Effect of strain on the stacking fault energy of copper: A first-principles study

Abstract

The intrinsic stacking fault energy (SFE) of copper under volumetric, longitudinal, and shear strains is investigated using density functional theory (GGA-PBE). Calculations are performed using a copper slab model aligned perpendicular to the (111) intrinsic stacking fault plane. The calculated SFE for unstrained copper is \ensuremath{\gamma} $=$ 41 mJ/m${}^{2}$. Results show a strong dependence of \ensuremath{\gamma} on strain and distinct behavior for different types of strain: (a) volumetric and longitudinal in the direction perpendicular to the stacking fault, (b) longitudinal parallel to the stacking fault, and (c) shear parallel to the stacking fault. In the first case (a), the SFE decreases monotonically with strain with a slope $d$\ensuremath{\gamma}/$d$\ensuremath{\epsilon}${|}_{\ensuremath{\varepsilon}=0}$ $=$ \ensuremath{-}0.44 J/m${}^{2}$ and \ensuremath{-}0.87 J/m${}^{2}$ for volumetric and longitudinal, respectively, and with ${d}^{2}$\ensuremath{\gamma}/$d$\ensuremath{\epsilon}${}^{2}$ g 0. In contrast, for longitudinal strain parallel to the stacking fault (b), the SFE dependence exhibits ${d}^{2}$\ensuremath{\gamma}/$d$\ensuremath{\epsilon}${}^{2}$ 0 with a maximum at \ensuremath{\epsilon} \ensuremath{\approx} \ensuremath{-}0.015. For the case of shear parallel to the stacking fault (c), the SFE is nearly constant at small and moderately large strain, but drops rapidly at very large strain (by a factor of 1/3 for $\ensuremath{\langle}\overline{1}10\ensuremath{\rangle}{111}$ shear at \ensuremath{\epsilon} $=$ \ifmmode\pm\else\textpm\fi{}0.1). For large $\ensuremath{\langle}11\overline{2}\ensuremath{\rangle}{111}$ shear strains, the SFE can either increase or decrease at large strain depending on the sign of the strain. In volumetric or longitudinal (perpendicular to the stacking fault) tension and longitudinal strain in the boundary plane (and for some shear directions), the SFE can become negative, implying a limit on the stability of the fcc crystal structure. The strong dependence of the SFE on strain suggests deep implications for the mechanical properties, microstructural evolution, and dynamic plasticity of metals at high pressure, during severe plastic deformation, and in shock-loading conditions.