Stabilization of High‐Pressure Phase of Face‐Centered Cubic Lutetium Trihydride at Ambient Conditions

Abstract Superconductivity at room temperature and near‐ambient pressures is a highly sought‐after phenomenon in physics and materials science. A recent study reported the presence of this phenomenon in N‐doped lutetium hydride [Nature 615, 244 (2023)], however, subsequent experimental and theoretical investigations have yielded inconsistent results. This study undertakes a systematic examination of synthesis methods involving high temperatures and pressures, leading to insights into the impact of the reaction path on the products and the construction of a phase diagram for lutetium hydrides. Notably, the high‐pressure phase of face‐centered cubic LuH3 (fcc‐LuH3) is maintained to ambient conditions through a high‐temperature and high‐pressure method. Based on temperature and anharmonic effects corrections, the lattice dynamic calculations demonstrate the stability of fcc‐LuH3 at ambient conditions. However, no superconductivity is observed above 2 K in resistance and magnetization measurements in fcc‐LuH3 at ambient pressure. This work establishes a comprehensive synthesis approach for lutetium hydrides, thereby enhancing the understanding of the high‐temperature and high‐pressure method employed in hydrides with superconductivity deeply.


Introduction
Over the past decade, there has been a burgeoning exploration into hydride-based superconductors with high critical temperature (T c ). [1][2][3][4][5][6][7][8] Two notable experimental achievements involve H 3 S with a high T c of 203 K, [9] and LaH 10 with a high T c of 250 K. [10] These milestones provide significant confidence in the pursuit of hydridebased superconductors at room temperature.A recent study reported the occurrence of superconductivity at room temperature and near-ambient pressures of 294 K and 1 GPa in N-doped lutetium hydride. [11]Subsequent to this report, a significant amount of experimental and theoretical work has been undertaken to reproduce and understand this superconducting phenomenon.  Howeve these efforts failed to observe the phenomenon of superconductivity in N-doped lutetium hydrides, leading to the retraction of the paper.[38] Several experimental studies have reported the absence of near-ambient superconductivity in N-doped lutetium hydride under various conditions.For instance, Ming et al. observed the absence of near-ambient superconductivity in N-doped lutetium hydride under pressure of 40.1 GPa through magnetic and electric measurements.[12] Similarly, Xing et al. found no superconducting transition at temperatures ranging from 1.8 to 300 K and pressures from 0 to 38 GPa.[13] Theoretical works contended that there is no stable ternary structure in the Lu-H-N chemical system at lowpressure conditions and proposed some Lu-H-N candidates, including Lu 8 H 21 N, [14] Lu 2 H 5 N, [15] and Lu 20 H 2 N 17 .[16] Despite extensive structure predictions by other groups, no explanations have been provided for the observed superconductivity near ambient conditions.[17][18][19][20] Multiple lines of evidence, including sample color, X-ray diffraction data, and thermal and dynamical stability, collectively support the assertion that the reported N-doped Lutetium hydride corresponds to N-doped LuH 2 (LuH 2±x N y ), as opposed to N-doped LuH 3 (LuH 3±x N y ). The attice parameter of cubic Ndoped lutetium hydride was determined to be 5.0289, [11] 5.032, [12] and 5.040 Å, [13] respectively, closely aligning with the lattice parameter of 5.033 Å for LuH 2 .The observed blue coloration of the samples is consistent with the characteristic color of LuH 2 .[11][12][13]26] Enthalpy calculations reveal that LuH 2 represents the ground state structure, whereas LuH 3 assumes a metastable Comparison between reported LuH 3±x N y [11] and fcc-LuH structure.[14,16,17,19] Furthermore, phonon spectrum calculations indicate that LuH 2 is dynamically stable, in contrast to the instability exhibited by LuH 3 .[11,19] Two structural forms of LuH 3 are identified: a hexagonal structure with P 3c1 space group (hcp-LuH 3 ) and a face-centered cubic structure with Fm 3m space group (fcc-LuH 3 ).Hcp-LuH 3 was found to be stable at ambient conditions and transformed to fcc-LuH 3 at 12 GPa.Fcc-LuH 3 , in turn, transformed back to hcp-LuH 3 upon releasing the pressure to ambient conditions.[39][40][41] The reported superconductivity of fcc-LuH 3 occurred at ≈12.4 K at 122 GPa.[42] In this work, we systematically prepared pure bulk samples of lutetium hydrides, including LuH 2 and hcp-LuH 3 , and notably managed to maintain fcc-LuH 3 to ambient conditions, using high-temperature and high-pressure method with large volume press (LVP) apparatus.We investigated the effect of the reaction pathway on the products and developed a preparation phase diagram.The fcc-LuH 3 exhibits obvious distinctions from LuH 2 , specifically, the lattice parameter for fcc-LuH 3 is 5.156(1) Å, larger than 5.033 Å observed for LuH 2 .Additionally, fcc-LuH 3 is characterized by a dark black coloration, in contrast to the blue color associated with LuH 2 . Densty functional theory (DFT) calculations, including anharmonic and temperature effects, confirm the stability of fcc-LuH 3 under ambient conditions.The hydrogen content of fcc-LuH 3 is confirmed using temperatureprogrammed desorption (TPD) and Nuclear Magnetic Resonance (NMR) methods.Importantly, our low-temperature resistance and magnetization measurements confirmed the absence of a superconducting transition in the fcc-LuH 3 phase.

