Orientational ordering of icosahedra in solidC60

Abstract

We determine the allowed structures for orientationally ordered icosahedral molecules on a fcc lattice such that there are four molecules per simple-cubic unit cell. The allowed space groups are Pm3, Pn3, and Pa3. In the latter two, an angle of rotation assumes a value not fixed by symmetry. The locations of all 240 atoms in the unit cell as deduced from the powder x-ray data of Heiney et al. are tabulated. We discuss a number of minima in the free energy which correspond to the observed Pa3 structure of solid ${\mathrm{C}}_{60}$. We introduce orientational order parameters which lead to a Landau free energy, from which we predict that the orientational transition is discontinuous.