Mechantsm and Kinettcs of the Reaction 1 Dolomite + 2

Canadian Mineralogist Yol.29, pp. 803-821(1991)

MECHANTSMAND KINETTCSOF THE REACTION 1 DOLOMITE+ 2 OUARTZ = I DIOPSIDE+ 2CO2 INVESTIGATEDBY POWDEREXPERIMENTS

ANDREASLUTTGE AND PAUL METZ Institut filr Mineralogie, Petrologie und Geochemie, Universifit Tilbingen, Wilhelmstr. 56' D-7400 Tiibingen, Cermany

ABSTRACT m€langede CO2 et de H2O, varie entre 80 et presque 10090.Les exp6riencesont dure jusqu'i 365 jours (8'760 heures). Un examen des mdlanges au microscope Experimentalinvestigation of the forward reaction I dlectroniquei balayage(MEB) demontre clairementun dolomite + 2 quartz = I diopside + 2 C02was carried m6canismede dissolution et de cristallisationpour toute out in a conventionalhydrothermal apparatus,in order valeur de X(CO), m0me dans les situations presque to determinethe mechanismand the kinetics at a total anhydres. Les donn6es sur le degr6 de conversion en pressureof 500 MPa and 680'C. The CO2 contents of fonction du tempset l'6videnceau MEB, pour unesurface the fluid phase,consisting of carbon dioxide and water, variable des r6actifs et desproduits, montrent was found to vary from 80 to nearly 100 mol9o. The spdcifique que les processusqui limitent le taux de rdaction sont experimentslasted up to 365 days (8,760 hours). SEM r6gis par I'interface, pourvu que les cristaux de examination of the reaction mixtures clearly shows a toujours recouvrent pas entibrement les grains de dissolution - crystallizationmechanism operating within diopside ne les 600 d 800premiBres heures, le taux the whole range of X(CO), even at almost "dry" dolomite. Pendant de I'interaction de la conditions.The data on degreeof conversionta,'sas time, de r6action h6t6rogdneddpend la (y inclus resultsof SEM studiesof experiments,and a variation of dissolution de la dolomite et cristallisation Compardei ces surfacearea of reactantsand products, have shown that nucl6ationet croissance)de la diopside. quartz trbsrapide dans rateJimiting processesare always interface-controlledas processus,la dissolutiondu semble Toutes ces long as the diopside crystals do not cover the dolomite toutes les conditions exp6rimentales6tudi6es. sont eUes- surfacescompletely. During the first 6@-800 hours, the "6tapes" de dissolution et de cristallisation qui plu- rate of the heterogeneousreaction is controlled by the mOmesdes processuscomplexes comprennent interplay of dolomite dissolution and diopside crysta! sieursrdactions 6l6mentaires. Les r6sultatsexp6rimentaux plus lization (including nucleation and growth). Compared montrent que I'identit6 du processusle lent change with these processes,quanz dissolution appears to be au cours de I'exp6rience,m€me of les conditionsP-T-X rapid in any case under the experimental conditions sont constantes,ou d peu prbs. Au d€but de la r6action, progrds applied. All of these dissolution and crystallization le taux de cristallisation de la diopside limite le plus ce sera la dissolution de la "steps" are themselvescomplex processes that consistof de la r6action; mrd, several elementary reactions. The experimental results dolomite qui en limite le progrds. Une fois I'armure de (-800 heures' show that the rate-limiting processchanges during the dolomite autour de la diopsidecompl6t6e d course of reaction, even if P-T-X(CO) conditions are - 3590de conversion),le transfert desespOces dissoutes constant, or nearly constant. At the beginning of the travers le liser6 devientle processusqui limite le progrbs reaction,diopside crystallization is rate-limiting,but later, de la r€action. De plus, nous avons confirmd l'influence dolomite dissolution becomesrate-determining; finally, catalytiqueessentielle de I'eau. when the dolomite-armoring diopside rim is complete (Traduit par la R6daction) (-800 hours, -3590 conversion), the transport of dissolvedspecies through the armoring rim becomesthe Mo*-clds: cin6tique,quanz, dolomite, diopside,micros- rateJimiting step.In addition, the essentialcatalytic effect copie dlectroniqued balayage,contr6le du taux de of water was verified in our experiments. r6action, contr6le de la surface, m€canisme de rdaction. Keywords;kinetics, quartz, dolomite,diopside, SEM, rate control. surfacecontrol, reaction mechanism. INTRODUCTION

SOMMAIRE During the last three decades, the P-T-X conditions of stability of numerous mineral as- 6tudi6 la rdaction I dolomite + 2 q\artz Nous avons The resulting = I diopside + 2 CO2 au moyen d'exp€riencesavec semblageshave been determined. appareilagehydrothermal conventionnel, afin de ddtermi- petrogeneticgrids allow us to quantify the equi- ner le m6canismeet la cindtique de cette r6action i 500 librium conditionsof many metamorphicreactions. MPa et 680'C. La teneur en CO2 de la phase fluide, Then "the focus of metamorphic petrology 803 804 THE CANADIAN MINERALOGIST shifted...... to a dynamic mode aimed at the dolomite (Algeria) with a Fe content of 0.7 wt9o quantification of the processesthat produced the FeO (Heinrich et al. 1986)and a single crystal of metamorphism" (Lasaga 1986), i.e., to questions syntheticquartz (KristallverarbeitendeGesellschaft, related to mechanismsand time dependence.One Neckar-Bischofsheim:Toyocom 1975),which were of the pioneering experimental studies of the usedto preparethe starting mixtures (40 mg). The mechanismand kinetics of a metamorphicmineral stoichiometry of the reaction requires 60.5 wt9o reaction was carried out by Greenwood (1963). (24.22mg CaMg(CO)2and 39.5wtVo (15.78 mg) Sincethen, severalheterogeneous mineral reactions SiO2. All cleavagepieces of dolomite (Dol) and havebeen investigated, e.g., by Kridelbaugh(1973), irregularly shapedquartz grains(Qtz) had a specific Matthews(1980, 1985), Tanner et al. (1985),Rubie grain-sizedistribution (given below, and see Fig. (1986), Rubie & Brearley (1987), Littge et al. lB) produced by ultrasonic sieving. A special, (1987), Schramke et al. (1987), Dachs & Metz improvedmethod of achievingrun conditions(e.9., (1988)and Heinrich et al. (1989). Tanner et al.1985) was not necessary,because the As pointed out in many of the papersmentioned grinding of powderscould not be observedto exert above, the dissolution of reactant minerals, along any influenceby SEM methods.The powdersused with the transport of dissolved species, are for the unseededruns H08-H50 and experiments important processes in the kinetics of H73-H82, which containeddiopside seeds, had an heterogeneousreactions among minerals. Conse- 80-100 pm grain-sizedistribution between80 and quently, much work has been devoted to under- 100pm. In runs H57-H66,20 mg of the dolomite standing mineral dissolution, e.9., b! Berner had a grain size of 5-10 g.m, and the remaining (1978),Berner & Holdren (1979),Berner & Morse 4.22 mg dolomite, and all the quartz, had a grain (1974),Berner & Schott (1982),Berner et ol. (1980), sizeof 80-100pm. In contrast,runs H67-H72 were Eugster (1982, 1986), Fein & Walther (1987), carried out with 13 mg of quartz from the 5-10 pm Novgorodov (1975), Petrovich (1976, 198la,b), size fraction plus 2.78 mg quartz and all dolomite Rimstidt & Barnes(1980), Walther & Orville (1982, from the 80-100 pm size fraction. 1983)and Blum et al. (1990).Our invesrigationsof The fluid phase (10 mg) used in the runs the mechanismand kinetics of a "simple" decar- mentioned above consistedof water and carbon bonation reaction, number (8) in the systemCaO dioxide IX(CO, = 0.901; it was produced by - MgO - SiO2- CO2- H2O(Winkler 1919,p.116), decomposition of silver oxalate (Ag2C2Oo).Low H2O contents of the very fine-grained Ag2C2Oa ldolomite+2quartz = ldiopside+2CO2 (8) have to be consideredeven after severaldays of drying at 60oC in the vacuum. contributes to the body of work directed toward All experimentswere carried out in a conven- an understandingof the kinetics of metamorphic tional hydrothermal apparatus (cold-sealpressure reactions. vessel).The experimentswith CO2 and H2O were run in sealedgold capsules.P-T conditions for EXPERIMENTAL METHoDS these experimentswere 500 MPa + 5 MPa and 680"C * 3oC (seealso Heinrich et ol. 1986).The Figure lA shows the optically clear natural equilibrium temperatureof the reactionat 500MPa

