Scholarly article on topic 'Exploration of stable compounds, crystal structures, and superconductivity in the Be-H system'

Exploration of stable compounds, crystal structures, and superconductivity in the Be-H system Academic research paper on "Materials engineering"

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Academic research paper on topic "Exploration of stable compounds, crystal structures, and superconductivity in the Be-H system"

Exploration of stable compounds, crystal structures, and superconductivity in the Be-H system

Shuyin Yu, Qingfeng Zeng, Artem R. Oganov, Chaohao Hu, Gilles Frapper, and Litong Zhang

Citation: AIP Advances 4, 107118 (2014); doi: 10.1063/1.4898145 View online:

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Exploration of stable compounds, crystal structures, and superconductivity in the Be-H system

Shuyin Yu,1,a Qingfeng Zeng,1 Artem R. Oganov,2,3,4 Chaohao Hu,5 Gilles Frapper,6 and Litong Zhang1

1Science and Technology on Thermostructural Composite Materials Laboratory, School of Materials Science and Engineering, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, PR China

2Department of Geosciences, Center for Materials by Design, and Institute for Advanced Computational Science, State University of New York, Stony Brook, NY 11794-2100, USA 3Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region 141700, Russia 4School of Materials Science and Engineering, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, PR China

5School of Materials Science and Engineering, Guilin University of Electronic Technology, Guilin 541004, People's Republic of China

6IC2MP UMR 7285, Université de Poitiers - CNRS, Poitiers 86022, France (Received 9 July 2014; accepted 30 September 2014; published online 10 October 2014)

Using first-principles variable-composition evolutionary methodology, we explored the high-pressure structures of beryllium hydrides between 0 and 400 GPa. We found that BeH2 remains the only stable compound in this pressure range. The pressure-induced transformations are predicted as I bam ^ P3 m1 ^ R3 m ^ Cmcm ^ P4/nmm, which occur at 24, 139, 204 and 349 GPa, respectively. P3m1 and R3m structures are layered polytypes based on close packings of H atoms with Be atoms filling all octahedral voids in alternating layers. Cmcm and P4/nmm contain two-dimensional triangular networks with each layer forming a kinked slab in the ab-plane. P3m1 and R3m are semiconductors while Cmcm and P4/nmm are metallic. We have explored superconductivity of both metal phases, and found large electron-phonon coupling parameters of A=0.63 for Cmcm with a Tc of 32.1-44.1 K at 250 GPa and A =0.65 for P4/nmm with a Tc of 46.1-62.4 K at 400 GPa. The dependence of Tc on pressure indicates that Tc initially increases to a maximum of 45.1 K for Cmcm at 275 GPa and 97.0 K for P4/nmm at 365 GPa, and then decreases with increasing pressure for both phases. © 2014 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License. []


The search for new high-temperature superconductors has attracted great enthusiasm in both fundamental and applied research. Owing to its low mass and high electron density, "metallic hydrogen" has been predicted to possess a high superconducting transition temperature (Tc > 200 K).1-3 However, hydrogen remains insulating at extremely high pressure (>320 GPa4), which are too high for any applications. Another feasible method of obtaining the properties of metallic hydrogen is to form hydrogen-rich alloys with other elements.5 Due to "chemical precompression," the pressure of metallization may be reduced significantly.

Inspired by the elusive state of matter, theoretical and experimental research has made considerable progress towards exploring superconductivity in hydrogen-rich compounds, e.g. for group IVa hydrides, calculations predicted that SiH4,6-9 SiH4(H2)2,10 GeH4,11-13 SnH41415 and PbH416 may become superconductors at high (yet lower than pure H) pressure. The origin of high-pressure superconductivity can be derived from the particular "H2" units, which are a feature common to

aElectronic address:

2158-3226/2014/4(10)/107118/10 4,107118-1 ~ " iilli if J nil \

hydrides of alkali metals,17 alkaline earth metals1819 and group IVa elements.1215 Experiments suggested metallization of SiH4 at ~60 GPa20 and its superconducting transition temperature (Tc) is 17 K at 96 and 120 GPa,21 though debates remain. In addition, the superconductivity of group Ilia hydrides (BH,22 AlH323 24 and GaH325) and alkaline earth metal hydrides (CaHn,26 SrHn19 and BaHn18) have also been extensively explored.

