THE AMERICAN MINERALOGIST, VOL. 50. SEPTEMBER, 1965

STABILITY OF : EXPERIMENT. THEORY, AND APPLICATION'

Dlvrn R. WoNes, U. S. GeologicalSuraey, Washington, D. C. AND HaNs P. Eucstnn, Deparlment of Geology,The Johns H opkins U niter sity, Baltimore, M arylond'.

AesrRecr on the join - react to form a number of assemblages and the reactions are governed by the independent intensive parameters, temperature, fugacity of HrO (fnro), and fugacity of (f6 r) . The most common of these assemblagesin natural occurrences are biotite-sanidine-; biotite-sanidine-magnetite; and biotite-leucite- olivine-magnetite. The compositions of biotites coexisting with sanidine and magnetite were determined for a variety of conditions of furo, fs, and temperature. The compositions lie in the ternary system KFes2+AlSLOro (OH)r, annite-KMg32+AlSraOro (OII)2, phlogo- pite-KFe3r+AlSigOu (H-J, "oxybiotite." Application of regular solution theory to KFerAlSiaOro(OH)s in ternary solid solution yields the following relationship: 3428- 4212(1 - x'), log fsrg : log xr l/2logfo,+ 8.23 - log aKArsi"or- log ap",e T * I where x1 is the mol fraction of KFeaAlSisOro(OH)z in biotite, ar<,rrsi.o,is the activity of KAISLOs in the various phases, and aFg,e,is the activity of FesOr in the various mineral phases. Neither molecular (a: x) or cationic (a: t') ideal solution theory describes the activities of KFedlSLOro(OH)e in "ternary" biotite solid solutions. The position of the fe.-Tcurvesfor biotite--magnetite-corundum/alumino-silicate-quartzassemblages were determined by the intersections of the stability curves of biotite and muscovite. Schematic fer-T curves are given for biotite-sanidine-pyroxene-magnetite-quartz assem- blages. Biotite crystallizing from a magma may follow either a more -rich trend or a more -rich trend, depending upon the fo, conditions during cooling. If fs, is decreas- ing with temperature, the Mg/Fe ratios oI the anhydrous phases and the amount of magne- tite either decrease or change very little. The magnesium-rich trend in the biotite composi- tions is represented by constant or increasing f6, (through loss of ) and leads to an increase in the amount of magnetite present and in the Mg-Fe ratios of the associated ferro- magnesian phases. The two trends may represent, respectively, undersaturation or satura- tion of the melt in regard to H2O. Extrapolation to natural biotites assumes that Ti, Al, and F substitutions are similar to Mg, Fe+s, and O substitutions. Biotite-K-feldspar-magnetite assemblages in low-grade metamorphic rocks ((500o C.) imply either disequilibrium or low HrO pressures. Assem- blages in the gneissesof the northwest Adirondacks imply HzO fugacities of 0.1-10 bars and COr fugacities of 400-10,000 bars during recrystallization of the interbedded and marbles. Intersections of biotite fsrs-T curves with the " minimum melting curve" sug- gest that most biotite-bearing and quartz latite magmas were at temperatures

I Publication authorized by the Director, U. S. Geological Survey. 1228 BIOTITE STABILITY 1229 greater than 750o C. and at HzO pressures of less than 1000 bars just before extrusion. Biotite phenocrysts permit an estimate of minimum H2O pressure in "granitic" melts; magnetite or orthopyroxene phenocrysts permit an estimate of maximum If3O pressures.

INrnonucrroN As biotites are very common constituents of igneous and meta- morphic rocks, knowledge of biotite stabilities and phase equilibria should aid in the determination of certain boundary conditions (tem- perature, water pressure,oxygen pressure and compositional variations) for magmatic and metamorphic processes. Previous investigators have determined the stability of the end members,phlogopite (Yoder and Eugster, 1954) and annite (Eugster and Wones, 1962), and this study attempts to examine the solid solution of those end members. The iron-magnesium ratio of biotites in igneous (Heinrich, 1946; Nockolds, 1947) and metamorphic (Thompson, 1957) rocks has been correlated with various types and grades of meta- morphism, and this study establisheslimitations of the intensive vari- ablesat which a particular biotite may be stable. Cation substitution of Fe and Mg in silicate lattices has been discussed by Ramberg (1952),Mueller (1960),Bradley (1962),Bartholom6 (1962), Ghose (1962) and Kretz (1964). Experimental studies have been limited to olivine and pyroxene equilibria, chiefly at liquidus temperatures and one atm. pressure(Bowen and Schairer,1935; Muan and Osborne,1955) whereas this study presents data on Mg-Fe substitutions in a hydrous silicate at elevated pressures.It may, therefore, serve as a model for other Mg-Fe solid solutions of hydrous silicates. The present study is an attempt to define the biotite-sanidine-magne- tite-gas equilibrium as a function of T, P(=Par*Prro), fo' and phase composition at temperatures between 400" and 900o C. On biotite compositions, at f6, values between the FeaOr-FerOaand Fer-'O-FerO+ buffers, no other assemblageswere encountered at the above conditions. This manuscript presents the experiments, their interpretation, and methods of extrapolation in the first part. In the second part applica- tions to some natural assemblagesare discussed.The biotite assemblages will provide, if properly studied, definite limits on the possible tempera- tures and fugacity of components such as H2O, Oz, and Hz in geologic processes.

ExpBnrurNIAL TECrrNreuES The techniques used have been discussed by Eugster and Wones (1962) and Wones (1963b). Cold-seal hydrothermal apparatus supplied temperature and pressure.Pressure measurements were good to t/p and I23O D. R. WONESAND H. P. EUGSTER the temperaturecontrol and measurementwas within 5" C. of the stated temperature.Individual experimentswere quenchedby slow cooling (20 minutes) of a sealedpressure vessel. As reactionrates are very slow, this techniquecreated no problemsrelated to "quench phases." Oxygen fugacitieswere controlled by the buffer techniqueof Eugster (1957).Table 1 lists the valuesof oxygenfugacity for the severalbuffers. Muan's (1963) results on the system Pd-Ag-Fe demonstratethe useful- ness of Pd-Ag alloys in hydrothermal experiments with iron-bearing systems.PdaoAgro alloys were used only in the most recent experiments. Phase equilibria were determined by examination of quenched prod- ucts obtained from experimentsusing biotite or phlogopitefsanidine {magnetite as starting materials.The phlogopite,sanidine and magne- Teela 1.Oxvcar.r Fucecrtms ol Oxvcru BumBns(Eucsrrn aNo Wonrs, 1962)

- A _ C(P_1) Logfsr:-i+B+ T Bufier

IrezOa-FerOr 24912 1l A1 0.019 FesOa-Fer-*O 32730 13.t2 0.083 Nio-Ni 24709 8.94 0 046 SiO:-FezSiO-Fe;Oa 27300 10.30 0.092 I tite were synthesizedas pure phasesand then mixed mechanically to avoid any ambiguity in results.The critical determinationin all experi- ments is the compositionof the biotite coexistingwith sanidine,magne- tite and gas. The exact location of the equilibrium is dependent upon attaining equilibrium by oxidizing a ferroan biotite to a magnesianbiotite-sani- dine-magnetite assemblage,and by reducing a phlogopite-sanidine- magnetite assemblageto a ferroan biotite-sanidine-magnetiteassem- blage. Completereversibility was establishedfor five points in addition to the data for the annite end member. The remainder of the data were obtained by oxidizing a biotite. Such experimentsshould yield a maxi- mum iron content. All indications are that they approach equilibrium within 48-100 hours, whereasthe reversingequilibrium requiresat least 250 hours. A sequenceof experimentstabulated in Table 3c at 750oC. and 800oC., 2070bars, demonstratesthat the approachto equilibrium proceededat highly variable rates. At 750o C., a 24-hour reducing experiment pro- BIOTITI], STABILITY r231 duced a biotite with Fe/Fe{Mg:0.63 whereas a 195-hour reducing experimentproduced a biotite with a value of Fe/Fe*Mg of 0.56. The value producedby oxidation of a ferroan biotite is 0.78 and is probably nearer the true equilibrium value. Where a large spreadbetween oxida- tion and reduction experimentsexists, the oxidation value is used. Experimentsusing oxide mixes as starting materials were given little credence.They were oniy usedin closeconjunction with experimentsus- ing biotites or phlogopite-sanidine-magnetiteas starting materials.

ColrposrrroN ol PHAsES As methods of extrapolation and interpolation of the biotite phase equilibria dependheavily on assumptionsconcerning the purity of sani- dine and magnetite,and on the compositionof the gas phase,as well as the biotite composition,discussion of the compositionalvariations of all the phasesis warranted.

Biotites.Biotite compositionswere determined by measuringindices of refraction and the (060,331) r-ray spacing using the data of Wones (1963b).Optical measurementsproved the most useful, as the r-ray re- flections are weak and broadenedby reflectionsfrom the inclusionsof original biotite flakes within the newly crystallized sanidine. The method of Gower (1957) was not used as the (004) biotite reflectionis coincidentwith the (311) of magnetite. A complicatingfactor in this study has been the formation of "oxybio- tite" in the biotite solid solutions.Consequently, the biotites are not a simple binary KMg3AlSi3Oro(OH)z-KFeaAISiBOr6(OH),but rather they are members of the reciprocal system (Ricci, 1951, p.371-389) KMgaAlSirOl0(OH)r-3 KFe2+Fe23+AlSiaOrz-KFes2+AiSi3O10(OH) r-3KMg . Fezs+AISieOrz.If the theoretical(and physically impossible)composition, KFes3+AlSieOrr(H-t),is used as a component,then the biotite composi- tions can be plotted in the additive ternary system shown in Fig. 1.'Ihe shadedarea represents those compositions that arephysically impossible. The advantageof this type of plot is that the annite concentrationsare assignedwith simplicity, whereasin the reciprocalsystem they may be ambiguousin certain cases. The concentrationsof "oxybiotite" have not been rigorously deter- rnined.However, as Wones (1963b)demonstrated, the c axis of the unit cell contracts with increasing"oxybiotite" content. This has not been lvell calibrated,but the availabledata in the abovestud-v indicate that c contractsabour 0.002 A for eachper cent "oxvbiotite.:'Figur*I plots the estimatedposition of the biotite solid solutionsfor eachof the buffer 1232 D. R. WONESANI) II P. EUGSTDR systemsinvestigated. It should be emphasizedthat these curves repre- sentlittle more than an "educatedguess." Another possible substitution is that of "ferriannite," KFstz*ps3+ Si3Or6(OH)2(Wones, 1963a).The formation of this componentrequires the formation of an aluminousphase and a changein the ph1,-sicalproper- ties of the biotites. No aluminousphases such as muscoviteor corundum were observed by optical or n-ray techniques. The compositions of natural biotites coexisting with feldspars, pyroxenes, olivines, and

Kreisltsiro,.{x-,)

K Mg'zF€;3Al si 3 orz

xrdo2arsi.o,otoH l" Annile Phlogopite

Ifrc. 1. The ternary system KIrel+AlSLOro(OH)z-KMg:'?+AISLOTo(OH)rKFer3+ Alsisorr(H1). Dashed lines indicated compositions of "buffered" biotites, the shaded area represents compositions physicallyimpossible to obtain. Dotted iine is that of appropriate composition of biotites that would provide a constant value for the heat of mixing. magnetites(Heinrich, 1946;Nockolds, 1947)indicate that such a substi- tution is not to be expected. In summarv, the Fe/Fef N{g ratio of the biotites hasbeen determined with confidence,but the Hz content is onlv estimated. Feld.spar.The expectedvariation in the feldsparcompositions are either the Fe3+3A13+substitution resuiting in KFeSirOs or solid solution of either FeaO+or FezOain KAlSiaOs.lleasurements of the indices of re- fraction of feldspars(Table 2) are all within 0.002 of the ideal value for 7 of 1.522 (Tuttle, 1952) and indicate less than I mol 16 KFeSigOs (7:1.608) (Wonesand Appleman,1961) and lessthan 0.4 rr.olToFezOz (G,:1.800) (Deer et al., 1962).The KAiSiaOspolymorph is apparently high sanidine(Donnay and Donnay,1952). BIOTITI,:, STABILITY t233

Magnet'ite.For the compositionsstudied, the possibletypes of substitu- tions causing deviations from the composition FeaOnare hercynite, FeAIzOa,n-iaghemite, Fe2O3,and magnesioferrite, MgFe2O+.The first two, FeAl2Oaand Fe2O3,may be checkedby unit cell measurements.The (333,511)reflection was measuredfor severalmagnetites at a variety of conditions,as well as for svnthetic magnetitessynthesized by the reduc-

Trsr-n 2.Imonx ol RnrnrcrroN*J"JT:lrr#D dsr or MncNnrrrrnsCorxrsrno

Starting Time, T,' C. P, bars Bufier "v, KAlSiaOa drr' Feror Materiall hrs.

