Exploring Hydrogen-Bearing Metallic Alloys: Phonon-Mediated Superconductivity in (Zr,Hf)H3 under High Pressure

Advanced structural forecasting of alloy hydrides, particularly through cluster expansion combined with first-principles calculations, opens up new possibilities for discovering novel phases in transition metal alloy hydrides like (Zr,Hf)H₃. Within this framework, significant findings have been made for compounds Zr₇HfH₂₄, Zr₄Hf₂H₁₈, Zr₂Hf₂H₁₂, and Zr₂Hf₄H₁₈, which demonstrate thermodynamic stability at 100 GPa. All identified structures exhibit metallic properties, suggesting a promising pathway to superconductivity. In terms of superconducting properties, Zr₇HfH₂₄, Zr₄Hf₂H₁₈, Zr₂Hf₂H₁₂, and Zr₂Hf₄H₁₈ show critical temperatures (T_c) of 15.9, 14.6, 8.2, and 12.8 K, respectively, at 100 GPa. Notably, Zr₄Hf₂H₁₈ achieves the highest T_c within the (Zr,Hf)H₃ series, reaching approximately 17 K at 150 GPa. Our analysis of the superconducting state is based on H-rich criteria under specific conditions, revealing that hydrogen’s contribution to the partial density of states is lower than that of hafnium and zirconium. The investigation also finds that these structures lack H clathrate configurations or H₂-like molecular units, suggesting they are unlikely to reach near-room-temperature T_c. These results highlight how structural frameworks supported by H or H₂-like molecules could potentially enhance superconductivity. Additionally, the alignment of the vibrational modes of the alloy with those observed in hafnium suggests that Hf-substituted Zr alloys support superconductivity and offer theoretical feasibility for achieving higher critical temperatures across a broader range of alloying combinations.