The crystal structure of Mg₂Ni is hexagonal and its space group is P6₂22 (No.180) [21] , as shown in Figure 1(a). The lattice constants of Mg₂Ni are a = b = 5.205 Å, c = 13.236 Å, α = β = 90˚, γ = 120˚. There are 12 Mg and 6 Ni atoms existing in the unit cell of Mg₂Ni. The spatial positions Mg and Ni atoms are respectively 6f(0.5, 0, 0.1187), 6i(0.16, 0.324, 0) and 3b(0, 0, 0.5), 3d(0.5, 0, 0.5). Single Y atom substituting for Mg and Ni atoms are investigated respectively. Moreover, it has been shown that Mg₂NiH₄ forms readily by hydrogenating the alloy Mg₂Ni [22] . The space group of Mg₂NiH₄ is monoclinic C2/c (No.15) and the lattice constants are a = 14.343 Å, b = 6.404 Å, c = 6.483 Å, β = 113.52˚, as shown in Figure 1(b). 16 Mg, 8 Ni and 32 H atoms are in the unit cell of Mg₂NiH₄ where Mg occupying the 8f, 4e, 4e sites and Ni the 8f site and H the 8f, 8f, 8f, 8f sites [23] [24] . The new systems of Y alloying Mg₂NiH₄ are studied.

All the density-functional theory (DFT) calculations are performed using a plane-wave basis set with the projector augmented plane wave (PAW) method as implemented in the Vienna ab initio simulation package (VASP)

[25] - [27] . Projector Augmented Wave (PAW) potentials are used to treat the core-valence interaction [28] . The PW91 [29] [30] generalized gradient approximation (GGA) is employed for the exchange-correlation functional. The electronic wave functions are expanded by plane waves with a kinetic energy cutoff of 350 eV to attain the required convergence. All of the self-consistent loops are iterated until the total energy difference of the systems between the adjacent iterating steps is less than 10⁻⁷ eV. The Brillouin zone is sampled by 6 × 6 × 2 mesh points in k-space based on Monkhorst-Pack scheme [31] for all systems. The valence electrons of 1s for H, 2p and 3s for Mg, 3p, 3d and 4s for Ni, and 4d and 5s for Y are considered in the calculations.

In order to check the accuracy of the calculations, we first optimize the structure of Mg₂Ni alloy and its hydride and compare the calculated lattice parameters with those determined experimentally. Then we consider the substitution of Mg and Ni by Y in independent spatial positions respectively. To single out a scenario that is most likely responsible for the stabilization of the crystal structure, the lattice parameters and enthalpies of formation ΔH for each case are calculated. The ΔH is calculated by taking the difference in total electronic energy of the products and the reactants [32] :

In the case of the crystal structure which including xMg, yY, zNi, the enthalpies of formation are calculated by the following equation:

where refers to the total energy of substituted Mg₂Ni by Y.

, and are the energy of every atom in HCP Mg, HCP Y and FCC Ni crystals, respectively. x, y, z are the numbers of Mg, Y and Ni atoms, respectively. Through the calculation, the values of, and are −1.595, −6.379 and −5.415 eV, respectively.

Table 1 displays the volume, lattice constant, total energy and enthalpies of formation of all the structures including Mg₂Ni, substituted Mg₂Ni by Y and their hydrides. The lattice constants of Mg₂Ni after geometry optimization are a = b = 5.180 Å, c = 13.232 Å, which agree well with the experimental data a = b = 5.205 Å, c = 13.236 Å [21] . The enthalpy of formation of Mg₂Ni is −3.211 eV, which means that the unit cell of Mg₂Ni is −51.612 kJ/mol. It is very close to the experimental values −51.9 kJ/mol [33] . When Y atom is added into Mg₂Ni, all the volumes of crystal structures will increase compared with the original structures. Moreover, it can be clearly observed that when the position of Mg (6f) is occupied by Y atom in Mg₂Ni, the total energy and the enthalpy of formation are the minimum. It indicates that the structure of Mg₁₁Y(6f)Ni₆ has the optimal stabilization among all the substituted structures.

Based on the stable structure of Mg₁₁Y(6f)Ni₆, we study the properties of substituted Mg₂NiH₄ by Y. Firstly, We have proved that the theoretical lattice constants and internal atomic positions of Mg₂NiH₄ are in good agreement with experimental results [23] . The states are displayed in Table 1. Various substitutive positions of Mg are considered. We find that the total energy of each new structure is very close. Thereby, a reasonable structure Mg₁₅YNi₈H₃₂ is selected to be investigated in detail, as shown in Figure 1(c).

