crystal growth in incongruently-melting compositions ... · recent advances in crystal growth...
TRANSCRIPT
American Mineralogist, Volume 66, pages 223-241, l98I
Crystal growth in incongruently-melting compositions:programmed cooling experiments with diopside
R. JeMes KrRKpATRrcK. LuNc-CHUAN Kuo
Department of Geology, University of lllinoisUrbana,Illinois 61801
auo JoHN Mnrcnron
S cripp s I nstitution of O c eano grap hyLa Jolla, California 92093
Abstract
Programmed cooling experiments using a synthetic diopside glass and constant coolingrates of from l0o to 300oC,/hr first crystallize forsterite and then with decreasing temperatureclinopyroxene + wollastonite. The forsterite grows as hopper-shaped crystals which then de-velop dendrites from external corners. The morphological development can be qualitativelyexplained by a model involving di-ffusion in the melt and interface attachment kinetics. Mi-croprobe traverses across forsterite-glass interfaces show that the magnitude of the MgO de-pletion in the melt near flat interface segments varies from 1.72 to 4.28 percent and increaseswith increasing run time for a given cooling rate and with increasing value of the product ofthe cooling rate times the run time for all cooling rates. The results are in qualitative agree-ment with theoretical predictions. Near a particular crystal MgO depletion is least at cornersand greatest in reentrants. The clinopyroxene is more magnesian than diopside (solid solu-tion towards enstatite) and grows as dendrites. The wollastonite occurs between the clinopy-roxene dendrite arms. The clinopyroxene first appears at nominal undercoolings (1391Iou",.n) of from l82o to 240"C, depending on the cooling rate. Unlike other sets of pro-grammed cooling experiments which show a continual increase in nominal undercooling withincreasing cooling rate, these experiments show a maximum in clinopyroxene undercoolingat 50"C,/hr. The undercooling is actually least for the 300oC,/hr runs.
IntroductionWhen crystals grow from a melt with a different
composition at least two processes must be involvedin the growth process: the molecular attachmentprocess occurring at the crystal-melt interface, andredistribution of chemical components in the melt inresponse to the selective removal of some of them bythe crystal. Removal of the latent heat of crystalliza-tion from the crystal-melt interface may be impor-tant if the growth rate is high. Traditional descrip-tions of the interaction of diffusion and crystalgrowth assume that the liquid and crystal composi-tions at the interface are the equilibrium composi-tions for the temperature at which growth is occur-ing (e.9., Elbaum, 1959). Such descriptions may notbe satisfactory for silicates and other materials whichgrow by a layer-spreading mechanism, because these0003-004x/8 l /0304-0223$02.00
materials require a finite supersaturation or under-cooling (really the same thing) at the interface forgrowth to occur (O'Hara et al., 1968; Hopper andUhlmann, 1974; Kirkpatrick, 1975). This layer-spreading growth mechanism also greatly affects thedevelopment of skeletal and dendritic crystal mor-phologies, allowing fully-faceted crystals to grow to alarger size than would be possible if interface kineticswere not important. Recent theoretical developmentshave shown how the effect of interface kinetics canbe taken into account for both interface stability andthe overall growth process.
This paper briefly reviews the recent theory, pres-ents the results of programmsd sssling experimentsin which forsterite, clinopyroxene, and wollastonitegrow from a synthetic stoichiometric diopside melt,and uses the theory to interpret these results.
223
KIRKPATRICK ET AL.: GROWTH IN INCONGRUENTLY.MELTING COMPOSITIONS
Theory
Recent advances in crystal growth theory can helpin the understanding of three major aspects of the ex-periments to be discussed here: (l) the origin of theskeletal morphologies of the forsterite and clinopy-roxene crystals, (2) the time (temperature), position,and cooling rate dependences of the liquid composi-tion at the forsterite-melt interface, and (3) the varia-tion in liquid composition away from the forsterite-liquid interface. This section will briefly review thesetheoretical developments.
Interface stability
When a crystal is growing freely (r.e., loss of latentheat through the melt) there is a tendency for the in-terface to break down into a cellular morphology.Theoretical analysis of this interface breakdown, tak-ing into account surface energy and a continuousgrowth mechanism, indicates that planar interfaceson freely growing crystals larger than a few micronsshould be unstable (Elbaum, 1959; Mullins and Se-kerka, 1963; see Lofgren, 1974, and Kirkpatrick,1975, for reviews).
As noted by O'Hara et al. (1968) and many otherssince, this is clearly at variance with observation.There are many situations where cm-size or largerfaceted crystals can be produced. The problem withthe older calculations is that they neglect the stabiliz-ing influence of layer-spreading growth mechanisms.These models correctly predict interface breakdownfor low entropy of fusion materials like metals, whichdo not grow by layer spreading, but apparently donot apply to high entropy of fusion materials like sili-cates (Jackson, 1958).
The interface stability of high entropy of fusionmaterials has been discussed by Cahn (1967), Tarshisand Tiller (1967), O'Hara et al. (1968), Chernov(1974), and Lawrence and Elwell (1976). Of these,Chernov's analysis is the most complete and will befollowed here.
Chernov has recognized three ways a faceted crys-tal may evolve into a non-faceted habit. These are:(l) random fluctuations on a flat interface, (2) ran-dom fluctuations at edges or corners, and (3) what wewill call macroscopic diffusional instability. For allthree, growth by a layer-spreading mechanism en-hances the morphological stability. For materialswhich grow by layer-spreading mechanisms, such asmost silicates, it appears that interface breakdownshould occur by random fluctuations at corners ormacroscopic diffusional instability.
The fundamental reason that layer-spreadinggrowth enhances morphological stability is that thespacing between the steps on the surface can changewith changing local undercooling or supersaturationin such a way that the growth rate of the face remainsconstant. If the undercooling is greater at one loca-tion, the spacing increases; if the undercooling is less,the spacing decreases. In this way the face can con-tinue propagating parallel to itself, although the av-erage slope of the interface with respect to the idealcrystallographic surface will change slightly. Accord-ing to Chernov (1974), slopes of about l" can com-pensate for inhomogeneities in the interface meltcomposition of about 20 percent for moderately ef-fective layer-spreading growth.
Chernov's analysis of instability by random fluctu-ations on flat interfaces indicates that growth by alayer-spreading mechanism is very effective at stabi-lizing the interface. When growth is by the continu-ous mechanism any protuberance from a freelygrowing crystal will see a larger uadlslsssling andwill grow more rapidly, causing the crystal to growwith a cellular morphology. For a crystal growing bya layer-spreading mechanism this effect is counter-acted by the sideways growth of the steps. Thus, as aprotuberance develops and the local slope increases,the protuberance generates many surface steps whichmove rapidly away, eliminating the irregularity fromthe surface.
The other two ways faceted crystals may breakdown are associated with corners and edges. Ofthese, macroscopic diffusional instability leads tohopper-shaped crystals, and random fluctuationleads to dendrite growth from corners or edges. Bothof these are common morphologies of silicate andoxide crystals in igneous rocks and in the experi-ments discussed in this paper.
Macroscopic diffusional instability occurs whenthe decrease in the spacing of the growth steps on thesurface with decreasing local supersaturation can nolonger compensate for variations in the super-saturation along the interface. When this happensgrofih stops or slows drastically in areas of low su-persaturation. [n most cases the low supersaturationoccurs in the center of a face because there is a muchlower volume of melt per unit area of interface at thecenter than there is at the corners. Lateral diffusionparal lel to the face helps el iminate this in-homogeneity, but as the crystal grows larger it be-comes less effective.
