Radiation Physics and Chemistry 64 (2002) 273–275

Dependence of the Doppler-broadening of the positron-annihilation radiation in C60 fullerenes on the temperature

Yutaka Ito*

High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tskuba, Ibaraki, 305-0801, Japan

Received 20 January 2001; accepted 10 April 2001

Abstract

A monotonic correlation of the Doppler-broadening of positron-annihilation radiation in solid C60 with the

temperature was observed between 77 and 299 K: Since the change in the spectrum due to the temperature was very

small, the spectrum was analyzed by a method which reduced the effect of the statistical uncertainties of the spectrum.

The observed temperature dependence is interpreted as being due to a thermal expansion of the lattice spacing between

the C60 molecules, where positron annihilation took place at the interstitial regions between the C60 molecules. r 2002

Elsevier Science Ltd. All rights reserved.

Keywords: Positron; C60; Fullerene; Doppler-broadening

It is well known that positron annihilation offers a

unique way to characterize the electronic and defect

structures of solids. In C60 fullerene specimens, a single

component of a positron lifetime of about t ¼ 390 ps

has been reported (Kri$sstiak et al., 1994; Be$ccv!aa$rr et al.,

1995; Ito and Suzuki, 1999; Jean et al., 1992). According

to a calculation of the positron density distribution in

C60; a positron cannot be localized inside the cavity of a

C60 molecule, but is distributed in the interstitial regions

between C60 molecules (Jean et al.,1992; Puska and

Nieminen, 1992). However, it is also pointed out that the

calculated positron distribution between C60 molecules

is quite different with respect to the approximation

model of the electron–positron correlation (Ishibasi,

1997). Unfortunately, in spite of a large difference in the

calculated distributions, the differences in the lifetimes

expected by these models are smaller than the un-

certainties of the measurements. Therefore, the positron

lifetime would not be an appropriate probe to estimate

the positron distribution in C60 fullerenes. On the other

hand, Doppler-broadening and=or the angular correla-tion of annihilation radiation (ACAR) has been known

to be a probe of the density in the momentum space of

electrons sampled by a positron. The Doppler-broad-

ening energy is proportional to the longitudinal mo-

mentum of the annihilation electrons. The same

proportionality exists between the angles and the

perpendicular momentum component in ACAR.

In a previous paper, the validity of the Doppler-

broadening spectrum used to characterize a fullerene

and other carbon phases was reported (Ito and Suzuki,

1999). It was one of the aims of this study, using the

Doppler-broadening spectrum, to obtain experimental

proof that the positrons distribute between C60 mole-

cules.

In this experiment, high-quality sublimation C60

specimens with a purity of better than 99.95% were

used. A positron source of 200 kBq 22Na; depositedonto a 1 mm mylar foil, was sandwiched between C60

specimens under a vacuum of 5� 10�6 Torr: Doppler-broadening spectra were obtained using a conventional

germanium detector with an energy resolution (full

width at half maximum, FWHM) of 1:16 keV for the

annihilation radiation energy. In order to avoid any pile-

up of the signal and the associated statistical uncertain-

ties, the spectrum was accumulated with sufficient

statistics under low counting rates.*Tel.: +81-298-64-5497; fax: +81-298-64-1993.

E-mail address: yutaka.ito@kek.jp (Y. Ito).

0969-806X/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved.

PII: S 0 9 6 9 - 8 0 6 X ( 0 1 ) 0 0 4 0 9 - 1

As will be shown, because the difference in the

Doppler-broadening due to temperature is very small,

a conventional analysis method, such as the S-para-

meter, is not useful for our purpose. In the present work,

the temperature dependence of the Doppler-broadening

parameter was revealed as follows: in order to normalize

the spectra, the height and center of the annihilation g-ray peak were estimated using a least-squares method

(MINUIT, 1994). The quality-of-fit was checked with

the w2 of the result. In Fig. 1, the spectra obtained at 299and at 77 K after this normalizing procedure are shown.

The longitudinal momentum distribution of electrons

(pL) sampled by positrons is shown regarding the

dependency between the count rate and the energy

difference (DE) from 511 keV; as given by

pL ¼ 2DE=c; ð1Þ

where c is the speed of light. As shown in Fig. 1, a

difference between the two temperatures can be clearly

observed in the tail of the annihilation g-ray spectra.

From the energy of the Doppler-broadening, the

difference of the two spectra is considered to be caused

by the p and s electrons on the surface of C60 (Haddon

et al., 1986; Haddon, 1992; Saito and Oshiyama, 1991).

