The effect of (Si, Cr, Fe, Ni, Nb, Sn) and monovacancy on hydrogen incorporation into Zr (0001): Ab initio insights
Introduction
Zirconium (Zr) based alloys are used in a wide range of industrial technologies such as aerospace and medical applications [1], [2], [3]. Depending on the application, hydrogen diffusion into Zr is either unfavorable or advantageous. In Light Water Reactors (LWRs), fuel rods are made up of Zr alloys, which offer an excellent combination of properties such as good mechanical behavior, low neutron absorption, high resistance to corrosion and the ability to operate at high temperature [4], [5]. In the Fukushima Daiichi accident, the harsh operating environment induced rapid oxidation of Zr because of its chemical interaction with steam, then a large quantity of explosive hydrogen and heat were released [4], [5], [6], [7], [8]. In such situations, hydrogen atoms may be adsorbed on the zirconium surfaces [9], which induces hydrogen embrittlement [10]. This phenomena has been widely investigated due to its consequences such as “Delayed Hydride Cracking (DHC)” failure [11], [12], [13], [14], [15], [16], [17], [18], [19], which causes weakness in the mechanical properties of the fuel rods.
Consequently, hydrogen behavior in the fuel cladding material has motivated researchers to both investigate and provide an understanding of the hydrogen adsorption on the surface mechanisms. A previous study [20] reported the H dissociation and diffusion process in doped Mg(0001) surface, while more specific research investigated the preferential H adsorption sites and the H diffusion into the Zr [9], [17], [21]. In addition, the heat of hydrogen segregation on Zr(0001) and Zr(1010) was discussed by [22]. Moreover, it was shown that the presence of dopants may affect the hydrogen adsorption and diffusion process in the Zr and Zr-H bulk properties [23], [24], [25], [26].
For energy applications, Zr is considered as an ideal element for hydrogen storage due to its high ability to form hydrides and store high densities of hydrogen [27], [28], [29], [30], [31]. Thus, Zr stores hydrogen in form of ZrH2 [32], [33]. The interaction of the Zr surface with Transition Metals (TMs) has gained more importance in the search for novel Zr alloys for hydrogen storage [34]. To achieve good efficiency in storing hydrogen, alloys based on zirconium have been investigated [35], [36], [37]. Distinct studies [38], [39] have analyzed the effect of doped Ti and Hf on the barrier energy when hydrogen diffuses into the ZrCo surface. Initial work in this field focused primarily on favorite adsorption sites on Zr clean Zr(0001) surface [9]. Another review of the literature done by [23] discussed the role of various impurities on the adsorption process, the dissociation of water and the diffusion of OH group hydrogen in the Zr (0001) surface.
However, there is still a need for a deep understanding of the influence of other impurities on hydrogen adsorption and diffusion between different Zr (0001) sites [40]. Additionally, it is not yet known whether the existence of vacancy defects is advantageous. Whereas hydrogen incorporation is distinct from hydrogen adsorption due to unsaturated surface atoms [41], the necessity of new studies of the hydrogen (H) diffusion into the subsurface sites of Zr at different coverages is strongly needed.
The outline of the present paper is summarized as follows. The modeling details used for all the present calculations are addressed in Section 2. The computational results of the structural parameters of clean Zr surface and the favorable hydrogen adsorption and incorporation sites in the clean Zr(0001) are computed in Section 3.1. The effect of monovacancy (Zr-Vac) on hydrogen adsorption/incorporation energies is discussed in Section 3.2. The ab initio results of the required substitution energy Esub of impurities and the influence of the various dopants on hydrogen adsorption are presented in 3.3 The substitution energy E, 3.4 H adsorption and incorporation into doped Zr(0001), respectively. In Section 3.5 the H diffusion from FCC site (on-surface) to inOcta site (sub-surface) is described through the Nudged Elastic Band (NEB) algorithm. Finally, conclusions of the entire study are given in Section 4.
Section snippets
Modeling details
All the calculations reported hereafter were performed using the Perdew-Burke-Ernzerhof (PBE) exchange–correlation functional [42] and the projector augmented wave (PAW) method implemented in the Vienna Ab initio Simulation Package (VASP) [43], [44], [45]. The integration over the Brillouin zone is performed with a 13x13x11 Monkhorst–Pack [46] k-points mesh for bulk calculations. To ensure accurate results, the cut-off energy of 500 eV for the plane wave expansion was used. The
Hydrogen adsorption and incorporation on clean Zr(0001)
To validate the surface models of H adsorption on the Zr (0001), the structural properties of the clean hcp Zr was first taken into consideration. By fitting the energy volume data in the third-order Birch equation of states [49], the obtained equilibrium lattice parameters and bulk modulus a = 3.232 Å, c/a = 1.599, and B = 93.78GPa are in good agreement with the experimental measurements of 3.233 Å, 1.592 and 92 GPa, respectively, as reported by Zhao et al [50].
The obtained surface energy of
Conclusion
Through first-principle calculations, we have studied the impact of additional impurities and monovacancy on the hydrogen adsorption, incorporation and diffusion into Zr (0001) surface as a function of the coverage. HCP and FCC adsorption sites have been found to be energetically the most stable, while both the incorporation sites, the Octahedral and Tetrahedral sites (inOcta and inTetra) have been determined to be energetically the more favorable for the H incorporation but less stable
CRediT authorship contribution statement
Farouk Mebtouche: . Toufik Zergoug: Writing - review & editing, Supervision. Saddik El Hak Abaidia: Validation. Johannes Bertsch: Supervision. AbouBakr Seddik Kebaili: . Arezki Nedjar: Software.
Declaration of Competing Interest
The authors declared that there is no conflict of interest.
Acknowledgments
The authors acknowledge the computational facilities of the Nuclear Research Center of Draria (CRND). The authors also thank the Laboratory of Nuclear Materials (LNM) at the Paul Scherrer Institute (PSI), Switzerland, and SwissNuclear for providing financial support.
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2022, International Journal of Hydrogen EnergyCitation Excerpt :The authors pointed out that for hydrogen adsorption, FCC (face-centered cubic) and HCP (hexagonal close-packed) sites are energetically the most stable, and the addition of Sn and Si reduced the incorporation energy at the tetrahedral site whereas Nb, Fe, and Ni increased it. Thus, Nb and Cr noticeably lower the minimum energy path of hydrogen migration [44]. Density functional theory (DFT) is a promising approach to understand the microscopic features of functional materials [45–49].