Beryllium hydrides can be an interesting subject of study, because low atomic mass of Be may lead to very high Tc values. The only known beryllium hydride is BeH2. The ground-state structure of BeH2 is body-centered orthorhombic with Ibam27 symmetry. At ambient conditions, BeH2 is an insulator with a pronounced band gap of 5.5 eV.28 Vajeeston et al.29 proposed that BeH2 undergoes a series of phase transitions a ^ ¡3 ^ y ^ 6 ^ e at pressures of 7, 51, 87 and 98 GPa, respectively, and reported that BeH2 remains insulating up to 100 GPa. Zhang et al.30 systematically investigated the pressure-induced metallization of alkaline earth hydrides, and found the metallization pressure of Pnma-BeH2 to be greater than 300 GPa. Wang et al?1 predicted that BeH2 reaches a metallic state by a R3m ^ Cmcm phase transition, instead of a direct band gap closure in R3m phase.


First-principles variable-composition evolutionary simulations were performed at 0, 50, 100, 150,200, 250, 300 and 400 GPa using the USPEX code,32-35 which has the capability of discovering possible stoichiometries and the corresponding stable and metastable structures at given pressure-temperature conditions, and has successfully predicted a large number of stable structures.36-38 The initial generation of structures and compositions was produced randomly with the use of space groups picked randomly from the total list of 230 groups. 50% of the lowest-enthalpy structures were used as parents for the next generation. In addition, 20% of structures in each new generation were produced by lattice mutation, 15% by atomic transmutation and 15% were produced randomly. Each generation contained 60 structures and runs proceeded for up to 50 generations.

The underlying structure relaxations were carried out using the Vienna Ab-initio Simulation Package (VASP) code,39 in the framework of density functional theory (DFT)40,41 within the Perdew Burke Ernzerhof generalized gradient approximation (PBE-GGA).42 The frozen all-electron projected augmented wave approach (PAW)43 was adopted to describe the core electrons and their effects on valence orbitals. A plane-wave kinetic energy cutoff of 600 eV and dense Monkhorst-Pack

44 ° -1

k-point grids44 with a resolution higher than 2n x 0.06 A were used for all structures. The most

stable structures were studied further at increased accuracy using a reciprocal-space grid better than

2n x 0.03 A .

Phonon calculations were carried out using the supercell approach as implemented in the PHONOPY code.45 Electron-phonon coupling (EPC) calculations were explored using the pseudopotential plane-wave method within PBE-GGA, as implemented in the Quantum-Espresso package.46 In these calculations, we used the kinetic energy cutoff of 60 Ry and Monkhorst-Pack k-point grids of 20 x 20 x 12 for the Cmcm phase and 16 x 16 x 8 for the P4/nmm phase with a Methfessel-Paxton47 smearing factor of 0.05 Ry. Additionally, q-meshes of 5 x 5 x 3 for Cmcm and 4 x 4 x 2 for P4/nmm were used to calculate the electron-phonon coupling matrix elements, respectively. We used the Allen-Dynes-modified McMillan equation48 to estimate Tc, as follows:

Tc = —exp

1.04(1 + A) ' A - ju*(1 + 0.622)

where is the logarithmic average frequency, A is the electron-phonon coupling constant and u* is the Coulomb pseudopotential, which is assumed to be between 0.10-0.13.5


Fig. 1 shows the convex hull phase diagrams for the Be-H system at selected pressures. The ground-state enthalpy of formation AHf is defined as AHf (BexHy) = AH(BexHy) - xAH(Be) -yAH(H). A compound is thermodynamically stable if it has lower enthalpy than any isochemical

mixture of the elements or other compounds. Such stable compounds form the convex hull. Based on our evolutionary searches, elemental Be adopts the P63/mmc structure below 390 GPa and bcc Im3m structure above 390 GPa. Our findings are in good agreement with previous calculations.49 Hydrogen undergoes a series of phase transitions: P63/m (P < 105 GPa), C2/c (105 < P < 207 GPa), Cmca-12 (270 < P < 385 GPa), Cmca (P > 385 GPa),50 in addition to the experimentally known Ibam,21 structure, we found a series of pressure-induced structural transformations (Ibam ^ P3ml ^ R3m ^ Cmcm ^ P4/nmm) with increasing pressure. Notably, we did not find other stable compounds besides BeH2 over the entire pressure range 0-400 GPa. The detailed structural parameters of these predicted phases are summarized in Table I.

