1 August 1975, Volume 189, Number 4200

Droplet Chond

Jetting on high-velocity collision of small meparticles may have produced droplet choi

Susan Wernt

Droplet chondrules are small spheroidalmeteoritic inclusions that appear to havesolidified from liquid droplets (Fig. 1).They are found in chondrites meteoritesthat most evidence suggests originated inthe early stages of formation of the solarsystem. The origin of the droplet chon-drules has been the subject of controversyever since Tschermak published the firstdetailed description of their microscopictexture in 1883 (1). Although a number oftheories have been proposed for their ori-gin, shock melting produced by impact ofmeteoritic bodies is favored by the bulk ofrecent evidence (2). The problem addressedin this article is the size of the bodies in-volved in the impacts. Cratering of pro-toplanets of asteroidal size by meteorites,favored by most authors, produces ejectawith the wrong distribution of sizes andshapes to form chondrites without furthersorting that is difficult to explain. This andother difficulties are precluded if dropletchondrules formed by breakup into drop-lets of "jets" produced by collisions be-tween small comparable-sized meteoriticbodies.

The Problem of the Origin of Chondrules

Petrographic and geochemical studies ofchondrules in unequilibrated ordinarychondrites (2-4) have placed several con-straints on theories for their origin:

1) The diameters of chondrules are lim-ited mainly to the range 0.1 to 5 millime-ters (3). In ordinary chondrites the distri-

The author is assistant professor of geology at theUniversity of California, Los Angeles 90024.

I AUGUST 1975

bution is strongly p2) Many chondrul

mensional and sphehalf are perfect sphei

3) Chondrules maor more of the mass

4) Chondrules cotemperature minerala variety of texture.chondrules are classolivine, (ii) radiatinphyritic, (iv) glassy,(vi) lithic. A numbetextural propertiesformed by rapid s

droplets: the spherorence of skeletalgrowth patterns, dertallites, the occurreimetastable preservaature phases (7).

5) The nonequilitchondrules and iodmarized in (2)] su,formed before theaccumulated, that iformed in situ in theThe term "chondi

authors to refer to .(or pieces thereof) inregardless of compo:clarity, I refer to chohave formed as the ruid droplets as drcmajor types of chonciv) have droplet rrvarying proportion:shaped members. Thlarly shaped chondrmany may be erodeschondrules, but som

SCIENCE

pieces of preexisting lithic material (6).Within the chondrites, chondrules are

embedded in a matrix of fine-grained crys-talline to partially glassy material. Few

Irules data are available regarding this matrixmaterial, principally because it is inter-stitial to and much finer than the chon-

teoritic drules. Olivine and pyroxene grains in thematrix have the same major element chem-

ndrules. ical compositions as those in the chon-drules and many fragments of dropletchondrules are observable in thin section;

er Kieffer it is therefore likely that at least some frac-tion of the matrix consists of crushed drop-let chondrules (7). Recent data on minorelement chemical fractionation patterns,

)eaked at 0.4 mm (5). however, suggest that at least some matrixles are roughly equidi- material has not experienced the samezroidal, but less than high-temperature history as the dropletres (6). chondrules (8).y comprise 70 percent Condensation of a gaseous solar nebulaof chondrites (2). or a Jovian protoplanetary atmosphere (9),nsist mainly of high- fusion of nebular dust by lightning (10),Is or glass and occur in and volcanism (11) have been proposed ass. The most common chondrule-forming processes, but shock-ified (3) as (i) barred melting due to hypervelocity impacts hasg pyroxene, (iii) por- been the hypothesis of most current inter-(v) agglomeratic, and est (2, 6, 12). The presence of ancient im-r of geochemical and pact craters on the moon, Mars, and Mer-suggest that they cury leaves no doubt that impact was an

solidification of melt active process in the early solar system.idal shape, the occur- The presence of glass spherules at terrestri-crystallites, parallel al impact craters and on the lunar surface

ldritic growth of crys- demonstrates that some glass spherulesnce of glass, and the similar to droplet chondrules are producedtion of high-temper- by impact (13).

The size of impacting bodies whichbrium composition of could have produced droplet chondrules is,ine-xenon ages [sum- unknown. Most authors have proposedggest that they were that the droplet chondrules were formed bychondritic meteorites impacts of meteorites onto "extended"s, that they were not protoplanets of roughly asteroidal size (6,chondrites. 12). I call such impacts in which one par-rule" is used by some ticle is small and the other large "particle-all rounded fragments to-parent" impacts. High-velocity impactschondritic meteorites, in which the target is sufficiently large thatsition and texture. For the projectile delivers less kinetic energyindrules that appear to than 107 ergs per gram to the target char-esult of cooling of liq- acteristically produce impact craters (14).plet chondrules. The (For spherical particles of equal density,irules listed above (i to this energy limit ioccurs approximately attembers, although in radius ratios of 8 and 37 for impact velo-s to the irregularly cities of 1 and 10 km/sec, respectively.)le origin of the irregu- If droplet chondrules were formed by*ules is still uncertain; particle-to-parent impacts, then it is rea-d fragments of droplet sonable to assume that they were at onee may be fragmented time part of ejecta assemblages much like

333

on

June

27,

200

9 w

ww

.sci

ence

mag

.org

Dow

nloa

ded

from

Fig. 1. Bishunpur L3 chondrite with chondrules of diverse sizes, shapes, and textures. Plane polarizedlight. [Photograph by W. R. Van Schmus; reprinted through the courtesy of Pergamon Press]

those found at terrestrial impact craters.If, on the other hand, the sizes of the im-

pacting bodies are such that the projectiledelivers more kinetic energy than 10' erg/gto the target, both particles are destroyedand no impact crater is formed (14). I callsuch impacts "particle-to-particle" colli-sions, using the word collision (in contrastto the word impact) to imply that the bod-ies are of the same order of magnitude insize. There are almost no data regardingthe nature of the products (particularly theglasses) formed by high-velocity particle-to-particle collisions, in contrast to parti-cle-to-parent impacts, for which a rela-tively large amount of field data exists. Inthis article I propose that there are sub-stantial differences between "particle-to-parent" impacts and "particle-to-particle"collisions and that some of the problems ofthe impact hypothesis for the origin ofchondrules are resolved if droplet chon-drules were formed by particle-to-particlecollisions.

