Effects of Ni doping on various properties of NbH phases: A first-principles investigation

Changes in the stability, hydrogen diffusion, and mechanical properties of the NbH phases from Ni-doping was studied by using first-principles methods. The calculation results reveal that the single H atom adsorption is energetically favorable at the tetrahedral interstitial site (TIS) and octahedral interstitial site (OIS). The preferred path of H diffusion is TIS-to-TIS, followed by TIS-to-OIS in both Nb16H and Nb15NiH. Ni-doping in the Nb15NiH alloy lowers the energy barrier of H diffusion, enhances the H-diffusion coefficient (D) and mechanical properties of the Nb16H phase. The value of D increases with increasing temperature, and this trend due to Ni doping clearly becomes weaker at higher temperatures. At the typical operating temperature of 400 K, the D value of Nb15NiH (TIS) is about 1.90 × 10−8 m2/s, which is about 80 times higher than that of Nb16H (TIS) (2.15 × 10−10 m2/s). Our calculations indicated that Ni-doping can greatly improve the diffusion of H in Nb.

Membrane reactors, used for the separation and purification of dense hydrogen, are one of the most important components in industrial hydrogen production by the steam reforming of natural gas 1,2 . Currently, although Pd and its alloys have been widely used for hydrogen separation and purification, their disadvantages such as high price and scarcity are also obvious. Over the last few decades, researchers have gradually shifted their attention to group VB transitional metals (V, Nb, and Ta) due to their potential of hydrogen permeability and relatively lower price 3 . Among them, niobium (Nb) has been well regarded as one of the most promising hydrogen separation materials, since Peterson et al. reported that it possesses excellent high-temperature mechanical properties as well as corrosion resistance [4][5][6] . Furthermore, Nb and its alloys also have been extensively used in hydrogen-related high-temperature structural applications, such as the diverter and nuclear material at the International Thermonuclear Experimental Reactor (ITER), due to their strong resistance to corrosion, high melting point, excellent mechanical properties, and small cross section of neutron absorption [4][5][6][7][8] . However, Nb alloys often have poor resistance to hydrogen embrittlement and therefore are limited in their practical applications [9][10][11][12] .
Further exploring Nb-based alloys with other elements is one solution to the above problem. Watanabe et al. revealed that the addition of W and Ru decreases the hydrogen solubility in Nb and therefore improves its resistance to hydrogen embrittlement 9, 11 . Hu et al. reported that the addition of W can improve the mechanical properties of the Nb 16 H phase, decrease the structural stability of the Nb 15 WH (TIS) phase, lower the diffusion barrier of H, and enhance diffusion paths for H 13,14 . In addition, Ni is an effective catalytic component and widely used in metal-based alloy compounds for hydrogen storage. Doping with Ni can decrease the sensitivity to impurity gas on the surface, thereby reducing the pollution caused by impurities. To the best of our knowledge, however, the fundamental work of Nb alloying with Ni has not been reported in the literature. It is necessary to study the structural and diffusion properties of Ni in the NbH phase by theoretical methods. Such calculations will contribute to the in-depth study of new Ni-based hydrogen permeation materials.
In this paper, we employ highly accurate first-principles method to investigate the effects of Ni doping on the structural stability, electronic structure, mechanical property, and H-diffusion behavior of the Nb 16