At ambient conditions, BeH2 crystallizes in the orthorhombic Ibam structure. This structure consists of a three-dimensional network of distorted tetrahedra with Be atoms sitting at the center of the tetrahedra and H atoms at the corner in a bridged position between two Be atoms. The ortho-rhombic phase transforms to a CdI2-type structure (P3ml; Fig. 2(a)) at 24 GPa, then it transforms to a related CdCl2-type structure (R3m; Fig. 2(b)) at 139 GPa (Fig. 3(a)). Both structures are made

TABLE I. Optimized structural parameters for the predicted BeH2 structures at selected pressures.

Pressure Lattice parameters Wyckoff positions

(GPa) Space group No. (A, deg) Atom Sites x y z

50 P3 ml 164 a = 2.085 Be la 0 0 0

c = 3.104 H 2d 0.667 0.333 0.721

150 R3 m 166 a = 1.886 Be lb 0 0 0.5

c = 8.316 H 2c 0 0 0.732

250 Cmcm 63 a = 1.796 Be 4c 0 0.139 0.75

b = 5.503 H1 4b 0 0.5 1

c = 2.840 H2 4c 0 0.819 0.75

400 P4/nmm 129 a = 1.906 Be 2c 0.5 0 0.707

c = 3.240 H1 2a 0 0 0

H2 2c 0.5 0 0.327

FIG. 2. Extended crystal structures of solid BeH2 for (a) the P3ml structure at 50 GPa; (b) the R3m structure at 150 GPa; (c) the Cmcm structure at 250 GPa; and (d) the P4/nmm structure at 400 GPa. The large blue spheres represent Be atoms, while the small red and green spheres indicate two symmetrically inequivalent H atoms.

of layers of edge-sharing BeH6-octahedra, but stacking sequences of these layers are different. The shortest interlayer H-H distances decrease from 1.83 A at 50 GPa to 1.51 A at 150 GPa (Fig. 3(b)).

We found a similar high-pressure structure in the B-H system:22 at P > 168 GPa, the P6/mmm-BH structure is the most stable phase, and may be described as stacking BH-layers with planar closely-packed arrays of boron atoms. On-top H atoms locate symmetrically between the boron layers. Note that if one assigns a formal charge of -1 to H (hydride-like), both the boron atoms in BH and beryllium atoms in BeH2 have a formal ns2 valence electron configuration. Notably, the structural transformation from Ibam to P3ml is accompanied by a large density jump of 9.81% while only 0.79% increase occurs at the transition from P3ml to R3m (Fig. 3(b)). The structures in Ref. 27 are metastable with respect to the P3ml structure.

At 204 GPa, the layered R3m structure transforms into an orthorhombic Cmcm structure (Fig. 2(c)). In this structure, Be atoms are coordinated by eight hydrogens, whereas hydrogens are in the fourfold coordination (H1 atoms - in planar square coordination, H2 atoms - in tetrahedral coordination). Note that H1 atoms form flat pure-hydrogen rectangular layers with shortest H-H distance of 1.42 A at 250 GPa. The tetragonal P4/nmm structure (PbClF-type) becomes stable at 349 GPa. In this structure, Be atoms are coordinated by nine hydrogen atoms (forming a capped tetragonal antiprism); H1 atoms are in a fourfold (planar square) coordination and H2 atoms in a fivefold (square pyramid) coordination. The structure can be viewed as layered, with double layers formed by Be and H2 atoms, alternating with square layers formed by H1 atoms. The Be-Be distances at 400 GPa are 1.901 and 1.906 A within the double layers, and 2.328 A between these layers, reinforcing cohesion of the highly delocalized covalent three-dimensional BeH2 structure. The shortest H-H distance is between H1 atoms, i.e. in the pure-hydrogen square layer - at 400 GPa this distance is 1.345 A. At such distances overlap of atomic orbitals is strong enough to make the material metallic. This is very similar to the Pbcn-SiH49 with the closest H-H distance of 1.35 A.

