Thermodynamics of Co-Existing Phases at Phase Transitions in Fullerenes
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ABSTRACT A thermodynamic model describing the co-existence of phases at orientational phase transition in solid fullerenes is developed. It is shown that for such a transition in fullerene C60 characterized by the comparatively low enthalpy, heterophase fluctuations can lead to the wide temperature region of the phase co-existence within about 30 K below the 260 K transition point, and mainly determine the anomalies of thermodynamic characteristics observed within that region. By comparison of the theoretical dependence obtained on this basis with the experimental data on the xray diffraction and heat capacity measurements for C60, the energetical characteristics of the heterophase cluster formation are evaluated. The relative contribution of homophase and heterophase fluctuations to breaking the orientational order is discussed. INTRODUCTION The processes of orientational ordering in solid fullerenes and the ensuing rearrangement of a crystal lattice are the matter of significant interest at the present time [1-5]. Physical properties of such crystals built of so many-atomic and highly symmetric molecules as fullerenes are closely connected with the orientational interaction as well as with the character of their vibrational, rotational and librational movement allowed by the symmetry of the crystal structure. So, solid fullerene C60 proved to be constructed of freely rotating molecules arranged in a fcc structure at room temperature. On cooling down to T, = 260 K the rotation freezes, which results in re-ordering the lattice to a sc structure with four fullerene molecules in an elementary cell (the symmetry Pa-3). The data of the numerous experimental studies [1, 6-11] of this phenomenon involving a great variety of tecniques have shown that is a first-order phase transition with the latent heat of 1.7 kcal/mol and the specific volume change of about 1%. The studies of orientational ordering in solid C70 revealed the similar but much more complicated picture of the sequence of the phase transitions in the range from 260 K to 360 K, which probably is due to nonequivalent rotation around various axes freezing at different temperatures [4,12]. At the same time, the experiments cited above also show a number of distinctive peculiarities for the phase transitions in fullerenes. The main of them consists in the wide temperature region below the transition point where the structure of the low-temperature phase is not homogeneous. So, the x-ray diffraction study [7] of the sc phase of C60 displayed that the relative fraction of reflections pertinent toPa3 symmetry began to decrease monotonically from unity at approximately 200 K, i.e. far below the transition point, down to about 60% at 260 K then falling to zero. Similar results indicating that the sc phase in C60 can not be considered as pure above 200 K have been obtained by infrared spectroscopy [10]. Both x-ray and neutron diffraction experiments performed in [8] have clearly revealed the co-existence of phases within 10 K below T.. Lastly, numerous calorimetric mea
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