{101¯2} Twin Interface Structure and Energetics in HCP Materials

This study systematically analyzes the {101¯2} twin in Hexagonally Close Packed (HCP) materials. Despite several propositions over 50 years, the Twin Boundary (TB) structure and twinning mechanism remain a debated topic, precluding determination of twinning energy barriers. This debate is resolved via Crystallographic Analytical Methods (CAM), Molecular Statics (MS) simulations in HCP Ti and Density Functional Theory (DFT) calculation of the Generalized Planar Fault Energy (GPFE) curve for several HCP materials. The {101¯2} crystallographic plane is “corrugated” comprising of two non-coincident sub-planes of lattice-sites (L-plane) and motif-sites (M-plane), causing ambiguity in determining the TB structure. This study resolves this ambiguity by establishing an energy-minimizing lattice-offset between the twin and matrix. At this offset, the TB forms by relaxation of both sub-planes into coincidence on a common atomic plane. A crystallographic calculation of this offset is proposed, extendable to non-single-lattice structures, in general. The twinning mechanism is determined, obtaining a shear-shuffle partition clarifying the motion of lattice and motif atoms. Nudged Elastic Band (NEB) simulations verify the mechanism along with disconnection-mediated migration of the twin. The GPFE is calculated for the first time in literature, to the best of our knowledge, revealing energy barriers for twin nucleation and migration. An absence of correlation of the unstable twinning energy barrier against twinning shear, Burgers vector magnitude or cohesive energy is shown, emphasizing the irreplaceability of the calculated barriers for predictive twinning models. Thus, a thorough clarification of the {101¯2} twinning mode is proposed, converging on the correct TB structure, twinning mechanism and energy barriers.