Formation of Frank-Kasper phases from interacting hard-spheres

The emergence of Frank-Kasper phases from interacting hard-spheres is studied using density functional theory. Specifically, the phase behaviour of the hard spheres with short-range attractive and long-range repulsive (SALR) interaction potentials is examined by using three version of hard-sphere models: the lattice gas model, the Carnahan-Starling approximation, and the fundamental measure theory. The competition between the attractive and repulsive interactions results in the formation of clusters composed of many particles, whereas the packing of these clusters leads to the formation of long-range ordered phases. Phase diagrams containing the commonly observed BCC and FCC phases, as well as the novel Frank-Kasper sigma and A15 phases, have been constructed. Similar phase transition sequences have been predicted using the three versions of density functional theory. However, the details of the phase diagrams could vary significantly. In particular, the local packing effect of particles within the clusters is obtained from the accurate fundamental measure theory. The results obtained from the study provide strong theoretical justification of the universality of phase transition sequences observed in various soft matter systems.