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The effect of water on the viscosity of a haplogranitic melt under P-T-X conditions relevant to silicic volcanism

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 The viscosities of hydrous haplogranitic melts synthesized by hydrothermal fusion at 2 kbar pressure and 800 to 1040° C have been measured at temperatures just above the glass transition and at a pressure of 1 bar using micropenetration techniques.
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  Contrib Mineral Petrol (1996) 124: 19 —  28   Springer-Verlag 1996 D.B. Dingwell · C. Romano · K.-U. Hess The effect of water on the viscosity of a haplogranitic melt under P-T-X   conditions relevant to silicic volcanism Received: 17 August 1995/Accepted: 8 January 1996 Abstract  The viscosities of hydrous haplograniticmelts synthesized by hydrothermal fusion at 2 kbarpressure and 800 to 1040 ° C have been measured attemperatures just above the glass transition and ata pressure of 1 bar using micropenetration techniques.The micropenetration viscometry has been performedin the viscosity range of 10   Pas to 10   Pas. Thesamples ranged in water content from 0.4 to 3.5 wt%.For samples with up to 2.5 wt% H  O, the water con-tentshave been determinedusing infrared spectroscopyobtained before and after each viscometry experimentto be constant over the duration of the measurements.Above this water content a measurable loss of wateroccurs during the viscometry.The viscosity data illustrate an extremely nonlineardecrease in viscosity with added water. The viscositydrops drastically with the addition of 0.5 wt% of waterand then shallows out at water contents of 2 wt%. Anadditional viscosity datum point obtained from theanalysis of fluid inclusions in a water-saturated HPG8confirms a near invariance of the viscosity with theaddition of water between 2 and 6 wt%. Thesemeasurements may be compared directly with the dataof Hess et al. (1995, in press) for the effects of excessalkali and alkaline earth oxides on the viscosity of HPG8 (also obtained at 1 bar). The viscosity of themelts, compared on an equivalent molar basis, in-creases in the order H  O ( (Li  O ( Na  O ( K  O ( Rb  O,Cs  O ( BaO ( SrO ( CaO ( MgO ( BeO). The extraordinarydecreasein melt viscosity withadded water is poorly reproduced by the calculationscheme of Shaw (1972) for the range of water contentsinvestigated here. The speciation of water in the quen- D.B. Dingwell ( ) · C. Romano, K.-U. HessBayerisches Geoinstitut, Universita¨t Bayreuth, D-95440 Bayreuth,GermanyEditorial responsibility: J. Hoefs ched glasses can be used to quantify the dependence of the viscosity on hydroxyl content. Considering only thehydroxyl groups as active fluidizers in the hydrousmelts the nonlinearity of the viscosity decrease and thedifference with the effects of the alkali oxides becomeslarger. Consequences for degassing calcalkalinerhyolite are discussed. Introduction A serious gap in present knowledge of the propertiesof degassing subvolcanic silicic magmas is thedescription of melt viscosity at the  P - ¹ - X  conditionsimmediately prior to and during volcanic eruptions.Modeling of the dynamics of such systems is flourish-ing at present and a further optimization of modelsfor the kinetics of melt degassing, vesiculation andfragmentation would be aided greatly by reliable vis-cosity data obtained under the appropriate  P - ¹ - X conditions.Equally important is the realization that fully gene-ralizable models for the  P - ¹ - X  dependence of meltviscosity will only be achievable when structure pro-perty relationships for the melts of interest, based onsystematicstudies of the variationof both structureandproperties with  P , ¹ and  X , are available.Both of these considerations, together with the ob-servations from glass transition studies (Dingwell andWebb 1992) and recent viscometry (Lejeune et al. 1994;Schulze et al. in press) that present methods of estima-ting melt viscosity are not very accurate at low watercontents, have led to the present investigation. Wehave chosen to study of the influence of minor amountsof water on the viscosity of a haplogranitic