sSi4010(OH)2 = 26' 162

log Ksp KMg2.sSi4Ol0(OH)2 = 25"429.

For Fe 2+-, Fe 3+- and AP+-celadonites, log Ksp was estimated following a similar procedure. Considering Al-celadonites:

log K~p Mg0.sAlv666Si4010(OH)2 = 1/6 log Ksp talc+ 5/6 log Ksp pyrophyllite = 5.080

this becomes

and

log Ksp (Mg0.5) A11.6668i4010 (OH)2---5'080 q-1 ---6-080

log Ksp KAll.666Si4010 (OH)2 = 5.345

after having exchanged Mg 2+ against K +. Clay solubility products of celadonite-type end-members, calculated on these bases, are

given in Table 1, column 5. The method is not yet applicable for hyperoctahedrally charged clays such as vermiculite, especially Palabora vermiculite (Table 2).

Solid solution model for clays 365

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SOLID S O L U T I O N M O D E L S

The possibility of considering clay minerals as solid solutions has been widely discussed in the past ten years. An early model proposed by Helgeson & Mackenzie (1970) is based on ideal solid solution of five components:

illite K0.60Mg0.25Alz.30Si3.50010(OH)2 K-beidellite K0.33A12.33Si3.67010(OH)2 Na-beidellite Na0.33Alz.33Si3.67010(OH)2 Ca-beidellite Ca0.167A12.33Si3.67010(OH)2 Mg-beidellite Mg0q 67A12.33Si3.67010(OH)2.

Calculations and considerations based on equilibria of such solid solutions with interstitial waters have provided some interesting results. However, the chemical composition of idealized minerals does not approach the actual clay composition. Lippmann (1977, 1979, 1980) discussed the stability relations of clay minerals considered as solid solutions and pointed out that the solubility of mixed crystals must be described in terms of several partial solubility products. For delineating the aqueous equilibrium solubility of clay minerals up to five or more partial solubility products would be necessary. Furthermore, Lippmann concluded that in these situations it is highly unlikely that these minerals form in nature under the conditions of thermodynamic equilibrium.

Recently, Stoessell (1979) proposed a regular solution site-mixing model for calculating illite stability. The four end-members chosen (pyrophyllite, muscovite, phlogopite and annite) did not include celadonites or Fe3+-minerals and the reasons for selecting these particular end-members were not given. Furthermore, even for the Fe3+-free illites, the parameters for ~alculating the mixing energies were not specified. The model is only speculative but it does give a complete set of theoretical relations for site-mixing.

The site-mixing approach was also followed by Aagard et al. (1981), who applied the method to montmorillonites, illites and mixed-layer clays. In their model, cations are distributed randomly (ideal site mixing) without any interaction between the different sites (tetrahedral, octahedral, interlayer). For calculation of the activities, four thermodynamic components--pyrophyllite, muscovite, paragonite and margarite--were used in order to relate the variations of the clay composition to the changes of the natural solution chemistry. However, application of this model is strictly limited to dioctahedral minerals and nothing is said on the way to select the thermodynamic Mg 2+ or Fe3+-components such as talc-phlogopite or Fe3+-pyrophyllite-Fe3+-muscovite, for example.

I D E A L SOLID S O L U T I O N M O D E L

A clay mineral of the illite, vermiculite or smectite type has the following general formula:

[N,+K+Ca2+ 2+ .4+ 3+ A13+ 3+ 2+ M 2+ O OH "~ ~ 7 Mg~ ][S14_xA1 x ][ y Fe~ Fep gq ] 10( )2. interlayer tetrahedral octahedral

The interlayer charge (I), the tetrahedral charge (T) and the octahedral charge (O) are respectively equal to:

I=c~+/3+27+26 T = x O=6-- (3y+ 3z + 2p+ 2q) I = T + O .


Clays normally have an octahedral charge and thus the interlayer charge is often greater than the tetrahedral. Some vermiculites show an excess of cations in octahedral positions but this case will not be considered here.

