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Volume105,Number1,January–February2000 Journal of Research of the National Institute of Standards and Technology [J.Res.Natl.Inst.Stand.Technol.105,81(2000)] Study of Interatomic Potentials in ZnS— Crystal-GRID Experiments Versus Ab Initio Calculations Volume 105 Number 1 January–February 2000 Timo Koch Crystal-GRIDmeasurementshavebeenper- Keywords: atomiccollisions;Crystal- formedwithZnSsinglecrystals.Forthe GRID;gammarayspectroscopy;inter- Forschungszentrum Rossendorf, firsttime,anasymmetricCrystal-GRIDline atomicpotentials;MolecularDynamics D-01314 Dresden, Germany shapecouldbeobserved.Theprelimi- simulations;nuclearlifetimes;ZnS. and narydataevaluationindicatesthatthere- portedlifetimeofthe3221keVlevelin Institut Laue-Langevin, F-38000 33Sistooshort.Avalueofabout60fshas Accepted: July22,1999 Grenoble, France beenfound.Duetothis“long”lifetime thelineshapeismuchlessstructuredthan Karl-Heinz Heinig calculatedwiththereportedlifetime. Availableonline: http://www.nist.gov/jres Forschungszentrum Rossendorf, D-01314 Dresden, Germany Michael Jentschel Institut Laue-Langevin, F-38000 Grenoble, France and Hans G. Bo¨rner Institut Laue-Langevin, F-38000 Grenoble, France 1. Introduction During the last decade the Gamma Ray Induced GRID”, should facilitate the study of interatomic solid Doppler broadening (GRID) technique has been opti- statepotentials,lifetimesofnuclearstates,andimpurity mised at the Institut Laue-Langevin (ILL). It has been locationsinthelattice.Inrecentworks[3,4,5]thegen- successfully applied to lifetime measurements. A de- eral applicability of the new method to the study of scription of the method can be found in Ref. [1]. interatomic potentials has been proven. Theuseofsingle-crystallinesamplesforGRIDexper- In this paper a preliminary report on measurements imentswasproposedduringthefirstGRIDworkshopin withZnSsinglecrystalswillbepresented.Theseexper- 1992 [2]. This special application, called “Crystal- imentsaimedtoobserveforthefirsttimeatheoretically 81 Volume105,Number1,January–February2000 Journal of Research of the National Institute of Standards and Technology predictedasymmetry[2]oftheDopplerbroadenedline it represents a sensitive indicator for the interatomic shapeforthe(cid:1)111(cid:2)crystaldirectionalignedtothespec- potential. trometer axis. It is expected that such an asymmetry Crystal-GRIDmeasurementscanbeperformedatthe allows the determination of interatomic solid state po- high-fluxneutronreactoroftheInstitutLaue-Langevin tentials and nuclear lifetimes to a higher precision than inGrenoble.Thecrystalstobeinvestigatedareplacedin with symmetric line shapes. adistanceof55cmfromthereactorcoreinatangential beam tube, where they are permanently irradiated by thermal neutrons (≈5(cid:2)1014 neutrons/cm2s). In gen- 2. The Crystal-GRID Technique eral, three oriented crystals of size 17 mm(cid:2)20 mm(cid:2)2mmareusedforthemeasurements.Twohigh- In a thermal neutron capture reaction the binding resolution gamma spectrometers, GAMS 4 and GAMS energyoftheneutronisdepositedinthenucleusandthe 5, are placed on either side of the beam tube at a dis- deexcitation takes place via a (cid:1)-cascade. The emission tance of 13 m and 17 m of the samples, respectively. of a first, primary photon (cid:1) entails a recoil of the still Bothoperateindoubleflatcrystalgeometry,i.e.energy 1 excitednucleusduetotheconservationofmomentump: resolution is gained by successive Bragg reflection on two almost perfect single crystals. p=mv =E /c, (1) 0 (cid:1)1 where m is the mass and v the initial velocity of the 3. RequirementsofCrystalsToBeStudied 0 recoilingnucleus,E theenergyoftheprimaryphoton (cid:1) 1 and c the velocity of light. As the