Impact Glasses Characteristic ofParticle-to-Parent ImpactsThe following four types of glasses are

found in the ejecta of impact craters:1) Glassesformed by bulk melting ofthe

rock (Fig. 2a). Impact glasses that arepolymineralic in composition or show evi-dence of flow of individual mineral com-ponents toward a mixed state are inferredto have been formed by bulk melting ofrock by high-pressure shock waves. Themelting may have occurred in a zone fairlyclose to the penetration path of the meteor-ite, or in a jet formed at the instant of con-tact of the meteorite with the ground (seenext section). Such glasses generally ap-pear extensively sheared and may havebeen significantly devolatilized (13). Theymay contain inclusions of lithic fragmentsincorporated while the glass was molten

Fig. 2. (a) Glass formed by bulk melting ofbasalt from Lonar Crater, India. Note regionswhich are reasonably homogeneous and regionswhich are inhomogeneous, vesicles, and re-crystallization around a small grain (upper left)and large lithic inclusion (lower right). Planepolarized light. (b) Thetomorphic labradoritegrain, maskelynite (msk), in contact with augite(pyx) and an opaque (opq) ulvospinel in shockedbasalt from Lonar Crater. Plane polarized light.(c) Melted labradorite (gls) surrounded byshocked augite (pyx) and including partiallymelted opaque (opq) grains. Maskelynite wasprobably formed as an intermediate phase be-fore melting of this grain. Shocked basaltfrom Lonar Crater. Plane polarized light. (d)Glass (isotropic material in center) formed bypressure melting of quartz (q) in shockedCoconino Sandstone at Meteor Crater, Ari-zona. Crossed polarizers.

SCIENCE, VOL. 189

on

June

27,

200

9 w

ww

.sci

ence

mag

.org

Dow

nloa

ded

from

(13, 15). The glass fragments range in sizefrom micrometers to centimeters in diame-ter; they range in shape from spherules toangular shards to large bombs (fladen).The size and shape of molten glass frag-ments are determined by the conditions ofejection from the crater. Impact-meltedspherules, shards, and bombs were foundintermixed with unshocked and shockeddebris in the fallout at Lonar Crater, India,by Frederiksson et al. (13). Lunar sphe-rules occur in similar association withshocked and unshocked ejecta fragments,as do some chondritic spherules (6).

2) Glasses without evidence offlow, pos-sibly formed by solid-state transformation(Fig. 2b). Monomineralic glasses that lackflow structures and vesiculation werecalled thetomorphic glasses by Chao (16)in recognition of the fact that they retainthe original shape of the grain from whichthey were formed. Such glasses are foundin rocks that have been shocked to low ormoderate pressures (17) and are generallybelieved to have formed by solid-state dis-ordering of the mineral lattices (18).Thetomorphic plagioclase glass occurs inthe Shergotty meteorite (1, 19), in lunarsamples (20), and in shocked rocks from anumber of terrestrial craters (21), and hasbeen produced in laboratory experiments(18); thetomorphic quartz glass and theto-morphic coesite glass are found at MeteorCrater, Arizona (22).

3) Glasses formed locally within a rockfrom a compressible component (Fig. 2c).In some shocked rocks, a single mineralcomponent has melted and flowed; for ex-ample, in some of the shocked basalts fromLonar Crater labradorite grains wereshock-melted but pyroxenes and opaqueminerals remained crystalline. The glassyregions are, on the average, equal to thegrain size of the minerals in the originalrock. High-pressure phases or thetomor-phic glasses may have formed as inter-mediate phases in this melting process(22), which occurs under shock-loading tomoderate pressures, insufficient to totallymelt the rock.

4) Glasses Jbrmed by high stresses atgrain boundaries (Fig. 2d). Observations ofshocked Coconino Sandstone from MeteorCrater (23) and of lunar breccias (24) re-veal small amounts of glass or devitrifiedglass at contacts between grains. Highpressures and shear deformation at grainboundaries during shock result in the for-mation of small amounts of glass in theseregions.The ejecta from impact craters charac-

teristically contains all four types of glassfragments listed above. These fragmentshave a variety of sizes, shapes, and rela-tionships to other rock components; the1 AUGUST 1975

glass is not simply in the form of smallspherules which resemble droplet chon-drules.

In addition to these four glasses, a fifthtype of melted material is produced if theimpact crater is formed in porous materi-als. This melt is formed by impact ofgrains as pores collapse under shock com-pression. The melt is injected into the porespaces, where it cools and, generally, crys-tallizes. I propose that this process, de-scribed in the next section, is similar to theprocess that occurs during particle-to-par-ticle collisions.

Melt Formed by Jetting

The fifth process by which melt is pro-duced during an impact event is jetting, theextrusion of hot material from the inter-section of obliquely colliding surfaces (25,26). I refer to the stream of hot materialthat emanates from the point of collisionas the "jet" and to the final products of thejetting process (cooled from high temper-ature) as "jecta."

1

-._ t bi 1 - IIf FI

Fig. 3. Geometries that may give rise to jetting: (a) a collapsing wedge and (b) impacting spheres.Schematic drawings of pore collapse in shocked Coconino Sandstone: (c) The shock (heavy line) im-pinges on a pore; irregularities of pressure in the shock wave are implied by the stippled pattern.Fractures in quartz are shown as thin lines, fractured quartz fragments as open circles, and coesitenuclei as black spots. These features are formed primarily in regions of shear along grain bound-aries. (d) The jet is formed from collapsing grains and injected into the pore. (e) A hot amorphousphase (SRO) exists temporarily in the collapsed pore. Stishovite (shown as stars) forms in small re-gions of high stress. (f) Upon pressure release the jet cools to form a jectum of coesite which nucle-ates and grows in the core. A thermal aureole forms around the jet as heat flows outward into thecooler quartz grains. The transformation of quartz to coesite is accelerated by the high temperatureswithin the thermal aureole and results in the formation of an opaque rim.

