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Cite This: Inorg. Chem. XXXX, XXX, XXX-XXX
Superconductivity of Pressure-Stabilized Vanadium Hydrides Xiaofeng Li and Feng Peng* College of Physics and Electronic Information & Henan Key Laboratory of Electromagnetic Transformation and Detection, Luoyang Normal University, Luoyang 471934, China S Supporting Information *
ABSTRACT: The study of the high-temperature superconductive property in compressed hydrogen (H)-rich hydrides has been motivated by hydrides, which become superconducting at low pressure due to chemical precompression. In the present study, we report the first-principles structure searches for stable vanadium(V) hydrides over a pressure scope 0−200 GPa, where stable unexpected stoichiometries of H-rich V hydrides (e.g., VH3, VH5, and VH8) emerge. These dense H-rich V hydrides are metallic with a strong ionic feature, and the coordination number of metal V gradually increases with H content. In particular, C2/m-VH8, which consists of infinite zigzag chains of sole H2 molecules, has the highest coordination number of 16. From our electron− phonon calculations, one can see that P63/mmm-VH5 and C2/m-VH8 are superconductors with estimated superconducting temperatures (Tc) of 18.5 and 71.4 K at 200 GPa, respectively. Our simulations not only uncovered the crystal structures of V hydrides, but also established the high-temperature superconductive nature of them.
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INTRODUCTION Metal hydrides have received wide attention for their unique physical properties and attractive applications, such as hydrogen (H) energy storage and potential high-temperature superconductivity. For example, a number of H-rich compounds that contain main group elements have been proven to have good superconductivity with highly superconductive temperatures (Tc) (e.g., 235 K at 150 GPa for CaH6,1 64 K at 220 GPa for GeH4,2 82 K at 300 GPa for LiH6,3 70 K at 166 GPa for KH6,4 38 K at 250 GPa for BeH2,5 and so on).6−11 Excitingly, H3S, a recent discovery of remarkably high superconductivity with a superconducting Tc of up to 203 K at 200 GPa,12 was perhaps formed from H2S by decomposition under pressure. For sulfur dihydride, H2S has not been regarded as having potential for superconductors, since it was suggested to be dissociated into solid sulfur and H before metallization. 13,14 H2 S was theoretically investigated and proved to be a potential superconductor with Tc as high as 80 K against elemental dissociation at 160 GPa; shortly thereafter, superconductivity was observed by compressing H2S.15 Moreover, shortly after this report, the observed high-temperature superconductivity in compressed H2S (H3S product) by breakthrough electrical measurement had an amazing high Tc of 190 K at some pressures.16 Transition metal hydrides, as typical metal hydrides, have also been a focus in searching for potential superconductors with high Tc under pressure. For example, PdH at ambient pressure has a superconducting temperature of approximately 9 K with an unusual isotope effect.17 In thorium (Th) hydrides, superconductivity was enhanced by interstitial H, and the Hrich compound of Th4H15 had a superconducting temperature of approximately 8 K, compared to 1.37 K for pure thorium.18 © XXXX American Chemical Society
For another known superconductor, PtH, Degtyareva and his coauthors19 assumed the formation of PtH at a certain pressure, which was not consistent with the experimental result in ref 20 in which the indirect evidence supported the formation of PtH. Theoretical investigations have also indicated that PtH had superconductivity with Tc of 10−25 K and a phase transition at high pressures.21,22 Recent theoretical calculation23 revealed that the potential high-temperature superconductors of YH4 and YH6 had an estimated maximum Tc of 95 and 264 K, respectively: Tc of 84−95 K and 251−264 K at 120 GPa, respectively. The superconductivity of osmium (Os) hydrides24 has been explored theoretically at high pressures, and its Tc has been predicted to be 2.1 K at 100 GPa. Furthermore, the Tc of NbH48 and CrH325 reached approximately 38 K at 300 GPa and 37 K at 81 GPa, respectively. In addition, pressurestabilized RuH3 with Pm3̅m symmetry has a Tc of 3.57 K at 100 GPa.26 The subsequent experimental work identified the stability of RuH.27 Among these transition metals, vanadium(V) exhibits a high transition temperature (Tc), which increases from 5 K at 0 GPa to 17 K at 120 GPa.28−30 However, at higher pressures, the superconducting temperature of V appeared to saturate and remain level up to 150 GPa.29 Moreover, V with bcc structure was not found to have a structural phase transition up to 154 GPa. At higher pressures, the phase uncertainty of V will influence the variety of its superconducting temperature.31 In addition, V also plays a very important role in the function of H storage due to stable V hydrides at ambient pressures. V can absorb H at moderate temperatures and pressures, and form a Received: July 14, 2017
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DOI: 10.1021/acs.inorgchem.7b01686 Inorg. Chem. XXXX, XXX, XXX−XXX
Article
Inorganic Chemistry hydride (VH2), which contains 3.8 wt % hydrogen.32 To date, few investigations33−38 have focused on V hydrides, such as VH2, V2H, and VH. However, these works only focused on the crystal structure, phase transition, and electronic structure of V hydrides at different pressures. The exploration for the superconductivity in V hydrides in the H-rich region at high pressures was performed in the present study. The phase diagram, its excellent properties, and possible superconductivity of the vanadium−hydrogen (V−H) system at pressures were explored using CALYPSO code.39,40 In addition to the known V2H, VH, and VH2, unusual stoichiometric V2H5, VH3, VH5, and VH8 compounds were uncovered, which can be energetically stable at high pressures. Using the Allen−Dynes-modified McMillan equation, H-poor hydrides of VH and VH2 have lower superconducting temperatures of only a few Kelvin. However, the H-rich phases of VH5 and VH8 have Tc’s that are estimated to be 18.5 and 71.4 K at 200 GPa due to the strong electron−phonon coupling (EPC).
