Synthesis, Structure, and Electric Conductivity of Higher Hydrides of Ytterbium at High Pressure

While most of the rare-earth metals readily form trihydrides, due to increased stability of the filled 4f electronic shell for Yb(II), only YbH2.67, formally corresponding to YbII(YbIIIH4)2 (or Yb3H8), remains the highest hydride of ytterbium. Utilizing the diamond anvil cell methodology and synchrotron powder X-ray diffraction, we have attempted to push this limit further via hydrogenation of metallic Yb and Yb3H8. Compression of the latter has also been investigated in a neutral pressure-transmitting medium (PTM). While the in situ heating of Yb facilitates the formation of YbH2+x hydrides, we have not observed clear qualitative differences between the systems compressed in H2 and He or Ne PTM. In all of these cases, a sequence of phase transitions occurred within ca. 13–18 GPa (P3̅1m–I4/m phase) and around 27 GPa (to the I4/mmm phase). The molecular volume of the systems compressed in H2 PTM is ca. 1.5% larger than of those compressed in inert gases, suggesting a small hydrogen uptake. Nevertheless, hydrogenation toward YbH3 is incomplete, and polyhydrides do not form up to the highest pressure studied here (ca. 75 GPa). As pointed out by electronic transport measurements, the mixed-valence Yb3H8 retains its semiconducting character up to >50 GPa, although the very low remnant activation energy of conduction (<5 meV) suggests that metallization under further compression should be achievable. Finally, we provide a theoretical description of a hypothetical stoichiometric YbH3.


■ INTRODUCTION
The enormous interest in diverse hydrogen-rich systems manifested in the last few decades can be linked mainly to two topics: energy storage in chemical compounds and phonon-driven superconductivity (SC), depending on the nature of systems studied. Due to the high gravimetric efficiency required for energy storage in most potential applications, the first area has been dominated by materials composed predominantly of light elements such as Li, B, Al, etc. 1−4 On the other hand, the hydrides that have been studied as potential superconductors are not limited in this respect and their components cover virtually the entire periodic table. 5−8 The recent upsurge in the search for high-temperature SC in hydrides under high pressure has been stimulated by Neil Ashcroft's idea of "chemical precompression" of hydrogen contained in hydrogen-rich chemical compounds. 9 In such hydrogen-dominated systems (in terms of an atomic fraction), the hydrogen sublattice is expected to contribute to the metallic state at drastically lower pressures compared to elemental hydrogen. This would finally allow for taking an advantage of the large phonon frequencies related to the lightweight hydrogen atoms to raise the critical temperature of SC. SC might occur provided the system features a high density of electronic states at the Fermi level and strong electron−phonon coupling. As a consequence of this concept, many binary and even more complex hydride-based systems have been screened theoretically, 10 leading ultimately to experimental discovery of superconductivity in some of them. Several hydrides, especially those containing the p-block and rare-earth (RE) elements, 7 were indicated as particularly promising by theoretical predictions, e.g., H 3 S 11,12 or YH 10 and LaH 10 . 13,14 The experimental verification of these predictions led to reports of strikingly high critical temperatures of superconductivity (T C ): compressed H 2 S forming a superconducting H 3 S phase of T C = 203 K at 155 GPa, 15 LaH 10 of T C = 250−260 K upon compression to ca. 200 GPa, 16−18 an incompletely identified C−S−H material synthesized in a diamond anvil cell (DAC) of T C = 288 K at 267 GPa, 19 or YH 6 of T C = 220 K at 166−183 GPa 20,21 and YH 9 of T C = 243−262 K at 182−201 GPa. 21,22 Considering the RE-based systems, in these superhydrides, the hydrogen sublattice is usually composed of clathrate-like and other complex geometrical motifs or contains mixed molecular and atomic units. 