Journalof CrystalGrowth 104 (1990)539—555 539North-Holland

ON THE FACET-SKELETAL TRANSITION OF SNOW CRYSTALS: EXPERIMENTS IN HIGHAND LOW GRAVITY

T. ALENA * andJ. HALLETT * *

Desert Research Institute, Reno,Nevada89506, USA

and

C.P.R.SAUNDERSUniversity of ManchesterInstitute of Science andTechnology,P.O. Box 88, ManchesterM60 I QD, UK

Received23 May 1989; manuscriptreceived infinal form 23 March1990

A Laboratoryinvestigationof theinfluenceof air velocity on thegrowthof columnarice crystalsfrom thevaporover therange— 3 to — 5 ° C showsthat thelinear growth velocityincreasesand thatcolumnstransform to sheathcrystalsor needlesas airvelocityincreasesfroma fewcms — to 40cm s — Comparisonwith a similar transition of platesto dendritesshows that,macroscopically,inboth casesthe facets sproutroundedtips at a critical velocity which is lower for higher ambient supersaturation.Studiesin lowgravity (20 s KC 135 aircraft parabola)show that chamberscaleconvection undernormal gravitymay havesignificant influenceongrowtheven in theabsenceof animposedair velocity.Fallingsnowcrystals,both plate like and column like, becomemoreskeletal inshapeastheygrow andfall with increasingvelocity.This developmentdependscritically on temperature(±0.5 ° anddemonstratesthat snowcrystal shapeis even moredependenton environmentalgrowthconditionsthanpreviouslythought.

1. Introduction plates to sector platesto dendrites,growing near— 150 C, can also be accomplishedby increaseof

It has long beenknown that the habit of ice ambientair velocity. The criterion for the transi-crystals growing from the vapor under super- tion is dependenton the relative orientation be-saturationtypical of the atmospherehas a corn- tweencrystalandair flow, but is otherwiseequiv-plex dependenceon temperature, withplates or alent to an increaseof supersaturation.Interpreta-dendrites growing above —3°C and between tion of the habit changeshas hypothesizeddiffer-—8°Cand —25°C,and prisms, hollow columns ent growth mechanismson different faces, the(sheathcrystals) and c axis needlesgrowing be- growth rateresulting fromdefects, surfacenuclea-tween —3 and —8°Cand below —25°C[1—3]. tion and rough growth on basal or prism face,Furthermore,this early work demonstratedthat being dependenton supersaturationandtempera-the transition from faceted growth to skeletal ture [5,6]. Thepurposeof the study presentedheregrowth, and ultimately to non-faceted needlesor is to describethe detail of the transition fromdendrites,was associatedwith increaseof super- prism to sheathcrystals to needles,compareitsaturation.Morerecent studiesby Keller andHal- with the plate—dendritetransitionstudiedearlierlett [4] havedemonstratedthat the transitionfrom and extendedto higher velocities.Laboratory re-

sults will be comparedwith a specificexperiment* . . . . . where relative air motion is reduced under lowPresent address:Quahmetncs,Inc., 1165 National Dnve, . ..

Sacramento,California 95834, USA. gravity, and the implicationsexarmnedfor further* * Correspondingauthor, experimentsin a microgravityenvironment.

0022-0248/90/$03.50© 1990 — Elsevier SciencePublishersB.V. (North-Holland)

540 T. Alena etal. / Facet-skeletaltransition ofsnowcrystals: experimentsin high and low g

2. Experimental empirically by finding the velocity at which thegrowth velocity decreasedas the flow rate in-

Foranyexperimental studyof icecrystalgrowth creasedat different positions in the chamber;from the vaporto be relatedto the atmosphere,it measurementsat 99% approachto equilibriummust simulate conditions under which crystals could be madeup to 40 cm s-‘ in a chamberofgrow as closely as possible.In principle this im- length 4 m. A further criterion was that the flowplies controlling temperature,supersaturationand be laminar. This was judged by lack of thermo-the diffusive propertiesof the air — heat, vapor, couplefluctuation(±0.1°C) in the growth regionmomentum.Air flow, throughthe fall velocity of and estimatedvisually by straight trajectoriesofthecrystal, is alsoimportantin controllinggrowth, ultrasonically produced 10 zm diameter waterso that it is always necessaryto add velocity to dropsusedas atracer.An overall error estimateofthese variables. This was achieved in the first growth temperatureis ±0.2°C,supersaturationstudyby Keller and Hallett[4]by usinga dynamic ±1.0% and velocity measuredby a hot wirethermaldiffusion chamber,a thermal water vapor anemometerand particletracer ±1 cm s~.Thisdiffusion chamberincorporatedinto a closedloop design is acompromise betweena shallowcham-wind tunnel [4]. The upper plate is maintained ber for small time constant and low Reynoldswarmer thanthe baseplatewhich stabilizesthe air number,anda deepchamberto spreadthe veloc-flow; each is coveredwith ice or water in filter ity gradientto permit crystalsto grow undernearpaper to maintain a constant vaporpressureat constantconditions.eachsurface,dependingon temperatureandphase. The walls are constructed of sealed doubleTo a first approximationboth temperatureand polycarbonatesheets,with 0.5 cm dry air sep-vapor pressure vary linearly withheight [7]. Since aration to prevent window fogging and restrictthe saturationvaporpressurevariesexponentially heat inflow. Excess insulation leads to con-with temperature,a supersaturatedregion is pre- densationon the wallswhich limits visibility andsent in the central part of the chamber,with a provides a water vapor sink, as crystals growmaximum just below the center. Crystal growth irregularly in the supersaturatedenvironment.It ismaybe studiedat aselectedtemperatureby choice thereforeadvantageousto allow someheat flow atof a mean temperature;choice of top and base the walls. This gives rise in practice to a smalltemperaturesas a departure(positive and nega- convectionof — 0.5—1 cm s’ on the scaleof thetive) from this meangives the supersaturationas chamber— up at the wallsand down towardstheanindependentparameter.In practice,experimen- center.Under unventilatedconditions, this circu-tal compromiselimits the precision in environ- lation extendsapproximatelythe chamberdepthmental control. Air, after enteringthe chamber, from the wall, with central circulationof a fewconditionedto be saturatedat the mean tempera- mm s— As the horizontalair velocity is increasedture, underconditionsof laminar flow relaxesinto beyond1—2 cm s~,this convectionvelocity is noa steadystatewith a time constant longerof importance.

