Origin of the distinct site occupations of H atom in hcp Ti and Zr/Hf

doi:10.1016/j.ijhydene.2024.10.197

International Journal of Hydrogen Energy

Volume 91, 19 November 2024, Pages 933-941

https://doi.org/10.1016/j.ijhydene.2024.10.197 Get rights and content

Highlights

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Hydrogen occupies octahedral interstice in Ti but tetrahedral interstice in Zr/Hf.
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H-metal atom Coulomb repulsion is responsible for the distinct site occupation of H.
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H-induced electron redistribution might matter to the distinct site occupation of H.
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H prefers the site with a trade-off between large space and high electron density.

Abstract

The location of the H atoms in Ti, Zr, and Hf is crucial to the formation of the hydrides in these metals as it influences the crystal lattice transformation and the hydrogen diffusion involved in the hydride formation process. Although Ti, Zr, and Hf are all of hexagonal close-packed structure with similar lattice parameters, the solute H atom occupies the octahedral interstice in Ti but the tetragonal interstice in Zr and Hf, of which the origin is still mysterious. In the present work, the origin of the distinct site occupation behavior of H atom in Ti and Zr/Hf is investigated through first principles calculations. The calculated solution energies confirm that H prefers the octahedral interstice in Ti but the tetrahedral interstice in Zr and Hf. We ascribe the distinct site occupations of H in Ti and Zr/Hf to the varying Coulomb repulsion between the H (as a screened proton in the metals) and the matrix atoms against the interstitial size. The competition between the H-induced electron accumulation effect and the matrix atom debonding effect might matter as well. We propose that, as a general rule, a H atom prefers the site with a trade-off between a large space and a high electron density in metals.

Introduction

Hydrogen (H) embrittles titanium (Ti) and zirconium (Zr) metals and their alloys [[1], [2], [3]] through the formation of brittle hydride, enhancing the atomic decohesion, accelerating the emission, multiplication, and motion of dislocations [[4], [5], [6], [7]]. The behavior of hydrogen in Ti and Zr based alloys is of fundamental interest and vital importance because these alloys are the key engineering materials for aerospace, marine, and energy resource applications [8,9].

The H atoms in solid solute state reside in the interstitial sites of the crystal lattice of the metals. In Zr, the H atom was determined to occupy the tetrahedral (T) interstice at room temperature by Narang et al. [10] and Fukai [11] using the inelastic neutron scattering experiments, which was afterward confirmed by many first principles calculations based on density functional theory (DFT) [[12], [13], [14], [15]]. The experimental investigation of H occupation in Hf is scarce. DFT calculations predicted that the T-site is preferable for H to occupy in Hf [[16], [17], [18]], similar to the case of Zr. The site occupation of H in Ti is, however, controversial. Based on their inelastic neutron scattering measurements, Khoda-Bakhsh and Ross concluded that H locates in the T-site of Ti at temperature of 315 °C [19]. The neutron diffraction experiment by Pinto et al. [20] and the nuclear magnetic resonance measurements by Korn et al. [21] suggested that H dissolved in Ti randomly in the T-sites at room temperature as well. However, the neutron scattering experiments by Hempelmann and Stritzker [22] indicated that a large part of H atoms occupies the octahedral (O) interstices in Ti around 300 °C, in agreement with the finding of Alperin et al. [23] Besides, advanced DFT calculations predicted consistently that H atom energetically prefers the O-site in Ti [24,25].

The possible different site occupation behavior of solute H atom in Ti and Zr/Hf as a fundamental issue is highly interesting and somehow unexpected because all three metals are of hexagonal close packed (hcp) structure and their lattice parameters

c / a

are very close to each other, and, therefore, their relative interstitial sizes are almost identical. More practically, the different locations of solute H are crucial to the understanding of the formation of the hydrides. Ti/Zr/Hf hydrides form through two accompanying processes, i.e., the transition of the crystal lattice from hcp to fcc (face-centered cubic) or fct (face-centered tetragonal) and the diffusion of the H atoms [[26], [27], [28], [29], [30], [31]]. For both Ti and Zr hydrides, the H atoms were detected to locate in the T-sites of the fcc or fct lattice [29,[32], [33], [34]], regardless of the chemical stoichiometry of the hydrides. The site-occupation of H influences the hydride formation process by affecting the hcp-fcc/fct lattice transition and the diffusion of the H atom. Therefore, it is important to reveal the origin of the distinct site occupations of H in Ti and Zr/Hf.

