Amerkan Mineralogist, Volume 76, pages 148-160, 1991

The A.EI of reaction and recalibration of garnet-pyroxene-plagioclase-quartzgeobarometers in the CMAS system by solution calorimetry

Jlnnns O. Ecxnnr, JR.,* R. C. NrwroNDepartment of the Geophysical Sciences, University of Chicago, 5734 South Ellis Avenue, Chicago, Illinois 60637-1434, U.S.A.

O. J. Kr-npp,c.James Franck Institute, University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637-1434, U.S.A.

Ansrnacr

Two of the potentially most useful barometers for the granulite facies are based on thefollowing reactions:

Enthalpy of reaction (AI1^) is one of the major sources of uncertainty in the calibration ofthese geobarometers. Solution calorimetry of stoichiometric mixes of synthetic phasesfrom each side of each reaction provides an improved method for determination of theenthalpies of reaction. Our results at 973 K are LH^: 8.23 (+2.52) kJ/mol and AiI" :6.02 (+3.a71kJlmol. These values discriminate among various AfI" values compiled fromprevious solution calorimetry and from internally consistent datasets. For the GAPESreaction there is agreement (though marginal) with all of the derived A,FI^ values, but forthe GADS reaction, only the AI1^ value compiled from the data of Holland and Powell(1985) is within the calorimetric uncertainty.

The resultant geobarometric equations, retaining entropy and volume data from Newtonand Perkins (1982), are (P in kbar, Z in K)

GAPES reaction: P:3.47 + 0.013072 + 0.0035042In Ko (+1.55 kbar) (8)GADS reaction: P :2.60 + 0.017182 + 0.0035961In K, (t1.90 kbar). (9)

A practical field test ofthese equations, for a well-characteized, granulite facies area insouthwestern North Carolina, indicates internal consistency for two-pyroxene-garnet gran-ulites and consistency with the experimental AlrSiOs diagram compared to a regionalkyanite-sillimanite isograd. The empirical adjustments of Newton and Perkins (1982),which subtracted 600 bars from the Reaction A scale and added 1600 bars to the ReactionB scale, are consistent with our calculations with no adjustment. Thus, previous barometriccalculations using their adjusted formulae, and tectonic interpretations based on thosepressures, should require little revision.

anorthite + enstatite :2/tpyrope * Vrgrossular + quartzanorthite + diopside : 2Agrossular * Vrpyrope + quartz

(GAPES) (A)(GADS). (B)

CaAlrSirO8 *CaMgSirO.morthile diopside

: %CarAlrSiror, + y3Mg3Al2Si3Or2 + SiOr. (B)grossulil pyrope quartz

Anorthite (An), enstatite (En), and diopside (Di) are, re-spectively, principal components of plagioclase, ortho-pyroxene, and clinopyroxene, and pyrope (Py) and gros-sular (Gr) are principal components of garnet. Quartz (Qz)is essentially pure SiOr.

Apparent metastable persistence of An + pyroxene as-semblages complicated previous attempts to determinestabilities of these reactions by phase-equilibrium exper-iments. All pyroxenes in these previous attempts werenot end-member compositions, but contained Al (as well

148

INrnonucrroN

Several mineralogical geobarometers applicable togranulite facies rocks are based on reactions among end-member substances of coexisting minerals. Two of thepotentially most useful barometers are based on the fol-lowing reactions:

CaAlrSirO8 + MgrSirOumorthite enstatite

:2AMgrAlrSirO,, * YrCarAlrSirO,, + SiO, (A)pyrop€ grossular quartz

t Present address: Department of Geological Sciences, Uni-versity of Tennessee, Knoxville, Tennessee 37996-1410, U.S.A.

0003-004x/9 r/0102-0 I 48$02.00

ECKERT ET AL.: GEOBAROMETERS IN THE CMAS SYSTEM t49

as Ca in orthopyroxene) substitution (perkins, 1983).Three of nine experiments attempting to determine thestability of Reaction A, though using garnets more py richthan would be stoichiometric, produced clinopyroxene atpressures > 17.3 kbar with garnet compositions of py*rlfor both Reactions A and B, equilibrium pressures deter-mined were strongly dependent on garnet composition(Perkins, 1983, Table 2). An attempt to evaluate AG val-ues and pressures, using compiled phase-equilibrium workon these reactions, produced calculated pressures fromthe Otter Lake, Quebec region which ranged from zeroto negative values, indicating a fundamental problem withthose phase-eqilibrium data (Newton and perkins, 1982,p. 205). Thus, direct investigation by high-temperature,high-pressure experiments is not feasible. However, mea-sured thermodynamic data may be used to calibrate thegeobarometer reactions, based on the equation of equi-librium

AGR: AIlg - ?"a'Sg + pavoR + RI ln K* : g. (l)

Here, AG*, Ar1g, A,SR are, respectively, the free energy,standard enthalpy, standard entropy, and standard vol,ume change of the reaction at I bar, ?". K* is the equilib-rium constant, defined for Reactions A and B by:

y u - d p v ' a L , ' a o " . ( 2 )4en 'dl ,

Activities of Py (Reaction A) and Gr (Reaction B) aresquared, as those components have coefficients of 24 inthese reactions, and activities of garnet end-membercomponents are cubed because mixing occurs among threesites. This is analogous to defining the garnet componentsas % of the formula units shown in Reactions A and B.The activities (a) are related directly to the concentrationsof the components of the solid solution phases; ao, iseffectively uriity. Knowledge or assumption of activity-concentration relations is necessary to formulate K* forcomplex rock systems. The other terms can be evaluatedby X-ray diflraction (for AZg), heat capacity measure-ments (for ASfl), and enthalpy of solution measurements(for A,FIR). The first two standard quantities may be com-piled from existing data based on precise measurementsand, in general, do not contribute major uncertainties tothe geobarometer calibrations. The enthalpy of solutionmeasurements are less precise; moreover, relatively fewmeasurements, especially duplicate studies of the impor-tant rock-forming end-member minerals, have been madeusing high-temperature oxide melt calorimetry. Input ofthe measured thermodynamic quantities into Equation Idefines implicitly the pressure (P) of recrystallization ofa garnet granulite, subject to an independently estimatedtemperature (Z) and to the assumption or documentationthat the minerals have not been reequilibrated subse-quently.

The geobarometer Reactions A and B, which may becalled, respectively, GAPES (grossular-anorthite-pyrope-enstatite-silica) and GADS (garnet-anorthite-diopside-

silica), were calibrated from thermodynamic data by Per-kins and Newton (198 l). Except for uncertainty regardinga small configurational entropy term for anorthite, theentropies, heat capacities, and volumes ofthe substancesare well constrained. The provisional calibrations alsowere based on enthalpy of formation values derived fromenthalpy of solution data available only since 1975-1980,and on simple activity-composition models based in parton enthalpy of solution measurements on garnet, plagro-clase, and pyroxene solid solutions. Newton and Perkins(1982) showed that their adjusted calibrations ofthe ba-rometers produced paleopressures for a wide variety ofgranulite-facies occurences that generally were consistentwith alternative pressure estimates. Their GAPES ba-rometer yielded pressures consistently about 2 kbar high-er than their GADS barometer for two-pyroxene granu-lites, and they considered that the former scale was moreaccurate than the latter. Accordingly, to produce agree-ment of the two scales, empirical adjustments of -500

bars for the GAPES scale and + 1500 bars for the GADSscale (Perkins and Newton, 1981, Eqs. 9), and of -600

bars (GAPES) and +1600 bars (GADS) (Newton andPerkins, 1982, p. 217), were suggested.