energy of the first Theoretically, Crystal-GRID studies can be per- photonisoftheorderofseveralMeV,theinitialvelocity formed with a large number of materials, however the v of the recoiling atom lies in between 10–5 c and sensitivity of the Doppler-broadened line shapes to the 0 2(cid:2)10–4 c, corresponding to an initial kinetic energy atomicinteractiondependsonanumberofcriteria.First E ofapproximately100eVto1000eV.Thedirection ofall,thematerialshouldcontainanisotope,whichhas kin,0 oftheinitialrecoilisarbitrary.Thefurthermotionofthe a simple (cid:1) cascade with a mostly primarily fed short recoiling nucleus is defined by the interatomic forces, living(5fsto40fs)level.Theprimaryfeedingguaran- i.e., by the interatomic potential in the solid. tees an almost monoenergetic recoil energy, the short At the time t' a second photon (cid:1) is emitted and lifetimetherestrictiontoafewcollisionprocesses.Fur- 2 observedbythespectrometerifemittedalongthedirec- ther, the coordination number of the material itself tionofobservation.Ifthenucleus[velocityv(t)]hasnot shouldbeaslowaspossible.Inthiscasetheanisotropy yet come to rest, the (cid:1) energy is Doppler shifted by of the recoil motion and therefore the fine structure in the Crystal-GRID line shape is strongly pronounced. v(t')(cid:4)n Inanexperimentanumberofadditionalrequirements (cid:3)E =E0 , (2) (cid:1)2 (cid:1)2 c have to be met: Currently, the intensity requirement is themostlimiting.Forthatreasonsufficientlybigsingle whereE0 istheunshiftedenergyofthesecondphoton crystals are needed. The typical size used up to now is (cid:1) 2 andntheunitvectorinthedirectionofobservation.Due three pieces 17 mm(cid:2)20 mm(cid:2)2 mm. As soon as to the total number of Doppler shifted photons a GAMS5isoperationalinbent-crystalmode,thinsingle- Dopplerbroadenedphotonenergyspectrumisobtained. crystallinefilmsshouldalsobeusable.Further,themea- The motion of the recoiling atoms within a single sured intensity depends on a number of quantities such crystal is highly anisotropic. For example, the slowing as the (cid:1) capture cross section, the absolute intensity of down in the direction of the nearest neighbour the (cid:1) transition, and the response function of the spec- (“blocking”) is more efficient than in the direction be- trometer, which itself depends on the (cid:1) energy as well tween two nearest neighbours (“channeling”). There- asthethicknessandthematerialofthecrystalsusedin fore,theisotropicdistributionofvelocitiesjustafterthe the spectrometer. According to the requirement of a recoil becomes anisotropic as soon as the interaction simple (cid:1)-cascade with short lived levels, light nuclei with nearest neighbours becomes non-negligible. In a would be preferential. However these isotopes do often powder target this anisotropy is averaged out by the have a very small neutron capture cross section. This arbitrary alignment of the micro-crystals. However, in limits currently the number of candidates for Crystal- thecaseofasinglecrystalthisanisotropyexistsmacro- GRID experiments to isotopes such as 36Cl, 49Ti, 56Fe, scopically and leads to a fine structure in the Doppler 59Ni,52Cr,and33S.Thereforeimprovementsofthespec- broadenedlineshape.Asthefinestructureiscausedby trometerefficiencyareurgentlyneeded.Afirststepwill theinteractionoftherecoilingatomwithitsneighbours be done with GAMS 5. An efficiency improved by a 82 Volume105,Number1,January–February2000 Journal of Research of the National Institute of Standards and Technology factor of 100 would be needed, in order to be able to (RMD) and is sufficient for Crystal-GRID simulations investigate alot of materials that are of great interest in [3]. solidstatephysics,forexample,anumberofimportant For ZnS 