The k-Nacci Sequences in Some Special Modular Groups

American Mineralogist, Volume 78, pages 607-61 1, 1993 A resolution of discrepantthermodynamicproperties for chamositeretrieved from experimental and empirical techniques Pnrnn J. Slccocl.l.r* Wrlr-rlru E. Srvrnrno, Jn. Departmentof Geologyand Geophysics,University of Minnesota,Minneapolis,Minnesota55455,U.S.A. AssrRAcr An important deficiencyin the thermodynamic data for common rock-forming minerals involves chamosite,the Fe2* end-memberof chlorite solid solution. The AG3 and Al13 values for chamosite reported in the literature, as computed from both phase-equilibria data and empirical approaches,exhibit huge discrepanciesof up to 210 kJ/mol. A small portion of the discrepancy(5-100/o)is related to inconsistenciesin the Al referencestate chosen for the thermodynamic retrieval calculations. It is shown that the remainder can be assignedto an improper applicationof the van't Hoffrelationship to computestandardstate thermodynamic properties (25 "C, I bar) for chamosite from equilibrium constants derived from high-temperature(575-625'C) and high-pressure(2.07-6.00 kbar) phaseequilibria experiments.We have reinterpretedthese previously published experimental resultsby taking explicit accountofheat-capacityand entropydata for chamositepredicted from additivity models.Following this approach,we computeAG; and AfIi for chamosite of -6495.13 + 4.17 and -7101.91 + 4.17 kJ/mol, respectively, valuesthat are in excellent agreementwith those computed from empirical techniques,after inconsistencies reIated to the Al referencestate are taken into account. In this way, major discrepanciesin previously reported thermodynamic data for chamosite are resolved. INrnooucrroN Chlorite is one of the most common mineralsproduced in low- to moderate-grademetamorphic environments. The compositionalvariability exhibited by natural chlorites (Foster, 1962) probably records important information pertainingto the for, temperature,pressure,aqueous solution composition, and protolith composition in a particular metamorphic or hydrothermal setting (e.g., Albee, 1962; Walshe, 1986; Shikazonoand Kawahata, 1987).Therefore,accuratethermodynamic data for the componentsof chlorite are a prerequisiteto model quantitatively how such intensive variables affect chlorite composition. Thermodynamic propertiesfor the Mg component of chlorite (clinochlore) have been constrained adequately by numeroushigh-temperature(>400'C) and high-pressure (> I kbar) phase-equilibria studies. Consistency among the various solid-solidand dehydrationequilibria have been evaluated,and standard-statethermodynamic properties for clinochlore calculated, using curve fitting routines(Helgesonet al., 1978),linear mathematicalprogramming (Berman, 1988),and least-squares techniques (Holland and Powell, 1990). Reliablethermodynamicdata for the Fe2+component of chlorite (chamosite)are lacking, although a number of high-temperature and high-pressurephase-equilibria ex* Present address: Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543, U.S.A. 0003-004x/93l0s06-0607$02.00 periments involving Fe-rich chlorite have been performed (seeChernoskyet al., 1988,for a comprehensive review). In many of these studies,problems with metastability and a lack of information pertainingto chlorite composition in experiment products hampered a thermodynamic analysisof the experimentalresults.An exception are the chlorite oxidation and sulfidation experiments of Bryndzia and Scott (1987). Thermodynamic properties