American Mineralogist, Volume 76, pages 458-469, I99I

Experimental determination of the pressure-temperature stability field andthermochemical properties of synthetic tremolite

D.l,vro M. JnNrrxsDepartment of the Geological Sciences and Environmental Studies, State University of New York-Binghamton,

Binghamton, New York 13901, U.S.A.

Trvrornv J. B. Hor-raNuDepartment of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, England

Apnrr, K. CL,IREDepartment of Geology, Rutgers University, New Brunswick, New Jersey 08903, U.S'A.

Ansrru,cr

New experimental data for the breakdown of synthetic tremolite to the assemblagediopsidic clinopyroxene * enstatitic orthopyroxene + B-quartz + H2O in the pressurerange of 1.5-7 kbar and to the assemblage diopside + talc in the range of 650-760 'C

were combined with existing experimenlal data for these reactions and all pertinent ex-perimenlal phase equilibria in order to obtain a refined value for the enthalpy of formation(AIlRrb*.2e8J of tremolite. Using the least-squares regression procedure and data base ofHolland and Powell (1990), the derived ArIRrb*.2e8K for tremolite is -12302.90 t 7.05(1o) kJ/mol for fixed values of entropy, volume, heat capacity, expansivity, and compress-ibility for tremolite. This analysis was performed with the assumption that all phases werepure and had unit activity. This agrees with the value of -12300.47 + 14.81 kJ/moldetermined for natural stoichiometric tremolite by Welch and Pawley (in preparation).Assuming that Ca and Mg mix ideally on the M4 site in Mg-enriched, synthetic tremoliteand that the compositions of the pyroxenes in equilibrium with synthetic tremolite areknown, the AIll,o*,re8* will be approximately I kJ/mol less negative or approximately-12302 kJlmol for stoichiometric tremolite. The dPldZ slope of the reaction tremolite :

2 diopside * talc is 8.8 barlK. Extrapolation of this univariant boundary to low temper-atures (200 "C) shows that tremolite is stable to at least 20 kbar and is not limited at lowtemperatures by this reaction at virtually any depth in the Earth's crust. The calculateddecomposition temperature of tremolite at I bar is 448 'C, which is about 350 oC lowerthan the observed dehydration temperature of tremolite. It is suggested here that thedissolution of silica, rather than the loss of hydroxyls, may control the decomposition oftremolite in hydrothermal environments.

fNrnooucrroN

Tremolite is an important calcic amphibole whosepressure-temperature (P- 7n) stability and thermodynamicparameters must be well known for it to be used quan-titatively in petrologic applications (e.g., Valley et al.,1983; Ghent, 1988). Our present knowledge of tremoliteis based heavily on the pioneering work of Boyd (1959),who investigated the upper-thermal stability of synthetictremolite according to the reaction

CarMg,Si.O,r(OH), : l.5MgrSi,Ou + 2CaMgSi,Outrcmolite enstatite diopside

- sio, + Hro (l) + MgrSioo'o(oH)r. (2)p-q!na. fluid talc

over the pressure range of 0.4-2.0 kbar. Surprisingly little The slope of Reaction 2 is approximately 23.3 bars/Kadditional experimental work on Reaction I has been according to Gilbert and Troll (1974, 1989 personal com-

0003-004x/9 1/0304-0458$02.00 458

reported since this study. Gilbert and Troll (1974) inves-tigated Reaction I at l0 kbar and above and found thatthe univariant boundary has a positive dP/d7: slope upto 915 "C and 15.5 kbar [sic], corresponding to the a- tol-quartz transition. Above this pressure, Reaction I in-volves a-quarlz and has a negative slope. Gilbert andTroll (1974) found the maximum pressure of tremolitestability to be approximately 26 kbar at 835 qC where itbreaks down according to the reaction

CarMgrSirO'lOH), : 2CaMgSirOutremolite diopside

JENKINS ET AL.: STABILITY OF SYNTHETIC TREMOLITE 459

30

28

a1

6

x

9 2 06q

Id rs

TemperaM ('C)

Fig. l. Experimental data and calculated univariant curvesfor Reaction I (tr: 1.5 en + 2 di + P-qtz + H,O), Reaction 6(tr + fo : 2.5 en + 2 d1 + HrO), and the o-B quartz transition.Symbols for reaction l: boxes : this study; triangles : Gilbertand Troll (1974); light arrows : Boyd (1959); dark arrows: Yinand Greenwood (1983). Symbols for Reaction 6: ovals : Jenkins(1983). Symbols for a-B qtz reaction: circles : Yoder (1950).Open symbols indicate growth of the low-temperature assem-blage, filled symbols indicate growth of the high-temperatureassemblage, stippled boxes indicate no reaction, and the arrowsindicate the maximum width of the reversal bracket. Abbrevi-ations: cpx : clinopyroxene; di : diopside; en : enstatite; fo :forsterite; opx: ofthopyroxene; qtz: qnaftz; trem: tremolite.

munication). Yin and Greenwood (1983) and Yin (1988,personal communication) investigated Reaction I in therange of0.l-1.4 kbar and found the position ofthe uni-variant boundary to be in fairly close agreement with thatof Boyd (1959). The experimental results for Reactions Iand 2 obtained by these investigators are shown in Fig-ures I and 2, respectively.

There are several aspects of the above experimentalstudies that require further attention. First, most ther-modynamic data for tremolite are based heavily on theexperimental data for Reaction I obtained over the lim-ited pressure range of 0. l-2.0 kbar. Obtaining tight ex-perimental reversals in the pressure range of 2-8 kbarwould help immensely in defining the thermodynamicparameters for tremolite by expanding the pressure rangeof experimental data without exceeding the P-Z rangewhere quartz becomes completely soluble in the ambientaqueous fluid (i.e., beyond the critical end-point pressureof 9.7 kbar at 1080'C in the system HrO-SiOr, Kennedyet al., 1962). Experiments performed above these P-Iconditions may suffer partial or complete loss of qvarlzvia dissolution and a significantly lowered activity of HrOin the ambient fluid. Secondly, the dP/dT slope andplacement of Reaction 2 is controversial. Gilbert and Troll(1974) place the univariant curve approximately 3 kbarlower than is reported here. The study by C-ao et al. (1986),who investigated this reaction indirectly in the systemHrO-CaO-MgO-AlrOr-SiO2 and in the presence of Al-bearing phases, would place this curve approximately 16kbar lower and with a steeper d,P/d,T slope (45 bars/K)

Temperature (oC)

