Effect of strain on generalized stacking fault energies and plastic deformation modes in fcc-hcp polymorphic high-entropy alloys: A first-principles investigation

The generalized stacking fault energy (GSFE) is a material property that can provide invaluable insights into describing nanoscale plasticity phenomena in crystalline materials. Lattice strains have been suggested to influence such phenomena. Here, the GSFE curves for sequential faulting pathways in dual phase [face-centered cubic (fcc) and hexagonal close-packed (hcp)] ${\mathrm{Cr}}_{20}{\mathrm{Mn}}_{20}{\mathrm{Fe}}_{20}{\mathrm{Co}}_{20}{\mathrm{Ni}}_{20}, {\mathrm{Cr}}_{25}{\mathrm{Fe}}_{25}{\mathrm{Co}}_{25}{\mathrm{Ni}}_{25}, {\mathrm{Cr}}_{20}{\mathrm{Mn}}_{20}{\mathrm{Fe}}_{34}{\mathrm{Co}}_{20}{\mathrm{Ni}}_{6}, {\mathrm{Cr}}_{20}{\mathrm{Mn}}_{20}{\mathrm{Fe}}_{30}{\mathrm{Co}}_{20}{\mathrm{Ni}}_{10}$, and ${\mathrm{Cr}}_{10}{\mathrm{Mn}}_{30}{\mathrm{Fe}}_{50}{\mathrm{Co}}_{10}$ high-entropy alloys are investigated on ${{111}}_{\text{fcc}}$ and ${(0002)}_{\text{hcp}}$ close-packed planes using density-functional calculations. The dependence of GSFEs on imposed volumetric and longitudinal lattice strains is studied in detail for ${\mathrm{Cr}}_{20}{\mathrm{Mn}}_{20}{\mathrm{Fe}}_{20}{\mathrm{Co}}_{20}{\mathrm{Ni}}_{20}$ and ${\mathrm{Cr}}_{10}{\mathrm{Mn}}_{30}{\mathrm{Fe}}_{50}{\mathrm{Co}}_{10}$. The competition between various plastic deformation modes is discussed for both phases based on effective energy barriers determined from the calculated GSFEs and compared with experimentally observed deformation mechanisms. The intrinsic stacking fault energy, unstable stacking fault energy, and unstable twinning fault energy are found to be closely related in how they are affected by applied strain. The ratio of two of these planar fault energies can thus serve as characteristic material property. An inverse relationship between the intrinsic stacking fault energy in the hcp phase and the axial ratio ${(c/a)}_{\text{hcp}}$ is revealed and explained via band theory.