The result of macroscopic diffusional instability isa hopper crystal. In some cases only the fastest-grow-
KIRKPATRICK ET AL.: GROW,TH IN INCONGRUENTLY.MELTING COMPOSITIONS
ing face of a crystal becomes hopper-shaped, whilethe more slowly-growing faces remain planar. Thisresults in a hopper crystal with some planar faces. Ifthere are other crystallographic planes on whichgrowth can occur at high angles to the one breakingdown, faceted macrosteps may develop. This leads tokins6a1ls waves which pass over the surface withgrowth taking place at any particular place onlywhen the macrostep passes over. Chernov's analysisindicates that this general kind of instability shouldbe common in silicate systems.
Chernov's analysis of interface instability by ran-dom fluctuations at corners has not been carried asfar, but his results indicate that, for crystals whichgrow by layer spreading, instability by fluctuations atcorners or edges should be much more common thaninstability by fluctuation on flat faces. His analysisindicates that even if a fluctuation does not developinto a dendrite it nay still result in a macrostepwhich will pass over the interface.
Instability spacing
In the traditional models the spacing (X) betweendendrite arms is proportional to the ratio of the diffu-sion coefficient (D) in the melt to the growth rate (Y)(X o< D/Y; Keith and Padden, 1963). In Chernov'sanalysis the transition to hopper morphology is di-rectly related to the efficiency of diffusion in the meltparallel to the interface. The critical crystal size foronset of hopper growth is related to the ratio of thediffusion coefficient in the melt to the kinetic coeffi-cient for growth times a number of system constants.1fos kinetic coefficient, b, is given by
Y : b A T
where AZ is the undslsssling and Y is the growthrate.
Traditional models may be sufficient to describesecondary dendrites (those growing on existing den-drites) because the surfaces bounding many dendritearms appear to be rounded and probably grow by acontinuous mechanism.
Whether the spacing between primary dendritearms growing from corners is also related to D/Y isnot clear. The process has not, to our knowledge,been analyzed in sufficient detail to determine ifthere is a critical initiation size.
I nt erfac e melt c o mp o sition
As for interface stability, the growth of crystals bylayer-spreading mechanisms complicates the inter-pretation of composition gradients near growing
crystals. One of the few analyses of this problemwhich include interface kinetics is that of Hopperand Uhlmann (1974). Their calculations indicate thatthe concentration of the rejected component in themelt at the interface, the composition gradient in themelt at the interface, and the difference between theinterface melt composition and the melt compositionfar from the interface all increase monotonically withincreasing time. Their results can only be used as ageneral guide for interpreting the results of the exper-iments discussed here because they assume a con-stant temperature, growth rate, and di-ffusion coeffi-cient.
Calculations more directly applicable to our exper-iments, although still difrcult to apply quantitatively,are those of Ghez and Lew (1973) and Miiller-Krumbhaar (1975). Both conclude that for samplescooled at a constant rate the supersaturation at theinterface increases with increasing time, the same asHopper and Uhlmann (1974). Miiller-Krumbhaar in-dicates that for a given starting material the interfacemelt composition for all cooling rates should fallalong one curve when plotted vs. the product of cool-ing rate, run-time, and some system constants. It isdifficult to use the Mtiller-Krumbhaar relationshipsquantitatively because the activation energy for crys-tal growth and the temperature and composition de-pendences of the diffusion coefficients 21s snknsvmand because a simple first-power relationship be-tween growth rate and supersaturation is assumed. Inthe absence of known phase relationships it is alsodfficult to distinguish this relationship from the equi-librium relationship, because sesling rate times runtime is simply temperature.
Composition gradients in the melt
The need for transport of components to and fromthe crystal surface leads to composition gradients inthe melt near the surface. For a binary system thecomponent enriched in the crystal is depleted in themelt near the crystal and the rejected component isenriched.
For a multicomponent system the diffusion coeffi-cient is ttsl 4 5ingle number but a matrix. The prob-lem of a three-component system has been treatedfor the interface equilibrium, isothermal case byCooper and Gupta (1971). Their results indicate thatexcept in the most unusual situations the composi-tion gradient will follow a curved path in composi-tion space with only the mean composition of the liq-uid lying on the depletion line. Quantitatively theirresults are not applicable to the experiments dis-
KIRKPATRICK ET AL.: GROWTH IN INCONGRUENTLY-MELTING COMPOSITIONS
cussed here because they assume constant diflusioncoemcients. However, the results should be qualita-tively the same for programmed cooling experiments.
Experiments
Procedure
Our experiments used programmed cooling meth-ods with the samples held on platinum wire loops(Lofgren et al., 1974). The starting material was syn-thetic stoichiometric diopside (CaMgSi,Ou) glass forwhich crystal growth rates have been measured atboth large and small undercoolings (Kirkpatrick,1974; Kirkpatrick et al., 1916). An experimentalcharge was made by pressing about 100 mg of pow-dered glass into a pellet and sintering the pellet ontoa platinum wire loop. Each run was started by plac-ing a charge in a MoSi, resistance furnace in the airat l400oC (9oC above the liquidus temperature) forten minutes. It was then cooled at a constant rate offrom 10" to 300'C/hr. The thermocouples were cali-brated against the melting points of gold and diop-side. A number of samples were run at each coolingrate but quenched at different temperatures in orderto observe the changes in mineralogy, composition,and texture as crystallization proceeds. The finalproduct is a bead approximately 4 mm in diameterwith varying amounts of glass and crystal.
The samples have been examined both whole andin polished thin section. Whole samples were exam-ined primarily by petrographic microscope while im-mersed in oil of n = 1.64 with the sample held in apiece of copper tubing epoxied to a glass slide. Thistechnique eliminated the lens effect of the glass bead,allowed the size and number of crystals in partially-crystallized samples to be determined, and permittedus to decide how to cut the sample. The partially-crystallized samples were then cast in epoxy and cutinto several slices by a diamond saw with a 250-pm-thick blade such that a crystal or crystals were cut ina predetermined way. Some crystals were cut length-wise; others were cut into serial slices about 250 p,mthick. These slices were then mounted as either thin(30 pm) or thick sections. The fully-crystallized sam-ples were cut in half and examined in thin section.
Analytical methods
Quantitative analyses of the glass, forsterite, andclinopyroxene were made with an ARL-EMX electronmicroprobe. The beam current was approximately0.07 microamps, the accelerating voltage 20 kV, and
the beam diameter I trrm. The standard was a syn-thetic diopside glass. Drift, background, and dead-time corrections were made with the computer pro-gram PRoBE. Absorption, fluorescence, backscatter,and stopping power corrections were made with amodified version of the program ABFAN (Boyd et al.,1969).
The composition gradients in the glass near crys-tals were measured by first running qualitative pro-files along the desired traverse with a JEoL JxA-50Aelectron microprobe at a scan speed of 40 pri perminute and then calibrating the scans with three toeight quantitative analyses along the traverse. Theglass compositions at the crystal-glass interface wereobtained by extrapolating the calibrated scans. In al-most all cases there is an analysis within 15 pm of theinterface, and extrapolation is never large.
Because the smallest grains in the fully crystallizedcharges are I to 5 pm across, several ofthese chargeswere powdered and X-rayed on a Norelco powderdiffractometer at lo 20 per minute with Ni-filteredCuKc radiation. Phase identification was made fromthe AsrM powder file.