335

eVI

6<9cr no jet forms

on

June

27,

200

9 w

ww

.sci

ence

mag

.org

Dow

nloa

ded

from

Obliquely impacting surfaces are neces-sary for jet production and they may arisefrom a variety of geometries: from impactof flat plates at oblique angles (Fig. 3a),from impact of spherical particles onto aplane or into each other (Fig. 3b), or fromcollapse of pores by shock waves propagat-ing through porous materials (Fig. 3, c tof). Jets, generated by geometries similar tothat shown in Fig. 3a, attained a practicaluse during World War 11 when they wereused as armor-penetrating devices becauseof the high velocities they can attain. Jetswere first observed in shock experimentsinvolving silicates by Gault et al. (27), whoimpacted aluminum spheres into basalttargets at high velocity. The theories of jet-ting, developed and experimentally verifiedfor aluminum and lead (25) and copper(26), demonstrate that the geometric con-ditions of impact shown in Fig. 3 are suffi-ciently similar to each other that much ofthe physics of the jetting process may beunderstood by considering the simplestcase, symmetrically impacting plates (Fig.3a).Analyses of pressures generated by

obliquely impacting plates show that jetsarise under certain specific conditions ofimpact (25, 26. 28). If two plates impact,each with velocity vP normal to its free sur-face, the pressure generated is a minimumfor head-on collision; for example, Walshet al. (25) calculated that for a head-on col-lision of aluminum plates, each with a ve-locity of 2.28 km/sec, the induced pressureis 450 kilobars. If the plates are cantedfrom the normal during impact by an angle20, they close along their interface with avelocity vi/tan 0 and, in so doing, createhigher pressures than are generated duringthe head-on collision. The geometry andshock configuration produced by such con-ditions of impact are referred to as the reg-ular regime (28). In this regular regime thepressure rises monotonically with increas-ing angle, giving rise to an increase in pres-sure by approximately a factor of 2. [Forexample, the pressure induced by twoaluminum plates impacting, each with ve-

locity v; = 2.28 km/sec normal to its freesurface, at angle 20 = 25044', is 820 kbar(25).] Pressure increases due to obliquity ofimpact in the regular regime are sufficientto generate melt locally at relatively lowervelocities than required for melting underhead-on collisions, and this process prob-ably accounts for some of the glass formedat grain boundaries in the Coconino Sand-stone or in lunar breccias (glass type 4).

If the impact angle is larger than a criti-cal angle, 20- which varies with impactvelocity, the regular regime breaks downand a squirt of hot material emanates fromthe point of collision (Fig. 3a). This streamof material is the jet. Shock configurations

336

that produce jets are complex and are re-ferred to as irregular regimes (28). Thepoint of emanation of the jet is a stagna-tion point; therefore, in accordance withBernoulli's theorem, all kinetic energy istransformed into enthalpy at this point(25). The pressure at the stagnation pointof two aluminum plates impacting at an-gles slightly above 20c, = 25044', eachwith velocity 2.28 km/sec, is, according toBernoulli's theorem, 2.25 Mbar (25). Theshock configuration that produces jetsgives rise to a directional focusing of shockenergy, with the consequent formation ofhigh-temperature melt; sufficient energy isdeposited to make jets in metals self-lumi-nous.

Jets may form in two regions of an im-pact crater: (i) upon initial contact of the

Fig. 4. (a) Two cryptocrystalline coesite cores

(c) in shocked Coconino Sandstone. These were

initially injected into pores as molten jets. Thedark rim which surrounds the coesite cores is a

thermal aureole (see text) and contains grains ofcoesite (typically less than I gm in diameter)and stishovite. The quartz grains (q) are rela-tively unshocked. Plane polarized light. (b) Elec-tron micrograph showing the characteristicequilibrated texture of coesite in the core. Dis-locations (d) are present in the coesite; twins

parallel to (010) cause streaking on the spots in-

dicated by small arrows on the diffraction pat-tern. [Micrograph by P. Thakey, S. Kieffer,and J. Christie]

meteorite and regolith surface, a jet can beextruded from the meteorite-target inter-face (27), and (ii) upon collapse of grainsacross pores in a regolith, jets may be in-jected into pores. The first process shouldproduce melt of the bulk composition ofthe target rock (glass type 1) perhaps en-riched in meteoritic components. The sec-ond process occurs only if impacts are intoporous regoliths and produces jets whichcool to form jecta of unique character-istics, described below.

Jetting in the Coconino Sandstone

A particular type of material found inshocked Coconino Sandstone from Mete-or Crater appears to be interstitial jecta(29); a study of this material, which wasformed by the collision of.quartz grains0.1 to 0.2 mm in diameter during shock,provides information about the productsformed upon high-velocity collision ofroughly equidimensional particles. Inmoderately shocked Coconino Sand-stone [class 3, defined in (23)] abundant"cores" of cryptocrystalline coesite occurin regions interpreted to be collapsed pores(Fig. 4a) (23). Transmission electron mi-crographs (22) show that these cores havea mosaic texture, with many grain bound-aries intersecting at angles of 1200 (Fig.4b). Such a texture is characteristically ob-served in annealed recrystallized metalsand single-phase mineral aggregates. Thetexture is referred to by metallurgists as amature polycrystalline structure, and in-dicates that grain boundary equilibriumwas nearly attained in these regions. Thesecores are the only regions within naturallyshocked rocks where textural evidence forequilibrium within shock waves has beenfound. Since the cores had only 10 to 45msec to form during the impact event atMeteor Crater (23), their equilibrated tex-ture implies that they formed from a veryhot precursor phase. Because of the steepslope of the SiO2 liquidus, it is probablethat the temperatures in the cores exceeded20000C.The cores are inferred to be jecta-the

cooled residue of jets injected into poresupon impact of quartz grains. The inferredprocess of formation of the jecta in theCoconino Sandstone is shown in Fig. 3, cto f; detailed discussion of the propagationof shock waves in porous media and theformation of jets is to be presented else-where (22). The shock wave generated bythe impact of the meteorite caused thequartz grains of the Coconino to impactagainst each other as pores collapsed (Fig.3c). Molten silica cores were formed as theleading regions of grains were jetted intothe pores (Fig. 3, d and e). These cores,

