A pair correlation function study of the structure of C₆₀

The inter- and intra-molecular structures of C₆₀ have been studied at 20 K and 295 K by means of the pair correlation function using low-angle pulsed neutron diffraction. Two methods of inversion of the structure factor data are presented. Direct inversion of the data using a Monte Carlo algorithm yields a model-independent combined intra- and inter-molecular pair correlation function. This clearly indicates, even at 295 K, the presence of two distinct C-C bond lengths of 1.377(15) AA and 1.458(6) AA. Further analysis was performed using a truncated icosahedral model for the intra-molecular behaviour in combination with a free-form Monte Carlo solution for the inter-molecular pair correlation function. This analysis confirms two distinct nearest-neighbour C-C bond lengths but indicates that the difference has a precision of order 0.005 AA. The optimal values at both 20 K and 295 K obtained from this analysis are 1.400 AA and 1.440 AA implying that the molecular structure is essentially unchanged between these two temperatures. There are, however, distinct differences between inter-molecular bonding at 20 K and 295 K that are consistent with an orientational ordering transition at 260 K. In particular, the room temperature data can be accurately modelled in terms of a face-centred-cubic structure in which the C₆₀ molecules adopt a completely random orientation with respect to one another.