ESperim_ental investigations and geological applicationsof equilibria in the system feO-fiOr-Al2O3-SiO2-H2O

SrpvBN R. Bour-eNr

Institute of Geophysics and planetary physicsUniversity of California, Los Angeles

Los Angeles, California 90024

V. J. Wnlr

Department of Earth SciencesMontash University

Clayton Victoria, 3168 Australia

eNo A. L. Boerrcsen

Institute of Geophysics and Planetary physicsand Department of Earth and Space Sciences

University of California, Los AngelesLos Angeles, California 90024

Abstract

A new mineralogic geobarometer for peraluminous rocks based on assemblages ofilmenite-Al2SiO5-quartz-garnet-rutile has been calibrated from the equilibrium relation: 3ilmenite * sillimanite + z quartz s almandine + 3 rutile. The reaction boundary waslocated (+0.2 kbar) using piston-cylinder apparatus at 11.5, lz.o,12.s,13.1,14.6,15.3 and15.9 kbar at750,800, 850, 900, 1000, 1050, and I 100"c, respectively. The geobaromerer iswidely applicable as the univariant assemblage occurs in numerous terranes spanningmiddle amphibolite to garnet-granulite facies metamorphites. Pressures calculated forseveral terranes are consistent with the appropriate Al2sio5 polymorph(s) and aregenerally in agreement with other well-calibrated geobarometers subjeci to choice ofmixing properties for Fe-Ca-Mg-Mn garnets.

American Mineralogist, Volume 68, pages 1049-1058

rocks, especially those of medium metamorphic grade.Historically, relative pressures have been inferred usingA12SiO5 index minerals. In rocks where two Al2SiO5minerals coexist, quantitative assessment of pressure ispossible if metamorphic temperatures are accuratelyknown. However, there may be substantial uncertainty insuch pressure estimates as a result of metastable growthor persistence of a given Al2SiO5 polymorph (Grambling,1981) or uncertainty regarding textural relations, particu-larly for fibrolitic sillimanite (Vernon and Flood, 1977).Alternatively, pressure and temperature have been simul-taneously inferred from assemblages containing twoAl2SiO5 minerals and the products and reactants of acalibrated dehydration reaction (Carmichael, l97E). Suchan approach is locally useful, but the necessary lowvariance assemblages are uncommon.

Another uncertainty inherent in geothermometry andgeobarometry based on dehydration reactions results

Introduction

Field and laboratory studies of peraluminous metasedi-mentary rocks have played a prominent role in shapingcurrent theories concerning the deformational and ther_mal processes in the crust. Consequently, geobarometryand geothermometry in pelitic rocks have been of consid-erable interest to metamorphic petrologists. As a result ofan abundance of relatively pressure insensitive dehydra-tion reactions in pelitic rocks, temperatures can be rea-sonably well established in amphibolite and transitionalamphibolite-granulite facies rocks. At higher grades, Fe_Ti-oxide (Buddington and Lindsley, 1964; Spencer andLindsley, 1981) and two-feldspar (Stormer, 1975) ther-mometry have been successfully applied. However, pres_sures have been more difficult to determine in pelitic

I Present address: Department of Earth and Space Sciences,State University of New York, Stony Brook, N. y. ll7g4.

0003-0M)983/l I I 2-1049$02.00 t0/,9

1050

from variable H2O activity. Geobarometers based onanhydrous equilibria do not suffer from this disadvantage.One such barometer is based on the assemblage plagio-clase-garnet-Al2SiO5-quartz wherein the grossular com-ponent of the garnet is buffered by the equilibriumrelation:

3 anorthite(in plag) : grossular(in garnet)

+ 2 A 1 2 S i O 5 * l q u a r t z ( l )

(Hays, 1967; Had.ya and Kennedy, 1968; Goldsmith,1980). In rocks the assemblage is multivariant as theresult ofsolid solution in plagioclase and garnet. The fourphase assemblage is stable over a wide range ofpressureand temperature and can be used to infer pressures ifequilibration temperatures are known (Ghent, 1976; New-ton and Haselton, l98l). The primary dfficulty in applica-tion of the barometer is that the garnet compositions inpelites containing the four-phase assemblage are typicallyless than 5 mole%o grossular component. Relatively largeerrors accompany analysis of minor components in addi-tion to errors resulting from uncertainty in the activity ofgrossular component in garnet at extreme dilution. An-other potentially useful barometer is based on equilibriabetween cordierite and garnet-sillimanite-quartz. Unfor-tunately, experimental (Hensen and Green, 1971; Currie,l97l) and theoretical and/or semiempirical (Thompson,1976; Newton and Wood, 1979; Perchuk et al., l98l;Martignole and Sisi, l98l) calibrations are in conflict;pressures inferred from this widespread assemblage havelarge uncertainties. Given the problems and uncertaintiesassociated with barometry in pelitic rocks, it is clear thatadditional, well-calibrated barometers are needed.

Assemblages containing ilmenite + Al2SiO5 + quartzand/or garnet + rutile are common in medium to high-grade peraluminous metamorphic rocks. The significanceof the equilibrium:

3 ilmenite + Al2SiOs * 2 qtartz

= almandine * 3 rutile (2)

has not been recognized previously. This equilibriumrelation forms the basis of a useful geobarometer. Naturalassemblages containing garnet-rutile-Al2SiO5-ilmenite-quartz (hereafter referred to as cRAIL) are multivariant asthe result of solid-solution in garnet and to a lesser extent,in ilmenite. Thus, to a first approximation the pressuresinferred from the cRAIL assemblage (at fixed tempera-ture) are a function of garnet composition. Therefore,application of equilibrium (2) in terranes for which meta-morphic pressures are well determined by other barome-ters will allow the activities of almandine to be deducedempirically. This in turn will allow a critical evaluation ofgarnet solution models. In addition equilibrium (2) willallow inference of accurate thermochemical data foralmandine. This is important as there are numerous,significant almandine-bearing reaction equilibria that are

BOHLEN ET AL.: EQUILIBRIA IN THE SYSTEM FeO-TiOz-AlzO3-SiO2-H2O

difficult to investigate experimentally, but whose positionin P-T-fo;-fs, space can be accurately calculated if ther-mochemical data for almandine are known' Therefore, inlight of the overall significance of reaction (2), experi-ments have been undertaken to determine the relativestabilities of ilmenite-Al2SiO5-quartz and almandine-ru-tile as a function of pressure and temperature.

