Structures and Properties of Osmium Hydrides under Pressure from

Article pubs.acs.org/JPCC

Structures and Properties of Osmium Hydrides under Pressure from First Principle Calculation Yunxian Liu, Defang Duan, Xiaoli Huang, Fubo Tian, Da Li, Xiaojing Sha, Chao Wang, Huadi Zhang, Ting Yang, Bingbing Liu, and Tian Cui* State Key Laboratory of Superhard Materials, College of Physics, Jilin University, Changchun 130012, P. R. China S Supporting Information *

ABSTRACT: The pressure-induced new structures and properties of osmium hydrides were systematically explored in a wide pressure range 0−300 GPa using ab initio methods. Three stable stoichiometries, that is, OsH, OsH3, and OsH6, are predicted above 50 GPa. The above hydrides exhibit metallic character with the notable band structures exception of OsH6. It is interesting to note that the phase P21/c of hydrogen-rich OsH6 adopts intriguing structures with H2 units. The electron−phonon coupling calculations indicate that the superconducting critical temperature (Tc) values of Fm-3m-OsH is 2.1 K at 100 GPa. Comparing to pure Os, the addition of hydrogen is in favor of improving the superconducting temperature.

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INTRODUCTION Hydrides have attracted a great deal of attention for several years due to the fact that they not only could be hightemperature superconductor at a relatively low pressure, but also can be used as a potential material for hydrogen storage. For example, sulfur hydrides was found having a high Tc with 190 K.1−3 And (H2)4CH4 can be used as a hydrogen storage material with 33.4 wt % molecular hydrogen.4 As we know, many transition metals can react with hydrogen to form hydrides under ambient conditions.5,6 However, platinum group metals, including Pt, Pd, Os, Ir, Ru, and Rh, do not form hydrides at ambient pressure, which owes to the fact that platinum-group metals are normally inert and resistant to react with other elements at normal conditions. High pressure can provide a different route to new material synthesis and manipulating novel physical properties. In the condensed and high pressure environments, the atoms close together and bonding patterns change, resulting in new materials that cannot be synthesized at normal conditions. With the pressure increasing, the chemical potential of hydrogen rises steeply and then hydrogen reacts with metals to form metal hydrides.7−10 The platinum-group metal hydrides, such as Rh, Pd, Ir, and Pt hydrides have been experimentally synthesized under high pressure.7,8,11−13 In addition, some of them have also been explored in theory.14−17 In recent years, the platinum-group metal hydrides have been of great scientific interest, which owes to their applications in the hydrogen economy and the potential substances of achieving metallic hydrogen at modest pressure. For example, RhH2 is a high volumetric hydrogen density compound, which theoretical volumetric hydrogen densities reach 163.7 g H2/L.11 And PtH is a superconductor with Tc = 12−16 K at 105 GPa.14 © XXXX American Chemical Society

As a platinum group metal, osmium is the densest and stiffest metal among transition metals, having a very large bulk modulus comparable to that of diamond. And it maintains the close-packed structure (P63/mmc) up to high pressures. To date, the various aspects of osmium and its compounds have been experimentally and theoretically investigated.18−20 However, no osmium hydrides are known at high pressures. Based on the applications of platinum-group metal hydrides materials, as well as the novel physical properties motivated us to perform a thorough search on osmium hydrides under high pressure. In addition, for most known D-metal hydrides, the metal atoms generally form a closed-packed host lattice in which hydrogen atoms occupy the octahedral or tetrahedral interstitial sites. A further motivation factor for the present investigations is to check whether the osmium hydrides are the above structural type or form some exotic structures. In the present work, we employed a first-principles global structural optimization method to extensively explore and search for the structures of hitherto unknown osmium hydrides at zero temperature. The phase stabilities of several stoichiometric binary osmium hydrides OsHn (n = 1−8) under various pressures were investigated. Then we obtain thermodynamically stable structures and identify a large number of stable phases which may be synthesized under proper pressure conditions. Particularly, we examined in detail their structures and calculated their dynamical stability, the corresponding electronic band structures, bonding patterns, as well as the superconductivity of Fm-3m-OsH. Received: April 20, 2015 Revised: June 11, 2015

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DOI: 10.1021/acs.jpcc.5b03791 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