This givesapracticallower limit to the velocityT — x2/~r2(D,ic, v), obtainablein this type of chamberin any earth-

bound laboratory; lower valuescan be achievedwhere x is the center—platedistance,and D, K only in a low gravity environment.From dimen-and v are thevapor,heatandmomentummolecu- sionalconsiderationsof equationsof motion,con-lar diffusivity. If V is the meanvelocity, this is vective velocitiesfall as local gravity is reducedasequivalentto a relaxationdistanceof L = VT. In or g dependingon conditions.A first attemptthe presentequipmentthis gives a time constant at growing snow crystals undera low gravity en-between1 and4 s. Selectinganupperlimit of the vironment was made in a static ice diffusionfall velocity of individual snow crystals of 40 cm growth chambercarried on a NASA KC 135s— [8] gives a distanceconstantbetween0.5 and2 aircraft in parabolic trajectory. The chamberwasm. In practice, the upper limit was determined approximatelythe samevertical height as thedy-

T. Alenaet al. / Facet-skeletaltransition ofsnowcrystals: experimentsin high and low g 541

GAS INLET VACUUM

PORT

Fig. 1. Schematicof staticvapordiffusion chamberfor ice crystalgrowthunderlow gravity.

- —COMPUTER

CONTROL

CAMERAS ________

~

~-... DIFFUSIONChAMBER

CRYSTAL GROWThsuppoRT

Fig. 2. Layout of staticdiffusion chamberfor ice crystalgrowth from the vapor, mountedon a paletteready for KC135 parabolictrajectoryflights.

542 T. Alenael a!. / Facet-skeletal transitionof snowcrystals: experimentsin high and low g

Q5

~ 0L- -~ --zP~ 05

~20 _____

.~ IC ~ ~ GRAVITY LOW GRAVITYz

Ccr~

~I-I.C10 20 30 40 50 60 70 80 90

TIME (s)

Fig. 3. Vertical and lateralg componentduringlow g KC135 parabolaand high g pullout. The effect of turbulence alongthe flightpathgives g uncertainty±0.05in low g and 1.8±0.1 in high g with lateralturbulenceeffects ±0.05g.

namic chamber,and diameter28 cm (fig. 1). The diameter — 0.5 mm insertedvertically into thetop and baseplates weremadeof 3/8 inch (0.95 chambercenter. At temperaturesnear 0°C it iscm) copperwelded to 1 mm sinterednickel sheet. necessaryto cool therod below —40°C in dry iceTemperaturecontrol of upper and lower plates prior to insertion to preventthe growth of super-was achievedby computer controlledthermoelec- cooled waterdroplets. Initiallybothchambers needtric cooling elementswhich could be set and to berun at high supersaturationto removenucleichangedduring flight, taking about 10 mm to which grow asdropletsand sediment; this takesreach a new equilibrium. The rangeof tempera- about 20 mm. The dynamic chamber operatesatture extendedfrom +20°Cto —30°C(±0.2°C) _____________________________

1.0for either plate. The upper plate was saturatedwith waterby flooding thebaseplate,cooling the _

upperplateandallowing vaporto diffuseuntil the ~~ 0.5sintered nickel on the upper plate became

>saturated.This chamberwas flown in the NASA ~

KC 135 aircraft (fig. 2)) in parabolic trajectories ~ 02

which gave — 102g for approximately20 s fol-

lowed by 1.8gduring pullout (fig. 3). Someten 20 .10 0

parabolaswere flown sequentially for any given TEMPERATURE (°C)

experiment.Supersaturationsare computedfrom measured

temperatureand the vapor pressuregiven by the

Region of growth=Clausius—Clapeyronequation. For both systems,selectionis madeof temperatureand supersatura- ~ a: ~eaojrernent

tion to be studied andthe top andbottomtemper-aturespre-set(fig. 4). A full reservoirlastsabout1day in the dynamic chamberand a few hours in 0.2

the staticchamber,dependingon the carrier gas _________________________________________composition and the imposed temperaturedif- 10 20 30 40 50

ference; this isadequatein the latter case since SUPERSATURATION 1% Iflight duration is not more than 2 h. The static Fig. 4. Temperatureand supersaturationprofiles for thermal

diffusion chamberfor ice crystal growth from vapor underchamber is designed to be evacuatedand can controlled temperature, and supersaturation. Temperaturereadily be operatedat any pressurewith gases gradients:(A) 0.59°Cmm’; (b) 0.47°Cmm1 (C) 0.37°C

other thanair. Crystalsare grown on a glassrod, mm1.

