The influence of artificial radiation damage and thermal annealing

60 Pages·2008·0.51 MB·English

by  David Shuster

Available online at www.sciencedirect.com
GeochimicaetCosmochimicaActa73(2009)183–196
www.elsevier.com/locate/gca
The influence of artificial radiation damage and thermal
annealing on helium diffusion kinetics in apatite
David L. Shustera,*, Kenneth A. Farleyb
aBerkeleyGeochronologyCenter,2455RidgeRoad,Berkeley,CA94709,USA
bDepartmentofGeologicalandPlanetarySciences,MS170-25,Caltech,Pasadena,CA91125,USA
Received15July2008;acceptedinrevisedform10October2008;availableonline21October2008
Abstract
Recentwork[ShusterD.L.,FlowersR.M.andFarleyK.A.(2006)Theinfluenceofnaturalradiationdamageonhelium
diffusionkineticsinapatite.EarthPlanet.Sci. Lett.249(3–4),148–161]revealingacorrelationbetweenradiogenic4Hecon-
centrationandHediffusivityinnaturalapatitessuggeststhatheliummigrationisretardedbyradiation-induceddamagetothe
crystalstructure.Ifso,theHediffusionkineticsofanapatiteisanevolvingfunctionoftimeandtheeffectiveuraniumcon-
centrationinacoolingsample,afactwhichmustbeconsideredwheninterpretingapatite(U–Th)/Heages.Herewereportthe
resultsofexperimentsdesignedtoinvestigateandquantifythisphenomenonbydeterminingHediffusivitiesinapatitesafter
systematically adding orremovingradiation damage.
Radiationdamagewasaddedtoasuiteofsyntheticandnaturalapatitesbyexposuretobetween1and100hofneutron
irradiationinanuclearreactor.Thesampleswerethenirradiatedwitha220MeVprotonbeamandtheresultingspallogenic
3Heusedasadiffusantinstep-heatingdiffusionexperiments.Ineverysample,irradiationincreasedtheactivationenergy(E )
a
andthefrequencyfactor(D /a2)ofdiffusionandyieldedahigherHeclosuretemperature(T)thanthestartingmaterial.For
o c
example,100hinthereactorcausedtheHeclosuretemperaturetoincreasebyasmuchas36(cid:2)C.Foragivenneutronfluence
themagnitudeofincreaseinclosuretemperaturescalesnegativelywiththeinitialclosuretemperature.Thisisconsistentwith
alogarithmicresponseinwhichtheneutrondamageisadditivetotheinitialdamagepresent.Indetail,theirradiationsintro-
ducecorrelatedincreasesinE andln(D /a2)thatlieonthesamearrayasfoundinnaturalapatites.Thisstronglysuggeststhat
a o
neutron-induced damagemimics the damageproduced byU andTh decayin natural apatites.
To investigate the potential consequences of annealing of radiation damage, samples of Durango apatite were heated in
vacuum to temperatures up to 550(cid:2)C for between 1 and 350h. After this treatment the samples were step-heated using
theremainingnatural4Heasthediffusant.Attemperaturesabove290(cid:2)CasystematicchangeinT wasobserved,withvalues
c
becominglowerwithincreasingtemperatureandtime.Forexample,reductionofT fromthestartingvalueof71to(cid:2)52(cid:2)C
c
occurredin1hat375(cid:2)Cor10hat330(cid:2)C.TheobservedvariationsinT arestronglycorrelatedwiththefissiontracklength
c
reduction predicted from the initial holding time and temperature. Furthermore, like the neutron irradiated apatites, these
samples plot on the same E (cid:3)ln(D /a2) array as natural samples, suggesting that damage annealing is simply undoing the
a o
consequences of damageaccumulation in terms ofHediffusivity.
Takentogetherthesedataprovideunequivocalevidencethatattheselevels,radiationdamageactstoretardHediffusionin
apatite,andthatthermalannealingreversestheprocess.Thedataprovidesupportforthepreviouslydescribedradiationdam-
agetrappingkineticmodelofShusteretal.(2006)andcanbeusedtodefineamodelwhichfullyaccommodatesdamagepro-
duction andannealing.
(cid:3)2008Elsevier Ltd. Allrights reserved.
* Correspondingauthor.
E-mailaddress:[email protected](D.L.Shuster).
0016-7037/$-seefrontmatter(cid:3)2008ElsevierLtd.Allrightsreserved.
doi:10.1016/j.gca.2008.10.013
184 D.L.Shuster,K.A.Farley/GeochimicaetCosmochimicaActa73(2009)183–196
1. INTRODUCTION log (kerma) (log(MeV/g))
10
14 15 16 17 18
Application of (U–Th)/He cooling ages to the solution
ofgeologicproblemsrequiresthatheliumdiffusionkinetics 90 hr
140
quantified in the laboratory be accurately extrapolated to
10 hr
conditions of interest in nature, specifically to lower tem-
0 hr 1 hr
peratures and over geologic timescales. The recent sugges- 120
tions that naturally occurring radiation damage modifies
He diffusion in apatite (Farley, 2000; Crowley et al., 2002;
100
Green et al., 2006; Green and Duddy, 2006; Shuster C) 90-100hr
etal.,2006)underscorethechallengeofthisextrapolation: o(C
helium diffusivity is anevolving function of time governed T 80 00 hhrr
by both temperature and effective uranium concentration
(eU)(Shusteretal.,2006;Flowersetal.,2007).Inthisstudy
60
wepresentresultsofcontrolledexperimentsinwhichweex-
ploretheresponseofHediffusioninapatitetoincreasesin
0 hr
crystal damage caused by artificial irradiation, and to 40 0-1hr
annealing of damage at elevated temperatures. In a subse-
quent publication, we will investigate the implications of -2 -1 0 1 2 3
theseobservations forapatite Hethermochronometry. log ([4He] ) (log(nmol/g))
10 eq
The interactions between radiation and crystalline mat-
ter involve ionizations, nuclear transmutations and direct Fig. 1. Neutron irradiation experiments: Helium closure temper-
scattering displacements of constituent atoms (Ewing ature (Tc) versus the log of the concentration of equivalent 4He
etal.,1995;Weberetal.,1998).Basedonthetotalnumber (log10([4He]eq) and the total kinetic energy released into matter
of atomicdisplacements perunit time,the mostimportant (log10(kerma)), as described in the text. Values of Tc were
calculated for a cooling rate of 10(cid:2)C/Ma using the formulation
of these interactions for He diffusion in minerals is likely
of Fechtig and Kalbitzer (1966) for diffusion kinetics determined
from alpha recoil of heavy nuclei in the 238U, 235U, and
from stepwise release fractions of proton-induced 3He or natural
232Th decay chains (Weber et al., 1997; Trachenko et al., radiogenic 4He. We estimated uncertainty in T (1r; shown as
c
2002),butmayalsoincludetheeffectsofthealphaparticles
vertical lines) solely from the linear regression statistics from the
themselves and spontaneous U fission. Regardless of Arrheniusplots.Theopen,light-graycirclescorrespondtonatural
source, the resulting displacements (Ewing et al., 1995) apatites and the solid black curve is the ‘‘trapping model” from
canmodifytheenergeticenvironmentalongdiffusionpath- Shuster et al. (2006). The gray circles plotting between T (cid:2)120
c
waysandmayeitherimpedeorpromotediffusion.Inasuite and140(cid:2)Caretheresultsofneutronirradiationexperimentsona
ofnaturalapatites,Hediffusivitiesbelow(cid:2)200(cid:2)Cdecrease synthetic fluorapatite sample shown in Fig. 2a. The dark gray
points (0 and 1h irradiations) and black points (90 and 100h
with increasing radiation damage (Shuster et al., 2006).