To parameterize the difference as a function of

temperature, each spectrum was compared with a

template formed from the average of the 299 K spectra.

The average deviation from the template (D.F.T.) was

given by summing the comparison on each channel,

D:F:T: ¼1

N

X nðiÞf ðiÞ

; ð2Þ

where N is the number of summations, nðiÞ is the

number of counts in the ith channel and f ðiÞ is the

number of counts expected by the template. The

template, f ðiÞ; was defined by the mean of six 299 K

spectra containing 1� 106 counts. Thus, the statistical

uncertainty in the template f ðiÞ is extremely small, and itcan be made possible to extract the change in the

Doppler-broadening by comparing the spectrum mea-

sured at each temperature with the template. The

correlation of D.F.T. and the temperature between 77

and 300 K is plotted in Fig. 2. The solid line in Fig. 2

was linearly fitted to all data points. These are the first

data to show the temperature dependence of the

Doppler-broadening of the annihilation radiation. The

variation in D.F.T. reflects a change in the momentum

space of the electron distribution annihilated with the

positron in C60: One can easily see that D.F.T. increases

linearly with decreasing temperature. The temperature

coefficient obtained from the best fit to the data is

ð�2:770:1Þ � 10�4 K�1; which was determined by

function minimization and an error analysis code,

MINUIT (MINUIT, 1994). This monotonic decrease

in D.F.T. as a function of temperature is considered to

be due to thermal expansion of the lattices between the

C60 molecules. A similar monotonic dependence is also

seen in the correlation between the positron lifetime and

the temperature (Han and Huang, 1995). The effect of

Fig. 1. Doppler-broadening of positron-annihilation radiation

in C60 measured at 299 K ð3Þ and at 77 K ðKÞ: The spectra

were normalized to the peak height and the energy difference

ðDEÞ from 511 keV: Fig. 2. Temperature dependence of the average deviation from

the template (D.F.T.), defined by Eq. (2). The variation of

D.F.T. reflects a change in the momentum distribution of an

electron annihilated with a positron in C60: One easily sees thatthe D.F.T. simply decreases with the temperature. The solid line

was linearly fitted to all data points.

Y. Ito / Radiation Physics and Chemistry 64 (2002) 273–275274

the thermal expansion of C60 molecules for the Doppler-

broadening of positron-annihilation radiation is not so

obvious, because it depends on the positron density

distribution in C60 and on the correlation of the electron

and positron wave functions. However, if a positron is

distributed in the interstitial sites between the C60

molecules, since the volume of interstitial sites decrease

at low temperature, due to thermal expansion of the

lattice, it is expected to increase the overlap of the wave

function of the positron and the electrons of the C60

molecule. Therefore, the ratio of the relative contribu-

tion of all p and s electrons of C60 for positron

annihilation would be changed as a function of the

temperature. In other words, these results also prove

that positrons are distributed in the interstitial sites

between the C60 molecules. If a positron is localized

inside the C60 molecular structure, the variation of

D.F.T. due to temperature would be much smaller than

that shown in Fig. 2. On the other hand, a phase

transition from orientational disorder to an ordered

structure is known to exist at 260 K (Prassides et al.,

1992). However, no distinct structure beyond the

uncertainty of the measurement can be observed in

Fig. 2. The statistical uncertainties accompanying the

counts in each channel of the Doppler-broadening

spectrum and template in Eq. (2) are included in the

error bar of each data point in Fig. 2. The Doppler-

broadening of the annihilation radiation seems to be

insensitive to this transition. A similar insensitivity was

also reported concerning the positron lifetime in C60

(Jean et al., 1992).

In summary, the temperature dependence of the

Doppler-broadening of positron-annihilation radiation

in C60 was observed for the first time. A new analysis

method presented in this report to compare the spectrum

with a template clearly revealed a change in the

annihilation spectrum. This result supports the idea

that positrons are located in the interstitial regions

between the C60 molecules. There exist two kinds of

open spaces between the C60 molecules: octahedral and

tetrahedral interstices. According to a calculation of the

positron state in C60; it is possible to distribute the

positron at both sites by an approximation model of

electron–positron correlation used in the calculation.

The method used to extract the temperature dependence

of the Doppler-broadening of positron-annihilation

radiation, as introduced in this report, will provide help

to obtain further information concerning the positron

density distribution between the C60 molecules, so as to

justify that the approximation of the calculation model

is realistic. The angular correlation of the annihilation

radiation method will also be available so as to obtain

similar information.

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