Experimental methods

Starting materials

A combination of synthetic and natural minerals were used inthe experimental investigation. Natural quartz from Brazil and alow Fe sillimanite from Brandywine, Delaware (Genth collection#399.15, The Pennsylvania State University) together with syn-thetic rutile, ilmenite, and almandine were used for startingmaterials. The quartz was prepared by grinding to approximately-200 mesh, followed by leaching in HNOr, and then firing at-800'C for 24 hours. The sillimanite was ground to -200 mesh.Several grains of sillimanite were analyzed by electron micro-probe to evaluate homogeneity and to obtain quantitative chemi-cal analyses (Table l). The sillimanite was homogeneous on the

scale of the microprobe beam and contained no elements abovebackground besides Al, Si, and very minor amounts of Fe. Rutilewas prepared from Baker Reagent Grade TiOz (anatase) byheating at 1000'C for 6 days. X-ray analysis of the product

indicated complete conversion to rutile. Ilmenite was synthe-sized by reacting at 1000'C in evacuated silica tubes appropriatemolar quantities of Fe-metal, hematite, and TiO2 (anatase) thatpreviously had been ground together and pellet pressed. Optical,X-ray, and electron microprobe analyses indicate that the ilmen-ite is homogeneous and stoichiometric FeTiOr. Almandine wasprepared using two different starting materials, a glass of alman-dine composition, and a mixture of appropriate molar quantities

of fayalite, sillimanite, and quartz. The glass was prepared byreacting Fe2O3, Al2O3, and SiO2 in a graphite crucible with atight-fitting graphite lid at 1375'C for 45 minutes. The result was

a black-green homogeneous glass. Optical examination of thematerial showed no unreacted starting material, and X-rayanalysis showed no diffraction pattern. Finely ground glass wasthen loaded into a 2.5 mm diameter Ag76Pd36 capsule withapproximately l-2 wt.% H2O and the capsule sealed. This

Table l. Electron microprobe analyses of sillimanite

31111-575 @dlte

(centh)Run /l 571 588 574

s10z 36 .2 37 .0

T i 0 z 0 . 5 0 . 7

A lz0r 62 .8 61 .0

F e o 1 . 0 0 . 8

Tota l 100.5 99 .5

s r 0 . 9 7 5 1 . 0 0 8

A.1 1 .993 r .959

T l 0 .010 0 .014

t re 0 .022 0 .018

r ( ' c ) 750 7s0

# polnts 7 a

3 6 . 8 3 5 . 9

0 . 4 0 . 6

62.4 63 .0

0 . 9 0 . 9

100.5 r00 .4

0 .990 0 ,957

1 . 9 8 0 2 . 0 0 1

0.009 0 .011

0 . 0 2 1 0 . 0 2 0

900 1000

36.4 35 .8

0 , 6 0 . 5

62.7 62 ,3

0 . 9 0 . 8

100.6 99 .4

0 ,980 0 .974

1 . 9 8 9 1 . 9 9 E

0.011 0 ,009

0.020 0 .018

1050 1100

36,7 36 .6

0 . 5 0 . 0

52.O 62.7

0 . 8 0 . 5

100.0 99 .8

0 .994 0 .999

1 . 9 7 E 1 . 9 9 r

0 .0r0 0 .000

0.016 0 ,010

1100

f >

capsule was then placed in a 5 mm diameter Pt capsule, alongwith -300 mg of Fe-metal powder and sufrcient water to react75Vo of the Fe to Fel-1O and the outer capsule was sealed.Garnet was synthesized at 900'C and 15 kbar for lZ-14 hours inpiston-cylinder apparatus. Optical examination of the productrevealed that the glass had reacted completely to garnet withtraces (<0.lVo) ofa low index crystalline phase, probably quartz.X-ray analysi-s gives the diffraction pattern of garnet (a =I 1.521 +0.001 A, determined from powder diffraction patterns,ll4' per minute scanning speed, with quartz as an internalstandard) with no indications of other phases. Electron micro-probe analyses indicate that the garnet is homogeneous, stoichio-metric almandine. Almandine was also prepared from finelyground mixtures of fayalite, sillimanite, and quartz using theprocedures outlined above. The fayalite used was stoichiometricFezSiOr, and its preparation has been described (Bohlen er a/.,1980). The sillimanite and quartz were those described above.Synthesis products were almandine (a = 11.520+0.0014) withtraces of quartz. Almandine prepared from crystalline startingmaterials has all of the same physical and chemical properties asthat prepared from glass. For both the almandine from glass andfrom fayalite-sillimanite-quartz the traces ofquartz in the garnetcould not be eliminated by fine grinding and re-reacting at 900.C,15 kbar on the iron-wi.istite bufer. Synthesis of almandine at avariety of different pressures and temperatures (7-20 kbar, 800-I100'C) gave similar results. However, almandine synthesized asdescribed above but with/6, butrered by quartz-fayalite-magne-tite resulted in a gamet with a slightly larger cell edge (a : 11.525- ll.528A) and very slightly increased amounts of additionalcrystalline phase(s). The only almandine used in this study wasthat synthesized on the Fe-Fe,-11O buffer.

Mrissbauer spectra of almandine and ilmenite were obtained atroom temperature using a constant acceleration, mechanicallydriven Mrissbauer spectrometer in order to check the startingmaterials for the presence of Fe3*. Samples of 70-90 mg wereused with a lOm Ci57Co in Pd source. Duplicate spectra wererecorded in 512 channels of a multichannel analyzer using avelocity increment of 0.03 mm per channel. Counting times weresuffcient to obtain several million counts per channel and peakdips of approximately 105 counts. The spectra were fitted withlorentzian doublets that in most cases were constrained to equalwidths and area for the low- and high-velocity components. Chi-squared and additional goodness-of-fit parameters (Ruby, 1973)were calculated for each fitted spectrum.

The M<issbauer spectrum of ilmenite consists of a singleferrous doublet and a very small, poorly defined ferric doubletthat appears in the spectrum as a low intensity "shoulder" on thelow velocity part of the ferrous doublet. For the octahedrallycoordinated ferrous iron in ilmenite the measured average isomershift and quadrupole splitting (ISF"": 1.058 mm/sec;Qs = 0.637mm/sec) are similar to previously reported values (Ruby andShirane, 196l; Syono et al., l98l). Observed peak widths are0.2E mm/sec. The intensity of the peaks attributable to ferric ironis so low that the location of the ferric doublet had to beconstrained in order to obtain convergence in the fitting proce-dure. The ferric doublet was constrained so as to be consistentwith isomer shifts and quadrupole splittings of octahedrallycoordinated Fe3* in other similar Fe phases. The relative areasof the ferrous and ferric count dips suggest that approximately3+15% of the iron is present as Fe3*. A slight, but significant,difference was noted in the areas of the two components of theferrous doublet. At first this was thought to be the result of

l05l

preferred orientation of the platy ilmenite grains. However,similar ferrous doublets with unequal areas are observed evenafter eforts have been taken to eliminate the preferred orienta-tion. Relaxation of the constraint of equal area results in aslightly better fit to the data but does not change the relativeamounts of inferred Fe3*. The relative areas of the ferrous countdips difer by 3+0.lVo, and a cause for this difference cannot bedetermined.