for chamosite retrieved by Bryndzia and Scott ( I 987) are shown in Table I , togetherwith those obtained from empirical estimationtechniques(Sverjensky,1985; Walshe, 1986)and natural Fe-Mg partitioning data (Holland and Powell, 1990).As originally indicatedby Cher(up to 2 l0 kJlmol) noskyet al. ( I 988),largediscrepancies exist between the AGi and A11; values obtained from the reversed phase-equilibria experiments of Bryndzia and Scott (1987)and thoseestimatedfrom various empirical approaches.Clearly, this level of uncertainty precludes reliable useof the chamositecomponentof chlorite solid solution in thermodynamic models of metamorphic or hydrothermal processesover a wide rangeof temperature and pressure.Thus, the purposeofthis paperis to review the possible sources of this important discrepancy and propose a resolution that brings into agreementthermodynamic data computed from phaseequilibria with those obtained from empirical estimation techniques. In this paper, the nomenclature for trioctahedral chlorites proposedby Bayliss(1975) has been adopted.Accordingly, the stoichiometryFerAlrSiro,o(OH), refersto chamosite 607 SACCOCIA AND SEYFRIED: CHAMOSITE THERMODYNAMIC 608 PROPERTIES TABLE1. Summaryof thermodynamicpropertiesfor chamositeat 298.15 K and 1 bar FesAlrSioO,o(OH)6 Chamosite: AGi (kJ/mol) s. AH? (kJ/mol) -6477.88' (-6490 88)t -6697.33+ 27 -6s34.36' -6486.46 (-6499.46)f (J/moUK) -7080.83 (-70s3.83)t -7222.84 + 46 -7148.44 Reference 596.22 Walshe(1986)" 594.96 r 54.4 559.00 BryndziaandScott(1987)+ Holland andPowell(1990)$ (1985)ll Sverlensky 'Calculated here from the correspondingvalues of AHi and S', together with S'data for the elements from Robie et al. (1979). .. The AH? calculated using the method of Tardy and Ganels (19741.S' value adopted by Walshe (1986) as taken from Helgesonet al. (1978)' t Values adiusted by -13.0 kJ/mol; see text for explanation. + Retrieved from reversed high I-P phase-equilibriaexperiments. $ Retrievedfrom natural Fe-Mg partitioningdata. ll Calculated using a linear free energy correlation technique that is equivalent to the terms "daphnite" and "14-A other data sets(Table l). Such an adjustment,however, daphnite" appearingin some thermodynamic data bases. can account for only 5-100/oof the total discrepancy. Moreover, the uncertainties associatedwith these estiSouncrs oF THE DTSCREPANCY mation techniques, beyond those related to thermodyA portion ofthe discrepancyshown in Table I can be namic referencestates,are thought to be on the order of attributed to the Al reference state selectedfor the ap- 4-8 kJ/mol (e.g.,Sverjensky,1985).Theseuncertainties proximation techniques.The AG; and AfIg estimated for are based on application of the estimation procedure to chamositeby Sverjensky(1985) and Walshe (1986) fol- predict AGgof solid phasesthat were not usedto calibrate low the Al referencestateof Helgesonet al. (1978),which the technique and that have AG; values already well eswas shown by Hemingway et al. (1982) to be in error by tablishedfrom phaseequilibria. Thus, the sourceof the approximately +6.5 kJlmol Al. As a consequence,the large discrepanciesin AG; and 4118for chamositecannot estimated values of AGPand Afli for chamosite must be be readily accountedfor by uncertainties associatedwith adjusted by -13.0 kJ/mol for proper comparison with thesepredictive schemes. An additional problem involves an improper application of the van't Hoff relationshipby Bryndzia and Scott 120 (19S7) to compute thermodynamicpropertiesfor cham1 bar osite at