Generalized Stacking Fault Energies of Diamond and Silicon under ⟨111⟩ Uniaxial Loading

The energy caused by atomic level shear in a crystal is called generalized fault energy (GSFE), This is an important material property for describing nanoscale plastic phenomena in crystalline materials, such as dislocation decomposition, nucleation, and twinning. During the shock loading process, the elastoplastic transition occurs after one-dimensional elastic strain, so the generalized stacking fault energy is of great significance in understanding the occurrence of plastic flow. Here, we calculate the generalized GSFE surface of glide (111) surface of silicon and diamond under uniaxial strain in [111] direction by using the first principles of density functional theory. Based on the translation symmetry of GSFE surface, we fit the GSFE surface expression obtained by Fourier series expansion and the generalized stacking fault energy curves for the $[{\overline{1}10}]$ (111) and $[ 11\overline{2}]$ (111) directions are given. With the increase of strain, the intrinsic fault energy (γ_I) and the unstable fault energy (γ_us) have obvious changes, and the ratio of the unstable stacking fault energy to the intrinsic stacking fault energy (γ_us/γ_I) decreases indicating that dislocations in crystals are not easily decomposed under uniaxial strain in the $\left\langle{111}\right\rangle$ direction. This result explains the results of dynamic experiments of dislocation evolution at four generations of light sources that the speed and strength of fault signals loaded along $\left\langle{111}\right\rangle$ direction are much lower than those loaded along $\left\langle{110}\right\rangle$ direction and $\left\langle{100}\right\rangle$ direction.