irradiations)correspondtothefiveneutronirradiationexperiments
Thisleadstotheideaofaradiationdamage‘‘trap”,alocal
conductedonasuiteofnaturalapatitessummarizedinTable1and
damaged region of the lattice in which He is preferentially
showninFig.2bandcandFig.EA1.Uptriangles=CJ50,down
sited. Diffusion through a radiation-damaged crystal in-
triangles=00mr18, circles=DYJS5, diamonds=01mr59,
volvestwoenergeticterms:onetoescapethedamagedsite,
squares=Durango.Timescorrespondtonumberofhoursinthe
and another to migrate through the undamaged lattice. CLICITfacilitywithinthenuclearreactor(seetext).
This model predicts a log-linear relationship between the
volume fraction of radiation damage in an apatite and
theheliumclosuretemperature;(Shusteretal.,2006)docu- ogical composition. Limited work on apatite (Farley,
mented such a correlation in a suite of natural apatites 2000) suggests that annealing enhances He diffusion, as
using 4He as a proxy for radiation damage (Fig. 1). These wouldbeexpectediftheradiation damagetrapsare elimi-
dataprovidedthecalibrationforakineticmodelforHedif- nated by this process. At present we have insufficient data
fusion that includes both temperature and radiation dam- toquantifyhowannealinginfluencesHediffusioninapatite
ageas independentvariables (blackcurve in Fig.1). oranyothermineral.Theradiationdamagetrappingmodel
At high enough radiation doses many solids approach of Shuster et al.(2006) included this effectonlyin an indi-
an aperiodic or glasslike state. Previous work shows that rect manner.
zirconsandtitanitesthatreachsuchastatediffuseHevery For thermochronometry, we are most interested in the
rapidly(Hurley,1952,1954;Nasdalaetal.,2004).Thefact extensivepropertiesofthedamagedmaterial,i.e.,theeffec-
thatapatitetendstohavelowerconcentrationsofUandTh tivebulkdiffusivityofthematerialatagivenpointintime.
and has a greater propensity to anneal radiation damage Ourgoalinthisworkistoconfirmandquantifytheeffects
may prevent it from reaching this condition, although at of damage accumulation and annealing on the kinetics of
presentthereare insufficient datato know. heliumdiffusion,ratherthanilluminatedetailsattheatom-
Annealingorreversionofdamagedsitesbacktoacrys- icscale.Ourapproachistwofold.First,tosimulatetheef-
tallinestateoccursinmanysolids.Therateofthisprocess fects of natural radiation damage we subjected apatites to
dependsonmanyvariablesincludingtemperature,thevol- neutron irradiation, a technique by which to induce vari-
ume fraction of damaged sites, and chemical and mineral- ableandcontrolledamountsoflatticedamagecomparable
Heliumdiffusionkinetics 185
to that produced by alpha recoil. Second, we subjected a held within the cadmium lined in-core irradiation tube
natural apatite to a suite of experimental conditions at (CLICIT) facility of the Oregon State University TRIGA
which lattice annealing is known to occur to varying ex- nuclear reactor for 1, 10, 90, or 100h. The samples
tents.Afterthesetreatmentswemaderoutinestepped-heat- were subjected to a 1MeV equivalent neutron fluence
ing measurements onthe samples to quantifythe resulting (U ) equal to (cid:2)2.3(cid:4)1016, (cid:2)2.7(cid:4)1017, (cid:2)2.0(cid:4)
eq, 1MeV, Si
changes in He diffusion kinetics. Throughout this paper, 1018, and (cid:2)2.7(cid:4)1018n/cm2, respectively. We calculated
we focus on the closure temperature (T) as a parameter these values of U from an external calibration
c eq, 1MeV, Si
whichencapsulatesthecombinedeffectsofmodifyingboth oftheCLICITfacility(referencedtosilicon)usingconven-
E andD /a2inourexperiments.However,ultimatelyitis tional techniques (ASTM, 1994). The energy spectrum
a o
thesetwofundamentalparametersofdiffusion(ratherthan within the CLICIT is dominated by moderate energies;
T) that are both directly observable in an Arrhenius plot roughly50%oftheincidentneutronshaveenergybetween
c
andmostrelevantforquantifyingHediffusivityonlabora- 1 and 4MeV (Figs. EA3 and EA4). We expect the higher
tory andgeologic timescales. energy neutrons to induce a greater proportion of damage
thanthoseatlowerenergies.Forthe90and100hirradia-
2. SAMPLES ANDMETHODS tions, the samples were not continuously exposed to the
neutron flux. The 90h irradiation was conducted in (cid:2)33
2.1.Samples consecutive steps between January 23 and February 23,
2006,andthe100hirradiationwasconductedin21consec-
The well-studied helium diffusivity (Zeitler et al., 1987; utive steps betweenNovember 29andJanuary 3, 2007.