Synthesis of fcc-LuH 3
The synthesis of the fcc-LuH 3 was investigated under extreme conditions of high temperature and pressure.LuH 2 was chosen as the starting material, with BH 3 NH 3 serving as the solid hydrogen source.The fcc-LuH 3 was synthesized at a high pressure of 5 GPa and temperatures exceeding 800 °C.A dual-phase composition of fcc-LuH 3 and hcp-LuH 3 was observed after recovery to ambient conditions from 5 GPa and 800 °C (Figure 1a).As the temperature increases to 1000 °C, the hcp-LuH 3 phase diminishes significantly, transforming into fcc-LuH 3 .Pure fcc-LuH 3 was obtained after recovery to ambient conditions from the conditions of 5 GPa and 1200 °C. Figure 1b presents a typically refined X-ray diffraction (XRD) pattern of the face-centered cubic structure.To confirm the reliability of the synthesis conditions, we conducted 10 sets of synthesis experiments.The XRD patterns indicate that the synthesis conditions of 5 GPa and 1100 °C (1200 °C) for 1 h are dependable for synthesizing pure fcc-LuH 3 (Figure S1, Supporting Information).We compared the XRD pattern of the fcc-LuH 3 produced in this study with the reported LuH 3±x N y , [11] which is actually LuH 2 .Each diffraction peak of fcc-LuH 3 exhibits a leftward shift in comparison to LuH 2 , indicating that the diffraction peaks of fcc-LuH 3 have a larger dspacing, i.e., fcc-LuH 3 has a larger lattice parameter (Figure 1c).The refined lattice parameter of fcc-LuH 3 is a = 5.156(1) Å, which is noticeably larger than a = 5.033 Å of LuH 2 .An earlier study indicates that the lattice parameter of fcc-LuH 3 extrapolated to ambient conditions through high-pressure volume is 5.12(2) Å, [40] a value closely resembling the 5.156(1) Å found in this study.Moreover, XRD exhibits limited sensitivity to hydrogen occupation, potentially allowing for dislocations within the material leading to non-stoichiometric composition, i.e., LuH 3-x , while still showing the overall fcc symmetry.The discussion about hydrogen occupations will be presented in the subsequent section.
In previous works, yttrium hydrides present comparable results, with two distinct compounds of fcc-YH 3 and hcp-YH 3 .The fcc-YH 3 is synthesized through a transformation to the hcp-YH 3 structure under conditions of high temperature and pressure, and it can be quenched to ambient conditions. [43,44]Despite the instability of the fcc-YH 3 at ambient pressure, it has been noted that high-temperature and high-pressure conditions play a crucial role in maintaining the presence of high-pressure phase fcc-YH 3 at ambient pressure.

