Reza Namakian1 George Voyiadjis1

1, Louisiana State University, Baton Rouge, Louisiana, United States

Anomalous basal type stacking faults (SFs) called partial SFs (PSFs) have been observed extensively within {10-12} 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 (1/3) <10-10> vector. Based on this special structural property of HCP metals, a new crystallographic model is developed for {10-12}<-1011> twinning system.
In the new model, PSFs are formed by (1/3) <101-0> displacement vectors (or relaxations) on every other basal plane and create a faulting plane on {101-2} plane. Subsequently, a zonal-twinning mechanism with a set of relatively simple shear and shear-shuffle atomic displacements having the smallest possible magnitudes is needed to accomplish {101-2}<1-011> twinning mode. Moreover, the pattern of atomic motions predicted in the new model is in excellent agreement with the ones obtained through molecular dynamic simulations in the literature.
The atomic displacement vectors associated with the zonal-twinning mechanism are derived analytically and expressed in a mathematical form generalized for the whole twinned domain of any HCP crystal with κ=c/a ratio within a practical range of 1.5<κ=c/a<1.9. This displacement field demonstrates that the atoms must move in a cooperative and coordinated manner during twinning.
For the special case of κ=√3, a pure shuffling mechanism is predicted by the current model in which the shear type atomic displacement vectors are zero, and shear-shuffle type atomic displacement vectors become net shuffle type atomic displacement vectors without varying magnitudes with respect to the height of the twinned domain.
For HCP metals with κ>√3, the twinning direction is reversed as reported in the literature previously. However, the new model reveals that the shear-shuffle type atomic displacement vectors are redirected toward the opposite of the twinning direction after some layers close to the twin boundary.
In contrast to the classical twinning mechanism, the new twinning mechanism suggests a simple and traceable pattern of atomic motions such that the associated absolute and relative magnitudes of the atomic displacement vectors are considerably smaller. Moreover, in the new mechanism, the resulted twinned lattice has a correct HCP structure, and the invariance of plain strain condition for {101-2} plane is preserved during twinning.
The new model describes a structural property of HCP crystals in which atoms can undergo spontaneous cooperative movements within these crystals, and consequently, substantial stress drops in the stress strain curves can be observed at the instance of twin formation. This macroscopic effect is expressed by a deformation gradient which is actually indicating that the macroscopic effect of the current mechanism is a simple shear process, in agreement with all experimental observations and simulation studies in the literature on the significance of shear during twinning.