Redetermination of the Anorthite Breakdown Reaction And

American Mineralogist, Volume 73, pages216-223, 1988

Redeterminationof the anorthite breakdownreaction and improvementof the plagioclase-garnet-AlrSiOr-quartzgeobarometer

ANonnl.M. Kozror,,Ronrnr C. Nrwrox Department of the GeophysicalSciences, University of Chicago, 5734 South Ellis Avenue, Chicago,Illinois 60637, U.S.A.

Ansrnq.cr The reaction 3 anorthite : grossular + 2 kyanite + quartz has been determined experimentally over the ranges 900-1 250"C and 19-28 kbar in a piston-cylinder apparatus using a NaCl pressuremedium. Two to four weight percent LirMoOo flux enabledreversal of the equilibrium 200'C lower than previouslyachieved. A point at 650.C, 13.5 + 0.6 kbar was calculated from published studies of 4 zoisite r quartz: 5 anorthite + gros- sularf 2HrOand2zoisite + kyanite+ quartz:4anorthite + HrO, andtheaddition of this point constrainsthe equilibrium curve to P (in kilobars):22.807 (in.C) - 1093. Use of this equation with the plagioclase-garnet-AlrSiOr-quartzgeobarometer results in reduction of the uncertainty of calculated pressuresby a factor of two over previous calibrations. Calculated paleopressuresare 400 bars higher for the assemblagewith sillimanite than those given by Newton and Haselton (1981). Analysis of the data provides an estimate of the I bar,298 K entropy of anorthite that is 3.3 J/K greaterthan the third- law entropy, implying 4oloAl-Si disorder in anorthite.

INtlnooucrtoN phic studies (e.g., Lang and Rice, 1985; Hodges and The reaction Crowley, 1985). We have undertaken a new experimental study of the 3 anorthite: grossular + 2 kyanite + quartz (l) anorthite breakdown reaction that reduces some of these uncertainties. Pressure cells of sodium chloride used in forms the basis of an important geobarometerfor meta- the piston-cylinder apparatus allowed greater accuracy in pelitic rocks. The assemblagegarnet * plagioclase * pressure determination. A nonaqueous molten flux, (kyanite, andalusite, sillimanite) + qtartz is common in LirMoOo, was used to promote equilibration of the ex- medium- to high-grade metamorphic rocks over broad perimental charges, making it feasible to attain tightly rangesoftemperature and pressure.The principal sources bracketed reversals at lower temperatures. In addition, a ofuncertainty in paleopressurescalculated from this ba- bracket of the equilibrium curve at 650 "C, 12.8-14.1 rometer are the P-7" location of the end-member reaction kbar, calculated from two zoisite-forming reactions pre- (i.e., Reaction l) and the activity-compositionrelation- cisely determined in gas-pressure apparatus at lower pres- ships ofthe garnet and plagioclasesolid solutions. sures, helps to constrain the curve in the P-7 range of Several experimental studies have been made of the crustal metamorphism. end-member reaction, starting with Boyd and England (1961),who first identifiedthe productsofthe breakdown ExpnnrlrnNTAl METHoDS of anorthite,and includingHays (1967),Hariya and Ken- All runs were performed in the piston-cylinder apparatus,us- nedy(1968), Schmid er al. (1978),Goldsmith (1980), and inga3/t in. (1.91 cm) diameterassembly with an NaCl pressure Gasparik (1984). Most of these experimentswere con- medium and WRe,-WRe' thermocouples.Temperature uncer- ducted at pressuresand temperatureswell above crustal tainties with these thermocouplesare less than +5 'C (Perkins metamorphic conditions and required long extrapolation et al., 1981).The salt was partially molten in runs at 1250"C for geobarometry.Hodges and McKenna (1987) have ar'd 27.3-28 kbar (Table l) as inferred from large inward-grow- pointed out that extrapolation of the equilibria, coupled ing quench crystals of salt next to the graphite furnace. The in- with wide bracketinguncertainties and limited P-Z ranges tersection of the melting curve of NaCl (Clark, 1959) with the of experiments,contributes a large proportion of the un- anorthite breakdown curve just above 1275'C and 28 kbar lim- certainty in any pressureestimate from this barometer. ited the upper temperaturerange of this study. The NaCl pressure medium with piston-out conditions re- An additional complication is the uncertain pressurecor- quires very small pressure corrections (Johanneset aL, l97I; rectionsin the ditrerent solid-media pressuredevices used Mirwald et al., 1975). However, a comparison of experimental in the studies.These factors contribute to an uncertainty reversalsofthe reaction anorthite + HrO : zoisite + kyanite + of at least 2 or perhaps 3 kbar in the P-?" location of quartz in a gas-pressurevessel and with the 3/+in. ( I .9 I cm) NaCl Reaction I in the temperature range 600-800 "C. Large piston-cylinder device by Jenkins et al. (1985) indicated that a uncertainties have also been cited in various metamor- 400-bar subtractive correction should be applied to piston-out 0003-004x/88/0304-0216S02.00 216 KOZIOL AND NEWTON: PLAGIOCLASE-GARNET-AI,SiO5-QUARTZ 217

