X-ray-diffraction and electrical-transport imaging of superconducting superhydride (La,Y)H_10

Domain: physics
Published: 2025-12-18
Editorial outcome: minor_revision

Abstract
Understanding how microscopic structural domains govern macroscopic electronic properties is central to advancing hydride superconductors, yet such correlations remain poorly resolved under pressure. We report the synthesis and characterization of (La0.9Y0.1)H10 superhydrides exhibiting coexisting cubic Fm3\bar{m} and hexagonal P63/mmc clathrate phases observed over the pressure range from 168 GPa down to 136 GPa. Using synchrotron-based X-ray diffraction imaging at the upgraded Advanced Photon Source, we spatially resolved μm-scale distributions of these phases, revealing structural inhomogeneity across the sample. Four-probe resistance measurements confirmed superconductivity with two distinct transitions: an onset at 244 K associated with the cubic phase and a second near 220 K linked to the hexagonal phase. Notably, resistance profiles collected from multiple current and voltage permutations showed variations in transition width and onset temperature that correlated with the spatial phase distribution. These findings demonstrate a direct connection between local structural domains and superconducting behavior.

Introduction
Dense hydrides exhibiting very high-temperature superconductivity are established as an extraordinary class of new materials of great fundamental and potential applied interest1. The remarkable quantum phenomena of these materials arise from the potential of dense hydrogen lattices to mimic atomic metallic hydrogen, which has long been predicted to exhibit room-temperature superconductivity under extreme pressures2,3. Advances in computational methods combined with experimental diamond anvil cell (DAC) techniques led to the discovery of rare-earth metal superhydrides with superconducting critical temperatures (T_c's) approaching room temperature at megabar (>100 GPa) pressures4–10. In particular, lanthanum decahydride (LaH10) was found to superconduct at temperatures up to 260 K at 188 GPa in the cubic Fm3\bar{m} clathrate phase8,9. This structure features a three-dimensional hydrogen cage network surrounding La atoms, enabling the strong electron–phonon coupling origin of this very high T_c superconductivity4–7. Notably, the near-room-temperature superconductivity was confirmed and has been independently reproduced by a growing number of groups10–12.

Recent research has focused on strategies to enhance T_c and stability of these materials by chemical substitution to form ternary and higher order phases13–21. Theoretical predictions for La superhydrides indicate that substituting a fraction of La with smaller elements such as yttrium (Y) chemically pre-compresses the lattice, modify phonon spectra, and extend the stability field of the clathrate phase13–15. In particular, (La,Y)H10 phases are predicted to retain the high symmetry of LaH10 while gaining enhanced structural stability through Y incorporation13–16. Experimental work has shown T_c values up to 253 K for (La0.8Y0.2)H10 at 183 GPa22, yet a comprehensive understanding of the pressure–composition phase space remains incomplete22,23.

Moreover, the coexistence of multiple structural phases together with stress-strain gradients and differences in synthesis conditions, in these and related samples further raises questions about how local structural heterogeneity affects superconducting behavior6,9,10,21,22. Traditional bulk measurements obscure this complexity by averaging over the entire sample volume, thereby masking domain-level interactions and local phase variations24,25. Resolving such structure–property relationships requires techniques that can spatially correlate structural and electronic properties, particularly under the extreme conditions in DAC experiments, where the length scales of structure–property variations fall in the μm to sub-μm range26.

Synchrotron-based scanning X-ray diffraction microscopy (SXDM) has emerged as a powerful tool for probing structural heterogeneity in compressed materials26–29. Enabled by the upgraded Advanced Photon Source (APS-U), SXDM offers high spatial resolution and sensitivity to local symmetry variations, strain, and phase coexistence. Combined with X-ray diffraction imaging (XDI) for visualization, this approach provides a direct view of heterogeneous states that remain hidden in conventional diffraction measurements26,29. Complementing this microstructural information, four-probe direct-current (DC) resistance measurements with multiple current/voltage probe permutations enables spatial sampling of superconducting behavior across a sample30. Although originally designed for homogeneous sheets, the van der Pauw (VDP) method can be adapted to probe inhomogeneous materials and correlated with spatially resolved XDI measurements to capture broadened or multi-step transitions arising from structural inhomogeneity30,31. Such spatially resolved transport techniques have yet to be applied to hydrides owing to the challenges of DAC experiments.

In this work, we synthesized (La0.9Y0.1)H10 at high pressure and employed SXDM in combination with multi-channel electrical transport measurements. Using a ~1 μm focused X-ray beam at HPCAT-U, SXDM revealed μm-scale structural inhomogeneity via XDI and correlated it with local superconducting transitions captured via spatially resolved resistance measurements. This represents the first direct correlation between crystal structure and superconductivity in hydrides. Two distinct superconducting onsets near 244 K and 220 K were found to correspond to regions dominated by the cubic Fm3\bar{m} and hexagonal P63/mmc clathrate phases, respectively, enabling unambiguous assignment of T_c values to specific structures. Yttrium substitution stabilizes the coexistence of both phases down to 136 GPa, without raising T_c above that of pure LaH10. Overall, our findings establish a clear, spatially resolved link between structural domains and superconducting behavior in hydrides.

Results
Structural characterization of (La,Y)H10
Prior to laser heating, the La0.9Y0.1 alloy compressed together with ammonia borane (NH3BH3) to high pressure adopted a distorted-cubic Fmmm structure32. At 158 GPa (DAC #1, Fig. 1), the X-ray diffraction (XRD) pattern showed spotty diffraction rings, a narrower accessible 2θ range at the longer wavelength, and additional peaks from Pt electrodes and the sample environment, which obscured weaker La-Y reflections. By contrast, at 172 GPa (DAC #2, Fig. S1), the shorter wavelength, absence of electrode and gasket contributions, and improved powder averaging yielded well-resolved La-Y reflections. A direct comparison of La0.9Y0.1 at 158 and 172 GPa is provided in Fig. S2, showing that the observed differences in the number and shape of peaks arise from experimental factors rather than intrinsic structural changes. In addition, the broader and asymmetric (002) profile at 172 GPa reflects pressure-induced lattice distortions and deviatoric stress, consistent with prior observations in elemental La under compression32.

Following laser heating, the diffraction pattern changed significantly, with alloy peaks disappearing and new reflections emerging from hydrogen-rich phases (Figs. 1 and S1), confirming successful hydrogenation. At 158 GPa (Fig. 1), the pressure relaxed to 153 GPa after laser heating, and the diffraction pattern revealed the formation of two clathrate structures: cubic Fm3\bar{m} and hexagonal P63/mmc, both of which have been previously reported in La–H and La–Y–H systems10,22. Optical images of the sample before and after laser heating are provided in Fig. S3. A second synthesis performed at 172 GPa (Fig. S1) produced the same two phases, demonstrating reproducibility across independent runs.

Le Bail refinements of the hydrogenated sample at 153 GPa yielded lattice parameters of a = 5.15(1) Å for the Fm3\bar{m} phase and a = 3.71(1) Å, c = 5.54(1) Å for the P63/mmc phase, corresponding to unit cell volumes of 136.6(1) Å³ and 66.1(1) Å³, respectively (Fig. 1, top panel). These values are comparable to those reported for undoped LaH10 at similar pressures6, with slight reductions in volume consistent with the expected lattice contraction from yttrium substitution14,22. As shown in Fig. S4, this systematic reduction provides direct structural evidence that ~10% Y is incorporated into the clathrate framework. Notably, no diffraction peaks from secondary LaH_n or YH_n phases were observed, indicating that Y substitution remains within the solubility limit for forming a single-phase clathrate or a mixed-phase clathrate solid solution13,22. Volume-based stoichiometry analysis yielded ~10 H per metal atom for both the cubic and hexagonal phases, consistent with the nominal (La0.9Y0.1)H10 composition (Supplementary Note 1).

