The effect of normal stress on stacking fault energy in face-centered cubic metals

TL;DR

This study quantifies how normal stress applied to the (111) plane modulates generalized stacking fault energies in six FCC metals using density functional theory, revealing that both stable and unstable stacking fault energies rise under compression and fall under tension, with SF formation accompanied by a small but finite out-of-plane expansion. The work demonstrates strong, cross-metal scaling of SFE, USFE, and related elastic properties, and links these trends to dislocation phenomena such as cross-slip and nucleation at interfaces. By benchmarking a suite of classical and machine-learning interatomic potentials, the authors show that ML potentials (notably MTP and PINN) generally outperform classical forms in high-stress regimes, while many classical potentials fail or yield unphysical results, especially under tens of GPa. They also discuss approaches to improve potential reliability, including training on large deformations and explicitly fitting the HCP-FCC energy difference under varying volumes. The findings have practical implications for predictive atomistic modeling of shock, nanoscale plasticity, and fracture in FCC metals, where accurate high-stress SF energetics are critical.

Abstract

Plastic deformation and fracture of FCC metals involve the formation of stable or unstable stacking faults (SFs) on (111) plane. Examples include dislocation cross-slip and dislocation nucleation at interfaces and near crack tips. The stress component normal to (111) plane can strongly affect the SF energy when the stress magnitude reaches several to tens of GPa. We conduct a series of DFT calculations of SF energies in six FCC metals: Al, Ni, Cu, Ag, Au, and Pt. The results show that normal compression significantly increases the stable and unstable SF energies in all six metals, while normal tension decreases them. The SF formation is accompanied by inelastic expansion in the normal direction. The DFT calculations are compared with predictions of several representative classical and machine-learning interatomic potentials. Many potentials fail to capture the correct stress effect on the SF energy, often predicting trends opposite to the DFT calculations. Possible ways to improve the ability of potentials to represent the stress effect on SF energy are discussed.

Figures (24)

• Figure 1: (a) Atomic structure of the cell used in the GSFE calculations. The cell contains 24 (111) layers, each with two atoms. The atoms are colored by their $Z$ positions to provide better visualization of the structure. (b) Illustration of the tilted-cell method. By tilting the $Z$ axis towards $Y$ by an amount $u$, a stacking fault is created at the boundary between the primary cell and its periodic image. The solid rectangle marks the primary cell, and the dashed rectangle marks its periodic image. The atoms in FCC and non-FCC environments are shown in green and red, respectively.
• Figure 2: GSFE versus shear displacement under applied normal stress $\sigma_{n}$ obtained by DFT calculations. (a) Al, (b) Cu, (c) Au, (d) Pt, (e) Ni, and (f) Ag. The curves were computed from Eq. (\ref{['eq:gsfe1']}). The triangular symbols represent SFE calculations from the exact Eq. (\ref{['eq:gsfe']}).
• Figure 3: SFE in six FCC metals obtained by DFT calculations. (a) Physical coordinates. (b) Normalized coordinates.
• Figure 4: USFE in six FCC metals as a function of normal stress obtained by DFT calculations. (a) Physical coordinates. (b) Normalized coordinates.
• Figure 5: The ratio of the SFE and the USFE as a function of normal stress for six FCC metals obtained by DFT calculations.