Table 1 Dimensions of supercells and corresponding k-point meshes used in the present DFT calculations.

Table 2 Lattice constants (a, b, c), the formation energy (ΔEf) of the B2 compound, the formation energies (ΔEf) of hydrides per one mol of H2 (Eqs. (7)?(9)), and the unit cell volume obtained by the present DFT calculations as compared with reported experimental and DFT results. Results for the B2 TiFe compound and hydrides (TiFeH and TiFeH2) are presented.

Table 3 The solution energy (Eq. (3)) and the volume expansion due to the presence of an H atom on each interstitial site obtained by the present DFT calculations.

Table 4 The site preference of additional alloying elements in the B2 TiFe compound obtained from the standard defect formation energy Eqs. (10)-((12)) and the defect formation energy based on non-stoichiometric compounds Eqs. (16)-((18)). The reference states for the atomic energies of pure Ti, Fe, and element X are hcp, bcc, and a single atom, respectively. Previous predictions of the site preference via the Bozzolo-Ferrante-Smith (BFS) method [51] (in parentheses) are compared to the present results.

Table 5 The role of additional alloying elements on the formation energies (ΔEf) of hydrides (TiFeH and TiFeH2) per one mol of H2 and the volume expansion (ΔV) considering partial Eqs. (7) and ((8)) and total (Eq. (9)) hydrogenation reactions obtained by the present DFT calculations. The results for stoichiometric hydrides without alloying elements are highlighted in bold. Underlined values indicate that the results correspond to the investigated site preference of each alloying element in the equiatomic TiFe compound (Table 4).

Table 6 The role of additional alloying elements in altering the plateau hydrogen pressure in the PCT curve. The predictions according to the present DFT calculations in Tables 4 and 5 are compared to the previous predictions via the Bozzolo-Ferrante-Smith (BFS) method [51] and previously reported experimental trends. The results for different compound stoichiometries (Equiatomic, Ti-rich, and Fe-rich) are specified. “Stabilized” and “Destabilized” indicate a decrease and increase in the plateau hydrogenation pressure, respectively.

Table 7 The solute-GB binding energy for possible segregation sites near the GB (Ti1, Ti2, and Fe1 shown in Fig. 1) and the maximum tensile stress (σmax) obtained by the present DFT calculation. In the solute-GB binding energy, the most probable site for the segregation of each ternary element considering the preferred sublattice site of the equiatomic B2 structure (Table 4) is highlighted in bold. The maximum tensile stress was obtained using the bi-crystal cell with an additional solute atom at the most probable site near the GB.