The calibrations of Newton and Perkins used calori-metric determinations of the enthalpies of formation forthe individual minerals by Charlu et al. (197 5, 1978) andNewton et al. (1977, 1980). These results were producedin three different batches of PbrBrO, calorimeter solventover a period offive years; the possibility exists of sub-stantial variation of results from one melt batch to an-other. Also, since boric acid was used to prepare the sol-vent, there were small, variable amounts of HrO in thesolvent. Possibly because oferrors arising from these fac-tors, the formation enthalpy for enstatite of Charlu et al.(1975) later was recognized to be incompatible with phaseequilibrium measurements (Perkins et al., l98l). Morerecent calorimetric work of Brousse et al. (1984) used analkali borate solvent and confrrmed that the earlier resultof Charlu et al. was too negative by almost 6 kJ/mol.Moreover, internally consistent thermodynamic datasetsderived from experimental phase equilibria (Holland andPowell, 1985, 1990; Berman, 1988) agree that theAIIj'To of pyrope reported by Charlu et al. (1975) is toonegative by about 6- I 3 kJ/mol. Conflicts of smaller mag-nitude also exist between the measured AIl! of anorthite,diopside, and grossular and deductions from phase equi-libria (Newton, 1987). These inconsistencies erode con-fidence in the earlier geobarometer calibrations and in-dicate that a redetermination of the enthalpies ofReactions A and B is needed.

This study redetermines AIl* of the geobarometer Re-actions A and B by solution calorimetry. Dissolution ofthe left-hand-side (LHS) or reactant assemblage and ofthe right-hand-side (RHS) or product assemblage givesA.Flo directly by subtraction. This method was used byNewton et al. (1974) ro define the dP/dT slopes of thehigh-pressure breakdown reactions of anhydrous mag-nesian cordierite and may be applied to any reaction,

150 ECKERT ET AL.: GEOBAROMETERS IN THE CMAS SYSTEM

stable or metastable, whose reactant and product assem-blages dissolve congnrently, and without effects of soluteconcentration, in the calorimeter solvent.

The calorimetric measurements reported here over-come several shortcomings of previous oxide-melt calo-rimetry on the individual phases, in terms of establishingAI1.. These improvements include:

l. A single master batch of PbrBrO5 melt was used inorder to eliminate errors arising from batch-to-batchvanatlon.

2. The BrO, used to prepare the oxide melt was obtainedin fused anhydrous disks that contained reported HrOcontents of less than 230 ppm, thus greatly reducingproblems of solute interaction with H.O. This couldbe a major source of error in dissolving the basic ox-ides CaO and MgO.

3. Measurements of heats of solution were made only onthe phases involved in the reaction, mixed in reactionproportions. Thus, this method involves no accruedinaccuracies associated with heats of solution of theindividual oxides, which, especially for MgO and CaO,could result in systematic inaccuracies of several kJ/mol. The stoichiometry (fixed bulk composition)maintained in the dissolution experiments shouldminimize effects of melt interactions resulting fromnonstoichiometry.

4. To maintain an inert atmosphere, dissolution eventswere undertaken, and the calorimeter solvent betweenexperiments was maintained, under a slight flow ofAr.

5. Additional improvements in technique include the useof a digitally integrated (rather than manually inte-grated) temperature-time curve to establish the heateffect, and the accumulation of more measurementsthan were used in previous work on any one bulkcomposltron.

The larger number of measurements gathered here, thoughapparently not improving precision, should produce moreaccurate mean values for the enthalpies of solution. Im-provement of accuracy neither implies nor requires im-proved precision.

ExpnnrunlwAr- METHoDS

Starting materials

All phases used for calorimetry, except quartz and en-statite, were synthesized from glasses made from stoi-chiometric mixtures of reagent-grade oxides. Puratronic"y-Al,O3 Q9.99o/o) and MgO (99.998o/o) and Alfa Co. SiO,(99.999o/o) were fired at - 1400 'C for 4-7 h prior to pre-paring the stoichiometric oxide mixes for glasses. Theweight of MgO was corrected empirically for weight gainfrom adsorption of atmospheric HrO. In addition, BakerUltrex CaCOr, dried at -300 "C for several hours, wasweighed into the stoichiometric oxide mixes for diopside,grossular, and anorthite; these mixes then were fired at-830 "C until decarbonation was complete, as indicated

by weight loss. The stoichiometric oxide mixes weremelted, quenched to glass, then ground and remelted forhomogenization, and again quenched.

Anhydrous mineral syntheses at high pressure weremade with thre !/q" piston-cylinder apparatus in graphitecapsules of -150-mg yield (except for most grossular)that were surrounded by an AlSiMg-ceramic inner assem-bly, graphite-sleeve heater, soft glass, and a talc outersleeve. Dry synthesis of most grossular was accomplishedin graphite capsules, of -600-mg yield, which formedpart of the graphite heater; this assembly was surroundedby soft glass and a talc outer sleeve. Nucleation in drysyntheses of garnets was assisted by mixing in smallamounts of seeds with ground glass. These garnet seedswere grown in hydrothermal syntheses from ground glass,sealed in Au capsules with -20 mg of deionized HrO, inthe 3/q" -diameter piston-cylinder apparatus with NaClpressure medium. Hydrothermal experiments at 1000 "Cused chromel-alumel thermocouples. Dry-synthesis ex-periments used 250lo Re-WW-30/o-Re thermocouples.Conditions and durations ofanhydrous syntheses are list-ed in Table l.

After opening the graphite sample capsules and burn-ing offexcess graphite at -830'C, all minerals synthe-sized were inspected for purity under immersion oils. Ex-perimental products estimated optically to contain morethan trace quantities of impurities were rejected. No spu-rious peaks appeared in X-ray diffraction powder pat-terns. Unit-cell values were determined by scanning att/s" 20/min (CuKa) with an annealed corundum internalstandard. Ten to 12 peaks of each substance were usedin least-squares refinement of the unit-cell values listedin Table l. Unit-cell indexing was accomplished using aprogram from the National Bureau of Standards. Addi-tional synthesis details follow.

Anorthite. CaAlrSirO, glass was obtained by meltingthe stoichiometric oxide mixture in a DelTech vertical-tube molybdenum-silicide furnace at 1600'C in a Pt cru-cible. Melts were drop-quenched into HrO. This glass wascrystallized in a Globar silicon carbide furnace at 1450'C for 160 h. X-ray diffraction powder patterns showedonly anorthite peaks.

Diopside. CaMgSi,Ou glass was obtained by melting thestoichiometric oxide mixture in the Globar furnace at1480 "C, then drop-quenched into HrO. This glass wascrystallized in the Globar furnace at 1285 .C for 168 h.X-ray diffraction powder patterns showed only diopsidepeaks.

Enstatite. Attempts to make MgSiO, glass in theDelTech furnace at 1570 'C and at 1600 'C (drop-quenched into HrO) failed to eliminate quench crystalsof forsterite, even for melting times exceeding 30 min.Thus, stoichiometric oxide mixes of MgSiO, compositionwere reacted in pressed pellets to a mixture of protoen-statite and clinoenstatite in a procedure similar to that ofBrousse et al. (1984). Sintering conditions in the Globarfurnace were 1300-1400 "C. After five sintering cycles,each of 24 to 16l h duration, interspersed with grinding

ECKERT ET AL.: GEOBAROMETERS IN THE CMAS SYSTEM

TABLE 1. Characteristics of synthetic minerals used for calorimetry

Synthesis conditions (kbar,'C, h)

Tempera-Pressure ture Time

Unit cell constants (A, degree, cms)

1 5 1

DiopsideCaMgSi,O6

EnstatiteMg,Si"O"

AnorthiteCaAlrSiros

GrossularCa3Al,Si3O,,

PyropeMg"Al,Si"O,,

0.001 1285 168

15-17 1400 41-118

0.001 1450 160

25-26 1200 42-170

30 1200 91-142

1 05.88(1 ) 66.1 1(2)

Notei All minerals crystallized from glass except enstatite (see text); garnets crystallized from glass + seeds (see text). Numbers in parenthesesrefer to one standard deviation (sample s.d.) in the last digit.