5,10,23 While the polyhydrides of exotic compositions may form in a megabar pressure range, they are preceded by more usual stoichiometries appearing at much lower pressures. Some of the latter also superconduct, as has been verified experimentally or as expected based on computational screening. 7 Obviously, lowering the pressure of synthesis of a superconducting hydride or the metastability of such phases under as close to ambient conditions as possible would be beneficial for more thorough macroscopic studies and possible applications. Recently, such high-temperature superconducting phases have been found for the hydrides based on lanthanides below the megabar pressure region. 24,25 With the exception of Eu and Yb, all lanthanides are easily hydrogenated at room temperature, absorbing up to 300 mol % hydrogen to form trihydrides, LnH 3 , already under the pressure of a few atmospheres; 26 see also Figure S1 in the Supporting Information (SI). However, due to the stabilization of half-filled or filled 4f electronic shells for Eu(II) and Yb(II), respectively, oxidation of these elements to the trivalent state by hydrogen is much more difficult. While the corresponding dihydrides can be readily prepared, 26 further absorption of hydrogen requires significantly higher pressure. The uptake of hydrogen by EuH 2 occurs only above 8.7 GPa, as has been reported by Matsuoka et al. based on X-ray diffraction and Eu−Mossbauer spectroscopy measurements. 27 At this pressure range, a tetragonal EuH 2+x containing trivalent Eu 3+ starts to form, and the latter remains the only detected oxidation state of Eu above 12.5 GPa. 28 Very recently, Semenok et al. 29 reported that EuH 9 is present in the samples already at 74 GPa, while the other europium superhydrides were detected within the range 74−130 GPa, some of them showing antiferromagnetic ordering. Unfortunately, the lower-pressure regime has not been studied in this work, leaving the gap between ca. 50 GPa for which EuH 2+x phases were reported and 74 GPa with the superhydride phases already formed.
In the case of ytterbium, some early reports indicated preparation of cubic YbH 2+x , x < 0.7 after reaction of this metal with hydrogen pressurized to ca. 120 bar. 30−32 These findings have been clarified by Auffermann, who prepared the metastable higher hydride of ytterbium via a high-pressure, high-temperature reaction (200−3200 bar, >600 K). 33 While the major features of the powder X-ray diffraction pattern of YbH 2+x are compatible with a face-centered cubic (fcc) unit cell reported earlier, application of powder neutron diffraction allowed for proper identification and refinement of its crystal structure. It appeared that the prepared compound can be described as YbH 2.67 , i.e., Yb 3 H 8 or Yb II (Yb III H 4 ) 2 , and it crystallizes in a trigonal unit cell with close packing of the nine ytterbium atoms (stacking sequence: ...ABC...), while hydrogen occupies all of the tetrahedral and 2/3 of the octahedral holes, and no disorder is observed in the structure. The crystal structures of the higher hydrides of Yb and Eu relevant to the current study are summarized in Figure 1.
The case of Yb(III) is special. 2 The vicinity of 4f shell closure for the 4f 13 electron configuration of Yb III resembles the 3d 9 configuration of parent oxocuprate superconductors, and the early DFT calculations indicated the possibility of the significant contribution of H 1s states to the electron density at the Fermi level even for the stoichiometric Yb(III) hydrides. 34 Markedly, the only hole in the f electron set usually resides on the orbital, which forms sigma* states with H(1s), which is analogous to a hole in the d set of Cu(II) residing in sigma* states with O(2p) in cuprates. Moreover, Yb(III) features a large magnetic moment of ca. 4.3−4.9 m B corresponding formally to spin-1/2, which again renders it similar to Cu(II) in parent compounds of oxocuprate superconductors; thus, one might expect that electron doping could affect magnetism and lead to SC, just like for Cu(II) oxides. Last but not the least, more recent theoretical considerations suggest that besides yttrium and the lightweight lanthanides (Ln), 13,14,35 the late lanthanides (Yb and Lu) should also form the superhydrides of T C > 100 K. 36 In the present work, we expand the chemistry of the Yb−H system far beyond the previously studied range of ca. 0.3 GPa. Using the DAC methodology, we investigate the reaction of metallic Yb with H 2 and attempt further hydrogenation of Yb 3 H 8 (YbH 2.67 ). We discuss the observed phase transitions as well as the possibility of formation of the higher hydrides of ytterbium, i.e., YbH 2+x , especially with x > 0.67. We have also studied the electronic transport of the mixed-valence Yb 3 H 8 in the function of external pressure. 