T Alenaet a!. / Facet-skeletaltransition ofsnow crystals:experimentsin high and low g 543

slight pressureover ambient(2 cm water) to pre- velocities in stepsas thecrystal grows,providingvent entry of outside air; the laboratory is at a the tip is well separatedfrom any neighborsandpressurelevel of approximately870 mbar. grows horizontally so that the temperatureand

Initially many small crystals grow on therod, supersaturationremainunchanged.After some 15 to 30 mm, favorably oriented Both chamberscan be operatedat ice super-crystalsgrow beyondtheir neighbors,to a length saturationof a fewpercent overice, throughwaterof 0.5 to 1 cm. Isolatedcrystals,growing into the saturation to high water supersaturation ap-air streamin the case of thedynamicchamber,are proaching200%. Crystalscan thereforebe grownselectedfor study. Growth is recordedby direct undera wide varietyof conditions. In particular,photographyor VCR througha zoom microscope the chambers canbe operatedat or somewhatto give a minimum field of view of 2 mm. Cham- below watersaturation(for a given temperature)berdesigngives minimum working distanceof 15 andprovidesimulationfor crystals growingin thecm in the dynamic chamberand — 25 cm in the atmospherein the presenceof supercooled waterstatic chamber;this limits resolutionin practiceto dropsor betweenwater and ice saturation.a fewmicrons.Limited adjustmentof crystalposi-tion is possibleby rotation,andverticalmotionoftheglass rod. 3. Results

In the dynamic chambertwo or three wellseparatedcrystal tips canbe examinedin a single 3.]. Experimentsin the dynamicdiffusion chamber-experimentat different levelsin the chamber, each Igwith its own temperatureandsupersaturation.Fora given crystal,it is possibleto examinethe effect Wedistinguishthefollowinggrowth terms: solidof air motion by increasingand decreasingthe column, with facets in prism and basal plane;

WI ND1mm

DIRECTION

~T~LL~Fig. 5. Transitionof hollow columnsto needlegrowthand back to thinnerhollow columnsas velocity is increasedfromzero to 18 cm

s~andreturnedto zero.Saturationratio over ice 20%, z.~p 0.56 gm3.

544 T. Alenaet al. / Facet-skeletaltransition ofsnowcrystals: experimentsin high and low g

hollow column, with the sameexternalperipherybut arbitrary internalfaces; sheath,an incomplete WIN Dhollow column; needle,a growth of one cornerof DI RECTIONa hollow column; spike, growth in a non-rationaldirection; plates, with facets in prism and basalplane; dendrites,branchinggrowth in directionofa axis; dorites, linear growth in directionof a axiswithout side branches.

The transitionfrom hollow column to needleorsheath,inducedby changeof air velocity,is shownin fig. 5. As the air velocity increasesfrom zero to18 cm s’, needlesgrow from eachcorner of theuppercolumn while sheathsgrow from the lowercolumn, which is partly shielded and in a lowersupersaturationenvironment.The column diame-ter does not revert with reduction of velocity;growth continuesas narrow hollow columns(fig.Sd). Fig. 6 shows thegrowth from a singlecornerof a column facing directly into the air stream;other corners,shieldedfrom the flow fail to de-velop. The effect of ventilation on sheathgrowthis shown in fig. 7. As ventilation increasesthegrowing tip narrows,becomingalmostcylindricalin cross section in fig. 7d. It is difficult to de-termine the exacttip shape,but it appears thatitis not faceted; facetsare only presenton thoseparts of the crystal downstreamfrom the leadingtip.

The effect of air velocity on dendrite growth ____________near —15°C is shown in fig. 8. At high velocitythe dendrites develop arms irregularly on eachside (fig. 8a); asthe velocity is reducedthe armdevelopmentis reduced(figs. 8b and 8c); at zerovelocity wall formed plates develop at each tip(fig. 8d).

