The role of entropy and enthalpy in high entropy carbides

Abstract

The thermodynamic stability of equiatomic mixed carbides, commonly referred to as high entropy carbides (HECs), is investigated via the CALculation of PHAse Diagrams (CALPHAD) approach for mixed carbides consisting of the group IVB and VB transition metal carbides as well as tungsten carbide. The Gibbs free energy of the B1-structured mixed carbides is computed using the compound energy formalism while that of the Bh-structured mixed carbides is evaluated using a point-defect model. The required thermodynamic data for the CALPHAD approach are obtained from density functional theory calculations and the Debye-Grüneisen model. The lower temperature limit at which the HECs mix in thermodynamic equilibrium is determined via numerical and analytical approaches. We find that enthalpy of mixing is at least as important as configurational mixing entropy in these mixed transition metal carbide compounds. The lower limit temperature where an equiatomic solid solution is present is largely independent of the number of components with the only exception being solutions containing tungsten carbide, where a weak temperature dependence is noted. Furthermore, the only equiatomic solid solutions that are thermodynamically stable below approximately 1000 K are those stabilized by enthalpy alone, indicating that many currently fabricated HECs are not at equilibrium at room temperature. Collectively, our results demonstrate that the formation of these carbides is controlled by the competition between entropy and enthalpy, or enthalpy alone, and thus these materials should be referred to as multi-principal component carbides since the former terminology can be misleading.