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Supporting Information Disappearance of the Superionic Phase Transition in Sub-5 nm Silver Iodide Nanoparticles Takayuki Yamamoto, Hirokazu Kobayashi,, Loku Singgappulige Rosantha Kumara, Osami Sakata, *, Kiyofumi Nitta, Tomoya Uruga and Hiroshi Kitagawa *,,,# Division of Chemistry, Graduate School of Science, Kyoto University, Kitashirakawa-Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan. PRESTO, Japan Science and Technology Agency (JST), 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan Synchrotron X-ray Station at SPring-8, Research Network and Facility Services Division, National Institute for Materials Science (NIMS), 1-1-1 Kouto, Sayo-cho, Sayo-gun, Hyogo 679-5148, Japan Japan Synchrotron Radiation Research Institute (JASRI), SPring-8, 1-1-1 Kouto, Sayo-cho, Sayo-gun, Hyogo 679-5198, Japan Institute for Integrated Cell-Material Sciences (icems), Kyoto University, Yoshida, Sakyo-ku, Kyoto 606-8501, Japan # INAMORI Frontier Research Center, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-3095, Japan Email: SAKATA.Osami@nims.go.jp, kitagawa@kuchem.kyoto-u.ac.jp S1

1. Experimental section General information All chemicals were purchased from Wako Pure Chemical Industries and used as received. Preparation of AgI nanoparticles The AgI nanoparticles were prepared by adding a 75 ml methanol solution of NaI (1.5 mmol) to a 375 ml methanol solution of AgNO 3 (0.37 mmol) in the presence of PVP K30 (0.75 mmol). The mixture was stirred for 2 h at 4 C, collected by centrifugation and washed with methanol. The resultant white precipitate was dried under vacuum. TEM observation and EDX analysis Transmission electron microscopy (TEM) was performed with a HITACHI HT7700 at an accelerating voltage of 100 kv. Energy dispersive X-ray spectroscopy (EDX) was performed with a Bruker XFlash detector 5030 with energy range of 2.4-4.8 kev. Synchrotron high-energy PXRD measurements Synchrotron high-energy powder X-ray diffraction (PXRD) measurements were performed at beamline BL04B2 of SPring-8 (λ = 0.202 Å). Powdered sample was loaded into a glass capillary and measured at room temperature. RMC modeling The Reverse Monte Carlo (RMC) modeling of the isolated and finite-size spherical AgI nanoparticles was performed by RMC_POT software with non-periodic boundary conditions. The simulation box contained 410 atoms (Ag: 205, I: 205) in random manner as the initial model. A number density of 0.028986 Å -3 corresponding bulk density of β-phase (5.67 g cm 3 ) was used in the simulation. The RMC calculated and experimental structure factor S(q) show good agreement with minimum Rw ~ 9.4 %. S2

DSC measurement Differential scanning calorimetry (DSC) was performed with NETZSCH Japan DSC3100SA at scanning rate of 5 K/min. Synchrotron XAS measurements Synchrotron X-ray absorption spectroscopy (XAS) was performed at beamline BL01B1 of SPring-8. AC impedance spectroscopy Alternating current (AC) impedance spectroscopy was performed with Keysight 4294A at an applied voltage of 100 mv. A pelletized sample with silver paste as electrodes were loaded into a chamber filled with Ar gas. The measurement temperature was controlled using Lake Shore Cryotronics Model 335 Cryogenic Temperature Controller. S3

2. EDX spectrum of the AgI nanoparticles Figure S1. EDX spectrum of the AgI nanoparticles. 3. Phase transition of PVP Many polymers are known to show glass transition and the glass transition can be changed by additives. The glass transition temperature of bare PVP was 170 C on the heating process as shown in Figure S2. In the DSC thermogram of 3 nm AgI nanoparticles, the phase transition of AgI was not observed but the glass transition of PVP was observed at 192 C. This change of glass transition could derive from additives to PVP. For a control experiment, PVP and NaI were mixed in water and collected by centrifugation. This PVP-NaI mixture showed the glass transition at 188 C. Figure S2. DSC thermograms of bare PVP (gray), PVP-NaI mixture (blue) and the AgI nanoparticles (red) on the heating process. S4

4. Comparison of PDF/RMC analysis with EXAFS analysis Figure S3. The distribution histograms of (a) Ag I and (b) Ag Ag bond lengths observed in the model generated by PDF/RMC analysis. Table S1. Bond lengths at room temperature determined from PDF/RMC and EXAFS analyses. Ag I / Å Ag Ag / Å PDF/RMC 2.85 2.86 EXAFS 2.77(1) 3.02(3) S5

5. Temperature dependence of parameters determined by EXAFS analysis Figure S4. Temperature dependence of (a) bond distances and (b) coordination numbers calculated from EXAFS analysis. S6

6. Ionic conductivity Figure S5. Nyquist plots of the AgI nanoparticles at 260 C. Figure S6. Temperature dependence of the ionic conductivity of bulk AgI. S7