The importance of air velocity in initiatinggrowth in anon-rationaldirection is shownin fig.9. Initial growth at a velocity of 13 cm s’ takesplaceat some15°to the c-axis;whenthe velocityis removed, growthreorientsto the c-axis direc- 1 mmtion. This is most noticeablein the lower twocrystals(arrowed)which resume growthparallel to Fig. 6. Sheathgrowth from onecorner of a hollow column at

the c axis of the original crystal. Growth direc- — 6.30C, 24% ice supersaturation,zip = 0.8 g m ~, asvelocityis increased fromzeroto 7 andfinally to 13 cm stions are inferred from the appearanceof crystalfacets; should there bedoubt, the crystal is raisedto a temperature near— 2°Cand a plate grown more dramatically in fig. 10 where the crystalon its end; a 90 ° angle shows that the original direction changestwice, as velocity isdecreased,directionwasthe c axis. This effect is showneven increasedand decreasedwith an interval of 365 s

T. Alenaet a!. / Facet-skeletaltransitionof snow crystals:experimentsin high and low g 545

a

WIND

DIRECTiON d

C

0.5mm

F1g. 7. Transition of sheathgrowth of a hollow columns to needlegrowth with increaseof ventilation at —5°C,3~ icesupersaturation,zip = 0.1 g m

(fig. lOc, arrowed).The rateat which this growth velocity, in contrast to the transitionfrom platesreorientation occurs, following a discontinuous to dendrites at — 15°C,which is considerablyvelocity change,is shown in fig. 11, with a time changedby air velocity.constantof about 100 s. The overall influence of The influence of air velocity on shapeandtemperatureand supersaturationon the form of linear growth velocityis displayedin fig. 14 for ccrystalsgrown between—4 to —8°C is shown in axis growth at —5.2°C and a axis growth atfig. 12 for zerovelocity (unventilated)crystal and — 14.5°C. This shows that a transitionof shapeat 20 cm s~air velocity. Atmosphericconditions associatedwith anincreasedgrowth velocity takesare representedby the region close to water place as the fall velocity increases.This impliessaturation(dotted), indicating that needlesgrow that for these temperatures,the atmosphericformin two regions,which extendto higher and lower will be sheathcrystals,at —5.2°C with all shapestemperatureas thevelocity increases.The linear possible at — 14.5°C. Thesecurves are highlygrowth rateof crystalspointing intothe air stream sensitiveto temperature,as shownin fig. 12. Evencan readily be measured.Theseare comparedin a differenceof 0.5°C may changethe shapeandfig. 13 for a and c axis growth for different air linear velocity by a factor of two. It is useful tovelocities. Eachfigure is derivedfrom some 100 plot the linear growth ratesas the squareroot ofpoints representinga temperature,excess vapor the velocity (fig. 15). This dependencefollowsdensity (supersaturation) andambientair velocity, from a considerationof laminar boundary layerThe critical transitionfrom hollow/solid columns theorywith thicknessproportionalto Re1”~2(Re=

to sheaths near —5°Cis unchangedwith air local Reynolds number).The upper curves ap-

546 T Alenaeta!. / Facet-skeletaltransition ofsnowcrystals:experimentsin high and low g

WINDp

DIRECTION

______ ~

~pir ~ ~- 11

/ 0.5mm

Fig. 8. Influence of air velocity on a axis dendritegrowthas air selocity is reduced.Sidearm developmentis reducedwith velocitydecrease,giving a singlearmdorite(c); at zerovelocity platesgrow on eachtip (d). There is agreatertendencyto form platesin the

shieldedregiondownwind of theleading tip at lowervelocity.

proximatethis idealized relationshipwhich is ap- zero air velocity but under normal gravity. Theproachedat higher vapor densityexcessand air situationwastherefore optimizedto give the maxi-velocity mum linear growth rate of ice from the vapor.

Simple theory [9] tells us that the rate of crystal

3.2. Experimentsin the static diffusion chamber growth dependsboth on the rateof heattransferunder low gravity in the carrier gas, which is enhancedby a high

thermal conductivity, and the rate of mass trans-The KC 135 environmentgives a maximum of fer, which is enhancedby increaseof vapordiffu-

20 s of 10 2 g, so that thekind of investigationis sion coefficient. The latter increase withdecreaseseverely restricted. The purposeof the experi- of pressureof thecarrier gas.Thesecontributionsmentswas to find out whetherconvectionwithin are of comparablemagnitudeunder the experi-the chamber was significantly influencing the mental conditionsfor air at — 10°C and pressuregrowth rate of a crystal tip underconditions of of 0.5 atm [10]. Theseconsiderationssuggestthat

T. Alenaet al. / Facet-skeletaltransitionof snow crystals:ezperimentsin high and low g 547

_________________ constraints.The maximumlinear growth velocity______________ of an ice crystal at 1000 mbar pressureis near

_________________________________________—5°C, where needlesor spikes grow. Ground

based experimentsshowedthat maximum growth

i lineargrowth rate with helium pressureat a fixedvelocity couldbe obtainedin helium at apressureof — 500 mbar. Fig. 16 shows thevariation of________ supersaturation.The conditions were chosen to

give —5°C near the chamber center, with anWIND

I. excessvapordensity1.3 g m2 this could not beDIRECTION too large, as thewater vaporreservoirwould be

1 mm ] depletedin flight..The operational procedurewas to preset the

plate temperatures,grow and sedimentany aero-sol in the chamber,and begin growth of a crystaljust after aircrafttakeoff. Growthof crystalswasrecordedas the aircraft flew through consecutive

_____ parabolic trajectories, withgravity varying be-______ tween1.8g and102g. Fig. 17 showscrystal forms

Fig. 9. Crystals resume growthparallel to the c axis with during the flight. Fig. 18 shows how thelength ofremovalof velocity.Temperature— 5.7°C,ice supersaturation thelong crystalchangeswith successiveparabolas.