SCIENCE, VOL. 189

on

June

27,

200

9 w

ww

.sci

ence

mag

.org

Dow

nloa

ded

from

which are inferred to have been hotamorphous material or to have short-rangeorder (SRO) only, subsequently crystal-lized to cryptocrystalline coesite jecta uponrelease of high pressure (Figs. 3f and 4).The trailing regions of impacting grains

which did not enter the jet were much lessstrongly shocked. These regions of thegrains (plus other quartz grains that werenot near pores) form a matrix of fracturedquartz which surrounds the jecta (Figs. 3fand 4). This quartz shows no evidence ofthermal recovery (22) and probably suf-fered initial heating of only a few hundreddegrees. However, as the jets cooled byconduction of heat into this surroundingmatrix of quartz, some of the quartz trans-formed into coesite on the periphery of thecore; that is, a thermal aureole about 100fim thick was formed (Figs. 3f and 4).Large temperature gradients existed in

these rocks, for if it is assumed that theoriginal distance between unjetted, rela-tively cold fractured quartz and the jettedcore was less than the 100- Mm thickness ofthe thermal aureole, the temperature gra-dients must have been at least 200 per mi-crometer. It may be concluded that jettingis an efficient mechanism for focusingshock energy into the regions of impactingparticles that enter the jet.

Jets are formed from material derivedfrom at least two interacting grains. There-fore, the composition of the jet is deter-mined by the composition of the collidingparticles and the degree of mixing attainedduring the jetting process. The CoconinoSandstone, which is composed almost en-tirely of quartz, provides no opportunity tostudy the composition of jecta formed bycollision of two grains of different compo-sitions, such as olivine and pyroxene. It islikely that collisions between particles ofdifferent compositions would yield jecta ofmixed compositions.The preexisting pores in the regolith im-

part two textural characteristics to the jec-ta which reflect their origin within a rego-lith and which contrast with properties ofdroplets that solidify in free space. Firstthe size and shape of pores in the regolithdetermine the size and shape of the jecta.Since most pores are, to first order, ellip-soidal, the jecta are also roughly ellipsoi-dal, but they do not have the perfect sphe-roidal form of cooled droplets. Secondly,jets formed by injection into pores cool rel-atively slowly. In contrast to droplets infree space, which cool primarily by radi-ative transfer, hot spots in a regolith coolprimarily by thermal conduction, and sincemineral grains are very poor conductors,the cooling is relatively slow (23). Quenchtextures therefore may not be as likely todevelop in jets cooling within a regolith.Furthermore, if the cratering events are ofI AUGUST 1975

roughly the same duration as the MeteorCrater event (10 to 45 msec), the jets maybe at high pressure for much of their cool-ing cycle (23), with the result that the jectaconsist of crystalline high-pressure phases,rather than glass or quenched high-temper-ature phases. It is possible that some irreg-ularly shaped chondrules that are rimmedand have a granular, rather than aquenched, texture were formed by jettingwithin a porous regolith on a protoplane-tary surface, and were subsequently bro-ken free to be reassembled even later intothe chondritic meteorites in which they arenow found. However, the spheroidal shapeand high-temperature phases of dropletchondrules suggest that they were notformed by jetting within a regolith.

Particle-to-Parent Impacts:Processes and ProductsUpon high-velocity impact of a projec-

tile against a target, shock waves that com-press the material are formed in both thetarget and the projectile; initial pressuresin the shock waves can be several mega-bars, depending on the velocity of impact.An initial jet may form at the surface ofcontact. During the first moments of im-pact the relative size of the two projectilesdoes not appreciably affect the shock con-figuration. The shock waves in each par-ticle initially form a roughly hemisphericalfront as they expand rapidly outward awayfrom the point of impact, and they there-fore engulf a continuously increasing massof material. The energy in the wave systemis relatively constant, so that as the shockis propagated through an ever-increasingmass of material, the induced pressuredecays quickly (approximately as the in-verse third or fourth power of the distancefrom the impact).The ratio of particle sizes becomes im-

portant as the shock propagates furtherfrom the point of impact. If one particle(called here the parent) is so much largerthan the other that it is effectively infinitein size, the wave front in the parent en-counters no free surfaces and the basichemispherical shape of the shock front re-mains undistorted. The compressive wavefront decays to a simple seismic distur-bance. Hence, an impact crater surroundedby a zone of broken and fractured targetmaterial is formed in the parent.The wide range of pressure and temper-

ature conditions associated with the essen-tially unlimited expansion of the compres-sive shock front in the parent gives rise tothe association of glasses and shocked andunshocked fragments typically found incrater ejecta from particle-to-parent im-pacts. In particular, the type 1 melted

glass, including shards and spherules, is in-termixed with the other types of glassesformed interstitially and intragranularly,and with moderately shocked and un-shocked fragments formed in different re-gions of the crater. Glass spherules com-prise only a small fraction (< 1 percent) oftypical crater ejecta from particle-to-par-ent impacts.

