consequences of intra.cascade clustering on defect

Radiation Effects & Defects in So/iy's, Vol. 144, pp. l19-143 Reprints available diratly from the publisher Phot@opying pemitted

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@ 1998OPA (OverseasPublishemAssrciation) N.V. Publishedby liense under the Gordon and BreachScien@ Publishcrsimprint. Printed in India.

CONSEQUENCES OF INTRA.CASCADE CLUSTERING ON DEFECT ACCUMULATION AND MATERIALS PERFORMANCE B.N. SINGH"'* and C.H. WOOb " Materials Research Department, Riss National Laboratory, D K-4000 Roskilde, Denmark ; oA EC L Research, lVhiteshell Laboratories, Pinawa. Manitoba ROE lLO. Canada (Received28 October1997) Considerationsof intracascadeclusteringof self-interstitialatoms (SIAs) and vacancies during the cooling-downphaseof a cascadeand of the differencebetweenthermal stabilities of SIA and vacancyclustersgive rise to the conceptofproduction bias. In recent years,variousaspectsof this conceptincluding the effectsof clusterannihilation by onedimensionalglide havebeeninvestigated.The salientfeaturesof theseinvestigationsand their resultsare summarized.The most important conclusionemergingfrom theseinvestigationsis that a realisticmodellingof accumulationof survivingdefectsunder cascade damageconditionsmust explicitly considerthe role of formation, thermal stability and mobility (glide and climb) of clustersproduced in the cascades.Examplesare shown whereappropriateconsiderationsofthesefeatureshaveled to predictionsregardingdose, temperatureand recoil energy dependenceof void swellingwhich are consistentwith experimentalresults.The specialfeature such as enhanceddamageaccumulationnear grain boundarieshas beensuccessfullyexplainedin terms of production bias and onedimensionalglide of small loops producedin the cascades.Finally, it is shown that the decorationof grown-in dislocationsby gliding SIA loops producedin the cascades may also explain the irradiation-inducedincreasein the upper yield stress. Keywords:Cascade;Production bias; Intra-cascadeclustering;SIAs; Vacancies; One-dimensionalelide

* Correspondingauthor

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In recent years,however, the problem has been, to a large extent, overcome by using atomistic computer simulation models such as moleculardynamics(MD) which haveyieldedthe detailsof the spatial distribution and morphology of lattice defectsand have shown that a substantial fraction of vacanciesand SIAs survives in the form of clusters[6-8]. Thepossibilityofintracascade clusteringof SIAshasbeen investigatedusing a diffusion-basedmethodology which also shows that a significant fraction of SIAs produced at the cascadeperiphery are likely to form clusters [9]. It is interesting to note here that the experimentalevidencesuggestingthe formation of clustersof SIAs and vacanciesin the cascades have,in fact, existedalreadysince1975(see Section2). In view oftheseresults,it is ratherunrealisticto treat the problemof damageaccumulationunder cascadedamageconditionsin termsof the conventionalrate theory basedon the assumptionthat all defectsare produced as singleSIAs and vacancies.Even the modified version of the rate theory treatmentdue to Bullough et al.ll0l is not appropriate since it considersthe clustering of only vacanciesand not SIAs and relieson dislocationbiasasthe only driving forcefor void growth. It was the recognitionof the significanceof the intracascadeclusteringof SIAs and vacanciesand of the differencein the thermal stability betweenthe clustersof SIAs and vacancieswhich led Woo and Singh [l l] to proposetheconceptof productionbias.The conceptwasshownto provide a potential driving force for void swelling in the steady-stateand to explain the temperaturedependenceof the steady-statevoid swelling. Subsequently,the evolution of void swellingin the transientregime(i.e. at very low doses)was studiedby Singhand Foreman [2] using the concept of production bias alone (i.e. without contribution of dislocationbias).The resultsdemonstrated that theproductionbiasmodel is indeed capableof predicting the swelling observedin the transient regime.Another important point emergingfrom this study was that in order to explain the observedvoid swelling at higher doses it was necessaryto assumethat l5o/oof the SIA clustersproducedin the cascadesescapedto sinks other than voids (e.g.grain boundariesand dislocations)by one-dimensional glide.This led to a detailedinvestigation of the role of one-dimensional glide of SIA clustersin controllingthe damageaccumulationundercascadedamageconditions[3,14].

