Influence of nickel addition on the stability, trapping, and diffusion behaviour of hydrogen in vanadium: A first-principles investigation


 Hydrogen embrittlement causes deterioration of materials used in hydrogen energy systems. Alloying is an effective means for overcoming this issue. In this study, the first-principles calculation method was used to investigate the effects of alloying Ni on the stability, dissolution, trapping, and diffusion behaviour of interstitial/vacancy H atoms in V. The calculated phonon spectra and solution energies of the vacancy/interstitial H atoms revealed that the V–Ni phase was dynamically and thermodynamically stable, and Ni addition could reduce the stability of V hydrides and improve their resistance to H embrittlement. H atoms in the interstitials and vacancies preferentially occupied the tetrahedral interstitial site (TIS) and octahedral interstitial site (OIS) with the lowest solution energies and diffused along the TIS → TIS and OIS → OIS paths with the minimum diffusion barrier energies. The trapping energy of the vacancy H atoms indicated that the addition of Ni could reduce the H trapping capability of the vacancies and suppress the retention of H in V. Detailed analysis of the calculated H diffusion barriers indicated that the presence of monovacancy defects blocked the diffusion of H atoms more than the presence of interstitials, and Ni doping did not enhance the H diffusion coefficient.


Introduction
Hydrogen, a clean, efficient, and renewable fuel, is regarded as an indispensable energy source for the future owing to the gradual depletion of fossil fuels 1,2 . However, to develop hydrogen energy on a large scale, the breakthrough lies in understanding the interactions between hydrogen and materials, such as those related to H-storage and H embrittlement, which can decrease the mechanical properties of metallic materials 3,4,5 . Dense metallic membranes are applied in high-purity hydrogen separation from gaseous mixtures and are likely to form hydrides, especially at high hydrogen partial pressures, thus degrading the mechanical properties of these membranes 6,7 . Similarly, the structural materials used in fusion and fission reactors generate several hydrogen impurities and vacancies that result in In such applications, the formed stable V hydride is a brittle phase and often becomes the source of fracture under the action of external forces 13 . Additionally, because of the occurrence of substantial vacancy defects, H bubbles are easily formed. This considerably affects the stability of the structural defects in the metal lattice and the mobility of H, leading to brittle fracture of pure V 14 . H embrittlement is a key problem that restricts the practical applications of V-based alloy materials.
Alloying is one of the effective ways to solve this problem, leading to improvements in several properties of these materials 18,19,20 . More specifically, decreased hydrogen solubility and restrained hydride formation are desirable. Experimental studies have shown that hydrogen solubility in transition metal alloys exhibits the following sequence: V-Ti > V-Cr > V-Mn > V-Fe > V-Co > V-Ni 13,15 ; adding Ni to V substantially reduces the hydrogen solubility of pure V, improving its resistance to H embrittlement 21,22,23 . Further, Ni, an effective catalytic component, is widely employed in hydrogen storage materials, chemical fuels, and organic chemical synthesis 24,25 . Moreover, the V-Ni binary alloy system is extensively studied owing to its high hydrogen permeability and mechanical strength 26,27 .
Several studies involving density functional theory (DFT) calculations have reported that alloying V with transition metals can decrease its H solubility and embrittlement and enhance the H diffusion coefficient 26,27,28,29 . However, the vacancy defect mechanism has not been investigated sufficiently. Until now, few studies have examined the fundamental mechanism of Ni substitution in transition metals and its effect on the interaction between V monovacancies and miscellaneous H atoms. The complex mechanism of the interaction between H and V vacancies has not been elucidated. Therefore, it is extremely significant to theoretically examine the influence of Ni addition on the stability and diffusion behaviours of interstitial and vacancy H atoms and the trapping of multiple H atoms in the vacancies. Therefore, to address the abovementioned issues, the formation energies of interstitial H, vacancy H, and H-vacancy clusters were determined using a highly accurate first-principles calculation method in this study. We comprehensively researched the stabilities, dissolution, trapping, and diffusion behaviour of H atoms in interstitial positions and vacancies, along with the influence of Ni substitution. We expect that the findings of this study will serve as a valuable reference for the industrial development of H-storage, H-separation, reactor first-wall, and blanket systems using V-based alloys, which are promising candidate materials for these applications.

