How the interface type manipulates the thermochemanical response of nanostructured metals: A case study on nickel: A case study on nickel

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ContentslistsavailableatScienceDirect

Materialia

journalhomepage:www.elsevier.com/locate/mtla

How the interface type manipulates the thermomechanical response of nanostructured metals: A case study on nickel

O. Renk

^a^,^∗

, V. Maier-Kiener

^b

, C. Motz

^c

, J. Eckert

^a^,^d

, D. Kiener

^d

, R. Pippan

^a

aErich Schmid Institute of Materials Science, Austrian Academy of Sciences, Jahnstraße 12, 8700 Leoben, Austria

bDepartment of Materials Science, Chair of Physical Metallurgy and Metallic Materials, Montanuniversität Leoben, Roseggerstrasse 12, 8700 Leoben, Austria

cSaarland University, Institute of Material Science and Methods, Saarbrücken, Germany

dDepartment of Materials Science, Chair of Materials Physics, Montanuniversität Leoben, Jahnstraße 12, 8700 Leoben, Austria

a r t i c le i n f o

Keywords:

Interface structure Boundary character Nanotwinned

Intergranular stress relaxation Nanoindentation

Nickel

Rate controlling process

a b s t r a ct

Thepresenceofinterfaceswithnanoscalespacingsignificantlyenhancesthestrengthofmaterials,butalsothe ratecontrollingprocessesofplasticflowaresubjecttochange.Duetotheconfinedgrainvolumes,intragranular dislocation-dislocationinteractions,thepredominantprocessesatthemicrometerscale,arereplacedbyemission ofdislocationsfromandtheirsubsequentaccommodationattheinterfaces.Bothprocessesnotonlydependon theinterfacialspacing,butalsoontheatomisticstructureoftheinterface.Hence,athoroughunderstanding how theseprocessesareaffectedbytheinterfacestructureisrequiredtopredictandimprovethebehavior ofnanomaterials.Thepresentstudyattemptstorationalizethiseffectbyinvestigatingthethermomechanical behaviorofsamplesconsistingofthreedifferentinterfaces.Purenickelsampleswithpredominantfractionsof low-andhigh-angleaswellastwinboundarieswithasimilaraveragespacingaround150nmareinvestigated usinghightemperaturenanoindentationstrainratejumptests.Dependingontheinterfacestructure,hardness, strainratesensitivityandapparentactivationvolumesevolvedistinctivelydifferentwithtestingtemperature.

Whileincaseofhigh-angleboundariesforallquantitiesapronouncedthermaldependenceisfound,theother twointerfacetypesbehavealmostathermalinthesametemperaturerange.Thesedifferencescanberationalized basedonthedifferentinterfacialdiffusivity,affectingthepredominantprocessofinterfacialstressrelaxation.

1. Introduction

Theenhanced fractions of grain boundaries (GBs) and interfaces makingup nanocrystalline(NC) materialsornanocompositessigniﬁ- cantlyaltertheirpropertyspectrum.Thetremendousdecreaseofthe meanobstaclespacingfordislocationsenhancesstrengthtounprece- dented levels [1–4]. Besides that, the rate-controlling processes of plasticﬂowarealteredcomparedtothecoarsegrainedreferencestate, astheprobabilityforstorageorinteractionofdefectswithinthegrains orphasesdiminisheswhentheirvolumeisreducedtothenanoscale.

ForFCCmetals,thisimpliesashiftfromforestcutting(i.e.dislocation- dislocationinteractions)todislocationemissionfromandinteraction with GBs or interfaces [5]. Accordingly, the measured strain rate sensitivity(SRS),m,ofplasticflowissignificantlyenhancedforNCFCC metals,accompaniedbyareductionofthe(apparent)activationvolume, V^∗,beingonlyontheorderofseveral10b³[6–9].Itisevidentthatthe interactionofdefectswithinterfacesstronglydependsontheiratomistic structure,consequentlyaffectingtheresultingproperties.Nanotwinned

∗Correspondingauthor.

E-mailaddress:oliver.renk@oeaw.ac.at(O.Renk).

(NT)metalsareoneofthemostprominentexamplesdemonstratingthis effect.Theintroductionofnanoscaledtwinsintomicrometer-sizedcop- pergrainsallowstounitehighstrengthwithexcellenttensileductility [10,11].Thissuperiorpropertycombinationisinclearcontrasttocon- ventionalNCorultra-finegrained(UFG)copper,offeringcomparable strengthbutextremelylimitedtensileductility[12,13].Thesynergyof strengthandductilityincaseofNTcopperisassociatedwiththesimul- taneouspossibilityofeasysliptransferandgenerationofsessiledisloca- tionsatthetwinboundaries(TBs).Thisensuresworkhardeningcapa- bility,notaccessibleforrandomhigh-anglegrainboundaries(HAGBs), wheredislocationseasilyannihilateattheoppositeGBs[14,15].Sim- ilarly,moleculardynamics(MD)simulationscomparingsampleswith HAGBsandlow-anglegrainboundaries(LAGBs)suggestastrongerwork hardeningabilityinthelattercase[16],inlinewithexperimentalobser- vationsonaluminum[17,18].Apartfrommechanicalproperties,also thethermalstabilityissignificantlyaffectedbyachangeoftheinterface structure.NanomaterialswithlargefractionsofLAGBsorTBsshowed significantlyimprovedthermalstabilitycomparedtostructuresconsist- ingmainlyofHAGBs,rationalizedbytheirreducedinterfacialenergies anddiffusivities[19–22].This emphasizesthatnot onlythemechan-

https://doi.org/10.1016/j.mtla.2021.101020 Received20January2021;Accepted22January2021 Availableonline24January2021

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icalbehavior,butalsootherproperties suchas thethermalstability arestronglydeterminedbytheinterfacetype.Hence,alsothethermo- mechanicalresponsewillbereadilyaﬀected,buthasremainedwidely unexploredsofar,especiallythecasefornanostructuresbuiltofLAGBs.

Focusingonthemechanicalbehavior,theinfluenceoftheinterface charactershouldbereadilyreflectedintherate-controllingprocesses ofplasticflow.However,studiesunravelingtheeffectoftheinterface characterandtakingapotentialsizedependence(i.e.effectsresulting fromtheinterfacialspacing)intoaccount,remain,exceptforthoseon NTcopper[14],scarceandarecurrentlymostlylimitedtoambienttem- perature.Unexpectedly,acomparisonofNTcopperwithconventional NCcoppersuggestedthattheSRSandactivationvolumeV^∗ofplastic flowdonotdifferforagiveninterfacialspacingandfollowthesame scalinglaws[14,23].Basedontheirfundamentallydifferentproperties discussedaboveandrecentresultsemphasizingtheimportanceofinter- granularstressrelaxation[9],thisagreementisastonishing.Infact,the measurementsobtainedonvariousUFGandNCFCCmaterialsshowed thattheSRSremainedconstantatlowlevelsuntilaboveacertaintem- peratureapronouncedincreaseoccurred[9].Abovethistransitiontem- peraturealsotheapparentactivationvolumesstartedtodecrease,ap- proachingsingledigit values,indicative ofdiffusion-basedprocesses.

Thisissupportedbyactivationenergiesatelevatedtestingtemperatures beingcomparabletothosereportedforGBdiffusion[9].Moreover,the transitiontemperatureswerefoundtobeonly50– 70Kbelowtheav- erageonesmeasuredforthermally-induceddislocationannihilationat randomHAGBsintheseparticularmaterials,cf.Refs.[9,24].Abovethe mentionedtransitionpoint,thetemperatureseemssufficienttoallow forthermallyfacilitatedstressrelaxation,reflectedinapronouncedtem- peratureandtimedependenceofplasticflow.Asawhole,theseresults pointtointergranularstressrelaxationasthecontrollingprocess.How- ever,modelsdescribingthekineticsofpurelythermally-inducedstress relaxation(Eq.(1))[25,26],indicatethatapartfrommaterialconstants suchastheshearmodulus,G,theatomicvolumeΩ,theboundarywidth 𝛿,andfundamentalconstantssuchastheBoltzmanconstant,k_B,anda pre-factorA(reportedtobeabout1/200forseverelydeformednanoma- terials[25,27]),therelaxationtime𝜏relaxonlydependsontheboundary diffusivityD_GBandthespreadingdistances,whichisnativelyrestricted tothegrainsizeasanupperlimit.