TABLE1. List of experimentalrun conditionsand results

Run Treatment. f fC) P (kbar) Time(h) Results 64 breathing 1250 28.O I gr growth; no zo oz breathing 1250 27.3 20 strong an growth; no zo 50 breathing 1200 zoJ 46 gr growth; trace zo 58 breathing 1200 260 46 an grew; no zo

cc 21" Li"MoOo 1150 zb.5 47 gr growth; zo present 47 <1"k v 2o5 1150 zcJ 47 gr growth; zo present 44 2h Li2MoO" 1150 251 23 an grew ol breathing 1150 25.O 43 an grew; no zo 21 2o/" LirMoOo 1100 z+.c 23 gr grew; tr. unknown 15 4"h Li2MoO, 1100 24.0 22 no reaction;minor unkn. 19 4% Li,MoOo 1100 23.4 22 an grew; trace zo, unkn. 49 2h ti2Mool 1050 23.4 66 gr grew; zo present 57 2o/" Li"MoOo 1050 23.0 116 an grew; zo present 72 4YoLi,MoO4 1000 22.s 229 gr grew ao 4% Li,MoO4 1000 22.O 69 no reaction; minor zo, unkn. 75 4"h Li"MoOo 1000 21.5 zto an grew 10 4"k Li2MoO4 9s0 21.3 47 gr grew; minorzo, unkn. 60 2kLi2MoO4 950 21.0 264 no reaction; minor unkn. 30 4% Li,MoO4 950 20.5 137 no reaction; minor zo, unkn 66 4"k Li2MoO4 950 20.5 261 an grew, minorzo, unkn. 74 4% LirMoO4 900 zu.5 286 gr grew 70 4% Li,MoO4 900 19.0 238 an grew A/ote:Pressures listed are uncorrectedgauge pressures(o: +0.5 kbar). zo: zoisite. unkn.: unknown phase (see text). . "Breathing" signifiesbreath-moistened charges. Values under "treatment" are in weight percent.

'C mns at temperaturesnear 600 and pressuresnear 10 kbar. form about 200loof intergranularmelt (Fig. 1). Extra kyanite and The correction is certain to be smallerat the higher temperatures quartz were added to the reversal mixes to ensure that all four of our study, which approach the melting point of NaCl. The phaseswere presentduring the runs. approachused here is to subtract200 bars from the experimental Reaction direction was determined by large (>300/o)changes gaugepressure and to add + 200 bars to the pressureuncertainty. in the ratios of the strengthsof anorthite and grossularX-ray Total uncertaintiesin run pressurefrom friction correction and diffraction peaks of quenchedcharges compared to the starting gaugedrift is +540 bars. material. Starting mixes were X-rayed 5 to 6 times to character- Starting materialswere a natural kyanite from Litchfield, Con- necticut(FeO content:0.16 wto/o),a natural quartz from Lis- bon, Maryland, and synthetic anorthite and grossular.Anorthite Taele 2. Syntheticanorthite unit-cell data was made from an ultrapure oxide mixture by sintering at 1300 'C and 1 bar for 2 d, and then treated at 1000 'C and 16 kbar Anorthite sintered Typical run product in a graphite capsuleto standardizethe material. Table 2 lists at 1300'C,1 bar Anorthite(AK14) (no.34) unit-cell parameters.Grossular (a : 11.850 + 0.002 A; was A. Refinedcell parameters synthesizedfrom stoichiometricglass at 1200'C and 26 kbar. a (A) 8.180+ 0.003 8.179+ 0.013- I 185 + 0.009 + + + Reversal mixes having nearly equal amounts of reactant and b (A) 12.857 0.004 12.873 0.008' 12 866 0.006 c (A) 14.175+ 0.006 14.168+ 0.026. 14.169+ 0.017 product phaseswere homogenizedthoroughly under acetonein a (') 93.333+ 0.026 93.047+ 0.082' 93.152+ 0.078 an agatemortar with small amounts of flux (seebelow), dried at Bf) 115.781+ 0.023 115.895+ 0.106. 115.942+ 0.073 450 .C, and sealedin welded Pt capsules. "r (') 91.101+ 0 022 91.256+ 0.073. 91.145+ 0.059 + + + To reverse a reaction in reasonablelaboratory times in the Y(4") 1338.38 0.94 1338.31 5.14- 1338.13 3.43 CaO-AlrO.-SiO2 system below 1200 'C, an intergranular fluid B. X-ray diffraction data (hkl, dspacings, Ad) compared to flux must be used in experimental runs. Water, an oxylate, and anorthite sintered at 1300 "C, 1 bar 202 4.0393 +0.0009-. -0.0055 PbO have been used in the past (Goldsmith, 1980; Gasparik, 130 3.7773 +0.0028-. +0.0049 1984). However, water or oxylate produces excessiveamounts 130 3.6189 +0.0025-- -0.0014 ofzoisite, which may obscurethe anhydrous reaction (Reaction 114 3.3510 -0.0112* 1), and incorporation ofPb into the feldspar structure may bias 220 3.2610 +0 0012-. +0.0012 the reaction. 220 3.1242 +0.0019" +0.0011 Therefore, two molten oxide fluxes, LirMoO. (Ito, 1975) and 132 3.0425 +0.0002* +0.0035 VrOr, were testedin this system.As little as I wto/oVrO, caused 042 2.9496 +0.0018.- -0.0002.- -0.0015 excessivelylarge amounts of melting, with elimination of some 132 2.8262 -0.0069-- of the reactantsin some runs. This flux was discardedbecause i34 2.6542 242 2.5014 0.0* -0.0011 of difficulty in controlling the amount of melting. Two to four 060 2.1397 -0.0003". +0.0003 weight percent of LiMoOo added yielded to the reversal mix 208 1.7689 +0.0008* +0.0005 better results.Runs without flux were successfulat 1200 and "C . 1250 "C (Table 1). At the temperature and pressureof most of AK14 treatedat 1000'C, 16 kbar. '- StartingAK14. the experiments,the LirMoOo dissolved some of the charge to 2r8 KOZTOL AND NEWTON: PLAGIOCLASE-GARNET-AI,SiO'-QUARTZ

