Abstract
Superhydrides have complex hydrogenic sublattices and are important prototypes for studying metallic hydrogen and high-temperature superconductors. Previous results for LaH10 suggest that the Pr-H system may be especially worth studying because of the magnetism and valence-band f-electrons in the element Pr. Here, we successfully synthesized praseodymium superhydrides (PrH9) in laser-heated diamond anvil cells. Synchrotron x-ray diffraction analysis demonstrated the presence of previously predicted F
INTRODUCTION
The idea that hydrogen-rich compounds may be high–critical temperature (Tc) superconductors can be traced back to 2004 (1), when chemical precompression of hydrogen by other elements was proposed as an effective way to reduce the metallization pressure of hydrogen. Recent experimental results of Tc exceeding 200 K in compressed H3S (2–4) and 250 to 260 K in LaH10 system (5–8) have indicated compressed hydrogen-rich compounds as potential room-temperature superconductors.
It is recognized that superconductivity in these hydrides owes its origin to electron-phonon coupling (EPC). Three parameters determine Tc: the characteristic phonon frequency, EPC, and Coulomb pseudopotential (9). Recent theoretical studies have covered almost all binary hydrides and found several metal superhydrides with extraordinary high-Tc superconductivity, such as CaH6 (10), MgH6 (11), YH6–10 (12, 13), AcH10–16 (14), and ThH9–10 (15). Peng et al. (16) first studied all the candidate structures of rare earth superhydrides with H-rich cages at high pressure and proposed that only several hydrides could be superconductors with Tc > 77 K. At the same time, superhydrides with H2 units are recognized to have relatively low critical temperature, e.g., LiH6 (17), NaH7 (18), Xe(H2)7 (19), and HI(H2)13 (20). The question is why some superhydrides are high-Tc superconductors, while others, with the same structure and stoichiometry, are not.
Continuing studies of lanthanide superhydrides, in this work, we studied high-pressure behavior of the Pr-H system above 100 GPa. Chesnut and Vohra (21) studied the crystal structure of metallic Pr and determined the phase sequence above megabar pressure. Pr can readily absorb hydrogen at high temperature and form hydrides: Face-centered cubic dihydride PrH2 and hexagonal close-packed trihydride PrH3 were found at ambient pressure. Subsequent filling of octahedral voids in the structure of dihydrides leads to nonstoichiometric PrH2+x composition, which exhibits considerable variations of magnetic structures (22). Here, through high-pressure and high-temperature (HPHT) synthesis, two unexpected Pr superhydrides were obtained and studied. In particular, we investigated superconducting behavior of synthesized Pr superhydrides by electrical resistance measurements. Theoretical calculations are used to unravel the relationship among their magnetic properties, electronic band structures, phonon spectra, and superconductivity. Comparison with already detailed studies of La and Ce superhydrides allows us to elucidate the great influence of metal atoms on superconductivity of superhydrides.
RESULTS AND DISCUSSION
The stability and structures predicted by theoretical calculations
Before describing the experimental results, we have compared our theoretical findings with the previous ab initio study (16), which is different from ours in a number of aspects. These differences are crucial for understanding our experimental results and motivated us to further perform independent variable-composition searches for stable compounds in the Pr-H system at pressures of 50, 100, and 150 GPa using the Universal Structure Predictor: Evolutionary Xtallography (USPEX) (23–25) package and Ab Initio Random Structure Searching (AIRSS) (26) code (see fig. S1). The current theoretical results performed by Vienna Ab-initio Simulation Package (VASP) (27–29) are also checked by an independent code Cambridge serial total energy package (CASTEP) (30). The results of CASTEP can be found in fig. S1. These two codes give the same results in principle. The only difference is the symmetry of PrH3 that CASTEP gives C2/m-PrH3, while VASP gives Pm
Results of the structure search exhibit large differences depending on including or excluding magnetism and SOC effects, which can be seen in Fig. 1 and fig. S1. However, previous calculations (16) did not include these effects. In agreement with previous results (16), our search gives Pm
Convex hulls for Pr-H system with the inclusion of SOC and magnetism at (A) 50, (B) 100, and (C) 150 GPa.
