Structure of Polydisperse fcc Nanocrystals: Implications for Crystal Fractionalization

Synthesis of nanocrystals yields polydisperse distributions, which not only implies a distribution of nanocrystal sizes but also of shapes. Noting that the synthesis products often reflect kinetic effects and may not reflect minimum energy states, we propose that the nanocrystals (of gold, silver, platinum, etc.) typically used in self-assembly and directed-assembly experiments consist predominantly of variations of single-crystal face-centered cubic truncated octahedra with closed shells of atoms. Between each consecutive pair of “magic number” (maximally symmetric) truncated octahedra, we identify 49 sizes with some degeneracy, for a total of 70 distinct closed-shell configurations. Energetic and geometric features of the nanocrystals for these special sizes are analyzed. Combining these results with previous theoretical models, we discuss the implications for crystal fractionalization, where polydisperse nanocrystals spontaneously phase-separate into single and multiple binary superlattices. We show that under very general conditions, the binary superlattice phases follow the order MgZn2, CaCu5, AlB2, and NaZn13 for increasing polydispersity. Other phases are less frequent but also possible.