9.744(11 8.927(11 5.248421

18.214(21 8.824(2) 5.171(1)

8.176(3) 12.862(3) 14.166(5)

11 .851(1)

1 1.455(1)

62.57(1)

93.14(2) 115.78(21 91.24(11 100.70(1)

12s.30(2)

113.16(1)

and repelletizing, no forsterite peaks were evident in X-raydiffraction patterns, which showed only peaks corre-sponding to protoenstatite and clinoenstatite. This ma-terial was converted to orthoenstatite at high pressure inthe piston-cylinder apparatus in graphite containers. X-raydiffraction powder pattems showed only orthoenstatitepeaks.

Pyrope. MgrAIrSirO,, glass was obtained by melting,grinding, and remelting the stoichiometric oxide mixturein the DelTech furnace at 1600 "C. Melts were drop-quenched into HrO. The glass was free of crystals. A por-tion ofthe glass was ground and crystallized to seed crys-tals in hydrothermal experiments at 1000 "C, 25 kbar for5.5-7.4 h. The seed crystals then were mixed with groundglass in dry synthesis experiments. Seed crystals com-posed 12.50/o by weight of these dry synthesis experi-ments. X-ray diffraction patterns showed only pyropepeaks.

Grossular. CarAlrSirO,, glass was obtained by melting,grinding, and remelting the oxide mixture in the Globarfurnace at 144CI 'C. Melts were drop-quenched into HrO.Seed crystals were obtained by crystallizing this glass inhydrothermal experiments at 1000 {, 24 kbar for 3-5 h.These seed crystals were mixed with ground glass in drysynthesis experiments and composed 9.lVo by weight ofthe dry syntheses. X-ray diffraction patterns showed onlygrossular peaks.

Quartz. The quartz used is a natural sample from Lis-bon, Maryland, which was purified by leaching.

Calorimetric technique

The oxide-melt calorimeter used is the Ni-block, twinCalvet-type apparatus first described with an Al block byKleppa (1960). Later modifications to this heat-flow cal-orimeter, including the replacement of the Al block witha Ni block, were described by Kleppa (1972) and byKleppa and Newton (1975). Our measurements weremade with this calorimeter operating at 700 (+3) "C (973K).

Calibration was accomplished by the Pt-drop method,whereby a length of Pt wire was dropped from room tem-

perature (25 'C) into the solvent, and the heat effect wascalculated using known values for the heat contents ofPt.Calibration was repeated for each set of measurements ofmelt, about 30 g in a single crucible. Each calibrationconstant was determined using three to five consistentdrops. The standard deviation (sample S.D. or ",S') of aset of calibration experiments was +0.21o/o to +0.97o/o ofthe mean calibration value.

The schematic diagram of Kleppa and Nefion (1975,Fig. l) shows a cutaway view of this calorimeter, includ-ing fused silica liners in which the dissolutions occur.Inside the fused silica liners. dissolutions occur within aPt crucible containing -30 g of Pb2B2O5 solvent. Thesesilica liners were flushed with dry Ar throughout and be-tween each experiment to maintain an inert atmosphere.The sample powder occupying the sample container wasa mixture of phases for the LHS or RHS in stoichiometricproportions. The sample container is attached to the bot-tom ofa thin fused silica tube passing through the centerof the liner. This thin silica tube is the means by whichthe sample container is moved in and out of the oxidemelt to insure that the powder is clear of the containerwhen dissolving. This stirring was perfbnned in an iden-tical manner for each experiment; at each of the first four60-s intervals of each experiment the stirring tube wasmoved up and down (sample container in and out of thesolvent) 20 times. After most individual dissolution ex-periments, a separate experiment was made to evaluateany heat effect associated with the stirring procedure forthe exact geometry of that particular experiment. Heateffects indicated by these stirring-effect experiments rangedfrom exothermic to endothermic and were equivalent tol.lolo to 3.4olo of the total heat signal in any given exper-iment. During several stirring-effect experiments, bothendothermic and exothermic values were reported by theintegrator over the course of a single experiment. As theseeffects were inconsistent, no stirring correction was ap-plied to any ofthe reported heat ofsolution values.

The calorimeter solvent was mixed in a master batchof Pb,BrO, from Aesar (99.99o/a) PbO powder and Pura-tronic, anhydrous BrO3 (99.9995%) fused disks. Four in-

t52 ECKERT ET AL.: GEOBAROMETERS IN THE CMAS SYSTEM

Eav

c

f

oI

1 A

oE-a5cof

ooI

1 D 170

E-I

c

5

oI

1701 C

oE?l<

c

l

.J'I

Anorthite + Enstatite, AnEn

A H s = 1 3 8 . 0 7 0 8 + 0 . 6 0 2 7 N

R = +0.22 d

E

E

sE E

E

E

E

0 1 2 3 4 5 6

Number of Dissolutions in Crucible of Solvent (N)

Anorthite + Diopside, AnDi

A H s = 1 5 9 . 2 8 2 5 - 1 . 0 6 6 1 N

140

Number ot Dissolut ions in Crucible of Solvent (N)

Fig. 1. Data for heats of solution are plotted vs. the corre-sponding dissolution event in a particular crucible ofsolvent, foreach stoichiometric mixture ofphases: anorthite + enstatite, AnEn(A), '?Apyrope * Yrgrossular + qtlartz, PGQ (B), anorthite +diopside, AnDi (C), and 2Agrossular * Vrpyrope + quartz, GPQ(D). Heat of solution values are plotted on the vertical axis; the

2l3Pyrcpe + 1/3Grossular + Qtz, PGQ

E

A H s = 1 3 3 . 1 0 3 8 - 0 . 4 5 0 5 N

R = + 0 1 2

g E E

EI

" : a E E

0 1 2 3 4 5 6 7

Number of Dissolutions in Crucible of Solvent (N)

2/3Grossular + 1/3Pyrope + Quartz, GPQ

AHs = 147.41!85 + 0.7435N

R = + 0 . 1 8 E

EE

Eo

E

E

E

0 ' l 2 3 4 5 6

Number of Dissolut ions in Crucible of Solvent (N)

dissolution event in the oxide-melt batch, which corresponds toeach heat-of-solution value, is plotted on the horizontal axis. Veryslight slopes and very low correlation coefrcients result fromlinear regression of these data. The absence of significant trendsfor solution values with successive measurements confirms thatthe assumption of infinite dilution of the solvent is justified.

1 B

R = -0.24

E

E

:EE

E

dividual subbatches of 400 g each were melted at -850

"C, then each subbatch was split into three approximatelyequal portions. Three subsets of the master batch wereformed by combining one portion from each of the foursubbatches. Each of these three subsets was remelted for> 30 min and was stirred to insure homogenization. Eachset ofcalibrations and five dissolutions was accomplishedin a single crucible f,lled with 30 g of solvent.

