Orientational phase transition in solidC60

Abstract

A simple model for the angular dependent interaction between C 60 molecules in face centered cubic lattice is proposed and analyzed by use of the rigorous bifurcation approach. The quantitative results for the orientational phase transition and the characteristics of the ordered phase are in good agreement with the experimental data.The orientational phase transition in solid C 60 is of much current interest. The orientational ordering has been a subject of extensive experimental investigations ͑see, e.g., Refs. 1-6͒; some theoretical researches were performed, too. 7-13 However, ab initio calculations fail to reproduce the experimental results.In this paper we develop a simple model for the angular dependence of the intermolecular potential in solid C 60 . The model is based on the ideas of preferred orientations due to David et al. 1 and to Lapinskas et al.,11 and on the maximal exploit of symmetry considerations. We apply to this model interaction the rigorous approach based on the LyapunovSchmidt theory of bifurcation of solutions of nonlinear integral equations and obtain quantitative results for the transition temperature and the distribution of molecular orientations in the ordered phase. These results occur to reproduce the experimental data.As is established in a number of experiments C 60 crystallizes in a face centered cubic ͑fcc͒ structure. At ambient temperature the molecules rotate almost freely with centers on the fcc lattice sites, so that the space group is Fm3 m ͑see, e.g., Ref. 2͒. When the temperature decreases to T S Ϸ260 K the first order orientational phase transition takes place: the sites of the initial fcc lattice become divided between four simple cubic sublattices ͑see Fig. 1͒ with its own preferable molecular orientation in each sublattice. The broken symmetry space group is Pa3 .Moreover, the neutron-diffraction experiments 1 have shown that the orientations in the ordered state are so that the electron-rich regions ͑the interpentagon double bonds͒ face the electron-deficient regions of the neighboring C 60 molecule: the centers of pentagons or the centers of hexagons. It was shown 1,3,5 that the ratio of the number of molecules in those two states is about 60:40 at the phase transition temperature and increases when the temperature decreases. This remaining orientational disorder is usually believed to cause the orientational glass transition at T G Ϸ90 K now confirmed by various experimental techniques ͑see, e.g., Ref. 14͒. These two minima of the intermolecular angle dependent energy were obtained by numerical calculations and were shown to be much lower than the energies of other mutual orientations of the pair of molecules ͑see, e.g., Refs. 8,9,13,15͒. In those calculations the previously obtained charge distribution for the isolated C 60 molecule 16 was taken into account. Usually recent calculations use the intermolecular potential of Sprik et al.: 17 a sum of 6-12 and Coulomb interactions between 60 atoms C and 30 double-bond centers D and between each other:

Nucleation of a sodium droplet onC60

“…57 We did not attempt to change any of the original parameters, but we added several fixed point charges to improve the electrostatic description of this molecule. Following Schelkachelva and Tareyeva, 58 60 charges +δq were placed on each C atom, while 30 charges −2δq were placed at the center of each C=C bond. Actually the full Tersoff potential is relatively costly, and we only used it for reoptimizing some stable structures.…”

Wetting-to-Nonwetting Transition in Metal-CoatedC60

“…This electrostatic model was further improved by including 90 fixed charges, 60 on each carbon site with value δq, 30 on the middle of each C=C bond with value −2δq. This was previously used by Schelkacheva Tareyeva in a study of bulk C 60 [16].…”

Full replica symmetry breaking in p-spin-glass-like systems

“…So there is no reflection symmetry. Behavior of this model is significantly different from what one usually has in the case of Ising-like operators [2,3,18,19,20,21,22,23,24,25,26,28]. We have done earlier calculations of 1RSB solution for various values of p that could change continuously [26].…”

“…For T < T 0 we have Almeida-Thoulles replicon mode λ (RS) repl < 0 and RS-solution becomes unstable. Similarly, when T < T 0 we have λ (1RSB) repl < 0 determining the condition when the 1RSB glass is unstable [19,24,26,27].…”

“…Replacing the simple Ising spins by more complex operatorsÛ dramatically expands the range of solvable tasks. The operatorÛ can be, for example, the axial quadrupole moment (quadrupole glass in molecular solid hydrogen at different pressures) or the role ofÛ can be played by certain combinations of the cubic harmonics (orientational glass of the clusters, for example, in C 60 in a wide pressure range), see [18,19,20,21,22,23,24,25,26].…”