Theoretically Thermal and Dynamical Stability of fcc-LuH 3
Theoretical calculations were performed on the fcc-LuH 3 compound, utilizing density functional theory (DFT).At 0 K, both LuH 2 and hcp-LuH 3 exhibit thermal stability, as indicated by their positions on the convex hull.However, fcc-LuH 3 is situated above the convex hull, with an enthalpy of 86 eV atom −1 higher than that of ground state hcp-LuH 3 , indicating fcc-LuH 3 is metastable (Figure S2).The calculated phonon dispersion of fcc-LuH 3 shows severe imaginary frequencies across the entire Brillouin zone at 0 K.These were obtained via the real-space supercell approach, considering solely interatomic harmonic interactions.The presence of imaginary frequencies implies lattice instability (Figure S3, Supporting Information), which is consistent with previous theoretical works. [11,14,45]However, it is important to note that anharmonicity corrections are particularly significant for hydrides, i.e., the zero-point vibration energy of hydrogen atoms can even modify the ground state structure.The interatomic anharmonic interactions may play a substantial role and likely need to be taken into account at finite temperatures.We used temperaturedependent effective potential (TDEP) to obtain finite-temperature renormalized phonon spectra by extraction ab initio molecular dynamics (AIMD) data.We conducted an AIMD simulation of fcc-LuH 3 using 128-atom supercells at 300 K with experimental lattice parameter (a = 5.156 Å).No evidence of phase transition was observed during 60 ps AIMD simulations (Figure 2a).We found that the system pressure fluctuated slightly at ≈0 GPa throughout the simulation (Figure 2b), implying the reliability of the AIMD simulation.Most importantly, no imaginary frequencies were observed in the phonon dispersion at 300 K (Figure 2c), demonstrating the dynamic stability of fcc-LuH 3 at ambient conditions.At a low temperature of 50 K, the structure of fcc-LuH 3 also maintains dynamic stability (Figure S4, Supporting Information).Figure 2d depicts the trajectories of fcc-LuH 3 , indicating vigorous movement of hydrogen atoms over a large area.A systematic study on the temperature and anharmonic lattice effects on lutetium trihydride is noted in the literature. [45]Finite temperatures are found to be imperative for stabilizing the fcc-LuH 3 phase, with dynamic stability observed above 200 K. Considering temperature, there is a significant expansion in lattice parameter.Our calculations using TDEP align with results obtained through stochastic self-consistent harmonic approximation (SSCHA).Owing to the weak X-ray scattering cross section of H, XRD does not provide constraints on the crystallographic position of H atoms.The H positions are also determined by geometry optimization of DFT calculation.Two types of hydrogen atoms are identified in fcc-LuH 3 : octahedral hydrogen (H O ) atoms located at the center of Lu octahedra, with Wyckoff position 4b (1/2,1/2,1/2), and tetrahedral hydrogen (H T ) atoms positioned at the center of Lu tetrahedra, with Wyckoff position 8c (1/4,1/4,1/4).

Synthesis of LuH 2
The synthesis of LuH 2 has been the subject of considerable investigation in recent studies. [12,13]In an effort to explore the formation of LuH 2 under high-pressure conditions, we conducted high-pressure experiments at extreme temperatures and pressures utilizing LVP.Lu pieces were selected as starting materials, and mixed powder of NH 4 Cl:CaH 2 (2:8) served as the solid hydrogen source.The synthesis of LuH 2 was accomplished under conditions of 3 GPa and 500 °C for a duration of 5 h.The XRD diffraction pattern shows a typical fcc structure of LuH 2 (Figure S5, Supporting Information).The refinement parameter, determined a = 5.036 (1) Å, was found to be in accordance with recently reported results for LuH 3±x N y [11] and LuH 2±x N y . [12,13]

Synthesis of hcp-LuH 3
Both LuH 2 and hcp-LuH 3 are stable on the convex hull.However, LuH 2 is the preferred structure due to insufficient hydrogen.It is hypothesized that the mixture powder of NH 4 Cl:CaH 2 (2:8) cannot provide enough hydrogen for this combination reaction, and CaH 2 may not undergo a replacement reaction with lutetium.A dual-phase of fcc-LuH 3 and hcp-LuH 3 is synthesized at 5 GPa and 800 °C for 1 h, using LuH 2 as the starting material and NH 3 BH 3 as the internal hydrogen source.The hcp-LuH 3 gradually transforms to fcc-LuH 3 from 800 to 1200 °C at 5 GPa (Figure 1a).To synthesize pure hcp-LuH 3 , Lu pieces were selected as the starting material and NH 3 BH 3 as the internal hydrogen source, given its superior ability to decompose hydrogen.The pure hcp-LuH 3 is synthesized under extreme conditions of 5 GPa and 1100 °C for 1 h. Figure S6 (Supporting Information) displays a typical XRD diffraction pattern of the hcp structure.The refinement parameters are a = 6.182(1)Å and c = 6.441(1)Å.

