JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 105, NO. Bll, PAGES 26,017-26,036, NOVEMBER 10, 2000

Dislocation and diffusion creep of synthetic anorthite aggregates

E. Rybacki and G. Dresen GeoForschungsZentrumPotsdam, Potsdam, Germany

Abstract. Syntheticfine-grained anorthite aggregates were deformedat 300 MPa confining pressurein a Paterson-typegas deformation apparatus. Creep tests were performedat temperatures rangingfrom 1140 to 1480K, stressesfrom 30 to 600 MPa, and strain rates between 2x 10 '6 and lx10-3 s 'l. Weprepared samples with water total contents of 0.004 wt % (dry)and 0.07 wt % (wet), respectively.The wet (dry) materialcontained <0.7 (0.2) vol % glass,associated with fluid inclusionsor containedat triplejunctions. The arithmeticmean grain size of the specimensvaried between2.7 _+0.1 lamfor the dry materialand 3.4 _+0.2 lamfor wet samples.Two differentcreep regimeswere identified for dry andwet anorthiteaggregates. The datacould be fitted to a power law. At stresses> 120 MPa we founda stressexponent of n = 3 irrespectiveof the water content, indicatingdislocation creep. However, the activation energy of wetsamples is356 _+ 9 kJmol 'l, substantiallylower than for dry specimens with 648 + 20kJ mo1-1. The preexponential factor is log A = 2.6(12.7) MPa -n s -• forwet (dry) samples. Microstructural observations suggest that grain boundarymigration recrystallization is importantin accommodatingdislocation creep. In the low- stressregime we observeda stressexponent of n = 1, suggestingdiffusion creep. The activation energiesfor dry and wet samples are 467 + 16and 170 + 6 kJmol '•, respectively.Log A is 12.1 MPa-n pm m s -1 for the dry material and 1.7 MPa -" pm m s '1 for wet anorthite. The data show that the strengthsof anorthiteaggregates decrease with increasingwater content in both the dislocationand diffusioncreep regimes. A comparisonof the creepdata of syntheticplagioclase from this study with publisheddata for feldspar,olivine, andquartz indicates a linearrelationship between activationenergy and log A similarto the suggestedcompensation law for diffusionin silicates.

1. Introduction and inferred deformationmechanisms exist for experimentally and naturallydeformed feldspathic and quartzo-feldspathicrocks Geological field studiesand laboratoryinvestigations of the and are discussedin a seminalreview by Tullis [1990]. mechanicalproperties of rockssuggest a rheologicalstratification The high-temperatureplastic strength of rockscan be reduced of the continentallithosphere [e.g., Brace and Kohlstedt, 1980; considerablyby the presenceof water-relatedspecies [Kohlstedt Kohlstedt et al., 1995] with a weak lower crustal layer et al., 1995]. Tullis and Yund [1980, 1991] and Tullis et al. sandwichedbetween stronger middle crust and upper mantle [1996] showed in their experimentsthat the presenceof water [e.g., Ranalii, 1987]. Independently, Meissner and Strehlau reducesthe strengthof feldsparand may causea changeof the [1982] and Chen and Molnar [1983] suggestedthat reduced dominant deformation mechanism. Dimanov et al. [1999] seismic activity of the lower crust indicateslow ductile flow demonstratedthat the strengthand activationenergy for grain strengthrelative to the uppercrust. However, mechanical data and boundary diffusion-controlledcreep of pure fine-grained flow law parameterson the rheologyof rockstypical for the lower anorthiteaggregates is reducedat atmosphericpressure when crust, i.e., gabbros,metabasites, etc., are still scarce[Caristan, tracesof water (0.05-0.1 wt %) are present.Likewise, the stressat 1982; Sheltonand Tullis, 1981; Kirby, 1983; Carter and Tsenn, the transitionfrom diffusion to dislocationcreep of feldsparis 1987; Mackwell et al., 1998]. The amount of stresstransfer and lower with trace amountsof water present. partitioningof strain betweencrustal layers and the mantle has In this studywe investigatedislocation and diffusioncreep of given rise to much controversy[e.g., Kirby, 1985; Ord and anorthiteaggregates at elevatedconfining pressures. We present Hobbs, 1989]. constitutiveflow laws for syntheticanorthite aggregates that are Feldspars,pyroxenes, and amphibolesare the most abundant dry or containtrace amounts of water. minerals constituting the deep continental crust. For monomineralicrocks composedof feldspar or pyroxenesome recentstudies of syntheticaggregates exist that yield constitutive 2. Starting Material and Experimental Methods equationsfor diffusioncreep [Lavie, 1998; Dimanov et al., 1998, 2.1. SpecimenFabrication 1999]. Bystricky[1998], Mackwell et al. [1998], and Xiao [1999] investigatedmixtures of clinopyroxeneor quartzwith feldsparat Anorthiteaggregates were fabricated from crushed CaA12Si2Oa various volume fractions. Detailed studies of the microstructure glass(Schott Glaswerke). The chemicalcomposition of the glass from fluorescentX-ray analysisis An9a.9Or0.2Ab0.9(normalized to 8 O) with majorimpurities of TiO2 (0.1 wt %), MgO (0.07 wt %), Copyright2000 by the AmericanGeophysical Union. Fe203(0.01 wt %), and H20 (•0.05 wt %). Papernumber 2000JB900223. The particlesize of the glasspowder was <60 pm. The powder 0148-0227/00/2000JB900223509.00 waspredried at 1073 K in air for 60 hoursand kept at 393 K for

26,017 26,018 RYBACKI AND DRESEN: CREEP OF ANORTHITE AGGREGATES severaldays before cold pressinginto steeljackets with 0.5 mm • I i I i I I I I I i • wet undeformed ...... wall thickness.A vacuumdye was usedto reducepressure to 1.5 kPa. To cold pressthe samples,an axial stressof 300 MPa was wetdeformed ...... /,•\ _ applied.The diameterof the jackets was 15 mm and the length ...... wetundeformed (78K) ...... -'" // \\ was 30 mm. Using a gas pycnometer(Micromeritics Accy Pyc / 1330), the porosity of the green bodies was determinedto be •30%. To fabricate "dry" specimens,we heat treatedthe cold- pressedpellets at 1073 K to 1173 K for more than 120 hours prior to hot pressing."Wet" sampleswere hot isostaticallypressed without the initial heat treatment.A Paterson-typegas apparatus was used to hot pressand annealboth wet and dry samplesin three stepsat a pressureof 300 MPa. First, sampleswere further densiftedabove the glasstransition temperature at 1173 K for 1 hour. Furtherannealing was performedat 1323 K for 2 hours,i.e., o ' I ' I ' I ' I ' I ' slightlyabove the nucleation temperature of 1297 K for•northite 2600 2800 3000 3200 3400 3600 3800 [Dresen et al., 1996]. Finally, the annealingtemperature was -1 wavenumber, cm increasedto 1473 K for 2 hoursto promotegrain growth. Heating andcooling rates were 20 and10 K min-•, respectively.After Figure 1. RepresentativeFTIR absorbancespectra of dry andwet sampleswere retrieved from the vessel, the iron jacket was anorthite aggregatessamples in the mid-IR range (3 I.tm dissolved in acid (50/50 vol % HC1/HNO3). For mechanical wavelength).Using the maximum peak heights near 3600 cm ~•, testing,the sampleswere precisionground to obtain cylindrical the calculatedwater contentof the wet sample(An10) is 9800 specimensof 10 mm diameter and 20 mm length. In this ppm H/Si before deformation(corresponding to 635 ppm H20 procedurethe initial samplesurface possibly contaminated by the (wt)) and 8400 ppm H/Si (545 ppm H20 (wt)) afterdeformation. acid was removed, and the samplediameter was reducedby 4 The dry undeformedsample (An28) contains•500 ppm H/Si (33 mm. The porosityof the samplesis lessthan •1%, as determined ppm H20 (wt)). An additionalpeak at a wavenumberof •3200 by Archimedes'method in water. cm-• wasfound in undeformedwet sample(An15, 10,400 ppm H/Si) when measuredat cryogenictemperature. The smallsharp 2.2. Water Content peaksat 2850and 2930 cm -• resultfrom resin used in sample preparation. A Fourier-transformedinfrared spectrometer(FTIR, Bruker IFS-66v) equippedwith a microscopewas used to measurethe water content of samples before and after deformation.The spectra were recorded at 293 K from >128 scans between feldsparscan contain up to severalthousand parts per million wavenumbers2500 to 4000 crn-• (resolutionof 2 crn-•).We H/Si [Kronenberg et al., 1986; Behrens, 1994; Beran, 1987; performedat least five separatemeasurements per sample.Since Hofmeisterand Rossman,1985]. the spotsize of the microscopeis roughly20 timeslarger than the 2.3. Microstructures averageanorthite grain size, our measurementsrefer to the total water contentof the samples.To quantitativelyestimate the water Figure 2a is an optical micrographtaken from an ultrathin contentof the aggregatesfrom 150-Hm-thicksamples, we used (<10 Hm) sectionof the wet startingmaterial. Prismatic anorthite Beer-Lambert's law and a molar extinction coefficient of 32 grains are common with an averageaspect ratio of 2.7. Grain L(H2O)mol -• crn-• [Beran,1987]. This technique probably yields boundariesare facetted, and 120ø triple junctions are scarce. an upperlimit for the watercontent [Bell et al., 1995]. Twins with fine-spacedlamellae are abundant.A few larger Absorbancespectra for typicalwet and dry samplesare given grains show undulatory extinction. In wet samples some in Figure 1. The spectrashow a broadbandabsorbance with a spheruliteswere foundwith needle-shapedgrains up to 200 I.tm maximumnear 3600 cm-•, characteristicof molecularwater or long and arrangedin radial fashion.Spherulites were previously hydroxyl[Aines and Rossman,1984]. Specimensreferred to as observedto crystallizefrom undercooledplagioclase melt [Abeet wet contain about 11500 _+2900 ppm H/Si (0.07 _+0.02 wt % al., 1991; Kirkpatrick et al., 1979; Lofgren, 1974]. Farver and H20) on averageand 640 _+260 ppm H/Si (0.004 _+0.002 wt % Yund[1995b] found spherulitictexture in hot-pressedorthoclase H20) if they are dry. Sampleto samplevariation is <40% and if the particlesize of the startingglass powder was >4 Hm. Since dependson the humidityduring cold pressing.On the basisof our startingglass powder contains particles <60 pm, it is possible spotmeasurements of a singlesample the distributionof water- that someof the largerglass particles crystallized as spherulites. relatedspecies is quitehomogeneous with <10% differencefrom Their volumefraction in the wet startingmaterial was 4 _+3 vol % averagevalues. We observedno significantdifference in water on average.No spheruliteswere found in the dry samples. content of samplesbefore or after deformation.No loss of The arithmeticmean grain size d wasdetermined from samples hydrogen by diffusion through the metal jacket during before and after deformationusing the line interceptmethod deformation runs could be detected. [Underwood, 1970]. Polished sectionswere etched with diluted FTIR spectraof a few specimensrecorded at liquid nitrogen hexafluorosilicicacid (34% H2SiF6)and examinedin a scanning temperatureshowed a weak ice peak around3200 cm-• electronmicroscope (SEM ZeissDSM 962). The meanintercept wavenumber,indicating the presenceof freezablewater in fluid length L was determinedalong 12 lines across the section inclusions [Aines and Rossman, 1984; K. R611er, personal oriented in 15ø intervals. L is convertedto grain size by communication,1999]. Extrapolation of the data of Behrens multiplyingL by a factorof 1.95 and assumingan averageaspect [ 1994] suggeststhat plagioclasemay incorporate0.05 wt % H20 ratio of 2.7 and a rectangularprism grain shape[Dimanov et al., at T = 1273 K and a waterpressure of PH20= 300 MPa. Natural 1998]. The meangrain sizeis 3.4 _+0.2 I.tm for wet samplesand RYBACKI AND DRESEN: CREEP OF ANORTHITE AGGREGATES 26,019

lOO 400 grains 8o

',-. 60

o • 40

c- 20

' I ' I ' I ' I ' I ' I ' I ' I ' I ' 0 1 2 3 4 5 6 7 8 9 10 grain size, pm

.