Ftc, l Starting materials.A. Photo of the syntheticquartz (Qtz) and natural dolomite (Dol) from Algeria, used to prepareall starting mixtures. B. SEM photo showing a part of the stafting mixture: a cleavagepiece of dolomite and two grains of quartz, all from the 8G-100pm grain-sizefraction. KINETICS OF THE REACTION DOI + QtZ = Di + CO2 805 and X(CO, : 0.9 is 615'C + 5'C (Gottschalk with a calibrated chromel-alumel thermocouple 1990; see also Fig. 2, curve 8). Thus, the situatedinside the autoclavesand in direct contact equilibrium temperature was oversteppedby ap- with the central part of the gold capsules.Run proximately 65oC. The temperaturewas measured durations were varied from 10 to nearly 3,000

1,000 1,000

P = 500MPa

O o

t-o f 700 y(U ao o- E 600 +to

v.z 0.4 0.6 0.8 0.9 1 Hro x(co, Cot Frc. 2. Isobaric T-X diagram (P = 500 MPa) for the systemCaO-MgO-SiO2- COI-H2O, with calculatedequilibria for reactions(1)-(13) (Gottschalk 1990)' Curve iA) showsthe equilibrium conditions for the reaction investigated,and the blaik squareindicates experimental T-X(CO, conditions.The arrow shows the direction and highestmagnitude of X(co) shift during all runs performed. 3Dol + 4Qtz + 1H2O = lTlc + 3Cal + 3CO2(1)'5Tlc+ 6Cal +,4 = Qtz : 3Tr + 6 CO2+ 2H2O(2),2Tlc + 3Cal I Tr + I Dol + I Cq2 i t uro(3), 5 Dol-+ SQtZ + I H2O = I Tr + 3Cal + 7co2(4)' I Tr + 3Cal +'2Qtz = 5Di + 3CO2t lH2O(6),lTr + 3Cal = 4Di + I Dol + I co2 i I H2o(7),I DoJ 2Qrz = lDi + 2CO2(8)'1Tr + 1l Dol = 8fo + t:Caf + 9CO2+ I H2O(9),3Tr+ 5Cal : 11Di + 2Fo + 5 CO2 + 3 H2O (lO), I Di + I Oot : 2Fo + 4 Cal + ZCO2Q\,ZCaI + 2Qtz-: 1 Wo1 2 CO2(13). Symbols:Cal calcite,Di diopside'Dol dolomite' Fo forsterite, Qtz quartz, Tlc talc, Tr tremolite, Wo wollastonite. 806 THE CANADIAN MINERALOCIST hours, 1.e.,up to 125days. Reactionprogress [= infiltration of nickel and chromium inlo the conversiono (0-10090)lwas determinedby weigh- capsulesis negligible during a run duration up to 'dry" ing the amountof CO2formed (e.9.,K?ise &Metz 182 days and is offset by the advantageof 1980)and using the stoichiometry of reaction (8). coz. The CO2 was weighedwith a Sartorius MP8 Ultra Micro Balancewith an accuracyof better than l9o. ExpEnrveNtel RESULTS The CO2 content of the fluid phase increased4 mol9o during the runs IX(COJ = 0.94]. This Mixed CO2-H2Ofluids procedureof determiningthe extent of conversion is correct, so long as reaction (8) is the only Results of experimentsinvolving mixed CO2- reaction.All solid phaseswere examined by optical, H2O fluids are given in Tables2,3, and 4, along SEM (Stereoscan250), EDX and X-ray powder with the experimentalconditions; Table I lists the diffraction. In specific cases,TEM and electron- definition of symbols used here. SEM photos of microprobe analysis (ARL) also were used. No run productsare given in Figures3A-D, 4A-F, and solid phases other than qtJarIz, dolomite and l0A. Figures 5-8 show the results of the experi diopside have been detectedby X-ray diffraction. ments designedto investigateextent of conversion By utilizing SEM studies,metastable formation of with time, and Figure 9 gives the results of talc was observed.The talc content is in any case so small that the error in the conversionmeasure- ment referred to above is not more than 0.590 TABI.E2 EXPERIMENTALDATA OFTIIE @NVERSION.TIME absolute. EXPERIMENTSCARRIED OUT AT 500MPa For comparison, experimentsalso were carried ro!tnt!(@2) t(@2) @21d. cos!. ro. 3olld out with a fluid phaseof nearly pure CO2,without r'cl lhl/tdl ffi tld Iryl trl addition of water. In this case, the pressure ao8 6ao 20lL 3a.79 0.90 0.90 o.l3 I go9 6AO 20lt 39.00 0.90 0.90 0.05 0.9 medium, which was carbon dioxide (99.995t/o u0 6ao Itf2 39.?3 0.r0 0.9! 0.93 A CO), also servedas the fluid phase,because earlier Btl 6ao 1Af2 40.30 0.90 EL2 6ao aot2 39.69 0.90 o.9l o.7t 6 results had shown that Ag2CrOoalways contains t13 6ao 5Ol2 39!34 0.90 o.9l 1.03 9 water, which cannot be expelledand which moves ala 6ao 7Lt3 39.?2 0.90 o.9l o.a2 7 415 640 7t/3 39.06 0.90 0.90 0.5J 5 the X(CO, to valuessomewhat lower than l. This Bl6 600 tot4 39.37 0.90 0.91 0.59 5 is in agreementwith resultsobtained by Tanner et El7 680 90t4 39.53 0.90 o.9l l.o3 9 (1985). srg') 540 95L 39.39 o.r0 0.91 0.79 7 al. Therefore, CO, from the pressure a!9 640 95/t 3a,a{ 0.90 0.91 l.a7 13 medium was introduced into the gold capsulesvia po 640 9614 39.a1 0.90 a small azl 640 L20t5 39.69 0.90 0.91 t.32 L2 tube-like channel. The disadvantageof v2 540 \20f5 ao.da 0.90 0.92 3.13 27 u3 640 L92tA 40.21 0.90 0.9! 1.69 15 u{ 640 L92lA 39.S6 0.90 0.91 1.46 13 t29 6ao 200fa 37.97 0.90 o. l.a2 13 TABLD ?1 I. DEFINITIONOF SYMBOLSUSED u6 6A0 2001a 39.04 0.90 o.9t suriace ag of miryal v7 640 239tt0 39.90 0.90 0.91 1.20 10 va 640 239/LO 39.64 0.90 0.91 t.?6 !5 04 iltlvity ol sp6i@ i w9 6go 2t0tl0 3?.39 0.90 o.92 2.76 26 @(tr+) divity of H+ 830 6ao 240lLO t9.28 o.9o 0.92 2.3t 2l t3l 540 2AalL2 t0.10 0.90 o.92 2.31 20 @!@intiot of epdi€ i 540 2AAtt2 39.73 0.90 0.92 2.a9 25 i spei6 i ia eltriio! or h Eitrsal. @peciiwly t33 5ao 3{5/t{ 39.S1 0.90 0.92 3.18 2A BI 6ao 3d6./1a 39.3? o.90 0.92 3.3a 30 A; @tioa equilibriqB @utet 135 5AO 358/15 39.30 0.90 o.92 3.13 2a t35 6AO 358/15 39.32 0.90 0.92 k+ late c@tet of diehil@ oiBinsal 2.81 25 B7 6ao 100tL7 39.07 9.eo 0.92 3,27 29 @tr@tetion prcdrct t3a 6a0 400tt7 39.62 0.90 0.92 2,96 26 B9 540 450/19 39.23 0.90 o.92 3.27 29 rcdtrced @r@!tniio! prcduct of mitr@l O at eqdlibriu t{0 6ao {50/t9 39.67 o.90 0.92 3.3? 29 ,ff,* Ehe ha to be o@tspped to iodtr@ lld€tion ol diopeide ltl 6ao 3l5f2t !9.83 o.92 0.94 3.lt 27 812 680 5t5l2t ao.t{ 0.90 0.92 3.5a 31 tu @tet ( dp€riestally detmiled) sa3 600 500t25 39.89 0.90 0.92 3.46 30 n @utut (qperieeltally det@ired) tal 680 600t23 39.t5 0.90 o:' 'jo ': rtg' 640 t0oo/42 38.49 0.90 P pruw(MPa) atc' 680 looo/t2 39.aa 0.90 a atlvity qrotlot Ea? 6AO 1950/81 39.03 0.90 0.93 5.lA 46 tta 680 1950/81 39.26 o.to 0.93 t.77 42 T tupentre (oC) !cg' 6ao 2r501L23 3a.92 0,90 a tia€ (hom) 640 2930/123 39.06 0.90 q.93 5.aa

