Effects of stacking fault energies on the interaction between an edge dislocation and an 8.0-nm-diameter Frank loop of self-interstitial atoms

ContentslistsavailableatScienceDirect

Nuclear

Materials

and

Energy

journalhomepage:www.elsevier.com/locate/nme

Effects

of

stacking

fault

energies

on

the

interaction

between

an

edge

dislocation

and

an

8.0-nm-diameter

Frank

loop

of

self-interstitial

atoms

S.

Hayakawa

a ,∗

_,

_Y.

_Hayashi

a

_,

_T.

_Okita

b

_,

_M.

_Itakura

c

_,

_K.

_Suzuki

b

_,

_Y.

_Kuriyama

b

a School of Engineering, the University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo, Japan, 1138656

b Research into Artifacts, Center for Engineering, the University of Tokyo, 5-1-5, Kashiwanoha, Kashiwa, Chiba, Japan, 2778568 c Center for Computational Science & e- Systems, Japan Atomic Energy Agency, 178-4-148-4, Wakashiba, Kashiwa, Chiba, Japan, 2770871

a

r

t

i

c

l

e

i

n

f

o

Article history: Available online xxx Keywords: Molecular dynamics Radiation-induced degradation Shear band

Austenitic stainless steels

a

b

s

t

r

a

c

t

Moleculardynamicssimulationswereconductedtoinvestigatetheeffectsofstackingfaultenergy(SFE) asasinglevariableparameterontheinteractionbetweenanedgedislocationandaFrankloopof self-interstitialatomswithadiameterof8.0nm.Thephysicalcontactbetweentheedgedislocationandthe loopcausesconstrictionoftheedgedislocation,followedbytheformationofaD-Shockleypartial dislo-cation.Thelatterprocessisassociatedwitheithertheformationofascrewcomponentanditscross-slip, orthedirectcorereactionbetweenthedislocationandtheloop.Theseprocessesinduceeitherthe ab-sorptionoftheloopintothedislocationorthetransformationoftheloopintoaperfectloop.TheSFE influencestheinteractionmorphologiesbydeterminingtheseparationdistanceofthetwopartial dislo-cationsandconsequentlytherateofconstriction.Thedependenceoftheinteractionmorphologyonthe SFEvarieswiththehabitplaneoftheloop.AhigherSFEincreasestheprobabilityoftheabsorptionor transformationinteraction;however,onlyloopshearingisobservedatthelowerlimitoftheSFErange ofausteniticstainlesssteels.

© 2016TheAuthors.PublishedbyElsevierLtd. ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).

1. Introduction

In austenitic stainless steels,which are used as in-core struc-turalmaterialsoflightwaterreactors(LWRs),weobservetwo sig-nificantchanges intheir mechanicalpropertiesduetoneutron ir-radiation.The first isan increase in yieldstress, which ismainly caused by irradiation-induced defects impedingthe glide motion ofdislocations.Theotheristhelocalizationoftheplastic deforma-tioninshearbands,aboveacertainirradiationdose.Thisiscaused by theremovalofirradiation-induceddefectsby dislocationsthat exist on ornearthe glide planes ofthe dislocation. The removal ofthesedefects makessubsequent dislocationsmove moreeasily inthesenarrowregions[1] .Thedominantirradiation-induced mi-crostructures are self-interstitialatom (SIA)-type Frank loops oc-curring within the temperature range of LWRs [2–4] ; thus, it is importantto evaluate theinteraction withadislocation to

inves-∗ _{Corresponding author. Fax + 81 3 5841 2904.}

E-mail addresses: [email protected] (S. Hayakawa), [email protected] (Y. Hayashi), [email protected] (T. Okita), [email protected] (M. Itakura), [email protected] (K. Suzuki), [email protected] (Y. Kuriyama).

tigate the micro-mechanisms responsible forthe aforementioned changes.