In order to describe these minerals by use of an unique solid solution, numerous end- members are needed as follows. (The end-member index is subscribed i, with i being any integer between 1 and 36.) (1) Four end-members of talc-pyrophyllite type:

Si4Mg3010(OH)2 (1) Si4Fe3Ol0(OH)2 (2) Si4Fe2Olo(OH)2 (3) Si4A120 Io(OH)2 (4)

(2) Four times four end-members of tetrahedral charged type with various interlayer cations:

(Na or K or Ca0.5 or Mg0.5)Si3A1Mg3010(OH)2 (5-8) (Na,K,Ca0.s,Mg0.5)Si3A1Fe3010(OH)2 (9-12) (Na,K,Ca0.5,Mg0.5)Si3A1Fe2010(OH)2 (13-16) (Na,K,Ca0.s,Mg0.5)Si3A1A12010(OH)2. (17-20)

When the interlayer cation is replaced by potassium those minerals are of the phlogopite-muscovite type. (3) Four times four end-members of the celadonite type with various interlayer cations:

(Na,K,Ca0.5,Mg0.5)SiaMg2.5010(OH)2 (21-24) (Na,K,Ca0.5,Mg0.5)SiaFe2.5Ol0(OH)2 (25-28) (Na,K,Ca0.5,Mg0.5)SiaFev666010(OH)2 (29-32) (Na,K,Ca0.5,Mg0.5)Si4All.666010(OH)2. (33-36)

For each end-member i, one defines: X; the mole fraction of the end member i in the solid solution; 2i the corresponding activity coefficient in the solid solution; Ai the corresponding activity in the solid solution; Ki the corresponding solubility product; Q~ the corresponding ion activity product in aqueous solution in equilibrium with the solid solution.

Applying general thermodynamics for solid solutions (Garrels & Christ, 1965) we obtain:

log Ki= log Qi- log Ai log Ki = log Qi - log X i - log 2i

If the solid solution is ideal:

2i= 1 and, log Ki = log Qi- log Xi.

For a given solid solution, an apparent overall solubility product K* is calculated by considering simultaneously n equilibrium relationships (one relationship per end- member) as follows:

i = n

log K* =log Q* = ~' Xi log Qi i=1

368

and, because

one has

Y. Tardy and B. Fritz

log Qi=log ~ .+ lo g Xi

i--n i=n log K* = ~ Xi log Ki+ ~ S~ log X~.

i=1 i=1

In the above expression Xi stands for the mole fraction of the ith end-member in the solid solution. By considering the mixing of talc-clay (i= 1) and pyrophyllite clay ( i= 4) one would have the formula

Si4All.aMg0.9Ol0(OH)2

corresponding to X~ = 0-3 and X4 = 0-7. There is only one set of (X~) values which is consistent with all the previous equations,

even if there is an infinite number of possibilities of combining n end-members with (Xi, i =n) mole fractions to obtain one given clay formula. The search for this unique (Xi) vector was made with a computer program called CISSFIT (Clay Ideal Solid Solution Fitting) in an iteration routine: from one clay formula plus one set ofn log Kvalues for the end-members, it calculates one set of n X~ (mole fraction values) and n constraints. These constraints are: mass balance equations for each element, independent equilibrium

i-n conditions, and the sum of the mole fractions equal to unity ~ Xi= 1

i=l For an end-member mixing model, the mole fractions are calculated on the basis of the

oxygen framework mixing and, in the above expression, the term ~. Xi log Xi derives i=n

from the entropy of ideal mixing of all the n end-members, with Xi previously defined. In order to clarify this calculation let us consider for example, the Mg-balance for the

general clay formula described above:

total Mg = octahedral Mg + interlayer Mg (Mg)t = 6 + q

Considering the n end-members, it follows, for each defined i= 1 to 36:

(Mg)t=~+q= 3(XI+ Xs+ X6+ XT+ Xs) -~-2"5(X2!-~-X22-~-X23--[-X24) ..~ 0.5(X8-I- XI2-]- X16-~- X20-~- X24-~- X28-l- X32-}- X36 )

which gives an example of the first type of relation between the different mole fractions. The second type is deduced from the n mass-action law relations previously described (Table 1). These n equilibrium relations are not all independent and if one considers magnesium and aluminium distribution in the general solid solution, where [aj] designates the activity of the aqueous species aj, one has

[Mg2+] 3 K1XI

[A13+] 2 K4X4

for the equilibrium between the solution and both talc and pyrophyllite end-members. For the same activity ratio there are also

