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Cubane (C8H8) and fullerene (C60) are famous cage molecules with shapes of platonic or archimedean solids. Their remarkable chemical and solid-state properties have induced great scientific interest. Both materials form polymorphic crystals of molecules with variable orientational ordering. The idea of intercalating fullerene with cubane was raised several years ago but no attempts at preparation have been reported. Here we show that C60 and similarly C70 form high-symmetry molecular crystals with cubane owing to topological molecular recognition between the convex surface of fullerenes and the concave cubane. Static cubane occupies the octahedral voids of the face-centred-cubic structures and acts as a bearing between the rotating fullerene molecules. The smooth contact of the rotor and stator molecules decreases significantly the temperature of orientational ordering. These materials have great topochemical importance: at elevated temperatures they transform to high-stability covalent derivatives although preserving their crystalline appearance. The size-dependent molecular recognition promises selective formation of related structures with higher fullerenes and/or substituted cubanes.

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A phase field theory of polycrystalline solidification is presented that is able to describe the nucleation and growth of anisotropic particles with different crystallographic orientation in 3D dimensions. As opposed with the two-dimensional case, where a single orientation field suffices, in three dimensions, minimum three fields are needed. The free energy of grain boundaries is assumed to be proportional to the angular difference between the adjacent crystals expressed here in terms of the differences of the four symmetric Euler parameters. The equations of motion for these fields are obtained from variational principles. Illustrative calculations are performed for polycrystalline solidification with dendritic, needle and spherulitic growth morphologies.

The short and intense pulses of the new X-ray free electron lasers, now operational or under construction, may make possible diffraction experiments on single molecule-sized objects with high resolution, before radiation damage destroys the sample. In a single molecule imaging (SMI) experiment thousands of diffraction patterns of single molecules with random orientations are recorded. One of the most challenging problems of SMI is how to assemble these noisy patterns of unknown orientations into a consistent single set of diffraction data. Here we present a new method which can solve the orientation problem of SMI efficiently even for large biological molecules and in the presence of noise. We show on simulated diffraction patterns of a large protein molecule, how the orientations of the patterns can be found and the structure to atomic resolution can be solved. The concept of our algorithm could be also applied to experiments where images of an object are recorded in unknown orientations and/or positions like in cryoEM or tomography.