The M<issbauer spectrum of almandine consists of a ferrousdoublet that is very widely split in comparison with other ferrousiron silicates and a very small, poorly defined ferric doublet thatappears in the spectrum as a low-intensity "shoulder" on thehigh velocity edge of the low velocity component of the ferrousdoublet. For ferrous iron (in the dodecahedral position) themeasured average isomer shift and quadrupole splitting (ISF.. :1.299 mm/sec; Qs : 3.546 mm/sec) are closely similar toreported values for gamets (Amthauer et al., 1976); however,these values are the first reDorted for the almandine end member.The observed peak widths are 0.3 mm/sec. The ferric doublet hasa measured average isomer shift and quadrupole splitting thatappears to be consistent with tetrahedral ferric iron. However,the intensity of the ferric iron count dips is so low that there arelarge errors in the fitted parameters, and, therefore, the datacould also be consistent with octahedrally coordinated Fe3*. Foralmandine synthesized on the iron-wtistite butrer the relativeareas of the ferrous and ferric doublets indicate thzt 2+ lVa of theiron is present as ferric iron. For almandine synthesized on theFMQ buffer somewhat higher Fe3* contents 14+l.5Vo) are in-ferred. This is consistent with the larger cell edge (a = 11.525 -

ll.528A) than for almandine synthesized on Fe-Fe'-yO andsuggests that the cell edge for almandine reported in a variety ofliterature sources as I 1.526-1 1.528 (e.g., Robie et al., 1966;Hsu,1968; Meagher, l9E0) was probably determined using almandinecontaining significant Fe3*. Based on the data described above,the cell edge for almandine is slightly less than I l.52lA.

Apparatus and experimental procedure

For every experiment, 9-12 mg of the cRArL assemblage inproportions consistent with the stoichiometry of reaction (2)were ground together and loaded into 1.6 mm diameter Ag66Pd26capsules that were sealed by arc welding. The 1.6 mm diametercapsules were loaded into 3 mm diameter Pt capsules along with150 mg of Fe metal powder and sufficient H2O to react 75Vo of theFe to Fel-1O. The outer capsules were also sealed by arcwelding. For experiments of <950oC 2-4 wt.Vo H2O was added tothe reactants in inner capsule to increase reaction rates. Thereactants in the inner capsule of experiments above 950'C wereloaded dry and the capsules sealed with no special measurestaken to eliminate moisture.

All experiments were conducted in piston-cylinder apparatuswith 2.54 cm diameter furnace assemblies similar to thosedescribed by Johannes (197E) and by Boettcher et al. (l99l).They consist entirely of NaCl and graphite and differ from thoseused by Johannes in the following ways: (l) The bottom (pistonend) graphite plug extends 3 mm into the internal portion of theassembly. (2) The sample is placed horizontally in the notchedtop surface of a cylinder of NaCl. (3) The thermocouple ceramicis sheathed by 3 mm diameter MgO tubing that in turn issurrounded by a cylinder of NaCl. Temperature was measuredwith Pt16s-Pte6Rh16 thermocouples with no correction for theefect of pressure on emf. We used the piston-in technique by

BOHLEN ET AL.: EQUILIBRIA IN THE SYSTEM FeO-TiO7-AlrOr-SiOz_H2O

1052 BOHLEN ET AL.: EQUILIBRIA IN THE SYSTEM FeO-TiO2-A\2O3-SiO2-H2O

Run #

Table 2. Electron microprobe analyses of ilmenite Results and discussion

Results of the experiments are given in Table 3 and inFigure 1. The reversals tightly constrain the equilibriumlocation and dPldT slope, providing a sound basis forcalculations of metamorphic pressures from natural as-semblages of ilmenite-Al2SiO5-quartz-garnet-rutile. Theexperiments using sillimanite have been carried out al-most entirely in the stability field of kyanite. The locationof the stable, kyanite-bearing reaction can be accuratelycalculated from the experimental data and those of Rich-ardson et al. (1968). Figure 2 shows the location of thestable kyanite-bearing equilibrium boundary calculatedfrom molar volume data (Robie et aI.,1966).

The intersection of the breakdown of staurolite-quartz(Richardson, 1968; Rao and Johannes, 1979) with thecnatl equilibrium generates additional reactions (Fig. 2).Such equilibria define the lower temperature stabilityIimit of garnet-rutile assemblages in the presence of H2Ovapor. The reactions:

staurolite + ilmenite + quartz

: almandine + rutile + H2O (3)

staurolite + rutile + qnartz

: ilmenite + kyanite + H2O (4)

Table 3, Experimental conditions and results

5 8 1

s 1 0 2 0 . 1 0 . 1

T102 54 .5 54 '2

A 1 z 0 r 0 , 0 0 . 1

FeO 46.2 47 ,3

Tota l 100.8 101.7

0 . 1 0 . 1

53 .8 53 .5

0 . 3 0 , 4

46.L 46 .8

100.3 100.8

0 .002 0 .003

0.008 0 .011

1.019 1 .007

0 . 9 7 I 0 . 9 8 0

900 1000

o . 2 0 . 1

5 2 . 8 5 2 . 8

0 . 8 0 . 9

4 7 . 5 4 6 . 2

101.3 100.0

o .004 0 .002

0,020 0 .027

0.987 0 .999

0 . 9 8 7 0 , 9 7 2

1050 1100

8 7

s1AI

T1

r ( ' c )

f po ln t6

bringing pressure to l0% below that ofthe final value, increasingthe temperature to that desired for the experiment and thenincreasing the pressure to the final value. During the period overwhich the temperature was increased, there was a concomitantincrease in pressure as a result of thermal expansion of NaCl.However, the piston was always advanced to the final value.

Our furnace assemblies have been calibrated over a wide rangeof P and Z using the melting points of CsCl, LiCl and NaCl(Clark, 1959, as modified by Bohlen and Boettcher, 1982), thereactions albite s jadeite + quartz (Hays and Bell, 1973) andferrosilite S fayalite + quartz (Bohlen et al., 1980). These dataindicate that our NaCl assemblies require no pressure correc-tion. Nominal pressures are listed in Table 3. The details of thecalibration are given by Bohlen and Boettcher (1982).

Experimental products

The products of all experiments were analyzed optically andby X-ray diffraction. Several of the experimental charges wereanalyzed by electron microprobe. Analyses were obtained usingan automated ARL-EMx electron microprobe analyzer with wave-length dispersive ADP, LiF, and TAP crystal spectrometers.Well-analyzed natural almandine-rich garnet (usNtr,t 107105 fromthe Smithsonian Institution), ilmenite, kyanite, and syntheticandradite were used as standards. An accelerating potential of 15kV and an emission current of 150 pA, and a sample current of0.010-0.012 p,A, were standard operating conditions. Countingtimes were sufficient to collect >10,000 counts for all majorelements in standards and unknowns. Spectrometer data werereduced using the correction procedures of Bence and Albee(l%E). The results for sillimanites and ilmenites are given inTables I and 2, respectively. Analyses of garnet were nearlyimpossible to obtain because of very fine intergrowths of garnetand rutile. Analyses of almandines showed a minimum of 1.5wt.VoTiO2 apparently the result of intergrown rutile. Neglectingsuch TiO2 resulted in garnet formulas that are stoichiometricwithin analytical uncertainty.

