VOL. 82, NO. 26
JOURNAL
OF GEOPHYSICAL
RESEARCH
SEPTEMBER
10, 1977
MassFractionationof the Lunar Surfaceby SolarWind Sputtering
Z. E. SWITKOWSKI x AND P. K. HAFF 9'
The Niels BohrInstitute,DK-2100Copenhagen
O, Denmark
T. A. TOMBRELLO AND D. S. BURNETT
California Institute of Technology,Pasadena,California 91125
The sputteringof the lunar surfaceby the solar wind is examinedas a possiblemechanismof mass
fractionation.Simpleargumentsbasedon currenttheoriesof sputteringand the ballisticsof the sputtered
atomssuggest
that mostejectedatomswill havesufficiently
highenergyto escapelunargravity.However,
the fraction of atoms which falls back to the surfaceis enrichedin the heavier atomic componentsin
relation to the lighter ones. This material is incorporatedinto the heavily radiation-damagedouter
surfacesof grains,whereit is subjectto resputtering.Calculationspredictthat an equilibriumsurface
layer, enrichedin heavier atoms, will form with •i(•80) • +20%0 • •i(8øSi)and that oxygenwill be
depletedon the surfacelayersof grainsrelativeto the bulk compositionby about 12.5%.Theseresultsare
in fair agreementwith experiment.The dependence
of the calculatedresultsupon the energyspectrumof
sputteredparticlesis investigated.We concludethat massfractionationby solarwind sputteringis likely
to be an importantphenomenonon the lunar surfacebut that the complexisotopicvariationsobservedin
lunar soilscannot be completelyexplainedby this mechanism.
ofthematerial
ejected
bysputtering
escapes
themoon's
grav-
INTRODUCTION
The bombardmentof the moon by the solar wind has long
been recognizedas an important erosive mechanismof the
surfacelayers of lunar material. Wehneret al. [1963a] irra-
diatedmetal,metaloxide,andmineraltargetswith low-energy
hydrogen and helium ions and concludedthat sputtering
would ejectmatter from the moon into spacewith a distribu-
tion of velocitiessufficiently
high that mostof this material
would escapelunar gravity. Additional investigations[Wehner
et al., 1963b]of the behavior of metal oxides under simulated
solar wind irradiation conditionssuggestedthat sputtering
ity, but somereturningmattersettlesbackonto the surface.
This material, which is somewhatricher in heavieratomsthan
the startingsurface,is incorporatedinto the heavilyradiationdamagedouter surfacesof grains,whereit remainssubjectto
resputtering.
Our calculations
showthat if lunargrainsurfaces
are in equilibrium with respectto sputteringerosion and
redeposition,a level of isotopicfractionationcloseto that
observedexperimentallyis producedon grainson a • 10a-yr
time scale.
CassidyandHapke[1975]havealsodiscussed
massfraction-
would lead to massfractionationof the lunar surface,with ation associatedwith gravitational escapeof the sputtered
heaviermasselements
beingpreferentially
enriched
in relation atoms.They concludethat directsputteringmassfractionation
to lighterelements.This conclusionwasbaseduponthe exper- is not important,althoughthe basisfor this conclusionis not
discussed.In this paper we come to the oppositeconclusion.
imental Observation that for the case of certain metal oxides
andHapkesuggest
thatsputtered
atomshavedifferthe surfaceof the targetbecameenrichedin the heaviermetal Cassidy
ent stickingcoefficients
and COnclude
that massfractionation,
There is considerable
experimental
evidencedemonstrating producedby multiple scatteringof sputteredatoms from a
thatthesurfaces
oflunarsoilgrains
areenriched
intheheavier rough lunar surface,must be consideredto accountfor the
isotopesof oxygenand siliconas well as indicationsthat the experimentalresultsfor lunar soils. Only qualitativeargusurfaceSi/O ratio is enhancedin relationto the bulk composi- mentsare givenfor this conclusion,however.The mostfundafollowing prolongedirradiation.
mental difference between our calculations and those of Cas-
tion [EpsteinandTaylor,1971,1972;TaylorahdEpstein,1973].
A detailedexplanationof thesesurface-correlated
effectshas sidy and Hapke is that we do not just considerthe mass
not been forthcoming.Nevertheless,it seemsclear that since fractionationfrom a singlestageof sputtering;we alsocalcuthe bulk isotopicabundancesin lunar samplesare rather con- late the steady state surfacecomposition,allowing for the
stant and similar to terrestrial minerals, surface effects have effectsof depositionand resputtering.
arisenfrom dynamic
processing
by agentsUniqueto the
It should
beemphasized
thatthepurpose
ofthispaper
isnot
moon's environment. In this context, several authors have to build a completemodel for the evolutionand composition
recognizedthat solar wind sputteringcould give riseto effects of the surfacelayers of lunar materials. Our objectivesare
qualitatively
similarto thoseobserved
[Epstein
andTaylor, more limited, viz., to define as quantitatively as possiblethe
role of a single mechanism,solar wind sputtering,in this
1971;Housleyet al., 1974;Cassidyand Hapke, 1975].
evolution.