37 ■ METHODS Experimental Section. Metallic Yb (99.9%, Sigma-Aldrich) and Au pressure standard (99.999%, Alfa Aesar) were loaded into the DAC. Diamonds of 200−300 μm culets and rhenium gaskets were used. Yb 3 H 8 was prepared according to the literature procedure 33 and analyzed at ambient conditions using powder X-ray diffraction, cf. Figure S2 and Table S1 in the SI. Ne, He, and H 2 , loaded at ca. 170 MPa in the custom-designed gas loading systems of GL CIW and Inorganic Chemistry pubs.acs.org/IC Article GSE CARS APS, 38 were applied as the pressure-transmitting medium (PTM). High-pressure angle-dispersive X-ray diffraction (XRD) measurements were performed using the Advanced Photon Source synchrotron facility of the Argonne National Laboratory. The measurements were carried out on sectors 13ID-D and 16ID-B operating at wavelengths from 0.2952 to 0.4066 Å. The sample-todetector distance and other geometrical parameters were calibrated using LaB 6 or CeO 2 standards. One of the samples of Yb in H 2 PTM was heated by the double-sided laser systems available at the beamlines to the maximum temperatures of about 2100 K measured by fitting gray body thermal radiation. 39 Heating was carried out in several pulses lasting for a few seconds; however, the overall amount of energy absorbed by the sample was not monitored. The heating was not uniform across the sample, which manifested as variable amounts of crystalline phases present in various areas of the sample.
The electronic transport properties were carried out in a custom, miniaturized diamond anvil cell in a classical four-electrode geometry, using a Quantum Design Physical Property Measurement System. NaCl was used as a PTM, and the pressure was measured using ruby fluorescence.
The two-dimensional diffraction images were analyzed and integrated using DIOPTAS software. 40 X-cell was used for pattern indexing. 41 The structures were refined in JANA2006. 42 The pseudo-Voigt function with the Berar−Baldinozzi correction for asymmetry was utilized for modeling the diffraction peak shape. The background was corrected by Legendre polynomials. Further details of the crystal structure investigations may be obtained from the joint CCDC/FIZ Karlsruhe online deposition service: https://www.ccdc.cam.ac.uk/ structures/ by quoting the deposition numbers CSD 2150168− 2150171. The third-order Birch−Murnaghan equations of state (EoS) were fitted using the EoSFit7-GUI program. 43,44 Computational. Density functional theory (DFT) calculations were performed using CASTEP. 45 Generalized gradient approximation (GGA) was used with the PBE functional adjusted for solids (PBEsol). 46 As hydrides usually require a large cutoff, here the value of 700 eV was applied to lead to very good energy convergence. The density of the k-point grid was set at 0.04 Å −1 ; ultrasoft pseudopotentials generated on the fly were used as they provide more accurate lattice parameters. The YbH 3 stoichiometry was assumed, and the I4/mmm structure type exhibited by YbH 2+x at elevated pressures was adopted. The sqrt2 × sqrt2 × 1 supercell (Z = 4) was applied to account for various magnetic ordering schemes; the formal spin of Yb(III) was used as the initial one in the first SCF step. For the magnetic structures, the DFT + U formalism was used, with U = 5 eV for the 4f electrons of Yb. Enthalpies of various magnetic models and that of a spin-unpolarized one were calculated at several pressure values. Electronic density of states (DOS) was computed for the lowest enthalpy solutions.