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COMPUTATIONAL METHOD We have employed the evolutionary algorithm USPEX, implemented in the USPEX code (Universal structure predictor: Evolutionary Xtallography),21−23 to search for the most stable stoichiometries and structures of OsHn (n = 1−8). The energetic and electronic structure calculations were carried out using density functional theory within the Perdew−Burke− Ernzerhof (PBE) parametrization of the generalized gradient approximation (GGA),24 as implemented in the Vienna ab initio simulation package (VASP).25 The adopted all-electron projector-augmented wave PAW26 pseudopotentials of osmium and hydrogen treat 5d66s2 and 1s1 electrons as valence electrons. And for hydrogen and osmium, the cutoff radii were taken 0.8 and 2.5 au, respectively. A plane-wave cutoff energy of 800 eV and appropriate Monkhorst−Pack-point meshes were used for all structures to achieve that the enthalpy calculations are converged to better than 1 meV/atom. Phonon calculations were performed by the direct supercell method using a supercell approach27 with the PHONOPY code.28 Electron−phonon couplings for superconducting properties were studied by within the framework of the linear-response theory as implemented in the Quantum ESPRESSO package.29 The convergence tests concluded that suitable calculation parameters are 100 Ry for kinetic energy cutoff, 20 × 20 × 20 k-point sampling mesh, and 5 × 5 × 5 q-mesh in Brillouin zone for Fm-3m-OsH.

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Figure 1. Enthalpies of formation (ΔHf, in meV/atom) of OsHn (n = 1−8) with respect to Os and H2 at selected pressures. The symbols on the solid line represent that the hydride is stable at the corresponding pressure.

RESULTS AND DISCUSSION

Here, we perform the evolutionary simulations with considering simulation sizes ranging from one to four for each stoichiometry OsHn (n = 1−8) formula units (f.u.) at 50, 100, 150, 200, 250, and 300 GPa, and find many different relaxed structures. The computed enthalpies of formation, ΔHf, of OsHn (n = 1−8) with respect to elemental solid Os and H2 at the selected pressures are provided in the convex hull, as shown in Figure 1. Moreover, the known structures of P63/mmc for Os and P63/m, C2/c, and Cmca for H230 are considered depending on the applied pressures. Structures which are thermodynamically stable relative to decomposing into other hydrides and/or pure elements are lying on the convex hull, whereas the structures above the convex hull are metastable (Figure 1). Principally, these structures can be synthesized in experiment. At the pressure of 50 GPa, the OsH6 becomes the preferred stable phase and also the only stoichiometry which can be formed, as depicted in Figure 1. At 100 GPa, OsH and OsH6 are thermodynamically stable species, and OsH6 has the most negative enthalpy of formation. With increasing pressure to 150 GPa, the enthalpy of the OsH was predicted as being the global minimum, with OsH3 and OsH6 falling on the convex hull. At the higher pressure of 200 GPa, OsH remains the most negative ΔHf, while other thermodynamically stable phase is OsH3. When the pressure reaches 300 GPa, OsH is the only most favorable hydride. We also calculated the enthalpy for the most stable structures and constructed the pressure−composition phase diagram of Os−H system, as depicted in Figure 2. It shows the stability ranges of Os, OsH, OsH3, OsH6 and H2, respectively. We can see that the P21/c of OsH6 is the most stable structure at 38 GPa. Then when the pressure reaches 155 GPa, OsH6 (space group Fdd2) becomes unstable and decomposes into OsH3 (Cmm2) and H2 (C2/c). At 140 GPa, OsH3 (space group Cmm2) is the most stable compound, and at elevated pressure

Figure 2. Pressure−composition phase diagram for Os−H system in the pressure of 0−300 GPa.

of 246 GPa it separates into OsH (Fm-3m) and H2 (C2/c). For OsH, the structure Fm-3m structure becomes favorable in the pressure range from 94 to 300 GPa. We can see that, for the stable stoichiometries, the general trend of n (n denotes the number of H in OsHn) is declining with pressure, which is similar to the case of Ir−H system.16 That is to say, the H concentration appears to decrease with increasing pressure. As we know, the electronegativity value (2.18) of hydrogen is comparable or smaller than those of Os and Ir (2.2), which may lead to the gradual instability of stable H-rich stoichiometries with the pressure increasing. The high pressure crystal structures of OsH, OsH3 and OsH6 were plotted in Figure 3. All the structures are represented in the form of a conventional cell with the addition of symmetry. At 300 GPa, OsH adopts a face-centered cubic Fm-3m (4 f.u./cell) structure, which can be B


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Figure 3. Crystal structures of the energetically stable Os−H system. (a) Fm-3m-OsH at 300 GPa, (b) Cmm2-OsH3 at 250 GPa, (c) P21/c-OsH6 at 100 GPa, and (d) Fdd2-OsH6 at 200 GPa. Purple and blue balls denote Os and H atoms, respectively. Yellow balls represent H2 units. The unit cell is drawn with black solid lines.