Other mechanismsare undoubtedlyalso important
In this paper we presentestimatesof the massfractionation
[Clayton
et
al., 1974].
of the lunar surfaceproducedby solarwind sputtering.Most
DETAILS OF THE PROCESS OF
•Now at School of Physics,University of Melbourne, Parkville
: Now at Wright Nuclear Structure Laboratory, Yale University,
New Haven, Connecticut 06520.
Copyright¸ 1977by theAmericanGeophysical
Union.
Paper number 7B0384.
DIFFERENTIATION
Whena beamof ionsstrikes
a solid,aninteratomic
cascade
3052, Australia.
3797
of particlesis initiated [Sigmund,1969]. Sputteringoccurs
when someof thesemoving atoms escapethrough a nearby
surface.Sputteringis thereforeexpectedto occuron the lunar
3798
SWITKOWSKI ET AL..' LUNAR SURFACEMASS FRACTIONATION
• escape
I
I
beam of an ion microprobe.This undoubtedlyrepresents
the
first stagein the abovemixingprocess.The mixingmechanism
II
has beentreatedtheoretically
by lshitaniet al. [1975],who
fallback
I
I
I
grainsurtace/" '\
•
mixing
[
I
'•
sputtered
portictes
region o!
radiation
damage
useda Monte Carlo approach,and by Haft and Switkowski
[1977], who considereda diffusionmodel in which the mixing
is assumedto haveits basis,as doessputtering,in the collision
cascadesgeneratedby the primary beam.
The exact thicknessof this enriched layer is uncertain.
Rather wide limits on the mixing depth Ax may be infersred
from, on the one hand, the immediatedepth of the sitesfrom
which the sputteredatoms are ejected(probably extending
downto a fewmonolayers,
•, 10,• [Sigmund,
1969;lshitaniand
Shimizu,1975]) to, on the other hand, the measureddepthof
the heavily radiation-damagedregion of the surfacesof dust
grains(•200-500 ,• [Borgetal., 1971]).Thepenetration
depth
of solarwindprotons,whichis • 100•, provides
a reasonable
Fig. 1. Schematicdiagram of processesinitiated at the lunar surface by solar wind irradiation. Material sputteredby the solar wind
largely escapesbeyondlunar gravity. The small (in the caseof lighter
elements)returning componentis enrichedin heavierisotopeswhich
are incorporatedinto a surfacelayer, Ax deep,by radiation-induced
mixing. As the lunar surfaceis eroded,the activelayer persists.Note
that in practice,sputteredatomsreturningon an area elementof the
lunar surfacedid not originatethere. Thereforegrain surfacesshould
reflect a homogenizedsamplingof a wide area of the moon.
surfaceas a result of bombardmentby solarwind protonsand
alpha particles[see,e.g., Maurette and Price, 1975].There is an
important difference, however, between the conditions of a
laboratory sputtering experiment and those encounteredon
the moon. In the former case,all the sputteredtarget material
is typically collected on a catcher foil or otherwise permanently separatedfrom the target. On the moon, gravitational forcesare an important consideration:sincethe energies
of ejected atoms are of the order of the energy required to
escapelunar gravity, some atoms escapeinto space, while
othersfall back to the lunar surface.Sinceat the sameenergy
the heavierof two particleshasthe lower velocity,there ought
to be a natural winnowing mechanismoperatingon material
tossedup from the moon by the solar wind. The fraction of
sputtered material which returns to the lunar surfacewill be
enriched in the heavier elementsand isotopesin relation to
their abundances in the undisturbed material. These returned
atoms are, of course,subjectto resputtering.Also, recoil implantation will drive atoms residing on a surface into the
substratefollowingdirectcollisionswith the primary ion [Nelson, 1969; Perkins and Stroud, 1972; Stroud, 1972; Moline et
al., 1974; Baranovaet al., 1974]. Such 'atomic mixing' of the
surface region by the solar wind will blend some of this enrichedmatter into the undifferentiatedsubstrate.Experimental
support for the idea of radiation-inducedmixing is found in
the work of Mertens [1975], who studiedthe sputteringof a
200-,4Cu film deposited
on AI. Duringbombardment
witha
250-keV Ar beam (whoserange [Lindhardet al., 1963]in Cu is
• 1400,4)a zonequicklydeveloped
aboutthetwo-metalinterface where the metals were well mixed over a region thicker
than •200 A. The useof a thickerCu coatingor lowerAr
beam energiesmight well have exposeda mixing depth that
was much closerto the range of the incident beam. Ion-beaminducedintermixingat a palladium/siliconinterfacehas also
been reported [van der Weg et al., 1974]. Cairns et al. [1971],
McHugh [1974], and Zinner et al. [1976] report distortionsin
implanted ion depth profilesproducedby the analyzingion
estimatefor Ax. Such a value is consistentwith computer
simulationcalculationsof atomicmixing [lshitaniandShimizu,
1975].
