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NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-021-21488-7 ARTICLE electrode, does not undergo any redox process. Thus, the net magnetization for NYZC should always be zero, therefore calculations were carried out without spin polarization. The pre-relaxed structures of Na3YCl6 (mp-31362) and Na3YBr6 (mp-29080) were extracted from the Materials Project (MP) database62,63. The corresponding ICSD64 IDs are #59886 and #82355, respectively. Aliovalent substitution on the Y3+ sites with charge compensation by Na+ vacancies were performed to generate Na3-(z-3)xY1-xMz+xCl6 (M = Ti4+, Zr4+, Hf4+, Ta5+) structures. DFT calculations were performed on all symmetrically distinct orderings of Y/M and Na/vacancies to identify the lowest energy structure. Candidate structures for the Na2ZrCl6 phase were obtained by performing ionic substitutions of all structures in MP database matching the formula of A2MX6. All candidate structures were fully relaxed using DFT prior to calculating their energies. The computed XRD pattern of the lowest energy candidate was successfully matched to the experimental XRD pattern. Other than the target phases of interest, the pre-computed energies of all other structures in the Na-Y-Zr-Cl phase space were obtained from the Materials Project database and used in the calculation of the energy above hull (Ehull), electrochemical stability window, and the interfacial reaction products following the methodologies established in prior publications21,65. Topological analysis of the framework chemistries was performed using Zeo ++, an open source topological analysis package66. The quantity of interest is the largest included sphere radius along the free sphere path Rinc. This gives an estimate of the diffusion channel size which is associated with the ionic conductivity of the material. Ab initio molecular dynamics. Non-spin polarized ab initio molecular dynamics (AIMD) simulations were carried out in the NVT ensemble. From the spin- polarized DFT calculations, the net magnetization is 0 for all ions, which supports the use of non-spin-polarized calculations for AIMD. A plane-wave energy cutoff of 280 eV, supercells with the minimum dimension larger than 10 Å and a minimal Γ-centered 1 × 1 × 1 k-mesh were used. The time step was set to 2 fs. Simulations were carried out at several temperatures between 500 K and 1200 K and the cor- responding diffusivities were extracted using the Nernst-Einstein relationship from the slope of the plot of the mean square displacement of Na ions with time. Machine learning interatomic potential and molecular dynamic simulations. The moment tensor potential (MTP)23–25 for NYZC0.75 was developed using the open-source Materials Machine Learning (maml) Python package. The training data comprises 800 snapshots extracted at 400 fs intervals from AIMD NVT simulations at 600 K, 800 K, 1000 K, and 1200 K. Static DFT calculations were then performed to obtain accurate energies and forces. A training:test split of 90:10 was used to train the machine learning model. The MTP cutoff radius and the maximum level of basis functions, levmax were chosen to be 5.0 Å and 14, respectively. The mean absolute error (MAE) on the energies and forces were 1 meV atom−1 and 63.5 meV Å−1, respectively (Supplementary Figure 18 and Supplementary Table 5). NPT MD simulations using the MTP were carried out using LAMMPS67. The simulation time was at a least amount of 10 ns with a 2 fs time step. A 4 × 4 × 4 supercell of the NYZC0.75 with 592 atoms was used. Material synthesis. All fabrication processes were conducted in an Ar-filled glovebox (mBraun 200B, H2O ppm <0.5, O2 ppm < 1), unless otherwise noted. Stoichiometric amounts of the precursors NaCl (>99%, Sigma Aldrich), YCl3, (99.9%, Sigma Aldrich) were hand-mixed in a mortar and pestle for 10 min and the powder mixture was placed in a 50 mL ZrO2 ball mill jar (Retsch Emax) with eleven 10 mm-diameter Y-ZrO2 milling balls. The mixture was milled for 2 h at 500 r.p.m. The material was extracted from the jars in the glovebox, pelletized at a pressure of 370 MPa with a 13 mm pellet die (Carver), loaded into a quartz tube, flame sealed, and heated in a box furnace (Lindberg Blue M) at 500 °C for 24 h. To homogenize the material, the material was ball milled again after heat treatment using 88 5 mm diameter Y-ZrO2 milling balls for a duration of 4 h. The material was extracted and stored in the glovebox before further testing. For the Zr substituted compounds, the same procedure was conducted with the addition of ZrCl4 (99.99%, Sigma Aldrich) as a third precursor, and the reagent ratios adjusted according to stoichiometry. Characterization—XRD. Powder samples were loaded into 0.5 mm-diameter boron-rich capillary tubes (Charles Supper). The tube opening was capped with clay and wrapped in paraffin film before it was brought outside of the glovebox to be flame-sealed with a butane torch. The samples were measured on a Bruker Kappa goniometer equipped with a Bruker Vantec 500 detector. The sample was placed in the Bragg−Brentano θ − θ configuration and the Debye−Scherrer method was used for measurements. XRD data was collected using Cu Kα radiation at 45 kV and 50 mA, over a 2θ range of 5 − 90° with a step size of 0.01°. Rietveld refinement was carried out with the FullProf software suite. For temperature-dependent capillary XRD, the capillary tubes were heated at a rate of 5 °C/min and held at the target temperature for one hour before the XRD measurement was taken. For Synchrotron XRD, the samples were prepared by loading the powders into polyimide tubes in the glovebox and were subsequently sealed with epoxy. Measurements were carried out at Beamline 28-ID-1 at NSLS-II. Characterization—electrochemical. 