450 2070 FerOq-FerOr annite 450 <1.523 nd. 480 2070 FerOr FezOa ph+sa+mt 250 <1.5223 1 6159 550 1035 Fesol-FerOs biotite 43

t Abbreviations:ph, phlogopite;sa, sanidine; mt, magnetite;Fe mix, KzC.6SiOz*FeiMgO*AlzOr;Oxmix KrO 6SiOr*FeCrOr 2HzOfMgOfAl0s. tion of hematite or by oxidation and decompositionof FeCzOr'2H2O. The resultsare listed in Table 2. The value of 8.396+.001 A for the unit cell edgeof magnetiteis larger than the value of 8.391given by Turnock and Eugster (1962) or the value of 8.394 given by Robie and Bethke (1963). The important point is that none of the measurementsdeviate from the of value 8.396by more than 0.0018.According to Turnock and Eugster this would indicate less than 0.5 mol per cent FeAlzO+in solid solution.The Fe:Oasubstitution only reachesmeasurable proportions at temperaturesin excessof 900oC. The unit cell data indicateless than 1.8 mol per cent Fe2O3(Donnay and Nowacki, 1954). 1234 D. R. WOND,SAND H. P. EUGSTER

The MgFezO4content is a matter of great importance and cannot be resolvedaccurately by data on the unit cell (Deer et al., 1962)although a limit of 10 mol per cent can be made. Three checkshave been made on the MgFezO4content of the magnetites.First, all experimentsin which Fe/Fe*Mg:0.94 yield large quantities of biotite. If the assemblage were only sanidine and magnetite, the maximum content of MgFe2Or would be 18 mol per cent. In the secondplace, visual estimatesof the biotite-magnetiteratio in such experimentsindicate that the spinel is close to pure magnetite. Finally, in experimentswithin the hematite field of stabilit.v,no spinelphases were observed, indicating that lIgFe2Oa is unstable in the presenceof KAlSieOi and HzO. However, in experi- ments buffered by magnetite-hematiteassemblages, both iron oxides occurred in assemblagesof biotite composition, indicating that the spinel phasewould be pure Fe3O+.These severallines of evidenceindi- cate that the spineiphase is essentiailypure Fe3Oa.

Gos. This phase is assumedto consistof the componentsHr and HzO. Eugster and Wones (1962,p. 92-93) have consideredthe problems of estimating both the Hr and H2O contents,the fugacitiesof those com- ponents, and the amount of dissolvedmaterial in the gaseousphase. Eugster and Wones presented methods for computinS fsro and fu" at specified temperatures and pressures.Shaw and Wones (1964) have given new estimatesof the fugacity coefficientsof hydrogen, and these values have been used in this paper together with the fugacity coeffi- cientsfor HzO calculatedby Holser (1954). Shaw (1963a)has shown that Hz-HzO mixtures are nonideal,but at the Hr/HzO ratios encounteredin this stud,v,only the Fe1-"O buffered experimentshave significant deviationsfrom the ideal mixing assumed by Eugster and Wones (1962).As the hydrogen fugacity data are used extensively in determining activity coefficientsand extrapolating the biotite data to iower temperatures,it is desirableto estimate the uncer- tainties in fsr. These are about 5/6 ol the actual value, and are largely due to uncertainties in the data for the oxl,gen buffers, especially FezSiOr-Fe3Or-SiOr. Shaw's(1963a) results for the severaloxygen buffers indicate that the Fe2SiO4-Fe3Oa-SiO:data may be questionableernd certainly need to be determinedmore rigorously. New data for FerOa-FerOahave been pub- Iishedby Blumenthal and Whitmore (1961)using emf measurementsof a magnetite-hematitecell. Their results yield oxvgen fugacities 2 to 3 orders of magnitude greater than those given by Norton (1955). The magnetiteprepared by Blumenthal and Whitmore, however,is probably BIOTIT]] STABILITY 1235 nonstoichiometricmaterial enrichedin FerOr, and hence, Norton's re- sults are used. In summary, the compositionof sanidineis assumedto be KA1Si3Os, that of magnetite,FeBO4, and the gas phaseof variable ratios of Hz and HrO. There is no evidencefor significantexchange of Fe and Al between sanidineand magnetite at the conditionsof theseexperiments, and the amount of iron oxidesdissolved in KAISi:rOsmust be less than 0.4 mol per cent. Biotite compositions are expressedin trvo ways. The first is as KFea*Mga(r-,)AlSLOr0+y(OH)r-uwhere y (and therefore Fe2+/Fe3+)is undefined and x is the ratio Fe/FefMg. The second method is KFe3*r2+Fe3*r3+Mgr*r2+AlSieOrzH(2-3x3)where x1 is the concentrationof KFerz+415ir6to(OH)r,annitel x2, KMg3A1Si3O10(OH)2,phlogopite; and xB,KFe33+AlSisOr2(H-1), "oxvbiotite." Throughout the remainderof this paper thesedefinitions of x, x1,X2, &rd x:rwill be retained.

ExponrlrpNIAL RESULTS The results of individual experiments are listed in Table 3 and the data for 1035 and 2070bars total pressureare plotted in Figs. 2 and 3. The plots representpseudobinary T-X projectionsfor experimentsbuffered by severaldifferent assemblagesand correspondto the lower portion of Fig. 14. It must be rememberedthat the oxygen and hydrogen contents changein thesediagrams, but the elementsremain in the ratio K: Al: Si: (Fe,Mg) of 1:1:3:3. The value of the experimentsvaries as a function of starfing material, length of time of the experiment,and precisionof the compositionalde- terminations.The location of the determinedequilibrium points is tabu- lated in Table 4 with the hydrogen fugacity of the experiment and the estimated "oxybiotite" contents. An important feature of the data is that the reversedequilibria, al- though few in number, do provide sufficient constraints on the un- reversedapproaches to equilibrium to permit judicious use of the latter data. Hence the boundary curvesgiven in Figs. 2 and 3 representa com- bination of reversed equilibria, nonreversedexperiments approaching equilibrium, and interpretation. A plot of thesedata in an f6r-T projection is given in Fig. 4. Contours representthe compositionsof biotites which coexist with sanidine and magnetitefor a given value of T and f6r.The contour labelled100 bounds the field of stability of annite from Eugster and Wones (1962) and the contour O representsthe upper stability limit of phlogopite and was calculatedfrom the data of Yoder and Eugster (1954).Luth (1964)pre- 1236 D. R. WONI;S AND H. P. EUGSTER

Teer,a 3. Exprnrurxrs Dnranurnrnc CouposnroN (l-e/.F'e*Mg) or Btotrtrs Conxrsrrnc wrnt Sl.ltrlrNn aNn M.tcNntrtn

Final Biotite Composition , Time Startins Material rt'L ) IlDars, - i - Remarks (hrs.) (Fe/Fe*Mg) v dooo Fe/Fe*Me

a) Experiments buftered by the assemblageFesOr FerOa 875 1035 8 bio(0.352) 1 591 1.646 1 5396 0.32t.06

850 103.5 28 bio(0.352) 1..587 | 634 1 5396 0 301 04

800 1035 66 bio(0.169) 1.571 r.602 1.5379 o.r1t.o2 oo reactlol 800 1035 45 bio(0 352) 1.587 r.634 1 5391 0 30t 05 800 1035 42 bio(0.550) 1 582 1 628 1.5392 0 301.05 800 1035 48 bio(0.765) 1 .582 1 628 n d. 0 30t 05 800 1035 50 bio(0.765) 1.582 1.628 1 5418 0.301 05

775 1035 61 bio(0.352) n.d. 1.629 n d 0.35+ 05 no reaction

750 1035 70 bio(0.352) 1.586 1 627 1.5397 0.351.02 no reactior 750 1035 38 bio(0 550) n d. 1.628 1.5397 0.361 .05 750 1035 42 bio(0.765) n.d. 1.622 1.5397 0 34t.05

700 1035 64 bio(0 169) 1 566 1.600 1.5380 O.17! 02 no reaction 700 1035 44 bio(0.550) n.d. 1 630 n d. 0 38t .04 700 1035 25O phfsafmt(O 765) n d. 1 631 n.d 0.381.02 teversed reaction

675 1035 6g bio(0.sso) n.d. 1.631 nd. 0.391.02

650 1035 94 bio(0 ss0) n.d. (1 612) nd. 0 39t 05 agg. index oI refrac- tion 1035 bio(0 76s) n.d. (1 607) 0.35t 07 agg. index of refrac- tion 1035 bio(0.76s) (1.614) nd 0.41i05 agg. index oI refrac- tioB

620 1035 44 bio(0.76s) 1.667 0.661.03

600 1035 63 bio(o.169) 1.561 1 600 1.5384 0.17+.02 no reaction 600 1035 13e bio(0 352) l 582 1.621 1.5411 0 35t 02 no reaction 600 1035 94 bio(0..550) 1.591 1 645 r.5426 0.551 02 some hema- trte 600 1035 42 bio(0.76s) 1.654 0.56i:.04

550 1035 140 bio(0.5s0) 1.586 | 646 | 5432 0.551.02 no reactton 550 1035 43 bio(0.76,{) 1.66s 0 651 04 only hema- tite

500 1035 64 bio(0.sso) 1 576 1 641 1.5455 0.5s1.02 no reaction 500 1035 83 bio(0.76s) 1.621 1 673 1.5486 0.77X .02 no reaction

485 1035 42 bio(0.76s) 1.625 L.679 1.5484 0.77X.02 uo reaction

900 2070 6.s bio(0.3s2) n q. l.oJJ 1.5388 0.27+.05 BIOTITE STABILITY LL.) I

T nw.n 3-(continued.)