Wolf et al., 1996; Farley, 2000) and annealing behavior Following the neutron irradiations, these samples were
(Green, 1988; Carlson et al., 1999; Ravenhurst et al., subjectedtoprotonirradiationatTheFrancisH.BurrPro-
2003)ofthefluorapatitefromCerrodeMercado,Durango, ton Therapy Center at Massachusetts General Hospital to
Mexico (Young et al., 1969) make it a logical choice to produce a uniform spatial distribution of 3He using previ-
investigatehere.OurspecimenofDurangoconsistsoffrag- ouslypublishedprocedures(Shusteretal.,2004).Forthese
mentsproducedbycrushingaslabcutfromtheinteriorofa experimentsweuseda220MeVprotonbeamandafluence
large, gem-quality megacryst. Two different grain sizes of of(cid:2)5(cid:4)1016p/cm2.Theirradiationstookplaceoveracon-
Durango were analyzed. Most experiments were done on tinuous(cid:2)8hperiodoneitherApril30,2006orOctober21,
shards of a standard we call CIT Dur-B, sieved to a mean 2007.
cross section of (cid:2)170lm. This fraction is from the same Note that the Durango aliquots used in the annealing
megacrystandissimilarinsizetotheCITDur-Amaterial experiments (see below) were neither neutron irradiated
studiedpreviously atCaltech and currently usedas anage nor protonirradiated.
standard (Farley, 2000). Dur-A shards have a helium clo-
sure temperature, T =71.7±1.9(cid:2)C (here and below 2.3. Initial treatment: thermalannealing
c
assuming dT/dt=10(cid:2)C/Myr). For a few experiments we
analyzed aliquots that consisted of a single large (few Asuiteofexperimentswasundertakentoassesswhether
mm) chipfrom the sameDurango megacryst. 4Hediffusionismodifiedwhenapatiteisheatedtotemper-
OnlyDurangowasinvestigatedintheannealingexperi- atures at which radiation damage annealing is expected
ments, but the irradiation experiments were performed on based on fission track annealing kinetics (e.g., Green,
Dur-Baswellasfournaturalapatitesfromgranitoidrocks 1988). For these experiments (cid:2)5–30mg aliquots of Dur-B
and a synthetic fluorapatite. The synthetic fluorapatite or Durango chips were loaded in copper foil pouches and
(WSAp) was synthesized in a flux of CaF (Prener, 1967; heatedinvacuumusingaprojectorlampapparatus(Farley
2
Cherniak,2005).Theanalyzedcrystalshadameancrosssec- etal.,1999).Thisdeviceiscapableofrapidtemperaturecy-
tionof(cid:2)300lm,andweassumethatthismaterialinitially cling and has an estimated temperature uncertainty of less
contains no radiation damage. Helium diffusion kinetics than2(cid:2)C.
andcompositionaldataforthefourgranitoidapatiteswere Annealing durations were between 1 and 350h at tem-
reported earlier (Shuster et al., 2005, 2006). They were se- peraturesrangingfrom20to500(cid:2)C.Duringtheannealing
lectedforneutronirradiationexperimentsbecausetheyhave step theevolvedHewasaccumulated,thenanalyzed using
significantlylowerheliumretentivitythanDurangoapatite isotopedilutionquadrupolemassspectrometryasdescribed
(T for 01mr59=49.2±6.6(cid:2)C, DYJS5=49.9±5.1(cid:2)C, elsewhere (Farley, 2000). Following the annealing step the
c
CJ50=49.4±3.7(cid:2)C(CJ50),and00mr18=47.2±9.6(cid:2)C). sample was subjected to a routine diffusion coefficient
ThelowerHeretentivityinthesesamplesisconsistentwith step-heatexperimentwithoutbreakingvacuum(seeSection
arelativelylowvolumefractionofradiationdamageandsug- 2.4).
geststhesesampleswillbereadilyaffectedbytheadditionof
damagefromneutronirradiation.Meancrosssectionsofthe 2.4. Diffusion experiments
analyzedgrainsrangefrom(cid:2)95to120lm.
For the neutron irradiation experiments, we quantified
2.2.Initial treatment: neutron irradiation–proton irradiation heliumdiffusionkineticsusingstepped-releaseofproton-in-
duced 3He (Shuster et al., 2004), while for the annealing
Toinduceradiationdamagethesixsampleswereloaded experiments we used the residual natural 4He as the diffu-
into an Al disk (routinely used for 40Ar/39Ar dating), and sant (Wolf et al., 1996; Farley et al., 1999; Shuster et al.,
186 D.L.Shuster,K.A.Farley/GeochimicaetCosmochimicaActa73(2009)183–196
2004).Aliquotsranginginsizefromasinglecrystaltomany et al., 2006). Below 600(cid:2)C, the samples were heated using
mgwereheldatacontrolledtemperatureforaknowntime aprojectorlampheatingapparatusinacontrolledfeedback
in a chamber under static vacuum (Farley et al., 1999). loop with a thermocouple, as described by Farley et al.
After heating, evolved helium was purified and cryogeni- (1999).Fortemperaturesbetween600and1200(cid:2)C,weused
callyseparatedfromothernoblegasesusingactivatedchar- a70Wdiodelaser(k=810nm)defocusedontothesample
coal held at 32K and analyzed using either a sector-field in the same thermocouple apparatus, which ultimately en-
mass spectrometer at BGC (3He) or a quadrupole mass abledcompleteheliumextraction.Bothheatingprocedures
spectrometer at Caltech (4He). Using the fraction of 3He weretunedforrapidresponseandtoavoidovershootofthe
or4Hereleasedandthedurationofeachstep,wecalculated set-point temperature. Temperature control across this en-
thediffusioncoefficient(D)normalizedtothecharacteristic tire rangewastypically better than±2(cid:2)C.
diffusive length scale a, (i.e., D/a2) using published equa- We used previously described criteria (Shuster et al.,
tions and the assumptions therein (Fechtig and Kalbitzer, 2006) to establish data subsets for Arrhenius regression
1966). modelsforthe3Hebasedexperiments:(i)weusedtheentire
We report D/a2 values (rather than D values) for all of setofmeasured3HereleasefractionstocalculateD/a2val-
our samples. The only exception is for the Durango large ues;(ii)weexcludedD/a2valuesfromregressionmodelsfor
chip experiments in which we scaled from the D/a2 values stepswhenRF3He60.5%(again,tominimizetheinfluence
actuallymeasuredtoa=85lm(equivalenttoDur-B)using of small dust fragments which may be present as well as
the measured grain dimensions and an equivalent sphere largeuncertaintiesatsmallyields),and(iii)excludedvalues
model(MeestersandDunai,2002).Giventhe complicated fortemperaturesP280(cid:2)C(toavoidtheinfluenceofanneal-
geometry of the analyzed chips this computation is fairly ing; see below). The only exception was for the synthetic
uncertain, so these data, especially the D/a2 and closure apatites,whichdidnotyieldappreciableamountsofhelium
temperaturevalues,aredeemedlessreliablethanthoseob- until well above 300(cid:2)C. Step numbers included in these
tainedonDur-B. regressions are indicatedin boldin Table EA1.