Molecular dynamics (MD) simulations for pure face-centered-cubic(FCC)metalshaveshownthattherearethreetypesof inter-actionmorphologiesbetweenanedgedislocationandanSIA-type Frankloop:loopdrag,transformation,andloopshearing[5,6] .The loopdragandtransformationinteractionsrequiretheconversionof anSIA-typeFrankloopintoaperfectloop.Thisprocessisinitiated bylocalconstrictionofthetwopartialsintoadislocation,anditis completedwithsweeping thestacking faultofthe loopeitherby asingle D-Shockleypartial orby two Shockley partials [6] . Since theseparationdistancebetweenthetwopartials isinversely pro-portionaltostacking faultenergy(SFE)[7] ,theSFE influencesthe probability ofconstriction andtheresultant interaction morphol-ogy[8,9] .

TheSFEofausteniticstainlesssteelsrangesfrom16–25mJ/m2

atroomtemperatureto31–34mJ/m2_{atapproximately330°C[10] ,}

whichis lowerthan that ofother pure FCC metalssuch asNi or Al.AlthoughtheSFEofCuisaslow astheupperlimitoftheSFE ofaustenitic stainless steels,the SFE ofaustenitic stainless steels is still lower, particularly at room temperature. Therefore, it is

http://dx.doi.org/10.1016/j.nme.2016.10.010

2352-1791/© 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ).

2 S. Hayakawa et al. / Nuclear Materials and Energy 0 0 0 (2016) 1–6

ARTICLE

IN

PRESS

JID:NME [m5G;October25,2016;17:54]

necessaryto evaluate the effectof the SFE on the interaction to utilizethedataobtainedwiththeCupotential.

In thisstudy,we conductedMDsimulations byusing recently developedembeddedatommethod(EAM)-typeinteratomic poten-tials toinvestigate the effectof the SFE on the interaction ofan SIA-typeFrankloopwithadiameterof8.0nmwithanedge dislo-cation.We performedadetailedanalysisofthe changeinthe in-teractionmorphologiesassociatedwiththecorereactionbetween thedislocationandthe8.0-nm-diameterloop.

2. Simulationmethods

WeusedtheEAM-typepotentialsdevelopedbyV.Borovikovet al.[11] . The SFE ranges from 14.6 mJ/m2 _{to 186.5mJ/m}2_{, while}

other material propertieswere kept almost identical. Four inter-atomicpotentials with SFEs of 14.6, 24.8, 44.1, and 186.5mJ/m2

were used in this study. The SFEs of the three lower potentials arewithintherangefortypicalausteniticstainlesssteels,andthe potential with the highestSFE was chosen to clarify the charac-teristicbehavior inlow-SFE metals.Byusingthesepotentials,we evaluatedtheeffectsoftheSFE asa singlevariableparameteron theinteractionbetweenanedge dislocationandaSIA-type Frank loop.

The large-scale atomic/molecular massive parallel simulator (LAMMPS),which wasdevelopedby SandiaNationalLaboratories anddesignedforparallelcomputers [12] ,wasusedin thisstudy.

Fig. 1 showsa schematicdiagram ofthesimulationcell.The x,y, andzaxesweretakenasthe[10_−1],[1₋₂1],and[111] direc-tions,respectively.Periodicboundaryconditionswereusedinthex

andydirections,whereasafreeboundaryconditionwasappliedin thezdirection.Thecelllengthsweresetat74.1,22.3,and22.1nm forthex,y,andzdirections,respectively.Anedgedislocationwas placedinthecellwiththeBurgersvectorofb=a0/2[10¯1]parallel

tothex-axisandalineparalleltothey-axis[13] .Ahexagonal SIA-typeFrankloop withthe



121



directionsontheiredgeswasalso insertedonthe

α

-,

γ

-,and

δ

-planes(Fig. 1 ).Thecenteroftheloop wason theglideplane ofthedislocation.The initialdistance be-tweenthecoreofthedislocationandtheloopwasapproximately 37nm.

Priortotheapplicationofshearstrain,thecellwasmaintained at100Kforapproximately70pswithapressurealmostzero.The microcanonicalensemblewithouttemperaturecontrolwaschosen for the simulations. Shear stress

σ

xz was applied to the cell by

exerting forces to the upper and lower layer of the z planes at aconstant strain rate of4.0× 106 _s−1_{.Timeintegration was}

per-formed by using theVerlet algorithm ata constant time step of 1.0_{× 10}−14s. Although the time step set in this study is slightly longerthan that inprevious studies [5,6] , weconfirmed that the energyisconservedwithin0.01eVateachtimestep.

