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Title: LARGE-SCALE MOLECULAR DYNAMICS SIMULATIONS OF SHOCK-INDUCED PLASTICITY, PHASE TRANSFORMATIONS, AND DETONATION

Author(s): Timothy C. Germann

Submitted to: http://lib-www.lanl.gov/la-pubs/00796201.pdf

LARGE-SCALE MOLECULAR DYNAMICS SIMULATIONS OFSHOCK-INDUCED PLASTICITY, PHASE TRANSFORMATIONS,

AND DETONATION

Timothy C. Germann�

AppliedPhysicsDivision (X-7),LosAlamosNationalLaboratory, LosAlamos,NM 87545

Abstract. Moderncomputersenableroutinemultimillion-atommoleculardynamicssimula-tionsof shockpropagationin solidsusingrealisticinteratomicpotentials,andoffer a directinsightinto theatomisticprocessesunderlyingplasticity, phasetransformations,andthedet-onationof energetic materials. Past, present,andprospectsfor future simulationswill bediscussedin thecontext of prototypicalsystemsfor eachof thesethreeclassesof problems.Initial samplesrangingfrom perfectsinglecrystals,to thosewith specificisolateddefects,tofull-fledgedpolycrystallinematerialswill beconsidered.

INTRODUCTION

Atomistic simulationmethods,particularlynon-equilibriummoleculardynamics(MD), offer agreatandlargely untappedpotentialfor the investigationof shockwaveprocessesin solids[1]. Only recentlyhas it beenconclusively demonstratedthat large-scaleMD simulationscan give steadyplastic (orsplit elastic-plastic)waves with a rich nanostruc-ture [2] that may be directly comparedwith ultra-fast X-ray diffraction measurements[3]. Shock-inducedphasetransformations(eithersolid-solidorsolid-melt),multiple shocks(including rampwaveloading), unloadingprocessessuch as rarefactionshocks,spallation,and ejecta,and shock-inducedchemistryarejustafew of thephenomenafor whichMD simulationsover thecomingdecadeshouldbeableto providea greatdealof insight.

This paperwill briefly review someof therecentachievementsusing classicalmoleculardynamics,andthosewhich mayreasonablybeexpectedin thenearfuture. Theuseof quantummoleculardynam-ics techniques,including density-functionalandtight-bindingmethods,to studyshock-compressed�Work done in collaborationwith Brad Lee Holian, Kai

Kadau, and PeterS. Lomdahl (LANL); Niels G. Jensen(UCDavis/LBL); Jean-BernardMaillet (CEA); and RamonRavelo(UT El Paso/LANL).

materials[4], is anotherpromisingfield,but will notbeconsideredfurther.

PROTOTYPICAL SYSTEMS

Three prototypical systemswill be discussedhere, representative of three classesof shock-inducedbehavior in solids,namely(1) plasticity, (2)polymorphicphasetransformations,and(3) detona-tion of energeticmaterials.

Themajority of moleculardynamicssimulationsfor solidshavefocusedonclose-packedmetals,rep-resentedeitherby pair potentialssuchasLennard-Jones6-12,or embeddedatommethod(EAM) po-tentials[5], which addan embeddingterm depen-dent on the local electrondensityto a pair poten-tial. Holian and coworkers [6] first demonstratedthatsteadyshockwavesin three-dimensionalsolidscouldbemodeledusingMD, with a transitionfroma purely elasticresponseto plastic flow when theHugoniot pressurejump is roughly equal to theshearmodulus. Theseearly (ca. 1980) simula-tions,with upto

�����atoms,exhibitedslippage(i.e.,

stackingfaults) along one, or at most two, � 111�planesfor shockstraveling in the ���� � direction.With the great advancesin computerpower andin parallelmoleculardynamicsalgorithms[7], Ho-lian andLomdahl[2] demonstratedthat3-D simula-

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tionswith�����

atomsarefeasibleonmoderate-sized(12-CPU)multiprocessorcomputers. Thesestud-iesconfirmedtheresultsof earliersimulations(e.g.,regardingthelinear ��� vs. ��� Hugoniot,thethresh-old for plasticity, . . . ), with patternsof intersectingstackingfaultsbeinggeneratedonall four available� 111� planes. Shortly thereafter, Zhakhovskiı etal. [8] showedthat smoothfine-grainedshockpro-files couldalsobeobtainedusinga time-averagingtechniquewith muchsmallersamplesthanthespa-tial averagingover large cross-sectionalsamples.Furthersimulationshave investigatedthecrystallo-graphicorientationdependencein both the elastic-plastic[9] andmelting[10] regimes.