Products of successful mineral syntheses were groundunder acetone and sized to -200 to -325 mesh (45-75pm). Extraneous organic materials were burned off fromthese sized fractions at -830 "C, then these fractions werehand picked under the binocular microscope at 15-40xuntil purity was estimated visually to be essentially 1000/0.The purified, sized fractions were used for the calorime-try. Total powder sample (LHS or RHS) was 30-40 mg.Individual mineral powders were weighed directly intothe calorimeter sample container preparatory to a solu-tion experiment. Extreme care was exercised during theweighing of these mixtures. The individual weight of eachphase was reproduced to 0.01 mg by two successive lift-

ings of the balance pan. ZEro on the balance was inspect-ed after each weighing and the drift from zero was re-corded. The maximum drift observed was less than 0.3mg, and the drift was typically less than 0.1 mg. Thismaximum zero-drift corresponds to a worst-case weigh-ing precision of < lol0.

Samples were thermally equilibrated in the calorimeterfrom 1.5 to 3 h before beginning dissolution; equilibra-tion was confirmed by steady background readings on theintegrator. The background assigned by the integrator isthe average ofthe last three background readings, each ofwhich is counted over a 60-s interval (Dickens et al.,1980). The maximum of six (five in all but one) sampledissolutions in a given crucible filled with 30 g of solventinsured that melt solutions were always very dilute. Nosignificant trends of measured heats of solutions with suc-cessive measurements are indicated by the data (Fig. l).The absence of a significant trend for heats of solutionwith successive measurements indicates negligible con-centration-dependent heat efects.

The heat effects of all dissolutions decaved to the cal-

ECKERT ET AL.: GEOBAROMETERS IN THE CMAS SYSTEM

TABLE 2. Heat of solution values (kJ/mol) from individual dissolution experiments

153

ExperimentA4tr..Time of experimentExperimentAH*'*Time of experiment

ExperimentAH-u*Time of experimentExperiment

Experiment:AH*."nTime of experimentExperimentA4r**Time of experiment

ExperimentAH-,*Time of experimentExperimentAH*t..Time ot experiment

I

14',t.78401 1

137.4136

,|135.32381 1

132.8036

1

143.73461 1

147.3542

llinelal mix: anodhite + enstatite (AnEn)2 3 4 5 6 7

146.15 139.90 141 .2O 142.77 t151 .861 140.1937 52 44 47 51 411 2 1 3 1 4 1 5 1 6

135.77 136.80 136.36 136.16 138.7241 40 36 40 43

Mineral mir: 2/tpyrope + yigtossular + quarlz (PGO)2 3 4 5 6

135.51 137.49 [146.9s] 13i].63 135.6738 46 46 39 431 2 1 3 1 4 1 5 1 6

126.83 128.50 125.25 126.68 126.3048 37 38 38 52

8 I 1 0138.16 134.99 139.2438 34 40

8 9 1 0126.15 128.13 133.2736 37 371 8 1 9

127.39 ',127.5242 38

I1s6.09491 8't49.7246

9 1 0152.41 152.3938 4419 20

162.56 152.2148 53

I 1 0151.19 147.8640 481 9

[161.81 ]47

7132.38421 7

135.7443

Minstal rnixr anonhite + diopside (AnDi)' t 2 3 4 5 6 7 8

t168.661 163.11 156.09 156.65 162.26 150.94 146.58 148.5649 41 45 39 39 41 41 401 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8

156.56 152.72 154.91 150.59 156.94 165.72 152.61 153.0039 42 39 47 47 44 45 50

ilineral mix:2/sgro33ular + %pyrope + quartz (GPO)2 3 4 5 6 7

157.56 153.42 154.49 147.02 140.18 140.9042 40 42 45 44 481 2 1 3 1 4 1 5 1 6 1 7

154.60 143.16 149.85 142.60 150.17 153.5038 49 51 54 38 50

Note.'Time ot experiment is the time elapsed (in minutes) until background readings returned to or near the original baseline value. Values in bracketsdenote the values for each suite of experiment excluded in the calculations. (See additional discussion in text.)

orimeter baseline values within 35 to 54 min after im-mersion of a sample (Table 2). The digital integrator printsvalues for peak and for background at 60-s intervals. Ex-periments were considered complete, and averaging ofthe digitally integrated values was terminated, within 15min after the temperature-time curye was restored towithin 0.150/o of the baseline value relative to the back-ground signal. Only one experiment of the entire opera-tion failed to restore to this level; this experiment wasdiscarded. For each suite of experiments (e.g., experi-ments on the LHS assemblage of Reaction A, AnEn),high or low outliers were omitted (see below), the meanvalues were calculated from the remaining experiments,and values of D ("twice the standard deviation of themean") (Robie et al., 1979) were computed. This crite-rion is given by

6 : 2

where x is the mean of measured values, xi are the indi-vidual measurements, and r? is the number of measure-ments. These 6 values have been recommended by calo-rimetry experts as the precision standard for calorimetry(Rossini, 1956, p. 319; Robie et al., 1979, p. 1l). Forsample standard deviation ^S, D : 2.SVt.

Rrsulrs oF cAr,oRrMETRY

The individual enthalpy of solution measurements areIisted in Table 2. Measurements enclosed in brackets werenot used in the averages. These omitted high or low val-ues from a suite of measurements. which were considered

outliers, deviated by more than 1.50/o of the mean valuefor the suite from the next highest or lowest measure-ment, respectively. Possible sources of the spread of val-ues in Table 2 include (but are not limited to) variationsin solution-time characteristics or dissolution kinetics(giving rise to somewhat different temperature-timecurves), uncorrected-for departure from perfect back-ground restoration and background drift during an ex-periment, possible slight variation in the master batch ofcalorimeter solvent, and weighing errors of the mineralmixtures for dissolution. Application to each value of acorrection for the heat efect of stirring would increasethe scatter of the data. Some portion of this variationlikely is produced as an artifact of calorimeter design andsample arrangement; however, the magnitude of theseeffects cannot be quantified at present. Further discussionof this problematic precision is beyond the scope of thispaper.

As a result ofthese uncertainties (and perhaps others),the relative precision (6) for the individual suites rangesfrom l.l0lo to l.7o/o. This is near the best precision real-izable by high-temperature solution calorimetry. The an-alytical precision reported by Charlu et al. (1975, 1978),when calculated for the geobarometer reactions (propa-gated as the square root of the sum of the squares of thestandard deviations for the solution enthalpies of indi-vidual phases; Newton and Perkins, I 982), appears betterthan that of our measurements. However, many solutionexperiments were omitted from those results as present-ed, and the apparent standard deviations for the geoba-rometer reactions are decreased more by the method ofpropagating a gtealer number of sets of measurements

(3)

154 ECKERT ET AL.: GEOBAROMETERS IN THE CMAS SYSTEM

TlaLE 3. Enthalpies of solution (kJ/mol) of individual minerals and of assemblages and enthalpies of reaction from calorimetry andinternally consistent datasets

Substance: Anorthite Enstatite Diopside pyrope Grossular euartz4g-" (970) 67.91 73.47 85.90 116.27 177.44 -5.15

oH 0.96 1 .09 1.05 1 .34 '1.72 0.29R e f e r e n c e 4 l 2 l g l

Assemblage: AnEnAH39;l'Gefs. 1-4) 141.38

Os

AH# (present)6H

Source of AHgraHl (973)

aHg (e73)6g

1.45

PGO131.52

1 . 1 0139.04 130.81 155.09 149.08

1.57 1 .97 2.38 2.s2Rets.1-4 Present H-P(85) RGB

9.77', 8.23 1 1 . 1 6 5 .14

AnDi cPQ153.80 151 .90

1.42 1.26

1.82 2.52 2.681.76- 6.02 5.06 1.02

H-P(90)8.49*

1 .61*1.90 3.47 2.86

_.Nofe.'Assemblages: AnEn: anorthite + enstatite. PGQ: %pyrope + T3grossular + quartz. AnDi : anorthite + cliopside. GpQ: %grossular +thpy tow+quar tz .References :1 :char lue ta l . (1975) ;2 :Newtoneta t . (1977) ;3 :char tue ta l . (1978) ;4 :newtoneta t . (198otH-p(85) :

l1o.!!1n! ?|{lgwell (1985); H-P(90): Holland and Powell (1990); RGB: Berman (1988). Heat contents (298-973 K) calculated from parameters inH-P(85), H-P(90), and RGB for the relevant reterence. Corrections for 1-4 (970-973 K) us; tabulated values for pyrope and estatite of H;etton (1979)and those ot Robie et al. (1 979) for other phases.* Values from references 1-4 at 970 K : 9.87 (GAPES) & 1.S1 (GAOS),

"' Heat capacity corrections use the H-p(85) value for quartz.

