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《Grain-Size-Governed Shear Failure Mechanism of Polycrystalline Methane Hydrates - Sveinsson et al. - 2021 - Unknown》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
pubs.acs.org/JPCCArticleGrain-Size-GovernedShearFailureMechanismofPolycrystallineMethaneHydratesHenrikAndersenSveinsson,*FulongNing,PinqiangCao,BinFang,andAndersMalthe-SørenssenCiteThis:J.Phys.Chem.C2021,125,10034−10042ReadOnlineACCESSMetrics&MoreArticleRecommendations*sıSupportingInformationABSTRACT:Theshearfailuremechanismofpolycrystallinegashydratesiscriticalforunderstandingmarinegeohazardsrelatedtogashydratesunderachangingclimateandforsafegasrecoveryfromgashydratereservoirs.Sincecurrentexperimentaltechniquescannotresolvethemechanismonaspatialandtemporalnanoscale,molecularsimulationscanassistwithproposingandsubstantiatingnanoscalefailuremechanisms.Here,wereporttheshearfailureofpolycrystallinemethanehydratesusingdirectmoleculardynamicssimulations.Basedonthesesimulations,wesuggesttwomodesofshearbehavior,dependingonthegrainsizes,d,inthepolycrystal:grain-size-strengtheningbehaviorwithad1/3grainsizedependenceforsmallgrainsizesandgrain-size-weakeningbehaviorforlargegrainsizes.Throughthecrossoverfromstrengtheningtoweakeningbehavior,thefailuremodechangesfromshearfailurewithafailureplaneparalleltotheappliedsheartotensilefailurewithafailureplanelyingatananglewiththeappliedshear,spanninganetworkofgrainboundaries.TheexistenceofsuchachangeinmechanismsuggeststhattheHall−Petchbreakdowninmethanehydratesisduetoachangefromgrainboundaryslidingtotensileopeningbeingthemostimportantfailuremechanismwhenthegrainsizeincreases.■INTRODUCTIONpermafrost,andonshorepermafrost.ThestabilityofmarineGashydrates,alsoknownasclathratehydrates,areice-likeslopesandArctictundrarelatestonaturallyoccurringcrystallinehost−guestcompounds.Ingashydrates,gasgeohazardssuchasunderwaterlandslidesandexplosive10moleculestheguestsareencapsulatedinanetworkformedmethaneblow-outsfrompingosintheArctic,whichmaybyhydrogen-bondedwatermoleculesformingahostlattice.1leadtomethaneemissionsthatreachtheatmosphere.TheGashydratesnormallyformoutofanaqueoussolutionofgasmechanicalpropertiesofhydratesarealsoimportantforriskDownloadedvia59.88.102.6onMay14,2021at10:34:32(UTC).andwaterunderhighpressureandlowtemperatures.Inassessmentinsubseaoperationsinvolvinghydrates,bothwhennature,mostgashydratesaremethanehydratesthataredrillingthroughhydrate-bearingsedimentsinconventionaloilembeddedinhydrate-bearingsediments.Suchsedimentsareandgasrecoveryandwhendrillingintohydrateformationsforprevalentundertheseabedoncontinentalmarginsandundertherecoveryofmethanefromthehydrate-bearingsedimentArctictundra,whereagassupplyandsuitablethermodynamicitself.Seehttps://pubs.acs.org/sharingguidelinesforoptionsonhowtolegitimatelysharepublishedarticles.2conditionsareprovided.GashydratescanalsoformasplugsThemechanicalpropertiesofgashydrate-bearingsediments3inoilproductionlines.Overthelastfewdecades,muchdependonthehydratedistributionpatterninthesediments,attentionhasbeendirectedtowardhydratesasanenergyhydratesaturation,porosity,particlesize,andmineralresource4,5andtheirpossibleenvironmentalimpact.6Esti-9,11−18compositionofthesedimentskeleton.Manystudiesmatesoftheglobalgashydrateinventoryvarybyordersofhavefocusedontheroleofthehydratedistributionandmagnitude,butacommonandconservativeestimateiscontentbutnotonthecontributionofthemechanical7approximately1500gigatonsofcarbon.Thisestimateisanbehaviorofthehydrateitselftothatofsediments.orderofmagnitudelargerthancurrentworldwideconventionalMillimeter-scaleobservationsoffailuremechanismsfornaturalgasreservesofapproximately120gigatonsofcarboncementedhydrate-bearingsedimentshaveshownthatbreakage38(approximately200trillionmSTP).Gashydratesmaybedistributedinvariouswaysinasedimentarymatrix.ThesedistributionpatternsarecommonlyReceived:January31,2021referredtoaspore-filling,load-bearing,andcementingRevised:March27,2021morphologies.Inload-bearingandcementingmorphologies,Published:April29,2021hydratesthemselvesmakeupanessentialpartoftheoverall9stabilityofhydrate-bearingsediments.Therefore,hydratesareimportanttothestabilityofmarineslopes,Arcticsubsea©2021TheAuthors.PublishedbyAmericanChemicalSocietyhttps://doi.org/10.1021/acs.jpcc.1c0090110034J.Phys.Chem.C2021,125,10034−10042
1TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticle17ofthehydratemassitselfoccursduringshearing,andhydrate-bearingsedimentstendtobecomebothstrongerand19morebrittlewithincreasinghydratesaturation.Therefore,understandingthemechanicalpropertiesofthehydratemassitselfisfundamentaltounderstandingthemechanicalresponse20ofgashydrate-bearingsediments.Todate,onlyasmallnumberofinvestigationsonthemechanicalbehaviorsofpuregashydratesundertensileandcompressionconditionshavebeenperformedbylaboratorymeasurementsandmoleculardynamicssimulations.Forexample,ithasbeenshownthatlaboratory-formedmethanehydrateis20-to40-foldmorecreepresistantthanice(Ih)andexperiencesextensivestrainhardeningfollowedbystrain21softening.Mechanicaltestsonmassivenaturalgashydratesampleshaverevealedbrittlefailureunderreservoirconditions,withastrengthofapproximately3MPa.Molecularsimulations22haveidentifiedmicromechanismsrelatedtoguestmolecules,shownsomeintrinsicdifferencesbetweenthefailureofflawless23singlecrystalsamplesoficeandhydrate,andestimatedthethermalactivationoffractureinitiationinmonocrystalline24methanehydrates.Recently,theroleoficeinthemechanicalresponseofice-containingmethanehydrateswaselaborated25basedonmolecularsimulations.Mostgashydrates,bothinnaturalandlaboratorysettings,26−28aregrain-texturedpolycrystallineicycompounds,andthegrainsizeisimportanttothestrengthofpolycrystallinematerials.Grainsizesoflaboratory-grownmethanehydratescanbeontheorderofamicrometerortensofmicrometers,withveryslowcoarseningafterinitialformationofa28polycrystal.Innature,duetolongeravailablecoarseningtimesthanincontrolledexperiments,thegrainsizescan29becomehundredsofmicrometers.Molecularsimulationshaveshownthatgrainsizeisamainfactorcontrollingthemechanicalbehaviorsofpolycrystallinehydratesundertensileloading30andthatthegrainsizedependenceexhibitsHall−Figure1.Conceptualviewofthisstudy.ThemotivationistoPetchbehavior:thesamplebecomesweakerwithincreasingunderstandthemechanicalbehaviorofgashydrate-bearingsediments(A).Inthisstudy,wefocusonthehydrateitselfatthenanometergrainsizeabovesomecriticalgrainsize.Thesamestudyalsoscaleusingmoleculardynamicssimulations.AnexampleofamodelshowedareverseHall−Petcheffectforsmallgrainsizes,withasystemwithagrainsizeof24nmisshowninpanelsBandC.Wecrossoveratapproximately20nm.However,mostinstabilitiesshowboththeinitial,relaxedstateandastrained,fracturedstateofgashydrate-bearingsedimentspresentasshearfailures,andduringasimulation.Fromthesesimulations,weidentifyfailureinvestigationsonthedeformationandfailuremechanismsofmechanismsatthegrainlevel(D)andfindfunctionalrelationshipspolycrystallinegashydratesundershearloadinghavenot,tothatdescribethebehaviorofhydratesasafunctionofconditionssuchourknowledge,beenperformedbefore.astemperatureT,axialstressσ,andshearstressτ.Thesemayinturnbeusedtoimprovethedescriptionofgashydrate-bearingsediments.Here,wereportthesheardeformationandfailurebehaviorsColorsinthepanelswithmolecularsystemsindicatewhetherofpolycrystallinemethanehydrateswitharangeofgrainsizesmoleculesarehydratesIcoordinated(red)ornot(orange).Methaneandthedestabilizationmechanismselucidatedbymolecularmoleculesareblue.Thiscoloringhighlightsthegrainboundaries,dynamicssimulations.WeobserveaHall−Petch-likebehaviorwheretheaccommodationoftwodifferentcrystaldirectionsalonga30similartothatfortensilefailure,butadditionally,weobserveplaneresultsinastructurethatisnotperfectlysI.aclearchangeinthefailuremechanismwithanincreasinggrainsizeofthepolycrystal.Forsmallgrainsizes,thedamage■SIMULATIONStotheinteriorofgrainsisappreciable,andthefailureplaneisWeperformedmultiplelargemoleculardynamicssimulationsparalleltotheappliedshear.Forlargergrainsizes,thefailureofpolycrystallinemethanehydratesundershearloading.Abecomesfracture-like,thestrengthdecreases,thefracturemoleculardynamicssimulationisasolutionofNewton’smodebecomestensile,andthefailureplanebecomesinclinedsecondequationforasystemofmanypointparticles.Thesewithrespecttotheappliedshear.Wequantifythisbehaviorparticlesactoneachotherwithforcesthatrepresent,inanandfitittoamodelforthestrengthofsmall-grainedsolids.approximatedway,theinteractionsbetweenatomsandFigure1showsanoverviewofthisstudy,withthegeologicalmolecules.setting,theselectionofamethanehydratepolycrystalastheFollowingWuetal.,30wepreparedcubicconfigurationsoffocusofthepresetstudyandthegoalofdiscoveringfailurepolycrystallinehydratesatfulloccupancybytheVoronoimechanismsandestablishingmathematicalmodelsforthetesselationofaBCCstructurewith2×2×2unitcellfailureprocess.repetitions,resultingin16grainsshapedlikecube-truncated10035https://doi.org/10.1021/acs.jpcc.1c00901J.Phys.Chem.C2021,125,10034−10042
2TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleoctahedra.Wecreatedsuchsystemswithgrainsizesrangingtokeepthecomputationalcostofrunningthemolecularfrom4to32nm,correspondingtosystemsizesrangingfromdynamicssimulationsatanacceptablelevel.Notethatifwe(10nm)3(31716particles)to(80nm)3(15877611translatethesehighstrainratesintoshearspeeds,theyarenotparticles).Figure1Bshowssnapshotsfromoneoftheunreasonablyhigh.Arepresentativesimulationwithaboxsimulationsinthepresentstudy.heightof40nmhasashearspeedof1m/s,whichisaThemethanehydratewasmodeledusingamonatomicreasonablereal-worldslidingvelocity.Thus,ahighstrainrate31waterandmethanemodel(mW).ThismodelhasthesamecanbewarrantedifthegoalofthesimulationsistodiscovermathematicalformastheStillinger−Weberforcefield(seemechanismsatplayclosetoafailinginterface,whereComputationalDetails).Monatomicwaterhasbeenshowntodeformationratesarehigherthantheglobalsteady-statereproducetheisotropicity,elasticmodulusandPoisson’sratiocreeprateoftheexperiments.ofsImethanehydrate(FigureS2).ThefracturetoughnessofmonocrystallinesIhydrateusingmWhasbeenestimatedtobe■COMPUTATIONALDETAILS240.08MPam,whichisclosetotheexperimentallyreportedCalculationofGrainBoundaryTraction.Themain32,33strengthsofpurewatericeandonlyslightlyhigherthanfacetsofthegrainsinourmodelpolycrystalhaveanormalthefracturetoughnessofsIhydratemodeledwithTIP4P/vectorn=(±1,±1,±1).Eachsuchgrainboundaryis34ice.Themonatomicwatermodelallowsforthegrowthofassociatedwithahexagonalfaceoftwoneighborgrainsinthebothamorphousandcrystallinehydratesandcansponta-polycrystal.Therefore,weconsiderthegrainboundaryregionneouslyproducehydrateswhereamorphous,sIandsIItobethehexagonalprismcenteredonthegrainboundaryand35hydratescoexist.Furthermore,ithasbeenshownthatthewithaheightof1nm.Wetaketheaveragevirialstress,S,mWmodelpresentssimilarmechanicalresponseofpoly-includingthevelocitycontribution,overthisvolume.We30crystallinehydratesasTIP4P/iceandTIP4P/2005.Thus,itaverageover1000consecutivetimesteps=10ps.ThevirialshouldbepossibletodiscovermechanismsofhydratefailureinstresshasbeenshowntoresolvethelocalstressfieldundertheemergentbehaviorofanmWmethanehydrate.mechanicalloadingofsolidmolecularsystems,evenunderNote,however,thatmonatomicwateriscoarsegrained,and38conditionsofdynamicfracture.inparticular,itusesathree-particleinteractionbetween”waterForeachparticle,i,thevirialstressistakenoverneighboringparticles”tomimicthegeometryandcharge.ThereareseveralparticlesjasissueswiththemWmodelthatshouldbenoted:Thei1ijij,pairdiffusivityoftheliquidphaseisfarfromexperimentalwater,σαβ=−mvvαβ+∑()rα−rFαβbothintermsoftheabsolutevalueandthevariationwith2j(1)changingtemperature.Theremovalofexplicithydrogensprohibitsprotondisorder,sofailuremechanismsdepending1iijk,threejjki,threekkij,three+∑rFαβ++rFαβrFαβcruciallyonprotondisorderwillnotbepresent.Proton3jk,(2)disorderhasforexamplebeenshowncrucialforachieving36elasticanisotropyofhexagonalice(Ih)insimulations.SincewhereαandβdenotethecomponentsofthestresstensorsIhydratesareisotropic,thisislessofaprobleminthepresent(e.g.,σxxorσxz).Thefirstsumisoverforcesfrompairstudy.Protondisordershouldalsoinfluencethemobilityofinteractionswithparticleiandneighborsjwithinthecutoffgrainboundaries,sincethenumberofpossiblegrainboundarydistancerc,andthesecondsumisoverforcesfromthree-bodyconfigurationsnecessarilymustincrease.Monatomicwaterinteractions.Thenotationrimeanstheαcomponentoftheαalsoenforcestetrahedralorderratherthanlettingitariseij,pairpositionvectorofparticlei.Fβistheβcomponentofthespontaneouslyfromtheshapeandchargedistributionoftheijk,threewatermolecule.Thisprohibits,forinstance,theformationoftwo-bodyforceactingonparticleiduetoparticlej.Fβis37high-densityliquidwateratextremepressures(0.7GPa).thethree-bodyforceactingonparticleiduetoparticlesjandThisis,however,farbeyondthepressuresweapplyinthisparticlek.Werotatethestresstensorsoastofindthenormalstudy.ThechoiceofthemWwatermodelinthisstudyisandsheartractiononallofthe(±1,±1,±1)grainboundaries.groundedinitssuperiorcomputationalperformance,goodWeonlyusethelocalstresscalculationtocomputetheratioofelasticpropertiesandtensilefracturestrengthvaluesforsInormaltosheartraction,theratioofmaximumshearandhydrateinadditiontoitsabilitytospontaneouslygrowingmaximumnormalstressandtoillustratethesignofthenormalseveraldifferenthydratephases.stressonparticulargrainboundaries.ThismeansthatwedoWesubjectedthepolycrystalsinthesimulationstosimplenotneedtocomputetheatomicvolume,whichwewouldhaveshearataconstantrateof2.5×107s−1andanormalpressurehadtodoifwewereaftertheactualvaluesofthelocalstress.of10MPa,correspondingapproximatelytoa1kmwaterThe(±1,±1,±1)grainboundariesgeometricallygroupintocolumn.Thesesimulationswereperformedfordifferenttwokindswithinwhichtheboundariesaregeometricallytemperaturesrangingfrom263.15to288.15K,spanningtheequivalentwithrespecttoxzshear.Thedifferencebetweenrelevanttemperaturerangeforhydratesinnature.Allthesearewhethertheyexperiencetensionorcompression,assimulationswererunlongenoughforthemethanehydrateillustratedinFigure4,partsEandF.Therefore,wetakethepolycrystalstofailmechanically,allowingustomeasureaaverageofthemagnitudeofthenormalandsheartraction,maximumshearstressandtoassesstheresidualstrength.Weseparately,foreachtypeofgrainboundary.39producedfourreplicatesimulationswithdifferentinitialPreparationofPolycrystals.Weusedliteraturevaluesvelocityseedsfortwoofthetemperature−grainsizefortheoxygenandhydrogensintheunitcellofsImethanecombinations,(273.15K,11.9nm)and(283.15K,15.9hydrate.SinceweusethemWmodel,thisisnotstrictlynm),toestimatethevariationinthemaximumstressduetonecessary,andwecouldhavejusttakentheidealizedspacechance.AnexamplesnapshotofasystemduringmechanicalgroupdescriptionalongwiththeoxygenandmethanefailureisshowninFigure1C.Ahighstrainratewasnecessarypositionsoftheprimitivecell.10036https://doi.org/10.1021/acs.jpcc.1c00901J.Phys.Chem.C2021,125,10034−10042
3TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleThepolycrystalswerecreatedlikeinref30:First,we10fs.Thepolycrystalswerefirstallowedtoannealfor10nsatgeneratea(2×2×2)periodicbody-centeredcubic(BCC)T=283.15KandP=10MPainorderforthegrainstructure.Thisstructureisusedasthesitesinathree-boundariestorelax.Afterannealing,shearstrainwasappliedatdimensionalVoronoidiagram.Sincethe(2×2×2)BCCarateof2.5×107s−1byshearingthesimulationdomain.structurecontains16points,thisprocedureresultsin16ShearwasappliedforlongenoughforthesystemtofailVoronoicells,eachofwhichdefinetheextentofarandomlymechanically.Duringshearing,thethermo-baro-couplewasorientedsinglecrystalofstructureImethanehydrateinourNPxPyPz(xy)(xz)(yz)T,withxzbeingtheappliedshearandxypolycrystal.andyzbeingkeptconstantat0.ThismeansthatweusedaForceFields.MethaneandwatermoleculesweredescribedmodifiedNPTensemblewithaconstantanisotropicpressureasoneparticlepermoleculeusingthemonatomicwaterandinthelateraldirections,whilethesheardirectionswereunder31methanemodel(mW)byJacobsonandMolinero.Thestraincontrol,withxy=0,yz=0,andxzbeingdictatedbythepotentialfunctionofthisforcefieldisthesameasthatfortheappliedstrainrate.Stillinger−Weberforcefield:■Ur=+∑∑ϕϕ()ij∑∑∑(,,)rijrikθijkRESULTS23Thebehaviorofthepolycrystaldependsstronglyonthegrainiji>≠ijikj>size.Figure2Ashowsthestress−strainrelationshipsforÄÅÅpqÉÑÑÅÅijjσσyzzijijjyzzijÑÑijjσyzzsimulationsatarangeofgrainsizesandT=273.15K.FortheÅÅjjijzzjjijzzÑÑjjijzzϕε2()rABij=−ijijÅÅÅÅijjjzzjjzzÑÑÑÑexpjjzz,ÅÅÇkrrrij{kij{ÑÑÖkij−aijijσ{ϕθ3(,,)rrijikijk2ijjγσijijyzz=[−]λεijkijkcosθijkcosθ0ijkexpjjjjzzzzkraij−ijijσ{ijjγσikikyzzexpjjzzjraik−ikikσz(3)k{withacutoffdistanceforinteractionsatrc=aσ,whereboththepotentialfunctionandtheforcesvanishsmoothly.ThemWforcefieldisabout2ordersofmagnitudemoreefficientintermsofsimulatedmass×timeperCPU-hourthantheall-atomTIPnPpotentials.TheparametersofthispotentialaregiveninTable1.SimulationSetup.Allsimulationswereperformedin4041Lammps.ANose−́Hooverthermo-baro-couplewithdampingcoefficientsofTpress=1psandTtemp=0.2pswasusedtomimicNPTconditions.TheequationsofmotionwereintegratedusingtheVelocityVerletschemewithatime-stepofTable1.ValuesofParametersintheMonatomicWaterand31MethanePotentialbyJacobsonandMolineroacommonparametersA7.049556277Figure2.Shearstrengthofpolycrystallinemethanehydrates.