NoClPressure Medium Li2Mo0a Flux

Grossulor+ Kyonite

o -o I

P(bor) = 22.80TfC)-1093

+ reoYlom f Z0+QZ+KY:ANHrO t zo*Qz=cR+1ru*Hlo

Fig. 1. Backscattered-electronimage (scalebar: l0 pm) of a 800 1000 1200 quenchedrun product. Lighest-graygrains are grossular,medi- T ("C) needlelike darkest grains are um-gray crystals are anorthite, Fig. 2. Experimentaldata (corrected downward 200 barsin quartz. mixture of kyanite or Medium-gray interstitial area is a pressure)for the reaction3 anorthite= grossular+ 2 kyanite+ Small bright aluminosilicate melt and tiny anorthite crystals. quartz.Open symbols indicate that productsgrew, closed sym- Li.MoOo. Photo courtesy of Laughlin. spots are bits of John bolsthat reactants grew. Half-filled symbols indicate no reaction. The curveplotted is a least-squaresfit to the midpointsof the brackets.The bracketat 650 'C, 12.8-14.14kbar is calculated ize variations in the peak intensities. The strong reflections of from two zoisitereactions (see text). The shadedarea indicates anorthite at d : 3.18 were comparedto the (400) and (420) peaks the sizeofthe uncertaintyenvelope as defined by theconfidence of grossular,and the (202) and (220) peaks of anorthite were limits of eachreversal of ReactionI (seetext). The areaat T < compared to the (422) and (431) peaks of grossular. Kyanite 900'C is extrapolatedfrom the experimentaldata. peak heights were not used because,as noted by Goldsmith (1980), natural kyanite shows strong preferred orientation that is diminished when it recrystallizesduring the run. showed insignificant differencesfrom the starting mate- Two extraneousphases were noted in some of the run prod- rial anorthite (Table 2), indicating that Li did not enter were presentin some charges,as ucts. Minor amounts of zoisite the anorthite structure. Thus, the presenceof LirMoOo noted in Table 1, even though the capsules,reversal mixes, and shouldnot have biasedthe P-Z position ofthe reaction. salt assemblieswere thoroughly dried previous to the run. Water by the consistencyof the results of may have been tenaciouslyadsorbed on the reversalmix, or Ht This was confirmed generatedfrom HrO decomposition in the salt medium may fluxed and unfluxed runs. have diffused through the Pt capsules(Goldsmith, 1986)during The eight reversal brackets (listed in Table l) at 900- the run. In addition, an unknown phase was detectedby a few 1250'C and 19-28 kbar cover a wider P-I range and very weak peaksin diffractogramsofnearly all run products with extend to lower temperaturesand pressuresthan previous 4 wt0/oLirMoOo and in a few of the runs with 2 wto/oLirMoOo studies.The experimental points are plotted in Figure 2. (noted as "unknown" in Table l). This phase could not be de- Also plotted is a calculated bracket of the equilibrium tected optically with transmitted light, but polished chargesun- curve at 650'C, discussedbelow. The straight line plotted in the intergran- der reflectedlight showed tiny acicular crystals is a least-squaresfit to the midpoints of the experimental ular melt patches, which could account for the unknown bracketsand the bracket at 650'C. The univariant curve peaks. The unknown phase has d values of 3.420, difraction P (in kilobars) : X-ray pattern can be described by the equation 3.105,and 2.918,as determinedby an diffraction - phase not 22.807(in'C) 1093. of a run with 8 wto/oLirMoOo. That the unknown is a 'C, polymorph or breakdown product of LirMoOo was determined The bracket at 650 12.8-14.14 kbar was calculated by the X-ray pattern of a quenched charge of LirMoOo run at thermodynamically on the basis of two zoisite-forming I I 00 'C and 23 kbar. The diffractogram of this chargeonly had reactions: d values corresponding to Li.MoOo. The unknown phase is 4 anorthite + HrO + 2 zoisite + kyanite + quattz (2) product probably a quench ofthe aluminosilicate intergranular 5 anorthite * grossular+ 2F{2O+ 4 zoisite + quartz. (3) melt. Rnsur,rsoFExpERrMENrs AND.ALCULATT.NS fiJf,i:liiffn:ltff'i.;'"Tffi"1*:lfui',tifl:: Electron-beam microanalysis of the quenched charges as cited in the caption. Each bracket, isobaric in the case confirmed that grossular, anorthite, kyanite, and qtartz ofgas-apparatusruns and isothermal in the caseofpiston- were all presentduring the runs. No Mo was detectedin cyclinder runs, is shown by a cross, where the long arm grossular or anorthite. Slow X-ray diffraction scans of representsthe confidenceinterval calculatedby the meth- severalprincipal peaks of anorthite in quenchedcharges od of Demarest and Haselton (198 l) and the short arm KOZTOL AND NEWTON: PLAGIOCLASE-GARNET-AI,SiO5-QUARTZ 219 the P or I uncertainty stated by the respectiveauthors. The uncertainty envelope shown is a subjective estimate ColculotedBrocket for ofwhat turns out to be an inconsistent data set. The calculated pressure of Reaction I at a given temperature 3An=:Gr + 2Ky+Q dependsonly on the pressuresof Reactions 2 and 3, the fugacity of HrO in the pressurerange betweenReactions 2 and 3, and the volumes of the solids, all of which are well known. Details of the calculation are given in Ap- pendix A. The uncertainties in the positions of the two zoisite reactions, which are smallest at 650 'C, are the o main sourcesof uncertainty in the calculatedposition of - the anorthite-breakdownreaction at this temperature.The resultingbracket of maximum width (1.3 kbar at 650 "C) takesaccount ofuncertainties in all ofthe input quantities.

