Article pubs.acs.org/IC
Pressure-Stabilized Superconductive Ionic Tantalum Hydrides Quan Zhuang, Xilian Jin,* Tian Cui,* Yanbin Ma, Qianqian Lv, Ying Li, Huadi Zhang, Xing Meng, and Kuo Bao State Key Laboratory of Superhard Materials, Jilin University, Changchun 130012, China S Supporting Information *
ABSTRACT: High-pressure structures of tantalum hydrides were investigated over a wide pressure range of 0−300 GPa by utilizing evolutionary structure searches. TaH and TaH2 were found to be thermodynamically stable over this entire pressure range, whereas TaH3, TaH4, and TaH6 become thermodynamically stable at pressures greater than 50 GPa. The dense Pnma (TaH2), R3m ̅ (TaH4), and Fdd2 (TaH6) compounds possess metallic character with a strong ionic feature. For the highly hydrogen-rich phase of Fdd2 (TaH6), a calculation of electron− phonon coupling reveals the potential high-Tc superconductivity with an estimated value of 124.2−135.8 K.
■
INTRODUCTION In recent years, the study of hydrogen-rich compounds under high pressure has seen wide progress, which has been focused mainly on two aspects: one is the search for new materials with high hydrogen capacity for hydrogen storage, owing to the fact that hydrogen is extensively regarded as a promising form of renewable and clean energy.1−3 The other is aimed at discovering conceivable high-temperature superconductors; for example, a significant number of hydrides (SiH4, Si2H6, SiH4(H2)2, GeH4, KH6, SbH4, GaH3, InH3, and others) at high pressures have been predicted to be superconductors with a superconducting transition temperature (Tc) ranging from 17 to 139 K.4−18 Furthermore, a high Tc of about 200 K has been predicted for sulfur hydride and affirmed by experiments.19−21 This stimulated a plethora of studies on sulfur hydride to analyze the factors contributing to its Tc and to examine anharmonicity as well as isotope effects.22−33 Moreover, the superconductivity of selenium hydrides, tellurium hydrides, and phosphorus hydrides has also been explored.34−38 Recently, the transition metal hydrides have also been the object of many investigations. Many late transition metals do not form hydrides under ambient pressure, but there are exceptions, such as Pd.39,40 Additionally, high pressure has been used to synthesize the hydride phase of some late transition metals, such as Rh,41 Ir,42,43 Pt,44 and others. Moreover, platinum and ruthenium have been proposed for use as hydrogen storage materials because they can adsorb a considerable quantity of hydrogen.45 As for the early transition metal hydrides, they may be synthesized under ambient conditions, which is attributed to their being less electronegative than hydrogen, such as the hcp-structured YHx, CaF2type (space group Fm3̅m) TiH2, ZrH2, VH2, and NbH2. However, at low temperature, the Fm3m ̅ form of TiH2 and ZrH2 will transform to tetragonal I4/mmm, and the tetragonal © 2017 American Chemical Society
structure is reported to be stable up to 63 and 103 GPa for TiH2 and ZrH2, respectively.46,47 With regard to group 5 element dihydrides, VH2 transforms to Pnma at about 50 GPa and NbH2 changes to P63mc at 45 GPa.48 Consequently, investigating the structures of early transition metal hydrides under high pressure is essential for comprehending the highpressure structural features of hydrides. Moreover, YHx (x = 3, 4, 6) are predicted to be superconductors with relatively high Tc of 40−264 K in the pressure range of 17.7−120 GPa.49 This motivated us to find high-temperature superconductors by compressing compounds of early transition metals with hydrogen. Tantalum, a group 5 element, is of fundamental interest due to its superconducting properties,50−52 and many aspects of tantalum and its compounds have been studied in depth.53,54 In recent decades, several stoichiometries of tantalum hydrides have been investigated at ambient pressure. Asano et al. reported that tantalum hydrides form an interstitial solid solution of hydrogen in tantalum over a wide composition range,55 and nine