THE AMERICAN MINERALOGIST. VOL.56. MARCH_APRIL, 1971

AN EQUILIBRIUM MODEL FOR BUCHAN-TYPE META-MORPHIC ROCKS, SOUTH-CENTRAL MAINE

Pnrrrp H. Osnnnc, LIn'iversity oJ Maine, Orono, Maine 04473

Arsrn.q.cr

Equilibrium relationships in andalusite-staurolite-cordierite-mica schists of the Buchan-

type from south-central Maine have been investigated. Samples containing assemblages

of eight to eleven minerals from compositionally distinctive beds and laminations of pelitic

schist in a single outcrop were studied by electron probe methods. The proximity of

samples enables one to consider that the values for external parameters (P, T, pJ are the

same over the sample area.Kp' values for Mg-Fe distribution between contacting cordierite and biotite in all

samples are identical, within experimental error. This equality indicates a close approach

to chemical equilibrium.Two models for equilibrium are considered. In the first model each lamination is treated

as a closed system, and the maximum number of determining components is taken as

eleven (SiOz, TiOz, AlzO:, FezOa, FeO, MnO, MgO, CaO, Naro, KsO and HzO). Thus,laminations associated with three different beds, and containing eleven minerals shouldbe invariant at arbitrary external conditions. However, analyses of individual grains of amineral species within each lamination are not identical, and a plot of

(x"* t /xueo_)\ x"* ,/ 0.r,.

uttt" \ x""o .,

"o,u,",,,.from these laminations does not define a unique point These observations indicate theinadequacy of this model.

In the second model the rock is considered to consist of compositionally distinct equi-librium mosaics of discrete grain clusters. Compositions of individual mineral grains be-Ionging to two- and three-grain clusters were examined. Difierent compositions of indi-vidual grains of the same mineral situated in different clusters in close proximity (4-6 mm)is consistent with this model. However, because a plot of

/Xueo \ /Xueo \

\ x"* ,/o.,,* versus

\-/"o,ai",itu

for these clusters does not define a unique point, the number of mineral species containedin a mosaic must be less than the number of determining components. By uniting thechemical data from contacting minerals, a seven component system is found to be adequateto describe the phase relationships within the mosaics.

The compositions of coexisting ilmenite and magnetite suggest that the temperaturewas -500'C and the/(O) for the sample analyzed, v'as -10-% bars.

GBNBner- Sraroun'xr

Rocks identified as the Waterville Formation (Osberg, 1968) in south-central Maine (Figure 1) have been recrystall ized by a Buchan-typemetamorphism. In this paper the degree to which chemical equilibriumhas been attained by the mineral associations in the Waterville Formationis examined and thermodynamic models representing large-volumeeauilibrium and mosaic eauilibrium are considered.

570

BUCHAN M ETAMORPHIC ROCKS

Frc. 1. Location and geologic map of the Waterville Formation south-central Maine.

At low grade the Waterville Formation consists oI quartz, plagioclase,muscovite, and chlorite. Within the area studied (Figure 1) the meta-morphic grade increases southward, and biotite, garnet, andalusite-staurolite, cordierite, and sillimanite isograds have been mapped.

Over most of the area the number of phases in the rocks are few andthe relationships between them do not give fruitful information for thepurposes of this study. Ilowever, an outcrop in a small roadcut exposed atWest Sidney (Figure 1) does provide an opportunity to investigateequilibrium relationships. The outcrop (Figure 2) contains six composi-tionally distinctive beds. Three beds contain associations of eleven rele-vant mineral soecies. whereas the others contain less than eleven.

J / l

572 PHILIP II. OSBERG

Frc. 2. Sketch of road-cut at West Sidney showing locationof samoles bv circles. Numbers refer to beds.

Prrnocnepuv

Modes of each bed are presented in Table 1. A minimum of two thin sections wereexamined for each bed and the modes are the averages of 2000 point-counts per slide forall slides pertaining to a given bed.

The beds consist of thin laminations of quartzite and pelite, 1 mm to 3 cm thick.Many of the pelitic laminations contain all of the modal minerals. Commonly, garnet,staurolite, cordierite, andalusite, and chlorite are porphyroblastic, and although theseminerals are mostly restricted to the pelite, they are locally developed in the qtarlzitelaminations. In some cases a single porphy'roblast extends across two or three laminations.

