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Chemical Trend of Pressure-Induced Metallization in Alkaline Earth Hydrides Chao Zhang,† Xiao-Jia Chen,‡,§ Rui-Qin Zhang,*,† and Hai-Qing Lin| Department of Physics and Materials Science, City UniVersity of Hong Kong, Hong Kong SAR, People’s Republic of China; Geophysical Laboratory, Carnegie Institution of Washington, Washington, D.C. 20015, United States of America; Department of Physics, South China UniVersity of Technology, Guangzhou 510640, People’s Republic of China; and Department of Physics and Institute of Theoretical Physics, Chinese UniVersity of Hong Kong, Hong Kong SAR, People’s Republic of China ReceiVed: May 1, 2010; ReVised Manuscript ReceiVed: July 19, 2010
The pressure-induced metallization of alkaline earth hydrides was systematically investigated using ab initio methods. While BeH2 and MgH2 present different semimetallic phases, CaH2, SrH2, and BaH2 share the same metallic phase (P6/mmm). The metallization pressure shows an attractive decrease with each increment of metal radius, and this trend is well correlated with both the electronegativity of alkaline earth metals and the band gap of alkaline earth hydrides at ambient pressure. Our results are consistent with current experimental data, and the obtained trend has significant implications for designing and engineering metallic hydrides for energy applications. 1. Introduction Metallic hydrogen is expected to show very unusual and amazing physical properties, such as high-temperature superconductivity1 and having the properties of a quantum liquid.2 In particular, achieving a superconducting state in hydrogen or related materials would be a breakthrough in the understanding of high temperature superconductivity and would probably open a path to room temperature superconductivity. Moreover metallic hydrogen could accumulate an enormous amount of energy, and thus it is considered to be one of leading candidates for clean energy in the future.3 Apart from the fields of modern chemistry and physics, metallic hydrogen is one of the basic objects in astrophysics, since it might be a main constituent in the giant planets and stars. However, hydrogen remains an insulator at extremely high pressures, at least up to 320 GPa.4 To circumvent this problem, it was proposed to achieve metallic hydrides by compression at lower pressures, which could present hightemperature superconductivity.5 This suggestion has motivated considerable theoretical and experimental studies on hydrides, especially group IVa hydrides.6-16 Experimentally, solid SiH4 exhibits both metallic and superconductive properties at 60 GPa.6,7 These discoveries are encouraging for exploring a wider range of hydrides. As a main class of binary hydrides, the alkaline earth hydrides are of great scientific and technological interest. They share clear common features: a large fraction (2/3) of H atoms and an average of four valence electrons per formula. The atomic radii of alkaline metals show a monotonic increment from 1.05 Å (Be) to 2.15 Å (Ba),17 while the Pauling electronegativities show a monotonic decrement from 1.57 (Be) to 0.89 (Ba).18 Since the Pauling electronegativity of H is 2.2, the electronic charge transfers from the alkaline metal atoms to hydrogen atoms under * To whom correspondence should be addressed. E-mail: aprqz@ cityu.edu.hk. † Department of Physics and Materials Science, City University of Hong Kong. ‡ Geophysical Laboratory, Carnegie Institution of Washington. § Department of Physics, South China University of Technology. | Department of Physics and Institute of Theoretical Physics, Chinese University of Hong Kong.