Consequently,on the lunar surface,after a sufficiently•ong
time haselapsed,a thin enrichedlayer will existin an equilibrium condition determinedby the balancebetweenatomslost
to outer space,atoms incorporatedupon fallback, and atoms
gainedfrom the admixedsubsurfacematerial. Sucha dynamic
situation is depictedin Figure 1.
THEORY
Two component
surface. Let us start with the simplepicture of a moon consistingof only two elements, Si and O,
present as their most abundant isotopesin the chemicalform
SiO2. (This assumptionwill be relaxedin the next section.)
Within this scenario,expressionsshall be derived for the evolution of the surface enrichment
of Si relative
to O and then
extended to calculationsof isotopic effects. It is useful to
definethe followingquantities:
The quantitynt is the normalizedstartingatomicabundance
at the lunar surface of the element whose mass number is i.
Thus n•6 = •, n28= •.
The quantity Nt(t) is the fractional abundanceof atoms of
speciesi after a time t of bombardment by the solar wind;
Nt(O) = nt.
The quantity S is the sputteringrate constant,definedas the
probability that an atom within Ax will be sputteredfrom the
surface in 1 yr; i.e., sputteringerosion rate in angstromsper
year is identical to SAx. Although S may in reality depend
(initially) upon the time t, we take its valueto be constant.Any
time variation of S would lead to changesin the estimatesof
equilibrationtimesbut would not affectgeneralconsiderations
of the equilibrium state with which we are mainly concerned.
The probability that an atom of speciesi is sputteredfrom Ax
in 1 yr is then in lowestapproximationNtS.
The quantity ft is the fractionof sputteredatomsi which
falls back to the lunar surface. This quantity is expressed
below in terms of the energyspectrumof sputteredparticles
and the lunar escapeenergy.
We can determineN•6(t) and N:8(t) in the following manner.
Considerthe surfacelayer Ax. With time, atoms are sputtered
away. Some atoms escape,so new unfractionatedmaterial is
introducedinto the activeregionfrom the interior sideof the
layer. We require that the total number of atoms comprising
this active region should be constant.An equation describing
the amount by which the fraction of oxygen atoms in Ax at
time (t + At) differsfrom that presentat t is given by
SWITKOWSKIET AL.: LUNAR SURFACEMASS FRACTIONATION
N•6(t + At)-
3799
N•6(t)= -N•(t)SAt + f•dV•(t)SAt
+ n•(l - f•)N•6(t)SAt+ n•(1 - f:8)N:8(t)SAt (1)
The first term on the right-handsideof (1) representsthe total
amount of O sputteredfrom Ax in time At, and the second
term reflects the amount
of O which returned
to the surface
õ
having failed to escapelunar gravity. The differencein these
two terms,(1 - f•)N•(t)SAt, is then the net lossfrom Ax of
the O componentthrough sputtering.In order to conservethe
number of atoms in Ax, fresh material is mixed in from the
reservoirof atoms within the grain in stoichiometricproportions. The filling of O 'vacancies'by O atomsis given by the
third term, while the last term representsthe filling of Si
vacanciesby underlyingO atoms.
Relation (1) is equivalentto the differentialequation
dN•6(t)
dt
i
0.0
i
EieV)
- -N•s(t)7 + C•6
(2)
where
7 = S[n:8(1- f•) + n•(1 - f:•)]
Fig. 2. Semilogarithmicplot of the energydistributionof sputtered particles;•,(E) dE - [dE/E2(1 + U/E) a] for U = I eV. The lunar
escapeenergiesfor atoms of mass 16 and 28 are indicated.
(3)
and
E
C•6- Sn•(1 - f:8)
(4)
with the solution,
C•6/7)e-•'t + C•/7
(5)
An analogous
equationpertainsto N•.•(t).In arrivingat (2)-(5)
we have usedthe fact that N•(t) + N•.•(t) = 1.
The time constantfor approachto equilibrium,T,q, is 3,-l.
For t >> T,o, the equilibriumconditionobtainedis
Nx•(m
) = Cx•/T
= n:•(1- n•(1
fx•)+- n•(1- f•)
(6)
The ratio C•/7 doesnot dependupon the value of S, and
thereforethe equilibriumconcentrations
do not dependupon
the absoluterate at whichparticlesare sputteredaway. The
equilibriumconcentrationis alsoindependentof the thickness
•x of the active surfacelayer. The sputteringfactor S does
appearin the argumentof the exponentialin (5) which determines how fast the steadg state condition is approached.
