PHYSICAL REVIEW 8 VOLUME 45, NUMBER 20 1& MAY 1992-II

Positrons as probes in C60 fullerites

H.-E. Schaefer, M. Forster, and R. WurschumInstitut fiir Theoretische und Angewandte Physik, Universitiit Stuttgart, Pfagfenwaldring 57, D 700-0 Stuttgart 80, Germany

%. KratschmerMax Pla-nck Ins-titut fur KernphysikPo, stfach 10 39 80, D 6900 -Heidelberg, Germany

D. R. HuA'man

Department of Physics, University of Arizona, Tucson, Arizona 85721(Received 20 December 1991; revised manuscript received 9 March 1992)

The single-component positron lifetime of 402 ps measured in C60-15-mole% C70 is compared tothat in the other carbon allotropic forms graphite and diamond. From the decrease of the positronlifetime in the fullerite specimen with quasihydrostatic pressure it is concluded that the positron is an-

nihilated on interstitial sites and not in the interior of the fullerene molecules.

After the recent breakthrough in preparing macroscop-ic quantities' of C6p carbon molecules ("fullerenes") thesolid-state properties of the molecular crystal ("fullerite")were studied.

For investigating the electronic properties of the fuller-ite solids or the processes of intercalation and compoundformation on an atomic scale, nuclear particles, e.g. , pos-itrons, may be used as specific and sensitive probes. Ear-lier positron annihilation studies by Azuma et al. yieldeda single positron lifetime in well-annealed C~-20-mole%C7p fullerites of 414 ps whereas Hasegawa et al. reportedfor commercial C60-C70 specimens a positron lifetimecomponent of 403 ps with an additional shorter com-ponent (r ~ 177 ps) the origin of which is not clear. Bothgroups attributed the long lifetime tentatively to a "free"delocalized positron state in the fullerite crystal. In thepresent paper we report on comparative positron lifetimestudies in the three allotropic carbon forms C60-15-mole% C7p fullerite powder, highly oriented pyrolyticgraphite crystals (HOPG), and natural diamond, and onpositron lifetime studies in fullerite under quasihydrostat-ic pressure in order to obtain information about the posi-tron annihilation site in the fullerite lattice.

The powder specimens with the typical compositionsC6p-15-mole% C7p (crystallite size 2 pm) were preparedand vacuum heated (I h at 573 K) for solvent removal in

the Heidelberg (specimen No. 1) and Tucson (specimenNo. 2) laboratories. For the positron lifetime measure-ments the NaCl positron emitter enclosed in a 0.8-pm-thick Al foil was embedded in or sandwiched between thespecimen material with quantitative positron annihilationin the specimens.

The observation of a single-component positron lifetimespectrum in the fullerite specimens demonstrates thepositron-electron annihilation from one state exclusively(see Fig. 1). The positron lifetime zt„=402 ps in the ful-lerite specimen at ambient conditions (see Table I) ismuch higher than in the denser graphite (interplanar dis-

tance 3.55 A) or diamond lattices. This long positron life-time originates from the large open volumes available in

the "foamy" fullerite structure with a C60 molecular di-ameter of 2rp =7.1 A (Ref. 6) and a cubic lattice constantap =14.17 A (Ref. 7).

For an assessment of the site (inside or outside the C6pmolecule) from which the positron is annihilated thepressure-induced variation of the positron lifetime zt„ in

fullerite was studied. A reversible decrease h, sf„=24 ps(see Table I) is observed by applying a quasihydrostaticpressure of p =3.2 Gpa.

lo'

10

+10

4

t (ns)F'IG. 1. Positron lifetime spectra in highly oriented pyrolytic

graphite and in C60-C70 powder.

12 164

POSITRONS AS PROBES IN C60 FULLERITES 12 165

TABLE I. Positron lifetimes in C60-15-mole% C70 fullerite at two temperatures and under quasihy-drostatic pressure (ambient temperature) together with the positron lifetimes in graphite (HOPG) andnatural diamond.

