Interfacial defect properties of high-entropy carbides: Stacking faults, Shockley partial dislocations, and a new Evans-Polanyi-Semenov relation

Abstract

Using first principles calculations, {111} intrinsic stacking fault (ISF) energies in Group IVB, VB, and VIB high-entropy transition metal carbides are shown to be predictable from an optimized rule of mixtures based on the properties of the single metal carbide constituents present near the stacking fault. A composition-independent linear relationship is demonstrated between the ISF energies and the unstable stacking fault (USF) energies along the <112>{111} gamma surface slip path. Treating the ISF and USF energies as analogous to the heat of reaction and transition state barrier in chemical reactions, this linear relationship represents a new application of the Evans-Polanyi-Semenov principle. Further, a full defect energy distribution can be obtained from the predicted ISF energies with only the composition as an input for the mixed early-transition metal carbides. Applying a model that balances the elastic repulsion between partial dislocations with the distribution of ISF energies, we show that Shockley partial edge dislocations should remain bound for all valence electron concentration values up to about 9.6, even when the average stacking fault energy is negative.