■ RESULTS AND DISCUSSION
As could be expected, the reaction between metallic ytterbium and hydrogen proceeds already at room temperature immediately after hydrogen loading to the cell. However, the unreacted metal is present in the whole pressure range studied, contributing to the strongest diffraction peaks (cf. Table 1), even for the largest pressure achieved for the sample compressed at room temperature to ca. 40 GPa; see Figures S3−S4. The evolution of the crystalline phases detected in this sample well corresponds to that described earlier, and YbH 2 remains the main hydridic phase. 47−49 The crystalline phase, which can be attributed to a higher hydride of ytterbium, YbH 2+x , is barely detected even at ca. 40 GPa; see Figure S3. However, the composition is variable from sample to sample, and in the case of the second DAC, the clear, although relatively weak, signals of the P3̅ 1m phase of YbH 2+x are visible already at 3.6 GPa, before heating of the sample; see Figure 2a. This may be attributed to a variable degree of surface oxidation, which should hamper further hydrogenation of the sample (this problem has been recently addressed using a thin Pd coating for the synthesis of yttrium superhydrides). 22   The in situ laser heating of the partially hydrogenated ytterbium sample up to ca. 2100 K, with several pulses lasting for a few seconds each, facilitates further hydrogenation and delivers the P3̅ 1m phase of YbH 2+x (Figure 1a), which predominates the powder diffraction pattern; see Figures 2b and S5−S7. The YbH 2 is detected in the sample in a minor amount, together with very weak signals from an unidentified crystalline phase(s); see Figure S7. Although the sample does remain not fully homogeneous, it can be concluded that both of these phases disappear after a few additional heating cycles on larger compression; see Figure S8. Above ca. 12.5 GPa, the P3̅ 1m phase of YbH 2+x undergoes a transition to the I4/m phase, which is isostructural to that reported for EuH 2+x at 8.7−9.7 GPa, 27 as indicated by the peak splitting (e.g., the peak b 4 of (0 0 2) and (3 1 0) reflections, while the (1 1 2) reflection of the trigonal phase contributes solely to the related a 4 peak) and the low-intensity reflections from the tetragonal superstructure (e.g., (1 1 0), (1 0 1), and (2 0 0), marked as b 0 , b 1 , and b 2 , respectively); see Figure 2c. During further compression, the latter phase symmetrizes to the I4/mmm structure (Figure 2d), similar to the EuH 2+x analogue reported for hydrogen pressures exceeding 9.7 GPa. 27 That second phase transition manifests itself as the vanishing superstructure signal and as a less-pronounced peak splitting for the main peaks (e.g., c 2 corresponding to (0 0 2) and (1 1 0) reflections).
To deal with more homogeneous samples including those with a fixed content of hydrogen, we also investigated Yb 3 H 8 (YbH 2+x , x = 0.67), which was prepared ex situ according to Auffermann's procedure; 33 Figure S20). The high-symmetry I4/mmm phase of YbH 2+x remains stable up to the highest pressures reached in our investigations of ca. 75 GPa; see Figure 3. The first phase transition (P3̅ 1m → I4/m) occurs with significant changes in the first coordinating spheres and is sluggish, as both phases are detected within the ca. 5 GPa range (this resembles the behavior of YbH 2 ). 49 These observations suggest a reconstructive phase transition, possibly of the first-order despite no significant volume discontinuity being observed. The second phase transition (I4/m → I4/ mmm) does not require significant changes in the coordination spheres but is rather related to symmetrization of the atomic positions. Therefore, it is a displacive phase transition apparently of the second order.
