Transformation from Weaire-Phelan packing to thermally stable Euler crystals in polycrystalline face-centered cubic metals

Abstract

Based on the least area principle to fill up space and Weaire-Phelan (W-P) conjecture, polycrystalline face-centered cubic metals Cu, Ni and Al consisting of triply-distributed coherent twin-boundaries were modeled at grain sizes below 10 nm. Atomistic simulations showed that grain boundaries in such W-P crystals may transform promptly into a unique structure characterized by three perpendicular catenoids of minimal surfaces formally proved by mathematician Leonhard Euler. The adopted Euler crystal can be thermally stable up to more than 80 % of the melting point. Densely embedded Σ3 {111} coherent twins are critical agents to trigger the transformation as well as to stabilize the resultant minimal-surface structures. Our results add further evidence that the evolution of 3-dimensional grain boundary networks into saddle-shaped minimal-surface morphologies may enhance the thermal stability of nanograined polycrystals.