To assess the stability of the observed phases during decompression, additional XRD measurements were performed on both samples. In DAC #1, the sample was gradually decompressed from 153 GPa, and an XRD was collected at 136 GPa from the sample center, with Fig. S5 illustrating the collection positions corresponding to the patterns in Figs. 1 and S6. At 136 GPa, both the cubic and hexagonal phases were still observed (Figs. S6 and S7). Fig. S7 presents XRD patterns of (La,Y)H10 at 153 and 136 GPa in DAC #1, collected from comparable positions in the sample chamber to confirm the persistence of both phases across this pressure range. At 136 GPa, minor distortions in the Fm3\bar{m} phase were also evident across different regions of the sample (Fig. S8), likely reflecting local pressure gradients and lattice relaxation. This pressure lies near the known structural phase boundary of undoped LaH10, where transitions to lower-symmetry structures such as R\bar{3}m or C2/m typically occur6,12. The persistence of both clathrate phases at 136 GPa suggests that Y substitution extends the structural stability of LaH10-type phases to lower pressures than observed in the undoped system6,12.

In DAC #2, after initial synthesis at 172 GPa and characterization at 168 GPa, the sample was decompressed to 161 GPa. At this pressure, both the Fm3\bar{m} and P63/mmc phases are clearly present (Fig. S4), in contrast to binary La hydrides where the cubic phase typically dominates6,10. The coexistence of both clathrate phases at this stage of decompression underscores the role of Y substitution in stabilizing structural polymorphism beyond that observed in undoped LaH106,9,10,12. The repeated observation of both phases across the 168−136 GPa range demonstrates persistent coexistence rather than distinct, pressure-stabilized states. Their simultaneous presence indicates that ~10% Y substitution promotes polymorphic coexistence under our synthesis and decompression conditions, rather than favoring a single dominant structure. This contrasts with LaH10, which transforms to lower-symmetry structures upon decompression6,9–12. The spatial variation and distribution of the cubic and hexagonal domains, further examined through diffraction imaging, highlight the complexity of phase coexistence near the clathrate stability boundary.

The pressure–volume (P–V) behavior of (La0.9Y0.1)H10, shown in Fig. S4, generally follows the trend reported for undoped LaH10, with modest phase-specific deviations that point to non-uniform compressibility and local strain effects. Similar trends were reported for (La0.8Y0.2)H10 synthesized at higher pressures22, where clathrate structures remained stable without decomposition. These results demonstrate that partial Y substitution preserves the hydrogen cage framework of LaH10 while extending phase coexistence across a broader pressure range22,23. Such structural robustness provides the basis for linking local phase heterogeneity to superconducting behavior, as discussed in the following sections.

Spatial mapping of structural domains via SXDM and XDI
Spatial phase mapping at 153 GPa revealed μm-scale coexistence of Fm3\bar{m} and P63/mmc clathrate domains. Using SXDM at HPCAT-U, diffraction patterns were collected across a 30 × 30 μm² region with ~3 μm steps. XDI-based analysis identified phase-specific intensity distributions by integrating the first two Bragg reflections unique to each structure, producing two-dimensional maps of local phase domains. Figure 2 shows XDI maps at 153 GPa resolving the FCC and HCP phases, correlated with the 2D X-ray scan and the optical image of the sample after laser heating. Image analysis of the domain maps indicates that the cubic phase covers approximately 42% of the mapped region, while the hexagonal phase accounts for 58%.

The Fm3\bar{m} phase is localized in discrete clusters near Pt leads #2, #3, and #4, with the largest fraction around lead #2 where excess ammonia borane was present (Fig. 2A). By correlating optical images before and after laser heating (Fig. S3) with the XDI maps, the interface between the sample and ammonia borane is identified between leads #2 and #3, consistent with regions of higher temperature and greater hydrogen availability favoring the Fm3\bar{m} phase, while regions farther from this interface exhibit a higher fraction of the P63/mmc phase, forming a continuous matrix between leads #1 and #4 (Fig. 2A). These correlations indicate that the observed structural inhomogeneity most likely arises from variations in hydrogen content and laser heating geometry9,10,12. As shown in Fig. S9, the local pressure gradient does not correlate with FCC/HCP boundaries, indicating that pressure is not the dominant factor in domain arrangement at synthesis conditions. While phase coexistence is common in multiphase hydride systems10,22, the ability to directly image μm-scale domain structure at this resolution provides a valuable framework for linking local structural environments with superconducting behavior, as discussed in the following sections.

Additional raster scans were performed at 136 GPa after decompression (Fig. 2A). Two maps, a broader 50 × 50 μm² grid and a focused 15 × 15 μm² grid, were collected from the same central region and are shown in Fig. 2. In the larger scan, the Fm3\bar{m} phase exhibits reduced intensity near Pt lead #4 compared to the 153 GPa map, while the P63/mmc phase remains more uniformly distributed across the sample chamber. The composite map again shows dominance of the hexagonal phase between leads #1 and #4, and clustering of the cubic phase around leads #2 and #3. The smaller scan offers a higher-resolution view of the local phase distribution and confirms the persistence of structural heterogeneity upon decompression.

The use of a micro-focused beam combined with SXDM enabled spatial mapping of phase-separated regions within the sample that may be challenging to resolve using conventional bulk XRD techniques. The spatial resolution in this study was chiefly governed by the ~1 μm beam size of APS-U and the small raster step size used during SXDM. Together, these parameters enabled fine spatial sampling across the sample chamber, allowing detection of μm-scale structural variations. Prior applications of XDI have demonstrated its effectiveness in visualizing structural gradients and preferred nucleation patterns in FeH_x33, H3S34, H335, and La–Y–Ce–H36 systems. However, earlier studies often had overlapping grids or had limited phase assignment capability due to reduced flux or detector sensitivity. The ability to resolve discrete Fm3\bar{m} and P63/mmc domains across the sample provides unique insight into structural heterogeneity. These spatially resolved maps form the foundation for linking local phase composition with superconducting behavior, as discussed below.

Superconductivity in coexisting phases
Four-probe DC resistance measurements were carried out on the (La0.9Y0.1)H10 sample in DAC #1 following structural characterization. As shown in Fig. 3A, resistance vs. temperature curves collected during warming cycles at four pressures between 153 and 136 GPa consistently display two distinct superconducting transitions. At 153 GPa, the first resistance drop begins at T_{c,onset} = 244 K, followed by a second transition near T_{c,onset} = 220 K (Fig. S10). The total transition width of ΔT ≈ 28 K is unusually broad for DC transport measurement and is characteristic of phase coexistence and electronic heterogeneity37.

