The American Mineralogist, Volurne60, pages 834-839,1975

ThermochemicalApproximations for Clay Minerals

JnnounO. Nnrncu CanadaCentre for Inland Waters,Burlington, Ontario, Canada

Abstract

The Gibbs energiesof formation for clay mineralshave been approximated by a model which assumesthat theseminerals are formed by the combinationof siliconhydroxide with metalhydroxides. The changein freeenergy during the polymerization ofhydroxides to form silicatesplus water is shownto be generallysmall and has beenrepresented by a correction term. The dispersionbetween the predictedand the experimentaldata of better than * 2.0 kcal mol-r is comparableto the total uncertaintyin the experimentallydetermined constants. The approximatedfree energies of formation for vermiculitesand ferromagnesiumchlorites are presented.

Introduction, bination("polymerization") of simplemetal hydrox- The study of the chemical constraints which ideswith siliconhydroxide, Si(OH),. The changein predicate the environmentsof formation (or free energyduring the polymerizattonof the hydrox- alteration)of clayminerals has been hindered by the ides to form clay mineralsis usuallysmall and has sparsity of relevant thermochemicalconstants. beenapproximated by a one parametercorrection Althoughseveral workers have determined the Gibbs term. The model in its presentform is essentially freeenergy of formation(AGi) for (e.g., see heuristicand the validity for its use restschiefly on Polzerand Hem, 1965;Kittrick, 1969;Reesman and the good agreementbetween the predictedand ex- Keller, 1968;Huang and Keller, 1973),few (if any) perimentaldata. AGy0for the other clay mineralsare available.The The mechanicsof the proceduremay be illustrated recentlyreported AGro for montmorillonitesand by consideringthe formation reaction of a typical (Reesmanand Keller, 1968;Helgeson, 1969; : Huang and Keller, 1973)pertain to specificor n,NaOH * nrKOH * naCa(OH), * naMg(OH), idealizedminerals and may beof limitedgeochemical * nuFe(OH)'+ n.Al(OH! + n,Si(OH). applicability.The AG10for ferromagnesiumchlorites - NaorKorCaorAlnrFeouMgorSirTO,o(OH), and vermiculitesremain to be determined. * (Znprl2)HzO (l) This report presentsa method for approximating where z1 is the reaction coefficient of the i-th the AG10for clay mineralswith an accuracywhich is hydroxide and z1 is the charge on the i-th cation adequatefor manygeochemical calculations. It is in- (including Si). Usually z1corrospoflds to the amount tended as a first step towards developingbetter of the i-th cation (or silicon) in the formula unit for methods for approximating the AGro for these the clay mineral. The free energy of formation for the minerals;the gambit will undoubtedlybe modified clay mineral whose formation is described by the and extendedas accurateexperimental data become above reaction is calculated by the expression: available.Obviously there is a needfor methodsto estimatethe AGrovalues for clay minerals.The ex- AGyo(Montm.) : Znt AGlo(r1) - perimental determinationsare difficult, and many - (2np1 l2)LGto(H,O)- Q Q) have considerableroom for improvement.Clay mineralsshow considerablevariations in composi- where AG10(r) is the free energy of formation of the tion, and it is unlikelythat the AGrofor everyone of i-th hydroxide component and Q is an empirical cor- them will ever be determinedexperimentally. rection factor defined as

The PredictiveMethod Q = o(n121- 12) (3)

The predictive method employedin this report i.e., Q is expressedas a function of the number of considersthe clay mineralsto be formedby the com- moles of water releasedduring the reaction.