volmo of the eloti,or (flrid phe) ia @ntet vtth eiasal Atle*pr'lnFh sbrEddritb 10 nSof sOO, - HrO lbidilase tx(@r) s 0r0l x(i) oole fretiot olspci6 i sd xrih 40 rry d I fu! d dls% by rdfo d-rdcn|'o oO lgsg fo ss% Tb@thgfui o conrenlor (7o) ddolsnlrB ardqtstzDrdalc8ys s[ to-lclp 8'eMo. . @ld c'Tsle sss l€aty rl tb d d 6s tra tBM stldy oly. .) I q calcfre vio Btoichiometlic c@ficielt of speie "d" ia miroal O (p€sm o nircd ls lowwd vsy rrd.ly !o 0.1 l,lPa b€fue qls{fiing tu Fnli€rdE!, wllh tu mt tu 6t aqale b€of& @d b flrdd da$ $q.es frm tb cqsle). KINETICS OF THE REACTION DoI + QtZ = Di + CO2 807

TABLE 3. EI(PERIMEMTAI DATA PERTAININC TO DECBEE TABLE 5. H(PEzuMENTAL DATA OF TTIE EXPERIMENTS CARRIED oF CONvmsIoN As A zuNCTIoN oF TIME AT 500 MPa, OUT WITTI A FLUID PHASE OF PURE CO, }IITII A VABIATION IN GRAIN SIZE ! D9 !{co2) x(co2) co2-Prd. No. t@al t'ct tbl / tdl 6olld std f,lul tD9l tsl TABLE3a. vr/3 500 6a0 \ooa/42 39,20 1.0 1.0 ? 700 roos/42 39.55 1.0 1.0 ? a9 r(cq) l(co2) co2-Prd. cotrv€r. w/9 300 fill 300 750 LOOA/42 37.?6 1.0 t.0 t'ct tbl/(dl 6oud !161 tosl IEI ta4 500 700 436a/\a2 39.55 1.0 t.0 7 BA5 500 6A0 8760/365 39.55 1.0 ? t5? 680 5012 39.04 0.90 0.91 0.99 t5a 6ao 5012 39.!5 0.90 0.91 o.6a The starting mixture of dolomite and quaflz had alwals an 80-100 pm gmin 859 640 aalA 39.36 0.90 0.91 fnction. The valuc of X(CO) wd nqrly 1. Extsnt of convcNion is only 960 540 aal4 39.54 0.90 0.91 1.50 mmble and not deteminable, b€ae gnvimetric mcthod.s annot bc t61 680 1201t 39.20 0.90 0.92 3.05 us€d on accoutrl of lhe open capsulc (s lexl). 862 680 a2015 39,65 0.90 0.92 u63 640 400/L7 39.02 0.90 0.93 864 580 100/!7 39.22 0.90 0.93 4.61 a65 680 a00/3a 38.83 0.90 0.93 5.22 (Fies. s66 680 ao0/3! a2.94 0.90 0.93 4.62 The SEM photos 10B-F) show some .IABLE characteristicaspects of the reaction mechanism 3b. u73 640 9514 4L.15 0.90 0.92 2.36 2\ operating under "dry" conditions. 814 640 95lt 42.56 0.90 0.91 1.64 t4 817 6S0 \2015 J8.69 0.90 0.92 2.O9 B7S 680 120/5 39.70 0.90 0.91 l.a5 16 DISCUSSIONOF EXPERIMENTAL RESULTS a79 680 \20/5 38.99 0.90 0.92 2.13 sao 6s0 12015 34,44 0.90 o.9l l.9a 11 ual 640 2101\0 39.92 0.90 0.92 3.26 2a Mixed COt-HtO fluids da2 580 430/1a 34.96 0.90 0.93 4.41 39 s83 6A0 t3o/1a 39.55 0.90 0.93 4.06 37 observationsconcerning the TABLE 3c. Somerepresentative t67 580 120/5 39.68 0.90 0.91 1.37 12 reactionmechanism are shown in Figures3.{ to D: t6a 680 !20/, 39.19 0.90 0.91 0.96 9 the diopside (Di) crystals nucleate and grow s69 640 2001a !9,13 0.90 0.91 1.70 15 d70 680 20014 34.32 o-90 0.91 1.34 13 exclusively(with one exception,see below) on the pr 580 1a5l\a 39.11 0.90 0.92 2.21 20 dolomite surfaces(Fig. 3A), beginningat the edges, a72 6A0 4361\a 37.95 0.90 0.92 2.46 22 corners and probably at sites of dislocations.At pm gmrn size 3a. AU lhe quaft aod 4.2 mg of lhe dolomite had an 80-100 in sirc' 680oC,but evenat 650oC,no nucleationbarrier fncrion, buirhe lut 20 mg of dolomite gEiN were 5-10 micrcG -- 3b. Diopide-seeded rum; 5 mg of diopaide in a gmin size fmction smaller was observedfor diopside, as was the casein the l0 micrctr have been added. pm grain sire work of Dachs& Metz (1988)on the diopside-form- i". eff ,ft" dolomirc and 2.18 mg of quare had an 8Gl0o - fmclion, but the 16l 13 mg of qurtz gniN were 5-10 microns in sizc' ing reaction, numbered (6) in the system CaO MgO - SiO2- CO2- H2O (seeFie.2): TABLE 4. EXPERIMENTAL DATA OF THE CONVERSION.TIME EXTERIMENTS CARRIED OUT AT 500 MPa WITH A VARIATION OF = x(cor-START I tremolite + 3 calcite * 2quartz Sdiopside+3CO2+lH2O (6) Tt llco2) t(co2) cq-Prd. coover !o. t'ct lbl/ldl rtnat tlsl ttl The newly formed diopsidecrystals usually range 50112\ 40.00 0.40 0.a7 6.13 54 (Fig. 38), and ,04/2L 39.61 0.80 0.97 5.9€ 52 from stalklike to needle-like 842 640 515/21.5 40.14 0.90 0.92 3.6{ 3l "whiskers" also can be observed.[By "whiskers", 841 540 515/21.5 19.85 0.92 0.9{ 3.11 21 mean crystals grown by special vt\13 680 50412\ 3a.93 0.95 0.95 2.54 23 we do not sal4 640 504/21 40.16 0.95 0.95 1.83 16 growth-mechanism (e.g, spiral growth), which used, but The saning mixtureof dolomitcand quartzhad alwaysan 80"1@ pm gnin cannot be investigatedwith the methods sie lBction. Thevalue of X(Cot-start ws varicd. rather the long hair-like diopside crystalsthat can be found in all reaction mixtures. We are not, experiments carried out with different startins therefore, using the term "whisker" in the narrow valuesof X(CO). sense.lThe surfacesof the dolomite not covered with diopsideshow dissolution features such as etch pits and terracedsteps (Fig. 3D). The quartz grains Pure CO2fluids (Figs. 3A,, B), however,are nearly free of diopside crystals.Their surfacesare generallycharacterized All experimentalparameters of runs carried out by the developmentof facets.In addition, etch pits using pure carbon dioxide (99.995v/oCO) as fluid with a 2-fold symmetry Giittge &Metz, in prep.) phase are given in Table 5. The exact value of and dissolution spikes(see Fig. 3B and Tanner el conversionis not determinable,because gravimetric al. 1985, plate 2b), called "hillocks" (Heimann methods cannot be used on account of the open 1975),are very common. The exceptionreferred to capsules.Thus, it was only possibleto estimatethe aboveconsists of nucleationof diopsidecrystals on extent of conversionfrom SEM studiesof reaction the top of somehillocks, which are the siteson the mixtures. The results are also given in Figure 9. mineral surfacehaving the slowestrale of removal 808 THE CANADIAN MINERALOGIST