[Mg2+] 3 K6X6 . . . . [AI3+] 2 - K~8~8 tpmogoplte and muscovite end-members),

Solid solution model fo r clays 369

and

so that

[Mg2+] 3 K22X22 M [Ap+]2 - ~ ( g and A1, K-celadonite end-members),

KIX1 K6X6 K2zX2z

K4X4 KisS18 /34X34

The boundary conditions correspond to X,--+0 or Xi~ 1 and do not contradict this relationship. It is obvious that if X1-+0, for example, there is no octahedral magnesium in the system and X6--+0 and )(22--+0; thus minerals such as talc, phlogopite and Mg-celadonite do not contribute to the solid solution. It is also clear that if X1 --> 1, one has

A set of solubility data is presented in Table 2. The corresponding values calculated by the ideal solid solution model, and solubilities of end-members previously given, are presented in Table 2, column 4. Solubility products of the different minerals (column 3) are derived from the following publications:

(I) Routson & Kittrick (1971) for the three illites. (2) Mattigod & Sposito (1978) for solubility of smectites measured by Kittrick

(1971a,b,c), Weaver et al. (1971), Weaver et al. (1976), Huang & Keller (1973), Misra & Upchurch (1976), Reesman & Keller (1968).

(3) Kittrick (1973) for the two vermiculites. (4) Trescases (1975) and Tardy et al. (1974b) for the nontronite of New Caledonia in

equilibrium with Al-goethite and an aqueous solution defined by pH=7.7 , log [Mg 2+] = -3-2 and log [H4SiO4]--- --3"44.

(5) Lemoalle & Dupont (1973), Carmouze (1976) and Gac (1979) for the nontronite in ferruginous oolites of Lake Chad, in equilibrium with goethite (log[Fe 3 +]/[H +]3 = _ 0"81), kaolinite (log[AP+]/[H+]3+log[HaSiO4]=-3.72) and aqueous solution in which pH = 7.0, log[Ca 2+] = - 3.398, log[Mg 2+] = - 3.438, log[HaSiO4] = - 3.332.

(6) Paquet (1970) and Gac (1979) for the beidellite ofvertisoils in Chad, in equilibrium with goethite, kaolinite and an aqueous solution characterized by pH=8.49, log[Ca 2+] = - 3-547, log[Mg2+/= -- 3-55, log[HaSiO4J = - 3-50.

(7) Tardy e t al. (1974a), Gac e t al. (1977a) and Gac (1979) for the saponite of Lake Chad in equilibrium with kaolinite, goethite and an aqueous solution characterized by pH = 8-1, log[Na +] = -1.48, log[Mg 2+] = -5.08, log[H4SiO4] = -2.70.

(8) Mackenzie et al. (1967), Patron et al. (1976) and Nahon (1976) for glauconite in equilibrium with quartz, kaolinite, goethite and sea-water at pH = 8-3. The glauconite formula is that of Cimbalnikova (1971) and Weaver & Pollard (1973). The chemical composition of sea-water is the one described by Garrels & Thompson (1962).

In Table 3, as examples, the contribution of each of the end-members to the solid solution is given for Goose Lake illite and sea-water glauconite. For the Goose Lake illite:

AI is explained by pyrophyllite > muscovite > Al-celadonite Fe is explained by Fe-muscovite > Fe-pyrophyllite = Fe-celadonite; Mg is explained by talc = Mg-celadonite >> phlogopite.

For the glauconite:

A1 is explained by Al-celadonite > pyrophyllite > muscovite;


TABLE 3. Mole fraction distribution in Goose Lake illite and sea-water glauconite

Goose Lake Sea-water No. End-members illite glauconite

4 Si4 A12 0.309 0.058 3 Si4 Fe2 0.016 0.090 1 Si4 Mg3 0.017 0-026

18 Si3 A1A12 0.267 0,031 14 Si3 A1 Fe2 0.081 0,317 6 Si3 A1 Mg3 0,001 0.001

34 Si4 A11.667 0,266 0,156 30 Si4 Fel.667 0.021 0.225 22 Si4 Mg2.500 0.023 0.080

Exi 1.001 0.984

Fe is explained by Fe-muscovite > Fe-celadonite > Fe-pyrophyllite; Mg is explained by Mg-celadonite > talc >> phlogopite.

D I S C U S S I O N

Large variations in solubilities appear in clays of the same composition and large discrepancies are also observed between measured and estimated values. Furthermore, the methods of estimation used by Tardy & Garrels (1974), Mattigod & Sposito (1978) and in the model presented here are in relatively good agreement.