2. COMPUTATIONAL METHOD
Figure 1. High-pressure phase diagram (convex hull) for the V hydrides with respect to V and H2 at (a) 0 GPa, (b) 100 GPa, and (c) 200 GPa. The solid and open symbols are the stable and metastable compounds, respectively. (d) Stable pressure range for the V−H system.
The energetic stability of V hydrides was performed by the CALYPSO method39,40 with a combination of first-principles calculations. The validity of CALYPSO has been proven by various compounds.41−45 The formation energies of V−H system are calculated by VASP code with the plane-wave pseudopotential method.46 The Perdew−Burke−Ernzerhof generalized gradient approximation47 was selected for the exchange-correlation function. The electron−ion coupling was dealt with PAW potentials with the 1s 1 and 3d 3 5s 2 configurations for H and V, respectively. The parameters are rough in the stage of structure search. However, the kinetic cutoff energy of 600 eV and Monkhorst−Pack schemes with a grid spacing of 2π × 0.03 Å−1 were chosen to ensure that the formation enthalpy converges to less than 1 meV/atom. Since V has partially filled d electrons, the calculations above were also performed within GGA+U to identify its influence. In the GGA+U method, we adopted the following parameter like Ueff = U − J, where U and J are the Coulomb and exchange parameters, respectively. For the V element, the U value was adopted to be 2.0 eV instead of Ueff. The lattice constants and band structure of the predicted P63/mmc-VH5 at 200 GPa were studied through the normal GGA and GGA+U schemes. As a result, the effects of U on the lattice constants (a = b = 2.450 Å [2.465 Å], and c = 3.147 Å [3.155 Å] in GGA [GGA+U]) and the electronic structure of P63/mmc-VH5 at 200 GPa (Figure S1) were hardly noticeable. Hence, only the electronic structure calculation within the GGA framework was performed. The effects of zero-point energy (ZPE) corrections based on the harmonic approximation are checked. In the case of VH5 with Cmcm structure (relative to the Im3̅m structure of V and the Cmca-12 structure of H at 300 GPa), ZPE is only about 5 meV/atom. Therefore, it is valid to neglect the contribution of ZPE when discussing the relative stability of V−H systems. Phonon dispersion and EPC parameters of these stable stoichiometries of hydrides were calculated by the quantum ESPRESSO package in the scheme of linear response.48 The Tc of V hydrides was calculated via the Allen−Dynes-modified McMillan equation.49
RESULTS AND DISCUSSIONS In the present study, the structure search focused on H-rich V− H compounds, in order to ensure high-Tc superconductivity. The variable-composition structure energy stabilities of V3H2, V2Hn (n = 1, 3, and 5), and VHn (n = 1−8) were predicted with the maximum formula units of 6 at 0, 100, and 200 GPa. The phase diagram of V hydrides (Figure 1) at various pressures was constructed via calculations of formation enthalpy relative to the products of the dissociation into the constituent elements, ΔHf = Η(VmHn) − mH(V ) − nH(H ), in which the enthal28 pies of the Im3m ̅ phase for V and the P63/m, C2/c, and Cmca phases for solid H under pressure50 were selected as the reference for thermodynamics. In general, on the convex hull, the phases are stable, do not decompose into other compounds, and were thereby expected to be experimentally synthesizable, while structures above the convex hull were unstable. From Figure 1a, the experimental confirmed stoichiometries of V2H and VH2 were energetically stable at ambient pressures, and were in agreement with the experiment.33 Up to 100 GPa, the new stoichiometries of VH, V2H5, and VH5 became stable due to emerging on the convex hull. Up to 200 GPa, V2H became unstable along with another two stable stoichiometries of VH3 and VH8; except for the above-mentioned stable stoichiometries of VH, VH2, and VH5, these are all clearly located on the hull. The stable pressure ranges of the corresponding phases of stable V−H compounds were shown in Figure 1d. The H-richest stoichiometry of VH8 was predicted to be stable at 200 GPa (Figure 1c), with a monoclinic structure (space group C2/m) (Figure 2a). From Figure 1c, it also showed that the C2/m phase of VH8 might be synthesized from compression on VH5 and H2. The reaction 2VH5 + 3H2→ 2VH8 can occur above 148 GPa (Figure S2). Structurally, the layered VH8 with a monoclinic crystal structure composed of Vcentered 16-fold VH16 polyhedrons and a H2 unit. In detail, along the b-axis, infinite H8 zigzag chains (...−H−H−H2−H2− H−H−...) with the covalent bonding of H−H were formed, and the character of the chemical bonding of the infinite H8 zigzag chains was identified by the electronic local function (ELF) (Figure 3f). In addition, the formed quasimolecular H2