We quantifiedthe temperature dependenceof the diffu-
sioncoefficientfromaseriesofstepsoneachsample.Such 2.4.2.Heatingscheduleandregressioncriteriaforannealing
datapermitlinearregressionofln(D/a2)against1/Tassum- experiments
ing the Arrhenius relationship D(T)/a2=D /a2exp((cid:3)E / Foraliquotsannealedattemperaturesabove250(cid:2)C,the
o a
RT),whereE istheactivationenergy,D isthediffusivity heatingschedulestartedattemperaturesatleast10degrees
a o
atinfinitetemperature,andRisthegasconstant.Theheat- lower thanthe initialannealingtemperaturesoastomini-
ing schedule and data selection criteria used in the regres- mize further annealing. It then included a series of retro-
sionsare described in the nextsection. grade steps, followed by prograde steps typically up to
Incalculatingandinterpretingourdataweareexplicitly 400(cid:2)C. Starting with a retrograde series was adopted to
assuming that 3He and 4He diffusion kinetics are inter- minimize the transient artifact known to occur when tem-
changeable despite a substantial mass difference. Previous peratures are dropped by a large amount between subse-
works suggests this conclusion isvalid for apatite (Shuster quent diffusion steps (Farley, 2000). For the experiments
et al., 2004). Similarly, other than for the coarse Durango where the initial temperature of annealing was <250(cid:2)C,
chipsforwhichwearecertainwecan(andmust)scaledif- only the prograde schedule was used. All of these experi-
fusivity from one grain size to another (Farley, 2000), we ments were performed with the projector lamp apparatus
are making no adjustments for the small grain size differ- described in Section 2.4.1. These experiments usually did
ences among our samples. This follows the approach of not degas the aliquot entirely, so the final yield necessary
our previous work in which the small range of grain sizes for diffusion coefficient calculations was obtained either
routinely analyzed for He dating yields variations in diffu- by atotal fusionstep in aresistance furnace (chips),orby
sivity far smaller than variations caused by the factors of calculation based on the mass of the sample and several
interestinthepresentstudy(Shusteretal.,2006).Theissue determinations of the concentration of He in Dur-B
of grain size will be considered further in a subsequent (8.2nmol/g).
publication. Arrheniusparameters weredeterminedfor eachaliquot
usingalldatapointsmeasuredattemperatures<280(cid:2)C(at
2.4.1.Heating scheduleandregression criteria forneutron whichpointfurtherannealingseemslikelybasedonfission
irradiatedsamples track experiments (e.g., Ketcham et al., 2007). In some
The heating schedule for the synthetic apatites began cases the first steps after annealing were isothermal, in
withasetofisothermalstepsateither150or250(cid:2)Ccontin- which case only the last of the isothermal measurements
uing with sets of isothermal steps up to 600(cid:2)C. All of the wasincludedintheregression(itwouldmakenodifference
natural samples were analyzed using a heating schedule if allisothermal pointswere included).
startingwithatleast3isothermalextractionsat200(cid:2)C,fol-
lowed by a series of decreasing temperature (retrograde) 3. RESULTS
steps, followed by increasing temperature (prograde) steps
up to 600(cid:2)C. Beginning our experiments at moderate 3.1. Neutron irradiation diffusionexperiments
(ratherthanminimum)temperaturesmoreefficientlymini-
mizes a potential artifact introduced by small dust frag- Results of the neutron irradiation and helium diffusion
ments containing 3He adhered to crystal surfaces (Shuster experimentsaresummarizedinTable1andthecorrespond-
Heliumdiffusionkinetics 187
ing Arrhenius plots for the six sets of experiments are today.While[4He]isaneasilymeasurableproxyforradia-
showninFig.2 andFig. EA1in theelectronic annex.Pri- tiondamage,itisnotidealforidentifyingthefundamental
mary datafor allexperiments are tabulatedin TableEA1. controls on helium diffusion. This is because correlations
For all samples, He diffusion coefficients define highly lin- betweenHediffusivityand4Hemightarisefromconcentra-
ear Arrhenius arrays at temperatures <280(cid:2)C (e.g., tion-dependentdiffusionratherthanradiationdamagecon-
Fig. 2). Exposure to a 1MeV equivalent neutron fluence trol, and because radiation damage accumulation (and
of 2.3(cid:4)1016n/cm2 causedno noticeablechange in helium annealing) in general will not correlate perfectly with the
diffusionkineticsinanyofthesixsamples.However,expos- accumulation of alpha particles. Here we improve on the
ing each to a fluence of 2.0–2.7(cid:4)1018n/cm2 caused in- [4He]proxybydeveloping analternativeindicator ofradi-
creases in both the activation energy (E ) and in ln(D / ation damage. This transformation requires a relationship
a o
a2),byasmuchas(cid:2)25kJ/moland6.4ln(s(cid:3)1),respectively. between the crystal damage caused by neutron irradiation
For example, E ranges from 139kJ/mol in an untreated andanequivalentamountofdamagecausedbynaturalal-
a
aliquot of Durango apatite to >161kJ/mol in those ex- phadecay.Tomakethetransformation,westartbyassum-
posedto90hofneutronirradiation.Ineffect,thedataar- ing that the amount of crystal damage caused by a
raysintheArrheniusplotsrotateclockwiseattemperatures particulareventisproportionaltothetotalamountofion-
below 550(cid:2)C. izing kinetic energy released into the matter of interest (or
Because the two diffusion parameters are so strongly kerma(ASTM,1994)).Withascalingrelationshipbetween
correlated (Fig. 3), for discussion of our observations it thekermaduetoneutronirradiationandthekermadueto
makessensetocombinethemintoasingleparameter,spe- alpha decay, we can inter-relate the amount of damage
cifically the closure temperature. As shown in Fig. 3, the caused by each process. This approach assumes that the
observedarrayofdiffusionparameterscutsobliquelyacross atomic displacements caused by neutrons are similar to
contours of closure temperature, with higher values of E those caused by alpha decay. In addition, we assume that
a
andln(D /a2)associatedwithhigherT.Thisindicatesthat damageassociatedwithinducedfissionof235Uisinsignifi-
o c
thepositivechangesinE duetoradiationexposurearethe cant,particularlybecauseweusedCdshieldingwhichmin-
a
dominantcontrolonlow-temperatureretentivity.Theradi- imizes the thermal neutron flux. We will focus our
ation resulted in lower values of D/a2 at lowest tempera- discussiononkerma,sinceitisaquantitythatismoreeas-
tures and diffusion kinetics with stronger temperature ilyrelatedtoradiationdamagethanis[4He],andallowsus
sensitivity. The resulting closure temperatures increased to compare damagecaused bydifferent types ofradiation.