Optically, the micaceous minerals of the pelite define a schistosity that is essentially

Taer,r 1. Monrs ol BBnorNc. Slncrurt Nunnnns Rrlrn roBnns ru Freunn 2

ModesMineral

Quartz \PlagioclaseJMuscoviteBiotiteStaurolite

CordieriteAndalusite

GarnetChloriteIlmenite \MagnetiteJ

3 4 . 6

1 2 7

o . /2 . 54 . 4

tro . 4

2 5 . 6

2 2 . 24 2 . 1

7 9

J I . J

1 2 . O2 7 . 90 26 . 1

0 . 6o . 7

1 . 2

2 3 . 6

6 . 149 14 . 02 . 0

11.2tr

l . J

2 . 7

8 73 4 311.6

1 . . )

tI

tr1 . 0

0 . 7

1 6 . 53 7 . O

3 . 9

If

7 . 4

4 2 . 2 3 2 . 6

1 . 3

BUCHAN M ETAMORP II IC ROCKS

parallel to the laminations. Porphyroblasts interrupt the schistosity but show no helicitic

structure. Textures indicative of alterations or reactions between grains were not observed,

and, thus, the minerals appear to be in stable association The foilowing contacting asso-

ciations were noted; biotite-chlorite-cordierite, biotite-chlorite-staurolite, chlorite-

staurolite-cordierite, biotite-chlorite-andalusite, biotite-chlorite-garnet, biotite-cordierite-

garnet, biotite-cordierite, biotite-staurolite, biotite-chlorite, biotite-garnet, garnet-

staurolite, garnet-cordierite, andalusite-biotite, andalusite-chlorite, staurolite-chlorite

cordierite-chlorite, and staurolite-cordierite. Quartz and muscovite are in close proximity

in each association.

Quartz occurs as anhedral grains 0.03 to 0.14 mm in size and commonly exhibits

undulatory extinction The grains of quafiz occur in a mosaic of generally rectangular

forms in section. Inciusions of opaques and muscovite are rare, and muscovite and biotite

embay quartz rather commonly.

Plagioclase was not positively identified in thin section, but difiractograms of quartz

separates consistently display the 22.1" peak of plagioclase. It is untwinned and has ap-

proximately the refractive index of quaftz. It probably makes up less than 3 percent of

the rock.Muscovite lorms subhedral plates 0.05 to 0 9 mm across. The plates are preferentially

oriented parallel to the schistosity. Grains of muscovite have simple contacts and contain

few inclusions.Biotite is subhedral. Grains have fair shape orientation, but it is not as good as that

of muscovite. Biotite is pleochroic; a:colorless, g:ry:brown. Grains range from .08

to 0.4 mm in size. Quartz, muscovite, and opaques occur as inclusions, and commonly

muscovite and chlorite embay biotite.

Staurolite forms subhedral to euhedrai porphyroblasts, 1 3 to 3.9 mm in size. Crystals

are commonly twinned on 1232} and contain such an abundance of qtatlz, garnet, and

opaque inclusions that they have a spongy appearance Pleochroic colors are d:colorless,

0:very light brown, and.y:yellowish brown.

Cordierite occurs as ameboid grains, 2.3 to 11.4 mm across, that include quartz,

biotite, muscovite, garnet, opaques, and chlorite. Included zircons are surrounded by

pleochroic haloes with colors that range from colorless to yellow. Boundaries of cordierite

crystals are penetrated by biotite, muscovite and chlorite. No tr,vinning was observed

in cordierite.Andalusite forms glomeroblastic prisms 2.5 to 15.5 mm long, consistin$ of small

euhedral needles. Quartz, biotite, and opaques are Locally included in the glomeroblasts.

Garnet crystals are euhedral. Crystals measure 0.5 to 0.8 mm across. They are clear

of inclusions and show no optical zoning.Chlorite occurs as porphyroblasts that cut across the schistosity. Crystals are sub-

hedral with generally simple contacts and measure 0.3 to 0 8 mm across. Chlorite is

optically positive and has pleochroic colors ranging from colorless to very pale green.

fnclusions within chlorite are quertz and opaques.