17%, zip=0.5gm3. The linear growth rate of the crystal varies be-tween2 and6 ±1 ~.tms~undertheseconditions.

in order to obtain a high crystal growth rate, to The accuracyof measurementis sufficient to giveprovideoptimum conditionsfor studyin the short an estimateof changesof growth velocityas mdi-time available, a high conductivity gas at low cated in this figure; the velocity increasesby apressureshould be used. There is, however, a factor of 3 ±1 as g increasesto its maximumsecondcriterion to be considered.At high vapor value. It is to be notedthat local gravity changesdiffusivities, the gradientof vapordensityacrossa are almost squarewave (fig. 3), sothat it wasgrowing crystal is reduced, showinga tendencyto impracticablein this experiment to observe theproducefacetsratherthandendritetips or needles growth in ig for direct comparison withlow or[11]. It is necessaryto optimize these opposing 1.8g; pre-parabolameasurementsusuallyinvolved

Table 1Transportpropertiesof growthenvironments

Kinematicviscosity, p Thermometricdiffusivity, ic Diffusivity, D Pr = v/Ic Sc = v/D ic/D(cm2 ~1) (cm2 ~1) (cm2 ~1)

Air 0.135 0.187 0.226 0.72 0.56 0.83(0°C,1000mbar) (0°C,1000 mbar) (water vapor,

0°C,1000 mbar)

Helium 1.09 2.56 0.77 0.42 1.4 3.4(0°C,1000 mbar) (0°C,1000 mbar) (0°C,1000 mbar)

1.5(0°C,500mbar)

Water 0.0179 0.0014 0.00002 13 1600 140(0°C) (NaC1)

548 T. A!enaeta!. / Facet-skeletaltransition of snowcrystals: experimentsin high and low g

c—axis ~

WIND

DIRECTION

I-

~~1

1 mm

Fig. 10. Sequenceshowingreorientationof a spike-sheathasvelocityis decreased,theincreased.Thekinksin directioncanbeseen inseveralcrystalsin (c), arrowed.

T. Alenaetat. / Facet-skeletaltransition ofsnow crystals:experimentsin high andlow g 549

25 I I I I I

ii

5,

*

~0 ke - SheathE 202~0~~—

2CD 1510 -

0.

‘~ 5.

5,1C

I I I I I I

0 50 100 150 200 250 300 350

TIME

Fig. 11. Reorientationof preferredgrowthdirectionfor two crystalsof fig. 10. At t = 0 air velocity was reducedfrom 18 cm s1to 5

cms~.

UNVENTILATED 20cm s1I 1 I’ I

I /I j I j

I j II j I30 ~ Spik I / 30 -

es SpikesI / III I I,

25-I I / 25-26 I I 26 IIz I ~I ~‘ ~ I’ Ii

0, jI 8;! ~ II ~‘/

jt ~ 20 h1 ~20- ~s ,~ ‘I

I I ~I / ‘~ I~ ,Ii /

C.’ / C.~ I\ / i /w 15 ‘~~I I / ~ 15 - I ~ / /

I I I Columns “ — I /I Sheaths I / and i / Columns

Ll.j I I / Scroll w 01% I / andC.~

‘I I!10 - / — 10 -~ Sheaths / / Scroll

‘t I~ I,II

hI,.. ~Sal‘,~ I/ tiOll

5.. I,\~,__ .4.

Hollow / Solid Hollow/Solid

a Columns b ColumnsI I I I

—4.0 —5.0 —6.0 —7.0 —8.0 —4.0 —5.0 —6.0 —1.0 —8.0

TEMPERATURE°C TEMPERATURE°C

Fig. 12. Compositeof crystalhabit and shapeat zero and 20 cms~ ventilation velocity from approximately100 points for eachgraph.Dottedline is watersaturationand shows abroadeningof the —5°Csheathregion with increasingvelocity. It also indicatestwo regionsof needlegrowthwhich changein temperaturewith velocity.The transitionto sheathgrowth is uninfluencedby velocity

at —5°C. Linesof demarcationareuncertainto ±0.25°C.

550 T. Alenaet a!. / Facet-ske!eta! transitionof snowcrystals: experimentsin high andlow g

UNVENTILATED “a” axis 7cm s~ “a’ axis

0.1 ~ 0.1

a I I

—12,0 —130 —140 —iSO 150 —12.0 —130 -140 —150 -100

TEMPERATURE ‘C) TEMPERATURE )~C)

UNVENTILATED “c’ axis 7cm s1 ‘c” axis 20cm S 1 “c’ axis

I ~ ~ oj +i 10~~

± ~

C d e—4,0 —5.0 —6.0 —7.0 —60 —40 —5.0 —60 —70 —UI) —40 —50 00 —10 —00

TEMPERATURE )‘~) TEMPERATURE ‘C) TEMPERATURE I C)

Fig. 13. Lineargrowth rates of isolatedcrystal tips pointing into theair streamfor a axis (a, b) and c axis (c, d, e) growth). Eachgraphis derivedfrom approximately100 experimentalpoints at a given temperature,excessvaporpressureand ventilationvelocity.

aircraft manoeuvres whichprecluded thismea- perimentally using optical techniques,as will besurement. describedelsewherefor solution growth.The opti-

