Nov 10, 1976 - Rates of linear crystal growth have been measured for diopside and ... by a surface nucleation mechanism, while diopside grows by a screw.
VOL. 81, NO. 32
JOURNAL
OF GEOPHYSICAL
RESEARCH
NOVEMBER
10, 1976
Kinetics of Crystal Growth From SilicateMelts' Anorthite and Diopside R. JAMESKIRKPATRICK,1 GILPIN R. ROBINSON, AND JAMESFRED HAYS Hoffman Laboratory,Harvard University,Cambridge,Massachusetts 02138 Rates of linear crystalgrowth have been measuredfor diopsideand anorthitegrowing from their own meltsby usinga microscopeheatingstage.Rateswere obtainedfor undercoolingsof as little as 13øC.The ratesare higherfor diopsidethan for anorthite. Maximum growth ratesobservedare 1.5 X 10-•' cm/s (AT = 194øC)for anorthiteand 2.2 X 10-•' cm/s (AT = 105øC)for diopside.For diopsidethis probably does not representthe maximumrate. Both phasesgrow with a facetedmorphology.Plotsof Y•/AT versusAT indicate that anorthite grows by a surface nucleationmechanism,while diopsidegrows by a screw dislocationmechanism.Theseplotscan alsobe usedto calculategrowthratesat undercoolings lessthan those at which data have been obtained.
the edgesof stepson the crystalsurface.Thesedifferentmechanismscan be distinguishedby the dependenceof the reduced The crystallization of igneous rocks occurs by nucleation growth rate Yr on undercooling. Y• is defined as and growth of crystallinephasesfrom a silicatemelt. In order to understand quantitatively the crystallization processit is Yr = (Yrt)/[1 - exp (-LAT/RTTL)] (1) necessaryto determinenumerical valuesfor the appropriate ratesof nucleation andgrowth.Thispaperpresenis datafor where Y is the growth rate, rt is the melt viscosity, L is the the rates of linear growth of diopsideand anorthite growing latent heat, T is the temperature in degreesKelvin, AT is the from melts of their own composition.The rates have been undercooling, R is the gas constant, and TL is the liquidus temperature[Uhlmann, 1972]. If good latent heat data are not obtained by using a microscopeheatingstagetechnique. The major objectivesof this study were (1) to develop the available, Yr can be approximatedby [NTRODUCTION
experimental techniquesfor measuringgrowth rates, (2) to obtain data for thesesimple systemsas a referencefor future studies of more complex systems,(3) to compare data obtained by the heating stage technique with results obtained previouslyby usingthe quenchingmethod [e.g., Kirkpatrick, 1974; Klein and Uhlmann, 1974], and (4) to determineif the data obtained can be used to interpolate into the very small undercoolingregion where ratescannot be directly measured.
Yr • Y•/AT
(2)
(see, for example, Klein and Uhlmann [1974]). Yr is a measure of the fraction of sitesavailablefor attachmenton the crystal surface.A plot of Yr versusundercoolingshouldyield a horizontal line for continuousgrowth, a straight line of positive slope for growth by the screwdislocationmechanism,and a curve with positivecurvature for growth by the surfacenucleIn addition,thegrowthratedataareused'toinferthemecha- ation mechanism [Uhlmann, 1972; Kirkpatrick, 1975]. These relationshipswill be usedto infer growth mechanismsfor both nismsby which the crystalsgrow. The anorthite glassusedin this studywaspreparedby Klein diopside and anorthite. A theoretical model is available which predicts the morand Uhlmann[1974] for their studyof anorthitegrowth kinetics. The diopsideglasswas preparedfrom reagentgrade cal- phology of growing crystals [Jackson,1958]. According to cium carbonate, magnesiumoxide, and General Electric 204 Jackson'smodel, materialswith low entropiesof fusion(50
AT
Fig. 5. Observed Y?7/AT versus undercoolingrelationship for anorthitegrowingfrom its Ownmelt. Viscositydat.aare from CUkierman and Uhlmann [1973].
