Mas A~Iro.K~Noo Ka^No,， T~Da?Tadao Lwataiwata合 Eiichieiich I Kurakuramot皿oto-- O ，, Minoruminor U Takenaka--Takenaka Andan D Sadaesada E Yayamaguch皿aguchi I

PrProcaadng田崎dinga s ofof 世帽民削白川町田信副首..itw Fourth Intamtional 5"Symposiu暗闘..... m 。oan ADVANCEDADVANCE D 鈍NUCLEAUCLEAII R ENERGYENERG Y RESTRESEARC由CHH ROLES ASDAXO DIRECTIO.... DIRECTIOX OF 且MATERIALrA TE RlA ι SCISCIEXCE E. ... CE 1: IX、.. .w' SVCLEARc. ιEAR TECHXOLOGYTECH I'> OLOG1'

POSITRONPOSITRO N ANNIBIANNIHILATIOL& TION N STUDYSTUD Y OFO P GlUlGRAPHITEPIUTE ,， GGLASSLIlS SYY CaRBONCARBO N JUQ)AN D C60/C70Cfi0 /C7o FULLDEFULLEREN蜘EE

阿Masayukasa 抑制i HHasegawa管記~gawa,， MasahirMas_a~iro.K~noo Ka^no,，_ T~da?Tadao lwataIwata合 EiichiEiich i KuraKuramot皿oto-- o ，, MinoruMinor u Takenaka--Takenaka andan d SadaeSada e YaYamaguch皿aguchi i

InstituteInstitut e forfo r MaterialsMaterial s Research ,， TohokuTohok u University ,， SendaiSenda i 980 ,， JapanJapa n _. * _. PhonePhon e 022-227-6200022-227-620 0 eext.2454.認 t.2454 ， FaxFa x 022-215-2061022-215-206 1 PhysicsPhysic s DeDepartmentpartment ,， JapanJapa n AtomicAtoni c EnEnergergy y ResearchResearc h lnstituteInstitute,， TOkaiTokai,， IbarakiIbarak i 319319-11・11 ,， JapanJapa n 合会 PhonePhon e 0292-82-5470 ,， FaxFa x 0292-820292-82-529・5297 7 * ResearchResearc h InstituteInstitut e forfo r App1iedApplie d MeMechanicschanics ,， Kyusyu Kyusy u UniversityUniversity,， Kasuga ,， FukuokaFukuok a 816 ,， JapanJapa n PhonePhon e 092-573092-573-961・9611 1 ext.ext . 566 ,， FaxFa x 092-582092-582-420・4201 1

且ABSTRACTBSTR 且.CT: : ACARACA R ( AnAngulagular r CoCorrelatior. relation n ofo f AnnihilationAnnihilatio n Radiation)Radiation ) andan d positronpositro n Keyword*K~yword.:: PositronPositro n AnnAnnihilationihilation ,， lifetimelifetim e measurementsmeasurement s havehav e beenbeen 皿madade e on,， Graphite, Glassy Carbon, C , Fullerene, Graphite ， G1assy Carbon ， C 6600' Fu11erene ， HOPGHOP G (High1y(Highl y OrientedOriente d PyrPyrolytio1ytic c Graph-Graph Void ,， Pore ,， VoidVoi d Trapping~-SoccerTrapping, Soccer 8a11Bal l ite) ,， isotropicisotropi c fine-grainedfine-graine d graphite ,， VacancyVacanc y glassyglass y carbonscarbon s andan d C60/C70C50/C7 Q P?wder._powder . HOPGHOP G showedshowe d markedmarke d bimodalitybimodalit y a10ngalon g theth e c-c- axisaxi s andan d anisotropyanisotrop y ini n ACARACA R momentummomentu m 1.1.INTRODUCTIOlM'l'R ODUCT l: ONN distribution ,， whichwhic h stemste m fromfro m character-character isticisti c annihi1ationannihilatio n betweenbetwee n "inter1ayer""interlayer " GraphiteGraphit e hasha s beenbee n emp10yedemploye d asa s theth e posipositron trons s andan d 1[T-electron -e1ectrons s ini n graphigraphite te. . 圃moderatooderator r andan d structura1structura l cocomponent岨lponents s ofo f ACARACA R curvescurve s ofo f theth e isotropicisotropi c graphitegraphit e fissionfissio n reactors ,， suchsuc h asa s gas-cooledgas-coole d andan d glassyglass y carbonscarbon s arear e eveneve n narrowernarrowe r one ,， becausebecaus e ofo f 10wlo w neutronneutro n crosscros s sec-sec thantha n tDattf^a t ofo f HOPGHOP G perpendicu1arperpendicula r tot o theth e tion ,， chemica1chemica l stabi1itystabilit y andan d highhig h melt-melt c-axis.c-axis . PositronPositro n 1ifetimeslifetime s ofo f 42042 0 and and ingin g point.point . FurtherFurthe r recentlyrecentl y carboncarbo n 39039 0 - 48048 0 psec ,， muchmuc h longerlonge r thantha n thattha t ofo f materia1smaterials,， forfo r exampleexampl e graphitegraphit e andan d 22122 1 psecpse c ini n HOPG ,， werewer e observedobserve d forfo r theth e cabon-carboncabon-carbo n composites ,， havehav beco e becom圃e oneon e isotropicisotropi c graphitegraphit e andan d g1assyglass y carbonscarbon s ofo f theth e keyke y materialsmaterial s ini n theth e fie1dfiel d ofo f respective1yrespectively,， which whic h arear e duedu e tot o positronpositro n plasma-wa11plasma-wal l lnteractioninteractio n ini n fusionfusio n reac-reac trappingtrappin g ini n structura1structura l voidsvoid s ini n them.them . torstor s becausebecaus e ofo f itsit s 10wlo w atomicatomi number c number PositroPositron n 1ifetimelifetim e anand d ACAACAR R widtwidth h (FWHM)(FWHM ) anand d high-temperaturehigh-temperatur e characteristics.characteristics . canca n beb e we11wel l correlatedcorrelate d tot o voidvoi d sizessize s ForFo r fusionfusio n reactorreacto r app1icationapplication,， absorp-absorp (1.7(1. 7 tot o 5.05. 0 nm)nm ) oro f g1assyglass y carbonscarbon s whichwhic h tiontio n andan d desorptiondesorptio n ofo f hydrogenhydroge n isotopeisotop e havenav e beenbee n determineddetermine d byb y sma11smal l ang1eangl e atomsatom s arear e veryver y iimportan田lportant t andan d sensensitivel!l!:t- tive1y y neutronneutro n (SAN)(SAN ) scatteringscatterin g measuremeasur e .-唖 •intsnts. . affectedaffecte d byb y structuralstructura l voids..void s J' andan d ACARACA R ..:urves curves andan d posipositro tron n 1ifetilifetiml' .e e ofo f radiation-inducedradiation-induce d vacanciesvacancie s andan d voidsvoids. . C60/C70CCQ/C7 0 powderpowde r agreag~ee we11wel l withwit h thosethos e ofo f Consequent1yConsequentl y atomisticatomisti c informationinformatio n andan d gIassy-carbons.glass y carbons. ThisThi s showsshow s thattha t positronpositro n characterizationcharacterizatio n ofo f structuralstructura l voidsvoid s andan d wavewav e functionsfunction s extend ,， asa s ini n theth e voidsvoid s radiation-inducedradiation-induce d defectsdefect s isi s veryver y necesneces- ofo f glassyglass y carbons ,， muchmuc h widerwide r thantha n openope n sary.sary . PositronPositro n annihi1ationannihilatio n hasha s beenbee n spacesspace s ofo f theth e octahedraloctahedra l intersticesinterstice s ofo f successivelysuccessivel y useduse d forfo r studiesstudie s ofo f vacan-vacan theth e face-centeredface-centere d cubiccubi c (FCC)(FCC ) structurestructur e ciescie s andan d voidsvoid s ini n meta1smetal s 【[1]1]. . ForFo r

ofo f C60C 60 crysta1crysta l andan d stro~g1ystrongly suggest~suggests carboncarbo n materia1smaterial s theth e usefu1nessusefulnes s ofo f thisthi s positionpositro n trappingtrappin g ini n thethe 町"soccesoccer r ballba11" " techniquetechniqu e hasha s beenbee n demonstrateddemonstrate d byb y vacancy.vacancy . Possib1ePossibl positron e positron statesstate s ini n theth e severa1severa l workersworker s [2[2-6]・6]. . carboncarbo n materialsmaterial s arear e discusseddiscusse d withwit h a simp1esimpl e modelmode l ofo f voidvoi d volume-trapping.volume-trapping . *) ' sometimessometime s ca1ladcal l 3d asa s cavitiescavitie s oro r Pre1iminaryPreliminar y resu1tsresult s ono n neutronneutro n irradia-irradia pores.pores . tiontio n damagedamag e ini n HOPGHOP G arear e a1soals o presented.presented .