the referencecondition of 25 "C and I bar from 80 high temperarure(575-625 'C) and high-pressure(2.076.00 kbar) phase-equilibriumexperiments.In their approach, equilibrium constantswere retrieved from 57540 Y 625 "C at 1 bar for the following reaction: o E - + %O, Fe,AlrSirO,o(OH)8 0 chamosite oo o : fFerOo + AlrSiOs+ 2SiO, + 4H,O -4Q magnetite -80 -120 0 200 400 600 800 ('C) Temperature Fig. l. The ACg.. of Reaction I in text computed as a function of temperature. The ACg. is distinctly nonzero above 25 oC, consistent with a nonlinear dependenceof log K^ on temperature. For the solid phasesin Reaction I other than chamosite, requisiteheat-capacitydata were from Berman (1988).Heatcapacity data for HrO and O, ga.swere from Haar et al. (1984) and Kelley (1960), respectively.Sincecalorimetric data for pure iron chlorite are lacking, the heat capacity of chamosite was computed using the algorithm of Berman and Brown (1985). Ky-An-Si (l) qvrtz which describesoxidation of the chamosite component of chlorite solid solution.The van't Hoffrelationship was then used to calculateA11?for chamosite;that is, the standard molal enthalpy of Reaction l, A-F13,was assumed to be independent of temperature, and the standard molal heat capacity of Reaction l, ACB..,was assumed to be zero. Similarly, a AGg for chamositewas retrieved from a linear extrapolation of the standardmol'C. The al Gibbs free energy of Reaction l, LG?, to 25 primary shortcoming of this retrieval technique is that equilibrium constantsoften appear to be linearly dependent on temperature if a small enough temperature interval is considered, which could lead to large errors if the referencetemperature (25 "C) is far removed from the experimentalconditions.For example,an analysisof the SACCOCIA AND SEYFRIED: CHAMOSITE THERMODYNAMIC 609 PROPERTIES TABLE 2, Summary of experimental properties resultsfromBryndzia andScott(1987)usedinthispaperto reevaluate thermodynamic of chamosite Expt. Charge' 27A E 28A 268 30A 31 B A B 348 36A 41 428 438 B A B rrc) P(kbar) 600 600 600 600 600 600 600 600 600 600 600 575 575 600 625 2.O7 2.07 2.O7 6.00 6.00 6.00 6.00 6.00 6.00 600 6.00 4.50 4.50 5.00 5.50 log fo, X"^". -16.44 -16.44 - 16.44 - 16 . 4 1 - 16.41 - 16.41 - 16.41 -16.41 - 16.41 - 17.05 - 17.05 -17.23 -17 23 - 16.48 - 15.80 0.155 0.136 0.120 o.222 0.252 o.264 0.223 0.258 o_241 0.399 0.397 0.369 0.334 0.219 0.197 Productst log 4n".-- -4.22 -4.50 -4.66 -3.25 -3.04 -2.93 -3.24 -2.93 -3.09 -2.O1 -2.02 -2.24 -2.45 -3.30 -3.53 Chl-Qtz-An-Py-Po-Mt-Sp Chl-Tc-Usp-An-Py-PGMt-Sp Chl-Tc-Usp.An-Py-Po-Mt-Sp Chl-Qtz-Ky-Py-Po-Mt-Sp Ghl-Qtz-Ky-Py-Po-Mt-Sp Chl-Tc-Otz-Ky-Usp-Py-Po-Mt-Sp ChLQtz-Ky-Py-Po-Mt Chl-Tc-Qtz-Ky-Usp-Py-Po-Mt ChLQtz-Ky-Gh-Py-Po-Mt Chl-Qtz-Ky-Gh-Po-Mt Chl-Qtz-Ky-Gh-Po-Mt Chl-Otz-Si-Py-Po-Mt-Sp Chl-Qtz-Si-Py-Po-Mt-Sp Chl-Qtz-Si-Py-Po-Mt-Sp Chl-Otz-Si-Py-Po-Mt-Sp ' l n i t i acl h a r g e c o m p o s i t i o( A n )sF: e - C h+lQ t z + A l , S i O s + M t + P y + S p + 0 . 1 ( B; )M g - C h+l Q t z + A l , S i O s + M t + T r + S p + mHl solution 01mHl solution '. Activity of FesAl,Si3O,o(OH)s based on an ideal site mixing approach (see text for explanation). Ky, kyanite;Mt, magnetite;Po, pyrrhotite;Py, pyrite;Qtz, quartz; I Mineralabbreviations:An, andalusite;Chl, chlorite;Gh, gahnite/hercynite(ss); Si, sillimanite;Sp, sphalerite;Tc, talc; Tr, troilite;Usp, ulvospinel/magnetite(ss). AC3. of Reaction I indicatesthat the van't Hoffrelationship cannot be properly applied, sinceACg.,is distinctly nonzero and is a complex function of