(8)
E >> C
(9)
and at high energies,
•,(E) '-• 1/E2
Nl•(t) = (n•-
E << u
The function•,(E) peaksat an energyof U/2. Values of U are
typically a few eV for oxides [Kelly and Lam, 1973], and we
shallreturnlater to a discussion
of the valueof U appropriate
to heavily radiation-damagedmineral grain surfaces.For the
purposesof illustrationan energyspectrumcalculatedfor U -1 eV is shown in Figure 2.
We assumethat the sputteredspeciesare atomic Si and O.
The fractionf• of sputteredatomsi which doesnot escape
from the moon is given by
f•= 1+ •
= 1+ m•gR
Referring
to thedefinition
of S in termsof •x, weseethat where E• is the lunar escapeenergyof elementof massm•. R
thecalculated
equilibrium
timewilldepend
onthethicknessand g are the lunar radius and gravitationalacceleration,and
of the layer •X, with a'larger thicknessrequiringa longer (1 amu)gR = 0.0292 eV. From (6) and (11) it is possibleto
calculatevaluesfor the equilibriumconcentrationof Si and O
with the appropriatevalue of U.
justifytheexist6nce
of a mixedlayer.It isworthemphasizing Multicomponentsurface. The formalism for differentiation
time to reach steady state.
In the above discussionwe cited severalexperimentsto
surface
havingbeendevelo.
ped,it isnow
that (6) is stillvalidevenif the mixedlayerdoesnot •xist. of a two-component
In this case, Nt• and N:• give the averagecomposition usefulto generalizethe theory to the caseof a homogeneous
mediumthat would be a more realisticapof the outeratomiclayer,whichis a mixtureof redeposited multicomponent
and unsputteredatoms.
proximation to the compositionof the lunar surface.It will
to assess
theeffectsof sputtering
on isotopic
In orderto proceedwe needto knowtheenergyspectrumof thenbepossible
enrichment
as
well
as
the
effects
on
arbitrary
pairs
of
elements.
sputteredparticles.In the absenceof experimentaldata for
Considerthe caseof a lunar surfacecomposedof k different
silicatematerialswe mustintroducea sputteringtheorywhich
If we labeleachconstituent
by a subscript
will thenallowcalculation
of f•. A frequently
usedenergy atomicspecies.
spectrumof sputteredparticles,derivedby Thompson
[1968] ranging from 1 through k, then after the surfacehas reached
equilibrium, the abundanceN• of species1 within Ax will
and consistentwith availableexperimentaldata, hasthe form
satisfythe equation
•,(E)= E:(1+ U/E)
a
(7) Nt = Ntft + ntN•(1 - ft)
+ n•N:(1 - f:) + ... + n•N•(1 - f•)
(12)
where•,ois a constantand U isa surfacebindingenergyfor the
material under bombardment.The behaviorof •,(E) at low Thefirsttermontheright-handsideisthenumberof sputtered
energiesgoes as
atoms of species1 which returns,and the subsequent
terms
3800
SWITKOWSKI ET AL.: LUNAR SURFACEMASS FRACTIONATION
reflectthe filling of speciesi (i - 1 throughk) vacancies
by
species1. Equation(12) may then be rewrittenas
N-•L
(1- f•)= • N,(1- f,)= const (13)
windsputtering
in thecurrentliterature
from0.5,4/yr [Borget
at., 1974]to 0.03,4,/yr [Zinneret al., 1976]thengives
S=
5 X 10-3
to
3 X 10-'yr -•
From (3) we obtain
since the summation covers all surface components. Since
thereis nothingspecialaboutthe choiceof species
i above,we
have in general
Teq = 240-4000 yr
In the following sectionswe compareestimatesof surface
isotopicand elementalfractionationsbasedon experimental
N,/n,= 1- fj
(14) data for lunar soil sampleswith the theoretical sputtering
Nj/nj
1 - fi
equilibrium surface fractionations as calculatedfrom (14).