Recently, simulationshave beencarriedout us-ing various EAM potentials for iron, to investi-gatethe ����� phasetransformationundershockloading [11]. It is ratherremarkablehow fast thetimescalefor this diffusionlessprocessis; for over-driven shocksin perfectsinglecrystals,the bcc �hcp transformationis basicallycompletewithin afew lattice planes,althoughsubsequentgrain an-nealingis observed over longer timescales.Sincethepublishedpotentialswereall fit to zero-pressuredata (or at best, an approximateRose“universalequationof state” for the bcc phase),it is not sur-prisingthatdetailsof theexperimentalHugoniotarenot quantitatively reproduced,especiallyabove thetransformationthreshold. But the fact that quali-tative aspectssuchasthe bcc-hcporientationrela-tionships,transformationkinetics,etc.,for differentshockdirectionsappearsto be independentof theactualpotentialleadsusto believe that theserepre-sentthe trueresponseof shock-compressedperfectsingle-crystaliron.

The third and final classof behavior concernsshock-inducedchemicalreactions,specificallydet-onation.Reactiveempiricalbondorder(REBO)po-tentialsdevelopedby Brenner, White, andcowork-ers[12, 13] in the early1990sexhibit many of thepropertiesof condensedphaseexplosives,includingacritical flyer platevelocityfor initiation [13], deto-nationvelocity independentof initiation conditions[13], delayed(homogeneous)initiation for low ve-locity impact[14], anda critical width for detona-tion of 2-D ribbons[15]. All of thesestudies(aswell asthe presentwork) arefor the original 2AB� A � + B � modelexothermicreaction,but shock

simulationsusingREBO potentialsfor ozone[16]andhydrocarbons[17] havealsobeencarriedout.

In the remainderof this paper, we will discusspast,present,andfutureMD simulationsfor eachofthesethreesystemswith threetypesof initial sam-ples:perfectsinglecrystals,singlecrystalswith iso-lateddefects,andpolycrystallinematerials.

PERFECT SINGLE CRYSTALS

Single-crystalsimulationsarebeginning to pro-vide quantitative predictionsaboutbehavior whichcan be measuredat the macroscale. Holian andLomdahl [2] demonstratedthat with samplecross-sectionsaslargeas

�������������unit cells,quantitative

measurementsof thestackingfault densitycouldbemadeand shown to closely follow the total volu-metricstrain � ��� � � acrosstheshockfront. Further-more,analysisof thesmoothstressprofilesobtainedby either time- or (in this case)space-averagingshows that the strain ratedependenceon the pres-surerise � is � "! ��#$ # , in remarkablygoodagree-mentwith experimentalmeasurementsfor metals.

Strachanand coworkers [18] have studied thespallationof perfectcrystalsof bcc Ta and fcc NiusingEAM potentials. Although the samplesizeswere relatively small (10 to 20 thousandatoms),they wereableto extract void volumedistributionsat differenttimeswhichexhibit apower-law behav-ior %'&)("*'+,(.-0/ over several ordersof magni-tude. The critical exponent13254 674 , which corre-spondsto that for 3-D percolation.Similar studiesusing larger sampleswith preexisting defectssuchasvoids, inclusions,or grain boundarieswould beof greatinterestsincespall failure at lesserstrainrates(closerto mostexperiments)couldberealized.

