Lattice dynamics of a rotor-stator molecular crystal: Fullerene-cubane ${\text{C}}_{60}\ensuremath{\cdot}{\text{C}}_{8}{\text{H}}_{8}$

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Lattice dynamics of a rotor-stator molecular crystal: Fullerene-cubane $C_{60} \cdot C_{8} H_{8}$

Colin Bousige, Stéphane Rols, Julien Cambedouzou, Bart Verberck, Sándor Pekker, Éva Kováts, Gábor Durkó, István Jalsovsky, Éric Pellegrini, and Pascale Launois

Phys. Rev. B 82, 195413 – Published 8 November 2010

Abstract

The dynamics of fullerene-cubane $(C_{60} \cdot C_{8} H_{8})$ cocrystal is studied combining experimental [x-ray diffuse scattering, quasielastic and inelastic neutron scattering (INS)] and simulation (molecular dynamics) investigations. Neutron scattering gives direct evidence of the free rotation of fullerenes and of the libration of cubanes in the high-temperature phase, validating the “rotor-stator” description of this molecular system. X-ray diffuse scattering shows that orientational disorder survives the order/disorder transition in the low-temperature phase, although the loss of fullerene isotropic rotational diffusion is featured by the appearance of a 2.2 meV mode in the INS spectra. The coupling between INS and simulations allows identifying a degeneracy lift of the cubane librations in the low temperature phase, which is used as a tool for probing the environment of cubane in this phase and for getting further insights into the phase transition mechanism.

Received 30 July 2010

DOI:https://doi.org/10.1103/PhysRevB.82.195413

Authors & Affiliations

Colin Bousige^1,2, Stéphane Rols¹, Julien Cambedouzou², Bart Verberck^2,3, Sándor Pekker⁴, Éva Kováts⁴, Gábor Durkó⁵, István Jalsovsky⁵, Éric Pellegrini¹, and Pascale Launois²

¹Institut Laue Langevin, F-38042 Grenoble, France
²Laboratoire de Physique des Solides, UMR CNRS 8502, Université Paris-Sud, F-91405 Orsay, France
³Departement Fysica, Universiteit Antwerpen, Groenenborgerlaan 171, B- 2020 Antwerpen, Belgium
⁴Research Institute for Solid State Physics and Optics, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary
⁵Department of Organic Chemistry, Eötvös Loránd University, P.O. Box 32, H-1518 Budapest, Hungary

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Vol. 82, Iss. 19 — 15 November 2010

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Figure 1
Visualization of the fullerene-cubane fcc lattice.Reuse & Permissions
Figure 2
X-ray scattering pattern of a $C_{60} \cdot C_{8} H_{8}$ crystal, recorded on a cylindrical image plate (a) at room temperature and (b) at 120 K. The [111] cubic axis is parallel to the x-ray beam (perpendicular to the pattern). Simulations are reported in (c) and (d) using the structural parameters refined in Ref. 11 to calculate Bragg peak intensities. Diffuse scattering intensity is calculated assuming that molecules take all orientations in (c) or that they can take 24 orientations in (d), as discussed in the text. Simulations are performed assuming that the crystal contains in identical ratio the “parent” crystal and its (111) mirror twin. Simple arrows point toward the $1, - 3, 1$ diffraction peak of the parent crystal and dotted arrows point toward the same peak for the twin crystal. Double arrows point toward the diffuse scattering halo around $3.3 Å^{- 1}$ characteristic of $C_{60}$ orientational disorder.Reuse & Permissions
Figure 3
Generalized density of states (GDOS) measured at 300 K and $3 Å$ . We consider three zones labeled low, mid, and high frequencies. Features at HF are mainly due to internal vibrations of cubanes (intense features from 75 meV up to 200 meV). Small peaks attributable to fullerene vibrations are visible (the $H_{g}$ vibration is visible at 33 meV). The two intense peaks in the MF region are due to cubanes intermolecular motions. The LF region shows a featureless intensity, associated to a quasielastic signal originating from slow reorientations of fullerenes.Reuse & Permissions
Figure 4
(Color online) (a) Experimental GDOS at $1.5 Å$ for temperatures between 180 and 100 K, at $1.65 Å$ for 50 and 10 K—(b) Simulated GDOS at 180 and 50 K. Simulations were shifted by 1 meV toward low energies. The Rigid Body Trajectory (RBT) allows us to separate translational and rotational motions: the peak at 11 meV is thus due to translations of cubanes, the one at 17.8 meV is due to librations of cubanes (see text).Reuse & Permissions
Figure 5
(Color online) (a) Temperature evolution of the susceptibility $χ^{″} (ω) / ω$ in the LF area (at $2.7 Å$ ) $S (Q, ω)$ for (b) $T = 180 K$ and (c) $T = 100 K$ at $2.7 Å$ . The $Q$ dependency is the same in both cases and the integrated intensity between 1.3 and 3 meV gives a peak at $3.4 Å^{- 1}$ , which is typical of coherent scattering of fullerenes (Ref. 19).Reuse & Permissions
Figure 6
(Color online) $ln (T_{c}^{i})$ as a function of $ln (a)$ at room temperature, as suggested by Ref. 10. $T_{c}^{i}$ is the transition temperature for the intercalated compound, $a$ is the corresponding lattice parameter at room temperature. Solid line is a linear fit with values of van der Waals compounds only (squares). Values collected from Refs. 3, 4, 5, 6, 7, 11.Reuse & Permissions

Physical Review B

covering condensed matter and materials physics

Lattice dynamics of a rotor-stator molecular crystal: Fullerene-cubane $C_{60} \cdot C_{8} H_{8}$

Colin Bousige, Stéphane Rols, Julien Cambedouzou, Bart Verberck, Sándor Pekker, Éva Kováts, Gábor Durkó, István Jalsovsky, Éric Pellegrini, and Pascale Launois

Phys. Rev. B 82, 195413 – Published 8 November 2010

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Physical Review B

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Lattice dynamics of a rotor-stator molecular crystal: Fullerene-cubane C60⋅C8H8

Colin Bousige, Stéphane Rols, Julien Cambedouzou, Bart Verberck, Sándor Pekker, Éva Kováts, Gábor Durkó, István Jalsovsky, Éric Pellegrini, and Pascale Launois

Phys. Rev. B 82, 195413 – Published 8 November 2010

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Lattice dynamics of a rotor-stator molecular crystal: Fullerene-cubane $C_{60} \cdot C_{8} H_{8}$