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(b) Only about one tenth of the NRT displacements survivesas lattice defects(i.e. SIAs and vacancies). (c) A substantialfraction of SIAs and vacanciesforms clustersduring the cooling-downphaseof thecascade; the high localconcentration of SIAs (i.e. closeproximity), the high temperaturein the cascade volume and the attractive elastic interaction betweenSIAs make clusteringof SIAs inevitable. (d) Both the sizeand the number of SIA clustersper cascadeincrease with increasingrecoil energy[6-8]. The observationof intracascadeclusteringof SIAs and vacanciesis not limited only to the MD simulationstudies.In fact, the transmission electronmicroscopy(TEM) and diffuseX-ray scatteringexperimentson irradiated pure metalshad provided ampleevidencefor the "athermal" clusteringofvacancies120-25landSIAs123-27lincascades evenbefore the intracascadeclusteringphenomenonwas firmly establishedby the MD simulationstudies[6-8]. Thus, the available evidencesuggeststhat under cascadedamage conditions a substantialfraction of SIAs and vacanciesis produced in the form of clustersand not as singleand isolated Frenkel pairs. Furthermore, the clusters of SIAs and vacanciesare spatially separated from eachother. At irradiation temperaturesabovestageV, vacancies would evaporate from the vacancy clusters and a large fraction of them would enter the medium (see next section). The evaporating vacancieswould contribute to the global vacancysupersaturation.At the same time, the density of SIA clusters would build-up with increasingdose.As shown later, the rate of observedvacancyaccumulation suggeststhat a fraction of the SIA clustersmust be escapingto extendedsinks.The interstitialclusters,on the otherhand,areexpected to remain thermally stable,at least up to peak-swellingtemperatures [28-30]andcannotprovidemobilesingleSIAsto themedium.It should also be noted that the fraction of vacanciesimmobilized in the form of clustersis not likely to be the sameasthat of SIAs.Thus,undercascade damageconditions, there is a large asymmetryin the production of mobile vacanciesand SIAs that can subsequentlybecomeavailablefor further interactionsand accumulationsin the form of dislocationsand voids. Theseconsiderationsof intracascadedefectclusteringand the thermal stability of the resulting clustersgave rise to the concept of productionbiasI l,l2].

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As describedin Section 2, the number of defectsproduced in the cascades is only about one-tenthofthe numberofdefectscalculatedby the NRT model [1]. To recognizethis loss of point defectsthrough mutual recombination in the cascadevolume, the calculations were carried out in terms of an effectivepoint defectgenerationrate G. G is taken to be the rate ofgeneration ofall point defectsthat are available for making contribution to the rate of defectaccumulationand is given by G: (l - o)Kwhere o is the fractionof defectsthat recombines in the cascadeand K is the point defectproduction rate as calculatedby the NRT model The influence of intracascadeclusteringon point defect accumulation under cascadedamageconditions is includedin the calculationby partitioningKinto threefractions:thosethat recombine(o), thosethat cluster()) and thosethat escapethe cascaderegion and undergolongrangediffusion(p).With theseconsiderations, Woo and Singh[l l]have shown that the effective point defect generation rute G is given by G : pjKl 0 - e) for j :i, v and ei : Ai(l - a). Using this definition of G, it has beenshown that the production bias is a potent driving force for the accumulationof vacanciesin voids under cascadedamageconditions [l]. In this analysis,it is implicitly assumedthat all the SIA clustersproduced in the cascadesare immobile and that the number densityof SIA clustersis maintained,at a steadystatevalue by some mechanismsuch as dislocation sweeping[11,33]which is also the mechanismvia which interstitial clustersare incorporatedinto the dislocation network. The problem of dislocationsweepinghasbeenfurther investigatedby Woo and Seminov[34]. using the effectivepoint defectgenerationrateG and experimentally derived quantities for various sink strengths describing the microstructure(seeTable I in [l 1]),the steady-state swellingratefor stainless steel has been calculated as a function of irradiation temperature. Figures I and 2 show the resultscalculatedfor an austeniticstainless steelirradiated with fission neutrons producing cascadesand l Mev electrons(e.g.in HVEM) producingFrenkel pairs, respectively.The results plotted in Fig. I illustrate severalimportant characteristicsof void swellingunder cascadedamageconditions: (i) The existenceof two sharply separatedtemperatureregimes;low swelling rate at lower temperaturesand high swellingrate at the