With improvedpotentialmodels,phasetransfor-mationsimulationsmayreachasimilar level of pre-dictive capacityas well. However, MD simula-tionsof detonationwill likely bemorevaluablein astrictly modelcapacity, sincetypical reactionzones(8 m to mm) of actualexplosivesare well beyondthecapabilityof MD simulationsfor atleastanotherdecade.SimulationsusingREBOmodelssubjectedto flyer plate[13, 14] or supportedpiston[12, 16]impacthavebeencarriedout in 2D and3D; herewefocusonour 2D supportedpistonresults.Themea-suredHugoniot is shown in Fig. 1. At very slowpiston velocities(below about300 m/s), a steady

2

0

2

4

6

8

10

12

14

16

0 1 2 3 4 5 6 7 8

D [k

m/s

]9

Up [km/s]

2-D supported piston simulations

plastic

overdriven melt

detonation

elastic

FIGURE1: MeasuredHugoniot(shockvelocityvs.par-ticle velocity) for the2-D AB crystal.

elasticwave is maintained,but soonthereafteronefindssplit elastic-plasticstructure(Fig. 2) followedby a fluid region dueto the extremelylow meltingpointof theAB model.For pistonvelocitiesgreaterthan 2 1.6 km/s, a steady-statedetonationis initi-ated.Velocitiesjust above this thresholdclearly in-dicatethatinitiation takesplaceby homogeneneousnucleationfar behindan intial compressive wave,which is subsequentlyovertaken by the detonationwave. The detonationvelocity is nearly constant,! 9.5 km/s, until for �0�;: 4.5 km/s an overdrivendetonationwaveexists.

STUDIES OF ISOLATED DEFECTS

Our simulationsindicatethat point defectssuchasvacanciesareinsufficiently strongstressconcen-trators to initiate plastic deformation[2] or phasetransformationsbelow the perfect single-crystalthreshold.Similarly, replacingan AB moleculeinthe molecularsolid by anA < radicalleadsto a fewlocalizedreactionsfor �0�>= 1.6 km/s,but doesnotseemto lower thedetonationthresholdappreciably(a few percentat most).

However, moreextendeddefectsor grainbound-ariesmay readily act as heterogeneousnucleation

FIGURE 2: Shockwave in a 2D AB molecularcrystalwith ?�@BADCFE GIH km/s (i.e., below thedetonationthresh-old), with moleculescoloredby theirorientation.Theun-shockedherringbonelatticeis atthetop,andatthebottomis theshockedstatecorrespondingto a (highly defective)90J rotationof theoriginal lattice.An intermediateelasticprecursorconsistsof diagonallines of singlemoleculeswhich have rotatedby varyingamounts,but returnto theoriginal configurationuponrelease.

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FIGURE3: Heterogeneousnucleationof detonationata10nmradiuscircularvoid, 6 psafteranonreactiveshockwave reachesthe left sideof the void. At later times,asteadyplanardetonationwaveis obtained.Atomsarecol-oredaccordingto their bonds,with bluefor productsandblackfor multiply bondedatoms.

FIGURE 4: Polycrystalline2-D Lennard-Jonessample(2 million atoms)before(top) andafter (bottom)shockcompressionfrom the left side. Atoms are coloredac-cordingthethelocalorientationof thehexagonallattice.

sites, as demonstratedby using a warped pistonto initiate plasticflow in fcc Lennard-Jonesium[2]well below the perfect-crystalthreshold. Simula-tionsof bcciron with a missinghalf-planeof atoms(whichcanrelaxinto aparallelpairof edgedisloca-tion lines) alsoshow thatphasetransformationnu-cleationmaybeinducedbelow theusualthreshold.

Oneimportantquestionwhich canbe addressedusingsuchsimulationsis whatrole varioustypesofdefects(voids, inclusions,dislocations,. . . ) playin “hot spot” initiation of detonation.For instance,we have found that large voids in a 2D AB crystalcan substantiallylower the perfect-crystaldetona-tion threshold,from 1.6km/sto around1.1km/sfor10nmradiuscircularvoids.An exampleof thispro-cessis shown in Fig. 3 for � �LK 1.38km/s.Onecanclearlyseeinitiation in thiscaseoccuringdueto theimpactof aconvergingjet of atomsejectedfrom theopposidesidesof thevoids,andnot by collision ofthetwo wavespropagatingaroundthevoid.