1400 trajectories r(t) with velocities v(t) i i semiconductors. havebeensimulatedwithanRMDprogram.Forbetter Becausethecrystaltemperaturecanreach1200Kin statistics the symmetry operations of the appropriate thereactor,thecrystalstructureneedstobestableupto pointgroupcanbeappliedtothetrajectories.Inorderto this temperature region. Furthermore reactor safety re- compare simulation and experiment the set of trajecto- quirements must be considered ((cid:5)-activity, no melting riesneedstobetransformedtoaprobabilitydistribution or evaporation of material, etc.). of velocities or energies. In an actual measurement the Oncethesebasicrequirementsarefulfilled,theoreti- directionofobservationisfixed.AsseeninEq.(2),the calcalculationscanbeperformed(seeSec.4).Ifaline Dopplershiftonlydependsontheprojectionv =v(cid:4)nof (cid:3) shape is very structured or not, depends mainly on the the velocity on the direction of observation. lifetimeandthecrystallattice.Shortlifetimesandopen For a given n the velocity projection distribution structures lead to the most pronounced line shapes. P(v,t) dv dt can be deduced by counting the trajecto- (cid:3) (cid:3) ries having a velocity projection v(t)(cid:4)n in the range i v...v +dv duringthetimeintervalt...t+dt.Anormal- (cid:3) (cid:3) (cid:3) 4. Theoretical Description isation of the distribution is not necessary, because the measurement does not yield absolute intensities. This Ananalyticalcalculationoftheoreticallineshapesis distribution is independent of the lifetime (cid:6)of the nu- only possible for simple assumptions on the slowing clearstate,becausethetrajectorieshavebeencalculated down process. Crystal-GRID line shapes can not be for a fixed period of time regardless of the second (cid:1) deducedwithsufficientaccuracyinthatway.Wehaveto decay. use computer simulations instead. As the recoil veloc- ThedistributionP(v)dv ofvelocityprojectionsv at (cid:3) (cid:3) (cid:3) itiesoftheatomsaremuchbelowtypicalelectronveloc- thetimeofthesecond(cid:1)decaycanthenbecalculatedfor ities(≈7(cid:2)10–3c),electronicexcitationsarenottaken a given lifetime (cid:6)by multiplying the radioactive decay into account. This allows consideration of the recoil law: motion within classical mechanics. The most exact (cid:4) (cid:5) (cid:6) computersimulationapproachwithinclassicalmechan- 5(cid:6) t' P(v) dv = exp (cid:7) P(v,t') dt' (3) icsaremoleculardynamics(MD)calculations.Inthese (cid:3) (cid:3) (cid:6) (cid:3) 0 calculations the motion of N atoms within a finite volume V is calculated assuming certain initial and Theintegraliscalculatedupto5(cid:6),where99.3%ofthe boundary conditions and the knowledge of the atomic secondaryphotonshavebeenemitted.UsingEq.(2)this interactionofallNatoms.Thetrajectoriesoftheparti- canbetransformedtotheprobabilitydistributionP(E ) (cid:1) 2 cles can be calculated by simultaneously integrating dE oftheDopplershiftedenergy,thesocalledCrystal- (cid:1) 2 Newton’s equations of motion of all N particles. In the GRID line shape caseofrecoilsimulationsforCrystal-GRIDexperiments (cid:5) (cid:6) theinitialconditionsaredefinedbythecrystalstructure c(cid:3)E ofthetargets,whereallatomsmoveataninitialvelocity P(E(cid:1)2) dE(cid:1)2(cid:7)P v(cid:3)= E(cid:1)0(cid:1)2 dE(cid:1)2 (4) 2 following a Maxwell distribution corresponding to the temperature of the crystal. The simulation volume is a Thislineshapewouldbemeasuredwithaspectrom- cubic cell, the size of which is adjusted such that the eteryieldinga(cid:8)-likeresponsefunction.Inthecaseofan recoiling atoms do not reach the boundaries within the ideal double flat crystal spectrometer the instrumental time of simulation. Periodic boundary conditions are response function can be calculated from diffraction