The conventionaldefinition for b in representingisotopicen- This comparisonis imperfectfor many reasons.In the context
richments, relative to some arbitrary laboratory standard, of the abovediscussionit is important to considerwhetherit is
reasonablethat the surfacesof lunar soil grains will have
(n,/nj)o, is
achievedsputteringequilibrium.The questionis thenwhether
there
are competingprocesses
whichbury or destroysputtered
• _=(nt/n•)o
Nt/Nj 1
(15)
surfacesin timeslessthan '-•11Yyr. Two plausibleprocesses
are
(1) impactmixingor volatilizationand (2) depositionof'fresh'
Combining(14) and (15) leadsto
surfacelayersof lunar materialsvaporizedby impactsat more
distantpoints.Constantinput (e.g., representing
vapor deposi1 + (•surf N,/N• _ (1 - f•)
(16)
tion) and/or constant rate terms (i.e., proportional to the
I + l•bulk n,/nj
(1 - f,)
number of atoms in the sputteredlayer representing,for exA somewhatmore natural quantity for expressingsurface- ample,impactburial) can easilybe addedto (2). In view of our
correlatedisotopicand elementalenrichmentsis definedby the limited objectiveof only definingthe role of sputteringmass
fractionation we feel that consideration of more complex
equation
equationsis not profitable,principallybecausethe appropriate
e(i/j)
-- (n,/nj)
N,/Nj 1- f'1-- fJ
f,
rates and rate constants to be used are not well known. There
(17) appearsto be nojustification,however,for assumingthat the
for any two speciesi•and j. Equation (17) makes a direct
comparisonbetweensurfaceand bulk concentrations,
without
referenceto an arbitrary standard.In practice,e and 6 differby
no more than about 5%0.(foroxygen),and it will be convenient
to make useof both definitions.Note that the final expression
in (17) is also the form that would have been derivedfor the
simplertwo-componentcaseby using(3), (4), and (6). This
then showsthat the equilibrium fractionationsare independent of the detailed compositionof the medium if the energy
spectrumof sputteredparticlesis not compositiondependent.
EQUILIBRATIONTIME
Beforeconsideringthe equilibriumelementaland isotopic
enrichmentsit is important to examinein more detail the time
scaleinvolvedfor achievingequilibrium.For the sakeof illustration we consider the case of SiO2 described by (5). In
general, equilibration times will depend upon the detailed
compositionof the medium, but until generallyacceptedsputteringratesare availablefor relevantlunar materials,it is not
possibleto deal with this complexity.
It is now necessaryto specifyvaluesfor the surfacebinding
energyU and sputteringconstantS. There existsno measurement of U for heavilyradiation-damagedmineralsof the kind
found on the lunar surface.Experiments[Kelly andLam, 1973]
havepointedto a valueof 4 eV for SiO2,but this is likely to be
significantlyhigher than the value appropriateto grain sur-
faceswhereextensiveradiationdamagehas disruptedthe
atomic bonding. We expectthat the effectivebindingenergy
may decreasewith increasingsolarwind irradiation.For the
purposesof estimatingthe equilibrationtime we take silicon
and oxygenboth to be characterizedby U = 1 eV, sothat their
energy spectra are the same. Noting that the lunar escape
energies
areE•6= 0.467eV andE:8= 0.818eV, (1 ! ) givesf•6 =
0.101 and f:8 - 0.202 (this factor of 2 beingcoincidental).
ratesof thosecompetingprocessesare negligible.Gault et al.
[1974] estimateimpact vaporization rates that would correspondto depositionof impact-volatilizedmaterialat a rate of
0.! ,•,/yr. This is withinthe rangeof sputtering
erosionrates
consideredabove. Consideration of more complex models
shows, in accord with intuition, that the effect of burial and
destructionprocesses
is to lengthenthe equilibrationtime scale
and, usually,decreasethe massfractionationsfrom thosecalculated above. For example,rapid impact mixing on a submillimeterscalehasthe effectof just rotatingsoil grainsin the
solar wind flux. This obviously increasesthe time to achieve
equilibriumbut also producesmore uniformly sputteredsurfaces,which makes a more realistic comparisonbetweenour
calculationsand experimentalmeasurements
on bulk soilsamples. If it is assumedthat annealing rates for the sputtered
layer are negligibly slow at cold lunar subsurfacetemperatures, the --,11Y-yrequilibration time can be accumulated
piecemeal;it neednot be in a singleexposure.It is reasonable
to regard lunar soil grainswith amorphouscoatings[Borget
al., 1971]as beingin sputteringequilibrium(seealsoBorg et
al. [1974]). The estimatedtime scalefor the formation of the
amorphouslayer (--•2000yr [Maurette and Price, 1975]) supports this assumption.Data presentedby Maurette and Price
[1975] on the fraction of grains having amorphouscoatings
indicatethat exceptfor someimmature soils,greaterthan 50%
of the micron-sizedgrains have amorphouscoatings.Since
most of the surfacearea in a lunar soil sampleresidesin the
smallergrains, there appearsto be somejustificationfor the
simplifyingassumption,one that we shall make in the following discussion,
that the surfacesof grainsin a maturelunar soil
sampleare in sputteringequilibrium.
COMPARISONOF CALCULATIONSWITH
,
EXPERIMENTAL
D
On the basisof (14) and (16) we now calculateenrichment
Takingax = 100/[ andthe rangeof erosionratesby solar effectsfor the isotopesof O, Si, and S. AssumingU = 1 eV, we
SWITKOWSKI
ET ALl LUNARSURFACE
MASSFRAETIONATION
3801
obtain = o. 0
= o.