Opaques include ilmenite, magnetite, pyrite, and pyrrhotite. Ilmenite and magnetite

were found in all beds, but pyrite and pyrrhotite were found in only two samples Ilmenite

is consistently the most abundant opaque. It occurs as euhedral hexagonal plates, approxi-

mately 0.03 mm across. Compositions judged from 2|ot>Fevrut and 20r116yFe6., and

Lindsley's (1963) determinative curves are Ilme7 Magnetite forms subhedral to anhedral

grains. The ceil dimension is o:8.404 which according to Lindsley's chart (1962) indicates

a composition of Mges. Pyrrhotite occurs as irregular lens-shaped grains that lie in the

schistosity. Pyrite is scarce relative to pyrrhotite. It forms subhedral to euhedral crystals

commonly associated with pyrrhotite.

Non-opaque accessories include zircon, tourmaline, and apatite.

573

574 PHILIP H. OSBERG

Crnursrnv

Bulk sampies from each bed were chemically anal1,2sd and the results are posted inTable 2. Approximately 500 g of sample were pulverized by a jaw crusher and processedin a Spex-Mixer/Mill until the grains passed through a 325 mesh sieve. The sample wasthen reduced to 20 g by passing it repeatedly through a splitter. The samples were analyzedby the method of Shapiro and Brannock (1962) as modified by Shapiro (1967).

The compositions of the beds have been recalculated to mole-ratios and plotted on aThompson projection (1957) in Figure 3. Before plotting the mole-ratios, iron was adjustedfor titania in ilmenite and the molar amount of alumina was adjusted lor soda and limein oligoclase and lime in garnet. None of the points representing the difierent beds haveidentical comoositions.

Tl'ntn 2- Crlnlrrcar, ANar,vsrs or Bnos. Nuuerns, OnrnnrneN G-2, RBlnn ro Bnns rN Frcunn 2

Sample SiOz TiOr A[Oo ZFeO MnO MgO CaO NazO KrO HrO+ HrO- PrOs

G-2I

23456

69.2 0 55 9 1 0 85 8 . 1 0 86 2 0 0 85 3 4 1 0s 9 . 7 0 85 5 . 9 0 9

1 5 . 4 2 . 4 N . D . O . 7 r 92 0 5 8 1 0 I 4 0 0 71 9 . 4 7 4 0 . 1 3 5 0 61 6 . 2 5 . 4 0 . 1 3 . 0 1 22 0 . 9 9 . 8 0 1 5 2 0 51 8 . 0 8 1 0 . 1 4 . 0 0 72 0 . 3 7 . 8 0 . 1 4 3 0 . 8

4 . t 4 5 0 6 6 0 . 1 7O 9 3 3 N A N AO 9 3 6 N A N A2 2 2 5 N A N A0 7 3 9 N A N AO 9 3 3 N A N A1 , 3 3 9 N A N A

0 . 1 6 9 9 6 9NA 97 50NA 94 40NA 93 40NA 95 50NA 95 60NA 95 30

Analyst: P. H. Osberg

Chemical analyses of contacting minerals in each bed were made using an AppliedResearch Laboratories EMX electron microprobe X.ray analyzer. The method of Benceand Albee (1968) was used to convert the data from the probe into weight percent. Primarystandards were as follows: Si-quartz, Al-kyanite, Fe-hematite, Mn-rhodonite, Mg-pyrope,Ca-grossularite, and K-orthoclase. Analyses oI minerals are presented in Tabie 3. Wet-chemical and probe analyses are shown for Sturbridge garnet and biotite standard to showcomparative values. All standards and reference minerals are from a collection in theHofiman Laboratory, Harvard University.

Except for garnet the minerals showed little chemical zoning. The rims of garnet areimpoverished in MnO and enriched in FeO relative to the cores.

TBsr non Equrr-rnnruu

One test for equilibrium consists of comparing distribution coefficientsfor exchangeable components between mineral pairs from beds of differ-ent bulk composition at the same set of external conditions. The deriva-tion and the form of the equation for the distribution coefficient, Kit,have been discussed by Kretz (196t,1964) and Albee (1965).