ation Shield.The growing crystalsare photographedwith a Super 8 motion picture camera using through-the-lenslight metering(Leicina special).The only filters in the systemare a cannotbe obtainedin this way, however,sincethe temperature heat absorberin.the light sourceand the polarizer and ana- is not constantduring the growth period. Thesefacetedmorarein agreement withthetheoryof Jackson [1958], lyzer. Films with an ASA rating of from 40 to 160havegiven phologies the bestresults,and color showsthe crystalsmuch better than which predicts faceted morphology for crystals with large black and white. The variableframe e•posurerate (9-56 (>2R) entropiesof fusion. The growth ratesare obtainedfor the tips of the crystals, framesper second)allows adjustmentof the exposure. The growthratesare obtainedby viewingth• film with a suchas thoseshownin Figure 2. For both phasesthe growth hand-operated flat screenviewer-editor.Time isobtainedfrom directionis parallel to the c axisas determinedby universal (diopside)or X ray study(anorthite[Klein the known frame exposurerate by countingthe frames.The stagemeasurement crystallengthis measuredas a functionof time, and the rate is and Uhlmann, 1974]). The growth ratesare independentof time, exceptwhen two obtained from the slope. Length calibrationis obtainedby crystalsconverge,therebycausingthe localtemperatureto rise photographinga microscopestagemicrometer. owing to buildup of latent heat and forcing the rate to deRESULTS
crease.
All crystalsof both anorthiteand diopsidefor whichgrowth rateshave been obtainedgrew as radiatingaggregatesof faceted crystals.Figures 2a and 2b illustratethe morphologies observed.Only diopsideis shown,becausethe motion pictures of anorthite, which were taken at higher temperatures,do not print well enough.The crystalsof both phases,however,look very muchthe same.It is not possibleto obtain singlecrystals of either phase by bumping seedsinto the melt, even when single-crystalseedsare used.Theseaggregatesare not spherulites, becausethe spacingbetweenthe individual crystalsdoes not remain constant and there is no branching of a crystallographic or noncrystallographicnature [Keith and Padden, 1963]. They are simply crystalswhich nucleateon the same seed. Large singlecrystalscan be obtained by melting back previouslygrown,crystalsuntil they are almostgoneand then rapidly dropping the temperature.These crystals, too, are facetedand show no signof interfaceinstability. Useful rates
The growthratesobtainedfor anorthiteare plottedagainst undercoolingin Figure 3. Rates could not be obtainedat undercoolings lessthan 13øCbecausethe crystalsfloat on the surfaceand move with the convectingmelt. In all casesthe crystalsgrownearthe surfaceof the melt in the sameposition asthe lastcrystalspresenton melting.The datapresented here wereobtainedon three separateoccasionswith the useof three differentbatchesof melt, and all gave similar results. The two pointsplottedassquaresin Figure3 are from Klein and Uhlmann [1974] for the same starting material, but a quenchingtechniquewas used.The agreementis excellentand givesusconfidence that the heatingstagemethodiscapableof yieldingaccurateresults.Most of the scatterin the data, at leastto 120øCof undercooling,wheretemperatureerrorsbecomesignificant,is within a temperatureuncertaintyof +5øC. The growth rate data for diopsideare plotted in Figure 4. The pattern is similarto that of anorthite,althoughthe abso-
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o
i
,
I
50
i
i
i
t
I
100
1,•o
0 UNDERCOOLING
Fig. 4.
(øC)
Observedgrowth rate versusundercoolingrelationshipfor diopsidegrowing from its own melt.
Fig. 6,. Observed D7/AT versusundercoolingrelationshipfor diopsidegrowingfrom its own melt. Viscositydata are from Kirkpatrick [1974].