834 THERMOCHEMICAL APPROXIMATIONS FOR CLAY MINERALS 835

The free energy data for the hydroxide components For the kaolinitegroup of minerals,Znrzr : 14. are given in Table l. It became apparent that the For the other groupsof clay minerals,the relation published AG10values for solid alkali metal hydrox- 2n61 : 22 (5) ides resulted in predicted data which were con- sistently higher than the experimental results. The is generallytrue, i.e., the sum of the hydroxylions of strategy was therefore adopted (I thank Professor the constitutivemetal hydroxidesis 22. Wherethere R. M. Garrels for the suggestion)to derivethe neces- is a chargeimbalance in the reportedcompositionS of sary free energies for KOH and NaOH from the the clay mineral(2n6 122 in mostcases), the clay publishedAGyo values for muscoviteand paragonite. mineralhas beenassumed to be in the H+ form. The The following reactionswere considered: compositionfor Aberdeenmontmorillonite reported by Kittrick (1971)serves to illustratethe calculative MOH + 3AI(OH)3+ 3S(OH)4: procedurefor clay mineralsin H+ form: MAlasisolo(oH)' + l0HrO (4) 0.445Mg(OH),+ 0.335Fe(OH)s+ 1.47A(OH)g+ Where M is K or Na. Employed in thesecalculations 3.82S(OH)4- were AG10() : -1330 kcal (Zen, Set 2, [(Alt * Mgo...u Feo rru) (Alo.18 Si3.82)Orr(OH)r] H*o.nru * 1972; Robie and Waldbaum, 1968) and AG10 9.79H,O (6) (paragenite): -1318 (Zen, kcal Set 2, 1972).The SinceAGyo (H*) : 0, therefore AGro for KOH and NaOH so derived are shown in AGro(Aberdeen -- 2n1 AGyo(r) Table l. montm.) - The expression for Q is empirical. According to - 9.79 AGro(H,O) Q, with Q = 0.39 x 9.79 (7) Equation (l), polymerize the hydroxides to form Although H+ does not figure in the free energy silicate + water, and may Q be envisagedas the sum calculation, it must be considered in the calculation of the dehydration energiesof the water molecules of activity products. split out. In other words, the dehydration of the Finally, the calculative procedure is illustrated ex- hydroxidesduring the formation of silicatesmay be plicitly by considering the formation reaction for analogous to the splitting out of water during the for- kaolinite: mation of a polymer. It was found during the study + - + (8) that the best fit between the experimental and 2AI(OH)3 2Si(OH). ALSi'O6(OH){ 5H,O predicted data was obtained when o was assigneda AG10(kaolinite) -- 2(-274.2)+ 2(-318.6)- 5(-56.69) constantvalue of 0.39.Thus Q : 0.39 X (the number -5 x0.39=-904.1 (9) of moles of water liberated). Attempts to fit the ex- perimentaldata with Q termswhich were functionsof This value is shown in Table 2 along with the mole fractions (see also Nriagu, 1974;Nriagu and predicted AG10values for other clay minerals. Dell, 1974)resulted in dispersionswhich were either larger or comparable to those obtained with Equa- Discussion tion (3). Table 2 compares the predicted and experimental AG10values for the various clay minerals. The error Tesle l. Thermodynamic for Ions and Constants Compounds predicted have been as- Used in the calculatio" EnergvData for clav bounds for the AG10dala il,;li",I"" sessedby means of the expression: Error range lon, compouno AG;, kcal mol-l source t" - AGr,o""ot"r"r,)'l - l-(AGr,*or.,, (10) Hzo - 56.69 Wagmanet al., 1968 LmJ KOH -|4.6 See +ex+ NaOH -102.6 See iexf wherem is the number of listed data for the particular

Ca(OH)2 -2t4.22 Garrels and Christ, 1965 group of clay minerals. -202. t4g(OH)2 t2 Helgeson,1969 (Table 2) the predicted AG10value for Al (OH)3 -214.2 Kit+rick,1969 It is seen that -|8.5 Fe(OH) 2 See, Nriagu and Del l, 1974 kaolinite agreesquite well (+ 0.6 kcal fw-1; fw : for- Fe(0H)3 - |66.5 Wagmanet al., 1969 mula weight) with the experimental data. The agree- HqSi0a (arcrpho!s) -3| 8.6 Wagmanet al., 1968 ment between the predicted and experimental data