In most cases, reaction direction was obvious upon opticalexamination of the experimental products. Where changes in therelative proportions of ilmenite-sillimanite-quartz and alman-dine-rutile were more subtle, the intensities of X-ray peaks ofthe minerals were used to infer reaction direction. A change ofX-ray peak intensities of less than 20Vo was taken as "noreaction. "

Pa?enthe,ee itulLeate nitu! to tPace Mnts p?esent-tlndetlini'ng indicdtes d@iffit phaees.

0.003 0 .002

0.000 0 .003

1 . 0 2 8 1 , 0 1 2

0.970 0 .983

750 7 50

0 . 2

5 3 , 0

0 . 9

46.2

1 0 0 . 3

0 .006

o.027

0 . 9 9 9

0 . 9 6 E

1100

7

Run # P(Kbar) r ( 'c) Duret ion( h r s )

Results

5 5 95 7 r581

5 7 05 7 25 7 7

578582678619

5 5 9560

s6s5 8 55 8 560r674

547

583584

588

580598599600

950

1000to00

105010501050

1r00r100r100r1001100r100

9 . 01 r . 0r t , 41 1 . 9

1 1 . 5I I . 9

1 2 . L

1 3 . 07 2 . 6

t2.4

1 0 . 01 4 . 01 3 . 01 5 . 01 3 . 41 3 . 0

1 3 . 0

1 3 . 8

t 4 . 5

1 5 . 0

1 5 . 61 5 . 0L 6 . 2

1 6 . 01 5 . 8

7 088

1 3 8 . 5t 6 8 . 7

9 7 . 5141

6 9 . 3r47t 2 t . 5L 2 0 , 5

20.52 12 6

2 6 . 54 96 97 06 9

7 2

3 24 1 . 6

rsQ(AR)ISQ (AR)flqAR4&ISQ

IqqARflqR43rsQ43ISQ

AR( ISq)4&rsaAr(rsq)rsQ(Ax)

ISQ

AR( ISQ)

flqARAR(IsQ)

4EISQIg!ARAR(ISQ)ISQ (AR)ISQ(AR)

-IEqAT

AR(ISQ)ISQ(AR)

AR(rsq)ISQ(AR)ISQ ( AT)

7501507507 5 0

800800800800

E50850850850

900900900900900900900900900

ISQ(AR)4EISQAR(ISQ)f99AR43ISQI9qAR

t82 52 4

88

181 92l

BOHLEN ET AL.: EQUILIBRIA IN THE SYSTEM FeO-TiO7Al2O3-SiOz-H2O 1053

are qualitatively located on Figure 2. Uncertainty in theformula and thermodynamic properties of staurolite pre-vent a quantitative assessment of the dPldT slopes of

-

reactions (3) and (4). However, these reactions are poten-tially useful for geobarometry or geothermometry. As-semblages containing both reactants and products ofreactions (3) and (4) have been reported in several fieldareas (Ghent, 1975; Pigage, 1976; Fletcher and Green-wood, 1978; Holdaway, 1978). One additional reactionthat emanates from the invariant point involving thecRAIL assemblage is:

staurolite + rutile + almandine

: kyanite + ilmenite + H2O (5)

We have omitted this reaction from Figure 2 for claritygiven that quartz-absent pelitic rocks containing the as-semblage appropriate for reaction (5) are practically non-existent.

Geobarometry

Using available volume data (Robie et al., 1966), ther-mal expansion and compressibility values (Skinner, 1966;Birch, 1966) and the equilibrium curve in Figure 2, wehave calculated a P-?-logleK diagram for cnarr- equilib-ria (Fig. 3), where K : @?ri@ar,sio)(a{,,)/(aarJ(aiu),the equilibrium constant for reaction (2) where unitactivity refers to the pure phase along the univariantequilibrium curve. The logleK curves were calculatedfrom the expression: 4ia : (-Rf hK)12.303AV. Theshallow dPldT slopes of the lo916l( curves emphasize theutility of these equilibria for geobarometry. Figure 3 canbe used for the evaluation of metamorphic pressures fromnatural assemblages given (l) the cRArL assemblage in-

700 800 900 t000 |.t00TEMPERATURE "C

Fig. l. Pressure-temperature projection showing the relativestabilities of almandine + rutile and ilmenite + sillimanite +quartz. A indicates that ilmenite + sillimanite + qtrartz grew atthe expense of almandine * rutile. V indicates that almandine *rutile grew at the expense of ilmenite * sillimanite + quartz.Kyanite-sillimanite and c-p quartz equilibria from Richardson era/. (1968) and Cohen and Klement (1967).

400 600 800 1000TEMPERATURE ('C)

Fig. 2. Pressure-temperature projection showing the relativelocations of the stable kyanite-bearing reaction of ilmenite +Al2SiO5 + quartz = almandine + ruti le. Brackets areexperimental reversals for the sillimanite-bearing reaction.Staurolite reactions are from Richardson (t968) and Rao andJohannes (1979). Al2SiOj phase relations from Holdaway (1971).a-B qvartz from Cohen and Klement (1967).

ferred to coexist at equilibrium, (2) the compositions ofthe phases, (3) appropriate solution models for the activi-ty of end-member components in impure minerals, (4) areasonable estimate of equilibration temperature.

Equilibrium coexistence of the cRArL assemblage issometimes difficult to demonstrate. In many rocks one ormore of the phases, usually the titanium oxides, arepresent at levels of less than one modal percent. Addi-tionally, ilmenite may have oxidized during retrogressionand/or weathering resulting in the formation of rutile oranatase. Rutile has also been noted as a product ofretrogression of titaniferous biotite. Such retrograde de-velopment of TiO2 is usually easily recognizable bytextural examination. In our experience the most reliablegeobarometry can be obtained from paragneisses inwhich ilmenite and rutile are present as inclusions ingarnet, the oxide inclusions commonly exhibiting grainboundary relations indicative of chemical equilibrium(Vernon, 1975, p.4l). The compositions of the ilmeniteand rutile in garnet grains and in the host rock matrix arecommonly similar, affording further evidence that theoxide phases and garnet comprised equilibrium assem-blages. Relicit garnets in some substantially retrogressedrocks may even preserye the former higher grade cnellassemblage.