Results
The phases occurring in these experiments areglass, forsterite, a clinopyroxene, and wollastonite.Figure I is a plot of temperature, run time, andphases present for each run. At nominal under-coolings (1391'C-quench temperature) less thanabout 140o to l60oC depending on the gesling rate,the only phase is glass. At somewhat larger nominalundercoolings, up to 240", only glass plus less than 5percent hopper or dendritic forsterite are present. Atthe largest undercoolhgs the samples appear to befully crystallized and contain mostly dendritic clino-pyroxene crystals with a small amount of wollaston-ite in the interstices between the clinopyroxene den-drite arms, along with the previously-crystallizedforsterite.
For cooling rates less than 50"C/hr the temper-ature of first appearance of clinopyroxene and wol-lastonite decreases with increasing cooling rate. Thisis similar to the variation observed in all previoussets of programmed cooling experiments (see, for in-stance, Walker et al., 1976; Grove and Raudsepp,1978). At larger cooling rates (100' to 300'C/h),however, the temperature of first appearance ofclinopyroxene and wollastonite increases (the nomi-nal undercooling decreases). This is opposite the pre-viouslv-observed variation. The variation in the tem-
KIRKPATRICK ET AL.: GROWTH IN INCONGRUENTLY-MELTING COMPOSITIONS
o= Gloss Onlyo= Forslerite+Glossr = Forslerite + Clinopyroxene + Wollostonile
TIME (HOURS)
Fig. L Ternperature vs. time plots for aU runs. Each point represents the quench tcmperaturc.
227
()gUJEf,F
" * lLd(L=lrJF
perature offirst appearanoe offorsterite has not beendetermined in sufficient detail to define a trend.
Forsterite
Forsterite is the first crystalline phase to appear atall cooling rates. It usually grows from and appearsto be nucleating on the platinum loop. In some sam-ples it is on the surface of the bead away from thewire and may have nucleated there. Table I presentselectron microprobe analyses, which show that it isvery close to ideal forsterite except for a smallamount of CaO.
All the forsterite crystals are hopper-shaped orhopper-shaped with external dendrites. Most havesome planar, crystallographically-controlled surf,aces.Figures 2 and 3 illustrate typical morphologies. Thesmaller crystals tend to be hopper-shaped with fac-eted external surfaces, while the larger ones tend tobe hopper-shaped with an externally dendritic mor-phology, although we can see no critical size for theonset of dendritic growth.
Figures 3a-3c illustrate a sequence of serial sec-tions cut perpendicular to the long axis of one crystal.The slice from within 250 pm of the growing end of
the crystal (Fig. 3c) is hopper-shaped and has amostly planar external morphology with only a smalldendrite developing at one oorner. The next slice to-wards the base of the crystal (Fig. 3b, 500 pm fromthe one above) is also hopper-shaped but has den-dritic anns developing from all corners. The sliceclosest to the base (Fig. 3a, 500 pm from the slice inFig. 3b and about 500 pm from the base) is similarbut shows more extensive dendrite development. Fig-
Table l. Electron microprobe analyscs of forsterite crystals
f0 ' /h r 20" /h r , l l62"C
l 2 0 f ' c | 2
20" lh r , l l71 'C 5O" lh r lOO" /hr
| 2 l l 7 7 . C i l 8 6 ' C
C a o 0 . 7 t
s i 0 2 \ 1 . 5 2
il90 57.t+9
Tota I 99 .72
C a 0 , 0 1 8
s i 0 . 9 7 9
Mg 2 .023
0 4 . 0 0 0
0 . 8 8 0 . 8 1
42 .07 \ z . 7 t
56.78 56.38
o o ? ? o o o n
0 .022 0 .020
0 . 9 9 1 1 . 0 0 3I o o c I o ? E
4 . 0 0 0 4 . 0 0 0
l . l | 0 . 8 7
42.42 43.28
) ) . o o ) t . 5 1
99. r9 99.49
0 .028 0 ,o22
1 . 0 0 3 r . 0 r 8
I . 955 1 . 9 \2
4 .000 4 .000
1 . 4 3 0 . 9 4
42.o5 42.35
56.84 56.22
l 00 .32 99 .51
0 .035 0 .024
0.987 0.999
| . 990 1 .978
4 .000 4 .000
228 KIRKPATRICK ET AL.: GRjWTH IN IN)7NGRUENTLY.MELTING COMPOSITIONS
Fig. 2. Photomicrographs of olivine crystals. (a) Hopper-shaped experimental forsterite nucleating on wire loop. Electron microprobescan along solid line is shown in Fig. 10. Striations on crystal are macrosteps on inside ofhopper. 10"/hr, Tr: l2l4oC. Planetransmitted light. (b) Hopper-shaped experimental forsterite crystal. Electron microprobe scans were done along transverses 3,{ to 3D.MgO depletion (AMgO) increases from294wt%oneat top to 3.68 ettEoneat base (lower left). 50'C/hr, Tq: ll71"C. Plane reflectedlight. (c) Hopper-shaped experimental forsterite crystal with dendrite arms developing at corners or external hoppers. Plane reflectedlight. 100'/hr, Tq : I 186'C. (d) Olivine phenocryst in mid-Atlantic ridge basalt. Note development of dendrite arms from corners, meltinclusions, and kinematic wave on lower right corner. Surfaces are curved, indicating a high step density. Plan€ transmitted light.
a
KIRKPATRICK ET AL: GROWTH IN INCONGRUENTLY-MELTING COMPOSITIONS 229
Fig. 3. Photomicrographs of serial sections through a hopper-shaped and dendritic experimental forsterite crystal, 10"/hr, 7o :
l20l'C. Plane transmitted light. (a) Slicc 500 prn from base of crystal showing extensive dendrite development. (b) Slice 500 pm fromthat in 3a, showing less well developed dendrites. (c) Slice 500 pm from that in 3b and about 250 rrm from the end ofthe crystal showinghopper development, but a mostly facet€d external morphology. (d) Close-up of slice in Figure 3c showing mostly flat crystal surfaceswith a kinematic wave starting at the corner.
23o KIRKPATRIzK ET AL.: cRowrH IN INj,NGRIIENTLv-MELTING coMposITIoNs
Table 2. Number of crystals and maximum crystal length for runscontaining only forsterite and glass
csqling rate, but there are many exceptions. The runat l25lo and 300'/h, for instance, contains forster-ite, while runs quenched from lower temperatures atthe same cooling rate do not. Neither the crystal sizenor the number of crystals increases consistentlyenough to calculate accurate nucleation or growthrates. Table 2 presents the maximum crystal size andthe number of forsterite crystals in each partially-crystallized run. Very roughly, the average growthrates are of the order of l0{ cm/sec for the fastest66sling rates and l0-' cm,/sec for the slower coolingrates. Nucleation rates are of the order of li/sample/hour for the fastest 66sling rates and l/sample/hourfor the slowest cooling rates. These nucleation ratesappear to reflect heterogeneous nucleation on thewire loop.
C omp o sition gradients near forsterite
Composition gradients in the melt near forsteritecrystals have been examined as a function of coolingrate, run time, and position on the crystal. Generallytwo to four microprobe traverses were made neareach crystal (Figs. 2, 3, and 4). For the crystal in Fig-ures 3a-3c several calibrated traverses were run oneach serial section. Figure 5 presents typical cali-brated scans. Figure 6 presents typical sequences ofpoint analyses. Table 3 lists the analyses used to cali-brate the scans in Figure 5. Table 4 presents the glassinterface compositions and compositions far from theinterface (CaO and MgO only) along with the differ-ence in CaO and MgO (ACaO and AMgO) betweenthe interface composition and the composition farfrom the interface for each scan.
