Structural and Superconducting Properties of Tungsten Hydrides Under High Pressure

Introduction

An important objective in condensed-matter physics and chemistry is to prepare hydrogen-rich (H-rich) compounds because of their broad applications and scientific significance [1–5]. In more detail, H-rich compounds are the excellent hydrogen energy storage materials [6–8] and high-temperature superconductors [9–11]. On the other hand, H-rich compounds, especially at high pressures, contain various kinds of chemical bonds (e.g., covalent, ionic, and van der Waals bonds) [12] and diverse hydrogen structure units [e.g., unpaired H [13], H₂ [14], H₃ units [15], and 3D hydrogen network resembling metallic atomic hydrogen [16, 17]], providing opportunity for us to fully understand physical and chemical properties of hydrogen.

Wigner et al. predicted that metalized solid hydrogen is the potential room-temperature superconductor due to its high phonon frequencies and strong electron-phonon coupling [18]. However, hydrogen metallization is rather difficult such as extreme high pressure [19, 20]. Fortunately, Ashcroft proposed that metallization of hydrogen-rich compounds needs relatively lower pressures [10], which also show high-temperature superconductivity [1, 2, 13, 21, 22]. Among the various H-rich compounds, metal hydrides as the potential superconductors have drawn much attentions because of large density of states at the Fermi level, high phonon frequencies, and strong electron-phonon coupling [23, 24]. Great progress has been made in metal hydrides [11, 25–28]. Interestingly, some of metal hydrides under high pressure show large T_c values [2, 29, 30]. For example, the T_c for LiH₆ reaches 82 K at 300 GPa [31]. The C2/c phase of KH₆ is a superconductor with an estimated T_c of 58.66–69.84 K at 166 GPa [5]. Recent theoretical calculation revealed that the potential high-temperature superconductor of CaH₆ has a T_c of 220–235 K at 150 GPa [2]. For Mg-H system, MgH₆ shows a T_c value of 263 K at 300 GPa [29]. Moreover, a theoretical work indicated that T_c value of 34.1–40.5 K for R-3 InH₃ at 200 GPa [15]. The P6/mmm SnH₄ was predicted to be a superconductor with a high T_c (73 K at 120 GPa) [21].

Among the various hydrides, transition metal hydrides have drawn a growing interest due to their lower synthesis pressure with respect to the other hydrides, multiple stoichiometries, catalytic transformations, and superconductivity [32–34]. These unique properties can be attributed to the diverse d electron configurations of transition metals. More interestingly, transition metal hydrides with higher hydrogen content become stabilized with increasing pressure [35, 36], consisting of diverse hydrogen structure units and exhibiting intriguing properties [6, 11–16]. For instance, FeH_x (x = 1–4) compounds have been reported [37–40]. Very recently, Pepin et al. reported synthesis of FeH₅ containing non-bonded hydrogen atoms above 130 GPa, which opens up a strategy to access metallic atomic hydrogen [41]. It is worth noting that finding metallic atomic hydrogen at a low pressure is the long-pursuit targets. In addition, FeH₅ shows a superconducting transition temperature of 51 K [42]. Inspired by these findings, Kvashnin et al. [43] and Zhang et al. [44] independently studied phase diagram and electronic properties of Fe-H binary compounds with diverse stoichiometries at high pressures. A new H-rich compound, FeH₆, was identified. Notably, Cmmm FeH₆ is metallic [43], whereas C2/c FeH₆ is non-metallic [44], which becomes rare example of pressure-induced non-metallicity among the transition-metal hydrides [45]. On the other hand, parts of transition metal hydrides especially at high pressures are metallization and exhibit superconductivity [9, 11, 13, 22, 33, 35]. In more detail, Li et al. revealed that the YH₄ and YH₆ are potential superconductors with the estimated T_c values of 84–95 K and 251–264 K at 120 GPa [13]. It is found that TaH₆ with an estimated T_c of 124.2–135.8 K under pressure is a candidate as a high-temperature superconductor [35]. As for vanadium hydrides, the high-pressure structures of VH₅ and VH₈ have been explored, their T_c values were predicted to be 18.5 and 71.4 K at 200 GPa due to the strong electron-phonon coupling (EPC) [36]. Consequently, these studies motivated us to search high-temperature superconductors of transition metal hydrides through compression.