phases of Ta−H compounds were reported by Schober et al.56 Simonović et al. synthesized tantalum hydrides of various compositions by equilibrating tantalum with hydrogen in the temperature range 573−823 K under a constant hydrogen pressure of 1 bar.57 Near Ta2H, hydrogen ordering occurs. Wanagel et al. studied the ordering of hydrogen in β-tantalum hydride and found a β-tantalum hydride with a composition estimated to be in the vicinity of Ta2H.58 Subsequently, several X-ray diffraction experiments were performed on Ta2H, confirming its structure in space group C222.59,60 Also, the stoichiometry of TaH2 has been studied and reported to adopt space group Fm3̅m.61 Recently, Received: November 23, 2016 Published: March 16, 2017 3901
DOI: 10.1021/acs.inorgchem.6b02822 Inorg. Chem. 2017, 56, 3901−3908
Article
Inorganic Chemistry Iturbe-Garciá et al. synthesized tantalum hydrides by utilizing a high-energy ball milling technique. Their XRD analysis demonstrated that Ta2H and TaH0.5 were obtained after 20 h of milling.62 As far as we know, the superconductivity of Ta−H compounds and the compressed tantalum hydrides have been barely investigated. Here, we extensively investigated the high-pressure structures of tantalum hydrides. The phase stabilities of several stoichiometries of binary tantalum hydrides were investigated. Then, we obtained thermodynamically stable structures and proposed many stable phases that may be synthesized under an appropriate pressure. Electronic structures, phonon dispersions, and superconductive behavior of Pnma (TaH2), R3m ̅ (TaH4), and Fdd2 (TaH6) were studied. The highly hydrogen-rich phase of Fdd2 (TaH6) was found to be a good superconductor with an estimated Tc of 124.2−135.8 K.
calculations were computed by QUANTUM-ESPRESSO.69 Ultrasoft pseudopotentials with a cutoff energy of 60 Ry were adopted for property calculations. The 5s5p5d6s and 1s were treated as valence electrons for Ta and H, respectively.
■
RESULTS AND DISCUSSION First, the stoichiometries of Ta2H, Ta5H, and TaH2 were investigated at ambient pressure and compared with those reported from experiments. By using the ELocR code, the three species are predicted to adopt space groups C222, C2, and P63mc, respectively. Their lattice parameters are listed in Table S1. Figure 1 shows a comparison of X-ray diffraction (XRD)
■
COMPUTATIONAL METHOD Tc can be estimated by the Allen−Dynes-modified McMillan equation63,64 Tc =
⎡ ⎤ 1.04(1 + λ) exp⎢ − ⎥ 1.2 ⎣ λ − μ*(1 + 0.62λ) ⎦
ω log
(1)
Figure 1. Comparison of XRD data based on reported experiments and our calculations at ambient pressure. (a) Upper black curve comes from experiments on Ta2H (TaH0.5) performed by Iturbe-Garciá et al., and bottom red curve represents the simulated XRD pattern from this work. The inset shows the C222 structure of Ta2H that we predict. (b) Upper black curve comes from experiments of TaH0.2 performed by Simonović et al., and bottom red curve represents the simulated XRD pattern from this work. The inset exhibits the C2 structure of Ta5H that we predict.
where λ and ωlog are the electron−phonon coupling constant and the logarithmic-averaged phonon frequency, respectively, and μ* is the Coulomb pseudopotential.65 λ and ωlog are given by λ=2
∫0
∞
α 2F(ω) dω ω
(2)
and ⎛2 ω log = exp⎜ ⎝λ
∫0
∞
⎞ dω 2 α F(ω) ln ω⎟ ⎠ ω
data based on reported experiments and our calculations. The XRD patterns of Ta2H (TaH0.5) reported by Iturbe-Garciá et al.62 and TaH0.2 given by Simonović et al.57 are shown as bold black curves in Figure 1a,b, respectively. Our calculations based on C222 (Ta2H) and C2 (Ta5H) agree well with the experimentally reported XRD patterns (see the red curves in Figure 1). Thus, the phases that we predict are consistent with the experimentally reported ones: C222 and C2 are the stable phases for Ta2H and Ta5H, respectively. For the TaH2 stoichiometry, Fm3̅m given by Müller et al.61 and the P63mc phase that we predict were also compared. It is worth mentioning that the same Fm3m ̅ structure was also found by utilizing the