Fig.2. Experimental data and calculated univariant curvesfor Reactions 2 (2 dr + ta : tr), 3 (tr : 1.5 en + 2 di + q +HrO),4 (ta: 1.5 en + q + HrO), and 6 (tr + fo :2.5 en + 2di + HrO). Also shown is the calculated boundary for the quartz: coesite reaction (q : coe). Symbols for Reaction 2: boxes:this study (open : tr growh, hachured : no reaction, filled :

di + ta); dark stippled triangles : Gilbert and Troll (1974)(pointing up : tr growth, pointing down : di + ta growth).Symbols for Reaction 3: light stippled triangles : Gilbert andTroll (1974) (pointing right : tr growth, pointing left : pyroxene

Erowth). Symbols for Reaction 4; circles : this study; diamonds: Chernos}ry et d. (1985) (open : ta growth, filled : en + qgrowth). Symbols for Reaction 6: ovals : Jenkins (1983) (filled: tr + fo growth, shaded : en + di growth). Abbreviations: coe: coesite; q: qlrartz (a-qtartz, unless otherwise shown); ta :

talc; tr : tremolite; others as in Figure l.

than is reported here. The implication of this study is

that the presence of other elements, such as Al, rnay have

an extreme effect on the lower-thermal or upper-pressure

stability limits of tremolitic amphibole and that the po-

sition of Reaction 2 in the Al-free system should be well

documented to correctly determine the effect of such el-

ements.The purpose of this paper is to report new experimental

data for Reactions I and 2, to review all extant experi-mental data for these reactions in order to provide a com-prehensive view ofthe upper-thermal and upper-pressurestability limits of tremolite, and to derive a value for the

en

\di\ q\ Hzo

460 JENKINS ET AL.: STABILITY OF SYNTHETIC TREMOLITE

TABLE 1. Phases used for experiments on Reactions 1, 2, and 4 in the text

Starting mixtures

Synthesis conditions R n 1R n 2Phase

(code no.) ComDosition (h)T P

("C) (kbar) FormTREM

1 3 1 7 T R 1R n 4TEO

Orthopyroxene(oPX 6-1)

EnstatiteClinopyroxene

(cPX 4-1)DiopsideDiopsideTalcTalcQuartzQuartzTremolite

I rREM 1-21)Tremolite

TremoliteIIREM 1€)

(MgosCaool)MgSirO6

MgSiO"(C&e5Mg105)MgSi106

CaMgSi.OuCaMgSi,O6MgssioO,o(OH),MgSioo,o(OH),sio,sio,CarMg5SioOrr(OH),

Ca,Mg5Sirorr(OHL

Ca,Mg5Si602(0H),

X Oo oX OoxooO Xo o

5 4 X X

4 0 09 5 X X

930 6.3

1000 15.0925 5.9

1 2501 250700750790

740806800730750750

1 atm18.017.512.02.O

2.02.O

13.022.O15.018.0

oxides

oxidesoxides

glassglassoxidesoxidesoxidenaturaloxidescrystalsgelcrystalsoxidescrystals

o

Xo

o o x o o

o o o x o

o o

o oo o

483

261 61 6

18821424724461

ooooXoX

ooooXoX

oXoXooo

/Vote.' Abbreviations: Rn : reaction; O = phase absent, X : phase present in mixture. Cotumn headings TREM 13,17; TR 1,2; and TEQ refer to theprefixes tor the experiment numbers in Tables 2-4.

enthalpy of formation of tremolite that is consistent withthese data.

Expnnrvrnr.ir.ll, METHODSApparatus

Experiments performed below 8 kbar were conductedat SUNY-Binghamton in internally heated gas vessels us-ing Ar as the pressure medium. Pressures were monitoredthroughout each experiment with both a bourdon-tubegauge and a factory-calibrated manganin cell. The citeduncertainties in pressure measurement include both theaccuracy (+50 bars) and any fluctuation in pressure dur-ing the experiment. Temperatures were measured by twoInconel-sheathed, chromel-alumel thermocouples thatwere calibrated against the freezing point of Sn (23 I .9 "C)and NaCl (800.5 .C). The tips of the thermocouples werepositioned at either end of the capsules and the entiresample and thermocouple arrangement packed with ce-ramic wool in a cylindrical copper cup to minimize ther-mal gradients. The cited temperature uncertainties in-clude both the accuracy of the thermocouple couples (+2"C) as well as any thermal gradient across the sample.

Experiments above 8 kbar were performed in piston-cylinder presses using 3Z-inch (1.905 cm) diameter NaClpressure media at the University of Chicago. Consider-able effort has been devoted toward calibrating the sam-ple pressure in this pressure medium. Detailed discus-sions of the calibration results can be found, for example,in Holland (1980), Jenkins (1981), and Jenkins et al.(1985). In briefl the procedure followed for generatingpressures involves pressurizing the NaCl assemblage atroom temperature to several kilobars below the desiredpressure and then using the well-calibrated thermal ex-pansion of the pressure medium to obtain the final pres-sure upon heating. This procedure does not strictly con-

form to either the hot or cold piston-out criteria describedby Johannes et al. (1971) but has been shown to giveresults on the albite : jadeite + quatlz reaction, as wellas several other reactions that require virtually no addi-tional friction correction. Pressure uncertainties, incor-porating accuracy as well as precision, vary from approx-imately 200-400 bars depending on the pressure rangeand diameter of the piston-cylinder assemblage used(Jenkins et al., 1985). For the pressure range ofthis study(20-30 kbar), uncertainties are estimated to be +200 bars.Temperatures were measured with chromel-alumel ther-mocouples, with the tip situated on top of the radiallymounted sample capsule, and are believed to be accurateto +5 oC.

Starting materials and procedures

The phases and starting mixtures used for investigatingReactions I and 2 are listed in Table l. All of the syn-thetic phases were made hydrothermally in Au or Pt cap-sules except for diopside, which was made at I atm byannealing glass of the composition CaMgSirOu at approx-imately 1250 "C. All of the tremolite samples were madein a two-step procedure, involving one intermediategrinding and retreatment. As discussed by Jenkins (1987),it is believed that all of these synthetic tremolite sampleshave approximately l0 molo/o Mg substituted for Ca inthe M4 site and that the compositions indicated in TableI are for the starting mixtures, not the actual phase com-posrtrons.