- 119-119 • --，

RecenRecent t excitinexciting g reporreport t oof f methomethod d merit国 ents s oon n HOPG,， glassg1assy y carboncarbons s anand d

fofor r preparinpreparing g larglarge e quantitiequantities s oof f ththe e CCQ/C~~0/C707Q _powderpowde r wilwi11 l bbee compareco 園 ipared d anand d

"socce"soccer r ballball" " CC60 60 moleculemolecules s [7[7] ] anand d ththe e discussediscussed d witwith h a simplsimple e void-trappingvoid-trappin g followinfollowing g discoverdiscovery y oof f superconductivitsUp'~rconductivityy modelmode1. .

iin n potassium-dopepotassium-doped d C民6nQ [8[&] ] havhave e raiseraised d greagreat t interesinterest t iin n ththe e structurstructure e anand d 2 2. . DPEXPERIMENTAEIUMEN'1' AL L propertieproperties s oof f thithis s allotropia11otropic c forform m oof f carbocarbon n [9,10][9 ，10]. . BecausBecause e oof f ththe e weaweak k FigurFigure e 1 showshows s crystacrysta1 l structuresstructure s intermoleculaintermo1ecu1ar r interaction,， ththe e solisolid d oof f diamondiamond d (a)(a )， , graphitgraphi te e (b )】 anand d ththe e C60 hahas s larg1arge e opeopen n spaces, fofor r example , (100(100) ) facface e oof f ththe e FCFCC C C - SampleSamples s useused d 6 ，， 60 ・ aat- t ththe e octahedraoctahedral l intersticeinterstices s wherwhere e i:L n thi悦1I s studstudy y arare e listelisted d iin n Tab.lTab.1. . A potassiupotassiurn m atomatorns s cacan n bbee accommodateaccornrnodated d iin n singlsingle e crystacrystal l platp1ate e oof f synthetisynthetic c diadia- itits s structurestructure. . ConsequentlConsequently y iit t iis s ververy y mon皿ond d witwith h (111(111) ) crystacrysta1 l facface e wawas s used.used . interestininteresting g tto o investigatinvestigate e positronpositro n HighlHighly y orienteoriented d pyrolytipyr01ytic c graphitegraphit e statestates s iin n soliso1id d CgC60 andQ and tto o comparcompare e thethern m (HOPG(HOPG) ) (2Y(ZYA A anand d ZYZYH H grade.， Unio Union n CarbideCarbid e witwith h thosthose e iin n graphitgraphite e anand d glassg1assy y ( Co.Co.) ) slabslabs s havhave e mosaimosaic c structurstructure e witwith h glass-likglass-like e ) carboncarbon. . ththe e well-orientewe11-oriented d c-axic-axis s bubut t witwith h randorandom m orientatioorientation n oof f ththe e crystallitecrysta11ites s iin n ththe e RecentlRecent1y positron y positron lifetimlifetime e measuremeasure- basabasal l planeplane. . ThThe e averagaverage e crysta11itecrystallit e mentments s havhave e beebeen n carriecarried d ouout t bby y severasevera1 l sizsize e alona10ng g ththe e a-axia-axis s iis s abouabout t 225μm5 a m groupgroups s [11-13](11-13] ,， includininc1uding g uus s [6][6]. . whilwhi1e e Turn7μ 皿 alona10ng g ththe e c-axic-axis s [3][3]. . H0PGHOPG- - FurtheFurther r theoreticatheoretica1 l calculationca1cu1ations s shoshow w ZYZYA A wawas s subjectesubjected d tto o fasfast t neutroneutrop_ n irrairra= ; 18 4 positropositron n statestates s anand d lifetime1ifetimes_in_C60 s in C60 anand d diatiodiation n witwith h fluencf1uence e oof-8.3-~-iõI8f 8.3 x 10 n/car~/C;2 potassium-dopepotassium-doped d fullerenefu11erenes s [14,15][14 ， 15]~-. A11Al l aat t abouabout t 150°150 ・C iin n ththe e JMTJMTR R reactorreactor. . TheTh e thesthese e experimentae 翠perimenta1 l studiestudies s havhave e reportedreporte d blochl~_ofk of HOPG-ZYHO fG -ZYH H 町wa'as s irradiateirradiated d tto o 1.41. 4 a positronpositro n 1ifetimelifetim e ofo f aboutabou t 40040 0 psecpse c ini n x 1010~u20 n/cmn/cm~2 ata t aboutabou t 6060 ・"CC inin 位田the JRR-2JRR- 2 C powders.powders . ThisThi s va1uevalu e isi s ini n ~oodgood reactor. 1sotropic fine-grained nuc1ear 606 0 reactor. Isotropic fine-grained nuclear agreemenagreernent t witwith h calculateca1cu1ated d onone e frofrom m graphitgraphite e ,， AXF-50AXF ・5Q1 1 (POC(POCO O GraphitGraph1te e 1nc.)Inc.),， theoreticatheoretica1 l modemode1 l iin n whicwhich h positropositron n wavewav e graphitizegraphitized d aat t 2502500 0 ・"CC ,， hasha s ana n averageaverag e functiofunction n iis s highlhigh1y y concentrateconcentrated d iin n ana n graigrain n sizsize e oof f abouabout t 4μrn4a m anand d voivoid d radiiradi i octahedraoctahedra1 l intersticeinterstices s oof f ththe e FCC FCC ranginrang1ng g frofrom m 0 tto o 0.4am0.4μm. . ThThe e grainsgrain s structurestructure. . ThThe e lifetim1ifetirne e oof f 40400 0 pseps 邑c iis s consiscons1st t リ'if crystallitecrysta111tes s ( abouabout t 40nm40n m mucmuch h longe10nger r thathan n thathat t iin n graphitgraphite e bulkbul k botboth h alonalong g ththe e a-axia-axis s anand d c-axic-axis s [8[8] ] ) ( aboutabou t 220psec220pse c )) oro r vacancyvacanc y (about(abou t 24524 5 pluplus s voidvoids among s among thethem m aas s schematicallyschematicall y psepsec c [4])[4J) ，, bubut t ververy y closc10se e tto o thathat t showshown n iin n FigFig. . 1 (e)[16](e)[16). . GlassG1assy carbon y carbon observeobserved d iin n glassglassy y carbocarbon n anand d irradiatedirradiate d iis s a kinkind d oof f non-graphitizablnon-graphitizable e harhard d graphite[3-6]graphite[3-6J. . TheThen n iit t is is ververy y necessarynecessar y carboncarbons s [17[17) ] anand hasd has a 皿microstructuricrostructure e iin n tot o rnakemake systemsystemati喧 tic c studystud y ono n carboncarbo n whichwhic h voidsvoid s arear e surroundsurrounde邑d byb y carboncarbo n

rnaterials.materials , suchsuc h asa s C60'C 6Q, graphitegraphit e andan d 1ayerslayer s ofo f graphitegraphit e oro r turbosraticturbosrati c stack-stack g1assyglass y carbons.carbons . 1nI n thisthi s paperpape r resu1tsresult s 1ngin g withwit h thicknessthicknes s 1essles s thantha n aboutabou t 101 0 ofo f ACARACA R andan d positronpositro n 1ifetimelifetim e measuremeasur e layerslayer s asa s depicteddepicte d 1ni n Fig.1(d)Fig.1(d) [19]【191. .

(a) (b)

ト 1.42nm --1 (d) (e) Fig.l.Fig.l . Crysta1Crysta l structuresstructure s ofo f (a)(a ) dia-dia mond ,， (h)(b ) graphitegraphit e andan d (c)(c ) theth e (100)(100 )

facefac e ofo f theth e FCCFC CιnC C60 unituni t ce11cell,， andan d Grain schematicschemati c representrepresentatio孟壬 ion n ofo fth th骨e micro-micro- structuresstructure s ofo f (d)(d ) isotropicisotropi c graphitegraphit e AXFAXF-5Q・5Q1 1 [16][16 ] andan d (e)(e ) glassyglass y carboncarbo n Crystallite [18].[18] .

120 -・圃 '9

Tab1eTabl e 1.1 . Specimens ,， theirthei r densities ,， ACARACA FWHM R FWHM widthswidth s andan d pos1tronpositro n lifetimes1ifetimes. .

SpecimenSpecime n DensityDensit y ACARACA FWHM R FWHM LifetimeLifetim e ReRemark田 arks s (g;αn3)(g/cm3 ) (mrad)(mrad ) (psec)(psec ) DiamondDiamon d 3.513.5 1 13.113. 1 107.1107. 1 HOPGHOP G 2.262.2 6 Unirrad.Unirrad . c//! 13.4 22221.1. 0 C 0.6700.67 0 runm n CJ/L cCJ/L Cj ./ z13.4: (ZYA)(ZYA ) 10.910. 9 a 0.2460.24 6 run皿n

Irrad.Irrad . C;;:c,,: 11.411. 4 283.1283. 1 8.38. 3 x 10181018n/cmn /cm 22 (ZYA)(ZYA ) ci':c i : 10.10.2 2 Irrad.Irrad . 1. 44 x x 1020n/cm210 20n/cm2 (ZYH)(ZYH ) C;/: : 9.9.1 1 363.9363. 9 I:l Ac/c/c c = 10.2 %告 C:// J. 8.58. 5 (96(96%告}) I:l Aa/a/a a = - 0.0.77%% IsotropicIsotropi c GraphiteGraphit e AXF-5Q1AXF-5Q 1 1.1.884 4 10.310. 3 38381.1. 0 G1assyGlass Carbon y Carbon GC-IQGC-1 0 1.1.449 9 10.310. 3 392.5392. 5 RgR g = 0.650.6 5 run皿n

GC-20GC-2 0 1.1.448 8 9.59. 5 480.7480. 7 RgR g = 1.1.229 9 nmn m

GC-30GC-3 0 1.1.445 5 9.39. 3 466.0466. 0 RgR g = 1.1.993 3 nmn m

1. 7* 】 Cc6060 ;C/c770 0 1.7*) 9.49. 4 416.7(300K)416.7(300K ) 405.6 (【 10K)10K)

