Growth modes of quasicrystals involving intermediate phases and a multistep behavior studied by phase field crystal model

Abstract

Understanding the microscopic kinetics of quasicrystal formation via nucleation and growth is crucial. Here, we report unusual pathways to nucleation and growth of dodecagonal quasicrystals via a phase field crystal model incorporating a two-length-scale potential. Under certain thermodynamic parameters, both quasicrystal growths via heterogeneous and homogeneous nucleation may be associated with a multistep behavior and the transient appearance of triangular and intermediate phases, different from classical nucleation pathways. The metastable intermediate phase spontaneously occurs to bridge the triangular phase and quasicrystal nuclei of different orientations to reduce the total free energy of the system. Decomposition of an undercooled fluid phase into quasicrystal phase shows a multistep pathway wherein the triangular phase and the intermediate phase may occur faster than the quasicrystal phase, when the growth rate of one length-scale ordering is significantly different from the other and the subsequent competing and coupling of both length scales are involved. The calculated structure factor, radial distribution function, and the aperiodic tiling structure of the intermediate phase explain why it appears during the quasicrystal formation.