KIRKPATRICK ETAL.: KINETICSOFCRYSTAL GROWTH
5719
lute rates for diopsideare higher. Useful rates could not be obtained at undercoolingsof lessthan about 14øC, and the scatterin the data is explainedby a temperatureuncertaintyof +5øC. At the largestundercoolingat which growth rateswere obtained(115øC) the ratesappearto be increasingwith further undercooling. Thus the highest rate obtained (2.2 X 10-•' cm/s) is probably not the true maximum growth rate for diopside.Again, the crystalsgrow near the surfaceof the melt. These data were also obtained
on three different occasions. No
comparativedata for diopsideare availablein the temperature range observed here, since quenching techniquescannot be usedfor diopsidein the smallundercoolingrange[Kirkpatrick, 1974]. o lO 20 One additional problem with diopsideis that it nucleates AT (oc) spontaneously.Initially, rates were obtained by using these Fig. 8. Calculated growth rate versusundercoolingrelationship spontaneouslynucleatedcrystals,but the scatter in the data for diopsidegrowingfrom its own melt in the very smallundercooling was largebecausethe crysfallographicdirectionfor which the region. Points plotted are observeddata. rates were obtained was not constant.With the seedingprocedure, rates can be obtained down to undercoolingsof as much as 115øC. At undercoolingslarger than this, sponIf experimentallydeterminedgrowthratesare to be usefulin taneousnucleationtakes place before the temperaturestabilizes. understandingthe crystallizationof igneousrocks, data must
beobtained fortheregion ofverysmallundercooling inwhich
DISCUSSION
most igneousrockI crystallizationprobably occurs[Kirk-
The mechanismby which anorthite and diopsidegrow from
patrick, 1975]. All crystallization,of course,must occur at
their own melts can be determined from the Y•/AT versus AT
some finite undercooling, or the rate would be zero. One
plotsshownin Figures5 and 6. The anorthiteviscositydata advantageof the heating stagetechniqueis that data can be come from Cukiermanand Uhlmann[1973], and the diopside viscositydata from Kirkpatrick [1974]. The relationshipfor anorthite, Figure 5, is a curve with an increasingslope, indicatinga surfacenucleationmechanism.This is in agreement with the resultsof Klein and Uhlmann[1974]. The data are also in agreement with their conclusion that the details of the classicalsurfacenucleationmechanismare not applicable in this case.The relationshipfor diopside(Figure 6) is a straight line, indicatinga screwdislocationmechanism.This contrasts with
the surface
nucleation
mechanism
determined
for the
obtained at moderat:elysmall undercoolings.These data can
thenbeusedto interpolate intotheverysmallundercooling range by using the fact that the rate must be zero at the liquidus.The bestmethodof interpolationis with the Y•/AT
versus aT plots inFigures 5 and6. The datahavebeenfit by
Y./AT = (1.8 X 10-6AT2) - (9.9 X 10-9AT3)
(3)
for anorthite andbY, . :
Yrt//XT= 6.6X 10-5/XT (4) pyroxenoidwhich grows from diopsidemelt at large undercoolings[Kirkpatrick, 1974]. It is also only the secondsilicate for diopside. Thecurves havebeenforcedto passthrough the .
material
known
which exhibits a screw dislocation
mechanism
over a wide rangeof undercoolings.Na2SiaO7growingfrom its own melt is the other [Schererand Uhlmann, 1975].
limitingvaluesof Y'•/AT = 0 at AT = 0.