Fig. 4 shows electronic densities of states (DOS) for the P3ml and R3m structures, from which it can be clearly seen that both structures are insulting. As we know, GW approximation can precisely estimate the materials band gaps in contrast to the GGA and LDA methods. For the P3ml and R3m phases, the gaps are 3.12 eV at 50 GPa and 1.80 eV at 150 GPa, respectively, indicating that both structures can be viewed as wide band gap semiconductors. In addition, it is clear that there is

0 50 100 150 200 250 300 350 -100 Pressure (GPa)

0 50 100 150 200 250 300 350 400 Pressure (GPa)

FIG. 3. (a) Enthalpy per atom for various BeH2 structures as a function of pressure with the P3ml structure taken as the reference; (b) Computed equations of state of BeH2 (solid lines) and shortest H-H distance (dotted lines).

substantial hybridization of the Be-p states and H-s states, suggesting large degree of covalency. The covalent bonds are mainly from the intralayer BeH6 octahedra while the interlayer interactions are mainly van der Waals forces.

Fig. 5 shows the band structures, partial DOS and electron localization function (ELF) for the Cmcm phase at 250 GPa and P4/nmm phase at 400 GPa, respectively. The band structures reveal that both structures are metallic with several bands crossing the Fermi level, and a pseudogap. The dispersed valence and conduction bands near the Fermi level signify a relatively large DOS at the Fermi level (0.098 and 0.107 electrons/eV/f.u., respectively), which may favor superconducting behavior. The valence band widths are greater than in the low-pressure phases, which indicates enhanced electron delocalization, thus, more electrons participate in bonding interactions, which promotes structural stability.

Distributions of the electron localization function (ELF) reveal electron accumulation on the H atoms. For the P4/nmm phase, the ELF between H atoms in the square H-layer is close to 0.5 (Fig. 5(e)), which equals to the value for the electron gas. This indicates that the square H-layer is metallic, which we think it is the origin of the superconductivity. In the Cmcm phase, Bader51 analysis reveals that Be atoms have charge +1.58 and the charges of H1 and H2 atoms are -0.82 and -0.76, respectively. The charges of Be, H1 and H2 atoms of the P4/nmm phase are +1.57, -0.94 and -0.63, respectively. It is obvious that there are large charge transfer from Be atoms to H atoms

20 -10 0 10 20 30

Energy (eV)

FIG. 4. Total and Partial density of states (DOS) for the (a) P3ml phase at 50 GPa and (b) R3m phase at 150 GPa.

for both structures, indicating the ionic character of the bonds. Together with the DOS and ELF analysis, the bonding nature can be characterized as mixed metallic, covalent and ionic bonds.

The calculated phonon spectra for the Cmcm and P4/nmm phases establish dynamical stability, as there are no imaginary phonon frequencies anywhere in the Brillouin zone (Fig. 6). We further explored the superconductivity for both structures by performing electron-phonon coupling (EPC) calculations. For the Cmcm structure at 250 GPa, the electron-phonon coupling parameter A is 0.63, indicative of quite strong EPC. Using the calculated of 1670.7 K and the commonly accepted values of the Coulomb pseudopotential u* (0.1-0.13),5 we obtained Tc in the range of 32.1-44.1 K using the modified Allen-Dynes-modified McMillan equation.48 Our results are similar to those of Wang et al.,31 the differences being due to different pseudopotentials. From Fig. 7(c), it is clear that Tc of the Cmcm structure first increases and then decreases with increasing pressure, and reaches a maximum (45.1 K) at -275 GPa.