These da+a have been found to give the leasi deviaflon befween fhe for of * 2.0 kcal fw-' should be predicted and experimen+al ly deiermined free ene.gies of formatron considered excellent. The consistently poorer agree- 836 J. O. NRIAGU

TesI-e2. Predictedand ExperimentalFree EnergyValues for Clay Minerals

Clay lt4ineraI Chemical Composifion Predicted AG!, Reported AGi, kca| /fw kca| /fw

Kaolinite Al2Si205(OH)a - 903.8 - 903.0 (Baranayand Kelly, l96l) qO1.A - (Palzer ^nd Hom, 1965) - 903.8 (Kittrick, 1969) - 902.9 (Robieand Waldbaum,1968) - 904.0 (Reesmanand Keller, 1968) - 902.87Qen, 1972) - 902,1 (Huangand Keller, 1973)

Georgiankaol inite - - rl Al r, geMgo.o3S i 205(0H)4 904.3 903,5 (Caq. 'l Arizona montmoriI lonite 19Na6.02K0.02)(At l.s2FeEtr,+llgo.33) -t253.1 -1252,| (S i 3.e 3A | 6.s7 ) 01 e (OH )2 Wyomingmontmori (Cao. (At -t252.6 - rr I lonife rNao.rrKo. o2) ,. rrr"llrruso,r, I 1249,2

(Si 3.eaAl s. e5)016(0H)2 -1251.6 (R,lt4.Garrels, Pers. Comm.)

Aberdeenmonfmori I lonite (Al (Al r. zgMgo.,*,rsfef+,rrl o, IBSi 3,B2) 016(0H)2 - t224.6 -1225,2(Kittrick, l97l)

[49-montmoriI Ioniie ( -t254,7 -1255.8 Mgo.ro Si .. rrn t,. r, rel+22tv196.r, )0, o toH ), (Weaveret al., l97l)

N4g-montmoriI lonite N490,67Al 2. 335 i 3.670r0 (0H)2 - t218,8 -1275,3 (Helgeson, 1969) (beidelI ite)

Ca-montmoriI lon ite Cuo.r ozAIz. i (OH) -r280.8 -1219.2 (Helgeson, 1969) (beidelI ite) 33S 3.670ro 2

K-montmoriI loni-te Ko,::Alz. 35i toH), -t282,5 -1219.6 rl (beidelI ite) " ,..t0, o

Na-monfmoriI lonife (OH N"o.agAlz. 3 i ) -1279,5 -1271,g rl (beidelI ite) 3S 3.6701o 2 -1278.8 ([4,E, Thompson,Pers,Comm. ) BeaversBend itlite ( Ko. ) (A| -1254,6 -1250.5 eoNuo.o,* ,. u,FejlurMso.,, ) (Huangand Keller, t973) (S i 3.48AIs. 52)01 s (OH )2 BeaversBend Ko. (A (s s3 | ,. urr"f*rugo.I 3) i 3.62A| 0.38) -tzoY.t -1267,6 (Routsonand Kiftrick, l97t) 010(0H)2

Fithian illite K9.5,a(A (S | 1.5af.f+29Mgs,19 ) i 3.51A|6. a9) -t210,0 - |270.6 ', 010(0H)2

GooseLake illite K0. (A (S se | 1.5srefll2alags.1s) i 3.6sA|0.3s ) -1266.1 - 1265,3 rl 016(0H)2

lllite Ko. (OH) olt4go.zsA lz, 39Si 3, 56019 2 -ll0r,5 -1301.0(Helgeson, 1969) Mg-chlorife It4g54l25i3019(OH)s -t955.4 -1954.8 rl Chlorite re6212M9a.snl2s i 3010(oH ) I - t938.2 'Fo- -0.5 Mn Al ei n /n!\ - vr+5,"2', 3"10."",8 t912.1 (OH) Fe'' MgaAl2S i 301I g -t870.3

ment betweenthe predicteddata and the experimen- fw-1) between the predicted and experimental AG10 tal resultsof Huang and Keller (1973)should be values as do montmorillonites. It should have been noted;without their data,the agreementbetween the recognized that the "predictability" of the AG10data predictedand experimentalresults is better than 2 for these minerals is comparable to the accuracywith kcal fw-1.Illites show the samedisparity (+ 2.0kcal which these constants are experimentally "known." THERMOCHEMICAL APPROXIMATIONS FOR CLAY MINERALS 837