In order to research the effects of Y on the properties of Mg₂NiH₄, We calculate the enthalpies of formation of Mg₂NiH₄ and Mg₁₅YNi₈H₃₂ respectively. In general, the formation of Mg₂NiH₄ can be expressed by the following reaction:

The enthalpy of formation of Mg₂NiH₄ can be expressed in Equation (4):

In the same way, the reaction of formation and the enthalpy of formation of Mg₁₅YNi₈H₃₂ can be respectively written as Equations (5) and (6):

where, , and are the total energy of Mg₂NiH₄, Mg₂Ni, Mg₁₅YNi₈H₃₂ and Mg₁₁Y(6f)Ni₆, respectively.

is the energy of free H₂ molecule. The calculated results are also shown in Table 1. For pure Mg₂NiH₄, the enthalpy of formation is −64.667 kJ/mol which coincides closely with the experimental result −64.4 ± 4.2 kJ/mol reported by Reilly et al. [22] . Furthermore, the enthalpy of formation of Mg₁₅YNi₈H₃₂ is −62.554 kJ/mol which is higher than that of pure Mg₂NiH₄. It can be clearly seen that the introduction of Y atom has effects on the destabilization of Mg₂NiH₄ in terms of energy. This is energetically favorable to perform the dehydrogenation reaction of substituted Mg₂NiH₄ by Y.

To make further investigation about the performance of dehydrogenation, we calculate the energies of Mg₂NiH₄ and Mg₁₅YNi₈H₃₂ which dissociate the nearest 2 H atoms around Ni atoms. The dehydrogenation energy is calculated by Equation (7):

The results are shown in Table 2. From Table 2 we can see that the addition of Y clearly decreases the dehydrogenation energy of Mg₂NiH₄ by about 47% to 0.983 eV. It suggests that although Y atom has poor effects on the destabilization of Mg₂Ni, it breaks down the stability of Mg₂NiH₄ positively and improve the dehydrogenation kinetics of Mg₂NiH₄ which as one of the hydrogen storage materials.

In order to further understand the effects of Y atom on the dehydrogenation properties of Mg₂NiH₄ alloy, the electronic properties of Mg₂Ni and Mg₁₅YNi₈H₃₂ are studied by calculating total density of states (DOS) and partial density of states (PDOS). Figure 2 displays the DOS and PDOS of Mg₂Ni and Mg₁₅YNi₈H₃₂ alloys.

Form Figure 2(a) we can see that there are two main peaks in total density of states below Fermi level. The bonding electron of the energy region between −9.2 and −3.7 eV is mainly dominated by Hs, Nis and Nid orbits, partial Mgs orbit. It is implied that H atoms tend to bond with Ni rather than Mg atoms in the structure of Mg₂NiH₄. The result is in correspondence with the conclusion that the interaction Ni-H is stronger than that of Mg-H which studied by Jasen [34] . There is a major contribution with Ni p, Ni d and Mg s orbits in the region from −2.4 eV to Fermi level. This indicates that Mg and Ni atoms have hybridization which keeps the structure of Mg₂NiH₄ stable. In addition, Ni d orbit plays the dominating role in the bonding electron.

Compared to pure Mg₂NiH₄, the enthalpy of formation and dehydrogenation energy change markedly due to the substituted Mg₂NiH₄ by Y. Figure 2(b) displays that below Fermi level Mg₁₅YNi₈H₃₂ has two main bonding peaks from −10.7 to −5.2 eV and −4.1 to −1.6 eV. It is not difficult to find that all the bonding peaks in total density of states move to the energy of deep potential well and the number of bonding electron reduces comparing to Mg₂NiH₄. It demonstrates that the substitution of Y alloying weakens the interaction of the atoms and destabilizes the structure of the hydride. The effects of Yd orbit on the bonding electron are significant especially for the energy region from −4.1 to −1.6 eV. What is more, Yp and d orbits contribute to the bonding electron and have mutual interaction with Nip and d orbits. It is also worth noting that the overlapping region between Nid and Hs orbits decreases obviously. It means that the interaction between Ni and H atoms become weak.