Ennon ANALysrs There has been much discussion of two problems of phase-equilibrium studies: first, of defining a "best" reaction curve (Chayes,1968), and second,ofdetermining the confidencelimits of such a curve (Bird and Anderson, 1973; Znn, 7977 ; Demarestand Haselton,198 l; Hodges and McKenna, 1987). The position and limits directly affectthe calculation and error estimation ofderived thermodynamic data(Zen, 1977).Moreover, sincemany ex- T ("C) perimental studies are performed well above average Fig. 3. Experimental data for the reactions 4An + H.O = metamorphic P-Z conditions, extrapolation of equilibri- 2Zo + Ky + Qz (Chatterjeeet aI., 1984;Goldsmith 1981;Jen- um curves generateslarge uncertainties(Essene,1982). kins et al., 1985)and 5An + Gr f HrO + 4Zo + Qz (Newton, The importance of the anorthite breakdowncurve, how- 1966;Chatterjee et al., 1984)and a calculatedbracket at 650 "C = ever, demandsthat a reasonableattempt be made at judg- for the reaction 3An Gr + 2Ky + Qz. Uncertainty envelopes for the two zoisite-forming reactionsare also plotted. They were ing the slope and error. Demarestand Haselton (198l) fit by eye to the confidenceinterval for each experimental re- have suggestedthat least-squaresanalysis is reasonable versal bracket (shown by crosses)as determined by the method phase-equilibrium for bracketswhere the standarddevia- of Demarestand Haselton(1981). tion of each point of a bracket is greater than the half- width of the bracket. They presenteda statistically rigorous method for assigningeffors to brackets where the standarddeviation ofeach point in pair the is equal.Since straints of the confidenceinterval. This is an important the present tightly bracketed reversalsmeet quali- their considerationfor the precision ofthe geobarometerbased fications,we follow their method in paper.We this assume on Reaction I and for calculation of the entropy of an- that the error in temperature is negligible and that the orthite, discussedbelow. standard deviation in pressure measurement,including the 200-baruncertainty ofour pressurecorrection, is 540 Appr,rc.LrroN To cEoBARoMETRY bars. Taking the midpoint of the bracket as the putative The presentdetermination of the reaction of anorthite position ofthe equilibrium curve, the standard deviation to grossular,kyanite, and quartz reducesthe uncertainty and confidencelimit of each bracket are calculatedfrom in calibration of an important geobarometerfor medium- Equations 6a and 6c and Figure 4 of Demarest and Has- to high-grade metamorphic rocks. Previous calibrations elton (1981).The confidencelimits are usedto definean (Ghent, 1976;Ghent etal., 1979;Newton and Haselton, uncertainty envelope for the equilibrium curve (Fig. l). l98l; Ganguly and Saxena,1984) made use of earlier This method is not as rigorous as that of Hodges and determinations of the end-member reaction, a collection McKenna (1987),but resultsin a reasonable,if intuitive of which is shown in Figure 4. The most preciseof these confidenceinterval. Lang and Rice (1985)have done an are the determinations of Goldsmith (1980) and Gasparik independentderivation ofthe P-Z equation for Reaction (1984).However, the studyof Goldsmith (1980)included 1 from the experimental studies of Hays (1967), Hariya only two wide brackets determined with the NaCl pres- and Kennedy (1968),and Goldsmith (1980)using linear sure medium, and Gasparik's(198a) study useda glass- programming. Their equation derived from A,F10and AS0 talc pressuremedium and relied on experimentally fixed for Reaction I with kyanite is P (in bars) : 22.77 T (in points ofother equilibria, suchas the albite-jadeite-quartz kelvins) - 7lll.9, with an uncertainty of +3 kbar at reaction (Holland, 1980) and the spinel peridotite-garnet metamorphic P-Z ranges.In our analysis, the slope can peridotite boundary (Gasparik and Newton, 1984) for vary betweenthe values21.80 and 24.96within the con- calibration. Gasparik (1984) also used a PbO flux which, 220 KOZIOL AND NEWTON: PLAGIOCLASE-GARNET-AI,SiO'-QUARTZ