Allotropic carbonsolids

Specimen 1

T (K.)295 118 3.2

r (ps)Specimen 2

p (GPa)10-4

Theory (Ref. 12)(semiconductorlikepositron shielding)

C60-15-mole% C70GraphiteDiamond

402+ I

212+ 4110

398+ 3 396 372 37019292

The pressure induced decrease of the positron lifetime isconsidered as a clear evidence for the annihilation of posi-trons from the compressible intermolecular space in thefcc fullerite crystal (see Fig. 2) and makes the annihila-tion from the interior of the highly incompressible ful-lerene molecules unlikely. These intermolecular or in-tramolecular elastic properties can be deduced from thelow fullerite bulk modulus xnb =18.1 GPa or the observa-tion that both the cubic lattice constant ao and the ratioao/rn exhibit the same relative change with pressure. Anextraordinary stiffness of the C60 molecules is also sug-gested by a theoretical estimate yielding an intramolecu-lar elastic modulus of xo„, =843 GPa (Ref. 9). On theoctahedral sites of the fullerite lattice large and cornpres-sible open spaces (interconnected by the narrowertetrahedral sites) with about the same spherical dimen-sions as inside the C60 molecule are available for the posi-tron (see Fig. 2).

It should be pointed out that the pressure-induced (24ps) or thermal changes (4 ps between 300 and 100 K) ofthe positron lifetime in the carbon fullerite are similar ifwe compare them either to the corresponding linearcompression of 5.9% or the thermal contraction of slightlybelow 1%. Similar changes of the positron lifetime by 16or about 20 ps are furthermore theoretically predicted inSi (Ref. 10) or Mo (Ref. 11) lattice vacancies if the va-

I14.17 A

7.O7 A

FIG. 2. (OOI) face of the C6o-fullerite unit cell with thespherical sizes of the octahedral (0) and the tetrahedral (T)interstices.

cancy sizes are changed linearly by 5% or 6%, respective-ly.

The annihilation of positrons from the intermolecularspace appears to be reasonable from both charge and spa-tial considerations. An enhanced electron density outsidethe C6n molecule and a corresponding Coulomb potentialdistribution may favor an intermolecular spreading of thepositron wave function. There arises now the question ofwhether the single positron lifetime observed here and byother groups ' is to be ascribed to a free delocalized or adefect-trapped state. Recent theoretical studies' of thepositron wave function in C60 fullerite yielded a positronspreading mainly on octahedral interstitial lattice sites be-tween the Csn molecules and a negligible positron densityin the interior of the molecule, in accordance with the con-clusions drawn from the pressure-induced decrease of rr„.Assuming a semiconductorlike positron-electron correla-tion interaction, which may be adequate for bulk C6o thelifetimes listed in Table I were calculated. Taking into ac-count that the free lifetime calculated for all the three al-lotropic carbon forms are slightly lower than the experi-mental values we may conclude that the 402-ps positronlifetime may be ascribed to the free delocalized positronstate. Positron annihilation from the crystallite surfaces isregarded as negligible if we compare the size of the fuller-ite grains ( = 2 pm) with a conventional positron diffusionlength in metals and semiconductors of about 0. 1 pm.However, an attribution of the 402 ps positron lifetime toa defect-trapped state should not be fully ruled out. Inhigh-resolution electron microscopy studies of our speci-mens' stacking faults and twins were detected. Further-more, we have to keep in mind that the positron lifetime of402 ps measured in C6n fullerite is not so far from the pos-itron lifetime r =550 ps in the low electron-density limitof a semiconductor as Si (Ref. 14) so that a change of life-time upon positron trapping at defects is small and not soeasy to detect.

In summary we point out that in comparison withtheoretical results the single-component positron lifetimemay be attributed to a free delocalized positron state al-though positron annihilation from a defect-trapped stateis not to be ruled out. From our measurements underquasihydrostatic pressure we conclude that the positron isannihilated from sites between and not in the interior ofthe fullerene molecules. Therefore, positrons are con-sidered as specific probes for studying intercalated fuller-ites and fullerite compounds.

12 166 H.-E. SCHAEFER et al.

e are indebted to M. J. Puska and R. M. Nieminen as well as to M. Hasegawa for communication of their results pri-or to publication. The support of A. Seeger and of the Deutsche Forschungsgemeinschaft is appreciated.

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