Article pubs.acs.org/IC
Structure and Electronic Properties of Fe2SH3 Compound under High Pressure Shoutao Zhang,†,‡ Li Zhu,§ Hanyu Liu,∥ and Guochun Yang*,†,‡ †
Centre for Advanced Optoelectronic Functional Materials Research and Key Laboratory for UV Light-Emitting Materials and Technology of Ministry of Education, Northeast Normal University, Changchun 130024, China ‡ State Key Laboratory of Superhard Materials, Jilin University, Changchun 130012, China § Geophysical Lab, Carnegie Institution of Washington, Washington, District of Columbia 20015, United States ∥ Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, Canada S7N 5E2 S Supporting Information *
ABSTRACT: Inspired by the diverse properties of hydrogen sulfide, iron sulfide, and iron hydrides, we combine first-principles calculations with structure prediction to find stable structures of Fe−S−H ternary compounds with various FexSyHz (x = 1−2; y = 1−2; z = 1−6) compositions under high pressure with the aim of finding novel functional materials. It is found that Fe 2SH3 composition stabilizes into an orthorhombic structure with Cmc21 symmetry, whose remarkable feature is that it contains dumbbelltype Fe with an Fe−Fe distance of 2.435 Å at 100 GPa, and S and H atoms directly bond with the Fe atoms exhibiting ionic bonding. The high density of states at the Fermi level, mainly coming from the contribution of Fe-3d, indicates that it satisfies the Stoner ferromagnetic condition. Notably, its ferromagnetic ordering gradually decreases with increasing pressure, and eventually collapses at a pressure of 173 GPa. As a consequence, magnetic and nonmagnetic transition can be achieved by controlling the pressure. In addition, there is a very weak electron−phonon coupling in Cmc21-structured Fe2SH3. The different superconducting mechanisms between Fe2SH3 and H3S were compared and analyzed. These findings open an irresistible impetus to search new hydrogen-containing superconductors. Iron chalcogenides (e.g., FeSe and FeS) have attracted considerable interest, because of their fascinating superconducting properties.19,20 Specifically, the Tc value for FeSe dramatically increases from 8 K to 36.7 K under compression.20 Moreover, the Tc value of the single-layer FeSe film on a SrTiO3 substrate reaches 65 K, which greatly exceeds the bulk Tc of the known iron-based superconductors.21,22 Very recently, superconductivity of tetragonal FeS has been observed.23−25 Because of its unique structure, FeS-derived superconductors with higher Tc are expected by intercalating various spacer layers between FeS layers.23 Under high pressure, the reaction of iron and hydrogen can form several stable compounds, such as FeH, FeH2, FeH3, and FeH4.26−29 These compounds exhibit interesting structures and electronic properties. For example, the ferromagnetic ordering of the dhcp-structured FeH collapses at a pressure of 48 GPa.27 FeH3 with Pm3̅m symmetry is metallic above 40 GPa, which is expected to be a superconductor.29 Based on diverse and interesting properties of sulfur hydrides, FeS, and iron hydrides, a natural and immediate thought is to examine whether stable
1. INTRODUCTION One of the main objectives in condensed-matter physics and chemistry is the preparation of compounds with novel structures and unique properties (i.e., superconductivity and hardness). It is because application of pressure can effectively overcome the reaction energy barrier1 and reorder atomic orbital energy levels2 that high pressure has become an important tool to prepare new materials.3 Until now, many unusual stoichiometric compounds (e.g., NaCl3 at 20 GPa and CsF5 at 50 GPa) with exotic properties have been discovered under high pressure.4−6 Superconducting transition temperature (Tc) of the compressed sulfur hydride (H2S) sample reaches 203 K.7 Notably, this observation was inspired by the theoretical prediction of high-Tc value in the compressed H2S.8 Subsequently, great efforts have been made to explore its superconductive mechanism and possible decomposition of H2S at high pressures.10−16 Until now, several stable H−S compounds (e.g., HS2, H2S3, H4S3, H3S2, H2S, H5S2, and H3S) have been found under high pressure.9,11,12,15 However, Im3̅m-structured H3S is mainly responsible for the observed high-Tc superconductivity.16 In addition, selenium (Se) or tellurium (Te) hydrides have been predicted to be good superconductors, with the estimated Tc reaching remarkably high values (e.g., 110 K for H3Se at 250 GPa,17 and 104 K for H4Te at 170 GPa18). © XXXX American Chemical Society
Received: August 11, 2016
A
DOI: 10.1021/acs.inorgchem.6b01949 Inorg. Chem. XXXX, XXX, XXX−XXX
Article
Inorganic Chemistry
composition of FexSyHz compound is thermodynamically stable, which must satisfy the following three criteria:50,51
compounds in the Fe−S−H ternary system could be formed at high pressures, which are expected to be potential functional materials. In addition, elemental sulfur and hydrogen are also considered as the constituent elements of the Earth’s core. To reveal phase relations and properties of Earth’s core materials, Fe−S and Fe−H binary compounds were broadly investigated under the conditions of the Earth’s core.30 To the best of our knowledge, the Fe−S−H ternary system has not been explored. In this work, we focus on exploring the structures and high pressure phase diagram of Fe−S−H ternary compounds with various FexSyHz (x = 1−2; y = 1−2; z = 1−6) compositions with the assistance of a swarm intelligence-based structural prediction, in combination with first-principles calculations.31,32 The magnetic Fe2SH3 is found to be stable at 100 GPa. In addition, its magnetism is strongly dependent on the external pressure, and eventually collapses at a pressure of 173 GPa. The charge transfer from Fe to S or H plays a certain role in determining structural stability. Our work is important to understand electronic properties and high-pressure phase diagram of Fe−S−H ternary system.