A questionariseson thescaleof the convection calpath length of air—watervaporsystemis, how-— whether the scaleis that of thecrystal (cm long, ever,too short in theseexperiments.It is of inter-mm tip diameter)or on thescaleof the chamber est to assess thetime requiredfor air motion to(2 cm deep). Ideally this could be answeredex- begin on each scale.The time constantfor a

T A/eisaet at / Facet-skeletaltransitionof snow crystals:experimentsin high and low g - 551

ICE SUPERSATURATION w~ ICE SUPERSATURATION (%l

a ID 15 2~ ‘~ b ~ 20 30 50 60

-5.2°C -14.5°C /

6 WATER / /6 SATURATION / 7I / AIR

AIR / VELOCITY / /VELOCITY / cm / /

cms~ 5 I / 3I / /

~37 / //— WATER . “ 20~’~

SATURATION - . -~ E

I3~ ~ -w

// 7_____ / ‘7

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 0.1 0.2 0.3 0.4 0.5 0.6 07 0.8 0.9

AMBIENT VAPOR DENSITY EXCESS (g rn-3) AMBIENT VAPOR DENSITY EXCESS (g m~)

Fig. 14. Linearcrystalgrowthvelocity andcrystalshapeatdifferentair velocitiesfor columns:at — 5.2°Cspikesandplates/dendritesat — 145° C. Dottedareasindicatetransitionregions.

vertical plate with helium distanceof 1 cm or 1 senting ratios of times for motion to begin bymm is 1.5 s or 0.5 s [12],which is quite long buoyancy and dissipationby heatloss or viscousenoughon eitherscalefor steadystateconvection damping respectively[13]. Values less than unityto begin and influence growthin the presentex- suggestthat the effect is unimportant. Table 1periment.This timescalewas verifiedqualitatively shows valuesof appropriate transportpropertiesby observingthe time for induced motionsto die and table 2 the values of Gr (Ra) which areaway under low gravity after admitting helium stronglydependenton the systemdimension(h3),gas,using smallice crystalsastracer, that is, either chambersizeor crystal size convec-

tion. This table shows that chamberscalemotionis important in 2g and ig in air and possiblyin

4. Discussion helium; it showsthat individual crystal convectionis barely important in air but is unimportant in

4.1. Criterion for convection helium. This raisesan importantquestionconcern-ing convectionin any cell designedfor study of

Enhancementof growth by buoyancyinduced growth of single facetedcrystals at a prescribedmotion canbeassessedin termsof a localRayleigh supercoolingor supersaturationin a gravitationalnumber (Ra),or Grashof number(Gr) repre- field. A thin crystal growing throughits environ-

552 T. Alenaet a!. / Facet-skeletal transitionof snow crystals:experimentsin high and low g

AIR VELOCITY (cms~) AIR VELOCITY (crns~)

I 4 9 6 25 49 I 4 9 16 25 49_________________________________________________ I I I

aI I

7b-5.2°C -14.5°C

6 6

0.90

/60

0.505 I—4 // /‘4 / / 0.40/I_ / /LI~J Q /050 / 0.35

~O4O /

/~ /e/ . / // - / .0.30/ce / /o ~ 0.35 -D / /(0 // - - 0.30 - // / 0.25/ / / 0.225

-- 0.25C, 2 2 /

0.200.225 / /

I //- 0.20 / /

- 0.150.10

0 I 2 3 4 5 6 7 8 9 0 I 2 3 4 5 6 7 8 9

[VEL0CITY]~ (cmsY2 [VELOCITY]~ (cms~)”a

Fig. 15. Data fromfig. 14 plottedas(velocity)1”2 thisidealization is approachedathighervelocity andvapordensityexcess.

B ment may give rise to convectivemotion because— of changesof density resulting from concentra-

—— —---

E / N N tion, or to a lesser extenttemperature,along its/ length andat its tip; motion may also result from

/>.

/ a bigger, lessdefinedgrowth, around the nuclea-/ tion and growth site on the scaleof the growth

0/ chamber.Convectivemotion is thereforedefinedw

> /0 / as intrinsicwhen initiatedby the crystal itself and/ will dependon the shapeand orientationof the

/0 crystal to the gravity vector; alternativelyconvec-I.)

I tion maybeextrinsic, whenthe crystal grows in a4 2. I velocity field prescribedby the growth chamberU,1- /

0 dimensionsand shape. The importanceof such

convectionis self-evidentif we are concernedwithdetailed growth rate, particularly if it is de-0 200 400 600 800terminedby a critical supersaturation requiredtoHELIUM PRESSURE 1 Torr)nucleatenew layers. It is ofinterest to compareFig. 16. Linear growth velocityof ice crystals in helium for

differentpressures. resultsobtainedin vaporgrowthin air with crystal

T. Alenael a/. / Facet-skeletaltransition of snowcrystals: experimentsin high and/owg 553

Table2Grashofand Rayleighnumbersng(~p/p)h

3/v2and ng(~p/p)h3/vsc

System Gravity

2g ig 102g

Grashof Rayleigh Grashof Rayleigh Grashof Rayleigh

Air Crystal 0.2 cm 3.2 2.3 1.6 1.2 0.016 0.011(0°C, 1000 mbar) Chamber2cm 3200 2300 1600 1200 16 11.5

