Supporting Information

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1 Supporting Information Chemical Pressure-induced Anion Order-disorder Transition in LnHO Enabled by Hydride Size Flexibility Hiroki Yamashita, Thibault Broux, Yoji Kobayashi, Fumitaka Takeiri, Hiroki Ubukata, Tong Zhu, Michael A. Hayward, Kotaro Fujii, Masatomo Yashima, Kazuki Shitara, Akihide Kuwabara, Taito Murakami, and Hiroshi Kageyama* Experimental details Polycrystalline LnHO samples (Ln = Sm, Gd, Tb, Dy, Ho, Er) were synthesized via high-temperature solid-state reactions using Ln2O3 (Wako, 99.9%) and CaH2 (ALDRICH, 99.9%). Ln2O3 was pre-heated at 900 C for one day to remove moisture. The 2H for O anion substitution reaction of lanthanide oxide was then conducted by weighing Ln2O3 powder with a 3M excess of CaH2 powder, grinding, mixing and palletizing. The pellet was then flame-sealed in an evacuated quartz tube (15 cm 3 ) at pressures below MPa. Each pellet into quartz tube was then heated to 650 C at a rate of 200 C/h, maintained at the temperature for 20 h, and cooled to room temperature at a rate of 200 C/h. The products were then washed with saturated NH4Cl/methanol in a nitrogen-filled dry glove box to remove CaH2 and CaO, and dried. After that, we obtained aimed lanthanide oxyhydrides. We characterized the purity and crystal structures of LnHO by powder X-ray diffraction (XRD) measurements using a D8 ADVANCE diffractometer (Bruker AXS) with Cu-Ka radiation (λ = Å). Since the obtained samples were possibly air sensitive, they were covered with Kapton tape during the XRD measurements. High resolution synchrotron powder XRD experiments (SXRD) were performed at room temperature using a camera with an imaging plate as a detector on instrument I11 at the Diamond Light Source, UK. Incident beams were monochromatized to λ = Å. Sieved powder LnHO (< 32 µm) were loaded into Pyrex capillaries with an i.d. of 0.18 mm. Data were analyzed using Fullprof suite. Absorption was computed from Argonne National Laboratory website. Sample µr ErHO 3.5 HoHO 3 DyHO 2.8 TbHO 2.6 GdHO 2.5 SmHO 2.2 S1

2 Neutron diffraction data were collected using the high resolution powder diffractometer imateria[s1] (BL20) in J-PARC, Japan. Sample was loaded into container with an i.d. of 6 mm, and the data was analyzed by Rietveld refinement using Z-Rietveld[S2]. We performed first-principles calculations of unitcells of anion-ordered LaHO and simple oxides of La2O3 (A-type and C-type rare-earth structures). Because a huge supercell should be considered to model the anion-disordered structure with the heterovalent ions, we only calculated the ordered structure and the simple oxides. First principles calculations were performed using the projector augmented wave method as implemented in the VASP code [S3,S4]. The exchange-correlation term was treated with the Perdew Burke Ernzerhof functional revised for solids [S5]. The atomic positions and lattice constants are relaxed until the residual atomic forces become less than 0.02 ev Å 1 and the plane-wave cutoff energies ware set to 520 ev. The spin polarization was considered. [S1] Ishigaki, T., Hoshikawa, A., Yonemura, M., Morishima, T., Kamiyama, T., Oishi, R., Aizawa, K., Sakuma, T., Tomota, Y., Arai, M., Hayashi, M., Ebata, K., Takano, Y., Komatsuzaki, K., Asano, H., Takano, Y., & Kasao, T. IBARAKI materials design diffractometer (imateria)-versatile neutron diffractometer at J-PARC. Nucl. Instruments Methods Phys. Res. A, 600, (2009). [S2] Oishi, R., Yonemura, M., Nishimaki, Y., Torii, S., Hoshikawa, A., Ishigaki, T., Morishima, T., Mori, K., & Kamiyama, T. Rietveld analysis software for J-PARC Nucl. Instruments Methods Phys. Res. A, 600, 94 96(2009). [S3] Kresse, G., & Furthmüller, J. Efficient Iterative Schemes for ab initio Total-energy Calculations using a Plane-wave Basis Set. Physical Review. B, Condensed Matter, 54(16), (1996). [S4] Kresse, G., & Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-wave Method. Physical Review B, 59(3), (1999). [S5] Perdew, J. P., Ruzsinszky, A., Csonka, G. I., Vydrov, O. A., Scuseria, G. E., Constantin, L. A., Burke, K. Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces. Physical Review Letters, 100(13), (2008). S2

