Molecular Form-Factor and Analysis of Diffraction Pattern of Fullerene Crystals
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E. V. SHULAKOV, R. A. DILANYAN, 0. G. RYBCHENKO, V. SH. SHEKHTMAN Institute of Solid State Physics, Russian Academy of Sciences, Chernogolovka, Moscow district, 142432, Russia.
ABSTRACT C60 molecules, in diffraction terms, is a quite novel object- covered by scattering points large sphere (D---0.5acub). The peculiarities of the diffraction distribution and its variation near the order-disorder phase transition are defined from the buckybal's molecular form-factor, fmol. The comparison of calculated diffraction distributions and experimental data proved advantage of the C60 "jump rotation" model at middle and high temperatures.
INTRODUCTION Based on diffraction data, we can state that the structural peculiarities of the fullerene family bye the conceptions of the molecular Fourier Transforms earlier developed by Wrinch H. Lipson and W. Cochran [I1]. A molecule C60, as a node of the unit cell, bears an extraordinary design of scattering centers on the rotation surface with diameter D = 0.704nm [2]. This fact gives rise to very peculiar diffraction patterns which immediately reflect the orientational ordering and structural transformations. This work is devoted to the above problem. We analyzed the Fourier-image molecule and considered the superposition of the obtained picture with the Laue interference function.
RESULTS AND CONCLUSION Let us clarify the notion of the molecular form-factor (MFF) [3] based on the traditional approach to the problem on a small crystal scattering. We shall consider an individual molecule as a structure element of the Bravais lattice. A scattering amplitude, attributed to one electron, can be put down as follows: 187 Mat. Res. Soc. Symp. Proc. Vol. 359 0 1995 Materials Research Society
M
A = Zfnexp(2 7Srn), n where fn is the atomic factor of an n - atom, S - the scattering vector (S = 2Sin(O)/X), M - a number of atoms in the crystal. If the molecules are in the lattice then we can represent the atom's coordinate as r. = rj + rm + rpm, where n is a serial number of a unit cell, m - a serial number of a molecule in the unit cell, mp - a serial number of an atom in the molecule. Then, approaching the problem traditionally, we may write down:
A = I exp(27zSrj)Z Fmexp(2 Srm) j
m
and distinguish the Laue interference function. MFF appears in the second factor, i.e. in the structure amplitude Fm, in an explicit form:
Fm =
fpmexp(2 7Srpm). p
The study of the Fm properties, using C60 as an example, immediately reveals a specific contribution of MFF to the intensity. Let us, first of all, consider the state of an orientational disorder of the molecules or, to put it otherwise, the state of a rotating spherical molecule. Then, a reasonable approximation must be a problem on scattering on a charged spherical surface [2]. Taking a sphere's diameter as D = 0.5a, where a is the constant of a cubic lattice, we obtain the Fourier-image shown in Fig. la. In this case MIFF is approximated by the function:
Fm
60fcJo(7D),
where fc - the carbon atomic factor, jo - the zero order Bessel spherical
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