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

Using first principles calculations, ${111}$ intrinsic stacking fault (ISF) energies in groups IVB, VB, and VIB high-entropy transition metal carbides (HETMCs) are shown to be predictable from an optimized rule of mixtures based on the atomic arrangement near the stacking fault. A composition-independent linear relationship is demonstrated between the ISF energies and the unstable stacking fault (USF) energies along the $\ensuremath{\langle}11\overline{2}\ensuremath{\rangle}{111}$ \ensuremath{\gamma} surface slip path. This relationship represents a new application of the Evans-Polanyi-Semenov principle by treating the ISF and USF energies as analogous to the heat of reaction and transition state barrier in chemical reactions. Further, a full defect energy distribution can be obtained from the predicted ISF energies for each early transition metal HETMC. Balancing the elastic repulsion between partial dislocations with the distribution of ISF energies, we show that Shockley partial edge dislocations should remain bound for HETMCs with valence electron concentration up to 9.6, even when the average stacking fault energy is negative.