net and plagioclaseactivities. Sincethe geobarometerhas a considerabletemperature dependence,accurate paleo- pressuredetermination depends on accurate knowledge of paleotemperaturesthrough independent geothermo- meters. Our experimental curve, determined with kyanite as the AlrSiO, polymorph, was combined with the experimental expressionof Holdaway (1971)for the kyanite: sillimanite reaction (seeApp. B for details), to obtain an o- expressionwith sillimanite as the polymorph. Our equations are (in "C, bars) P,.n": 22.807"- 1093 (5a) P,,.irr: -0.00018727^'z+ 23.417 - 25. (5b) Equations 5a and 5b give pressuressomewhat greater than the Newton and Haselton (1981) formulas, basedupon the experimental work of Goldsmith (1980) (in oC,bars): P,,*,:23.207- 2100 (6a) T-C P,,,ir,:23.607- 600. (6b) Fig. 4. Comparisonof variousexperimental studies on the The secondformula is also basedon the Holdaway (1971) reaction3An = Gr + Ky + Lengthof line showsrange of Qz. kyanite-sillimanite curve and is in error by about +300 experiments.Dotted line showsthe extensionof the present (cited in and Saxena, study'sresults to a calculatedbracket at 650'C, 12. 8-l 4.I 4 kbar. bars,as shown by E. Froese Ganguly 1984).The presentformulas (Eqs.5a and 5b) give pres- suresgreater than the Newton and Haselton(1981) for- in our experience,enters into solid solution with the feld- mulas by about 750 bars at 600 "C for the anorthite spar. breakdown with kyanite and by about 400 bars for the For any temperature,Newton and Haselton( 198l) have reaction with sillimanite. Paleopressurescalculated with written the equation for the barometer as the new formulas and using the same assumptionsabout grossularand anorthite activities as did Newton and Has- -PjAV? + RT ln(a","/a."),+ PAV, = g, (4) elton (1981)will be higherby about theseamounts. For where P0 and AVI are the pressureand volume change, example,Ghent (1976) estimatedpaleopressures at Es- respectively,of the end-memberreaction (1), a denotes planade Range, B.C., of about 8.6-9.0 kbar, whereas the activity ofgrossular in garnet and anorthite in plagio- Newton and Haselton(1981) calculated 7.8-8.4 kbar and clase,P is the estimated pressureof the assemblage,and this study suggests8.6-9.2 kbar. AZ, is the partial molal volume change at I bar. The Uncertainties in the paleopressuresdue to uncertainties approximation sign is usedbecause ofneglect ofthe effect in the location of the end-member curve are much re- of thermal expansionand compressibilityon A,Vland AV,. duced as a consequenceof the new work, being +$59 Becauseconsiderable extrapolation from the experimen- bars at 600 "C and +400 bars at 1000 "C. Further refine- tal P-T rangesto metamorphic conditions of the equilib- ment of the geobarometerawaits clarification of the ther- rium adds uncertainty to the lD term, the precision of the modynamic mixing properties of the solid solutions. geobarometer calibration depends greatly on the P-I control of the experiments and the tightness of the ex- ENrnopv oF ANoRTHITE perimental bracketing nrns. A remaining source of error Numerous authors have consideredthat the third-law is the uncertainty inherent in the formulations of the gar- entropy of anorthite should be supplementedwith a con-

Tnaue3. Thermodynamicdata used in entropycalculation

5 Phase 6x 10*, bx1O2 6 x 10*6 d x 10*g e x 10 ax105 Bx.lQz Anorthite (synthetic) 199.30 5.1683 -9.2492 - 1.4085 -4.5885 4.1883 10.079 1.42 12.9 Grossular(natural) 255.50 16.333 -75.99 9.113 -20.873 26.690 12.s30 2.39 6.3 Grossular(synthetic) 260.12 5.1633 3.2184 -9.9419 - 1.4031 12.530 2.39 6.3 Kyanite 82.30 3.039 - 1.339 -0.8952 -2.9043 4.415 2.54 4.3 Ouartz 41.46 1.044 0.607 0.034 - 1.070 2.269 5.91 22.9 Note: Third-law entropies (J/mol.K), heat-capacitycoefficients (J/mol. K), volumes at 298 K and 1 bar (J/bar),thermal-expansion coefficients (deg-'), and compressibilities(bar 1). Cp: a + bT + c/T2 + dl(T,t2l+ eT2. References:Anorthite-Robie et al. (1978),Krupka et al. (1979).Synthetic grossular-Haselton (1979). Natural grossular--Westrum et al. (1979), Krupkaet al. (1979).Kyanite-Robie and Hemingway(1 984). Quartz-Holland and Powell(1985). Volume parameters from Hollandand Powell(1985). KOZIOL AND NEWTON: PLAGIOCLASE-GARNET-AI,SiO,-QUARTZ 22r