Particle-to-Particle Collisions:Model for Processes and Products

In both bodies of a particle-to-particlecollision, and in the smaller body of a par-ticle-to-parent impact, the expandinghemispherical compressive wave frontsgenerated initially are disturbed by reflec-tion from the boundary surfaces of theparticles. The reflected waves are rarefac-tion waves, complex systems of tensionand shear waves. In brittle substances,such as rocks and minerals, these rare-faction waves cause extensive spallationand fracture of material near the boundarysurfaces (14). Hence, the shock history ex-perienced by material at a particular dis-tance from the point of impact in a smallparticle may be very different from thatexperienced by material at the same dis-tance from the point of impact in a largeparticle.On the basis of these considerations of

the shock conditions that exist in smallparticles during impact, and the descrip-tion of grain-to-grain collisions givenabove, I propose the following model forthe high-velocity collision of two roughlyequidimensional particles of zero porosity(30). Upon impact, material near the pointof collision is melted by high shock pres-sures and jetting. A roughly hemisphericalcompressive shock wave propagates intoboth particles, but is disturbed by reflec-tion of the shock from boundary surfaceswith the result that much of the unmeltedmaterial is pulverized by spallation andfracturing initiated at the free surfaces.Very little material experiences a shockhistory intermediate between the two ex-tremes of melting and fracturing.

it is necessary to consider the amount ofmelt that might be formed by particle-to-particle collisions, for in order to producechondrites that are 50 to 70 percent chon-drules without a sorting or chondrule-en-richment episode following their forma-tion, the collisions must be relatively effi-cient in converting the mass of the collid-ing particles to melt. The amount of meltthat is generated will depend on the veloci-ty of impact of the particles. Although wecurrently do not have laboratory data onthe amount of melt produced by particle-to-particle collisions as a function of veloc-

337

on

June

27,

200

9 w

ww

.sci

ence

mag

.org

Dow

nloa

ded

from

ity, it is possible to obtain rough estimatesof the amount of melt produced and thevelocities of impact of grains in the Coco-nino Sandstone. The jecta (the cryptocrys-talline coesite cores) typically comprise 10to 20 percent of the shock-metamorphosedclass 3 samples, and if every quartz grainof the original rock had been involved in ajet-forming collision, then on the averageat least this fraction of quartz was trans-formed to melt by a typical collision. Theaverage velocity of impact of grains can beestimated from the equation of state ofquartz (31) and Coconino Sandstone (32),and from a model for the behavior of indi-vidual grains during shock compression ofa porous material (23). The average pres-sure experienced by the class 3 shockedCoconino Sandstone fragments was be-tween 150 and 250 kbar (23); the equationsof state suggest that the average relativevelocity of impact of grains was between2.0 and 4.5 km/sec at these pressures. Athigher relative velocities of impact, alarger fraction of the mass of impactinggrains was converted to jecta. In class 4shocked Coconino Sandstone samples(23), which are interpreted to have experi-enced pressures above 250 kbar, and there-fore higher particle velocities, 50 to 60 per-cent of the quartz was converted to jecta.[The jecta in these rocks are much moredifficult to recognize because the jets in-verted to vesicular glass on cooling (23).]

In summary, the geometric differencesbetween particle-to-parent impacts andparticle-to-particle collisions cause twosubstantial differences in the impact pro-cesses: in particle-to-particle collisions (i)initial jetting causes melting of a muchlarger fraction of the total mass of theparticles, and (ii) disturbances of the ex-panding shocks by the reflected rarefactionwaves cause much of the unmelted materi-al to be pulverized by spallation and frac-turing. Very little material experiences ashock history intermediate between thesetwo extremes.

Origin of Droplet Chondrules

The texture of ejecta from impact cra-ters made by particle-to-parent impactsdoes not resemble the texture of chondriticmeteorites in detail. The dissimilarity leadsto two well-recognized difficulties with thehypothesis that chondrules were formed byimpacts of meteorites into protoplanets ofasteroidal size: (i) ejecta from impact cra-ters show a wider range of shapes and sizesthan the chondrules and chondrule frag-ments in chondritic meteorites, and (ii)crater ejecta consist of a mixture ofshocked and essentially unshocked debris,

338

of which glass spherules that resemblechondrules comprise only a small fraction.Impact theories for the origin of chon-drules must account for the unimodal andnarrow size distribution and textural char-acteristics of chondrules by providing ei-ther a process of chondrule formation thatproduces only such particles, or a processthat sorts a larger distribution of sizes andtextures subsequent to chondrule forma-tion. [For example, Dodd (6) proposed thatmaterial formed by impact cratering wasrecycled back into the nebular cloud by the

(a) to

(b) t1

V4V.

lvi

IVj

iVIVj

tVi

(c) t =-x

vj4-

?I

V.

(d) t3

_0

Fig. 5. Schematic drawing of the formation ofchondrules. (a) Two spheres of diameter d im-pact with relative velocity 2v.. (b) Material fromthe segment of height x flows into the centralplane of the impact and out into the jet, which isextruded at average velocity v.. (c) The segmentscollapse in time t = x/v., during which the ma-

terial from the segments has been transferredinto an annulus around the collapsed particles.(d) Instabilities develop in the annulus, whichbreaks down into columns (rays) and droplets.The trailing portions of the spheres are frac-tured by rarefaction waves. A cone of fracturedmaterial erupts from the antipodal point of eachsphere (14).