To further investigate the origin of these transitions, the temperature dependence of eight partial resistance traces [R_{ab,cd}(T)] were collected using the standard VDP permutations, involving four voltage pairs and two current paths, as shown in Fig. 4. Each measurement configuration was overlaid onto the composite XDI phase map, enabling direct spatial correlation between structural domains and electronic behavior. Notably, configurations such as R_{34,12}, R_{34,21}, R_{41,23}, and R_{41,32} (Fig. 4B, D) exhibited a sharp superconducting drop near 240 K, with a narrow transition width of ΔT < 10 K. These measurements probed regions between electrodes #3 and #4 and between #4 and #1, with voltage recorded across electrodes #1 and #2 or #2 and #3. Based on the spatial maps shown in Fig. 2, these current–voltage pathways intersected domains where the Fm3\bar{m} phase was concentrated, particularly near electrode #2. This spatial correlation supports the assignment of the higher-temperature superconducting transition to the Fm3\bar{m} clathrate phase.

In contrast, other partial resistance configurations, such as R_{12,34}, R_{12,43}, R_{23,41}, and R_{23,14} (Fig. 4A, C), exhibited broader, two-step transitions, with onsets near 241 K and 218 K, respectively. These configurations passed through regions where both Fm3\bar{m} and P63/mmc phases were present, with a higher fraction of the hexagonal phase observed between electrodes #1 and #4. The lower-temperature transition was thus attributed to the P63/mmc clathrate phase. This interpretation is consistent with previously reported superconducting transition temperatures in undoped and Y-substituted LaH10 systems (Fig. 3B)9,10,22. Notably, both transitions occurred at lower onset temperatures than in pure LaH10, where T_c typically exceeds 250 K under similar pressures9–11. The observed T_c suppression provides complementary evidence of successful Y incorporation and its influence on the electronic structure, particularly through added intermediate-frequency phonon modes15,22. Furthermore, the direct correlation between partial resistances and spatial phase distribution underscores the utility of structural mapping for interpreting superconducting transport behavior in mixed-phase systems.

To evaluate the pressure dependence of superconductivity in the coexisting clathrate phases of (La0.9Y0.1)H10, resistance measurements were performed during decompression from 153 to 136 GPa (Fig. 3A). Across this pressure range, the resistance–temperature profiles consistently displayed two distinct superconducting transitions, indicative of phase coexistence. Additional support for superconductivity comes from current–voltage (I–V) curve measurements at 146 and 136 GPa (Fig. S11), which exhibit nonlinear behavior below ~230 K at 146 GPa. Notably, the overall resistance behavior and partial resistance traces remained similar down to 142 GPa (Fig. S12). Consistent with measurements at higher pressure, all transition temperatures at each pressure during decompression occurred within experimental uncertainty across the eight configurations, confirming that the observed features are intrinsic to the sample. At 136 GPa, a marked departure from the previous R–T profiles were observed (Fig. 3). The two-step superconducting features became less distinct, and the transition width narrowed (ΔT ~ 20 K), particularly in partial resistances such as R_{12,34}, R_{12,43}, R_{23,41}, and R_{23,14} (Fig. S13). These current paths intersect regions where the spatial phase map (Fig. 2) indicated reduced Fm3\bar{m} intensity near Pt lead #4, consistent with diminished cubic phase contributions at lower pressures.

Meanwhile, traces such as R_{34,12}, R_{34,21}, R_{41,23}, and R_{41,32} still exhibited sharp superconducting drops, with more pronounced secondary features. These traces traverse regions around Pt leads #2 and #3, where the Fm3\bar{m} phase remained spatially concentrated even after decompression. The persistence of sharp transitions in these configurations suggests that residual cubic domains retain superconductivity near 228 K, albeit with reduced volume fraction. Structural data at 136 GPa revealed minor distortions in Bragg positions of the Fm3\bar{m} phase (Fig. S8), as previously discussed in the structural characterization section. These distortions likely reflect lattice relaxation and non-uniform pressure gradients, and correlate with the observed suppression of the higher-T_c onset from 238 K at 142 GPa to 228 K at 136 GPa, a more rapid decline than typically reported in binary LaH10 systems9,10,12. While pure LaH10 transitions to lower-symmetry C2/m or R\bar{3}m phases near this pressure, no such transformations were evident here6,12, suggesting that the observed T_c suppression arises from phase dilution, lattice strain, and microstructural inhomogeneity, mechanisms known to influence superconductivity in clathrate hydrides9,10,12,38.

Methods
Sample preparation and high-pressure synthesis
A La–Y alloy with a nominal composition of La0.9Y0.1 was obtained from Ames Laboratory, prepared by arc melting high-purity La (93.36%) and Y (6.64%) metals under an argon (Ar) atmosphere40. Scanning electron microscopy–Energy-dispersive X-ray spectroscopy (SEM–EDS) analysis at 5 µm resolution confirmed a uniform single-phase alloy with a measured composition of 92.33% La and 7.67% Y (Table S1, Fig. S14). Ambient-pressure XRD likewise showed no evidence of phase segregation prior to loading (Fig. S15), confirming that the alloy was a homogeneous precursor. DACs equipped with double-beveled diamonds (~65 μm culet) were used for high-pressure synthesis and subsequent characterization. DAC #1 was configured for transport measurements: the Re gasket was electrically insulated from the sample by prefilling the chamber with a compressed cubic boron nitride (cBN) and epoxy mixture, followed by laser drilling to form the sample chamber. Thin platinum foils (~2 µm thick) were manually positioned on the diamond culet to form electrical contacts in a VDP geometry for four-probe DC resistance measurements30, with secondary connections made externally using fine copper wires and silver epoxy. DAC #2 employed a Re gasket for synthesis experiments.

Sample loading was performed in an argon-filled glove box to avoid air exposure. A piece of the La–Y alloy was placed in direct contact with ammonia borane, which acted as both the hydrogen source and the XRD measurements collected at intermediate pressures. Pressure was determined from the Raman shift of the diamond edge42,43, representative spectra at different pressures are shown in Fig. S16. In situ laser heating was performed at 158 GPa on DAC #1 at beamline 16-ID-B of the APS-U; this sample was subsequently used for both XDI and transport measurements (Fig. 1). A second synthesis was carried out at 172 GPa using DAC #2 at beamline 13-ID-D of the APS, with results shown in Fig. S1. Laser heating in both cases was performed at the interface between the metal and ammonia borane using a modulated Yb fiber laser, delivering ~300 ms focused pulses, reaching estimated temperatures of 1200–1800 K44,45. Each synthesis involved multiple laser heating cycles, which ensured complete hydrogen uptake and phase formation.

Synchrotron X-ray diffraction and imaging
Synchrotron XRD measurements were performed at beamline 16-ID-B of the APS-U (DAC #1, λ=0.4859 Å at 158 GPa on the LH table and λ=0.4246 Å at 136 GPa on the GP table) and at beamline 13-ID-D of the APS (DAC #2, λ=0.3344 Å) at Argonne National Laboratory. Diffraction patterns were collected using PILATUS 2D area detectors and integrated into one-dimensional intensity profiles using DIOPTAS46. Structural parameters were extracted via Le Bail refinements using Jana200647,48. This approach was necessary due to spotty diffraction and overlapping contributions from multiple coexisting phases, some with partially known or unknown structural models.

At 13-ID-D, the pre-upgrade X-ray beam was focused to ~3.8 × 2.7 μm². At 16-ID-B, the beam profile improved significantly with the APS-U upgrade: the beam size was reduced from ~6.3 × 3.1 μm² (pre-upgrade) to ~1.4 × 1.2 μm² (post-upgrade), with enhanced brilliance and minimal tails. This improvement enabled high-resolution spatial mapping with minimal signal overlapping between adjacent positions.