At first, it seems difficult to determine the significance of the various measurements. It appears that most of them correctly reflect the stability field of clays in natural conditions and that a few, such as Arizona montmorillonite (Cheto) or Wyoming montmorillonite (Clay Spur) of Huang & Keller (1973), the Houston Black Clay smectite of Carson et al. (1976) or the Colony montmorillonite of Weaver et al. (1971), are in error. However, solubility data are all suspect for several reasons: (i) the time needed to be sure that equilibrium is really reached is undetermined but certainly long; (ii) the investigators rarely know what the secondary phases produced during dissolution and the secondary mineral solubilities controlling the activity of A13+ and Fe 3+ in solution really are; (iii) a so-called pure clay mineral is in fact a mixture of several phases differing in size or chemical composition, reacting as different minerals, and dissolving at different rates; (iv) clay particles are probably solid solutions between many end-members. This last reason is perhaps the most important and provides an alternative for interpretating solubility measurements. In fact, when the ratio of clay to solution is low, either the equilibrium is reached, but the end product must differ from the initial one, or the end and initial products are identical and the equilibrium is not effectively reached (Wollast, 1976, personal communication).

Beside these reasons for suspecting solubility measurements, there are also reasons for suspecting the data obtained from field observations (Tardy et al., 1974a,b; Trescases, 1975; A1-Droubi, 1976; Van Breemen, 1976; Gac et al., 1977a,b; Gac, 1979). Two major difficulties are encountered: (i) waters analysed are percolating, and thus not strictly 'in

Sol id solution mode l f o r clays 371

con tac t ' with the supposed c lay mineral ; (ii) c lay minera ls in soils are mixtures and chemical compos i t ions o f indiv idual crystals are no t k n o w n exactly.

C O N C L U S I O N

The mode l presented here is based on the solubi l i ty p roduc t s o f thir ty-s ix end-members and on an ideal solid so lu t ion o f those end-members .

This mode l provides the o p p o r t u n i t y o f obta in ing , by s imulat ion, the pr inc ipa l clay compos i t ions found in nature . The ca lcula ted solubil i t ies were also c o m p a r e d with solubi l i ty measurements ob ta ined exper imenta l ly and those der ived f rom field observations. Such solubil i t ies are known to be suspect a l though they are roughly in accordance

with the solubil i t ies ca lcula ted using the model . However , the exper imenta l solubil i t ies are no t rel iable enough to be used to decide (i) whether c lay minera ls are sol id solu t ions or not and, if so, wha t are the different componen t s which real ly con t r ibu te to the solid solut ion, (ii) wha t is the type o f sol id so lu t ion and (iii) how to choose between a s i te-mixing mode l and an end -member mixing model .

The app l i ca t ion o f the end -member mixing mode l presented here to the s imula t ion o f na tu ra l cases requires tha t the solubi l i ty o f the componen t s con t r ibu t ing to the ideal solid so lu t ion mus t be greater than the solubi l i ty o f the co r respond ing well-crystal l ized minera ls such as ph logopi te , muscovi te and talc. The log K solubi l i ty is a l inear funct ion o f the p a r a m e t e r AO 2- ca t ion in bo th series: (i) well-crystal l ized phyl losi l icates and (ii) poo r ly crysta l l ized c lay minera l end-members o f a same compos i t ion . The slopes o f the l inear funct ions are different, so tha t the difference in solubil i t ies decreases in the fol lowing order : magnes ium, ferrous iron, a lumin ium and ferric iron.

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AAGARD P., HELGrSO~q H.C. & BENSON L.V. (1981) Chemical and thermodynamic consequences of preferential site occupancy in montmorillonite, illites and mixed layer clays. Am. 3. Sci. (in press).

AL-DRouBI A. (1976) G~ochimie des sels et des solutions eoncentr~es par ~vaporation. ModUle thermodynamique de simulation. Application aux sols sal~s du Tchad. Mdm. Sci. G~ol. Strasbourg, 46, 177 pp.

CARMOUZE J.P. (1976) La r~gulation hydrogdochimique du Lac Tchad. Contribution d l'analyse biogdodynamique d'un systdme lacustre endordique en milieu continental. Th~se Doct. es-Sciences, Univ. Paris VI, 418 pp.

