Lattice distortion in high-entropy carbide ceramics from first-principles calculations

The idea of high-entropy alloys (HEAs) has profoundly stimulated the recent development of novel entropy-stabilized ceramics. Herein we explore the local lattice distortion, one of the core effects in HEAs responsible for their extraordinary properties, in typical high-entropy ceramic (HEC) carbides with single-phase rock salt structures. We first quantify the local distortions based on first-principles calculations, and then investigate their influences on the structural properties, lattice stability, electronic structures, mechanical deformation, defect energetics, and thermodynamic properties. Our results show that carbon generally exhibits the most substantial distortion. On average, large local distortion is found in (NbTiVZr)C and (MoNbTaVW)C. Such distortion plays a crucial role in stabilizing HECs by lowering their enthalpy of formation. The electronic structure of HECs depends strongly on the local distortion, which can enhance charge transfer between transition metals and carbon atoms. We further show that distortion makes HECs soft and ductile due to the delocalization of electronic charges. The formation energies of C vacancies decrease significantly due to local distortion, resulting in high concentrations of C vacancies. The presence of high-concentration C vacancies release distortion and helps to retain the high strength of HECs. Finally, we show that lattice distortion has a great impact on the thermodynamic quantities of HECs, such as thermal expansion coefficient and Debye temperature.