ambient conditions. Under the application of pressure, the charge may transfer from the hydrogen atoms to the metal atoms. A metallic phase is expected once sufficient charge can be transferred onto the alkaline earth metals. The pressure-induced charge transfer would help to promote the emergence of a metallic state. The pressure-induced metallization and related properties are interesting.19,20 Despite many high pressure studies on individual alkaline earth hydride,21-33 the rule and trend for pressure-induced metallization of these hydrides remains unclear. In this work, we report systematic studies on phase transitions and metallization of alkaline earth hydrides under pressure within density functional theory. We found that the metallization pressure decreases with increasing the radius of the alkaline earth metal in this main group hydride. This trend is well correlated with both the band gap of alkaline earth hydrides at ambient pressure and the electronegativity of alkaline earth metal. 2. Computational Details The enthalpies of alkaline earth hydrides at pressures were calculated using the Vienna Ab-Initio Simulation Package (VASP),34 within the density functional theory formalism with plane-wave pseudopotential. The Projector Augmented-Wave (PAW)35 and the Perdew-Burke-Ernzerhof (PBE)36 exchangecorrelation functional were used. The plane-wave energy cutoff was set to be 400 eV and the convergence of the force on each atoms to be less than 5 × 10-3 eV/Å. Monkhorst-Pack37 k-point grids, 24 × 24 × 24, 16 × 16 × 16, and 8 × 8 × 8, were used for Brillouin zone sampling of one, two, and four formula units, respectively. To simulate the hydrostatic conditions in the diamond anvil cell, the pressure was applied on the material from three directions. Under hydrostatic conditions, the stress tensor components are equal and correspond to the external pressure.38 3. Results and Discussion BaH2, the heaviest hydride among alkaline earth hydrides, possesses typical phases and a simple evolution path under pressure, especially its lowest metallization pressure. Figure 1 shows the band structures and projected density of states (PDOS)
10.1021/jp103968c 2010 American Chemical Society Published on Web 08/05/2010
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Figure 1. Electronic band structures (left panel) and projected densities of states (PDOSs) (right panel) of BaH2 for (a) Pnma phase, (b) P63/mmc phase, and (c) P6/mmm phase at favorable pressures. Inset: the crystal structures of three phases. The green and purple spheres represent Ba and H atoms, respectively. For Pnma phase, Ba atom and two inequivalent H atoms occupy Wyckoff 4c positions. For P63/mmc phase, Ba and two H atoms locate at Wyckoff 2c, 2d, and 2a positions. For P6/mmm phase, Ba and H atoms are at 1a and 2d positions.
of three phases of BaH2, inserted with crystal structures. At ambient condition, the BaH2 stabilizes in orthorhombic cotunnite-type structure with Pnma symmetry, with a primitive cell containing four formula units (Z ) 4). The Pnma phase of BaH2 is insulating with an indirect band gap of 2.88 eV, which is in agreement with other theoretical calculations.39 In the pressure range studied, BeH2 and MgH2 adopt this phase as their high pressure structure, while CaH2 and SrH2 take this phase as their ambient pressure structure, up to 15 and 8.5 GPa, respectively. It is interesting that the Pnma phases of alkaline earth hydrides show nonmetallic character, with the exception of BeH2. The Pnma BaH2 was predicted to transform into a hexagonal structure with P63/mmc symmetry at 3.5 GPa. The calculated lattice parameters at 4.8 GPa are a ) 4.330 Å and c ) 5.670 Å with c/a ratio of 1.31, which is in agreement with experiments.30 The atomic arrangement in this P63/mmc structure is the same as that of Ni2In-type structures of several AX2 compounds, such as BaF2.40 The P63/mmc phase of BaH2 has an indirect band gap of 1.22 eV at 40 GPa [Figure 1(b)]. Similar to BaH2, CaH2 and SrH2 adopt this phase as the second phase with nonmetallic character. However, this phase in MgH2 is valid after 165 GPa, showing metallic character. Applying further pressure on BaH2, a phase of space group P6/mmm becomes favorable at 42 GPa, which is in agreement with recent measurements.33 The band structure [Figure 1(c)] reveals its good metallic feature. In other words, the second structural transition is accompanied by electronic phase transition. This metallic phase can be taken as energetically stable structures of CaH2 and SrH2 above 102 and 177 GPa, respectively. The electronic projected density of states (PDOS) of Pnma phase, P63/mmc phase, and P6/mmm phase of BaH2 at favorable pressures are plotted in Figure 1. For these three phases, the valence band of Pnma phase is mainly constituted by H s, Ba p, and Ba d electrons, while the conduction band is dominated by Ba d electrons. Under the application of pressure, the PDOS of Ba d electrons move downward, especially the conduction part. If this effect is sufficient, then a metallic state (P6/mmm phase) emerges. Comparing the P63/mmc phase to the P6/mmm phase, we found that the states of H s electrons of P6/mmm decrease sharply, especially near the Fermi level. Correspondingly, the states of Ba d electrons of conducting band increase, suggesting the charge transfers from H s to Ba d electrons. This charge transfer from H to Ba, particularly the electronic s-d transition, drives the phase transition. As noted, CaH2, SrH2,
Figure 2. Electronic band structures (left panel) and PDOSs (right panel) for metallic states for (a) Pnma BeH2 at 400 GPa, (b) P63/mmc MgH2 at 170 GPa, (c) P6/mmm CaH2 at 180 GPa, and (d) P6/mmm SrH2 at 110 GPa.