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DOI: 10.1021/acs.inorgchem.7b01686 Inorg. Chem. XXXX, XXX, XXX−XXX
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Figure 2. Crystal structures of stable V hydrides under high pressures. (a) VH8 in C2/m phase; (b, c) P6/mmm and Cmcm phase of VH5, respectively; (d) VH3 in Fm3̅m phase; (e) V2H5 in Ibam phase; (f, g) Fm3̅m and Pnma phase of VH2, respectively; (h) VH in R3̅m phase; (i, j) I41/ amd and C2/m phase of V2H in the structures, respectively. The large and small spheres are V and H atoms, respectively.
Figure 3. (a−f) ELFs of R3̅m-VH, Pnma-VH2, Ibam-V2H5, Fm3̅mVH3, P63/mmm-VH5, C2/m-VH8 at 200 GPa. (g) The Bader charge of V and H in various VHn compounds at 200 GPa. Figure 4. Phonon spectrum and phonon density of states (PDOS) for (a, b) VH5 and (c) VH8.
unit had the shortest H−H covalent bond length (approximately 0.911 Å) with the isosurface value of approximately 0.92 for quasimolecular H2 units at 200 GPa. The formation of the H−H bond was attributed to the accepted charge of approximately 0.4e per H2 donated by the V atom. The ELF plots reveal the ionic nature of H−V bonding due to the nonlocalization between the H atom and the V atom.
The energetically favored structure of VH5 (stability above 82 GPa, Figure S3) is a layered-arranged P63/mmm phase (Figure 2b) that consists of the hexagonally packed V-centered VH12-polydron layer and H layer. The layers of H and VH12polyhedron can be connected by means of V−H−V (V−H length is 1.61 Å at 200 GPa) with H located between the C
DOI: 10.1021/acs.inorgchem.7b01686 Inorg. Chem. XXXX, XXX, XXX−XXX
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Figure 5. Electronic band structure and DOS for (a, b) VH5 and (c) VH8.
number of H increases from 12 to 15 accompanying the formation of an H-sharing VH15 octadecahedron (Figure 2c). VH3 can be stable in the Fm3̅m structure (Figure 2d) above 127 GP (Figure S4), where V and H atoms located in a bodycentered and face-centered cubic sublattice, respectively. In two cubic sublattices, each V atom is 8-fold coordinated by H, and one H atom is surrounded by four V atoms. These structural units form a symmetric cage connected by the V−H bond and face-centered H atom located at the center point of the cage. The stable phase of V2H5 (stable above 53 GPa, Figure S5) adopted the Ibam structure Figure 2e) with a three-dimensional network frame, in which V atoms form a network with a coordination number of 10, while each H atom is surrounded by three V atoms. For VH2, at low pressure, the cubic CaF2 structure (space group, Fm3̅m, Figure 2f) was reproduced. When pressure increased up to 49 GPa (Figure S6), the CaF2 phase transformed into an orthorhombic Pnma phase (Figure 2g), which is consistent with results in ref 29. VH can possibly be synthesized through the reaction of VH2 + V2H → 3VH above 80 GPa (Figure S7), which adopts a unique hexagonal R3̅m structure (Figure 2h) in our considered pressure region. For the R3̅m phase, V and H atoms occupied the vertex of the distorted cubic sublattice, nested within each other, forming an interpenetrating polymeric network. The bond lengths of V− H are all 1.713 Å for the R3̅m phase at 100 GPa. The H-poor V2H stoichiometry reproduced a tetragonal structure with I41/amd symmetry at ambient conditions (Figure 2i), which is in good agreement with the experiment.27 When compressing to 19 GPa, an energy-favored stable C2/m phase is uncovered (Figure S8). In this monoclinic phase, a ladder-type and layered structural characterization is observed with each H atom surrounded by the six V atoms, and each infinite ladder plane along the b-axis is composed of two V atoms and two H atoms. Moreover, the bond length of V−H decreases from 2.705 Å (I41/amd phase) at ambient condition to 1.657 Å (C2/m phase) at 100 GPa. Above 103 GPa (Figure S8), V2H becomes unstable and decomposes to VH and V as
Figure 6. Eliashberg EPC phonon function α2F(ω), and EPC constant λ(ω) for (a) P63/mmm-VH5 at 200 GPa, (b) Cmcm-VH5 at 300 GPa, and (c) C2/m-VH8 at 200 GPa.