Figure 7 plots the composition gradients in part ofthe system CaO-MgO-SiOr. They do not plot on the
Coo l i n9ra fe
(" /nr)
RunN o .
Tqu "nch No . o f Hax imum- 7 ; ; i c r y s t a l s c r y s t a l
l eng th (mm)
6
36A
2985 l A554
q3A28A44A52A54A
\7A48A66A68A78A
724
o>Ao / A
754
45A46A49A50A55A57A7047\A
300
200200200
t00t 0 01 0 0r00t 0 0
5050)u5050
30
202020
t 0l 0l 0t 0l 0l 0l 0l 0
l25t
l 2 0 lI l 9 r| 1 8 6
t 2 t It 2 0 ll l 9 lr r86l l 8 r
I t75I 1 6 4I r 5 8i l54I t52
r r55
l l T rI r 5 l| 152
1235t23l1225t2 t6r 2 l 4t 2 0 l| 1 9 8| 197
0 . 3
0 . 2 50 . 30 . 8
0 . 80 . 81 . 70 . 80 . 8
> 2 , O3 . 02 . 94 .0 ' t4 . 0 *
3 . 0
3 . 03 . 03 . 0
r . 60 . 7
2 . 7
2 . 8z . ut . 0
2
4
9963
22
6?
3Iea
zI
* l e n g t h o f s a m p l e
ure 4 illustrates in more detail the crystal in Figure3a.
In general, the size and the number of forsteritecrystals increases with increasing run time at a given
Table 3. Electron microprobe analyses ofglass near forsterite crystals(points correlate with Figs. 5, 6, and l0)
Run 57n-3nt 2
Run 57A-38l 2
C a O 2 7 , 9 1 2 7 . 2 0 2 7 . 2 5 2 7 . 1 5 2 7 . 0 9 2 6 . 8 2 2 6 . 8 3 2 6 . 9 0
s i02 57 ,25 57 . t7 57 .09 56 . t3 56 .55 56 .5 \ 56 .61 55 .35t ' f g o 1 5 . 1 0 t 5 . 7 1 1 6 . 4 8 1 6 . 8 7 1 7 . 3 1 1 7 . 2 8 t 7 . 3 5 1 7 . 3 8
T o t a l 1 0 0 . 2 5 1 0 0 . 0 8 r 0 0 . 8 2 1 0 0 . l 5 t 0 0 . 9 5 t 0 0 . 6 4 t 0 0 . 7 9 t 0 0 . 6 3
t . 0 7 5 1 . 0 4 8 l . 0 4 32 . 0 5 8 2 . 0 5 5 2 . 0 4 0
0. 809 0 . 842 0 . 878
5 . 0 0 0 6 . 0 0 0 6 . 0 0 0
r . 0 4 9 t . 0 3 8 t . o z 9 t . o z 9 r . 0 3 42 .022 2 .021 z .oz5 z .oz [ z .o t90 .905 0 .92 t 0 .921 0 .924 0 .9286 . 0 0 0 6 . 0 0 0 5 . 0 0 0 6 . 0 0 0 6 . 0 0 0
2 7 . 6 5 2 6 . 6 5 2 6 . 8 6
56.36 56.\6 56.69
f 6 . 4 8 r 7 . 4 8 1 7 . 2 7
r 0 0 . 4 9 1 0 0 . 5 9 r 0 0 . 8 2
l . 0 6 5 | . 0 2 3 1 . 0 2 9
2.026 2 .022 2 .025
0 . 8 8 3 0 . 9 3 3 0 . 9 1 9
6 . 0 0 0 6 . 0 0 0 5 . 0 0 0
Ca
5 l
I't9
0
KIRKPATRICK ET AL.: GROWTH IN INCONGR(IENTLY.MELTING COMPOSITIONS
Table 3. (cont.)
Run 55A
I
Ca0
s i 0 ^
Mgo
Tota I
5 l
M g
0
2 7 . 5 1
56.9\| ) . l o
1 0 0 . 2 |
l . 050
2 . 0 4 8
0 . 8 4 5
5 . 0 0 0
27 .30
r 5 . 7 8
a o n ?
t . u o o
2 . 0 3 8
0 . 8 5 7
5 . 0 0 0
2 7 . 1 8
56.6\
99 .77
1 . 0 5 I
2 . 0 4 5
0 . 8 5 8
5 ,000
2 7 . 3 \E E 1 '
r 6 . 6 4
q q ? n
I . 0 5 9
2 . O t 3
0 . 9 0 4
5. 000
2 7 . 0 8
5 5 . l 0
1 7 . 1 5
9 9 . 3 3
| .057
2.006
0 . 9 3 0
5 , 0 0 0
to . o: l
) ) ' { |I I . O I
o a 7 7
I . 0 3 5
2 . 0 0 6n q ( ?
5 . 000
5 \ . 8 9r 8 . 2 8
99.60
I . 0 2 8I q o ?
n q A q
5 . 0 0 0
2 6 . \ \
t 7 . 9 7
99.78
| .025
2 . O 0 3
0 . 9 6 9
5 . 0 0 0
forsterite (with about l%o CaO) depletion line, but arecurved. The melt near the crystal is enriched in SiO,relative to forsterite depletion. Going away from theinterface the gradients cross or come to the forsteritedepletion line and then curve towards the originaldiopside bulk composition. Even the most MgO-de-
pleted compositions at the interface are still wellwithin the diopside primary phase field.
The MgO value in the glass at the interface andAMgO vary systematically with location on the inter-face, run time at a given cooling rate, and the prod-uct of run time and cooling rate for all the cooling
Fig. 4. Close-up plane reflected light photomicrographs of the slice shown in Fig. 3a. (a) Dendrite arm showing nonfaceted secondary
arms (except on a few external surfaces) and entrapment of melt by secondary arms growing from bottom. (b) Dendrite arms showing
entrapm€nt of melt by growth of secondary dendrites perpendicular to overall growth direction, non-planar internal surfaces and planar
extemal surfaces.
' 2 3 2 KIRKPATRICK ET AL.: GROWTH IN INCONGRT]ENTLY-MELTING C1MP1SITI1NS
Table 4. Glass compositions in forsterite plus glass runs
C 1RunN o .