impacts and that subsequent gravitationalsettling provided sorting.]These problems associated with the for-

mation of droplet chondrules by impact onprotoplanets can be resolved by the follow-ing model. It is assumed that the dropletchondrules were formed by collisions be-tween small particles of restricted size ra-tios by particle-to-particle collisionsrather than particle-to-parent impacts.The collisions were at sufficiently highvelocity that molten jets were extrudedinto space (see Fig. 3b). As these jetsbroke into small globules because of in-herent instabilities in the flow of liquidsthey cooled to form spherical jecta, whichbecame the droplet chondrules. The fine-grained matrix material observed inchondritic meteorites may be the fractionof the impacting grains which did notenter the jet; it experienced a relativelylow-temperature, low-pressure history.(Some matrix material may also consistof particles which never attained suffi-ciently high velocities to become in-volved in chondrule-forming collisions,and some might also consist of chondrulescrushed by impacts after their formation.)The following simple model of the par-

ticle-to-particle collision process is in-troduced to estimate the size of impactingparticles which could have formed dropletchondrules. Two spherical particles ofequal diameter d, volume Vsph, and den-sity p are assumed to impact with equaland opposite velocities v; relative to thecentral point of contact P, as shown in Fig.5a. A radially symmetric jet begins to formas material flows from the edges of thespheres into the plane of symmetry per-pendicular to v; (Fig. 5b). Let m = m(vi)denote the mass fraction of each incomingprojectile which enters the sheet, and as-sume that this fraction is derived from thefirst segment of each colliding sphere to in-teract, as shown in Fig. 5, b and c. The seg-ment from which the jet is derived has vol-ume Vseg and height x, which is related tothe mass fraction m as

Vseg = m - x2(3d-2x) (1)Vsph d3

If m is small and x < < d, this gives xd(m/3)1/2.The spheres collapse the distance x in

time t = x/vi, during which the sheetforms. A three-dimensional sheet wouldthin with distance from the point of im-pact, in order to satisfy conservation ofmass, and because of instabilities of fluidflow, the sheet would break into filamentsand droplets after a short distance, as illus-trated in Figs. 5d and 3b. In this model,however, the mass fraction m is assumedto be completely transferred to an annulus

SCIENCE, VOL. 189

on

June

27,

200

9 w

ww

.sci

ence

mag

.org

Dow

nloa

ded

from

surrounding the colliding spheres beforethis breakup begins (Fig. 5c). The annulusis assumed to have average thickness 6 andaverage radial velocity vj at time t = x/vi.The outer radius at this time is then vjx/viand the inner radius is (xd - x2)'12; hence,the volume is

Viet = 7r 6( X2 -dx + x2) (2)

where, for simplicity, the density of the jethas been taken equal to p. Conservation ofmass requires that Viet = 2m VSph; hence

d =6

[ vi2 ( )/2+] (3)V2 m

The diameter d obtained from this equa-tion will be the largest for maximum val-ues of vj/vi and 6 and a minimum value ofm, and is relatively independent of reason-able values for these parameters.A limit may be placed on the velocity ra-

tio vj/vi by considering conservation of en-ergy, which requires that mv-2 < v2 Thechoice vj/v1 = (M)-1/2, which is equivalentto assuming that all projectile energy istransferred to the jet, maximizes the calcu-lated particle radius r. In fact, because ofdissipative processes within the shock(such as heating) and deposition of someshock energy in material of the sphereswhich does not enter the jet, the velocity ofthe jet will be substantially less than thevalue given by this assumption.

In order to relate the thickness 6 of theannular sheet (the jet) to the mean diame-ter of chondrules (the jecta), it is assumedthat the sheet breaks into columnar fila-ments of average diameter 6 and that thesefilaments then break up into droplets (thedroplet chondrules). Laboratory data onliquid jets (33) demonstrate that such co-lumnar filaments break up into primary,secondary, and even tertiary droplets dueto the growth of instabilities. The size ofthe droplets depends on the initial jet di-ameter, its velocity, viscosity, and surfacetension, and a characteristic wavelengthfor the initial disturbance. Assuming invis-cid flow, the largest droplet formed typi-cally has a diameter 1.8 times that of thejet and the smallest (tertiary) has a diame-ter 0.2 times that of the jet (33). The pa-rameters for viscous breakup are not sig-nificantly different for the purpose of thismodel. In order to maximize the estimatedvalue of d, it is assumed that droplet chon-drules are the smallest (tertiary) dropletsfrom jetting events; the average chondrulediameter, 0.4 mm, is then taken to be 0.2times the sheet thickness; that is, 6 is 2mm.With the assumptions, then, that m =

0.1, vj/vi = 3.3 and 6 = 2 mm, Eq. 3 givesa diameter of 1 cm for the particles fromI AUGUST 1975

which the droplet chondrules of average di-ameter were formed.

In order to produce ejecta characteristicof particle-to-particle collisions ratherthan particle-to-parent impacts, the Gault-Wedekind criterion (14) specifies that theratio of particle sizes involved in the colli-sions must be fairly small. The maximumratio of particle sizes depends on the veloc-ity of impact, vi, which is not specified bythis model; however, an estimate of theminimum velocities may be made. It wasconcluded in the previous section that ve-locities between 2.0 and 4.5 km/sec wererequired for the conversion of 10 to 20 per-cent of impacting quartz grains to jecta inthe class 3 Coconino Sandstone. Experi-ments of Gault and Wedekind (14) suggestthat very little glass is produced on impactof aluminum spheres into Pyrex spheres atvelocities of I to 3 km/sec, so it is likelythat 3 km/sec is the minimum impact ve-locity at which an appreciable fraction ofquartz (say, 10 percent) can be convertedto melt by jetting. Jetting may occur atsomewhat lower velocities on impact ofbronzite and dunite particles, which aremore typical of meteoritic compositionthan are quartz particles (34).

If the average impact velocity was 3km/sec, the Gault-Wedekind criterion thatparticle-to-particle collisions have morethan 107 erg/g delivered to the target massdictates that the ratio of particle sizescould not exceed 20; if the average velocitywas 10 km/sec the limiting ratio is 40. Thissuggests that, if the average particle diam-eter was 1 cm, most particles were in therange 0.5 mm to 20 cm diameter. It shouldnot be concluded that particles of larger orsmaller size were absent at the time of for-mation of droplet chondrules. It is sug-gested, however, that collisions of particleswithin this size range were the dominantevents of the chondrule-forming epoch.

Summary

I have proposed that droplet chondruleswere formed by jetting during collision ofmeteoritic particles with diameters rangingin order of magnitude from 0.5 mm to 20cm. This conclusion, based on a dynamicmodel for the collision process, supportsthe hypotheses of Wasson (2) (based ongeochemical considerations) and Whipple(35) and Cameron (36) (based on dynamicmodel considerations) that chondruleswere formed from objects less than 1 m inradius.