ΔHf (FexSy Hz) = xΔμFe + yΔμS + zΔμH
(1)
(i = Fe, S, H)
(2)
Δμi ≤ 0
mjΔμFe + njΔμS + qjΔμH ≤ ΔHf (FemjSnjHqj)
j = 1 , ..., t (3)
where Δμi is the deviation of actual chemical potential of atomic species during growth (μi) from that of bulk elemental solid (μi0) (defined as Δμi = μi − μi0), ΔHf the formation enthalpy, and FemjSnjHqj represents all of the known j competing phases. Equation 1 represents the equilibrium growth, eq 2 is used to prevent FexSyHz compounds from decomposing into elemental solids, and eq 3 is used to guarantee FexSyHz compounds stable against the formation of competing phases. To determine the stabilities of FexSyHz compounds, we fully considered stable binary compounds at the given pressure as the competing phases (e.g., Fe3P-type structure Fe3S52 (space group I4)̅ , MnP-type phase FeS53 (space group I4̅), orthorhombic structure FeS254(space group Pnnm), FeH329 (space group Pm3̅m), H3S9 (space group Im3̅m), and H4S315 (space group Pnma)). Among the considered FexSyHz compositions, only Fe2SH3 (space group Cmc21, 4 f.u.) is thermodynamically stable. According to the formation enthalpies of the considered compounds, we are able to calculate their chemical potential ranges and determine the stable region of studied ternary compounds. Detailed description of this procedure can be found in the Supporting Information (Figure S1). The two-dimensional phase stability diagram of Fe2SH3 at 100 GPa is shown in Figure 1; the area marked green represents its stable region.
2. COMPUTATIONAL DETAILS To determine the preferred structures of the Fe−S−H ternary system at high pressures, we used the swarm-intelligence-based structure prediction method as implemented in the Crystal structure AnaLYsis by Particle Swarm Optimization (CALYPSO) code,31,32 which can efficiently search the stable structures for the given compositions. CALYPSO determines the stable structure by just depending on the known chemical composition. As a consequence, CALYPSO is unbiased by the already known structures, which has been successfully applied to various known compounds, ranging from elemental solids to binary and ternary compounds.8,33−37 Detail structural predictions can be found in the Supporting Information. The ab initio structural relaxations and electronic properties calculations were performed by using density functional theory (DFT) within the Perdew−Burke−Ernzerhof (PBE) of generalized gradient approximation (GGA),38 as implemented in the Vienna ab initio Simulation Package (VASP) code. 39 The electron−ion interaction was described by using an all-electron projector augmented-wave (PAW) method40 with 3d74s1, 3s23p4, and 1s1 treated as valence for Fe, S, and H atoms. The plane-wave kinetic energy cutoff of 600 eV and appropriate Monkhost−Pack k-meshes with grid spacing of 2π × 0.03 Å−1 were chosen to ensure that the total energy calculations are well-converged. The phonon calculations were performed to determine the dynamical stability of the predicted structures by using the finite displacement approach,41 as implemented in the Phonopy code.42 The electron−phonon coupling for superconducting properties of stable phases are performed within the framework of the linear-response theory via the Quantum-ESPRESSO package.43 To study the interatomic interaction, integrated crystal orbital Hamilton populations (ICOHPs) was calculated as implemented in the LOBSTER package.44 Electron localization function (ELF)45 was used to analyze the chemical bonds as done in VASP.39 Bader’s Quantum Theory of Atom in Molecules (QTAIM) analysis was adopted for the charge transfer calculation.46
Figure 1. Phase stability diagram of the Cmc21-structured Fe2SH3 at 100 GPa. Each line represents a known competing phase. The stable region of Fe2SH3 is indicated in green.