used.Startingwithaninitialrecoil,possibletrajectories theory. Due to small imperfections of the used spec- can be simulated. The method is exact within classical trometer crystals an additional broadening has to be mechanics. Hence the result of MD simulations is as taken into account by folding the ideal instrument re- goodastheinteratomicpotential.However,MDsimula- sponse function with a Gaussian of width (cid:9) , the so EW tionsareverytimeconsuming.Forourpurposeonlythe called “excess width”. The later can be determined ex- interaction of the recoiling nucleus with all its neigh- perimentally. When folding P(E ) with the obtained (cid:1) 2 bouring nuclei needs to be known. The interaction of realisticresponsefunction,thelineshapetobefittedto two nuclei far away from the recoiling nucleus has no theexperimentaldatacanbecalculated(fordetailssee appreciable influence and can be neglected. This ap- [1]). proximation is called “restricted molecular dynamics” 83 Volume105,Number1,January–February2000 Journal of Research of the National Institute of Standards and Technology As can be seen, the measured Crystal-GRID line of the crystals. Crystals having an inversion symmetry shapesaredirectlycorrelatedtotheslowingdownpro- yieldsymmetriclineshapesforallorientations,because cess in the crystal. For a given crystal structure and thenucleusslowsdowninthesamewayforanemission alignment of the crystal, the calculated line shape de- withvelocity+v or(cid:7)v.TheGRIDmethodisinsensi- 0 0 pends only on the classical potential used in the RMD tive to rotations of the sample around the direction of calculationandonthelevellifetime.Therefore,bycom- observation. Therefore a symmetric line shape is also paringsimulationandmeasurement,theinteratomicpo- producedifthelatticeonlyhasarotation-inversionsym- tential may be improved in the energy region of 10 eV metry around this axis. to 1000 eV. Thezincblendestructurehasnoinversionsymmetry. However a rotation-inversion symmetry exists for some axes,e.g.,forthe(cid:1)100(cid:2)andthe(cid:1)110(cid:2)directions,butnot 5. The Zincblende Structure for the (cid:1)111(cid:2) direction. Consequently the expected line shape in the latter case is asymmetric. Undernormalconditions,Zincsulfide(ZnS)hasthe zincblendestructure(pointgroupF43m).Thetwocon- stituentsarefoundontwoface-centredcubicsublattices 6. Experiments respectively,displacedwithrespecttoeachotherbyone forth of the diagonal of the cubic unit cell. In GRID DuringtwomeasuringperiodsweexaminedtheZnS experimentsthedirectionofobservation,i.e.,thedirec- crystalswiththe(cid:1)111(cid:2)and(cid:1)110(cid:2)directionsrespectively tionoftheaxisbetweenthesampleandthespectrome- oriented towards the spectrometer. The measurements ter, is well defined. usedthe2380keVtransitioninthe33Snucleus,depop- InpreviousCrystal-GRIDmeasurementstheDoppler ulatingthe3221keVlevel.Thislevelismostlydirectly broadeningofthelineshapewasalwayssymmetricwith fed, 91% of the populating nuclei decay directly from respect to the unshifted photon energy. This symmetry the capture state (see Fig. 1). Two two-step cascades wasduetotheexistinginversionsymmetryinrealspace furthercontributetothefeeding[6].Theirinfluenceis Fig.1. Partiallevelschemeof33S[6].ForeachlevelofenergyE thereportedlifetime level (cid:6)isgiven[7].ForthetransitionsthephotonenergyE(cid:1),thecorrespondinginitialrecoil velocityv oftheSnucleus,andtheabsoluteintensityofthetransition(%meansper100 0 neutrons)aregiven. 