The Rule of Mixtures, a New Evans-Polanyi-Semenov Relation and Twinning Predictions for High Entropy Transition Metal Ceramics

High entropy ceramics, typically characterized by five or more components in roughly equimolar concentrations arranged randomly on one or more crystal sublattices, have the potential for outstanding mechanical properties as well significant challenges for understanding and predicting these properties. In this work, we have used first-principles calculations to probe the {111} twinning properties of Group IVB, VB, and VIB high-entropy transition metal carbides. We find that the twin boundaries are predictable through an optimized rule-of-mixtures based on the properties of individual metal carbide constituents near the twin plane. We also find that the unstable twin energy, which is a barrier along the <112> {111} gamma surface slip path, can be related to the twinning and stacking fault energies through an Evans-Polanyi-Semenov (EPS) relation. Typically used to describe a linear relation between activation energy and heat of reaction in a series of related chemical processes, we will show how this new application of the EPS relation leads to analytic relations for twinnability as a function of valance electron concentration for these materials.