Extended Data Fig. 8: Further analysis of the reaction mechanism on discharge of Al-Se cells fitted with molten NaCl-AlCl₃ electrolyte.

a, The χ_red² of linear combination fittings using three components (χ_red²_best, bottom) and using only two of the three components (ratio over χ_red²_best, top). The significantly higher χ_red² using only two components proves that three components are necessary to capture the information of the entire data set; the almost constant χ_red²_best across all scans indicates further that 3 components faithfully reproduce the entire data set, in complete agreement with the PCA analysis (Extended Data Fig. 6d, e). More importantly, the low χ_red² of using Components A and B for scans 1–6 (χ_red²/ χ_red²_best ~1) indicates that only A and B are present in these 6 scans, and similarly, the high χ_red² of using B and C for scans 10–15 (χ_red²/ χ_red²_best = 4~11) indicates that A is necessary and present in these scans. b, The operando X-ray diffraction patterns of the crystalline Se cathode during discharge at D/10 and 180 °C, featuring the Se (101) and Se (010) peaks. The Se peaks do not disappear until the end of discharge. c, d, Nyquist plots of the in-situ measured impedance data on an Al|Se cell, as a function of the state of discharge (SOD) from bottom to top (c); the evolution of charge transfer resistance (R_ct) and electrolyte resistance (R_s) of the cell, as fitted from the Nyquist plots (d). For consistency amongst all impedance data, circle fitting of the Nyquist plots on the high-frequency semicircle was performed (instead of finding one equivalent circuit for all), and the first intercept (of the fitted circle with the real-axis) is regarded as R_s and the distance between the two intercepts is regarded as R_ct. The error bars are the standard deviations based on three measurements at the corresponding SOD. The R_s remains constant at around 1.5 ohm cm² for all SOD, indicating there is minimal change of the electrolyte composition and dissolution of formed species. The R_ct experiences initial decrease (SOD: 0–30%, due to formation of partially soluble Al₂(Se_n)₃ species), slight increase (SOD: 30–55%, probably due to initial formation of Al₂Se₃), stabilization (SOD: 55–85%), and eventual increase (SOD: 85–100%, eventual formation of Al₂Se₃). This is consistent with the trend in the proposed reaction mechanism in Fig. 3e. e, The picture of Al₂(Se₆)₃ (targeted stoichiometry) and selenium in the molten NaCl-AlCl₃ electrolyte placed on a hot plate (around 180 °C); partial solubility is confirmed by the darkened color. The nominal Al₂(Se₆)₃ was prepared by mixing the targeted amount of Se and Al₂Se₃ in the melt; thus, it may not reflect the exact ratio and serves only as demonstration of partial solubility of such compounds. Note that elemental selenium appears to have some solubility as well. f-h, the ex-situ XAFS studies on the fast-charged selenium electrodes: the XAFS spectra of fully discharged and charged electrodes collected operando and ex-situ for comparison (f); as the fast-charging study has to be performed ex-situ due to the limited time resolution of the XAS scan (~10 min), the very similar XAFS features using two measurement approaches indicates that the chemical states of selenium species remain unchanged if we stop and cool down the warm cell at a certain SOC (the electrolyte freezes). The ex-situ Se K-edge XAFS spectra of the selenium electrodes charged at 20C (g) and 50C (h) respectively; the spectra were collected using transmission mode on the retrieved fast charged electrode, and fitted by linear combination fittings using the three principal components. By quantifying the components using linear combination fitting, we observed that the cathode recharged at 20C contains 10.5% of the Al₂(Se_n)₃ and 89.5% of Se⁰, and the one recharged at 50C contains 17.3% of the Al₂(Se_n)₃ and 82.7% of Se⁰. No component C was observed in both electrodes.