c

Figure 2. (a) Opticalmicrograph of hot-pressedanorthite (An21, crossednicols, scale bar 12.5 pm). The ultrathin sectionphotograph reveals fine grains with high aspectratios of about 2 to 3 that are randomly oriented. The averagegrain size is •3.5 pm. (b) Grain size distributionof sampleAn23 (wet, undeformed).The arithmeticmean grain size is 3.2 _+1.6 pm. (c) TEM bright-field micrographof sampleAn 24 showstwins and suturedgrain boundaries.Spacing of the twins is <20 nm. (d) Intracrystallinesubmicron-sized fluid inclusions (arrows) surroundedby a glass rim are abundantin the wet starting material (sample An12). The trace of small contaminationspots at a distancefrom the centralbubble stemfrom EDX analysisthat showeda Si enrichmentin the center of the inclusion.

2.7 +_0.1 pm for dry samples.For somespecimens we measured microscopeimages (TEM, PhilipsCM 200). The volumefraction the grain size distributionwith the aid of a digital imaging of submicron-sizedgrains is •5% afterhot pressingat 1323 K for system.It is typicallyleft-skewed (lognormal), as shownin Figure 4 hoursand <1 vol % after annealingat 1473 K for 10 hours. 2b. Since grains smaller than 0.5 pm diameter could not be To investigate the grain growth kinetics of wet anorthite resolved from etched SEM sections, we estimated their volume aggregates,we hot isostaticallypressed four samplesbetween proportion in two samples using transmission electron 1323 K and 1473 K for 4 hours and annealedfour samplesat 26,020 RYBACKI AND DRESEN: CREEP OF ANORTHITE AGGREGATES

1473 K between 4 and 10.5 hours. No significantgrain growth data processing,the uncertaintyof stressand strainrate data is occurred under these conditions. However, Dresen et al. [1995] <3 %. Temperaturesare accurateto within 0.5%. found substantialgrain growth in anorthitein the presenceof water. In their case the sampleswere crystallizedfrom a glass 3. Results block. Sincethe glasspowder contains water adsorbed on particle surfaces,grain growth may be inhibited by pinning causedby 3.1. Mechanical Data abundantpores [Olgaard and Evans,1988]. For rigid inclusions 3.1.1. Stress exponents. About 190 creep tests were the stabilizedgrain size dmax depends on secondphase diameter ds performedon 20 wet and 5 dry samplesat stressesbetween 30 to and volumefractionfi 600 MPa; the resulting steady state strain rates were between 2x10-6 s-• andlx10 -3 s-• (Table1). The strainfor eachstep at ttmax= C (tt•/fm). (•) constant load was •3%, and the total strain accumulated in individual sampleswas 25% on average.Steady state creep was observed after 1-1.5% strain, but the amount of transient C is a constant of •1; rn is a measure of second phase (primary) creep increasedat higher loads, probablydue to the dispersion.For a random distribution,particle distributionrn = elongatedgrain shape[Deng et al., 1999]. 1.0, and if particles lie on comers, rn = 1/3 [Olgaard, 1985; Figure 3a showstypical examplesof the variation of strain Evans et al., 2000]. For a sampleporosity of 1% and an average rate with applied stress.The reproducibilityof strainrate for a pore size of ds= 0.5 pm with porespreferentially located at grain givenstress is betterthan a factorof 2 (e.g., samplesAn10, An45, boundaries(m = 0.5), equation(1) gives a roughestimate of the and An4). For temperaturesbelow •1473 K, wet samplesare stabilizedgrain size of •5.0 pm. weaker than dry specimens;e.g., at T = 1393 K, wet samples The dislocationand fluid inclusiondensity of undeformedand An10, An45, and An4 are weaker than sample An39 (partially deformedspecimens was determinedfrom 300 TEM micrographs dried), which itself is weaker than the dry sampleAn42 (Figure [Underwood, 1970]. The dislocationdensity p of undeformed anorthiteis •5 x 10•m-2. This is a lowerbound, since we didnot 3a). The strainrate sensitivityincreases with stressfrom n • 1 to F/•3. quenchthe samplesafter hot isostaticpressing. Most dislocations In mostcreep tests the load was increasedstepwise at constant are gentlycurved, suggesting that climb is relativelydifficult even temperature.We also performeda few testsat constantload and at 1473 K. Twinning is common in the undeformed material varied T. Here the resultingstrain rates were systematicallyhigher (Figure 2c). It may result from misfit stressesthat accrueduring when T was increased and lower when T was decreased, as crystallizationand orderingof anorthite[Putnis, 1992; Xu et al., compared to the respective stress-steppingtests at the same 1997]. conditions.This may be due to small variations in grain size The undeformed wet specimens contain abundant betweensamples subjected to differenttemperature treatments. If intracrystallinefluid inclusionsup to severalhundred nanometers the stresswas back-steppedat constantT, the resultingstrain rate in diameter(Figure 2d). As shownin the low-temperatureFTIR was higher comparedto the precedingstrain rate at similar load. measurements,the inclusionsare partially freezable. The amount Possibly, the microstructureof the specimensdid not fully of fluid inclusionsin wet (dry) material is 0.2 (0.01) vol % on equilibrate with stress in these experiments.In addition, we average,equivalent to about 0.07 (0.004) wt % H20 in anorthite performed a displacement-controlledexperiment at constant if all inclusionsare filled with water.These values agree very well displacementrates on a wet specimenat T = 1373 K. Strainrates with the hydrogencontent determined by FTIR, suggestingthat werevaried in threesteps between lx10 -3, lx10 -4, and lx10 -s s -•. most of the water is incorporatedas fluid inclusionsduring hot The flow stress-strainrate data from theseexperiments agree with isostaticpressing. In both undeformedand deformedwet samples results from creep tests within the observedsample to sample we found<0.7 vol % glass,and in dry samplesthe glasscontent variation. was <0.2 vol %. Frequently, the glass surroundingthe fluid The mechanicaldata were fitted using a multilinearregression inclusionsforms a shell(Figure 2d); in wet specimenssome triple to a powerlaw creepequation of the form junctionscontained glass. In TEM, no glass was observedalong grain boundariesto a • = A a nd-m exp (-Q/RT), (2) resolutionof 2 nm. Energy dispersiveX-ray analysis(EDX) of the glass in 19 different locations shows a significant Si enrichmentwith respectto the adjacentanorthite crystal. This Si where• is strainrate (s-l), A is a preexponentialconstant, o-is enrichmentmay be due to local nonstoichiometriccomposition of stress(MPa), d is grainsize (pm), Q is the activationenergy (kJ the startingglass powder or due to meltingof anorthiteunder the mol-1),T is temperature(K), R is thegas constant, and n andrn experimentalconditions in the presenceof water. are the stressexponent and the grain size exponent,respectively. The resultsof regressionanalysis are given in Table 2. For analysiswe excludedall data from temperatureor stressback- 2.4. Mechanical Tests and Data Processing steppingexperiments. Furthermore, data that appearedto be in We performed constant load (creep) tests at 300 MPa the transitionalregime (see Figure 3a) and somehigh stressdata confiningpressure in a Paterson-typegas apparatus.Temperature that are likely to be in the power law breakdownregime [e.g., was varied from 1093 K to 1493 K. Specimenswere jacketedin Tsennand Carter, 1987] were excludedfrom regression.Figures iron with 0.3 mm wall thicknessand nominally drained to the 3b and 3c show plots of log stressversus log strainrate. The atmosphere.Force was correctedfor strengthof the iron jacket slopen, i.e., the stressexponent, increases from n • 1.0 + 0.1 to n and convertedto axial stressby taking sample distortioninto • 3.0 + 0.1 with increasingstress, indicating a transitionfrom account. True (natural) strain and strain rates were determined diffusionto dislocationcreep. The dashedlines representthe fit from axial displacementand correctedfor systemcompliance. of the multilinearregression to the data. The boundarybetween Consideringthe propagationof errorsassociated with testingand the two creepregimes is differentfor dry andwet samples. RYBACKI AND DRESEN: CREEP OF ANORTHITE AGGREGATES 26,021

Table 1. MechanicalData for Creepof SyntheticAnorthitea

Sampleb T, K c•,MPa g, s'• •, % Comment

An4 1389 32.4 1.76 x 10-5 3.26 OH = 12,520 ppm H/Si 1393 65.2 3.39 x 10'5 2.98 d = 3.15 + 0.27 pm 1393 140.5 1.07 x 104 3.25 O= 0.9% ct=0% axial splitting

An10 N c 1393 32.1 1.99 x 10'5 2.73 OH = 9720 ppm H/Si N c 1389 52.4 2.58 x 10-5 2.89 d = 3.26 + 0.12 gm N c 1392 83.4 3.97 x 10-5 2.69 cI)= 1.1% N/P 1392 184.9 1.12 X 10-4 3.60 ct=2% pc 1391 290.0 3.01 X 10'4 5.44 stressbackstep pc 1391 417.0 1.57 x 10-3 9.48 P 1391 300.5 9.12 X 10'4 5.24

An12 1493 32.2 6.21 x 10-5 3.14 OH = 8510 ppm H/Si 1442 31.0 2.34 x 10-5 3.10 d = 3.68 _ 0.22 [tm 1341 30.1 3.08 x 10-6 1.71 cI) = 1 .O% 1341 62.0 6.04 x 10-6 1.78 ct=1% 1341 146.2 1.44 x 10'5 1.73 temperature steps 1341 267.8 4.21 x 10-5 2.34

An15 1293 55.4 9.95 X 10-6 2.67 OH = 9320 ppm H/Si 1293 31.9 7.88 x 10'6 1.13 d = 3.34 _+0.35 pm 1292 31.2 8.66 x 10'6 0.88 ß = 1.2% 1292 53.7 1.19 x 10'5 1.12 ct=5% 1292 82.1 1.58 x 10'5 2.27 stressbackstep 1292 134.5 2.58 x 10'5 2.78 1292 195.2 4.10 x 10-5 2.63 1291 292.1 7.17 x 10'5 2.23 1291 463.1 1.66 x 10'4 2.79 1291 618.5 4.44 X 10'4 3.71