(five per reaction) than are the standard deviations cal-culated from our results (two sets per reaction).

Table 3 compares our enthalpies of solution for thefour assemblages to the composite enthalpies predictedby compilation from four previous studies of the individ-ual minerals. The agreement appears reasonably good: allof the compiled AfI of solution values (within uncertain-ty) are within the precision limits of this study. Appar-ently, systematic errors in the previously reported solu-tion values for the individual phases, though producingcomposite solution enthalpies for each assemblage thatoverlap, within precision, our measured values, createdsystematic shifts in the mean values for each assemblage(see Table 3). Small relative differences in AfI of solutionfor each assemblage are magnified in calculating Aflo.Similarity of Afl^ from the previous measurements to thepresent value suggests that compensating errors for en-thalpies of the predominating Mg phases on each side ofthe reaction (En and Py) produced a previous value thatwas reasonable. Discrepancies between the measured en-thalpies of formation and phase equilibrium deductionsmay have arisen, in part, from problems in determiningenthalpies of solution of the component oxides CaO, MgO,AlrOr, and SiOr. These oxides were measured separately,rather than together in proportions ofthe reactions, andthere may have been specific concentration-dependentheat effects violating the limiting dilution law. The for-mation enthalpies of the individual phases, where possi-ble, should be remeasured by dissolution of stoichiomet-ric oxide mixes, with or without other anchor phases.

Table 3 also lists A.Flo for Reactions A and B from ourwork, along with those derived from solution values ofthe individual minerals and from the internally consistentdatasets of Holland and Powell (1985, 1990) and of Ber-man (1988). The latter three values were correctedto 973K using the heat-capacity corrections presented by the

respective authors. For each AII^ value derived from so-lution calorimetry, the uncertainty is listed as the squareroot of the sum of the squares of the two d-values. Ourvalue of AIl[ at973Kis marginally compatible with thevalue compiled from earlier calorimetry, is very near thevalue calculated from the dataset of Holland and Powell(1990), and lies midway between the values obtained fromthe datasets of Holland and Powell (1985) and Berman(1988), marginally compatible with both. Our value ofAtlg is marginally compatible with that of Holland andPowell (1985) but excludes the value compiled by New-ton and Perkins (1982) and the values ofBerman (1988)and Holland and Powell (1990), being 4-5 kJ larger thanthese other values. Our work supports generally theA,F/ff compiled by Newton and Perkins (1982) but indi-cates that their A,Hg is roughly 4.5 kJ too negative. Therevision of A.Flg is of the correct sign and magnitude toobtain reasonable agreement between pressure values cal-culated from Reactions A and B for two-pyroxene gran-ulites without empirical adjustments, as demonstrated inthe next section.

Although the precision of our results does not appearimproved over those reported previously, the larger num-ber of measurements and improvements in techniquesuggest that our results may be more accurate.

Appr,rc.lrroN To cEoBARoMETRy

The calorimetric results reported here define AIlg ofthe GAPES and GADS Reactions A and B. For purposesofevaluating explicitly the effect ofthis work on the geo-barometer calibrations, pressure calculations are present-ed (Table 4) which were made by replacing only the A,FI*term in the pressure equations of Newton and Perkins(1982). Prior to comparison of these calculations, somediscussion is necessary of the other terms in Equations Iand,2.

ECKERT ET AL.: GEOBAROMETERS IN THE CMAS SYSTEM

TABLE 4, GAPES and GADS pressures (kbar) for two-pyroxene-garnet and selected one-pyroxene-garnet granulites, southwestNorth Carolina

GAPES GADS

155

Sample Present' Present Present*

FQ42E.AAwB1866E-AWB1866E-FFQSOEwB1575EFQ75EFQ107EFO106EWB112OEW B l 1 1 6 EWB1762EFQ88E

8.40

8.037.238.04

8.03

7.167.87

,Vote.' Pressures calculated at 750 qC. Present calculations are from Equations I and 9. Present' calculations use the present results (AH') combinedwith the AyF calculated at 1023 K (750 "C), 3.5 kbar, using the expansivity and compressibility parameters in Holland and Powell (1985). P-N : adlustedformulation of Perkins and Newton (1981). P-H : linearized formulation of Powell and Holland (1988). RGB : tormulation using the Berman (1988)intemally consistent dataset corrected to 1023 K (750 rc), 3.5 kbar (see texg. WB1866E-A and WB1866E-F are amphibolitic and felsic gneisses froma single thin section. FO1O7E and FQ1OOE are GAPES and GADS assemblages separated by less than 200 m. All data are trom Eckert (1988); thelast three samples and WB1575E are also in Eckert et al. (1989).

8.467.627.197.827.437.838.28

8.568.87

8.938.047.598.2s7.848.268.73

9.039.36

8.517.627 .167.837.427.848.32

8.628.96

7.806.926.467 .136.727 .147.6'l

7.918.24

9 .16 7.70

7.316.467.31

7.31

6.387.'14

8.40

8.017.178.01

8.01

7.'to7.84

8.787.948.78

8.77

7.878.61

8.81

8.447.648.45

8.44

8.497.657.227.857.467.868.31

8.598.90

7.578.28

The AS" term

The entropy changes of the reactions, A,SR, are basedon very precise low-temperature heat capacity measure-ments to establish the 298 K entropies of the substancesand also on quite precise high-temperature heat-contentmeasurements to establish AS^ at elevated temperatures.The maximum uncertainty in AS* for both reactions is+2.68 J/Kat 1000 K (see Newton and Perkins, 1982, forsources of data). Some disagreement remains about apossible configurational entropy term for anorthite re-sulting from tetrahedral Al-Si disorder. According to thephase equilibrium deductions of Koziol and Newton(1988), Gasparik (1986), and Wood (1988), all based onexperimental reactions involving anorthite, a mean con-figurational entropy of 3.3 J/K (range: 1.3-7 .7 J/K), cor-responding to 40lo (range: 1.4-l2o/o) disorder, is indicated(Koziol and Newton, 1988). The internally consistent da-tasets of Holland and Powell (1985) and Berman (1988)use much smaller values (1.3 J/K and 0.5 J/K, respec-tively). Inasmuch as larger values seem in accord withthe phase equilibrium data and heat capacity data forsynthetic anorthite and grossular, and since these syn-thetic phases were used in our calorimetry, configuration-al entropy of 4.18 J/K is retained as in Newton and Per-kins (1982, p.206, Table l, Eqs. l2).

