Energy landscape of deformation twinning in bcc and fcc metals

Abstract

Energy landscapes of $(2\overline{1}\overline{1})⟨111⟩$ deformation twinning in bcc Mo and $(111)⟨11\overline{2}⟩$ deformation twinning in fcc Al and Cu are determined using density functional theory for sliding of layers numbering up to 7. In bcc Mo, the minimum thickness of a metastable twin is two layers, while twin embryos of three and four layers are unstable. Starting from five layers, the Mo twin can grow in a layer-by-layer fashion. The twin boundary formation and migration energies are found to be 607 and $40\phantom{\rule{0.3em}{0ex}}\mathrm{mJ}∕\mathrm{m}$, respectively, implying that partial dislocations on twin boundaries will have wide cores and high mobilities. The stress to homogeneously nucleate a partial loop on the boundary of a thick twin is determined to be only $1.4\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, indicating that once a deformation twin in Mo reaches a critical thickness, which we estimate to be six layers, it can grow rather easily. Based on simple defect mechanics considerations, we estimate the condition for runaway defect growth requires twin embryo thickness to be tens of layers. Comparing the twinning energy landscape for Mo with those of Al and Cu, we find the former to have a longer ranged interlayer mechanical coupling, which is due to angular bonding and weaker electron screening in the intervening layers. Between Al and Cu, interactions in the former are relatively longer ranged.