Final Biotite Composition Starting Material T(o C.) p (b"rr) Ti.. Remarks ' (hrs.) rFelFe*Mg) t dooo Fe/Fe*Mg

800 2070 7l bio(0. 16e) n.d. 1 613 1.5373 O.17X .O2 no reaction 800 2070 73 bio(0.3s2) 1.581 1.631 1.5391 u.J)f .ul no oxrqes 800 2070 28 bio(0. ss0) 1 584 1.630 1 5390 0.351.04 800 2070 43 bio(0.5s0) 1.580 1 630 t.5397 0.35t.0.1 800 2070 42 bio(0.76s) 1.587 1 632 n.d. 0.37+.0.1

750 2070 51 bio(0.550) 1.632 0 371 .04 750 2070 42 bio(0.76s) 1.635 | 54t7 0.411.03

725 2070 o/ bio(0.ss0) 1.626 0.331.03 Onlyhema- tite

?00 2070 bio(o 169) 1 571 1 605 1.5375 O 17! .02 no reaction 700 2070 r22 bio(0.3s2) 1.581 1.628 1.5399 0.351.02 no reaction 700 2070 68 bio(0.5s0) t.634 0 391 .03 700 2070 t22 bio(0.ss0) 1.629 0.36t.03 700 20?0 40 Ox mix(0. 765) 1.627 0.35t .03 700 2070 65 bio(o 76s) 1.637 0 43t 03

680 2070 64 Ox mix(0.765) 1.633 0.40t.04 '1..640 680 2070 42 bio(0. 765) 0.441 .0.1

650 2070 94 bio(0.sso) 1.596 1.651 1.5430 0.551.02 somehema- tite pres- ent 113 bio(0.76s) 1.639 0.451.04

625 2070 94 bio(0.76s) i .640 0.461.04

600 2070 115 bio(0 169) 1.569 1.591 1.5374 O,17+ ,02 no reaction 600 2070 bio(0.352) 1.576 1 623 !.5397 0 351.02 no reaction 600 2070 94 bio(0.550) 1 591 1.645 r.5426 0.55:t 02 somehema- tite and magne- tite pres- ent 600 bio(0.765) 1 649 0 52t 02

o.) bio(o 76s) r.667 0 66t .03

bio(0.765) 1.674 0.72+.03 only hema- tite

bio(0 765) 1.680 u.llt u2 noreacuon

bio(0.880) (1.6s7) 0.80t 05 (Ass index of refrac- tion

b) Experiments buffered by the assemblageNi-NiO 850 1035 816 ph+sa+mt(0.765) 1.672 0 40:t 0,1 reversed reaction 850 1035 138 bio(0.352) 1 s82 | 622 0.351 .02 no reaction 850 1035 94 bio(0.76s) t.637 0 46t 04 850 1035 92 Fe mix(0.880) l.oJl 0.43+ 05 1238 D R. WONDS AND II. P. EUGSTER

Trpl-e 3-(continued)

Final Biotite Composition StartingMaterial Tf c.) P Titl Remarks tu"*t {}e/Fe*Mg) rhrs.) 'y dooo FelFe*Mg

800 1035 21O Fe mix(0.550) r 589 1.629 1 5466 0 441 03 800 1035 165 bio(0 550) 1 589 1.636 1.5436 0 47t 05 800 1035 1,23 Fe mix(0. 765) 1 .593 1 636 1 5494 0 49+ 05

7.50 103.s 116 bio(o 880) I .643 0.541 03

700 1035 32o bio(o s50) | 647 1 5487 0 551 .02 no reaction 700 1035 94 bio(o 76s) |.622 1 5493 0.69i.02 700 1035 los bio(0.880) l 654 0.631.03 700 1035 116 Fe mix(0 880) 1.660 0 68t 02

800 2010 118 bio(0.169) 1.564 1.597 1 5387 0 17t.02 no reaction 800 2070 l2I bio(0 352) 1 575 1.61,2 1 5440 0 351.02 no reaction 800 2070 168 bio(0.5s0) 1 599 1.643 1 5479 0 55+ 02 no reaction 800 2070 700 ph*sa*mt(O.765) 1.595 1 651 1 5468 0 561 .04 reversed reactron 800 2070 140 bio(0.76s) 1 596 1,642 1.5471 0 541.04 800 2070 178 bio(0 880) 1.597 1 642 1.5469 0 55t .03 800 2070 118 bio(o.880) 1.598 1.646 1 5496 0.561 .06 800 2010 160 bio(0.939) 1 642 0 531 .03

750 2070 2O9 bio(0 i6s) 1 663 0 70+.03 750 2070 597 ph*sa*mt(0.765) I .650 0.601.03 reversed reaction 750 2070 20e bio(o 880) 1 660 0 67t 03 750 2070 2O9 bio(0.939) r.658 0.66+ 03

700 2070 139 bio(0.169) 1 s64 1.597 1 5385 0 17! 02 no reaction 700 2010 139 bio(0 352) 1.575 I 616 1.5410 0 35t ,02 no reaction 700 2010 rig bio(0 550) I 595 1 654 1.5475 0-551 02 no reaction 700 2070 160 bio(0 76.5) 1 620 r.613 1 5518 0.77+ -02 no reaction 700 20io 1110 ph*sa*mt(0 765) I.642 0.53 teversed reaction 700 20io 132 bio(o 880) 1 683 0 88t 04 magnetite present 700 20io 164 Fe mix(0.880) r.676 0 821 .03

650 2070 336 ph*sa*mt(0.765) 1.613 O 17L 02 complete reversal 650 20io 89 bio(0.765) 7 6t'3 1.5511 O 71X 02 no reaction

600 2070 92 bio(0.76s) 1.623 1 668 1 5519 O i7! 02 no reaction 600 2070 r32 bio(o 880) 1.622 1 681 1.5534 0.881 02 no reaction 600 20io 14o bio(0.939) 1.628 1 690 I 5544 0,q4+ 02 no reaclion

c) Experiments bufiered by the assemblage I'eSiOr-FeaOr-SiOz

900 1035 6 bio(0.s50) 1 591 1 646 1 5450 0.50+ 05

8s0 1035 91 bio(0 352) 1 581 1.622 t.544.5 0 35+ 02 no reaction 850 1035 \29 bio(0.5.50) 1 595 1 641 0.541.04 850 1035 105 Fe mix(0 5.50) 1 592 1.636 o 49X 02 850 1035 105 Fe mix(0.765) 1 587 1 629 0.42+.04

25O ph*sa*mt(0.76.5) 1.586 1632 0.4Jj.02 reversed reaction BIOTITI' STABILITY t239

Trnlr 3 (continueiJ)

Final Biotite Composition stilting Malerial Tr.c' - ) P- rburrr---- Tit" Remarirs lhrs.) (Fe/Fe I Mg) Y dooo Fe/Fe*Ms

800 to35 94 bio(0. ss0) 1.644 0.551 .02 no reaction 800 1035 49 bio(o 76s) 1.64+ 0 54t .04 800 1035 89 Fe mix(0.880) 1.602 I .650 0.611.03 800 1035 123 Fe mix(0 880) 1.596 1.637 0.52t 04

775 1035 229 phfsa*mt(0.765) 1.635 0.461.04 reversed reaction

750 1035 229 ph+sa+mt(0 765) 1.612 0.52:t.04 reversed reaction 1035 91 bio(0 ssO) |.644 0.551 -02 no reaction 750 1035 86 bio(0.765) 1 660 0 67t 04 750 1035 r76 bio(o 880) (1 644) 0.75t.05 (agg index ref)

700 1035 250 ph*sa*mt(0 765) I 665 0.71t 04 reversed reaction 700 1035 229 ph*sa*mt(0.765) 1.672 o.77X 02 complete reaction

850 2070 132 bio(o 3s2) 1.570 1.612 0.251 04 no oxides present

825 2070 118 bio(0.3s2) 1.580 1.620 1.5142 0.351 .02 no reaction

800 2070 89 bio(0 3s2) 1.578 r.617 1.5432 0.35t 02 no reaction 800 2070 122 bio(0.ss0) 1 600 1.648 n.d. 0.55+.02 no reaction 800 2070 432 ph+sa+mt r 607 1.664 o 70t.o2 reversed reactron 800 2070 250 1 591 | .639 0.49+ 02 reversed reaction 800 2070 142 bio(0. 76s) 1.607 1.664 0 70+ .02 800 2070 65 bio(0 76s) 1.603 1.666 0.69f.04 800 2070 48 bio(0.880) 1.605 1 660 0.671.04

775 2070 96 bio(0.76s) 1.672 0.77! 02 no reaction 775 2070 ph*sa*mt(0 765) 1.645 0 541 04 reversed reaction

750 2070 89 bio(0 ss0) 1 ..597 1 643 1.5489 0 55t.02 no reaction 750 2070 231 ph*sa*mt(0 765) 0.631 04 reversed reactron 750 2070 195 ph*sa*mt(0 765) 1.647 0.501 04 reversec reaction 750 2070 122 ph*sa*mt(0 ?65) 1 650 0.591.04 reversed reactron 750 2070 7l bio(0.76s) 1 672 O.77! 02 no reaction 750 2070 48 ph*sa*mt(0. 765) l 654 0 62t 04 reversed reactlon 750 2070 24 ph*sa*mt(0.765) 1.655 0.63:t 04 reversed reaction 750 2070 48 bio(o 880) 1 673 0.i81 02

740 2070 bio(0. 76s) 1.672 O.77+ .O2 no reaction D. R. WONES AND H. P. EUGSTL,R

'l tnrx. 3-(continued)

Final Biotite Composition Time Starting Material T('C P (bars) ) (hrs (Fe/FeiNIe) ) FelFe*Mg

72s 2070 168 ph*sa*mt(0.765) 1 655 0 6J1.04 reversed reactiol 725 2070 167 bio(0.76s) 1.677 I 5500 0 77!.02 no reaction

715 2070 92 bio(0 880) L623 l 684 1 5546 0 88t 02 no reaction

700 2070 92 bio(O 352) 1.575 1 616 1 5435 0.35t 02 no reaction 700 2070 1s0 bio(o ss0) 1.597 1 644 1.5478 0.55+ 02 no reaction 700 2070 4.50 bio(0.76s) 1.612 1 670 I 5514 0.77!.02 no reaction ?00 2070 250 ph*sa*mt(0.765) | - o).) 0.63:,04 reversed reaction 700 2070 113 bio(o 880) 1 620 | 682 I 5544 0.88t .02 no reaction 700 2070 140 bio(o 939) 1.629 1 690 1.550 0.s41 02 no reaction

d) Erperiments bufiered by the assemblageFer-*O FeaOr

850 1035 177 bio(0.ss0) 1.597 1 6+6 1.5475 0 55t 02 no reaction 850 1035 94 bio(0.76s) 1 615 1 666 1 5516 0.72!.04 850 1035 96 bio(0 765) 1.615 r.666 1 5507 0.72! 04

sentsa revision of thesedata. The phlogopitecontour curvessharply at low f6, values, becausethe gas phase becomesincreasingly enriched in hydrogen and the fugacity (and activity) of HzO decreasesrapidly. Hydrogen acts as an inert gas with respect to the phlogopite decom- position, but becausefsr6 decreaseswith decreasingf6r, the decomposi- tion temperaturemust be lowered.This points up the important fact that equilibria of hydrous silicatesfree of iron are also subject to the com- position of the gasphase and thereforeto changesin fe, if an appreciable amount of h1'drogenis present. The high temperature relationshipsare further complicated by the fact that silicatemelts form at those conditions (Luth, 1964).The sani- dine*magnetite+biotite assemblageswill react, with increasing tem- peratures to form leucite*olivinefmagnetite*biotite assemblages, kalsilite*leucite+ olivine assemblages,or olivine{ melt assemblages. The contoursof biotite compositionshave beeninterpolated from Fig. 3 and Table 3. Only those portions of the contours which are well establishedby the experimentaldata are shown. The shapesof complete contoursare suggestedin Fig. 13.Because of the temperaturelimitations, contours are complete within the magnetite field only for iron-rich biotites (Fe/Fe*MgX100>70), but they do extendto magnesium-rich biotites in the upper portion of the magnetitefield. A particular contour indicatesthat a biotite of that Fe/Fe*Mg ratio is stable anywherebe- Iow that contour, but not above it, where the biotite is replacedby the assemblagem agnesianbiotite-sanidine-m agnetite. BIOTITE STABILITTI L24r

Euflcr: F€^Sioa -F.50. - Si02

. Biotile + Sonidine o qno - - +I'lognellle+Gos <(a ,oo tj-v< F - Eiolile + Gos f' r 700 i-;-

.o 9O0 E eoo 700 600

Butflr: F.30. - F.2Oi tooo

Biotile Ssnidin6 900 "

o 800

700

600

500 | o^^ | o0 02 04 06 08 to Fe' 'Fe+Mq

l.rc. 2. Position of biotite-sanidine-magnetite-gas equilibria at 1035 bars total pressure as a function of temperature and Fe/FefMg at oxygen fugacities of the given bufier assemblages Open blocks represent biotite-sanidine-magnetite assemblages; shaded blocks, biotite assemblages; partially shaded blocks, biotite-sanidine-hematite assemblages. Brackets and triangles indicate composition of biotites coexisting with sanidine and magnetite. Shaded triangles represent high reliability, open triangles fair reliability, open brackets low reliability.