Tungsten (W) is one of transition metal elements. At atmospheric pressure, molecular tungsten hydrides such as WH₂, WH₄, and molecular complex WH₄(H₂)₄ were identified using spectroscopy at low temperatures and in neon matrix [46, 47]. However, they are unstable with respect to hydrogen and bulk W at ambient conditions. In other words, there is no stable solid tungsten hydride at ambient conditions. Once, it was thought that W hardly reacts with H₂ under pressure [48], and was used as a sealing material in high-pressure experiment [19]. However, finding near-stoichiometric WH above ~30 GPa arouses much attention to studying tungsten hydrides at high pressures [49]. Specifically, variable composition structural prediction was performed to investigate structures and phase stability of WH_n (n = 1–6, 8, 10, and 12) up to 150 GPa [46, 50]. Three W-H compounds (i.e., WH, WH₂, and WH₆) are found to be stable [46, 51]. Subsequently, Gregoryanz et al. studied the formation, decomposition, and mechanical properties of tungsten hydrides in a diamond anvil cell up to 115 GPa [52]. Notably, these studies mainly focus on structures and stabilities of tungsten hydrides below 150 GPa. To the best of our knowledge, their electronic properties and superconductivity have not been explored so far.

Generally speaking, most of metal hydrides exhibit superconductivity, and high pressure is in favor of stabilizing H-rich compounds [e.g., LaH₈ [11], BaH₆ [53], YH₁₀ [16], and LaH₁₀ [17]]. On the other hand, H-rich compounds show larger T_c value [54]. Therefore, we expect that tungsten hydrides with a higher hydrogen content become stable under high pressure. Moreover, understanding electronic structures and superconductivity of tungsten hydrides is important to explore their potential applications. In this work, we studied the structural stabilities of tungsten hydrides containing various W_xH_y (x = 1, y = 1–12; x = 2, y = 1) compositions at pressures of 100, 200, and 300 GPa via first-principle structure search calculations. Besides reproducing the reported tungsten hydrides, we find a new stable stoichiometry WH₅ consisting of unique H network and tetrahedron H units, exhibiting the highest T_c value among the tungsten hydrides.

Computational Details

The structural prediction of W-H system was performed via particle swarm optimization as implemented in CALYPSO code [55, 56] at the selected pressures of 100, 200, and 300 GPa. The main merit of this code is capable of finding the ground-state structures only depending on the given chemical composition. Its efficiency and validity have been proven by applying different kinds of systems, ranging from elemental solids to binary and ternary compounds [2, 57–62]. Considering these advantages, CALYPSO becomes a leading structure prediction method in the field. Then, the structural relaxations for the considered W-H compounds were performed through the Broyden-Fletcher-Goldfarb-Shanno (BFGS) [63] method as implemented in Cambridge Serial Total Energy Package (CASTEP) program [64]. The Perdew-Burke-Ernzerh (PBE) of generalized gradient approximation (GGA) was selected for the exchange-correlation functional [65]. The electron-ion interaction was described by using the ultrasoft pseudopotential [66] plane-wave method, in which 5s²5p⁶5d⁴6s² and 1s¹ were taken as valence electrons for W and H atoms, respectively. The kinetic cutoff energy of 400 eV and the Monkhorst-Pack scheme [67] with a k-point grid of 2π × 0.03 Å⁻¹ were chosen to ensure that the total energy well-converged. The phonon spectra and the electron-phonon coupling were calculated within the framework of the linear-response theory as carried out in the Quantum-ESPRESSO package [68]. The kinetic energy cutoff for wave-function expansion is chosen as 80 Ry. A k-point mesh of 15 × 15 × 14 and a q-point mesh of 5 × 5 × 2 for WH₅ were used in the first Brillouin zone. More detailed calculated information can be found in the Supporting Information.

Results and Discussion

To obtain higher T_c value, high hydrogen content in compounds is one of the necessary prerequisites [9, 11, 54]. As a consequence, we carried out the crystal structure search on W_xH_y (x = 1, y = 1–12; x = 2, y = 1) stoichiometries at the selected pressures of 100, 200, and 300 GPa through first-principles swarm structure searching calculations. First, based on the predicted stable structures, we studied the relative phase stability of each stoichiometric compound by calculating its enthalpy of formation (ΔH = [H(W_xH_y) – xH(W) – yH(H₂)/2]/(x + y)) relative to elemental W and H₂ solids at the selected pressures. Here, H(W_xH_y) is the enthalpy of considered structure, H(W) and H(H₂) are the enthalpies of elemental W and H₂ solids, respectively. Then, convex hull data for considered W-H compositions at selected pressures are constructed using enthalpy of formation per atom ΔH for each composition to determine its stability (Figure 1A). In general, a structure whose enthalpy of formation sits on the convex hull (i.e., solid line) is thermodynamically and is experimentally synthesizable. At 100 GPa, the known WH, WH₂, and WH₄ are well-reproduced by our structural search, validating that our adopted method is suitable to the W-H system. At 200 GPa, WH, WH₂, and WH₆ are stable, whereas WH₄ becomes unstable with respect to WH₂ and WH₆. With further compression, a new stoichiometry WH₅, is thermodynamically stable in addition to WH and WH₂ at 300 GPa, whereas WH₆ decomposes into WH₅ and H₂. It is noted that WH is the most stable composition in the whole considered pressure range. To provide more information for experimental synthesis, we determine the pressure stability region of W-H compounds, as displayed in Figure 1B. Intriguingly, these stable compounds do not undergo any structural transitions. This is in sharp contrast with other transition metal hydrides, such as VH₃ [71] and ScH₆ [9].