The compositions of qtrairrz, Al2SiO5 and rutile com-

oltY

uiEfoolrlEo

,r6

t5

14

,t3

=12ocl5roUJE,l 8a@

peo'

"'d

ILMENITE + SILLIMANITEA +QUARTZ

of, o*rbf,,xo,=$ix1'o6'

c'' r ! oarroH,

GARNET + RUTIL

ILMENITE+ SILLIMANITE

t ro l-oY 1v l

UJE.faatrJEo-

1054 BOHLEN ET AL.: EQUILIBRIA IN

TEMPERATURE ("C)Fig. 3. Pressure-temperature-log K (to base l0) plot for

ilmenite-Al2SiO5-quartz-almandine-rutile geobarometer.Al2SiOs phase relations from Holdaway (1971). a-B quartz fromCohen and Klement (1967).

monly differ little from those of end-member components.Rutile with appreciable Nb and Fe have been reported,but application of ideal solution models will not lead tosignificant errors in calculated pressures. Ilmenite inperaluminous rocks may contain significant proportionsof hematite and pyrophanite. Ilmenite-hematite solutionsare probably appreciably nonideal at moderate tempera-

TH E S Y S TEM F e O-T\O rAl zO 3-S iO 2-H zO

tures (i.e., middle amphibolite facies) becoming ideal ornearly so under granulite facies conditions (Anderson andLindsley, l98l). Hematite-rich ilmenites may not be com-patible with almandine-rich garnets, the latter being unsta-ble with respect to oxide-aluminum silicate assemblages atthe relatively high /e, required by hemo-ilmenite' Fe3+enriched ilmenites are probably products of retrogradealteration. In nearly all the cases examined (Table 4)'ilmenite in the cnetl assemblage contained less than 15moleVo hematite and pyrophanite combined, and we haveadopted an ideal-solution model for these and other lesssignificant components. It should be noted that Fe-Mnpartitioning between ilmenite and garnet is strongly depen-dent on temperature. When adequately calibrated, Fe-Mnpartitioning will provide a useful check on garnet-ilmeniteequilibrium relations in natural assemblages.

Garnets in medium-grade rocks commonly exhibitgrowth zoning whereas those in high-grade paragneissesare usually relatively homogeneous, aside from retro-grade rim compositions. In this context accurate geobaro-metry requires careful assessment of the garnet composi-tions in equilibrium with the other phases. Zoned garnetsthat have remained saturated with ilmenite-Al2siorquartz-rutile could conceivably yield information on pro-grade, peak and retrograde metamorphic pressures.

The solution properties ofgarnet potentially present anobstacle to accurate geobarometry. In many pelitic rocks,especially those of high metamorphic grade, the garnetsare essentially almandine-pyrope solutions with spessar-tine, grossular and andradite components, together com-prising less than 5-15 moleVo. Empirical determinations

Table 4. Pressures calculated from assemblages of ilmenite-Al2SiO5-quartz-garnet-rutile

Loca l i t y Reference Sep le No. *Observed

Al-SiI lcateTmperature

( " c )other Barmetera

Pressure (Kbar) (Kbar)

Lake Bonapar te , Eenson

Mines , Ad l rondacks

wes lern Malne

quesne l Lake,

Br i t i sh co lub la

Esp lanade Range

Br l t l sh Co lunb la

south ls land

New Zeal.and

Northern Idaho

Barho l l rh

Funera l Mts . , Death

va11ey, Ca l l fo rn ia

Kllbourne Hole

Neu Mexlco

Y a l e , B r l t l s h

Co1@bla

Iv rea Zone, N. I ta ly

Co l ton , New York

Cent ra l i lassachuseEts

Bohlen, unpubl l .shed 78-LB-20, 78-Ben-l

Evaos and Guldott l 9, 24( 1 9 5 5 )

Fletcher and creenrcod 6, 9, 13

c-74[t C-798I, C-7982c-74R, C-79L, C-74c-629, c-532, C-529

8 7 1 , 1 1 1 y , c 2 6 A ,M 3 4 , 5 9 5 C

s 1 1 r

s i t r

Ky,Ky-St1 1 ,Ky-S1I l

Ky

Ky-St l I

Ky

Ky-S lII

s 1 1 1

Ky, Ky, Sl l I

s 1 1 t

s11l

slr l

7 , 5 , 7 , A 7 . 5 * *

6 . 7 , 7 . 5

8 . 4 , 8 . 4 , 7 . 7 7 . 6 "

7 . 7 t . g t

t l6 . 3 6 . 5 ' l

8 . 5

7 . 3 7 . 2 t 1

7 . 2 , 7 . 3 , 8 . O , 7 . 3a . t , 7 . 8 , 7 . 9' t l

7 . 8 , 6 . 9 , 8 . 0 7 . 3 ' ,

7 . 2 , 7 , O , s . s t7 . 4

+ + +7 , 5 , 7 . 5 , 1 , 6 5 . 8 ' | , 7 . 07 . 3 , 7 . 4 , 7 . L7 . 2 , 7 . L , 7 . O

7 . O , 6 , 3 , 7 . 2 6 . g i6 . 5 , 5 . 3

7 3 O , 7 3 O

600, 600

680, 680, 680

540

620

6 5 0

660

8 o o , 8 0 0 , 8 o o , 8 0 0 ,800, 800, 800

6 0 0 , 6 0 0 , 6 5 0

7 1 0 , 7 r 0 ,710

7 3 0 , 7 3 0 , 7 3 01 3 0 , 7 3 0 , 7 3 O7 3 0 , 7 3 O , 7 3 O

6 7 5 , 6 7 5 , 6 1 56 7 5 , 6 7 5

( 1 9 i 9 )

chen! (1975)

H a E E o r l ( 1 9 6 7 )

Hietanen (1969)

Labotka (1980)

cv-150

11468

2r27

FML-] 10

Padovanl and carter 4, 18, 51, 54,( 1 9 7 7 ) 5 7 , 6 2 , 6 8

P i g a g e ( 1 9 7 6 ) 3 , 4 , 5 ,

scl@idt and wood (1.976) SD-I2I, sD-139,sD-4 30E

SEoddard (1976)

f tacy (197E)

*sanpfe No., Af-siTicate. tenFrature and pressure ate Tisxeil in cortespniliDg colvtu and tow trDsitions.**otthopgtoxene-oTivina-Nattz, whfen and tuetxcher, 7982

t e lag iocJase-garnet -a l

"s io . -quar tz , i le f ton and Ease l ton , I 98 l .

tlorttupcroxene-pfaqiocTase=garnet-quartz, Bohleh et a2., 198 3.

llKganixe-silli@nite at hom xenperaxute, Richarilson ec a7., 1968.