Elimination of Impurities of Lu and Lu 2 O 3
Considering potential impurities, we have ruled out the presence of Lu and Lu 2 O 3 with careful consideration (Figure 1d; Figure S7, Supporting Information).The lack of LuH 2 diffraction peaks indicates that all LuH 2 react with excess hydrogen and form LuH 3 .The hexagonal phase of Lu metal is known to be stable up to at least 40 GPa. [46]Our XRD pattern reveals the absence of Lu peaks, indicating that excess hydrogen facilitated the complete reaction of Lu with hydrogen, forming lutetium hydrides.On the other hand, the cubic phase of Lu 2 O 3 remains stable up to 12 GPa, undergoing a transformation to a monoclinic phase at higher pressures. [47,48]In our observations, the monoclinic phase of Lu  S9, Supporting Information).Because the XRD peaks are too weak, the impurities could not be identified.Here we assume that the impurities might be lutetium oxides or hydroxides since our synthesized fcc-LuH 3 is pure and it's probable that these impurities will be reduced by hydrogen and transformed into hydrides through reactions.

Comparison of Colors, Crystal Structure, and Lattice Parameters between Lu and Lutetium Hydrides
Commercially available Lu pieces and LuH 2 powder were used as starting materials.The Lu pieces exhibit a metallic silver color (Figure 3a), while LuH 2 synthesized under high-temperature and high-pressure conditions displays a bright blue color (Figure 3b).Both hcp-LuH 3 and fcc-LuH 3 are black and dark black respectively, each with a metallic sheen (Figure 3c,d).Lu possesses a hexagonal crystal structure with a P6 3 /mmc space group (Figure 3e).LuH 2 has a fcc structure with an Fm 3m space group, with H atoms occupying the interstices of Lu sublattice tetrahedrons (Figure 3f).Hcp-LuH 3 has a hexagonal structure with a P 3c1 space group (Figure 3g).Fcc-LuH 3 has an fcc structure with Fm 3m space group, H atoms occupy the interstices of Lu sublattice tetrahedrons and octahedrons.The phase transition sequence of high-temperature and high-pressure synthesis is depicted in Figure 3e-h.Lattice parameters and unit cell volume are presented in Figure 3i,j, illustrating a gradual increase in the volume of unit cells from Lu to LuH 2 to hcp-LuH 3 due to hydrogen absorption.However, there is a 2.61% collapse in the unit cell volume from 35.19(2) Å 3 f.u−1 .for hcp-LuH 3 to 34.27(2) Å 3 f.u.−1 for fcc-LuH 3 .Figure 3k visually represents the hydrogen-induced volume expansion, with ΔV/H values of 1.23 Å 3 f.u.−1 for LuH 2 and 1.90 Å 3 /f.u. for hcp-LuH 3 .Due to the volume collapse from hcp-LuH 3 to fcc-LuH 3 , the volume expansion ΔV/H is reduced to 1.59 Å 3 /f.u. Figure 3l

