Orientational ordering in solid orto-H2 and para-D2

Tareyeva, E. E.; Trapezina, T. I.

doi:10.1016/0375-9601(75)90249-2

Cited by 9 publications

(5 citation statements)

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“…In the case of the full interaction one can obtain all possible broken symmetry phases compatible with the initial symmetry and the condition of positive temperature value ͑see, e.g., the case of hydrogen 20,22,25 ͒. Now we have truncated the interaction and reduced the problem.…”

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confidence: 97%

“…We shall follow our papers on hydrogen [20][21][22]25 to obtain quantitative results. In the mean-field approximation from the first equation of BBGKY hierarchy for the orientational distribution functions or by minimizing the orientational free energy one can obtain the following nonlinear integral equation: 21…”

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confidence: 99%

“…This means the first order phase transition. [20][21][22] The bifurcation points are the eigenvalues ␣ of the linearized system corresponding to Eq. ͑5͒:…”

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Orientational phase transition in solidC60

Schelkacheva

Tareyeva

2000

Phys. Rev. B

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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:

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Orientational phase transition in solidC60

Schelkacheva

Tareyeva

2000

Phys. Rev. B

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“…These orientational trasitions can be conveniently described by changes in the n-particle orientational distribution functions f n (ω 1 , ..., ω n ). This kind of problems was treated by use of bifurcation approach, for example, in the papers [2,3,4,5,6]. Here we will follow our papers [2,3,6].…”

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“…This kind of problems was treated by use of bifurcation approach, for example, in the papers [2,3,4,5,6]. Here we will follow our papers [2,3,6]. Let us describe briefly the main steps of the method.…”

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