of wFt"rure for garnet yield 2580, 2979+185,2580+ 140, and1509-11392 callgm atom (Saxena, 1968; Ganguly andKennedy, 1974; Oka and Matsomoto, 1974; Dahl, 1980),respectively. Experimentally determined values are sub-stantially lower. Kawasaki and Matsui (197D determineda value of 2120+350 caVgm-atm at high pressure andtemperature. O'Neill and Wood (1979) infened that Fe-Mg garnet mixing is significantly more ideal at 1000.Cthan it is in olivine. Heat of solution measurements onolivines by Wood and Kleppa (1981) indicate that l,l/p"y*for olivines is in the range of 1200 caUgm-atom for Fe-richcompositions. This implies that Wp"y, for garnets mustbe in the range of 500-1000 cal/gm-atom. If one acceptsSack's (1980) value of W6gy, : 800 callgm-atom forolivines, then Vllp"y, for garnets of 0-300 caVgm-atom arerequired by the experimental data. After a review of theavailable data, Perkins (1979) proposed a I dependentexpression for lryf,t"y* (3480-L.ZT,C) that yields WFLMg of2500+100 caUgm-atom for granulite temperatures. How-ever, in light ofthe recent experimental data, this expres-sion has been rejected in favor of an ideal mixing model(Wr"Nae : 0) by Newton and Perkins (1982), although theynoted that such a choice is at the lower limit of permissi-ble values. An additional empirical test of WFlr'rg can bemade by comparing cRArL barometry with estimates interranes for which pressures have been reliably estab-lished. Choice of 17f,'"y, below 1000-1500 caVgm-atomyields sillimanite pressures for kyanite-bearing rocks andin a few cases, andalusite pressures for some sillimanite-bearing rocks. In terranes where pressures are wellknown, such as the Adirondacks (see Bohlen et al.,1982,for a review) empirical evaluations of lVF.t"v* give valuesof 2200-2500 callgm-atom. Therefore, we hive adoptedthe Perkins model for almandine-pyrope because it isconsistent with the bulk of empirical data and yieldspressures consistent with the appropriate Al2SiO5 mineralin all but one of 45 ilmenite-Al2siO5-quartz-garnet-ruti1eassemblages evaluated. It should be noted, however, thatour conclusion regarding lVFt"1,a, is based primarily on Fe-rich compositions, whereas the data of O'Neill and Wood(1979) were determined for Mg-rich garnets. The apparentdiscrepancy between the two sets of Fe-Mg mixingproperties could be an indication of marked asymmetry ofthese parameters in Fe-Mg garnets. The Perkins modelfor almandine-grossular garnets has also been acceptedfor calculations in this study (see Bohlen et al., 1982,forjustification). Spessartine is a significant component ofsome garnets in peraluminous rocks, but there are fewdata on the mixing of Fe-Mn and Mg-Mn garnets. Forthose garnets with significant Mn we have assumed thatFe-Mn garnets mix ideally (Ganguly and Kennedy , 1974)and that interactions of Ca and Mg with Mn are the sameas those for Fe. In any case the loglsK-pressure-tem-perature plot (Fig. 3) derived from the experimental datais not dependent on the garnet mixing models and poten-tial users can make their own choice of solution modelsfor geobarometry applications.

1055

A Iiterature search indicates that the assemblage ofilmenite-Al2siorquartz-garnet-rutile is common, butthe compositions of all of the phases are rarely reported.There are a number ofterranes that probably contain theassemblage but accessory phases in the rocks are com-monly combined in the modes, and there is no distinctionbetween oxides, sulfides, etc. As can be seen in thisstudy, it is important that the presence of even traceamounts of a given phase be clearly reported. Pressureshave been calculated from 14 areas for which at leastgarnet analyses are reported (Table 4). Table 4 indicatesthat the cnan geobarometer yields accurate pressuresthat agree well with a variety of other well-calibratedbarometers. Precision of the inferred pressures is alsoexcellent, especially considering that some of the spreadmay be the result of real pressure variation. With theexception of one assemblage in western Maine (Evansand Guidotti, 1966), pressures inferred from all of theassemblages predict the correct Al2SiO5 polymorph. Thediscrepancy for the Maine assemblage may be the resultof a low estimated temperature; increase of the estimatedequilibration temperature by 50-60'C would eliminate theconflict and still be consistent with other phase relations.Generally the pressures in Table 4 are in agreement withthe estimates of the original workers. Our pressure for thePicuris Range, New Mexico (Holdaway, 1978) is about Ikbar below the value given by Holdaway of 3.7 kbarbased on occurrences of Al2SiO5 minerals. However,only a garnet analysis (containing 40 moleVo spessartine)is available and, therefore, the pressure given is a mini-mum. The accurate and precise pressures are evidencethat generally, on at least the scale of a thin section, allminerals in these pelitic rocks, even those present in veryminor to trace amounts, are in equilibrium.

A range of geobarometers applicable to high-grademetamorphic rocks are now available (see Essene, 1982,for a review) but few precise and accurate "sliding"equilibria that are independent of water activities may beused for pressure estimates in medium-grade terranes.Our cnell barometer has the advantage that the loci ofiso-activity product curves are nearly independent oftemperature (Fig. 3). Temperature uncertainties of -r50'C

result in maximum errors in inferred pressure of about 0.5kbar. We suggest that the cRAIL barometer has particularapplication to Barrovian-style metamorphic terranes. Be-cause the phases involved (other than garnet) depat littlefrom end-member compositions, garnet-rutile assem-blages can be used to infer minimum pressures for rockslacking the requisite cnerl assemblage.

The cne,tl geobarometer may be used to clarify retro-grade metamorphic pressure-temperature-time paths.England and Richardson (1977) and Wells (1979) haveemphasized the importance of evaluating thermal relax-ation histories for understanding the tectonic evolution ofmetamorphic belts. The oxide phases are known for theirreactivity, and for the cnen assemblage to remain inequilibrium during retrogression a nearly isobaric cooling

BOHLEN ET AL.: EQUILIBRIA IN THE SYSTEM FeO-T\O2-AI2O7S\O2-H2O

1056 BOHLEN ET AL.: EQUILIBRIA IN THE SYSTEM FeO-TiOrAlzOs-SiO2-H2O

path is required (Fig. 3). Garnet rim compositions areknown for several terranes listed in Table 4. The extremerims are commonly richer in Fe and Mn than internalportions of the garnet. Such rim compositions are consid-ered to result from retrograde adjustments consonantwith increased Mn-Fe partitioning between ilmenite, bio-tite, and garnet. If it is assumed that the garnet rimcompositions are in equilibrium with other phases in therock during retrogression, then retrograde pressures canbe evaluated. The loglsK values for the garnet-rim-rutile-ilmenite-Al2SiO5-quartz assemblage are smallerthan the log K values for nonrim garnet compositions.This requires that the retrograde pressure paths be lesstemperature-dependent than the loci of constant log K(Fig. 3) which further implies the early retrograde coolingpath is nearly isobaric. Similar nearly isobaric retrogradetrends have been noted in several metamorphic terranes.The inferred retrograde P-T paths of these terranes areconsistent with diminishing heat supply during the waningstages of metamorphism. This suggests, following thethermal models of England and Richardson (1977), thatheat from the addition of magma into the crust may be animportant component of the heat budget of many meta-morphic terranes.

Acknowledgments

This research was supported by National Science FoundationGrant EAR-16413 to ALB, EAR E2-06268 to SRB, and Austra-lian Research grants to VJW. Les Faus, Chris West, ScottBoettcher, Curt Boettcher, and Duane Ottens assisted us withmachining and maintenance of the high-pressure equipment.Mcissbauer data were collected in the M<issbauer AnalysisLaboratory, UCLA under the direction of Professor WayneDollase who helped with interpretation of Mtissbauer results.Mr. Robert Jones assisted us with the collection of electronmicroprobe data. The manuscript was improved by a carefulreview by Dr. Robert C. Newton.