meltcomposition serving as a model for calcalkalinerhyolite. The results provide the most precise compari-son of the effects of differing network-modifyingcomponents on the melt viscosity hitherto possible andsystematics emerge in the temperature and composition  dependence of the viscosity of granitic melts in general,one of the outstanding problems remaining in meltphysics.The present measurements are focused on the vol-canologically vital but previously underinvestigatedre-gion of water contents of 0.4 to 3.5 wt%. By investigat-ing such melts at 1 bar pressure and very low temper-atures of 500 to 750 ° C we access a range of viscositiesof 10   to 10   Pas which corresponds to those of cal-calkaline rhyolites during the final stages of degassing,vesiculation and/or fragmentation. The results pro-vided below are unfortunately not well predicted byavailable calculation schemes based on data obtainedat much higher water contents. We conclude that thediscrepancies between experiment and calculation arelarge enough that the predictions of much modelingwork regarding the degassing of rhyolitic melts, i.e.,those melts involved in highly explosive, rhyolitic anddacitic volcanic systems, are in need of revision. Method SynthesisFor our investigations we have chosen as a base composition a hap-logranitic melt composition (designated HPG8 by Holtz et al. 1992)which lies near the 1-kbar (pH  O) ternary minimum in the systemSiO  -NaAlSi  O  -KAlSi  O  . This melt composition was chosen toenable a direct comparison of the present results for the influence of water on melt viscosity with the data provided by Hess et al. (1995,in press) for the effects of alkali and alkaline earth oxides and toserve as a model for a calcalkaline rhyolites.The base melt used in the present study was generated by directfusion of powder mixes of oxides and carbonates at 1 atm and1400 —  1650 ° C. The fusions were performed in thin-walled platinumcrucibles with a MoSi   box furnace. The partially fused products of this initial fusion were transferred in the crucibles to the viscometerfurnace and a stirring spindle was entered into the samples fromabove. The samples were fused for hours to days until inspection of the stirring spindle, removed periodically from the melt, indicatedthatthe meltswerecrystal- andbubble-free. Themelts were removedfrom the furnace and allowed to cool in air in the Pt crucibles. Theglass composition was analyzed by solution-based ICP-AES (induc-tively coupled plasma-atomic emission spectrometry) methods. Theresults of a bulk anhydrous analysis are presented by Holtz et al.(1992).Glass cylinders (diameter: 3 mm; length: 3 —  4 mm) were drilled bywater-cooled diamond coring tools, cleaned ultrasonically inacetone and then dried at 110 ° C to remove any residue of acetone.Glass samples ( & 100 mg) were then loaded together with knownamounts of doubly distilled H  O in capsules formed from platinumtubing (outer diameter:3.2 mm; length:10 mm; wall thickness0.1 mm) and sealed with an arc-welder.The capsules were checked for possible leakage by testing forweight loss after drying in an oven at 110 ° C for at least one hour.After an hour at 110 ° C, the added water was considered to bedistributed randomly in the platinum capsule, and thus around theglass sample. Synthesis of hydrous glasses was performed with twodifferent apparatus.The experiments performed at 800 ° C were carried out in ex-ternally heated rapid quench cold seal bombs operating vertically(water as a pressure medium). In this apparatus the temperature iscontrolled by Ni —  NiCr thermocouple (accuracy $ 10 ° C). The pres-sure has an accuracy of  $ 20 bar. The experiments at 1040 ° C and2 kbar were placed in TZM bombs (Ar as a pressure medium) Thetemperature was recorded by a Ni —  NiCr thermocouple (accuracy $ 15 ° C) and the pressure was monitored with a strain-gaugemanometer (accuracy $ 50 bar). The samples were held for a timesufficient to allow complete homogenizationof H  O dissolved in themelt by diffusion through the sample (run durations ranged from7 to 17 days).After the high pressure - high temperature dwells, the sampleswere quenched rapidly and isobarically by