The common neighbor analysis (CNA) was employed for vi-sualization [14] . In a color version, the blue regions indicate a hexagonal-closed-pack(HCP)structure,whichissynonymouswith astackingfault inan FCCstructure. Thered regionsindicate nei-theranFCCnorHCPstructure,whichdescribesthecoreofthe dis-locationortheloopinmostcases.FortheBurgersvectoranalysis, thedislocationextractionalgorithm(DXA)wasemployed[15,16] .

Different distributions oftheinitial atomicvelocitysometimes resultedindifferentinteraction morphologies[17] .Hence, we re-peatedthecalculationsatleasttwiceforeachconditionby chang-ingtherandomseedoftheinitialvelocitydistribution.Ifa signif-icantdifference in the interactionmorphology was obtained(the cases of the

α

-plane at an SFE of 24.8 mJ/m2 _{and those of the}

γ

-plane at an SFE of 186.5mJ/m2_{), we conducted up to five}

re-peatedcalculations,andalltheobtainedinteractionmorphologies andtheirreactionprobabilitiesarepresentedintheresultssection.

Fig. 1. Schematic diagram of the simulation cell. The Burgers vector of the disloca- tion follows the CA direction in the Thompson tetrahedron. The planes BCD, ABD, and ABC are denoted by the Greek letters α, γ, and δ, respectively.

Table 1

Summary of the interaction morphologies. S, D , and T denote the loop shearing, drag, and transforma- tion, respectively. SFE (mJ/m 2 ) 14 .6 24 .8 _{44 .1 186 .5} α-plane S S or D D D γ-plane S S S D or T δ-plane S S S S 3. Results

Table 1 summarizestheinteractionmorphologiesforeachhabit plane. The probability ofloop shearing increases withdecreasing SFE. Inthe following subsections,we will show the effect ofthe SFEonthedetailedinteractionmorphologiesineachhabitplane.

3.1.Interactionofthelooponthe

α

-plane

Fig. 2 showssnapshotsoftheinteractiononthe

α

-planeatan SFE of44.1 mJ/m2_{. When thedislocation starts to move and}

ap-proaches the loop because of the applied shear strain, the lead-ing partial bends owing to the repulsive interaction (Fig. 2 (a)). Then, the dislocation physically touches the loop, which locally constrictsthedislocationatitstop,wherethescrewcomponentis formed(Fig. 2 (b)).Thedislocationstartstocross-slipontheplane alongtheloopedge,whichisdifferentfromtheoriginalslipplane.

Fig. 2. Sequential snapshots of the interaction on the α-plane at an SFE of 44.1 mJ/m 2 . The left- and right-hand side figures show the DXA and CNA visualization, respectively.

Through thisprocess, a D-Shockleypartial is createdonthe loop edgebythefollowingreaction(Fig. 2 (c)):

a0/2[10¯1]+a0/3[¯1¯11]→a0/6[1¯2¯1]. (1)

Thescrewcomponentagainchangestheslipplanetothenext loop edge,whereitprogressivelycreatesanotherD-Shockley par-tialasitcontinuesto cross-slip(Fig. 2 (d)).TheseD-Shockley par-tials eliminate the stacking fault of the loop toward the bottom (Fig. 2 (e))untilthishalfpartoftheloopbecomescompletely un-faulted (right half of Fig. 2 (f)). The right half of the loop is ab-sorbedbythedislocation.Astheshearstrainincreases,the dislo-cationdetachesfromtheremaininghalfoftheloop,andadouble superjogformsonthedislocation(Fig. 2 (g)).Theinteraction mor-phologyforthecasewiththehighestSFEof 186.5mJ/m2 _is

fun-damentallythesame.Notethatthistypeofinteractionwas previ-ouslyobservedbyNogaretetal.inCuwithanSFEof44.4mJ/m2_,

despitethedifferenceinloopsizeandtemperature[5] .

