American Mineralogist.Volume 78, pages68 I-693, 1993

Geothermobarometryin pelitic schists:A rapidly eyolyingfieldx

M. J. Hor,o,q.wav, Brsw.l;rr MuxrroploHyAy Department of Geological Sciences,Southern Methodist University, Dallas, Texas 75275, U.S.A.

Ansrnrcr The study of pelitic rocks for the purpose of deciphering pressure-temperature(P-Z) information is an important area for collaboration betweenmineralogists and petrologists. Accurate geothermobarometryis especiallyimportant for studiesof pressure-temperature- time paths of terranesduring tectonism and for studies of the movement of metamorphic fluids. During the past decade, new developments have included thermodynamic data bases,sophisticated crystal structure determinations and associatedsite assignments,and analysesfor Fe3+ and light elements (especially H and Li) for many within a petrogeneticcontext. It is now necessaryto apply thesenew findings to geothermobarome- try in several important ways: (l) The stoichiometric basis for hydrous minerals should be revised in light of highly variable H and variable Fe3*, which can now be estimated with considerableaccuracy as a function of grade or assemblage.(2) Mole fraction (activity) models should be based on the best crystal chemical considerations.For some minerals, H may be omitted from the model if all the substitutionsinvolving H are coupled substitutions. (3) Thermodynamic data should be basedon careful analysisof all available experiments and secondarycomparison with natural assemblages.(4) The possibility of nonideal solid solution should be considered,as ideality is merely a specialcase of nonide- ality. It is better to estimate binary interaction parameters than to assumethat they are zero. However, it is difficult to determine ternary interaction parameters.In such cases, little error is likely to result from assumingthat strictly ternary interaction parametersare zero, while evaluating all the binary terms. Our understanding of and solu- tions has improved, and the garnet-biotite geothermometerhas undergonenumerous re- finements, but additional information on theseminerals and improvements in the garnet- biotite thermometer are still necessary. As the P and ?"determinations become more precise,we can better evaluate Xnro, X"o, and X.ro in the fluid phase. In all probability, patterns will be discovered in the compo- sitions of pelitic metamorphic fluids, especially when graphite is present. The hematite- ilmenite solid solution system is potentially useful for determining .fo2,oree the solvus is better understood. In graphitic rocks at known P and T, knowledge of /o, from coexisting hemoilmenite and rutile or hemoilmenite and magnetite enables one to determine the mole fraction of all fluid species. Careful application of the present state of knowledge,combined with modest improve- ments, should allow accuracyapproaching +250 bars and +25 "C in rocks formed at low to moderate pressures.It is very important to continue to revise thermochemical data, activity models, Margules parameters,and stoichiometric information, and it is equally important for petrologistsand tectonicists to make use of these revisions as they become available.

INrnooucrroN if we are not continually watching for them and correcting possible, get preci- In recent years, we have become concernedabout the them wherever we will not the best simplified view taken by some petrologists and tectoni- sion, especiallyin the P-T ratge outside of the range of cists regardingquantitative estimation of the pressureand calibration. This is an ideal area for collaboration be- temperature of formation of metamorphic rocks. There tween mineralogists and petrologists. Mineralogists pro- are many possiblesources of error in this procedure,and, vide valuable information on mineral structure and site assignments,and petrologistsapply the results to activity models. Both mineralogists and petrologists are making t This report is a revised, expanded version of the Mineral- ogical Society of America Presidential Address given by M.J. important contributions to careful, complete chemical Holdaway at the Geological Societyof America Meeting in Cin- analysis of common metamorphic minerals. cinnati, Ohio, on October 27, 1992. Interesting work is being done on pressure-tempera- 0003-004x/93l0708-o68I $02.00 681 682 HOLDAWAY AND MUKHOPADHYAY: GEOTHERMOBAROMETRY IN PELITES

P difference between these two estimates is 450/oof the lower value. Here we review the processof P, T, and X"ro estima- tion, focusing on five important areas:(l) determination of mineral stoichiometry, (2) mineral mole fraction (ac- o tivity) models, using the mixing-on-sites model, (3) non- E (4) and use o ideality in mineral solid solutions, derivation U) -6 of thermodynamic data, and (5) fluid composition and o petrologists carefully consider c its use to test results. If E l what is known in eachofthese areasand continue to heed z developmentsas they becameavailable, we will converge on a consistent P-T-Xtro grid for all metamorphic ter- ranes and grades.In our analysis, we will focus on me- dium-grade pelitic , but some of what we have to say is equally applicable to other gradesor bulk compositions. The major silicate minerals we will be dis- Wt.%Water cussing are muscovite, biotite, garnet, staurolite, cordi- Fig. 1. Histogramof H.O contentof all muscoviteand bio- erite, aluminum silicates, and chlorite; the Fe-Ti oxides tite samplesanalyzed by M.D. Dyar.After Dyaret al. (1993), and rutile, as well as reprintedwith the kind permissionof PergamonPress. ilmenite, hematite, magnetite, graphite, will also come up for discussion.We will con- sider mainly the dominant mineral end-membersand will ture-time paths (e.9.,Spear and Selverstone,1983) and not be consideringsulfide equilibria. The effectsofsulflde on fluid composition and movement in metamorphic ter- on Xrro in medium-grade reduced pelites can be ignored ranes(e.9., Ferry and Dipple, l99l). There are also sig- ifthe sulfideis pyrrohotite and not pyrite (Shi, 1992). nificant controversies over how much P-Z information MrNsnAl, SToICHIoMETRY one can learn from zoned minerals (e.g.,Frost and Tracy, 1991) and how much fluid actually passedthrough the Extensiveand, commonly, exclusiveuse of the electron rocks (e.g.,Gray et al., l99l). The quality of the results microprobe for mineral analysis has left us short on im- of many of these studies may well be only as good as the portant data for many minerals, especiallyhydrous ones. quality of the geothermobarometryused. Only when sig- In many studies, mineral chemistry is based on micro- nificant improvementsare made to the accuracyof P-T probe data alone. The resultant shortcomings include a determination will we possibly be able to answer these lack of data for Fe3+/(Fe2++ Fe'*) and a lack of light- questions. That alone is an important justification for elementanalyses, such as H, Li, B, and Be, on minerals continuing our efforts to improve geothermobarometry. as diverse as micas, chlorite, staurolite, garnet, and tour- To illustrate the seriousnessof the problem, we com- maline. In this list all may contain significant amounts of pare two recent studiesinvolving geothermobarometryin Fe3+,all but garnethave variable H, biotite and staurolite pelitic rocks. In Acadian M3 in Maine and in the Dela- may have significant Li, and tourmaline has variable B merian of South Australia. near Adelaide. isobaric ther- (Dyar et a1.,1992,1993; Holdaway et al., 1986a,1986b; mal metamorphism produces assemblagescontaining Dutrow et al., 1986). The assumptionof ideal or zero staurolite * andalusite followed by sillimanite at higher content of light elementsand zero Fe3* may have pro- grade. In both areasthe appearanceof sillimanite corre- ducedinaccurate stoichiometry, and it has precludedthe sponds approximately to the disappearanceof both an- possibility of several important substitutions that are dalusite and staurolite. In both areas,cordierite is locally coupledwith thoseof major elements.Depending on the present,probably becauseofan earlier, lower-P subevent, mineral, the H content of hydrous minerals may be a a local decreasein P, or a differencein bulk composition. function of metamorphic grade,of mineral assemblage, All petrologic evidenceindicates that thesetwo localities or both. With light-elementand Fe3* analyticaldata for have enjoyed about the same P-T conditions. Average representativeminerals, we can make appropriatecorrec- metamorphic conditions for the staurolite-bearingrocks tions to the stoichiometricbasis. Here we summarizewhat p":+1 deducedby Holdaway et al. (1988) for Maine M3 are P we know about Fe3*/(Fe2+* and light elements, : 3.1 kbar, T : 531 'C; conditionsdeduced by Dymoke how they affect stoichiometry,and possiblesite assign- and Sandiford (1992\ for the Delameriannear Adelaide mentsfor Fe3*. are P : 4.5 kbar, T : 594 oC, corresponding to an ap- parent P difference of 1.4 kbar or a depth difference of Muscovite nearly 5 km. Whereaspetrologists who work in rocks at Muscovite suffers from two compositional problems. higher P and I might not consider these to be serious (l) Preliminary Mdssbauerstudy (M. D. Dyar, unpub- differences, we believe it should be possible to obtain lished data) shows that half to two-thirds of the Fe in much greater accuracyin low- to moderate-P rocks than muscovite is Fe3+.Except for highly oxidized, Iow-grade, is implied by this comparison. It is worth noting that the or high-P rocks, this efect can be ignored becauseit has HOLDAWAY AND MUKHOPADHYAY: GEOTHERMOBAROMETRY IN PELITES 683