= 0.202,f8o= 0.218,fs•.= [Greenet al., 1976]. If this is true, our fi('80) valuesare over0.234, and f•4 = 0.249.Thesevalueslead to the following estimated, and our estimates of Si/O elemental fractionation
surfaceheavy isotopeenrichments,
b(•O) = 26.0%0
b(aøSi)-- 20.2%0
fi(•'S) = 19.1%o
using(•bulk(180)
"- "{"5%0,
(•bu•k(80Si)
= -2%0, and 8bulk(•4S)
=
+0.5%o.The approximateconstancyof the surfaceb valuesis a
consequenceof assumingthat U = 1 eV (see discussionof
Figure 4).
Epsteinand Taylor [1971, 1972, 1975] and Taylor and Epstein[1973]chemicallyetchedlunar soilswith exposures
to F•
gasand monitoredthe isotopicenrichmentasa functionof the
amountof oxygenremovedfromthegrains.For Si andO they
found strongenhancements
of the heavierisotopesin the O
and Si removedwith verybriefexposure;
however,the isotope
ratios approachedthe bulk valuesonce approximately1% of
the massof the grainshad beenremoved.The early fractions
presumablyapproximatethe isotopiccompositionsof the surfacelayers.Noting that measurements
of specificsurfacearea
in submillimeter
lunarfinesrangefrom0.2to 0.6 mug [Cadenheadet al., 1972;Holmeset al., 1973], we have assumedan
will be low.
We have emphasizedin the above discussionthat our calcu-
lated massfractionationsare independentof the depth (Ax)
chosen for our mixed layer and, in fact, independentof
whether the mixed layer even exists. However, it should be
equally stronglyemphasizedthat the existenceand thickness
of the mixed layer are critical in comparingour calculations
with the Epsteinand Taylor experimentalresults.If the mixed
layer is only the first atomic layer, then the massfractionation
in this layer mustbe enormous,because(1) eventhe firstcut of
the F• strippingcontainsmuch more material than the first
atom layer and (2) it is very unreasonableto believe that
alternativeisotopicfractionationmechanisms(e.g., diffusion)
wouldproducea 50- to 100-•-thickisotopically
anomalous
layer for Si and O. Thus if there is no mixed layer, our
calculatedisotopicfractionationsfor Si and O would be much
lessthan what mustactuallybe present,and somemechanism
other than sputteringwould be dominant.However, our inter-
pretationisthat thereissufficient
evidence
that themixedlayer
really existsand that the sputteringshouldbe regardedas a
plausiblemechanismfor producingobservedSi andO isotopic
fractionations.
effectivegrain diameter of 10 u, so that the measurementsof
Bearing the above qualificationsin mind, we return to a
more detailed comparisonwith lunar data. Equation (11)
whichthereare measurableisotopicfractionations.The values showsthat the fraction of sputteredatoms escapingis not
b(•O) and b(aøSi)
were found to vary quicklywithin this layer. linear in mass; however, because of the small fractionations
Our modelis unrealisticin that it doesnot considerthe depth involved in fi(x•O)/b(x70), we calculate this ratio to be 2, in
dependence
of the isotopicdistribution.The observeddepth accord with the general expectationfor a physicalisotope
dependence
of the isotopicvariationsprobablyreflectsa com- separationprocessas well as with the measurements
of Clayplex gardeningof the surfaceby atomic projectilesas well as ton et al. [1974].
some diffusionof the surfacespecies.This processis quite
EpsteinandTaylor notealsothat total oxygenis depletedby
likely a complicatedone whichdoesnot lend itselfto any •40% relativeto Si in the first cutsof the fluorinestripping.
plausiblebut straightforward
description;
andthe assumption Qualitativelysimilar effectsin the outermostatomic layers
of a well-defined
layer,Ax deep,is only a roughapproxima- havebeenobservedby HousleyandGrant[1976]usingelectron
tion. However,the first cutsof thesefluorination'stripping' spectroscopyfor chemical analysis(ESCA). The fact that
experiments
correspond
to an effectivesamplingdepthof 440 larger variations were not observed in the ESCA measure•,, andtheenrichment
effects
weremuchdilutedfor depths ments is an argumentfor a well-mixedlayer in at least the
EpsteinandTaylordefinesurfacelayersup to 170• thickin
greater
than• 100• (i.e.,a depthof approximately
Ax). For outer40 •,. In a manneranalogous
to theisotopic
variations
this outermostpart of the sputteredlayer it doesappearreasonableto assumea well-mixedzoneof materialin sputtering
equilibrium,asdescribedby our equations.Thuswe think that
it is fair to comparethe model predictionsto the maximum
measuredenrichments,i.e., thosewhich apply to the thinnest
surfacelayers.Experimentally,
•(1•O)wasfoundto rangeupto
•50%o and •(3øSi)up to •25%o in the fluorination fractions.