Methods
First-principles calculations based on DFT were conducted using the Vienna Ab initio Simulation Package 30,31 . The generalised gradient approximation with the Perdew-Burke-Ernzerhof forms for the exchange-correlation interaction and the projected augmented wave methods for the core-electron interaction were used 32,33,34 . A 54-atom supercell containing a 3 × 3 × 3 unit cell was used. The V 3d3 4s2, Ni 3d8 4s2, and H 1s1 electrons were regarded as the valence electrons. A kinetic cut-off energy of 360 eV and k-meshes with dimensions of 4 × 4 × 4 were applied. While optimising the supercell size, shape, and atomic positions, the convergence threshold for the self-consistency energy was less than 1 × 10 −6 eV atom −1 , and the force acting on each atom was less than the maximum of 1 × 10 −2 eV Å −1 . The optimum diffusion paths and energy barriers of H atoms between the initial and final configurations were calculated by employing the extremely well-known climbing-image nudged-elastic-band (CI-NEB) method 35 . The phonon spectra and thermodynamic properties were calculated using the PHONOPY code 36 .
The solution energy of an interstitial (vacancy) H atom for a metal or alloy is defined as follows 14 : The vacancy formation energy is calculated as follows 10 : Here, E(VNiH), E(VNi), E(V), E(Ni), E(H2), and E(vac) concretely represent the total energies of the respective systems; N is the number of V atoms.
There are two ways to trap H atoms in vacancies, namely trapping them simultaneously and sequentially (one by one). Hence, the trapping energies associated with these two different trapping methods should be defined separately 37 . The average trapping energy of each H atom trapped simultaneously is defined as The H atoms are sequentially placed in the monovacancy, and the trapping energy of each H atom is given as where Evac+nH and Evac+(n-1)H are the total energies of n H atoms and (n-1) H atoms in the vacancy of the system, respectively, and EV,H(TIS) refers to the total energy of the H atoms in the tetrahedral interstitial site (TIS).
According to the statistical method described by Maroevic et al. 38 and Rao et al. 39 , the vacancy concentration can be written as

Results
To determine the accuracy of our calculations, we calculated the stability of H atoms in V at the interstitial sites (TIS, diagonal interstitial site (DIS), and octahedral interstitial site (OIS)) and substitution site (SS), as plotted in Fig. 1

Influence of Ni substitution on structural stability of V
To examine the influence of Ni substitution on the structural stability of metallic V, we employed the density functional perturbation theory to optimise the linear response function and lattice dynamics matrix of a 2 × 2 × 2 body-centred cubic (bcc) supercell containing 15 V atoms and 1 Ni atom to calculate the phonon dispersion and phonon state density. The obtained phonon density of states was then used to calculate the thermal properties. As shown in Fig. 1(b), there are 48 branches in the phonon spectrum, and each branch corresponds to a vibration mode; among these branches, 3 branches with low frequencies correspond to acoustic phonons and 45 branches with high frequencies correspond to optical phonons. The calculated phonon spectrum of the V-Ni binary alloy has no imaginary frequency, so the structure exhibits dynamical stability. Fig. 1(c) shows the phonon density of states in the bcc phase of V-Ni, including the total density of states and partial density of states. The V-Ni peak is at approximately 8 THz, whereas that of Ni occurs at 5.2 THz. Fig. 1

Stability of H atoms near multiple Ni atoms
We next investigated the H solution properties in TIS and OIS, which are composed of multiple (n = 1-6) Ni atoms. The H atom was placed in the TIS and OIS, and Ni atoms replaced its nearest neighbouring V atoms. A series of possible structure models were tested; finally, the most stable configurations were obtained, as shown in Fig. 3; the corresponding H solution energies are summarised in Fig. 4

Interactions between monovacancy and multiple H atoms
Vacancy defects are one of the common point defects occurring in metals and alloys. We To investigate the interaction between multiple H atoms and a monovacancy, we first calculated the energetic stability of multiple H atoms at a monovacancy in V. The solution energies of multiple H atoms at the most suitable sites are summarised in Fig. 6(a) Fig. 6 We calculated all the possible configurations involving multiple H atoms when an Ni atom is added. As shown in Fig. 6(c),

Monovacancy and Vac-nH cluster concentrations
To study the equilibrium concentrations of vacancies, we employed a statistical method 38,39 to estimate the intrinsic vacancy and Vac-nH cluster concentrations. The calculation results are presented in Fig. 7. As observed in Fig. 7(a, b), the concentrations of V and V-Ni vacancies gradually increase with the increase in temperature, which means that the vacancy concentration can easily damage metals or alloys at high temperatures. As for the Vac-nH cluster concentration shown in Fig. 7(c, d)

H diffusion in interstitials and vacancies
To further study the influence of Ni substitution on the H atom diffusion in interstitials and vacancies, we calculated the possible diffusion paths and migration energy barriers of H diffusion using the CI-NEB method 35 , as shown in Fig. 8 After adding Ni atoms, as illustrated in Fig. 8

Discussion
We investigated the influence of adding Ni on the stability, dissolution, trapping, and

Data availability
The datasets generated and analyzed during the current study are available from the corresponding author on reasonable request.       [14] .