POLYCRYSTALLINE MATERIALS

We have recentlybegun carryingout somepre-

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FIGURE 5: Polycrystallineiron sampleat 2.2 ps, 4.5ps, and9.5 ps after impactwith a pistonat the left (notshown). Thesamplecontains32 grainsanda total of 24million atoms;thesizebeforeshockcompressionwas58nm M 58 nm M 87 nm. Atoms are color-codedby thenumberof neighborsN within 2.75A: theunshockedbccsample( NOAQP ) is grey, uniaxially compressedbcc( NRAS C ) is blue,thetransformedclose-packedregion( NBA SUT )is red, andothervalues(colors)primarily correspondtograinandtwin boundaries.

liminary simulationsof nanocrystallinematerials.Thedifficultiesherearetwofold: (1) sampleprepa-ration thatgeneratesa realisticdistribution of grainsizes,orientations(texturing), andrelative orienta-tions (grain boundaryenergies); and (2) samplessufficiently largethatmany grainsareaveragedoverin the transversedirections,andthat a steady-stateshockwaveisachievedin thelongitudinaldirection.

A two-dimensionalexampleis shown in Fig. 4.The sampleis generatedwith a Voronoi construc-tion: we randomlyselect80 grain centerpositionsandorientations,andfill eachgrainwith a triangu-lar latticeof thegivenorientationuntil themidpointbetweentwo grain centersis reached.This initialstateis thenannealedfor VB& ��� # * timesteps(corre-spondingto a few ps) to at leastpartially relax thegrain boundaries,beforebeingsubjectedto shockloading.In thiscasethepistonvelocity is below theperfect-crystalHugoniot elastic limit (at least forthe varioustriangularlatticeorientationswhich wehave studied),but animationsclearlyshow disloca-tionspropagatingfromthegrainboundariesthrougheachcrystallite. As seenin the bottom panelofFig. 4, this processgreatly distortsthe previouslylineargrainboundaries,andleavesbehinda signif-icant dislocationdensityin severalof the grainsaswell. The shockwave is considerablybroadeneddue to the distribution of shockvelocitiesin eachgrain andthescatteringoff of grain boundaries,soeven for this 2 million-atomsystem,a steady-stateshockprofile is notyet attained.

Suchsimulationsmayalsobecarriedout in 3-D,but simulationsizesof W �� � atomsarenecessaryto have a reasonablenumberof grainsand suffi-ciently smallsurface-to-volumeratio of eachgrain.Onepreliminaryexamplefor iron is shownin Fig.5,wherea32-graininitial configurationwasgeneratedin a mannersimilar to that for the previous exam-ple,andthendrivenat � ��K 725m/stowardsamo-mentummirror [2] at the left. For this particularEAM potential, this piston velocity is about15%below the perfect-crystaltransformationthresholdfor shocksin the �����X� direction[11]. Again,weseenucleationof thebcc � hcptransformationatgrainboundaries,whichthenslowly proceedsinwardsforeachgrain. As before,a steadyshockprofile is notyet attained,but in this casethe numberof grainsin eachtransversecross-sectionis too small to ever

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expectsteady-statebehavior.

CONCLUSIONS

Theprospectsarevery goodfor usingMD sim-ulationson perfector nearlyperfectcrystalsto sys-tematically study shock phenomena,particularlythe effects of variousheterogeneities,in a quanti-tative capacityfor metalplasticityandphasetrans-formationprocesses.On the otherhand,energeticmaterial and polycrystal studiesare more likelyto remain in a qualitative, model-building capac-ity for the forseeablefuture. Even

��FYatomsare

not enoughto representa micron-scalecubeof ma-terial, so direct MD simulationsof realistic poly-crystallinesampleswith grainsizeson theorderof�� 8 m are impractical,andunnecessary. Insteadamorebeneficialapproachwould involve usingMDsimulationsto calibratethe governing interactionsfor models(suchas the discreteelementmethod)usedin mesomechanicalstudiesof shockcompres-sion[19], thusproviding alink betweeninteratomicpotentialson the sub-nanometerscaleand meso-scopicbehavior on thesub-millimeterscale.