An18 1275 31.7 6.10 X 10-6 1.53 OH = 11,480 ppm H/Si 1273 57.4 1.06 x 10-5 1.72 d = 3.30 _+0.35 pm 1273 88.7 1.56 x 10-5 2.49 ß = 1.2% !273 211.9 4.08 x 10'5 1.84 ct=9% 1273 409.6 1.04 X 10-4 2.43 temperature steps 1273 594.5 2.33 X 10'4 3.88 lateral fractures 1191 569.6 5.92 x 10'5 2.97 1093 557.3 4.84 X 10'6 1.66

An20 N t 1142 87.7 2.20 X 10-6 1.27 OH = 9740 ppm H/Si N c 1142 144.7 4.16 X 10-6 1.72 d = 3.66 + 0.37 [tm N t 1142 218.5 7.03 X 10-6 2.46 ß = 1.0% N t 1141 422.4 1.29 x 10-5 2.48 ct=2% N/P 1140 619.3 1.98 x 10-5 2.87 temperature steps P 1193 496.4 6.24 x 10-5 2.33 P 1273 475.2 2.37 X 10'4 3.54 P 1346 447.8 6.08 x 10-4 4.78

An21 1347 32.5 9.12 X 10'6 1.89 OH = 10,770 ppm H/Si 1347 53.3 1.38 x 10-5 2.18 d = 3.47 _+0.47 [tm 1346 84.7 2.17 x 10-5 2.10 cI) = 0.9% 1346 212.7 7.06 x 10'5 2.00 ct=2% 1346 310.4 1.41 X 10-4 3.13 temperature step 1346 392.8 2.69 x 10'4 4.45 1346 457.8 5.67 X 10-4 5.50 1442 212.0 8.18 X 10-4 5.49

An22 N t 1373 89.6 3.15 x 10'5 1.79 OH = 10,710ppm H/Si N c 1373 145.4 5.68 x 10'5 2.33 d = 3.26 _+0.43 N/P 1372 217.5 1.13 X 10-4 2.15 cI) = 0.9% pc 1372 315.7 2.55 x 10'4 3.70 ct=3% pc 1372 394.8 5.55 x 10'4 5.70 stressbackstep P 1373 451.6 1.74 x 10'3 5,47 few axial fractures N 1373 42.3 5.02 x 10'5 3.00

An23 N c 1474 32.5 6.49 x 10'5 1.95 OH = 9670 ppm H/Si N t 1473 55.3 1.01 X 10'4 2.31 d = 3.27 _+0.45 pm N/P 1473 139.9 2.94 X 10'4 3.29 •=0.9% N c 1472 81.5 1.74 x 10-4 3.32 ct=3% N c 1471 100.8 2.07 X 10'4 2.75 stressbackstep 26,022 RYBACKI AND DRESEN: CREEP OF ANORTHITE AGGREGATES

Table 1. (continued)

Sampleb T, K c•, MPa Comment

N/P 1470 148.4 3.39 x 10-4 3.70 P• 1470 176.1 5.05 x 10-4 4.70 P• 1471 218.5 9.67 x 10-4 6.23 An24 N • 1441 84.9 1.12 x 10-4 3.32 OH = 9230 ppm H/Si N/P 1439 135.3 2.06 x 10-4 3.57 d = 2.94 + 0.41 gm N/P 1437 161,7 2.55 x 10-4 3.50 (I) = 1,0% pc 1437 179.1 3.29 x 10-4 3.68 cz=9% pc 1437 190.0 4.06 x 10-4 4.02 initial length= 17 mm P• 1436 217.0 5.53 x 10'4 4.53 pc 1437 234.3 7.89 x 10-4 6.81 P 1437 270.1 1.70 x 10-3 8.34

An25 N c 1442 55.0 7.78 x 10-5 2.05 OH = 8500 ppm H/Si N • 1442 85.0 1.15 x 10'4 2.06 d = 3.32 + 0.45 gm N/P 1442 134.8 1.94 x 10-4 3.03 (I) = 1.0% pc 1441 199.5 3.76 x 10-4 3.62 c•=9% pc 1441 215.9 5.09 x 10-4 4.41 pc 1440 236.8 6.37 x 10-4 5.14 pc 1439 239.9 8.13 x 10-4 7.01 P 1440 255.6 1.18 x 10'3 5.74

An27 N/P 1317 318.3 6.92 x 10-5 2.04 OH = 8660 ppm H/Si pc 1317 353.1 1.12 x 10-4 2.33 d = 3.50 + 0.35 gm pc 1317 394.7 1.65 x 10-4 3.01 (I)= 2.5% pc 1317 426.2 2.32 x 10-4 3.41 (x= 12% pc 1316 446.2 3.66 x 10-4 3.74 p c 1317 506.7 5.56 x 10-4 4.16

An28 N 1468 48.6 1.12 x 10-4 2.02 OH = 500 ppm H/Si N c 1467 58.8 1.23 x 10-4 2.12 d = 2.72 + 0.41 gm N c 1468 90.0 1.76 x 10-4 2.22 ß =0.9% N c 1468 102.4 1.94 x 10-4 2.17 cz=0% N c 1467 157.0 3.03 x 10-4 2.60 pc 1467 180.0 3.65 x 10-4 3.23 pc 1467 197.7 4.57 x 10-4 3.82 pc 1467 211.8 5.41 x 10-4 4.35 pc 1467 245.1 7.94 x 10-4 5.13

An29 N c 1368 61.6 6.95 x 10-6 2.02 OH = 460 ppm H/Si N c 1368 83.3 8.69 x 10-6 1.76 d = 2.72 + 0.51 gm N c 1367 157.0 1.62 x 10-5 2.17 • = 0.9% N c 1365 232.1 2.69 x 10-5 2.40 cz=0% pc 1366 400.3 6.82 x 10-5 2.42 pc 1366 428.2 9.53 x 10-5 2.34 pc 1366 477.0 1.55 x 10-4 1.82

An31 N c 1223 105.5 7.14 x 10-6 2.14 OH = 12,360ppm H/Si N c 1222 216.7 2.17 x 10-5 2.44 d = 3.42 + 0.05 gm N 1222 275.3 3.31 x 10-5 2.25 (I) = 0.9% N/P 1222 326.1 4.68 x 10-5 2.92 (x= 12% P 1220 377.1 6.52 x 10-5 2.53 microfractures P 1220 433.6 7.08 x 10-5 2.57 P 1220 524.9 8.81 x 10'5 2.50 P 1220 595.7 9.21 x 10-5 3.16

An32 N c 1421 86.1 7.02 x 10-5 2.21 OH = 12,210 ppm H/Si N c 1420 96.5 7.89 x 10-5 1.93 d = 3.01 + 0.10 gm N c 1420 127.2 1.09 x 10'4 2.24 (I) = 0.8% N/P 1420 152.9 1.57 x 10-4 2.43 c•= 10% p c 1420 189.5 2.13 x 10-4 2.68 pc 1419 212.6 2.92 x 10-4 3.03 pc 1419 216.2 3.68 x 10-4 2.57 pc 1418 247.7 4.83 x 10-4 3.12 pc 1418 284.7 7.35 x 10-4 4.75 P 1419 289.3 1.08 x 10'3 4.73

An33 N c 1374 110.5 3.55 x 10'5 2.09 OH = 14,830ppm H/Si N c 1373 107.3 2.78 x 10-5 2.57 d = 3.18 +0.58 gm N c 1374 159.1 4.64 x 10-5 3.01 (I) = 1.1% N/P 1373 189.4 7.13 x 10-5 2.88 (x = 70% N/P 1373 243.7 1.14 x 10-4 2.56 Table 1. (continued) 26,023

Sampleb T, K c•,MPa g, s4 e, % Comment

pc 1371 264.5 1.74 x 10'4 3.03 pc 1372 280.4 2.21 x 10-4 3.45 pc 1372 300.7 3.10 x 10-4 3.96 pc 1372 322.6 4.67 x 10-4 4.35 P 1371 319.6 9.37 x 10'4 7.17 An35 Nc 1372 131.2 6.63x 10'5 2.05 OH= 14,850ppm H/Si Nc 1373 127.3 6.43x 10-5 2.01 d = 3.59+ 0.17pm N c 1372 157.8 8.57 x 10-5 2.63 tI) = 0.9% N/P 1373 208.8 1.98x 10-4 1.45 {x= 40%

An36 N 1191 131.1 1.08x 10'6 1.23 OH= 4390ppm H/Si N 1191 237.5 1.62x 10'6 1.46 d = 3.83+ 0.13pm N c 1190 348.8 1.91 x 10-6 1.94 tI) = 1.0% N c 1190 479.8 2.73x 10-6 1.70 {x=0%, dried

An39 Nc 1387 87.5 2.28x 10-5 2.58 OH= 7350ppm H/Si Nc 1386 134.9 3.45x 10-5 2.47 d = 3.48+ 0.59pm N/P 1388 199.3 6.14 x 10-5 3.22 tI) = 0.7% pc 1388 264.3 1.13x 10-4 3.41 {x=0%, dried pc 1388 294.6 1.56 x 10-4 4.23 pc 1388 319.3 2.23 x 10-4 4.22 pc 1388 367.4 3.42 x 10-4 5.58

An41 N 1430 50.0 3.70x 10-5 1.90 OH= 710ppm H/Si Nc 1429 72.9 4.38x 10-5 2.52 d = 2.55+ 0.21pm N c 1430 97.2 5.74 x 10-5 2.62 tI) = 1.0% N c 1429 148.4 8.46 x 10'5 3.20 {x= 0% pc 1428 236.4 1.64 x 10-4 4.06 pc 1429 261.4 2.28 x 10-4 4.30 pc 1429 289.1 2.86 x 10'4 4.67 pc 1429 331.2 4.12 x 10'4 5.66 pc 1429 355.5 5.95 x 10-4 6.06

An42 Nc 1389 77.2 1.13x 10-5 2.07 OH= 450ppm H/Si N• 1391 194.4 2.98x10 -5 3.14 d= 2.61+0.19 pm N • 1390 246.9 3.76 x 10-5 3.20 tI) = 0.9% P• 1390 312.5 5.70 x 10-5 3.91 ct = 0% pc 1390 331.5 7.24 x 10-5 3.97 P• 1390 366.5 9.80 x 10'5 4.34 pc 1390 424.1 1.48 x 10-4 3.65 pc 1390 453.6 1.98 x 10-4 4.23

An43 N 1253 77.3 5.96x 10-6 1.61 OH= 19,250ppm H/Si N• 1253 122.5 1.36x 10-5 1.79 d = 3.93+ 0.23pm N c 1250 169.4 1.88 x 10-5 2.59 tI)= 1.6% N c 1251 245.9 3.15 x 10-5 3.21 {x= 90% N 1251 314.4 4.38 x 10-5 2.75 microfractures N 1251 347.1 4.94 x 10-5 3.16 N/P 1245 402.9 5.30 x 10'5 3.48

