Atomic Structures of Symmetric Tilt Grain Boundaries in Hexagonal Close-Packed (hcp) Crystals

Molecular dynamics simulation and interface defect theory are used to determine the relaxed equilibrium atomic structures of symmetric tilt grain boundaries (STGBs) in hexagonal close-packed (hcp) crystals with a tilt axis. STGBs of all possible rotation angles theta from 0 deg to 90 deg are found to have an ordered atomic structure. They correspond either to a coherent, defect-free boundary or to a tilt wall containing an array of distinct and discrete intrinsic grain boundary dislocations (GBDs). The STGBs adopt one of six base structures, , i = 1, aEuro broken vertical bar, 6, and the Burgers vector of the GBDs is related to the interplanar spacing of the base structure on which it lies. The base structures correspond to the basal plane (theta = 0 deg, ); one of four minimum-energy, coherent boundaries, , and ; and the plane (theta = 90 deg, ). Based on these features, STGBs can be classified into one of six possible structural sets, wherein STGBs belonging to the same set i contain the same base boundary structure and an array of GBDs with the same Burgers vector , which vary only in spacing and sign with theta. This classification is shown to apply to both Mg and Ti, two metals with different c/a ratios and employing different interatomic potentials in simulation. We use a simple model to forecast the misorientation range of each set for hcp crystals of general c/a ratio, the predictions of which are shown to agree well with the molecular dynamics (MD) simulations for Mg and Ti.