Starting mixtures for Reaction I and for the TR-l se-ries of experiments for Reaction 2 consisted of reactantsand products mixed in stoichiometric proportions. Thestarting mixture for the TR-2 series of experiments con-sisted of a 3:l ratio of talc * diopside to tremolite inorder to make the intensities of the diopside 220 and,221

JENKINS ET AL.: STABILITY OF SYNTHETIC TREMOLITE 461

Tlale 2. Experimental results for Reaction 1 in the text

Experi- Tem-ment no. Pressure Derature TimeOREM-) (kbar) (rC) (h)

Tmle 3. Experimental results for Reaction 2 in the text

Experi-ment no.

crR-)1-13 24.0 650 31-15 2s.0 650 31-16 27.O 650 31-5 26.0 700 11-12 26.5 700 31-7 27.0 700 31-14 27.5 700 31-6 28.0 700 12-22 25.0 725 22-24 26.0 725 32-26 26.0 725 32-28 26.5 725 32-25 27.O 725 31-10 27.O 740 31-11 28.0 740 22-21 26.0 750 42-19 27.0 750 12-20 28.0 750 11-9 27.O 760 2

Results'

Tem-Pres- pera-sure ture Time(kbar) (qC) (d)

17-1 1.50(s)13-16 1.58(5)17-6 1.52(5)17-9 1.53(5)17-4 1.50(5)13-1 3.2s(8)13-3 3.07(s)13-5 3.02(6)134 2.87(5)13-2 3.00(5)13-6 4.92(6)13-8 5.02(5)13-9 4.97(5)13-10 4.98(5)13-7 5.05(10)17-2 7.08(13)1&15 7.05(15)17-3 7.19(17)13-13 6.85(18)13-12 7.4(6)

830(3) 215840(3) 217851(3) 331860(3) 81868(3) 112852(4) 96874{3) s5880(3) 31688q2) $2901(2) 136891(2) 188905(3) 69914(3) 145919(s) 144e30(5) 53828(3) s2916(3) 92929(4) s2933(4) 769s0(4) 69

tr growth (m)tr growth (m)no reactionpyroxene growth (s)pyroxene growth (vs)tr growth (vs)tr growth (s)tr growth (m)pyroxene growth (m)pyroxene growth (vs)tr growth (vs)tr growth (s)tr growth (s)no reactionpyroxene growth (vs)tr growth (vs)tr growth (vs)pyroxene growth (m)pyroxene growth (vs)pyroxene groMh (vs)

tr growth (m)no reaction (XRD only).'ta + di growth (m, XRD only)-'tr growth (m, XRD only)"ta + di growth (s)ta + di growth (m, XRD only)"ta + di growth (s, XRD only)-'ta + di growth (s)tr growth (w)ta + di growth (w)ta + di growth (m)ta + di growth (vs)ta + di growth (vs)no reactionta + di growth (s)tr growth (s)ta + di growth (m)ta + di growth (s, XRD only)'-tr growth (s), minor enstatite

nucleatedNotej Results arranged in order of increasing pressure. Uncertainty in

last digit shown in parentheses. Abbreviation: tr : tremolite.'Extent of reaction indicated in parentheses by the symbols m : mod-

erate, s : strong, and vs : very strong, mrresponding to a change of 20-50%, 50-80'/", and greater than 80%, respectively, in the relative peakheights of the X-ray diffractometer patterns.

reflections about the same as the tremolite 240 and l5lreflections on an X-ray diffractometer pattern. This wasdone in an attempt to enhance the reaction signal de-duced from the X-ray pattern.

Each experimental sample was prepared by sealing aportion of the starting mixture in a Pt capsule with 15-30 wto/o HrO. At the conclusion of the experiment, thecapsule was checked for leakage by examining the seamsfor any signs of rupture and by checking for any weightloss.

Analytical methods

All experimental products were analyzed with a No-relco X-ray diffractometer using Ni-filtered Cu radiation.The reaction direction for Reaction I could be readilydetermined from the relative peak heights of the phaseson the X-ray diftactometer pattern. In particular, the 310,I 5 I , and 240 reflections of tremolite , 220 and 221 reflec-tions of diopside, and the 6 I 0 reflection of enstatite werefound to be sensitive indicators ofthe extent ofreaction.A minimum of 20o/o change in the relative peak heightswas considered necessary to indicate a significant amountofreaction. Reaction 2 could not be analyzed so readilyin this manner. As a consequence of the much lower tem-peratures and smaller energetics (i.e., AS and A11), theextent of reaction for Reaction 2 was too small to discernvia X-ray criteria within a few kilobars of the univariantboundary. Greater sensitivity was achieved by examiningthe infrared (IR) spectra of the experimental products andmonitoring the variation in the peak-height ratio of thetalc 665 cm ' to tremolite 755 cm-l vibrations. A detailed

Nofe.' Results are arranged in order of increasing temperature. Uncer-tainty in pressure and temperature are 0.2 kbar and 5'C, respectively.Abbreviations: di : diopside; ta: talc; tr: tremolite.

' Extent ot reaction indicated in parentheses by the symbols w : weak,m : moderate, s : strong, and vs : very strong, corresponding to achange of 10J0%, 30-50%, 5H0%, and >80%, respectively, in theband intensities of the infrared (lR) spectrum. Note that as little as 10%relative change in band heights is considered significant owing to thegreater sensitivity of lR spectroscopy.

" Results based only on X-ray difftaction data, no lR spectrum obtained.Extent of reaction estimate as in Table 4.

description of this analytical method and a comparisonof the sensitivity of the IR vs. X-ray diffractometer meth-od is given in Jenkins and Clare (1990).

ExpBnrprnNTAL RESLTLTS

The experimental results for Reaction I are listed inTable 2 and are shown by the solid and open squares inFigure l. For comparison, the lower-pressure data of Boyd(1959) and of Yin and Greenwood (1983) are shown bylight and dark double-headed arrows, respectively, whilethe higher-pressure data of Gilbert and Troll (1974) areshown by triangles. There is very good agreement be-tween all of the experimental reversals even though theywere obtained by four different studies in four differentlaboratories. The univariant curves drawn on Figure Ihave been calculated from thermodynamic data derivedin this study as discussed below.

Experimental results for Reaction 2 are listed in Table3 and are shown by the solid and open squares in Figure2. The experimental results for Reaction 2 from Gilbertand Troll (1974) arc shown by the triangles pointing upand down. Notice that Gilbert and Troll (1974) foundtalc and diopside gowth to occur approximately 3 kbarlower than was observed in this study. Several of theexperimental samples from the study of Gilbert and Troll(197 4) were kindly made available to the first author forexamination. Analysis of one of these lower-pressure talc

462 JENKINS ET AL.: STABILITY OF SYNTHETIC TREMOLITE

TABLE 4. Experimental results on Reaction 4 in the text

Experi- Tempera-ment no. Pressure ture Time(rEO-) (kbar) fC) (h) Resutts.

ta growth (s)ta growth (vs)ta growth (s)ta growth (vs)en+qg row th (m)en+qg row th (vs )

A/ote.' Results arranged in order of increasing temperature. Uncertaintyin pressure and temperature are 0.2 kbar and 5.C, respectively. Abbr+viations: en : enstatite, q : @4uartz, ta : talc.- Extent of reaction indicated in parentheses based on a qualitativeassessment of the changes in the relative peak heights of the X-ray dif-fraction patterns; m : moderate, s : strong, and vs: very strong.