To visualize spatial phase distributions and structural inhomogeneity, SXDM was performed at 16-ID-B by raster scanning the laser-heated region over a two-dimensional grid. Each scan consisted of an 11 × 11 array of diffraction patterns acquired with step sizes of 2–5 μm. The collected datasets were processed using the X-ray Diffraction Imaging (XDI) software26. For each scanned point, XDI converts the 2D diffraction pattern into a radial intensity profile and integrates the signal within user-defined 2θ regions of interest corresponding to specific Bragg reflections. The resulting integrated intensities were compiled into two-dimensional maps, where each pixel represents a scanned position. The color intensity in these maps reflects the relative strength of the selected reflection, providing a direct visualization of local domain structure, spatial phase distribution, and structural heterogeneity26,36.

Electrical transport measurements
After synthesis and XRD analysis, DAC #1 was transferred to a continuous-flow cryostat for temperature-dependent resistance measurements down to 80 K. Electrical resistance measurements were carried out at 153, 147, 142, and 136 GPa. Data was collected during both cooling and warming cycles; however, only the warming cycle (at ~1 K/min) was analyzed due to reduced thermal gradients upon the slow warmup reducing temperature uncertainty. Resistance measurements were performed using a Keithley 6220 current source (100 μA excitation), a 2182A nanovoltmeter, and a Keithley 7001 switching matrix to acquire voltages across multiple electrode configurations49. Current and voltage leads were permuted in the standard VDP configuration30. Measured partial resistances are then processed to account for thermoelectric offsets. Distinct drops in resistance indicate superconducting transitions that persist across the entire pressure range. Because the sample did not satisfy the assumptions required for extracting sheet resistivity (R_s) using the standard VDP equation, e^{-\pi R_{12,34} / R_s} + e^{-\pi R_{23,41} / R_s} = 1, primarily due to sample inhomogeneity, the resultant R_s values are not expected to represent the bulk electronic properties of a single phase. Nonetheless, VDP-averaged resistances are reported, as the superconducting transition is clearly observed (Fig. 3A). Correlations between individual partial resistances and the spatial phase distribution are explored in this work.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Please see the attached pdf version.", "reviewer_2": "The manuscript reports (La0.9Y0.1)H10 synthesized ≥150 GPa with coexisting cubic and hexagonal clathrate phases from 172 → 136 GPa, mapped by SXDM/XDI at APS-U with ~1 µm beam, and correlated to eight van der Pauw permutations showing two superconducting onsets (~244 K and ~220 K) that spatially associate with FCC-rich vs HCP-rich domains. The core contribution is the spatial co-analysis linking local structure to transport signatures in a mixed-phase superhydride—compelling and timely. A few minor comments need to be addressed before final acceptance. 1. To evaluate the homogeneity of the as-cast La-Y ingot, specify the grain size of the SEM-EDS in Table S1. How can you confirm the uniformity of the alloy, considering your sample size, ~30 um? Put a larger font of the scale bar in Fig. S2. 2. Evaluate the actual stoichiometry of FCC and hcp phases after laser heating. 3. Provide the Raman data demonstrating surplus hydrogen remained after LH. 4. Clarify pressure gradients across the chamber (e.g., diamond edge Raman at multiple azimuths) and map how they correlate with domain distribution."}, "author_response": "Reviewer #1: This paper reports the synthesis and characterization of (LaY)H10 superhydrides. Two coexisting cubic 𝐹m-3m and hexagonal 𝑃63/mmc phases were observed over the studied pressure range. The m-scale structural inhomogeneity was revealed and visualized via SXDM and XDI. Four-probe DC resistance measurements confirmed superconductivity with two distinct transitions. The first Tc is 244 K associated with the cubic phase and the second Tc near 220 K linked to the hexagonal phase. However, a few points need clarification before it can be recommended for acceptance. Response: We sincerely thank the reviewer for their thoughtful and encouraging summary of our work. We are especially grateful that they highlighted the synthesis, phase coexistence, and superconducting transitions in (La,Y)H₁₀, as well as the observation of µm-scale structural inhomogeneity via SXDM/XDI and the identification of two distinct superconducting transitions from four-probe resistance measurements. We truly appreciate the constructive suggestions and have carefully addressed each point in detail below. Comment #1: Why the number and shape of the XRD diffraction peaks are different at 158 GPa and 172 GPa for La0.9Y0.1? such as the peaks at 7, 10, and 13.5 degrees at 158 GPa. Response: We carefully compared the La Y diffraction patterns at 158 and 172 GPa and revised the 0.9 0.1 manuscript to clarify differences between the number and shape of the diffraction peaks. Three main factors contribute: (i) measurement geometry, since the 172 GPa data were collected at λ = 0.3344 Å at Sector 13-IDD of GSECARs and the 158 GPa data at λ = 0.4859 Å at Sector 16-IDB of HPCAT, resulting in different Q-ranges; (ii) microstructure, with the 172 GPa sample producing uniform powder rings, while the 158 GPa sample showed textured arcs that redistributed intensity; and (iii) sample environment, as the 158 GPa transport cell contained Pt electrodes, NH BH and 3 3 a c-BN+epoxy gasket, whose reflections overlapped with weak La peaks. These effects explain why fewer La reflections are visible at 158 GPa. We also clarified that peak-shape differences, such as broadening of the (002) reflection, are due to pressure-induced distortions and texture, which are well documented in high-pressure La studies1,2. Finally, we explicitly labeled Pt peaks and marked the weak features near 7° and 10° as unknown impurity reflections to avoid confusion. Changes in the manuscript: From Results – Structural Characterization of (La,Y)H 10 “At 158 GPa (DAC #1, Fig. 1), the diffraction pattern showed spotty diffraction rings, a narrower accessible 2θ range at the longer wavelength, and additional peaks from Pt electrodes and the sample-environment, which obscured weaker La-Y reflections. By contrast, at 172 GPa (DAC #2, Fig. S1), the shorter wavelength, absence of electrode and gasket contributions, and improved powder averaging yielded well-resolved La-Y reflections. A direct comparison of La Y at 158 0.9 0.1 and 172 GPa is provided in Fig. S2, showing that the observed differences in the number and shape of peaks arise from experimental factors rather than intrinsic structural changes. In addition, the broader and asymmetric (002) profile at 172 GPa reflects pressure-induced lattice distortions and deviatoric stress, consistent with prior observations in elemental La under compression.” From Methods – Sample Preparation and High-Pressure Synthesis “DAC #1 was configured for transport measurements: the Re gasket was electrically insulated from the sample by prefilling the chamber with a compressed cubic boron nitride (cBN) and epoxy mixture, followed by laser drilling to form the sample chamber. Thin platinum foils (~2 µm thick) were manually positioned on the diamond culet to form electrical contacts in a VDP geometry for four-probe DC resistance measurements3, with secondary connections made externally using fine copper wires and silver epoxy. DAC #2 employed a Re gasket for synthesis experiments. Optical images of the sample chambers for both DACs are shown in Fig. S2, and a schematic of the DAC assembly is provided in Fig. S3.” From Methods – Synchrotron X-ray Diffraction and Imaging “Synchrotron XRD measurements were performed at beamline 16-ID-B of the APS-U (DAC #1, λ = 0.4859 Å at 158 GPa on the LH table and λ = 0.4246 Å at 136 GPa on the GP table) and at beamline 13-ID-D of the APS (DAC #2, λ = 0.3344 Å) at Argonne National Laboratory.” From Figure 1 - XRD patterns and structural refinement of coexisting (La,Y)H phases 10 Figure 1: Bottom Panel: Experimental XRD patterns of La Y at 158 GPa before and after 0.9 0.1 laser heating. The pre-heating pattern corresponds to the distorted-cubic Fmmm phase. After laser heating, the diffraction pattern shows the formation of (La,Y)H₁₀ phases, consistent with the refined structures shown above. Reflections from Pt electrodes are explicitly labeled, while peaks marked with “*” correspond to unidentified or sample-environment contributions. Insets show representative 2D diffraction images for reference. From Figure S2 - Comparison of La Y samples at 158 and 172 GPa 0.9 0.1 Figure S2: Comparison of La₀.