Orientational phase transition in solid C60: Bifurcation approach

Orientation ordering and the transition to the orientational glass state in fullerite C60

“…We recall some results given in [20], [21] that we need for developing orientational glass theory. Our main physical assumption is that according to the foregoing, we restrict ourself to considering a finite number of permitted molecular orientations instead of continuous rotations about the crystal lattice sites.…”

“…We note that in addition to the H and P states, solution (7)-(11) also includes equiprobable molecular orientations K 1 (ω) describing rotations in the cubic lattice (see, e.g., [25]). The equations given in [20], [21] can be rewritten in a more compact form, which is needed below. For this, we use the fact that in the ordered phase, all lattices are equivalent from a physical standpoint and transform into one another when the crystal is rotated through 90 • about the z axis.…”

“…We established [20], [21] that a first-order transition occurs, and we found the branch temperature, the ordered-phase symmetry, and the fraction ρ P (or ρ H ) of molecules whose pentagons (or hexagons) are directed toward the double bonds of the nearest neighbors in the vicinity of the phase transition. In this case, our data agree well with the experimental data…”

“…In the vicinity of the branch point T b (see [20] for the details), we can write a linearized system of equations of the form…”

“…But we think that it is natural to seek an analogy between the glass state in C 60 and ordinary spin glasses, more precisely, orientational glasses in systems with molecules that are simpler than the C 60 molecule, such as either a mixture of orthohydrogen and parahydrogen or an N 2 -Ar mixture. Our aim here is to try to describe low-temperature orientational glass in C 60 on a microscopic level in the spirit of spin glass theory based on our previous papers: on one hand, a rather successful description of quadrupole glasses [18], [19] and, on the other hand, a microscopic theory of the orientational phase transition in C 60 at 260 K proposed in [20], [21].…”