Twinning pathway in BCC molybdenum

– The (21̄1̄)〈111〉 twinning energy landscape of BCC Mo is determined using the density functional theory for embryos containing 2 to 7 layers. The 2-layer embryo is metastable, whereas the 3and 4-layer ones are unstable. Layer-by-layer growth starts at 5 layers. The twin boundary formation and migration energies are found to be 607mJ/m and 40mJ/m, respectively, indicating that twin partial dislocations have wide cores and high mobilities. The stress to homogeneously nucleate an additional partial loop on the boundary of a sufficiently thick twin is only 1.4GPa; this implies that once a deformation twin reaches critical thickness, which we estimate to be 6 layers, subsequent growth in thickness is easy. Deformation twinning [1] is a primary mode of strain-energy relaxation [2] which competes with dislocation slip as the dominant carrier of plastic deformation. The outcome of the competition depends on the stress level [3], temperature, nature of existing defects like cracks [4], and intrinsic material properties [5]. It is generally believed that at low-to-intermediate stress levels, the activation energy of the nucleating deformation twin is greater than that of the slip. However, once nucleated, a deformation twin is able to produce a large amount of plastic strain within a very short time. Therefore, deformation twinning tends to occur more frequently under high strain-rate loading such as laser shock [6], at lower temperatures [7], and near stress concentrators [2, 8]. The mesoscopic kinematics of twin growth has been proposed to involve the pole mechanism [9] and variants [10,11], and the double-cross-slip mechanism [12,13]. On the other hand, microscopic energetic information, even for simple metals, is lacking. Recently, Tadmor and collaborators have established an intrinsic material property called the “twinnability” [4], which is the ratio of γus, the unstable stacking energy, to γut, the unstable twinning energy, both in J/m. Basically, γus and γut are the barriers for a 1-layer partial