These relationships yieldthecalculated curves plotted in
Figures7 and 8 for!anorthite and diopside,respectively.The
dataobtainedat u.ndercoolings lessthanabout25øCarealso plotted.The calculated ratesfor diopsideincrease morerap-
idlyintheverysmallundercooling range thandotheratesfor anorthite. Thusat AT = 1øCtheratefordiopside isinferred to be about100timesfasterthanthe ratefor anorthite,whileat AT = 20øCthe difference is only abouta factorof 10.This
ß
contrast in temperaturedependenceis due to the different
mechanisms by whi6hthetwo phases grow. :
The rates obtained for thesesyntheticcompositionsare, of
course, notdirectly applicable to anynatural system. Many additionalfactorssuchas compositionaleffects,pressure,and volatile content must be examined before we can understand
crystalgrowthkineticsin eventhe simplest naturalsystems, The ratesobtainedare, however,limitingdataandcanbe Used to placeboundson the conditionsof crystallization in natural systems. ::
-7
:
-8
lO o
lO
20
AT
Fig. 7. Calculated growth rate versus undercooling relationship for anorthitegrowingfrom its own melt in the very smallundercooling region. Points plotted are observeddata.
CONCLUSIONS
Themicroscope heating stage-technique hasbeenshown to be usefulfor obtaining crystalgrowthratesin geologically important systems t0..temperatures over1500øC. Growthrates havebeenobtainedi:for anorthiteand diopsidegrowingfrom :
,
5720
KIRKPATRICK ET AL.: KINETICS OF CRYSTAIr GROWTH
their own melts. The rates for diopside are higher at a given undercooling than those for anorthite becauseof diopside's lower viscosity. The rates for anorthite agree well with the rates obtained by Klein and Uhlmann [1974] using the quenching method on the samematerial. Diopside and anorthite grow as faceted crystals in agreement with the theory of Jackson [1958]. Plots of Yq//XT versus /XT indicate that anorthite grows by a surface nucleation mechanismand that diopside growswith a screwdislocationmechanism.Theseplots can be used to calculate growth rates in the very small undercooling region where direct observation is not feasible. Acknowledgments. We thank D. Walker, D. R. Uhlmann, and G. Lofgren for discussionsand helpful advice.This work was supported by NSF grant GA 44002 and by the Committee on Experimental Geology and Geophysicsof Harvard University. REFERENCES
Cukierman, M., and D. R. Uhlmann, Viscosityof liquid anorthite, J. Geophys.Res., 78, 4920-4923, 1973. Eagan, R. J., J.P. DeLuca, and C. G. Bergeron,Crystal growth in the system PbO-B•.O3, J. Amer. Ceram. Soc., 53, 214-219, 1970.
Jackson,K. A., Interface structure, in Growthand Perfectionof Crystals, edited by R. H. Doremus, B. W. Roberts, and D. Turnbull, John Wiley, New York, 1958. Keith, H. D., and F. J. Padden,A phenomenologicaltheory of spheru-
litic crystallization,J. Appl. Phys.,34, 2409-2421, 1963. Kirkpatrick, R. J., Kinetics of crystal growth in the system CaMgSi•.O6-CaAI•.SiO6,Amer. J. Sci., 274, 215-242, 1974. Kirkpatrick, R. J., Crystal growth from the melt--A review, Amer. Mineral., 60, 798-814, 1975. Klein, IL., and D. R. Uhlmann, Crystallization behavior of anorthite, J. Geophys.Res., 79, 4869-4874, 1974. Meiling, G. S., and D. R. Uhlmann, Crystallization and melting kinetics of sodium disilicate, Phys. Chem. Glasses,8, 62-68, 1967. Scherer,G., and D. R. Uhlmann, Crystallization behaviorof a-phenyl o-cresol,J. Cryst. Growth, 15, 1-10, 1972. Scherer, G., and D. R. Uhlmann, Crystallization kinetics of Na•.O.3SiO•., J. Cryst. Growth, 29, 12-18, 1975. Uhlmann, D. R., Crystal growth in glassforming systems--A review, Advancesin Nucleation and Crystallization in Glasses,Spec. Publ. 5, edited by L. L. Hench and S. W. Freiman, Amer. Ceram. Soc., Cleveland, Ohio, 1972.
(Received March 10, 1976; revisedJuly 8, 1976; acceptedJuly 16, 1976.)