Determination of Nitrogen Doping in fcc-LuH 3
The N-doped LuH 3 ±xNy reported by Dasenbrock-Gammon et al. is identified as a dual-phase of LuH 2 and LuN, based on the XRD patterns and the color of the sample.In our study, we also detected the LuN phase in the fcc-LuH 3 sample when only the surface of the sample was cleaned (Figure S10, Supporting Information).The LuN, with a lattice parameter of a = 4.753(1) Å, aligns with the recent work. [11]It forms readily on the surface of the fcc-LuH 3 sample due to the decomposition of NH 3 BH 3 .Upon meticulous abrasion and cleaning of the sample surface, we successfully obtained pure fcc-LuH 3 samples (Figure 1b; Figure S1, Supporting Information).Energy-dispersive X-ray spectroscopy (EDS) was performed on fcc-LuH 3 samples.The EDS spectrum is in agreement with the reported LuH 3±x N y and shows a weak peak from nitrogen and indicates a slight nitrogen doping in fcc-LuH 3 (Figure 4a).Given the facile formation of LuN, we attribute this doping phenomenon to the presence of LuN. Figure 4b,c shows a scanning electron microscope (SEM) image and EDS mapping of a cross-section of fcc-LuH 3 , respectively.The EDS mapping reveals the spatial distribution of nitrogen in our fcc-LuH 3 sample and illustrates that nitrogen is widespread homogeneously in the sample with an average nitrogen composition of 1.3 wt.%.Despite theoretical predictions of various metastable Lu-N-H compounds, such as Lu 8 H 21 N and Lu 2 H 5 N, with lattice parameters consistent with LuH 2 , [15,19,49] quantifying the N content and doping structure in our investigation is a challenge.

The Hydrogen Content of fcc-LuH 3
To quantify the hydrogen content in the synthesized fcc-LuH 3 , we utilized both temperature-programmed desorption (TPD) and Nuclear Magnetic Resonance (NMR) measurements.These techniques provide semi-quantitative evaluations of the hydrogen content.To investigate the thermal desorption behavior of the sample, a TPD experiment was conducted under a helium gas flow.Two prominent peaks were clearly observed in the temperature range of approximately 300-440 and 550-950 °C, respectively, which indicates hydrogen release with temperature increasing (Figure 5a).The area ratio of low and high-temperature peaks was ≈1:2, indicating a correlation with H O and H T sites, respectively.Notably, H O atoms exhibited lower stability, evidenced by their release at lower temperatures compared to H T atoms.The 1 H-NMR spectroscopy served as a tool for the investigation and analysis of hydrogen occupancy.The 1 H-NMR spectrum of fcc-LuH 3 , as illustrated in Figure 5b, revealed distinct chemical shifts at +0.1 and +5.4 ppm.The two H chemical shifts suggest an association with H O and H T sites, respectively, aligning consistently with the outcomes of TPD results.
The observed broad and extensive peak band is attributed to the presence of a paramagnetic Lu ion.Consequently, the integration of the peaks to determine the area and subsequently estimate the ratio of the two hydrogen atom sites becomes challenging.Based on the comprehensive analysis involving TPD and NMR, we have deduced that the fcc Lu hydride obtained under high-temperature and high-pressure synthesis corresponds to fcc-LuH 3 .

The Absence of Superconductivity in fcc-LuH 3 at Ambient Conditions
The non-superconductivity of fcc-LuH 3 at ambient conditions was confirmed through low-temperature electrical and magnetic measurements.Following the successful synthesis of the polycrystalline sample, its electrical and magnetic properties were analyzed using a Physical Property Measurement System (PPMS).exhibiting the typical diffraction pattern of fcc-LuH 3 (Figure S12, Supporting Information).

Conclusion
In conclusion, we have successfully synthesized bulk lutetium hydrides of LuH 2 , hcp-LuH 3 , and fcc-LuH 3 , and constructed a synthesis phase diagram.The high-pressure phase fcc-LuH 3 is retained at ambient conditions through a high-temperature and high-pressure method using LVP.DFT calculations of lattice dynamics with anharmonic and temperature effects confirm that fcc-LuH 3 is stable at ambient conditions.The hydrogen content of fcc-LuH 3 is confirmed through the TPD and NMR methods.Low-temperature electrical and magnetic measurements reveal the absence of superconductivity in fcc-LuH 3 under ambient conditions.This study establishes a comprehensive synthesis strategy for lutetium hydrides, and this approach enhances our understanding of the high-temperature and high-pressure method used in hydrides with superconductivity.