TABLE1. HrO content of Maine peliticmicas as a functionof Trale 2. Stoichiometryof micas,specimen 143' grade- Muscovite.* Biotitel

Muscovite No H, Fe3* No H, Fe3* Average Average correction corrected correction corrected (%) ('/") No. No. rrlSi 3 034 3 076 2.666 2.696 Garnet 8 3.54 0 86 16 4.52 0.30 rrlAl 0.966 0.924 1.334 1.201 Staurolite 10 3.78 0.39 10 4.16 0.47 rrlFe3r 0.000 0.000 0.000 0 103 Sillimanite 26 4.06 0.35 29 3.83 0 35 rMrAl 1.866 1.947 0 390 0.542 Ksp-Sil-Mus 4 3.84 020 5 3.21 0.30 rMtTi 0.038 0.039 0 173 0.175 Atl 48 3.90 0.49 60 4.02 0.51 rMtFe2+ 0.060 0.031 1.277 1.136 rMtFes+ 0.000 0.030 0.000 0.052 . Data of Dyar et al. (1993and unpublisheddata) lutMg 0.05s 0.056 0.952 0.963 tMtMn 0 001 0 001 0.011 0.011 rM1! 0.980 0.896 0197 0.121 ratK 0.917 0.930 0.971 0 982 IAINa 0.064 0.065 0 018 0.018 a trivial effect on stoichiometry and activity. (2) Dyar et OH 2.000 1.666 2 000 1.602 al. (1993and unpublisheddata) have determined the HrO Mole fraction+ 0 781 0.785 0.066 0.044 content of 48 pelitic muscovitesamples from Maine that 'Holdaway et al. (1988) F neglected. show a range from 2.5 Lo 4.8o/oHrO. Data for all the .* Assumesall IMrAI is on M2, all IMrnis on M1i tor correctedvalues, half biotite and muscovite samplesthey have analyzedare of Fe is Fe3* t Assumingdisorder of all specieson M1 and M2, Guidottiand Dyar summarizedin Figure l; the two minerals have similar (1991)Fe3+. rangesof HrO content. There is a generalpositive rela- t See Table 4 for mole fraction models. Biotite mole fractions are for tionship betweenHrO content and gradefor muscovite, annite with a slight decreaseat the highestgrade (Table 1).Note however, that most pelitic muscovite has less than the stoichiometricvalue of 4.5o/oHrO. This is also important titatively significant amounts of Li, as shown by Dutrow becauseit may affectthe nature of ionic substitutionsin et al. (1986)and Dyar etal. (1992and unpublisheddata). muscovite.For a muscovite in the potassiumfeldspar- This effect can commonly be ignored but may be the sillimanite-muscovite zone, estimating3.80/o HrO from cause of P-I discrepanciesin individual specimens.(3) the resultsofDyar et al. (1993and unpublisheddata) has According to the work of Dyar et al. (1993 and unpub- a small effecton the stoichiometry(Table 2). For a mi- lished data) on 60 specimens,pelitic biotite rangesbe- croprobe analysis,with O substitutingfor OH , the O tween 2.9 and 5.2o/oin HrO, whereasthe ideal value is basisbecomes I 1.15 insteadof I 1, slightly increasingthe 4o/o.As with muscovite,that affectsthe nature of ionic total cationic content. The H* deficiencymay compen- substitutions.Biotite shows a negativerelationship be- sate for excesscharge in the octahedrallayer over that tween HrO content and grade (Table l). For a biotite necessaryto chargebalance the tetrahedrallayer. F con- samplein the potassiumfeldspar-sillimanite-muscovite tents of muscoviteare low and insufficientto explain the zone, Dyar's averageHrO content of 3.2o/oincreases the H* variations (Dyar et al., 1993 and unpublisheddata). O basisto I 1.2,increases the content ofcations, and re- Correctingfor H and Fe3+increases activity slightly (Ta- ducesthe vacancycontent of the octahedralsites (Table ble 2). 2). The deficiencyof H in many pelitic biotite samples cannot be explainedby F (Dyar et al., 1992and unpub- Biotite lished data) but may compensatefor increasedcharge of Metamorphic biotite hasthree problems associatedwith Fe3*, Al, and Ti in the octahedralsites above that bal- composition. (l) An pelitic biotite that grew under re- ancedby tetrahedralsubstitution (Dyar et al., 1993).In duced conditions with graphite and ilmenite has about this case,note that making correctionsfor H and Fe3* l2oloof Fe as Fe3*,as shownby wet-chemicaland Moss- reducesactivity substantially,mainly becauseof the effect bauer studies.Guidotti and Dyar (1991) interpretedthe of Fe3*. Miissbauer spectraon reducedpelitic biotite from Maine to indicate on average80/o of the ps 4s t+lps:+and 4oloas Staurolite I6lFe3+.Both the amount and the siteassignments for Fe3+ Work on staurolite shows that determination of stau- in these pelitic biotite samples (Dyar, 1990) have been rolite stoichiometry suffers from the same problems as questionedby Rancourt etal. (1992) in a study ofbiotite biotite. (l) Staurolite that grew under reducing conditions of different composition and origin. However, Dyar (1993) containson average3.50/o of the Fe as Fe3* (Dyar et al., pointed out that detection oft4lFe3+requires random ori- l99l; Holdaway et al., 1991),probably in the tarFe(T2) entation in micas, I41Fe3+has often been identified in bi- sites.(2) Most staurolite containsLi (Dutrow et al., 1986), otite and other phyllosilicates,and the Fel;f has been con- and in the absenceof a Li analysis or evidence of high firmed by many independent wet-chemical studies, such Li, it is best to assumethe averagevalue of 0.2 Li ions as that of Williams and Grambling (1990). Guidotti's to avoid systematicerrors (Holdaway et al., l99l). Better (1984) review of chemistry of pelitic biotite also showed yet, representative specimensfrom a telTane should be substantial Fe3*. (2) A few biotite samplescontain quan- analyzed for Li with the ion microprobe or proton-in- 684 HOLDAWAY AND MUKHOPADHYAY: GEOTHERMOBAROMETRY IN PELITES