Synthesis of polyhydrides Fm3 ¯
To synthesize previously unknown hydrides, we carried out several experiments by directly compressing Pr and hydrogen in the Diamond Anvil Cells (DACs). The diamond used in this experiment was coated with 150-nm alumina film by magnetron sputtering. The metallic Pr sample was loaded and sealed with a little pressure in the argon-protected glove box. After loading hydrogen into the cell, the sealed pressure was about 10 GPa, and selected x-ray diffraction (XRD) patterns are shown at various pressures (see fig. S3C). Figures 2 and 3 summarize the data for PrH3 and PrH9, respectively. Before laser heating, the diffraction pattern at 30 GPa included peaks from Fm
(A) Refinement of the experimental XRD patterns obtained in Pr + H2 cell by cold compression to 30 GPa. arb. units, means arbitrary units. (B) Refinement of the XRD pattern by Fm
The experimental volumes of cubic PrH3 are in good agreement with those predicted for Fm
(A) Refinement of the XRD pattern by F
It is well known that experimental studies of hydrides are greatly affected by the hydrogen permeability contributing to the failure of diamonds in the high-pressure experiments. To minimize this problem, we synthesized the new hydrides by replacing of pure hydrogen with ammonia borane (AB), which is an excellent source of hydrogen (released during decomposition of AB). Several experiments were performed according to the reaction: Pr + NH3BH3→PrHx + c-BN through HPHT treatment (31–33). Figure 2B shows the diffraction pattern after laser heating at 43 GPa. The reaction products are dominated by Fm
Synthesis of F4 ¯
To obtain higher hydrides of Pr, we conducted further experiments at pressures above 100 GPa. To overcome problems with hydrogen permeation, we also used NH3BH3 (AB) as the source of hydrogen, which proved to be effective for synthesis of superhydrides at megabar pressures (7, 34). The original sample containing Pr with AB was laser-heated to 1650 K at 115 GPa. Measurements after laser heating did not show any changes in pressure, and Raman signal of H2 was detected at 4147 cm−1, indicating the generation of hydrogen. Figure 3A shows the XRD pattern with the presence of two praseodymium superhydrides F
Both structures have almost the same volume and energy on convex hull at studied pressure range (Fig. 1, B and C). The stability of F
Properties of F4 ¯
We performed a series of experiments to investigate superconductivity of PrH9 via measurements of electrical resistance R(T) in the range of 1.6 to 300 K at pressures from 100 up to 150 GPa (see Fig. 4). The XRD pattern of the prepared sample at 126 GPa, deposited with four electrodes, shows presence of both F
(A) The sample inside the diamond anvil cell connected with four electrodes before and after laser heating for sample 1. (B) The photos of sample 2 from different sides of cell after heating. (C) XRD pattern proves that cubic and hexagonal PrH9 were synthesized in the sample at around 120 GPa from a mixture of Pr and AB. (D) Resistance steps of sample 1 at different magnetic fields. (E) Resistance steps of sample 2 at different pressures.
Further theoretical calculations were aimed at understanding why both F
Calculations demonstrate that both PrH9 structures are dynamically stable (fig. S6) and exhibit metallic properties (Fig. 5). However, only 6 to 9% of the total densities of electron states (DOS) at the Fermi level comes from the hydrogen atoms, the rest being due to f-electrons of Pr. Relatively high values of the density of states above 3 to 4 eV−1 f.u.−1 (per eV per formula unit) at or near (±1 eV) the Fermi level, caused by a series of Van Hove singularities make it impossible to use constant DOS approximation when calculating parameters of the superconducting state in PrH9 (41). Low contribution of hydrogen to DOS is associated with weak EPC at 150 GPa, resulting in low superconducting Tc. EPC calculations for both PrH9 with the selected pseudopotential (PP) give the estimated Tc of 0.8 K for cubic PrH9 and 8.4 K for hexagonal PrH9 at 120 GPa with μ* = 0.1, which is in good agreement with experiments (see figs. S10 to S12).
Electron localization function of (A) F
We summarized magnetic properties for all studied praseodymium hydrides at the pressure range of 0 to 150 GPa in Fig. 6. We find that all Pr-H compounds are magnetic: Fm
(A) Magnetic moments of Pr-H compounds at high pressure and (B) magnetic map of Pr-H system as a function of pressure.
CONCLUSIONS
Using in situ decomposition reaction of NH3BH3 under HPHT conditions previously used for synthesis of lanthanum superhydrides, we synthesized two novel metallic superhydrides F
METHODS
Experimental method
The praseodymium powder samples were purchased from Alfa Aesar with a purity of 99.99%. Molybdenum electrodes were sputtered onto the surface of one diamond anvils in the van der Pauw four-probe geometry. A four-probe measurement scheme was essential to separate the sample signal from the parasitic resistance of the current leads. We prepared an isolated layer from cubic boron nitride (or a mixture of epoxy and CaF2). We performed laser heating of three diamond anvil cells (100- and 150-μm culets) loaded with metallic Pr sample and ammonia borane in the argon-protected glove box. The diamonds used for electrical DACs had a culet with a diameter of 100 μm. Thickness of the tungsten gasket was 20 ± 2 μm. Heating was carried out by pulses of infrared laser with a wavelength of 1 μm (Nd:YAG), and temperature measurements were carried out by the MAR 345 detector. Pressure was measured by the edge position of diamond Raman signal (42). XRD patterns studied in diamond anvil cells samples were recorded on the BL15U1 synchrotron beamline (43) at Shanghai Synchrotron Research Facility (China) with the use of a focused (5 μm × 12 μm) monochromatic beam. Additional syntheses with electrodes were carried out at the 4W2 High-Pressure Station of Beijing Synchrotron Radiation Facility (China). The beam size was about 32 μm × 12 μm. Both facilities are with the incident x-ray beam (20 keV, 0.6199 Å) and a Mar165 charge-coupled device two-dimensional detector. The experimental XRD images were integrated and analyzed using the Dioptas software package (44). The full profile analysis of the diffraction patterns, as well as the calculation of the unit cell parameters, was performed in the Materials Studio (45) and Jana2006 program (46) by the Le Bail method (47).
