Local electronic structure rearrangements and strong anharmonicity in YH3 under pressures up to 180 GPa

The discovery of superconductivity above 250 K at high pressure in LaH10 and the prediction of overcoming the room temperature threshold for superconductivity in YH10 urge for a better understanding of hydrogen interaction mechanisms with the heavy atom sublattice in metal hydrides under high pressure at the atomic scale. Here we use locally sensitive X-ray absorption fine structure spectroscopy (XAFS) to get insight into the nature of phase transitions and the rearrangements of local electronic and crystal structure in archetypal metal hydride YH3 under pressure up to 180 GPa. The combination of the experimental methods allowed us to implement a multiscale length study of YH3: XAFS (short-range), Raman scattering (medium-range) and XRD (long-range). XANES data evidence a strong effect of hydrogen on the density of 4d yttrium states that increases with pressure and EXAFS data evidence a strong anharmonicity, manifested as yttrium atom vibrations in a double-well potential.


Supplementary
: XANES spectra. Pressure-dependent experimental Y K -edge XANES spectra (a and b) and their first derivatives (c and d) for YH 3 samples S1 and S2.

Supplementary Note 2. XRD Data and pressure determination
For pressure determination, the lattice parameters of the sample were obtained from X-ray diffraction (XRD) measurements made concomitantly with collecting the XAS spectra. For the XRD measurements, the beam was switched to 20 keV (λ = 0.62 Å). The pressure was evaluated from the known pressure-volume (P-V) equation of state (EOS) for YH 3 . For the hcp phase, the Birch-Murnagan EOS was used with the parameters: V 0 = 23.39 cm 3 /mole (38.675 Å 3 /f.u.), K 0 = 71.9 GPa, K 0 = 5.0 S2 . For the fcc phase the P-V data from a separate XRD study in the region 17 -180 GPa ( Supplementary Fig. S4) complemented with the ambient-pressure volume per formula unit V 0 = 36.87 Å 3 /f.u. from Ref. S3 were fit with the Vinet function with V 0 fixed. S4 The obtained bulk modulus and its derivative respectively are: K 0 = 91.17 GPa, K 0 = 3.576. Figure S3: XRD data. X-ray diffraction patterns for YH 3 , samples S1 (a) and S2 (b).  The Y K -edge XANES spectra of metallic yttrium (hcp phase) were calculated within the full-multiple scattering (FMS) formalism by the ab initio real-space FDMNES code. S5, S6 The calculations were performed using real energydependent Hedin-Lundqvist exchange-correlation potential S7 and the self-consistent cluster potential for the clusters with radii R = 3.6, 4.0, 6.0, 7.0, 8.0 Å around the absorbing yttrium atom. The results of the calculations are compared with the experimental spectrum of yttrium foil measured at 300 K in Supplementary Fig. S6(a). To identify the origin of the XANES peaks, the partial p(Y) and d(Y) density of states (DOS) are shown in Supplementary Fig.  S6(b) for the excited and ground states, i.e., with and without the core hole at the 1s(Y) level of the absorbing yttrium atom.

Supplementary
As one can see, the core hole effect is relatively small. All main features of the experimental Y K -edge XANES of yttrium foil are reproduced by a small cluster of 3.6 Å radius containing six yttrium atoms of the first coordination shell only. The shoulder at the absorption edge is due to the mixed p − d states of yttrium, whereas other peaks located above the edge are due to the features in p(Y)-DOS.

Supplementary Note 5. Reverse Monte Carlo (RMC) analysis of EXAFS spectra
Supplementary Figure S7: EXAFS spectra. Pressure dependence of the experimental Y K -edge EXAFS spectra χ(k)k 2 (a and c) and their Fourier transform moduli (b and d) for YH 3 samples S1 and S2. The FTs were not corrected for any phase shifts; therefore, the positions of peaks differ from crystallographic values. Figure S8: RMC EXAFS analysis. The results of RMC/EA-EXAFS calculations for fcc-YH 3 at selected temperatures: circles -experimental data, lines -calculated spectra. The Y K -edge EXAFS spectra χ(k)k 2 of YH 3 are compared in the left panels and their Fourier transform moduli -in the right panels. Figure S9: Structure characteristics. a Pressure dependence of the three nearest Y-Y shells radii and b temperature dependence of MSRD at 39 GPa for three nearest Y-Y shells, obtained from the RMC analysis of the Y K -edge EXAFS spectra of YH 3 .

Supplementary
The EXAFS oscillations were extracted using the ATHENA code, S8 taking care to remove the low-frequency oscillations. The EXAFS-functions χ(k)k 2 obtained from absorption spectra were Fourier transformed using Kaiser-Bessel windowing function in the range of wavenumber k from 1.5 to 16.5 Å −1 .