Coo l ing ra te(6 /h r \
Tquench
( ' c )
c-_ci
Acao 1s190
I n t e r f a c e
trFsi t ion*
S c a n
N o .Mgo
43A
44A
45A
49A
r00
1 0 0
I 2 1 l
L l 91
1 1 8 6
I L 1 7
2 - 7 . 5 02 7 . 5 22 7 . 4 6
2 ' 7 . 3 02 7 . 6 L2'1 -74
2 7 . 4 7
2 7 . 5 72 7 . 5 32 7 . 3 02 7 . 4 4
2 7 . 9 0
2 8 , 4 02 4 . 6 42 4 . 6 62 8 . 5 02 a . 7 6
2 A - 2 62 4 . 6 02 4 . 0 22 8 . I 5
2 8 . 5 024.602 8 . 5 82 4 . 2 2
2 8 . 1 82 9 . 2 0
2 7 . 5 22 7 . 2 3
2 7 . 6 4
2 1 . 7 0
2 7 . 9 42 1 , 1 4
2 7 . 4 22 7 . 1 6
2 7 . 7 42 7 . 4 6
2 7 . 3 62 7 . 3 0
2 7 - ' 7 22 7 . r 42 1 . 2 8
2 7 . 6 0
2 8 . 3 02 8 . 3 0
24. r32 8 . 1 0
2 8 . 0 82 7 . 4 2
1 AI Blc
2A2B2 D
3A
3c3D
IA
I B3AJ B
3c3D
1 B2A
2c
3Al 6
3D
6C
2A3B
3A
5A5 B
6A
2A
3A
3 C
1 0 0
1 0
1 0
1 0
t o
1 1 8 6 2 6 . 2 2 r A - 2 92 6 . I 2 1 8 . 2 02 6 . 1 6 1 8 . 4 6
2 6 . 3 0 1 8 . 5 02 6 . r O 1 8 . 0 72 6 . 2 0 I 7 . 9 8
2 6 . 7 2 1 8 . 0 6
2 6 . 0 4 I 8 . 0 02 5 - A 9 t 8 . I 62 5 . 7 5 L 7 . 9 22 6 . r O r 8 , 0 0
2 6 . 9 L 1 8 . I 8
2 7 . 3 8 1 8 . 0 02 7 . 5 0 1 8 . 0 22 7 . 5 1 I 7 . 8 22 1 . 3 2 L 7 . 6 42 7 . 5 0 I 7 . 7 2
2 6 . 7 6 1 8 . 0 02 6 . 7 5 1 8 . 5 22 6 . ' 7 0 L A . 4 22 6 . 5 0 1 8 . 3 0
z o . o t L t . 6 2
2 6 . 6 6 I 8 . 0 02 6 . 5 2 L 7 - 7 62 6 . 5 0 1 8 . 0 0
2 6 . 3 0 1 8 . 0 02 6 . L 4 I 8 . 2 5
2 6 . 4 8 1 7 . 0 62 6 . 2 2 1 6 . 4 8
2 6 , 5 0 L 7 . 4 2
2 6 . 5 4 1 7 . 3 0
2 6 . 5 2 r 7 . 2 42 6 . 3 0 1 7 . 0 8
2 6 - 5 2 1 7 . 3 82 6 - 4 8 I 7 . 4 0
2 6 - 5 0 1 7 . 0 02 6 . 4 A 1 7 , 0 3
2 6 . 5 0 1 8 . 0 02 6 . 4 0 1 8 . 0 6
2 6 . 6 4 1 8 . 6 02 6 . 2 4 1 8 . 5 02 6 . 2 6 1 8 . 4 8
2 6 . 5 0 1 8 . 0 6
2 7 - L 8 I 7 . 7 32 6 . 9 7 I 7 . 6 9
2 6 . 7 6 ) , 7 . 4 42 7 . O L t 7 - 7 4
2 6 . 6 6 1 7 . 5 02 6 . 4 O 1 7 . 3 0
1 4 . 9 9 - 1 . 2 8 3 . 3 0
1 4 . 6 1 - 1 . 4 0 3 . 5 91 5 . 4 0 - r . 3 0 3 . 0 6
1 5 . 6 8 - 1 . O 0 2 - 8 2r 5 . 1 0 - 1 . 5 1 2 - 9 71 5 . l - 2 - 0 . 9 4 2 . 8 6
1 5 . 8 6 - O . 7 5 2 - 2 0
L 3 . 7 4 - I . 5 3 4 - 2 61 3 . 8 8 - L . 6 4 4 . 2 A1 3 . 9 6 - 1 . 5 5 3 . 9 61 4 . o 4 - 1 . 3 8 3 . 9 6
1 5 . 3 6 - 0 . 9 9 2 . 8 2
L 4 . 6 2 - 1 . 0 2 3 . 3 81 5 . 0 8 - 1 . 1 4 2 . 9 41 4 . 7 t - 1 . 1 5 3 . 1 11 4 . 2 4 - 1 . 1 8 3 . 3 6L 4 . O 4 - 1 . 2 6 3 . 6 8
1 4 . 3 8 - 1 . 4 0 3 . 6 21 4 . 5 6 - 1 . 8 5 3 . 9 61 4 . 6 2 - r . 3 2 3 . 8 0t 4 . 5 6 - 1 . 6 5 3 - 7 4
1 3 . 9 6 - r . 8 3 3 . 8 61 3 . 9 0 - r . 9 4 4 . r 01 3 . 5 2 - 2 . 0 6 4 . 2 4r 3 . 8 8 - L . 7 2 4 . I 2
1 4 . I 2 - t . 8 8 3 . 8 8L 4 - L 6 - 2 . O 2 4 . O 9
1 4 . 4 8 - 1 . 0 4 2 . 5 41 3 . 4 8 - 1 . 0 1 3 . O 0
1 4 . o O - 1 . I 8 3 . 4 2
1 3 . 7 8 - 1 . L 2 3 . 5 2
1 4 . 1 3 - t . 4 2
1 3 . 7 6 - t . 4 83 . 1 r3 . 3 2
1 4 . 1 0 - 1 . 3 0 3 . 2 4I 3 . 8 4 - I . 2 8 3 . 5 6
L 3 . 6 2 - r . 2 a 3 . 3 8I J . J b - I . J d J . b /
L 6 . 2 0 - 0 . 8 6 1 . 8 01 6 . 3 2 - 0 . 9 0 t . 7 4
1 6 - 5 7 - I . 0 4 2 . 0 31 6 . 7 4 - 0 . 9 0 r . 7 2L 6 . 5 2 - t . 0 2 r . 9 6
1 5 . 9 8 - 1 . 1 0 2 . O A
1 5 . 5 3 - r . r 2 2 . 2 01 5 . 1 8 - 1 , 3 3 2 . 5 r
1 5 . 0 6 - L - 3 7 2 - 4 21 5 . 9 0 - 1 . 0 9 I . 8 4
1 5 . 0 2 - L . 4 2 2 - 4 4t 5 . 5 6 - r - O 2 r . 7 4
F
F
F
F
F
D
F
F
F
F
F
F
l l 58
1 1 5 2
57A
1 1 7 1
L I 6 2
r235
L225
L 2 I 4
I 201
4 B
n
R
D
F
R
F
R
F
F
D
F
FD
D
1 A1 B
2A
3 A3B
,-Interface posLtLon: F = fLat, R = reent?dnt, D = dendtit ic t ip or conner
KIRKPATRICK ET AL.: GROWTH IN INCONGRUENTLY-MELTING COMPOSI?IONS
Run 57A-38
200
BFig. 5. Calibrated electron microprobe scans showing the MgO gradi€nts in the glass near forsterite crystals. Off-scale peaks are
crystal. Both scans are for same crystal. 57A-3A is across a flat interface segment; 57A-38 is across a dendrite tip (see Fig. 4). Low MgOvalues on the left side of 57A-3A scan are melt inclusions. Note even lower MgO than at th€ interface.
233
o33;
t 8
o;g 17CD=i re
rooPm
rates. These variations are in good agreement withthe theory discussed above.
The data in Table 4 indicate that the nature of theinterface greatly influences the interface composition.Relative to the composition next to flat interface seg-ments, AMgO near dendrites or corners (those partsof the crystal protruding into the melt) is lower andMgO at the interface is higher. At reentrants, on theother hand, AMgO is greater and MgO at the inter-face is lower. Because of this we use only data fromflat interface segments to compare data from di-ffer-ent runs.