*)* ) theoretica1theoretica l densitydensit y GlassG1assy y carboncarbons s witwith h differendifferent t heathea t 33. . RESULTSRESULTS 昆1mUNO DDISCUSSIOl: SCUSS l: ON N treatmenttreatmen t temperaturestemperature s (HTT)(HTT ) fromfro m TOKAITOKA I CARBONCARBO N Co.Co . werewer e examined:examined : GC-10 ,， GCGC-2・20 0 33-・1 DiaDiamon・ond andd and GraphiteGraphit e andan d GC-20GC-2 0 heat-treatedheat-treate d ata t 1300.C1300°C,， 2000 2000°・cC andan d 3000.C3000° C respective1y.respectively . 5ma11Smal ang1el angle FigureFigur e 2 showsshow s ACARACA R curvescurve s ofo f neutronneutro n scattscatterin邑 ring g measurementsmeasurement s havehav e diamond ,， unirrad1atedunirradiate d HOPG-ZYAHOPG-ZY A samplessample s revealed that these samples contain revea1ed that these samp1es contain forfo r Pz'p z, momenτUUlmomentum 邑examinedxamined ,， (a)(a ) para11elparalle l voidsvoid s ofo f near1ynearl y uniformunifor m sizesiz e withwit h radiiradi i tot o theth e c-axisc-axi s [PZPC][PZPC ] andan d (b)(b ) norma1norma l tot o ofo f gyrationgyratio n (Rg)(Rg ) givengive n ini n Tab.1Tab. l [19][19]. . theth e c-axisc-axi s [PZNC][PZNC ] asa s we11wel l asa s AXF-5Q1AXF-5Q1. . ForFo r fu11erenefulleren e samp1esample,， powderpowde r ofo f cC60;C7060 /'c70 AlthoughAlthoug h stat1sticsstatistic s forfo r diamonddiamon d 1si s poorpoo r (C : 90%) of 98% purity (MER Co.) (C60 60 90%) of 98 者 pur1ty (MER~~Co;í becausebecaus e ofo f itsit s veryver y sma11smal l size ,， theth e werewer e emp1oyed.employed . ACARACA R curvecurv e isi s clearlyclearl y foundfoun d tot obe be veryver y broad ,， whichwhic h isi s duedu e tot o smallsmal l latt1celattic e Long-s1itLong-sli t ACARACA R measurementsmeasurement s werewer e constantconstan t andan d hencehenc e 1argelarg e Bri110uinBrilloui n zonezone. . performedperforme d withwit h a usua1usua l machinemachin e havinghavin g a AsA s 1istedliste d ini n Tab.lTab. l positronpositro n lifet1melifetim e 1ni n geometrica1geometrica l r~resolutio害o1utionn ofo f 0.630.6 3 mradmra d diamonddiamon d 1si s veryver y short ,， beingbein g comparecompar e 64 (FWHM)(FWHM ) andan d u~CuCu sourcesources s ooff 11 CiCi withwit h typicaltypica l semiconductorssemiconductor s suchsuc h asa s Si5i. . strength.strength . LifetimeLifetim e measurementsmeasurement s werewer e ThisThi s isi s a1soals o duedu e tot o highhig h densitydensit y ofo f theth e accomp1ishedaccomplishe d usinuSing g a conventionaconventiona1 l appaappa- valencva1 月nce e electronselectron s ini n diamond.diamond . ACARACA R ratusratu s withwit h a timetim e res01utionresolutio n ofo f aboutabou t curvescurve s ofo f HOPG-ZYHHOPG-ZY H arear e ini n goodgoo d agreementagreemen t 17017 0 psecpse c (FWHM)(FWHM ) ，, much muc h higherhighe r resolutionresolutio n withwit h thosethos e ofo f HOPG-ZYHH0PG-ZY H andan d ththe邑n notno t thantha n 内主 thahat t ofo f theth e precedingprecedin g paperpape r [6][6] ,， shownshow n here.here . ForFo ther the unirradiatedunirradiate d statestat e and 22Na (20#Ci) source deposited on and L. ...Na (20μCi ) source deposi ted on theth e PZPCPZP C distributiondistributio n isi s bimodalbimoda l withwit h a tot o a thinthi n my1armyla r fi1m.film . MeasurementsMeasurement s arear e saddle point at p =0 and peaks around p carried out at room temperature other sadd1e point at Pz=O z and peaks around p~2 carried out at room temperature other- z 土±3 mrad ,， whereaswherea s bellbell-shape・shaped d forfo r wisewis e stated.stated . AfterAfte r source-backgroundsource-backgroun d PZNC.PZNC . TheTh e b1modalbimoda l distribut10ndistributio n 1si s duedu e tot o subtraction ,， lifetimelifetim e spectraspectr a werewer e high1yhighl y concentratedconcentrate d wavewav e functionfunctio n ofo f decomposeddecompose d intoint o oneon e oro r twotw o lifetimelifetim e component using a fitting program. positronpositro n withinwithi n a graphitegraphit e layerlaye r (inter(inter- - component using a fitting program. layerlaye r positronpositro n ) andan d itsit s consequentlyconsequentl y enhancedenhance d ann1hilationannihilatio n withwit h n-electronsn-electrons

- 121 - ーー司

whosewhos e wavewav e functionsfunction s arear e extendingextendin g a10nqalon g heightheigh t ofo f theth e sadd1esaddl e point.point , insteadinstea d ofo f theth e c-axisc-axi s withwit h noda1noda l p1anesplane s ofo f theth e theth e peakspeak s ata t -3" 3 mrad.mrad , is is given.given . graphitegraphit e hexagona1hexagona l networknetwor k p1anesplane s [20[20- - 23].23] . TheTh e sa1ientsalien t bimoda1bimoda l distributiondistributio n LifetimeLifetim e spectraspectr a ofo f unirradiatedunirradiate d observedobserve d showsshow s thattha t a1mostalmos t a11al l positronspositron s HOPGHOP G (ZYA(ZY A andan d ZYH)ZYH ) werewer e we11wel l representedrepresente d havehav e annihi1atedannihilate d fromfro m de1cca1izeddelccalize d B10chBloc h byb y singlesingl e lifetimelifetim e ofo f 22122 1 psecpse c (Tah.l).(Tab.l) . state.state . TheTh e resultsresult s arear e consistentconsisten t withwit h previouspreviou s workwor k [4[4,5]，5 】.. TheTh e 10werlowe r dosedos e irradiationirradiatio n 18 18 _1__2 2 IrradiationIrradiatio n ofo f 8.38. 3 xlOx10~g n/cm n/cm~ ono n (HOPG-ZYA)(HOPG-ZYA ) causedcause d ana n increaseincreas e ini n life11fe- HOPG-ZYAHOPG-ZY A causedcause d disappearancedisappearanc e ofo f theth e timetim e tot o 28428 4 psec.psec . ShimotomaiShimotoma i ete t al.al . havehav e bimoda1bimoda l shapeshap e andan d markedmarke d narrowingnarrowin g ini n reportedreporte d tha~hatt theth e 1ifetimelifetim e ofo f positronspositron s tht~ee PZPCPZP C distributiondistributio n (Fig.3).(Fig.3) . ThisThi s isi s trappedtrappe d ata t vacanciesvacancie s i8i s aboutabou t 24524 5 psecpse c duedu e tot o trappingtrappin g ofo f positronspositron s ini n defectsdefects: : [4].[4] . ThisThi s indicatesindicate s theth e lifetimelifetim e ofo f theth e vacanciesvacancie s - vacantvacan t sitessite s ata t theth e networknetwor k irradiatedirradiate d HOPG-ZYAHOPG-ZY A isi s ana n averageaverag e bebe- p1anesplanes,， wherewher e theth e positronspositron s dod o notno t seese e tweentwee n lifetimeslifetime s comingcomin g fromfro m positronpositro n 1l 1l n-electrons-electrons [[44] ] - oro r microvoidsmicrovoid s asa s trappingtrappin g ata t vacanciesvacancie s andan d veryver y sma11smal l statedstate d be1ow.below. 工It shou1dshoul d beb e notednote d thattha t microvoids ,， becausebecaus e ofo f finitefinit e timetim e depthdept h ofo f theth e sadd1esaddl e pointpoin t fromfro m theth e reso1ution.resolution . TheTh e higherhighe r dosedos e irradiationirradiatio n bimoda1bimoda l peakpea k isi s veryver y sensitivesensitiv e tot o (HOPG-ZYH)(HOPG-ZYH ) gavegav e a 10ngerlonge r 1ifetimelifetim e compocompo- presencepresenc e ofo f vacancy-typevacancy-typ e defects.defects. 工In theth e nentnen t ofo f 36436 4 psecpse c ( Tab.lTab. l ) andan d a shortshor t PZNCPZN C distribution ,， narrowingnarrowin g byb y irradiairradia- componentcomponen t ofo f ahoutabou t 25025 0 psecpse c withwit h veryver y tiontio n waswa s observedobserve d tot o nearlynearl y theth e samesam e sma11smal l intensityintensit y ofo f aboutabou t 4% ,， whichwhic h isi s extentexten t asa s ini n usualusua l meta1smetals，, whichwhic h a1soals o veryver y closeclos e tot o positronpositro n 1ifetimelifetim e ini n suggests positron trapping at the vacan vacancy as stated above. The longer suggests positron trapping at the vacan- vacancylifetim e as is stateddu e toabove. radiation-induceThe longer d cy-typecy-typ e defects.defects . HigherHighe r dosedos e irradiationirradiatio n 1ifetime is due to radiation-induced on HOPG-ZYH has induced further narrow microvoidr as stated below. on HOPG 回 ZYH has induced further narrow- microvoid= as stated be10w. ingin g ini n theth e ACARACA R curvescurve s forfo r bothbot h orienta-orienta tion. This implies that higher dose tion.result sThis in positron-trappinimplies that ghigher in largedose r LifetimeLifetim e spectraspectr a ofAXF-5Qlof AXF-5Q1 isi s wellwel l vacancy-typresults in e positron-trappingdefects . As a measurin largere of decomposeddecompose d tot o a sing1esingl e componentcomponen t ofo f grosvacancy-type s shape of defects.ACA R curveAs ,a FWHmeasureM width ofo f 38138 1 psec ,， muchmuc h 10ngerlonge r theth e vacancyvacanc y life1ife- grossth e ACAshapeR curveof sACAR are curvepresente， FWHMd inwidth Tab.1of , time.time . ACARACA R curvecurv e andan d itsit s FWHMFWH M widthwidt h forfo r wherthe ACARe focurvesr HOPG are a presentedful l width in at Tab.1a half， AXF-5Q1AXF-5Q 1 arear e shownshow n ini n Fig.3Fig. 3 andan d Tab.1Tab. l where for HOPG a fu11 width at a ha1f respective1y.respectively . TheTh e FWHMFWH M widthwidt h isi s lessles s

Rd o0 55 10 10 .5 0 5 10 15 AngleAngl e (mrad(mrad) ) Angle (mrad) Fig.2.Fig.2 . ACARACA R curvescurve s ofo f (a)(a ) diamond ,， (b)(b ) Fig.3.Fig.3 . ACARACA R curvescurve s ofo f theth e unirradiatedunirradiate d HOPG ,， PZPCPZP C ( 0O ) ) andan d PZNCPZN C ( • )， ), (c)(c ) andan d irradiatedirradiate d HOPGHOP G forfo r (a)(a ) PZPCPZP C andan d (b)(b )

AXF-5Q1 ,， andan d (d)_C60~C70(d) C60/C70 powdpowder邑r. . AllAl l theth e PZNCPZN C orientations.orientations . curvescurve s arear e normalizednormalize d toto theth e samesam e heightheigh t ata t zerozer o angleang1e. .

