George Voyiadjis1 2 Reza Namakian1

1, Civil and Environmental Engineering, Louisiana State University, Baton Rouge, Louisiana, United States
2, Computational Solid Mechanics Laboratory, Louisiana State University, Baton Rouge, Louisiana, United States

Generalized stacking fault energy (GSFE) analysis is a valuable technique to provide some insights and information on dislocation core structures and mobilities which are controlled by crystal resistance to shearing along a specific crystallographic plane. This technique is composed of the following steps: 1) cutting a single crystal along a fault plane, 2) shifting rigidly the upper half of the newly created bi-crystal along an arbitrary fault vector which belongs to the fault plane, 3) releasing the shifted crystal on the top of the lower half crystal, 4) relaxing the bi-crystal atoms in the direction perpendicular to the newly generated fault plane. By generating GSFE profile, one should be able to recognize the local minima on the profile correspond to stable stacking faults (SFs).

However, the stability of the SFs should be checked once the atoms are allowed to relax in all directions. This issue could be heightened in metals with hexagonal close-packed (HCP), like magnesium or Mg, due to the unsymmetrical feature of atomic configuration on the two sides of the slip direction. In this work, two relaxing directions are considered, out-of-plane (N-direction) and in-plane (P-direction). N-direction is normal to the slip plane which is {10-11}, the first pyramidal or compression twinning plane in HCP metals. P-direction is parallel to the slip plane and perpendicular to the slip direction which is <-1012>. Accordingly, N-direction relaxation (one direction relaxation) and N-P-directions relaxation (two directions relaxation) schemes are used here.

To study the effect of different relaxation schemes on GSFE profile for {10-11}<-1012> slip system, a sample with 80,000 atoms is constructed in which the height of the sample is large enough to minimize the effect of free surface on the fault plane. Four different empirical potentials, three of which designed by embedded-atom method (EAM) and one with modified EAM (MEAM), available in the literature for Mg are employed in Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) to generate GSFE profile as described above with N-direction and N-P-directions relaxations.

We report here that results of N-direction and N-P-directions relaxations both coincide partly along direction, however, N-P-directions relaxation shows significant oscillations in the GSFE profile for all four potentials. This deficiency could be attributed to the following reasons. First, GSFE is a nonphysical projection of crystal slip. Dislocation emission and motion incorporate two energy components: (1) initial elastic deformation and (2) breaking of atomic bonds. While the second term can be assessed by the GSFE, the contribution of elastic deformation is absent from the rigid GSFE model. Second, the traditional way of cutting, shifting, releasing, and finally relaxing the atoms to generate GSFE profile due to the unsymmetrical feature of atomic configuration on the two sides of the slip direction causes a force along the P-direction, which influences not only the value but also the location of the calculated GSFE. Therefore, one may observe the fluctuations in the GSFE profile.

To resolve all the above mentioned issues related to the rigid GSFE profile, nudged elastic band method (NEBM) as a minimum path energy finder (MEP) is employed to find precise values of the saddle points in the GSFE profile. The SFE profile obtained by NEBM along direction shows a completely different energy profile in shape and magnitudes with respect to the GSFE one such that the magnitude of the energy barriers are reduced significantly thanks to the incorporation of elastic deformation energy in NEBM and non-straight shape of the slip trace obtained by NEBM. Therefore, NEBM can provide more accurate and robust results about SFEs compared to GSFE method.