Nanoparticle Superlattices as Quasi-Frank Kasper Phases*

I show that all phases reported experimentally in binary nanoparticle superlattices can be de-
scribed as networks of disclinations in an ideal lattice of regular tetrahedra. A set of simple rules
are provided to identify the different disclination types from the Voronoi construction, and it is
shown that those disclinations completely screen the positive curvature of the ideal tetrahedral lat-
tice. In this way, this study provides a generalization of the well-known Frank-Kasper phases to
binary systems consisting of two types of particles, and with a more general type of disclinations,
i.e. Quasi-Frank Kasper phases. The study comprises all strategies in nanoparticle self-assembly,
whether driven by DNA or hydrocarbon ligands, and establishes the universal tendency of superlat-
tices to develop icosahedral order, which is facilitated by the asymmetry of the particles.