Figure 4. Phonon dispersion curves and phonon density of states (PDOS) projected for Fm-3m-OsH, Cmm2-OsH3, P21/c-OsH6, and Fdd2-OsH6 at 100, 200, 100, and 150 GPa, respectively.

viewed as NaCl-type (see Figure 3a). At the pressure of 250 GPa, OsH3 prefers the stable structure of orthorhombic Cmm2 (8 f.u./cell) and we carried out three times expanding cell in caxis direction in the Cmm2 phase to better describe its structural feature, as shown in Figure 3b. We note that the structure segregates into layers, in which one is consistent with

Os and H atoms, and the other is formed by only H atoms. For OsH6, we predict monoclinic P21/c and orthorhombic Fdd2 at 100 and 150 GPa, respectively. Remarkably, P21/c (4 f.u./cell) can be viewed as being composed of H2 units, H atoms and Os atoms, as shown in Figure 3c. The Fdd2 (8 f.u./cell) structure consists of H atoms and Os atoms, in which Os atoms can be C


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Figure 5. (a−c) Electronic band structures and (e−h) calculated total and partial density of states (PDOS) of the Fm-3m-OsH, Cmm2-OsH3, P21/cOsH6, and Fdd2-OsH6 at different pressures. The vertical dashed line at zero is the Fermi energy level.

addition of a certain element may make OsH6 become a good hydrogen storage material at mild condition. Dynamic property of the phase is one of the basic criteria when considering the structure stability. Figure 4 presents the calculated phonon dispersion curves and projected phonon density of states (PHDOS) for Fm-3m (OsH), Cmm2 (OsH3), P21/c, and Fdd2 (OsH6) at accessible pressures. There is no sign of imaginary frequencies in the entire Brillouin zone, which indicates that the above phases are dynamical stability in their corresponding studied pressure range. A striking feature of PHDOS is the two separate regions: the high frequency region and the low frequency modes (below 10 THz) are related to H and Os atoms, which attributes to osmium much heavier than hydrogen atom. To investigate the electronic properties of Os−H system, we explore the electronic band structures and partial density of states (PDOS) for Fm-3m (OsH), Cmm2 (OsH3), P21/c, and Fdd2 (OsH6) at 100, 200, 100, and 150 GPa, respectively, as plotted in Figure 5. Note that, for Fm-3m OsH and Cmm2

seen to form a distorted simple orthorhombic structure, as seen in Figure 3d. Detail parameters of these structures at different pressures are listed in Table S1 in the Supporting Information. Figure S1 in the Supporting Information shows the enthalpy curves of OsH6 with respect to Os and H2 as a function of pressure. OsH6 become stable at 38 GPa, meaning that it can be synthesized in the recent diamond anvil cell experiment. Under compressing, Fdd2 stands out as lowest-enthalpy phase in 104−300 GPa. It is noted that RhH2 was synthesized above 8 GPa and released H at 4 GPa.11 Based on Rh and Os belong to platinum group metals, the OsH6 with hydrogen content of 3.1 wt % may be have same property in terms of hydrogen storage. In addition, Mg base hydrogen storage alloys perform excellent properties on hydrogen storage at proper conditions, for example, Mg3Pr, Mg (In, Al) and CeH2.73−MgH2−Ni.31−33 The studying of structures and deuterium desorption for Ca3Mg2Ni13 can provide a blueprint for the mechanism of hydrogen desorption.34 The above reaches inspire us that the D


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point, the Tc was estimated by using the standard Allen−Dynes modified McMillan equation.35

OsH3, the conduction and the valence bands are overlapped, suggesting that the two phases are metallic (as shown in Figure 5a and b), while for P21/c and Fdd2 of OsH6, they are semiconducting phases due to their energy band gaps (Figure 5c and d). A visual inspection of the PDOS of Fm-3m OsH and Cmm2 OsH3 (Figure 5e and f) shows that Os-d orbits mainly dominate the density of states at the Fermi level. Whereas for P21/c and Fdd2 OsH6, the PDOSs show significant hybridization between the Os-d and H-s orbits in the energy range (Figure 5g and h). To further visualize the interactions between the atoms in the polymeric hydrogenic sublattice for P21/cOsH6, we calculated electron localization function (ELF), as depicted in Figure 6c. The ELF value located between H2 unit