122 -

thantha n eieithe ther r afo f PZPCPZP C oro r PZNCPZN C orientationorientatio n 3-23- 2 GlassyGlass y CarbonsCarbon s ofo f theth e unirradiatedunirradiate d HOPG.HOPG . TheseThes e resultsresult s arear e possiblepossibl e onlyonl y ifi f mostmos t ofo f positronspositron s ACARACA R curvescurve s ofo f theth e g1assyglass y carboncarbo~哩，s , annihjlateannihjlat e fromfro m trappedtrappe d statesstate s ofo f strucstruc- especia11yespeciall y ofo f GC-10.GC-10 , werewer e foundfoun d tot o beb e turaltura l voidsvoid s butbu t notno t fromfro m de10ca1izeddelocalize d veryver y simi1arsimila r tot o thattha t ofAXF-5Qlof AXF-5Q1 , asa s statestat e ini n theth e isotropicisotropi c graphite:graphite : annihia~~ihi seensee fromn from theirthei r Fin倒FWHM (Tab.1( Tab.l ). ). ACARACA R lationlatio n fromfro m delocalizeddelocalize d statestat e wouldwoul d givegiv e curvescurve s ofo f GC-20GC-2 0 (shown( show n 1aterlate r ini n a ana n intermediateintermediat e widthwidt h betweenbetwee n thosethos e forfo r comparisocam~~risonn withwit h C60/C70C^Q/C^ Q ofo f Fig.Fi~.55 ) andan d theth e PZPCPZP C andan d PZNCPZN C orientationsorientation s andan d GC-30GC-3 0 arear e broader-broader thaDthan -thattha t ofo f GC-10GC ・10. . ratherrathe r flatfla t shapeshap e aroundaroun d zerozer o angle.angle . IIt t LifetimeLifetim e spectraspectr a ofo f theth e g1assyglass y carbons,， shouldshoul d beb e notednote d thattha t vacanciesvacancie s orox theirthei r forfo r examp1eexampl e GC-20GC-2 0 asa s pzesentedpresente d ini n Fig.4 ,， very small microvoids can not exist very small microvoids can not exist arear e we11wel l decomposeddecompose d tot o singlsing~ee lifetimelifetim e becausebecaus e theth e samplesampl e hasha s beenbee n heat-treatedheat-treate d componentscomponent s ofo f 39039 0 - 448自o0 psecpse c ( Tab.1Tab .1 )】.. ata t highhig h temperaturetemperatur e ofo f 2500°C2500"C. . TheseThes e resu1tsresult s indicateindicat e thattha t positronspositron s ini n theth e glassyglass y carbonscarbon s arear e trappedtrappe d 1ni n struc-struc WeW e considerconside r possiblepossibl positron e positron tura1tura l voids.voids , asa s ini n theth e isotropicisotropi c graph-graph trappingtrappin g ini n theth e structuralstructura l voids.voids . Arti-Arti ite.ite . ForFo r samp1essample s ofo f higherhighe r heat-heat- ficialficia l graphitesgraphite s arear e characterizedcharacterize d byby a treatmenttreatmen t temperaturetemperatur e (GC(GC-2・20 0 andan d GC- GC- significantsignifican t ( closedclose d andan d openedopene d ) porosporos- 30)30 )，, narrawingnarrowin g ini n ACARACA R curvecurv e andan d in-in ityit y amongamon g grainsgrain s andan d voidagevoidag e withinwithi n creasecreas e ini n positronpositro n 1ifetimelifetim e arear e observedobserve d grainsgrain s (Fig .‘ l(d)).1(d)) . AXF-5QlAXF-5Q 1 isi s a finefine- (Tab.1(Tab. l ). ). TheseThes e changeschange s byb y heathea t treat-treat grained isotropic graphite which are ment are presumably due to growth of the grained isotropic graphite which are voids,ment are presumab1yas seen iduen increasto growth e ooff the R„ extremextremel巴 1y y isotropicisotropi c andan d ofo f veryver y smal1smal l vOids ， a.5 seen in 孟ncrease of Rn and uniform crystallite size [16]. (Tab.l)[10]. Voids in glassy carbons are and uniform crystallit 邑 size [161. wel(Tab.1) l know【10]. n Voidsto havin e g1assynearl y carbons sphericaare l PositronsPositron s ini n graphitegraphit e bulkbul k arear e wellwel l we11 known to have nearly spherica1 characterized as "interlayer positrons" polyhedra bounded by graphite layer characterized as "interlayer positrons" polyhedraplane s ( Fig.1(ebounded ) ) byan d graphiteto be unifor1ayerm in ，1 betweenbetwee n theth e hexagonalhexagona l networknetwor k planesplane s andan d planes ( Fig.l(e) ) and to be uniform in may have marked anisotropy in positron size as revealed by Guinier plot of may hav 邑 marked anisotropy in positron smalsize l anglas erevealcd scatterinby g Guinierintensit yp10t ( X-raof y diffusion.diffusion . HoweverHoweve r tto o ourou r knowledgeknowledg e non o sma11 angle scattering intensity ( x-ray experimental information on the diffu [25] and neutron [19] ) and give well experimental information on the diffu- definit[25] and e valuneutron e of R[19] as ) listeand d give in Tab.lwe11 . sionsio n hasha s beenbee n reported.reported . ThenThe n wew e simplysimpl y definite value of Rg as g 1isted in Tah.l. assume positron diffusion constant of assume positron diffusion constant 2 of perfectperfec t graphitegraphit e crystalscrystal s D=D = 1 cmιIseccm /sec,， as seen in metals and semiconductors NaturalNatura l questionquestio n isi s aboutabou t trappingtrappin g as seen in meta1s and semiconductors state of positrons in the voids inin the [24], and get a diffusion length (D y-'*- state of positrons in the voids the [24]. 200nand m get which a idiffusions much longelength r tha(D n )...，，，， the isotropicisotropi c graphitesgraphite s andan d glassyglass y carbons.carbons . crystallit200nm whiche sizeis omuchf 40nmlonger. This than suggestthe s VariousVariou s void-trappingvoid-trappin g statesstate s ini n metalsmetal s crystallitetha t most ofsize positronof 40nm. s inThis the crystalsuggests havehav e beenbee n reportedreporte d sos o far:far : void-surfacevoid-surfac e thatlit e most diffusof e positronst o the inter-crystallitin the crystal- e ofo f manyman y metalsmetal s [1J[1]，, freefre e positroniumpositroniu m voidlite s diffu, get宮 etrappeto the d therinter-crysta11itee and give the (Ps)(Ps ) ini n voidsvoid s ini n V andan d NbNb [26][26 ] andan d PsPs- - voidslonge r ，lifetimget trapped e componenthere t andan d givea narrothe w 1ikelik e statestat e ata t voidvoi d surfacesurfac e ofo f A1 Al [27][27]. . ACA10nger R curvelifetime . Delocalizecomponent d positroand an narrowstate s ForFo r meta1smetal s iti t isi s we1!wel l knownknow n thattha t ACARACA R ACARi n thescurve. e voidDe10ca1ized ar e discussepositron d later.states FWHMFWH M widthwidt h decreasesdecrease s andan d lifetimelifetim e inin- in these void are discussed later. creasescrease s withwit h theth e radiusradiu s upu p tot o aboutabou t 0.50. 5

10' 10'

-+- C60/ C 70 ir ir ;'ヘ¥ ・GC-20 2ト/¥ 持諸蜘制 10: 10: i~/\ IO ，) '--' ~OO 60060 0 70700 0 800 ChanneJChanne l numbeDU 田 b.r r Fig.4.Fig. 4. PositronPositro n lifetimelifetim e spectraspectr a ofo f 5 o0 -5 -5 15 A 円91e (mrad) HOPGHOP~,， glassyglass carbon y carbon (GC-20)(GC-20 ) andan d CCgg/Cy60 /C 7Q0 Angle (mrad) powder.powder . TimeTim e scalescal e isi s 23.223. 2 psec/channel.psec/channel: ACAR curves of C /C powder FigFi~.~:, 5. ACAR curves of C60fio/C70 7n powder andan d GC-20.GC-20 .