An44 N 1480 36.6 9.30x 10-5 2.51 OH= 1060ppm H/Si Nc 1479 51.3 1.14x10 -4 2.87 d= 2.89+0.38 pm N c 1479 71.7 1.44x 10-4 3.20 tI) = 0.9% N c 1478 105.2 1.80 x 10-4 3.57 {x= 1% N c 1478 105.5 1.98 x 10-4 2.86 N c 1480 154.4 2.77 x 10-4 4.05 pc 1479 177.7 3.68 x 10-4 4.60 pc 1479 197.6 4.87 x 10-4 3.85 pc 1479 225.8 6.48 x 10'4 4.68

An45 N 1392 47.5 2.50x 10'5 2.16 OH= 16,220ppm H/Si Nc 1392 53.0 2.54x 10-5 2.49 d = 3.45+ 0.30pm N c 1391 76.2 3.42 x 10-5 2.61 tI) = 1.1% N c 1391 122.0 6.07 x 10-5 3.18 ct = 90% N/P 1391 178.0 1.17 x 10-4 3.30 pc 1390 216.6 1.88 x 10-4 4.05 P• 1390 245.0 2.82 x 10-4 4.70 pc 1390 253.2 3.55 x 10-4 5.69 P 1391 290.4 6.06 x 10-4 6.61

• T is temperature,c•is flow stress,• is (natural)strain rate, e is strain,OH is watercontent determined by FTIR, d is meangrain size, 4) is porosity,and {x is vol % of spheruliticgrains. bIndex N andP indicatediffusion and dislocation creep regime, respectively. cData are used for datafit to a powerlaw. 26,024 RYBACKI AND DRESEN: CREEP OF ANORTHITE AGGREGATES

stress, MPa 2O 4O 60 80100 200 400 600

i i i i

•I, 450 ppm H/SI (42) ß 500 ppm H/SI(28) • a X 7350ppmH/Sl(39)O 9670ppmll/Sl(23) - 10-3 •' 9720ppm H/SI (10) A 12520ppmH•i (4) O • -3,5 0 16220ppmHi(45) • oe• ,- -4,0 e• . .c_ o •

m -4,5 •o v x .

o

-5,0 10'5

' I ' I ' I ' I " 2,9 log

stress, MPa 40 60 80 100 200 400 600 -3,0 I I i I . ß I I 10 '3 drysamples z•' O, b [] 1388K 0 1368K -3,5 • 1478KV 1468 K0 1428 K ß ß ß zvß'•"•;;• .- ''" \\0.' ' .0[] o &.•.....-' -'' \ F'I'O,' 10.403 -4,0 . •-• ß- ' .O-" \ •ss •- •. ßß .. ,,[] -4,5 .-- - t•?.$•.' ø ' . ß ...' I• ß o .'' x\n=3

.10-5 -5,0 . •355•" ' ' Q- ' ' '

. 0 ß .. - n=l ß

ß. •3s5 •'- ' ' -5,5 ' / ' I " I ' I ' I ' 1,6 1,8 2,0 2,2 2,4 2,6 2,8 log stress, MPa

stress, MPa 20 40 60 80100 200 400 600 I I I I I I I I wetsamples ' ' $ ' C .- 10'3 (•)[] 1393K1493K 0[] 1373K1473K •(•) 1343K1443K (•(]:) 1423K1323K ß.• •, •'' ,' ß' • 1293K• 1273K • 1253K • 1223K • •,• O' O • Vl,-. •,e•• •' .

• -4,0 10'4 • • . . • v.' •-.. n=3 ' .'''' .'''' •-'' '•0 '• .-• • ' .c:_ -4,5 ...-" ' ..-"g • -5,0 .10-5 03 o •'• -'"' _.-"•' -5,5 tt13•' ' ' ' '. , -' ' ' ' r

' I ' I ' I ' I ' I ' I ' I ' 1,3 1,5 1,7 1,9 2,1 2,3 2,5 2,7 2,9 log stress, MPa

Figure3. Logstress versus log strain rate plots for deformedanorthite aggregates. (a) Strainrate which increases withincreasing stress, temperature, and water content over the investigated range of conditions.(b) and(c) Data for all dryand wet samples are separated into two deformation regimes with stress exponent n = 1 andn = 3, indicating diffusioncreep and dislocation creep, respectively. The boundary between the two regimes is shiftedtoward higher stresseswith decreasing temperature and water content. Dashed lines are best-fit regression lines. Experimental error is indicatedfor one datapoint. RYBACKI AND DRESEN: CREEP OF ANORTHITE AGGREGATES 26,025

Table 2. PowerLaw CreepParameters for Diffusionand Dislocation Creep of Dry andWet SyntheticAnorthite a

Regime n Q, kJmol 4 logA b, MPa-" pm'" s-1 mb

DiffusionCreep Dry 1.0 _+0.1 467 _+16 12.1 _+0.6 3 Wet 1.0 _+0.1 170 _+6 1.7 _+0.2 3

DislocationCreep Dry 3.0 _+0.4 648 _+20 12.7 _+0.8 0 Wet 3.0 _+0.2 356 _+9 2.6 _+0.3 0

"n is stressexponent, Q is activationenergy, A is preexponentialfactor, and m is grainsize exponent. hFor determination ofA thegrain size exponent was set to m = 0 fordislocation creep, and m = 3 for diffusion creep (see text for discussion).It shouldbe noted that given uncertaintiesare standard deviationsof multipleregression analysis and do not considerexperimental accuracy.

temperature, K 1500 1400 1300 1200 I , I , I • I • -4,5 - a diffusioncreep •. (•= 10 MPa -5,0 - 10-5 .

• -5,5 t.• - ._ ß.,-, -6,0 - 10-6

-6,5 Qdry----467ñ16 kJ mol '• •

6,5x10-4 7,0x10'4 7,5X10'4 8,0X10'4 8,5x10-4 9,0X10'4 1FF,K '1

temperature, K 1500 1400 1300 I • I • I -7 - 10'7 b dislocation(• = 10creep MPa . 8\\\\ • AQwet =356 ñ9kJ mof - 10-8

10'9

6,5x10-4 7,0x10-4 7,5xl0 '4 8,0x10-4 l/T, K'1

Figure4. Arrheniusdiagrams for (a) diffusionand (b) dislocationcreep of dryand wet specimens, normalized to 10 MPa differentialstress. The activationenergy for dry samplesis •300 kJ mol-• higherthan that for wet specimensin bothregimes. Experimental error is indicatedfor onedata point. 26,026 RYBACKI AND DRESEN: CREEP OF ANORTHITE AGGREGATES

3.1.2. Grain size sensitivity. Since we were not able to the smallerdislocation-free recrystallized grains show dihedral measurethe grain size exponentm explicitly, we set m = 0 for anglesclose to 120ø, especiallyat high temperatureand in dry dislocationcreep. For diffusion creep,m was assumedto be 3. samples.However, larger acicularor tabular grainscontaining Wang et al. [1996], Dimahoy et al. [1999], and Xiao [1999] few deformation twins are more common. Grain boundaries of the reportedm valuesfrom 2.5 to 2.9 +_0.3, implyinggrain boundary originalgrains are stronglysutured. Grains with high dislocation diffusion-controlledcreep for similar material in uniaxial and density and twin lamellae appear to be consumedby less triaxial creepexperiments. deformed grains (Figure 5a). The dislocations are 3.1.3. Activation energy. The activation energy Q for inhomogeneouslydistributed and very high dislocationdensities diffusioncreep of anorthitevaries from 170 + 6 kJmo1-1 for wet are foundwithin individualgrains. Dislocations show curved and aggregatesto 467 + 16kJ mo1-1 for dry samples (Figure 4a). For straightsegments. The dislocationpatterns are variablewith free dislocationcreep we foundactivation energies of 356 + 9 and648 dislocationsegments and some dislocationwalls (Figure 5b). + 20 kJmo1-1 for wet and dry samples, respectively (Figure 4b). Dislocationnetworks are scarcebut more frequentat higher The ratios of activationenergies for diffusion and dislocation temperatures.Theaverage dislocation density is p •1.4 x 1012m'2, creepare between1.4 for dry samplesand 2.1 for wet specimens. i.e., •3 times higher than in the startingmaterial. However, for This is in agreementwith activation energy ratios commonly technicalreasons, samples could not be quenchedunder load, so observedfor volumeto grainboundary diffusion-controlled creep the dislocationdensity represents a lowerbound. rangingfrom 1.5 to 2 [e.g., Schmidet al., 1977]. In deformed specimens,fluid inclusionsdecorate grain Two samples(An36 and An39) were dried but still retained boundaries.Intracrystalline fluid inclusionsare commonly 4500-7500 ppm H/Si (Table 1). Regressionanalysis of the few surroundedby glass.More triple junctionsare filled with Si- creepdata on these samples yields n = 1 andQ = 268_ 1 kJmol '1 enrichedmelt in deformedsamples than in the startingmaterial in the diffusion creep regime, which is betweenthe activation (Figure 5c). The amountof intracrystallineglass is small (<0.2 energiesof dry andwet samples(Table 3). vol %) in dry samplesand decreaseswith increasingannealing temperaturein dry specimens.At T>1323 K, wet samplescontain 3.2. Microstructure of Deformed Samples moreglass than at lower temperatures.In a few caseswe observed In almostall experimentsthe load was increasedin stepsuntil melt on two-grain boundariesin samplesdeformed at high sampleswere deformedin the dislocationcreep field. In SEM, no temperature. strongshape-preferred orientation of the grainswas observed, and no marked lattice-preferredorientation was seen in optical 4. Discussion microscopy using a gypsum plate. The deformed synthetic anorthite aggregatesshow more submicron-sizedrecrystallized The log stress-logstrain rate plots in Figure 3 indicatea low grainsand lessbig twins than the startingmaterial. Occasionally, stresssensitivity of the strain rate for dry and wet anorthite

Table 3. Compilationof PowerLaw CreepParameters for Diffusionand Dislocation Creep of SyntheticSilicate Aggregatesa

No. Rock log A Q n m H/Si, ppm Remark Reference

DislocationCreep Regime 1 An•0o 12.7 + 0.6 648 + 20 3 0 640 + 260 dry thisstudy 2 An•00 2.6 +_0.3 356 + 9 3 0 11500+ 2900 wet this study 3 O1 3.28 420 3 0 1500- 3000 wet, Q estimated Ka86 4 Qtz -7.18 135 3.1 0 1000 - 12600 wet, estimationof parameters Pa90