The AZ. term

Nefion and Perkins (1982) used the 298 K, I bar vol-umes of the phases to calculate A'V^, and chose to ignorethermal expansivities and compressibilities. The uncer-tainties in the 298 K, I bar volumes measured by X-raydiffraction contribute negligible error (Table l). A slightimprovement of the calibration might be obtained bytaking the AZ*'s calculated for 1000 K and 3.5 kbar (for7 kbar paleopressure), conditions representative for gran-ulite facies calculations. The pressure of 3.5 kbar is as-

signed for 7-kbar pressures by evaluating the volume cor-rection as a definite integral from I bar to 7 kbar {Jfroo'dVdP : Im' - ,rlorntl/2: -(V)35). This correctiondecreases AZ"'s by about 4-5o/o, and raises calculatedpressures by 300-350 bars (GADS) and 370460 bars(GAPES), as shown in Table 4 for corrections of Hollandand Powell (1985). However, replacement of a by A qvartzat 298 K, I bar (calculated from Berman, 1988), resultsin AZo's that differ by -3o/o from values calculated withno expansivity or compressibility corrections. At 750'C,o. quartz would be stabilized above -8.45 kbar (Berman,1988, Table 3b, Fig. 4), so the choice of quartz poly-morph will have a significant effect on volume calcula-tions at higher pressures. Substituting the volume ofB-quartz for a-quartz constitutes most of the differenceamong calculated values of AV^ at I bar, 298 K and,given this and other uncertainties regarding volume cor-rections, may be a more straightforward approach. How-ever, to emphasize comparison to the Newton and Per-kins calibrations by replacing only the Afl^ terms,calculations presented here retain the 298 K, I bar vol-umes using a quartz.

Activity-composition relationships

An uncertainty of unknown magnitude that affects allthermodynamically based geothermometers and geoba-rometers arises from uncertainties in the activity-concen-tration relations used to calculate the equilibrium con-stant (Eq. 2). The actiyity-composition relations in useinvolve a certain number of measured data together witha considerable amount of crystal-chemical interpretationand empirical adjustment based on natural parageneses.The equilibrium constant is therefore the least-con-strained parameter in Equation l.

For garnet components, simple activity expressions usedby Newton and Perkins (1982) are of the following form:

156 ECKERT ET AL.: GEOBAROMETERS IN THE CMAS SYSTEM

lw^ . . Iao, : X."expl-# (Xi"u + Xr"Xo,) | t+lL r \ t

I

..n: x,pxplk (x?^ + x*x,")] (5)

where X is the atomic fraction in a ternary lta,Vtg,neygarnet and W.^*"is a grossular-pyrope binary interactionparameter evaluated as 13.807 - 0.00637"kJ (for four Oatoms), independent of composition (Newton and Ha-selton, l98l). These expressions are of the type for mul-ticomponent regular solutions used by Ganguly and Ken-nedy (1974) and originally from Prigogine and Defay(1954), in which the assumption is made that the otherbinary interaction parameters W.^r,and W*"r., and a sec-ond-order term from ternary interactions, are negligible.The expressions follow from more general equations forsubregular multicomponent solutions by assuming that,over a restricted compositional range, the garnets behaveapproximately as regular solutions. The binary parameterW"^*" may be split into enthalpic and entropic parts:

W*-": W*" - TWt-". (6)The enthalpic term Wr*-" (excess enthalpy parameter)was evaluated using the solution calorimetry measure-ments of Newton et al. (1977) on synthetic pyrope-gros-sular garnets, and the entropic term I4f.., (excess entropyparameter) was evaluated using the heat capacity mea-surements of Haselton and Westrum (1980) on syntheticpyrope, grossular, and a pyrope6o-grossular4' solid solu-tion. Recent phase equilibrium work on pyrope-grossularsolid solutions by Wood (1988) upholds the general mag-nitude of lZ."r, expressed by the Newton and perkinsformula but indicates that the excess entropy term maybe somewhat dependent on composition and may not besymmetric as assumed here.

Bohlen et al. (1983a) and Ganguly and Saxena (1984)found reasons from experimental phase equilibria andnatural parageneses to infer that the binary Mg-Fe inter-action may not be negligible. They 5r,ggested that the in-teraction parameter was asymmetric and particularly sig-nificant near the Fe end-member. This conjecture wassupported by the enthalpy of solution measurements onalmandine-pyrope garnets by Geiger et al. (1987) and bydeductions based partially thereon by Sack and Ghiorso(1989). However, standard deviations of the measure-ments of Geiger et al. (1.81-7.15 kJ/mol) are large rela-tive to their derived excess enthalpy [-3 kJlmol atMg(Mg + Fe) : 0.251. In contrast, recent deductions fromexperimental Fe-Mg exchange between garnet and olivineby Hackler and Wood (1989), as well as deductions fromphase equilibria and natural parageneses by Berman andBrown (1988), indicate much smaller, perhaps negligible,Fe-Mg nonideality. Most recently, experimental mea-surements at 1000 qC on the displacement of the GRAILequilibrium indicate nearly ideal Fe-Mg mixing for Fe-rich garnets (Koziol and Bohlen, 1990).

Solution calorimetry by Geiger et al. (1987) on Ca,Fegarnets and phase equilibrium measurements in the samejoin by Koziol (1990) indicate negligible Ca-Fe interac-tions; this has been verified for ternary Ca,Mg,Fe garnetsin the Fe-rich (almandine-dominated) range with about20 molo/o grossular by the phase equilibrium measure-ments of Koziol and Newton (1989). These recent obser-vations tend to justify the selection of interaction param-eters made by Newton and Perkins (1982). Forcomparison to previous calculations, the barometer cal-ibrations presented here employ the garnet solution pa-rameters used by Newton and Perkins (1982).

The pyroxene activity models used in the Newton andPerkins (1982) geobarometer calibrations (and most oth-ers) are essentially the two-site ideal models of Wood andBanno (1972). In these models, the activity of MgrSirO.in orthopyroxene is given by XMI.XM|, where each X isthe fraction of Mg atoms on each of the two octahedralM sites. The presence of nonquadrilateral components(Al,Mn,Ti) in natural pyroxenes prevents the applicationof macroscopic components and requires calculationsemploying the two M sites. Solid-state emf measurementsof orthopyroxenes (Sharma et al., 1987) suggested sub-stantial positive excess free energy, in contrast to recenttheoretical studies (Sack and Ghiorso, 1989; Davidsonand Lindsley, 1985) that predict small or even slightlynegative excess free energy. Thus, apparently there is noirrefutable reason at present to defer to a model morecomplex than that of Wood and Banno (1972\. Deduc-tions based on experimental Fe-Mg exchange between il-menite and clinopyroxene (Bishop, 1980) and on mod-eling of experimental data on the quadrilateral pyroxenesolvus (Saxena et al., 1986) show substantial nonidealityof diopside-hedenberyite clinopyroxenes, with a maxi-mum excess free energy of about 2 kJ at intermediatecompositions. However, modeling of the experimental Fe-Mg distribution between garnet and clinopyroxene (Pat-tison and Newton, 1989) indicated nearly ideal clinopy-roxene, or even slightly negative deviations from ideality,in the Mg-rich range of most granulite clinopyroxenes,regardless ofwhether an ideal or a nonideal garnet is as-sumed. Thus, uncertainty remains as to whether any im-provement in clinopyroxene component activities isachieved by adopting a model more complex than theideal two-site model. For comparison to previous results,pressure calculations using the present calibrations em-ploy these same ideal two-site models for pyroxene.