by16to27(cid:2)Cafterirradiation.ChangesinT (DT)nega- Thekermaforaparticularneutronirradiationisafunc-
c c
tivelyscalewiththeT priortoirradiation,indicating that tionoftheenergyspectrumandtheamountoftimeasam-
c
apatites with higher initial T were less perturbed by the ple resided within a specific nuclear reactor. The energy
c
neutron irradiation thansamples withlower initial T. spectrumwithintheCLICITfacilityatOSUiswell-known
c
at the location of our samples, shown in Fig. EA3. Using
3.2.Thermal annealing diffusionexperiments the American Society for Testing and Materials (ASTM)
standardpracticeforcharacterizingneutronenergyfluence
Completestepped-heatingdatafortheannealingexper- spectra for radiation hardness testing (ASTM, 1994), the
iments are compiled in Table EA2 and the segments used 1MeV equivalent monoenergetic damage function for sili-
forcomputationofArrheniusparametersplottedinSupple- con has been calibrated for the OSU CLICIT facility by
mentaryFig.EA2.TypicalresultsareshowninFig.2c.All S. Reese (personal communication), equaling 6.3(cid:4)109n/
aliquots yielded highly linear Arrhenius arrays including kWscm2. From this calibration, we can estimate the
both the retrograde and the prograde sequences. Both the 1MeV equivalent neutron fluence (U ) for each
eq, 1MeV, Si
slope and the intercept of the He diffusion arrays vary experimentalcondition(notetheOSUreactorwasoperated
among the aliquots (Table 2). For example, the activation at 1MW for ourexperiments). Since the kerma for silicon
energy(E )rangesfrom139kJ/molinanuntreatedaliquot hasalsobeenquantified(Namesonetal.,1972),wecansim-
a
(identicaltopreviousresults(Farley,2000))to<100kJ/mol plyrelateU totheSikermabyusingtheASTM
eq,1MeV,Si
in thoseexposed to the most intense annealing conditions. standard 1MeV neutron displacement kerma factor (K
D,
For a given annealing duration, both activation energy ) of 95±4MeVmb (ASTM, 1994) and the mean
1MeV, Si
andD /a2generallydecreasewithtemperatureand,aswith atomic mass of Si asshown inFig. 4a.
o
theneutronirradiationexperiments,thereisastrongcorre- The kerma for a-decays along the U- and Th-decay
lation between the two Arrhenius parameters (Fig. 3). Ta- chainsisgivenbythemeanQ-valueforthesetofa-decays
ble 2 shows that T of the variably annealed Durango ((cid:2)5.7MeV/a-decay).Byassumingquantitativeretentionof
c
aliquots rangesfrom (cid:3)2 to78(cid:2)C. 4He, which will be true at temperatures below (cid:2)40(cid:2)C, we
can relate the kerma resulting from a-decay to an
4. DISCUSSION equivalentradiogenic4Heconcentrationinapatite(‘‘alpha
equivalent units”, or [4He] ) (Fig. 4a). Note that the
eq
4.1.Relating neutrondamageto naturalalpha damage reaction Q-value carries all available energy for causing
crystal damage, including both the kinetic energy of the
Inourpreviouswork,weconsideredtheradiogenic4He a-particleandtherecoiledparentnucleus.Here,weignore
concentration([4He])tobeaproxyforthevolumefraction thesmallamountoftotalkermaduetonaturallyoccurring
ofnaturallyoccurringradiationdamagewithineachsample butrelatively infrequentspontaneous 238U fissionevents.
1
8
8
Table1
Neutronirradiationexperiments.
Sample [4He]o Reactor J 1-MeVeq.neutron [4He]eq [3He] [4He]tot Ea(kJ/ (+/(cid:3)) ln(Do/a2) (+/(cid:3)) Tc (+/(cid:3)) D.L
(nmol/g) time(h) fluence(1016n/cm2) (nmol/g) (nmol/g) (nmol/g) mol) (kJ/mol) ln(s(cid:3)1) ln(s(cid:3)1) ((cid:2)C) ((cid:2)C) .
S
h
WSAp_A 0.000 0 0.00000 0.0 0.00 0.0037 0.037 132 0.8 5.66 0.14 117.2 0.9 u
s
WSAp_B 0.000 1 0.00027 2.3 0.13 0.0017 0.038 133 1.1 5.82 0.21 118.4 1.3 ter
,
WSAp_D 0.000 10 0.00260 26.8 1.56 0.0042 0.410 132 1.8 4.77 0.32 126.5 2.2 K
WSAp_C 0.000 90 0.02343 204.1 11.86 0.0036 2.150 149 0.6 8.04 0.10 143.8 0.6 .A
.