In this paper the distribution of iron and magnesium between contact-ing pairs is analyzed in exchange reactions of the type

FeAlzSisrzOg * KvsMgA1173SiO1673(OH)273

: MgAlzSir lzOe I K173FeAI173SiOrora(OH)srs.

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The distribution coeffi.cient may then be written

- o o r d i e r i t e - b i o t i t e^MEO ^ FeO

Kn' :"

lfcordlerite XbiotiteFeO MgO

The value of the distribution coefficient depends on temperature,pressure, chemical potential of water, concentrations of other exchange-able components, and deviations from ideality of solid solutions. Theoutcrop at West Sidney is sufficiently small that the external conditions(7, P,pt,o) can be considered constant. In addition to iron and magne-

sium, aluminum, manganese, and titanium are exchangeable componentsin the mineral pairs analyzed, but their effect on the ratio of magnesiumand iron is probably small. Finally, the effect of non-ideality is regardedas approximately constant in each comparison because of the constancy

of external conditions and the similarity of chemical compositions of thephases involved.

The resulting Kp' values are presented in Table 4. The similarity ofvalues within pairs of contacting minerals indicates that at the time thechemistry was frozen into the rock mutual exchange of chemical com-

ponents existed at least between contacting minerals. Such relationships

suggest a close approach to equilibrium.It might be argued that the Mg-Fe ratios in biotite, chlorite, cordierite,

garnet, and staurolite change so little in response to changing external

T.lnr,n 4. Ko'Var,ues lon CoNr.tcrrNc Mrxrxals.

NuMerns ARE THE Smm a.s Tasln 3

Kr' (cordierite/ Kp' (staurolite/ Kp

biorite) biotite)

' (garnet-rim/ Kp' (chlorite/

biotire) biotite)

1 A

rb2a3a3b4a4b4c4d

5b6a6b

1 . 9 31 . 9 1

1 .95

1 . 9 81 . 9 1

1 . 9 51 . 9 3

. 2 5

. 26

1 . 1 1

1 . 1 5

. I J

. 1 6

. 25. 1 6

BUCHAN M ETAMORPHIC ROCKS

Tanr,n 5. CoupamsoN ol KDlloR MrNrnar, P,uns .lrDtrlnnnwr Mnreatotpnrc Gnaon

577

Location Kp' (garnetrim-biotite) Kp' (chlorite-biotite)

0 1 60 . 1 3

conditions that their K/p values are poor indicators of equilibrium. Theaverage Kp' values for contacting chlorite-biotite and garnet rim-biotitefrom the outcrop at West Sidney compared with an outcrop in the lowintensity part of the staurolite zone are tabulated in Table 5. Thesecomparisons indicate that Kot is sensitive to changes in metamorphicconditions.

Whether or not the values of Ko' at West Sidney were established byprograde or retrograde reactions is unknown, i.e., whether or not thechemistry was frozen in at the climax of metamorphic conditions or atsome set of conditions slightly below the climax. It is reasoned, in eithercase, that the common values of Kot for parts of coexisting minerals fromrocks of differing bulk composition indicates a close approach to equilib-r ium in volumes at some scale

TnnnlrolyNAMrc MoDELS

Having demonstrated that the mineral associations approach chemicalequilibrium, the question arises as to the thermodynamic model that isconsistent with the mineral relationships. Two models are considered.The first is a "large volume model" in which a lamination constitutes thesystem, and the second is a "mosaic model" in which clusters of grainsare considered to constitute the system.

Large aolume model. In considering the "large volume model", three bedsare of interest: 1. 4. and 5. In these beds individual laminations containall of the modal minerals and, in the case of 4 and 5, the probe analyses ofminerals were all from single layers.

These beds have slightly different bulk compositions (Table 2, Figure3), and modal analyses (Table 1) indicate that each contains eleven rele-vant minerals including ilmenite and magnetite. Following Korzhinskii(1959, p. 62) at fixed external conditions (T, P, 2p:) the phase rule re-duces to the form

West SidneyComparison outcrop

1 . 1 31 . 0 2

where

f : q - P

578 PHILIP H. OSBERG

o.ctlgO

r66ffi6rfi

Fro. 3. Bulk compositions of beds.

/:number of degrees of freedomci: number of buffered components

2: number of phases.