Trele 3. Stoichiometryof natural staurolite samples at ex- Moln FRAcrroN MoDELS tremesof H content. The proper choice of a mole fraction (activity) model 3-3 71-627 is crucial for all subsequentcalculations. The best possi- rMltAl 7.70 7.70 ble choice of models is always a problem, and it is im- tM1lR2+ 030 0.30 portant to be as correct as possible. Also, petrologists IMrtAl 779 7.79 should acceptthe fact that as our understandingof crystal {Mrr(Rr+ ,Ti) 0.21 0.21 rM3tAl 187 1.59 structure, site assignments,and composition improves, rM3t(R,ts,n) 0.13 0.41 we must continue to allow activity models to evolve. A lM4lFe2+ 002 051 points (l) {M4r(Zn,Li,!) 1.98 149 number of important are as follows: It is better rrltSi 763 to make an incorrect decision on disorder or even site rrltAl 0.37 041 assignmentthan to make an error that renders the activ- tr2tFe2+ 3.01 218 rr4(Rr+, R3+,Li,!)** 0.99 192 ity model inconsistent. For example, both the mole frac- H 2.68 4.56 tion basis of an ion and its exponentmust be the same -%Li+2/sTi+Fe3+ si +Al 25.53 25.38 number. The equation for mole fraction must flt the . Analyticaldata from Holdawayet al (1986b)and Dyar et al. (1991), model. (2) Care should be taken to avoid accounting for site assignmentsfrom a model based on Hawthorneet al. (1993a)and two substitutions when the ions are individually coupled Holdawayet al (1991),modified by Holdawayet al. (in preparation). .'ExcludingFe'z+. by charge balance constraints. In staurolite, H substitu- tion is alwayscoupled to other major substitutions.(3) If a given model was necessaryfor retrieval of thermody- duced 7 emission.(3) Staurolitehas variable HrO con- namic data, then that model, if reasonable,should also tent. That which occurs with biotite or garnet has about be used for geothermobarometry. (4) Any mineral that 3 H+ pfu, whereasthat which occurs with aluminum sil- has two or more independent sites also has the potential icate and no biotite or garnet has about 4 H+ pfu (Hol- for site interaction energies.When we ignore this possi- dawayet al., 1986a;Dyar et al., 1991).This observation bility, we are assuming these energiesare zero. Even if can be used to determine the stoichiometry of staurolite mixing on the independent sites is ideal, this cross-site that occurs with in the absenceof a HrO analysis, interaction can have an efect on the mole fraction cal- but in our opinion it is better to take advantage of the culation. (5) In most cases,it is not yet possibleto test constancyof Si + Al and normalize the stoichiometry to alternative mole fraction models, although more such ef- Si + Al - VtLi + 2/tTi + Fer+ : 25.55 (Holdawayet al., forts should be attempted. With thesepoints in mind, we 1991;Table 3, this report). This approachpreserves the present possible models for some of the common min- constancy of Si and Al while correcting for the minor erals (Table 4). substitutions in natural staurolite that involve Si and Al. Activity models for micas are still very much open to With this approach, subtraction of the total cation charge question; the ones presentedhere are simply reasonable from 96 estimatesH+ within about I pfu. Either of these approximations. We assume octahedral sites in biotite approachesis significantly better than the previously used are disordered. This is-supportedby the lack ofcontrary method of assumingeither 2 or 4 H pfu. X-ray diffraction evidenceand the factthat, at metamor- Comprehensivecrystal structure studiesby Hawthorne phic T, disorder is even more likely than at room Z. We et al. (1993a,1993b, 1993c) enable one to apportionthe assumetatAl avoidance in micas, as advocatedby Circone ions of a staurolite analysis into all the sites (Table 3). and Navrotsky (1992), and make the simplifying as- These two Fe-rich staurolite samplesrepresent extremes sumption that alternate tetrahedral sites are occupied by ofthe known rangeofH content. Note that the Fe content Si and show no solid solution. We suggestthat the re- of the T2 site is considerablyless in the high-H staurolite maining two tetrahedral sites, occupied by one Al and becauseof the vacancy content of about one ion. This one Si in end-member micas, and by Al, Si, and possibly approachof assigningions to their proper sitesusing crys- Fe3* in natural micas, should be incorporated into the tal structure determinations as a model considerably im- mole fraction model. Ackermann et al. (1993)presented proves the quality of stoichiometry and the resulting mole spectroscopicevidence that OH- replaces some apical fraction calculations for stoichiometric staurolite end- I4lO2-in synthetic germanium muscovite. This observa- members. tion and compositional data suggestthat at least some torAl is charge compensatedby adjacent OH replacing Chlorite O'-. The t4rAlin micas is probably not chargecoupled to We only wish to mention chlorite briefly. The work of octahedralsubstitutions on an ion by ion basis.However, Dyar and Guidotti (1992) showed that the stoichiometry Essene(1989) suggestedthat the tetrahedralsites should of chlorite in pelites is affectedby two main variables: (1) be omitted from mica models. The l2-fold site vacancies Chlorite contains Fe3+ (about I lolo of Fe). (2) Average in many micas might be occupied by some form of H HrO content is 100/ocompared with the ideal value of (e.g.,Miller et al., l99l). H* deficiencyin the OH po- 12010.These observations should be taken into account sitions is almost certainly H+ vacanciesrather than OH when determining chlorite stoichiometry and activity. vacancies and is probably coupled to cation charge in HOLDAWAY AND MUKHOPADHYAY: GEOTHERMOBAROMETRY IN PELITES 685