temperature(Fig. I ). The largeincreasein ACF..at 575 "C is a consequence of the tr transitionsexhibited by quartz and magnetiteat this temperature,causedby structural and magneticphase transitions,respectively(Berman, I 988). Furthermore,the effectof thesetr transitionson the thermodynamicproperties of Reaction I is magnifiedby reaction stoichiometry, sinceboth quartz and magnetiteappearon the same side ofthe reactionand have reactioncoefficientsgreater than unity. In view of the fact that Bryndzia and Scott (1987) investigateda small temperatureinterval (575625 "C), this heat-capacityanalysissuggeststhat misuse of the van't Hoff relationship may explain the grossly discrepantAG; and Al1; values for chamositeretrieved from experimentand empirical techniques. RuNrnnpnsrATroN EQUILIBRIUM oF pHASE knowledgeof the /o, and the activity of chamosite in chlorite solid solution at the termination of eachexperiment. In this study, chamositeactivities were evaluated by assumingideal site mixing of five Fe atoms and one Al atom over six octahedralsites in the chamositeformula unit (e.g.,Helgesonand Aagaard, 1985). A summary of experimentalresultsrequired for the calculation of Kr, is given in Table 2. Once K' has been determined, AG; and A,FI; values for chamositecan be retrieved from the solution of the familiar thermodynamicrelationships: AG: : -2.303Rf log K,, (3) AGr : (4) ? n,aG7, AG7: 66"rr.h"- + ^S.(f - 7".) c B d z +r RESULTS A more rigorous retrieval of AGg and A.F1;values for chamositecan be made by taking into account,explicitly, the heat capacity of chamositepredicted with the algorithm of Berman and Brown (1985). On the basis of a standardstateof unit activity of the pure solid and HrO at the temperatureand pressureof interest and on unit fugacity of the hypothetical ideal gas at I bar and the temperature of interest, the equilibrium constant for Reaction I at the temperature and pressureof interest (K.r) can be written as: log Kr, : 4 log eszo - 5/6log fo, - log 4.n"-. (2) Sincethe aqueousphasein theseexperimentswas dilute (distilled H,O and 0.10 m HI solutions),the activity of HrO can be closelyapproximatedas unity (Helgesonet al., l98l). Valuesof Kr, can thereforebe computedfrom AH?: AGfl + ..A,SP [',anr_ w ( P -P , ) ( s ) (6) where n, is the reaction coefficientof the rlh species,which is positive for productsand negativefor reactants,A@" is the apparent standard Gibbs free energy of formation of i at the temperatureand pressureof interest, following the conventions of Benson (1968) and Helgesonet al. ( I 978), and S', V' , and Cg are the standard molal entropy, volume, and heat capacityof chamositeat the referencetemperature(I.) and pressure(P.) of 298.15 K and I bar, respectively.Thus, in addition to the CF of chamosite, the only information required is AG7" values for the other product and reactant speciesin Reaction I and V. and S. data for chamosite (Table 3). Supporting AGi, values were computed using thermodynamic data from Berman(1988)for quartz,magnetite,and the AlrSiO5 polymorphs,Haar et al. (1984)for H,O, and Kelley (1960) SACCOCIA AND SEYFRIED: CHAMOSITE THERMODYNAMIC 610 -6400 TABLE3. Values of y", S", and Cg coefficients.used in this study to compute AGi and LH? tot chamositefrom experimentsof Bryndzia the high I-P phase-equilibria and Scott (1987) vo 21.34 Jlbal S" 583.20J/mol/K ko 1229.233 o E -6800 ? oF- and Wagmanet al. (1982)for O, gas.Tl;,eV" of chamosite is well establishedfrom measurementsof unit-cell parameters(e.g.,McOnie et al., 1975).Owing to a lack