3.2. Geometry Structure. Fe2SH3 stabilizes into an orthorhombic structure (space group Cmc21, 4 formula units per cell, Figure 2a) at 100 GPa. The structure contains two inequivalent Fe atoms occupying 4a (0.5000, 0.8744, 0.0630) and 4a (0.000, 0.8919, 0.6718) positions, one equivalent S sitting at 4a (0.5000, 0.7925, 0.4209) position, and three inequivalent H atoms occupying 4a (0.5000, 0.9681, 0.7965), 4a (0.5000, 0.5109, 0.4496), and 4a (0.0000, 0.9252, 0.2186) sites. For clarity, these inequivalent atoms are labeled with different colors in Figure 2. The former Fe atom, labeled as Fe1, is coordinated by three S and two H atoms, while the later Fe atom, marked as Fe2, is surrounded by three S and four H atoms. The two different Fe polyhedrons through coplanar constitute the basic building block with a Fe−Fe distance of
3. RESULTS AND DISCUSSION 3.1. Phase Stability. Hydrogen-rich compounds are promising candidates for high-Tc superconductivity.47−49 As a consequence, we mainly focus our structure search on FexSyHz (x = 1−2; y = 1−2; z = 1−6) chemical compositions at 0 K and 100 GPa. For each composition, structural search was performed up to 4 formula units (f.u.) per simulation cell. Among the predicted structures, the structure with the lowest enthalpy is used to investigate its relative stability. A B
DOI: 10.1021/acs.inorgchem.6b01949 Inorg. Chem. XXXX, XXX, XXX−XXX
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Inorganic Chemistry
Figure 2. Crystal structure of Fe2SH3 compound at 100 GPa. (a) Fe2SH3 with the Cmc21 symmetry. (b) View of Fe-polyhedron in Fe2SH3. (c) View of Fe−S polyhedron in Fe2SH3. (d) View of Fe−H polyhedron in Fe2SH3. Panels (b)−(d) show the coordination environment of Fe, S, and H atoms, respectively. In the structure, the small red, green, and blue spheres represent H atoms; the mediumsized purple spheres represent S atoms, and large golden or pink spheres represent Fe atoms. Structural information is shown in Table S1 in the Supporting Information.
2.435 Å (Figure 2b), which is comparable to the Fe−Fe distance of 2.482 Å in bulk Fe with Im3̅m symmetry55 and 2.489 Å in Ti9Fe2Ru18B8 under ambient conditions.56 The Cmc21-structured Fe2SH3 can be constructed by extending the basic building block through interconnecting S and H3 atoms in the bc plane, and stacking edge-sharing basic building block along the a-axis. Each S atom forms a 6-fold coordination with Fe atoms (Figure 2c). The three different hydrogen atoms directly bond the Fe atoms (Figure 2d). Specifically, each H1 atom is coordinated with two Fe2 atoms, each H2 atom has one neighboring Fe2 atom, and each H3 atom is surrounded by two Fe1 atoms and one Fe2 atom. 3.3. Lattice Dynamic Stability. To identify the lattice dynamics of the Cmc21-structured Fe2SH3, we calculated a phonon dispersion curve (see Figure 3a). The absence of
Figure 4. Electronic and electron−phonon coupling (EPC) properties of Fe2SH3 with Cmc21 symmetry: (a) electronic band structure and (b) projected density of states (PDOS) of Fe2SH3 at 100 GPa, where the color in panel (a) represents the Fe-3d electron contributions (the horizontal and vertical solid lines indicate the Fermi energy level); (c) Fermi surface in Brillouin zone of Fe2SH3; (d) magnetic moment of Fe2SH3, as a function of pressure; (e) Eliashberg EPC spectral function α2F(ω), EPC integration λ(ω), and phonon density of states (PHDOS) of Fe2SH3 at 173 GPa; and (f) and (g) contour plots of electron localization function (ELF) within the (1 0 0) and ( 0 1.76 −1) plane at 100 GPa.