The transition pressure between the I4/m and I4/mmm phases of YbH 2+x is markedly higher than that of EuH 2+x containing larger metal ions. 27 This trend remains in line with the known relations observed for the Ln 3+ compounds, e.g., following the row of contracting Ln 3+ ions, the hexagonal-tocubic transition in the LnH 3 series gradually requires a higher pressure, 50,51 and a similar trend was noticed for the phase transitions of Ln 2 O 3 . 52 Clearly, the smaller cations require higher compression to mimic the larger ones, which is a common trend in high-pressure chemistry. 53 The diffraction patterns from Yb 3 H 8 samples in H 2 and Ar PTMs (Figure 4) are quite similar to each other. All key reflections may be assigned to the same crystalline phase in both data sets. Such a qualitative picture alone may suggest that an additional H 2 uptake does not occur for Yb 3 H 8 even at 74.5 GPa, the highest pressure reached in our experiments. However, for the I4/mmm phase, the corresponding diffraction signals are shifted toward lower Q values for the sample of Yb 3 H 8 compressed in H 2 PTM, indicating a larger unit cell volume. This phenomenon is noticeable around 30 GPa, becoming obvious for larger pressures ( Figure S23). EoS for Yb 3 H 8 was derived independently for the YbH 2+x crystalline phases present in the samples compressed in H 2 and Ne PTMs for the experimental runs covering a sufficient number of V(p) data points; see Figures S24−S29. The obtained fit parameters are presented in Table 2, while some of the available EoS parameters for the related lanthanide hydrides are summarized in Table S2. In general, the V 0 of the low-pressure trigonal form is slightly larger than the highpressure I4/mmm phase, and the inverse trend is observed for their bulk moduli. The P3̅ 1m form of Yb 3 H 8 reveals V 0 comparable to the Pnma YbH 2 of V 0 = 35.63(7) Å 3 , but the former remains significantly less compressible ( Figure 5) (for Pnma YbH 2 B 0 = 40.2(22) GPa). 48 The I4/mmm phase of YbH 2+x present above ca. 27 GPa has a slightly smaller molecular volume with an increased bulk modulus. These values fulfill a similar trend for the europium hydrides: the I4/ mmm phase of EuH 2+x of V 0 = 38.8(1) Å 3 (slightly bulkier than the Yb analogue, according to the relation of Eu and Yb ionic   Table S2. One key issue is that of the composition of the YbH 2+x specimen studied and that of a possible H 2 uptake by the sample in the H 2 atmosphere. Inspection of Figure 5 reveals that the differences in the molar volume of the Yb 3 H 8 specimen compressed in various PTMs are only marginal, which is also reflected by the respective EoS curves; see Figure  S30. However, on larger compression, the V(p) curve seems to be slightly less steep for the sample pressurized in H 2 . Although the discrepancy is rather small and it may be caused by the errors in the determination of pressure in both types of samples, it is fairly consistent across the pressures for which the tetragonal phases are favored, especially 25−75 GPa. The EoS curves fitted for the I4/mmm YbH 2+x in H 2 and Ne PTM fall apart by ca. 1.5% in terms of V(p); see Figure S31. At the same time, a simple addition of 1/3 atomic volume of hydrogen would increase the molecular volume of I4/mmm YbH 2+x by ca. 4.8% at this pressure range. Altogether, this might suggest that the composition of the sample compressed in excess H 2 is similar to YbH 2.77 rather than YbH 2.67 .
Indeed, one might speculate that the amount of 1/3 of vacancies is not a natural value for the tetragonal I4/mmm cell and that 1/4 would be a more natural value (hence, YbH 2.75 would be a more appropriate composition for such a specimen,  The estimated standard deviations (E.S.Ds.) are given in parentheses. B 0 ′ was fixed for the final refinement. N represents the number of data points. The molecular volume of YbH 2 48 and the volume roughly estimated for YbH 3 have also been plotted. The crystallographic phases of YbH 2+x , detected under a specific pressure range, are indicated at the bottom. Notice that the sample (d) represents a system of variable stoichiometry due to gradual H 2 uptake. Inorganic Chemistry pubs.acs.org/IC Article very close to YbH 2.77 suggested above from the EOS analyses). However, due to lack of direct evidence supporting such a scenario, one must refrain from making any firm conclusions here. In any case, the stoichiometry of the samples studied must be still far from the one expected for the Yb(III)H 3 stoichiometry ( Figure 5, n.b. the V/N Yb curve of YbH 3 may only serve as a rough estimation as the effects of the strain introduced during crystal formation were not considered).
Resistance of Yb to be fully oxidized to Yb(III) in the hydride environment is remarkable; it turns out that only if a negative charge density on the hydride is reduced, e.g., by binding it to B(III) in the form of the BH 4 − anion, the stoichiometric Yb(III) species may form and yet they are thermodynamically metastable at ambient (p,T) conditions. 55−58 The electric conductivity of formally mixed-valence species, be it YbH 2.67 , YbH 2.75 , or YbH 2.77 , is of great interest in the context of potential generation of superconductivity in this material. Figure 6 (top) shows the electric resistivity versus temperature plot for a sample of Yb 3 H 8 embedded in NaCl PTM. It is clear that the low-pressure phases of Yb 3 H 8 show a semiconducting behavior as their resistivity strongly decreases with the temperature increasing. A large drop in resistivity may be seen between 20.2 and 25.2 GPa, roughly corresponding to the second structural phase transition from the I4/m to the I4/ mmm polymorphs.