75 mg of powder was pressed at 370 MPa into a 10 mm polyether ether ketone (PEEK die) using two titanium plungers and the dimensions were measured with calipers. The relative density of the pellets was determined by comparing the measured dimensions with the XRD results. On both sides of the pellet, acetylene black (AB) was added for better contact with the current collectors; once added, the AB was also pressed at 370 MPa using the titanium plungers. The cell configuration was secured into a cell holder and con- nected to a Solartron 1260 impedance analyzer. Impedance measurements were taken with an applied AC potential of 30 mV over a frequency range of 1 MHz to 1 Hz. Temperature-dependent EIS measurements were also conducted within the glovebox; the sample was heated from 20 °C to 100 °C and EIS measurements were recorded at every 20 °C increment. Measurements were taken only after the sample was held at the target temperature for over an hour to allow for equilibration. The heating rate was 2 °C/min. The activation energy (Ea) was calculated from the slope of the resulting Arrhenius plot. DC polarization was also conducted by the Solartron 1260 impedance analyzer. The cell setup was similar as before; the powder was pressed at 370 MPa into a 10 mm PEEK die using two titanium plungers and subsequently secured into a cell holder. The applied DC potential was 50 mV and the current response was measured over time. The model SSSB is composed of NaCrO2 as the positive electrode, Na-Sn (2:1) as the negative electrode, and Na3PS4 as the electrolyte. The positive electrode is mixed into a composite with a weight ratio of 11:16:1 of NaCrO2: Na3PS4: VGCF (VGCF from Sigma Aldrich; length 20–200 μm, <100 ppm iron, average diameter: 130 nm, average specific surface area: 24 m2 g−1). The battery is fabricated through mechanical pressing; 75 mg of Na3PS4 powder is pressed first at 370 MPa, then about 12 mg of the composite NaCrO2 powder is placed on one side of the Na3PS4 pellet and pressed at the same pressure, and finally on the opposite side of the Na3PS4, an excess of Na-Sn 2:1 alloy (35 mg) is pressed at the same pressure. After securing the cell in a cell holder, the electrical leads were connected to an electrochemical cycler (Landhe). For a rate of C/10, the current density used was 64 μA cm−2. To incorporate Na2.25Y0.25Zr0.75Cl6 (NYZC0.75) into the model SSSB, NYZC0.75 replaced Na3PS4 in the composite cathode (still hand-mixed with the same 11:16:1 ratio). For cells cycled at 40 °C, the cell assemblies were placed into a compact box furnace (MTI KSI-1100X) within the Ar-filled glovebox. Current densities ranged from 64 μA cm−2 (C/10) to 640 μA cm−2 (1 C). After cycling, the cell was disassembled to characterize any material changes. Characterization—23Na solid-state NMR. All 23Na solid-state NMR experiments were performed on a 3.2 mm HX probe on a Bruker Avance III Ultrashield Plus 800 MHz (18.8 T) NMR spectrometer. A 1 M NaCl aqueous solution, with a reported 23Na chemical shift of 0.04 ppm68 was used as reference sample to cali- brate the chemical shift scale. 23 Na NMR spectra were collected on NYZCx (x = 0, 0.25, 0.5, 0.75, 1) compounds with a simple pulse and acquire (zg) sequence and at a magic angle spinning (MAS) rate of 12 kHz as no spectral enhancement was observed at higher spinning speeds. The solid electrolyte samples were packed inside 3.2 mm sapphire rotors in an Ar-filled glovebox to avoid contamination with air or moisture. In addition, a flow of N2 gas was used to spin the samples, providing an inert atmosphere during 23Na NMR signal acquisition. Due to the quadrupolar nature of 23Na nuclei (I = 3/2), the calibrated pulse durations differed for the various 23Na local environments in the samples. Hence, all spectra were obtained using a 30° radiofrequency (RF) excitation pulse in lieu of a standard 90° pulse angle to uniformly excite all 23Na spins in the sample and provide internally quantitative 23Na NMR spectra. The quantitative nature of the so-obtained spectra was confirmed by collecting data using a pulse angle as low as 5°, which showed no change in the relative amounts of each resonance compared to the 30° pulse data. The power level used for all measurements was 100 W (~93 kHz) with a 90° pulse duration of around 2.7 μs, therefore, a 30° pulse duration of either 0.9 or 0.95 μs was used depending on the optimization of each sample. A 30 s delay was applied before each scan when signal averaging in order to allow full relaxation, where the relaxation times of these samples are 2 s or below. Characterization—XPS. The powders were adhered onto a small metallic sample stub (Shimadzu) with carbon tape. The metallic stub was secured into a metallic canister and sealed inside the glovebox with clamps. The metallic canister was placed into a N2 glovebox that is attached to the XPS tool (Kratos Axis Supra), where the sample can be transferred into the analysis chamber without any exposure to ambient air. All measurements were taken using 15 kV Al Kα radiation at a chamber pressure less than 5 × 10−8 torr. For the wide survey scans, a pass energy of 160 eV and a dwell time of 100 ms was used, but for specific element regions, a pass energy of 20 eV, a dwell time of 300 ms, and a step size of 0.05 eV was used. The charge neutralizer was enabled during all the measurements. Data calibration and analysis were conducted using the CasaXPS software, and all region spectra were calibrated using the C 1 s peak. Characterization—focused ion beam (FIB). The Na3-xY1-xZrxCl6 powders were pressed into a 10mm-diameter pellet at 370 MPa. The pellet was extracted and then NATURE COMMUNICATIONS | (2021)12:1256 | https://doi.org/10.1038/s41467-021-21488-7 | www.nature.com/naturecommunications 9PDF Image | cathode-solid electrolyte composite sodium-ion
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