In this model, the formation of chon-drules is viewed as a textural, but not sub-stantial chemical, change in the material ofthe early solar system. Droplets of melt

produced by jetting are mixtures of materi-al derived from two parent grains. Jets are

probably not appreciably fractionated (ex-cept in volatile elements) either in the shortduration of the shock events (several mi-croseconds) or in subsequent cooling.

This model for the formation of dropletchondrules implies that they were formedat a time in the history of the solar systemwhen particle sizes were small. The mostlikely time for this condition is early in theprocess of accretion of nebular dust toplanetary matter. Since velocities less thanapproximately 1.5 km/sec are required forthe agglomeration and accretion of par-ticles (37), the relatively higher velocitiesindicated for droplet chondrule-formingcollisions indicate an early high-velocitydestructive epoch amidst the general trendtoward accretion of material.

References and Notes

1. G. Tschermak, Sitzungsber. A kad. Wiss. WienMath.-Naturwiss. KI. 85 (No. 1), 347 (1883).

2. J. Wasson, Meteorites (Springer-Verlag, Berlin,1974); Rev. Geophys. Space Phys. 10, 711'(1972).

3. W. R. Van Schmus, Earth Sci. Rev. 5, 145 (1969).4. R. T. Dodd, Geochim. Cosmochim. Acta 33, 161

(1969); and W. R. Van Schmus, J.Geophys. Res. 70, 3801 (1965).

5. R. T. Dodd, Trans. Am. Geophys. Union 48, 159(1967); Y. I. Stakheev, G. V. Baryshnikova, A. K.Laurukhina, A kad. Nauk SSSR Meteoritica 32,103 (1973).

6. R. T. Dodd, Contrib. Mineral Petrol. 31, 201(1971).

7. A. M. Reid and K. Fredriksson, in Researches inGeochemistry, P. H. Abelson, Ed. (Wiley, NewYork, 1967), vol. 2, pp. 170-203.

8. J. W. Larimer and E. Anders, Geochim. Cosmo-chim. Acta 31, 1239 (1967).

9. J. A. Wood, Icarus 2, 152 (1963); M. Blander andJ. Katz, Geochim. Cosmochim. Acta 31, 1025(1967); J. W. Larimer and E. Anders, ibid., p.1239; M. Podolak and A. G. W. Cameron, Icarus23, 326 (1974).

10. F. L. Whipple, Science 153, 54 (1966); A. G. W.Cameron, Earth Planet Sci. Leti. 1, 93 (1966).

11. A. E. Ringwood, Rev. Geophys. 4, 113 (1966).12. H. Urey, Astrophys. J. 124, 623 (1956); K. Fred-

riksson, Trans. N.Y. Acad. Sci. 25, 756 (1963); G.Kurat, Geochim. Cosmochim. Acta 31, 491 (1967);F. Wlotzka, in Meteorite Research, P. M. Mill-man, Ed. (Reidel, Dordrecht, 1969), pp. 174-184.

13. K. Fredriksson, A. Dube, D. J. Milton, M. S. Bala-sundaram, Science 180, 862 (1973).

14. D. E. Gault and J. A. Wedekind, J. Geophys. Res.74, 6780 (1969).

15. W. von Engelhardt, Contrib. Mineral Petrol. 36,265 (1972).

16. E. C. T. Chao, in Researches in Geochemistry, P.H. Abelson, Ed. (Wiley, New York, 1967), vol. 2,p. 204.

17. The pressures at which various shock features areformed vary considerably depending on the com-position and porosity of the material and the shockconditions associated with the impact. Very ap-proximately, the following values apply: low pres-sure (P < 200 kbar), moderate pressure (P = 200to 500 kbar), high pressure (P > 500 kbar).

18. D. J. Milton and P. S. DeCarli, Science 140, 67(1963); P. S. DeCarli, in Shock Metamorphism ofNatural Materials, B. M. French and N. M. Short,Eds. (Mono, Baltimore, 1968), p. 129.

19. M. B. Duke, in Shock Metamorphism of NaturalMaterials, B. M. French and N. M. Short, Eds.(Mono, Baltimore, 1968), p. 613.

20. W. von Engelhardt, J. Arndt, D. Stoffler, H.Schneider, in Proceedings of the Third Lunar Sci-ence Conference, E. A. King, Jr., Ed. (MITPress, Cambridge, 1972), vol. 1, p. 753.

21. N. M. Short and T. E. Bunch, in Shock Meta-morphism ofNatural Materials, B. M. French andN. M. Short, Eds. (Mono, Baltimore, 1968), p.255.

22. S. W. Kieffer, P. P. Phakey, J. M. Christie, in prep-aration.

23. S. W. Kieffer, J. Geophys. Res. 76, 5449 (1971);thesis, California Institute of Technology (1971).

24. J. M. Christie, D. T. Griggs, A. H. Heuer, G. L.

339

on

June

27,

200

9 w

ww

.sci

ence

mag

.org

Dow

nloa

ded

from

Nord, S. V. Radcliffe, J. S. Lally, R. M. Fisher,Proceedings of the Fourth Lunar Science Confer-ence, W. A. Gose, Ed. (Pergamon, New York,1973), vol. 1, p. 365.

25. J. M. Walsh, R. G. Shreffler, F. J. Willig, J. Appl.Phys. 24, 349 (1953).

26. W. A. Allen, H. L. Morrison, D. B. Ray, J. W.Rogers, Phys. Fluids 2, 324 (1959).

27. D. E. Gault, E. M. Shoemaker, H. J. Moore,NASA Tech. Note D-l 767 (1963).

28. L. V. Al'tshuler, S. B. Kormer, A. A. Bakanova, A.P. Petrumin, A. I. Funtkov, A. A. Gubkin, Sov.Phys. JETP 14,936 (1962).