Fig. 3 showsthedifferenceintheinteractionatthelowestSFE of 14.6 mJ/m2_{. D-Shockley partials are created on the two loop}

edges accordingto the reactionin Eq. (1) , whichis sameforthe

case with an SFE of 44.1 mJ/m2 _{in Fig. 2 (d). They temporarily}

eliminate the stacking fault of the loop (Fig. 3 (a)). However, the separationdistance betweenthe twopartials isso large that the dipolesegments of the leading partial join and closebefore the D-Shockley partials complete unfaulting the loop (Fig. 3 (b)). The temporarilyunfaultedpartoftheloopreturnstotheoriginalFrank loopwhenthetrailingpartialdetaches(righthalfinFig. 3 (c)).This results in the loop shearing interaction. This type of interaction waspreviouslyobserved by Terentyevetal.inFe-20Cr-10Niwith anSFEofapproximately20mJ/m2 _{[6] .}

For the interaction at an SFE of 24.8 mJ/m2_{, repeated}

calcu-lationsprovided differentresultsin theinteraction morphologies, i.e., either loop drag (1/5) or loop shearing (4/5), depending on theinitialvelocitydistributionoftheatoms.Theseresultsindicate thatthecriticalSFEatwhichtheinteractionmorphologychanges from loop shearing to loop dragis near 24.8 mJ/m2 _{for an}

8.0-nm-diameterloop.Notethat thecriticalSFEexistswithin theSFE rangeofausteniticstainlesssteels—atleastforan8.0-nm-diameter loop—whichindicatesthatevenifweusetheCu potential,which

4 S. Hayakawa et al. / Nuclear Materials and Energy 0 0 0 (2016) 1–6

ARTICLE

IN

PRESS

JID:NME [m5G;October25,2016;17:54]

Fig. 3. Sequential snapshots of the interaction on the α-plane at an SFE of 14.6 mJ/m 2 . The left- and right-hand side figures show the DXA and CNA visualization,

respectively. In (c), the dislocation has moved out from the visualized region near the loop.

hasbeenusedasaprototypelow-SFEmetal,itisdifficulttoreveal thelowestSFEbehaviorsonthishabitplane.

3.2.Interactionofthelooponthe

γ

-plane

Fig. 4 showssnapshotsoftheinteractiononthe

γ

-plane atan SFEof186.5mJ/m2_{.When thedislocationstartstomove and}

ap-proachestheloopbecauseoftheappliedshearstrain,theleading partialbends owingto theattractive interaction (Fig. 4 (a)).Then, thetwopartials are constrictedatboth oftheintersectionpoints (Fig. 4 (b)). The constricted dislocation detaches fromthe bottom andcontinuesto glide insidethe stacking fault ofthe loop. Dur-ing this process, the dislocation reacts with the loop, creating a D-Shockleypartialbythefollowingreaction(Fig. 4 (c)):

a0/2



10¯1



+a0/3



¯111



→a0/6



12¯1



. (2)

The D-Shockleypartial eliminatesthe stackingfault ofthe en-tirehalfoftheloop,whichresultsincreatingaperfectcomponent (righthalfinFig. 4 (d)):

a0/6



12¯1



+a0/3



1¯1¯1



→a0/2



10¯1



. (3)

The sameprocess progressivelyoccursontheotherhalfofthe loop(lefthalfinFig. 4 (e)).Then,theentireloopconvertstoa per-fectloopwiththeBurgersvectorofa0/2[10¯1],whichisparallelto

thatofthe dislocation.The loop edgeis cutatthe top,andeach endisseparatelyconnectedtothedislocation(Fig. 4 (f)).Whenthe dislocationglidesbecauseofthefurtherapplicationofshearstrain, theloopmay(2/5)ormaynot(3/5)beabsorbed,dependingonthe initialvelocity distribution.Ifitis absorbed,theconnectedshape

oftheloopisretainedthroughtheglidemotionofthedislocation (Fig. 4 (g-1)),whereasifitisnotabsorbed,theperfectloopremains afterthedislocationdetaches(Fig. 4 (g-2)).