For runs done at the same cooling rate but for dif-ferent lengths of time AMgO increases and MgO atthe interface decreases with increasing run time. Fig-ure 8 shows this variation for runs at 50o and lO"C/hr.
Figure 9 shows the ratio of MgO at the interface toMgO in the bulk melt vs. the product sf sssling rateand run time. This plot allows comparison with theo-retical prediction (Miiller-Krumbhaar, 1975). MgO atthe interface would show the same decrease, andAMgO would increase. Almost all the MgO ratiosplot on the same convex-upward curve. The one
Run 57A- 3A
2 34 5 6 7 8r t r t t l l
Pm
234
pm
Fig. 6. Electron microprobe analyses (MgO) rs. position used tocalibrate scans in Fig. 5.
crystal (3 data points) at 100'C/hr that does not ismuch larger than other crystals at the same coolingrate and may have nucleated at a higher temperature.The other data at this cooling rate fall on the overalltrend.
A number of forsterite crystals contain numerousmelt inclusions trapped between dendrite arms.Table 3 and Figure 5a prescnt analyses of the in-clusions in the sample illustrated in Figures 3a and 4.The inclusion compositions are somewhat scatteredbut are all signfficantly lower in MgO (forsterite)than even the glass composition at the external inter-face. This is probably due to continued growth offorsterite onto the inclusion wall after it was trapped.The inclusion compositions are poor estimates of thebulk liquid composition from which the crystals are
KI RKPA TRI C K ET A L. : GRO\|ITH I N I N C O N cRIt E N TLY- M ELTI N G C O M p O S I TI O N S
r8
l 7
t6
r5
t4
>sC D += ]
growing, a conclusion also reached by Roedder andWeiblen (1977) for lunar mare basalts.
Figure l0 presents a calibrated microprobe scandown the axis of the hopper crystal illustrated in Fig-ure 2a. Table 3 gives the analyses used to calibratethis scan. The continual decrease in MgO from themouth of the hopper to its base also indicates contin-ual growth on the inside of the crystal.
The partitioning of Ca and Mg between the meltand olivine shows no systematic temperature or cool-ing rate dependence, and the olivine is much richerin calcium than the equilibrium value predicted byextrapolating the data of Watson (1979) for experi-ments in the system NarO-CaO-MgO-AlrOr-SiOr.Figure I I shows the otvine-liquid partition coeffi-cients, (CaOlMgO)o,/(CaO/MgO),,0, using the ex-trapolated interface liquid compositions at flat inter-face segments plotted vs. l/T"K, along withWatson's equilibrium data. Care was taken not to an-alyze the forsterite within about 15 pm of the inter-face because ofsecondary fluorescence effects. Simi-larly, there is no systematic variation when thepartition coefficients are plotted vs. cooling rate. In-deed, the data for one crystal at 104/T"K: 6.83 inFigure I I span nearly the entire range. All the parti-tion coefficients from the programmed cooling exper-iments are much larger than the equilibrium valuesof Watson. This reflects the much higher CaO valuesin our olivines (0.71 to 1.43 wt%o, Table l) relative tohis (0.03 to 0.53 wtvo).
o 57A-3Ar 574-38
a 44Ar 7 8 AA 7 5 A
W7. % CoOFig. 7. Composition gradients in glass close to forsterite crystals plotted in the system CaO-MgO-SiOr. Points near the diopside
composition are far from the interface; points away from the diopside composition are next to forsterite crystals. The curvature of thegradients in composition space is in agreement with the theory of Cooper and Gupta (1971) and is due to multicomponent diffusioneffects.
KIRKPATRICK ET AL.: GROWTH IN INCONGRUENTLY-MELTING COMPOSITIONS
OUENCH TEMPERATURE Fc)( o )
qJENCH TEMPERATURE Cc)(b)
Fig. E. AMgO vs. time for flat interface segments: (a) 50"Ar; @) 10"/hr.
23s
.Rgott=
Ag
3ott=
C linop yr o x ene and w o ll ast onit e
A clinopyroxene (Wo47-Wo.n) and wollastonitecrystallize after forsterite, beginning at temperaturesranging from 1209" to I 15loC, depending on coolingrate. There is a minimum in the appearance temper-ature at a cooling rate of 50"C/ht (Fig. l). No glasscan be seen in thin sections of any nr1 ssnfsiningclinopyroxene and wollastonite.
The clinopyroxene crystals are all dendritic, withas many as three levels of branching. The surfaces ofthe dendrites are rounded and appear to be non-crys-tallographic. There are from 2 to 13 clinopyroxenecrystals in each thin section. The wollastonite crystalsare located between the clinopyroxene dendrite anns,often in opticaly continuous networks. The morerapidly-cooled samples are often highly vesicular.Figure 12 illustrates typical clinopyroxene and wol-lastonite morphologies.
The clinopyroxene compositions are more magne-sian than diopside and fall along the diopside-ensta-tite join. Table 5 lists typical electron microprobeanalyses of the clinopyroxene. Figure 13 plots theanalyses in the forsterite-wollastonite-silica system.
There appears to be no systematic variation of clino-pyroxene composition with cooling rate or temper-ature. The wollastonite grains are too small to ana-lyze with the microprobe.
It has been suggested (Kirkpatrick, 1975; Walkeret al., 1976; Grove and Walker, 1977) that dendritearm spacing decreases with increasing undercooling(higher growth rate) and that the spacing may be
COOLING RATE X TIME
Fig. 9. MgO (intcrface)/MgO Oulk) vs. spreling rate timcs runt'me for all flat intcrfacc scgneots examincd. 100o,/hr data thatfall below trend are from unusually large crystal.
T I M E ( H R S )
KIRKPATRICK ET AL.: GROIVTH IN INCONGRUENTLY-MELTING COMPOSIIIONS
Run 564
p.mFig. 10. Calibrated scan (MgO) of glass down the length of a hopper forsterite. Calibration points are given in Table 3, crystal is
illustrated in Fig. 2a.
dg
goE l=
used as a measure of relative cooling rate. In our ex-periments the relationship between the temperatureof crystallization and the spacing is poor. Figure 14 isa plot of the spacing of the finest-scale dendrites ys.cooling rate. These spacings were measured by rotat-ing the thin section on a universal stage until the
6.0 too/;,"K
Fig. ll. Olivine-liquid partition coefficients, Ko : (CaO,zMgO)"r/(CaO/MgO)riq, using the cxtrapolated interface liquidcompositions for the programmed moling experiments (squares)along with the equil ibr ium values of Watson (19?9) forexperiments in the system Na2O-CaO-MgO-Al2O3-SiO2.
anns were most clearly resolved and the spacing wasa minimum. Although there is considerable scatter, itis clear that the spacings are the largest (about l0pm) at the slowest cooling rates, have a minimum ofabout 4 pm in the range 50o to 200"C/hr, and in-crease slightly to about 6 pm in the 300'C/hr runs.The scatter in the data is real and not analytical.There are patches of different spacing, even within asingle crystal. This variation in spacing may be dueto variation in melt composition (and therefore liq-uidus temperature and therefore undercooling) asso-ciated with the composition gradients near forsteritecrystals. We have not, however, been able to associ-ate alay changes with any specific forsterite crystals.