+ diopside growth experiments (750'C, 25 kbar) by IRspectroscopy as well as X-ray diffractometry confirmedthe growth of talc and diopside and indicated that a gen-uine discrepancy, i.e., one that is not an artifact of theanalltical technique, exists between this study and thatofGilbert and Troll (1974). The origin ofthis discrepancyis not obvious. It probably stems from the different pis-ton-cylinder pressure media used by the two studies:%-inch diameter NaCl assemblage used in this study vs.aVz-inch diameter talc + BN + pyrophyllite assemblageused by Gilbert and Troll (1974). The latrer assemblage,however, normally tends to over- rather than underesti-mate the true sample pressure (Johannes et al., 1971) andshould lead to higher observed pressures. The presenceof "positive anvil effects" (Johannes et al., l97l) mayexist for an assemblage that involves pyrophyllite partsdirectly surrounding the sample yielding sample pres-sures that are apparently higher than the nominal (gauge)pressure. Other factors such as experiment duration andsample preparation appear to be comparable. Until thesource ofthis discrepancy is resolved, we prefer the datathat were obtained in this study with the NaCl pressuremedia, which has been studied extensively in terms of itspressure calibration (e.g., Johannes et al., l97l; Holland,1980).

Experimental results for the reaction

CarMg,SirOr,(OHL : l.5MgrSirOu * 2CaMgSirO.trcmolit€ enstatile diopside

F sio, + H2o (3)d{uartz ftuid

which was studied by Gilbert and Troll (1974) are shownin Figure 2 by the triangles pointing left and right. Thefilled and open circles in Figure 2 refer to the reaction

Mg,Sioo,o(oHr,: ,.ry"?,|;,o. * :rrg

. |;?

(4)

which was studied here. The phases used for studyingReaction 4 are listed in Table I and the experimentalresults are listed in Table 4.

Reaction 3 was also investigated in this study (byT.J.B.H.) but the results were inconclusive because quartzcould not be identified among the products. These ex-periments were performed with starting mixtures con-sisting of equal proportions of tremolite and the anhy-drous break-down products with excess HrO (2G40 wto/o).It is surmised that quartz was dissolved into the vaporphase because ofthe relatively high ratio of HrO to qtartzand because of the high pressures of these experiments(above 15 kbar). The experiments performed by Gilbertand Troll (1974) involved starting mixtures which wereeither predominantly tremolite with a trace of the break-down products or predominantly the breakdown prod-ucts with a trace of tremolite. In this approach there issufrcient quartz to ensure its presence during the $owthof tremolite but probably not enough to ensure its pres-ence during the breakdown of tremolite. Therefore, thetremolite growth experiments of Gilbert and Troll (1974)at 10, 15, and24 kbar are considered more reliable thanthe breakdown experiments. The calculated curve for Re-action 3 is in excellent agreement with these data below24 kbar.

Reaction 4 was investigated primarily to provide ad-ditional experimental control on the location of the in-variant point arising from the intersection of ReactionsI and 2. The data define a fairly tight bracket for thelocation ofthis univariant reaction between 800 and 820'C at 25 kbar.

THnnrvronylm,Mrc ANATYSTS

A thermodynamic analysis of the experimental datadiscussed above has been performed with the twofoldobjective of(l) discerning whether or not all ofthe extantdata for a given univariant reaction are consistent witheach other based on existing entropy, volume, heatcapacity, and frro data and (2) using Reactions l-3 torefine a preferred value for the enthalpy of formation(AFIPT b".re8J of tremolite.

The fundamental thermodynamic expression whichseryes as the basis for our analysis is given in Equation5 below:

AGr,r: AHopo,ro - 7A,S9o,&

* [ ' ,rctdr - r I"^# *

+ Plazittfi + a(aV)(T - 7",) - A@nP/21

+ RIln K, + RIln /fi,ro (5)

where AGr. is the Gibbs free energy of the reaction at Pand T', M%^, AS9o..o, and AC$ are the change in theenthalpy, entropy, and heat capacily, respectively, ofthereaction at the reference pressure (%) and temperature(fr); aZi:llii is the volume change of the solids for thereaction; a and B are the thermal expansivity and isobariccompressibility, respectively, of the solid phases; /is the

367

1 11 21 3

28.025.025.O25.025.025.0

770 22770 72790 22800 5.0820 5.0830 6.5

JENKINS ET AL.: STABILITY OF SYNTHETIC TREMOLITE

TABLE 5. Thermochemical values at 298 K and 1 bar used in this study

463

G

At+(kJ/mol) "(LH)

S(kJ/mol) (J/mol K)

V a(J/ba0

bx10 -s

a V B Vx10 5 x10 -3

TremoliteEnstatiteForsteriteDiopsideTalca-QuartzB-QuartzCoesiteH,O (steam)

-12302.90-3089.38-2171.87-3200.15-5894.90-910.80-909.07-908.17-241.81

7.0s 550.002.08 132.501.62 94.101.90 142.703.70 260.800.74 41.500.74 43.54o.74 39.000.03 188.80

2.6528-0.2990

0.1 0690.00413.7416

-0.3350-0.3350-0.4387

0.8656

-12362.O-596.9-542.9

-2745.9-8805.2-636.2-636.2

0.0487.5

-7.3885-3.1853- 1.9064-2.0201-2.1532-0.7740-o.7740-1.0725-o.2512

84.5 36.0018.0 4.6016.0 3.2022.0 5.5037.0 26.008.0 5.920.0 2.602.2 2.00

27.270 1.21446.262 0.35624.366 0.23496.619 0.3145

13.625 0.53432.269 0.09792.367 0.09792.064 0.1087

0.0401

/vofe.' The heat capacity coefticients apply to the experiment (kJ/K): C" : a + bT + "7-z

a 6ltfT; aV in kJ/kbar K; py in kJ/kbar'z.

fugacity of HrO at the P and Z of interest; and K. is theequilibrium constant for the reaction. The standard stateis that of unit activity for the solids at the P and Z ofinterest and of unit fugacity for HrO at I bar and the fof interest. At equilibrium LG.r is zero by definition. Itis a basic simpliffing assumption that all of the thermo-dynamic values except for AHi'"o,ro are known and haveno uncertainty (or at least have much less uncertaintythan enthalpy data). The major advantage of this as-sumption is that one can determine the uncertainties of,and correlations between, any derived values ofAflj"o,rofor the phases involved. The reader is referred to thediscussions of Powell and Holland (1985) and Hollandand Powell (1990) for further justification for this as-sumptron.