𝜏_{𝑟𝑒𝑙𝑎𝑥}=𝐴 𝑘_𝐵𝑇𝑠³

𝐺Ω𝐷_𝐺𝐵𝛿 (1)

BasedonEq.(1),itisevidentthatforagivenmaterialandinter- facialspacing,therelaxation timemainlydependson theinterfacial diffusivity.Accordingly,differentrelaxationtimesandhencedeforma- tionbehaviorareexpectedfordifferentinterfacetypes.Inotherwords, differentvaluesoftheSRSorworkhardeningrateswouldbeexpected, contrastingthementionedagreementinpreviousstudies[14].Although thereportedsimilaritiesbetweenHAGBsandTBscouldresultfromthe restrictiontoambienttestingtemperatures,theobviouscontroversies motivatedadetailedstudyunravelingtheeffectoftheinterfacetypeon thedeformationbehaviorofnanostructuredmetals.Duetoitshigher meltingpointweusednickelasamodelmaterialtoallowformeasure- mentsinawidertemperaturerangewithouttheoccurrenceofsignif- icantmicrostructuralmodifications.Inaddition,NCnickelandnickel alloyshavebeenwidelystudiedatroomtemperature(e.g.Refs.[8,28–

31])whatallowsforacomparisonwiththegathereddata.Hightem- peraturenanoindentationstrainratejumptestsperformedonsamples withLAGBs,HAGBsandTBsofsimilarspacingallowedtoassesstheef- fectoftheinterfacetypeonthedeformationresponseandtoprovethe raisedhypothesis thatinterfacialstressrelaxationisthepredominant rate-controllingprocess.

2. Experimental

Tounderstand howtheinterface typeaﬀectsthedeformationbe- havior, nanostructurednickel sampleswithdiﬀerent boundarytypes

butsimilarinterfacialspacingweresynthesized.Thesamplesconsidered inthisworkconsistpredominatelyofHAGBs,LAGBsandTBs,labelled HAGB,LAGBandNTsamplehereafter.TheHAGBandLAGBsamples wereprocessedbyhighpressuretorsion(HPT)andcyclichighpressure torsion(CHPT)atambienttemperature.Nickel(99.99%,fromGoodfel- low)sampleswith10mmdiameterand1 mmheightweredeformed byquasi-constrainedmonotonicHPT[32]atambienttemperaturefor 10 rotationsatarotationalspeedof 0.2rotmin⁻¹underanapplied nominalpressureof5.1GPa.Suchseveremonotonicstrainsresultinan UFGstructureconsistingofrandomHAGBswhichmakeupto75–80%

ofthetotalboundarylength[33,34].Tocreateananoscaledstructure ofsimilardimensionsbutconsistingmainlyofLAGBS,recrystallizedNi samples(773K/1h)havingthesamedimensions(10mmdiameterand 1mmheight)werecyclicallyHPTdeformed(5° twistangle)forﬁve cyclesusingasetupintroducedearlier[35,36].Thelargeplasticstrain amplitudesappliedallowedtocreateadistinctfractionofdislocation cellshavingapproximatelythesamespacingasobtainedincaseofthe monotonicallydeformedsamples.TheNTnickelsamplesweresynthe- sizedusingpulsedelectrodeposition.Sheetsofseveralmillimeterthick- nessconsistingofNTnickelstructuresweregrownoncoppersubstrates.

Butindiol(0.02gl⁻¹)andsodiumsaccharin(3gl⁻¹)wereaddedtothe electrolyteasgrainreﬁners.Adetailedchemicalcompositionoftheelec- trolytecanbefoundelsewhere[37,38].Depositionwasperformedus- ingsquarepulseswithacathodiccurrentdensityof45mAcm⁻²and ananodiccurrentdensityof65mAcm⁻²withapulsedurationof5ms, respectively.

BoundaryspacingsandfractionsofboundarycharactersoftheHAGB andLAGBsampleswereanalyzedusinganelectronbackscatterdiffrac- tion(EBSD)detectorattachedtoaLEO1525fieldemissiongunscanning electronmicroscope(SEM,CarlZeissMicroscopy,Germany),whilefor theNTnickelsamplestransmissionKikuchidiffraction(TKD)inanon- axisconfiguration[39]withasetupfromBruker,Germanywasused.

ThestepsizeincaseoftheTKDscanswassetto10nm,while25 nm wereusedfortheconventionalEBSDscans.ForconventionalEBSD,a finalelectrolyticalpolishingstep(StruerselectrolyteA2)wasusedto remove anydeformationlayerpresentfrommechanicalgrindingand polishing.ForTKD,anelectrontransparentNTsamplewasprepared followingstandardTEMpreparationroutinesofmechanicalgrinding, polishinganddimpling,followedbygentleionpolishing.Theobtained datawasanalyzedusingastandardsoftwarepackage(OIManalysis5.3, EDAX).FortheHAGBandLAGBsamplesthemicrostructureswerean- alyzedinradial(RAD)directionoftheHPTdiskataradiusof4mm, whiletheNTstructurewasobservedperpendiculartothegrowthdirec- tion.Toexaminethethermalstabilityofthesamplesandtodetermine themeaningfultemperaturerangeforthehightemperaturenanoinden- tation protocolusedtoassessthedeformationbehavior,thesamples wereisochronallyannealed(30min)atvarioustemperatures.Vickers microhardnessmeasurements(0.5gfload,15s)atambienttemperature accompaniedbymicrostructuralanalysisasdescribedbeforeenabledto determinethethermalstabilityrange.PleasenotethatincaseofVick- ershardness,nottheprojectedarea,butthecontactareaisconsidered forevaluatingthehardness.Hence,forthesametesttemperatureand materialcondition,thesevaluesareslightlyreducedcomparedtothe nanoindentationdata.Minoreffectscouldfurtherarisefromdifferences inappliedstrainrate.

Toobtaininsightsintothedeformationbehavior,nanoindentation strainratejumptestsatroomtemperatureandelevateddeformation temperatureswereperformed[40].IncaseoftheHPTdisks(HAGBand LAGBsamples)theindentationdirectionwaschosenalongtheaxialdi- rection,whilethenanotwinnedsampleswereindentedalongthegrowth direction,i.e.perpendiculartotheTBs.Priortotheteststhesamplesur- facesweremechanicallygroundandpolishedfollowedbyaﬁnalelec- trolyticalpolishingstep(StruerselectrolyteA2)toremoveanydeforma- tionlayers.IncaseoftheHPTdisks(LAGBandHAGBstructures),the indentswereperformedataradiusofabout4mm,i.e.whereallmi- crostructuralinvestigationswereperformed.Fromthenanoindentation

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strainratejumptests hardness,H,strainratesensitivity, m, andap- parentactivationvolumes,V^∗,asafunctionofthetestingtemperature canbeextracted.Hence,insightsintotherate-controllingdeformation processesofthediﬀerentnanostructuresandinterfacescanbegained.

AlltestswereperformedonaplatformNanoindenterG200(KLA,CA, USA)equippedwitha continuousstiﬀness measurement(CSM)unit.