nearest two V atoms. The isosurface value of ELF (Figure 3e) located between the two closest H atoms was quite small (approximately 0.3), verifying the isolated H atoms. The phase transition of P6/mmm → Cmcm in VH5 was found at 273 GPa (Figure S3) with a volume collapse, and the coordination D
DOI: 10.1021/acs.inorgchem.7b01686 Inorg. Chem. XXXX, XXX, XXX−XXX
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Table 1. Calculated EPC Parameters λ, Electronic DOS at the Fermi Level N(Ef) (States/Spin/Ry/Unit Cell), ωlog, and Tc for VHn (n = 1−3, 5, 8) at Different Pressures phase
P (GPa)
ωlog (K)
N (Ef)
λ
Tc (μ* = 0.1)
Tc (μ* = 0.13)
R3m ̅ -VH Pnma-VH2 Fm3̅m-VH3 P63/mmm-VH5 Cmcm-VH5 C2/m-VH8
200 200 200 200 300 300
567 493 466 1210 936 876
3.655 5.723 5.577 6.392 5.337 7.144
0.396 0.503 0.475 0.530 0.663 1.135
2.24 6.12 4.59 18.5 25.1 71.4
0.96 3.71 2.62 11.8 18.3 62.8
the reaction of V2H → VH + V. The detailed structural information on the predicted V−H stoichiometries is presented in Table S1. The thermodynamic stabilities of VHn (n = 1, 3, 5, and 8) and V2Hn (n = 1 and 5) were investigated at different pressures, as shown in Figure S9 and Figure 4. These results revealed the absence of imaginary frequency throughout the Brillouin zone, identifying the dynamical stability of the above phases. Moreover, two distinct frequency branches could be observed in Figure 4. The contribution of the low-frequency region less than 20 THz mostly comes from the vibrations of the V atoms, and the high end of the frequency corresponded to H atoms owing to the higher atomic mass of V. The electronic band structures and projected density of states (PDOS) of these stable V−H compounds were calculated so as to to understand their nature of the chemical bonding and the formation mechanism. The results were exhibited in Figure 5 and Figure S10. These results revealed their metallic characterization under favorable pressures. Both VH5 and VH8 (Figure 5) revealed a strong density of states (DOS) peak originating mainly from the V-d and H-s orbitals. Furthermore, there was a strong hybridization of the V-d orbitals and H-s orbitals around the Fermi level, indicating the strong interaction between V and H atoms. To characterize the bonding nature between these atoms, ELFs of the concerned phases of V hydrides were investigated at 200 GPa, as shown in Figure 3a−f. Merely monatomic HH appeared in VH and VH2 with different stacking (Figure 3a,b). In detail, each H atom was located between two V atoms, forming an ionic bond for R3m ̅ VH. For Pnma-VH2, each V atom was surrounded by three H atoms, which formed zigzag chains. Interestingly, monatomic H and hexagonal “H6” appeared in V2H5, and hexagonal H6 consisted of two nonequilibrium H atoms (Figure 3c). Different from V2H5, the H atoms of hexagonal H6 in VH3 were completely equivalent (Figure 3d). For P63/mmm-VH5, in addition to hexagonal H6, square H4 units also appeared (Figure 3e). In the H-richest stoichiometry VH8 with C2/m symmetry, the unusual structural feature of the H2 molecule, a “H8−V−H8” one-dimensional infinite chain (Figure 3f) and VH16 polyhedrons were found. Bader charge analysis revealed analysis that each HH atom has obtained 0.22 e, which is not enough to dissociate the H2 molecule. Charge localization between monatomic HH and molecular H2 indicates their strong covalent bonding, leading to the formation of a onedimension infinite extended H−V chain. In order to describe the charge transfer of V → H, the Bader charge of VHn (n = 1− 3, 5, and 8) at 200 GPa was calculated (Figure 3g). The Bader charge on V was nearly identical when n > 1, while the acquired H decreases almost linearly with H content, which indicated that the negative oxidation state of V remained constant with the H content. In fact, small charge transfer of V → H is the main reason to form the H2 molecule and the high coordination