₉Y₀.₁ samples at 158 and 172 GPa. Left: Optical images of the loaded chambers in DAC #1 and DAC #2, illustrating differences in sample environment. Center: 2D diffraction images, showing spotty rings at 158 GPa and uniform powder rings at 172 GPa. Right: Integrated XRD patterns. At 158 GPa (DAC #1), additional reflections from the cell assembly are present: peaks at d ≈ 1.79 and 2.2 Å correspond to fcc-Pt, while broad features at d ≈ 2.80 and 4.0 Å are marked as impurity and likely arise from amorphous gasket contributions. At 172 GPa (DAC #2), the pattern is cleaner and dominated by La–Y reflections. Comment #2: Although the author used the Le Bail method for fitting, several peaks remain unknown, as shown in the figure below. Moreover, the fitting deviation for the 102 peak is excessively large. Could these peaks originate from a new structural phase? Additionally, the authors should provide the XRD diffraction pattern alongside the integrated intensity plot. Response: We carefully re-analyzed the diffraction data to address these points. The revised Le Bail refinements now explicitly account for the reflections near 13.5° and 15.5°, which originate from fcc-Pt electrodes. Other very weak reflections remain unidentified and are labeled as impurity peaks from sample-environment in the updated figures. Their intensities are too low and isolated to support assignment to a new structural phase. Similar minor impurity features have been reported in previous studies of La–H and La–Y–H superhydrides4,5. The apparent deviation in the 102 reflection is now minimized after re-refinement. Residual mismatches at this pressure (153 GPa) are consistent with nonhydrostatic stress and lattice distortions, which are known to broaden or slightly shift reflections in lanthanum under megabar conditions1. This does not indicate the presence of a new phase. To increase transparency, we updated the manuscript by (i) labeling Pt and impurity peaks in the Le Bail fits, and (ii) providing corresponding 2D diffraction images alongside the integrated intensity plots so that azimuthal distributions can be compared directly. Changes in the manuscript: From Figure 1 - XRD patterns and structural refinement of coexisting (La,Y)H phases 10 Figure 1: Top: XRD patterns and structural refinement of coexisting (La,Y)H₁₀ phases. Top: Experimental synchrotron XRD patterns and Le Bail refinements of the Fm-3m and P6 /mmc 3 (La,Y)H₁₀ phases at 153 GPa. The experimental data, fit, and residuals are shown in red, black, and gray, respectively. Refined lattice parameters for both phases are indicated. The peaks marked with “*” correspond to unidentified or sample-environment contributions. Insets show representative 2D diffraction images for reference. Comment #3: I suggest changing \"DAC#2\" to \"DAC#1\" in the main text to enhance clarity for readers. Response: We revised the Methods section to clarify the DAC numbering and improve readability. DAC #1 is now described as the transport cell, and DAC #2 as the synthesis-focused cell, with the corresponding beamline and wavelength details specified. Changes in the manuscript include: From Methods – Sample Preparation and High-Pressure Synthesis “DAC #1 was configured for transport measurements: the Re gasket was electrically insulated from the sample by prefilling the chamber with a compressed cubic boron nitride (cBN) and epoxy mixture, followed by laser drilling to form the sample chamber. Thin platinum foils (~2 µm thick) were manually positioned on the diamond culet to form electrical contacts in a VDP geometry for four-probe DC resistance measurements, with secondary connections made externally using fine copper wires and silver epoxy. DAC #2 employed a Re gasket for synthesis experiments.” From Methods – Synchrotron X-ray Diffraction and Imaging “Synchrotron XRD measurements were performed at beamline 16-ID-B of the APS-U (DAC #1, λ = 0.4859 Å at 158 GPa on the LH table and λ = 0.4246 Å at 136 GPa on the GP table) and at beamline 13-ID-D of the APS (DAC #2, λ = 0.3344 Å) at Argonne National Laboratory.” Comment #4: Why do the positions of the unknown peaks differ between 153 GPa and 136 GPa in DAC#2? What is the origin of these unknown peaks? Were the XRD patterns collected from the same sample location for these two measurements? The XRD diffraction pattern and micrograph of the collection positions should be provided. Response: We revised the manuscript to clarify the origin of these peaks and added new supplementary figures to show the measurement locations. Figure S5 now presents the XRD collection positions at 153 GPa and 136 GPa in DAC #1, corresponding to the patterns in Fig. 1 and Fig. S6. Figure S7 shows paired XRD patterns at 156 GPa and 136 GPa collected from equivalent positions, confirming the coexistence of cubic and hexagonal phases at both pressures. Figure S8 provides diffraction images from different regions at 136 GPa, highlighting distortions in the fcc lattice upon decompression. The apparent differences between the 153 GPa and 136 GPa patterns are explained by: Sampling location: the 153 GPa dataset was collected near the electrode region, where Pt reflections appear, whereas the 136 GPa dataset was collected at the sample center, with negligible Pt contribution. Stress-related distortions: decompression leads to distortions in the fcc (La,Y)H₁₀ phase, producing weak features as seen in Fig. S8. Instrument configuration: the 153 GPa pattern was collected on the LH table with λ = 0.4859 Å, while the 136 GPa pattern was measured in a separate run on the GP table with λ = 0.4246 Å. This difference naturally shifts 2θ values even when d-spacings remain unchanged. To remove ambiguity, we also included a comparison in d-spacing (Fig. S7 Right), which shows that all observed shifts are consistent with decompression and do not indicate a new phase. Changes in the manuscript: From Results – Structural Characterization of (La,Y)H 10 “To assess the stability of the observed phases during decompression, additional XRD measurements were performed on both samples. In DAC #1, the sample was gradually decompressed from 153 GPa, and an XRD was collected at 136 GPa from the sample center, with Fig. S5 illustrating the collection positions corresponding to the patterns in Fig. 1 and Fig. S6. Electrical resistance measurements were carried out in the intermediate pressure range. At 136 GPa, both the cubic and hexagonal phases were still observed (Fig. S6 and S7). Figure S7 presents XRD patterns of (La,Y)H at 153 GPa and 136 GPa in DAC #1, collected from comparable 10 positions in the sample chamber to confirm the persistence of both phases across this pressure range. At 136 GPa, minor distortions in the 𝐹𝑚3̅𝑚 phase were also evident across