Internal consistency among a set of experimental datacan be shown in the following manner. Knowing valuesfor S, C", V, f^ro, and K,, one can solve Equation 5 ex-plicitly for values of Aflgo,ro by assuming AG.., is zero atthe extreme P and T range of each pair of experimentsthat bracket the univariant boundary. Each experimentbracketing the univariant boundary yields a correspond-ing maximum and minimum value for AHopo,ro, i.e., a setofbracketing enthalpy values. Internal consistency for aset of experimental data is demonstrated if at least onevalue of AH%,ro lies between all of the maximum andminimum values obtained from the experimental brack-ets.

The enthalpy of formation for tremolite was initiallyderived by the least-squares regression technique ofPow-ell and Holland (1985) and Holland and Powell (1990)using the new experimental data presented here and theentire mineral data base (123 minerals) of Holland andPowell (1990). It soon became apparent that only theenthalpies of tremolite and talc were significanfly changed;the enthalpies of all other phases were changed onlyslightly (generally less than 0.05 kJlmol). Rather than re-vise the entire data base of Holland and Powell (1990)with new enthalpy values that are well within the existinglo range of uncertainty, we have performed a least-squaresregression only for the enthalpies of formation of trem-olite and talc and have fixed the enthalpies of all other

phases to those values given in Holland and Powell (1990).Further details of the least-squares refinement procedure

are given below.Values or expressions for S, Cr, V, aY, and 0 Z for all

of the phases were taken from Holland and Powell (1990)and are given in Table 5. For pressures above 0.3 kbar,the frro data were calculated from the equation of Hol-land and Powell (1990), which represents the variation ofRZln /as function of P and ?"over the range of 0.1-40kbar and 300-1200 "C. This equation is based on the /'rodata ofBurnham et al. (1969) below 10 kbar and that ofDelany and Helgeson (1978) and Halbach and Chatterjee(1982) above l0 kbar. The equation is formulated on thepremise that the Gibbs free energy of formation of HrO(: RZln /) varies as a relatively simple monotonic func-tion ofpressure and temperature, especially above l0 kbar(Delany and Helgeson, 1978). This equation is well suitedfor the purposes of thermochemical data extraction be-cause it is designed to cover the P-T range over whichmost experimental phase equilibria involving hydrousphases are obtained and covers certain pressrue rangesthat other equations ofstate do not, e.g., Equation 15 ofDelany and Helgeson (1978) is best above l0 kbar, theequation of Haar et al. (1984, Appendix A) does not goabove I 0 kbar, and Equation I 4 of Saxena and Fei ( I 987)is not recommended below 2 kbar. For pressures below0.3 kbar, the equation of Holland and Powell (1990) wasfound to be insufficiently accurate (especially in the vi-cinity of 0.2 kbar) and a Berthelot equation of state invirial form was used instead:

/ n \R7"ln /: RIln P +

lt + V)r

where parameter A : 2.564 and B : -5.0966 x tOu(units: J, bar, K). For the range of l-300 bar and 300-1200'C this equation fits the available data for HrO (seereferences in Haar et al., 1984) with an avera5e absolutedeviation of ll0 J, except in the immediate vicinity ofthe critical point.

The value of IL will be treated in two ways as discussedbelow.

464 JENKINS ET AL.: STABILITY OF SYNTHETIC TREMOLITE

J'; 23'l

R 236a)

: 2isil

234

233

600 700 800 900

Temperature oC

Fig. 3. (A) Intemal consistency analysis of the data from thisstudy for Reaction 1 (per two moles of tremolite), showingAIl?*,rrr^ of reaction derived from the bracketing experimentsfor tremolite gowth (open symbols) and tremolite breakdown(filled symbols) as a function of temperature. Thin lines: consis-tent region or overall enthalpy bracket used in the regression asdefined by Holland and Powell (1990). Stippled line: least squaressolution for the enthalpy of reaction. (B) Internal consistencyanalysis ofthe data from Boyd (1959) and from yin and Green-wood (1983). Shaded area: consistent region or cumulativebracket from A. Bold line: least squares solution for the enthalpyof reaction, same as in A.

Assumption of pure phases

Although there is solid solution occurring in tremolite,diopside, and enstatite and probably dissolution ofat leastquartz into the ambient HrO, our initial thermodynamictreatment will be made under the assumption that eachphase is pure and that K. is unity. This assumption stemsfrom the lack of a well verified activity-composition re-lationship for the solution of Mg into tremolite (Jenkins,1987) and from the largely unknown amount of dissolu-tion of quartz into the ambient fluid along the univariantcurves of Reactions I and 3. It is also true, to a firstapproximation, that the reduction in the activities of the

components on both sides of the reaction will be similarin magnitude and tend to keep the value of K, near l.

Figure 34, is a plot of the derived values of AF1?b".,2e8Kof reaction as a function of temperature for Reaction I(per two moles of tremolite) for the four experimentalreversals reported in this study. The solid squares rep-resent the bracketing experiments for the breakdown oftremolite while the open squares are those for the growthof tremolite. There is a narrow range of feasible valuesbetween 234.40 and 236.75 U which can satisfu (passbetween) all of the bracketing experiments if one takesinto consideration the uncertainties in pressure and tem-perature associated with each experiment.

In order to derive an enthalpy of formation for trem-olite that is internally consistent with a large number ofother phases, it is necessary to relax the extremely tightconstraints placed on the feasible range ofenthalpy val-ues by the experimental data as exemplified by the ex-periments shown in Figure 3A. Powell and Holland (1985,p. 334) discuss the reason and method for defining aminimum width for the feasible or consistent region ofAHopo,roof reaction. The method used here and in Hollandand Powell (1990) is slightly different. The experimentaluncertainty in P and Z associated with the ends ofeachexperimental bracket gives rise to a corresponding uncer-tainty in the derived enthalpy ofreaction, referred to hereas uH (see Appendix). A consistent region, or overallbracket (A), is sought which satisfies all of the data andhas a width ofat least 3(211). This is equivalent to sayingthat the narrowest a bracket can be is three times theexperimental uncertainty on its ends. The factor of 3 islarger than the factor of 2 used by Powell and Holland(1985) but still obeys the criterion established by Dem-arest and Haselton (1981) that the quantity (uII)/(O.1A): 1.5 (:d/s of Demarest and Haselton, l98l) be less than2 for a Gaussian probability curve for the overall enthal-py of reaction bracket. If this interval is less than 3(uII)then the consistent region is widened as follows. (l) Themedian of the low enthalpy bracket ends and the medianof the high enthalpy bracket ends are determined. (2)These two values are averaged and set equal to the mid-point ofthe consistent region (: C). (3) The location ofthe consistent region is then centered on this average val-ue C and has a width given by C + 1.5(uI{) and C -1.5(uII). For weighting purposes, the standard deviationof Afl is taken as 7+ the width of the consistent region,that is to say, oM: 0.75(uI{). The upper and lower hor-izontal lines in Figure 3,A, are the consistent region oroverall bracket (: A) for the experiments performed inthis study. The thicker middle line is the Af/go,.o of re-action obtained from the least-squares regression of theentire experimental data set (see below).