FIGURE 1

Figure 1. (A) Phase stabilities of various W-H compounds at 100, 200, and 300 GPa. The elemental W solid phase with symmetry Im-3m [69], and P6₃/m, C2/c, Cmca-12 elemental H₂ solids [70] are adopted to calculate the formation of enthalpy. (B) Pressure-composition phase diagram for the W-H compounds.

WH₅ becomes stable above 230.2 GPa and stabilizes into a hexagonal structure (space group P6mm, one formula unit per cell, see Figure 2). This structure contains two inequivalent H's occupying 2b (0.3333, 0.6667, 0.6985) and 3c (0.0000, 0.5000, 0.0825) sites and one equivalent W's sitting at 1a (0.0000, 0.0000, 0.4728) position. Each W atom forms a twelve-fold coordination with H atoms (Figure 2A), having two different W–H distances of 1.70 and 1.71 Å. Mulliken charge analysis [72] shows W atom transfers 0.17 e to each H atom, indicating that W-H bonding is ionic. There are two kinds of H coordination. The H atom at 2b site is coordinated by three W atoms, while H atom at 3c site is shared by two W atoms (Figure 2B). Notably, H atoms form intriguing H network with alternate triangle and hexagon rings along c axis with equal H-H distance of 1.38 Å (Figure 2C), which is called a kagome lattice [73–75]. Moreover, the H atom in the ab plane constitutes vertex-sharing tetrahedron units having H-H distance of 1.28~1.38 Å (Figure 2D). These H-H distances in WH₅ is much larger than H₂ (0.74 Å) [16] at ambient conditions and monatomic H (0.98 Å) at 500 GPa [76], and comparable to lanthanum and yttrium hydrides (1.02~1.54 Å) [11]. indicating that WH₅ might has high T_c value as observed in CaH₆ [2], LaH₈ [11], and YH₁₀ [13].

FIGURE 2

Figure 2. Crystal structure of WH₅ with P6mm symmetry at 300 GPa. (A) View of W-H polyhedrons in P6mm WH₅. (B) Two inequivalent H atoms with three- and two-fold W atoms. (C) H network with alternate triangle and hexagon rings along c axis is a kagome lattice. (D) Vertex-sharing tetrahedron unit consisting of four H atoms in the ab plane.

Dynamic stability of a compound strongly correlates with its practical application. Thus, we calculated phonon spectra of P6mm WH₅ as implemented in Quantum-ESPRESSO package (Figure 3A). The absence of any imaginary frequency in the entire Brillouin zone obviously confirms its dynamic stability. Based on the analysis of projected phonon density of states (PHDOS, Figure 3B), there are two separate regions. The high frequency modes (above ~30 THz) mainly originate from the contribution of H atoms, whereas the low-frequency modes (below ~15 THz) associate with W atoms, which is attributed to that H atom has a lighter atomic mass than W. Moreover, P6₃/mmc WH, Pnma WH₂, P4/nmm WH₄, and C2/m WH₆ are also dynamically stable (Figure S2).

FIGURE 3

Figure 3. (A) Phonon dispersion curve, (B) Eliashberg spectral function α²F(ω), electron-phonon coupling integration λ(ω), and projected phonon density of states (PHDOS) on W and H atoms, (C) electronic band structure, and (D) PDOS for P6mm WH₅ at 300 GPa.

Subsequently, we probe the electronic band structure and corresponding projected density of states (PDOS) of the stable W-H compounds as depicted in Figures 3C,D and Figure S1. As we expected, all the W-H compounds exhibit metallic character due to several bands across their Fermi levels. For these W-H compounds, there is a common character of their electron properties (i.e., the main contribution to PDOS near the Fermi level comes from W 5d orbital). Moreover, there is large overlap between H 1s orbital and W 6s or 6p orbital. The appearance of “flat band-steep band” [3, 77, 78] at Fermi level and large N(E_f) indicate that W-H compounds are the potential high-temperature superconductors [79].