different regions of the sample (Fig. S8), likely reflecting local pressure gradients and lattice relaxation.” From Figure S5 - XRD collection positions for (La,Y)H₁₀ at 153 GPa and 136 GPa Figure S5: XRD collection positions for (La,Y)H₁₀ at 153 GPa and 136 GPa in DAC #1, corresponding to the patterns shown in Fig. 1 and Fig. S5. Left: XDI map of the sample chamber at 153 GPa and 2D scan of the chamber at 136 GPa, with electrodes and sampling locations marked for spatial reference. Right: representative 2D diffraction images collected at the indicated locations. The 153 GPa pattern was collected near the electrode region, where Pt peaks are visible, while the 136 GPa pattern was collected at the sample center, where Pt contributions are within the signal-to-noise ratio. From Figure S7 - XRD patterns of (La,Y)H₁₀ at 153 GPa and 136 GPa in DAC #1 Figure S7: XRD patterns of (La,Y)H₁₀ at 153 GPa and 136 GPa in DAC #1, collected from comparable positions in the sample chamber to confirm the presence of cubic and hexagonal phases at both pressures. The data were taken from the central square (55th and 56th positions in a 110-square grid) to ensure consistent sampling. Left: XDI maps of the sample chamber. Middle: representative 2D diffraction images from the selected positions. Right: integrated diffraction patterns in d-spacing, demonstrating that the two datasets are directly comparable. From Figure S8 - Spatially resolved XRD analysis of the cubic phase at 136 GPa Figure 2: Spatially resolved XRD analysis of the cubic phase at 136 GPa. XDI map of the Fm3 ̅m (cubic) phase of (La,Y)H₁₀ at 136 GPa, showing its spatial distribution across the scanned region. Diffraction patterns extracted from two high-intensity regions of the grid (right) confirm the presence of the cubic phase with slight peak shifts between locations, likely arising from local pressure gradients and lattice relaxation effects. Comment #5: In the main text, the author named the sample as (La0.9,Y0.1)H10, How did the author arrive at this ratio? And What evidence supports the successful incorporation of Y for the reaction product? Response: We clarified in the manuscript how the composition was determined and provided multiple lines of evidence for yttrium incorporation. The La–Y alloy precursor was prepared by arc-melting 90% La and 10% Y at Ames Laboratory. SEM–EDS confirmed a uniform single-phase alloy with 92.33% La and 7.67% Y (Fig. S14 & S15), and ambient XRD showed no segregation. Following hydrogenation, we performed a volume-based stoichiometry analysis for both phases. For the cubic Fm-3m phase at 153 GPa, the refined unit-cell volume corresponds to ~9.96 H per metal atom. For the hexagonal P6 /mmc phase, the expansion corresponds to ~9.34 H per metal 3 atom. Both are consistent with decahydride stoichiometry. Evidence of Y incorporation includes: Slightly contracted unit-cell volumes relative to LaH₁₀ at the same pressure (Fig. S4), consistent with substitution by the smaller Y atom. Persistence of both cubic and hexagonal clathrate phases down to 136 GPa, whereas undoped LaH₁₀ typically transforms to lower-symmetry phases. A measured reduction in T compared to LaH₁₀, consistent with prior reports that Y lowers T c c while stabilizing the clathrate lattice5. We also added a new Supplementary Note 1 detailing the stoichiometry analysis. Changes in the manuscript: From Results – Structural Characterization of (La,Y)H 10 “As shown in Fig. S4, this systematic reduction provides direct structural evidence that ~10% Y is incorporated into the clathrate framework. Notably, no diffraction peaks from secondary LaH or n YH phases were observed, indicating that Y substitution remains within the solubility limit for n forming a single-phase clathrate or a mixed-phase clathrate solid solution. Volume-based stoichiometry analysis yielded ~10 H per metal atom for both the cubic and hexagonal phases, consistent with the nominal (La Y )H composition (Supplementary Note 1).” 0.9 0.1 10 From Results – Structural Characterization of (La,Y)H 10 “In DAC #2, after initial synthesis at 172 GPa and characterization at 168 GPa, the sample was decompressed to 161 GPa. At this pressure, both the 𝐹𝑚3̅𝑚 and 𝑃6 /𝑚𝑚𝑐 phases clearly present 3 (Fig. S4), in contrast to binary La hydrides where the cubic phase typically dominates. The coexistence of both clathrate phases at this stage of decompression underscores the role of Y substitution in stabilizing structural polymorphism beyond that observed in undoped LaH . The 10 consistent observation of both phases across the entire pressure range studied (172–136 GPa) confirms that they coexist rather than represent distinct, pressure-stabilized states. Their simultaneous presence indicates that Y substitution does not strongly favor one structure over the other but instead promotes a mixed-phase state. This contrasts with LaH , which transforms to 10 lower-symmetry structures upon decompression.” From Results – Structural Characterization of (La,Y)H 10 “The pressure–volume (P–V) behavior of (La Y )H , shown in Fig. S4, generally follows the 0.9 0.1 10 trend reported for undoped LaH , with modest phase-specific deviations that point to non-uniform 10 compressibility and local strain effects. Similar trends were reported for (La Y )H synthesized 0.8 0.2 10 at higher pressures5, where clathrate structures remained stable without decomposition. These results demonstrate that partial Y substitution preserves the hydrogen cage framework of LaH 10 while extending phase coexistence across a broader pressure range.“ From Methods – Sample Preparation and High-Pressure Synthesis “A La–Y alloy with a nominal composition of La₀.₉Y₀.₁ was obtained from Ames Laboratory, prepared by arc melting high-purity La (93.36%) and Y (6.64%) metals under an argon (Ar) atmosphere40. Scanning Electron Microscopy - Energy-Dispersive X-ray Spectroscopy (SEM– EDS) analysis at 5 µm resolution confirmed a uniform single-phase alloy with a measured composition of 92.33% La and 7.67% Y (Table S1, Fig. S14). Ambient-pressure XRD likewise showed no evidence of phase segregation prior to loading (Fig. S15), confirming that the alloy was a homogeneous precursor.“ From Supplementary Information Note 1 – Volume-Based Stoichiometry Analysis of (La,Y)H10 “To estimate the hydrogen content of the synthesized clathrate phases, we compared the atomic volumes of the La–Y alloy precursor and the hydrogenated phases, following procedures established for rare-earth hydrides. All values reported here were obtained from DAC #1 (Fig. 1). The alloy measurement was performed at 158 GPa, while the hydride phases were measured at 153 GPa; the ±5 GPa difference is within the experimental uncertainty of pressure determination and therefore allows direct comparison. La Y alloy precursor (Fmmm, 158 GPa): 0.9 0.1 Unit cell volume = 58.5 Å3 with 4 metal atoms → atomic volume = 14.63 Å3/atom. Cubic 𝐹𝑚3̅𝑚 phase (153 GPa): Unit cell volume = 136.6 Å3 with 4 formula units → atomic volume = 34.15 Å3/metal atom. Expansion relative to alloy = 19.52 Å3/atom. Hexagonal 𝑃6 /𝑚𝑚𝑐 phase (153 GPa): 3 Unit cell volume = 66.1 Å3 with 2 metal atoms → atomic volume = 33.05 Å3/metal atom. Expansion relative to alloy = 18.42 Å3/atom. Hydrogen reference: The atomic volume of hydrogen at 153 GPa is taken as 1.961 Å3/atom, derived from the Vinet EOS of H , using parameters: B =0.162 GPa, B ′=6.813, V =21.116 Å3 6. 