TABLE4. Possiblemole fractionmodels for some peliticminerals in the FASH system

End-member Composition Activity model- IM1lXtrtrlxAr ttlx", Muscovite KAlrtSisAlOlo(OH), 4.I^lX

octahedral layers above that of the Tschermak substitu- cordierite with garnet using the Ganguly and Saxena tion (Dyar et al., 1993). (1984) garnet mixing model. Much of this nonideality The staurolitemole fraction models and end-member disappears if more recent gamet mixing and cordierite formulas (Table 4) result in significantpart from the ef- hydration data are incorporated into the approach. Fe- fortsofHawthorne et al.(1993a,1993b, 1993c). The first Mg end-membersof biotite may also show some nonide- threepositions in the formula are coupledas demonstrat- ality, which is not yet well understood.Hoisch (1991)has ed by their work. The best way to model a 2H staurolite shown from natural occuffencesthat Ti and Al substi- end-memberis with the mole fraction of vacancyon M4 tutions in biotite are nonideal solid solutions, and Cir- (formerly U), with an additional correction for dilution coneand Navrotsky (1992)have confirmed Hoisch's con- ef tarFsz+by other ions on T2, and the bestway to model clusion for phlogopite-eastonite.Examples of probable a 6H stauroliteend-member is with the mole fraction of nonideality betweenmajor end-membersthat have com- t6lFe2+on M4. Even simple FASH staurolitesamples re- monly been overlooked include iron-magnesium stauro- sultingfrom experimentalstudies contain nonstoichiom- lite and hematite-ilmenite. etric amountsof Fe2+-H+solid solution(Holdaway et al., Even though there is some question regardingthe strict l 993). applicability of the Margules approach, it seems to be For cordierite, there has been a problem concerningthe useful in most cases,and it is far better than assuming correct HrO content for the fully hydrous end-member. ideality. There appear to be severalinconsistencies in the Carey and Navrotsky (1992) have shown that the cordi- literature regarding the nature of Margules equations for erite-hydrous cordierite solid solution fits an ideal one- multicomponent systems.Mukhopadhyay et al. (1993) site model (Table 4). have derived all the equations for an excessparameter These suggestionsshould make it clear that mole frac- such as Gxs and for RZ ln 7 in symmetrical and asym- tion models for many of these minerals will continue to metrical n -component systemsfrom first principles using evolve as additional information comes to light. a Taylor seriesexpansion. From a strictly mathematical standpoint, ifthe constituent binaries in a ternary system NoNrrn.l,lrrY rN MINERALS are symmetrical, there are no ternary interaction param- There is a tendencyfor petrologiststo believe that many eters. Both Helffrich and Wood (1989) and Mukhopa- minerals may be modeled as ideal solid solutions, when dhyay et al. (1993)showed that, for a ternaryasymmetric in fact this is commonly not the case.In our view, ideality solution, if it becomesnecessary to assume that ternary is merely a special caseof nonideality, and some degree interaction parameters are zero for want of better infor- of nonideality is common in most solid solutions. When mation, we must be careful to use formulations that in- one seesindications of a solvus or irregular partitioning clude all of the binary interactions. For an asymmetric of major ions betweenmineral pairs, it is likely that there regular ternary solution, G*s is given by is nonideality.In our opinion, when there are no exper- imental data, it is better to estimate the nonideality from G": X,Xr(XrWn + XtWr,) -l XI3(X3WB + XtW3t) petrochemical natural data than to assume ideality. A -f analysis by Guidotti et al. (in preparation) may provide + x2x3(x3wn + x2wrr) xtx2x|cD3 for the best muscovite-paragonitesolvus information and where shows clearly that the solvus is affectedby phengite con- t/z(Wr, tent; the Margules parametersfor the 12-fold site in mus- Cr.r: + W, + WB + W, + Wn + Wi2) covite should be corrected for the new muscovite-parag- - wrrr. onite data and for the effect of phengite component. Bhattacharyaet al. (1988) showedthat Fe-Mg mixing in It is far better to assumeWrz.:0 than to assumeC,r. : cordierite is nonideal with computations basedon natural 0 becauseC,r, is significantly basedon the binary param- 686 HOLDAWAY AND MUKHOPADHYAY: GEOTHERMOBAROMETRY IN PELITES

TreLe5, RecommendedMargules parameters for garnet,per than most Zbased on more sophisticatedthermodynam- threecations ic data bases.This is becausethe thermometry is little affected by other intensive variables, and nonideality is lnteraction WH(kJl ws (J/K) W, (Jlbatl' Source.* corrected. Mg-Fe 6350 0 0.020 1 -0.030 Fe-Mg 2080 0 1 Gnon-q,norrnrnns Mg-Ca 15000 eo o.'t77 2 Ca-Mg 56s20 2.1 0.0s0 Severalgeobarometers have met with considerablesuc- Fe-Ca 7770 0 0.099 3 (Table Ca-Fe -3270 0 0.064 3 cess 6). Most have the advantage of being reac- Mg-Mn 0 0 0? 4,5 tions that involve no fluid component, which means that Fe-Mn 0 0 o? 4,6 P rnay be estimated independently of XH2o.Almandine Ca-Mn 0 0 0 3,4 Mg-Fe-Ca o? 0? 0 182 * muscovite + biotite * aluminum silicate has potential - becauseit involves only major components,but it sufers Values determined by statistical analysis of synthetic garnet molar volumesusing data from Haseltonand Newton(1 980), Geiger et al.(1987), from low A,V and AS (Essene,1989). Almandine * cor- Wood (1988),Koziol and Newton(1989), and Koziol(1990). dierite + sillimanite also has potential, mainly for high- .'Sources : tot WH,and l\ls: 1 Hackler and Wood (1989); 2 : Wood grade rocks, but does involve HrO. Ultimately, both P (1988);3: Koziol(1990);4: Berman(1990);5: Wood(1991); and 6 : o'Neiil et ar.fi989). and l'can be determined with this assemblage,providing something is known about Xg,o. We are in the processof revising this geobarometer.The presenceof garnet in all of thesegeobarometers emphasizes the importance of re- eters. Comparison shows that although the equations of solving garnet Margules parameters and the problem of various authors appear to be quite different, most are the obtaining P from garnet-absentpelites. Even with signif- sameand are. with lew exceptions,correct. icant improvements in thermodynamic data, mole frac- The garnetsrepresent an example of a four-component tion models, and Margules parameters, some of these system that has been extensively studied for the past de- geobarometersmay never be more accuratethan +0.5 cade.The data used are from both experimental and nat- kbar. ural occurrences.We have carefully reviewed the avail- able resultsand arrived at what is probably the best overall TrmnrronvuAMlc DATA AND DATA BASES set of Margules parametersfor determining Gxs and t'xs The most important single aspectof geothermobarom- (Table 5). One of the problemsthat arisesin this type of etry is the quality of the thermodynamic data on which analysis is the failure to adequately account for error in P-7" results are based. These data come from a combi- the data. This is important, as sometimeserrors are great- nation ofthree sources:(1) calorimetricdata, (2) experi- er in magnitude than the mean parameter because (l) mental data, and (3) natural occurrences.Ideally, we would experimental data were collected without proper design Iike to have agreementbetween these sources,but that is in the statistical sense,and (2) the number of data points not common. The following cautions should be noted for is not statistically large enoughto put tight constraints on deriving thermodynamic data: (l) Calorimetric enthalpy the amounts of the errors.As a result,in someinstances (II) data derived from solution calorimetry tend to have more complicated expressionshave been advocatedthan errors larger than what can be obtained from the analysis are warranted by the data. of good experimental data. On the other hand, calori- metric entropy (,S),specific heat (C"), and X-ray diffrac- Excn.c.Ncp GnorunnnroMETERS tion molar volume (V) data are likely to be more precise Exchange geothermometers are especially useful for than H. (2) Methods of experimental studies should be medium-grade pelites becausethey have low sensitivity checked carefully to be sure that the experiments repre- to P and no sensitivity to XHro. However, at granulite sent true reversalsof stable alternative assemblagesand grade they are easily reset and may have serious difficul- that experimental starting materials and products have ties. Although it still has some problems, the garnet-bi- been characterizedas well as possible. (3) Each reversal otite geothermometer,corrected for at least garnet non- should be independently judged, and conditions should ideality, is by far the best exchangegeothermometer. Ferry be extended away from equilibrium to the limit of ex- and Spear(1978) emphasized the kinds ofrocks bestsuit- perimental error. We have found this to be especially ed and the error limitations of the method. For best re- important with the aluminum silicates,as seenbelow. (4) sults, graphite-bearingrocks should be used, and Fe3+in Comparison with natural assemblagesshould be a sec- both minerals should be accounted for, as done by Wil- ondary processand should be done with extreme caution. liams and Grambling (1990). Where garnet is present in (5) If natural assemblagesare to be used for calibration, medium-grade pelites, garnet-biotite geothermometry correctionsshould be made for mineral composition, Fe3+, approachesan error of +25 "C under reducing conditions and fluid composition, where appropriate. The presence and a high biotite/garnet volume ratio. At high grades, of graphite reduces the X",o in fluid to 900/oor less, de- or under conditions ofresetting during cooling, accuracy pending on P-T conditions. It is even possible that fluid is considerably worse. In appropriate rocks, I based on in micaceouspelitic schistsescapes more rapidly than in garnet-biotite geothermometry is probably more accurate quartzites, and so P,".in micaceousrocks would be slight- HOLDAWAY AND MUKHOPADHYAY: GEOTHERMOBAROMETRY IN PELITES 687