84 Volume105,Number1,January–February2000 Journal of Research of the National Institute of Standards and Technology small but taken into account in the RMD simulations. Duetothelonglifetimethelineshapesaremuchless Theenergyofthefirstphotonis5421keV,correspond- structured than predicted by the computer simulations ingtoaninitialrecoilenergyoftheexcitedSnucleusof performedbeforetheexperimentwiththereportedlife- 478eV,i.e.,arecoilvelocityof1.76(cid:4)10–4cor0.529Å/fs. time.Thus,theinformationwhichcanbegainedforthe Thenuclearstatehasareportedlifetimeof(40(cid:10)12)fs interatomic potentials will be reduced. [7]. The double crystal spectrometer was used with one crystal in first and the other in second reflection order. 7. Ab Initio Results For each orientation of the crystal 35 scans have been measured.Everyscanconsistedof90datapoints,each Our second, purely theoretical approach to ZnS po- of them being measured for 320 s. Thereby a peak tentialsconsistsofquantummechanical—socalledab intensityofabout40countsperscancouldbeattained. initio—calculations.Thesecalculationsallowtoobtain Thedataevaluationisstillinprogress.Uptonowwe the total energy of an arbitrary configuration of typi- obtained two preliminary results. On the one hand, for cally64atomswithoutrequiringanyinformationabout thefirsttime,thepredictedasymmetryofthelineshape classical interatomic potentials. By calculating the en- in the (cid:1)111(cid:2) direction could be confirmed (see Fig. 2). ergyofaseriesofatomicconfigurations,aninteratomic Ontheotherhandthelifetimeofthenuclearstateunder potential can be developed theoretically. investigation was found to be much longer than the re- InafirststeponeoftheSatomswithinasimulation portedvalue[7].Consideringtwodifferentinteratomic cellof64atomswasdisplacedalongthe(cid:1)111(cid:2)direction potentials (ZBL [8], KrC [9]) in our theoretical model towardsitsnearestneighbour.Fordifferentdistancesthe and fitting the results of the two crystal orientations total energy has been calculated. The difference to the independently,weobtainalifetimearound60fsascan totalenergyoftheideallatticegivesafirstapproachto beseeninFig.3.Thefittedlifetimesforthetwodiffer- anabinitiopotential(seeFig.4).Eventhoughnotonly ent directions are not identical. This indicates that the the Zn—S interaction between two particles is consid- interatomicpotentialsusedinthesimulationdonotwell ered, the contribution of other atom pairs should be describe the interaction. Consequently a new potential comparatively small. will be developed. Fig.2. Doppler-broadenedlineshapeofthe2380keVtransitionin33Sforthe(cid:1)111(cid:2)direction.Thelinerepresents thefittedtheoreticallineshapeobtainedwithRMDsimulationsusingtheZBLpotentialandalevellifetimeof 65fs.Theasymmetrycanbeseeninthewingsofthecurvearound120eVandinthesmallpeaksbetween200 eVand300eV. 85 Volume105,Number1,January–February2000 Journal of Research of the National Institute of Standards and Technology RMDcalculationshavebeenperformedwiththisde- duced ab initio potential. As can be seen in Fig. 3 the obtainedlifetimeisabout70fs.Theminimum(cid:11)2value of the fit, however, is higher, i.e., worse, than for the screenedCoulombpotentials.Thisindicatesthattheab initiopotentialdoesnotwelldescribetheslowingdown inthecrystal.Thismaybeduetosomecrucialapprox- imations within the ab initio calculations, e.g., with respect to the exchange energy, that have to be made. Furtherapproacheswillbemadeinordertoimprovethe potential. 