of phase-equilibria constraints over a wide rangeof temperature, it was necessaryto estimate S' for chamosite from the additivity model of Holland (1989). Following this approach, an S" of 542 J/mol/K is computed that representsthe calorimetric and magneticcontribution but does not include provisions for site configurational entropy terms. Sincethe degreeof order in chamositeis not presently well established,we have elected to add the ideal configurationalentropy for chamosite(41.2 J/mol/K) to the calorimetric contribution; that is, we assumecomplete disorder. Although direct analogies cannot necessarily be drawn to the Mg componentof chlorite, a comparison of the ,S"for clinochlore regressedfrom a large number of phase-equilibriaexperimentswith the calorimetric value doesindicate substantialdisorder(Berman, I 988). The resultsof our thermodynamic analysisof the phaseequilibrium data of Bryndzia and Scott (1987) are outlined in Table 4. Reinterpretedin this way, the data yield AG; and Aflp valuesfor chamositeof -6495.13 + 4.17 valuesthat and -7101.97 + 4.17 kJ/mol, respectively, are in excellentagreementwith those computed from various empirical techniques,after corrections related to the Al referencestateare considered(Fig. 2). Such agreement is encouraging and strongly suggeststhat the large discrepanciesin AG; and A11;values for chamositereported in the literature are related to heat-capacityeffects.The Chamosite 1 bar -6600 k, -102.565 x 10'z k2 -122.769 x 10u k3 212.151 x 1O' * For cafcufationof heat capacity in J/mol/K from CB : ko'r k,T 05 + k2T-2+ k3T 3. CBcoefficientswere computed using the algorithm of Berman and Brown (1985).See text for sourceof y'and S'data- PROPERTIES <l -7000 l-This Study O Walshe(1986) -7200 '\ A Sverjensky (1985) ' "" Holland andPowell(1990) A Bryndzia andScott(1987) -7400 200 400 600 800 (oC) Temperature Fig. 2. Summary of AGi, values for chamosite (at 25 "C, AG9., is equivalent to AGF). The approach taken in this study was to first compute AGir for chamositeal 575-625'C (solid circles)from the experimentaldata ofBryndzia and Scott(1987). A AG3 could then be computed by taking into account S" and Cg data for chamosite determined from additivity models. The resulting free energy function is shown by the solid line. Note the excellent agreement between the results of this study and AGg values computed from various empirical techniques,after adjustments related to the Al referencestate are taken into account. results also serve to emphasize the utility of adopting heat-capacity and entropy data predicted from additivity models when direct constraints from calorimetry are absent. Some disagreement still exists, however, between the results of this study and AGi, values predicted using the chamosite (daphnite) data from Holland and Powell (1990), which are based on natural Fe-Mg exchange equi- experiments TABLE 4, Summaryof thermodynamicpropertiesfor chamositeretrievedin this study from the high I-Pphase-equilibria of Bryndziaand Scott (1987) r('C) P(kbar) 575 600 600 600 62s 4.50 2.o7 5.00 6 00 5.50 l.o9 K,." 16.71+ 0.15 18.16+ 0.22 17.03 16.62+ 0.27 16.69 AGP-* -271.99 + 2.49 -303.59 + 3.68 -284.68 -277.86.