TesI-n 2, Continued

2+ 3+ (Mgz. -1326.9* - Vermiculite zrF"o. o2Fe0.46cao. ooKo. r o) (Si2. 91Al 1. 1a)016 (0H)2 (Mgr.,rFei-- ,+ - ?+ -137,-.6 * - orFej-u rCao. o:Ko. o r )

(Si2.e1Al 1. 1a )016(OH)2

5T -t361 Vermicullte (Mg3Fee.s) (Si2. e5Al 1. 1)0i6(OH)2 .9 (idealized focmula) 3+ 2+ rAveragermontmori -1261 -1260.6 xx I lon i te K6.a (Mgs. 34Fe9. 17Fe6. 64A | 1. 56) .4 (Alo, 175 i 3.s3)016 (OH)2 3+ 2+ rEnd -1289.0 -1291.8xx memberrillite Ks.a (Mgs, 34Fe6. 17Fe6. 0qA | 1. s0) (0H (A| 6.175 i 3.s 3 )01s )2 x These compositions correspond approxima+ely to those of Libby (Montana) vermiculifes reported by Boettcher (1968). rx Predicfed by the methodof Tardy and Garrels (1974).

The agreement between the predicted and ex- stantialdecreflse in the AGyoof the resultantchlorite perimental AGlo shown by the data in Table 2 is phase. rather remarkable considering (a) the wide range in Table 3 cofnparesthe predictedand experimental composition of the clay minerals representedand (b) LGf data for other layer silicates.Except for the the differencesin experimental techniquesused to ob- resultsof Beane(1973), the predicteddata are in good tain the listed data. There are also differencesin the agreementwith the experimentalAGro values. The methods of data interpretation. For example, Kit- "predictability" of the free energy data for these trick (1971), Routson and Kittrick (1971), and mineralsis about2.0 kcal mol-1, which is thesame as Weaver,Jackson, and Syers(1971) assumed that Fes+ for the clay rninerals.For greenaliteand ferric min- was conserved in their system as hematite. on the nesotaite,the presentmodel gives results which differ other hand, Huang and Keller (1973) believedthat from thosechlculated by the method of Tardy and most of the iron remained in solution as ferric hy- Garrels(197$; such a disparityis discussedbelow. droxide complexes.In this regard, it is worth men- The free dnergy data predicted by the present tioning that Helgeson(1969) compiled his AGlo values methodshould be usedas first approximations,to for the idealized clay minerals from the solubility be corrected as more experimentaldata become data in the literature. The small deviations between available.It cannot be usedto obtain the various the predicted and experimental data (differences in AG10for mineralswith the sameformula; for exam- methodology notwithstanding) lend considerablesup- ple, it cannot discriminatebetween the AGyovalues port to the suggested method for approximating for kaolinite. , and . In spite of the the AGlo values for clay minerals. short-coming,the dispersion of thedata in Table2 in- Few solubility measurements have been reported dicatesthat the predictedAGlo valuesare adequate from which AGy' for chlorites or vermiculites may be for: (a) evaluating the relative stabilities of clay derived. The AG10of magnesium chlorite calculated minerals;(b) assessingthe diageneticmodifications of by Helgeson (1969) from the reported solubilities of clay mineralsin soilsand sediments. chlorite and kaolinite in seawater is in good agree- ln a recentpaper, Tardy and Garrels(1974) have ment with the value predicted by the present method. presentedanother method for estimatingthe AGrofor The AG10values for ferromagnesium chlorites have layer silicates.Their methodis basedon the assump- been predicted and are shown in Table 2. Also given tion that eachsilicate can be representedas an ideal in Table 2 are the AG10values for vermiculites with solid solutionof oxide and hydroxidecomponents chemical compositions which are similar to the sam- which possessGibbs energiesof formationwithin the ples from Libby, Montana (seeBoettcher, 1968). Un- silicatestructures which are constantbut may differ fortunately there are no experimental data to check from AG10values assignedto the componentsas these predicted constants. Notice however that the separate phases. Their model thtis essentially substitutionof Fe2+for Mg2+ in chlorite causesa sub- operateson the oxidesand doesnot includethe cor- 838 J, O, NRIAGU