Ftc. 3. A. Reactionmixture after 358 h at run conditions(H36, o = 250/0);surfaces of dolomiteare coveredby diopside (Di), whereas the quartz grains are completely uncovered. B. Quarrz grain from A at a higher magnification, showing a specialtype of dissolution feature: hillocks. C. Stemlike to needlelike crystalsof Di have grown on the dolomite surfaces,which becomedissolved. D. Dissolution features(etch pits, terracedsteps) on a surfaceof dolomite(H62, a = 22a/o). during dissolution. sequenceof reactions,as shown, for example,by From thesetextures, we concludethat the overall Rimstidt & Barnes (1980) in the case of quartz reaction mechanismoccurs by dissolution - crys- dissolution. This means that the overall tallization, as has also been suggested,e.g., by heterogeneousreaction is composedof oneor more Matthews (1980, 1985), Tanner et al. (1985), complex reactions or processes (dissolution, Heinrich et al. (1986), Ltrttge et a/. (1987), and precipitation),which consist,in turn, of a number Schramke et al, (1987) for some other reactions of elementaryreactions. involving metamorphic minerals investigated by powder methods. It should be emphasizedthar KlNsrrcs: ExpsnrvsNreL many observationsconcerning the mechanismof the reaction investigated here are either com- It is evident from a study of the literature that parable, or nearly identical, to those made by there is little agreementconcerning the identity of Tanner et al. (1985) during their study of the the process(es)that control(s) the kinetics of a kinetics of the reaction: I calcite * I quartz : I heterogeneousreaction involving metamorphic wollastonite+ I CO2. minerals(e.g., Ridley & Thompson 1986).At the Figure I I showsschematically a simpletwo-path same time, there are few experimental data reaction model, as was also usedby Dachs& Metz pertaining to reaction rates that could provide (1988)in a similarfashion. The overallmechanism supportfor the theoreticalwork of Avrami (1940, of reactionconsists of the dissolutionof dolomite l94l), Aargaard& Helgeson(1982), Fisher (1973, and quartz, transport of dissolvedspecies through 1978),Helgesonet al, (1970,1984),Helgeson (1971, the fluid phase,and nucleation and growth of the 1972),Lasaga (1984, 1986)and Walther & Wood diopsidecrystals. It is clearthat eachof thesemain (1986). To achieve progress in understanding processesmay, in turn, consistof a reactionor a reactionkinetics, it is essentialto know much more KINETICS OF THE REACTION Dol + Qtz = Di + cO2 809

Frc. 4. Scanningelectron micrograph showing the metastableformation of talc and the increaseof a with run duration' : resriltingarmoring iim on the dolomite surfaces.Ptot = 500 MPa, T = 680oC,XCOZI at stan 0'90' and the -- A. H08, a -- lbo,20 h; iirst crystalsof Di are observable(ieearrow). B. H27, a 27t/0,239 h; Dol surfaces are pan-lycovered by Di crystals,C. H62, q = 220/0,120h, Dol in a 5-10 pm sizefraction; metastableformation E. of tatc litc; on dolomire. D. H48, a : 42t/0, 1,950h; Dol surfacesare completelycovered by Di crystals. Armoring rim of Di crystalsafter 2,950h (H50, a = 490/o).F. Samerun as E; cleavageplane of a dolomite grain surroundedby a diopsiderim (about 3 pm thick). about the rate-determining process or processes of for the experimental investigation of the kinetics the overall heterogeneous ieactions. In general, the despite the fact that this reaction is not very experimental investigation of these processes is common in nature. complicated by the complexity of the mineral Experiments H08-H50 (Table 2, Fig- 5) were reaciions. Theiefore, *e.hose'a simple reaction carried out with dolomite and quartz, both in a 810 THE CANADIAN MINERALOGIST

40 g30 .91E 6l2s >l c 82a

o.2 o.4 1.2 1.4 t.6 1.8 2.O 2.2 2.4 2.4 ---+> tlmetxl0'3 thl

zo zs do ds so 95 100 110 120 125 ----> tlme [days] Frc. 5. Resultsof the unseededruns H08 - H50. At the start of the experiment,the grain-sizefraction was always 80-100pm for both dolomite and quartz.

80-100 pm grain-size fraction. Figures 4A-F reactionkinetics might be surface-controlledduring illustrate some important stagesof the reaction: the first 800 hours of the experiment. When the r After 20 hours, the first diopsideneedles can dolomite grains becomearmored, after about 800 be observed(Fie. A). During the course of the hours, the reaction rate decreases.We must now reaction,the dolomite surfacesbecome increasingly assume,as did Tanner et al. (1985),that diffusion overgrown by diopsidecrystals. through the product layer is rate-limiting. The o Figure 48 showsthe situation after 239 hours difference with their study is one of time. In the (a : l09o). There are still areasfree of diopside caseof the wollastonite-producingreaction, only on the dolomite surfaces. By this time, the six hours are necessaryto close the product rim metastableformation of very thin plates of talc under the P-T-X conditions of the experiments (Tlc) can be established,as shown in Figure 4C. performed by Tanner et al. (1985),but more than r The nucleation period of diopside persists 600 hours were necessaryto close the rim in the during the first 600 hours (a : 3090), which is caseof the diopside-producingreaction investigated much longer than expectedat the beginningof this here. Betweenthe 2,000th and 3,000th hour, the investigation.The increaseof conversionis almosr reaction rate approachesbut does not reach zero. linear during this period, ascan be seenfrom Figure Lasaga(1986) presented a theoreticaldiscussion of 5. the interplay of surface-controlledprocesses be- . After about 800 hours (a 3590), all tween a reactant that becomesdissolved, and a dolomite grains are covered by diopside crystals. product mineral that crystallizes from an over- This diopside rim is closed, as can be seenfrom saturatedsolution. The two-path model (Fig. ll) Figures4D-F, after nearly2,000 hours (o : 45Vo). consists also of two interplays: 1) dolomite On the basis of the SEM observations, we dissolution- diopsidecrystallization, and2) quartz concludethat the reactionobeys a dissolution-crys- dissolution - diopside crystallization. tallization mechanism,and we suggestalso that the To study the influence of surfaces of the 8ll KINETICS OF THE REACTION Dol + Qtz = Di + Coz 60

F g 830 E30 o '0+o 'al ol ol trl cl ol o o 3zo il20 o U P: 500MPa T : 680'C X(COr)-start: 0.90

o,2 0.4 0.6 0.E 0 0.2 0.4 0.6 0.E '3 -----> '3 --l> tlme [h] x 10 tlme [h] x 10 0 510'152025 303540 n ri 1n 15 20 25 30 35 40 -> _-> tlme ldays] tlme ldays] - H57 - H66' with a Ftc. 7. Resultsof the diopside-seededruns H73 H83' Frc. 6. Resultsof the unseededruns and surface-areaof Dol. At the beginningof the At the beginningof the experiments,-quartz higher from the 80-100pm size experiments'quartz was from the 80-100pm size dolomite were always powder,however, consisted of iraction,with about 5 mgof diopsideof a sizefraction fraction,The dolomite area represents pmsize fraction and 4.22 mg in 80-100 smallerthan 10 pm. The stippled 20mg in 5-10 in Fig' 5' Lm size fraction. The stippled area represents experimentalresults shown experimentalresults shown in Fig. 5. dolomite. This can be reactantsand product upon reaction kinetics,three the dissolution rate of only when values of con- types of expeiimentswere carried out: runs with Jetermined, however, measured.lThus, at the P-T-X enlargedsurface-area of dolomite (Table 3a)' runs centration can be study, it is evidentthat addeOdiopside crystals (Table 3b) and runs .onaitiont applied in this wittr This result is in with an enlargedsurface-area of quartz (Table 3c)' itre reactionli surface-controlled. of Tanner et ol' (1985) and The results of these runs (Figs. 6-8) show that a agreementwith those (1988).The experimentaldata also distinct increaseof reactionrate is observableafter Dlchs & Metz of path I (dolomite hours, as the surfacearea of dolomite increases huue sho*n thai the interplay 120 - is slowerth.an (Fig. 6). A similar effect is seen in the case of dissolution diopsidecrystallization) quartz dissolution and diopside diopside-seededruns (Fig. 7), and no.increaseof ihe interplay of Therefore,from the experimen- reaction rate can be observed in the case of formation (path 2). made with SEM, we increased surface-areaof quartz (Fig. 8). [The tal data and the observations processesalong.path l^are reason for the lower rate of the overall reaction can point out that the reactionduring the first (seeruns H7l and IJ72in Fig. 8) might be the rapid rut.ii*iting for the overall not possibleto decide which dissolution of quartz, which could have reduced 800 hours, but it is 8t2 THE CANADIAN MINERALOGIST

a \0 o c .E El o c,t E cl o o o o il U P:500MPa T:680"C run duEflon:504 h flHl*i so.ioopm