ACKNOWLEDGEMENTS

Fruitful discussionswith Mark Elert, Jerry Er-penbeck,Jim Hammerberg, Ed Kober, JohnMint-mire,AlejandroStrachan,CarterWhite,andSergeyZybin aregratefullyacknowledged.This work wascarriedout underthe auspicesof the U.S.Dept.ofEnergy at Los AlamosNational LaboratoryunderContractW-7405-ENG-36.

REFERENCES

[1] Holian, B.L., Germann,T.C., Lomdahl,P.S.,Ham-merberg, J.E.,andRavelo, R., in Shock Compres-sion of CondensedMatter–1999, edited by M.D.Furnish et al., AIP ConferenceProceedings505,New York, 2000,pp.35–41.

[2] Holian, B.L., and Lomdahl, P.S., Science280,2085–2088(1998).

[3] Loveridge-Smith,A., et al., Phys. Rev. Lett. 86,2349–2352(2001).

[4] For instance, see Kress, J.D., Bickham, S.R.,Collins, L.A., Holian, B.L., and Goedecker, S.,Phys.Rev. Lett.83, 3896–3899(1999).

[5] Daw, M.S., Foiles,S.M., andBaskes,M.I., Mater.Sci.Rep.9, 251–310(1993).

[6] Holian,B.L., Phys.Rev. A 37, 2562–2568(1988).

[7] TheSPaSM(“ScalableParallelShort-rangeMolec-ular dynamics”) code is describedin: Lomdahl,P.S, Tamayo,P., Grønbech-Jensen,N., and Bea-zley, D.M., in Proceedingsof Supercomputing93, edited by G.S. Ansell, IEEE ComputerSo-ciety Press,Los Alamitos, CA, 1993, pp. 520–527; Beazley, D.M., and Lomdahl, P.S., Comput-ers in Physics11(3), 230–238(1997); see alsohttp://bifrost.lanl.gov/MD/MD.html.

[8] Zhakovskiı, V.V., Zybin, S.V., Nishihara,K., andAnisimov, S.I., Phys. Rev. Lett. 83, 1175–1178(1999).

[9] Germann,T.C., Holian, B.L., Lomdahl, P.S., andRavelo,R.,Phys.Rev. Lett.84, 5351–5354(2000).

[10] Zhakovskiı, V.V., Zybin, S.V., Nishihara,K., andAnisimov, S.I.,Prog. Theor. Phys.Supp.138, 223–228(2000).

[11] Kadau,K., Germann,T.C., Lomdahl,P.S.,andHo-lian, B.L., theseproceedings.

[12] Robertson,D.H., Brenner, D.W., andWhite, C.T.,Phys.Rev. Lett.67, 3132–3135(1991).

[13] Brenner, D.W., Robertson,D.H., Elert, M.L., andWhite,C.T., Phys.Rev. Lett.70, 2174–2177(1993);76, 2202(E)(1996).

[14] Robertson,D.H., Brenner, D.W., andWhite, C.T.,Mat. Res.Soc.Symp.Proc.296, 183–186(1993).

[15] White, C.T., Robertson,D.H., Swanson,D.R., andElert, M.L., in Shock Compressionof CondensedMatter–1999, editedby M.D. Furnishet al., AIPConferenceProceedings505,New York, 2000,pp.377–380.

[16] Barrett, J.J.C.,Robertson,D.H., Elert, M.L., andWhite, C.T., in Shock Compressionof CondensedMatter–1997, edited by S.C. Schmidt et al., AIPConferenceProceedings429,New York, 1998,pp.329–331.

[17] Stuart, S.J., Tutein, A.B., and Harrison, J.A., J.Chem.Phys.112, 6472–6486(2000); Elert, M.L.,Swanson,D.R., and White, C.T., in Shock Com-pression of CondensedMatter–1999, edited byM.D. Furnishet al., AIP ConferenceProceedings505,New York, 2000,pp.283–286.

[18] Strachan,A., Cagin, T., andGoddard,W.A., Phys.Rev. B 63, 060103(R)(2001).

[19] For instance,seeBalokhonov, R.R.,Makarov, P.V.,Romanova,V.A., andSmolin,I.Y., Comput.Mater.Sci. 16, 355–361(1999);Yano,K., andHorie, Y.,Phys.Rev. B 59, 13672–13680(1999).

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