number of V. The strong interaction between cation and anion enhances the Madelung energy of the ionic component of the V−H bonding and the stability of V hydrides. H-rich V hydrides may be high-temperature superconductors due to their metallic character. Therefore, their potential for phonon-mediated superconductivity can be estimated within the scheme of the BCS theory. The Tc of the predicted V hydrides was evaluated via Allen−Dynes-modified McMillan equation.51 Figure 6 shows the Eliashberg EPC phonon function α2F(ω), and EPC constant λ(ω) for P63/mmm-VH5 at 200 GPa, Cmcm-VH5 at 300 GPa, and C2/m-VH8 at 200 GPa. The EPC parameter of VH8 arrived high to 1.13. For the Coulomb pseudopotential parameter, it is obvious that it cannote be accurately calculated from first principles. Our calculated Tc has an uncertainty that originates from the empirical value of μ*. In general, μ often varied within the range 0.1−0.2. For comparison, we applied μ* = 0.1 and 0.13 to predict the superconducting temperature of V−H compounds. When observed, as μ* changed from 0.1 to 0.13, the Tc values of Cmcm-VH5 and C2/m-VH8 changed from 25.1 and 71.4 K to 18.3 and 62.8 K, respectively. The calculated ωlog, N(Ef), λ, and Tc at pressure are summarized in Table 1. As presented in Table 1, this obviously indicates that Tc increases with the content of H in the V−H system, and logarithmic average frequencies ωlog, DOS at the Fermi level, and EPC parameters play a key role in superconducting temperature. The high superconducting temperature possibly resulted from the strong EPC (high EPC parameter λ) from the light mass of H, and enhanced from modes containing H/V and H/H vibrations. These results would provide useful theoretical guidance for investigations on the superconducting mechanism of transition metal hydrides.
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CONCLUSIONS The methods of unbiased structure searching and density functional total energy calculations were performed to explore phase stabilities and the superconductivity of V hydrides at high pressures with an effort to obtain various compounds with possible exotic physical properties. We identified the formation of six stoichiometric V hydrides (V2H, VH, VH2, VH3, VH5, and VH8) with unforeseen structural features. Moreover, the coordination number of the V atom increases with the H content under high pressures. The experimentally synthesized V2H became unstable and decomposed into VH and V above 103 GPa. The electronic band structures of all the stable V−H compounds indicated their metallicity, and the Bader charge analysis suggests a nearly identical transfer of charge from the V atom to the H atom with the H content. The strong interaction between cation and anion enhances the Madelung energy of the ionic component of the V−H bonding and the stability of V hydrides. Furthermore, from electron phonon calculations, as derived by the direct solution of Allen−Dynes-modified E
DOI: 10.1021/acs.inorgchem.7b01686 Inorg. Chem. XXXX, XXX, XXX−XXX
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McMillan equation, one can see that P63/mmm-VH5 and C2/ m-VH8 are superconductors with the predicted Tc of 18.5 and 71.4 K at 200 GPa, respectively. Our simulations enriched the crystal structures of the V−H system and uncovered the superconductivity character with the high Tc of V hydrides.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b01686. Table S1 and Figures S1−S10 (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Xiaofeng Li: 0000-0003-4370-430X Feng Peng: 0000-0001-6501-5148 Author Contributions
X.L. and F.P. contributed equally to this work. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was financially supported by the National Natural Science Foundation of China Grants 11774140 and 1150400, and the Henan Key Teacher Project 2014GGJS-114. This research is also supported by China Postdoctoral Science Foundation under 2016M590033, Program for Science and Technology Innovation Talents in University of Henan Province Grant 17HASTIT015, the Natural Science Foundation of Henan Province Grant 162300410199, and Open Project of the State Key Laboratory of Superhard Materials, Jilin University, under 201602, and the Scientific and Technological Research Project of the ‘“13th Five-Year Plan”’ of Jilin Provincial Education Department under Grant 201648.
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DOI: 10.1021/acs.inorgchem.7b01686 Inorg. Chem. XXXX, XXX, XXX−XXX
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DOI: 10.1021/acs.inorgchem.7b01686 Inorg. Chem. XXXX, XXX, XXX−XXX