0.75 0.80 0.85 0.90 0.95 1.0 x(co, 0 0.2 0.4 0.0 0.8 --> '3 Ftc. 9. Degreeof conversiono (unseededruns, Tables 4 tlme [h] x 10 and 5) plotted as a function of the X(CO2) values. The arrows indicate direction and rnagnitude of 0 5 10152025 303540 X(CO) shift during the run. The starting mixture of -> dolomite and quartz was from the 80-100 pm size fime [days] fraction in eachcase. Ftc. 8. Resultsof the unseededruns H67 - H72, with a greatersurface-area of quartz.At the beginningof crystallization are congruent. Thus, we can write experiments,13mg ofthe quartzwas from a 5-10pm (see the appendix for a derivation): sizefraction, and 2.78 mg consisted ofparticles 80-100 Term 1 of equation (A9) takes into consideration pm across.The grainsof Dol, however,were also 80-100pm in size. The stippledarea represenrs experimentalresults shown in Fig. 5. processinvolved in path I is rate-determining.

KrNnrrcs: THEoRETTcAL

The following theoretical discussion is an attemptto understandthe kineticsof path I in more detail. Despite the fact that there is as yet a lack Ierm 2 of data requiredfor many of the variablesinvolved, we suggestthat the discussion of equation .A.9, madein a qualitative manner and not violating the + nLn'arn(r - experimentalresults, is informative. For the following discussion, we make the assumption, which is perhaps an oversimplifica- tion, that dolomite dissolution and diopside (Ae) = CO2 813 KINETICS OF THE REACTION DOI + QtZ Di +

Frc. 10. A. Di crystalsformed in a diopside-seededrun (H81, a = 28t/o):seeds have grown, whereasnew.crystals (run of Di also have formed (seethe very small ones),B. Part of a reaction mixture after 365 days run duration magnification; Di wirh "pure,, CO). Only very small crystalsof Di are present.C. Marked area.of B at a higher whiskirs and et& pits (seearrows; .un b. r..n on the bol surface.D. On the edgesof the Dol grain, crystallization F. Dissolution of Di has increased.E. Qtz grain after 365 days run duration: sharp edgesare still observable. features(hillocks) on a Qtz surfaceafter 182 days at experimentalconditions. the dissolution of dolomite, and term 2 describes in path l. The parametersk$ol and kli are the the formation of diopside;dcldt is the net change overallrate-constants of both processes.Aoor(Aoi) in concentrationof speciesI (Ca or Mg), causedby is the surface of dolomite (diopside). Z is the the overall reaction, that is to say, by the interplay volume of the fluid phase in contact with the of dissolutionand precipitation processesinvolved minerals; oca, QMsand a(H+) are the activities of 814 THE CANADIAN MINERALOCIST

A- t+ lfco->o ot

occott dolomite dt

Mgt* dc rr €Ftn'"t o 0> tulg AT dt

''oi li ' o

Flc. I I . Simplified schematicillustration of the "two-path model" of reaction(8). Each "path" includesthe dissolution of a reactant (Dol or Qtz, respectively),the transport of dissolvedspecies (Ca and Mg, respectively,in the case of path I, and SiOf- in the caseof path 2, and the crystallizationof diopside.The dissolutionand precipitation processesare describedby changesin concentration.

Ca-, Mg-speciesand H+ in the solution. L"S,ois the dcco d,cus reducedactivity-product of diopside (dolomite) at equilibrium, which has a definite but unknown dt dt value for the P, T and X(CO2) of the experiments carried out. We write the index * becauseZ* is tertn"l, valid for specificconstant values of a(CO), a(H2O) and a51.The experimentalresults (H67-H72) have (o(a+)) shownthat an increasein the dissolutionof quartz Bo,'Ana does not increasethe rate of the overall reaction. V 0-w) This implies that csiis at a steadystate after a few hours at run conditions. If this is so, dcalldl is equal to 0, and ca;is constant. The total systemof differential equationsfor all concentrationsinvolved in the overall reaction has to be solved for each generalcase. In the caseof reaction(8), however,the problem is much simpler, as mentionedabove: cs1has a constant value, and c6ualways equals cyo, if congruent dissolution of dolomite and precifitation of diopside €ue assumed, respectively.Thus we can write: (A10) KINETICS OF THE REACTION DOI + QtZ = Di + CO2 815

(see p' 7), The changeof c6u(cyr) with time is qualitatively about 20 hours at run conditions the sameas the changeof the product c6" ' cy, (if indicated as l2oin Figure 12. At /26,the nucleation is equal we assumethe specialcase in which cqo : cyu, i.e,, barrierfor diobsideis overstepped,i.e., L* when the congruent behavior). Therefore, we can examine or greater thin L"6ucteotior.At the time (Al0) qualitatively the change of Z* with time. The firsi crystal of diopside appears' equation In the outcome of this discussionis presentedgraphically describes the behavior of the system. 1, in Figure 12. following, we look upon the changesin term csu The initial period (phaseI) lastsabout 20 hours, which takes into considerationthe increaseof of dolomite' 1.e., from to to t20Gig. l2). During this time, (cna")resulting from the dissolution of c6u crystallization of diopside was not detected ex- attd-tetm 2, which describesthe decrease perimentally.The concentrationsof all specieswill (c-.) resulting from the formation of diopside' At in term increase rapidly because of the dissolution of the'beginningof diopsideformation, ,4po1 same dolomite and quartz. During tsto t2s,equation (A7) I is much higherthan.4pi in term 2.lf at the and an analogousequation for quartz dissolution time kf,o1is not too different from kf,',-the^first describethe behavior of the system. term oT-equation (Al0) should be, therefore, case, The period of diopside nucleation begins after determinativefor I*. As long as this is the

fi I () rJ - o I "r

tI I I I I I P = 500 MPa T=680oC X(CO, = 0.90{.94

lo tt t' trt t.o* t.no ------> time t lhl (A10). Phasel:.initial period Fra. 12. Concentrarionproduct L8 plorted as a function of time r, deducedfrom eq. phaseIV: the reaction is (only dissolutionof quartz and d'olomite);phases II, III: period-pro..tt.r, of diopsidenucleation; (Li:f of Ihe,reduced controlled by the dissolution of dolomite o, truniport respectively. .= lalu: of diopside' concentration-product of diopside at equilibriumj 1fi'trcteation: value of nucleation barrier infbrmation, see Ostwald-Mierjrung. =-..yituigrowth occurs,but no nI'cleationis possible).For more detailed text. 816 THE CANADIAN MINERALOGIST