TheCSMunitsuperimposesasinusoidalloadsignal(2nmamplitude and45Hzfrequencyusedhere)thatallowstodeducecontactstiffness andthusmodulusandhardnesscontinuouslythroughoutthetest.For elevatedtestingtemperatures,alaserheatingstage(SurfaceTec,Hück- elhoven,Germany)wasused.Both,thetipandthesampleareheated independently,allowingtoadjustandstabilizethecontacttemperature carefully,minimizingthermaldrift[41].Duetothelaserheating,the selectedtemperaturesandsubsequentstabilizationarereachedwithina fewminutes,reducingtheexposurepriortotheindent.Thisalsoguaran- teedawell-definedandhomogenoustemperaturedistributionthrough- outtheindentationsequence.Thewholesystemincludingsampletray andthecoppercoolingshieldsurroundingtheindentationtipwaswa- tercooledandthechambertemperaturewascloseto291K.Aninert gasatmosphere(forminggas– N₂containing5%H₂)wasobtainedby twoindividualvalvesthatcontrolledthegasflowaroundthesample trayandtheheatedtip.Thiscreatedanoven-likeatmosphereanden- suredthatoxidationofthesamplescouldbeprevented.Afterthehigh temperaturetests,allsampleswereinspectedvisuallyand,althoughnot quantified,noobviousoxidationwasrecognized.Forallmeasurements Berkovichtipswereused.Incaseoftheelevatedtestingtemperatures sapphiretips(Synton-MDP,Nidau,SwitzerlandtogetherwithSurface Tec,Hückelhoven,Germany)wereusedtominimizechemicalinterac- tionsbetweentip andsample[42],whileatambienttemperaturedi- amondtips(Synton-MDP,Nidau,Switzerland)wereused.Framestiff- nessaswellastipshapecalibrationsweremadeonfusedsilicaregularly betweentheindividualsamplesaccordingtotheOliver-Pharrmethod [43].Athermaldriftoflessthan0.1nm/swasallowedpriortoanytest andwasdeterminedateachtestingtemperaturebeforeaswellasafter eacharrayofindents.

Ateverychosentesttemperatureatleastfourindentations,separated by50μm,wereperformedwithintheheatingcycle,rangingbetween roomtemperature(RT)and573K,depending onthethermalstabil- ityoftheindividualsamples,respectively(NiHAGBs:298,373,398, 425,448,473and498K;NiLAGBs:298,373,423,473,498,523,548 and573K;NiNT:298,373,398,423,448,473,498,523,548and 573K). Thenanoindentationtests wereperformedinconstantstrain rate-controlledmode[44].Theappliedstrainratewasalteredabruptly afterevery500nmindentationdepth,starting with0.05s⁻¹,reduc- ingitfurtherto0.01s⁻¹,increasingitbackto0.05s⁻¹,droppingto 0.005s⁻¹beforejumpingbacktotheinitialstrainrateof0.05s⁻¹.All hardnessandmodulusdatareportedinthefollowingareaveragedval- uesobtainedatastrainrateof0.05s⁻¹between 1050and1450nm indentationdepth.Basedonthestrainratejumptests,thestrainrate sensitivity,m,andtheapparentactivationvolumes,V^∗,canbecalcu- latedaccordingtoEqs.(2)and(3)[30],respectively,whereHdenotes thehardness, ̇𝜀thestrainrate,C^∗aconstraintfactorbeing2.8,k_Bthe Boltzmanconstant,andTtheabsolutetemperature.

𝑚= 𝜕(ln(𝐻))

𝜕(ln(̇𝜀)) (2)

𝑉^∗ =𝐶^∗∗√

3∗𝑘_𝐵∗𝑇

𝑚∗𝐻 (3)

ItshouldbenotedthatthevaluescalculatedaccordingtoEqs.(2) and(3)coulddependontheappliedstrain(i.e.indentergeometry)and strainrate,withthelatterchosenratherhighwithinthisstudy.Notably, forhighstrainratetestsconstanthardness(ﬂowstresses)priortoan- otherstrainratejumpmaynotalwaysevolve,complicatingthisanalysis.

Thiswas,however,notthecasehere,asforthemajorityoftheapplied ratejumpsrather constanthardnesslevelsevolved,compareFig.6b.

Furthermore,whilethedislocationdensitycanaffectthecalculatedSRS orV^∗valuesformetalssubjectedtocomparablylowstrains[45],this issueisnotpronouncedfornanostructuredmaterialstestedhere.Previ- ousresultsindicatethatBerkovichtipsimposingastrainof~7%strain alreadynecessitatealargenumberofdislocations.Thus,nosignificant differenceoftheSRSorV^∗atagiventemperaturewasevidenced,inde- pendentifmeasuredduringtheheatingorcoolingsequence(i.e.testing alreadyarelaxedstate)[9].

Asthetestprotocolincludestwostrainratejumpsbacktoapre- viousstrainrate(̇𝜀=0.05s⁻¹),thehardness-contactdepthcurvescan beusedasafirstindicatorforstructuralmodificationsduetothether- momechanicalexposureofthenanostructures.Aswillbedetailedlater, forHAGBsamplestestedatspecifictemperatures,thesecurvesalready suggestedgraingrowthbeneaththeindentertip.Therefore,thecross- sectionsofparticularindentswereextractedandinspectedaswell.After depositingaprotectiveplatinumlayerontopoftheindentusingagas injectionsysteminafocusedionbeam(FIB)workstation(ZeissAuriga, Zeiss,Germany),aslicethroughtheresidualimpressionwithathickness ofabout2μmwasextractedfromthesampleusinganOmniprobe200 micromanipulator(OxfordInstruments,UK).Subsequently,thesamples wereattachedtoacoppergridbyplatinumdepositionandanalyzed usingconventionalEBSDasspecifiedbefore.

AllresidualimprintswerefurtherimagedusingaKeyencelaserscan- ningconfocalmicroscopetodeterminetheheightofthepile-upsand theirevolutionwithtemperature.Therecordeddatawasanalyzedus- ingthesoftwarepackageGwyddion2.56.Linearproﬁleswereapplied totheimagedindentstomeasurethepile-upheights.Thereportedval- uesareaverageswiththestandarddeviationastheerrorbar.Itshould benotedthatforsomeconditions(testtemperature,interfacetype)the errorbarseemsratherlarge,whichisnotaresultofpronouncedscatter betweentheindentstakenatagiventemperature,butratherduetodis- tinctdeformationdiﬀerencesbetweenthethreefacesoftheBerkovich tip.

3. Results

3.1. Microstructuralcharacteristicsandthermalstabilityofthethree diﬀerenttypesofnickelsamples

Fig.1showsrepresentativemicrographsofthethreediﬀerenttypes ofnickelsamplesunderinvestigation.TheHAGB samples(monotoni- callyHPTdeformed,Fig.1a)exhibitatypicalUFGmicrostructurewith slightlyelongatedgrainsalongthetangential(TAN)direction,consist- ingpredominantlyofHAGBswithfractionsofupto75%ofthetotal boundarylength.Itshouldbementionedthatafterseverestrainingno preferredmisorientationangleoraxispaircanbedetermined,asre- portedearlier[33,34,46,47].Thus,thegeneratedHAGBscanbecon- sidered asrandom. This is alsoevident from themisorientationdis- tribution,Fig.2a.Averageboundaryspacingsweredeterminedusing thelineinterceptmethodandsettingacriticalmisorientationangleof morethan15°,yieldingaverageminimumdimensions(alongtheaxial direction)ofabout190nm.TheLAGBsamples(Fig.1b)appearsimilar toconventionalcold-workedstructures.Insidethestilldistinguishable coarsegrains,well-deﬁneddislocationboundarieswithlowmisorienta- tionanglesdeveloped.Thefractionofboundarieswithamisorientation anglebelow15° inthesesamplesmakesup75%ofthetotalboundary length.BecausetheaveragespacingoftheLAGBswasdeterminedby conventionalEBSD,thethresholdangletoidentifyagrainwassetto 2°,althoughdislocationboundarieswithanevenlowermisorientation anglemayexist.Accordingly,theaveragespacingalongtheaxialdi- rection(minimumdimensions)determinedforthiscondition(265nm) canonlybeconsideredasanupperboundfortheactualspacing.For both,theHAGBsamplesandtheLAGBsamples,dislocation-basedplas- ticityisevidentfromtheODFsections,whichshowagoodagreement withtheidealtexturecomponents[48]inFig.2c.TheNTnickelsam- plesconsistofcolumnargrainsingrowthdirection,havinganaverage

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Fig.1. Representativemicrostructuresofthetestednickelsampleshavingthreedistinctinterfacetypes.(a)HPTdeformednickelconsistingpredominantlyofHAGBs;

(b)Recrystallizedandcyclicallycold-workednickelwithamajorityofLAGBs(boundariesintheinsetimageinblackdenoteHAGBs),and(c)electrodepositedNT nickel.Forallspecimentypestheaverageinterfacialspacingiswith150–250nmrathersimilar.