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review).This behaviourcannotbe explainedin termsof conventional rate theory and dislocationbias(seefor example[44]),particularly when the dislocationdensityis very low. The situation,on the other hand,is very suitablefor testingthe production biasmodel sincethe production biasis expectedto be the most potent driving force for the void swelling at very low doseswhen the densityof the biasedsink (i.e.dislocations) is negligiblylow. The temporalevolutionof SIA clusters,void sizeand swelling was calculatedby Singh and Foreman [12] for pure copper under neutron irradiation at 523K. Thesecalculationswerecarried out taking the production bias to be the only driving force. The escapeof vacanciesfrom the cascadevolumewastakenasthe effectivegeneration rate of vacanciesand wascalculatedusingcascadeparametersobtained from MD simulations.Sincethe dislocationdensityin fully annealed pure copper is generallyfound to be very low [45], the density of dislocationsinkswas taken to be zero. The calculationsdemonstratedthat the productionbiasdoesindeed havethe potential of providing the driving force for void swellingeven in the absenceof dislocationsand without the contributionof dislocation bias.Furthermore,the generaltrendsof the calculateddosedependenceof swellingare in agreementwith experimentalresultsshowingthe high swelling rate at low dosesand a decreasein the swelling rate at higher doses(Fig. 4). However,in order to explainthe experimental resultsquantitatively it was found to be necessaryto assumethat small sIA clustersproducedin the cascademust be mobile and about r5Toof them must be escapingto sinks other than voids. According to MD simulationresultsit seemsquitepossiblethat about I 5% of SIA clusters producedin the cascadeduring fissionneutron irradiation of copperin the peak swellingregimemay contain as few as only 4-6 SIAs [46]. Thesesmallclustersarelikely to be highly glissile[7,8].Indirectexperimental evidencefor the one-dimensionalglide of small sIA clusterscan be deducedfrom the results on the evolution of SIA clustersin the annealing stage II after low temperature irradiation with electrons [47,48]and fast neutrons[48-50]. It shouldbe addedthat at void swellingtemperaturesevaporationof vacanciesfrom vacancyclustersproduced in the cascadeswould generate vacancysupersaturationin the medium. In the presenceof this supersaturation,the sessileSIA clusters produced in the cascades would shrink and eventually disappear.This processwould ensure,

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(ii) That at high dislocationdensities(> l0r2m-2) voids may nucleate during the transientmaximum of the vacancysupersaturationeven though they may not be stableduring the subsequentsteady-state condition. It shouldbe pointed out that the loop glideis not the only mechanism of cluster removal. Various possibilitiesincluding conservativeclimb have been consideredby Trinkaus et al. 114,331. Possibleeffects of production bias and clusterannihilation on the dislocationcomponent of the microstructure, including the nucleation and growth of SIA loops and the climb of the network dislocationshave beenstudied by Woo and Seminov [34]. These authors conclude that the observed evolution of the dislocation structure can be understood as a consequence of the operationof the productionbias,despitea net flux of freevacancies to SIA clusters.In order to understandthe nucleationof SIA loops in the environmentof a net flux of free vacancies,Seminov andWoo [51]haveuseda Fokker-Planakequationapproachto include stochasticeffectson the evolution of the primary clusters.They have shown that despitea much higher flux of freely migrating vacanciesat the peakswellingtemperatures,the nucleationand growth of SIA loops are possible. 4. DAMAGE ACCUMULATION IN THE VICINITY OF GRAIN BOUNDARIES It is well establishedthat grain boundariesact as neutral and unsaturable sinks for both vacanciesand SIAs. This givesrise to a grain-size dependentvoid swellingdue to the depletionof point defectsfrom the grain interior, i.e. within a certaingrain sizerange,the void swelling would decreasewith decreasinggrain size.The grain sizeeffect under I MeV electron irradiation (i.e. where all defectsare produced as Frenkelpairs)was,in fact, establishedexperimentallyalreadyin l973by Singh[52].The calculationofthe steady-state vacancysupersaturation profiles as a function of grain size[53] led to a satisfactoryexplanation for the observedgrain sizeeffect. It should be noted that thesecalculations were carried out using the conventionalmean-field approach and dislocationbias.Thus, it can be concludedthat under Frenkel pair production conditions, the vacancysupersaturationin a relative large

