Asymmetric equilibrium core structures of pyramidal-II 〈c+a〉 dislocations in ten hexagonal-close-packed metals

Abstract

The structures of pyramidal-II $\ensuremath{\langle}c+a\ensuremath{\rangle}$ dislocations, one of the most important defects in structural hexagonal-close-packed (HCP) metals, have not been fully characterized for many of the HCP metals in use today. Here, we employ ab initio informed phase-field dislocation dynamics to determine the minimum energy structure of pyramidal $\left\{\overline{1}\overline{1}22\right\}\ensuremath{\langle}11\overline{2}3\ensuremath{\rangle}$ dislocations in ten HCP metals, including Be, Co, Mg, Re, Ti, Zn, Cd, Hf, Y, and Zr. As input for the simulations, we calculate, using first-principles density functional theory, the $\left\{\overline{1}\overline{1}22\right\}$ generalized stacking fault energy (GSFE) curves for all ten metals. From these calculations, it is found that magnetism in Co is necessary for achieving a local minimum in the GSFE curve. We observe in simulations that edge and screw character dislocations split into two partials separated by a low-energy intrinsic stacking fault. The splitting distance is shown to scale inversely with the local minimum energy normalized by the product of its shear modulus and Burgers vector. Interestingly, some HCP metals exhibit an asymmetric structure, with either unequal partial Burgers vectors or widths, in contrast to the symmetric configuration expected from linear elastic dislocation theory. We explain these structures by properties of the local maxima in their GSFE curves. Metals with larger degrees of elastic anisotropy result in dislocations with larger splitting distances than would be expected under the commonly used assumption of elastic isotropy. These findings on the sizes and asymmetry in the structures of pyramidal-II $\ensuremath{\langle}c+a\ensuremath{\rangle}$ dislocations are fundamental to understanding how these dislocations glide and interact or react with other defects when these metals are mechanically strained.