Fig.2. (a)UncorrelatedmisorientationdistributionoftheHAGBandLAGBsamplessynthesizedbyHPTandcyclicHPT,respectively,withtherandomdistribution (opencircles)givenforcomparison;(b)distributionofthelineinterceptsforthediﬀerentinterfacetypes;(c)RepresentativeODFsectionsoftheHAGBandLAGB sampleswiththeblackdotsindicatingthepositionofidealtexturecomponentsexpectedfordislocation-basedplasticity[48].

thicknessofabout 2.5μm,withthelargest onesbeingup to10μm thick.Insidethecolumnargrainshighdensitiesoftwinboundariescan befound,seeFig.1c.Thisresultsina{111}ﬁbretextureingrowthdi- rection.Themajorityofthetwinboundariesarecoherenttwinbound- aries(fraction~ 85%)andtheiraveragespacingbasedonlineinter- ceptsisabout120nm.Thus,sampleswithrelativelysimilarboundary spacingscouldbe synthesizedandassessedwithrespecttotheirme-

chanicalproperties andthermalstability.Itshouldbe notedthatthe purityoftheNTnickelsamplesislowercomparedtotheothertwoin- terfacetypes,withsulphurbeingknownasmainimpurityinEDnickel samples.However,asthepreferredsegregationsitesarethecolumnar HAGBs,ratherthanthecloselyspacedTBswhichdeterminetheme- chanical properties,this isnot expectedtocause aneﬀect, compare Ref.[49].

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Fig.3. ThermalstabilityofthethreediﬀerentnickelmicrostructuresasrevealedfromroomtemperatureVickersmicrohardness(0.5gfload)testsperformedafter isochronal(30min)annealingandcomplementarymicrostructuralinvestigations.Circlescorrespondtotheimagesinb).DataoftheHAGBspecimensistakenfrom Ref.[50].PleasenotethatthediﬀerenceoftheRThardnesscomparedtoFig.6originatesfromtheuseofthecontactareainsteadoftheprojectedareatodetermine theVickershardness.

Fig.4. RepresentativeSEMimagesoftheindents;

samples containing HAGBs (upperrow), LAGBs (middlerow)andTBs(bottomrow)atindicated testingtemperatures.

Asimilarboundaryspacingforallthreetypesofspecimensisalsoev- identfromthehardnessmeasurementstakenatroomtemperature.For alldifferenttypesofspecimensacomparablehardnessof2.5–3.2 GPa wasmeasured,seeFig.3.Totesttheirthermalstability,thesamples weresubjectedtoisochronal(30min)annealingtreatmentsatdifferent temperatures.Vickersmicrohardnessmeasurementsatroomtempera- tureaccompaniedwithstructuralcharacterizationallowedtodetermine anystructuralchanges.Thesethermalstabilitylimitswereusedtoset thetestingtemperaturerangeforthenanoindentationexperiments.It canbenoticedthattheHAGBsampleshaveasignificantlylowerthermal stabilitycomparedtotheLAGBandTBsamples.Alreadyabovetemper- aturesof423KmassivegraingrowthoccurredfortheHAGBspecimens, whileatthistemperaturepronouncedchangesstillremainabsentforthe LAGBandTBspecimens.Atannealingtemperaturesof523Kalsointhe LAGBsamplesfirstrecrystallizationnucleicanbe observed(Fig.3b), explainingtheratherlargestandarddeviationofhardnessforthispar- ticularannealingcondition.Atthisannealingtemperaturethehardness slightlydropsalsoin caseof theNTsamples, butchangesof theTB

spacingremainsmall.Evenafterannealingat773K,theTBspacingre- mainswellbelowamicron,indicatingasuperiorthermalstability.The improvedthermalstabilityincaseoftheLAGBandTBspecimenscom- paredtotheHAGBsamplesisinlinewithinvestigationsonNTcopper [20,21]andnanolaminatednickelconsistingofnanoscaledLAGBs[19]. Itcanberationalizedbytheirlowerinterfacialenergyanddiﬀusivity comparedtogeneralHAGBs,consequentlyreducingthedrivingforces forgrowthandtheatomicmobilitywithintheinterfaces[19,22].Apart fromthermalstability,pronounceddiﬀerences betweenthethreedif- ferenttypesofnickelsamplesarealsoevidentwhenconsideringtheir mechanicalbehavior,aswillbeoutlinedinthefollowingsection.

3.2. Deformationbehavioratambientandelevatedtemperatures

Alreadyfromtheshapesoftheremanentimpressionsafterroomand elevatedtestingtemperatures,adistinctivelydifferentdeformationbe- haviorforthethreeinterfacetypesisevidenced.RepresentativeSEMim- agesoftheindentsfromthethreedifferenttypesofsamplesatdifferent

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Fig.5. Analysisofthepile-upheightofthediﬀerentnickelsamplesasafunction oftemperature.ThelargeerrorbarsfortheLAGBandTBsamplesarejusta consequenceofthediﬀerenceofthepile-upheightalongthethreesidesofthe Berkovichtip.

testingtemperaturesarepresentedinFig.4.Itshouldbenotedthatthe micron-sizedgrainstructurevisibleinsomeimagesisjustaconsequence of recrystallizationoccurring in thesample, whichwas continuously heatedduringtheindentationsequencesandcertainlydoesnotaﬀect anyinterpretation.Forallthreeinterfacetypes,distinctpile-upforma- tion(i.e.aconvexdeviationfromtheidealindentshape)occursduring indentationatroomtemperature.Thisisexpectedformaterialshaving alreadyhighstrengthand,accordingly,limitedwork-hardening capa- bility[51,52].Quantitativeanalysisoftheindents(Fig.5)revealedthat foralltestingtemperaturespile-upformationismorepronouncedwhen LAGBsandTBsareinvolved.Thelargeerrorbarforthesetwosamples isnotcausedbyscatterbetweenmultipleindentstakenatagiventem- perature,butbythepronounceddiﬀerenceofthepile-upheightalong thethreesidesoftheBerkovichtip.Uptotemperaturesof475K,the pile-upheightoftheLAGBandTBspecimensismoreorlessconstant, beforereducingtolowerlevels.Incontrast,thepile-upheightmeasured ontheHAGBspecimensalreadydecreasedatmuchlowertemperatures, Fig.5.Attestingtemperaturesof423K,stillbelowthethermalstability limit,theindentsresemblealreadyanalmostperfectandstraightshape, withthepile-upheightbeingsimilartotheonestakenat473Kwhere graingrowthalreadyoccurred.

Apartfromthecleardifferencesoftheindentshapesforthethree sampletypesandtheirevolutionwithtemperature,alsothetempera- turedependenceofthemeasuredhardnessvaluesexhibitsquitediffer- enttrends.WhileforthesamplescontainingLAGBsandTBsthehardness doesnotchangesignificantlywithanincreaseofthetestingtempera- ture,theHAGBsampleshowsadistincttemperaturedependence,see Fig.6a.DatatakenfromRef.[9]obtainedonaUFGNi4.5Alalloycon- sistingpredominantlyofHAGBsisaddedforcomparison.Asforthepure nickelsamplewithHAGBsalsoforthealloyedvariantthehardnessis extremelytemperaturesensitive.Thealloyingcontentonlyshiftsthe testingtemperaturesthatcauseasubstantialdropinhardnesstowards highervalues.Althoughmeasuringwellbelowthethermalstabilitylimit (~ 0.25T_m),thehardnessoftheHAGBsamplesdecreasesalreadyre- markably.Becauseboth,theLAGBandNTsamplesdonotshowadis- tincttemperaturedependence,above~ 0.22T_mthehardnessofthese twospecimensexceedsthoseoftheHAGBsamples.However,itiswell- establishedthatnanostructuresconsistingpredominantlyofHAGBsare pronetograingrowthduringdeformation,evenundercryogeniccon- ditions,asevidencedforavarietyoftestingtemperaturesanddeforma-

tionmodes,seeforinstanceRefs.[36,53–58].Therefore,graingrowth incaseoftheHAGBsamplesmayalreadyoccurbelowthethermalsta- bilitylimitduetothedeformation(7%equivalentstrain)imposedby theBerkovichindenter,explainingthereducedhardnessvalueswithin- creasingtestingtemperature.Astheindentationprotocolconsistedofa seriesofstrainratejumps,includingtwojumpsbacktoapreviousstrain rate,therecordedhardness-contactdepthcurves(Fig.6b)alreadyallow todeducemicrostructuralinstabilities.Nevertheless,fromthehardness- contactdepthdata,thisisnotexpecteduptotestingtemperaturesof 398K,sincefortestingtemperaturesbelow398K,astrainratejump backtoapreviousstrainrate(i.e.0.05s⁻¹)alwaysleadstoidentical hardnesslevels,indicatingmicrostructuralstability.Thisisdiﬀerentfor highertestingtemperatures.Alreadyat423K,thehardnessforthelast strainratesegmentremainsbelowtheonesobtainedintheprevioustwo segments,presumablyalreadyaconsequenceofmeasuringclosetothe thermalstabilitylimit.

