Ab initio calculations based on the density functional theory have been performed to investigate the migrations of hydrogen(H) and helium(He) atoms in β-phase scandium(Sc),yttrium(Y),and erbium(Er) hydrides with three different ratios of H to metal.The results show that the migration mechanisms of H and He atoms mainly depend on the crystal structures of hydrides,but their energy barriers are affected by the host-lattice in metal hydrides.The formation energies of octahedral-occupancy H(H oct) and tetrahedral vacancy(V tet) pairs are almost the same(about 1.2 eV).It is of interest to note that the migration barriers of H increase with increasing host-lattice atomic number.In addition,the results show that the favorable migration mechanism of He depends slightly on the V tet in the Sc hydride,but strongly on that in the Y and Er hydrides,which may account for different behaviours of initial He release from ScT2 and ErT2. Ab initio calculations based on the density functional theory have been performed to investigate the migrations of hydrogen (H) and helium (He) atoms in β-phase scandium (Sc), yttrium (Y), and erbium (Er) hydrides with three different ratios of H to metal. The results show that the migration mechanisms of H and He atoms mainly depend on the crystal structures of hydrides, but their energy barriers are affected by the host-lattice in metal hydrides. The formation energies of octahedral-occupancy H (H tet) and tetrahedral vacancy (V tet) pairs are almost the same (about 1.2 eV). It is interest to note that the migration barriers of H increase with increasing host-lattice atomic number. In addition, the results show that the favorable migration mechanism of He depends slightly on the V tet in the Sc hydride, but strongly on that in the Y and Er hydrides, which may account for different behaviors of the initial He release from ScT2 and ErT2.