Tlnl-B 3. Comparisonof Experimentaland PredictedFree Energiesof Formation for SilicateMinerals

Pred i cted AG9 t Mineral Name Chemical composition kcal.mol-l Qannr*oA ^Co Ln^| mnI-I

Microcl i ne KAtSi308 - 892.8 - 892.817 (Robie and Waldbaum,1968) )+ Minnesotaite Fe3Sia016(OH)2 -t070.I -1069.9 (Melrnik, 1972) MgrSi u0ro (OH), -132t.o -lll9.0 (Hostetler et al., l97l) -1320.0 (Bricker et al.,1913) -1324.486(Robie and Waldbaum,1968) -1323.28 (Meltnik, 1912) ,+ Annite KFe!AlSi301o(0H)2 -|35.6 -1145.8 (Beane, 1973) )+ -t -1148.2 (Zen, KFe[ 3Fer.TAlSi30l2Hr. 7 t5t.2 1973) KMg3AlSi 301e(OH)2 - |]88 -1401.4 (Beane, 1973) x Mg2Si 305(OH ) 2 -t023.8 -t020.5 Chrysoti le Mg3Si205(OH)r+ - 963.8 - 965.11 (Melrnik, 1972) - 962.08 (Bricker et al., 1973) - 964.92 (Hostetler and Chris+, 1968) PyrophylI ite AlzSi'+Oro(OH)z -t26t.9 -1260.0 (Zen, Sef |, 1912) t+ GreenaI i te Fel Si205(OH)a - 7t3.A --720 xx Ferric minnesotaite Fe! Siu0ro(OH), -t046.5 - |055.0 xx

* Recalculated by Tardy and Garrels (1914) from the data of Chri st et al . , 1973. )r* Predic-fedbv Tardv and Garrels ( 1974) wi-fh fhelr method. rection (i.e., Q) term. On the other hand, my model present model. Thus one could write basically demonstratesthat the change in free energy Al,Oa + 3H,O: 2AI(OH)B (11) during the combination of metal hydroxides to form silicates plus water is usually small (except for the aG6o(Alro3) alkali metal hydroxides). : 2AG'0[AI(OH),] - 3AG/o(H,O)- q Superficially, it would appear that the major difference between the two models involves the : -379.5 kcal (r2) replacement of the "silication" energiesof Tardy and whereAGu' is the Gibbs energyof Alros boundin the Garrels (1974) by "hydroxylation" energies in the mineral lattice.By definition,

- Tnslr 4. Comparison of the Free Energy Data (For Silicate AGorva"o*"rrtioo: AGao AGro, (13) Minerals) Predicted in This Report with Those Cafculated by the Method of Tardy and Garrels (1974)* so that : -379.5 - (-378'1) (14) l{i ne.a I Name AG;, kc6l.1w-r AGuhvd.o*vr'ti.^

ardv -l'4 Thi s reportxi Exper i mentaI AGor"a.o*vtoti" :