However, already for testing temperatures of 398 K, where the hardness-contactdepthsignalsuggestsastablemicrostructure,thehard- nessdiffersalreadymorethan30%comparedtoroomtemperature.To elucidatethereasonsforthishardnessreduction,anotherHAGBsam- plewas preparedandindentedat398K.Alift-out ofathin lamella throughtheindentperformedat398Kwastakenandthevolumebe- neath theindentsubsequently analyzed. Theobtained backscattered electronimagesanddetailedcolorIPFmapsofthemicrostructuresare showninFig.7.Obviously,thegrainsizebeneaththeindentissignifi- cantlylargerthaninunaffectedregionsfurtheraway.Onacloserlook theregionwherenoticeablegraingrowthoccurredislimitedtoacircu- larshapearoundtheindent.Estimatingtheplasticzonesizeaccording toRefs.[59,60]indicatesthatgraingrowthisconfinedtothisvolume, highlightedbythedashedline.Despitetheindentation-inducedgrowth issignificant, itisnotreflectedinthehardness-contactdepthcurves, showingidenticalhardnesslevelsforajumpbacktothesamestrain rate(i.e.0.05s⁻¹).Thiscouldberelatedtothefactthatfortheself- similarBerkovichindenttherealizedequivalentstrainand,hence,the amountofgrowthisindependentofthepenetrationdepth,butjustthe sizeoftheplasticzoneincreases.

3.2.1. Strainratejumptests

Fromthehightemperaturenanoindentationtests,strainratesensitivity, mandapparentactivationvolumes, V^∗,weredeterminedasa functionoftemperatureaccordingtoEqs.(2)and(3).Thevaluesre- portedin thefollowingareaverages,with thestandarddeviationas theerrorbar.Fig.8summarizesthesequantitiesforthethreediﬀerent specimentypesasafunctionofthetesttemperature.Inaddition,data obtainedonaNCNi4.5AlalloyconsistingofamajorityofHAGBs(Ref.

[9])isplottedforcomparison.Asforhardnessandindentmorphology, alsothetemperaturedependenttrendsofstrainratesensitivityandap- parentactivationvolumedifferremarkablyforthethreeinterfacetypes investigated.Again,thesetrendsarecomparablefortheLAGBandNT specimens butdiffersubstantially fortheHAGB samples,Fig.8a.At ambienttemperature,SRSislow(0.01– 0.02)andrathersimilarforall threeinterfacetypes,althoughslightlyhighervaluesweremeasuredfor theHAGBnickelandNi4.5Alsamples.Alreadyforslightlyelevatedtest- ingtemperatures,thedifferencesbetweenthesamplesbecomeapparent.

WhileforthepurenickelsampleswithHAGBstheSRSquicklyincreases withtemperature,theLAGBandNTspecimensbehaveratherathermal.

Thisalsoholdstrueforthealloyednickelsampleconsistingpredomi- nantlyofHAGBs.However,similartothepurenickelHAGBsamples, above~ 0.25T_mtheSRSoftheNi4.5Alalloyquicklyincreases.Incase ofthepurenickelHAGBsamples,theSRSreachesvaluesofabout0.05 at423K,beforedecreasingagain.ThisdropoftheSRScanbeattributed totheoccurrenceofsigniﬁcantgraingrowth,asthetestingtemperature exceededthethermalstabilityofthesamples,Fig.3.Evenhighervalues of0.1canbemeasuredincaseoftheNi4.5AlHAGBsamples,although foragiventemperaturetheSRSofthepurenickelsamplesisalways higher.Incontrast,fortheLAGBandNTsamples,nochangeoftheSRS

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Fig.6. (a)Hardnessasafunctionoftestingtemperaturefornickelsampleswithdiﬀerenttypesofinterfaces.DataobtainedonaNCNi4.5Alalloy(Ref.[9])witha predominantfractionofHAGBsisaddedforcomparison.Circleddatapointsin(a)refertothehardness-contactdepthcurvesoftheHAGBsamplesdisplayedin(b).

Fig. 7. Backscattered electron image showingmicrostructuralchangesbeneath anindent ofaHAGBsampleindentedat 398 K. The dashed line corresponds to the maximumdepth of theplastic zone, estimated according to Refs. [59,60].

Pleasenotethediﬀerentscalebarsofthe images.

couldbemeasureduptotemperaturesof473K(~ 0.25T_m).Evenfor highertestingtemperatures,theincreaseremainsrathersmallandfor bothtypesofsampleswithinthewholetemperaturerangetested,the SRSexceedsonlyslightlythatmeasuredincaseofHAGBsalreadyatam- bienttemperature(m~ 0.02).Nevertheless,alsoforthesetwointerface typesasimilartrendasmeasuredfortheHAGBsamplescanbeexpected, giventhatthestructuresremainstableuptowaylargertemperatures thantestedhere.Thisissupportedbydataobtainedduringlargestrain deformationofpurecoarse-grainednickel(i.e.incompressionandtor- sion),suggestingthatatleasttemperaturesof873Kwouldberequired tomeasureadistinctratedependenceofﬂowstress[61,62].Whilethis wouldbepossiblefortheNTsamples(compareFig.3),incaseofthe LAGBsamplesrecrystallizationoccurredalreadyatabout0.32T_mand causedadropoftheSRStoevenlowervalues.

Ascanbeexpectedfornanostructures,theapparentactivationvol- umesV^∗areontheorderofseveraltensofb³forallspecimenstested

atroomtemperature,seeFig.8b.With~ 40b³theapparentactivation volumesincaseoftheLAGBandNTspecimensareslightlylargerthan theonescalculatedfortheHAGB samples.Forthepureandalloyed HAGBsamples,valuesofabout20b³weremeasured.AstheSRSofthe LAGBandNTsamplesdoesnotchangesignificantlywithtemperature accordingtoEq.(3),theapparentactivationvolumesofthesesamples increasemoderatelyuptoabout60 b³ withtestingtemperature.Sig- nificantly largervaluesof almost400b³ aremeasuredfor theLAGB specimenafterrecrystallization,asexpectedforacoarse-grainedFCC metalatmoderatetestingtemperatures,withforestcuttingbeingthe ratecontrollingprocess.Incontrast,V^∗ofboth,thepureandalloyed HAGB specimens,remainsratherconstantbeforestartingtodecrease oncereachingthetemperatureswheretheSRSquicklyincreases.This trendofdecreasingV^∗isrestrictedtoanarrowtemperaturerangein caseofthepurenickelHAGBsamplesasgraingrowthoccurs,reflected inadistinctincreaseoftheactivationvolume.However,incaseofthe

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Fig.8. (a)Strainratesensitivity,m,and(b)apparentactivationvolume,V^∗,ofthenickelsampleshavingdiﬀerentinterfacesasafunctionoftestingtemperature.