Fig. 5 showssnapshots ofthe interaction at the lower SFE of 44.1mJ/m2_{.Constriction ofthetwopartials seldomoccursatthe}

loopedges(Fig. 5 (a))becausetheseparationdistancebetweenthe two partials is larger than that at the higher SFE. Consequently, thereactiondescribedinEq. (2) isnotinduced.Instead,the lead-ing partial detaches (Fig. 5 (b)), followed by the trailing partial (Fig. 5 (c)).Thisresultsintheloop shearinginteraction.The inter-actionsatthelowesttwoSFEsarefundamentallythesame.

The interaction on this plane is categorizedinto two groups: thehighSFEof186.5mJ/m2_{,andlowSFEsof44.1mJ/m}2 _orlower.

BothCuandausteniticstainlesssteelsforallpossiblerangeofSFEs belong to thelow SFEgroup. Therefore, theatomistic interaction fortheausteniticstainlesssteelscanbesimulatedbyusingCu po-tentialsonthishabitplane.

3.3. Interactionofthelooponthe

δ

-plane

Fig. 6 showssnapshotsoftheinteractiononthe

δ

-plane atan SFE of 186.5mJ/m2_{. In this case, the normal vector of the habit}

plane is perpendicular to the Burgers vector of the dislocation. Whenthedislocationentersthestackingfaultoftheloopbecause oftheapplied shearstrain,neithertheshapeoftheloopnorthat ofthedislocation changesstrongly (Fig. 6 (a)). Thedislocation de-taches from the loop with the formation of a step on the loop edge(Fig. 6 (b)).ThisinteractionisobservedforalltheSFEs, soit islikelyacommonfeatureofFCCmetals.

4. Discussion

Weconfirmedthe existenceofthree typesofinteraction mor-phologies that occur between an edge dislocation and an SIA-typeFrankloop:loopdrag,transformation,andloopshearing.One mechanismfortheloopdrag,whichoccursonthe

α

-plane,isthe local constrictionof the dislocation, followed by the screw com-ponentcross-slip.Unfaultingoftheloopisaccomplishedbya sin-gle D-Shockley partialsweeping the loop—amechanism thatwas previously observed by Nogaret et al [5] . In this study, a differ-entmechanismfortheloopdragisobservedonthe

γ

-plane.The reaction between the dislocation and the loop directly creates a D-Shockley partial inside theloop, which by itself completes the unfaultingof theentire loop.Although thistype ofinteraction is observed only at the highest SFE and not for the SFE ranges of austeniticstainlesssteels,wefoundthattheunfaultingofan SIA-type Frank loop occurs without formation of screw components oritscross-slip.Sincethesemechanismsstartfromconstrictionof thedislocation,followedbytheformationofaD-Shockleypartial, theSFEisacrucialparameterfordeterminingtheinteraction mor-phologiesbycontrollingtheprobabilityofconstriction.

The critical SFE, which changes the interaction morphologies from loop shearing to loop drag, depends on the habit plane. The critical SFE forthe

α

-plane in particular lies within the SFE rangeof austeniticstainlesssteels. Aprevious studyshowed that loopshearingisthedominantinteractionwithanedgedislocation, whileloopdragisobservedonlyonthe

α

-planeinCuwithanSFE of44.4 mJ/m2 _{[5] .However, even onthe}

_α

_{-plane, we found that}

theloop dragmaynotoccur forausteniticstainless steelswitha lowerrangeofSFEs.

In thisstudy, the temperaturewas set to justabove the zero kelvinat100K.However,highertemperatures,includingthe oper-atingtemperatureofnuclearreactors,maychangethecriticalSFE, whichwillbeevaluatedinafuturestudy.

Fig. 4. Sequential snapshots of the interaction on the γ-plane at an SFE of 186.5 mJ/m 2 . The left- and right-hand side figures show the DXA and CNA visualization, respec-

tively. A snapshot from a different angle is shown in (a) to clearly visualize the attractive interaction. In (g), two different interaction morphologies depending on the initial velocity distribution are shown by means of CNA visualization: (g-1) and (g-2).

5. Conclusions

We conducted MD simulations at 100Kto investigate the ef-fectsoftheSFEontheinteractionbetweenanedgedislocationand an8.0-nm-diameter SIA-typeFrankloopwiththe



121



directions ontheiredges,byusingtherecentlydevelopedEAMpotentialsfor FCCmetals.Theinteractionmorphologiesandtheirdependencyon theSFEdifferamongthehabitplanesoftheloop.