In these laminations (in beds t,4, and 5), if the assemblages of elevenminerals are considered to be in equilibrium, the number of bufferedcomponents must be at a minimum eleven. Because there is no a prioriway of knowing which components are buffered, the simplest procedureis to parcel out the buffered components among the major rock formingoxides-SiOz, TiOz, AI2O3, Fe2O3, FeO, MnO, MgO, CaO, NarO, KrO, andHzO. To satisfy the minimum requirement of the eleven phase assem-blages, all of the major oxides are used, and water must be consideredbuffered. These circumstances suggest that these laminations with elevenphases as systems have zero degrees of freedom at constant T, P, E,ui,and consequently the phase relationships are determined completely bythe eleven major oxides. ft is doubtful that trace amounts of other com-ponents would materially affect the ratios of the major components.

BUCHAN M ETAMORPHIC ROCKS

The possibility that the assemblages of eleven minerals contain non-reactive phases, phases stabilized by additional components, or representphases involved in an incompleted reaction must be considered. Becausegarnet is zoned it might be thought to be a nonreactive phase. Althoughdiffusion between the inner parts of the crystal and its environment isobviously diffi.cult, the rims of garnets are reactive as shown by thechange in values of Ko' between garnet rims and contacting biotite withmetamorphic grade (see table 5). The presence of zinc might stabilizestaurolite and thus reduce by one the number of phases that are deter-mined by the major rock forming oxides. This question was not studied,but it is questionable that a trace amount of zinc in the rock serves tostabilize up to eleven modal percent of staurolite. Finally, the absence ofreaction rims between minerals and the occurrence of the same phaseassemblage at other outcrops seems to argue against the notion that theassemblage represents an incomplete reaction.

A test for the adequacy of the "large volume model" is to compare thecompositional invariancy of phases from beds of different bulk composi-tion. This comparison can readily be made on a diagram in which the Mg-Fe ratios of contacting minerals are plotted. For invariant conditions thisplot should define a unique point, whereas if the conditions are not invari-ant, the coordinates for contacting minerals should lie along a curve.Figure 4 shows the plots for contacting biotite-garnet rims, biotite-staurolite, biotite-chlorite, and biotite-cordierite. The uncertainty of the

Fro. 4. Plot of MgO/FeO for biotite against MgO/FeO for minerals in contactwith biotite. Ellipses show precision at 95/s confldence level.

519

tora

o,!b o eo

=

(MgOlFcO)gorn, rtour, chlor, cord.

580 PHILIP H. OSBERG

values at the 95 percent confidence level is indicated by the dimensions ofthe ellipses.

The plot of the MgO-FeO ratios for contacting biotite and cordieriteis instructive. It is obvious that the coordinates for these minerals fromlaminations in beds 1,4, and 5 are not the same, and in fact they differby an amount far greater than any conceivable error in analysis. Al-

though phase considerations suggest that these laminations are composi-tionally invariant, the plot indicates that they are not. This contradictionleads the writer to judge the "large volume model" inadequate.

Mosaic model. In the "mosaic model" the rock is thought to consist ofgrain clusters that have bulk compositions that may difier from that ofadjacent grain clusters. Exchange of chemical species between adjacentclusters is incomplete, but the external conditions are uniform for all

clusters.A test for the "mosaic model" would be to show that the compositions

of a particular mineral varied from potnt to point in the rock. Becausebiotite is the dominant Mg-Fe mineral in all samples, a comparison of theMgO-FeO ratios of biotite from different parts of a lamination shouldshow the validity of the model.

MgO-FeO ratios of selected biotites along a ten millimeter traverseare shown in Figure 5. The precision of the ratios at the 95 percent con-

fidence level is represented by the lengths of the line-segments. A stauro-lite crystal occupies the left margin of the traverse, followed by a biotite-concentration, a cordierite porphyroblast, a muscovite-rich seam, and aquartz-rich layer as indicated. The MgO-FeO ratios of bioite vary frompoint to point along the traverse.