the increaseof L*, i.e,, c.u and cyn, in the fluid of thesespecies by diopsideformation. The slope phase, which originatesfrom the dissolutionof of the curveshowing L* as a function of time will dolomite, exceedsthe decreaseof I* originating thereforebecome negative at I greaterthan l*. The from the consumptionof Ca and Mg, respectively, changeof slope indicatesthat the rate-controlling by the nucleationand growth of diopside.In other step of the overall reaction has changed.For times words,I* increasesfurther, but its slopeis reduced greaterthan l*, the dissolutionof dolomite is slower continuously starting at /20. From 126to l" (/* is than the nucleation and growth of diopside. That defined below), the kinetics of the overall reaction is to say, beyond t" it is the dissolutionof dolomite should be controlled by the processesof crystal- and not the nucleationand growth of diopsidethat lization of the diopsideand not by the dissolution is the rate-limiting processof the overall reaction of dolomite. This period is called phase II (Fig. (8). The period betweent* and t666is called phase 12). III. This conclusion is supported by an important SEM studiesof reactionmixtures after about 600 observationmade during SEM studies: in seeded hoursshow that the nucleationprocess of diopside runs (H73-H83,Fig. l0A), ir is commonlypossible has cometo an end. From l6njon, only the growth to observenot only the seeds,which have grown of diopside crystals could be observed. This bigger, but also newly formed diopside crystals, observationcan be understoodby consideringthe which have nucleatedand grown at the sametime. decreaseof ADotby dissolutionand, in addition, This showsthat the concentrationproduct I* was the armoring effect of the diopsidecrystals, which not only greater than Liif but also higher than or cuts down the surface area of dolomite in direct equal to Lfiucteotion.This is achievableonly if the contactwith the fluid phase.Consequently, cq6 ard dissolution of the dolomite is faster than the crn will decreaseso much that the value of I* has nucleation and growth of diopside. The length of to-become smaller lhan L/1'cteatio,.On the other time that this state of affairs lasts will be hand, c5;should still be constant,because all quartz determinedby the extent to which the assumption surfacesare still free. During the further courseof of similarrate-constants for kf,o,and kf,i is coirect. the reaction, the concentration product Z* will Equation (Al0) does not consider any processof converge with Liif . The period between l6s0and nucleationexplicitly. Therefore,it is necessary,for lro* (longest-durationexperiment) is called phase the formulation of a more detailed model, to IV. consider also the consumptionof Ca and Mg The assumptionmade earlier, that the reaction species by processesof nucleation. It will be rate is not transport-controlled,is valid so lorlg as essentialfor future work to accountfor nucleation the rim of diopsidecrystals around all dolomite in equation(Al0). grainsis not closed.As soonas this is the case,the As the reactionproceeds,,4pol will progressively diffusion of dissolvedspecies through the armoring rim will be rateJimiting. decreasewhile .4o, will increase,conditioned by The rate-determining process the continued nucleation and growth of diopside. has changedagain. At the same-time, a6u, a*r/ Liff approachesI , and aru . a*"/Llf becomesinireasingly greaterthan 1; MECHANISMAND RATE UNDER ALvosT this meansthat the absolute value of term I will Werrn-FRrr CoNurtoNs decrease,whereas the absolutevalue of term 2 will increase. As a result of this process,the absolute An SEM examinationof reaction mixtures held valuesof term I and term 2 will becomeeoual at for nearly 1,000hours at run conditionsshows thar a cefiain point. At the time when this o..urr, the conversiondecreases drastically under almost dcru/dt = = dcya"/dt 0. The time that this happens water-freeconditions (Liittge 1985;see also Fig. 9). is not determinableby our experiments.Therefore, However, in the caseof a significant overstepping it is called (Fig. t* here l2). At t*, the consumption of the reaction(150 - 200oC),the reactionrate is of Ca and Mg species at the diopside-fluid faster (Table 5, VI/1 and VIl9). With respectto interfaces equalsthat of speciesproduction at the natural systems,the latter conditions may not be dolomite-fluid interfaces.It is obvious that dL*/dt very relevant. In order to have readily perceptible also is zero. ThereforeZ* as a function of I has a conversionin the presenceof nearly pure CO, with maximum at l*. an oversteppingof only 60oCor 80oC,respectively, With further conversion,.4po1 will decrease,and (Table 5, runs H84, H85), it was necessaryto have the absolutevalue of term I will therefore become run durationsofup to oneyear (8,760hours). The progressivelysmaller, whereas z4pi and the absolute SEM photos (Figs. 108-F) show some charac- value of term 2 will increase. In general the teristicaspects of the reactionmechanism operating production of Ca- and Mg-bearing species by under "dry" conditions. The reaction mixtures dissolutionof dolomite is lessthas the consumotion from which these pictures were made representa KINETICS OF THE REACTION Dol + Qtz = Di + CO2 817 run durationof 4,368or 8,760hours, respectively. considerationthe fact that the reaction consistsof Both dolomite and quartz clearly show dissolution a dissolution-crystallizationmechanism even under featuressuch as etch pits (Fig. l0C), hillocks (Fig. such H2O-poorconditions, we can agreethat most l0F), and slightly rounded edgesand corners.The metamorphicreactions in nature are controlled by diopside crystals nucleate and grow at the same water-rock interactions, and not by solid-state sites, but exclusivelyon dolomite surfaces (Figs. diffusion. Moreover, the formation of diopside l0C, D). The habit of thesediopside crystals (Fig. from dolomite and quartz, even under such lOD) differs greatly from that observedin reaction CO2-rich conditions, is rapid in comparison with mixtures formed with a fluid phase containing geologicaltime, i.e., it takes place within decades water. It appears that the number of diopside or centuries,instead of millennia. whiskershas increased (Fig. l0C). Our observations It is important to determinewhether or not the are consistentwith a dissolution - crystallization results obtained from the experimentson mineral mechanism(Ltittge et al. 1987).This result is not powderswill hold also in natural systems,in view in agreementwith studiesof the reaction 1 calcite of critical points that have been raised (e.9., + I quartz : I wollastonite + I CO2 done by Thompson& Rubie1985). Therefore, a comparison Kridelbaugh (1973), who postulated a mechanism of the resultsgiven abovewith thoseof experiments of solid-statediffusion involving calcium, silicon with cylindersof rocks hasbeen carried out (Liittge and oxygen, with diffusion of oxygen as the most &Metz, in prep.). likely rate-determiningstep. From the SEM photos of the dissolution-crys- SUMMARY tallization textures.we assumethat small amounts of water, which are adsorbed on the reactant In summary, we conclude that a dissolution- surfaces(c/. Steinike et al. 1985, Moore & Rose crystallizationmechanism is operative throughout 1973), are responsible for the dissolution. The the entire range of X(CO) investigatedexperimen- catalytic effect of water is well known and hasbeen tally. This is the caseeven if there is only a very discussedin detail by Rubie (1986).On the other small amount of water present.During the course hand, CO2should not be able to break bonds in of the experimentson powders,the overall reaction silicate minerals, e.9,, quarlz, on account of the is characterizedby the changeof the rate-limiting absenceof a dipole, and the small quadrupole processesduring the first 2,000 hours of run moment of CO2.By contrast,Novgorodov (1975) duration: inferred (by extrapolation) a solubility of SiO2 of 1. The reaction is interface-controlledduring the 0.0166wt.9o in pure CO2 (300 MPa and 700'C) first 1,000 hours of the experiment.This stage from studies of quartz solubility in CO2-H2O includesan initial period of dissolutionof both mixtures. The dependenceof conversion on the reactants(-20 hours). At the beginningof the X(CO, value can be shown experimentally(Table nucleationperiod the interplay betweendissolution 4, Fig. 9). Note that the results are perhaps of dolomite and crystallization of diopside is somewhatinfluenced by the small decreasein the determinative. In this stage, (from l2s to lr), the degreeof oversteppingof the temperature [OoC nucleation and growth of diopside determine the betweenX(CO) = 0.87 and X(CO) : 0.981. rate of the reaction. After l" (maximum value of However, theseresults are in closeagreement with the concentrationproduct), the rate is controlled those of Tanner et al. (1985). by the dissolutionof dolomite.This periodlasts up Solid-statediffusion will alwaysoperate at high to nearly 1,000hours. temperatures,but in comparison with a simul- 2. When all dolomite grains are armored by taneous mechanism of transport of dissolved diopsidecrystals, i.e., afrerabout 1,000hours, the speciesthrough a fluid phase,solid-state diffusion rate-determining step changes again. Now the is less effective, becauseof the higher activation overall reaction is transport-controlled, i.e., the energiesrequired. At the temperaturesused for diffusion of dissolvedspecies through the diopside these experiments,solid-state diffusion is a much rim is ratelimiting. This processis, of course,much slower process than diffusion through the fluid slower than the interface-controlled processes. phaseand, therefore, is not rate-limiting. Thus it After 1,000 hours, nearly 4090 conversioncan be follows that the rate-determiningprocess is evident- observed.The next 2,000 hours give only an ly a dissolution-precipitation mechanism, even additional 20s/oof reaclion progress. under "dry" conditions and at temperaturesup to at least700"C. ACKNowLEDGEMENTS Drier conditions than those used in our experimentswith "pure" CO2should not be expectedto The authors thank M. Gottschalk, W. Bayh, E. be very conunon in crustal rocks. If we take into Dachs, S.M. Fortier, W. Heinrich, H.W. Alten, 818 THE CANADIAN MINERALOCIST