D!ffusionCreep Regime 5 O1 4.83 290 1 2 dry, Q, m estimated Ka86 6 O1 6.18 250 1 3 wet, Q, m estimated Ka86 7 An•00 12.1 + 0.6 467 + 16 1 3 640 + 260 dry this study 8 An•0o 1.7 + 0.2 170 + 6 1 3 11500+ 2900 wet thisstudy 9 Anmo 1.5 + 0.3 162 + 8 1 3 11500 +_2900 wet, parameterfit for T<1343 K this study 10 An•00 5.3 _+0.5 267 + 13 1 3 11500+ 2900 wet, parameterfit for T_>1343K this study 11 An•00 5.1 + 0.1 268 + 1 1 3 5870 + 2090 driedsamples An36 andAn39 this study 12 An•00 1.5 + 1.2 170 + 29 1 2.8 8500 + 1500 wet, predried,(refitted) Xi99 13 Anm0 1.4 +_0.4 151 + 40 1 2.8 22000 + 8000 wet, as received, (refitted) Xi99 14 An•00 15.8 +_0.6 585 +_45 1 2.9 430 + 120 dry (HUP), uniaxial Di99 15 An•00 8.6 +_0.6 377 +_38 1 2.5 5530 + 2470 wet (HIP), uniaxial Di99 16 An•00 9.0 + 0.8 388 + 22 1 2.5 3800 + 750 wet (HIP1), uniaxial, (refitted) Di99 17 An•00 8.1 + 0.5 361 + 13 1 2.5 7000 + 1000 wet (HIP2), uniaxial, (refitted) Di99 18 Anm0 10.6 420 +_38 1.3 2.5 wet, uniaxial Wa96 19 An60 7.2 338 + 27 1 2.7 wet, uniaxial,partial melt Di98

anis stressexponent, Q is activationenergy (kJ mol-•), A is preexponentialfactor (MPa -n •tm m sq), m is grainsize exponent, and T is temperature.The data indicatedwith "uniaxial"are derivedat 1 atm conditions,all othersare derivedat 300 MPa confiningpressure. Referencesare 1-2 and 7-11, anorthite(An10o), this study;3, 5-6, olivine (O1), Ka86 [Karato et al., 1986]; 4, quartz (Qtz), Pa90 [Patersonand Luan, 1990]; 12-13, anorthite(An•0o), Xi99 [Xiao, 1999] (the flow law parametersare refitted using multiple linear regressionanalysis); 14-17, anorthite(An•0o), Di99 [Dimanovet al., 1999](14 arehot uniaxially pressed, HUP, specimens,16 and 17 are separaterefits for hot isostaticallypressed, HIP, samples,subdivided into HIP1 andHIP2 sampleswith slightlydifferent water content); 18, anorthite(An•00), Wa96 [Wanget al., 1996]; 19, labradorire(An60), Di98 [Dimanovet al., 1998]. RYBACKI AND DRESEN: CREEP OF ANORTHITE AGGREGATES 26,027

..

Figure 5 TEM bright-fieldmicrophotographs of deformedanorthite aggregates. (a) Grainboundary migration of a strain-freerecrystallized grain toward grains with very high (tangled)dislocation density (arrow, sample An12). (b) Dislocationswhich are oftengently curved or straightsometimes form walls or networks(arrows, sample Anl 8). (c) Fluid inclusionssurrounded by glasslocated in triplejunctions or areintracrystalline (arrows, sample An4). 26,028 RYBACKI AND DRESEN: CREEP OF ANORTHITE AGGREGATES aggregatesat low stresseswith n = 1 and a transitionto a higher grain boundariesand the melt contentis <1 vol % [Hirth and stresssensitivity of n = 3 at high stresses.A transitionbetween Kohlstedt, 1995a; Dimanov et al., 1998]. the dislocationand diffusion creep field was also observedin 4.1.1. Activation energy. We found an activationenergy of other studiesof fine-grainedsynthetic aggregates, i.e., olivine 648+ 20kJ mol -• fordislocation creep of dry samples, whereas in [Hirth and Kohlstedt, 1995a, 1995b; Karato et al., 1986], the presenceof water it was reducedsignificantly to 356 + 9 kJ feldspar[Dimanov et al., 1998; Ji and Mainprice, 1986;Meyer et mo1-1.The activation energy for creepat hightemperatures T > al., 1993; Tullis and Yund, 1991; Xiao et al., 1996], calcite 0.5Tin (Tin is melting temperature)has been suggestedto be [Walker et al., 1990], anhydrite [Dell•4ngelo and Olgaard, similar to that of self-diffusion[Takeuchi and Argon, 1976]. 1995], and natural granitic aggregates[Dell'Angelo et al., 1987]. However, when dislocationclimb is difficult and recoveryis The stress at the transition between regimes decreaseswith slow,dynamic recrystallization will contributemore significantly increasingtemperatures (Figure 3a). to the release of stored strain energy [Cahn, 1983], and the Raj and Ghosh [1981] and Freeman and Ferguson [1986] observedactivation energy may reflecta mixed mechanism. suggestedthat the transitionbetween dislocation and diffusion Althoughthe processlimiting the creeprate in plagioclaseis creepwould depend on the grainsize distribution of the deformed not clear, it probablyinvolves breaking of Si-O and A1-O bonds aggregate;a broad grain size distributionresults in a broad in the feldsparlattice. Carpenter[ 1991] studiedthe kineticsof Si- transitionalregime. Wang [1994] found that the stressexponent Al exchangein syntheticdry anorthiteaggregates at 0.1 MPa may vary considerablydue to a small variation in grain size pressure using antiphase domain coarsening. He obtained around the critical size for which both mechanisms contribute to activationenergies ranging from 506 to 637kJ mol '1, depending the overall strainrate. The grain size distributionof our starting on the growth exponent. Recently, Liu and Yund [1992] material(Figure 2b) andthe bimodalgrain size distribution due to investigated NaSi-CaA1 interdiffusion by lamellar dynamic recrystallizationprobably both contributed to the homogenization.In the presenceof 0.1 wt % water, at 1.5 GPa observedtransition between regimes. pressure and temperatures<1248 K they found activation energiesof 371 and 303 kJ mo1-1for homogenizationin Huttenlocherplagioclase and peristerite,respectively. Baschek 4.1. Dislocation Creep Regime and Johannes[1995] also investigatedthe homogenizationof a At T • 1273 K the stressesrequired to deformthe samplesat peristeriteat 1 GPa pressureand an H20 mole fraction of 0.5. strainrates between•lx104 and lx10-5 s-• in the dislocation Theyobtained an activation energy of 465kJ mo1-1. Grove et al. creepfield exceededthe confiningpressure by a factorof •2. For [1984]determined a Q of 517 kJ mol-• for homogenizationof stressesexceeding the confining pressure,Goetze's criterion Huttenlocherlamellae in dry plagioclaseat 0.1 MPa pressure. [Evans and Kohlstedt, 1995] predicts the onset of dilatant Theseactivation energies for Si-A1 exchangeindicate that the microcracking.Also, at high stresses,power law creepbreaks kineticsof NaSi-CaA1interdiffusion are stronglyaffected by the down and the stressexponent increases with stress.Power law presenceof water. They are in the range of values that we breakdownstresses O'pL B are proportionalto the shearmodulus p; determined for dislocation creep, suggestingthat Si or A1 for metalsand ceramics, C•pt•B • 10 '3 p [Frostand Ashby, 1982] diffusion may control creep in the high-stressregime. This butmay be ashigh as • 10'2 p for silicates[Tsenn and Carter, conclusion is also consistent with the observation that the 1987]. This suggeststhat the power law breakdownstress for activation energiesdetermined for lattice diffusion of O and Ca anorthiteaggregates C•pLBis •200-250 MPa. However, we did not aresubstantially lower. For oxygen self-diffusion inanorthite the observea nonlinear increase ofn withstress upto stresses of values range from 162 _+ 36 kJ mol '1 [Ryerson andMcKeegan, •500MPa. Only in some experiments atthe highest stresses did 1994]to 236 _+ 8 kJmo1-1 [Elphick etal., 1988] under dry we observeaccelerated creep rates due to cracking.Since we did conditions.An activationenergy Q of 110+ 5 kJmo1-1 was found not measure volumetric strain, it is possible that cracking under wet conditions [Giletti et al., 1978]. For Ca lattice occurredat thehighest stresses but remainedundetected. diffusion,Behrens et al. [1990]obtained 313 kJ mol-• in dry The slightlycurved dislocation segments commonly found in Anco. the deformedanorthite samples suggest that climb is relatively 4.1.2. Comparison with other deformation studies. difficult. Strongly suturedgrain boundaries,bulging of grains, Experimentallyderived flow laws for dislocationcreep of and numeroussmall recrystallizedgrains suggest that grain plagioclaseare scarce.Montardi and Mainprice [1986] found a boundarymigration recrystallization is common [Tullis, 1983; stress exponent ofn •3.9and a very high Q of 1332 _+ 80 kJ mol '1 Tullisand Yund,1985]. In quartzite,Hirth and Tullis [1992] for uniaxialcreep of dry-synthetic anorthite samples with •,50 identifiedthree different dislocation creep regimes characterized grain size, which was possibly influenced by melting.Meyer et al. by differentrecrystallization mechanisms. At low temperatures,[1993] performed uniaxial creep tests on dry syntheticanorthite Hirth and Tullis[1992] describe dislocation creep accommodated aggregates with •,3 pm averagegrain size. Theydetermined n by grainboundary migration recrystallization (regime I). The 2.5,suggesting that the samples were deformed in thetransitional microstructuresof our deformed wet and dry anorthite samples regime with Q = 660+ 60 kJ mo1-1.Dimanov et al. [1998] aresimilar to themicrostructures described by Hirth and Tullis deformedfine-grained synthetic Anco with 0.1 wt % H20 in [1992]and to feldsparmicrostructures recently described by Post uniaxialcompression. At the transition between the diffusion to andTullis [1999] typical for low-temperature dislocation creep. dislocation creep field they reported Q= 670kJ mo1-1 and n •, 2- However, in our anorthitesamples deformed at elevated 3. Ji and Mainprice[1987] deformedalbite aggregates at 0.1 temperatures,subgrain boundaries were more frequently observed MPa andfound similar strength for "as-received"and predried thanin previousstudies. This suggestsan increasingamount of samples.For temperaturesbelow 1333 K theyobtained a stress recovery-accommodatedcreepat high T. Theslight increase in exponentn = 2.1 and an activation energy of524 _+ 23 kJ mo1-1. melt content in our experimentsshould not contribute With the exceptionof Montardiand Mainprice[1986] the significantlyto the deformationrate sinceit doesnot wet the reportedactivation energies are close to thevalue of Q = 648+ 20 RYBACKI AND DRESEN: CREEP OF ANORTHITE AGGREGATES 26,029 kJ mo1-1that we foundfor dislocationcreep of dry anorthiteand wet and dry Ab96, measured at 1.5 GPa pressure, plot 2 orders aggregates.However, composition, water content, and grain size of magnitudelower in strainrate at T • 1500K. The reasonfor variedbetween the studies.The activationenergy for dislocation this discrepancymay be againa differencein water fugacity. creepof oursamples with traceamounts of waterand deformed at Owingto the low activationenergy Shelton's [1981 ] datapredict 300 MPa confiningpressure is much lower than that for dry faster strain rates for deformationof plagioclaseat low samples,but it is alsolower than that for samplesdeformed at temperaturescompared to our results and those of Ji and atmosphericpressure in the presenceof water. The significant Mainprice[1987]. reduction of Q suggeststhat dislocation creep is strongly 4.2. Diffusion Creep Regime influencedby water fugacity. Shelton and Tullis [1981] and Shelton [1981] deformed In the low-stressregime we determineda stressexponent n = 1 naturalanorthosite and albite rocksin a solid-mediumapparatus for wet and dry samples.Since grain growth was slow in our at temperaturesbetween 973 K and 1373 K and 1.5 GPa experiments,we did not determinegrain size sensitivityof the confiningpressure. For stressesbetween 200 and 600 MPa they creep rate. As already mentioned,the grain size sensitivityis foundn = 3.2 andQ = 239 kJ mol-• for anorthosite.The stress assumedto be rn = 3 basedon the findingsof Dimanov et al. exponentwas found to be stress-dependent[Shelton, 1981], and [ 1999], Wang et al. [ 1996], and Xiao [ 1999] on similar material steady state was probably not reached in these experiments with comparablegrain size and range of stresses.An rn = 3 [Tullis, 1990]. For albite,Shelton and Tullis [1981] reportedn = suggeststhat grain boundarydiffusion-controlled creep operates 3.9and Q = 235kJ mol -•. Deformationof albite samples dried at in fine-grainedanorthite at low stresses.Tullis et al. [1996] and 873 K gavea stressexponent of •4 and Q = 431 kJ mol-• Tullis and Yund [ 1991] also describedgrain boundarydiffusion [Shelton,1981]. The reportedactivation energies are significantly creep in triaxially deformedfine-grained feldspar. At 600-1200 lower than for the dry and wet syntheticanorthite samples MPa confiningpressure and 1173 K temperaturewith •0.7 wt % investigatedin this study.The reasonfor this discrepancyis not water added, syntheticfeldspar aggregateswere deformedby clear but may be partly related to a substantiallyhigher water diffusion creep. However, in drier samples(•0.2 wt % H20), fugacityin the experimentsof Sheltonand Tullis [ 1981]. dislocationcreep dominated. The existing mechanical data for dislocation creep of 4.2.1. Comparison with other studies on feldspar plagioclaseare compiledin an Arrheniusdiagram (Figure 6). deformation.We found an activation energy of 467+ 16kJ mol -• Two setsof curvescan be distinguished:(1) dry Ab94is obtained for grainboundary diffusion creep of dry samples.The activation at 0.1 MPa [Ji and Mainprice, 1987], and our dry and wet An•00 energy for diffusion creep of wet samplesdeformed in the data intersectat •1500 K. The dry albite is strongerthan dry temperaturerange of 1153K to 1493K is 170 + 6 kJ mol-•. anorthite at low T, which may be related to different water However, the data may be subdividedinto a high- and a low- fugacity.(2) In comparison,Shelton's [ 1981] data for wet An?s, temperatureregime at •1343 K (Figure 4a). A separateregression