References

Birch, F. (1966) Compressibility: elastic constants. In S. P.Clark, Jr., Ed., Handbook of Physical Constants, p.97-174.Geological Society of America Memoir 97.

Bohlen, S. R. and Boettcher, A. L. (1981) Experimental investi-gation and geological applications of orthopyroxene--olivine-quartz geobarometry. American Mineralogist, 66, 951-965.

Bohlen, S. R. and Boettcher, A. L. (1982) The quartz s coesitetransformation: a precise determination and the efects ofother components. Journal of Geophysical Research, 87,7073-:t078.

Carmichael, D. M. (1978) Metamorphic bathozones and batho-grads: a measure of post-metamorphic uplift and erosion on aregional scale. American Journal of Science, 278,769-797.

Clark, S. P. (1959) Etrect of pressure on the melting points ofeight alkali halides. Journal of Chemistry and Physics, 31,1526-153 l .

Cohen, L. H. and Klement, W., Jr. (1967) High-low quartzinversion: determination to 35 kilobars. Journal ofGeophysi-cal Research, 72, 42454251.

Currie, K. L. (1971) The reaction 3 cordierite = 2 Earnet + 4sillimanite + 5 quartz as a geologic thermometer in theOpinicon Lake region, Ontario. Contributions to Mineralogyand Petrology, 33, 215-226.

Dahl, P. S. (1980) The thermal-+ompositional dependence ofFe2*-Mg2* distributions between coexisting garnet and clino-pyroxene: applications to geothermometry. American Miner-alogist, 65, 852-866.

England, P. C. and Richardson, S. W. (1977) The influence oferosion upon the mineral facies of rocks from different meta-morphic environments. Quarterly Journal of the GeologicalSociety of London, 134,201-213.

Essene, E. J. (1982) Geologic thermom€try and barometry. InJ. M. Ferry, Ed., Reviews In Mineralogy, 10, p. 153-2M.Mineralogical Society of America, Washington, D.C.

Evans, B. W. and Guidotti, C. V. (1966) The sillimanite-potashfeldspar isograd in western Maine, U.S.A. Contributions toMineralogy and Petrology, 12, 25-62.

Fletcher, C. J. N. and Greenwood, H. J. (1978) Metamorphismand structure of Penfold Creek area, near Quesnel Lake,British Columbia. Journal of Petrology, 20,743-:794.

Froese, E. (1976) Applications of thermodynamics in metamor-phic petrology. Geological Survey of Canada, Paper 7543.

Ganguly, J. and Kennedy, G.C. (1974)The energetics ofnaturalgarnet solid solution. I. Mixing of the aluminosilicate end-members. Contributions to Mineralogy and Petrology, 4E,t37-148.

Ghent, E. (1975) Temperature, pressure, and mixed-volatileequilibria attending metamorphism of staurolite-kyanite-bear-ing assemblages, Esplanade Range, British Columbia. Geolog-ical Society of American Bulletin, 86, 1654-1660.

Ghent, E. A. (1976) Plagioclase-garnet-AlzSiOs.{uartz: a poten-tial geothermometer-geobarometer. American Mineralogist,61,7r0-714.

Goldsmith, J. R. (1980) The melting and breakdown reactions ofanorthite at high pressures and temperatures. American Min-eralogist, 65, 272-284.

Grambling, J. A. (1981) Kyanite, andalusite, sillimanite, andrelated mineral assemblages in the Truchas Peaks region, NewMexico. American Mineralogist, 66, 702-722.

Grew, E. S. (1981) Granulite facies metamorphism at Molodezh-naya Station, East Antarctica. Journal of Petrology, 22,297-336.

Bohlen; S. R., Essene, E. J., and Boettcher, A. L. (1980) Hariya, Y. and Kennedy, G. C. (1968) Equilibrium study ofReinvestigation and application ofolivine-quartz--orthopyrox- anorthite under high pressure and high temperature. Americanene stability. Earth and Planetary Science Letters, 47, l-10. Journal of Science, 266, 193-203.

Bohlen, S. R., Wall, V. J., and Boettcher, A. L. (1983) Experi- Hattori, H. (1967) Occurrence of sillimanite-garnet-biotitemental investigation and application of model garnet granulite gneisses and their significance in metamorphic zoning in Southequilibria. Contributions to Mineralogy and Petrology, 83, 52- Island, New Zealand. New Zealand Journal of Geology and61. Geophysics,10,269-299.

Buddington, A. F. and Lindsley, D. H. (1980) Iron-titanium Hays, J. F. (1967) Lime-alumina-silica. Carnegie Institution ofoxide minerals and their synthetic equivalents. Journal of Washington Year Book, 65,234-239.P€trology, 5, 310-357. Hays, J. F. and Bell, P. M. (1973) Albite-jadeite-quartz equilib-

BOHLEN ET AL.: EQUILIBRIA IN

rium: a hydrostatic determination. Transactions of the Ameri-can Geophysical Union, 54,482.

Hensen, B. J. and Green, D. H. (1971) Experimental study of thestability of corderite and garnet in pelitic compositions at highpressures and temperatures. L Compositions with excessaluminosilicate. Contributions to Mineralogy and Petrology,33 ,309-330.

Hietanen, A. (1969) Distribution of Fe and Mg between garnet,staurolite and biotite in aluminum-rich schist in various meta-morphic zones north of the Idaho Batholith. American Journalof Science, 267, 422-456.

Holdaway, M. J. (1971) Stability of andalusite and the aluminumsilicate phase diagram. American Journal of Science, 2j1,97-l 3 l .

Holdaway, M. J. (1978) Significance of chloritoid-bearing andstaurolite-bearing rocks in the Picuris Range, New Mexico.Geological Society of America Bulletin, 89, 1404-1414.

Hsu, L. C. (1968) Selected phase relations in the system Al-Mn-Fe-Si-O-H: a model for garnet equilibria. Journal of Petrolo-gy, 9, 40-83.

Johannes, W. (1978) Pressure comparing experiments withNaCl, AgCl, talc, pyrophyllite assemblies in a piston-cylinderapparatus. Neues Jahrbuch fiir Mineralogie Monatshefte, 2,84-92.

Kawasaki, T. and Matsui, Y. (1977) Partitioning of Fe2* andMg2* between olivine and garnet. Earth and Planetary ScienceLetters. 37. 159-166.

Labotka, T. C. (1980) Petrology of a medium-pressure regionalmetamorphic terrane, Funeral Mountains, California. Ameri-can Mineralogist, 65, 670-689.

Martignole, J. and Sisi, J. C. (1981) Cordierite-garnet-H2oequilibrium: a geological thermometer, barometer and waterfugacity indicator. Contributions to Mineralogy and petrology,77,3846.

Meagher, E. P. (1980) Silicate garnets. In P. H. Ribbe, Ed.,Reviews in Mineralogy, 5,p.25-66. Mineralogical Society ofAmerica, Washington, D.C.