There is also some uncertainty in plagioclase activitymodels. The Al avoidance model of Newton et al. (1980)is based on solution calorimetry ofplagioclase in the highstructural state synthesized at 1200 9C in conjunction withthe entropy-of-mixing model of Kerrick and Darken(197 5). The activity of CaAlrSirO, is given by

26X^,,47T

T

"*:&L*e*o(r032

(7)

ECKERT ET AL.: GEOBAROMETERS IN THE CMAS SYSTEM t57

This formula reproduces rather closely the activities foundby Orville (1972) in his aqueous alkali chloride exchangeexperiments with plagioclase at 700 oC and 2 kbar in thecomposition range An2o-An50. At higher anorthite con-tents there may be a slight discontinuity in the activityat the transition from the face-centered to the body-cen-tered structures (Carpenter and Ferry, 1984). At compo-sitions below Anro and temperatures below 600 "C, Equa-tion 7 probably underestimates the anorthite activity(Ashworth and Evirgen, 1985). In the temperature-com-position range of recrystallization of most intermediateand mafic granulites, Expression 7 may be adequate; italso has been incorporated into several general ternaryfeldspar models (Haselton et al., 1983; Ghiorso, 1984;Fuhrman and Lindsley, 1988). For comparison to pre-vious calculations, Expression 7 is retained in the calcu-lations ofpressure given herein.

At present the net errors in geobarometry contributedby all of the uncertainties in activity-composition rela-tions cannot be evaluated precisely. A worst-case esti-mate formulated by Hodges and McKenna (1988) con-cluded that the accuracy of the most commonly usedgeobarometer formulations applicable to crustal rocks islikely to be t-5 kbar, which would make most of thebarometer scales virtually useless on an absolute basis.Nevertheless, several barometers have proven to be gen-erally consistent with geologic criteria in various meta-morphic belts and to provide useful information whenused in a relative sense to distinguish pressure variationin individual metamorphic progressions [see Newton(1983) and Bohlen et al. (1983b) for summariesl.

Reformulation of the barometers

Equations for geobarometry may be reformulated withthe new Afl^ values and otherwise the same input termsas those used by Newton and Perkins (1982); this allowsdirect comparison of the effect of replacing only Afl*. Therevised equations are (P in kbar, ?" in K)

GAPES reaction:

P : 3 .47 + 0.013072 + 0.00350421n K"

(+1.55 kbar) (8)

GADS reaction:

P - - 2.60 + 0.01718r + 0.0035962In K"

(+1.90 kbar). (9)

Uncertainty for each reaction is propagated as the squareroot ofthe sum ofthe squares ofthe standard deviationsof the enthalpy and entropy terms (Nefion and Perkins,1982), scaled to the pressure calculation by dividing byAV^.

Equations were derived by linear regression to establishthe variation of pressure as a function of pyrope content(X*) in garnet, using the experimental results of Perkins

(1983) at 1300 oC, on Reactions A and B. These equa-tions are (P in kbar)

P: 48.22 - 0.318Xp", R: -0.9997 (GAPES)(10)

and

P:4:0. t3 - 0.235Xw R: -0.6194 (GADS).( l l )

For the stoichiometric garnet compositions of ReactionsA and B, at 1300 "C, equilibrium pressures of 25.00 (A)and 32.29 (B) kbar were calculated. Pressures calculatedfrom Equations 8 and 9 for end-member compositionsin Reactions A and B (all a : l), at 1300 "C, are 24.03(A) and 29.62 (B) kbar, in reasonable agreement despitethe inherent uncertainties and the problems of metasta-bility in the phase equilibrium results.

An evaluation of the present calorimetric results andtheir contribution to the geobarometer calibrations is at-tempted below, in spite of the intrinsic uncertainties in-volved. The test is based on the consistency of the twobarometers for pyroxene-garnet granulites from a well-characterized and well-mapped metamorphic area.

Pressure calculations for southwestern North Carolina

Comparative pressure calculations were made for agranulite-facies core of Paleozoic metamorphism in theBlue Ridge province of the North Carolina Appalachians(Fig. 2) (Eckert et al., 1989). Structural, petrologic, andstratigraphic evidence indicates a continuous metamor-phic progression from the staurolite zone to the horn-blende granulite subfacies ofthe granulite facies (Eckert,1988; Eckert and Mohr, 1988; Eckert et al., 1989). GADSassemblages, with or without GAPES assemblages, occurin the granulite-facies area of Figure 2 in mafic (amphi-bolitic) rocks; GAPES assemblages also occur alone infelsic (tonalitic) gneisses.

GAPES and GADS pressures, using five different for-mulations for each barometer. were calculated from thecompositional data in Eckert et al. (1989) and Eckert(1988), at an inferred temperature of 750 'C. All calcu-lations were made with the activity models used by New-ton and Perkins (1982) as discussed above. Pressures list-ed in Table 4 were calculated (l) with the adjustedformulation of Perkins and Newton (1981), (2) withEquations 8 and 9 ofthis study which apply our new AfI"values, (3) with Equations 8 and 9 and AV* corrected to750'C and 3.5 kbar (parameters in Holland and Powell,1985), (4) with the linearized formulation of Powell andHolland (1988) (which is based on the internally consis-tent dataset of Holland and Powell, 1985), and (5) withan equation derived from the internally consistent datasetof Berman (1988), corrected to 750 qC, 3.5 kbar. Pres-sures calculated for two-pyroxene + garnet assemblages

1 5 8 ECKERT ET AL.: GEOBAROMETERS IN THE CMAS SYSTEM

KENTUCKY

TENNESSEE 10ts"/ . ' -.-! l- CAROLINA

3,:"I

AI.ABAMA

PLAIN

GEORGTA

Calculated GAPES & GADS PressuresWith Respect to lsograds, SW North Carol ina

S i l l i m a n i t e - |

Kyan i te

Fig. 2. Map relationships of GAPES and GADS pressurescalculated (using Equations 8 and 9) for two-pyroxene + garnetassemblages in westem North Carolina (Table 4). In the small-scale map, major subdivisions of the southern Appalachians areshown (simplified after Hatcher, 1987). The inset shows isogradsin the Noland Creek-Wayah amphibolite/granulite transition(Eckert and Mohr, 1988; Eckert, 1988) and pressures calculatedusing our formulations of the GAPES and GADS barometers.

Metamorphic zones: stawolite (St), staurolite-kyanite + kyanite-almandine (Kyanite), sillimanite-muscovite (Sillimanite-I), sil-limanite-orthoclase (Sill-I), and the hornblende granulite subfa-cies of the granulite facies (HGD. For each locality, the GAPESpressure is positioned above the GADS pressure. Data are fromEckert (1988); data from the southwesternmost locality(WBl575E) are also in Eckert et al. (1989).

(both GAPES and GADS) are plotted by sample localityin Figure 2.

All of the GAPES calculations are in reasonable to goodagreement, and indicate that the pressures fall in the sil-limanite field of the experimental AlrSiO, diagram (Fig.3), consistent with the kyanite-sillimanite isograd (Fig. 2)and with the presence of peak-metamorphic sillimanitein nearby metapelites. The smaller Afl^ from the Berman(1988) dataset (Table 3) contributes to lower pressuresfrom his calibration. Calculated pressures of7.5-8.5 kbarat 750 "tC are in the range expected ifthere is a generallycoherent increase of temperature and pressure from in-side the kyanite field to the granulite facies, across thekyanite-sillimanite isograd (compare Figs. 2 and 3).