Theoretical calculations
We have carried out variable-composition searches for stable compounds in the Pr-H system at pressures of 50, 100, and 150 GPa using the USPEX (23–25) package coupled with the VASP code (27–29)and AIRSS (26) code coupled with the CASTEP plane-wave code (30) and on the fly pseudopotentials (48). The first generation of USPEX search (120 structures) was created using a random symmetric generator, while all subsequent generations (100 structures) contained 20% random structures and 80% created using heredity, soft mutation, and transmutation operators.
We calculated the EoS for PrH, both PrH3, and two PrH9 phases. To calculate the EoS, we performed structure relaxations of phases at various pressures using DFT (49, 50) within the generalized gradient approximation (Perdew-Burke-Ernzerhof functional) (51, 52) and the projector augmented-wave method (53, 54) as implemented in the VASP code (27–29). Plane-wave kinetic energy cutoff was set to 1000 eV, and the Brillouin zone was sampled using Γ-centered k-points meshes with a resolution of 2π × 0.05 Å−1. Obtained dependences of the unit cell volume on pressure were fitted by three-order Birch-Murnaghan equation (55) to determine the main parameters of the EoS, namely, V0, K0, and K′, where V0 is equilibrium volume, K0 is bulk modulus, and K′ is derivative of bulk modulus with respect to pressure using the EosFit7 software (56). We also calculated phonon densities of states for studied materials using finite displacement method [VASP (57) and Phonopy (58)].
Calculations of phonons, EPC, and superconducting Tc were carried out with Quantum ESPRESSO package (59) using density-functional perturbation theory (60), using plane-wave pseudopotential method and local density approximation exchange-correlation functional (61). Norm-conserving pseudopotentials for H (1s1) and Pr (5s25p64f36s2) were used with a kinetic energy cutoff of 90 Rybderg (Ry). In our ab initio calculations of the EPC parameter λ, the first Brillouin zone was sampled using a 6 × 6 × 6 q-points mesh with a denser 24 × 24 × 24 k-points mesh for F
SUPPLEMENTARY MATERAILS
Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/6/9/eaax6849/DC1
Table S1. Crystal structure of predicted Pr-H phases.
Table S2. Experimental parameters of DACs.
Table S3. Experimental cell parameters and volumes of lower praseodymium hydrides along with calculated cell volumes (VDFT).
Table S4. Experimental cell parameters and volumes of two praseodymium superhydrides along with calculated cell volumes (VDFT).
Table S5. EoS of metallic Pr from reference.
Table S6. Calculated EoS parameters of third Birch-Murnaghan equation for all studied Pr-H phases.
Fig. S1. Calculated convex hulls for Pr-H system at various pressures.
Fig. S2. Convex hulls without and with zero-point energy (ZPE) correction of found praseodymium hydrides at 120 GPa.
Fig. S3. Experimental XRD patterns dependence of pressure in the range of 0 to 130 GPa.
Fig. S4. Pressure dependence of the nearest H-H distances and nearest Pr-H distances from experimental cell parameters.
Fig. S5. Raman spectra of Z1 cell under decompression.
Fig. S6. Calculated phonon density of states and band structure for PrH9.
Fig. S7. Calculated phonon density of states and band structure for PrH8 and PrH3.
Fig. S8. Electron density of states for PrH3.
Fig. S9. Enlarged figure of electrical resistance measurements of PrH9 in sample 2.
Fig. S10. Calculated superconducting parameters of F
Fig. S11. Eliashberg spectral functions, the electron-phonon integral λ(ω), and critical transition temperature Tc(ω) calculated at 120 GPa for cubic PrH9 with σ = 0.035 Ry.
Fig. S12. Calculated superconductivity of hexagonal PrH9 by Eliashberg spectral functions at 120 GPa.
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REFERENCES AND NOTES
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