Considera biotite with (Fe/Fe*MgX 100)of 70. This biotite (and all biotitesfor which Fe/Fef MgX 100< 70) is stableat any value of fe, and T on or below the 70 contour.If an increasein fo" (or decreasein'f) above (below) this contour occurs, the originally homogeneousbiotite must react under Ozto form magnetite,sanidine, and H2O and a biotite whose compositionis given by the contour appropriateto the new f6,-T condi- tions.The amount of magnetiteand sanidineformed during oxidationcan be calculatedfrom the initial and final compositionof the biotite. Thus, the decompositionof biotite to biotite-sernidine-magnetiteat 2070bars is defined between 400oand 900" C. b;- I'ig. 4. A similar figure can be con- 1242 D. R WONFS AND II . P. EUCSTER structed for 1035bars from Fig. 2. For a given biotite composition,the assemblagebiotite-sanidine-magnetite-gas is divariant in the system KAISiaO8-MgO-Fe-O-Hand is representedb1' a curved surface in the fe.-fgro-T space.A more completef6,-T diagram will be discussedlater (Fig. 13). The most important feature of Fig.4 is the steepintersections

Buft.r: F.2Sioa- Fr3Oa-Si02

Bioiile+ Sonidine g soo \ +Mognelite+Gds --Y---x_- E OUV = - F blollle+bos ) r 700

Bufl.r:Ni-NiO rooo Bioiile ' Sonidine o 9OO +Mognetite + Gos - 9 800 t{- Biolile + Gos f---{ ' 700

Buffar: F.roa - Fr203

)o oz ol", 06 os lo

' Fe +Mq Fro'3' Positio"t 2070bars totar pres- "::lt"*-'#*:[T:"-#."*x'J;'r?,;ir" of the biotite curveswith the "buffer" curves.Presumably the stability curvesof most of the anhydrousferromagnesian siiicates will be parallel to the "buffer" curves,so that the resulting assemblagesof biotites and olher ferromagnesianminerals for a given bulk compositionare highly dependenton f6r, fsr6 and temperature. In effect, the biotites represent a two-volatile equilibrium, the two volatilesbeing oxygenand water. Consequentlythe effectof temperature changeson biotite compositionsis very dependenton the activitiesof the BIOTITE STABILITY 1243

a d' dr4b4 qqq q \o€r +1 o\4 N \o4 o o\N

s c) oQ rQ tQ.Q N - : O n + \O O.4 s - + \O 4 O +, O - O € @ N N N € € .O 'O € € \O .O 4 + + 4 - 4 4 + + + N r O O S H N N

+ \o r o c) N - +, + 4 0 co r N \o N N c) o N i a \o N € + c) + - i - N N N N N N N N O 4 4 \O \O \O € N r N I S A + + +

N O N 4 4 N cO O O O n € +:4 N Ctr € +r 4 O \O O O\ O N N @ a NO€90aOOA+ .+44+€++444€€r\Or€Nr 4. + +

NON€O\Oo.-+O ONN:Oo-NO-d+O-4+-F M \ o $ N o\ <. 4 JJ-jJJJJJJJ J-i JdJdJ-jo'-i so-joJd6i J lltlttttttttttl H

,Y ,Y. ,i; ,! ,9 U) TTTT*T o."d h dodidddddd-o;1-d-,r-bbEbx -,r ddi d g SjcS-a. 0 d m b-dE b 4 ij6 4 ,4 t 6 h ;^, + ;& Ir tr'+'*'a'*?'a fr L fLa,;! ^ -ii-: a'] ,,,-,,vAv-A^+'E -) -;^ + + + + ! i ; i ! + : : !.i 5.ivri.Fv :.Fv.rv.rY_v o_eqqqo_qqo_qo_o_o_? a_4 q4 4 qo_4q4 q,4 i4. X ri r,:d ri r;r,: r; d d d d,;dzizdZzdlzdzizEi lTr

d o4Do4O40nn o 4 0 4 n 4 4 o 4 4 0 O o 4 4 o 4 0 rosNororoo roNsooQrQorsr€QNoN

Ni:NdNiNii * HN*:N iNHN NiN:: NNi a (-) + 83S8f;888R9 4OO 440 nO 40O nOO nO 44 a o\@r@rrNr\o\o \o \o \o 0o 4 € @ €N € ns @rNN €s F V

E .9O\ON+ +@O4o., NH*O o.\:ONO\a\O<14@Q46r € O @ N H € c|' A n H cN cr' @ O c|. \O 4 O 0O 4 c) 4 N r a 4 € H cr at € o € r, o i F cN \o o F o N D + a - o o o € r € 4 + + +<.<,ddd;-j i-i -; JJ-i-i=i-;J-idciioooo lllllltttt ttttttlttttttttltl"j-; tl X w o j 1214 D. R WON]iS ANI) II. P. IJUGSTER two volatile constituents. However, the activities of oxygen and water are related to that of h1'd16g.tr by the dissociation of water, and useful resuits are obtained in considering the hydrogen-biotite equilibrium.

o

= Sonidine+ Hemollle+ Gos C) o -to ctr J IL C (D olr x o -20 erl o Kolsilite+ Leucilo+ J Biotite+ Gos // Olivine+ Gos

300 500 700 900 Temperoture,oC

Frc. 4. A projection from the Fe/Fef Mg axis of the biotite equilibria onto the f6r-T plane at 2070 bars total pressure.The positions of biotite-sanidine-magnetite equilibria as determined in this study are shown by heavy contours of constant Fe/FelMgX 100 values for the biotites and are taken from Fig. 3. Heavy curve labeled O represents maximum phiogopite stability, area bounded by curve labeled 100 is the annite stability field. Light r,r'eightlines and dotted lines represent "bufier" curves (see Table 1). See also Figs. 13 and 14.

BrorrrB Sor-ro SoruuoNS; Acrrvrry CoEFFTcTENTS The reaction between annite and sanidine and masnetite can be written as follows:

KFe:AlSirOro(OH)r=KAISLO3 f !-e3Oa{ H: (I) annite sanidine magnetite gas Eugster and Wones (1962) derived an expressionrelating hydrogen fugacity to temperaturefor that reaction. Using the hydrogen fugacity coefficientsof Shaw and Wones (1964), that expressionbecomes o?41 Iogffi" : - ,lrt * 11.05(+0.111 (1)

where T is in oK. BIOTITE STABILITY 1245

%Anni le, KFe';Alsi3oro(oH)z 20 40 80 too Iooo

900

I 800 A'1

h\ 700 o o E b F \^ 600 v \

Feroa -Fe2O5

500 \c)

400 oo o.2 o.4 06 o8 to Fe, 'Fe +Mq

Frc.5. Comparison of annite concentration (mol per cent)-temperature data and Fe/IrefMg-temperature data for biotites coexisting with sanidine, magnetite, and gas (Hr-|HrO) at a total pressure of 2070 bars. Solid lines indicate Fe,zFefMg data; dashed lines, annite concentration data. Solid lines are from Fig. 3, dashed curves are based on the 'Iable data of 4. Circles indicate points bufiered by l'e3OsFe2Or; triangles, Ni-NiO; squares, FezSiOrFerO+-SiOz.

As all of the phasespresent are pure end members (assurringfor the presentthat "oxyannite" is of low concentration),equation (1) is equaily well an expressionfor an equilibrium constant,K^..i1", where

&xAlsiros'atrF."ror.fEr 9341 logKo"i1u : at : - -T + 11.05(t0'11) (1') "*"**,"..* We may now use equation (1') to define the standard state for KFesAlSiaOro(OH)rkeeping in mind the problem of variations in the quantity of "oxyannite" in the solid solution. The effects of total pressure are very small. From the compilation of Robie and Bethke (1963),the molar volumes (cc/mol) are Fe3O4,44.53; KAlSi3O8, 108.98; and KFerAlSiaOro(OH)2,t54.32. This results in a volume change of about 1 cc/mole for the solids, which correspondsto 1246 D. R. WON]'S AND H. P I],UGST]]R

-25 calories/1000bars. Wones (1963b) has demonstrated the partial molar volume of KFeaAISirOro(OH)zin biotite solid solutions to be a constant,so that all PAV".liaterms may be neglected. As can be seenfrom the data in Table 4 the KFe3AlSirOro(OH)zcon- centration of the biotites coexistingwith sanidineand magnetite are not directlv equivalent to the Fe/Fe+Mg (or x) ratios becauseof the pres- enceof "oxybiotite" (x3).This differenceis shown very clearly in Fig. 5 where KFeeAlSirOro(OH)zconcentration (x1)-temperature plots are com- pared with the Fe/Fe-FMg-temperature plots for 2070 bars. When no "oxybiotite" is present,x:xr. The deviationsare not seriousfor Ni-NiO and FezSiOr-Fe:rO+-SiOzbuffered arssemblages,but thev are quite Iarge for the FeaO+-FeuOsdater. For this reason,the KFerAlSi;Oro(OH)zcon- centrationrather than Fe/Fef Mg will be usedhenceforth in the deriva- tion of activity coefficients.Figure 5 again points up the fact that, at a given temperature,biotites from biotite-sanidine-magnetiteassemblages are much more iron-rich at low values of fe, and that this effectis more pronouncedat lower temperatures. The activity of KFe3AiSirOro(OH)2,oKFesArsiaoro(ony, in a solid solution of biotite coexistingwith sanidine,magnetite and gas, may be readily obtained through expression(1'):

t IH" aXFe3AISi3olo(oH) (2) r: * rH2 where fs, is the fugacity of hydrogenin the particular biotite assemblage and fog, is the fugacity of H2 in the analogousassemblage containing pure annite at the same temperature.Values of log axr".lrsi31110(oH)2are given in Table 4. Plots of log a11p"ra1siror.(oH)2versus log r and log 11are given in Fig. 6 and 7. If the biotites are ideal molecularsolutions of KFeeAISiaOl0(OH)r, KMgrAlSirOto(OH)r,and KFe33+AlSi3O10(H-1),then the activities would be characterizedby a:x or a:xr. However, an ideal cationic substitu- tion (Bradley,7962), in the three octahedralsites would correspondto a:x3 or a:Xr3. As can be seenfrom Figs. 6 and 7 neither solutionis ade- quate. Figure 7 aisodemonstrates that the variablex1 gives a consistency to all data, whereasin Fig. 6 the variable x Ieadsto a discontinuity be- tween data collectedwith the differentbuffers. This consistencysuggests a model of random mixing of 3 molesof (Fe, Mg) over two distinct sites, but until further work is done, another model is proposedfor extrapola- tion. Consequentlyxr is the appropriatevariable, as it is the concentra- tion of KFeaAlSirOro(OH)r,the component whose standard state is de- finedb1'equation (1'). BIOTITh:, STABILITY t247

rtr ! E tl ! E

! 'h I o_. o^ E Oa ; na

o_a\--'

-0 U 025 05 075 lO _LOGX

Frc. 6. Logarithm of the activity of KFe:AlSirOro(OH), plotted as a function of the logarithm of Fe/Fe*Mg of biotites (X) coexisting rvith sanidine and magnetite. Squares represent experiments buffered by Fe3OsFe2O3;triangles, Ni NiO; circles, I'ezSiOr-FeaOr- SiOzi crosses, Fer *O-Fe:Or Solid symbols represent reversed equilibria. The lower line (a:x) represents molecular ideal solution theory; the upper line (a:x3), ideai cationic substitution theory.