TABLE6. Some geobarometersfor peliticrocks.

Geobarometer(from high- to low-P) Reference Comment

Almandine-rutile-ilmenite-aluminumsilicate Bohlenet al. (1983) very good Almandine-grossular-rutile-ilmenite-anorthite Bohlenand Uotta (1986) very good Grossular-anorthite-aluminum silicate Newtonand Haselton(1981)-' very good Pyrope-grossular-muscovite-anorthite- phlogopite Ghentand Stout (1981)f gooo Almandine-grossular-muscovite-anorthite-annite Ghentand Stout (1981)t good Almandine-muscovite-annite-aluminumsilicate McMullinet al. (1991) good Almandine-cordierite-aluminumsilicate-H"O Holdawayand Lee (1977) needswork 'Listed by end-membercomponents for use in quartz-bearingrocks. -- Also Kozioland Newton(1988). t Also Hoisch(1990). ly lower than that in adjacent quartzites, as suggestedby able reversalsand half-reversalsare totally consistent for Holdaway and Goodge(1990). eachofthe threephase boundaries (e.g., Fig. 2) and con- oC,3.75 There are a number of possiblenaturally occulTingpe- sistentwith a triple point at 504 + 20 + 0.25 litic assemblageswhose presenceor absenceshould serve kbar. We also evaluated all the available molar volume as a test of the quality of thermodynamic data bases, data; our best estimates are given in Table 7. Kyanite, provided correctionsare made for mineral and fluid com- with only two determinations, needs more carefully de- position. These include (l) biotite * andalusite + mus- termined unit-cell data on low-Fe3* samples.Using these covite + quartz, a common assemblagethat should not results and the calorimetric data of Robie and Heming- occur, according to calculations based on the published way (1984)and Hemingway etal. (1991),we have refined version of the Holland and Powell (1990) data base (see H and S (Table 7). These values are recommended for also Powell and Holland, 1990); (2) cordierite + stauro- aluminum silicate thermodynamic data. lite + muscovite + quartz, which does not occur in na- The iron cordierite stability results of Holdaway and ture except in apparent disequilibrium or perhaps when l-ee (1977),Weisbrod (1973),and Richardson(1968) have stabilized by high Zn orLi in staurolite; (3) cordierite + been criticized on theoretical grounds. We now tealize garnet + muscovite + quartz, which can only occur if that in our work, unstable hercynite in the synthesized the garnet is stabilized by high Mn; (4) chloritoid + sil- cordierite and almandine favored growth of metastable limanite + qvarlz, which has a narrow stability range in graphite-free, Fe-Al-rich rocks over a range of fo,; and (5) paragonite + sillimanite * quartz, which has a naffow stability range in Na-Al-rich rocks. A necessarybut not sufficient test of a thermodynamic data base is whether Sillimanite these conditions are met. A problem with thermodynamic data basesin general is that, by their mathematical nature, they are self-con- sistent. Therefore, they tend to produce self-consistency 6 5 among various reactions in a rock or group of related (I) rocks. This self-consistencydoes not necessarily mean 32. that the data base is accurate. It may very well be dis- c) placedin P and Ifrom the correctposition or be incon- L sistent with P and T determined from other bulk com- positions and reactions. 1.0 Andalusite An advantageof data basesis that retrieving ,FIand S of minerals from experiments and from natural occur- rencestends to correct for disorder and nonidealities that 0.0 may not be easily correctedwith direct calorimetric mea- 450 650 750 850 surementson stoichiometric end-members.Examples are Temperature( oC) end-member disorder, minor amounts of solid solution phase diagram for the andalu- such as l2-fold-site H or vacancy in micas, and partial Frg.2. Pressure-temperature reaction showing all valid reversalsand half-re- replacementof Si by Al in staurolite. site-sillimanite versalsadjusted to their error limits away from the phasebound- Many of the important pelitic reactions used in data ary. Closed symbols : andalusite-stable half-reversals; open basesdepend critically on aluminum silicate and, to some symbols : sillimanite-stable half-reversals.This boundary and extent, on cordierite equilibria. Using studies since 1966, similarly determined boundaries for kyanite * andalusite and Holdaway and Mukhopadhyay (1993) have carefully kyanite + sillimanite are consistent with the thermochemical evaluated all experimental work on aluminum silicates. data given in Table 7. After Holdaway and Mukhopadhyay If each reversal is judged independently, all the accept- (l 993). 688 HOLDAWAY AND MUKHOPADHYAY: GEOTHERMOBAROMETRY IN PELITES

TABLE7. Thermodynamicdata for aluminumsilicates.