Filhian i lite -t211.7 Beavers Bend illite -t214.1 Goose Lake illi+e -t212. I The AGro (Alros) is taken from Tardy and Garrels -t230.6 Aberdeen monircri I lonite (1914). Table 5 summarizesthe calculated hydroxyla- Bel le Fourche monim.t -1240.6 Average mon+rcrl I lonite tion energies for the other metal oxides. It becomes End member rcn+m. Clinochlore t96t. I immediately apparent that the differencebetween the Ann i te -t t5t.1 Greenal i+e two models is deeper than the mere replacement of Ferric minneso-faite the silication energy by hydroxylation energy. * The chemicalfomulae for these minerals are given in Tables 2 and J, For clay minerals, the two models give results unless specified otherwise. ** A correc+ion of -f.5 kcal. pe. mole of Al has been madefor species which are quite comparable (see Table 4). The AG10 containing aluminum;Tardy and carrels used +his correc+ion faclor fo. ihei. rcdel and in their recalcuia+ionof +he publishedexperimenial values for and ferric minnesotaite ob- resulls (lis+ed in-fheTable). + Basedon struc+ural formulaof H;.28[(All.5tsF";:225i4g6,29)(Al tained by the two methods differ appreciably (see (At o,o6ssi 3.e3s)olo (oH2l Tables 3 and 4). For each of the two mingrals, the diS- THERMOCHEMICAL APPROXIMATIONS FOR CLAY MINERALS 839