In this paper, first-principles calculations are performed to explore the physics underlying the distinct site-occupations of H in Ti and Zr/Hf. The solution energies of H in the T and O interstices of Ti, Zr, and Hf are calculated and compared to determine the stable occupation site of H. The lattice structures and electronic structures of the systems are analyzed, with which the distinct site occupations are discussed. The paper is arranged as follows. In Section 2, we describe the method and computational details. In Section 3, we present the solution energy, crystal structure, and electronic structure from the calculations. In Section 4, we discuss the physical origin of the distinct site occupations of H in Ti and Zr/Hf. Finally, we conclude our work in Section 5.

As strongly requested by the reviewers, here we cite some references [[35], [36], [37], [38], [39], [40], [41], [42], [43], [44], [45], [46], [47]] although they are completely irrelevant to the present work.

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Section snippets

Method and computational details

The stable occupation site of solute H in the Ti, Zr, and Hf is determined by comparing the solution energies of H in the O- and T-sites. The solution energy of a H atom is defined as

E_{sol} = E_{M - H} - E_{M} - \frac{1}{2} E_{H_{2}}

where

E_{M - H}

E_{M}

and

E_{H_{2}}

are respectively the total energies of the supercell of M (M = Ti, Zr, Hf) containing one H atom, H-free M supercell, and the H₂ molecule. A lower solution energy corresponds to a more stable occupation state. We adopt 4 × 4 × 2 times of the hcp unit cell to calculate the

Solution energy of H

The solution energies of H in Ti, Zr, and Hf, calculated with various types of exchange-correlation functionals, are listed in Table 1. As seen in Table 1, all the XC functionals generate consistently lower solution energies of H in O-site (

E_{sol}^{O}

) than those in T-site (

E_{sol}^{T}

) for Ti, suggesting that H prefers the O-site. This prediction supports the experiments by Hempelmann and Stritzker [22] and Alperin et al. [23] but in contrast to those by Khoda-Bakhsh and Ross [19], Pinto et al. [20], and

Discussion

Our first principles calculations of the solution energies demonstrate that the H atom prefer the O-site in Ti but the T-site in Zr and Hf (see Table 1). However, the three systems share the same geometric and electronic structure characteristics: (1) smaller size of the T interstice than that of the O interstice (Table 2); (2) larger distortion energy induced by the T-site H than that by the O-site H (Table 4); (3) higher electron density around the T-site H than that around the O-site H (Fig.

Conclusion

First principles calculations demonstrated that the solute H atom occupies octahedral interstice in Ti but tetragonal interstice in Zr and Hf although Ti and Zr/Hf are of the same lattice structure. In the present work, first principles calculations were carefully performed to investigate the distinct site occupations solute H in Ti and Zr/Hf. Our calculations demonstrated that the Ti–H, Zr–H, Hf–H systems share some geometric and electronic structure characteristics.

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smaller size of the T

CRediT authorship contribution statement

Fan-Xi Yang: Writing – original draft, Methodology, Conceptualization. Yi-Fei Zhu: Validation, Formal analysis. Shuo Cao: Supervision, Conceptualization. Chao-Ming Wang: Writing – review & editing, Methodology. Ying-Jie Ma: Writing – review & editing, Resources. Rui Yang: Writing – review & editing, Resources. Qing-Miao Hu: Writing – review & editing, Supervision, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

The authors gratefully acknowledge the financial supports from the National Natural Science Foundation of China (grant Nos. U2106215, 52071315, and 52001307) and the National Key Research and Development Program of China (grant No. 2021YFC2801803).