+ 4.52 -287.02 AG?"'t -6959.54 + 2.43 -703703 + 3.68 -6975.86 -6356.95 + 4.52 -699s.94 aHi.,ll Acp. $ -6501.35+ -7055.55 + 2.43 -6492.94 + -7081.18 + 3.68 -6494.28 -7082.54 -6496.71 + -7084.97 + 4.52 -6490.35 -7113.29 Averaoe: -6495.13 + 2.43 3.68 4.52 4'17 -7108.19+ 2.43 -709978 + 3'68 -7101'12 -7103.55 +4'52 -7097.19 -71A1.97 + 4.17 . Values are in kJ/mol. .. Standard molal Gibbs free energy of Reaction 1 at T and P. t Apparent standard molal Gibbs free energy of formation of chamosite at T and P. y'(P - 0.001) from AG?', where * Abbarent standard molal Gibbs tree energ! of formation of chamosite at f and 1 bar calculatedby subtracting y" is the standardmolalvolumeof chamositeat 298.15K and 1 bar (21.34kJ/kbar). g Standard molal Gibbs free energy of formation of chamosite from the elementsat 298.15 K and 1 bar. -2035.35 J/mol/K, ;i StanOarOmolal enthalpy ot tormition of chamosite from the elements at 298.15 K and 1 bar, consistent with a AS? value of which was comouted from tire estimated S. of chamosite in Table 3 and S'data for the elements from Robie et al. (1979). SACCOCIA AND SEYFRIED: CHAMOSITE THERMODYNAMIC libria (Fig. 2). It is interesting to note that the two data sets agree reasonably well at high temperatures but divergeas the referencecondition (25'C) is approached,a result that can be largely attributed to differencesin the S" values adopted for chamosite. In effect,the smaller S" for chamosite(559.0 J/mol/K) reported by Holland and Powell (1990) implies a more ordered crystal structure and leadsto a lesssteepdependenceof AGi, on temperature. CoNcr-uorNc REMARKS The thermodynamic properties for chamosite derived in this study will undoubtedly require further refinement as additional phase-equilibriaand calorimetry data become available.In particular, additional constraintson the magnitude of the configurational contribution to S" for chamositeare needed,and the assumption of ideal mixing of atoms on sitesin chlorite requiresfurther testing. Nevertheless,the resolutionoflarge discrepancies in AGg and AtI; for chamositeproposedhere will greatly increasethe accuracyof thermodynamicmodelsof metamorphic and hydrothermal settingswhere chlorite solid solution is a ubiquitous phase.In this regard,it should be emphasizedthat the retrievalcalculationsin this study relied upon supportingthermodynamicdata for minerals from Berman( I 988) and, therefore,the resultingAG3and 4113values for chamositeshould only be used with this data base.If the retrievalcalculationsare performedwith supporting thermodynamic data for minerals from Helgesonet al. (1978),the AGf and A1l; valuesfor chamositeare -6491.56 + 6.95 and -7098.41 + 6.95 kJlmol, respectively. AcxNowr,nocMENTS We thank Mark Ghiorso and an anonymousreviewer for critical comments, which significantlyimproved this paper This study was supported by NSF grant OCE-8817341to W.E.S.and representsa portion of the first author's Ph.D dissertation. RrrnnnNcns cITED Albee, A.L (1962) Relationshipsbetweenthe mineral association,chemical composition and physical properties ofthe chlorire series.American Mineralogist,47, 85 | -870. Bayliss, P. (1975) Nomenclature ofthe trioctahedral chlorites. Canadian Mineralogist, 13, 178- 180. Benson,S.W. (1968)Thermochemicalkinetics,223 p.Wlley, New York. Berman, R.G (1988) Internally-consistentthermodynamic data for minerals in the systemNa,O-K,O-CaO-MgO-FeO-Fe,O.-AI,O.-SiO.