Atomic Structures of $$ [0\bar{1}10] $$ Symmetric Tilt Grain Boundaries in Hexagonal Close-Packed (hcp) Crystals

Abstract

Molecular dynamics simulation and interface defect theory are used to determine the relaxed equilibrium atomic structures of symmetric tilt grain boundaries (STGBs) in hexagonal closepacked (hcp) crystals with a ½0 " 110 tilt axis. STGBs of all possible rotation angles h 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, P ðiÞ B , i = 1, …, 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 (h = 0 deg, P ð1Þ B ); one of four minimum-energy, coherent boundaries, ð " 2111Þ; ð " 2112Þ; ð " 2114Þ, and ð " 2116Þ P B ). 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 P ðiÞ B and an array of GBDs with the same Burgers vector b ðiÞ GB , which vary only in spacing and sign with h. 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.

Energetics of vacancy segregation to symmetric tilt grain boundaries in hexagonal closed pack materials

“…Figure 2 shows grain boundary energies as a function of the misorientation angle for the 12 10 and 01 10 tilt axes in Mg, Ti, and Zr. The trend observed for the grain boundary energy as a function of a misorientation angle is comparable to what has been previously reported for Mg and Ti 34,35 The energy cusps for the 12 10 system were identified as 1 013 θ 32.15°, 1 012 θ 43.31°, 1 011 θ 62.06°, and 2 021 θ 75.21° twin boundaries for magnesium, in order of increasing misorientation angle. Similarly, in the case of the 01 10 tilt axis, the energy cusps were 2 116 , 2 114 , 2 112 , and 2 111 twin boundaries.…”

“…[29][30][31][32][33] In addition, grain boundary energies can be computed through theoretical formulations and computational methods. The role of the grain boundary plane in determining the grain boundary energy was investigated by Wang and Beyerlein, 34,35 who performed extensive calculations of the symmetric tilt grain boundary (STGB) energies for hexagonal closed pack (HCP) metals. The aforementioned research notwithstanding, the role of grain boundary character on the energetics of point defects' segregation at the interface has received less attention, especially in HCP materials with varying degrees of grain boundary SUs.…”

Strain rate and temperature effects on the selection of primary and secondary slip and twinning systems in HCP Zr

“…Later, using a homogeneous twin nucleation model, it was argued that f1 1 2 2gh1 1 2 3i twinning is preferred over f1 0 1 1gh1 0 1 2i twinning when the twin-boundary energy for f1 0 1 1g h1 0 1 2i twins is within 10% of or greater than that for f1 1 2 2gh1 1 2 3i twins and that transition arises because their relative boundary energies change with temperature [87]. However, both MD and first principles calculations find that the f1 0 1 1gh1 0 1 2i twin boundary energy is substantially lower than the f1 1 2 2gh1 1 2 3i twin boundary energy [88][89][90][91], with 74.3 mJ/m 2 compared to 123.8 mJ/ m 2 . Likewise, differences in the mobility of f1 0 1 1g h1 0 1 2i and f1 1 2 2gh1 1 2 3i twinning dislocations cannot provide an explanation [90].…”

Toward understanding twin–twin interactions in hcp metals: Utilizing multiscale techniques to characterize deformation mechanisms in magnesium

“…This feature is a consequence of the relatively low energy that the B-P boundary exhibits [45], and will play a role in continued boundary mobility, especially in the case of detwinning under cyclic loading. The faceted nature of the boundaries may facilitate dislocation motion along the twin boundaries and potential shuffling of atoms across the boundaries.…”