temperature, K 1500 1400 1300 1200 -3 , ' i , , 0-3 "•,• ... dislocationcreepofplagioclasec•=100MPa [•1 '-.:'-... [r .7J --...... -_..._-_.... ß ß1:--wet An,oo,this- study"-... - _

• -9' 3:..... wet Ab,,,Shelton [19811 -•.•.'...

- ß 6: .... dry Ab94,Ji and Mainprice[1987] -11 , • .... • .... • .... • .... • 10'• 6,5xl0 '4 7,0xl0 '4 7,5xl0 '4 8,0xl0 '4 8,5xl0 '4 l/T, K'1

Figure 6. Arrheniusplot of dislocationcreep of dry andwet plagioclase,normalized to 100 MPa flow stress.Dry (1) and wet (4) Anw0;confining pressure P = 300 MPa; wet (2) An?s;as-received material, P = 1.5 GPa, n = 3.2, Q = 239kJ mol -•, log A = -3.7MPa -n s -•' wet(3) Ab96; as-received, P = 1.5GPa, n = 3.9,Q = 235kJ mol -• logA =- 5.6MPa -n s '•' dry(5) Ab96; samples dried at 873 K, P = 1.5GPa, n = 4, Q = 431kJ mol -•, log A = 0.9MPa -n s'l; dry (6)Ab94; as-received material and specimens dried at 1303K, P = 0.1MPa, n = 2.1,Q = 524kJ mol -•, logA = 11.2 MPa-n s -•. Exceptfor ouraggregates all samples were obtained from natural rocks. Note that Carter and Tsenn [1987] refittedthe datafor wet Ab96using multiple linear regression analysis. They foundn = 2.8, Q = 245 kJ mol- •, andlog A =-2.3MPa -n s -•. 26,030 RYBACKI AND DRESEN: CREEP OF ANORTHITE AGGREGATES

temperature, K 1500 1400 1300 1200 -4 • I • I • I , I ! 10'4 grainboundary diffusion creep o f anorthosite .,...•,._•...•_.•,....•.•_(• = lO MPa, d 5 pm 10'6 -

, ß, --. 2 10'8

1' wet,triaxial, thisstudy 4 '•, 10'1ø 2:- -- wet, uniaxial, Dimanov et al. [1999] %• - ' 3:.... dry,triaxial, this study '• r

- 4: --- dry, uniaxial, Dimanovet al. [1999] :. -12 10'12 6,5X10'4 7,0X10'4 7,5x10'4 8,0X10-4 8,5X10'4 l/T, K'1

Figure 7. Arrheniusdiagram of grainboundary diffusion creep of syntheticanorthite aggregates, calculated for 10 MPa stressand 5 pm grainsize. Dry samplescontain a few hundredparts per million H/Si andwet materialseveral thousandparts per million H/Si. Uniaxial data were obtainedat atmosphericpressure, and triaxial data were obtainedat 300 MPa confiningpressure. Flow law parametersfor uniaxiallydeformed samples are given in Table3 (14 and 15).

for the data above and below temperaturesof 1343 K yields aggregatesat 300 MPa confiningpressure. His resultsare quite activationenergies of 267+ 13and 162 + 8 kJmol -• forhigh- and similarto ours (Table 3). low-temperaturediffusion creep, respectively(Table 3). We 4.2.2. Activation energy. Farver and Yund [1995a] found no microstructuralevidence for a changein deformation investigatedCa grain boundary diffusion in dry anorthiteand mechanismwith temperature.At elevated temperaturessome oxygen grain boundary diffusion in wet albite. They found melting may have occurredin the wet samples,leading to a activationenergies of 291and 68-83 kJ mol -•, respectively.Both weakeningand a higher activationenergy [Hirth and Kohlstedt, values are substantiallylower than the activation energies 1995a]. We thereforeconsider an activationenergy of 170 + 6 kJ measuredin this study, suggestingthat neither the diffusion of mol'• basedon the whole temperature range as a lowerbound for calciumnor oxygencontrol grain boundary diffusion creep of dry diffusion creep of wet anorthite aggregates.This value is and wet anorthiteaggregates. significantlylower than the activationenergies reported from Recently,Yund and Farver [1999] reportedactivation energy deformationexperiments on plagioclaseaggregates performed at of 176+ 61 kJmol -• forSi grainboundary diffusion in anorthite atmosphericpressure in the diffusioncreep regime [Dimanovet aggregates.The diffusionexperiments were performed at 0.1 MPa al., 1998, 1999; Ji and Mainprice, 1986; Mercer and Chokshi, pressure,and the sampleswere considereddry from sample 1993; Meyer et al., 1993; Wang et al., 1996; Montardi and preparation,but no FTIR data are available.A1 grain boundary Mainprice, 1986]. Recently, Dimanov et al. [1999] compiled diffusivitiesin feldsparsare not known. Dresen et al. [1995, diffusion creep data for anorthite aggregates.The activation 1996]obtained activation energies of 365 and425 kJ mol-• for energiesfrom these studies range from 590 to 770 kJ mol -• for dry grain growth of as-received(200 ppm H/Si) and dry (60 ppm and from 370 to 420 kJ mol-• for wet anorthitesamples, H/Si) anorthite, respectively, at atmosphericpressure. These respectively. values are in the range of activation energiesmeasured for In Figure 7 we compareour data with thoseof Dimanovet al. diffusion creep of dry anorthite,but a comparisonmay not be [1999]. At T < 1500 K all samplesdeformed at atmospheric straightforwardsince grain growth involves diffusion acrossthe pressureare considerablystronger than when deformedat 300 boundaryas opposedto diffusioncreep, which requirestransport MPa confiningpressure irrespective of water content; at 1173 K alongthe boundary. the differencein strengthis •,2 ordersof magnitudefor both wet 4.3. The Effect of Water and Confining Pressure and dry samples.At atmosphericpressure and high temperatures, Dimanov et al. [1999] observedfast dehydrationof waterpresent A major difficulty in investigatingplastic flow of silicatesin at grain boundaries.However, in the samplesdeformed at 300 deformationexperiments at elevatedpressures is to establish MPa confiningpressure, no significantdehydration was observed. chemicalequilibrium with respectto water [Patersonand Luan, In addition to the differencein water fugacity this differencein 1990]. This requiresthat the kineticsof volumediffusion of water dehydration may also account for the different strengthsof are fast enough to attain local equilibrium at experimental anorthite aggregatesobserved at 0.1 and 300 MPa confining temperatures and that the chemical environment is well pressure.Xiao [1999] also deformed syntheticwet anorthite controlled.Kronenberg et al. [1986] investigatedthe mobilityof RYBACKI AND DRESEN: CREEP OF ANORTHITE AGGREGATES 26,031

wt % H20 wt % H20 10'3 10'2 10'1 10'3 10'2 10'4 ,,,I , , , , , ,,,I ' ' ' ' , ,,'1 I 700 ,, ,i , i i I I i I I • i ' ' ' ' I Ill (• = 100 MPa, T = 1273 K, d = 10 pm i b 2' 600 - -6 12

500 - I m I

400-

300- 11

200 - [] diffusioncreep (P = 300 MPa) . [] diffusioncreep (P = 300 MPa) •._..,/, 1 a • (•)r-I dislocationdiffusion creep creep(P (P = 0.1=300 MPa)MPa) r-I diffusion creep (P= 0.1 MPa) ' -lO • dislocationcreep(P=300 MPa) lOO lOO 1000 10000 lOO 1000 10000 water content, ppm H/Si water content, ppm H/Si wt % H20 10'3 10'2 10'1 18 I I I • i • ß • , •l•l ' • I I I Illl 700 , I , I , I , I , I , I , I , I , I , I , I , I

. ß feldspar 16 C 60O - •I, quartz //ß1 ß7 14 ß olivine / / '•'" . •E 12 500 - . 3 / 18..,,, 10 '•400- •. 8 6 • I 6 / 2 5 6 11 •300 - o / 1 . c• 4 / ,- 6 o (•) dislocationcreep (P = 300MPa) 2 200 - / 12 ,' -- 2 . [] diffusion creep (P = 3000.1 MPa)MPa) 12• / -'13 d lOO ' "1 ' I ' I '"1 ' I ' I ' I ' I ' I ' I ' I ' I lOO 1000 10000 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 water content, ppm H/Si logA, MPa'" pm m s '1