Fig. 7 shows the total and partial phonon density of states together with the Eliashberg phonon spectral function a2F(w) and electron-phonon integral A(u) as a function of frequency for the P4/nmm structure at 400 GPa. Low-frequency (<35 THz) vibrations are mostly related to Be atoms, while higher-frequency (>45 THz) modes mainly come from the vibration of H1 and H2 atoms. At 400 GPa, The calculated EPC parameter A is 0.65, indicating rather strong EPC in the P4/nmm structure. Using the calculated of 2170 K and u* (0.1-0.13), we obtained Tc in the range of 46.1-62.4 K. The vibrations of Be below 35 THz contribute about 44.3% of total A, while the vibrations of H1 and H2 above 45 THz contribute about 55.7% with no obvious difference between H1 and H2 vibrations to A. In addition, the pressure dependence of Tc displays the same trend as observed in the Cmcm phase and reaches a maximum of 97.0 K at 365 GPa. This is one of the highest Tc values predicted in the literature. Note that the Allen-Dynes formula is expected to be reliable when A is less than 1-1.5,52 which is the case here.

0 0.2 0.4 0.6 0.8

- -\ /- • ---A

■zA. — Hp


metallic H-layer

FIG. 5. (a) and (b) band structures and partial DOS for Cmcm phase at 250 GPa and P4/nmm phase at 400 GPa, respectively; (c), (d) and (e) electron localization function (ELF) through specific surfaces.


In summary, using variable-composition evolutionary simulations for crystal structure prediction, we investigated the high-pressure phases of solid beryllium hydrides in the pressure range of 0-400 GPa. BeH2 is found to be the only stable beryllium hydride. The pressure-induced transformations are predicted to be Ibam ^ P3ml ^ R3m ^ Cmcm ^ P4/nmm, which occur at 24, 139, 204 and 349 GPa, respectively. The layered P3ml and R3m structures belong to the well-known CdI2 and CdCl2 types, respectively. The Cmcm and P4/nmm phases contain 8- and 9-coordinate Be atoms, respectively, and layers of H atoms with short H-H distances, responsible for metallic conductivity. The entire phase transformations are first-order with volume shrinkage values of 9.81%, 0.79%, 2.71% and 0.43%, respectively. The P3ml and R3m structures are semiconductors while the Cmcm and P4/nmm phases are metallic. Electron-phonon coupling calculations show that the Cmcm and P4/nmm structures are phonon-mediated superconductors, with large electron-phonon coupling parameters of 0.63 for the Cmcm phase with a Tc of 32.1-44.1 K at 250 GPa and 0.65 for the P4/nmm phase with a Tc of 46.1-62.4 K at 400 GPa. Dependence of Tc on pressure indicates that Tc will increase initially to a maximum value of 45.1 K for the Cmcm phase at 275 GPa and 97.0 K for the P4/nmm phase at 365 GPa, respectively, and then decrease with increasing pressure for both structures.

0 0.01 0.02 0.03 0.04 O 0.02 0.04 0.06 0.08 20 25 30 35 40 45 50 55

p a2F(w)/ w / Cmcn^ 4Tc (K) i i *> i

V / i i ♦ A / ' / ' ♦ " ; '

i A' P4/nmm ♦ A » (cf f Tc (K)

f__ \S** —-Total f Be(2c) . ............. "1(2«) (a) ---H2(2c) (b) ;.(»■)

220 240

300 ï C

360 380 400


0.2 0.4 0.6 40 50 60 70 SO 90 100

FIG. 7. (a) Total and partial phonon density of states (PDOS) for P4/nmm phase; (b) Eliashberg phonon spectral function a2F(^) and electron-phonon integral A(w>) as a function of frequency at 400 GPa; and (c) calculated superconducting transition temperature (Tc) vs pressure for Cmcm and P4/nmm phases, triangles and squares represent i* = 0.1 and 0.13, respectively.

We thank the Natural Science Foundation of China (Grants No. 51372203, No. 11164005 and No. 51332004), the National Basic Research Program of China (973 Program, Grant No. 2014CB643703), the Basic Research Foundation of NWPU (Grant No. JCY20130114), the Foreign Talents Introduction and Academic Exchange Program (Grant No. B08040), the National Science Foundation (Grants No. EAR-1114313 and No. DMR-1231586), DARPA (Grants No. W31P4Q1310005 and No. W31P4Q1210008), and the Government of the Russian Federation (Grant No. 14.A12.31.0003) for financial support. The authors also acknowledge the High Performance Computing Center of NWPU, Shanghai Supercomputer Centre, and the National Supercomputing Center in Shenzhen and the GENCI-CINES (France) for the allocation of computing time on their machines.

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