Isotropic grain boundaries and size-dependent thermal stability of Schwarz crystals Cu and Al at nanoscales

Abstract

Schwarz crystals consisting of triply periodic minimal surface grain boundaries of different shapes were studied for face-centered cubic metals Al and Cu via atomistic modeling and simulations. The thermal stabilities of those curvy grain boundaries depend on shape, spacing between grain boundaries and how closely the grain boundary energies fulfill the isotropic condition. Schwarz crystals consisting of energetically less anisotropic grain boundaries are thermally more stable. Destabilization occurs when shapes of grain boundaries deviate significantly from the ideal minimal-surface morphologies. A thermodynamic model was proposed to describe the size-dependent thermal stability exhibited by primary Schwarz crystals at nanoscales.