Formation of Stable Schwarz Crystals in Polycrystalline Copper at the Grain Size Limit

A prototype Schwarz crystal (SC) structure of dividing--space minimal grain boundaries (GBs) constrained by coherent twin boundaries (CTBs) was recently discovered in extremely fine-grained polycrystalline Cu. In this Letter, constraining effects of $3D$ CTB network on the formation and thermostability of SC are addressed via atomistic simulations. GB migration and evolution of CTB network trigger formation of SC diamond. CTB constraints are critical to generate GBs of zero mean curvature underlying vanishing capillary pressure, and to counterbalance the elastic driving forces of lattice. GB motion can be suppressed at temperatures close to the melting point with GB aperture down to 3 nm.