2 0 0 0 From these values, the estimated hydrogen content per metal atom is: ∆𝑉 𝑛 = 𝐻 𝑉 𝐻 Cubic phase: 19.52 / 1.96 ≈ 9.96 H/metal atom Hexagonal phase: 18.42 / 1.96 ≈ 9.34 H/metal atom These results indicate that both phases are consistent with decahydride stoichiometry, within experimental uncertainty, and support the assignment of the composition as (La Y )H . This 0.9 0.1 10 conclusion is further supported by the pressure–volume trends shown in Figure S4, where the data for both FCC and HCP phases closely follow the reported equation of state of LaH , consistent 10 with ~10 H per metal atom.” Comment #7: The images in Figure 2 at 153 and 136 GPa should be presented in the same orientation to facilitate direct comparison and interpretation. Response: We revised Figure 2 so that the 153 GPa and 136 GPa XDI images are displayed in a nearly common reference frame. This improves direct comparison while retaining the full uncropped raster grids to avoid loss of peripheral features. The difference in raster orientation between runs (due to stage angle/zoom) prevents exact pixel alignment, but the updated figure enhances clarity without compromising completeness of the dataset. Changes in the manuscript: From Figure 2 - Spatially resolved XRD imaging of phase domains in (La0.9Y0.1H₁₀ at high pressure Figure 2: Spatially resolved XRD imaging of phase domains in (La0.9Y0.1H₁₀ at high pressure. (A) XDI maps of the laser-heated (La,Y)H₁₀ sample at 153 GPa (top) and 136 GPa (middle and bottom), obtained via raster scanning with a ~1 μm micro-focused synchrotron beam. The 30 μm × 30 μm scan at 153 GPa resolves spatial distributions of cubic Fm3 ̅m (red) and hexagonal P6_3/mmc (blue) domains, with Pt leads mapped in dark gray or brown. Electrode positions are annotated directly on the Pt to enable spatial correlation with electrical transport measurements. The rightmost column overlays all phases to show the composite spatial distribution. At 136 GPa, a 50 μm × 50 μm scan (middle) and a higher-resolution 15 μm × 15 μm scan (bottom) show continued coexistence of FCC and HCP domains with spatial variation. (B) 2D X-ray scan overview showing the raster grid layout at respective pressures. (C) Optical image of the sample at 153 GPa after laser heating. Comment #8: The Raman spectroscopy data used for pressure calibration should be provided in the supplementary materials. Response: We added the requested data to the Supplementary Information. Figure S16 now presents the diamond-edge Raman spectra used for pressure calibration. In each case, spectra were collected at the culet center of the sample, and they confirm the pressure values reported in the manuscript. Changes in the manuscript: From Methods – Sample Preparation and High-Pressure Synthesis ”Pressure was determined from the Raman shift of the diamond edge, representative spectra at different pressures are shown in Fig. S16.” From Figure S16 – Diamond-edge Raman spectra for pressure calibration (DAC #1) Figure S16: Diamond-edge Raman spectra for pressure calibration (DAC #1). Representative spectra at 158 GPa (before laser heating), 153 GPa (after laser heating), and 136 GPa (during decompression). The diamond edge was measured at the center of the sample. Reviewer #2: The manuscript reports (La0.9Y0.1)H10 synthesized ≥150 GPa with coexisting cubic and hexagonal clathrate phases from 172 → 136 GPa, mapped by SXDM/XDI at APS-U with ~1 µm beam, and correlated to eight van der Pauw permutations showing two superconducting onsets (~244 K and ~220 K) that spatially associate with FCC-rich vs HCP-rich domains. The core contribution is the spatial co-analysis linking local structure to transport signatures in a mixed- phase superhydride—compelling and timely. A few minor comments need to be addressed before final acceptance. Response: We sincerely thank the reviewer for their thoughtful and encouraging assessment of our work. We are especially grateful that the reviewer recognized the significance of correlating spatially resolved structure with superconducting behavior in superhydrides, which we see as the central contribution of this study. We appreciate the constructive suggestions and have carefully addressed each of them below. Comment #1: To evaluate the homogeneity of the as-cast La-Y ingot, specify the grain size of the SEM-EDS in Table S1. How can you confirm the uniformity of the alloy, considering your sample size, ~30 um? Put a larger font of the scale bar in Fig. S2. Response: We revised the Supplementary Information to clarify the SEM–EDS analysis and to document alloy homogeneity across multiple length scales. The caption of Table S1 now explicitly states that the listed values correspond to EDS spectra acquired at 5 μm resolution (Fig. S14). SEM images were acquired over a 100 μm field of view, and additional EDS measurements were collected at 25 μm, 10 μm, and 5 μm resolutions, all of which showed consistent La and Y distributions. These results demonstrate compositional uniformity at scales well below the ~30 μm DAC sample size. This conclusion is corroborated by ambient-pressure synchrotron XRD (Fig. S15), which shows a single-phase dhcp alloy with no evidence of segregation, and by high-pressure diffraction prior to hydrogenation, which reveals only a single distorted-Fmmm phase above 150 GPa. Together, these datasets confirm that the alloy precursor is homogeneous across both microscopic and macroscopic scales. In addition, Figure S3 has been updated with a larger, clearer scale bar as requested. Changes in the manuscript: From Methods – Sample Preparation and High-Pressure Synthesis “A La–Y alloy with a nominal composition of La₀.₉Y₀.₁ was obtained from Ames Laboratory, prepared by arc melting high-purity La (93.36%) and Y (6.64%) metals under an argon (Ar) atmosphere40. Scanning Electron Microscopy - Energy-Dispersive X-ray Spectroscopy (SEM– EDS) analysis at 5 µm resolution confirmed a uniform single-phase alloy with a measured composition of 92.33% La and 7.67% Y (Table S1, Fig. S14). Ambient-pressure XRD likewise showed no evidence of phase segregation prior to loading (Fig. S15), confirming that the alloy was a homogeneous precursor.“ From Table S1 – Results of SEM-EDS analysis for La0.9Y0.1 alloy Table S1: Results of SEM–EDS analysis for La₀.₉Y₀.₁ alloy. The listed values correspond to EDS spectra acquired at 5 µm resolution (Fig. S14). SEM imaging was performed over a 100 µm field of view. Additional EDS measurements at 25 µm and 10 µm gave consistent results, supporting alloy homogeneity across multiple length scales. La Y 0.9 0.1 Line Apparent Wt% Standard Element k-Ratio Wt% Type Concentration Sigma Label Y L series 1.08 0.01082 7.67 0.15 Y La L series 35.12 0.31512 92.33 0.15 LaB 6 Total: 100.00 From Figure S3 – Schematic illustration of the DAC assembly configured for four-probe electrical transport measurements Figure S3: Left: Schematic illustration of the DAC assembly configured for four-probe electrical transport measurements. Right: Optical images of the (La,Y)H₁₀ DAC #1 sample at 158 GPa before laser heating (transmitted and reflected light) and after heating at 153 GPa (transmitted light). A clear volume expansion is observed following synthesis, as evidenced by the transition of the initially transparent ammonia borane region to an opaque state on the right side of the culet. Comment #2: Evaluate the actual stoichiometry of FCC and hcp phases after laser heating. Response: Thank you for this important point. We performed a volume-based stoichiometry analysis for both the cubic and hexagonal clathrate phases, using the alloy precursor and the refined unit-cell volumes after hydrogenation. Both phases are consistent with ~10 H per metal atom, i.e., a nominal decahydride stoichiometry. The slightly lower hydrogen count in the hexagonal phase is attributed to small structural distortions or partial hydrogen occupancy, as expected for this metastable structure. To provide full transparency, we added a new Supplementary Note 1 that details the calculations, including reference to the hydrogen equation of state. Changes in the manuscript: From Results – Structural Characterization of (La,Y)H 10 “As shown in Fig. S4, this systematic reduction provides direct structural evidence that ~10% Y is incorporated into the clathrate framework. Notably, no diffraction peaks from secondary LaH or n YH phases were observed, indicating that Y substitution remains within the solubility limit for n forming a single-phase clathrate or a mixed-phase clathrate solid solution. Volume-based stoichiometry analysis yielded ~10 H per metal atom for both the cubic and hexagonal phases, consistent with the nominal (La Y )H composition (Supplementary Note 1).” 