f,gurational entropy, most plausibly of a small amount of quire substantial corrections of unknown reliability for tetrahedralAl-Si disorder. This would give an optimal fit nonternary components.As a possibleillustration of this, to many experimental phaseequilibria, including the an- another set of measurementsis available (Kolesnik et al., orthite breakdown reaction. X-ray diffraction studies of 1979) on a natural grossularwith total impurities about somenatural high-temperatureanorthite also indicate the a factor of two less than those in the grossular used by existenceof such disorder (Smith, 1974,p. 139).How- Westrum et al. (1979). The third-law entropy of this gros- ever, some recent thermodynamic summaries of many sular is much closerto that of the Haselton and Westrum experimental equilibria involving anorthite suggestlittle (1980) synthetic grossular,which may indicate that the (Wood and Holloway,1984; Holland and Powell, 1985) effectsof impurities are greater than allowed for by the or no (Halbachand Chatterjee,1984;Robie et al., 1978) correctionprocedures of Westrum et al. (1979). configurational entropy. The present work allows an improved calculation of AcrNowr,BocMENTS the thermodynamic properties of anorthite becausehigh- part quality measured heat-capacity data (Table 3) exist for This work is of the Ph D thesisresearch of Andrea M. Koziol. Our thanks to David Pattison and Tom Chacko for reviewing an earlier ver- all the participating phases. A fundamental ambiguity sion of this manuscript. Thanks also to Dexter Perkins and Helen Lang arises in the two conflicting heat-capacity and entropy for constructive reviews This researchwas supportedby a National Sci- data setsfor grossular.Measurements on a natural, nearly enceFoundation grant, EAR-841 I 192, with additional support from the pure end-membergrossular (Westrum et al., 1979;Krup- Materials ResearchLaboratory (NSF), University of Chicago. ka et al., 1979) gaveheat capacitiesand standard entropy values significantly smaller than measurementson a pure RnrnnrNcns crrrn syntheticgrossular sample (Haselton and Westrum, 1980). Berman,R.G., Brown, T.H., and Greenwood,H.J. (1985)An internally Estimates of a possible non-third-law entropy of anor- consistentthermodynamic databasefor minerals in the systemNarO- thite basedon Reaction I dependon which grossulardata KrO-CaO-MgO-FeO-FerOr-AlrO3-SiOr-TiOr-HrO-COr.TR-377. Sci- set is accepted.In spite of the uncertainties of the semi- entific Document Distnbution Office, Atomic Energyof CanadaLim- ited, Research River, lJ0, empirical correction of the heat-capacity Company, Chalk Ontario KOJ Canada. data for impur- Bird, G.W., and Anderson,G.M (1973)The freeenergy of formationof ities (principally FeO and HrO) in the natural grossular, magnesiancordierite and phlogopite.American Journal ofScience,273, severalauthors (e.g, Haas et al., l98l; Berman et al., 84-9l. 1985)have preferredthis data set.Others (e.g.,Halbach Boyd, F R., and England,J.L ( I 96 I ) Melting of silicatesat high pressures. and Chatterjee,1984; Wood and Holloway, 1984; Hol- CarnegieInstitution ofWashington Year Book 60, 1l3-125. Burnham,C.W., Holloway, J.R., and Davis,N.F. (1969)Thermodynamic land and Powell, 1985)have preferredthe measurements properties of water to 1000"Cand 10,000 bars. Geological Society of on synthetic grossular. AmericaSpecial Paper 132,96 p. The entropy of anorthite at 1000 K can be computed Chatterjee,N.D., Johannes,W., and Leistner,H. (1984)The systemCaO- from the measureddP/dT slope of the anorthite break- AlrOySiOr-HrO: New phaseequilibria data, somecalculated phase re- petrological down reaction by the : lations, and their applications.Contnbutions to Mineral- Clapeyron equation, dP/dT AS/ ogyand Petrology.88. l-l 3. AZ. A slopeof 22.80is our bestexperimental fit, but the Chayes,F. (1968) On locating field boundariesin simple phasediagrams slopecan vary between21.80 and 24.96,whilch adds a by meansof discriminant functions. American Mineralogist, 53, 359- measureof uncertainty to the calculation. Details of the 371 (1959) points calculation, including error analysis,are in Appendix C. Clark, SP., Jr. Effectofpressure on the melting oferght alkali halides. of ChemicalPhysics, 31, 1526-1 procedure Joumal 531. Our is to compare the entropy of the reaction Demarest,H.H, Jr, and Haselton,HT., Jr. (1981)Error analysisfor at 1000K, 15.5 kbar as determinedby the experimental bracketedphase equilibrium data. Geochimica et CosmochimicaActa, data with the value calculated from the data in Table 3. 45,217-224 Any discrepancywe assumeto be due to configurational Essene,E.J. (1982) Geologic thermometry and barometry Mineralogcal Societyof America Reviews in Mineralogy, 10, 153-206. entropy in anorthite. Ifthe data set for synthetic grossular Ganguly,J , and Saxena,S.K. (1984)Mixing propertiesof aluminosilicate is used, the configurational entropy of anorthite comes garnets:Constraints from natural and experimentaldata, and applica- out to be, on average,3.3 J/K (range:1.3 to 7.7 J/K) at tions to geothermo-barometry American Mineralogist, 69, 88-97. 1000 K. This is equivalentto 4o/o(tange: 1.4 to 12.4o/o) Gasparik,T. (l 984) Experimentalstudy of subsolidusphase relations and properties pyroxene tetrahedral Al-Si disorder. If, however, the C, data for mixing of in the system CaO-AlrOr-SiO, Geo- chimicaet CosmochimicaActa. 48. 2537-2545. natural grossularare used, the amount of anorthite con- Gasparik,T., and Newton,R.C. (1984)The reversedalumina contents of figurational entropy necessaryto model the dP/dT slope orthopyroxenein equilibrium with spinel and forsterite in the system of Reaction I is 0.07 J/K (range:-2.1 to 4.3 J/K), essen- MgO-AlrO,-SiOr. Contributions to Mineralogy and Petrology,85, 186- tially zero. 196 (1976) potential geo- The present experimental Ghent, E.D. Plagioclase-garnet-AlrSiO5-quartz:A data cannot, of course, dis- barometer-geothermometer.American Mineralogist, 61, 7 10-714. criminate betweenthese disparate results. Our preference Ghent, E.D, Robbins,D.B., and Stout,M.Z. (1979)Geothermometry, is for the C, data ofthe synthetic grossularand, therefore, geobarometry,and fluid compositionsof metamorphosedcalc-silicates the existence of some configurational entropy of anor- and pelites,Mica Creek, Bntish Columbia. American Mineralogist, 64, thite. This is largely based on the fact that the Haselton 87zt-885. Goldsmith, J.R. (1980)The melting and breakdownreactions of anorthite and Westrum (1980) Cp data are more straightforward at high pressuresand temperatures American Mineralogist, 65,272- than the measurementson natural grossular, which re- 284 222 KOZIOL AND NEWTON: PLAGIOCLASE-GARNET-AI,SiO5-QUARTZ