Figure 1 .
Figure 1.XRD patterns of the synthesized lutetium hydride samples.All XRD patterns are obtained utilizing Cu K radiation ( = 1.5406Å) at ambient conditions.a) XRD patterns corresponding to various synthetic conditions.The phases of fcc-LuH 3 and hcp-LuH 3 are indicated by pink dots and blue diamonds, respectively.b) Experimental XRD pattern and Rietveld refinement of fcc-LuH 3 .The experiment data, refinement result, and residues are denoted in black circles, pink line, and gray line, respectively.The expected positions of diffraction peaks for fcc-LuH 3 are indicated by pink ticks.c)Comparison between reported LuH 3±x N y[11] and fcc-LuH 3 .d) Indexing of sample and identification of impurities.The gray circles, pink line, blue line and orange line represent the experimental XRD pattern, simulated XRD of fcc-LuH 3 , simulated XRD of hcp-LuH 3 , and LuN, respectively.The expected positions of diffraction peaks for fcc-LuH 3 , hcp-LuH 3 , and LuN are marked by pink, blue, and orange.
Figure 1.XRD patterns of the synthesized lutetium hydride samples.All XRD patterns are obtained utilizing Cu K radiation ( = 1.5406Å) at ambient conditions.a) XRD patterns corresponding to various synthetic conditions.The phases of fcc-LuH 3 and hcp-LuH 3 are indicated by pink dots and blue diamonds, respectively.b) Experimental XRD pattern and Rietveld refinement of fcc-LuH 3 .The experiment data, refinement result, and residues are denoted in black circles, pink line, and gray line, respectively.The expected positions of diffraction peaks for fcc-LuH 3 are indicated by pink ticks.c)Comparison between reported LuH 3±x N y[11] and fcc-LuH 3 .d) Indexing of sample and identification of impurities.The gray circles, pink line, blue line and orange line represent the experimental XRD pattern, simulated XRD of fcc-LuH 3 , simulated XRD of hcp-LuH 3 , and LuN, respectively.The expected positions of diffraction peaks for fcc-LuH 3 , hcp-LuH 3 , and LuN are marked by pink, blue, and orange.

Figure 2 .
Figure 2. The thermal and dynamic stability of fcc-LuH 3 at ambient conditions.a) Convex hull of Lu-H system at 300 K. b) Energy minimization for molecular dynamics simulation.The inset image is the crystal structure after MD simulation.c) Anharmonic phonon dispersions of fcc-LuH 3 at 0 GPa and 300 K. d) AIMD trajectories of fcc-LuH 3 at 0 GPa and 300 K. H-ions are represented with small green spheres, and Lu ions are shown with red spheres.
FigureS7, Supporting Information).The lack of LuH 2 diffraction peaks indicates that all LuH 2 react with excess hydrogen and form LuH 3 .The hexagonal phase of Lu metal is known to be stable up to at least 40 GPa.[46]Our XRD pattern reveals the absence of Lu peaks, indicating that excess hydrogen facilitated the complete reaction of Lu with hydrogen, forming lutetium hydrides.On the other hand, the cubic phase of Lu 2 O 3 remains stable up to 12 GPa, undergoing a transformation to a monoclinic phase at higher pressures.[47,48]In our observations, the monoclinic phase of Lu 2 O 3 was not detected, thus ruling out its presence.Although the main peak positions of cubic Lu 2 O 3 closely resemble those of fcc-LuH 3 , there exists a discernible difference between them, ≈0.2°.The larger lattice parameter of Lu 2 O 3 (a = 8.4 Å) results in additional diffraction peaks, such as those at 23°and 45°.The absence of these peaks further substantiates the absence of Lu 2 O 3 in the sample.We also examined the purity of the starting materials Lu and LuH 2 , and there are only tiny traces of impurities (FiguresS8 and S9, Supporting Information).Because the XRD peaks are too weak, the impurities could not be identified.Here we assume that the impurities might be lutetium oxides or hydroxides since our synthesized fcc-LuH 3 is pure and it's probable that these impurities will be reduced by hydrogen and transformed into hydrides through reactions.

Figure 4 .
Figure 4. Elemental composition of fcc-LuH 3 at ambient conditions.a) EDS spectra of synthesized fcc-LuH 3 .b,c) SEM image and EDS mapping image for N element at same sample surface area of LuH 3 .

Figure 6 .
Figure 6.Low temperature electrical and magnetic measurement of fcc-LuH 3 .a) Electrical resistivity measurement in the temperature range of 2 to 300 K. b) The magnetic susceptibility (left axis, filled symbols) and inverse magnetic susceptibility (right axis, open symbols) normalized per mole for fcc-LuH 3 .