Structural aspects ofC82andC76crystals studied by x-ray diffraction

Abstract

A precession photograph of a ${\mathrm{C}}_{82}$ single crystal cocrystallized with toluene shows a striking tenfold symmetry in the plane normal to its elongated ten-sided columnar axis. This pattern can be perfectly explained by superposition of ten domains systematically twinned and nearly equally distributed, each of which consists of a monoclinic lattice with a=18.36 Å, b=11.36 Å, c=11.41 Å (a/c=1.609), and β=108.07°. Such extraordinary lattice parameters as its axial ratio a/c nearly equal to the golden ratio (τ=1.61 803. . .) and monoclinic angle β nearly equal to 108° result in a highly unusual twinning. A toluene-solvated ${\mathrm{C}}_{76}$ is also found to have very similar structural features as a=17.68 Å, b=11.08 Å, c=11.02 Å (a/c=1.604), and β=108.10°. Combining the previous results of pentane-solvated ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{70}$ by Fleming et al. which also crystallize into a monoclinic lattice, we have found that among all four fullerides the similarity with respect to the unit-cell shape, a:b:c=τ:1:1 and β=108°, holds extraordinarily well within less than 1% accuracy regardless of kinds of fullerenes and solvents. We have also successfully analyzed these crystal structures with the space group P$2_1$ (z=2) by assuming the ${\mathrm{C}}_{82}$ or ${\mathrm{C}}_{76}$ cage to be spherical, which can be driven from the ‘‘sphere packing model’’ previously proposed by Fleming et al.