and BaH2 have the same structural sequences, and these heavier alkaline earth hydrides are dominated by d electrons. Thus, the charge transfer from hydrogen to metal atom, in particular s-d transition, can be applied to the CaH2 and SrH2, and drives the nonmetal to metal transition. Figure 2 shows electronic band structures and PDOSs of the metallic phases for other alkaline earth hydrides. Clearly, the metallization of BeH2 and MgH2 takes place via the closure of the indirect band gap, shown in Figure 2, parts (a) and (b). The electronic band structure of BeH2 calculated at 400 GPa [Figure 2(a)] shows that the valence band cross the Fermi level along the Γ f Z f T directions, while the conduction bands cross the Fermi level along the S f X f U directions. These crossing Fermi level bands are relatively flat, showing the well-localized properties. The PBE-GGA calculations give this indirect band gap overlap of about 1.6 eV. Compared to BeH2, the band structure of MgH2 [Figure 2(b)] shows more bands crossing the
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Figure 3. The Fermi surfaces of metallic states for (a) BeH2, (b) MgH2, (c) CaH2, and (d) SrH2. The center point (Γ) of Brillouin zone is not shown.
Figure 4. The metallization pressure (PM), band gap (∆E), and Electronegativity (EN) of alkaline earth hydrides vs the radius of the alkaline earth metal. The triangle is taken from the data in ref 31.
Fermi level with steep dispersion. The valence bands cross Fermi level at Γ and A symmetry points, and conduction bands cross Fermi level at H point. The crossing develops a lot of electron-hole pockets along the Fermi level, which facilitate the conduction. The PDOS of the metallic phase for BeH2 [right panel of Figure 2(a)] shows a strong hybridization between H s and Be p states below Fermi level, both of which mainly contribute to the valence band. The conduction band mainly originates from the Be p states. Slightly different from BeH2, the valence band of MgH2 mainly originates from H s states, and Mg s and p states contribute to the conduction band. Carefully examining the PDOS of BeH2 and MgH2, the density of states at Fermi level is small, thus these two phases should be best described as semimetal. CaH2 and SrH2 have the same metallic phase as BaH2, P6/ mmm phase. Their electronic properties are thus very similar [Figure 1(c), Figure 2(c), and Figure 2(d)]. The band structures reveal metallic character with large dispersion bands crossing the Fermi level. There are two bands crossing the Fermi level around Γ, A, and H symmetry points for CaH2 and SrH2, while BaH2 leaves the A point. This leads to a slight difference in the configuration of the Fermi surface, as we will discuss in detail below. The PDOSs show significant hybridization between alkaline earth metal atoms and H atoms below the Fermi level. The d states of alkaline metal atoms dominate the range above the Fermi level. The density of states at the Fermi level has a significant value, indicating good metallic character. The mechanism of nonmetal to metal transition is driven by the charge transfer from the H s states to the metal d states. Fermi surface (FS) topology plays an important role in understanding the metallic characteristics. Figure 3 shows the three-dimensional FSs of metallic states of alkaline earth hydrides. The FSs were calculated by Quantum-ESPRESSO package41 using VASP-optimized structures employing the same PBE functionals on much denser k-meshes. There are four electronic bands crossing the FS for BeH2 Pnma phase, and identified by different colors. However, only two ship-typed structures locate around X and Z points, which mirror the high degeneration of bands. Constituted by flat bands, the ship-typed structure is very thin, showing the localized properties. The lowest energy band (green color) and the second lowest energy band (red color) degenerate around Z point and come from valence band having hole-type character. The other ship-typed structure, centered at the X point, contains the third (blue color) and fourth (dark yellow) band. The MgH2 P63/mmc phase also