Figure 8. (a-c) Variation of log strainrate, Q, and log A with log water contentof syntheticanorthite aggregates. Flow law parametersare given in Table 3. Strainrates were normalizedto T = 1273 K, cr= 100 MPa, and d = 10 pm. They increaseconsiderably with increasingwater content. However, the activation energy Q and the preexponentialconstant (log) A stronglydecrease with increasingwater content. The given error barsare thoseof the flow laws,reflecting the statisticalstandard deviation of regressionfits. (d) Plot of Q versuslog A showinga linear interdependenceand suggestsa compensationlaw for diffusion(open symbols) and dislocationcreep (solid symbols).The lines are calculatedby linearregression of the creepparameters for anorthiteobtained in this study. The resultsfor otherplagioclase rocks and for quartzand olivine are in reasonableagreement, suggesting that the SiO4tetrahedral structure with the incorporationof water determinesthe parametersof powerlaw creep.See text for discussion. hydrogen in potassium feldspar, and Dimanov et al. [1999] and diffusion creep strainrates in anorthiteincrease with water estimated diffusivities of molecular water in the same anorthite content at 300 and 0.1 MPa confining pressure,at least up to a materialas used in this study.Their resultssuggest that the water concentrationof 0.1 and 0.05 wt %, respectively.A diffusiondistance at 1423 K is •2 mm for hydrogenand •4 I.tm comparisonof the data setsindicates that the effect of confining for molecularwater in 2 hours.For the rangeof temperaturesof pressureappears to be smallrelative to changesin watercontent. this study,even the smallerdiffusion distance for molecularwater Paterson [1989] suggestedthat the dislocation creep rate is of the order of the average grain size of the anorthite increaseswith water fugacityfmo. Providedthat the rock is water aggregates. saturatedand in equilibriumwith respectto the chemicalpotential Figure 8a is a plot of log strainrate-log water content.The of water,this may be expressedby a relationof the form data are from this study, Xiao [1999], and the deformation experimentsat 0.1 MPa of Dimanov et al. [1999]. Dislocation • • fPH20- (3) 26,032 RYBACKI AND DRESEN: CREEP OF ANORTHITE AGGREGATES

For quartzite,Kohlstedt et al. [1995] and Gleasonand Tullis •0.1 wt % (Figure 8b). The data from experimentsperformed at [1995] inferred an exponentp • 1.0, suggestingthat (2OH)o is 300 MPa confining pressureshow reducedactivation energies the dominantpoint defect and an oxygenatom is replacedby a when comparedto experimentsperformed by Dimanov et al. (OH)2 group.Post et al. [1996] obtainedp • 2.0 from their data, [1999] on sampleswith comparablewater contentdeformed at indicatingthat (4H)si is the major defect where four hydrogen 0.1 MPa pressure.However, at atmosphericpressure the water atomsreplace a silicon atom. Post et al. also demonstratedthat fugacity is poorly defined. For this reason we estimatedthe quartz samples show a decreasein strengthwith increasing fugacity for our sampleswith different water content but a amountof water up to 0.3 wt %, with no furtherweakening for constantconfining pressureof 300 MPa using a multilinear higher water contents.McDonnell [1998] recently found that regressionto the data.This procedureyields an estimatedfugacity fine-grained synthetic forsterite aggregatesdeformed triaxially coefficient of •0.5 for both diffusion and dislocationcreep. with up to 0.1 wt % water presentare substantiallyweaker than However,as alreadymentioned above, this approachis only valid dry samples.On the basis of experimentaldata for quartz and if sampleswith low andhigh traceamounts of waterdeform with olivine, Ord and Hobbs [1989] suggestedthat the activity a similarrate-limiting mechanism, which has not beenconfirmed exponentis less than the stressexponent since large changesin yet. water activity lead to relatively small changesin flow stressat a given strain rate. Solution-precipitationprocesses appear to be 4.4. Isokinetic Effect relevantfor creepunder laboratoryconditions only if more than Figures 8b and 8c show that activationenergy Q and log A •0.5 wt % water is presentin fine-grainedfeldspar aggregates decreasewith increasingwater content.Q and log A are linearly [lhllis et al., 1996; Tullis and Yund, 1991] and quartzite [den related for diffusion and dislocation creep (Figure 8d). For Broket al., 1994; den Brok and Spiers,1991 ]. anorthite the Q-log A pairs obtained at different confining The water fugacityin samplesdeformed in this studycan be pressureand water content for a given creep regime form a estimatedfrom the water contentmeasured using FTIR and the straightline. The data from other studieson syntheticaggregates porosityof the samples.Behrens [1994] estimatedthe solubility of feldspar(e.g., points18 and 19 in Figure 8d), olivine (points3, of waterat 300 MPa PH20and 1273 K to be •7500 ppm I-I/Si. The 5, 6), and quartz (point 4) fit to a similar trend providedthat the watercontent in the dry samplesis substantiallyless, but cooling stressexponents n are close to 3 and 1 for dislocationand stage FTIR measurementssuggest that some of the inclusions diffusion creep, respectively.The data for quartz and olivine contain freezablewater. We considerit unlikely that the water deviate somewhatfrom the regressionlines determinedfor the precipitated during cooling and subsequentpressure release. anorthitesamples, but they containestimates of Q only (seeTable However, Doukhan and Trepied [1985] suggestedthat the 3). For olivine, data points 5 and 6 representtwo different criterion of chemicalequilibrium for isolatedwater bubblesis diffusionregimes with rn = 2 and 3, respectively.However, Hirth differentfrom that for a constantpressure reservoir. and Kohlstedt[1995a] found rn = 3 for olivine. To estimatewater fugacities,we assumethat the total amount This kind of relation between Q and log A is known as the of water measuredby FTIR is distributedin the pores.The ratio "compensationlaw" or "isokinetic effect" of diffusion. The of pore volume to water contentyields the specificvolume of temperaturedependence of the diffusioncoefficient D is usually water for which the temperaturedependent fugacity can be expressedin the form of an Arrheniuslaw retrieved from steam tables [Burnham et al., 1969; Haar et al., 1984]. For the range of experimentaltemperatures and at a D = Do exp (-H/RT), (4) pressureof 300 MPa this procedureobviously yields only a rough estimateof the fugacities;they range from •10 MPa for dry whereDo is preexponentialfactor and H is activationenthalpy. samplesto •150 MPa for wet specimens.Since we used an iron The compensationlaw describesthe linearrelation jacket, the oxygenfugacity is probablybuffered by iron wustite. Using the modifiedRedlich-Kwong equation of statefor H2-H20 logDo = logD*+ H/2.303RT* (5) fluid mixtures[Grevel and Chatterjbe,1992] predictsthat the water fugacityat experimentalconditions is •40% lower than the whereT* andD* arethe "isotemperature" and"isodiffusion first estimate. coefficient",respectively. T*,D* is thecrossover point in a logD- For anorthite, water can be incorporatedby the reaction 1/T plot where the Arrheniuslines for differentdiffusing species 2(CaA12Si208)+ 2xH20 <--->Ca2A14Si4_xH4xO16 + xSiO2, with x = 4 in a given mineral, or for a given speciesin different materials, for thesubstitution Si4+ <---> 4H +, or x < 4 forpartial substitution. intersect [e.g., Hart, 1981; Sorokin, 1992]. For example, the Alternatively,replacing 02- by 2(OH)'gives 2(CaA12Si208)+ compensationlaw may be applied to self-diffusionof ionic 2xH20 <--->Ca2A14Si4016_4x(OH)4x + 2xO, again with x = 4 for speciesin feldsparand olivine [Hart, 1981], siliconself-diffusion completereplacement, or lower otherwise.In both cases,the in silicates [Bejina and Jaoul, 1997], and divalent cation fugacityexponent p equalsx, suggestingp valuesbetween 0 and diffusionin olivine and garnet[Jaoul and Sautter, 1999]. 4. The compensationlaw is still not well understood.It may be To interpretthe effect of trace amountsof water and pressure due to the commonrelationship between activation enthalpy H on the creeprate of anorthiteaggregates, at leasttwo alternative and the preexponentialfactor Do to the Debye temperature, approachesare conceivable.First, it may be possiblethat the althoughit predictsa nonlinearinterdependence [Lasaga, 1981]. activationenergy for creepitself dependson waterfugacity since Dowry [1980] and Zheng and Fu [1998] found a stronglinear the concentration of extrinsic water-related defects in correlationbetween anion porosityand oxygendiffusivity for a thermodynamicequilibrium changes with fugacity.Second, the wide rangeof minerals.Fortier and Giletti [1989] establisheda rate-limitingcreep mechanism may changeas a functionof water similarrelation between oxygen diffusion in silicatesand the total content.A combinationof both processesis possible. ionic porosity,suggesting that Do and H are both affectedby the Our observationis that the activationenergies for diffusion ionic porosity. Hart [1981] and Bejina and Jaoul [1997] and dislocationcreep changewith water contentat least up to explainedthe interdependenceof H and Do by the relation RYBACKI AND DRESEN: CREEP OF ANORTHITE AGGREGATES 26,033 betweenDo and the activationentropy S (of defectformation and 1500 • I I .... I .... I • , , • I , , \ \ '. hydrostaticpore pressure migration). The compensationlaw then infers a relationship betweenS and activationenthalpy H. Bejina and Jaoul [1997] pointedout that D* hasa pureentropic significance, e.g., it is the "" __ - - value of D at H = 0. 1000 - A similar compensationbehavior may be expected for t .. 3o .... diffusion and dislocation creep of feldspar since both creep mechanismare probablyrate limited by Si or A1 diffusion,with Do incorporatedin the preexponentialfactor A. Performinga 500 linear regressionon our data pointsyields Q = 281 + 28.9 log A for dislocationcreep of anorthiteand Q = 121 + 28.6 log A for diffusion creep. From the slope b of these regressionlines the ..... - ...... •';:...... -. NF, 30 •m compensationtemperatures T* are calculated from the relation T*

= b /2.303 R. T* is •1510 K and 1495 K for dislocationand 0 ' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' diffusioncreep, respectively. Subdividing our data for diffusion 700 750 800 850 of wet anorthiteinto temperatureregions above and below 1343 T,K K (see Figure 4a), resultsin parametersQ and log A that are in good agreementwith the compensationline (points9 and 10 in stress, MPa Figure 8d). Moreover,creep parameters of dry and wet anorthite o 2O 40 60 80 lOO match a singlecompensation line. We concludethat even when 500 i I I [ I • I , extrinsic(H20) defectschange the activationenergy for diffusion, •, = 10'•4S'1 the creep rate is probably still controlledby a single (rate o o . limiting) species,i.e., Si or A1. ,,,/ 600- Bejina and Jaoul [1997] found a compensationlaw behavior • 7oo- for silicon self-diffusion in silicates as a first-order approximation,suggesting a commonmechanism for Si migration 8oo- in minerals with structures based on the SiO4 tetrahedron. However,in detail, forsteriteand quartzshowed slightly different E 900- compensation lines, possibly related to their different crystallographicstructures. A similar explanationmay hold for 1000 - the compensationbehavior shown in Figure 8d. A differencein 1100 - .... quartz, Paterson and Luan [1990] the structure between different silicate minerals may be / / responsiblefor the small deviationof quartzand olivine from the -- -- - anorthite,olivine, Karatothis studyet al. [1986] b 1200 plagioclasecompensation line. ' I ' I ' I ' I '

