1. Introduction

Hastelloy N, a Ni-based alloy, is the special structural material for molten salt reactor (MSR) [1, 2] with excellent corrosion resistance against molten salts. Tritium (T), produced by neutron reactions with FLiBe molten salt, can flow readily through the Hastelloy N walls of various systems in MSR. With radioactivity, T release to the environment must be controlled. Knowledge of H behavior in Ni-based alloy is essential for predicting T behavior in MSR and guiding T control processes [3]. Also, H behavior in alloys is a fundamental subject for understanding hydrogen embrittlement [4, 5] suffered by alloys.

While it is difficult to experimentally explore H behaviors in alloys, first-principles calculations can be used to study H behaviors in alloys and their underlying physical mechanisms at the atomic and electronic levels [6, 7]. Since the alloying additives can directly modify H behavior in alloys, the interactions between them are very important.

In our previous first-principles calculations [8], the interactions between H and 3d transition metal (TM) alloying atom in Ni were found to be influenced greatly by the electron distribution, which do not obey the elastic mechanism [9] or the “reverse stability” rule [10]. In this work, we further investigated the interaction between 4d TM atoms and H in Ni with first-principles calculations, and the differences between 4d and 3d elements in their interaction with H.

2. Computational details

The computational method is stated in detail in our previous work [8], and spin-polarized electronic state calculations are performed within the density functional theory [11, 12] using Vienna ab-initio simulation package (VASP) [13]. A 2×2×2 Ni supercell containing 32 Ni atoms is used with a Monkhorst-Pack 7×7×7 k-point mesh. In the Ni-4d supercell, a Ni atom is replaced by a 4d atom. In the Ni-4d-H supercell, one H atom is placed in the octahedral or tetrahedral interstitial site (O-site or T-site) nearest to the substitutional 4d atom. Energies of H vibrations are taken into account by calculating the zero point energy (ZPE). To a first-order approximation, only H vibrations are calculated and network vibrations are neglected [14].

The computational method of the interaction energy between 4d element and H is the same as our previous work [8] according to Refs.[9] and [10]. A positive value of the interaction energy means the rejection to H in the Ni-TM-H system, and a negative value refers to the attraction to H.

3. Results and discussion

The calculated total energy of the Ni-4d-H supercell with H in O-site or T-site is shown in Fig. 1. It can be seen that H in O-site is more energetically preferable than in T-site, since O-site is larger than T-site. This is the same as the case of 3d elements [8]. Furthermore, the T-site in the Ni-4d-H supercell for the cases of Zr, Nb, Mo, Ag and Cd is unstable for H atom. Thus, only the cases of H in O-site are taken into account in the following sections.

Fig. 1.Full-screen View

Total energy of the Ni-TM-H supercell with a H atom in the O-site or T-site with and without the ZPE correction.

The calculated 4d-H interaction energies are shown in Fig.2(a). In order to validate the 32-atoms supercell, the interaction energies calculated in 108-atoms supercell (denoted by ‘108’ in parentheses) are also shown in Fig. 2(a). The change trends of interaction energies in 32-atoms and 108-atoms supercells are almost the same. However, the interaction energies calculated in 32-atoms are all positive, and those calculated in 108-atoms are negative (expect Cd). This difference can be attributed to the influence of H concentration (i.e. the supercell size), which is shown in the results of 3d-H interaction [8].

Fig. 2.Full-screen View

Interaction energy between 4d and H atoms in Ni with and without the ZPE correction (a) and electro-negativities (in Pauling) of the 4d element (b). ‘108’ in parentheses in (a) means the energies are calculated in the 108-atoms Ni supercell. The solid and dash lines in (b) indicate the electro-negativities of Ni and H, respectively.

In later text, only the results calculated in 32-atoms supercell are analyzed, which represents the case of a relatively high H and 4d TM atoms concentrations and can be used to compare with our results of the 3d-H interaction conveniently [8].

The TM-H interaction can be decomposed into the mechanical and chemical effects. The mechanical effect is caused by the atomic size effect mechanism, and the chemical effect is induced by the electron distribution. Since the change trends of the bond length and binding energy in Fig. 3 do not have evident correlation with that of the interaction energy shown in Fig. 2(a), neither the bond length nor the binding energy can explain the 4d-H interaction energy in Fig. 2(a) alone, as displayed in Fig. 3, which is consistent with the results of the 3d-H interaction [8].