As for the forsterite, it is not possible to determineaccurate nucleation or growth rates for the clinopy-roxene. Because the crystals must have grown en-tirely between the run time of the longest run whichcontains only forsterite and glass and the run time ofthe shortest run which contains clinopyroxene, it ispossible to estimate minimum average growth rates.For the 300"C/hr runs the crystals must have grownabout 4 mm in less tlan I minute, so the growth ratemust have been greater than about 7 x l0-3 cm/sec.For the l0oC/hr runs they must have grown about 4mm in less than 18 minutes, so the growth rate musthave been greater than about 4 x l0-o cm/sec. Theserates are in good agreement with growth rates of theorder of l0-' cmlsec for this bulk composition ob-tained in this temperature range from microscopeheating-stage experiments (Kirkpatrick et al., 1976).Because the samples are fully crystallized, it is notpossible to determine the crystallographic directionwith the highest growth rate.
oYg
I
E n d o f C r y s t o l
6.5p+/toK
KIRKPATRICK ET AL.: GROWTH IN INCONGRUENTLY.MELTING COMPOSITIONS 237
Fig. 12. Photomicrographs of dendritic clinopyroxene crystals. (a) l0'/hr, plane transmitted ligbt. Wollastonite is in dark areas
between dendrites. (b) 200'lh, plane reflected ligbt. Wollastonite is between dendrite arms.
Discussion
O ccurrence of forsteriteThe forsterite in these experiments is cleady me-
tastable and only occurs because of the failure ofclinopyroxene to nucleate. The highest temperatureat which forsterite occurs is l25l"C. Fitting the
stable part of the forsterite liquidus surface in thejoin forsterite-diopside with the relationship
wtTo Fo5o,1a : 1.495 x 103 exp [-ll '96 x lD'/Rn
(Fig. 598 in Leven et al., 1964) and extrapolating tothe diopside composition gives a metastable liquidustemperature of about 1260"C. The accurary of this
Table 5. Electron microprobe analyses of clinopyroxene crystals in fully-crystallized samples
l 0 ' / h r , I 1 9 6 ' c
t 2 3
t 0 0 " / h r , l l 5 l " C
t 2 3
2 0 0 ' l h r , l l S l ' C
1 ) ?
1 00 ' / h r
I t 7 2 " C
3oo" lhr
l 2 0 l o c
Ca0
s i 0z
Mgo
To ta l
5 l
Mg
0 . 9 5 rI O O O
I . 0 4 2
6 . 000
2\ . \9 z \ .89 25 .00
55.56 55 .30 55 .712 0 . 1 3 1 9 . 7 6 1 9 . 4 9
1 0 0 . 1 8 9 9 . 9 5 1 0 0 . 2 0
2 5 . 7 0 2 5 . 1 1 2 5 . 5 9
55.?2 56 .13 55 .63
1 8 . 7 1 1 9 . 1 9 1 8 . 9 2
9 9 . 6 3 I o o . 4 3 l o o . l 4
0 . 9 9 6 0 . 9 6 2 0 . 9 8 5
t . 9 9 8 2 . 0 0 8 2 . 0 0 0
I .009 | '023 I .01r {
5 . 0 0 0 6 . 0 0 0 6 . 0 0 0
25.61 24 .65 25 .54
55.32 55 .57 55 . \2
f 8 . 9 7 1 9 . 6 7 1 9 . 3 0
9 9 . 9 0 9 9 . 8 9 l o o . 2 5
o . 9 9 0 0 . 9 4 9 0 . 9 8 3
1 . 9 9 5 1 . 9 9 8 1 . 9 9 2
l . o 2 o r . 0 5 4 1 . 0 3 4
5 . o o o 5 . 0 0 0 5 . 0 0 0
2 5 . t \ 2 \ . 8 4
5 5 . 0 7 5 6 . 1 2
1 9 . I 3 1 9 . 5 o
9 9 . 3 4 1 0 0 . 4 5
0 . 9 7 6 0 . 9 5 I
1 . 9 9 5 2 . 0 0 6
1 . 0 3 3 r . 0 3 8
6 . o o o 6 . 0 0 0
0 . 9 4 0 0 . 9 5 9
t . 9 9 2 r . 9 9 1
| . 0 7 6 r . 0 6 0
5 . 0 0 0 5 . 0 0 0
PROTOENSTATIT
FORSTERITE
PSEUOOWOL LASTON I T E
238 KIRKPATRICK ET AL.: cRowril IN INj1NGRUENTLY-MELTTNG coMposrrroNs
sioz//
+ GoSiou 23
ToMgSiO.
'ToMSrSiO.
45 50 Mgrsioo+
predictions of the theory of Chernov (1974). The fun-damental shape of almost all of the forsterite crystalsis a hopper. Only a few of the thinnest crystals showa fully-faceted morphology, and this may be an acci-dent of the way they were cut during sample prepara-tion. The smallest crystals are usually hopper-shapedwith some planar surfaces (Fig. 2a). Most of thelarger ones are hopper-shaped with dendrite arms de-veloped from corners. There is no evidence of break-down of flat interfaces by random fluctuations. Thisimplies that the forsterite is growing by a layer-spreading mechanism, that signifisanl super-saturation at the interface is necessary to drive crystalgrowth, and that models which assume interfaceequilibrium will be insufficient to describe thegrowth.
Fig. 13. clinopyroxene compositions plotted in part of the system Sio2-casio3-Mg2Sioa.
extrapolation is difficult to determine, but forsteritemay be supercooled a few degrees. This result is ingood agreement with other programmed 666ling ex-periments u5ing platinum loop methods (Donaldsonet al.,1975).
Forsteite morphologt
The development of the forsterite norphologies inttrese experirnents is in very good agreement with the
9
= 8\
7
6
5
4
3
2
I
CLINOPYrcXENE DENOflTE ARM SPACIIVG
cooLtNG RATE (7HR.)
Fig. 14. clinopyroxene dendrite arm spacing vs. cooling rate for all fully-crystallized runs.
KIRKPATRICK ET AL.: GROWTH IN INCONGRUENTLY-MELTING COMPOSITIONS
It appears that breakdown of a euhedral forsteritecrystal takes place first by macroscopic diffusional in-stability and only later by random fluctuations atcorners. The critical crystal size for the onset of hop-per morphology appears to be about 12 trrm. This isprobably small enough to be affected by surface en-ergy (capillarity), although this still needs to be con-sidered in the theoretical analysis. There appears tobe no critical size for the onset of dendrite develop-ment from comers, and we can see no systematicrelationship between the presence of dendrites andcrystal size. More theoretical and experimental workis needed.
It is not clear why the secondary dendrite arms de-velop. Figures 3 and 4 show that they start devel-oping near the end of the primary dendrite arms andthat in many cases their external surfaces appear tobe crystallographically controlled. Their inner sur-faces and in some cases their outer surfaces do notappear to be crystallographically controlled.
One possible mechanism for their origin is thatthey develop after the primary dendrite tip pene-trates, at least partially, the diffusion halo surround-ing the crystal. Figure 4 indicates that there must besome statistical factor in their development, since thespacing of the secondary arms, while of the same or-der of magnitude, is neither constant nor variable ina uniform way.
From a purely geometric standpoint these experi-ments show, especially in Figure 4, that melt in-clusions in olivine crystals are trapped primarily bythe growth of secondary dendrite arms parallel to theoriginal interface.