(PDOS). There are several bands crossing the Fermi level (Figure 4a), indicating that it is metallic. The valence band below −4 eV is composed mainly of S 3p orbitals hybridized with Fe 3d states (Figure 4b), and there is a dominant Fe 3d character (see Table S2 in the Supporting Information) at the Fermi energy (EF). The calculated DOS per Fe atom at the Fermi level is 1.42 eV−1, satisfying the Stoner criterion (DOS(EF) · I = 1.42 with I ≈ 1.0 for Fe57). This is also in agreement with the calculated magnetic moment of 1.85 μB per cell. Thus, Cmc21-structured Fe2SH3 is the ferromagnetic ground state at 100 GPa. Its Fermi surface (Figure 4c and Figure S2 in the Supporting Information) is composed of relatively small pockets around points T, Y, S, and R, indicating that there is no obvious Fermi surface nesting. Generally, pressure has a great effect on the magnetic properties.58 Subsequently, the magnetic moment, as a function of pressure, was calculated and shown in Figure 4d. It is found that the magnetic moment is gradually decreasing as the pressure increases, and collapses at a pressure of 173 GPa, similar to the hcp-structured FeH compound.27 In addition, the DOS value at EF at 173 GPa becomes smaller in comparison with its magnetic state at 100 GPa (Figure S3 in the Supporting Information). We again conducted structural prediction at this pressure, and found that the structure of Fe2SH3 still retains Cmc21 symmetry. Based on the above discussion, the large DOS at EF and high vibrational frequency suggest that Cmc21-structured Fe2SH3 may be a superconductor. Based on BCS theory,59 the
Figure 3. Phonon dispersion curves and phonon density of states (PHDOS) projected on Fe, S, and H atoms of Cmc21-structured Fe2SH3 at 100 GPa. For the sake of clarity, the PHDOS of Fe, S, and H atoms are shown as blue, green, and red lines, respectively.
imaginary modes in the entire Brillouin zone confirms its dynamical stability. As illustrated in Figure 3b, the motion of the H atoms mainly dominates the vibrational states in the high-frequency regimes (18−55 THz), while the coupling Fe− S pairs in the lattices contribute to the low-frequency regimes (0−18 THz). Generally, the high-frequency vibration of H atoms plays a significant role in superconductivity.47 It is found that both the highest vibrational frequency region of H atoms in the Cmc21-structured Fe2SH3 are comparable to those observed in the Im3̅m-structured H3S.9 3.4. Electronic Properties. Figure 4 shows the electronic band structure and corresponding partial density of states C
DOI: 10.1021/acs.inorgchem.6b01949 Inorg. Chem. XXXX, XXX, XXX−XXX
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Inorganic Chemistry
further experimental investigations of the Fe−S−H ternary system.
electron−phonon coupling (EPC) calculations were performed. The integrated EPC parameter λ(ω), Eliashberg spectral function α2F(ω), and phonon density of states (PHDOS) at 173 GPa are shown in Figure 4e. The calculated EPC constant (λ) is just 0.30 and far below 2.19 of H3S.9 The main contributor to the λ originates from low-frequency vibrations (86.1% of λ) of the heavy Fe and S atoms, which is in sharp contrast with dominant high-frequency vibrations contribution (82.6% of λ) of H3S. Its Tc was estimated by using the Allen− Dynes-modified McMillan equation.60 With a Coulomb potential (μ*) of 0.1, the estimated Tc value is only 0.3 K, which is lower than 5 K in FeS23 and 191 K in H3S9. Here, we are mainly concerned with the difference of superconductor mechanism between Fe2SH3 and H3S. In H3S, H and S atoms form a strong covalent bond, whereas Fe−S and Fe−H bonds in Fe2SH3 are apparently ionic, and the Fe−Fe bond is metallic, as will be discussed later. On the other hand, in H3S, the EPC comes from the s and p electrons, while the Fe-d electron dominated the Fermi level in Fe2SH3. These results suggest the superconductivity nature of Fe2SH3 is dramatically different from that of H3S. To detect the interatomic interaction in the Fe2 SH3 compound, we calculated the integrated crystal orbital Hamilton populations (ICOHPs) for Fe−Fe, Fe−S, and Fe− H pairs at 100 GPa. The ICOHP has a tendency to scale with bond strength (metallic or covalent) in compounds by counting the energy-weighted population of wave functions between two atomic orbitals for a pair of selected atoms. In the Cmc21structure Fe2SH3, the values of ICOHP between Fe−Fe, Fe−S, and Fe−H pairs are −4.896, −1.994, and −1.074 per pair, illustrating that the Fe−Fe interaction is much larger than that of Fe−S and Fe−H. The major contribution of Fe−Fe interaction originates from 4s−3d, which corresponds to the decomposed ICOHP of −2.844 eV per pair. More information on the Fe−S and Fe−H interaction can be found in the Supporting Information (Table S3). Subsequently, we calculated the electron localization function (ELF) to analyze the bonding features of the Cmc21-structured Fe2SH3. Generally, the large ELF values (>0.5) correspond to the lone electron pairs, core electrons, or covalent bonds, whereas the ionic bonds are represented by smaller ELF values (