Tc =

⎡ ⎤ 1.04(1 + λ) exp⎢ ⎥ ⎣ λ − μ*(1 + 0.62λ) ⎦ 1.2

ω log

This equation has been found to be highly accurate for materials with λ < 1.5. The electron−phonon coupling strength (EPC) λ, the logarithmic average phonon frequency ωlog, and the electronic DOS at the Fermi level N(Ef) were calculated to explore the possible superconductivity. According to our calculations, with the Coulomb parameter set μ* = 0.1, the EPC parameter λ becomes 0.42, ωlog is 347.84 K, N(Ef) is 4.22 (states/spin/Ry/unit cell), and the Tc is 2.1 K (at 100 GPa). Moreover, to our best knowledge, the Tc of Os is only 0.65 K. Therefore, we considered that the addition of hydrogen is in favor of improving the superconducting critical temperature. Besides the above stable structures, we also observed some interesting metal-stable phases, and their structural motifs are presented in Figure 7. At 100 and 150 GPa, we predicted two monoclinic phases with Cm (4 f.u./cell) and P21 (4 f.u./cell) for OsH5, which are composed of Os, H atoms and H3 units. However, the morphology of H3 is different: the H3 is linear in Cm phase, but it becomes bent in P21 structure. OsH7 adopts a monoclinic C2/m (4 f.u./cell) and a orthorhombic Ima2 (2 f.u./cell) at 150 and 300 GPa, respectively. Both phases consist of H, Os atoms and H2 units, in which the H−H distances are 0.87 and 0.79 Å. For OsH8, a structure with P21/c symmetry containing four formula units (Z = 4) was predicted at 200 GPa. The P21/c contains H, Os atoms and H3 units, and the H3 units form triangles with the distance of 0.87 Å, 0.90 Å, and 0.96 Å. The map of the electron localization function (ELF) for P21/c-OsH8 (Figure 6d) shows localized electron density within the H3 ring (ELF over 0.9), implying that localized spin paired electron density exist.

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CONCLUSION In summary, we have employed the evolutionary algorithm USPEX in combination with first-principles calculations to investigate the high-pressure crystal structures of Os−H system (H-rich). Three stoichiometries (OsH, OsH3, and OsH6) are found stable, and OsH6 become stable relative to pure elements above 38 GPa. The hydrogenic sublattices of osmium hydrides are composed of H atoms and H2 and H3 units. The band structures of stable phases reveal that Fm-3m (OsH) and Cmm2 (OsH3) are metallic phases. Moreover, the estimated super-

Figure 6. Calculated ELF of (a, b) P21/c-OsH6 with isosurface value of 0.8 and (c, d) P21/c-OsH8 with isosurface value of 0.8.

is close to 1.0, which is significantly larger than the ELF value between Os and the nearest H atom (ELF < 0.5), implying that the former form strong covalent bonding in H2 unit, while no bonds were present between the Os and H atoms. The density of states for the Fm-3m OsH phase at the Fermi level has a significant value, suggesting that it may be a superconductor at accessible conditions. Further examining this

Figure 7. Crystal structures of the metastable Os−H system at different pressures. Purple and blue balls denote Os and H atoms, respectively. Yellow balls represent H2, H3 units. E


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conducting critical temperature Tc of OsH reaches 2.1 K at 100 GPa by application of the Allen−Dynes modified McMillan equation. Our findings help to shed light on understanding the rich and complex crystal structures of osmium hydrides, which have broad implications for further exploring other platinumgroup metal hydrides.

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ASSOCIATED CONTENT

S Supporting Information *

Calculated structural parameters of our predicted stable structures for Os−H system at their corresponding pressures; enthalpy curves (relative to Os and H2) for OsH6 in the pressure range from 5 to 300 GPa. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b03791.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel/fax: +86-431-85168825. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Basic Research Program of China (No. 2011CB808200), Program for Changjiang Scholars and Innovative Research Team in University (No. IRT1132), National Natural Science Foundation of China (Nos. 11204100, 51032001, 11074090, 10979001, 51025206, 11104102, and 11404134), National Found for Fostering Talents of basic Science (No. J1103202), China Postdoctoral Science Foundation (2012M511326, 2013T60314, and 2014M561279), Graduate Innovation Fund of Jilin University (2015102). Parts of calculations were performed in the High Performance Computing Center (HPCC) of Jilin University.

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Structures and Properties of Osmium Hydrides under Pressure from

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