has four bands crossing the complex FS. The lowest energy band (green color) locates at A symmetry point. The second lowest energy band displays tubular shape along the Γ f A direction. These two bands originate from the valence band and have a hole-type character. The other two bands located at the H symmetry point with a similar shape have an electron-type character. Due to the similar electronic band structures, the metallic phases of CaH2 and SrH2 have very similar FSs. Although there are only two bands crossing the Fermi level, the FSs of the P6/mmm phase are particularly rich showing a good metallic character. To better view the shape of the FS, two colors are used for one band such that one side is colored by purple and other side is colored by green for the first band. Interestingly, each band consists of two parts. The first band has a hexagonal cup portion along the Γ f A direction and a hemisphere portion near A point. The second band has circle shape around Γ point, and other portion locates at L point. The BaH2 has a very similar FS as CaH2 and SrH2 have, and the only difference is the absence of the hemisphere portion near the A point. The rich FSs for CaH2, SrH2, and BaH2 show good metallic properties. Figure 4(a) shows the trend of the metallization pressure as a function of the alkaline metal atom radius in alkaline earth hydrides. Clearly, the metallization pressure of these hydrides decreases with the radius of the alkaline earth metal, with the exception of MgH2 whose calculated metallization pressure is 165 GPa. The metallization pressure of CaH2 differs slightly from the previous calculation31 probably due to the difference in pseudopotentials. For comparison, we presented the radius of the alkaline metal atom dependence of both the band gap of alkaline earth hydrides at ambient pressure and electronegativity of the alkaline earth metals in Figure 4, parts (b) and (c), respectively. The band gap of the alkaline earth hydrides at ambient condition is strongly related to the metallization pressure. Electronegativity, which represents the electronholding energy of an atom, provides the primary information on microscopic electronic structures during chemical bonding. The electronegativity difference between the hydrogen and the metal atoms increases as the metal atomic radius increases, indicating that the bonding is becoming more active. The most active bonding (Ba-H) in these alkaline earth hydrides is quite sensitive to external conditions. When pressure is applied, the Ba-H bonding is more easily changed, resulting in the charge redistribution between the H and Ba atoms. Therefore, BaH2 is most likely to transform into a metallic state. On the contrary,
Induced Metallization in Alkaline Earth Hydrides the little electronegativity difference between Be and H makes BeH2 with a unique covalent bond different from the rest of the alkaline earth hydrides. The special bonding between Be and H leads to a large band gap. Thus BeH2 becomes difficult to compress. Therefore, both the band gap of alkaline earth hydrides and the electronegativity of the alkaline earth metals provide a consistent origin for the obtained metallization trend in these hydrides. 4. Conclusions We have investigated the pressure-induced metallization of alkaline earth hydrides using ab initio methods. The metallization pressure shows a clear decrease with an increasing radius of the alkaline earth metal in these materials. This trend is well correlated with both the band gap of alkaline earth hydrides at ambient pressure and the electronegativity of alkaline earth metal. The obtained metallization trend on alkaline earth hydrides could guide the search, design, and fabrication of artificial metals. Acknowledgment. This work was supported by the HKRGC (Nos. CityU 103408 and CUHK 402108) and NSFC (10874046). The work at Carnegie was supported as part of EFree, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award No. DE-SC0001057. We gratefully acknowledge R. J. Hemley for reading this paper and comments. References and Notes (1) Ashcroft, N. W. Phys. ReV. Lett. 1968, 21, 1748. (2) Babaev, E.; Sudbo, A.; Ashcroft, N. W. Nature 2004, 431, 666. (3) Nellis, W. J. Rep. Prog. Phys. 2006, 69, 1479. (4) Loubeyre, P.; Occelli, F.; LeToullec, R. Nature 2002, 416, 613. (5) Ashcroft, N. W. Phys. ReV. Lett. 2004, 92, 187002. (6) Chen, X. J.; Struzhkin, V. V.; Song, Y.; Goncharov, A. F.; Ahart, M.; Liu, Z. X.; Mao, H. K.; Hemley, R. J. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 20. (7) Eremets, M. I.; Trojan, I. A.; Medvedev, S. A.; Tse, J. S.; Yao, Y. Science 2008, 319, 1506. (8) Feng, J.; Grochala, W.; Jaron´, T.; Hoffmann, R.; Bergara, A.; Ashcroft, N. W. Phys. ReV. Lett. 2006, 96, 017006. (9) Martinez-Canales, M.; Bergara, A.; Feng, J.; Grochala, W. J. Phys. Chem. Solids 2006, 67, 2095. (10) Pickard, C. J.; Needs, R. J. Phys. ReV. Lett. 2006, 97, 045504. (11) Yao, Y.; Tse, J. S.; Ma, Y.; Tanaka, K. Europhys. Lett. 2007, 78, 37003. (12) Tse, J. S.; Yao, Y.; Tanaka, K. Phys. ReV. Lett. 2007, 98, 117004.
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