Analysis of the activation energy for conductivity, E a ( Figure  6 bottom), suggests that E a is already quite small (ca. 0.07 eV or 812 K) for Yb 3 H 8 at a low pressure (2.4 GPa). This feature comes certainly from the mixed-valence nature of the compound. One sharp drop of the E a value is seen between 11.0 and 13.9 GPa, roughly corresponding to the first crystallographic phase transition. The second drop of the E a value between 20 and 29 GPa is more subtle, which suggests that the second phase transition affects E a less considerably, and it is followed by the flattening of the curve above ca. 29 GPa. The E a value determined at 48.5 GPa is as small as 0.005 eV (58 K) yet not null. Thus, Yb 3 H 8 retains its semiconducting character even at ca. 50 GPa; this makes it similar to Fe 3 O 4 . 59 Metallicity, which would correspond to the formulation of Yb(III) 3  To learn what properties might be expected from fully stoichiometric YbH 3 , we performed quantum mechanical calculations for this compound; we assumed that it would adopt the I4/mmm structure observed here, similar to the europium analogue for which solely the Eu 3+ oxidation state has been detected above 12.5 GPa. 28 Both the magnetic and spin-unpolarized models were considered. The molecular volumes calculated for these models of YbH 3 fall within the range of experimentally observed values for the YbH 2.67 and YbH 2.67+x compounds ( Figure S33), which may indicate a slight underestimation of the lattice parameters by the applied DFT formalism. At the same time, the molecular volume computed for the YbH 4 polyhydride (I4/mmm, isostructural with the proposed YH 4 and other REH 4 ) 60 remains significantly larger.
The DFT calculations for all magnetic states converge to solutions characterized by extremely small remnant magnetic moments. The corresponding spin-nonpolarized band structure and DOS (Figure 7) suggest that the compound would have a metallic nature, with several broad bands crossing the Fermi level. Both Yb(f) and H(s) states contribute to the states at the Fermi level; such strong hybridization was noticed previously. 34 The fact that the spin of Yb(III) would not localize but instead give rise to itinerant electrons may seem surprising, but this could be due to strong hybridization with broad H(s) states (and this was the reason why we were targeting YbH 3 composition in experiments).

■ CONCLUSIONS
We have attempted synthesis of the yet-elusive ytterbium trihydride utilizing both metallic Yb and its currently most hydrogen-rich hydride, YbH 2.67 , as the precursors in highpressure hydrogenation (up to ca. 75 GPa). Our results point to the lack of a marked qualitative difference between these systems compressed in H 2 and the samples of YbH 2.67 pressurized in He or Ne PTM. In all of these cases, a sequence of phase transitions from the unit cells of the P3̅ 1m symmetry to the I4/m and I4/mmm systems occurred within ca. 13−18 GPa and around 27 GPa, respectively. The same tetragonal phases were observed upon compression of EuH 2 in H 2 PTM: the I4/m Eu 2+ /Eu 3+ mixed-valence system formed from the P6 3 /mmc dihydride above 8.7 GPa and the high-symmetry I4/ mmm phase was detected above 9.7 GPa. 27 The fact that Eu 3+ in a hydride environment forms at a pressure as large as 8.7 GPa, while analogous species of Yb 3+ may be prepared at several kPa, is following the standard redox potentials of the Eu 3+ /Eu 2+ and Yb 3+ /Yb 2+ pairs, which are −0.35 and −1.05 V, respectively. In other words, Yb 2+ can be easier oxidized by H 2 to Yb 3+ than its Eu 2+ analogue.
For the highest pressure investigated here (25−75 GPa) corresponding to the I4/mmm phase, the molecular volume of the systems compressed in H 2 PTM consistently remains ca. 1.5% larger than that for the systems compressed in inert gas  The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

Notes
The authors declare no competing financial interest.