The variation in MgO-FeO ratio from biotite grain to biotite grain

indicates the existence of compositional realms. This compositionalvariation coupled with the existence of equilibrium partitions indicates a

condition of mosaic equilibrium.Compositional realms are apparently controlled by the growth of por-

phyroblasts that as they grow extend their compositions over largevolumes of rock. In their growth the porphyroblasts replace certainminerals in the rock, incorporating some chemical constituents and ex-changing others with neighboring minerals, the exchange partitions beinga function of the factors of state. Diffusion within porphyroblasts is gen-

erally faster than diffusion through multicrystalline volumes of rock,and, therefore, chemical constituents that diffuse out of the porphyro-blast into the environment tend to be concentrated in a selvage of min-

erals immediately adjacent to the porphyroblasts.Porphyroblasts seeded in different parts of the rock may have slightly

BUCHAN M ETAMORP II IC ROCKS 581

-. llourolila{*qflffi,ornc,dirrrtr-:,fi

i:';'""nurcovlle -rlch rcom

nrn

Frc. 5. MgO/FeO for biotite along a 10 mm traverse. Mineralogy is indicated at top

of diagram. Five segments indicate precision at 95/6 confidence level. Data are from

beds 5.

different compositions because of initial differences in bulk chemistry. Asa consequence, the compositions of coresponding paired porphyroblasts

and selvage minerals may difier from place to place in the rock.

NurrsBn op DB'rnpurNrNG CoMpoNENTS

Because mosaic equil ibrium was established in these rocks, the totalmineral assemblage of a lamination is in disequilibrium, and the totalnumber of phases is undoubtedly greater than the maximum number pos-

sible for the smaller equilibrium volumes. The question of the maximumnumber of phases, and therefore the number of determining components,contained within an equilibrium mosaic has not been answered, mainly

because (1) most compositional realms contain less than the maximumnumber of phases, and (2) the plane of the thin section nearly always

shows f ewer than the number of minerals that makes up the compositionalrealm. However, some insight into the maximum number of minerals(and therefore the number of determining components) can be obtainedby studying the compositional relationships between contacting minerals

belonging to many equilibrium mosaics. With this information it shouldbe possible to piece together a phase diagram consistent with the ob-

served relationships. We are looking for the minimum number of com-

o n i a l r a i t t t (

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582 PHILIP H. OSBERG

Frc. 6. Thompson projection showing tie-lines between chemically analysedmineral pairs. Data are for minerals that appear in Table 3.

ponents required in the constructions of a consistent diagram, i.e., adiagram in which phase polyhedra do not intersect.

Figure 6 shows tielines connecting compositionally analyzed mineralpairs. Optical observations of contacting minerals indicate the existenceof additional tie-lines as follows: andalusite-chlorite, chlorite-cordierite,chlorite-staurolite, andcordierite-staurolite. Garnet, althoughnot plotted,has tie-lines extending to all minerals shown in Figure 6. The andalusite-biotite tie l ine intersects both the staurolite-chlorite and the staurolite-cordierite tie lines. In addition the andalusite-chlorite tie-line intersectsthat of staurolite-cordierite. Because these mineral pairs exhibit equilib-rium partitions, the intersecting tie-lines indicate a need to considerchemical components other than those specificed in the Thompson pro-jection.

Garnet contains a relatively high percentage of MnO, and a considera-tion of this oxide does separate the intersecting tieJines in Figure 6. The

BUCHAN M T,TAMORPHIC ROCKS

43'

Frc. 7. Modified Thompson projection showing the separation of tie-linesthat results when MnO is considered as a component.

MnO-content of the minerals is as follows: andalusite(biotite:chlorite< cordierite ( staurolite ( garnet. These chemical relationships are shownon a modification of the Thompson projection similar to that employedby Drake (1969). In Figure 7 the vertical axis is AlrOr-3KrO/FeOf MnO*MgO and triangles of composition with apices FeO, MnO, and MgOare erected on the plane of projection. This geometric modification servesto move the compositions of cordierite and staurolite off the projectionplane, thereby separating the intersecting tie-Iines.