12. 123- '1 ー・回

nmnm. . However,， furthefurther r increasincrease e iin n ththe e imagimage e potentiapotential l coulcou1d d bbe e supposesupposed d t~oo bbe e radradius i us doesdoe s notno t givegiv e anyan y changechang e ini n ACARACA R ververy y limitelimited d iif f wwe e noticnotice e thathat t th沿 le e curvcurve e anand d lifetimlifetime e anany y more,， whic which h iis s electroe1ectron n pile-upile-up p tto o forform m ththe e imagi 皿 age e interpreteinterpreted d aas s appearancappearance e oof f positronpositron- - potentiapotentia1 l iis s onlon1y y dondone e bbyy r. -e1ectrons-electron s trappintrapping g aat t ththe e voivoid d surfacsurface e (Fig.6(a))(Fig.6(a)). . whicwhich h cacan n freelfree1y y movmove e alona10ng g graphitgraphite e ThThe e trappintrapping g statstate e aat t ththe e voivoid d surfacsurface e hexagonahexagona1 l networnetwork k planep1ane ,， bubut t nonot t perpenperpen- hahas s essentiallessentially y ththe e samsame e physicaphysical l oriori- diculad :i cu1ar r tto o it:i t. . gingins s aas s thathat t aat t frefree e surfacesurface: : positronspositron s arare e repellerepelled d towartoward d vacuuvacuum m bby y surfacsurface e SferlazzSfer1azzo o eet t ala1. . [28]，, fro岨m slos10w w dipoldipole e potentiapotentia1 l induceinduced d spilled-outspilled-ou t positropositron n experiment,， havhave e demonstrateddemonstrate d electronelectrons s whilwhile e attracteattracted d bby y imagimage e thathat t surfacsurface e twtwo o dimensionadimensiona1 l (2D(2D) ) ACAACAR R forceforce. . ArAre e tt^etrey y possiblpossible e iin n carboncarbo n spectruspectrum m iis s ververy y similasimi1ar r tto o thathat t oof f ththe e materialmaterials? s ? OOn n ththe e contrarcontrary y tto o ththe e cascase e bulbu1k k iin n HOPG,， iin n contrascontrast t tto o ththe e cascase e oof f oof f conductioconduction n electronelectrons s iin n metals,， metameta1 l wherwhere e ththe e surfacsurface e spectrum皿 iis s valencvalence e electronelectrons s iin n graphitgraphite e cannocannot t substantiallsubstantia11y y differendiEferent t frofrom m ththe e bulbu1k k spilspi11 l ouout t frofrom m surfacsurface e becausbecause e oof f covacova- - oneone. . TTo o explaiexplain n ththe e similaritsimilarity y thethey y havhave e lent bonding. Further formation of the 1ent bonding. Further formation of the proposeproposed d twt田 o possibilitiespossibilities: : (1(1) ) ththe e surfacsurface e trappintrapping g statstate e doedoes s nonot t exexist:i sts s (a) (a(a) ) anand d ththe e positropositron n annihilatann :i hi1ate e iio n ththe e las1ast t Bul Bulk k VoiVoid d BulBu lk k fefew w graphitgraphite e layerlayers s (2)】 ththe e e1ectronselectron s samplesa 皿pled d bby y ththe e surface-bounsurface-bound d positronspositron s 一一一一 arare e ververy y similasimilar r tto o thosthose e samplesampled d bby y ththe e interlaye:i nter1ayer r positronpos :i trons s iin n ththe e bulkbu1k. . WeW e havhave e tto o notnote here e here thathat t formatiofor 湖 ation n oof f a surface-boun~urface-boundd statstate e fofor r positropositron n shou1dshoul d bbe e accompanieaccompanied d bby y significansign :i f:i cant t changchange e ini n ththe e surface-electrosurface-electron n states,， espespeciall邑cia11y y oof f nll-electrons-electrons,， whicwhich h wilwi11 l bbe e detecteddetecte d iin n ththe e 22D D ACAACAR R spectruspectrum m aas s statedstate d aboveabove. . TheThen n wwe e supporsupport t ththe e firsfirst t possipossi- (bJ (bJ bility,， nno o surface-trappinsurface-trapping g statstate e ofo f positronspositrons. . ThiThis s iis s furthefurther r supportesupported d byb y ththe e resultresu1ts s oofAXF-5Q1f AXF-5Q 1 whicwhich h iis s defi-defi nitelnite1y y characterizecharacterized d aas s smalsma11 l crystalcrystal- lite1ites s oof f nearlnear1y y perfecperfect t graphitgraphite e crys-crys talta1s p1uss plus voidvoids s amonamong g ththe e crysta11itescrystallite s anand d inter-granulaint 邑r-granular r voidsvoids. . Ilf f ththe e sursur- face-trappinface-trapping g iis s possiblepossibl e iin n graphitegraphit e andan d ACARACA R momentummomentu m distributiondistributio n isi s nearlynearl y theth e samesam e asa s thattha t ini n theth e bu1kbulk,， a1mostalmos t a11al l positronspositron s shouldshoul d beb e trappedtrappe d ata t theth e voidvoi d surfacesurfac e andan d givegiv ACAR e ACAR curvecurv e correspond-correspond ingin g tot oan an intermediateintermediat e bet'betwee回een n theth e c-c- axisaxi s para11e1paralle l [PZPC][PZPC ] andan d perpendicularperpendicula r 〉 [PZNC][PZNC ] ACARACA R curves.curves . ThisThi s isi s notno t concon- -24 sistentsisten t withwit h theth e presentpresen t result:result : theth e curvecurv e forfo r AXFAXF-5Qー円 Q11 is is narrowernarrowe r thantha n eveneve n thattha t forfo r PZNC.PZNC . ThenThe n wew e havehav e tot o seeksee k a Fig.6.Fig.6 . SchematicSchemati c representationrepresentatio n ofo f possiblepossibl e a1ternativealternativ e mode1mode l ofo f voidvoi d possiblepossibl positron e positron trappingtrappin g statesstate s ini n trapping.trapping . voi~svoids ofo f graphitegraphit e andan d glassyglass y carbon ,， (a)(a ) surfacesurfac e trappingtrappin g andan d (b)(b ) vo1umevolum e traptrap- InI n HOPGHOP G theth e positronpositro n statestat e arear e we11wel l ping.ping . 1nI n (b)(b ) theth e vertica1vertica l 1inesline s showsho w exp1ainedexplaine d ini n termsterm s ofo f a twotw o dimensiona1dimensiona l facingfacin g hexagona1hexagona l graphite-1ayersgraphite-layers,， withwit h statestat e ofo f de100a1izeddelocalize d inter1ayerinterlaye r positronpositro n effectiveeffectiv e separatiseparatio口n ofo f d ( ( diameter) ,， samplingsamplin g preferentia11ypreferentiall y theth e n-e1ectronsn-electrons ata t theth e voidvoi d surface.surface . TheTh e limitlimi t ofo f d - [22[22,29]，29] ,， asa s schematicallyschematicall y depicteddepicte d ini n c/2c/ 2 cou1dcoul d beb e assumedassume d tot o correspondcorrespon d tot o Fig.6(b)Fig.6(b ) withwit h a separationseparatio n ofo f d = 0/2c/ 2 interlayerinterlaye r positronspositron s ini n theth e bulkbul k ofo f betweenbetwee n theth e hexagona1hexagona l graphitegraphit e layers1ayers. . graphite.graphite . SchematicsSchematic s ofo f effectiveeffectiv e poten-poten 1tI t shou1dshoul d beb e notednote d thattha t theth e positr~nspositrons tia1tia l energyenerg y (V+)(V +) ofo f a positronpositro n nearnea r theth e existexis t most1ymostl y ini n theth e inter1ayerinterlaye r regionregio n graphitegraphit e 1ayerlaye r andan d ofo f positronpositro n wavewav e butbu t hardlyhardl y uponupo n theth e graphitegraphit e layer.layer . functionfunctio n (W( V ++)) iion ththe e voivoid d arare e shownshown.σ , a VoidsVoid s ini n glassyglass y carboncarbo n arear e boundedbounde d byb y andan d n e1ectronselectron s ofo f theth e graphite-layersgraphite-layer s graphitegraphit e layerlaye r planplane邑s ( ( asa s shownshow n ini n arear e a1soals o shown.shown . Fig.1(e)Fig.1(e ) )， ), sometimessometime s acoompaniedaccompanie d withwit h