DataforaNCNi4.5Alalloy(Ref.[9])consistingpredominantlyofHAGBsandEDNCNi(Refs.[28,31])areaddedforcomparison.Trendlinesareaddedasguide fortheeye.

morestableNi4.5AlHAGBsamples,thedecreaseisclearlyvisibleand singledigitactivationvolumes,indicativefordiﬀusiveprocesses,are approached,Fig.8b.

Basedonthemeasuredhardnessandactivationvolumes,theappar- entactivationenergiesoftheratelimitingprocessescanbeestimated accordingtoEq.(4)[63].Thisapproachdescribestheactivationbarrier, Q,asstress-dependentGibbsfreeenergy,ΔG,toactivateplasticﬂow.

Sinceitisgenerallyassumedthatcontributionsfromtheentropyterm arenegligible[29,64],ΔGiscloselyrelatedtotheactivationenthalpy ΔH_act,expressedas:

𝑄 ∼ Δ𝐻_𝑎𝑐𝑡= 𝐻𝑉^∗

√3𝐶𝑇

𝜕(ln𝐻)

𝜕(₁

𝑇

) (4)

withHandV^∗beingthehardnessandapparentactivationvolume,respectively,T,theabsolutetemperatureandCaconstraintfactorof2.8.

AscanbeseenfromFig.9a,forallthreeinterfacetypesthelogarithm ofthehardnessasafunctionoftheinversetemperaturecanbereason- ablydescribedbyalinearfitwithintwodistincttemperatureranges.In caseoftheHAGBsamples,onlytheoneatlowertemperatureswascon- sideredfurther,asthatathighertemperaturesalreadycorrespondsto a(partially)coarsenedmicrostructure,compareFigs.6and8.Thecal- culatedactivationenthalpiesandtheirchangewithtestingtemperature aredisplayedinFig.9b.FortheHAGBspecimensatRTanactivation enthalpyofabout2eVcanbedetermined,whichimmediatelydecreases toabout1eVwithanincreaseofthetesttemperature.FortheLAGBand NTsamples,activationenthalpiesofabout3eVarederivedatelevated testingtemperatures,wherepropertiesbecomeslightlytemperaturede- pendent.ThesevaluesarecomparabletothoseexpectedforGBdiffusion (~ 1eV)andbulkdiffusioninnickel(~ 3eV),respectively,compare Refs.[65,66].

4. Discussion

4.1. Eﬀectoftheinterfacetypeandthedeformationtemperatureonthe indentshape

Distinctdiﬀerencesarenotonlyobservedforthemechanicalprop- erties,butalreadyfortheindentshapes,Fig.4.Whilepile-upforma- tionforhighstrengthmaterialswithlowwork-hardeningcapacityis

expected[51,52], thediﬀerences betweenthethreetypesof samples (Fig.5)needtobebrieﬂydiscussedintheremainder.AlthoughLAGBs andTBsareknowntohavehigherwork-hardeningratescomparedto HAGBs[10,13],largerpile-upsareformedforthesetwosamples.More- over,pile-upformationincaseoftheHAGBsamplescontinuouslydimin- isheswithincreasingtestingtemperature, whichisunexpectedgiven thereductionofhardnessandwork-hardeningratewithtemperature [51].

Independentofthesampletype,duetofixedgeometryandindenta- tiondepthaconsistentvolumeofmaterialneedstobedisplacedbythe indentertip.However,thisoccursmorelocalizedincaseoftheLAGB andNTsamples,presumablybecausetheseinterfacesaremorerigid comparedtotheHAGBs.Whilemoredetailedstudiesarerequiredto assessthisissueindetail,investigationsonNTcoppersupportthisno- tion[67].Asdetailedinthenextchapter,detwinningandlocalcollapse of thetwinstructurewasreported, favoringlocalplasticflow,hence largerpile-upheights.AsthemechanicalpropertiesincaseoftheLAGBs andTBsarelargelyunaffectedbythetesttemperature,apronounced changeofthepile-upheightisthusnotexpected.Incontrast,thermo- mechanicallyinducedmigrationoftheHAGBscaneasilyoccur(Fig.7).

Thisisinlinewithdetailedobservationsshowingthatatlowhomolo- goustemperaturesunderanappliedstressfield,foragivenGBcrystal- lography,HAGBsmigratemuchfasterthanLAGBsdo[68].Asanymov- inginterfacerealizesplasticstrain,theeasiermigrationofHAGBscould facilitateamorehomogenousplasticflowoverlargervolumes,leading tosmallerpile-upsheights.Thelargeaffectedzonebeneaththeindent atmoderatetestingtemperaturestogetherwiththeenhancedratesen- sitivityincaseoftheHAGBspecimens(Fig.7andFig.8)supportthis picture andalsoexplainsthefurtherdiminishingpile-upheightwith increasingtesttemperature.

Apartfromalargeraveragepile-upheightincaseoftheLAGBand NTspecimens,alsotheheightdiﬀerencebetweenthethreefacesofthe Berkovichtip,givingrisetothelargeerrorbarsinFig.5,ismorepro- nounced.Thiscanbe rationalizedbytwofactors.First,forthesetwo specimens,onlyasinglecrystallographicorientationisprobed(i.e.the sizeofthegraincontainingtherigidinterfacesismuchlargerthanthe volumeaﬀectedbytheindent).Indentationstudiesonsinglecrystalsin- dicatethattheorientationofthefacetsoftheindentertipwithrespect totheavailableslipsystemsdeterminestheanisotropyofthepile-up

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Fig.9. (a)PlotoflnH(hardness)asafunctionoftheinversetemperature,withslopeofthelinearﬁtsintherespectivetemperatureintervalsdisplayed.(b)Calculated activationenthalpies,ΔH_actasafunctionoftesttemperatureforthethreeinterfacetypes.

height[69–71].Thisanisotropymightbeenhancedifadditionallyin- terfacesrestrictingplasticﬂowareintroduced[71],especiallyifthey areperfectly alignedandhardlymobileastheLAGBsandTBsinves- tigatedhere(i.e.paralleltothesheardirectionorperpendiculartothe growthdirection,respectively).However,asthepronouncedanisotropy diminishessomewhatatelevatedtestingtemperatures,theeﬀectofthe interfaceseemsmoreimportant.

4.2. Pronouncedtemperaturedependenceofmechanicalpropertiesincase ofHAGBs

Besidethedifferentappearanceoftheindentshape,thepresented resultsalsoreveal,dependingontheinterfacetype,adistinctivelydif- ferentthermomechanicalresponse,cf.Figs.6and8.Alreadythehard- nessvaluesmeasuredatRTindicatethatnotsolelytheinterfacialspac- ing,butalsotheinterfacetypeplaysapredominantroleindetermining themechanicalresponse.AlthoughtheaveragespacingoftheTBswas smallerthanthatoftheHAGBs,theRThardnessoftheHAGB speci- menswasthehighest,seeFig.6a.Basedonpreviousresearch,thiscan beexplainedby(partial)collapseoftheNTstructure.Straininduced detwinningwasclearlyobservedbeneathnanoindentsperformedonNT copper,withdetwinningbecomingmorepronouncedforhigherequiva- lentstrainsapplied[67].Further,forNTstructuresahugeanisotropyof theflowstresscanbemeasured,differingbyafactorofthreebetween thehardandsofttestingmodesforNTcopper[72].Althoughlesspro- nounced,suchanisotropicflowbehaviorwasalsoreportedformetallic nanolaminates[73,74].Beneaththeindentsbendingorrealignmentof thelayersand/orshearbandformationwasfrequentlyobserved[75–

77].Alignmentofthelayerswithrespecttothefacesoftheindentercor- respondstotheweakesttestingdirection,thusfacilitatesplasticﬂow.

Convertedhardnessvalues(usingaconversionfactorofthree)yielding resultsclosetotheuniaxialﬂowstressoftheweakesttestingorientation, furthersupportthispicture.Hence,theslightlylowerhardnessvalues measuredincaseoftheNTnickelaremostlikelyaconsequenceofsuch instabilitiesoccurringduringindentation.