The GADS calculations, based on our calorimetry, agreereasonably well with the GAPES pressures from the samerock or adjacent outcrops, although GADS pressures aresystematically higher than GAPES by 130-590 bars (Ta-ble 4). The agreement suggests that the activity models

pertinent to the two equilibrium constants, which involvemostly the same components, either are reasonable orhave comparable errors, at least in the composition rang-es considered. This agreement implies further that theassumption of frozen-in paleopressures is valid. A smallempirical pressure adjustment of - 350 bars could be ap-plied to GADS calculations; this would force agreementof the two scales, on average. Such a small empirical ad-justment would be well within the calorimetric uncer-tainties but is not required and remains a matter of in-dividual preference. The Powell and Holland (1988)GADS pressures are substantially (l.l-1.2 kbar) belowthose calculated with Equation 9; this results largely fromthe smaller value of AfI" employed (Table 3). Althoughthe small AfI" of Berman (1988) (Table 3) should lowercalculated pressures, the larger AS calculated from thatdataset contributes an upward shift to calculated GADSpressures. Pressures calculated from the Berman (1988)dataset agree reasonably well with our values and ex-

ECKERT ET AL.: GEOBAROMETERS IN THE CMAS SYSTEM 159

1 0E

+GAPESGADS

*f

KYANITE

SILLIMANITE

able in future work to improve measurement of enthalpiesof formation of silicates.

AcxNowr,roctrlnxrsThe present work was supported by National Science Foundation grant

EAR-8707156 (R.C.N.). Calorimetry maintenance and some supplies weresupported by NSF grant CHE-8700937 (O.J.IC). Additional support wasprovided by the central facilities of the Material Research Iaboratory(NSD al the University of Chicago. We acknowledge gratefully the vastamount of advice and instruction in calorimetric technique given by I,e-titia Topor throughout this work. Use of the DelTech melting furnace wasprovided by B.J. Wood; assistance in the melting and quenching to glassof starting material using the DelTech fumace was provided by AlanWoodland. Assistance by Joe Pluth in setting up the program to indexthe unit-c€ll calculations is acknowledged. Conversations with Tom Chackoprovided valuable feedback throughout this study. Reviews by H.T. Ha-selton and J. Ganguly, and comments by R.O. Sack, helped clarifi themanuscript.

RrrnnrNcns crrEDAshworth, J.R., and Evirgen, M.M. (1985) Plagioclase relations in pelites,

central Menderes Massif, Turkey. II. Perturbation of garnet-plagioclasegeobarometers. Joumal of Metamorphic Geology, 3, 219-229.

Berman, R.G. (1988) Internally-consistent thermodyanamic data for min-erals in the system NarO-KzO-CaO-MgO-FeO-Fe'Or-AlrO,-SiOr-HrO-CO,. Journal of Petrology, 29, 445-522.

Berman, R.G., and Brown, T.H. (1988) A general method for thermo-barometric calculations, with a revised garnet solution model and ge-ologic applications. Geological Society ofAmerica Abstracts with Pro-grams, 20, A98.

Bishop, F.C. (1980) The distribution ofFe'z* and Mg between coexistingilmenite and pyroxene with applications to geotlermometry. AmericanJournal ofScience, 280, 46-77.

Bohlen, S.R., Wall, v.J., and Boettcher, A.L. (1983a) Experimental in-vestigations and geological applications ofequilibria in the system FeO-TiOr-Al,Or-SiO,-HrO. Arnerican Mineralogist, 68, 1049-105E.

-(1983b) Experimental investigation and application of garnet gran-ulite equilibria. Contributions to Mineralogy and Petrology, 83, 52-6 l.

Brousse, C., Newton, R.C., and Kleppa, O.J. (1984) Enthalpy of forma-tion of forsterite, enstatite, akermanite, rnonticellite and merwinite at1073 K determined by alkali borate solution calorimctry. GeochimicaCosmochimica Acta, 48, l08l-1088.

Carpenter, M.A., and Ferry, J.M. (1984) Constraints on the thermody-namic mixing properties of plagioclase feldspars. Contributions to Min-eralogy and Petrology, 87, 138-14E.

Charlu, T.V., Newton, R.C., and Kleppa, O.J. (1975) Enthalpies of for-rnation at 970 K of compounds in the system MgO-Al'OySiO, fromhigh remperature solution calorimetry. Geochimica Cosmochimica Acta,39, 1487-1497.

-(1978) Enthalpy of formation of some lime silicates by high-tem-perature solution calorimetry, with discussion of high pressure phaseequilibria. Geochimica Cosmochimica Acta, 42, 367-37 5.

Davidson, P.M., and Lindsley, D.H. (1985) Thermodynamic analysis ofquadrilateral pyroxenes. Part II: Model calibration from experimentsand applications to geothermometry. Contributions to Mineralogy andPetrology, 91, 39O-4O4.

Dickens, I(J., Kleppa, O.J., and Yokokawa, H. (1980) Microcomputercontrolled inte$ator for Calvet-type twin calorimeters. Reviews ofSci-entific Instruments. 5 l. 67 5-677.

Ecke(, J.O., Jr. (1988) Petrology and teclonic implications of the mela-morphic transition from the staurolite-kyanite zone to the Wayah gran-ulite-facies metamorphic core, southwest North Carolina Blue Ridge:Including quantitative analysis ofmineral homogeneity, 337 + xii p.Ph.D. thesis, Texas A&M University, College Station, Texas.

Eckert, J.O., Jr., and Mohr, D.W. (1988) Conditions in the metamorphictransition from the staurolite-kyanite zone to the hornblende granulitefacies core near Franklin, North C.arolina: Petrologic evidence for acontinuous Paleozoic progression. Geological Society of America Ab-stracts with Prognms, 20, 262.

o(E

ll.!a

EJooE4

24 0 0 5 0 0 6 0 0 7 0 0 8 0 0

Temperature ('G)

Fig. 3. GAPES and GADS pressures calculated (using Equa-tions 8 and 9), for two-pyroxene + garnet assemblages in thearea of Figure 2, are plotted in P-7 space relative to the alumi-num silicate diagram of Holdaway (1971). All pressures are cal-culated at 750 t. Symbols for GAPES pressures are open squares;those for GADS are frlled symbols with crosses. Four pressuresare plotted each for GAPES and for GADS, but the essentiallyidentical pressures for FQ75E and FQ50E (Table 4) cannot beresolved as distinct symbols.

tremely well with the adjusted values of Perkins andNewton (1981, Table 4).

Previously calculated GAPES pressures using the ad-justed Perkins and Newton (1981) formulae were shownto compare favorably to pressures calculated from nearbymetapelitic rocks using the Newton and Haselton (198 l)garnet-AlrSiO,-plagioclase-quartz (GASP) barometer(Eckert, 1988; Eckert et al., 1989). The pressure spreadof the present GAPES and GADS calculations, to someextent, may reflect real pressure variations, notably aneastward pressure increase (Fig. 3) which is similar to atrend indicated by pressure calculations from nearbymetapelites using the Newton and Haselton (1981) GASPbarometer (Eckert, 1988).

CoNcr.usroNs

l Results from solution calorimetry of reaction assem-blages define the possible ranges ofthe enthalpy changesof two geobarometer reactions important to the granulitefacies and discriminate among various AfI^ values com-piled from previous solution calorimetry and internallyconsistent datasets.

2.The AH"values determined at 973 K for the GAPESand GADS reactions are, respectively, 8.23 (+ 2.52) and6.24 (+ 3.47)k1/mol.

3. A practical field test ofresultant equations indicatesinternal consistency for two-pyroxene-garnet granulitesand consistency with kyanite-sillimanite phase relation-ships.

4. Solution calorimetry of reaction assemblages is a po-tentially important technique for calibrating geother-mometer and geobarometer scales and may prove valu-

t60 ECKERT ET AL.: GEOBAROMETERS IN THE CMAS SYSTEM

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MeNuscnrpr RECETvED JeNuanv 2, 1990MeNuscnrrr AccEprED Nowlraen' 15, 1990