Results and Discussion
In order to compare to the experimental results 15-17 , a 2 × 2 × 2 super cell containing 16 Nb atoms was built, and one of the Nb atoms was substituted by Ni. To study the diffusion behavior of H atom between the nearest sites, one H atom was placed at the tetrahedral interstitial site (TIS) and octahedral interstitial site (OIS) of Nb and Nb 15 Ni, respectively. In Nb 15 NiH (TIS), the Nb-H and Ni-H bond lengths are about 1.96 and 1.65 Å, respectively. After the doping of Ni atoms, the structure was changed from bcc to simple cubic due to the smaller atomic radius of Ni compared to Nb. However, the structure remained as the cubic type. As a typical example, Fig. 1(a) shows the schematic illustrations of Nb 15 NiH with H atom in TIS and OIS. For clarity, the corresponding atomic configurations of TIS and OIS are displayed in Fig. 1     where r and ν are the jump distance and vibration frequency, respectively. We can calculate the vibration frequency ν according to Zener and Wert's theory 24 , which is approximately expressed by    28,29 . The Young's modulus (E) is determined by means of E = 9BG/(3B + G) 29 . After a series of calculations, the lattice constants (a), three independent elastic constants (C 11 , C 12 , and C 44 ), and elastic moduli (B, G, and E) of various Nb 16 H and Nb 15 NiH phases are obtained ( Table 2). The calculated values of pure Nb are also listed and compared with experimental results. The consistency between the calculated and experimental values proved the reliability of our calculation method. (i) We use the following criteria for mechanical stability: 11 12 , = > 3 11 12 < < C B C 12 11 30 . Table 2 presents the computed values of C 11 , C 12 , and C 44 for the materials, showing that they are all mechanically stable. (ii) The shear modulus G represents the resistance to plastic deformation, while the bulk modulus B represents the resistance to fracture 31    phases. According to the empirical criterion proposed by Pugh 32 , if the value of B is about 1.75 times larger than G, the material will be ductile, otherwise fragile. The calculated B/G values listed in Table 2 show that all phases are ductile. These results suggest that the Ni-doping could help to improve the mechanical properties of Nb 16 H phase, and enhance the resistance to hydrogen embrittlement.  16 H, which will result in improved structural stability and stronger mechanical properties. Figure 6 shows the charge density of Nb and Nb 15 Ni with H atom at the TIS and OIS sites, respectively. As shown in Fig. 6(a) and (c), the charge density distribution between H and Nb is symmetrical. However, from Fig. 6(b) and (d), the charge density between H and Ni is obviously higher than that between H and Nb after substituting Ni for Nb. This suggests the Ni-H bond is stronger than Nb-H bond, which is also in agreement with the above DOS analysis.

Conclusions
We have investigated the structural stability, mechanical property, and hydrogen diffusion properties of H in pure Nb and Nb 15 Ni, using first-principles calculations in combination with empirical theory. The results show that Ni-doping can enhance the mechanical properties of Nb 16 H phase, decrease energy barrier of H diffusion, and improve H diffusivity in the Nb 16 H phase. The calculated density of states and charge density distribution reveal that the Ni-H chemical bond formed after Ni-doping is stronger than Nb-H in Nb 15 NiH, and this is directly responsible for the improved mechanical properties in Nb 15 NiH. The CI-NEB calculations indicate that the single H atom is energetically favorable for adsorption at the tetrahedral interstitial site (TIS) and octahedral interstitial site (OIS) in both Nb 16  Computational methods. Our calculations were carried out using the well-known Vienna ab initio simulation package (VASP) 34,35 , in the framework of density functional theory (DFT). The core-electron interactions were described by projected augmented wave (PAW) method 36,37 . The exchange-correlations term was approximated by Perdew-Burke-Ernzerhof (PBE) corrected generalized gradient approximation (GGA) functions 38 . The electronic configurations 4d 4 s 1 and 3d 8 4s 2 were treated with the valences of Nb and Ni. The cutoff energy of plane wave was set to 360 eV, and the k-mesh of 5 × 5 × 5 was used in the Brillouin zone, which turns out to be sufficient to obtain convergence to less than 1.0 × 10 −6 eV. Then, the atomic coordinates and crystal volume were relaxed with the conjugate gradient method, until the forces acting on all atoms are less than 0.01 eV/Å. These parameters ensured good convergence in the total energy. The migration barriers were calculated using the climbing image nudged elastic band method (CI-NEB) 18 . The calculation convergence and parameters stay the same for the ground state calculations.