F
DAp_A 8.200 0 0.00000 0.0 8.20 0.0023 8.200 139 2.2 13.54 0.55 73.1 1.5 a
r
DAp_B 8.200 1 0.00027 2.3 8.33 0.0022 7.500 138 0.9 13.38 0.21 72.1 1.0 le
y
DAp_C 8.200 90 0.02343 204.1 20.06 0.0022 8.633 161 2.0 19.25 0.50 86.7 1.1 /G
DAp_D 8.200 90 0.02343 204.1 20.06 0.0022 8.824 164 2.1 19.92 0.51 87.8 1.1 eo
c
01mr59a 0.500 0 0.00000 0.0 0.50 0.0025 0.500 121 1.5 10.50 0.40 49.2 6.6 him
01mr59_A 0.500 1 0.00027 2.3 0.63 0.0019 0.793 123 1.2 11.73 0.29 44.5 1.2 ic
a
01mr59_B 0.500 90 0.02343 204.1 12.36 0.0022 3.016 134 2.1 11.55 0.53 74.5 1.5 e
t
01mr59_C 0.500 90 0.02343 204.1 12.36 0.0022 2.926 135 1.0 12.79 0.25 69.6 0.7 C
o
s
DYJS5b 0.300 0 0.00000 0.0 0.30 0.0020 0.300 122 1.2 10.50 0.30 49.9 5.1 m
o
DYJS5_A 0.300 90 0.02343 204.1 12.16 0.0022 2.545 128 2.1 10.32 0.52 67.5 1.6 ch
im
CJ50b 0.010 0 0.00000 0.0 0.01 0.0020 0.010 121 0.9 10.20 0.20 49.4 3.7 ic
a
CJ50_A 0.010 100 0.02645 267.8 15.56 0.0026 1.668 136 0.8 10.86 0.16 85.0 0.8 A
c
00mr18b 0.040 0 0.00000 0.0 0.04 0.0020 0.040 149 2.7 21.40 0.70 47.2 9.6 ta
7
00mr18_A 0.040 100 0.02645 267.8 15.60 0.0024 1.443 165 4.7 21.15 1.19 81.9 2.4 3
(2
[4He] istheinitialradiogenic4Heconcentration;Jistheneutronirradiationparameter(GrastyandMitchell,1966);the1-MeVequivalentneutronfluenceisestimatedfromempiricalcalibration 0
o 0
asdescribedinthetext;[4He]eqisthealphaequivalentconcentrationforeachirradiationestimatedfromFig.4and[4He]o;[3He]and[4He]totarethemeasuredheliumisotopeconcentrations;Eais 9)
theactivationenergyforheliumdiffusion;ln(Do/a2)isthenaturallogofthefrequencyfactor,andTcistheheliumclosuretemperaturecalculatedfordT/dt=10(cid:2)C/Ma.nmol=10(cid:3)9mol. 183
a Shusteretal.(2005). –1
b Shusteretal.(2006). 96
Heliumdiffusionkinetics 189
T (oC) T (oC)
600 500 400 300 400 300 250 200 150
-12 -10
(a) Synthetic Fluorapatite (b) 01mr59
-12
-14
-14
-16
1)) 1)) -16
-s -18 -s
n( n(
2a) (l -20 2a) (l -18
D/ D/ -20
n( n(
l -22 l
-22
01mr59; no neutrons
WSAp_A; no neutrons (Shuster et al., 2005)
-24 WSAp_B; 1 hr irradiation -24 01mr59_A; 1 hr irradiation
WSAp_C; 90 hr irradiation 01mr59_C; 90 hr irradiation
-26 -26
12 14 16 18 14 16 18 20 22 24
4 4 -1
10 /T (1/K) 10 /T(K )
T (oC)
400 300 250 200 150
-10
(c) Durango Apatite
-12
-14
1)) -16
-s
n(
2) (l -18
a
D/ -20
n(
l
-22
DUR-B; 414oC 1 Hr anneal
-24 DUR-A untreated
DUR-B; 90 hr irradiation
-26
14 16 18 20 22 24
4
10 /T (1/K)
Fig.2. ExampleHediffusionArrheniusplotsfor(a)syntheticapatiteWSApbeforeandafterneutronirradiation,(b)01MR59beforeand
afterneutronirradiation,and(c)DurangoapatiteshowingresultsfromuntreatedDUR-A(Farley,2000),andDUR-Bsubjectedto90hof
neutronirradiationandDUR-Bsubjectedto1hofannealingat414(cid:2)C(graysquares).Linesaretheheliumdiffusionkineticsdeterminedby
linearregressiontosubsetarraysselectedusingthecriteriadiscussedinthemaintextandindicatedinTablesEA1andEA2.Opensquaresare
the control experiments without any time in the nuclear reactor or thermal annealing, circles are 1h irradiations and diamonds are 90h
irradiations.InallcasesneutronirradiationcausesArrheniusarraystorotateclockwise,yieldinghigherclosuretemperatures.Incontrast,
annealingdoesjusttheopposite.Arrheniusplotsforallsamplesareincludingintheelectronicannex.
By assuming that the kerma for silicon during the time clearlyanoversimplification,wediscussbelowanddemon-
in the OSU reactor is approximately equal to the kerma strateinFig.1thattherelationshipinFig.4bappearstobe
for apatite for the same irradiation conditions, we can set valid. The relationship also allows us to express the previ-
thetwofunctionsinFig.4aequaltooneanothertoderive ous results ofShuster et al. (2006)in terms of kerma(e.g.,
arelationshipbetweenU and[4He] .Thisallows Fig. 7).
eq,1MeV,Si eq
ustosemi-quantitativelyexpresstheexpectedcrystaldam-
agecausedbyneutronirradiation(mostlikelyduetonucle- 4.2. Experimental complications
ar scattering reactions) in terms of alpha equivalent units
andtocomparetheseresultswiththenaturalvariationsob- Therelativelysmallamountofkermaintroducedbyour
servedbyShusteretal.(2006).Althoughthisrelationshipis proton irradiation (Summers et al., 1993), as well as
190 D.L.Shuster,K.A.Farley/GeochimicaetCosmochimicaActa73(2009)183–196
25 temperature ofa samplewhilein the reactor. Asdiscussed
natural samples intheelectronicannex,wecanestimatethe4Heproduction
1 hr rateinoursamplesfromknownreactioncrosssectionson
10 hr
20 100 hr 40Ca,16O,and19F.Sinceweknowthetotalamountoftime
350 hr spent in the reactor, we can use the measured diffusion
-1n(s)) 15 1n ehurt rboign cirhraipds. kmineaentictsembpoethrabtuerfeoroefathnedsaafmteprleirurasidnigat4ioHne/t3oHseotlhveermfoorcthhre-
2) (l otrnoollmedetreyxp(SerhiumsetenrtainndvoFlvairnlegy,s2im00u4lt)a.nIneoeuffsecitn,-tghrioswisthacaonnd-
a
D/o 10 diffusionof4He.Fig.EA5showstheresultofthisanalysis,
n( clearlyindicatingthatthesamplesreachedameantemper-
l
ature of (cid:2)260(cid:2)C. This temperature corroborates a previ-
ous, independent measurement of maximum temperature
5
(270(cid:2)C) made in the same facility using a thermocouple
20o C 40 oC 60 oC80 oC100 0C eimmpboerdtdaendt iimnpalincaatilounmsinfourm40bAlor/c3k9A. rThgiesocthemropneorlaotguyr,ephaars-
0
80 100 120 140 160 ticularlywhenconductedonKbearingglasswhichislikely
Ea (kJ/mol) to diffuse Ar at (cid:2)260(cid:2)C during irradiation (Shuster et al.,
2005).