The activity coemcientfor KFeeAlSi3Ol6(OH)2,7r, is derived from the f ollowing relationship:

- - (3) a: T1xr: P; log"r: logfs, logfon, logxl rHo If cationic substitutionsare used: - 3 log 7r : log fx, - log f"n, 3 log xy As the number of substitutionsis not merely the octahedralcation sub- stitutions, but alsoinvolve the O3OH anionic substitution, a molecular model has beenused to describethe activitl' of KFeaAlSiaOro(OH)zin the solid solutions consideredhere. The theory of regularsolutions (Guggenheim ,1952) was appliedto the data with somesuccess, but the problem of the "ox1'biotite" content has prevented final resolution of the problem until better data on the con- centration of that component are obtained. From regular solution theory - , (1 *,)tW rog 71 : (4) l.ntRT 1248 D, R. WONES AND H. P. EUGSTI],R

F tr E 5

E t ,/ tr '*.'z' o d:;' 0

- o o.25 0.5 0.75 l.o

Frc. 7. Logarithm of the activity of KFe3AlSi3Olr(OH), plotted as a function of the logarithm of the mol fraction of KFe:AlSisOro(OH):(xr). Symbols are identical to Figure 6. whereW is the heat of mixing per mole. Figure 8 is a plot of log 71versus (l-x)2/T. The slopeis about -4212, and from this a heat of mixing of -870 cal/mole has been derived. The lack of agreementbetween the high temperature Fe3Oa-FerOabuffered data and the remainder of the data may be due to any one or all of the following:

-5

.?

^ -rifil- -lY- ^ " . lnA0-- ,E-v o 0t2345678 \rf"'o'

Frc. 8. Logarithm of the activity coefficient of KFerAlSiaOro(OH)z(a/xr) plotted as a function of (1-xr)'/T. Symbols are identical to Fig.6.) BIOTITE STABILITY 1249

(1) because of their short duration, the high temperature experiments do not represent equilibrium; (2) the fundamental values for the fo, of the FerOrFqO3 equiiibria given by Norton (1955) are incorrect; (3) the heat of mixing of the oxybiotite-annite substitutions is a function of compositionl or (4) the estimates of the "oxybiotite" compositions are in- correct, due either to inefficient calibration of the physical properties or to changes during the quench procedures. If (4) were the main problem, the appropriate composition of the biotites in the ternary system which would provide a constant value for the heat of mixing are plotted as a dotted line in Fig. 1. In our opinion both (3) and (a) could be responsiblefor the observed discrepancies in Fig. 8. Until more precisework is done on the composition,regularr solution theory provides a satisfactoryempirical model for the energy of mixing of KFeaAlSirOto(OH),"moiecules" in a biotite solid solution serieswhere the KFedISLOto(OH), concentrationis greater than 25 mole percent (Fig.8; Table 4). The activitl. of KFedlSi3Or0(OH), in a solid solution seriesis given by combiningequations (3) and (4):

loga6p",1;s1,6,0(0H), : log*' -n""1- "t)l 1+o.zo; (5)

For biotites coexistingwith sanidineand magnetite,an expressionfor the hydrogenfugacity may be obtained by combining equation (1') and (5): 9341+ 4212(1 - x,)' log f11, : - * Iosxr + 1105 (+0.20) (6)

Adding an approximationfor the equiiibrium constant for H2O, the fol- lowing expressionis obtained: 3428- 4212(1 - x)z log fTrr6 : -f losxr I I/2logfs,+ 8.23(+0.20) (6')

For an assemblagecontaining impure K-feldspar and impure magnetite the expressionexpands to: 3428- 42! (i:'!* Iog f11,6 : los xr I t/2tog fo.

+ 8.23 - logaxersi,o,- logap",6, (tO.ZO; (.6") The agreementbetween regular solution theorv and the actual run data is shown in Fig. 9, a plot of hydrogen fugacity versus the inverse temperature ('K). The actual run data (Table 4) are given as well as the curves calculatedfrom equation (6) for the severalmol fractions of KFeaAISirOro(OH)r.Biotite is stableon the right hand side of the curves and biotite-sanidine-magnetite-h)'drogenon the left hand side. In- dividual points give the mol fraction of KFerAlSieOro(OH)2,taken from Table 4. The agreementwith the curvescalculated from regular solution theory seemsvery satisfactorl.. A more direct comparisonwith respectto Fe/FeiMg ratios is given in Fig. 10 which is a comparison between the experimental curves' 1250 D. R. WONES AND IT, P, FUGSTER regular solution theory curves, and molecular ideal curves at a total pressureoI 2070bars. The molecularproportions (moI 0/6KFeaAlSieOro (OH)r) were adjusted to Fe/Fe+Mg by means of Fie. 1. The data for

= o Cll =ctl L c o oll oo o -

Or -l o J

-3 na l.o t.2 t.4 '" t 'o'

l'rc. 9. Logarithm of hydrogen fugacity plotted as a function of inverse temperature (oK) and composition of biotite for biotite-sanidine-magnetite-gas assemblages.Open circles give the position of experimental points with determined biotite compositions. The lower group of points u'ere determined at 1035 and 2O7Obars rvith a Fe3Oa-Fe2O3buffer rvhile the middle groups refer to FezSiOa-FerOr-SiOzand Ni-NiO data. (mol per cent KFerAlSiaOro(OH)). Heavy lines are equilibrium positions calculated by regular solution theory for specifiedvalues of mol per cent KFe:AlSLOro(OH)r. the FesOr-Fe2O3assemblages show the deviationbetween predicted values and actual measuredvalues. It is obvious that there is a close corre- spondencebetween measuredvalues and regular solution values,except for biotites on the hematite-magnetitebuffer above600' C. It is equally obviousthat an ideal solution model is far from satisfactoryin describing biotite solid solutions. BIOTITE STABILI:TY lzJl

ilo0 ro00- Bufler'FezSi04-Fe304-Si02

900 o

o 800

700

600 ilo0 - tooo Bultrr' Ni Nio ?- soo .E eoo F 700

600

lloo 1000 Buffcr: FeJoa-FczO5

900 800 \o o ..\ 700

600 lr I 5OO F I 400 L oo o2 0 4 0.6 08 l'o F%"*ue

Frc. 10. Biotite composition-temperature plots comparing experimental results (circles and heavy lines), regular solution theory (dashed lines), and molecular ideal solu- tion theory (dotted lines) for a total pressure oI 2070 bars. Solid lines are from Fig. 3; circles from Table 4.

ExrnapolatroN To OrnBn Assn'Nrsracr'sCoNTATNTNG BrorrrE Biotite-muscolite-magnetite-corund,umor (AlzSi.Or-quartz)-gas.Chinner's (1960) discussionof the gneissesand at GIen Clova, Scotland, pointed out that the interrelation of biotite-muscovite pairs need not be restricted to the considerationsof chlorite and reactions' The relation pertaining to oxygen fugacity as the intensive variable is the followine:

KFe:AISLO'o(OH),+ Alros I LO": KAleAlSLOro(OH),f Fe:On (II) annite corundum muscovite magnetite 1252 D. R. WONIIS AND IL P. EUGSTER or by adding qrartz:

KFerAlSi:Oro(OH): f ALSiO; + +Or: KAl,AlSi3Or0(OH), f Fe3Oaf SiO: (III) annite muscovite magnetite quartz the position of reaction (II) plotted as a function of f6, and T is given in Fig. 11. The position of the calculatedpoints is obtained from the inter- sectionof equation (6') with the new data for the reaction KAlrAlSiBOl1

-c $e$trI)

() -z "#fy (t f r z. u (t .'.4,$ .'.2'. *0" )< /^tv' o -30 a," aNNtTE.5+ AtzSior * MUSCOVITE+OIJARTZ + (, TIT E o MAGNE J --- aNNlTEro *AlzSiOs+ MUSCOVITE+ QUARTZ + MAGNETITE -_ ANNITE+ CORUNDUM+ MUSCOVITE+ MAGNETITE -40 300 400 500 600 700 TEMPERATURE."C

Frc. 11. Biotitefcorundum-:magnetitefmuscovite and biotite+Al:SiOasmagnetite fmuscovitefquartz oxidation reactions plotted as functions of fo, and temperature. Ellipses indicate intersections of the annite data of Eugster and Wones (1962) with that of Velde (1964) for muscovite. Triangles indicate intersection of annite data ryith that of Segnit and Kennedy (1962) for muscovitefquartz Solid lines indicate boundaries between iron oxide and fayalite assemblages.The three dashed curves are calculated from equations (a), (8) and (9).

(OH), (muscovite)SKAISi3O8 (sanidine)*AIzOr (corundum){H2O (gas) obtained by Velde (1961). The temperature value obtained for a given fs,6 by Velde was substituted with the value for fsr6 in equation (6') in order to obtain the f6, value at which annite (biotite), muscovite, sanidine, corundum and magnetite coexist at the given temperature (seeellipses in Figure 11). Reaction (III) is also plotted in Fig. 11. The values of those plotted points were obtainedby using the data of Segnitand Kennedy (1962)for the muscovite+quartzSK-feldsparfcorundum*HzO with equation (6'). The essentialfeatures of these reactions are that they are inde- BIOTITE STABILITY

1 :

o

Tempctotuao+

Fro. 12. Schematic for-T relationships for the bulk compositions biotitef3 quattz at some arbitrary value of total pressure (Pnrf Pnro). Curves labeled "annite," BI, and BII represent biotites of arbitrary KFerAlsisoro(oH)2 content coexisting with sanidine, magnetite/hematite, and quartz. curve labeled o is the boundary marked by the reaction phlogopitef3 quartz=sanidinefenstatite. Dash-dot curves represent the assemblages fayalite-quartz-magnetite (Fa-Qz-Mt), olivine-pyroxene-magnetite, (Ol-Px-Mt), and pyroxene-magnetite-quartz (PII). The dashed curve through points D, DI, and DII repre- sents the maximum thermal stability of a given biotite in the presence of qtattz. See dis- cussion under " Biotite-quartz- gas." pendent of the activity of H2O, are parallel to the other silicate f6,-T curves, and indicate that, in an aluminous environment' pure annite is stable with qtrartz and magnetite only over extremely limited f6r-T re- gions. Approximate equations have been derived graphicalll' for reactions (II) : : - (8) rog16, t'ffi + r7.zr:lsYa and (III): rogrs":-fffi +rc.s+lsok (e)

The effect of pressureis small as the AV"oua"is about 5 cc/mol for reac- tion (II) and 3 cc/mol for reaction(III). The effect of diluting the KFeeAlSirOro(OH)rcomponent in biotite solid solutions is to displace the curves to higher values of fe" at constant temperature. The approximate curve representing the assemblage biotite (50 mole /6 KFe3AlSLOlg(OH)r)-muscovite-magnetite-Al2sio5- quartz is plotted. as the dotted line in Fig. 11. The maximum thermal t254 D. R. WONES AND I]. P. L,UGSTER

stability of both biotite and muscovite is a function of fg,6, and Fig. 11 was constructedwith the assumptionthat fs,6 wirs high enoughfor the to be stable. Chinner (1960) has shown how the increased"oxygen content,, in a biotite-quartz-muscovite-kyanite-magnetite-(hematite) corre- sponds to increasesin fo,. In Fig. 11, for a given isotherm, the biotite

o - lO

600 700 aoo 900 tooo ttoo Temperofure,oC

Irrc. 13. Stability of biotites as a function of fs, and temperature compared to the approximate stability of olivines (and pyroxenes) at a total pressure (Hrf HrO) of 2070 bars. The fields are labeled as follows: a) biotite-sanidine-hematite-(gas); b) biotite- sanidine-magnetite; c) biotite-leucite-olivine-magnetite (c': hematite) ; d) biotite-kalsilite- leucite-olivine; e) biotiteJeucite-olivine-iron; f) biotite (annite); g) kalsiliteJeucite-olivine. Solid and dashedlines show the stability of a given biotite (Fe/FetMgX 100); dotted lines, olivines. Biotite equilibria for a number of biotite bulk compositions have been projected along the Fe/Fef Mg axis upon the f6r-T plane. Lables of fields are not unique and high temperature areas are labeled for magnesium-rich bulk compositions onll'. [1yorl'. labeled I and II show oxidizing and reducing trends in crystalizing magmas. compositionwill becomemore magnesiumrich with increasingfugacity of oxygen,a relation recognizedqualitatively by Chinner. Tilley (1957), in a discussionof the alkalic rocks of the Haliburton- Bancroft areain Ontario, Canada,gives an analysisof a very iron-rich biotite. As this biotite coexistswith corundum, the annite-corundum curve of Fig. 11 helpsto definethe intensivevariables during crystaliiza- tion of those rocks. The curvesrepresenting these assemblages indicate that biotites with intermediate Fe/Fef Mg ratios will be stable in a smaller range of f6, BIOTITT, STABILITY I Z.).)

and temperature values if they coexist with k1'anite, sillimanite, an- dalusite, or corundum tharnif they exrst in a non-aluminousenviron- ment. The f6,-T curve above which biotites with more than 50/6 annite cannot coexist with aluminous silicatesIies somewhat above the curve for the Ni-NiO buffer. Figure 4 shows the contrasting curve for biotite (50/p annite)-sanidine-m agnetite assemblages.

