Exploring Hydrogen-Bearing Metallic Alloys: Phonon-Mediated\nSuperconductivity in (Zr,Hf)H<sub>3</sub> under High Pressure

Advanced structural\nforecasting of alloy hydrides, particularly\nthrough cluster expansion combined with first-principles calculations,\nopens up new possibilities for discovering novel phases in transition\nmetal alloy hydrides like (Zr,Hf)H<sub>3</sub>. Within this framework,\nsignificant findings have been made for compounds Zr<sub>7</sub>HfH<sub>24</sub>, Zr<sub>4</sub>Hf<sub>2</sub>H<sub>18</sub>, Zr<sub>2</sub>Hf<sub>2</sub>H<sub>12</sub>, and Zr<sub>2</sub>Hf<sub>4</sub>H<sub>18</sub>, which demonstrate thermodynamic stability at 100 GPa. All\nidentified structures exhibit metallic properties, suggesting a promising\npathway to superconductivity. In terms of superconducting properties,\nZr<sub>7</sub>HfH<sub>24</sub>, Zr<sub>4</sub>Hf<sub>2</sub>H<sub>18</sub>, Zr<sub>2</sub>Hf<sub>2</sub>H<sub>12</sub>, and Zr<sub>2</sub>Hf<sub>4</sub>H<sub>18</sub> show critical temperatures (<i>T</i><sub>c</sub>) of 15.9, 14.6, 8.2, and 12.8 K, respectively,\nat 100 GPa. Notably, Zr<sub>4</sub>Hf<sub>2</sub>H<sub>18</sub> achieves\nthe highest <i>T</i><sub>c</sub> within the (Zr,Hf)H<sub>3</sub> series, reaching approximately 17 K at 150 GPa. Our analysis\nof the superconducting state is based on H-rich criteria under specific\nconditions, revealing that hydrogen’s contribution to the partial\ndensity of states is lower than that of hafnium and zirconium. The\ninvestigation also finds that these structures lack H clathrate configurations\nor H<sub>2</sub>-like molecular units, suggesting they are unlikely\nto reach near-room-temperature <i>T</i><sub>c</sub>. These\nresults highlight how structural frameworks supported by H or H<sub>2</sub>-like molecules could potentially enhance superconductivity.\nAdditionally, the alignment of the vibrational modes of the alloy\nwith those observed in hafnium suggests that Hf-substituted Zr alloys\nsupport superconductivity and offer theoretical feasibility for achieving\nhigher critical temperatures across a broader range of alloying combinations.