CARSON C.D., KITTR1CK J.A., DIXON J.B. & MCKEE T.R. (1976) Stability of soil smectite from a Houston black clay. Clays Clay Miner. 24, 151-155.

CI~BALNnCOVA A. (1971) Chemical variability and structural heterogeneity of glauconites. Am. Miner. 56, 1385-1392.

EU~STEK H.P. & CHOU I.M. (1973) The depositional environments of Precambrian banded iron formations. Econ. Geol. 68, 1144-1168.

FRITZ B. (1975) Etude thermodynamique et simulation des r~actions entre min~raux et solutions. Application la g~ochimie des alt6rations et des eaux continentales. Mdm. Sci. Gdol. Strasbourg, 41, 153 pp.

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FRITZ B. & TAe, DY Y. (1976) Sequences de min~raux secondaires dans l'alt6ration des granites et roches basiques; modules thermodynamiques. Bull. Soe. geol. France, 18, 7-12.

GAC J.Y., AL-DRouBI A., FRITZ B. & TARDY Y. (1977a) Geochemical behaviour of silica and magnesium during the evaporation of waters in Chad. Chem. Geol. 19, 215-228.

GAC J.Y., AL-DRouBI A., PAQUET H., FRITZ B. & TARDY Y. (1977b) Chemical model for origin and distribution of elements in salt and brines during evaporation of waters. Application to some saline Lakes of Tibesti, Chad Pp. 149-158 in: Origin and Distribution of the Elements (L. H. Arhens, editor), Pergamon Press, Oxford.

372 Y. T a r d y a n d B. Fr i t z

GAr J.Y. (1979) G~ochimie du Bassin du Lac Tchad. Bilan de l'alt&ation, de l'&osion et de la s~dimentation. Th6se Univ. Louis Pasteur, Strasbourg, 249 pp.

GARRELS R.M. & THOMPSON M.E. (1962) A chemical model for sea water at 25~ and one atmosphere total pressure. Am. J. Sci. 260, 57-66.

GARRELS R.M. & CHRIST C.L. (1965) Solutions, Minerals and Equilibria. Harper & Row, London. HELGESON H.C. & MACKENZIE F.T. (1970) Silicate sea water equilibria in the ocean system. Deep Sea Res. 17,

877-892. HEL6ESON H.C., DELA~ J.M., NESBITT H.W. & BIRD D.K. (1978) Summary and critique of the thermodynamic

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RI~ S U M 1~: Une m&hode d'estimation de l'+nergie libre de Gibbs et de la stabilit6 des min6raux argileux est proposre en vue de son utilisation dans les programmes d'ordinateurs drterminant l'~volution chimique des syst~mes eau-roches naturels. On prrsente d 'abord un modrle pour des solutions solides idrales d 'un grand nombre de constituants puis on propose un ensemble de produits de solubilit6 estimrs pour 36 constituants. Finalement on discute de l'application de la m&hode h la pr6vision des stabilitbs des argiles dans la nature ou dans les conditions exp+rimentales.

K U R Z R E F E R A T : Zur Absch/itzung von freien Gibbs Energien und Stabilit/iten von Ton- mineralen mit Computerprogrammen wird eine Methode zur Berechnung der cbemischen Entwicklnng natfirlicher Wasser-Gesteins Systeme vorgesteltt. Diese basiert auf: (a) einem Modell yon idealen Mischkristallen aus einer groBen Anzahl Endgliedzusammensetzungen und (b) einem Datensatz gesch/itzter Lrslichkeitsprodukte von 36 Endgliedern. Es wird die Brauch- barkeit der Methode zur Vorhersage experimenteller oder natiirlicher Tonstabilit/iten er6rtert.

R E S U M E N : Se propone un mrtodo para la estimacidn de las energias fibres de Gibbs y de la estabilidad de los minerales de la arcilla para uso con programas de ordenador con el prop6sito de determinar la evolucirn quimica de los sistemas naturales rocagua. EstS. basado en (i) un modelo para soluciones srlidas ideales de un gran mimero de composiciones del miembro final de la serie y (ii) los productos de solubilidad de 36 miembros final de serie. Se discute la aplicaci6n del m&odo para la prediccirn de la estabilidad de arcillas naturales o sintbticas.

an ideal solid solution model for calculating solubility of clay...

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