Such a manipulation, however, does not alleviate the problem of cross-ing tie-lines in the immediate vicinity of biotite in Figure 6. In this dia-gram the biotite in contact with cordierite has larger AlzOr-3KrO/FeO*MgO and smaller MgO/FeO*MgO values than does the biotite thatcontacts staurolite. On the other hand, biotite contacting chlorite hasvalues of ALOa-3KzO/FeOtMgO and MgO/FeO*MgO that in somecases approach those of biotite associated with cordierite and in othercases those of biotite-associated with staurolite. These relationships canbe explained by either of the following solid solutions in biotite:

Mg+z5i+r a Fe+3Al+3

Mg+22Si-4 = Ti+42A1+3

583

584 PHILIP H. OSBERG

The writer favors the second possibil i ty because although Ti enters

staurolite, it does not. enter into cordierite, and consequently the biotite

associated with cordierite should be Ti-rich relative to the biotite asso-

ciated with staurolite. This circumstance causes the biotite contacting

cordierite to have higher values of AlzOs-3KzO/FeO*MgO and lower

values of MgO/FeO+MgO than does biotite contacting staurolite.

When MnO is considered to be a component, the biotite solid solution

Mg+251+a e 2Al+3

can explain the chemistry of biotite contacting cordierite and staurolite.

However, it cannot explain the chemistry of biotite associated with

chlorite. These assumptions cause some of the chlorite-biotite tie-Iines to

cross the surface containing the cordierite-biotite tie-l ines.An alternative interpretation explaining the crossing tie-lines in the

vicinity of biotite (Figure 6) is that mosaics consisting of a given mineral

pair were hozen in at external conditions that differed from those at

which other mosaics consisting of different mineral pairs were frozen in.

This interpretation is rejected on the basis that mosaics consisting of a

triad of minerals, for example a biotite crystal that contacts both garnet

and cordierite (see Tables 4, 3a, and 6a) has a biotite composition that is

homogeneous within the l imits of the experimental technique. Moreover,

the Ko' values for biotite and the other two minerals of the triad are

comparable to those for mosaics consisting only of mineral pairs.

These relationships suggest that the number of determining compo-

nents is seven (SiOz, TiOz, AlzOa, FeO, MnO, MgO, and KzO). Water is

considered mobile.

TolrppnaruRE AND FUGACTTY ol oxYGEN

The existence of i lmenite and magnetite in the rocks at West Sidneyallows an estimate of the temperature of the equil ibrium to be made using

the method of Lindsley (1963). The temperature estimates of this method

are somewhat uncertain. Because of the small grain size of both i lmenite

and magnetite and because of the scarcity of magnetite, the compositions

are averages of grain separates. There is no glrarantee that the composi-

tions are those of contacting magnetite and ilmenite.The 2dlrroy and 20pzq lines for ilmenite and the cell edge for magnetite

were measured using a 114.6 mm Debye-Scherrer camera. The value

for the cell edge of magnetite was determined using Talyor and Sin-clair 's (1945) and Nelson and Riley's (1945) extrapolations. Applying

these values to Lindsley's graphs (1962, 1963) leads to compositions ofIlmeT and Magso. Util izing the/(O) projections of Lindsley (1963), the

BUCIIAN M ETAMORPH IC ROCKS

compositional coordinates indicated lie in the lower left corner. Extrapo-lating Lindsley's data for these compositions indicates that the tempera-ture was approximately 500'C. The/(Oz) average specifi,c to this samplewas of the order of 10-24 bars, but might vary from sample to sample.

Sulrlrany

Although beds contain up to eleven minerals, chemical relationshipsindicate that the minerals are not all in mutual equilibrium. Instead,compositional realms have been established within which local equilib-rium exists. A minimum of seven determining components is necessary todescribe the phase relationships within the mosaics. The compositions ofcoexisting i lmenite and magnetite suggest that the temperature atequilibrium was r:500oC.

AcrNowr,rncnwnts

The work leading to this paper was in part supported by National Science FoundationGrant GA-933. In addition the writer gratefully acknowledges Professors Clifford Frondel,

James B. Thompson, Jr., and Cornelis Klein, Jr. for making the electron probe at theHofiman Laboratory, Harvard University, available for his use. Finally, Professors ArdenAlbee, Cornelis Klein, Jr , Peter Robinson, and James B. Thompson, Jr. critically readthe manuscript. Their suggestions for revision are appreciated.

RernruNcrs

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586 PHILIP H. OSBERG

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Manuscript receired,, Ju,ne 21, 1970; aceepted' Jor publi'cation, Detember 11, 1970.