turbostrturbostrati目atic c stacking.stacking . ThenThe n w 邑e proposepropose a

124 -

simplsimp1e e modemode1 l thathat t ththe e positronpositrons s arare e iin n a layelayer r spacspace e anand d are are supposesupposed d tto o bbe e frefree e statstate e bubut t effectiveleffective1y y confineconfined d bby y emitteemitted d easileasi1y y alona10ng g ththe e basabasa1 l planep1ane. . ththe e inner-most,， namel namely y void-wallvOid-wal1 ,， graph graph- ConsequentlConsequent1y y iif f ththe e void-walvoid-wa1l l containcontains s itite e layer1ayers s oof f ththe e voidsvoids. . SincSince e valencva1ence e ththe e edgedge e (suc(such h aas s zig-zazig-zag g oor r arm-chaiarm-chair r electron巴1ectrons s oof f graphitgraphite e arare e essentiallessentia11y y oof f [17][17]) ) oof f graphitgraphite e hexagonahexagonal l networksnetworks. , twtwo o dimensionaldimensiona1 ,， ththe e electroe1ectron n statstate e aat t frefree e positronpositrons s cacan n bbe e emitteemitted d therethere. , ththe e inner-mosinner-most t graphitgraphite e layelayer r iis s alsa1so o perpendiculaperpendicular r tto o <0001>,， tto o bbe e confineconfined d nearlnear1y y ththe e samsame e aas s thathat t oof f graphitegraphit e iin n ththe e voidsvoids. . laye1ayer r iin n ththe e bulkbu1k. . I工n thithis s modemode1 l ththe e wavwave e functiofunction n oof f ththe e positropositron n iis s extendextend- FoFor r simplicitsimplicity y wwee assumassume e ththe e voidsvoid s eed d oveover r ththe e wholwho1e e oof f ththe e voidvoid. . FoFor r smalsma11 l iin n glassglassy y carboncarbons s arare e sphericaspherica1 l iin n theitheir r voids with diameter less than about 5 voids with diameter 1ess than about 5 shapesh~pe., thethen n ththe e voivoid d radiusradius. , RRy. v, iis s runnm ，, ththe e positropositron n statstate e wilwil1 l bbe e givegiven n related to Rg. related to R.9 ' welwe11 l bby y thathat t oof f zero-poinzero-point t motio四otion n (ZPM)(ZPM). . Therefore the void diameter, or an 2 Therefore the void diameter ， or an RV2=t5/3mg2. (5/3)Rg . effectiveffective e separatioseparation n betweebetween n ththe e facinfacing g graphitgraphite e void-walvoid-wall l layerlayers s (Fig.6(b)),， I1n n FigFig. . 7 ACAACAR R FWHFWHM M widthwidths s anand d lifetimeslifetime s determinedetermines s positropositron n annihilatioannihi1ation n life1ife- arare e plotteplotted against d against ththe e voivoid d radiusradiu s time and ACAR distribution. Hereafter we time and ACAR distribution. Hereafter we calculateca1culat 邑d frofrom m th邑e resulresult t oof f smalsmal1 l calca11 l thithis s void-volumvoid-vo1ume e trappintrapping g tto o makmake e anglangle e neutroneutron n scatterinscattering g showshown n iin n Tab.lTab.l. , distinctiodistinction n frofrom m conventionaconventiona1 l voidvoid- - anand d furthefurther r ACAACAR R widthwidths s ( PZPPZPC C anand d surfacsurface e trappintrapping g iin n metalsmeta1s. . InteractionInteractio n PZNC and 1ifetime of HOPG are a1so between the void-wall and the volume- PZNC ) and lifetime of HOPG are also betweentrappe d positrothe vOid-wall n will and b thee subjecvo1ume- t of showsh ロwnn fofor ther the effectiveffective e separatioseparation n ofo f futurtrapped e studypositron . Howevewi11 r we be notesubject a volumof e c/2c/2. . IIt t is is clearlc1early y seeseen n thathat t ACAACAR R widthwidt h effecfuture t stestudy. m fromHowev ZPM邑. rPositronwe note sa confinevo1ume d decreasedecreases s anand d lifetim1ifetime e increaseincreases s withwit h effectin sphericastem from l ZPM. infinitPositrons e square-welconfined l increasincrease e iin n ththe e effectiveffective e separatioseparation n upu p potentiain spherica1 l with radiuinfinite s R will square-we11hav e the tto o abouabout t 3 runm n bubut t arara e saturatesaturated d fofor r the the potentia1 with radius Rv v wi11 have the furthefurther r increaseincrease. . ThiThis s definiteldefinite1y y demondemon- ZPM energy, E0, ZPM energy ， EO' stratestrates s ththe e overlappinover1 日.pping g betweebetwean n theth e 2-2 positropositron n wavwave e functiofunctiun n anand d ththe e electronelectro n 百一R Enu z一~ "1 1 1 「一ーー1 τ-.-1- 宅 1515 wherwhere e m iis s ththe e positropositron n massmass. . EEn g amountsamount s I咽 ' 色，ロ tto o 1.1.5 5 eeV V fofor r R^-0.~.=O.55 nnm m anand d 0.40.4B 8 eeV V fofor r ε RRu y = 1 nmnm. . ThiThis s square-welsquare-we11 l potentia1potentia l mighmight t bbe e totoo o simplsimp1e e bubut t coulcou1d d givgive e usu s correctcorrec t orderorde r ofo f theth e ZPMZP M energy.energy . TheTh e ifh ← o sma11ersmalle r ZPMZP M energyenerg y forfo r theth e 1argerlarge r voidvoi d is ,， ata t 1eastleas t oneon e of ,， reasonreaso n forfo r theth e voidvoi d vo1ume-trapping.volume-trapping . 5 Here we adopt an over-simp1ified H 1 h Here we adopt an over-simplified 6 picturepictur e thattha t theth e positronspositron s ini n theth e bu1kbul k 60∞0 graphitegraphit e arear e confinedconfine d ini n a voidvoi d withwit h %~ r ._0- 0 diameterdiamete r ofo f theth e interlayerinterlaye r separationseparatio n to ( name1ynamel y c/2)c/2 )，, neglectingneglectin g ana n effecteffec t 340R4 ∞0L.yt-- comingcomin g fromfro m differencedifferenc e ofo f dimensiona1i-dimensionali ε ト i 〆 tyt y of of theth e confinementconfinemen t spacespac e : twotw o dimendimen- e siona1siona l forfo r graphitegraphit e bu1kbul k andan d threethre e 主520200 0ぽ 000 dimensiona1dimensiona l forfo r voidsvoids. . :::J 1)<' ← N 円 u - 「言 888 o OneOn e mightmigh t supposesuppos e thattha t positronpositro n V14i l t よ }6t emissionemissio n fromfro m theth e voidvoi d surfacesurfac e isi s ener-ener getica11ygeticall y unfavorab1eunfavorable,， becausebecaus e positronpositro n Effective Effective Separation Separation(nm) (nm) workwor k functionfunctio n ofo f HOPGHOP G i5i s reportedreporte d tot o be be aboutabou t 1.51. 5 eVe V [28[28,30]，30]. . ItI t shouldshoul d beb e notednote d Fig.7.Fig.7 . RelationsRelation s betweenbetwee n positronpositro n anni-anni thattha t thisthi s workwor k functionfunctio n isi s forfo r theth e hi1ationhilatio n characteristicscharacteristic s ( ACARACA R FWHMFWH M emissionemissio n a10ngalon g <0001><0001 > directiondirectio n fromfro m theth e widthwidt h andan d lifetimelifetim e ) andan d theth e effectiveeffectiv e basa1-p1anebasal-plane,， andan d correspondscorrespond s tot o energyenerg y separationseparatio n (void( voi d diameterdiamete r ). ). ForFo r ACARACA R barrierbarrie r tot o beb e overcomeovercom e byb y theth e positronpositro n widthwidt h ofo f HOPG ,， circ1escircle s standstan d forfo r PZNCPZN C whenwhe n passingpassin g throughthroug h theth e outermostoutermos t andan d squaressquare s forfo r PZPCPZP C orientation:orientation : openope n graphitegraphit e hexagonalhexagona l networknetwor k planeplan e ata t theth e symbolssymbol s arear e forfo r unirradiatedunirradiate d andan d so1idsoli d surface.surface . HoweverHoweve r theth e positronspositron s canca n movemov e onesone s arear e forfo r irradiatedirradiate d HOPG-ZYH.HOPG-ZYH .

12.') 12.') 125 ー・・『

wavewav e functionsfunction s ofo f theth e void-wa11void-wal l graph-graph 0.71nm0.71n m andan d consistsconsist s ofo f 121 2 pentagonspentagon s andan d ite.ite . FromFro m Fig.7Fig.7 首w'e e Cealca n makemak e roughroug h 202 0 hexagonshexagon s [9[9,10]，10]. . 1nI n ththe e cagecag e bondbon d estimationestimatio n ofo f theth e voidvoi d diameterdiamete r fromfro m 1engthslength s betweenbetwee n C-CC- C arear e 0.1400.14 0 andan d 0.1460.14 6 ACARACA R widthwidt h oro r 1ifetime.lifetime . TheTh e resu1tsresult s nmn m , whichwhic h arear e veryver y closeclos e tot o tha tt" ini n aboutabou t theth e irradiatedirradiate d HOPG-.YHH0PG-2Y H arear e shownshow n graphitegraphit e hexagonalhexagona l networknetwor k (0.142(0.14 2 nm)nm). . ini n Fig.7Fig. 7 byb y a c10sedclose square d square andan d circ1escircle s ThisThi s structurestructur e rnakesmake s itsit s electronicelectroni c ata t c/2c/ 2 ofo f theth e unirradiatedunirradiate d state.state . TheseThes e structurestructur e veryver y simi1arsimila r tot o thattha t ini n graph-graph datadat a indicataindicat e thattha t theth e irradiation=irradiation = ite ,， nanamel皿ely y trigonaltrigona l uo andan d 1I iz elec-elec inducedinduce d defectsdefect s arear e voidsvoid s withwit h theth e trons.trons . WhWhilile e withinwithi n theth e cagecag e theth e C-CC- C near1ynearl y theth e samesam e diameterdiamete r asa s thosethos e ofo f GC=GC = bondingbondin g isi s veryver y strong ,， theth e interrnolecu-intermolecu- 101 0 oro r GC-20 ,， name1ynamel y 2020-3・30 0 nm.nm . BeBecauscause e lar_(la r ( C60-C60)C6 0-C60) bondingbondin g isi s !eryver y weakwea k andan d vacancyvacanc y ini n graphitegraphit e canca n migratemigrat e ababovロ've e analogousanalogou s tot o theth e interlayerinterlaye r bondingbondin g 1000.C1000° C [31] ，, thesethes e voidsvoid s arear e notno duet due tot o betweenbetwee n graphitegraphit e 1ayerslayer s andan d a1soals o duedu e tot o vacancyvacanc y c1usteringclusterin g butbu t t白血o mierocracki<.:rocracks s vanva dern der WaalsWaal s attraction.attraction . BeBecausc包.u se e ofo f theth e producedproduce d byb y markedmarke d anisotropicanisotropi c changechang e ini n weakwea k interrnolecintermolecula.u lar r interaction ,， theth e theth e 1atticelattic e constants:constants : 10.2%10.2 % di1atationdilatatio n solidsoli d CCgQp hasha s largelarg e open spaces ,， forfo r in the c-axis whereas 0.7% shrinkage in example, 60P at the octahedra~pe~l interstices in the c-axis whereas 0 蜘 7% shrinkage in exarnple ，--at the octahedral interstices theth e a-axisa-axi s ( Tab.1Tab. l ). ). ThisThi s markedmarke d aniso-aniso- wherewher e potassiurnpotassiu m atornsatom s canca n beb e accornrnodat-accommodat tropytrop y isi s duedu e tot o carboncarbo n interstitia1interstitia l ede d in.in . Th e distance ,， vanva n derde r WaalsWaal s clusters, such as C2 anc* c3' formed in separation, between adjacent cages is c1usters ， such as C~ and C角， formed in separation ， between adjacent cages is theth e inter1ayerinterlaye r space ,， andan d i5i s significantsignifican t aboutabou t 0.290.2 9 nrn nm,， asa s cornparedcompare d withwit h theth e after irradiation at temperatures below interlayer distance ( 0.335 nm ) of 200°after C [31]irradiation . at temperatures below graphiteinterlayer . Puskdistance a and Niemine(0.335 n [14 nrn ] calcuof 200.C [31]. graphite.late d the puska positroand n Nierninen wave functio[14] ncalcu- and latedlifetim ethe withipositron n the waveloca l functiondensit y andap WeW e makemak e a shortshor t remarkremar k aboutabou t PsP s proximatiolifetime withinn and the suggestelocal d density that ap-the formationformatio n 1ni n theth e voids.voids . FreeFre e PsP s emissionemissio n proximationpositro n densitand y issuggested highl y concentratedthat the , isi s possib1epossibl e sincesinc e positroniumpositroniu m workwor k positronbu t not delocalizeddensity is , highlyi n theconcentrated open volume， functionfunctio n isi s negativenegativ e (ー( -0.6eVO.6eV) ) [28][28]. . buto f not the delocalizedoctahedral ，ininterstices. the open volurne They Actua11yActuall y a narrownarro w p-Psp-P peak s peak withwit h smal1smal l ofals o the calculateoctahedral d positrointerstices. n lifetime verThey y intensityintensit y aroundaroun d theth e zerozer o momentummomentu m alsosimila calcr .u tolated the positronexperimenta lifetirne l one. very The portionportio n ofo f ACARACA R curvecurv e werewer e foundfoun d forfo r nearlsirnilar y tosam e the calculationexperirn 邑ntals havone. e beeThe n HOPGHOP G [22][22 ] andan d Grafoi1Grafoi l (from(fro m UnionUnio n Car-Car nearlyreporte d sarne by Ishibashcalculations i et al.have [15] beenan d bidebid e Co.)Co. ) [32][32 ] whichwhic h isi s ana n pexfoliate.x fo1iated d reportedJea n et alby . 1shibashiri-2] . Howeveret ,al. lifetim[15] e and of recompressedrecompresse d sheetshee t rnademade frornfrom graphitegraphit e abouJean t et 40a0l. pse[1 c2]. haHowevers been ，commonllifetime y obof partic1es:particles : 0.350.3 5 % andan d 2.5%2.5 % ofo f theth e p-Psp-P s aboutserve d 400 in glasspsec yhas carbonbeen s commonlya s well ob- as intensityintensit y forfo r HOPGHOP G andan d Grafoi1Grafoi l respec-respec servedisotropi cin graphitglassy e carbonsan d irradiateas welld KOPas G tive1y.tively . 1nI n presentpresen t study ,， however ,， suchsuc h aisotropics shown abovegraphi . Thte e andsignifican irradiated t observa f:OPG a narrownarro w p-Psp-P s peakpea k hasha s notno t beenbee n detect-detect astio nshown of above.presen t The studsignificanty is that thobserva-e ACAR ed. ed. tioncurv e ofo fpr C6Q/C邑 sent 70 alsstudy o agreeis that s quitthe e ACARwel l witcurve h thaof t C60/C10_~lsoof GC-20. I nagrees vie w ofquite the wellfac t