Fig. 3. He diffusion parameters ln(D/a2) and E for natural Althoughthesmallamountofconcurrentannealingex-
o a
apatites (Shuster et al., 2006), for neutron irradiated natural pectedatthistemperatureinthereactorwillcausethesam-
apatites, and for the annealed Durango apatite aliquots. The ples to plot at higher kerma in Figs. 1 and 7 than is
specified number of hours corresponds to the Durango apatite appropriate, the shift is relatively small given the logarith-
annealing experiments conducted at different temperatures, as mic x-axis.
shown in Figs. 4 and 5. All samples define a roughly linear
trajectory on this figure, which we associate with the effects of
4.3.Theinfluenceofneutronirradiationonsyntheticapatite
radiation damage. Increasing damage moves samples to the
northeast, annealing moves them to the southwest. Also shown
ThetrappingmodelofShusteretal.(2006)predictsthat
andlabeledarecontoursofclosuretemperature(calculatedfordT/
dt=10(cid:2)C/Ma). Note that the sample array crosses closure proton-irradiated apatite otherwise devoid of radiation
temperaturecontoursatanobliqueangle,showinghowincreasing damage should have diffusion kinetics defined by the two
or decreasing amounts of radiation damage propagates into parameters: E =120kJ/mol and D /a2=1.58(cid:4)104s(cid:3)1,
a o
changesinclosuretemperature. correspondingtoT (cid:2)52(cid:2)C.Ourexperimentsonsynthetic
c
fluorapatite were designed, in part, to test this prediction.
thermal annealing during the neutron irradiations may Assuming that the synthetic apatite has exactly the same
complicate our ability to relate neutron-induced damage propertiesasnaturalapatite,weexpectedT tobeatorbe-
c
to the observations of Shuster et al. (2006). However, due low the least retentive apatites observed in Shuster et al.
to the log-linear relationship between kerma and T, each (2006). However, this is not observed. Instead, even in the
c
introduces only a small bias in Fig. 1. The kerma intro- untreated specimen we found helium diffusion kinetics
duced during the 8h of proton irradiation is only approximately equal to the most retentive natural apatite,
(cid:2)1014MeV/g,comparedwith(cid:2)1016ormoreinmostnatu- or (cid:2)117(cid:2)C (Figs. 1 and 2a). We do not understand why
ralsamples.Wethereforeexpectproton-induceddamageto the synthetic apatite is so He retentive, but we suspect it
be insignificant relative to a sample’s initial or neutron-in- is related to large differences in defect density between the
duced damage except for those samples containing very synthetic and natural specimens.
low amounts of initial kerma (particularly the synthetic Another striking feature of the synthetic apatite Arrhe-
apatite, CJ50 and 00mr18). Comparison of Fig. 1 with nius plot is a lack of curvature between 270 and 900(cid:2)C, a
Fig.7(whichincludeskermaduetoprotonirradiation),re- linearity that is almost never observed in natural apatites
veals only a slight difference in the location of these sam- (See Fig. EA1 and Farley, 2000; Shuster et al., 2004,
ples. However, we now believe that the trapping model as 2005, 2006). While these discrepancies make the synthetic
calibratedinShusteretal.(2006)(Fig.1)maybebiasedto- apatite an imperfect analog system, the sample’s response
wardshighT forkermavaluesbelow(cid:2)1014MeV/g.Since to neutron irradiation is remarkably similar to natural
c
T is expected to rapidly increase with relatively small samples.
c
amountsofkerma,undermostcircumstancesthisisamin- The 10 and 90h neutron irradiations of the synthetic
orartifact (see below). apatite caused E and D /a2 to increase dramatically
a o
Inadditiontocausingcrystaldamage,theneutronirra- (Table1).TheresultingchangeinT from90hofneutron
c
diations caused two bi-products during irradiation: 4He irradiation (DT (cid:2)+27(cid:2)C) spans most of the observed
c
(primarily from (n,a) reactions while in the reactor) and range in T for natural apatites (Fig. 1). When plotted
c
heat. Although the latter introduces the potential for a against alpha equivalent units ([4He] ) or kerma, we find
eq
smallamountofbiasinFig.1duetoconcurrentannealing the relative increasesin T are in good agreement with the
c
during neutron irradiations, we show that these complica- trapping model of Shuster et al. (2006) when shifted up-
tionsalsoprovideaninterestingwaytomonitortheaverage wards to have a base T (cid:2)117(cid:2)C (gray curve in Fig. 1).
c
Table2
Thermalannealingexperiments.
Aliquot AnnealingT((cid:2)C) Annealingtime(h) E (kJ/mol) (+/(cid:3))(kJ/mol) ln(D/a2)ln(s(cid:3)1) (+/(cid:3))ln(s(cid:3)1) T ((cid:2)C) (+/(cid:3))((cid:2)C) Fractionlostinannealing
a o c
step
Shards
Nopretreatment 141 1.7 14.23 0.40 72.5 1.3
H1-T75 75 1 140 2.5 14.21 0.60 71.2 1.9 1.00E(cid:3)04
H1-T300 300 1 137 1.7 12.98 0.40 72.0 1.3 7.30E(cid:3)02
H1-T325 325 1 133 1.6 12.90 0.39 63.9 1.3 1.14E(cid:3)01
H1-T350 350 1 127 1.5 10.75 0.37 62.4 1.3 9.50E(cid:3)02
H1-T354 354 1 123 2.3 10.17 0.55 57.4 2.1 1.50E(cid:3)01
H1-T365 365 1 121 1.2 9.05 0.38 59.4 0.4 1.80E(cid:3)01
H1-T375 375 1 117 1.5 8.54 0.35 52.4 1.2 1.99E(cid:3)01
H1-T397 397 1 112 1.9 7.21 0.46 46.6 1.7 2.14E(cid:3)01
H1-T414 414 1 108 1.3 6.78 0.32 39.2 1.1 3.13E(cid:3)01
H1-T450 450 1 94 1.3 4.57 0.32 14.1 1.1 8.70E(cid:3)01
H1-T500 500 1 79 1.3 0.50 0.32 -2.1 1.2 9.40E(cid:3)01 H
e
liu
H10-T250 250 10 142 1.7 13.97 0.42 76.9 1.4 5.60E(cid:3)02 m
H10-T275 275 10 135 1.7 12.67 0.40 68.8 1.3 1.14E(cid:3)01 d
iff
H10-T300 300 10 125 2.0 10.82 0.37 58.0 2.3 2.27E(cid:3)01 u
s
H10-T315 315 10 125 1.5 10.41 0.37 59.2 1.3 2.75E(cid:3)01 io
n
H10-T330 330 10 119 1.5 8.66 0.35 55.1 1.2 2.59E(cid:3)01 k
H10-T345 345 10 109 1.3 6.16 0.32 46.3 1.1 2.79E(cid:3)01 ine
tic
H100-T250 250 100 135 1.7 12.33 0.40 72.8 1.4 8.90E(cid:3)02 s
H100-T275 275 100 129 1.6 11.35 0.38 62.7 1.3 3.27E(cid:3)01
H100-T300 300 100 118 1.5 7.35 0.35 62.0 1.3 2.88E(cid:3)01
H100-T325 325 100 118 1.9 7.29 0.46 63.7 1.7 7.70E(cid:3)01
H350-T250 250 350 133 1.8 12.23 0.44 68.1 1.5 2.95E(cid:3)01
H350-T270 270 350 126 1.7 9.93 0.41 65.4 1.5 3.59E(cid:3)01
Chips(diffusivitiesrecomputedtor=85lm)
Nopretreatment 141 2.7 14.00 0.60 74.1 2.3
BH1-T150 150 1 145 3.5 16.24 0.85 70.6 2.7 1.67E(cid:3)05
BH1-T250 250 1 143 2.0 14.74 0.47 73.7 1.5 1.20E(cid:3)03
BH1-T325 325 1 135 1.9 12.80 0.45 67.7 1.6 1.00E(cid:3)02
BH1-T350 350 1 133 1.6 12.65 0.39 63.4 1.3 2.00E(cid:3)02
BH1-T375 375 1 127 1.5 11.89 0.37 53.9 1.2 3.20E(cid:3)02
BH1-T391 391 1 115 1.4 9.97 0.33 35.7 1.1 5.40E(cid:3)02
BH1-T415 415 1 115 1.4 9.57 0.33 39.2 1.1 5.90E(cid:3)02
1
9
1
192 D.L.Shuster,K.A.Farley/GeochimicaetCosmochimicaActa73(2009)183–196
1e+18 initial Tc indicates that the neutron-induced damage was
(a) kerma functions additivetothenaturaldamage,butinalogarithmicsense.