J,V. Chernosky,and an anonymousreviewer for Bluu, A.E., Yuro, R.A. & Lrsncn, A.C. (1990):The critical commentsand helpful discussions,which effect of dislocation density on the dissolution rate 283- considerablyimproved this paper. We also are very of quartz. Geochim. Cosmochim. Acta 54, grateful to C. Hemleben and H. Hiittemann for 297. providing SEM facilities, R. Schulz for his Decns, E. &Mprz, P. (1988):The mechanismof the manifold assistanceduring the performanceof this reaction I tremolite + 3 calcite + 2quartz = 5 study,M. Mangliers,J. Miillich and N. Walker for diopside + 3 CO2 + 1 H2O: results of powder technical assistanceand preparatory work. We experiments. Contrib. Mineral. Petrol. 100, 542' expressour thanksto S.M. Fortier and L. Vantine 551. for linguistic improvementsto the text, and to Mrs. A. Metz for the excellent and fast typing and Eucsrrn, H.P. (1982): Rock-fluid equilibrium sys- retyping of the manuscript. This work forms part tems. ft High-PressureResearches in Geoscience. of the researchprogram "Kinetics of rock- and E. Schweizerbart'scheVerlagsbuchhanlung, Stutt- mineral-forming processes" of the Deutsche sart (501-518). Forschungsgemeinschaft.Funds were provided by (1986): Minerol. gratefully Minerals in hot water. Am. this institution and are acknowledged. 71,655-673.

REFERENcES -& BeunrcenrNen,L. (1987):Mineral solubilities and speciationin supercriticalmetamorphic fluids. Aancaeno, P. & HelcesoN, H.C. (1982): Ther- In Thermodynamic Modeling of Geological (I.S.E. modynamic and kineiic constraints on reaction Materials: Minerals. Fluids and Melts rates among minerals and aqueous solutions. I. Carmichael& H.P. Eugster, eds.). Rev. Minerol. Theoretical considerations. Am. J. Sci. 282, r7. 361-403. 237-285. FrrN, J.B. & WalrHEn, J.V. O987): Calcite solubility fluids. Geochim. Cos' AvnaMr, M. (1940): Kinetics of phase change. II. in supercritical CO2-H2O 1665-1673. Transformation - time relations for random mochim. Acta 51, distribution of nuclei. J. Chem. Phys. E,212-224. Frsurn, G.W. (1973): Nonequilibrium thermodynamics as a model for diffusion-controlled (1941):Kinetics of phasechange. III. Granula- metamorphicprocesses. Am. J. Sci. 273,891-924. tion, phase change, and microstructure. J. Chem. Phys. 177-184. 9, (1978): Rate laws in metamorphism. Geochim. Cosmochim.Acta 42, 1035-1050. BrnNrn, R.A. (1978): Rate control of mineral dissolution under earth surface conditions. Am. J, GorrscHnrr, M. (1990): Intern konsistente ther- Sci. 278. 1235-1252. modynamische Daten im System SiOz-Al2O3- CaO-MgO- K 20- Na 20- H 2O-CO2. Ph.D. disserta- & HoloneN, G.R., Jr. (1979):Mechanism of tion, Universitiit Tiibingen, Ttibingen, Germany. feldspar weathering. II. Observations of feldspars from soils. Geochim. Cosmochim. Acta 43. GnprNwooo,H.J. (1963):The synthesisand stability I 173-l186. of anthophyllite. J. Petrol. 4,317-351.

& Monse,J.W. (1974):Dissolution kinetics of HgrruenN, R.B. (1975): Aufldsung von Kristallin. calcium carbonate in sea water. IV. Theory of Springer, Wien. calcitedissolution. Am. J. Sci. 274. 108-134. HrrNnrcu, W., Mrrz, P. & Bavu, W. (1986): - & Scuorr, J. (1982): Mechanism of pyroxene Experimentalinvestigation of the mechanismof the and amphibole weathering. II. Observations of soil reaction:ltremolite + lldolomite + 8forsterite grains. Am. J. Sci. ?-82,1214-1231. + 13 calcite + 9 CO2 + I HzO. An SEM study. Contrib. Mineral. Petrol. 93. 215-221. -, Stonenc,8.L., VElnal, M.A. & Knou, M.D. (1980): Dissolution of pyroxenesand amphiboles & GorrscHalr, M. (1989):Ex- during weathering. Science207, 1205-1206. perimental investigation of the kinetics of the reaction l tremolite + 1l dolomite + 8 forsterite BLrNcor, J.G., MEnrel, C.A. & Ssrr-,M.K. (1982): + 13 calcite + 9 CO2 + I H2O. Contrib. Mineral. Thermodynamics of crystal - fluid equilibria, with Petrol. 102, 163-173. applications to the systemNaAlSi3Os - CaAl2Si2Os - SiO2 - NaCl - CaCl2 - H2O. In Advances in HrLonsoN,H.C. (1971):Kinetics of masstransfer Physical Geochemistry 2 (S.K. Saxena, ed.). amongsilicates and aqueoussolutions. Geochim. Springer-Verlag,New Y ork (l9l-222). Cosmochim.Acta 35, 421-469. KINETICS OF THE REACTTONDol + Qlz = Di + COz 819

(1972): Kinetics of mass transfer among PernovrcH, R. (1981a): Kinetics of dissolution of silicatesLesand aqueoussolutions: correction and mechanicallycomminuted rock-forming oxidesand clarification. Geochim. Cosmochim. Acta 36. silicates. I. Deformation and dissolution of quartz 1067-1070. under laboratory conditions. Geochim. Cos- mochim. Acta 45, 1665-1674. -, Bnowr, T.H., NtcntNI,A. & JoNns,T.A. (1970): Calculation of mass ransfer in geo- (l98lb): Kineticsof dissolutionof mechanical- chemicalprocesses involving aqueoussolutions. ly comminuted rock-forming oxides and silicates. Geochim.Cosmochim. Acto 34, 569-592. II. Deformation and dissolution of oxides and silicates in the laboratory and at the Earth's , MunRuv, W.M. & AancaanD, P. (1984): surface. Geochim. Cosmochim. Acta 45' 1675- Thermodynamicand kinetic constraints on reaction 1686. ratesamong mineralsand aqueoussolutions. II. Rate constants,effective surface area and the Pr,tnovtc, R., BEnNtrn,R.A. & Got-oH,rnrn,M'B' hydrolysisof feldspar.Geochim. Cosmochim. Acta (1976): Rate control in dissolution of alkali N,U05-2432. feldspars. I. Study of residual feldspar grains by X-ray photoelectron spectroscopy. Geochim. Cos' KAse, H.-R. & Merz, P. (1980): Experimental mochim. Acta 40, 537-548. investigationof the metamorphismof siliceous dolomites.IV. Equilibrium data for the reaction: I Diopside + 3 Dolomite + 2 Forsterite + 4 Rrrlev, J. & Tuor',rpsoN,A.B. (1986): The role of mineral kinetics in the development of metamor- Calcite + 2 CO2. Contrib. Mineral. Petrol. 73, - l5l-159. phic microtextures. /n Fluid Rock Interactions during Metamorphism(J.V. Walther& B.J. Wood, New York (154-193). KRlDELrAucu,S.J. (1973): The kinetics of thereaction: eds.). Springer-Verlag, calcite+ quartz = wollastonite+ carbondioxide at elevatedtemperatures and pressures. Am. J, Sci. RrMsrror, J.D. & BenNrs, H.L. (1980):The kinetics n3,757-777. of silica - water reactions. Geochim- Cosmochim. Acta 4,1683-1699. Lasacn, A.C. (1984):Chemical kinetics of water - rock interactions.J. Geophys.Res. 89, 4@9-4025. Runm,D.C. (1986):The catalysisof mineral reactions by water and restrictions on the presence of (1986):Metamorphic reaction rate laws and aqueous fluid during metamorphism. Mineral. developmentof isograds. Minerol. Mog. 50, Mag. 50,399-415. 359-373. & Bneanmv, A.J. (1987):Metastable melting LUTrcE,A. (1985):Experimentelle Untersuchungen during the breakdown of muscovite + quartz at I zum Mechanismusder Reaktion: I Dolomit + 2 kbar. Bull. Mindrol. 110, 533-549. Quartz = I Diopsid + 2 Co2.Diplomarbeit,Inst. f. Mineralogie,Petologie u. Geochemie,Univ. Tiibingen,Tiibingen, Germany. Scunaurc, J.A., Kpnntcr, D.M. & Lesncn, A.C. (1987): The reaction muscovite + quartz = andalusite + K-feldspar + water. l. Growth R. (1987):Concepts ,Merz, P. & RrHr-ANoen, kineticsand mechanism.Am. J. Sci. 287,517-559. of the mechanism of decarbonation reactions in siliceous carbonates. Terra Cognita ?,253 (abstr.). SrerNrrs, U., HeNNtc, H.P. & Esenr, I. (1985): und MerrHews, A. (1980): Influences of kinetics and Beziehungenzwischen Strukturvertinderungen Z. mechanism in metamorphism: a study of albite Sorption am mechanisch aktivierten Quarz. phys. crystallisation. Geochim. Cosmochim. Acta 44, Chem. X;6(2), 302-310. 387-402. TaNNBn,S.8., Krnntcr, D.M. & Laseca,A.C. (1985): (1985): Kinetics and mechanisms of the Experimental kinetic study of the reaction: calcite reaction of zoisite to anorthite under hydrothermal + quartz + wouastonite + carbon dioxide, from conditions: reaction phenomenologyaway from the t to 3 kilobars and 500 to 850oC.Am. J. Sci. 285, equilibrium region. Contrib. Mineral. Petrcl. E9, 577-620. r l0-121. THoMRsoN,A.B. & Ruatr, D.C., eds. (1985): Moonr, G.S.M. & Rosr, H.E. (1973):The structure Metamorphic Reactions. Advances in Physical of powderedquartz. Noture U2, 187-190. Geochemistry,Vol. 4. Springer-Verlag,New York.