Biotite-quartz-gos.The most common biotite-bearingmineral assemblages are those containing qttartz. The stability of annite-quartz was deter- mined by Eugster and Wones (1962) and we were able to show that it doesnot differ from the annite stability at f6, values above those of the FezSiOa-Fe:rO+-SiOzbuffer becausethe addition of quartz does not lead to the formation of new phases.The high-oxygenfugacity assemblages arehematite*sanidinef qttartz and magnetite*sanidine* quartz. How- ever, at fe, valuesbelow those of the FezSiOa-FerO+-SiOzbuffer, the sta- bility field of annitef quartz is drastically reduced,because of the reac- tion of qttartz rvith magnetite to form fayalite. The annite*sanidine f magnetite]_quartz boundary terminatesat the intersection'with that buffer curve, representedby point D in Fig. 12 (f.orthe rragnitudes of fo, and T of point D for a given P*u"see Eugster and Wones,1962). Below point D the annitef quartz field is bounded b1'the curve repre- senting the reaction KFerAlSirOro(OH)z-t 3/2 SiO,= KAISLOz I 3/2 FerSiOr* H:O (IV) annite q.uartz sanidine favalite which originatesat point D. For bulk compositionsof increasingmagnesium content, fayalite is replacedat first by an iron-rich olivine and later by a pyroxene (see,for instance,Bowen and Schairer,1935). Hence for biotiteswith intermediate Mg/Mgf Fe ratios, the biotitef qtartz field must be bounded by a reactionof the type K(Fe,Ms):AlSi3Oro(OH), + 3SiO, = KAISLOs* 3(Fe,Mg)SiO: * HzO (V) biotite BII- qrartz sanidine pyroxene The field boundary representedby this reaction must intersect the biotite*quartzfsanidine{magnetite boundary for the same biotite composition(B II) at a point D II (seeFig. 12). D II is also a point on the fer-T curve representingthe coexistenceof the intermediate py- roxeneof reaction V rvith magnetite and qvartz (curve P II in Fig. 12). Any p1'roxenericher in FeSiOawould be oxidized along this curve ac- cording to the reaction 3FeSiOrI1/2Oz=Fe"On f 3SiOu (VI) ferrosilite magnetitequartz t256 D. R. WONES AND H. P. ]i.UGSTER

No data are availableon the oxidation of intermediatepyroxenes, but it is reasonableto assume,that the for-T curvesfor pvroxene-magnetite(or hematite)-quartz assemblagesbehave similar to those for the oxidation of intermediate olivines, which will be discussedlater and are shown in Fig. 13. If they do behavein that way, they will lie essentiallyparallel to the oxygen buffer curves. They will also have the property that for iron- rich pvroxenesa large changein Fe/Fef Mg will causea smali changein f6r, while for magnesiumrich pyroxenesjust the oppositeis true. Point D II of Fig. 12 represents the assemblagebiotite{ quartz *sanidine*pyroxenef magnetite.It is an isobaricinvariant point and lies on the biotite+ quartz contour B II, which is identical with the biotite contour of Fig. 4 for the samebiotite composition.The composi- tion of the pyroxene of point D II and curve P II is not known and will have to be established experimentally. The location of the biotite *quartz*sanidinef magnetite boundary' is not known (reaction V), but it must originatein point D II and move subparallelto boundary IV towards lower values of f6, and T. Point D II, therefore,is the highest temperature,for a given Pgu"2&t which a biotite of compositionB II can coexistwith quartz. Somewherebetween points D and D II of Fig. 12, olivines must be replaced by pyroxenes. Point D I has been drawn to represent the assemblage biotite+olivine{pyroxene*sanidinefmagnetite *quartzlgas. The following field boundaries, for a fixed bulk composi- tion, biotite B If quartz, intersectin point D I; biotite*quartzf sani- dinefmagnetite (B I), biotite*quartz{sanidine*olivinefpyroxene (VII) and olivinef pyroxenef magnetite{quartz (Ol-Px-}It), whereby curve Ol-Px-Mt must lie betweenthe f6r-T curve for the FezSiOa-FeaOn- SiOzbuffer and curve P II; but the differencein fe, betweenthese two curves is probably exceedinglysmall (seediscussion of Fig. 13). Figure 12 also contains a contour labelled 0 which representsthe assemblagephlogopitef quartzf enstatite*sanidine{ gas.This contour behaves similarly to the phlogopitef forsterite*leucite*kalsilitef gas curve of Fig. 4, but lies at lower temperaturefor a given gas pressure. With increasing Mg content, the biotite+ quartz contours of Fig. 12 (biotite+ quartz* hematitef sanidine, biotite{ quartzf magnetite fsanidine, and biotite*quartzf pyroxene+sanidine) must move to- wards higher temperatures without crossing each other and they will eventually, in the absenceof iron, merge with the phlogopite+quartz contour (0). Therefore,the path describedby all points D II must curve upwards and asymptotically approach the 0 contour at high f6, values. Figure 12 has been drawn with the assumption that, at that particular gas pressure,enstatite+sanidinef gas is the stable high-temperature BIOTITE STABILITY 1257 assemblage.Recent data by Wones (unpublished) indicate that at a temperature of about 840" C. and a gas pressureof 2000 bars the as- semblage phlogopitefquartzfenstatite+melt*gas is stable. Hence, of the biotite contours drawn for Pg.":2000 bars in Fig.4, only those ivhich lie at temperatureslower and at fo2values higher than the corre- sponding pvroxene-magnetite-quartzboundary (P II) remain unaf- fected b1' the addition of quartz. A similar argurxent holds for the reac- tion sanidinefquartzfgas-melt at temperatures above 765" C. (Shaw, 1963c).

Appr,rcerroN To NATURALBrorrrBs Determinat'ionof annite concentrationIn the foregoing discussionof biotite reactions,emphasis has been on the end member annite, KFeaAISiaOro (OH)r. fn all assemblagesconcerning -rich feldspar andf or muscovite and magnetite a critical variable is the KFesAlSLOl0(OH), concentration.In most natural biotites, and especiallythose occurring in igneousrocks, the determination of the concentrationof this com- ponent is a probiem of someinterest In exarriining analyses of natural biotites, one is immediately struck brr the diversities in composition. There are three groups of cationic sub- stitutions possible in biotites: "interlayer" substitutions (K+iNa+ -Ca2+-H3O+), octahedral layer substitutions (Fe2+3Mgz1iMn2+ 3Fe3+3Ai3+=Ti4+=I [vacancy]), and tetrahedral layer substitu- tions (Si+a3Al3+rFe3+).In addition there are the anionic substitutions (OH-=F-=CI-=O'-). The problem remains of determining the con- centration of KFesAlSiBOl0(OH),within a given biotite. For the ideal end member,the only inter-layer cation is K, the only octahedralcation is Fe2+,Al occupiesI of the tetrahedral sites, and the anions are 2(OH) groupsin addition to 10 .Decrease of any of the ideal quantities will decreasethe concentration of KFesAlSirOto(OH)zand affect the activity of that component. A great deal of work will be required to establishthe effect of other sub- stitutions, but probably the (Na, Ca)=K and the 3Fe,+i2Al3+* n substitutions are the only ones which will tend to decreasethe stability of annite. This deductionis basedon the effectof paragonitecomponent on the stability of muscovite (Eugster and Yoder, 1956)and the known Iimitation of soiid solutionbetween trioctahedral and dioctahedralmicas (Foster, 1960). Until more complete data on the effect of thesesubstitutions are avail- able, simplicity requires the determination of the maximum concentra- tion of K, Fe2+,[AlSi3], and OH within their respectivesites, and the assignmentof the smallestof thoseconcentrations to KFeTAISLOT6(OH)r. 1258 D. R. WONES AND H. P. T,UGSTER

A cursory examinationof most biotite analysesindicates that Fe2+in the octahedralsite is the most commonlimitation. As the present study has been concernedwith that substitution, it would seem that the determination of the mol fraction of Fe2+in the octahedrallayer and the substitution of that value for "x1" in equations (5, 6) above is the most direct means of applying the results of this study to natural biotite assemblages. A final remark may be in order concerningthe useof physicalproperties to estimate the mol fraction of KFeaAlSi3Ol0(OH)2.The most easily' measuredproperties are the unit cell dimensions,r-rav reflectioninten- sities, the indices of refraction, density, zrnd more recentlv, magnetic ^.. ^ ^^-+i Lit I +. - SUbLCprruurr). The optical measurementsare limited in that the birefringenceof bio- tites changesverv little, and in a majority-of cases,2V is so small as to provide very little information. This reducesthe optical data to effec- tively one measurementand one or two estimates. As pointed out by Smith and Yoder (1956), the majority of biotite unit cellshave a B of 99'55'+20' (1M) or 95o00'(2M) and a 1/3:b. Henceb andc provide two measurements. The remaining properties (r-ray reflection intensities, density and magnetic susceptibility) may provide sulficient accurate data if done under optimum conditionswith a great deal of care. Ifence 6 parameters are available to estimate some dozen common substitutions. Although there are some limiting effects, a chemical analysisstill seemsto be the most satisfactory technique and, with the presentdav advancesin fluorescencespectrometry, will probably prove the simplest.