-TiO.H.O-COr. Journal of Petrology, 29, 445-522. Berman,R.G., and Brown, T.H. (1985)Heat capacityof mineralsin the system Na,O-K,O-CaO-MgO-FeO-Fe,O,-Al,Or-SiOr-TiOr-H.O-CO,: Representation,estimation, and high temperatureextrapolation. Contributionsto Mineralogyand Petrology,89, 168-183. Bryndzia, L.T., and Scott, S.D. (1987) The cornposirion of chlorite as a PROPERTIES 6ll function ofsulfur and oxygen fugacity: An experimental study. American Journal of Science,287, 50-7 6. Chernosky,J V, Berman, R.G., and Bryndzia, L.T. (1988) Stability, phase relations, and thermodynamic properties ofchlorite and serpentinegroup minerals. In Mineralogical Societyof America Reviews in Mineralogy, 19,29s-346. Foster, M.D. (1962) Interpretation ofthe composition and a classification of the chlorites. United StatesGeological Survey ProfessionalPaper, 414-4,33p. Haar, L., Gallagher, J., and Kell, G. (1984) NBS/NRC steam tables. Hemisphere,Washington, DC. Helgeson, H.C., and Aagaard, P. (1985) Activity/composition relations among silicatesand aqueoussolutions.L Thermodynamics of intrasite mixing and substitutional order/disorder in minerals American Journal of Science.285- 7 69-844. Helgeson,H.C., Delaney,J.M, Nesbitt, H.W., and Bird, D.K. (1978) Summary and critique of the thermodynamic propertiesof rock-forming minerals. American Journal of Science,278-4, l-229. Helgeson,H.C., Kirkham, D.H., and Flowers,G.C. (1981) Theoretical prediction of the thermodynamic behavior of aqueouselectrolytesat high pressuresand temperatures. IV. Calculation of activity coefficients, osmotic coefficients,and apparent molal and standard and relative partial molal properties to 600"C and 5Kb. American Journal of Science.281. 1249-1516. Hemingway,B.S.,Haas,J.L., and Robinson,G.R. (1982)Thermodynamic properties of selectedminerals in the system AlOr-CaO-SiO;HrO at298.15 K and I bar (105pascals)pressureand at higher temperatures. United StatesGeological Survey Bulletin, 1544,70 p. Holland, T.J.B. (1989) Dependenceofentropy on volume for silicate and oxide minerals: A review and a predictive model. American Mineralogist,74,5-13 Holland, T.J.B., and Powell, R. (1990) An enlargedand updated internally consistentthermodynamic dataset with uncertaintiesand conelations: The system KrO-Na,O-CaO-MgO-MnO-FeO-Fe,O.-Al,O,TiO,-SiO.-C-Hr-O,.Joumal of MetamorphicGeology,8, 89-124. Kelley, K.K. (1960) Contributions to the data in theoretical metallurgy XIII. High temperatureheat content, heat capacitiesand entropy data for the elements and inorganic compounds. United States Bureau of Mines Bulletin, 584,232 p. McOnie, AW., Fawcett,J.J., and James,R.S. (1975) The stability of intermediate chlorites ofthe clinochlore-daphniteseriesat 2 kbar P,,o American Mineralogist, 60, 1047- 1062. Robie, R.A., Hemingway,B S., and Fisher,J.R. (1979)Thermodynamic properties of minerals and related substancesaf 298.15 K and I bar (105pascals)pressureand at higher temperatures.United StatesGeologicalSurveyBulletin, 1452,455p. Shikazono,N., and Kawahata,H. (1987) Compositionaldifferencesin chlorite from hydrothermally altered rocks and hydrothermal ore deposits. Canadian Mineralogist, 25, 465-474. Sverjensky,D.A. (1985) The distributlon ofdivalent trace elementsbetween sulfides, oxides, silicates and hydrothermal solutions. I. Thermodynamicbasis.Geochimicaet CosmochimicaActa, 49, 853-864 Tardy, Y., and Garrels, R.M. (1974) A method of estimating the Gibbs energiesof formation of layer srlicates.Geochimica et Cosmochimica A c t a .3 8 . I l 0 l - l I 1 6 . Wagman,D.D, Evans,W.H., Parker,V.8., Schumm, R.H., Halow, I., Bailey,S.M., Churney,K.L, and Nutall, R.L. (1982)The NBS tables of chemical and thermodynamic properties. Journal of Physical and Chemical ReferenceData, 11,392 p. Walshe, J.L. (1986) A six-component chlorite solid solution model and the conditions of chlorite formation in hydrothermal and geothermal systems.EconomicGeology,81, 681-703. Apnrr 6, 1992 Maruscnrsr RECETvED Meroscmsr ACcEFTED JeNurny 15, 1993