Thisagreeswiththelog-linearrelationshipobservedinnat-
1e+17
uralsamplesandpredictedbythetrappingmodel(Shuster
et al., 2006). This is most clearly observed in Fig. 1. For
1e+16 example,samplesCJ50and00mr18,whichcontainasmall
g) amount of initial kerma and a T (cid:2)50(cid:2)C, end up with
V/ c
e T (cid:2)82 and 85(cid:2)C, (or differences of +32 and +35(cid:2)C).
M c
a ( 1e+15 On the other hand, Durango, which initially contains a
m far larger amount of kerma and initial T =72(cid:2)C is only
ker 1e+14 perturbedby+14(cid:2)C.Whenplottedagaincst[4He]eqorker-
ma,allfivesamplesplotveryclosetotheclosuretempera-
tures observed for natural apatites with an equivalent
Φ
1e+13 eq,1Mev,Si amountofdamageandclosetothatpredictedbythetrap-
[4He] ping model.
eq
ThemainobservationofShusteretal.(2006)wasacor-
1e+12
0.01 0.1 1 10 100 1000 relationbetweenTcandlog([4He])inasuiteofnaturalapa-
(1016 n/cm2) or (nmol/g) tites. While radiation damage trapping of 4He is a
reasonable explanation for this correlation, the possibility
of concentration-dependent-diffusion could not be ruled
2m) 10000 (b) scaling relationship out. The neutron irradiation experiments described here
n/c provideatestbetweenthesepossibilities,asdotheanneal-
160 ing experiments (see Section 4.5). Only a small fraction of
1 1000 neutrons produce 4He (see electronic annex), but almost
ce ( all participate in damage production. In contrast, in the
n
e case of a-decay, the production of radiation damage is
u
nt fl 100 genetically tied one-to-one with 4He production. Thus,
e the neutron irradiated samples accumulate radiation dam-
al
v age faster than 4He. For example, the measured 4He con-
ui
q 10 centrations following 90 and 100h neutron irradiations
e
V ([4He] in Table 1) are typically (cid:2)1 order of magnitude
e tot
M Q-value relationship lowerthanthealphaequivalentunitsofradiationdamage.
1 Mev,Si 1 9190 hh hrr rnp neroeututortonron irn rir ariradradiadiatiioationtionn irraFdiiga.ti1onshioswcsotrhraeltattheedrwesipthondsaemoafgHeeadcicffuumsiuolnattioonneruattrhoenr
Φeq,1 0.1 than 4He accumulation. For example, the 100h experi-
0.01 0.1 1 10 100 1000 mentsforsamplesCJ50and00mr18plotaspredictedfrom
their increased kerma (Fig. 1), yet if they were plotted
[4He] (nmol/g)
eq against [4He] , they would plot significantly higher in T
tot c
than the main population. The distinction between radia-
Fig. 4. Kerma scaling. (a) The relationships between the total
tion damage and [4He] is perhaps most clearly seen in the
kinetic energy released into matter (kerma) and (i) the 1MeV
Durango apatite results. The in-reactor 4He production
equivalent neutron fluence (U ) and (ii) the alpha
eq, 1 MeV, Si
equivalent units due to U- and Th-decay series assuming quanti- and diffusive loss were fortuitously balanced such that the
tative4Heretention([4He]eq).(b)Thescalingrelationshipbetween final 4He concentration after neutron irradiation ([4He]tot
U and[4He] derivedby settingthe twolinesequal to (cid:2)8.7nmol/g) was approximately equal to the initial 4He
eq,1MeV, Si eq
one another in (a). Shown are the equivalent 4He concentrations concentration ((cid:2)8.2nmol/g). Despite nearly equivalent
for90and1hintheOSUnuclearreactor,and9hofirradiationin [4He], the T after 90h of neutron irradiation was higher
c
the200MeVprotonbeamattheFrancisH.BurrProtonTherapy by(cid:2)15(cid:2)C.Thisclearlyindicatesthatavariableotherthan
Center. [4He]iscontrolling heliumretentivity in thesample. When
plottedagainst[4He] orkerma(Fig.1),theincreaseinT
eq c
is close to that predicted by the trapping model, again
This agreement corroborates the parameters E =29kJ/
t
mol and w=1.26(cid:4)10(cid:3)4g/nmol of Shuster et al. (2006) stronglyindicatingthatradiationdamageisthecontrolling
variable.
and also indicates that the kerma scaling relationship in
Fig. 4 isnotgrossly inaccurate.
4.5. Kermaas a predictive variable
4.4.The influenceof neutron irradiation onnaturalapatite
Whenscaledtothetotalkineticenergyavailablefordis-
Justlikeinthesyntheticapatite,inallfivenatural apa- placing atoms, the neutron irradiations caused changes in
tites,exposuretoincreasingamountsofneutronirradiation helium diffusion kinetics that are in good agreement with
caused E , D /a2 and the He closure temperature to in- the observed range in natural apatites and the model of
a o
crease (Table 1). The fact that DT negatively scales with Shusteretal.(2006).Becausewedidnotinducesignificant
c