An atomic displacive model for [formula omitted] twinning in hexagonal close packed metals with the emphasis on the role of partial stacking faults in formation of [formula omitted] twins

Abstract

Anomalous basal type stacking faults (SFs) called partial SFs (PSFs) have been observed extensively within {101¯2} or extension twins for a variety of hexagonal close packed (HCP) metals. The formation of PSFs can generate a stacking sequence in which every other basal plane has been displaced by a 1/3101¯0 vector. Based on this special structural property of HCP metals, a new crystallographic model is developed for 101¯21¯011 twinning system. In contrast to homogenous lattice shearing process in classical twinning model, the new model describes that formation of PSFs can provide transient locations of atoms in such a way that a subsequent zonal-twinning mechanism including a set of relatively simple shear and shear-shuffle atomic displacements toward twinning direction is sufficient to accomplish 101¯21¯011 twinning. These shear and shear-shuffle atomic displacements are formally determined, and their analytical expressions are given in a generalized explicit form for a whole twinned domain of any HCP crystal with c/a ratio between 1.5 and 1.9. It will be shown that the macroscopic effect of spontaneous cooperative movements of atoms in the new mechanism is a simple shear, and the invariant plane strain condition of {101¯2} or twinning plane is preserved.