Universal self-assembly of one-component three-dimensional dodecagonal quasicrystals.

Using molecular dynamics simulations, we study computational self-assembly of one-component three-dimensional dodecagonal (12-fold) quasicrystals in systems with two-length-scale potentials. Existing criteria for three-dimensional quasicrystal formation are quite complicated and rather inconvenient for particle simulations. So to localize numerically the quasicrystal phase, one should usually simulate over a wide range of system parameters. We show how to universally localize the parameter values at which dodecagonal quasicrystal order may appear for a given particle system. For that purpose, we use a criterion recently proposed for predicting decagonal quasicrystal formation in one-component two-length-scale systems. The criterion is based on two dimensionless effective parameters describing the fluid structure which are extracted from the radial distribution function. The proposed method allows reduction of the time spent for searching the parameters favoring a certain solid structure for a given system. We show that the method works well for dodecagonal quasicrystals; this result is verified on four systems with different potentials: the Dzugutov potential, the oscillating potential which mimics metal interactions, the repulsive shoulder potential describing effective interactions for the core/shell model of colloids and the embedded-atom model potential for aluminum. Our results suggest that the mechanism of dodecagonal quasicrystal formation is universal for both metallic and soft-matter systems and it is based on competition between interparticle scales.