Fig. 3.Full-screen View

Bond length between the 4d atom and its nearest Ni atom in Ni-4d supercell,$d_{NiTM}^{Ni-TM}$, relative to the Ni-Ni bond length in pure Ni supercell,$d_{Ni}^{Ni-Ni}$. Binding energy of the 4d atom in Ni matrix, and the horizontal line indicates the value of Ni.

For the 3d-H interaction, the interaction energies are all (except Zn) negative (Fig.3 in Ref. [8]). However, for the 4d-H interaction, the interaction energies are all positive (Fig. 2a). Comparing Fig. 3 in this work with Fig. 2 in Ref. [8], the Ni-4d bonds in Ni-TM supercell are longer than the Ni-3d bonds due to the bigger atomic sizes of 4d elements. The bigger 4d atomic size induces a stronger extrusion in the supercell resulting in a stronger repulsive force to H atom. So, the effect of atomic size plays a dominant role in the 4d-H interaction, which is mainly different from the 3d-H interaction.

To explore the chemical components, of the electro-negativities of the 4d elements [15] shown in Fig. 2(b), the calculated charge density and the charge density difference [16] are demonstrated in Figs. 4 and 5.

Fig. 4.Full-screen View

Calculated charge densities (a–e) and the corresponding charge density (in electron/Bohr³) differences (f–j) of the Ni-4d-H system with H in the O-site for Ni, Zr, Nb, Mo and Tc.

Fig. 5.Full-screen View

Calculated charge densities (a–e) and the corresponding charge density (in electron/Bohr³) differences (f–j) of the Ni-4d-H system with H in the O-site for Ru, Rh, Pd, Ag and Cd.

For Zr, the atomic size is relatively big and close to those of Ag and Cd in Fig. 3, so we can expect that Zr should exert a strong repulsion to H. However, the repulsion of Zr is obviously weaker than those of Ag and Cd as displayed in Fig. 2(a), which can be attributed to the chemical component. Due to the lowest electronegativity of Zr in Fig. 2(b), Zr loses electrons easily, and the electrons are gained by the Ni-H bonds (e.g. Ni1-H bond in Fig. 4b) which become stronger than those in the Ni-H supercell (e.g. Ni1-H bond in Fig. 4a). The stronger Ni-H bonds reduce the repulsive interaction in the Ni-Zr-H supercell, which can explain the difference between Zr and Ag (or Cd). However, with the increase of electronegativity from Zr to Mo, the Ni-H bonds become weak as shown in Fig. 4(b–d), hence, the repulsive interaction to H in the Ni-4d-H supercell become strong. This agrees with the interaction energy in Fig. 2(a).

For Tc, the reduced electronegativity (Fig. 2b) and the smallest atomic size (Fig. 3) are both helpful to reduce the repulsive interaction to H (Fig. 2a). For Ru, Rh and Pd, there are no obvious differences in the calculated charge density and the charge density difference (Figs. 5a-5c, 5f-5h), thus the corresponding interaction energies change little Fig. 2a).

However, for Ag and Cd, the repulsive interactions to H become strong as judged by the interaction energies in Fig. 2(a), which has a close association with the apparent charge depletion between the Ag (or Cd) and H atoms (Figs. 5i and 5j) and the relatively big atomic size (Fig. 3). Especially for Cd, the biggest atomic size and the stable electronic configuration with completely filled 4d and 5s orbitals result in the strongest repulsive interaction to H.

The structure of the alloys (e.g. Hastelloy N alloy) is complex and also involves many kinds of defects, which will be addressed in our future works. So far there has been little research on the direct 4d-H interaction in Ni-based alloys by the experimental studies. However, the study of the 4d-H interaction in this paper is helpful for further experimental studies.

4. Conclusion

In this work, we use first-principles calculations to investigate the interaction between H and 4d TM elements in Ni-based alloy. The interaction energies between 4d elements and H are calculated. The TM-H interaction has been decomposed into the atomic size effect and electron effects, and both of these effects are analyzed. The effect of atomic size plays a dominant role in the 4d-H interaction, which is mainly different from the 3d-H interaction. We believe that this work is very helpful for the future experimental studies.