Comparison to natural hopper and dendritic morpholo-gies
The development of the hopper and dendritic mor-phologies of the forsterite crystals in these experi-ments is similar to the development of generally simi-lar morphologies of many natural phases. In mostcases the interface breakdown of crystals in igneousrock is associated with edge effects rather than withrandom fluctuation on flat interfaces. (Whether thisis due to macroscopic diffusional instability or ran-dom fluctuations at corners is not always clear.) Themorphologies of many olivines in terrestrial and lu-nar basalt (Drever and Johnston, 1957; Donaldson etal., 1975'. Donaldson, 1976) arc basically hopper-shaped with dendrite anns extending from the cor-ners. Figure 2d shows a typical skeletal olivinephenocryst in glass from a mid-Atlantic ridge basalt.It is not hopper-shaped but does have dendrite arms
growing from corners. There is a kinematic wave onthe lower right arm. Even the net dendrite olivinesthat grow in the margins of basalt pillows start theirbranching at corners (Kirkpatrick, 1979).
Other phases show generally similar morphologies.The arrowhead morphologies of chrome spinels andmagnetites are due to development of dendrite armsfrom corners. The hopper and skeletal morphologiesof pyroxene crystals (Walker et al., 1976) are prob-ably also due to edge or corner effects.
Note that the development of spherulites is a nu-cleation effect and unrelated to the development ofhopper and dendritic morphologies (Keith and Pad-den, 1963; Kirkpatrick, 1979), although all form inresponse to composition gradients in the melt. Thetheory discussed here is not applicable to spherulites.
Interface melt compo sition
With the addition of effects associated with cornersand reentrants, the melt compositions at the inter-faces of forsterite crystals are in good qualitativeagreement with theory. For a given crystal the ditrer-ence between the melt compositions at the interfaceand far from the interface is least at corners and ondendrites and greatest in reentrants (Table 3). This issirnply due to the geometrical effects of the melt vol-ume to interface area ratio (Chernov, 1974).
For flat interface segments the increase in AMgOwith increasing run time (Fig. 8) agrees well with thepredictions of both Hopper and Uhlmann (1974\ andMiiller-Krumbhaar ( 1 975).
The continual decrease in MgO at the interfacewith increasing value of the product of run time andcooling rate (Fig. 9) is also in good agreement withthe theory of Miiller-Krumbhaar. The reason therelationship is convex upward, rather than linear orconcave upward as he shows it, is that the diffusioncoefficients in the experiments are decreasing withdecreasing temperature while he assumes a constantv5lue. The upturn predicted by his theory is not ob-served. This may be because clinopyroxene nucleatesbefore it can occur.
These results are also consistent with modelswhich assume interface equilibrium, but the largeCaOlMgO partition coefficients, their lack of system-atic variation, the large variation for one crystal (Fig.I l), and the large variation in AMgO and ACaO evenfor a single crystal (Table 3) all argue for dis-equilibrium at the interface. The metastable olivineliquidus surface is not known, however, and it is pos-sible (although we feel it unlikely) r1tu15sns1hing ap-
KIRKPATRICK ET AL.: GROWTH IN INCONGRUENTLY-MELTING COMPOSIZONS
proximating interface . equilibrium is being main-tained.
Composition gradients in the melt
The composition gradients in the melt near the in-terfaces are in good quattative agreement with thetheory of Cooper and Gupta (1971). Figure 7 showsthat the melt composition at the interface lies on thesilica-rich side of the forsterite depletion line. Goingaway from the interface the compositions move to-wards the original bulk composition along a curvedpath that crosses or cogres to the forsterite depletionline and then curves back towards the bulk composi-tion. This is precisely the variation predicted by Coo-per and Gupta. The point where the compositiongradient crosses the forsterite depletion line is themean composition of the liquid influenced by the for-sterite growth.
It is not possible to analyze the quantitative appli-cability of the Cooper and Gupta theory to these ex-periments because the multicomponent exchange dif-fusion coefficients are not known and because theexperiments were not isothermal. It is clear, however,that if we are to understand the growth of crystalsfrom incongruently-melting compositions, we needvalues for this kind of difusion coefficient. valueswhich are in very short supply.
Occurrence of clinopyroxene and wollastonite
The first occurrence ofclinopyroxene is suppressedmore in these experiments than is the first occurrenceof the liquidus phase in any other set of programmedcooling experiments in the same range of cootngrates. This is clearly associated with difficulties in nu-cleation and not slow growth, because the clinopy-roxene growth rates are so high that if a small crystalwere present it would rapidly fill the entire charge.This easy suppression of nucleation also occurs inmicroscope heating-stage experiments with the samecomposition (Kirkpatrick et al., 1976).
The reason for the minimum in the clinopyroxenenucleation temperature at the intermediate coolingrates is not clear. The decrease from lD"/ht to 50"/hr can be explained kinetically-with increasingseeling rate the probability of nucleation of a crys-tal at a given temperature decreases because the timeavailable decreases. Thus, a larger undercoolingmust be reached for nucleation to occur in a finitesample. This is the explanation usually given for sim-ilar variations observed in many sets of programmedcooling experiments (Walker et al., 1976; Grove andRaudsepp, 1978).
The increase in the clinopyroxene nucleation tem-perature from SOolhr to 300'/hr is unexpected and isthe only such variation yet observed. The data inTable 4 indicate that heterogeneous nucleation onforsterite once a critical interface melt composition isreached cannot explain the variation. The interfacecompositions follow the cooling rate X time relation-ship, and there is nothing unusual about the interfacecompositions in the runs quenched just prior to clino-pyroxene nucleation. Neither is it likely that clinopy-roxene is nucleating by a different mechanism in thehigher cooling rate experiments. If this mechanismwere available. it should be used at the slower cool-ing rates also. If this increase in nucleation temper-ature with increased cooling rate is found to be acommon occurrence, more work on its origin may bejustified.
The occurrence of wollastonite in these charges isthe result of crystallization of forsterite and MgO-rich clinopyroxene, which leaves the melt enriched inCaO. Its occurrence between the clinopyroxene den-drite arms is a kinetic effect. Figure 7 shows that theliquid compositions before clinopyroxene forms arewell within the clinopyroxene primary phase field.Once the clinopyroxene begins to grow, however,CaO builds up at the clinopyroxene-melt interface,and because the growth rate is so high it cannot dif-fuse far. Eventually wollastonite saturation (or super-saturation) is reached at the clinopyroxene interfaceand wollastonite crystallizes there.
AcknowledgmentThese experiments were done in the experimental petrology lab-
oratory at the NASA-Johnson Space Cent€r in Houston. We aregrateful to Gary Lofgren for allowing us the use ofthese facilitiesand Oscar Mullins for helping with the experiments. We are alsograteful to Tim Grove and D. M. Henderson for their reviews ofthe manuscript. This work has been supported by NSF grantsEAR 7682185 and EAR 7903923.
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Chernov, A. A. (1974) Stability of faceted shapes. Journal of Crys-tal Growth, 24/25, ll-31.
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Donaldson, C. H. (1976) An exfrerimental investigation of olivine
KIRKPATRICK ET AL.: GROWTH IN INCONGRUENTLY-MELTING COMPOSI?IONS 241
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Donaldson, C. H., Usselman, T. M., Williams, R. J., and LofgrerlG. E. (1975) Experimental modeling of the cooling history ofApollo 12 olivine basalts. Proceedings of the Lunar ScienceConference, 6th, 843-869.
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Manuscript received, Augast 22, 1979;accepted for publication, August 6, 1980.