Helium Crystal 0.2 cm 0.04 0.017 0.01 0.004 0.0002 0.0001(0°C,500 mbar) Chamber2cm 40 17 12 5 0.25 0.1

K = thermometric diffusivity, g = surface gravityacceleration,n = gravity factor, ~1p/p = buoyancy estimated fromtemperatureexcess1°C,v= kinematicviscosity, h = dimension.

growth in solution. Some insight into this dif- of Schmidt number(table 1) results in the prin-ferencemay be obtainedby considerationof dif- cipal resistanceto growthby solutediffusion ratherfering environmental conditions andtransport than heat conduction[19]. For most salts, super-processesin the two cases.Crystalsgrow by diffu- saturationis readily producedby cooling in thesive transportof water vaporthroughaninert gas absenceof nucleation.The effect of motion mayor solute moleculesthrough an inert solvent; in be studied by moving the crystal through thebothcasesthereis latent heattransportaway from solution [14] or with the solution flowing over athe crystal. In the case of icegrowth from the crystalat a fixed velocity [15—18].Growth ratesofvapor, the resistanceto growth resulting from facetedcrystals (potashalum, sodiumnitrate)arevapor transferand heat transfer are comparable. found to increase withfluid velocity with theBy contrast, in the case ofsolution growth, the growth rateapproachinga nearconstantvalueforsmall valueof solution diffusivities or large value fluid velocity of 20 cm s’.

.. —. —4CC

___ 4

Fig. 17. Ice crystals growingin thestatic diffusion chamberat temperature—5°C.ice supersaturation40%. ~p = 1.3 g m ~, inheliumat 500 rnbarpressure.

554 T Alenaetal. / Facet-skeletaltransition ofsnow crystals:experimentsin high and low g

/ practical interestsince thin facet crystal growth/

/MEAN under theseconditionsoccurringinto the aircraft/ GROWTH boundary layer could influence its transition to

/ VELOCITYI000 / y 3.4pm ~‘ turbulenceand influence lift; this would only be

MAXIMUM /5.9 ,um s-’/ of importanceat modestspeed whereaircraftdy-

E /..• ,, namic heatingfails to raisethe temperaturesuffi-ciently to destroythe supersaturation.2• -‘

‘MINIMUM..,~ 2.1 ~m S~ 4.2. The transition from faceted to non-faceted

~ 500 •..‘ (curved)growth

Results presentedabove and in the previousU)>-

paper [4] show that increaseof supersaturationU

and/orair velocityleadsto abreakdownof faceted100 E—~ ~ Og growth andthe onsetof growthwith tips which, at

theresolutionavailable,havecurvedgrowthfronts.100 200 300 400 Nevertheless,the growth direction is related to

TIME Is)distinct crystallographicdirections(dendritesare

Fig. 18. Growthof ice crystals in helium (500 mbar)showing nearthe a axis observation;needlesin the c axislower growth rate in low g (10—2) and higher growth rate inhigh g (1.8). Estimatederror of velocity measurement±1 pm direction)althoughchangesin air velocity andthe

s~. symmetryof air flow leadto growth and anangleto such rational directions both in c axis growth

In vapor growth, the Reynoldsnumber at ice describedaboveandin a axisgrowth (seefig. 5 incrystalterminalvelocity in air has avalueof 1 to 5 ref [4]). Intermediate to these transitions is thecomparedwith a few thousandrequiredto reach appearanceof hollow columns, sheathsor sectorthe asymptoticlimit in solution growth. For the plates,partially formed“idealized” solid columnscrystalsstudiedin solution,skeletalgrowthis not or plates. Thesechangescan be interpretedinreportedas fluid motion is increased[18]. Indeed, termsof surface nucleationat protrudingcornersandmost important, conventional wisdomfor the at higher supersaturationand air velocity, withgrowth of well-developedfacetedcrystalsin ig is incomplete layer formation in shielded regionsthat stirring gives better facets: spatial gradients away from the corners. This conceptis consistantof solution concentrationare removed.This situa- with suchcrystal forms in solution growth undertion is to be distinguished fromlow g growth of low air velocity.facetedcrystals,whereconvectivemotion andas- The transition to curved growth, from an em-sociated fluctuationsare removed.There is evi- pirical view point, is associatedwith a tip instabil-dently a major distinction betweenvapor growth ity which couldwell developfrom a local fluctua-of a facet in air — whereincreaseof velocity and tion of growth conditions such that lateral layersupersaturationgive enhancedtip growth and a growth is no longerableto give rise to facets,eventransformationto skeletal growth— andgrowth of at thetip as thelocaldriving force for growth is sofacets in solution where substantialincreaseof large that molecular mobility is sufficient tosolution flow enhancesfacetedgrowth. nucleateeverywhereandso thatno facetedsurface

