Metallurgy of soft spheres with hard core: from BCC to Frank-Kasper phases

Understanding how soft particles can fill the space is still an open question. Structures far from classical FCC or BCC phases are now commonly experimentally observed in many different systems. Models based on pair interaction between soft particle are at present much studied in 2D. Pair interaction with two different lengths have been shown to lead to quasicrystalline architectures. It is also the case for a hard core with a square repulsive shoulder potential. In 3D, global approaches have been proposed for instance by minimizing the interface area between the deformed objects in the case of foams or micellar systems or using self-consistent mean field theory in copolymer melts. In this paper we propose to compare a strong van der Waals attraction between spherical hard cores and an elastic energy associated to the deformation of the soft corona. This deformation is measured as the shift between the deformed shell compared to a corona with a perfect spherical symmetry. The two main parameters in this model are: the hard core volume fraction and the weight of the elastic energy compared to the van der Waals one. The elastic energy clearly favours the BCC structure but large van der Waals forces favors Frank and Kasper phases. This result opens a route towards controlling the building of nanoparticle superlattices with complex structures and thus original physical properties.Comment: To appear in EPJ

Geometric study of a 2D tiling related to the octagonal quasiperiodic tiling

International audienceA quasicrystal built with three types of tiles is related to the well-known octagonal tiling. The relationships between both tilings are investigated. More precisely, we show that the coordinates of the vertices can be obtained in two different but equivalent ways. The structure factor is calculated exactly. We emphasize the difficulty one can have to define the order of the symmetry of a quasicrystal, from a practical point of view, exhibiting a quasiperiodic tiling whose spectrum has a « quasi » eight-fold symmetry. Finally, we show how to recover easily a class of octagonal-like quasicrystals.Au moyen de trois tuiles, nous construisons un pavage quasipériodique du plan, que nous relions au quasicristal octogonal. Ainsi, nous montrons que les coordonnées des nœuds peuvent être obtenues de deux manières différentes. Le facteur de structure est calculé exactement. Ce pavage qui possède « presque » une symétrie d'ordre huit, soulève la difficulté de la détermination pratique de la symétrie d'un quasicristal. Finalement, nous montrons comment construire une large classe de pavage du type de l'octogonal, à partir de ce nouveau pavage