Figure 3B is a plot ofthe data from Boyd (1959) andfrom Yin and Greenwood (1983), where the solid sym-bols correspond to tremolite breakdown and the opensymbols to tremolite gowth. The consistent region fromFigure 3,A, is reproduced here as the shaded band ("Brack-

h 238'l4

a€ 236aq)

g 234

230

lIvi"-acr.'nwood 1983

t[""r0'rrn I I l3

Cumulative bEcket ild best fit frcmthis srudy

JENKINS ET AL.: STABILITY OF SYNTHETIC TREMOLITE 465

et from this study") to show that there is fairly goodagreement in the derived enthalpies of reaction betweenthis study and those of Boyd (1959) and of Yin andGreenwood (1983).

An internal consistency analysis of the data for Reac-tion 2 from this study is shown in Figure 4. Figure 4shows the values of AIl?rar,2e8r of reaction for the brack-eting experiments demonstrating talc + diopside $owth(open squares) and tremolite gowth (closed squares).There is no range of enthalpy values that will satisfy allof the experiments. Ifthe highest temperature experimentis rejected because of the possible complications from thenucleation ofenstatite, then a narrow consistency rangeexists between -7.65 and -7.77 kJ. The width of thisconsistent region does not quite obey the 3(211) criterionand was widened further to -7.83 to -7.55 kJ (thin hor-izontal lines on Fig. 4).

As mentioned above, a least-squares regression wasperformed according to the procedure of Holland andPowell (1985) but allowing only the enthalpies of for-mation of tremolite and talc to vary. The enthalpies ofall other phases were fixed at those values given by Hol-land and Powell (1990). The enthalpies of formation oftremolite and talc were refined using the phase equilibriadescribed here together with all reactions in the data baseof Holland and Powell (1990) that involve tremolite andtalc. The experimental phase equilibria, low and high en-thalpy ofreaction values, widened enthalpy ranges (I1: x* y), and the resultant least-squares-determined enthalpyofreaction [calc(I{)] for these equilibria are listed in Ap-pendix Table l. The derived values of A}1l,o",,rnr* fortremolite and talc can be found in the first column ofTable 5 and their associated uncertainties (lo) in the sec-ond column. Also given in Table 5 are the AF181 b*2e8K,S, V, C", Va, and VS tenns for all of the phases consid-ered in Figures I and 2. The value obtained for tremoliteis -12302.90 + 7.05 kJlmol, which is in excellent agree-ment with the value reported by Berman (1938)(-12305578 kJlmol) but considerably more positive thanthe values reported by Helgeson et al. (1978) (-12319.696kJlmol) and Robie er al. (1978) (- 12355.080 + 17.3 W/mol).

Solid solutions

It is important to consider how solid solution in trem-olite and the coexisting phases might affect the derivedAlt"o,o of the component CarMgrSi8Orr(OH), (: trem).At present there is no experimental information on thecompositions of orthopyroxene (opx) and clinopyroxene(cpx) in equilibrium with tremolitic amphibole and quartz(Reaction l) or on the composition of cpx in equilibriumwith talc and tremolite (Reaction 2) in the system HrO-CaO-MgO-SiOr. For the purposes of this analysis, there-fore, it is assumed that the compositions of opx and cpxin equilibrium with tremolitic amphibole and quartz arethe same as those of coexisting opx and cpx in the absenceof these phases and that the composition of cpx in equi-

600 ?00 800Temperature (oC)

Fig. 4. Internal consistency analysis of the data from thisstudy for Reaction 2. Open squares : di + ta growth; Filledsquares : tr growth. Lines as in Figure 3,A,.

librium with talc and tremolite is pure diopside. Both ofthese assumptions are supported by the lack of any shiftsin X-ray peak positions, appearance ofextraneous phases,or unaccounted for changes in the proportions ofphasesthat would be expected to accompany an extensive re-equilibration of the pyroxenes used in the starting mix-tures. As argued by Jenkins (1987), it is assumed that thesynthetic tremolite used in all of these reactions is notstrictly that of tremolite, but is that of an Mg-enrichedtremolite with the composition Ca,,Mgr rSirOrr(OH)r.Furthermore, the composition of synthetic tremolite isassumed to be constant over the pressure and tempera-ture range considered in this study.

The compositions of coexisting opx and cpx over thetemperature range of interest (600-900 lC) are essentiallyconstant (Lindsley et al., l98l) and are listed in Table 1.The activity expressions for the components MgrSirOuand CaMgSirOu in opx and cpx, respectively, used in thisanalysis were those of Lindsley et al. (1981), who mod-eled the nonideal mixing in opx with a one-parameterMargules expression and in cpx with a two-parameterMargules expression. A simple ideal activity model fortremolite was used where the activity of trem is given bythe expression d i€* : (XW),. For the synthetic tremoliteused here, the activity of trem is (0.9)'z : 0.81.

Using the above activity-composition relationships, thecalculated values of K, do not deviate more than ap-proximately 5olo from 1.0 at even the highest tempera-tures encountered for tremolite stability. Considering theuncertainties in phase compositions and activity-com-positions, it was deemed unwarranted to perform a least-squares regression ofthe ILll data seq however, an inter-nal consistency analysis of the experiments for ReactionsI and 2 was performed. The results of this analysis sug-gest that the bracketing values ofAfl$o,ro are shifted ap-proximately 0.61 kJ lower for Reaction I (per I mol oftremolite) and approximately 1.73 kJ lower for Reaction2. Although these shifts do not change the status of in-

o&J - d

Reaction: 2 diopside + talc = kemolit€

466

Temperoture, (oC)

Fig. 5. Calculated locations of Reactions l, 2, and,3 thatdelimit the upper-thermal and upper-pressure stability of syn-thetic tremolite in the system HrO-CaO-MgO-SiOr. Also shownis the univariant boundary for the reaction d.-quartz: g-q:uarlz(q : bq). The boundary for Reaction 2 from Cao et al. (1986) isshown for comparison. Abbreviations as in Figures I and 2.Arrow indicates the thermal stability of tremolite at I bar cal-culated according to Reaction 3.

ternal consistency within a given set of experiments, theydo affect the derived value of AI/!, u,,e* for tremolite.It is suggested here that provision for the solid solutioneffects in tremolite and pyroxene,with our crurent knowl-edge of the compositions and activity-composition rela-tions in these solid phases, results in an increase of ap-proximately I kJlmol, or a value of -12302 kJ/mol, inthe Aflf , *.rrr* of tremolite. This compares very well withthe value of -12300.47 + 14.8 kJlmol derived from theexperimental study of natural, on-composition, tremoliteby Welch and Pawley (in preparation).