(A)B0.6022245584showsloadingcurvesforT=273.15K.Thelegendshowsthegrainγ1.2size,d,calculatedfromthegrainvolume:d=V1/3.(B)Strengthofa1.8hydratesamplesasafunctionofthegrainsizefordifferentθ0109.5°temperatures.(C)DatafrompartBwithalogarithmicscaleonwater−waterbothaxes,withlinescorrespondingtograinsizedependenceexponentsof1/(dashedblacklines)and−1/(dottedblacklines).εww6.189kcal/mol32A1/powerlawisalsoindicated(dashedgraylines)tocontrasttheσww2.3925Å21/powerlaw.(D)DatafrompartBonaxesthatshouldrevealtheλwww23.153methane−methanegrainsizedependenceoftheshearstrengthgiventhateq4describesthetemperaturedependenceoftheshearstrengthcorrectly.Grainsizeεmm0.340kcal/mol11dependenceexponentsof/3and−/2areindicatedwiththickgrayσmm4.08ÅlinesinthesmallgrainsizeandlargegrainsizepartsofpanelD,λmmm0respectively.Noticethatfortwoofthetemperature−grainsizewater−methaneinteractionscombinations,(273.15K,11.9nm)and(283.15K,15.9nm),fourεwm0.180kcal/molsimulationswithdifferentrandominitialvelocityseedhavebeenrunσwm4.00Åtoshowthatthevarianceofthemaximumstressisverysmallλwm(m|x)0comparedtothedifferencebetweenthetemperaturegroups.TheseshowupasmostlyoverlappingmarkersinpanelB,andasseveralaSameasintheoriginalStillinger−Weberpotential.loadingcurveswiththesamegrainsizeinpanelA.10037https://doi.org/10.1021/acs.jpcc.1c00901J.Phys.Chem.C2021,125,10034−10042
4TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticlesmallestgrainsize,4nm,thehydrateshowsductilecharacteristicswitharelativelylowmaximumstrength.Theloadingcurvestartselasticallyatlowstrainsbeforereachinganinitialyieldstressofapproximately120MPaatastrainofapproximately0.08.Thehydratethenhardensbeforeitreachesitsultimateyieldstressofapproximately150MPa.Then,strainsofteningfollowsbutnotcatastrophicfailure.Increasingthegrainsizeleadstoashorterhardeningphase,amoreabruptfailureprocessandasmallerresidualstrengththehydratebehavesinmorebrittlefashion.Forgrainsizesfrom19.8nmandup,thefailureismoreorlessinstant.Wealsoseethatthemarkersforthedatapointswithreplicates,(273.15K,11.9nm)and(283.15K,15.9nm),fallalmostontopofeachother,showingthatthevarianceismuchsmallerthanthedifferencebetweenthetemperaturegroups.Toassesstheeffectofthegrainsizeandtemperaturesimultaneously,weestimatetheshearstrengthbytakingthemaximumofthestress−strainrelationshipfromeachsimulation.Figure2Bshowsthemaximumshearstressasafunctionofgrainsizefordifferenttemperatures.Itshowsgrainsizestrengtheningforsmallgrainsizes,uptoacriticalgrainsizeofd≈22nm,andgrainsizeweakeningforlargergrainsizes.Increasingtemperaturesleadtoadecreasingstrength.Figure2Cshowsthesamedatawithalogarithmicscaleonbothaxestorevealpower-lawrelationships.Wefindthatanexponentofapproximately1/fitswellinthegrainsize3strengtheningregime.Wedonothaveenoughdatainthelargergrainsizelimittomakeanystrongconclusions,butwedrawa1/drelationshipforreference.Beyondthecriticalgrainsize,theslopesofthemaximumstress−grainsizerelationshipsseemtovarysystematically:theyaresteeperforhighertemperatures.Weexpectthatthetemperaturedependenceofthestrengthcanbeexplainedbyanenergyactivationmodel.SuchanFigure3.Damagepatternchangesfromgraininteriordamageforapproachhasworkedpreviouslytodescribetensilecracksinsmallgrainsizestograinboundaryopeningforlargergrains.Thisishydratesbymoleculardynamicssimulations.24Followingaillustratedbysinglegrainstakenoutfromsimulationswithgrainsizesstudyonnanocrystallinemetals,42weassumeagrainslidingof8nm(A,B),12nm(C,D),and24nm(E,F)andT=273.15K.modelforthestrength:ThecolorsshowwhetherparticlesaresIcoordinatedhydrate(red),nonsIcoordinatedhydrate(orange)ormethane(blue)andthusσε=AdTe()̇UkTs/B(4)visualizedamagetothegrainsandinparticularshowthegrainmaxboundary.PanelsBandDshowthatforsmallgrainsizes,theinteriorofgrainsisdamaged,whilepanelFshowsthatthedamagepatternforHereA(d)capturesthegrainsizedependence,ε̇isthestrainlargergrainsboundariesistensileopening.rate,Tisthetemperature,kBistheBoltzmannconstant,andUsisanenergybarriertograinboundarysliding.Wethereforeseektocollapseallthemaximumstressesmeasuredinoursizesjustafterfailureofthesample.Forsmallgrains,at8nm,itsimulationsontoacommonscalingfunctionA(d)bydividingseemsthatgraincornersarewornoff.Forslightlylargergrains,themwithTeUks/BTforsomeactivationenergyU.Sincethisat12nm,weobserveintragrainfracture,resultinginpartsofsactivationmodelwasdevelopedforthenanocrystallinebranch,certaingrainsbeingtornoff.Whenintragrainfracturesoccur,weprioritizethedatapointsbelowthecriticalgrainsizeinthetheyareaccompaniedbytheformationofamethanebubble.modelfit.WeobtainthedatacollapseshowninFigure2DbyForgrainsat8and12nm,theoverallfailureplaneinthewholesettingUs=0.095eV.Thisdatacollapseshowsthatthedatafitsystemisparalleltotheappliedshear.However,forlargertheproposedmodelwellbelowthecriticalgrainsizeandgrains,especiallyford≥19.8nm,thefailuremechanismslightlylessaccuratelyforgrainsizesbeyondthecriticalgrainchangescompletely.Failurenowoccursexclusivelyatthegrainsizeofd≈22nm.Inadditiontothecollapseddatapoints,weboundariesbytheopeningofcavities.Thefailureappearsasadraweye-guidinglinescorrespondingtoad1/3grainsizetensilefractureoftheboundaries,resultinginafailureplanedependencebelowthecriticalgrainsizeandd−1/2beyondthethatliesonaslopewithrespecttotheappliedshearandcriticalgrainsize.spanninganetworkofgrainboundaries(seealsoFigureS1).Morethanjustshowingthebehavior,moleculardynamicsToverifyquantitativelythatthefailuremodechangesfromsimulationsallowfordirectobservationofwhichmechanismsshearfailuretotensilefailure,wecheckhowthenormalandchangeduringachangeinbehavior.Wefindthatthegrainsizesheartractiononthegrainboundarieschangewithgrainsizestrengtheningtoweakeningbehaviorisaccompaniedbyaandtemperature.ThegrainsresultingfromVoronoitesselationchangeinthefailuremechanismthatisbothvisuallystrikingofabody-centeredcubicstructuremainlyhavegrainandnumericallymeasurable.Figure3showsgrainsofdifferentboundarieswithnormalvectorsinthe(±1,±1,±1)10038https://doi.org/10.1021/acs.jpcc.1c00901J.Phys.Chem.C2021,125,10034−10042
5TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticlecoordinatedirections.Thesegrainboundarieshavetwo■DISCUSSIONfeatureswithrespecttotheappliedshear:thoseundertensionWehaveshownthattheshearfailureofpolycrystallineandthoseundercompression,sinceoneofthexz-planemethanehydratesfollowsareverseHall−Petchrelationshipupdiagonalscontractsandtheotherexpandsunderxzshear.Thetoacriticalgrainsizeofd≈22nmandaregularHall−Petchstressesonthetwokindsofgrainboundariesareshowninrelationshipbeyondthiscriticalgrainsize.ThecrossoverFigure4,partsEandF.Wefindanormalandsheartraction,σnbetweentheseHall−Petchregimesisaccompaniedbyapronouncedchangeinthefailuremode;itchangesfromsheartotensile.Wealsofindthatthetemperaturedependencebelowthecriticalgrainsizefitswithanactivationenergyof0.095eV.Thisactivationenergydoesnotcapturethetemperaturevariationtothesameextentbeyondthecriticalgrainsize.Thisisconsistentwithachangeinmechanism.Wehavenotfoundexperimentallymeasuredactivationenergiesfornanocrystallinemethanehydrates,sowesettleoncomparingthemwithnanocrystallinemetals:InmoleculardynamicssimulationsofnanocrystallineNiattemperaturesfrom300to500K,an43activationenergyof0.2eVhasbeenmeasured.Thisishigherthaninthepresentstudy,whichisexpectedforastrongermaterialwithahighermeltingpoint.ThemeltingpointofNiis1728K,itsYoung’smodulusisaround200GPa,anditsfracturetoughnessisontheorderof50MPam1/2.Comparetovaluesofaround290K,7GPa,and0.1MPam1/2forsIhydrate.Thefailureisbrittleabovethecriticalgrainsize.Consequently,shearfailuresofhydratepolycrystalsinexperiments,whosegrainsizesarefarlargerthanthoseinoursimulations,shouldbebrittle.Thisiscompatiblewithexperimentalobservations,suggestingthathydrate-bearingsandsbecomeincreasinglybrittlewithincreasinghydrate19saturationandthatcrushingofthehydratemassitselfis17,44importantduringthefailureofhydrate-bearingsands.Thisisalsoconsistentwithexperimentsonmassivenaturalgas45hydratesshowingbrittlebehavior.Intheexperimentonmassivehydrates,theyalsoconstructedarangeoffailurestressesasafunctionofgrainsizebasedontheirexperiments,previousmolecularsimulations,andpreviousexperimentsonice.Oursimulationsfromthegrain-sizeweakeningregimeallfallinsidethisrange,increasingourconfidenceinthequantitativeaccuracyofourresults.Weexpectthatdecreasingthestrainratewill,toafirstorderapproximation,reducethemaximumstressesinoursimulations.AsecondordereffectofthisispresumablythatthebrittlemechanismforlargegrainsizesisimpededmorethantheductilemechanismatsmallFigure4.Ratioofnormaltosheartractionon(111)grainboundariesgrainsizes.Thus,foralowerstrainrate,wewouldexpecttheundertension(A,C)andcompression(B,D)asafunctionofgraincrossoverlength,dm,toincrease.sizefordifferenttemperatures.TherelativenormaltractionincreasesThecomputationalcostofincreasingthesystemsizeisdrasticallywithgrainsize,indicatingachangeinthefailuremode.PanelsEandFillustratethepartsofthesystemoverwhichtheconsiderablesincethenumberofatomsincreases8-foldfortractioniscalculated(seemethodssectionfordetailsontheeachdoublingofthegrainsized.Wehaveestablishedthatthecalculation).ThecolorsinpartsEandFindicatelocalstressfrominteriorofgrainsstaysintactduringthefailureoflargegrains.blue(tension)tored(compression).Therefore,ratherthanjustscalingupthesimulationsofthepresentstudy,multiscaleapproachesusingexplicitmoleculesandτn,respectively,onthesesurfaces.Thesetractiononlyongrainboundariesandgrainjunctionscanbeawaytocomponentsshouldacttowardaperfectlytensile(σn)orrevealthemechanismsonlargerscalesandtoaccuratelyperfectlyshear(τn)failureofthegrainboundary.Theratioofdeterminewhetheranenergyactivationmodel,andifsowhatthenormaltosheartractionisshowninFigure4,partsAandactivationenergy,holdsabovethecriticalgrainsize.ThisB.Inaddition,partsCandDofFigure4showtheratiooftheactivationmodelcould,forinstance,beofasimilarnaturetomaximumnormaltomaximumshearstressascalculatedfromthatforslowtensilecrackevolutioninmonocrystalline24theprincipalstresses.Theabsolutevalueoftheratioσn/τnhydrates.Inthatmodel,forpenny-shapedcrackswithaincreasesandthenstabilizeswithgrainsize,butthevaluelengthof8nm,anactivationenergyonthesameorderaswhereitstabilizesdependsonthetemperatureforboththemeasuredinthepresentstudy(0.095eV)couldbeachievedbytensileandcompressiveboundaries.settingthemaximumstresstoapproximately560MPa,and10039https://doi.org/10.1021/acs.jpcc.1c00901J.Phys.Chem.C2021,125,10034−10042
6TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleloweringthemaximumstresswouldincreasetheactivationtemperatureeffectsinteractwiththegrainsize.Futurestudiesenergy.couldthereforebenefitfromsystematicallyexaminingtheThepossiblenumberofpolycrystalconfigurationsisvast,slidingpropertiesofvarioushydrategrainboundaryconfig-bothintermsoftherotationsandgeometriesofthecrystalurations.grainsconstitutingthepolycrystal.ThepolycrystalsintheThemeasuredgrainsizesinrealhydratesarelargerthan30,46presentstudyrepresentsanidealizedcase.Previousstudiesthosewemodeledinthisstudy.However,smallergrainsmayhaveshownthatpolycrystalswithuniformlyrandomlyformduringfailure.Forinstance,duringlaboratory-controlledVoronoi-centeredgrains,presentsimilartensilebehaviorasfailureofoldAntarcticwaterice,small,recrystallizedicegrainstheirregularlyconstructed(BCCstructure)counterparts.Weofapproximately100μmformedinthegrainboundaries48maythereforereasonablyconjecturethattheeffectsobservedbetweentheoriginalmillimeter-sizedgrains.Ifasimilarinthepresentstudywillholdformoredisorderlypolycrystals.mechanismexistsforhydrates,theslowcoarseningof28Thegrainsizedependencerevealedinthisstudyissimilartohydratescouldpossiblyleadtoastrongsmall-grained30thatobservedundertensionandcompression.However,boundaryzonefacilitatinghighcreepresistance.undershearloading,wefindthatthechangeinthefailuremechanismasthegrainsizecrossesthecriticalgrainsizeis■CONCLUSIONSmuchmorepronounced.ThereisaclearchangefromfailureUnderstandingthefailuremechanismsofpolycrystallinethattearsoffpartsofhydrategrainstofailurethatonlyinvolvesmethanehydratesisimportantforpredictingthebehaviorofgrainboundaryopening.Duringthischange,wecanmeasuregashydrate-bearingsediments.Inthispaper,wehaveshownthatthetensileproportionofthegrainboundarytractionsimulationssuggestingthatthemechanismofshearfailureofincreasesandthatitstabilizeswithgrainsizeonatemperature-polycrystallinemethanehydratesisgrain-sizedependent,withdependentvalue.Wearenotcomfortableestimatingtheatransitionfromlocalshearfailuretolocaltensilefailurewithactivationenergyduringtensileopeningbecausethedataincreasinggrainsize.Thischangeinmechanismcoincideswithbeyondthecrossoverlengtharesparse.However,theorderofacrossoverfromgrainsizestrengtheningtograinsizethedatapointsinthedatacollapse(Figure2D)showsthattheweakeningbehavior,indicatingthatachangefromlocalhigh-temperaturedatapointsstillliebelowthelow-temper-sheartolocaltensilefailureisresponsiblefortheHall−Petchaturedatapointsafterapplyingscalingaxes.Wecanthereforebreakdowninpolycrystallinemethanehydrates.withreasonablecertaintystatethatthisactivationenergywouldhavetobelargerthantheactivationenergycontrolling■thesmall-grainedregime.ASSOCIATEDCONTENTGrainsizeweakeninginpolycrystallinematerialsisoften*sıSupportingInformationexplainedbytheHall−Petcheffect.IntheHall−Petcheffect,TheSupportingInformationisavailablefreeofchargeatdislocationspileupatthegrainboundary,resultingintheyieldhttps://pubs.acs.org/doi/10.1021/acs.jpcc.1c00901.strengthfollowinga1/ddependence,wheredisthegrainIllustrationofthechangeofmechanismoffailurewhensize.Whenthegrainsizedisverysmall,ontheorderofafewthegrainsizeincreasesandYoung’smodulusandcrystalunitcells,thepolycrystalcommonlystrengthenswithPoisson’sratioasafunctionoftemperaturefortheforcegrainsize.However,inoursimulations,wedonotfindfieldusedinthepresentstudy(PDF)dislocationspilinguppriortofailure.Rather,alldamageisconcentratedonthegrainboundariesandjunctions,andonly■atcriticalfailuredosomegrainsinthesmall-grainregimeAUTHORINFORMATIONexperienceinteriordamage.Mechanismsotherthandisloca-CorrespondingAuthortionpile-uphavebeenproposedtoexplaingrainsizeHenrikAndersenSveinsson−TheNJORDCentre,weakeningandstrengtheninginnonmetals,suchasceramics,47DepartmentofPhysics,UniversityofOslo,0371Oslo,whereacriticalgrainsizeof18.4nmisfound,whichisNorway;orcid.org/0000-0002-3651-0710;explainedbytherelativefractionsofbulk,grainboundary,andEmail:h.a.sveinsson@fys.uio.notriplejunctionvolumeinapolycrystal.Inthatstudy,suchanηAuthorsanalysiswasconsistentwithagrainsizedependencedwiththeexponentηbeingsmallerthan1/belowthecriticalgrainFulongNing−FacultyofEngineering,ChinaUniversityof2Geosciences,Wuhan,Hubei430074,China;Laboratoryforsize.MarineMineralResources,QingdaoNationalLaboratoryforApolycrystalcanabsorbsimpleshearinvariousways.IfweMarineScienceandTechnology,Qingdao266237,China;assumethatthegrainboundaryslidingisinsensitivetonormalorcid.org/0000-0003-1236-586Xtractionandiscorrectedfortheconfiningpressure,thePinqiangCao−FacultyofEngineering,ChinaUniversityofcompressivenormaltractiononthe(111)grainboundariesGeosciences,Wuhan,Hubei430074,China;SchoolofundercompressionwouldbeequaltothetensilenormalResourceandEnvironmentalEngineering,WuhanUniversitytractiononthe(111)grainboundariesundertension.ofScienceandTechnology,Wuhan,Hubei430081,China;Conversely,ifthegrainboundaryslidingdependedonnormalorcid.org/0000-0003-1469-4288traction,thecompressiveboundarieswouldhaveadifferentBinFang−FacultyofEngineering,ChinaUniversityofratioofsheartonormaltractionduetopreservingshearGeosciences,Wuhan,Hubei430074,Chinatractionintheabsenceofgrainboundarysliding.TheAndersMalthe-Sørenssen−TheNJORDCentre,symmetricandgrain-sizeincreasingtendencyshowninFigureDepartmentofPhysics,UniversityofOslo,0371Oslo,4,partsAandB,indicatesthatthetensionandcompressionNorwaybuiltupfromgrainboundaryslidingplaysanincreasinglyimportantroleasthegrainsizeincreases,thatgrainboundaryCompletecontactinformationisavailableat:slidingislargelyinsensitivetonormaltraction,andthathttps://pubs.acs.org/10.1021/acs.jpcc.1c0090110040https://doi.org/10.1021/acs.jpcc.1c00901J.Phys.Chem.C2021,125,10034−10042
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