Type-I clathrate calcium hydride and its hydrogen-vacancy structures at high pressure

Recently, the first predicted metal clathrate hydride CaH₆ was successfully synthesized experimentally and shown to have a superconducting critical temperature Tc exceeding 200 K. However, experimental findings suggest the existence of additional unidentified phases besides CaH₆. In this study, we performed an extensive structure search of the Ca--H system at 200 GPa, revealing a thermodynamically stable type-I clathrate hydride, Ca₈H₄₆, along with two analogous structures featuring hydrogen vacancies. Ca₈H₄₆ exhibits a high Tc range of 210--223 K at 150 GPa, and the presence of hydrogen vacancies shifts the Tc. Our simulated x-ray-diffraction patterns, calculated equation of state, and Tc's for Ca₈Hₓ (x=44-46) agree with the experimental results, confirming their presence in multiple synthesized phases. Our findings serve to revise the Ca--H phase diagram under high pressure and offer valuable insights into the effects of hydrogen vacancies in Ca₈H₄₆, which explain the anomalous decrease in Tc observed in experiments.