- (l 98 l) The join CaAlSiOr-H'O (anorthite-wa1er)at elevatedpres- Al,O3-SiO,at 1540 kbar and 900-1600'C.Contributions to Mineral- suresand temperatures.American Mineralogist, 66, I l8 3-1 188 ogyand Petrology,78, 99-109. -(1986) The role of hydrogenin promotingAl-Si interdiffusionin Robie,R A., and Hemingway,B S (1984)Entropies of kyanite,andalu- albite (NaAlSi.O) at high pressuresEafth and PlanetaryScience Let- site, and sillimanite: Additional constraintson the pressureand tem- ters,80, 135-138. perature of the AlrSiO, triple point. American Mineralogist, 69,298- Haas,J.L., Robinson,GR, and Hemingway,BS. (1981)Thermody- 306 namic tabulations for selectedphases in the system CaO-AlrOrSiOr- Robie,R.A , Hemingway,B S., and Fisher,J.R (1978)Thermodynamic H,O at 101.325kPa (l atm) between273 l5 and 1,800K. Journalof properties of minerals and related substancesaI 298 15 K and 1 bar Physical Chemistry ReferenceData, 10, 575-669. (105pascals) pressure and at higher temperatures.U S. GeologicalSur- Halbach,H., and Chatterjee,N.D. (1984)An internallyconsistent set of vey Bulletin 1452. thermodynamic data for twenty-one CaO-AlrO,-SiOr-HrO phasesby Schmid,R., Cressey,G., and Wood, BJ. (1978)Experimental determi- linear parametric programming Contributions to Mineralogy and Pe- nation of univariant equilibria using divariant solid-solution assem- trology,88,l4-23. blagesAmerican Mineralogist, 63, 5 I l-515. Hariya, Y, and Kennedy,G C. (1968) Equilibrium study of anorthite Smith, J V (l 974) Feldsparminerals, vol. I Crystal structureand physical under high pressureand high temperature.American Joumal of Sci- properties Springer-Verlag,New York. ence,266, 193-203. westrum.EF, Jr., Essene,EJ., and Perkins,D,III (1979)Thermo- Haselton,H.T (1979)Calorimetry of syntheticpyrope-grossular gamets physical propertiesof the garnet grossular Journal of Chemical Ther- and calculatedstability relations. Ph.D. thesis,University ofChicago, modynamics,ll,57-66. Chicago,Illinors Wood, B.J , and Holloway,J R. (1984)A thermodynamicmodel for sub- Haselton,H.T., Jr , and Westrum,E F., Jr (1980)Low-temperature heat solidusequilibria in the systemCaO-MgO-Al,O.-SiOz. Geochimica et capacitiesof syntheticpyrope. grossular,and pyropeuogrossularoo.Geo- CosmochimicaActa, 48, 159-176 chimicaet CosmochimicaActa. 44,701-'709. Zen, E. (1977) The phase-equilibriumcalorimeter, the petrogeneticgrid, Hays,J F. (1967)Lime-alumina-silica. Carnegie Institution of Washing- and a tyranny of numbers. American Mineralogist, 62, 189-204 ton Year Book 65. 234-239 Hodges,K.V., and Crowley,P. (1985)Error estimationand empincal MeNuscnrm RECEIvEDMlv 8, 1987 geothermobarometryfor pelitic systems American Mineralogist, 70, M.LNuscnrprAccEmED Novetusen 13, 1987 '702-709