These considerationssuggest that at higher forms.This is consistentwith the observation thatvelocity, with Reynoldsnumber > i03, and local very thin crystals grow as discsfrom the vaportransport controlled by small scaleeddies, even andonly developedgefacetsas they thicken[20].vapor growth may revert to faceted form. Thissituationis well beyondthecapabilityof the pres- 4.3. Application to the atmosphereent laboratory system,but it could occur duringfrost growth on a cold aircraft surfaceduring In the earth’satmosphere,snow crystalswhichdescent intowarmer, moist air. This is of some reach the surfacegrow overa rangeof tempera-

T Alenaet at / Facet-skeletaltransition ofsnow crystals:experimentsin high and low g 555

ture between0 and —40°C, andover a rangeof supportedby NASA HeadquartersMicrogravitypressurefrom 1000 to a few 100 mbar. Growth Scienceand Applications Division. The KC135often takes placeclose to water saturation,al- aircraft work was carriedout underthe directionthoughunderconditionsof highcrystalconcentra- of Robert Shurney,MarshallSpaceFlight Center,tion, with mutual competitionfor availablemois- Alabama, whosehelp was vital to the success ofture (concentrationbetween 100 to 500 l1 de- the project. Subsequentanalysiswas supportedinpendingon updraft velocity), growth takes place part by a NASA contractthroughJet Propulsionbetweenwater and ice saturation.It is clear from Laboratory,Pasadena,CA, Contract # 957764.Itfig. 13 thatsmall changesin conditionsof temper- fulfills in part the requirementsfor a higher degreeature, and saturationratio near — 50 C, can give (T.A.) in the Departmentof Physics,University ofsignificant changesin crystalshape;fig. 15 shows Nevada,Reno.that differentfall velocity at specifictemperaturealso hassimilar effects. Regimessimilar to fig. 15can be producedfor each0.25°Cchange,which Referencesdiffer asin fig. 13, so thata three-dimensionalplotof crystal form with temperature,excessvapor [1] U. Nakaya,SnowCrystals,NaturalandArtificial (Harvard

density andvelocity (combining fig. 13 and a University Press,Cambridge,MA, 1954) p. 510.[2] T. Kobayashi, J. Meteorol. Soc. Japan75 Anniversarysequenceof graphicssimilar to fig. 15) will reveal Volume(1957) 38.

a complex picture.A crystal falling in the atmo- [3] B.J. MasonandJ. Hallett,Proc. Roy.Soc. (London) A247

spherewill increasein fall velocity as it grows, (1958) 440.

usually falling into air at higher temperature. The [4] V. Keller, J. Hallett, J. CrystalGrowth 60 (1982)91.

distribution of saturationratio along its trajectory [5] J. Hallett, Phil. Mag. 6 (1961)1073.[6] T. Kuroda,J. CrystalGrowth 65 (1983) 27.is dependenton the particular weather system, [7] J.L. Katzand P. Mirabel, J. Atmos. Sci. 32 (1975)646.

andis in generalunrelatedto temperatureandfall [8] M. Kajikawa, J. Meteorol. Soc. Japan50 (1972) 577.

velocity. Phenomenologically,a falling crystalcan [9] H.R. Pruppacher and J.D.Klett, Microphysicsof Clouds

take a large numberof pathways,some ofwhich and Precipitation(Reidel, Dordrecht,1978)p. 714.

can give similar growth. For example, needles [101 J. Hallett, J. Opt. Soc. Am. A4 (1987) 581.[11] T. GondaandM. Komabayasi,J. Meteorol. Soc. Japan49occur in two regionsin fig. 13; dendritesoccur in (1971) 32.

two regionsnear — 15 ° C. Interpretationof differ- [12] R. Siegel, Trans.ASME 80 (1958)347.

ent shapedcrystals is therefore even morecorn- [13] J.S. Turner,BuoyancyEffects in Fluids (CambridgeUni-

plex than realized before,and a specific crystal versity Press, Cambridge,1973) p.367.

shapeor shapesequencein the samecrystal may [14] J. Hallett, N. Cho, K. Harrison,A. Lord, E. Wedum andR. Purcell, Final Report,NASA Contract *NAS8-34605,be subject to several interpretations. Remern- Marshall Space Flight Center, Huntsville, AL. 1987, and

bering that the atmosphereis aturbulentmedium, submittedfor publication.

the probability of two crystals which can be ob- [15] J.W. Mullin and J. Garside,Trans. Inst. Chem. Eng.45servedand which follow the sametrack is there- (1967) 285.fore remote; an upperprobability canbe placed [16] J.R. Garside,R. Janssen-VanRosmalenand P. Bennema,

J. CrystalGrowth 29 (1975) 353.from conditionsof the variability outlined above. [17] R. Janssen-VanRosmalen,P. BennemaandJ. Garside,J.

Crystal Growth 29 (1975) 342.[18] E. Kirkova and R. Nikolaeva, Crystal Res. Technol. 18

Acknowledgements (1983) 743.[19] M. O’Hara and R.C. Reid, Modelling Crystal Growth

Rates fromSolution (Prentice-Hall,EnglewoodCliffs, NJ,Thiswork wassupportedin part by NSF Grant 1973) p.274.

ATM-8715636. The low gravity studieswere car- [20] V. Keller, C.V. McKnight andJ. Hallett, J.CrystalGrowthnedout throughNASA Grant#NAS8-32977and 49 (1980)458.