0.9 0.1 10 From SI Note 1 – Volume-Based Stoichiometry Analysis of (La,Y)H10 “To estimate the hydrogen content of the synthesized clathrate phases, we compared the atomic volumes of the La–Y alloy precursor and the hydrogenated phases, following procedures established for rare-earth hydrides. All values reported here were obtained from DAC #1 (Fig. 1). The alloy measurement was performed at 158 GPa, while the hydride phases were measured at 153 GPa; the ±5 GPa difference is within the experimental uncertainty of pressure determination and therefore allows direct comparison. La Y alloy precursor (Fmmm, 158 GPa): 0.9 0.1 Unit cell volume = 58.5 Å3 with 4 metal atoms → atomic volume = 14.63 Å3/atom. Cubic 𝐹𝑚3̅𝑚 phase (153 GPa): Unit cell volume = 136.6 Å3 with 4 formula units → atomic volume = 34.15 Å3/metal atom. Expansion relative to alloy = 19.52 Å3/atom. Hexagonal 𝑃6 /𝑚𝑚𝑐 phase (153 GPa): 3 Unit cell volume = 66.1 Å3 with 2 metal atoms → atomic volume = 33.05 Å3/metal atom. Expansion relative to alloy = 18.42 Å3/atom. Hydrogen reference: The atomic volume of hydrogen at 153 GPa is taken as 1.961 Å3/atom, derived from the Vinet EOS of H , using parameters: B =0.162 GPa, B ′=6.813, V =21.116 Å3 6. 2 0 0 0 From these values, the estimated hydrogen content per metal atom is: ∆𝑉 𝑛 = 𝐻 𝑉 𝐻 Cubic phase: 19.52 / 1.96 ≈ 9.96 H/metal atom Hexagonal phase: 18.42 / 1.96 ≈ 9.34 H/metal atom These results indicate that both phases are consistent with decahydride stoichiometry, within experimental uncertainty, and support the assignment of the composition as (La Y )H . This 0.9 0.1 10 conclusion is further supported by the pressure–volume trends shown in Figure S4, where the data for both FCC and HCP phases closely follow the reported equation of state of LaH , consistent 10 with ~10 H per metal atom.” Comment #3: Provide the Raman data demonstrating surplus hydrogen remained after LH. Response: We did not observe any hydrogen vibron after laser heating synthesis. This outcome is consistent with complete consumption of the hydrogen released from ammonia borane. Multiple cycles of pulsed laser heating were performed, which promote full uptake of available hydrogen by the alloy. The presence of a large fraction of the hexagonal P6₃/mmc phase in the recovered sample further suggests hydrogen deficiency relative to the cubic phase, again consistent with full reaction. This interpretation is supported by other datasets Post-LH XRD shows only the clathrate phases (Fm-3m and P6 /mmc), with no reflections 3 attributable to solid H . 2 Volume-based stoichiometry (Supplementary Note 1, Fig. S3) yields ~10 H per metal atom for both phases, matching decahydride stoichiometry and indicating full hydrogen uptake. Similar absence of H vibrons following synthesis has been reported in prior La–H and La– 2 Y–H studies4,5, where it was attributed to complete incorporation of hydrogen into the clathrate framework. Changes in the manuscript: From Methods – Sample Preparation and High-Pressure Synthesis “Laser heating in both cases was performed at the interface between the metal and ammonia borane using a modulated Yb fiber laser, delivering ~300 ms focused pulses, reaching estimated temperatures of 1200–1800 K. Each synthesis involved multiple laser heating cycles, which ensured complete hydrogen uptake and phase formation.” Comment #4: Clarify pressure gradients across the chamber (e.g., diamond edge Raman at multiple azimuths) and map how they correlate with domain distribution. Response: We quantified the pressure distribution across the chamber and correlated it with the XDI maps. Figure S9 shows local pressures at the electrode–sample junctions determined from Pt(111) reflections using the Pt EOS. The electrodes span 164–170 GPa (ΔP ≈ 6 GPa). FCC/HCP domain boundaries do not coincide with the local pressure gradient, indicating that pressure is not the primary control on domain arrangement at synthesis conditions. To place these results in context, we also added the center diamond-edge Raman measurement (153 GPa), which differs from the Pt-EOS values near the electrodes. Such offsets are common at ≥150 GPa due to differences among pressure scales and nonhydrostatic stress in XRD measurements. Accordingly, we emphasize relative ΔP rather than absolute pressure. We note that, in this experiment, our priority was transport measurements. Raman mapping at multiple azimuths was not performed to minimize laser exposure of the diamond culets, which can trigger damage at these pressures. Changes in the manuscript: From Results – Spatial Mapping of Structural Domains via SXDM and XDI “The Fm-3m phase is localized in discrete clusters near Pt leads #2, #3, and #4, with the largest fraction around lead #2 where excess ammonia borane was present. By correlating optical images before and after laser heating (Fig. S3) with the XDI maps, the interface between the sample and ammonia borane is identified between leads #2 and #3, consistent with regions of higher temperature and greater hydrogen availability favoring the Fm-3m phase, while regions farther from this interface exhibit a higher fraction of the P63/mmc phase, forming a continuous matrix between leads #1 and #4. These correlations indicate that the observed structural inhomogeneity most likely arises from variations in hydrogen content and laser heating geometry. As shown in Fig. S9, the local pressure gradient does not correlate with FCC/HCP boundaries, indicating that pressure is not the dominant factor in domain arrangement at synthesis conditions.” From Figure S9 – XDI maps with local pressure variation at 153 GPa Figure S9: XDI maps with local pressure variation at 153 GPa. A 30 µm × 30 µm raster shows Pt leads (dark gray), cubic Fm-3m (red), and hexagonal P6 /mmc (blue). Local pressures at the 3 electrode–sample junctions were derived from Pt(111) using the Pt EOS (K₀ = 266 GPa, K₀′ = 5.81, V₀ = 60.3793 Å³ per fcc cell). The electrodes span 164–170 GPa (ΔP ≈ 6 GPa). ΔP values relative to the median (=166 GPa) are displayed on both the Pt map and the FCC+HCP overlay. Domain boundaries do not align with pressure gradients: FCC and HCP phases coexist across the full ΔP range, indicating pressure is not the primary control on domain arrangement at synthesis conditions. The center diamond-edge Raman measured 153 GPa, slightly lower than Pt-EOS values; such offsets are common above 150 GPa due to scale differences and nonhydrostatic stress. For correlation, we emphasize relative ΔP rather than absolute pressure."}, {"round": 2, "reviewer_comments": {"reviewer_1": "I can accept the publication of the article and have no further suggestions", "reviewer_2": "The authors have sufficiently addressed my concerns. I have no additional comments and recommend this manuscript for publication in Nature Communications."}, "author_response": "Response to Reviewer #1: We appreciate your recommendation for publication and your supportive comments. Response to Reviewer #2: We thank you for your thorough review and for confirming that our revisions have fully addressed your previous concerns. We are grateful for your recommendation for publication in Nature Communications."}]

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