3 ErHO Synchrotron XRD Er (1) 1 O (2) 0.66(1)** H (2) 0.33(1)** Space group Fm3"m ; a = (1) Å; **sum constrained to be 1 χ 2 = 7.3, RBragg = 2.71%, RF = 1.44% S3

4 HoHO Synchrotron XRD Phase 1: 73% weight fraction Ho (1) 1 O (2) 0.59(4)** H (2) 0.41(4)** Space group Fm3"m ; a = (1) Å; **sum constrained to be 1 χ 2 = 21.5, RBragg = 4.13%, RF = 5.03% Phase 2: 27% weight fraction Ho (1) 1 O (2) 0.58(4)** H (2) 0.42(4)** Space group Fm3"m ; a = (1) Å; **sum constrained to be 1 χ 2 = 21.5, RBragg = 4.21%, RF = 5.05% S4

5 DyHO Synchrotron XRD Phase 1: 60% weight fraction Dy (1) 1 O (2) 0.62(2)** H (2) 0.38(2)** Space group Fm3"m ; a = (1) Å; **sum constrained to be 1 χ 2 = 13.6, RBragg = 6.37%, RF = 4.89% Phase 2: 40% weight fraction Dy (1) 1 O (2) 0.52(2)** H (2) 0.48(2)** Space group Fm3"m ; a = (1) Å; **sum constrained to be 1 χ 2 = 13.6, RBragg = 6.29%, RF = 5.03% S5

6 TbHO Synchrotron XRD Tb (1) 1 O (2) 0.57(1)** H (2) 0.43(1)** Space group Fm3"m ; a = (1) Å; **sum constrained to be 1 χ 2 = 25.7, RBragg = 8.03%, RF = 4.46% S6

7 GdHO Synchrotron XRD Gd (1) 1 O (2) 0.42(1)** H (2) 0.58(1)** Space group Fm3"m ; a = (1) Å; **sum constrained to be 1 χ 2 = 9.8, RBragg = 1.9%, RF = 1.71% S7

8 SmHO Synchrotron XRD Phase 1: 64% weight fraction Sm (1) 1 O (2) 0.49(2)** H (2) 0.51(2)** Space group Fm3"m ; a = (1) Å; **sum constrained to be 1 χ 2 = 20.6, RBragg = 6.21%, RF = 3.52% Phase 2: 36% weight fraction Sm (1) 1 O (2) 0.42(2)** H (2) 0.58(2)** Space group Fm3"m ; a = (1) Å; **sum constrained to be 1 χ 2 = 20.6, RBragg = 5.95%, RF = 4.8% S8

9 Intensity (a. u.) HoHO Neutron powder diffraction yint ycal delta TOF (µs) Figure S1 Rietveld refinement of neutron powder diffraction of HoHO Ho (1) 1 O (2)* 0.474(2)** H (2)* 0.526(2)** Space group Fm3"m ; a = (1) Å; *constraint to be equal, **sum constrained to be 1 χ 2 = 5.53, Rwp = 5.22%, Rp = 4.53% Note: Contrary to what has been observed with synchrotron data, only one phase could have been detected here. The resolution provided by the neutron experiment does not allow the detection of such subtle differences in cell parameters. S9

10 BVS H - BVS in disordered case O 2- BVS in disordered case H - BVS in ordered case O 2- BVS in ordered case Shannon radius (8-coordination) Figure S2 BVS values for oxygen and hydrogen. Experimental values for La Nd are taken from Refs. 23, 24. The disordered structure for La Nd is hypothetical. The bond valence parameters have been taken from Ref. 29 (Brese, N. E.; O Keeffe, M. Bond-Valence Parameters for Solids. Acta Crystallogr. B 1991, 47, ). The BVS values of hydride show that H is always over-bonded. However, no obvious evolution is observed with the lanthanide ionic radius, and most importantly the size flexibility of hydride anions (and the limited number of oxyhydride materials) makes it difficult to argue hydride BVS itself; the flexible size in H, the upmost feature of this anion (Ref. 22), means that tabulated parameters for lanthanide hydride should have a certain range of errors, leading potentially to a misestimation of the calculated BVS values. For these reasons, we did not address the bonding nature of hydride in the main manuscript. S10