Elementary Mechanisms of Shear-Coupled Grain Boundary Migration

A detailed theoretical study of the elementary mechanisms occurring during the shear-coupled grain boundary (GB) migration at low temperature is performed focusing on both the energetic and structural characteristics. The migration of a $\Sigma 13(320)$ GB in a copper bicrystal in response to external shear displacements is simulated using a semiempirical potential. The minimum energy path of the shear-coupled GB migration is computed using the nudge elastic band method. The GB migration occurs through the nucleation and motion of GB steps identified as disconnections. Energy barriers for the GB and disconnection migrations are evaluated.

Figure 1

(a) Sketch of the simulation cell. (b) Configurations of the $\Sigma 13$ GB projected in the ($x$, $y$) plane: Black (gray) and red (pink) atoms belong to different grains. Black (red) and gray (pink) atoms do not have the same $z$ coordinate. For black and white printing, red, gray, and pink atoms appear as dark gray, gray, and light gray atoms.

Figure 2

(a) Shear stress and (b) potential energy variation (black, red, and green) as a function of the shear displacement. Black and red curves correspond to the initial and final configurations of the GB. The blue curve reports the energy of the transition state from the initial to the final configuration. Dashed lines are a guide to the eyes. $c_i$ and $c_f$ denote the initial $\mathrm{RC}=0$ and final $\mathrm{RC}=1$ configurations used in the NEB method with $d=0.066\mathrm{nm}$ [cf Fig. 3a]. The cell $y$ and $z$ sizes are 1.3 nm and 1.4 nm. For black and white printing, red and blue curves appear as dark and very dark gray curves.

Figure 3

(a) MEP energy profile as a function of the RC. (b) Same as Fig. 1b for the initial, metastable, and final GB configurations. Black curves are guides to the eyes. Blue and green squares display the main moving atoms. The cell $y$ and $z$ sizes are 1.3 nm and 1.4 nm.

Figure 4

(a) Minimum energy path per unit area as a function of the RC for $d=0.066\mathrm{nm}$ for 5 different cell $y$ sizes ranging from 1 to $5L_{[2\overline{3}0]}$ ($z$ size is 1.4 nm). (b) Minimum energy path (solid line) per unit disconnection length as a function of the RC for $d=0.066\mathrm{nm}$ (the cell $y$ and $z$ size are 6.5 nm and 1.4 nm) and energy variation (dashed line) for stable configurations, as fitted from elasticity theory Eq. (1). The quantities $\Delta {\zeta }_{\mathrm{bar}}^{\mathrm{GB}}$ and $\Delta {\zeta }_{\mathrm{bar}}^{\mathrm{disc}}$ are roughly reported.

Figure 5

Energy barrier per unit disconnection length $\Delta {\zeta }_{\mathrm{bar}}^{\mathrm{GB}}$ as a function of the shear displacement for 5 different cell $y$ sizes ranging from 1 to $5L_{[2\overline{3}0]}$ ($z$ size is 1.4 nm).