8. Conclusion Crystal-GRID measurements have been performed withZnSsinglecrystals.Forthefirsttime,thetheoret- icallypredictedasymmetriclineshapecouldbeverified experimentally. At the actual state of data evaluation it seemstobeclearthatthelifetimeofthe3221keVlevel in33Sisabout60fs.Thisvalueiswellabovetheprevi- ouslyreportedvalue.Thereforethelineshapesareless structured than predicted. Duetothereducedinformationthatcanbeextracted fromthelineshapes,athirdZnSmeasurementhasbeen Fig. 3. Determination of the lifetime of the 3221 keV level in 33S. proposed. It should be performed in the (cid:1)100(cid:2) orienta- Computer simulations have been performed for different screened tion.Withtheadditionalresultsitshouldbepossibleto Coulombpotentials(KrC,ZBL).Foreachcrystalorientationtheoret- validate interatomic potentials even though, due to the icallineshapesfordifferentlifetimescanbefittedtotheexperimental data. The calculated (cid:11)2 values are plotted against the lifetime. The “long”lifetime,thetransitionisnotoptimalforCrystal- minimaofthecurvesgivetheresultinglifetimes.Theyvaryaround60 GRID studies. fs.Usingthepreliminarypotentialobtainedfromabinitiocalcula- tions, a lifetime around 70 fs would be obtained. However the (cid:11)2 values are worse than for the screened Coulomb potentials. The ab initioresultsneedtobeevaluatedmorecarefully. Fig. 4. The energy of a 64-atom lattice with one S atom displaced along the (cid:1)111(cid:2) directiontowardsthenearestneighbourhasbeenabinitiocalculated.Thedifferenceto theenergyoftheideallatticeisplottedversustheZn—Sdistance.Thenearestneighbour distanceintheideallatticeis2.33Å.Theobtainedrelationcanbeseenasanabinitio potentialandiscomparedtotheclassicalscreenedCoulombpotentialsusedinthiswork (KrC,ZBL). 86 Volume105,Number1,January–February2000 Journal of Research of the National Institute of Standards and Technology Thefirstabinitioresultsdonotyetyieldsufficiently goodresults.Neverthelessthesimultaneousexperimen- talandtheoreticalapproachesallowadirectcomparison of the results, leading to an increased reliability of the obtained potentials. 9. References [1] H.G.Bo¨rnerandJ.Jolie,Sub-picosecondlifetimemeasurements by gamma ray induced Doppler broadening, J. Phys. G: Nucl. Part.Phys.19,217–248(1993). [2] K. H. Heinig and D. Janssen, The fine structure of Doppler profilesinmoleculardynamicschannellingcalculation,ILLIn- ternalReport92HGB16T(1992). [3] M.Jentschel,Crystal-GRID:EineneuenukleareSondezurUn- tersuchung atomarer Bewegung im Festko¨rper. PhD thesis, TU Dresden(1997). [4] M. Jentschel, K. H. Heinig, H. G. Bo¨rner, J. Jolie, and E. G. Kessler, Atomic collision cascades studied with the Crystal- GRIDmethod,Nucl.Ins.Meth.B115,446–451(1996). [5] M.Jentschel,H.G.Bo¨rner,andC.Doll,Newapplicationsofthe GRID-techniqueinnuclearandsolidstatephysics,inProceed- ingsofthe9thInternationalSymposiumonCaptureGamma-Ray Spectroscopy and related topics (CGS 9, Budapest, Hungary, 8–12October1996),G.L.Molna´r,T.Belgya,andZ.Re´vay,eds., Springer(1996)pp.755–768. [6] S.Raman,R.F.Carlton,J.C.Wells,E.T.Jurney,andJ.E.Lynn, Thermalneutroncapturegammaraysfromsulfurisotopes:Ex- perimentandtheory,Phys.Rev.C32,18–69(1985). [7] R. B. Firestone, Table of Isotopes. New York, Wiley-Inter- science,8thed.(1996). [8] J.F.Ziegler,J.P.Biersack,andU.Littmark,TheStoppingand RangeofIonsinSolids,Vol.1ofTheStoppingandRangesof IonsinMatter.NewYork,PergamonPress(1985). [9] W.D.Wilson,L.G.Haggmark,andJ.P.Biersack,Calculations of nuclear stopping, ranges, and straggling in the low-energy region,Phys.Rev.B15,2458–2468(1977). Abouttheauthors: TimoHauschild(TimoKochatthe time of the meeting) is a thesis student at ILL/FZ Rossendorfwithspecialinterestsininter-atomicpotentials. Dr. Karl-Heinz Heinig is a Staff Scientist at FZ Rossendorf, Institute of Ion Beam Physics and Materi- alsResearch.Hisspecialinterestsincludemodelingof ionimplantationprocessesandnanoclusterformation. Dr.MichaelJentschelisaPostDoctoralfellowatILL. His special interests are high resolution gamma spectroscopy and atomic collision processes. Dr. Hans Bo¨rner is the Group Leader for Nuclear and Particle PhysicsatILLwithspecialinterestsinhighresolution gamma spectroscopy, nuclear structure at low excita- tion energies, and fundamental physics with neutrons. 87