3-33- 3 C60/C70C60 /C70 FuFulleren11erene e withtha t ththat e ACAó圭R GC~20.curve an1n d viewth e oflifetim the e fact of ththat e c60/the c7ACAR 0 powdecurve r arand e verthe y lifetirnesimila r tofo ACARACA R curv~urvee ofo f theth e Cgg/C^C60~C70g _~owderpowder thosthe eC60/C70 o f the glassp~wdery carbonsare_ very , sirnilar positronto s agreesagree s veryver y we11wel l withwit h thatoftha t of GCGC-2・200 as as thoseshoul d of btbee inglassy th e nearlcarbons y the， sampositronse state shownshow n ini n Fig.4.Fig.4 . LifetirneLifetim e spectrumspectru m ofo f theth e shouldin bothbe carboin the n materialsnearly the . sameFurthe rstate we powderpowde r isi s a1soals o sirni1arsimila r tot o thattha t ofo f GCGC-2・20 0 havin eboth t o notcarbone thatrnaterials. C60 has basicallFurther y thwe e same chemical bonding character as those ( Fig.4Fig. 4 )) andan d isi s representedrepresente d byb y aa sing1esingl e have to note_that_C 60 has basically the componentcomponen t ofo f 41741 7 psecpse c whichwhic h isi s in in goodgoo d sarnein graphitcaernical e anbondingd glasscharactery carbon, as namelthose y trigonal sp and -electrons. agreernentagreemen t withwit h theth e previouspreviou s resu1tsresult s in and glassyn carbon ， na 皿ely Then graphit~we coul d reasonably assume that byb y otherothe r groupsgroup s [11-13].[11-13] . 1tI t shouldshoul d beb e trigonal sp~ and lI -electrons. notednote d thattha t thesethes e positronpositro n annihilationannihilatio n Thenth e positronwe could s arereasonably trappe d inassume ope n volumthat e characteristics of Cgg/CyQ are complete which size is given by the void volume- characteristics of C60/C70 are cornplete- thetrappin positrons g modelare fortrapped the glassin openy carbonsvolurne . lyl y theth e samesam e asa s those-observedthos e observed forfo r theth e which size is given by the v01d volume- glassy carbons and isotropic graphites. The present results are shown by dashed glassy carbons and isotropic graphites. linetrapping s in Fig.model 7 anfor d the indicateglassy s thatcarbons. posi ThisThi s indicatesindicate s a positronpositro n trappingtrappin g statestat e The present results are shown by dashed in open volume which is very similar to trons are trapped in open volume with in op 邑n volume which is very similar to lines in Fig.7 and indicates that posi- the voids in glassy carbons. diameter jf about 2 nm, which is much the voids in g1assy carbons. tronslarge r are tha七n rapped that in at openth e volume octahedrawith l diameterinterstice s~f about( 0.71 2 IUnrn I ，).which T o illustratis rnuch e TheTh e CCC刷、 Q fu11erenefullerene crystallitecrystallit e thilarger s a spherthan that e of radiuat s the2 nm centereoctahedral d on powderpowde r consistsconsist s ofo f theth e soccersocce r ballbal l thintersticese soccer-bal(0.71l lattic~~ e). poinTo t ill is.u strateshow n rnolecu1esmolecule s ofo f 6060-ato・atorn m cagecag e ，, whichwhic h formfor m thisi n Fig.8a sphere. The spherof radius e is clearl2 n 皿 centery foun邑d ton o FCCFC C structurestructur e withwit h a latticelattic e constantconstan t ofo f bthe e mucsoccer-ballh bigger thalatticen an inscribepoint dis sphershown e 1.1.442 2 四nmn (9)(Fig.1).[9](Fig.l) . TheTh e soccersocce r ba11bal l hasha s ain t Fig.8.th e octahedraThe sphere l intersticis clearly e pointfound , foto r a hollow-cagehollow-cag e structurestructur e ofo f truncatedtruncate d be rnuch bigger than an inscribed sphere icosahedronicosahedro n whichwhic h hasha s a diarneterdiamete r ofo f a

126 ー・『

exampl 色e O0守、，T, andan d tot o havehav e theth e near1ynearl y theth e C60C^ Q arear e 10ca1izedlocalize d oro r near1~_ioca~izednearly localized ini n samesam e open"v01umeope n volume asa s thattha t estiestimate田 ated d forfo r openope n vo1umevolum e butbu t notno t theth e voidvoi d surfacessurface s oro r theth e soccer-ba11soccer-bal l vacancyvacanc y wherewher e oneone 皿moleole ‘ soccer-ballsoccer-bal l surface.surface . culecul e ofo f C Q isi s missing.missing . ThisThi s strongly 606 strong~y suggestssuggest s tfie the positronpositro n trappingtrappin g ata t theth e 1nI n summary.summary , wew e havehav done e done systematicsystemati c soccer-ba11soccer-bal l vacancyvacanc y withwit h amp1eampl e trappingtrappin g studystud y ofo f variousvariou s kindkin d ofo f carboncarbo n materj.-- materi raterat e fromfro m theth e de1delocalize口ca1 :i zed d state.state . a1sals,， HOPG ,， isotrop:isotropi二c fine-grainedfine-graine d graph-graph™

ite ,， glassyglass y carboncarbon 凱and C60/C70C^Q/C 7O powder.powder , W 邑e considerconsider pOSSibi1itypossibilit y ofo f positronpositro n andan d uavehav e foundfoun d similarsimila r ACACA且R curvescurve s andan d trappingtrappin g ini n inter-granu1arinter-granula r openope n spacespac e ofo f 1ifetimeslifetime s commoncommo n tot o them.them . TheseThes e arear e comecom e theth e powder:powder : ~raingrain sizesiz e ofo f theth e powderpowde r isi s fromfro m theth e void-volumevoid-volum e trappingtrappin g andan d exper-exper orderorde r ofo f lO-'m.1 0 m. IfI f positronspositron s arear e trappedtrappe d imentallyimentall y correlatedcorrelate d tot o theth e voidvoi d sizesiz e there ,， theirthei r 1ifetimelifetim e wi11wil l showsho w non o obtainedobtaine d fro 田m smal1small ang1eangl e neutronneutro n fscat!.cat- - changechang e uponupo n co01ing.cooling . PositronPositro n 1ifetimelifetime,， tering.tering . BasedBase d ono n th 邑e correlationcorrelation theth e however ,， waswa s foundfoun d tot o decreasedecreas slightly e slightly positron-trappingpositron-trappin g openope n volumevolum e isi s rough1yroughl y withwit h temperaturetemperatur e downdow n tot o 10K:10K : aboutabou t 101 0 estimatedestimate d aboutabou t 2 nmn m ini n diameterdiamete r andan d psecpse c shortershorte r ata t 10K10 K tha~than thattha t ata t roomroo m ShOshowWTl n tot o correspondcorrespon d tot o theth e volumevolum e aroundaroun d temperature ,， asa s shownshow n ini n Tab.1.Tab.l . ThisThi s isi s theth e soccersocce r ba11bal l vacancy.vacancy . ThisThi s strong1ystrongl y duedu e tot o theth e sma11smal l reductionreductio n ofo f theth e openope n ssuggestl! ggests s existenceexistenc e ofo f theth e soccer-ballsoccer-bal l v01umevolum e causedcause d byb y 1atticelattic e shrirkageshrirkag e ata t vacancyvacanc y ini n C60/C70Cgg/Cy Q crystal1ite.crystallite . lowlo w temperature:temperature : shrinkageshrinkag e ini n aOa 0 ata t 111 1 K isi s aboutabou t 1告% [33].[33]. ThisThi s reductionreductio n canca n beb e 同We thankthan staffk staff membersmember s ofo f theth e evidenceevidenc e ofo f theth e v01ume-trappingvolume-trappin g ofo f Oarai BranchBranc h ofo f lMRIMR， TohokuTohok u UniversityUniversit y nanometer-scale rather than of micron- # nanometer-sca1e rather than of micron- forfo r theirthei r helphel p ini n handlinha~dlingg irradiatedirradiate d sca1escal e forfo r theth e inter-granu1inter-granulaョr openope n spacespace. . samplessample s andan d positronpositro n sourcessources. .

1nI n thisthi s contcontext邑xt ,， wew e notenot e thattha t nearlynearl y theth e samesam e reductionreductio n hasha s beenbee n a1soals o REFERENCESREFERENCE S predictpredicte邑d theoretica11ytheoreticall y forfo r theth e delode10 ・ ca1izedcalize d positronspositron s byb y PuskaPusk a andan d Nieminen.Nieminen . (1)(1 ) Brandt ,， W.W . andan d Dupasquier ,， A.(Ed.):A.(Ed.) : 工In theirthei mode1 r model theth e positronspositron s ar 邑e concen・ "Positron"Positro n Solid-StateSolid-Stat e Physics"Physics " (North(North- - tratedtrate d ini n thethe ロoctahedractahedra1 l intersticesinterstices. . Holland ,， AAmsterdam皿sterda 皿， , 1983).1983) . ThenThe n iti t shou1dshoul d beb e pointedpointe d outou t thattha t positronpositro n 1ifetimelifetim e isi s sensitivesensitiv e tot o theth e (2){2 ) Aravin ,， L.G. ,， Salukvadze ,， R.A. ,， latticelattic e parameterparamete r andan d thattha t positronspositron s ini n Shantarovich ,， V.P.V.P . andan d KhKhomenkoomenko ,， A.A.:A.A. : phys.phys . stat.stat . so1.(a)sol.(a ) 50.50 , K213K21 3 (1978).(1978) .