Hodges,K.V , and McKenna, L W. (1987)Realistic propagation of uncertainties in geologicthermobarometry American Mineralogist, 72, 67I -680 AppnNllrx A Holdaway,M.J (1971)Slability of andalusiteand the aluminum silicate phasediagram. American Journal of Science,21 l, 91-131. Note that two times Reaction 2 minus Reaction 3 will 'C, Holland, T.J.B (l 980) The reaction albite : jadeite + qvafiz determined result in Reaction L Referring to Figure 3, at 650 experimentally in the range 600-1200"C. American Mineralogist, 65, 5.55-5.75kbar (Pr),AG, : 0, but at 650'C, 8.5-8.9kbar 129-134. (Pr), < The latter free-energychange Holland, T.J.B.,and Powell,R. (1985)An internallyconsistent thermo- LG2: 0 and AG3 0. dynamic data set with uncertaintiesand correlations:2 Data and re- can be expressedby sults.Journal of MetamorphicPetrology, 3,343-353 - (A1) Ito, J. (1975)High temperaturesolvent growth oforthoenstatite, MgSiO,, AG3: +2RT lnj/f3) + AV3(P' P3)' in air. GeophysicalResearch Letters, 2, 533-536 where is the fugacity of water at the equilibrium pres- Jenkins,D.M., Newton, R C, and Goldsmith,J R. (1985)Relative sta- / bility of Fe-freezoisite and clinozoisite Journal of Geology, 93, 663- suresof Reaction 2 and Reaction 3, respectively.AZ, is 672 a characteristicvolume changeof the solids of Reaction Johannes,W., Bell, P M , Mao, H K, Boettcher,A L., Chipman,D.W, 3 at 650'C and can be closelyapproximated by the mean Hays, J.F, Newlon, R.C, and Seifert,F (1971)An interlaboratory volume change over the pressureinterval P3 to P2. We pressure comparison of piston-cylinder calibration using the albite- (1969) vol- breakdown reaction Contributions to Mineralogy and Petrology, 32, used fugacity data from Burnham et al. and 24-38 ume data (including cvand B) from Holland and Powell Kolesnik,Y N., Nogleva,V.V., Arkhipenko,D.K., Orekhov,B.A., and (1985).The free-energychange is -27.85 kJ to -33.86 Paukov, I Y (1979) Thermodynamics of pyrope-grossularsolid solu- kJ. tions and the specific heat ofgrossular at 13-300 K" Geochemistry The free-energychange ofReaction I at 650'C and P, International,16, 57-64. Krupka, K, Robie,R.A., and Hemingway,B.S. (1979) High-temperature may be expressedas heat capacitiesof corundum, periclase,anorthite, CaAlrSirO,glass, muscovite,pyrophyllite, KAlSirO8 glass, grossular, and NaAlSiO, glass. -AGl : AG3- 2AG2: AG: - O: AVtdP' (A2) AmericanMineralogist, 64, 86-101 L"' Lang,H.M, and Rice,J.M. (1985)Geothermometry, geobarometry and I-X (Fe-Mg) relations in metapelites, Snow Peak, northem Idaho where AZ, is the volume changeof Reaction l. From Journalof Petrology,26, 889-924. Equation A2, Pt (the equilibrium pressureof the anor- Mivald, P W (1975) , Getting,I.C., and Kennedy,G C Low-frictioncell reaction) may be obtained by iteration. for piston-cylinder high-pressureapparatus. Journal of Geophysical thite-breakdown Research,80, l5l9-1525. Given the errors in the two lower curves, P, is between Newton,R.C. (1966)Some calc-silicate equilibrium relations.American 12.8and 14.14kbar. Journalof Science,264, 204-222. Newton,R C , and Haselton,H.T. (1981)Thermodynamics of the garnet- plagioclase-AlrSiOr-quartzgeobarometer. In R C Newton, A Navrot- sky, and B.J Wood, Eds, Advancesin physicalgeochemistry, vol. l, AppnNorx B p 131-147 Springer-Verlag,New York. Perkins,D., III, Holland,T.JB, and Newton,RC (1981)The AlO, The standard free-energychange of Reaction I at a contents of enstatite in equilibrium with garnet in the system MgO- given temperature is obtained by multiplying a charac- KOZIOL AND NEWTON: PLAGIOCLASE-GARNET-AI,SiO5-QUARTZ 223

teristic volume changeby the equilibrium pressureat this P,,"u,: AG?,"'rl-AZ?,,'r temperature. A volume changeappropriate for the tem- : -0.00018727'1+ 23.417- 25. (B6) peraturerange 600-1000 "C is that at 800 "C and l0 kbar; the equilibrium pressuretimes this AZ differs negligibly from the integralof AZwith respectto pressuresfrom I bar to the equilibrium pressure over this temperature AppnNorx C range. The thermal-expansion and compressibility data For the reaction 3 anorthite = grossular* 2 kyanite + for the minerals of Reaction I compiled by Holland and quarlz,at 1000 K and 15.5 kbar, the volume changeis Powell (1985) give AV : -6.210 J/bar for the reaction -6.105 J/bar. Our experimentaldata indicate a dP/dT with kyanite and -5.154 J/bar for the reactionwith sil- slopeof 22.80(range: 21.8-24.96). The changein entropy 'C), limanite. From the former value (in J, of this reaction (AS) is AG?u":t4t.59T - 6788. (Bl) As,,.: A,s"p+ o{on no, (cl) The standard free-energychange of the anorthite-break- f ,"'oo given down reaction with sillimanite is by where a is the thermal expansion, and this integral is AG?,"u: AG?.k,+ 2AGP":"i,,. (82) approximatedas aZ(l5500). The pressurecorrection is 3.545J/K, so then AS,.,: -135.65. The data setlisted Using the experimental expressionfor the kyanite to sil- in Table 3 is used to calculateAS at 1000 K, I bar by the limanite reaction of Holdaway (1911): equation Pkv-sirr: 20(T - 315) + 0.0009(Z- 315)'z, (B3) AS,,,:A^sn, * or. (c2) and a characteristicvolume changeof0.536 J/bar at 800 f"Or"'' 'C and 5 kbar (Holland and Powell, 1985), This value is - 126.73 using the S0 and C, data for syn- -135.87 AG?v:"irr: -0.000482 4T' - l0.4l4T + 3329, (B4) thetic grossularand for natural grossular.We assumethat the discrepancybetween the experimentally from which derived value and the thermodynamically derived value is non-third-law entropy in anorthite. Then the anorthite AG9..u,:-0.0009648r2 + 120.67r - 130. (B5) configurationalentropy is 3.31 J/K (range:1.3-7.7 J/K) The equilibrium pressureof Reaction I with sillimanite using the synthetic grossulardata set and 0.07 J/K (range: is then (in bars) -2.14.3 J/K) usingthe natural grossulardata set.