Tnnvror,rrn rHASE EeurLrBRrA

The univariant boundaries for Reactions l-4 have beencalculated using the thermochemical data listed in Table5, the fr,o equations of Holland and Powell (1990) andthe Berthelot equation given above, and the computerprogram Thermocalc (Holland and Powell, 1990). Thesecnryes are shown in Figures I and 2. There is, in general,excellent agreement between the calculated univariantboundaries and the experimental brackets for essentiallyall reactions except Reaction2 (2 diopside * talc : trem-olite), where it is simply not possible to satisfu the rever-sals obtained both in this study and in studies of Gilbertand Troll (1974) with one univariant curve. As discussedin the Experimental Results section, we have favored theexperimental results obtained in this study because theywere obtained with a pressure medium (NaCD that is be-

JENKINS ET AL.: STABILITY OF SYNTHETIC TREMOLITE

of 2 0o€:o

ooc l o

lieved to be more hydrostatic than the pressure mediumused by Gilbert and Troll (1974).It might be pointed outthat the calculated curve for Reaction 3 is in excellentagreement with the 15 kbar reversal of Gilbert and Troll(197 4), which su ggests that there is better agreement con-cerning the measurement of temperature than of pressurebetween this study and that of Gilbert and Troll (1974).The univariant boundary for the a-B quaftz transition, ascalculated from the data of Holland and Powell (1990)based on the review of Mirwald and Massone (1980), isalso shown. The calculated boundary for the reaction

CarMgrSirOrr(OH), + MgrSiOotremolite fosterite

:2.5MgrSj,Oo + 2CaMgSirO. * T;?

(6)

is shown in Figures I and 2 along with the experimentaldata ofJenkins (1983) for this reaction (open and closedovals). This reaction demonstrates that the thermody-namic data derived here are consistent with reactionslimiting the stability of tremolite in quartz-free as well asquartz-bearing assemblages.

The univariant curves delimiting the stability field ofsynthetic tremolite in the system HrO-CaO-MgO-SiO,have been combined into one diagram in Figure 5. It canbe seen in Figure 5 that tremolite by itself has a wide P-Zrange of stability, having a maximum thermal stability of918 qC at 7.5 kbar and a maximum pressure stability of26.8 kbar ar 798 "C. The slope of Reaction 2, as men-tioned in the Introduction. is ofconsiderable interest be-cause the lower-thermal stability of tremolite may be dic-tated by this reaction. The dP/dT slope observed in thisstudy is approximately 8.8 barlK. This is much less thanthe 45 barlK slope observed by Cao et al. (1986) whoindicated that tremolitic amphibole has a minimum tem-perature of stability of approximately 500 t (Fig. 5).These authors recognized that the reaction boundaryshown by Gilbert et al. (1982) and thermodynamic cal-culations using the data of Robie et al. (1978) or Helgesonet al. (1978) indicated that Reaction 2 occurs at muchhigher pressures and with a shallower slope. Cao et al.(1986) conducted their experiments in an Al-bearing sys-tem and suggested that this may explain the difference inthe location of this boundary; however, there is not enoughinformation on the compositions of the experimentalproduct phases in the Cao et al. (1986) study to allow amore detailed analysis of the effect of Al. At least in thesystem HrO-CaO-MgO-SiOr, tremolite should be stableup to pressures of 2l kbar even at the lowest grades ofmetamorphism (200'C) and should not transform to atalc + diopside assemblage, by Reaction 2, at typicalcrustal metamorphic conditions.

The l-bar stability of tremolite was calculated usingthe newly refined thermodynamic data obtained in thisstudy by assuming an ambient f'ro of I bar and by as-suming that it decomposes at this pressure according to

Reaction 3. The calculated decomposition temperature is448'C. This is nearly 350 oC lower than the dehydroxyl-ation (and presumably decomposition) temperature fornatural tremolite in the presence of an HrO-free environ-ment (N) reported by Freeman (1966). Two possible ex-planations are proposed here for the large difference be-tween the calculated and observed l-bar decompositiontemperature. First, it is possible that tremolite dehydratesat very low pressures (i.e., near I bar) to a single Mg-richclinopyroxene and quartz and that this process occurs ata much higher temperature than Reaction 3. This decom-position mechanism has been proposed by Freeman andTaylor (1960, cited by Ghose, l98l) and has its counrer-part in the dehydration ofgrunerite to clinoferrosilite andsilica (Ghose and Weidner, l97l). Second, the experi-mentally observed higher decomposition temperature mayresult from a simple overstepping of the theoretical tem-perature because ofslttggish kinetics, especially when seedsofthe breakdown products are not present. Unfortunatelythe magnitude of this overstepping (350 "C) is far greaterthan one would predict. A mixture of forsterite + trem-olite, for example, will decompose (unseeded) to enstatiteand diopside with only approximately 50 'C overstep intemperature af 12-15 kbar in a hydrothermal environ-ment (Jenkins, 1980). Similar overstep temperatures havebeen observed for the breakdown of layered silicates inhydrothermal experiments performed in the range of 2-7 kbar (Ridley and Thompson, 1986). Based on the ob-servation of Jenkins (1987) that the incongruent disso-lution of tremolite is largely controlled by silica solubilityin the ambient fluid of hydrothermal experiments, it isproposed here that the greatly enhanced breakdown oftremolite with only a few tens of bars of HrO pressure isinfluenced more by the dissolution of silica than by theloss of HrO from the tremolite structure. The enhancedsolubility of quartz with increasing HrO pressures in therange of200-1000 bars has recently been studied by Rag-narsdottir and Walther (1983). A careful crystallochem-ical study of the I bar decomposition of tremolite is need-ed before one can choose between these two explanations.