Novoonooov,P.G. (1975):Solubility of quartz in Tovocopr (1975): Quality standards for the inclusions H2O-CO2mixtures at 700oCand pressuresof 3 of TOYO quartz. TOYOCOM Equipment Co, and 4 kbar. Geochem.Intern. l2(5),122-126. Ltd., Tokyo, Tech. Bull. C-5. 820 THE CANADIAN MINERALOGIS'I

VaN Lren,J.A., Dr BnuvN,P.L. & Ovensrrr, J.T.C. where dc'/dt is now lhe net changein concentrationof (1960): The solubility of quartz. J. Phys. Chem. speciesI in the solutionthat is in contactwith a mineral 64, 1675-t682. O. Q is the activityquotient, and Kcqis the valueof this quotient in the case of equilibrium. Both m and n are constantsthat usuallyhave to be determinedexperimen- WeLTHER,J.V. & OnvrLLr, P.M. (1982): Volatile tally. FollowingLasaga (1984), it is assumedhere that la production and transport in regional metamor- and ro equal I as a first approximation. The phism. Contrib. Mineral. Petrol. 79,252-257. stoichiometriccoefficient z equals I also if congruent dissolutionand precipitationare assumed. Equation (A2) & - (1983): The extraction-quenchalsoshould hold for crystalgrowth of themineral O from technique for determination of the thermodynamic an oversaturatedsolution, e,g., for the crystallizationof properties of solute complexes: application to diopsidein the caseof reaction(8). quartz solubility in fluid mixtures. Am. Mineral. The dissolution of dolomite may be described 68,731-74r. schematicallyas follows:

& Wooo, 8.J., eds. (1986):Fluid - Rock CaMg(Co3)2solid + H2O = ca(OH)zdit"tlu"d + Interactions during Metomorphism. Advances in Mg(OH;rdissorvco+ 2CO2 (A3) Physical Geochemistry,Vol. 5. Springer-Verlag, New York. At present,it is not possibleto write a more descriptive equation,because the speciesin COz-richfluid phaseare WrnrLrn, H.G.F. (19'79): Petrogenesis of Metomor- not well known (Eugster& Baumgartner1987). We phic Rocks(sth ed.). Springer-Verlag,New York. therefore use the following schematicreaction for the crystallizationof diopsidealso: WoooLnNo, A.B. & Welruen, J.V. (1987): Ex- CaMg[Si2O6]'olid1 16 HzQ : perimental determination of the solubility of the assemblage paragonite, albite, and quartz in Ca(OH;rdissotvca+ Mg(OH;rdi$olvca * supercritical H2O. Geochim. Cosmochim. Acta 51, 2[Si(OH)4.2H20]dis$olved (A4) 365-372. Using equations (A2) and (A3) and inserting the Received December 17, 1990, revised manuscript activitiesof the dissolvedspecies, we obtain for dolomite: acceptedMay 30, 1991.

t, a- - - p+y1 -'Dd=*!.^D4 1"1t-t- dt Y . ("=*ffi) (A5) APPENDIx -r[",ff14n.rrW

In casesfar removed from equilibrium, it is possible to write the following equation for the dissolution of a mineralO (Lasaga1984): If )l(CO) and X(H2O) are nearly constant,as can be approximatedin the caseof the experimentsperformed = (At) here, a(CO) and a(H2O) can be assumedto be constant # +.2;6rg1o1fl+))"o also. In addition, we consideralso, as a first approximation, that a51has a constantvalue over time (steadystate), where dq/dt is the changein concentrationof soeciesI and that ac.. is equal to c6u (ay* is equal to cy"). This in the fluid phasewith respectto the changein time, kd simplificationis allowedif we usethe Henrianstandard is the overall rate-constantof the dissolution processof state (e.9., Blencoeet al. 1982),which is justified if tne mineralO, and le is its surface.V is the volumeof the concentrationsof dissolvedspecies in the fluid phaseare solution(fluid phase)in contactwith mineralO. Equation not too high. In our case,it is reasonableto assume (Al) should hold for the dissolutionof quartz and Henrian behavior. Even if there is a deviation from dolomite, respectively,at rhe very beginning of the Henrian behavior,the statementsmade from equationA9 experiments.As equilibrium is approached between a (Al0) are still qualitatively correcr. The activities of reactant and the solution, the rate of precipitation will dolomite,apop and diopside,ap;, eeualI as long as both become more and more important. Lasaga (1984) mineralsremain pure phases.For this case,equation (A5) proposed equarion (A2), which takes precipitation into will becomemuch simpler: account,in additionto dissolution:

n?:-_ - A^r h = Ae .rt. ,L,..@(E+))"e = kB"#(o(.E*)) ; 7 kt gLv (A6) -f;',o'r[ftP1a+Y"e {a2) -*5",!p1n.r(ffi) KINETICSOF THE REACTIONDol + erz = Di + CO, 821

The product at&.aiffn is the reduced activity-product in equilibrium of Ca- and Mg-bearingspecies in the solution, which we cal ff1q. We write the index * because L* is valid for specificconstanl values of a(CO), a(Hr,O) and as;.Howevir, note that Zifr is clearly'afunction'of P, T, X(CO2) and a51.Under the experimentalconditions applied, Zfi$ has a definite but unknown value. Equation (A6) can be rewdtten:

#=ut",P(o(E+))tW) (A7)

An equation such as (A7) can also be written for the dissolutionof quartz. [For a more detaileddescription of the dissolution of quartz, the readershould consult Van Lier et al. (1969), Rimstidt & Barnes(1980), Walther & Orville (1983)and Woodland & Walther (1987).1If it can be assumedthat csiis at a steadystate after a short period of somehours, then dc(SiO)/ dt is equalto 0, and a(SiO2) is constant.Using equations(A2) and (A4) in consideration of the assumptionabove, we can write equation (A8) for the crystallizationof diopsidein a manner analogous to equation (A7)

#=ut,?r{a+))(r-W) (A8)

Notice that Z,$iq is the reduced activity-product of diopside at equilibrium; it has a definite but unknown value for P, T and X(CO) of the experimentscarried out, and the above-mentionedconstant activitiesof SiO2 and H2O. Now we combine equations(A7) and (A8):

ilc; dt

,ertu | (o(r+)) I --v-l|kBot.Arot(r-W) L lertu 2 +*g,.u;(r- --w-)acd'aMc\

(Ae)

where dq/dt is now the net changein concentrationof speciesI (Ca or Mg) causedby the overall reaction, that is to say, by the interplay of the dissolution of dolomite and the precipitation of diopside (path l).