  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.