RMC simulations
The experimental Y K -edge EXAFS spectra were analysed using the RMC method with an evolutionary algorithm (EA) approach, as implemented in the EvAX code. S9 In the RMC method, the material is represented by a 3D structural model, and atomic coordinates are randomly changed at each iteration of the simulation to minimize the difference between experimental and configuration-averaged calculated EXAFS spectra.
The initial models of YH 3 structure at different pressures were constructed based on the lattice parameters estimated from the experimental diffraction data. For instance, the model of the low-pressure hcp YH 3 phase was constructed based on the structure determined by neutron powder diffraction for the hcp YD 3 phase with the space group P3c1 (163) S10 leaving the Wyckoff positions of atoms but modifying the lattice parameters a and c. The model of the high-pressure fcc YH 3 phase was constructed by changing the lattice constant a and leaving the Wyckoff positions corresponding to the cubic F m3m (225) phase.
The RMC simulations of pressure-dependent EXAFS data were performed with the 3 × 3 × 3 large supercell containing 648 atoms for the hcp structure or 432 atoms for the fcc structure. Temperature-dependent EXAFS data measured at the pressure of 39 GPa were simulated for the fcc structure using the 4 × 4 × 4 large supercell containing 1024 atoms. Periodic boundary conditions were applied to avoid surface related effects. 32 atomic configurations were used simultaneously in the EA method. At each iteration, a new atomic configuration was generated by randomly displacing all atoms in the supercell with a maximum permissible displacement of 0.4 Å.
The configuration-averaged Y K -edge EXAFS spectra were calculated by ab initio real-space FEFF8.50L code S11 including multiple-scattering contributions up to the 4-th order. The complex energy-dependent exchange-correlation Hedin-Lundqvist potential S7 was employed to account for inelastic effects. The amplitude reduction factor S 2 0 was set to 1.0. As a criterion for the agreement between the experimental and calculated EXAFS spectra, we used a comparison of their Morlet wavelet transforms. S12 Calculations were performed in the k-space range from 3.5 to 13 Å −1 and the R-space ranges from 2 to 6 Å for the fcc structure and from 2.5 to 7.5 Å for the hcp structure. No significant improvement in the agreement was observed after 3000 iterations. At least three RMC/EA simulations with different sequences of pseudo-random numbers were performed for each experimental data set.
The RMC simulations performed with and without hydrogen atoms gave close agreement with the experimental data, indicating that due to hydrogen is a weak scatterer, its contribution cannot be reliably evidenced. Therefore, further discussion will be limited to the Y-Y correlations. As a result of the RMC simulations, sets of atomic coordinates were obtained. They were used to calculate partial pair radial distribution functions (PRDFs) g Y-Y (R) and to estimate structural parameters, as interatomic distances R(Y-Y) and mean-square relative displacement (MSRD) factors σ 2 (Y-Y) for Y-Y atom pairs.

Supplementary Note 6. EXAFS spectra analysis in the case of strong anharmonicity
The experimental Y K -edge EXAFS spectra treatments for the first Y(0)-Y(1) shell around the absorbing atom of YH 3 were analysed in real-space using VIPER program package. S13 The EXAFS functions χ(k)k 2 obtained from the absorption spectra were Fourier transformed in the range of wavenumber k from 1.5 to 16.5 Å −1 , using the Kaiser-Bessel windowing function. Fourier back-transformation (BFT) was carried out using a Hanning window in the real-space range corresponding to the nearest interatomic Y(0)-Y(1) distance. The model EXAFS function was fitted to the BFT filtered experimental one.
The model EXAFS function χ(k) for atomic pair absorber-scatterer oscillations is constructed as follows. Suppose we know the potential of these oscillations as a parametric function of interatomic distance. Solving the stationary Schrödinger equation numerically for the particle with the reduced mass of the atomic pair, one obtains a pair radial distribution function (PRDF) of atoms in the i-th shell: where N i is the coordination number, and E n and Ψ n are the n-th energy level and its corresponding wave function. Given the PRDFs, the model EXAFS function is calculated as where k = 2m e / 2 (E − E th ) is the photoelectron wavenumber referenced to the ionization threshold E th , and r min and r max are determined by the windowing function of the back Fourier transform. The phase shift φ i (k) and the scattering amplitude F i (k) were calculated using the FEFF8.50L code S11 for the fcc structure of YH 3 , using the 4 × 4 × 4 large supercell containing 1024 atoms with crystallographic data from neutron diffraction study S10 and our s-XRD data. The potential parameters were extracted from the model-to-experimental EXAFS-function fits. The model for the oscillatory Y-Y potential for the YH 3 C/2m phase at 39 GPa was constructed as follows. Let us imagine the position of the angular Y(0) atoms as fixed, and the octahedron of 6 Y(1) atoms in the centers of the faces (see Fig. 5b in the main text), squeezed to the center of the cube. In six neighboring cells being joined through the faces of the cube, these internal octahedra will, on the contrary, be stretched. This compression-tension occurs dynamically and, apparently, due to the dynamic instability of the hydrogen subsystem. Such a movement exchanges the roles of two inequivalent Y positions and requires a double-well form of the oscillatory Y-Y potential. Here, we take a parabolic form for each well, U 1 = k 1 (r − r 1 ) 2 /2 and U 2 = k 1 (r − r 2 ) 2 /2, and these are joined continuously.
Angular atoms Y(0), of which a fraction of 1/4, see this displacement perpendicular to the nearest neighbor. Therefore, they do not fill the double-well potential and oscillate in a single-well one. Atoms Y(1) in the octahedron, of which a fraction of 3/4, are seen by 4 atoms at a short distance, 4 at a long distance and 4 (almost at the face of a cube) on average distance. Total, coordination number with short distances = 12 × 3/4 × 1/3 = 3, the same as for long ones. For medium: 12 × (1/4 + 3/4 × 1/3) = 6. I.e. as a result, we have one single-well potential with a coordination number of 6 and one double-well potential, also with the number 6 (3 in each well). Given the calculated χ(k), defined by equations (1) and (2) in addition to single-well potential, we performed a least-squares fit between the model and experimental χ(k)k 2 over the range k = 2-16 Å −1 and extracted the full potential parameters (see