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523K. Generally, the enhancementin vacancy accumulation in the peak zone extends over distancesof - 20 cavity spacingsfrom the boundary. The peak cavity density seemsto occur at about 10 cavity spacingsfor all cavity densities,so that the peakdistancefrom the grain boundary decreases with increasingcavity density(seeTable I in [5a]. The formation of the peak zone implies that the vacancy supersaturation must be considerablyhigher in the peak zone than in the grain interior. This requiresa preferentialtransport of SIAs from the peak zoneto the grain boundary. Calculationsof the swellingrate as a function of distance from a grain boundary demonstratedthat the enhanced accumulation of vacanciesin the peak zone cannot be explained in terms of conventional three-dimensionaldiffusion and biasedannihilationof mono SIAs at dislocations[55].Thesecalculations did show,on the other hand, that a one-dimensionaltransport of SIAs via long-rangechannellingcan produce a peak zone. However, this was not consideredto be a realistic mechanismunder cascade damageconditions. Recently,the problem has beentreatedwithin the framework of production bias and one-dimensionalglide of small SIA clusters.Calculationsof the void swellingasa function of distancefrom a grain boundary show that the observedformation of peak zonein the vicinity of grain boundariescan be properly rationalized in terms of transport of SIA loops from the peak zone to the grain boundary by glide [ 3,l4]. one-dimensional

5. DAMAGE ENERGY DEPENDENT DEFECT ACCUMULATION As describedin Section3, one of the major predictionsof the PBM is that at a given temperature and damage rate, the rate of vacancy accumulation should depend on the recoil energy which determines the nature of damage production and the efficiency of intracascadeclusteringof SIAs and vacancies.In order to test this prediction, specimensof fully annealedpure copperwereirradiated at about 523K with 2.5MeV electrons,3 MeV protonsand fissionneutrons[56]. All irradiation experimentswere carried out at a displacementrate of about 5 x l0-8dpa (NRT)/s. Irradiationswith electronsand protons were carried out at Jiilich, whereasfission neutron irradiations were

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component for the proton irradiated sample is clearly intermediate between the electron and the neutron irradiated caseswhich gives evidenceof a similar relationshipbetweenthe void densities. The resultsshowingthat the clusterdensityas well as void swelling increasewith increasingrecoil energy demonstratethe sensitivity of void swellingto intracascadeclusteringof SIAs. Theseresultsare fully consistentwith the main predictionof productionbias that the magnitude of void swelling is strongly dependent on the intracascade clusteringefficiencyof SIA (e.g. see Fig. l). Furthermore,it was demonstratedalmost ten yearsago that the high swellingrate observed in the neutron-irradiatedcopper could not be explainedin terms of the standardrate theory and dislocationbias l44l.lt is quite interesting to note here that the swellingrate in the electronirradiated copper at

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are fundamentallydifferent from that of the Frenkelpair production at low recoil energies.While consideringthe problem of defect accumulation under cascadedamageconditions,it is necessary, therefore,to treat explicitly the impacts of intracascadeeventssuch as clusteringof SIAs and vacanciesand one-dimensionaltransport of small SIA clusters. Considerationsof thesefeaturesand the thermal stability of the resulting clustersof SIAs and vacanciesform the basisof the production biasmodel. Various aspectsof the damageaccumulationunder cascadedamage conditions have been investigatedwithin the framework of the production bias and one-dimensionalglide of small SIA clusters. The calculateddependencies, for example,of void swellingon irradiation dose and temperatureagreevery well with the availableexperimental results. Experimental results on the effect of recoil energy on void swelling are also in good agreementwith the prediction of the production bias model. A larger number of experimental observations showingan enhancementin damageaccumulationnear grain boundaries in metals and alloys irradiated under cascadedamageconditions can be satisfactorilyunderstoodin terms of production bias and onedimensionalglide of small SIAs to grain boundaries.It should be emphasizedhere that none of these experimental results could be explainedin terms of standardrate theory using dislocationbias as the only driving force. Finally, it should be mentioned that mechanical properties such as irradiation creep and irradiation hardening of materials irradiated under cascadedamage conditions can be also understoodin termsof productionbias and one-dimensional glide of small SIA clusters. It is reasonableto conclude,therefore,that the standardrate theory approachbasedon dislocationbiasalonemust be modified. The kinetic equations describing damage accumulation under cascadedamage conditions must account for the production,annihilationand dissociation of the clusters,their function assrrks,and their reactionwith otner defectsin the medium. Acknowledgements This work was partly funded by the European Fusion Technology Programme.CHW is gratefulfor CANDU OwnersGroup for frnancial

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