dropping the sample intothe cold part of the bomb (estimated quench rate 200 ° C/s). Specialcare was given during the quench to maintain isobaric conditions byopening the vessel to the pressure line (2000    bar).The quenchedrun products consistedof crystal-freelimpid glass-es. Doubly polished sections of 1 mm thickness were prepared formicropenetrationviscometry by grinding with alumina abrasive andthen polishing with diamond paste using water as a lubricant.Polished samples were cleaned with acetone to remove epoxy. Thehomogeneity of the glasses was tested by analysis with an infraredspectrometer (see below).Micropenetration viscometryThe viscosities were measured using a micropenetration technique.This involves determining the rate at which an Ir-indenter undera fixed load moves into the melt surface. These measurements wereperformed in a BAHR DIL 802 V vertical pushrod dilatometer. Thesample is placed in a silica rod sample holder under an Argon gasflow. The indenter is attached to one end of an alumina rod, which isattached at the other end to a weight pan. The metal connectionbetween the alumina rod and the weight pan acts as the core of a calibrated linear voltage displacement transducer (LVDT). Themovement of this metal core as the indenter is pushed into the meltyields the displacement. The present system uses hemispherical Ir-indenters with diameters of 2 mm, and a force of 1.2 N. The absoluteshear viscosity is determined from  " 0.1875  Ptr     (1)(Pocklington 1940; Tobolsky and Taylor 1963) for the radius of thehalf-sphere  r , the applied force  P , indent distance   , and time t ( t " 0,   " 0 upon application of the force). The measurements areperformed over indentation distances of less than 100   m. Thetechnique yields an absolute determination of viscosity up to1100 ° C in the range of 10   to 10   Pas. Viscosities determined onthe DGG-1 standard glass using 3 mm samples have been repro-duced within an error of  $ 0.06 log units (see Fig. 1).All samples were heated up to the measuring temperature, heldat this temperature for 1 hour to allow thermal equilibration andcomplete structural relaxation of the sample and then the viscositymeasurement was performed. After the measurement, each samplewas cooled at approximately 20 K/min.The advantages of the micropenetrationtechnique are the abilityit provides of using relatively small amounts of sample and simplesample geometry constraints compared to other high-viscositymethods such as parallel plate or fiber elongation (cf. Dingwell et al.1993; Dingwell 1995a). Using the formulation of Pocklington (1940)the penetration distance should be small compared to the sampleheight. As this criterion cannot always be honored in our presentexperiments,wehave evaluatedthe effect of samplesize on a DGG-1standard glass with a thickness of 1 mm (Fig. 1). Between 10   to10   Pas appears a slight, but significant deviation to highervalues of the determined viscosities from the calculated values re-ported in the Deutsche Glastechnische Gesellschaft data sheet. Thedata listed in Table 2, all performed on samples of 1 mm thickness,are corrected for this sample size effect.20  Fig. 1  Viscosities determined on the Deutsche GlastechnischeGesellschaft soda-lime glass-melt viscosity standard (DGG-1) usingthe micropenetration method. Micropenetration viscometry has theadvantage of applicability to very small sample dimensions. Themeasurable influence of reducing size to 1 mm thickness is incorpor-ated as a small correction factor based on the data presented hereAn important aspect of the present study is the demonstration of the stability of water-bearing samples during measurement at 1 atm.On each of the samples 526 —  3, 527 —  1, 527 —  2 and 144 —  1 three to fourviscosity measurements were performed with no drift in viscosityvalues as a function of time. This observation, combined with thelack of evidence for concentration gradients of water in spatiallyresolved IR measurements (described below), argues against signifi-cant water loss. Nevertheless the shapes of the indentation curvesfrom the present experiments show minor irregularities which mayindicate a very thin ( ( 10   m) boundary layer. Although theseirregularities add noise to the viscosity determinations, the influenceof such effects on the derived viscosities remains within the quoteduncertainties previously obtained by this method (Hess et al. 1995 inpress). This is consistent with the evidencefrom the sample size effectnoted above that the stress and resultant strain are distributed overthe lengthscale of the entire sample ( " 1 mm).Control of water contentWater contents of the samples, both as total water dissolved in themelt and as the fractions of water dissolved as molecular water andas hydroxyl groups, were determined by IR spectroscopy. Becausethe present samples are investigated under water-oversaturated con-ditions at 1 bar, samples were analyzed before and after each viscos-ity measurement to check for water loss during viscometry. Sampleswere then positioned over an aperture in a brass disc in order to aimthe beam at areas of interest in the glasses. A Bruker IFS 120 HRfourier transform spectrophotometer was used to obtain transmis-sion infrared spectra in the NIR region (2500 —  8000 cm   ), usinga W source, CaF   beamsplitter and a narrow band MCT detector.The spectrophotometer operated at a resolution of 4 cm   witha scanning speed of 20.0 KHz and the objective used was a Casseg-ranian 15X. Typically, 200 —  1000 scans were collected for each spec-trum. Background was recorded and subtracted from every spec-trum. The two bands of interest of this regions are at 4500 cm   and5200 cm  .TheH  O contentof the sampleshasbeen determinedby measur-ing the heights at the maximum of the absorption bands near 4500and 5200 cm   attributed respectively to the combination stretch-ing # bending mode of X-OH groups and a combination of stretch-ing # bending modes of molecular water groups (Stolper 1982a;Newman et al. 1986).For evaluation of the spectra we have applied a baseline correc-tion different to that used by Stolper and coworkers (Stolper1982a,b; Newman et al. 1986; Silver et al. 1990). For the band due tothe stretching and bending of molecular water at 5200 cm  , thebackground is essentially flat, so a linear background tangent to theminima on either side of the peak was chosen. The procedureadopted is different for the OH band at 4500 cm  , where thebackground is complicated because of the contribution from thehigh-energy tail of the fundamental OH-stretch band at 3570 cm  and the band at 4000 cm  . We have adopted linear backgroundtangent to the minima in the 5200 cm   peaks for the determinationof the heights of the 4500 cm   band. This procedure assumes thatboth bands do not overlap and that the low frequency bands at4000 cm   do not contribute to the band at 4500 cm   at itsmaximum (Behrens et al. in press).This procedure allows extremely precise and reproduciblemeasurements of the height of the peaks and we prefer it to themeasurements of the integrated absorptivities because of the higherrelative uncertainty of the latter arising from problems in accuratefitting of the background.Theprecisionof the measurementspresentedhere is basedon thereproducibility of the measurements of glass fragments repeatedover a long period of time as well as on the uncertainty assigned tothe background subtraction procedure. We estimate that the typicaluncertainty in our measurements for the 4500 cm   and the5200 cm   band is approximately 0.003 absorbance units.The concentration of dissolved ‘‘water’’ in a glass contributing toa given band can be determined as follows: c " (18.02)(absorbance)/(  )(  )(  ) (2)where  c  is the H  O concentration in weight fraction, 18.02 is themolecular weight of water, absorbance is the height of the absorp-tion peak,    is the thickness of the specimen in cm,    is the molarabsorptivity (or extinction coefficient) in liter/mol-cm and    is thedensity of the sample in g/liter.Density measurements have been performed using a BermanBalance with toluene as a reference liquid (Table 1). Precision, forsamples whose masses range from 0.02 to 0.06 g, is estimated to be $ 3 g/liter based on reproducibility of measurements on differentsamples. The thickness of each glass plate was measured witha digital Mitutoyo