Recognit'ionof usefwl mineral assemblages.The composition of a biotite within a given rock merely permits an estimationof either the maximum fo" or temperature or the minimum fsre or fn, at which the biotite formed. This does not provide much more than an estimate of one or two variables,if the third is known or estimated. Ifowever, the presenceof the equilibrium assemblagesanidine-mag- netite-biotite immediately permits the determination of the univariant fsr-T (or the divariant fe,-fsr6-T) conditions of the formation of the mineral assemblagewhich containsbiotite of a specificcomposition. The analogous assemblage muscovite-corundum (aluminosilicerte-quartz)- magnetite permits the determination of f6r-T conditions. Hence the critical determination of the presenceof sanidine or muscovite, mag- netite, qrartz, and the aluminosilicatesis most important in making full useof the biotite eauilibrium data. BIOTITF STABILITY t259

Perhaps one of the most useful applicationsof the biotite data is in establishingmaximum (or minimum) H2O activities in processesinvolv- ing igneous (and some metamorphic) rocks. Here the divariant equi- librium involving fqr-fHr6-T (equation 6') for the biotite-sanidine-mag- netite assemblageis the one of interest. The presenceof with the magnetite permits an estimate of fe,-T conditions and the substitu- tion of thesein equations(6') or (6") then permits limits to be placedon fs,6 (Lindsley, 1963). In metamorphicassemblages the biotite*muscovite*magnetitef alu- minosilicate-l qrartz assemblagepermits f6r-T estimates independently of fsr6, (reactionsII and III) and consequentlydoes not permit the estimateof HzO activities.IIowever, if combinedwith chlorite:

KFe3AlSlOro(OH)z * FeaAlzSi:Oro(OH)s| 4/3 Oz = 3SiO, + KAITAISLOIo(OH), * 8/3 FesOr+ 4HrO, such an estimatewould be possible(see Turnock, 1960).This equilibrium will be dependent on the composition of the chlorite as well as the biotite. The critical relationship, in all the above assemblages,is the co- existenceof biotite, magnetite,and sanidine or muscovite. However, in many alteration sequences,the iron-rich are sulfides rather than oxides,and consequently,the biotite mineral assemblagescan pro- vide usefulconstraints on intensivevariables during the alteration. In all theseapplications the maximum amount of information mav be obtainedonly if the entire assemblageis considered,not merely the pres- ence,absence, or compositionof a singlemineral. It is particularly valu- able to determine the nature and composition of the opaque minerals ("ores") which are present.Also of great importance is the problem of contemporaneityof the severalminerals.

Br,ctttn, Rplcrrolr Senros The reaction principle of Bowen (1922, 1928)applies to the biotites. The relations of biotite to a magmatic or metamorphic system will be quite sensitiveto variations in temperature, pressure,or the activities of componentssuch as 02, I{2O, F, SiOz.The types of reactions which can occur are highly varied but may be generalizedto the form: biotite*(Or+(SiO,) - K-feldspar (or feldspathoid) * Fe-Mg silicates (or oxides) fHzO. The particular phasesma-v be qnartz, tridymite, sanidine,leucite, kalsil- ite, olivine, pyroxene, amphibole, magnetite, hematite, and/or a melt containing any or all of the critical componentsKzO, AlrOs,SiO2, MgO, Fe, Oz,Hz and F. 1260 D. R. WONL,SAND H. P. DUGSTER

The negative free energy of mixing for KMgrAISisOro(OH)r and KFerAlSirOro(OH),indicates that biotites of intermediate compositions will coexist with more magnesianolivine, pyroxene or melt for mag- nesian bulk compositionsand with more ferroan minerals for ferroan bulk compositions.Such relations are implied by Thompson (1957) in AFM diagramsfor metamorphicassemblages, and by Larsenand Draisin (1948) for the igneous rocks of the southern California batholith. In other words, tie lines, biotite-ferromagnesianphase(s), are more con- centratednear the middle of the phlogopite-anniteseries than thev are near either of the two end members. Heinrich (1916)and Nockolds (1947),in their anaiysesof biotite com- positionsin various rock types, showedsome generaltrends which may be summarizedby stating that the biotites from the more siliceousig- neousrocks tend to be more iron-rich than biotites from the lesssiliceous rocks.There are two reasonableinterpretations of thesetrends, one that the bulk compositionsof these lock types are related and the biotites merel1'reflect that effect,or that the lesssiliceous rocks representhigher temperatures of crystallization and hence only Mg-rich biotites are stable at those magrnatic conditions. The two interpretations are cer- tainly not mutually exclusive. The biotite data can be used to estimate the relative importance of intensivevariables in establishingthe distribution of iron and magnesium betweenvarious phases.Ileretofore, temperatureand the nature of the coexisting phases were consideredthe most important variables. Figure 13 is an attempt to demonstlate,as shown by Muan and Osborn (1956),that f6, is as important as temperature,if the oxidesare included as nafic phases.This figure also servesto summarizethe biotite data. It is drawn for a constant (Hr+HrO) pressureof 2010bars and is a.projec- tion along the compositionaxis onto the fer-T plane. Figure 13 showsthe projection of five sectionsmade at constant bulk composition,represented by a specificbiotite composition. These sec- tions appear as the contourslabelled 100, 70, 40, 30, and 0 and are the biotite-sanidine-magnetitecontours of Fig. 4. The,v are drawn solid where the-v*were located experimentaliy and are dashed where their position has been inferred. The contour Iabelled0 representsthe assem- blage phlogopite+forsterite*leucite*kalsilite*gas. For annite bulk composition Eugster and Wones (1962) have shown that the sanidine {magnetite field cannot be in direct contact with the fayaiite{leucite *kalsilite field, but must be separatedfrom it by a narrow field repre- senting the coexistenceof fayalitefleucitefmagnetite. The biotite fsanidinefmagnetite field of Fig. 13 (field b), therefore,must also be separated from the biotite+olivinetleucite*kalsilite field (d) by a BIOTITD STABILITY 1261 narrow fer-T area representing biotite+olivine*Ieucite*magnetite (field c, Fig. 13). Sincefield c must existfor all biotite bulk compositions,the boundaries between fields b and c as well as c and d cannot crossthe phlogopite con- tour, but must approachit gradually at somehigh fs, at which neither the biotite nor the olivine will contain much iron. Thus a narrow strip of

So+Lc Ks+Lc+Ol+C +Ol+Ml +G

Biotite+ (b) () Sonidine+ o o 5 o o CI E o F

loo 80 60 40 20 0 FelFe*Mg xloo

'I-X Irrc. 14. projection of K(Fe,Mg)3AlSLO10(OH)r-l-H:tHzO bulk composition, buffered by Fe2SiOa-Fe3Oa-SiO2,at a constant total pressure oI 2O70 bars. Only the boun- dary between fields (b) and (f) is experimentally determined. the biotite-olivine-leucite-kalsilite field extends to high ft1, values, but only for very magnesianbulk compositions.Where field c comesin con- tact with the fs,-T curve of the FeaOa-Fe2O3buffer, magnetiteis repiaced by hematite and the equivalentfield c' (biotite+olivine*leucite*hema- tite) extends into the hematite field. It should be noted that a discontinuit,vmust exist in the biotite con- tours wherethey crossboundaries between fi.elds b, c (or c') and d. With the exception of fieid g, Fig. 13 onl-v shows equilibria involving biotites. To clarify the high temperature relationships,Figure 14 has been constructedfrom Figure 13. It representsa T-X section along the f6,-T curve of the FezSiOa-FesOr-SiOzbuffer (curve labelled 100 in Fig. 13). The biotite-sanidine-magnetite-gasboundary has been determined t262 D. R. WONES AND II. P. EUGSTER experinientaliyup to a temperatureof 900" C. (seeFig. a). Above that temperature phase relations have been inferred from Fig.13. In par- ticular, the two isobaricinvariant equilibria, biotitef sanidinef leucite * olivine* magnetitef gas and biotitef leucite+ kalsilitef olivine {magnetite*gas, are shown which define the limits for field c. Fe/Fe {Mg ratios shown in Fig. 14 are those of coexistingbiotites, olivines, and mzr.gnetites.At the highest temperaturesand magnesiumrich com- positionsa simpletransition loop exists,enclosing the field of biotite+ol- ivinef leucite*kalsilite*gas. At fe,-T valueswithin the field of stabilit-v of wiistite, this transition loop would be continuousfrom the magnesium- free to the iron-freesystem. In Fig. 13, equilibria existing at very low values of fs, have been par- tially omitted. Specifically,no field is shown for biotite*sanidine*iron. This assemblagewould occupy a narrow strip within field e. In this f6r-T area a figure analogousto Figure 14 could be constructed,but with iron taking the place of magnetite. Becauseof the rapid decreaseof fsre at verv low valuesof f6, for a P*u"of 2000bars, all biotite contoursmust be crowdedinto the field representingbiotite*sanidinef iron (within field e), as they passtowards lower temperaturesand f6, values. As mentionedabove, Fig. 13 has alsobeen constructed to elucidatere- lationships between several ferromagnesian phases. Therefore, the oxidation curvesfor fa.valite100, fayalite 10 forsterite 90, and fayalite 1 forsterite99 have beenprojected onto the biotite-sanidine-magnetitefield (in Fig. 13 thesecurves are labelled100, -19 and -1, respectiveiy.The 100curve is, of course,the fo"-T curve of the FerSiOr-FeeOa-SiOrbuffer. The curves -10 and -1 were calculatedassuming ideal cationic solid solutionsin the oiivines,an assumptionjustified by the theoreticalanaly- sis of Bradley (1962). The Faro and Fa1 contours indicate the fayalite contents of olivines from olivine-pyroxene-magnetiteassemblages and representthe highest FezSiOEcontent possiblefor the given f6"-T values. The olivine and biotite contours intersect at steep angles,because the olivine contours represent redox reactions while the biotite contours representhydrogenation-dehydrogenation reactions. If we considerbiotite-olivine bulk compositions,that is, the assem- blages biotite-olivine-sanidine-magnetite-(quartz)-(pyroxene),we can predict accurateiy the effectsof both fe, and T on the magnesium-iron distribution between biotite and olivine. At constant temperature,for example, an increasein oxygen pressurewill not onl1. result in a de- creasein the iron content of both the stablebiotite and the stabieolivine. Pyroxenesshould behavevery simllarly to olivines,since pyroxene con- tours (Fig. 12) also representsimple redox reactions. Consequently,if the fsr-T conditionsare appropriate,the iron-magnesiumdistribution of BIOTITE STABILITY t263 biotite-olivine or biotite-pyroxene pairs may favor either iron-rich biotite coexistingwith magnesianolivine and pyroxene (Pecora, 1941; Ram- berg, 1952) or magnesium-rich biotite coexisting with iron-rich py- roxene(Larsen and Draisin, 1948). Changesin Hz*HzO pressurebasically have little effect on the spatial relations of the equilibria shown in Fig. 13. Increasing pressure merely shif ts the biotite contours towards higher temperatures, while the olivine contours remain practically unaffected. Figure 13 represents,of course,unusual bulk compositions.Amphiboles and pyroxenes are much more commonly associatedwith biotites than are olivines. But for such assemblagesno data are available and no valid extrapolationsare possible at this time. We may now attempt to discussbiotites in equilibrium with a melt. The biotite contours of Fig. 13 can probably be safely extended to in- clude biotite*sanidine*magnetite{melt. These four phasesact as fo, buffers and changes in the Mg/Fe ratio of the melt would simply be reflected in the amounts of biotite and magnetite coexisting with the melt. Osborn (1962) has emphasized the importance of fo, on the courseof crystallization of magmas and on the end products. In a similar way we may considertwo contrastingtrends of crystallization(Fig. 13). Trend I represents a magma, which, during crystallization and cool- ing, becomessaturated in HrO, reacts with that component, and loses hydrogen to the environment. fn such a situation fo2 remains constant or increasesslightly with little changeor a decreasein the Fe/Fe*Mg ratio of the biotites crystallizing from the melt. The final crystallization products will be magnesium-rich biotite and considerable quantities of magnetite. Grout (1923) describedsuch phenomenain the granite of St. Louis County, Minnesota. Potapiev (1964) has describedsuch phe- nomenain the Kolyvanian massif,and one of us (D.R.W.) on field trips with P. C. Bateman has observed such sequencesin the late stages of crystallizationin the plutons of the SierraNevada batholith (Bateman et al.. 1963\. Trend II, representsa magma which, becauseof the low H2O content, is "buffered" by the anhydrous mineral assemblages.The final result would be the crystallization of iron-rich biotite and other ferromag- nesian silicates and very little magnetite. Larsen and Draisin (19a8) in- dicate that this may be the casefor portions of the southern California batholith, and the data of Heinrich (1946) and Nockolds (1947) imply this situation may be the more generalcase. It would seem that the relations of the several ferromagnesian min- erals in a crystallization sequencemight indicate a probable f6r-T path of the crystallizing magma, and this, in turn, might give some indication t264 D. R. WONb'S AND H. P. EUGSTER of HrO saturation of undersaturation.The problem of Hr solubility and diffusionin silicatemelts alsomust be considered.

