Symmetry analysis of the 2aphase ofC60

A symmetry analysis of the 2a phase recently observed in some samples of ${\mathrm{C}}_{60}$ is presented. This phase is described by a unit cell with eight molecules in inequivalent orientations. We first show that if this structure is assumed to be exactly cubic, there are only three allowed space groups, none of which corresponds to the PA3¯ arrangement of threefold axes previously established for ${\mathrm{C}}_{60}$ by several groups. Our calculated powder diffraction spectra for these space groups are not consistent with existing experimental data. Second, if the symmetry of the PA3¯ structure is lowered by a doubling of the unit cell, we show that the resulting structure is trigonal, space group R3¯. We calculate powder diffraction spectra for this scenario and thereby place upper limits on both the angular distortion and the trigonal lattice distortion. Third, since the microscopic origin of this distortion probably involves defects of some presently unknown type, we consider a phenomenological scenario for the origin of this trigonal distortion. Within this scenario, we study the symmetry of the interactions needed to explain this structure. We start by giving an analysis of the structural distortion within harmonic lattice dynamics. However, to obtain the correct (R3¯) symmetry structure we were forced to study the cubic coupling between zone-corner librons and macroscopic strains. In this way we relate the development of R3¯ symmetry from the PA3¯ structure in terms of a phenomenological model of lattice dynamics. Fourth, we extend the above arguments to construct a Landau theory for the hypothesized PA3¯→R3¯ phase transition, which occurs as a function of the concentration of the presumed defects. The resulting free energy has no cubic terms (so the transition can be continuous) but has five fourth-order invariants.