micrometer (precision $ 3.10   cm) (Table 1).In order todetermine quantitatively thewt% of the water speciesin the samples investigated, the molar absorptivities are required.We considered for our study molar absorptivities values presentedbyNowak andBehrens (1995) for an haplograniticcompositionverysimilar to that here investigated (   " 1.56;      " 1.79). The pro-cedure to derive molar absorptivities is extensively described inNewman et al. (1986) and it is based on a weighted linear leastsquare method. An extended discussion of the procedures adoptedfor the derivation of the absorptivities and the errors involved isprovided by Behrens et al. (in press). Several measurements, per-formed along sections perpendicular and parallel to the length,showed no difference in the background subtracted peak area, at4500 cm   (hydroxyl groups) and at 5200 cm   (molecular H  O)and therefore indicate that H  O is homogeneously distributedthroughout the sample and that the run durations were long enoughto produce complete hydration via diffusion of water through thesample.Infrared determination of the water content (molecular waterand water dissolved as hydroxyl groups) were performed after eachviscosity measurement in order to test the homogeneity of thesample and to rule out significant water loss.Two samples were cut in slices perpendicular to the indentationpoint of micropenetration viscometry and traverses were made inorder to investigate possible water gradient across the samples.21  Table 1  Synthesis conditionsand spectroscopic data Sample Time   P  ¹  Density   Thickness   AOH   AH  O  (h) (kbar) ( ° C) (g/l) (cm)528 —  1-1 168 2 1100 2356 0.160 0.133 0.005528 —  1-2 168 2 1100 2356 0.161 0.129 0.009528 —  1-3 168 2 1100 2356 0.164 0.130 0.011526 —  2-0 168 2 1100 2346 0.149 0.260 0.062526 —  2-2 168 2 1100 2346 0.150 0.235 0.077526 —  2-3 168 2 1100 2346 0.150 0.229 0.073526 —  3-0 168 2 1100 2346 0.147 0.256 0.058526 —  3-2 168 2 1100 2346 0.148 0.232 0.075526 —  3-3 168 2 1100 2346 0.149 0.227 0.071526 —  3-4 168 2 1100 2346 0.149 0.228 0.069527 —  1-1 168 2 1100 2340 0.151 0.286 0.148527 —  1-2 168 2 1100 2340 0.152 0.285 0.144527 —  1-3 168 2 1100 2340 0.153 0.283 0.140527 —  2-1 168 2 1100 2340 0.154 0.297 0.148527 —  2-2 168 2 1100 2340 0.155 0.291 0.142527 —  2-3 168 2 1100 2340 0.157 0.290 0.142527 —  2-4 168 2 1100 2340 0.158 0.290 0.141144 —  1-1 408 2 800 2331 0.101 0.231 0.176144 —  1-2 408 2 800 2331 0.101 0.226 0.174144 —  1-3 408 2 800 2331 0.102 0.222 0.171280 —  2-1 288 2 800 2327 0.099 0.237 0.244280 —  1-1 288 2 800 2327 0.099 0.243 0.246300 —  1-1 168 2 800 2318 0.079 0.274 0.295300 —  1-3 168 2 800 2318 0.107 0.283 0.321   Duration of the experiments   Density measurements; error $ 3 g/l (relative error " 1%)   Thickness; error "$ 3.10   cm (relative error " 1%)   Absorbance; error "$ 0.003 units; values reported refer to multiple spectraSingle spots of 100   m were used to evaluate the presence of a gradi-ent. The samples all appeared homogeneous and no evidence of waterconcentrationgradients wasobservable withinthe uncertaintyof the infrared determinations. The infrared measurements cannotrule out the possibility of some water loss in the immediate vicinityof the indentation point ( ( 10   m from the surface). Such smallgradients are however unlikely to influence the present viscositydeterminations in a significant way, as discussed above.The water contents of all samples with the exception of no. 300remain unchanged during the high temperature dwells employed toassure fully relaxed viscosity determinations in the viscometrymeasurements. The viscosity data obtained thus pertain to struc-turally equilibrated, fully relaxed, water-bearing melts at 1 bar pres-sure and the temperatures of measurement. The results for sampleno. 