Withincreasingtestingtemperature,thediﬀerencesbetweenthein- dividualsampletypesbecomeevenmorepronounced.WhiletheLAGB and NTsamples behave quite similar andtheir properties are only weaklytemperature-dependent,thesamepropertiesvarystronglywith temperatureincaseoftheHAGBsamples.Ascanbenoticedfromthe

Ni4.5AlHAGBsample,thispronouncedtemperaturedependencecan- notbeavoidedbyalloying,butjustthetemperatureswherepronounced changesoccurareshiftedtowardshighervalueswithalloyingcontent, cf.Figs.6aand8.Thisemphasizesthatalreadyatcomparablylowtem- peraturesof~ 0.2T_m,mechanicalpropertiesarenotsolelydetermined bytheaverageinterfacialspacing,buttheinterfacetypeplaysadeci- siverole.Thisstrongtemperaturedependenceofhardnessincaseofthe HAGBsamplesisunexpectedforFCCmetalsthatconventionallyhave atemperature-independent yieldstress[78–80].Althoughduetothe temperaturedependenceoftheworkhardeningratetheﬂowstresses determinedatlargerstrainscandiﬀersubstantiallyalsoforFCCmetals [80],thisisnotexpectedforseverelydeformedmaterialshavingalready anegligiblework-hardeningcapacity.Moreover,consideringthelimited equivalentstrainsrealizedwiththeBerkovichtip(i.e.~ 7%),adecrease ofhardnessbymorethan30%whilemarginallyincreasingthetesting temperaturefrom0.17T_mto0.23T_mwouldnotevenbeexpectedfora FCCmaterialwithapronouncedwork-hardeningrate[80].

Thepronouncedtemperaturedependenceofhardnessisalsoevident forthealloyedNi4.5AlHAGBsamples(Fig.6),inperfectagreement withliteratureﬁndingson variousnanostructuredmaterials,butalso fornanocompositesornanolaminates[28,31,81–85]. Thesameholds trueformetallic thinﬁlms,usuallycomposedofNCgrainstructures.

Earlynanoindentationstudiesalreadyreportedareductionofhardness by morethan50%whenthetesting temperaturefor goldorcopper thin filmswas increasedfromRTto400K,althoughthemicrostruc- tureswereclaimedtobethermallystableuptothispoint[86],similar towhatwasfoundinthepresentstudy.Contrary,thehardnessofthe LAGBorTBsamplesremainsalmostunaffected(i.e.reductionby8%) inthesametestingtemperatureinterval.Thissuggeststhatthedistinct temperaturedependenceoftheflowstresshasitsorigininthepresence of large fractionsofrandomHAGBs orinterfaces.Astrongtempera- ture dependencein caseof theHAGB samplesis,however,alsoevi- dentfortheotherpropertiesdetermined.SRSoftheHAGBspecimens showsindependentofpurityapronouncedincreasewithtemperature, accompaniedbyadropintheapparentactivationvolume,V^∗,aslongas themicrostructureremainsstable,Fig.8.Incontrast,theSRSvaluesof theLAGBandNTspecimensarealmostathermal(Fig.8a),causingto- getherwiththealmostconstanthardnessslightlyincreasingactivation volumeswithincreasingtemperature.FocusingontheHAGBspecimens, itappearsthatpronouncedpropertychangesofH,mandV^∗withtem-

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peratureoccuratsimilar testingtemperatures,suggesting acommon origin,cf.Figs.6and8.Fromthedeformationtextures(Fig.2)ofthe LAGBandHAGBsamplesanddetailedresultsonNTmetals(e.g.Refs.

[72,87,88]),itisevidentthatforallsamplesdislocation-basedplasticity prevails.Hence,asthedeformationmechanismremainsthesameforall threetypesofsamples,thediﬀerencesinthemechanicalbehaviorneed tooriginatefromachangeoftheinteractionofdislocationswiththe respectiveinterfaces.Thestrongtemperaturedependenceofproperties incaseofHAGBsseemstobeapeculiarityoftheinteractionofdislo- cationswiththem,occurringonlyatmuchhighertemperaturesincase ofinterfacesconsistingofdislocationarrangements(LAGBs)oralmost atomicallysharpinterfacessuchasTBs.

Interactionsofdislocationswithdifferentinterfaceshavebeenstud- ied previously, andgiven thenecessary temperatureand/or applied stress,latticedislocationscanenter aGB,forminganextrinsicgrain boundarydislocation(EGBD),i.e.adislocationbeingnotpartoftheGB structurebutcomingfromoutsidetheGB[26].Variousprocessescan becoupledtotheabsorptionofanEGBD,suchasdislocationemission, GBmigrationorgrainrotation,justtonameafew[26].Althoughthe actualprocessescandifferdependingonboundarycrystallographyand theBurgersvectoroftheincomingdislocation[26,87,89,90],thisaspect isnotconsideredintheremainderbecauseindividualinteractionevents arenotaccessiblewiththeexperimentsusedinthiswork.Nevertheless, probingmultipleboundariesofagiventypeatthesametimeallowsto drawconclusionsabouttheiraveragebehaviorandrespectivedistinc- tions.Inanycase,aftertheinjectionorabsorptionofalatticedisloca- tion,theGBwillbeinastateofhigherenergy.Eveninthecaseofdirect transmission,aresidualBurgersvectorcouldbeleftattheinterface,if thoseofthein-andoutbounddislocationsdiffer.Consequently,thein- terfaceaimsatreducingitsenergyagainbyintergranularstressrelease, involvingthermallyactivatedprocesses.Theseprocessesdeterminethe behaviorofpolycrystalstoagreatextent,asdislocationemission,GB migrationorgrainrotationarecloselyrelatedtothem[26].Indeed,our recentstudyfocusingonUFG/NCFCCmetalsreportedgoodagreement betweentheaveragetemperaturesforthermally-induceddislocationan- nihilationinrandomHAGBswiththosewhereSRSincreasedtoremark- ablyhighvalues[9].Thesameholdstrueforthenickelsamplestested here.AverageannihilationtemperaturesfordislocationsinHAGBsof purenickelof about490 Kwerereported [24], agreeing reasonably wellwiththetemperatureswheremaximumratesensitivityandinitia- tionofgraingrowthoccurred,compareFig.8.Itshouldbenotedthat theincreasingtemperaturedependenceofpropertiesintheHAGBsam- plesalreadybelow490Kisnotcontradictingthisidea.Astheaccom- modationofdislocationsatGBsandtheassociatedrelaxationoftheir stressfieldsinvolvethermallyactivatedprocesses,thethermalenergy requiredcanbereducedbythepresenceofmechanicalstresses,com- pareEq.(5).There,GdenotestheGibbsfreeenergy,FtheHelmholtz energy,𝜏theresolvedshearstressandVthe(physicalorreal)activation volumeoftheprocess[91].

𝐺=𝐹− 𝜏𝑉 (5)

Accordingly,partoftheenergycanbeprovidedbythemechanical workdonebytheappliedshearstress,whilemodelsdescribingtheki- neticsofintergranularstressrelaxation(i.e.Eq.(1))orthementioned temperaturesfordislocationannihilation [24]justconsiderthepure thermallydrivencase.Hence,theappliedstressesduringindentation cansigniﬁcantlyreducetherequiredthermalcontributionstoovercome theactivationbarrier.Thiswasindeedobservedinin-situTEMstraining experimentsonUFGaluminum,wherethedislocationcontrastatthe GBsdecreasedmorerapidlywhensmalldislocationpile-ups,i.e.locally higherresolvedshearstresses,werepresent[92].Thisisinlinewiththe developmentofapronouncedtemperaturedependencealreadybelow theaverageannihilationtemperaturesreported.