(3)(3) 工Iwatawata ,， '1'.， T., FuFukushimakushima ,， H. ,， ShimotoShimoto- -

mai,， MM. . anand d DoyamaDo yama ,， M.M.: : 噌""3plp. . JJ. . AppADpll. . Phys.,， 20，, 1791799 9 (19B1).(1981) .

(4(4) ) Shimotomai,，阿" M., Iwata1wata ,， T.,， TakaTaka- - hashi,， TT. . anand d Doyama,， M.M.: : JJ. . PhysPhys. . SocSoc. . JapanJapan. , 52,， 69694 4 (1983}.(1983) . (5(5) ) KuiamotoKU1amoto ,， E.E.. , Takenaka,， M.M.. , HasegaHasega- - 官waa,， MM. . anand d Tanabe'1' anabe ,， T.T.: : JJ. . NuclNuc l. . Mat.Mat.. , 179-181,， 20202 2 (1991).(1991) . (6(6) ) HasegawaHasegawa. , M.,， Kajino,， M.,， Kueahara,， H.,， Kuramoto,， E.,， Takenaka,， MM. . anand d Yamaguchi,， S-S.: : MaterM 己ter. . Sci5c i. . Forum,， 105盟主=- 110,， 1041041 1 (1992).(1992) .

- 110 — l.OOnm—- (7)Kratschraer(7) Kr atscbrner ,， W. ,， Lamb,， L.D.,， FostiroFosti r. o- - poulos,， K K. . an己£ Huffman,， K.J，.: : NatureNat l¥ re ,，笠'1， 347. Fig.8Fig.8. . ThThe e soccer-balsoccer-ba11 l arraarray y iin n ththe e 35354 4 (1990)(1 990). . (110(110) ) planp1ane e anand d possiblpossib1e e opeopen n volumvo1ume e iin n CCQC 刷、. - DasheDashed d circlecirc1es s represenrepresent t ththe e socce50ccer r (8(B) ) Hebard,， A.F.,， Rosseinsky,， M.J.,， balb亙I1 l oon n ththe e neighborinneighboring g (110(110) ) planep1ane. . Haddon,， R.C.,， Murphy,， D.W.,， Glarrum,， OctahedraOctahedra1 l intersticinterstice e ii5 s showshown n bby y a S.H.,， Palstra,， T.T.M.,， RamierezRam~邑rez,， A.PA.P. . circlcirc1e e witwith h mesmesh h (0™)(0 中). . Larg邑e circlcirc1e e anand d KortanKort 卸 , A.R.:: NatureNature. . 主盟350, 60600 0 representrepre5ents s a sphersphere e witwith h diametediameter r oof f 2 (1991)(1991). . nnm m : approximatinapproximating g sizsize e oof f ththe e soccersoccer- - balball l vacancyvacancy. .

- 127 寸

(9)(9 ) Huffman ,， D.R.:D.R. : Pbys.Phys . Today ,， 44 ,， 222 2 (26)(26 ) Hasegawa.Hasegawa, 問.，M., Yoshinari.Yoshinari , 0.O.,， MatuiHatui ,， (1991).(1991) . H.H . andan d YYamaguchiaaa. guchi ,， S.:S. : J.J . Phys.Phys . CondensCo ndens. . HaMattertter .， 1,， SA77SA7 7 (1989).(1989) . (10)(10 ) Prassides ,， K.K . andan d Kroto ,， H.:H. : PhysPhys. . Wor1dWorld,， 5,， 141 4 (1992).(1992) . 【(2727) ) Jensen ,， &.0. K.O.,， Eldrup ,， M. ,， Singh ,， B.N..B.N. , Linderoth ,， S.S . andan d BeBenzonnzon ,， M.D.:M.O. : J. J. (11)(11 ) Azuma ,， T. ,， Saito ,， H. ,， Yamazaki ,， Y. ,， Phys.Fhys . F.F . 晦，Mett. . Phys. .，主宣18. 10911091 (1988).(1988) . Komaki ,， K. ,， Nagashima ,， Y. ,， Watanabe ,， H. ,， Hyodo ,， T. ,， Kataura ,， H.H . andan d Kobayashi ,， (28)(28 ) Sfer1azzo.Sferlazzo . P..P. . BeBerkorko .， 5.S..， Lynn .， N.:N. : J.J . Pbys.Phys . Soc.Soc . JapJapan凱，盟, 60, 28122812 K.G. ,，腕 Mills,Jr.ills ，Jr.. , A.P. ,， Roe11ig.Roellig , L.O. .， (1991).(1991) . viescasViescas.， A.J.A.J . andan d West ,， R.R . N.:N. : PhysPhys. . RevRev. . Lett.Le tt. ,，盟. 60. 53538 8 (1(1988)988). . (12)(12 ) Jean ,， Y.C. ,， Lu ,， X. ,， LoLouu,， Y. ,， Bb~rBhern昂- tbithi.， A. ,， 5underSunder,， 5.C.S.C.,， Lyu ,， Y. ,， R¥;c H^r,， (29)(29 ) 5aito.Saito . R. .， SShima hiIIl a,， N.N . andan d KamimKamimuraura. , P.H.P.H . andan d Cbu Chu,， C. C.W.凶.: : Phys.Phys . Rev. ,，笠， 45, H.:H- : 5cntheticSyntheti c MeMetalsta1s ,，笠. 23, 21721 7 (1(1988)988). . 121261212 6 (1(1992)992). . (30)(30 ) Gu11ikson.Gullikson, EE.M‘H. . andan d Mi11s.Mills , Jr.Jr.. , (13)(13 ) Schaefer ,， H.E. ,， Forster ,， M. ,， Wur-Wur- A.P:A.P : Pbys.Phys . ReRev.v.. , 里呈~，B36, 8777877 7 (1(1987)987). . schum ,， R. ,， Kr Kratschmeratscbmer ,， W. W . andan d Huff:Huffman園 an ,，

D.R.D.R . : Phys.Phys . Rev. ,，空室， 45, 121641216 4 (1(1992)992). . 【(3131) ) KKellye1 1y ,， B.T.:B.T. : .Physics"Physic s ofo f Graphite "愉 iApplied•Applie d ScienceScienc e PuPub.b. ,， Lo Londonndon ,， 1981).1981) . (14)(14 ) Puska ,， M.J. M.J . andan d Nieminen ,， R.M.:R.H. : J. J. Phys.:Phys. : Condens.Condens . Matter ,， !' 4, L149L14 9 (1992).(1992) . (32)(32 ) Hasegawa.Hasegawa , M. ,， Kajino ,， H.M . andan d Yama-Yama guchi ,， S.:S. : ToT o beb e publishea.published . (15)(15) 工Ishibashishibashi ,， 5.S.,， Terada ,， N. ,， Tokumo-Tokumo- to ,， M. ,， KinosbitaKinoshita,， N.N . andan d lharaIhara,， (33)(33 ) Heiney ,， P.A.P.A,,， FiscberFischer,， J.E. ,， H.H.:ibid :ibid ,，生， 4, L169L16 9 (1(1992)992). . McGMcGhiehie ,， A.W. ,， RomRomanowanow ,， W.J. ,， DeDenensteinnenstein ,， A.M. ,， McCMcCauleyauley ,， Jr. ,， JJ.P.‘P. ,， 5mithSmith,， III111 ,， (16)(16 ) Eng1eEngle,， G.B.: Carbon ,， ~，8, 48548 5 (1970).(1970) . A.B.A.B. 聞an.d d Cox.Cox , D.E.:D.E. : Phys.Phys . Rev.Rev . LeLetttt. . 66堕，, 2911291 1 (1991).(1991) . (17)(17 ) MarsbMarsh,， H.(Ed.}:H.(Ed.) : "rntroduction"Introductio n tot o CarbonCarbo n SCience".Science" , (Butterworths ,， LoLondonndon ,， 1989).1989) . (18)(18 ) Shiraishi ,， M.:M. : "Introduction"Introductio n tot o CarbonCarbo n r.t Materialateria 1. s .. " (in(i n Japanese) ,， Sd.Ed . byb y Inagaki ,，阿 M., (Carbon(Carbon Materia1sMaterial s 5OC.Soc.,， Tokyo ,， 1984) ,， p29.p29 . (19)(19 ) Aizawa ,， K. ,， YamagucbiYamaguchi,， 5.S.,， Niimura ,， N.N . anaan d Hasegawa ,， M.:M. : 5ci.Sci Rep. . Rep. R1TURIT U (Tohoku(Tohok u Univ.) ,， 35 ,， 18918 9 (1991(1991)】..

(20)(20 ) Berko ,， 5.S.,， Ke11ey.Kelley , R.B.R.E . andan d PlasPlas- - kett.kett , J.5.:J.S. : Phys.Phys . Rev. ,，主 10606 ,， 82482 4 (1(1957)957). .

(21)(21 ) Colombino ,， P. ,， Fisce11aFiscella,， B .‘ andan d Trossi ,， L.:L. : NuovoNuov o CiCimento田ento ,，呈7.， 27, 58958 9 (1963).(1963) .

(22)(22 ) LeLeee,， R.R. ,， vonvo n 5tettenStetten,， E .‘ C. ,， Hasegawa ,， M.M . andan d Berko ,， 5.:S. : Phys.Phys . Rev.Rev . Lett. ,，豆宣， 58, 2363236 3 (1(1987)987). .

(23 )】 Yongming ,， L. ,， Johansson.Johansson , B.B . andan d Nieminen ,， R.M.:R.M. : J.J. Phys.:Phys. : CondensCondens. . Matter ,，主， 3, 2057205 7 (1991).(1991) . (24)(24 ) 5chu1tzSchultz,， P.J.P.J . andan d Lynn ,， K.G.: K.G. : Rev.Rev . Mcd.Mod . Phys. ,， 60 ,， 70170 1 (198(1988)自). . (25)(25 ) Rothwe11Rothwell,， W.5.:W.S. : J.J. Appl.Appl . Phys. ,，翌， 39, 1840184 0 (1968).(1968) .

-128- 128-