We performe first-principles density functional theory calculations to investigate the stability and mechanical properties of various HfHx (0 ≤ x ≤ 1) phases.For pure Hf phases,the calculated results show that the HCP and FCC phases are mechanically stable,while the BCC phase is unstable at 0 K.Also,as for various HfHx phases,we find that H location and concentration could have a significant effect on their stability and mechanical properties.When 0 ≤ x ≤ 0.25,the HCP phases with H at (tetrahedral) T sites are energetically most stable among various phases.The FCC and BCC phases with H at T sites tu to be relatively more favorable than the HCP phase when H concentration is higher than 0.25.Furthermore,our calculated results indicate that the H solution in Hf can largely affect their mechanical properties such as the bulk moduli (B) and shear moduli (G).