Molarvolume Entropy Enthalpy (J/ba4 (J/mol K) (kJ/mot) (1973) Kyanite 4.408(21 82.86(50) -2593.70(300) Weisbrod Andalusite 5.146(2) s1 60(s2) -258s.66(300) \ Sillimanite 4.984(2) 9s.08(52) 2586.37(300) 'Holdaway and Mukhopadhyay(1993), based on analysisof experi- .v Holdawayand lre mentalreversal data since 1966 and on calorimetricdata of Robie and (r977) Hemingway(1984) and Hemingwayet at (1991). I cordierite, especially at lower Z. Mukhopadhyay et al. o-

Kyanite

,-t + 741 ' /- a ^ ..-' ,,-- Almmdine y ,.,-- + 'tt't / Quartz

"", E740 t--t--1 6

6 o ?39

7381( 734 ?39 740 741 742 Measured Volume Fig. 4. Plot of measuredvs. calculatedmolar volume for 22 staurolitespecimens using a multiplelinear regression model in Sillimanite which compositionalvariables are fictive end-membersFez*, Mg,Zn, Li, Mn, Ti, Fer+,and fl. Si andAl areassumed to have Almandine averagevalues. After Holdaway et al. (1993). + Quartz events (producing andalusite and sillimanite) are Acadi- 4s0 500 t:o 600 6so ?oo an, and the high-grademetamorphism (locally producing femperature (oC) kyanite) is late Paleozoic,and the region was more deeply Fig. 5. Phasediagram for FASH staurolitewith variableH buried at that time. In an analysis of rocks by Holdaway from 2.8 to 4.4 coexistingwith quartz.Heavy lines showalu- et al. (1988) in an area between Augusta and Rangeley minum silicatestability relations and the limit of stauolite-quartz (McMullin et a1.,199 I , p. 901),later plutonism and post- stability.Solid contours show H contentof staurolitecoexisting metamorphic folding are advocated as causesfor P vari- with aluminum silicate,dashed contours show H contentof ation. In fact, the area suffered posttectonic metamor- staurolitecoexisting with almandine.Limit of staurolite-quartz givenH content.After phism, and the observed sharp reentrants in isogradsare stabilityoccurs where contours meet for a et al. (in preparation). the result of overlapping nonsynchronous adjacent gra- Holdaway nitic heat sources(Holdaway et al., 1982, 1988).All the metamorphism is synchronous with plutonic intrusion, semblage,seen in several specimens,is andalusite + sil- and intrusion occurredover at least 75 m.y., during which limanite + muscovite * potassium feldspar * cordierite time P increasedsignificantly. In both of the casescited + biotite + quartz * graphite, lying on Carmichael's above, P increasedfrom north to south and with decreas- (197S)bathograd. The first occurrenceof sillimanite and ing age of the metamorphism. the first occuffence of sillimanite * potassium feldspar The application of a data baseto only a very few spec- consistentlyare found in the sameplace in the field. Dick- imens from an areais of concernto us. Thesespecimens ersonand Holdaway (1989)estimated metamorphic con- may not be representativein their degreesof equilibra- ditions of 2.35 kbar, 600 "C, usingthree independent ex- tion, or they might representlimiting values of the P and perimental P-I reactions.One problem with this locality T rangeor mineral compositions. is the total absenceof garnet, the result of low P. The As an example of the kinds of problems that may oc- Berman data base(1988, updatedin 1992)gave similar cur, we use a contact metamorphic assemblagefrom P-I conditions (Table 8). Berman's unpublished cordi- western Maine at the north end of the Lexington batho- erite data do not account for HrO and are provisional. lith, studiedby Dickersonand Holdaway (1989).The as- His iron cordierite data arebased on experimental results

Trele 8. Estimatesof P-f conditionsof formationfor a rock from Maine"

P (kba4 rfc) Details 235 600 Dickersonand Holdaway(1989) three experimentalreactions, activity-corrected 2.45 600 Berman(1988, updated 1992) includingiron cordierite,excluding magnesiumcordierite 2.25 595 Berman(1988, updated 1992) excludingall cordierite,aluminum silicate' muscoviteonly 3.00 635 Hollandand Powell(1990, updated 1992) includingiron cordierite and magnesiumcordierite north . Mineralassemblage : andalusite+ sillimanite+ muscovite+ potassium feldspar + cordierite + biotite + quartz + graphite' Locality: lobe of Lexingtonbatholith, Maine (Dickerson and Holdaway,1989) 690 HOLDAWAY AND MUKHOPADHYAY: GEOTHERMOBAROMETRY IN PELITES

clude the following: (l) In many medium-grade pelitic terranes, coexisting thin metacarbonateunits commonly exhibit minerals like grossularor epidote and sometimes contain no carbonate, indicating high Xsro even in the metacarbonateunits. (2) Many metamorphic terraneshave granitic heat sources,which are by nature HrO-rich. (3) The dominant prograde HrO-consuming mass-transfer reaction in most graphitic pelites is the reaction of HrO with graphite C + HrO : CO, + CH4 and when this reaction, combined with simple dehydration reactions, controls fluid composition, it controls it near 800/oHrO, 100/oCOr, 100/oCHo, and at,fo, values near the QFM buffer, depending on P and T, as shown by Ohmoto and Kerrick (1977). (a) This observation is confirmed by the highly reducing nature of most graphitic schists,with no hematite component in the ilmenite. We can take advan- FeO Fe3Oa FerO3 tage of this by assuming that the graphite * HrO equi- librium dominates, with either a closed system or one Fig.6. FeO-FerO.-TiO, diagramshowing possible hematite- partially open to fluid movement, which allows X.o, to ilmenitephase relations at about 600 .C. The dashedline is a be equal to or somewhat greater than X."r. Using schematicO, isobar. this method, Holdaway et al. (1988)assumed X.o, was up to ten times X.r". This approach enablesus to estimate the ofMukhopadhyay et al. (1991) and can be expectedto composition of pelitic fluids in graphitic rocks. It will not be most accurate close to the experimental P-T condi- work well if the graphitic rocks are at all oxidizing, with tions. The Holland and Powell data base(1990, updated hematite component in the ilmenite, or if the pelites are in 1992) gave conditions ar higher P and T (Table 8). deepand undergoinganatexis. The accuracyofthe results Cordierite data in this data baseaccount for HrO in cor- also dependson the accuracyof the thermodynamic data dierite but have not been adjusted to the new iron cor- and mixing models for fluids. Great strides have recently dierite experimental results. In our opinion, the main beenmade concerningthermodynamic data for fluids and problem with the Holland and Powell data base is that fluid solutions, especiallyby Shi and Saxena(1992) and their thermodynamic data for aluminum silicare are nor by Shi ( I 992).At presentthe aboveapproach may be the based on a careful analysis of all available experimental bestway to estimatefluid compositionin appropriatepe- data (e.g.,see Holdaway and Mukhopadhyay, 1993). lites. For the same assemblagein the Ballachulish aureole, This approach can be strengthenedby an accurate,in- (1992) Pattison deduced condirions of 3 kbar, 645 "C, dependentdetermination of /o, becauseall fluid compo- using, in part, thermodynamic data for cordierite. Two sitional variables in graphite schists are uniquely deter- differences between the Lexington and Ballachulish lo- mined by knowing P, T, and fo,, and the assumption of calities are that in most specimensthe Ballachulish as- subequal Xro, and X.ro becomes unnecessary.We are semblagedoes not contain graphite and that in several hoping to determine the hematite-ilmenite solvus exper- specimensandalusite appearsto have been stabilized by imentally. The schematic plot of Figure 6 incorporates high Fe3+.Pattison assumedthe fluid was pure HrO. We what we know from petrologic observationsat about 600 do not believe theseconditions can be defendedas a point oC and illustrates that the system is nonideal and has a on the andalusite-sillimaniteP-Zboundary, asadvocated solvus. The dashed line is a schematic O, isobar, which by Pattison(1992). shows that for a constant composition of ilmenite, /o, In summary, much more careful work is neededbefore varies with the nature of the coexisting phase. Experi- petrologistscan dependon the useof thermodynamic data mental determination of this system should enable one basesfor P and T estimation. Eventually one should be to determine fo, for the ilmenite * rutile equilibrium, able simply to use the data bases,with appropriate mole 2FerOr..,"u- + 4TiO, : 4FeTiOr.. + Or, or the ilmenite fraction models and corrections for nonideality, to eval- + magnetiteequilibrium, 6FerO,ss in irm : 4FerOo* Or, uate P from the various geobarometersgiven in Table 6. in rocks, and to estimate a limited rangeof fo, for ilmen- Until that time, thesedata basesshould not be usedwith- ite-only assemblagesby constraining f, from the ilmen- out careful critical examination of the results. ite + rutile and ilmenite + magnetite equilibria. The alternative approach for determining fluid com- Fr,urn coMposrrroN position is to use geothermometersfor ?nestimates, use In sulfide-absentmedium-grade pelitic rocks, the pre- fluid-absent geobarometersfor P estimates,and, with the dominant fluid speciesare H.O and COr, and, where estimated T and P, use dehydration reactionsto estimate graphite is present,CHo as well. Qualitative argumentsto Xrro from the compositions of coexistingphases. In some indicate the approximate composition of pelitic fluids in- casesthe results of such efforts indicate Xn,o values far HOLDAWAY AND MUKHOPADHYAY: GEOTHERMOBAROMETRY IN PELITES 691