29. I thank E. M. Shoemaker for first suggesting to methat jetting might occur locally in porous materi-als.

30. The phenomenology would be qualitatively similarif the particles were porous (fluffy); however, intra-

particle jetting within the fluffy particles might beprominent, as it is within a porous regolith, and theconditions required for jetting at the interface ofcollision might be substantially different. There arenot sufficient data at this time to consider the de-pendence of this model on material properties orto consider the problem of scaling from small tolarge impacts.

31. J. Wackerle, J. Appl. Phys. 33, 922 (1962).32. T. J. Ahrens and V. G. Gregson, J. Geophys. Res.

69, 4839 (1964); F. H. Shipman, V. G. Gregson, A.H. Jones, Final Report MSL-70-14 (General Mo-tors Corporation Technical Center, Warren,Mich., 1970).

33. B. Scarlett and R. E. Buxton, Earth Planet Sci.Lett. 22, 177 (1964); a review of the theory of thebreakup of liquid jets is given in G. A. Young, ThePhysics ofBase Surge (NOLTR 64-103 U.S. Nav-

al Ordnance Laboratory, Indian Head, Md.,1965),pp. 139-187.

34. S. W. Kieffer, Trans. Am. Geophys. Union 56,1142 (1974).

35. F. L. Whipple, in Nobel Symposium No. 21: FromPlasma to Planet, A. Elvius, Ed. (Almqvist &Wiksell, Stockholm, 1972), p. 211.

36. A. G. W. Cameron, Icarus 18,407 (1973).37. J. F. Kerridge and J. F. Vedder, Science 177, 161

(1972).38. I thank the following people for helpful comments

during this study: J. Christie, R. Dodd, J. Kerridge,G. Oertel, P. Phakey, E. Shoemaker, R. Shreve,and J. Wasson. V. Doyle expertly drafted the il-lustrations. Supported by NASA grant NSG-7052and the Smithsonian Foreign Currency Program,which covered field expenses at Lonar Crater, In-dia.

Compartments and Polyclonesin Insect Development

Clones made in early development keep within certainfixed boundaries in the insect epithelium.

F. H. C. Crick and P. A. Lawrence

divide in all about 10 or 11 times (on aver-age) to give a total of some 50,000 cells (5).Shortly after puparium formation cell divi-sion of the disc stops. The disc has now acharacteristic size and shape, being some-what like a flattened and heavily foldedballoon (7).At metamorphosis a complicated set of

cell movements occurs, and these result inthe disc being turned inside out so that itcan form the adult structure. The wing it-self, for example, is first formed as a bag.The bag is then collapsed to form the adultwing, which thus becomes a single sheet ofepithelial cells folded and collapsed toform a double layer of epithelial cells.

In this article our aim is to describe re-Sent work on the development of intact-pithelia and in particular the importantresults and ideas of Professor AntonioGarcia-Bellido (1) and his group in Madridwhich are not yet widely known. We tryto explain as clearly as possible what theseideas are and what sort of experimentshave been done to support them. Some ofthe more obvious questions arising fromthe results and how the new concepts mayrelate to other ideas such as "gradients"are listed.

Development of Drosophila

The development of an adult Drosophilais a complex process. The nucleus of thefertilized egg divides a number of times toform a compact mass of about 250 nuclei,near the center of the egg, without cellwalls. These nuclei then migrate outwardto the inner surface of the egg where forthe first time cell membranes are formed.The cells divide several more times to forma single layer of cells, about 4000 in all, lin-

Drs. Crick and Lawrence work in the Cell BiologyDivision of the Medical Research Council Laboratoryof Molecular Biology, Cambridge, CB2 2QH, En-gland.

340

ing the inside of the egg. This is called theblastoderm. Behaving as a sheet of cells,the blastoderm undergoes complex foldingmovements generating a multilayeredgerm band, which soon becomes visiblysegmented. The egg hatches after 24 hoursand the animal then goes through three lar-val stages each separated by a molt. Afterthese larval stages, lasting in all about 96hours, the animal then pupates and meta-

morphoses into the adult fly.This adult is formed mainly from special

groups of cells in the larva which them-selves take little or no part in larval devel-opment or function. These are the histo-blasts and the imaginal discs. There are 19of the latter (nine pairs of discs plus thesingle genital disc). We shall concentratemainly on one pair of these, the so-calledwing disc. The left wing disc, within the leftside of the larva, produces the left wing ofthe insect and that part of the dorsal leftside of the thorax next to the wing.The wing disc is seen in the first larval

stage as a small patch of embryonic epider-mal cells (2). These cells remain diploid,while the surrounding larval epidermalcells become polyploid (3). There are prob-ably only about 15 to 30 cells forming thewing disc at this early stage (4-6). Duringthe course of larval growth these disc cells

Basic Ideas of Clonal Analysis

For the purposes of exposition we nowtemporarily leave the wing and describe ahypothetical sheet of "white" epithelialcells on the adult fly. We imagine that wehave at our disposal a special techniquethat enables us to mark (say black), at ran-dom, a single cell in a developing disc. Themark is such that it does not interfere inany way with the normal development ofthe animal. Moreover, all the descendantsof this marked cell retain the mark and canbe recognized in the adult. The method ofmarking has the advantage that we canchoose fairly precisely when, in devel-opment, we mark the cell; but it has thedisadvantage that we cannot mark a par-ticular cell at that time, but only one cho-sen at random, and in early stages we usu-ally mark only one cell in any one individ-ual. If we assume that the significant fea-tures of the process are effectively the samein all individuals, we can piece togetherwhat is happening in development by com-bining experiments on many different indi-viduals.What do we find? Naturally, we see a set

of black cells in the adult, but how many ofthem are there, and how are they ar-ranged?The first observation is what might be

SCIENCE, VOL. 189

on

June

27,

200

9 w

ww

.sci

ence

mag

.org

Dow

nloa

ded

from