Brorrrns AS INDTcAToRS oF INTENSTvE VARIABLES The biotite stabilit.v has been shown to be bounded bv a trivariant equilibrium such that in the assemblagebiotite-K-feldspar-magnetite three of the four variables,mol fraction of KFe3AlSi;Orn(OH):,oxygen fugacity, H2O fugacity, and temperature, must be defined before the fourth can be determined.Additional complicationsinvolve the mol frac- tions of KAlSiaO8and FerO+in the feldspar and spinel phases,as well as the structural state of the feldspar.For such casesexpression (6") must be used.The problem of estimatesof arrrsiro,and a3'"6rnis best solved by using the data or Orville (1963) for KAlSiaOs activities, and those of Lindslev (1963)and Turnock and Eugster (1962)for the FeaO+activities. Once that assemblagehas been established,however' it is relatively straightforward to determine fsr6, given fe, and T. The remaining problems thus consist of getting estimatesof two intensive variabies. Lindsley's(1963) data on the systemFe-Ti-O provide meansof estimating fe,-T conditions from the composition of the coexisting iron and ti- tanium oxides. Biotite analvsesmay also provide rough estimatesof f6r-T conditions at constant fsr6. From Fig. 1it can be seen that Fe3+/Fe2++Fe3+is about 0.25 for FerO+-FezOebuffer conditions;0.10 for Ni-NiO; 0.05for Fe:SiOr-FeaOa-SiO2;and (0.02 for Fer-*O-FerOr. For temperatureestimates there are such possibilitiesas the feldspar solvus(Yoder, et a|,.,1957; Wyart and Sabatier,1962;and Orville,1963), the calcite-dolomite solvus (Goldsmith, 1959) muscovite- solvus (Eugster, 1956),and isotopefractionation (Epstein, 1959). The fugacitl- of HrO is probably one of the more interestingvariables to attempt to define,as fsre influencesmelting points (Tuttle and Bowen, 1958),viscosities (Shaw, 1963b; Friedman et al., 1963;Burnham, 1964) eruptive phenomena (Boyd, 1961; McBirney, 1963) and metamorphic grade (Fyfe, et o1.1958).If f6, and T can be estimated,the biotites should serveas indicatorsof fsr6. Even in the absenceof K-feldspar and magnetite the mol fraction of KFeeAlSiBOl0(OH),in biotite permits minimum estimatesof fsr6 to be made. Of the many biotite-K-feldspar-magnetiteassemblages described in the literature, the two selectedhere demonstrate different applications of the biotite data. The study of Larsen et al. (1937) on phenocrystsin volcanic rocks demonstratesthe usefulnessof the stability data with even a limited amount of information on the compositionof the biotite. The combined data of Engel and Engel (1960) and Buddington (1963) BIOTITE STABILITY r265

provide an examplewhere a more rigorous application can be made be- causeof an abundance of mineraloeical information.

VolcanicRocks. The data of Larsen et al. (1937)on the biotites found in the quartz-latites of the San Juan Mountains, Colorado, lvhen com- bined with the Tuttle and Bowen (1958)minimum melting curve,permit averyrough estimateof the fsre-T conditionsof the magma chamberat the time of eruption. The biotites in question have been badly oxidized

o -

TEMPERATURE,'C

Frc. 15. Plot of fHrs versus T for G, "granite minimum melting" as determined by Tuttle and Bowen (1958). Curve 1 represents the stability a biotite of 0.15 mol fraction KFesAlSi3Oro(OH)2coexisting with magnetite and hematite. Curve 2 representsthe stabil- ity of a biotite of 0.25 mol fraction KFerAlSirOro(OH), coexisting with quartz, magnetite, and fayalite.

during the eruptive history so that it is difficult to obtain an estimate of f6r. In the example of the Piedra Rhyolite, the mol fraction of KFeaAlSiaOro (OH)z end member is about 0.28+0.03. Assuming that FerOa-FezOaand FezSiOa-SiOz-FeaO+are the limiting fs,-T boundaries,the stability curves for a biotite of this compositionmay be caiculatedfrom equation (6') and are shownintersecting Tuttle and Bowen's (1958)minimum melting curve at either 730oC., 600 bars fs,6 or 875oC., 125 bars fHrc,in Fig.15. Tuttle and Bowen'sdata were recastin fugacitiesrather than pressures. The need for most preciseinformation is obvious, and careful examina- tion of the oxide mineralscould permit a better estimate. In the above examplethe mol fraction of KFeaAlSieOro(OH)zwas as- sumedto be 0.15in the first caseand 0.25in the second.These values re- t266 D. R. WONES AND H. P, EUGSTER fer to Fig. 1 which showsestimates of KFeaAlSigOro(OH)zconcentrations in biotites buffered b_vFezSiOa-FeaOa-SiOr and FeaOa-FezOa.The major assumption in this treatment is that components other than n[g2+ have the same efiect on the stability of the annite end member. Minor assumptions are that the activities of KAlSiaOs and Fe3Oaare 1, and that the melting curve of the Piedra Rhyolite is comparable to the "granite minimum" melting curve. The presenceof a biotite phenocryst of known composition permits a minimum H2O fugacity to be estimated for a given temperature, whereas the presenceof magnetiteor pyroxene(Carmichael, 1960) to the exclusion of biotite permits a maximum estimatefor the H2Ofugacity.

MetamorphicRocks. The completedata of Engel and Engel (1958,1960) on biotite-sanidine-magnetiteassemblages, when combinedwith the ap- proximate magnetite compositionsgiven by them, permit fairly good estimatesof fs,e during regional of the gneissesof the Northwest Adirondacks.In this casethe f6, estimatesare much better, as both Lindsley's (1963)data on the system Fe-Ti-O and the Fe3+content of the biotite permit estimatesto be made of f6r-T conditions. Engel and Engel (1958,1960) have estimatedthe temperaturesof two assemblagesin gneissicrocks to be 500oand 600", respectivell'.For the 500'C. assemblage(Emeryville), the Fe2+content of the biotite octa- hedral layer is about .38, the Fe3+content is about 0.04. The feldsparis about Orsr and the ulv

fo, at 500oC. was 10-2abars then fgre must be about 0.1 bar;.at 600'C. fsr6 must vary between1-10 bars. The gneissesin the Adirondacksare interlayered with graphitic marbles and amphibolites.T'he amphiboliteshave clinopyroxene-pvroxene-horn- blende assemblages(Engel and Engel, 1962). Exftapolating the data of Boyd (1959) on the tremolite3diopsidef enstatite+quartziIHzO reac- tion to 500oand 600oC., the equilibrium HzO pressuresare about 0.1 and 1 bar. The graphite-COzreaction has beenrecently studied by French (1964) using the data of Wagman et al. (1945). For graphite one may obtain, at 500o C., the expressionlog fs6,:1og161126.64 and at 600" C., Iog f66, :log f6r{23.60. The values of log fge, obtained for the Adirondack assemblagesare 2.60 at 500oC. and 4.00 at 600' C. This disparity may be explained in terms of disequilibrium, a lack of graphite in the 600. C. assemblage,or the actual gradient in the fugacity of COz from 435 to 10,000bars. The high ratios of COzto HzO are consistentwith the min- eral assemblagesof the marblesand the interbedded.gneisses, so that the gradient may well exist and be due to dehydration and decarbonation re- actionsleading to the high temperatureassemblage. If the biotites are not in equilibrium with the magnetites,then the Hzo fugacities are minimal values. However, the decreasein the quantity of biotite, the variations in magnetite composition,and the presenceof graphite in the marbles all combine to give a uniform model. A further implication of the data is that the existenceof biotite-K- feldspar-magnetite assemblagesin rocks of low metamorphic grade ( < 500' C.) impliesvery low valuesfor water pressure,and perhapsmany modelsin which water pressureis consideredequal to Ioad pressureneed revision.

Detectionof Grad'ients.The fact that the composition of biotite coexisting with sanidineand magnetiteis dependentor frr,o,f6, and T implies that gradients in any of these three intensive variables should be reflected in changesin the compositionof biotite. peikert (1963) applied this argu- ment with somesuccess to rocks of the canadian shield in northeastern Alberta. He found that biotite compositions were closely related t. spe- cific rock types. He assumedthat rocks of such closeproximitl, would be isothermal,so that variationsin f6, or fs,6 w€r€ responsiblefor the devi- ations in the composition of the biotites. ff the gneissesare formed by the alteration of metasedimentaryrocks, the model of cation exchange from an ubiquitous vapor phase in such a system is difficult to reconcile with the persistenceof steep gradients in fs, observed in manl' Iocalities (Chinner, 1960;Eugster, 1959).Pitcher and Sinha (1957) have observed t268 D. R. WONES AND H. P. EUGSTER mineraiogicchanges easily explainedby gradients in the f6, of contact aureolesaround granite intrusives. The changes in the compositions of biotites in wall rock alteration processes(Anderson et at., 1955)very clearly show gradientsin the ac- tivities of oxvgen and sulfur which also match the activity gradients pro- posedfor H+ and K+ in suchphenomena. The stability of biotite in such phenomenais alsoa function oI other variablessuch as the hydrogenion and potassiumion concentrations.

Brorrres rN GEocHRoNoLoGY The high K and Rb contentsof biotites have made them valuable for studiesin geochronology,using the K-Ar and Rb-Sr methodsfor dating the tine of crystallization of the biotite' As this study has shown, the biotite-K-feldspar-magnetiteassemblage represents a trivariant equi- librium in which changesin P, T,fsr6, or fo,will necessitatea changein the compositionof biotite through recrystallizationin order to reestab- lish equiiibrium. The classicstudy of Tilton et at. (1958)on the Baltimore Gneissdem- onstrated that the agesof the biotites are Paleozoic,but the agesof the zirconsand feldsparsare Precambrian.As all the biotites examinedare in K-feldspar and magnetitebearing assemblages (C. A. Hopson, 1964,and pers. comm.), recrystalTizationof the biotites during metamorphism seens entirel1,'reasonable. Jaeger el al. (196t) have also demonstrated variationsin biotite agesin which the biotites are partially recrystallized. Recentl.v,however, Tilton and Hart (1963)have shown that diffusion of and strontium out of biotite crystals during metamorphism will reduce biotite ageswithout recrystallization. It is readily apparent that biotite ages are particularly subject to metarnorphic changes.Careful petrographic studies to ascertaineither the homogeneitvof the biotites being analysedor the existenceof the tri- variant assemblagesdiscussed certainly should add a great deal to the interpretationof biotite ages.Biotites occurringin K-feldspar,muscovite, or magnetite free erssemblages(marble, quartz-plagioclase-biotite gneisses)should. have less tendency to recrystailize, and might be ex- pected to y-ieldolder ages.

AcxNowTBoGMENTS This studl' was initiated at the GeophysicalLaboratory, Carnegie Institution Washington,while D. R. Wones held a Vannevar Bush Fel- lowship and H. P. Eugsterwas a staff member.D' R. Woneswould like to expresshis gratitude to the Geology Department of the Massachusetts BIOTITE STABILITY r269

Institute of Technology and to the GeophysicalLaboratory for making this opportunity available, as well as to Profs. H. W. Fairbairn and G. J. F. MacDonald of M.I.T. and to Prof. J. B. Thompson, Jr. of Harvard University for much help and stimulation at the beginning of this study. We are much indebted to our colleaguesat the GeophysicalLabor- atory, the U. S. Geological Survey and The Johns Hopkins University for encouragementand many helpful discussions.The manuscript was critically reviewedby J. J. Hemley, H. R. Shaw and Priestl,u:Toulmin, III, and their commentsled to a considerableimprovement of the manu- scrlpt.

RnpnnrNcrs

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Monuscript receizted.,January 29, 1965; acceptedJor publication, May 4, 1965.