ELocR code. The total energy calculations show that the formation enthalpy of Fm3̅m is about 0.03 eV/atom higher than that of P63mc. Therefore, the employed computational method is valid and the calculations under high pressure can give reasonable results. Next, the crystal structures of tantalum hydrides of various stoichiometries (TaHn) under high pressure were explored, and many different structures were obtained. Figure 2a shows the thermodynamic convex hull at selected pressures, which is defined as the enthalpies of formation per atom with respect to those of solid Ta and H2 at selected pressures. Structures with their enthalpy on the convex hull are thermodynamically stable and experimentally synthesizable, whereas the structures above the convex hull are metastable. At ambient pressure, TaH and TaH2 are the preferred stable phases, and other stoichiometries lie above the convex hull, demonstrating that they are unstable. Up to 50 GPa, TaH3 and TaH4 become thermodynamically stable species. As for TaH6, which decomposes into other stoichiometries and H2 at low pressure, it lies nearly on the
(3)
The parameter ω denotes the phonon frequency, and α F(ω) is the Eliashberg spectral function66 γqv 1 α 2F(ω) = ∑ δ(ω − ωqv) 2πN (ϵF) qv ωqv (4) 2
The line width γq,υ is written as v γqv = πωqv ∑ ∑ |gmn (k, q)|2 δ(ϵm , k + q −ϵF) × δ(ϵn , k −ϵF) mn
k
(5)
where ϵn,k is the energy of the bare electronic Bloch state, ϵF is the Fermi energy, and gνmn(k, q) is the electron−phonon matrix element. Structure prediction at different pressures was explored by utilizing the ELocR code.67 Structural relaxation was performed with the Vienna ab initio simulation package (VASP 5.3.2) within density-functional theory using the Perdew−Burke− Ernzerhof generalized gradient approximation.68 The “hard” PAW pseudopotential for H and “GW” pseudopotential for Ta were adopted, and for hydrogen, the 1s cutoff radius was 0.8 au. For tantalum, the radius for 5p6s6d was taken as 2.5 au. There are 13 and 1 valence electrons in the pseudopotentials for Ta and H, respectively. A plane-wave cutoff of 950 eV and appropriate Monkhorst−Pack k-meshes were employed with a resolution of 2π × 0.025 Å−1 for Brillouin zone (BZ) sampling to ensure that all enthalpy calculations are well converged to less than 1 meV per atom. Phonon and electron−phonon 3902
DOI: 10.1021/acs.inorgchem.6b02822 Inorg. Chem. 2017, 56, 3901−3908
Article
Inorganic Chemistry
Figure 3. High-pressure structures of tantalum hydrides. (a) Pnma phase of TaH2 at 200 GPa, (b) R3̅m (TaH4) at 250 GPa, and (c) Fdd2 (TaH6) at 300 GPa. Purple and blue balls depict Ta and H atoms, respectively.
Mechanical properties are one aspect in the determination of phase stability. According to mechanical stability criteria, the stable structures possess a positive crystal deformation energy. The elastic constants of Pnma (TaH2), R3̅m (TaH4), and Fdd2 (TaH6) were calculated and are listed in Table 1. Obviously, Table 1. Elastic Constants Cij (kBar) for Pnma (TaH2) at 200 GPa, R3̅m (TaH4) at 250 GPa, and Fdd2 (TaH6) at 300 GPa
Pnma (TaH2) R3̅m (TaH4) Fdd2 (TaH6)
Figure 2. (a) Enthalpies of formation (ΔH) of TaHn (n = 1, 2, 3, 4, 6) with respect to Ta and solid H2 at selected pressures. Solid symbols imply that the hydrides are thermodynamically stable at the corresponding pressures, and open symbols represent metastable stoichiometries. (b) Stable pressure ranges of Ta−H compounds in the 0−300 GPa range.
C11
C22
C33
C44
C66
C12
C13
C23
8629 5452 11 652 5368 10 432 5390
1483 5531 2597
2478
2125 6518
3777
9660 2557 10 018 2113 11 560 3668
9537 5019 5819 10 471 5383
C55
the elastic constants of matrix Cij meet the Born−Huang stability criteria,70 indicating the mechanical stability of the proposed phases. The phonon dispersion curves and projected phonon density of states (PHDOS) are presented in Figure 4. All structures exist with no imaginary frequency in the entire Brillouin zone, which demonstrates their dynamical stability. For all structures, the low-frequency (