Tlrle 5. Hydroxylation and Silication Energies for the Metal Gennrrs, R. M., lNo C. L. Csnrsr (1965)Solutions, Minerals, and Oxides* Equilibria. Harper and Row, 450 p. HnI-cosoN, H. C. (1969) Thermodynamicsof hydrothermal AGohyd.oxy 2oH) systemsat elevatedtemperatures and pressures.Am. J.Sci.267, I ut i on( Per sr I tcaTton 729-804. Hosrrrun, P. B , eNo C. L. Csnrsr (1968)Studies in the system Kzo -95.9 -il t.0 MgO-SiOz-COz-HzO.I: The activity-productconstant of Na20 -58.1 - 72.6 14S0 - 9.1 - l3.l chryostile. Geochim.Cosmochim. Acta, 32, 482-497. Fe0 - 2.1 _ 4.0 -, J. J. Hnulnv, C. L. Cnxrsr,AND J. W. MoNrovl (1971) -t3.5 Ca0 -chrysotileequilibrium in aqueoussolutions. Geol. Soc. Am. A1203 - t.4 (-8.4)*x - 4.3 Abslr. Programs,3, 605. FezOg +t3.6 0.0 Hu,rNc, W. H., eNo W. D KELLER(1973) Gibbs freeenergies of - Si0z 1.4 0.0 formation calculated from dissolution data using specific HzO 0 - 2.5 mineral analyses-Ill: Clay minerals.Am. Mineral. 58, 1023-1028. * The si I ication energies I isted are from Tardy and Garrels KIrrnrcr, J. A. (1969)Soil minerals in theAtOg-SiOg-HrO system (1974). The hydrcxyla-l-ionenergies are based on the AG; da-i'efor the mej-al hydroxides tisted in Table l. and a theory of their formation. Clays Clay Minerals, 17, 157-167. x* The value in brackets includes the correction factor of - (1971)Stabiliry of montmorillonites-Il: Aberdeenmonr- 3.5 kcal for each mole of Al(0H)3. morillonite.Soi/ Sci. Soc.Am. Proc. 35,820-823. M er-'Ntr,Y . P. (1972)Thermodynamic constants for the analysis parity in the predicteddata is about twicethe differ- of conditionsof formation of iron ores.Inst. Geochem.Phys. ence between the silication and hydroxylation Minerals, Acad. Sci. Kiets, 193 p. energiesfor MgO in Table 5. It may be recalled, Nntncu, J. O. (1974)Lead orthophosphates-Iv:Formation and however,that Tardy and Garrels stability in the environment. Geochim.Cosmochim. Acta, 38, assumeda priori 887-898. that the hydroxyl ions of the layer silicateswere -, AND c. I. Drll (1974) Diageneticformation of iron derivedfrom Mg(OH)r. Wherethere is insufficientor phosphatesin recentsediments. Am. Mineral. 59,934-946. no Mg in the mineralcomposition to accountfor the PoLzER,W. L., rro J. D. Hrnr (1965)Dissolution of kaolinite.J. hydroxyl ions, their model calls for the appropriate Geophys.Res. 70, 6233-6240. RrrsurN, A. L., rNo W. D. KELLER(1968) amountof watermolecules to be includedin Aqueoussolubility the forma- studiesof high-aluminaand clay minerals.Am. Mineral. 35, tion reaction.Such a strategymay lead to inconsis- 929-941. tenciesas evidencedby substitutingthe listedvalues for Ronrr, R. A., ANDD. R. WILoSAUM(1968) Thermodynamic AGro,",,,""r"0,of Mg(OH), and MgO into the follow- propertiesof mineralsand relatedsubstances at 298.15oKand- ing equation one atmosphere(1.013 bars) pressure and at higher temperatures.U.S. Geol.Suru. Bull. 1259,255p. MgO+H,O=Mg(OH), (15) RoursoN, R. C., nuo J. A. Krrrnrcr (1971)Illite solubility..Sorl ,Sci.,Soc.Am. Proc.35. 715-718. The resultingAGro,"u,",r"a1 for water is -54.1 kcal, Trnoy, Y., eNo R. M. Gennrls (1974)A methodfor estimating whichmay be comparedwith the valueof -59.2 used the Gibbs energiesof formation of layer silicates. Geochim. in their calculation.Obviously experimental data will Cosmochim.Acta, 38. I101-1116. TILLER,E. (1968) be neededto decideas to which G. Stability of hectorite in weakly acid setof the predicted solutions-Il: Studiesof the chemicalequilibrium and the AGrovalues for greenaliteand ferric minnesotaiteis calculationof free energy.Clay Minerals,7,26L-27O. more nearly correct. Weculr.r,D. D., W. H. Evrxs, U. B. Penrrn, I. Hlr-ow, S. M. Berrrv, eNo R. H. ScHUMM(1968; 1969). Selected values of Acknowledgments chemical thermodynamic properties. Nat. Bur. Stand. Tech. Note 270-3(1968), 270-4 (1969). I thank Professor R. M. Garrels for generous his comments on Wrlvrn, R. M., M. L. JncrsoN, AND J. K. Svrns (1971) the manuscript. Magnesiumand siliconactivities in matrix solutionsof mont- References morillonite-containingsoils in relationto clay mineralstability. Soil Sci.Soc. Am. Proc.35,823-830. BneNn,R. (1973),cited in Y. Tardyand R. M. Garrels,1974. ZnN, E-ar (1972)Gibbs free energy, ethalpy, and entrophyof ten BoerrcHrn, A. L. (1968)Vermiculites, hydrobiotite, and biotitein rock forming minerals:Calculations, discrepancies, and impli- the Rainy Creekigneous complex near Libby, Montana.Clay cations.Am. Mineral. 57, 524-553. Minerals. 6. 283-296. - (1973) Thermochemicalparameters of minerals from Bnrcrnn,O. P., H. W. NEsBrrr,AND W. D. GuNrrn 0973)The oxygen-bufferedhydrothermal equilibrium data: method, ap- stability of talc. Am. Mineral. 58, U-72. plicationto anniteand almandine.Contrib. Mineral. Petrol.39, CHnrsr,p. L,, P. B. Hosrnrrnn,nr.rp R. M. Sresrnr(1923) Studies 65-80. in the systemMgO-SiO:-COr-HrO. lII. The activity-product Manuscript receiued,April I, 1974; accepted constantof sepiolite.Am. J. Sci.273, 65-83. for publication,May 6, 1975.