Subsequently, we investigate their superconductivity based on Bardeen-Cooper-Schrieffer (BCS) theory [80]. Among the stable tungsten hydrides, WH₅ has the largest electron-phonon coupling parameter, λ, which is comparable to those predicted for H₂S [59] and H₃Se [78], and slightly smaller that of H₃S [77], indicating that there is strong EPC in WH₅ (Table 1). The combined projected phonon density of states (PHDOS) with Eliashberg spectral function α²F(ω) (Figure 3B) can be used to determine the origin of λ. For WH₅, the low-frequency vibrations from the heavy W atoms (below ~15 THz) contribute 38.7% of the total λ, whereas the high-frequency vibrations (above ~30 THz) resulting from H atoms account for 61.3% of λ. For WH₆, the low-frequency vibrations (below ~15 THz) from the W atoms contribute 50% of the total λ (Figure S3), which is in sharp contrast with WH₅. The λ (0.74) in WH₆ is smaller than 0.93 in WH₅, indicating a weak electron-phonon coupling in WH₆. On the other hand, compared PHDOS (Figure 3B and Figure S3) between WH₅ and WH₆, the high-frequency and low-frequency modes of WH₅ are clearly separate, unlike the situation of WH₆ in which the H-stretching vibrations mix together within the mid-frequency region. These observations can be attributed to the unique H network and the tetrahedron H units in WH₅, whereas hydrogen atoms in WH₆ directly bond W atoms (Figure S4). Based above results, WH₅ with unique H network shows good superconductivity, as will be discussed below. Similar observation has been found in CaH₆ [2], LaH₈ [11], and YH₁₀ [16].

TABLE 1

Table 1. The logarithmic average phonon frequency ω_log, the electronic density of states at the Fermi level N(E_f), the electron-phonon coupling parameter λ, and the superconducting transition temperature T_c of W-H compounds at selected pressures.

The superconducting T_c values of the stable tungsten hydrides are evaluated through the Allen-Dynes modified McMillan equation [81] by using the calculated logarithmic average frequency, ω_log. The typical Coulomb pseudopotential μ* usually adopts the value in the range of 0.1 to 0.13 for many metal hydrides [10]. Thus, μ* with 0.1 and 0.13 was adopted here. The calculated T_c values are shown in Table 1. As expected, WH₅ shows the highest T_c value of 51.3–60.8 K, which is attributed to its large λ and high ω_log. The T_c values of W-H compounds decrease when μ* increases from 0.1 to 0.13, similar to V-H [36] and In-H compounds [15]. Meanwhile, we calculated the pressure-dependent T_c value of WH₅. As shown in Figure 4, the effect of pressure on T_c values is rather small. This is different from the decreased T_c for CrH₃ [82] and ThH₁₀ [83] and the increased T_c in ScH₈ [9] with increasing pressure. In more detail, as the pressure increases, ω_log becomes larger, whereas λ becomes smaller, and N(E_f) remains nearly unchanged (Figure 4).

FIGURE 4

Figure 4. The logarithmic average phonon frequency ω_log, the electronic density of states at the Fermi level N(E_f) (states/Ry/cell), the electron-phonon coupling parameter λ, and the superconducting transition temperature T_c of P6mm WH₅ at the selected pressures of 230, 250, 270, and 300 GPa.

Conclusions

To determine phase diagram and superconductivity of W-H binary compounds, we have explored their crystal structures and stabilities with various chemical compositions with the aid of first-principles swarm structural calculations. We identify a hitherto unknown WH₅ compound, consisting of unprecedented H network and tetrahedron H units, which can be synthesized from compression of C2/m WH₆ and Pnma WH₂ above 230.2 GPa. All the stable tungsten hydrides are metallic in their stable pressure region. The P6mm WH₅ shows high T_c value up to 60.8 K at 300 GPa, which is much higher than WH₆. This work provides an opportunity for full understanding of crystal structures, electron properties, and superconducting mechanism of tungsten hydrides at megabar pressures.

Author Contributions

GY and AB contributed conception and design of the study. ShoZ organized the database. YS, JZ, and JL performed the statistical analysis. ShuZ wrote the first draft of the manuscript. GY and AB wrote sections of the manuscript. All authors contributed to manuscript revision, read and approved the submitted version.

Conflict of Interest Statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Acknowledgments

This work is supported by the Natural Science Foundation of China under Nos. 21573037, 11704062, and 51732003; the Natural Science Foundation of Jilin Province (No. 20150101042JC); the Postdoctoral Science Foundation of China (under Grant No. 2013M541283); and the Fundamental Research Funds for the Central Universities (2412017QD006).

Supplementary Material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fphy.2018.00101/full#supplementary-material

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