Theoretical predictions and experimental verification on the phase stability of enthalpy-stabilized HE TMREB₂s

Transition metal diborides (TMB₂s) are the materials of choice in extreme environments due to their excellent thermal and chemical stabilities. However, the degradation of oxidation resistance of TMB₂s at elevated temperature still hinders their applications. To cope with this challenge, it is effective to incorporate rare earth elements to form high-entropy transition and rare-earth metal diborides (HE TMREB₂s). To obtain thermodynamically stable single-phase structures for HE TMREB₂s, a “16 × 16 mixed enthalpy matrix” is constructed using first-principles calculations to predict the single-phase formation ability of 120 two-component diborides (TCBs). Through the use of the “16 × 16 mixed enthalpy matrix” of TCBs, specific combinations of TMB₂s and REB₂s that are most likely to form single-phase HE TMREB₂s are confirmed. Subsequently, based on the energy distribution of the local mixing enthalpies of all possible configurations, the enthalpy and entropy descriptors of HE TMREB₂s (RE = Sc, Lu, Tm, Er, Ho and Dy) are investigated. It is found that the mixing enthalpy plays a critical role in the stability of the single-phase HE TMREB₂s, i.e., HE TMREB₂s are enthalpy-stabilized materials. The experimental results further confirm that enthalpy dominates the thermodynamic domain and drives the stability of REB₂s in HE TMREB₂s. This study validates that enthalpy-stabilized HE TMREB₂s can further expand the compositional space of ultrahigh temperature ceramics (UHTCs) and is expected to further improve the oxidation resistance and high temperature properties of UHTCs.