300 must be treated more cautiously. The high temperatureexcursions employed here involved (as noted above) a 1 hour dwellatthe measurementtemperaturefollowedby loadingthe indenteronthe melt surface and measuring viscosity over approximately 5 min.Given that the viscosity is determined in the last 13% of the hightemperature dwell time, the postviscometry water content is likelya very good approximation to the water content during the visco-metry determination. With sample no. 300 we have identified thelimit of water content for which the present methodology can beapplied. Results The results of the viscosity determinations aretabulated in Table 2 together with the total watercontents and species concentrations as determined byIR spectroscopy. The viscosity data are presented ver-sus the reciprocal absolute temperature in Fig. 2. Themicropenetration viscosity measurements show a de-creasing viscosity and an approximately constant tem-perature dependence of viscosity with increasing watercontent. The decrease is extremely nonlinear, beinghigher at low water content. These data have been fit tothe Arrhenius equation (1) to describe the temperaturedependence of viscosity. log    " a # b /  ¹  (3) These fits are used as the basis for interpolation of viscosity data to construct the isothermal and isovis-cous comparisons used below. Figure 3a illustrates thedata extrapolated to isotherms of 700, 800 and 900 ° C.Due to the likelihood of significantly non-Arrhenianbehavior of these melts (see D.B. Dingwell, in press,Dingwell et al., in press) the Arrhenian extrapolation of the present database to viscosities as low as 10   Pas inFig. 3a is somewhat uncertain. An alternative repres-entation is to plot the temperature at which a constantviscosity is obtained (an isokom) as a function of watercontent. This involves no extrapolation of the presentdata set and is presented in Fig. 3b. All of the essentialfeatures of Fig. 3a are retained. 22  Table 2  Viscosity and water contentsSample OH   H  O   H  O total   T Viscosity(wt%) (wt%) (wt%) ( ° C) (Pa s)528 —  1-1 0.41 0.01 0.42 648.7 11.80528 —  1-2 0.39 0.02 0.41 703.6 10.76528 —  1-3 0.39 0.03 0.42 687.3 11.40526 —  2-0 *   0.86 0.18 1.04  — —  526 —  2-2 0.77 0.22 0.99 649.6 9.68526 —  2-3 0.75 0.21 0.96 611.4 10.45526 —  3-0 *   0.86 0.17 1.03  — —  526 —  3-2 0.77 0.22 0.99 611.1 10.48526 —  3-3 0.75 0.21 0.96 593.7 10.98526 —  3-4 0.75 0.20 0.95 666.6 9.42527 —  1-1 0.93 0.42 1.35 528.4 11.39527 —  1-2 0.93 0.41 1.33 549.4 10.96527 —  1-3 0.92 0.39 1.31 602.8 9.88527 —  2-1 0.95 0.41 1.37 567.4 10.58527 —  2-2 0.92 0.39 1.32 582.9 10.38527 —  2-3 0.91 0.39 1.30 621.4 9.60527 —  2-4 0.90 0.38 1.28 612.5 9.83144 —  1-1 1.13 0.75 1.88 546.6 10.09144 —  1-2 1.11 0.74 1.85 507.0 11.30144 —  1-3 1.08 0.72 1.80 576.6 9.69280 —  2-1 1.19 1.07 2.25 545.3 9.62280 —  1-1 1.22 1.07 2.29 501.9 10.49300 —  1-1 1.73 1.62 3.35 515.1 9.93300 —  1-3 1.31 1.30 2.61 548.7 9.12   Water content as derived from IR determination of absorbances;average relative error is 2%   Average relative error is 7%   Total water content is derived as a sum of molecular and waterdissolved as hydroxyl groups   Samples indicated by ! 0 are referred to IR measurements per-formed before the first viscosity determination Fig. 2  The viscosities of HPG8 melt containing up to 3 wt% waterdetermined using micropenetration viscometry on samples annealedat 1 bar at various temperatures above the glass transition for1 hour. The viscosities decrease strongly whereas the temperature-dependence of viscosity is little affected within the range of watercontents presented in this study Fig. 3a  Isotherms at 700, 800 and 900 ° C for the influence of wateron the viscosity of HPG8 melt at 1 bar pressure. The estimatedviscosity for this range of conditions using the method of Shaw(1972) at 700 ° C is included for comparison ( line ). The viscositydecrease is much more nonlinear than the method predicts. b  ‘‘Isokoms’’ or lines of constant viscosity at 10  , 10  , 10   Pasversus the prediction of the 10   Pas isokom from the method of Shaw (1972) ( solid line ) Discussion Comparison with the scheme of ShawFor over two decades estimates of the viscosity of hydrous silicate melts have been possible using thecalculational scheme of Shaw (1972). The input of hy-drous melt viscosities upon which the Shaw (1972)scheme was based are the data obtained by the sameauthor on a calcalkaline rhyolite sample with approxi-mately 4 and 6 wt% of added H  O (Shaw 1963). Those 23
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