for cor- from the predicted rangeof70-900/o in sulfide-absentgra- in cordierite: Constraints from natural data and implications geothermometry in granulites. American Mineralogist, phitic pelites. might be taken to indicate that such dierite-garnet That 73,338-344 metamorphic rocks have a wide range of fluid composi- Bohlen.S.R., and Liotta, J.J.(1986) A barometerfor gametamphibolites tions. We believe it commonly indicates a compounding and gamet granulites.Journal of Petrology, 27, 1025- 1056. of errors in T, P, thermodynamic data, mole fraction Bohlen,S R., Wall, v J., and Boettcher,A.L. (1983)Experimental inves- geological of equilibna in the system FeO- model, and corrections for nonideality. tigations and applications TiO,-Al.O.-SiO,-H.O. AmericanMineralogrst, 68, I 049- 1058. point In our opinion, when we reach the where various Brown.T.H . Berman,R.G., and Perkins,E H' (1988)Ge0-Calc: Software dehydration equilibria in graphitic schistsindependently packagefor calculation and display of pressure-temperature-composr- and consistently give us reasonablevalues of Xr,o, then tion phasediagrams using an IBM or compatible computer. Computers we will be making real progressin geothermobarometry and Geosciences,14, 27 9-289. and Navrotsky, A. (1992)The molar enthalpy of dehydration homing in on the best thermodynamic data for all Carey,J.W., and of cordierite. American Mineralogist, 77, 930-936. the minerals. Knowledge of fluid compositions can then Carmichael. D.M (1978) Metamorphic bathozones and bathograds:A serve as a check on the quality of the geothermobarome- measure of the depth of post-metamorphic uplift and erosion on a try and the thermodynamic data. At that stage,we will regional scale.American Journal of Science,27 8, 769-7 97. A. (1992) Substitution of164rAlin phlogopite: be able to say much more about the nature of fluids in Circone, S., and Navrotsky, Hrgh-temperaturesolution calorimetry, heat capacities,and thermo- pelitic rocks and perhaps test models for fluid behavior dynamic propertiesof the phlogopite-eastonitejoin. American Miner- and movement. alogist,7 7, I 19 l- 1205. Dickerson, R P., and Holdaway, M.J (1989) Acadian metamorphism as- Suunrlnv AND RECOMMENDATIONS sociated with the Lexington batholith, Bingham, Maine American of Science,289, 9 45-974 In summary, we recommend the following: (l) We Journal Dutrow, B.L , Holdaway,M.J., and Hinton, R.W (1986)Lithium in stau- should use all information available to determine the best rolite and its petrologic significance'Contributions to Mineralogy and possiblestoichiometry and site assignments.(2) We should Petrology,94,496-506 carefully think out mole fraction models and continue to Dyar, M.D. (1990) Mdssbauerspectra of biotite from metapelites.Amer- 656-666. experiment with and test them. (3) Nonideality should ican Mineralogist,'l 5, - ( 1993)M6ssbauer spectroscopy of tetrahedralFer* in trioctahedral be evaluatedwhenever possible. (4) Thermodynamic data micas- DiscussionAmerican Mineralogist, 78, 665-668. basesshould be continually reevaluated,should be treat- Dyar, M D , and Guidotti, C.V. ( 1992)Controls on ferric iron in chlorite ed with some degreeof skepticism,and should be applied Geological Society of America Abstracts with Programs,24, 130' M'J', with care. (5) Fluid reactions should be used to test and Dyar, M D, Perry,C.L, Rebbert,C R, Dutrow, B.L, Holdaway, H.M. (1991) Mijssbauer spectroscopyof synthetic and nat- methods.(6) Consistentwith the times, we must and l-ang, refine our urally occurring staurolite American Mineralogst, 76' 27-41' be willing to accept change. Dyar, M.D, Guidotti, C V, Meadows,E', and Robertson'J.D (1992) As we home in on the best activity models, values for PIGE analysesof F and Li in muscovite and biotite from metapelites thermodynamic data, and corrections for nonideality, it and associatedgranites of W. Maine Abstracts to AGU Fall Meeting, be possible to approach accuraciesof +25 'C, Supplementto Eos,618 should C.V., Holdaway, M.J., and Colucci, M (1993) + Dyar, MD., Guidotti, +250 bars,and l0o/oXr.oin low- to medium-P rocks. Nonstoichiometnc hydrogen contents in common rock-forming hy- droxyl silicates.Geochimica et Cosmochimica Acta,57, in press. AcxNowr-nucMENTs Dymoke, P, and Sandiford, M (1992) Phase relationships in Buchan facies seriespelitic assemblages:Calculations with application to an- We acknowledgewith thanks the following people for allowing use of dalusite-stauroliteparageneses in the Mount Lofty Ranges,South Aus- their unpublisheddata and for helpful drscussions:M. Darby Dyar, Charles tralia. Contributions to Mineralogy and Petrology, ll0, lzl-132' Guidotti, Frank Hawthorne, Barbara Dutrow, Klaus Langer, and Steven Essene,E.J (1989) The current status of thermobarometry in metamor- Guggenheim.M Darby Dyar provided a thoughtful review. We thank pbic rocks. In J.S. Daly, R A. Clitr, and B W.D Yardley, Eds., Evolu- Rob Berman for making the latest version of his Ge0-Calc data base tion of metamorphic belts, p. 1-44 Geological Society Special Publi- (Jan92.RGB)available to us, and Roger Powell for running the lrxington cation, Cambridge,England. batholith data on Thermocalc. This researchis supported by research Ferry,J.M., and Dipple, G.M (1991)Fluid flow, mineral reactions,and funds from the National ScienceFoundation, grants EAR-89-04777 and metasomatismGeology, 19, 2ll-214. EAR-90-r9277. Ferry,J.M, and Spear,FS. (1978)Experimental calibration ofthe par- This work is dedicated to the memory of Patricia Piercy Holdaway, titioning of Fe and Mg between biotite and garnet. Contributions to t937-199t. Mineralogyand Petrology,66, I l3-l 17. Frost, B R., and Tracy, R J (l 99 l) P-f paths from zoned :Some RnrnnnNcss crrED minimum criteria American Journal of Science,29 1' 9 17-939. Ackermann, L., Langer, K., and Rieder, M. (1993) Germanium musco- Ganguly, J., and Saxena,S.K. (1984)Mixing propertiesof aluminosilicate and applica- vites with excesshydroxyl water, KAl,[Ge3 ,Al'*-,O'o ,(OH),(OH),] gamets:Constraints from natural and experimental data, and the questionofexcess OH in natural muscovites.European Journal tions to geothermobarometry.American Mineralogrst, 69' 88-97. mixing of Mineralogy, in press. Geiger,C.A., Newton, R.C , and Kleppa,O.J. (198?)Enthalpv of gamets from Berman, R.G (1988) Internally-consistentthermodynamic data for min- of synthetic almandine-grossularand almandine-pyrope erals in the systemNa'O-K,O-CaO-MgO-FeO-FerO,-Al'O,-SiOr-TiO,- high-temperaturesolution calorimetry. Geochimica et Cosmochimica H,O-COr. Journal of Petrology, 29, 445-522 Acta,51, 1755-1763. -(1990) Mixing properties of Ca-Mg-Fe-Mn garnets. Amencan Ghent. E.D.. and Stout, M.Z. (1981) Geobarometryand geothermometry Mineralogist.7 5. 328-344. of plagioclase-biotite-gamet-muscoviteassemblages. Contributions to - (1991) Thermobarometry using multi-equilibrium calculations:A Mineralogy and Petrology, 76, 92-97. new technique,with petrologrcalapplications. Canadian Mineralogist, Gray,D.R., Gregory,R.T., and Durney,D.W. (1991)Rock-buffered fluid- 29,833-855. rock interaction in deformed quartz-rich turbidite sequences,eastern Bhattacharya,A, Mazumdar,A.C., and Sen,S.K. (1988)Fe-Mg mixing Australia. Journal of GeophysicalResearch ' 96' 19681-19704. 692 HOLDAWAY AND MUKHOPADHYAY GEOTHERMOBAROMETRY IN PELITES