Newton, R. C. and Haselton, H. T. (1981) Thermodynamics ofthe garnet-plagioclase-Al2SiOs-quartz geobarometer. In R. C.Newton, A. Navrotsky, and B. J. Wood, Eds., Thermodynam-ics of Minerals and Melts, p. 129-145. Springer, New York.

Newton, R. C. and Perkins, D., III (1982) Thermodynamiccalibration ofgeobarometers for charnockites and basic granu-lites based on the assemblages garnet-plagioclase-orthopyrox-ene(clinopyroxene)-quartz with applications to high-grademetamorphism. American Mineralogist 67, 203-222.

Newton, R. C. and Wood, B. J. (1979) Thermodynamics of waterin cordierite and some petrologic consequences of cordieriteas a hydrous phase. Contributions to Mineralogy and Petrolo-gy, 68, 391-405.

Oka, Y. and Matsumoto, T. (1974) Study on the compositionaldependence of the apparent partition coefficient of iron andmagnesium between coexisting garnet and clinopyroxene solidsolutions. Contributions to Mineralogy and Petrology, 48,tl5-121.

O'Neill, H. St. C. and Wood, B. J. (1979) An experimental studyof Fe-Mg partitioning between garnet and olivine and itscalibration as a geothermometer. Contributions to Mineralogyand Petrology. 70. 59-70.

Padovani, E. R. and Carter, J. L. (1977) Aspects of the deepcrustal evolution beneath south central New Mexico. Ameri-can Geophysical Union Monograph, 20, 19-55.

TH E S YSTEM FeO-TiOy-Al2O 3-SiOz-H 20

Perchuk, L. L., Podlesskii, K. K., and Aranovich, L. Ya. (1981)Calculation of thermodynamic properties of end'member min-erals from natural parageneses. In R. C. Newton, A. Nav-rotsky, and B. J. Woods, Eds., Thermodynamics of Mineralsand Melts, p. lll-129. Springer, New York.

Perkins, D., III (1979) Application of new thermodynamic datato mineral equilibria. Unpublished Ph.D. Thesis, The Univer-sity of Michigan.

Pigage, L. C. (1976) Metamorphism of the Settler schist, south-west of Yale, British Columbia. Canadian Journal of EarthSciences, 13,405421.

Rao, B. B. and Johannes, W. (1979) Further data on the stabilityof staurolite + quartz and related assemblages. Neues Jahr-buch ftir Mineralogie, Monatshefte, 10, 437-447.

Richardson, S. W. (196E) Staurolite stability in a part of thesystem Fe-Al-Si-O-H. Journal of Petrology, 9, 467488.

Richardson, S. W., Bell, P. M., and 6ilbert, M. C. (l%8)Kyanite-sillimanite equilibrium between 700 and 1500"C.American Journal of Science. 266. 513-541 .

Robie, R. A., Bethke, P. M., Toulmin, M. S., and Edwards, J. L.(1966) X-ray crystallographic data, densities and molar vol-umes of minerals. In S. P. Clark, Jr., Ed., Handbook ofPhysical Constants, Geological Society of America Memoir,97,27J4.

Robie, R. A., Hemingway, B. S., and Fisher, J. R. (197E)Thermodynamic properties of minerals and related substancesat 298.15K and I bar (105 Pascals) pressure and at highertemperatures. United States Geological Survey Bulletin, 1452.

Ruby, S. L. (1973) Why misfit when you already have 12?M<issbauer Etrect Methodology, 8, 263-277.

Ruby, S. L. and Shirane, G. (1961) Magnetic anomaly inFeTiO3-aFe2O3 system by M<issbauer effect. Physical Re-view,23, 1239-1240.

Sack, R. O. (1980) Some constraints on the thermodynamicmixing properties of Fe-Mg orthopyroxenes and olivines.Contribution s to Mineralogy and Petrology, 7 l, 237 -246.

Saxena, S. K. (196E) Distribution of iron and magnesium be-tween coexisting garnet and clinopyroxene in rocks of varyingmetamorphic grade. American Mi neralogist, 53, 20lE-2024.

Schmid, R. and Wood, B. J. (1976) Phase relationships ingranulitic metapelites from the lvrea-Verbano Zone (NorthernItaly). Contributions to Mineralogy and Petrology, 54, 255-279.

Skinner, B. J. (1966) Thermal expansion. In S. P. Clark, Jr., Ed.,Handbook pf Physical Constants. Geological Society of Amer-ica Memoir. 97.75-96.

Spencer, K. J. and Lindsley, D. H. (1981) A solution model forcoexisting iron-titanium oxides. American Mineralogist, 66,I I 89-l 201 .

Stoddard, E. F. (1976) Granulite facies metamorphism in theColton-Rainbow Falls area, northwest Adirondacks, NewYork. Unpublished Ph.D. Thesis, University of California,Los Angeles.

Stormer, J. C., Jr. (1975) A practical two-feldspar geothermo-meter. American Mineralogist, 60, 667-67 4.

Syono, Y., Ito, A., and Morimoto, S. (1981) Systematics ofMrissbauer parameters in Fe57-doped titanate and germanateilmenites. Journal of Physics and Chemistry of Solids, 42, 4E3-486.

Thompson, A. B. (1976) Mineral reactions in pelitic rocks. II.Calculation of some P-I-X (Fe-Mg) phase reactions. Ameri-can Journal of Science, 276, 425454.

1057

l05E BOHLEN ET AL.: EQUILIBRIA IN THE SYSTEM FeO-TiOrAlzOrSiOz-H2O

Tracy, R. J. (1978) High-grade metamorphic reactions and partial Archaean sialic crust, southern West Greenland. Journal ofmelting in pelitic schist, west-central Massachusetts. Ameri- Petrology, 20, 187-226.canJournalof Science,278, 150-178. Wood, B. J. and Kleppa, O. J. (1981) Thermochemistry of

Vernon, R. H. (1975) Metamorphic Processes. John Wiley and forsterite-fayalite olivine solutions. Geochimica Cosmochi-Sons, New York. mica Acta, 45,529-534.

Vernon, R. H. and Flood, R. H. (1977) Interpretation of meta- Zen, E. (1973) Thermochemical parameters of minerals frommorphic assemblages containing fibrolitic sillimanite. Contri- oxygen-bufered hydrothermal equilibrium data: method, ap-butions to Mineralogy and Petrology, 59,227-235. plication to annite and almandine. Contributions to Mineral-

watl, V. J., Clemens, J. D., Essene, E. J., Treiman, A. F., and ogy and Petrology, 39,65-80.Westrum, E. F., Jr. (1980) Thermodynamic properties andphase equilibria for ilmenite (abstr.) Transactions of the Amer-ican Geophysical Union, 46, 1146-1147. Manuscript received, October 29, l9E2;

Wells, P. R. A. (1979) Chemical and thermal evolution of acceptedforpublication, May 16, 1983.