| Based on the generalized gradient approximation (GGA) of density theory and Full-potential linearized augmented plane wave (FLAPW), the equilibrium geometric structure, density of states, charge density structure and potential structure have been calculated for the LaNi5-based alloys. Finally, the enthalpies of formation for the LaNi5-based alloys and its hydrides are worked out by thermodynamic method. We compared the data with the corresponding experimental data, the results show that our calculated data are perfect agreement with the experimental data.By using two different methods, the intermetallic compound LaNi5 has been optimized. The results indicate than the spin-polarization has not obvious effect on the optimized geometric structure and energy. From the optimized calculation on five nonequivalent interstices for the hydrogen storage material, we can know that 12n site is the most stable position, which is easily occupied by hydrogen atom during the absorbing process.The intermediate phase (β-phase) has been fully studied theoretically. The optimized geometric structure agrees exactly with the experimental results. The density of states and charge density for β-phase have also been first calculated.By analyzing the primary solid solution phase (α-phase:LaNi5H0.5), the intermediate phase (β-phase: LaNi5H3) and the hydride phase (γ-phase: LaNi5H7), the results show that the volumes of the hydrogen storage alloys incessantly expand, when the hydrogen atoms are absorbed into the interstitial sites. The volume of the hydride phase (γ-phase: LaNi5H7) expands 27.1%. In the processes of the absorbing hydrogen atoms, the a axis and the c axis have different transformation, and the orderliness of the transformation agrees with that of the experiments. At the sametime, their Ef energies are falling in turn. However, in the low energy regions, DOS and the gap of the energy band structure is continuously broadening. The interaction is weakened among lanthanun atoms and nickel atoms because of the absorption of the hydrogen atoms and the expanded volume in the LaNis alloy, and the interaction among hydrogen atoms and nickel atoms is stronger than among hydrogen atoms and lanthanun atoms.For the first time, the model of LaNi5H8 is constructed, and the corresponding parameters are computed. The results show that the volume expands 31.9%, also a large increase in the lattice parameter of a axis is found, but that of c axis has a relatively small increase.The energies for two different models of LaNi4Al have been calculated. The results show that the nickel is most likely substituted by aluminum atom on the 3g site, which is better agreement with the experiments. We also discussed the effects which were taken by aluminum atom on LaNis alloy from DOS, the charge density and the potential structure. For the first time, the structure for LaNi4.5Al0.5 is calculated, which is exactly agreement with the experimental results. At the same time, the whole energy band structure and DOS are also given.The alloying effects of the substituted elements have been investigated on the hydrogen storage alloys. It is important meaning that the aluminum, the manganese, the cobalt and the copper elements keep to improving the performance of the hydrogen storage alloy from the analysis of their DOS and charge density.Finally, the enthalpies of formation for LaNi5 and its hydride were calculated out. We can also conclude that the increasing enthalpy of formation can be used to improve the stability of the hydride for the hydrogen storage materials through the analyses of the formed enthalpy. Among the LaNi4M(M=Al, Mn, Co, Cu), the enthalpies of formation of LaNi4Al is the lowest, but the formed enthalpies of the others are higher than the one of LaNis.
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