Figure 9. (a) Extrapolationof wet anorthitedislocation creep data 5. Geological Applications to naturalstrain rates of 10-•3-10-•5 s -•. Also the intersectionwith Feldsparis a majormineral constituent of the Earth's crustand friction strengthcalculated with Byerlee'sfriction law under often containstrace amountsof water [Beran, 1987; Hofmeister hydrostaticpore pressureconditions is indicated. The mean and Rossman, 1985]. Crustal shear zones commonly show crustaldensity was set to 2.8 g crn-3. TF is thrustfault evidencefor deformationin the presenceof aqueousfluids [e.g., (compressive)regime, NF is normal fault (extension)regime. Kenkmann, 1997; Kronenberg et al., 1990; Nakashirna et al., Geothermalgradients of 20 and30 K km-• areassumed. (b) 1995]. To extrapolateour experimentaldata to naturalconditions, Stress-temperaturediagram of dislocationcreep at 10-•4 S -• strain we focus on the deformation behavior of wet anorthite. rate for wet syntheticquartz, wet syntheticanorthite, and wet Passcrierand Trouw [1996], Pryer [1993], and Tullis [1983] syntheticolivine. Power law parametersare given in Table3. reviewed the deformationmechanisms operating in naturally deformed feldspars.A transition between dislocationcreep accommodatedby grainboundary migration recrystallization (low ratio of porepressure to overburdenpressure. The transitionfrom T) and by subgrainrotation recrystallization(high T) was brittle frictional sliding to crystal-plasticflow of wet anorthite suggestedto occur under amphibolitefacies conditions.In aggregatesoccurs at temperaturesof z725-780 K for a strainrate quartzo-feldspathicultramylonites deformed at greenschist-to of 10-•4 s '•, geothermalgradients ranging from 20 to 30 K km-•, granulite-faciesconditions, high ductilitysuggesting superplastic and a hydrostaticfluid pressuregradient (Figure 9a). The flow and diffusion creep accommodatedby grain boundary temperatureat the transitionchanges by •25 K for +_1order of slidingprocesses has been commonlyobserved [Allison et al., magnitudechange in strainrate. This temperaturerange is in 1979; Jensen, 1985; Olsen and Kohlstedt, 1985; White, 1990; goodagreement with temperatureestimates of 723-773 K for the White and Mawer, 1986; Fliervoet et al., 1997; Kenkrnann, onsetof dislocationcreep in naturallydeformed feldspars based 1997]. on microstructuralobservations [Voll, 1976; Pryer, 1993]. Figure 9a shows calculatedflow stressprofiles for wet De Bresseret al. [1998] proposedthat grain growth anorthitein comparisonwith frictionalstrength determined by during diffusioncreep and grain size reductiondue to dynamic Byedee's[1978] law. The frictionstress for a thrustfault is given recrystallizationaccompanying dislocation creep may reach a by CrTF= [2 % COS{b+2 Sv (1-,;1,) sin{b] / (1-sin½),and for a normal dynamicequilibrium at the boundaryof the two creepregimes. faultby O'NF= [2 r0 COS{b+2 Sv (1-,;1,) sin• / (l+sin½),where r0 is Extrapolatedflow laws for dislocationand diffusioncreep of wet cohesion(50 MPa), {bis angleof internalfriction (31 o), and,;1, is anorthiteintersect at a grain size of •15-70 !.tmfor strainrates of 26,034 RYBACKIAND DRESEN:CREEP OF ANORTHITEAGGREGATES

10-•-10-•3s-•. That is in agreementwith grain size distributions Aines, R.D., and G.R. Rossman, Water in minerals?A peak in the foundfor mylonitesand ultramylonites in shear zones. infrared,J. Geophys.Res., 89, 4059-4071,1984. A comparisonof strength profiles for quartz,feldspar, and Allison,I., R.L.Barnett, and R. Kerrich, Superplastic flowand changes in crystalchemistry of feldspars,Tectonophysics, 53, T41-T46, 1979. olivineextrapolated toa strain rate of 10-•4 s -• isgiven in Figure Baschek, G., and W. Johannes,The estimationof NaSi-CaA1 9b.The effect of water fugacity on dislocation anddiffusion creep interdiffusionrates in perisriteby homogenizationexperiments, Eur. rateof theseminerals is not alwayswell constrained.Therefore it J. Mineral., 7, 295-307, 1995. wasnot consideredin extrapolatingthe data.The flow lawsare Behrens,H., Structural,kinetic and thermodynamicproperties of basedon experimentsperformed on wet,fine-grained synthetic hydrogenin feldspars,in Kinetic Processesin Minerals and Ceramics:EFS workshop on CationOrdering, pp. 1-7,Eur. Sci. aggregatesusing a gas deformationapparatus at 300 MPa Found.,Cambridge, England, 1994. confiningpressure. Considering these flow laws as the most Behrens,H., W. Johannes,and H. Schmalzried,On the mechanismsof reliableones with respect to equilibriumwith water, quartz is cationdiffusion processes in ternary feldspars, Phys. Chem. Miner., muchweaker than plagioclase in the dislocation creep regime up 17, 62-78, 1990. Bejina,F., andO. Jaoul,Silicon diffusion in silicateminerals, Earth to •1100 K temperature,and olivine is severaltimes stronger Planet.Sci. Lett., 153, 229-238, 1997. even at 1200 K. Bell,D.R., P.D. Ihinger, and G.R. Rossman, Quantitative analysis oftrace OH in garnetand pyroxenes, Am. Mineral., 80, 465-474, 1995. 6. Conclusions Beran,A., OH groupsin nominallyanhydrous framework structures: An infraredspectroscopic investigation of Danburite and Labradorite, Phys.Chem. Miner., 14, 441-445,1987. We examinedthe deformationbehavior of fine-grainedBrace, W.F., and D.J. Kohlstedt, Limits on lithospheric stress imposed by syntheticanorthite aggregates at 300 MPa confiningpressure. laboratoryexperiments, J. Geophys. Res., 85, 6248-6252, 1980. Wet samplescontain •0.07 wt % water,and dry specimensBurnham, C.W., J.R. Holloway,and N.F. Davis,Thermodynamic contain•0.004 wt % H20, incorporatedas fluid inclusionsand propertiesof water to 1000øCand 10000 bars, Spec. Pap. Geol. Soc. Am., 132, 1-96, 1969. probablyas pointdefects. Depending on the appliedstress, Byerlee,J., Friction of rocks, Pure Appl. Geophys., 116, 615-626, 1978. temperature,and water contentof samples,we observeda Bystricky,M.J., High temperaturedeformation of clinopyroxene- transitionfrom diffusion creep with a stressexponent n • 1 to plagioclaseaggregates, Ph.D. thesis, 159 pp., Dep. of Geosci.,Pa. dislocationcreep with n • 3. Microstructuralobservations of StateUniv., UniversityPark, 1998. Cahn,R.W., Recovery and recrystallization, in Physical Metallurgy, vol. samplesdeformed in thedislocation creep regime suggest that 2, editedby R.W.Cahn and P. Haasen,pp. 1595-1671, Elsevier Sci., grain boundarymigration recrystallization is an important New York, 1983. accommodationprocess. Grain boundary diffusion is expectedin Cadstan,Y., Thetransition from high temperature creep to fracturein thelow-n regime based on comparisonwith published creep Marylanddiabase, J. Geophys.Res., 87, 6781-6790,1982. experimentson similar material. Carpenter,M.A., Mechanism and kinetics of A1-Siordering in anorthite, I, Incommensuratestructure and domain coarsening, Am. Mineral., In thetemperature range investigated drysamples are stronger 76, 1110-1119, 1991. thanwet samples.The activationenergy for bothdiffusion and Carter,N., andM. Tsenn,Flow properties of continental lithosphere, dislocationcreep of wet specimensis about300 kJ mol-• lower Tectonophysics,136, 27-64, 1987. thanthat for dry samples. This difference may be due to a gradual Chen,W.P., and P. Molnar, Focal depth of intracontinental andintraplate changefrom intrinsic to extrinsicwater-related point defects earthquakesand their implicationsfor the thermaland mechanical propertiesof thelithosphere, J. Geophys. Res., 88, 4183-4214,1983. controllingthe creep rate or dueto a dependenceof Q onexternal DeBresser, J.H.P., C.J. Peach, J.P.J. Reijs, and C.J. Spiers, On dynamic variables(water fugacity) for theseaggregates when only trace recrystallizationduring solid state flow: Effects of stressand amountsof waterare incorporated. temperature,Geophys. Res. Lett., 25, 3457-3460,1998. In the diffusioncreep regime, anorthite deformed at 300 MPa DelrAngelo,L.N., andD.L. Olgaard,Experimental deformation of fine grainedanhydrite: Evidence for dislocationand diffusion creep, J. pressureis considerablyweaker than when deformed at 0.1 MPa, Geophys.Res., 100, 15,425-15,440,1995. probablydue to differencesin waterfugacity and due to different DelrAngelo,L.N., J. Tullis, and R.A. Yund, Transitionfrom dislocation amountsof water specieson grain boundaries.For dislocation creepto melt-enhanceddiffusion creep in fine-grainedgranitic creepwe foundhigher activation energies in comparisonto aggregates,Tectonophysics, 139, 325-332, 1987. Den Brok, S.W.J.,and C.J. Spiers,Experimental evidence for water publisheddata under dry and wet conditions, predicting higher weakeningof quartziteby microcrackingplus solution-precipitation strengthat low temperatures. creep,J. Geol. Soc.London, 148, 541-548, 1991. A compensationlaw-like behavior was observed for Den Brok, S.W.J.,J. Meinecke,and K. R611er,Fourier transform IR dislocationand diffusioncreep of plagioclase,similar to the determinationof intragranularwater contentin quartzites isokineticeffect found in manydiffusion experiments. This experimentallydeformed with and withoutadded water in the ductile deformationfield, J. Geophys.Res., 99, 19,821-19,828,1994. suggeststhat diffusion is controlledby the same ionic species (Si Deng,Z.Y., J.L. Shi, Y.F. Zhang, T.R. Lai, and J.K. Guo, Creep and and/orA1) over a widerange of conditions inboth regimes. creep recovery behaviourin silicon-carbide-particle-reinforced alumina,J. Am. Ceram.Soc., 82, 944-952,1999. Acknowledgments.We are verygrateful to RichardWirth for the Dimanov,A., G. Dresen,and R. Wirth,High-temperature creepof TEM investigations.Alexandre Dimanov contributed through partiallymolten plagioclase aggregates, J. Geophys. Res., 103, 9651- constructivediscussions, and Michael Naumann afforded experimental 9664, 1998. assistance.We thank Klaus R611erfor low-temperatureFFIR Dimanov,A., G. Dresen,X. Xiao,and R. Wirth,Grain boundary measurements,Stefan Gehrmann for preparationof thin sections,Karin diffusioncreep of syntheticanorthite aggregates: The effect of water, Peachfor preparation of TEM sections,Ursula Glenz for SEM assistance, J. Geophys.Res., 104, 10,483-10,497,1999. andRudolf Naumann for performingfluorescent X-ray analysis. We Doukhan,J.C., and L. Trepied,Plastic deformation of quartz single acknowledgethehelpful and constructive comments provided by Jan crystals,Bull. Mineral., 108, 97-123, 1985. Tullis,Greg Hirth and an anonymous reviewer. 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