The results of our calculations are therefore in reasonable
the amountof oxygendepletioncausedby sputteringis calculated to be 12.5%.As is the casewith fi(•O), the calculated
fractionation
is less than that measured. This is not what
wouldbe expected
if thesurfaces
of thesoilgrainsanalyz•:d
had not attained sputteringequilibrium. Possiblead hoc explanationsfor the lowercalculatedfractionationsare that (1)
volatilizationand recondensation
are important mechanisms
for mass fractionation, (2) our adopted sputteringenergy
•spectraare incorrect,(3) our calculatedresultsreflect the
average mass fractionation over a layer that is thicker than
what is actually analyzed,or (4) the sputteringyield is mass
dependent(seethe sectionon massdependence
of the sputtering process).
Rees and Thode [1974] have used S isotopicanalysesof
grain-sizefractionsto estimatea surfacefi(a•S)enrichmentof
about 20%0,in excellentagreementwith our calculations.
accordwith the data of Epsteinand Taylor, althoughthe
measuredisotopicenrichmentfor O is morepronounced
by a
factor of 2 than for the Si isotopesin contrastto our calculations.We cautionthatthereareseveralfeaturesWhichprohibit comparisonbeyondthe order of magnitudelevel. The
assumptionof sputteringequilibriumhas alreadybeen discussed.The interpretationof the fluorinationexperimentsis
alsocomplex.As experimentsare performedon a distribution
of grain sizes,shapes,and compositions,uncertaintiesexistin
Relativelylargea•K/•XKdepletionshavebeenreportedfor
theconversion
of thefractionof oxygenremovedto anequiva- bulk soil samples(5-10%o),but thesedo not appear to be
lent depth of surfacelayer. Furthermore,grains without surfacecorrelated[Barneset al., 1973;Garneret al., 1975].A
amorphouslayers (10-50% in mature soils [Maurette and speculativepossibilityis that the large bulk isotopicenrichPrice,1975])mayhavenormalsurfa•:e
compositions.
Another mentsfor K (and S), comparedto the absenceof equivalent
oversimplification
in our calculationsis the assumption
that effectsfor Si andO, mayindicatethat a largefractionof theK
the sputteredspeciesare Si and O atoms. There is some evi- and S in lunar soilshasbeenon surfaces.For example,mostK
dencefor the sputteringof molecularspeciessuchas sio and S may haveoriginallybeeneraplacedasvapor depositson
3802
SWITKOWSKI ET AL.: LUNAR SURFACE MASS FRACTIONATION
surfacesand later incorporatedinto larger grains by impact Figure 3 illustratesthe variation in • as a function of U for the
three systemsof interest.DecreasingU tendsto increaseall b
melting or agglutinateformation.
Equation(14) is alsovalid for the caseof an elementsuchas values and thereby to improve slightly the match to experiC, which is usually consideredto be absent in lunar rocks ment. Thus if U = 025'eV, we find •(Si/O) = 395%0,•(*øSi)=
exceptfor solar wind implantation.In this case,n, in (14), 48%0,and •(•O) = 67%0.Massfractionationby the mechanism
refers to solar wind, not bulk, abundance. For our standard proposedhere will of courseapply to all elementsacrossthe
assumptions(U = 1 eV) we would predict e(xsC)to be only periodic table. Figure 4 demonstrateshow isotopic enrichabout 10%o.This is reasonablycloseto a bulk soil value, but ments will vary as a function of massnumber for isotopes
surface carbon isotopic enrichmentsmay be much larger differingin massby two units.
An interestingfeature of the form of the energyspectrum
(>•50%o)[Epsteinand Taylor, 1975].If the Epsteinand Taylor
resultsare acceptedat facevalue,they would indicatethat (1) adoptedhere is the asymptoticbehaviorof • when U • 0. In
our adoptedsputteringenergyspectrumis incorrect,(2) diffu- this case,•(i/j) = At/A• - 1 whereAt.• are the massnumbers
sion lossand reimplantationaccompaniedby largemassfrac- of the elementsunder consideration.Therefore if the energy
tionation is the dominant effectcontrollingthe surfaceC iso- spectrumof sputteredparticlesis peakedat very low energies,
topic composition,or (3) the solar wind (•(15C)is •40%o. The as might happen if the sputteredmaterial which returnsand
data of Epsteinand Taylor[1975]indicatethat the surface-and adheresto the grain surfacesis only very weakly bound, then
volume-correlated(bulk) C in lunar soil representsdifferent rather large heavy atom enrichmentsmight result.
Sucha discussionis speculativeuntil experimentalmeasuresourcesand that the bulk C isotopiccompositionis irrelevant
...... n,,r •._.•.