Guidotti, C.V. (1984) Micas in metamorphic rocks. In Mineralogical So- and Ca-Mn garnetsdetermined by reversed,displaced equilibrium ex- ciety of America Reviews in Mineralogy, 13, 357-467. perients American Mineralogist, 75, 319-327. Guidotti, C.V., and Dyar, M.D. (1991)Ferric iron in metamorphrcbiotite Koziol, A.M., and Newton, R.C. ( 1988)Redetermination of the anorthite and its petrologrcand crystallochemicalimplications. American Min- breakdownreaction and improvement of the plagioclase-garnet-Alrsio5- eraloglSt,/tr, lOl-l /) quartz geobarometer.American Mineralogist, 73, 216-223. Hackler, R.T., and Wood, B.J (1989) Experimental determination of Fe - (l 989) Grossularactivity-composition relationshipsin ternary gar- and Mg exchangebetween garnet and olivine and estimation of Fe-Mg nets determined by reverseddisplaced-equilibrium experiments Con- mixing propertiesin gamet. American Mineralogist, j4,994-999. tributions to Mineralogy and Petrology, lO3,423-433. Haselton,H.T., and Newton, R.C (1980)Thermodynamics of pyrope- McMullin, D W A, Berman,R.G., and Greenwood,H.J. (1991)Calibra- grossular garnets and their stabilities at high temperaturesand high tion of the SGAM thermobarometer for pelitic rocks using data from pressures.Journal of GeophysicalResearch , 85, 69'73-6982. phase-equilibrium experiments and natural assemblages.Canadian Hawthorne, F.C., Ungaretti, L, Oberti, R , Caucia, F., and Callegari,A. Mineralogist,29, 889-908 ( I 993a)The crystal chemistry of staurolite I. Crystal structure and site Miller, A.K., Guggenheim,S., and Koster van Groos, A.F. (1991)The occupanciesCanadian Mineralogist, 31, in press. incorporation of "water" in a high-pressure2:l layer silicate: A high - (1993b) The crystal chemistry ofstaurolite. II. Order-disorderand pressuredifferential thermal analysisof the l0 A phase.American Mrn- the monoclinic ' orthorhombic phase transition. Canadian Mineral- eralogist,76, 106-112. press ogist,31, in Mukhopadhyay,B , Holdaway,M.J., Gunst,R.F., and Dyar, M.D. (1990) -(1993c) The crystal chemistry of staurolite. III. Local order and Endmember thermochemical parameters and mixing properties of chemical composition. Canadian Mineralogist, 31, in press. 3-hydrogenFe-staurolite GeologicalSociety of America Abstractswith Helffrich, G., and Wood, B.J. (1989) Subregularmodel for multicompo- Programs,22, 349. nent solutions.American Mineralogist, 74, l0l6-1022. Mukhopadhyay,B., Holdaway,M.J., and Dyar, M.D. (1991)New exper- Helgeson,H.C , Delany,J.M., Nesbit, H W., and Bird, D K. 097g) Sum- imental determination of the reaction Fe-cordierite : almandine + mary and critique of the thermodynamic properties of rock-forming sillimanite + quartz under hydrous condition Geological Sociely of minerals. American Joumal of Science,278A, 229 p. AmericaAbstracts with Programs,23,391-392. Hemingway, B.S, Robie, R.A., Evans,H.T., and Kenick. 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(1981)Metamorphic petrology, min- covite + biotite + gamet + plagioclase,and implications for the mix- eral equilibria, and polymetamorphism in the Augusta Quadrangle, ing properties of octahedrally-coordinatedcations in muscovite and south-centralMaine. American Mineralogist, 66, 5 l-69. biotite. Contributions petrology, to Mineralogy and 108, 43-54 Ohmoto, H., and Kerrick, D.M. ( I 977) Devolatilization equilibria in gra- Holdaway,M.J, and Goodge, W. (t990) pressure J Rock vs. fluid pres- phitic systems.American Joumal of Science,277 , 1013-1044. sure as a controlling influence on mineral stability: An example from O'Neill, H.St.C.,Pownceby, M.J., and Wall, V.J. (1989)Activity-com- New Mexico. AmericanMineralogist, 75, 1043-1058. position relationsin FeTiO,-MnTiO, ilmenite solid solutionsfrom EMF Holdaway, M J., and I-ee,S M. (1977) Fe-Mg cordierite stability in high- measurementsat 1050-1300K. 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