Sutvrpr.c.nv

New experimental data for Reactions 1,2, and 4 werecombined with existing experimental data for these re-actions, Reaction 3, and all of the experimental phaseequilibria data pertinent to tremolite phase equilibria inorder to obtain a refined value for the enthalpy of for-mation (AFIR1 b"..2e8J of tremolite. Based on the least-squares regression procedure and data base of Hollandand Powell (1990), the derived AIl8r b",.2e8K for tremoliteis - 12302.90 + 7.05 kJ/mol for the values of entropyand volume for tremolite given in Table 5. This analysiswas performed with the assumption that all phases werepure and had unit activity. Assuming that Ca and Mgmix ideally on the M4 site in synthetic tremolite and thatthe compositions of the pyroxene coexisting with syn-thetic tremolite are known, then this value will be ap-proximately I kJlmol more positive, or approximately

467

-12302 kJ/mol for stoichiometric tremolite. This is inexcellent agreement with the Al/fl, o",,rrr" of -12300.47

+ 14.81 kJ/mol determined for on-composition naturaltremolite by Welch and Pawley (in preparation). The cal-culated univariant boundaries for Reactions l-3 indicatean upper-thermal stability for tremolite of 918 'C at 7.5kbar and an upper-pressure stability of 26.8 kbar at 798"C. The dPldZ slope of Reaction 2 that is consistent withboth the experimental and thermochemical data in thesystem HrO-CaO-MgO-SiO, is approximately 8.8 barlK(approximately constant over the temperature range of200-800 "C), much less than the 45 barlK slope predictedby Cao et al. (1986) in the system H,O-CaO-MgO-AlrOr-SiOr. In view of this, the lower-temperature stability oftremolite does not appear to be limited by Reaction 2 atpressures within the Earth's crust. The calculated decom-position temperature of tremolite at I bar is 448 "C, whichis approximately 350 "C lower than the observed dehy-dration temperature of tremolite. It is suggested that thedissolution of silica, rather than the loss of HrO, fromtremolite may be the ratelimiting step for tremolite de-composition in hydrothermal environments.

AcxNowr,nncMENTS

Financial support for this study was provided by National ScienceFoundation grants EAR-81071 10 to Robert C. Newton at the Universityof Chicago and EAR-E803437 to D.M.J. Financial support was also pro-vided by an NSF Summer Research Fellowship ro A.K.C. while at theUniversity of Chicago. The authors are indebted to M. Charles Gilbe(and Hui-An Yin for their assistance in supplying experimental samples,data, and details ofexperimental procedure that would not otherwise bereadily available. The carefirl manuscript reviews by J.V. Chernosky andR.G. Berman are greatly appreciated. Special thanks are given to AnneDarling and Dave Tuttle for assistance in manuscript preparation.

Rnrnnrxcns crrEDBerman, R.G. (1988) Internally-consistent thermodynarnic data for min-

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MaNuscnrm RrcErvED Mencs 12, 1990Mexuscnrgr AccEprED JeNuenv 14. l99l

JENKINS ET AL.: STABILITY OF SYNTHETIC TREMOLITE

AppENDrx TABLE 1. Data pertinent to the enthalpies of formation of tremolite and talc

469

Reaction and source l n Kx

(co,) P (kbar) rrc) H(low) H(high) mrss calc 2scl Summary

1. 2tr:3en + 4di+2W+ 2H2O

(Yin and Greenwood,19&t)

(Boyd, 1959)

ohis study)

2. 2di + ta: tr[Ihis study)

4. 2ta:3en + 2bq+ 2H2O

(Skippen, 1971;(Chernosky, 1976;Chernosky et al.,1985)

4. 2ta = 3en + 2q+ 2H2O

(Chernosky et al.,1985)

4. 2ta:3en + 2q+ 2H2O

[rhis study)

6. 2tr + 2to:s e n + d i + 2 H r O(Jenkins, 19&!)

0.1 655

0.25 725

0 0.3 7550 0.8 8000 1.4 8200 0.6 7950 1.0 8350 1.5 8400 2.0 8600 1.s 8400 3.0 8800 2.90 5.0 9140 7 .1 916

27.O 24.026.5 26.026.0 25.027.0 26.0

0 0.5 6560 1.0 7000 2.0 725

0 10.0 7900 13.00 13.6 7850 17.0 7950 25.0 8000 28.0 770

675 231.57 236.20

745 234.00 238.24

775 2U.75 239.01820 232.58 236.32840 230.50 233.96820 2U.95 239.85850 236.60 239.3s870 233.28 238.48880 233.94 237.28860 233.28 236.74

233.76888930 235.77929 234.97650 -8.41700 -7.99725 -7.66750 -8.02672 217.04721 219.35735 218.11

235.29238.16236.82-7.O5-7.76-7.20-7.56220.21223.19219.79

820

214.67 216.04215.51

213.50214.83216.48 218.88213.54

218.64 221.54216.91 219.61216.U 219.45217.59 219.91

758 2815 3

8 8 4 8 3797 3

-7 828 3852 3868 3852 3890 3888 3

-3 911 3918 325.43 0.38

-0.14 25.86 0.380.08 26.08 0.38

26.31 0.38670 2703 2

1 7 3 6 2

3 8 0 3 37 8 0 7 3

807 3808 3800 3795 4

t+ (232.94 - 235.96)

calqr0 : 235.29 (sd 0.3s)within bracketuH : 1.01, ds: -0.4

H: (235.33 - 238.03)caqt,) : 235.29 (sd 0.3s)within bracketuH: 0.90, cls: 0.4ft (234.40 - 236.7s)caqr0 : 235.29 (sd 0.35)within bracketuH: O.78, d/s : -0.3

ft (-7.83 - -7.55)caqo: -7.70 (sd0.11)within bracketuH: 0.09, d/s: -0.5

H: (217.82 * 220.49)calc(r, = 219.90 (sd 0.32)within bracketuH: 0.89, ctls: O.2t*. (214.21 - 216.16)calc(r, = 216.44 (sd 0.321too high but OKuH: 0.65, d/s: 0.5H: (216.48 - 218.88)caqf, : 216.44 (sd 0.32)uH: 0.60, dls = 2.0

H: (217.43 - 219.58)caq4:218.41 (sd0.46)within bracketuH : Q.72, d/s : 0.6

671 2

731 2

0 0

0 0

0000000000000000000

000000

800800

-2 818 3801 4782 4i l 7 4

0 0 5.0 820 8400 0 8.0 790 8100 0 10.0 770 7900 0 20.o 640 660

/Vote.'Results from the least-squares analysis of experimental data pertinent to the enthalpies of formation of tremolite and talc. Reaction numberscorrespond to those given in the text.

Abbreviations: |n 11 : gquilibrium @nstant used for the reaction under consideration; XCOJ : the mole fraction of CO, for the reaction underconsideration; P and T : the pressures (kbar) and temperatures ('C) of each particular experimental bracket unadiusted for experimental uncertainties;H(low) and fftigh) : enthalpy brackets used in the least squares regression; m,bs: misfit of the calculated to observed temperature (K) or pressure(kbar) range ot a bracket; calc : calculated pressure or temperature and its associated uncertainty (2 so) based on the least-squares rElression; H:(x - ll: expanded enthalpy bracket; calql0 : enthalpy of reaction and its associated uncertainty (so) from the least-squares r€gression; uH:enthalpy uncertainty due to pressure and temperature measurement uncertainty at the extremes of the brackets; d/s: a bracket width parameter asdefined in Holland and Powell (1985). All enthalpies are in kJ.