For interactions on the

α

-plane, higher SFEs induce the loop drag interaction through the constriction of two partial disloca-tions, formation of the screw component and its cross-slip, fol-lowed by the formation of a D_{-Shockley partial. The loop} shear-ing interaction is observed atlower SFEs. The critical SFE,which

changestheinteraction morphologies,isnear24.8 mJ/m2_.For

in-teractions on the

γ

-plane, higher SFEs induce the loop drag or transformationinteraction throughtheconstriction oftwopartial dislocationsattheloop edges, followedby theformationof a D-Shockleypartial.Thisreactionis notinduced fortheSFEs of44.1 mJ/m2 _{orlower,resultingintheloopshearinginteractioninstead.}

Forinteractionsonthe

δ

-plane,nosignificantchangeintheshape ofthedislocation orintheshapeoftheloopisobservedthrough thephysicalcontact.Theloopshearinginteractionoccurs,whichis independentoftheSFE.

Forausteniticstainlesssteels,theinteractiononthe

γ

-and

δ

-planesisloop shearing,whereas onthe

α

-plane, itiseitherloop dragorloopshearingdependingontheSFEwithintheirrange.

6 S. Hayakawa et al. / Nuclear Materials and Energy 0 0 0 (2016) 1–6

ARTICLE

IN

PRESS

JID:NME [m5G;October25,2016;17:54]

Fig. 5. The CNA visualizations of the interaction on the γ-plane at an SFE of 44.1 mJ/m 2 . Two snapshots from a different angle are shown in the left- and right-hand

side figures in (a).

Fig. 6. The CNA visualizations of the interaction on the δ-plane at an SFE of 186.5 mJ/m 2 .

Acknowledgments

Thispaperincludesresultsoftheprogram“Developmentof In-novativeResource-renewableBoilingWaterReactorasHigh Perfor-manceTransuraniumBurner”,supportedbytheMinistryof Educa-tion,Culture,Sports,ScienceandTechnology(MEXT)inJapan.We wouldliketothankEditage(www.editage.jp )forEnglishlanguage editing.

References

[1] D. Rodney , Nucl. Instrum. Methods Phys. Res. B 228 (2005) 100–110 . [2] P.J. Maziasz , J. Nucl. Mater. 205 (1993) 118–145 .

[3] S.J. Zinkle , P.J. Maziasz , R.E. Stoller , J. Nucl. Mater. 206 (1993) 266–286 . [4] C. Pokor , Y. Brechet , P. Dubuisson , J.-P. Massoud , A. Barbu , J. Nucl. Mater. 326

(2004) 19–29 .

[5] T. Nogaret , C. Robertson , D. Rodney , Philos. Mag. 87 (2007) 945–966 . [6] D. Terentyev , A. Bakaev , Y.N. Osetsky , J. Nucl. Mater. 442 (2013) S628–S632 . [7] D. Hull , D.J. Bacon , Introduction to Dislocations, third ed., Pergamon, Oxford,

United Kingdom, 1984 .

[8] D. Rodney , C. R. Phys. 9 (2008) 418–426 .

[9] D. Terentyev , A. Bakaev , J. Nucl. Mater. 442 (2013) 208–217 . [10] C.C. Bampton , I.P. Jones , M.H. Loretto , Acta Metall 26 (1978) 39–51 .

[11] V. Borovikov , M.I. Mendelev , A.H. King , R. Lesar ,Model. Simul. Mater. Sci. Eng. 23 (2015) 055003 .

[12] LAMMPS Molecular Dynamics Simulator: http://lammps.sandia.gov/ . [13] Y.N. Osetsky , D.J. Bacon , Model. Simul. Mater. Sci. Eng. 11 (2003) 427–446 . [14] H. Tsuzuki , P.S. Branicio , J.P. Rino , Comput. Phys. Commun. 177 (2007) 518–523 . [15] A. Stukowski , K. Albe , Model. Simul. Mater. Sci. Eng. 18 (2010) 085001 . [16] A. Stukowski , V.V. Bulatov , A. Arsenlis , Model. Simul. Mater. Sci. Eng. 20 (2012)

085007 .