.............
fnr
n,,rnn•oe
Tho bulk o may be ,•t,,,,,,,,, or lunar in mentsare •u• a•u out of "-- energydistributionof eachspecies
origin. Significantlunar C inputs into the regolith are also of sputteredatoms under • 1-keV/amu hydrogenand helium
requiredif suggestions
are correctthat CO in lunar rockshas bombardmentof targetswhosecomposition,surfacestructure,
producedmetalliciron [Satoet al., 1973;Sato, 1976]or vesicu- and radiation historyresemblesthat of the lunar surface.The
lation [Goldberget al., 1976].
absenceof data in this area atteststo the difficulty of such
Large b(•SN)values(up to 100%o)for lunar soils[Kerridge, measurements.
1975] do not appear to be related to lunar surfaceresidence
Mass dependence
in thesputtering
processitself This topic
and thusprobablycannotbe explainedby sputtering.Further- is receiving increasingtheoretical [Andersenand Sigmund,
more, it should be noted that to the extent that the form of our
1974] and experimentalattention [Shimizuet al., 1973; Poate
sputteringenergyspectrumis correct(regardlessof the value et al., 1976].While simpleconsiderations
of massconservation
of U adopted) the b(•SN)producedby sputteringshouldnot requirethat after prolongedsputteringthe compositionof the
exceed 70%o.
ejectedmaterial should reflectthe compositionof the target,
dynamic
'effects
occurring
duringthe
For U = 1 eV we also expect "Ca/4øCa variations corre- theremaybeimportant
;•oa;o,;,.. which might produceanomalous•u•
.... ••t• composispondingto about b("Ca) • 20%o.Experimentsto date [Rus- ............
sell et al., 1976, 1977] suggestthat no variationsgreaterthan tions even in the absenceof gravitationalredeposition.Thus
the sputteringratesof differentatomicor isotopicspeciesmay
3%0are present.This is difficultto understandin view of the O,
differ from one another.Within certainapproximations[Haft
Si, and S data, regardlessof the fractionationmechanism.
In summary,it seemslikely that sputtering/gravitational andSwitkowski,1976]the partial sputteringrate of speciesi is
massfractionationis oneof the importantprocesses
determin- predictedto be NtS, where S is the total rate. We have made
ing the chemicaland isotopiccompositionof lunar surface this assumptionabove.In principle,however,it is possiblefor
layers,but this mechanismcannot accountfor all isotopic each speciesto be characterizedby its own sputteringfactor,
data. We are still far from a comprehensive
picture of the so that St • S•. In this case,(17) may be generalizedto
sourcesand mechanisms
for the concentrations
and isotopic
compositionsof light elementsin lunar soils.
St(l DISCUSSION
e(i/j)
= Sj(1
- f•)_ 1
(18)
It is worthwhilehere to reiteratethe fundamentalassumptions upon which the calculationsdependand to note those
aspectswhich requirefurther experiments.
Energydistributionof sputteredparticles. In order to producesignificantmassfractionationthe velocitydistributionof
lOO
the sputteredatomsmustextendto sufficientlyhigh velocities
80
- 800
that thereis significantmasslossfrom the moon.Althoughit
is possiblethat heavy atoms tend to be emitted at lower .-.
60
600
energiesthan light atoms, as might be expectedfrom argumentson the efficiencyof collisionalenergytransfer,we have
40
400
adoptedthe conservative
assumptionthat the energyspectra
are identical for all atomic species.An energy spectrum
20
200
weightedmore to lower energiesfor the heavier particles
would, of course,magnify surface• valuesstill further.
0.01
0.1
1.0
10.0
The energyspectrum(7) wasdeveloped
primarilyto explain
U(ev)
sputteringexperiments
with projectilesboth heavierand more
energeticthan solar wind particles;however,it seemsto hold
Fig. 3. Semilogarithmicplot of calculatedvaluesof • versusU.
alsofor lighterprojectiles
[Wehneret al., 1963a].In anycase,it Curvesare shownfor •O-•O, aøSi-a•Si,
and Si-O (dashedcurve). The
is a usefulparametrization,
sinceby simplyadjustingU, one scalefor •(Si-O) is notedto the right of the figure.As U ---,0, •(•O) ---,
can controlthe positionof the peakof the energydistribution. 125%o,e(aøSi)-• 71%o,and •(Si/O) ---,750%o.
SWITKOWSKIET AL.' LUNAR SURFACEMASS FRACTIONATION
80
the periodictable.Enrichments
can alsobe predictedfor any
pair of elements.
70
Acknowledgments.This work was supportedin part by the National ScienceFoundation (PHY76-83685) and the National Aeronauticsand SpaceAdministration(NGR 05-002-333).
60
U=o.z
• so
•
•o
•
•o
3803
ev
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