However,despiteconsideringthethermalpartonly,thementioned modelsdescribingthekineticsofinterfacialstressrelaxationcanstill beusedtoqualitativelyrationalizetheobviousdiﬀerencesbetweenthe

HAGBandtheLAGB/NTsamples,astheappliedstressisroughlythe sameforallthreeinterfacetypes.Asstatedpreviously,therequiredre- laxationtimedependsmainlyonmaterialproperties(i.e.shearmodulus, atomicvolume,interfacialspacingandwidth)andinterfacialdiffusivity [25,26],cf.Eq.(1).Consideringthatthenickelsamplestestedherehave aquitesimilarboundaryspacingandassumingaratherconstantbound- arywidth,theonlyparameterthatfundamentallydiffersistheinterfa- cialdiffusivity.FortheLAGBandNTsamples,theactivationenergies forboundarydiffusionareexpectedtobesimilartobulkdiffusion,i.e.

adifferencebyafactorofabouttwocomparedtotheHAGBspecimens [93].Availableinterfacialdiffusiondatafornickelalongdeformation- inducedLAGBs[22]andHAGBs[27]attemperaturesclosetothehigh- estonestestedhereyieldvaluesofD_LAGB₍₄₅₈_K)=5.14×10⁻¹⁹m² s⁻¹ andD_HAGB₍₄₄₀_K)=5.03×10⁻¹⁷m²s⁻¹,respectively.Forcomparison, thebulkdiffusivityatthistemperaturewouldbeonlyontheorderof D_V₍₄₅₀_K)=5×10⁻³⁷m²s⁻¹[65].Withallotherparametersbeingap- proximatelythesameforthenickelsamplesstudiedhere(Eq.(1)),the expectedrelaxationtimesdifferbyatleasttwoordersofmagnitudebe- tweenthesetwosampletypes.Theaccordinglyreducedrelaxationtime- scalesincaseoftheHAGBspecimensarereflectedintheirpronounced temperaturedependenceofmechanicalproperties,whilethelowdif- fusive,‘dense’TBsorLAGBsrequirehighertemperaturestothermally activatesuchprocesses.Thisisreflectedintheiralmosttemperature- independentpropertiesintheinvestigatedtemperaturerange,butalso in activationenthalpiesbeingcomparabletobulkdiffusion,compare Fig.9bandRef.[65].Thesimilaractivationenthalpiescalculatedfor theTBsandLAGBsissupportedbysimulationwork,emphasizingthat both,TBsandLAGBs,canprovideeasysliptransferacrossthebound- ary,butcanalsoresistdislocationslip.Exceptforthecaseofascrew dislocationimpingingaTB,oradislocationwithproperBurgersvector impingingattherightpositionoftheLAGB,locksorjunctionsareeas- ilycreated.Thesesessileresidualsoftheinteractionprocessmayonly beremovedorovercomefromsubsequentdislocationsbyclimb,neces- sitatinginbothcasesascenarioclosetobulkself-diffusion[89,94,95].

Similarly,althoughnotaspronounced,thereduceddiffusivityofHAGBs causedbyalloyingorimpuritiesinducesashifttowardshighertesting temperaturesuntilrelaxationprocessescanbethermallyactivated.The reductionofV^∗towardssingledigitvalues,foundfortheHAGBspeci- mensonceapronouncedtemperaturedependenceofpropertiesismea- sured(Fig.8b),andtheactivationenthalpiesbeingclosetoexpectations forGBdiffusion(compareFig.9bandRef.[66]),furtherhighlightsthe importanceofdiffusiveprocessesattheGBsatthesetestingtempera- tures.

Thermally-inducedstressrelaxationattheboundariesthusnotonly explainstheobservedpropertydifferencesbetweenthethreeinterface types,butalsoallowstorationalizethepronouncedtemperaturedepen- dentpropertiesincaseoftheHAGBsample.IncaseofHAGBs,relaxation canoccuratmuchsmallertimescales,thusenhancedtestingtempera- turesorprolongedtestingtimes(i.e.reductionofthestrainrate)already allowfor diminishingstressfields.Their interactionwithsubsequent latticedislocationsishencereducedandlowerflowstressesaremea- sured.ContrarytheretardedrelaxationatLAGBsorTBs,whichoccurs bydislocationclimb[96],explainsnotonlythereportedhigherwork- hardeningratesinthiscase[14–18],butalsotherathertemperature- invariantpropertiesmeasuredinFigs.6and8.Thisinterpretationisin linewithrecentinvestigationsonNTcoppersuggestingthattherate limitingprocessisdislocationclimbalongtheTBs,causingalsoanin- creaseoftheratesensitivityatsufficientlyhightemperatures[88].Since stressrelaxationatGBscanalsoresultintheirmigration,theobserved graingrowthbeneaththeindentoftheHAGBsampleswell-belowthe thermalstabilitylimitmaynotbetoosurprising(Fig.7).Althoughfre- quentlyobservedfornanostructuressubjectedtovariousloadingsitu- ations(e.g.Refs.[36,53–55,97]),initiationofdistinctgraingrowthby applyingjust7%additionalstrainmayappearintriguingatfirstview foraseverely deformedsample. However,theequilibriumgrain size wasadjustedatRT,whileHPTdeformationat418Kalreadyyieldsan

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increaseoftheminimumgraindimensionsby60%[98].Inadditionto theincreaseofthetestingtemperature,thechangeoftheloadingsit- uationitselfcouldacceleratethemigrationrates[99].Disconnections, GBlinedefectsresponsiblefortheirmigration[100–102],canalsobe generatedbyimpinginglatticedislocations[100,103].Thestepheight andBurgersvectorofthedisconnectionwill,however,notonlydepend onboundarycrystallography,butalsoontheinteracting dislocation.

Hence,astrainpathchange,activatingdiﬀerentslipsystems,couldal- tertheactivedisconnectionmodesandaccordinglytheGBmigration rates.Thethermalandmechanicalstabilityofananomaterialcanthus largelydiﬀer,compareFigs.3and6.

5. Summaryandconclusions

Thepresentresultsrevealapronouncedinfluenceoftheinterface type on the deformation behaviorof nanostructured nickel. Despite havingasimilarinterfacialspacing,thepresenceoftwinorlow-angle boundariesresultsinanalmostathermalbehaviorofhardness,ratesen- sitivityandactivationvolume.Incontrast,thepropertiesofHAGBsbe- comestronglytemperature-sensitivealreadyatlow homologoustem- peratures(≥0.2T_m),whilealloyingonlyinducesashifttowardshigher onsettemperatures.Thesedifferencescanberationalizedbasedonthe importantroleofinterfacialstressrelaxationforthedeformationbe- haviorofnanomaterialsanditsdependenceonboundarydiffusivity.As observedfortheHAGBspecimens,interfacialstressreleasecandistinc- tivelymodifythenanostructurestested.Noticeablegraingrowthbelow thethermalstabilitylimitisreflectedinapronouncedtemperaturede- pendenceofhardness.Theseobviousdifferencesinducedbytheinter- facetypecannotbecapturedinpredictionsusingmodelssolelybased ontheinterfacialspacing(i.e.modified Hall-Petchconcepts).Hence, conceptsincludingkineticsofaccommodationandstressrelaxationpro- cessesofdislocationsatinterfacesneedtobetargetedanddevelopedto ensuremorereliablepropertydescriptions.Whiletheirkineticsarerea- sonablydescribedforthepurethermallyactivatedcase,itsstressdepen- denceyetneedstobeassessed.However,withfutureworkinthisfield, amajorsteptowardsageneralizedmodelcapturingeffectsofchemistry, interfacetypeorloadingsituationand,hence,ageneralpredictionof mechanicalpropertiesofnanomaterials,seemsaccessible.

DeclarationofCompetingInterest

Theauthorsdeclarethattheyhavenoknowncompetingﬁnancial interestsorpersonalrelationshipsthatcouldhaveappearedtoinﬂuence theworkreportedinthispaper.

Acknowledgments

Financial support by the European Research Council under ERC GrantAgreementsNo.340185USMSandNo.771146TOUGHIT,the AustrianAcademyofSciencesviatheInnovationFundIF2019-37and underthescope of theCOMETprogram withinthe K2Center‘Inte- gratedComputational Material,ProcessandProductEngineering(IC- MPPE)’(ProjectNo859480)supportedbytheAustrianFederalMin- istriesforClimateAction,Environment,Mobility,InnovationandTech- nology(BMK) andfor DigitalandEconomicAﬀairs(BMDW),repre- sentedbytheAustrianresearchfundingassociation(FFG),andthefed- eralstatesofStyria,UpperAustriaandTyrolisgratefullyacknowledged.

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