# Fileset [jmca2024_NaSulfideConductor_esi_rj.pdf](https://mdr.nims.go.jp/filesets/25ed9f80-9f93-4ca2-9f6f-f161461bdc86/download) ## Creator [Seong-Hoon Jang](https://orcid.org/0000-0001-6026-636X), [Randy Jalem](https://orcid.org/0000-0001-9505-771X), [Yoshitaka Tateyama](https://orcid.org/0000-0002-5532-6134) ## Rights ## Other metadata [Computational discovery of stable Na-ion sulfide solid electrolytes with high conductivity at room temperature](https://mdr.nims.go.jp/datasets/cb755371-f4a7-4ef5-8959-52de2abf5320) ## Fulltext Template for Electronic Submission to ACS JournalsSupporting InformationComputational Discovery of Stable Na-ion Sulfide Solid Electrolytes with High Conductivity at Room TemperatureSeong-Hoon Jang,1,2* Randy Jalem,2 and Yoshitaka Tateyama2,3 1 Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, 980-8577, Japan2 Research Center for Energy and Environmental Materials (GREEN), National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan3 Laboratory for Chemistry and Life Science, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama, 226-8501, Japan*Corresponding author: jang.seonghoon.b4@tohoku.ac.jpS1Electronic Supplementary Material (ESI) for Journal of Materials Chemistry A.This journal is Β© The Royal Society of Chemistry 2024Discussion S1 Details of sampling protocolSampling space. The space group for each is as follows: (with the orthorhombic Ξ© π‘π‘Ž5𝐴𝑙𝑆4 symmetry),1, 2 (monoclinic ),3 (monoclinic ),1 π‘ƒπ‘π‘π‘Ž π‘π‘Ž5𝐼𝑛𝑆4 𝑃21/π‘š π‘π‘Ž4.5𝐴𝑙0.5𝑆𝑖0.5𝑆4 𝐢𝑐 π‘π‘Ž4𝑆𝑖𝑆4(orthorhombic ),1, 4-6 (tetragonal ),7-9 (tetragonal ),10-12 and 𝑃212121 π‘π‘Ž4𝑆𝑛𝑆4 𝑃4Μ…21𝑐 π‘π‘Ž3𝑉𝑆4 𝑃4Μ…21𝑐 (tetragonal ).1, 13-15π‘π‘Ž3𝑆𝑏𝑆4 𝑃4Μ…21𝑐Ewald summation sampling. cases of at were taken in total: 112 (𝑀, 𝑀',Ξ©) π‘š = π‘š' = 0.5 cases of for and and cases of . We conducted 105 π‘π‘Ž4𝑀0.5𝑀'0.5𝑆4 𝑣(𝑀) = 3 𝑣(𝑀') = 5 7 π‘π‘Ž3.5𝑆𝑖0.5π‘‡π‘Ž0.5𝑆4supercell operations on the abovementioned parent structures. We modified the number of Na-ions when necessary, and replaced host metal ion sites with and . This resulted in supercells with 𝑀 𝑀'varying numbers of ion sites: for , , , , and 144 Ξ© = π‘π‘Ž5𝐴𝑙𝑆4 π‘π‘Ž5𝐼𝑛𝑆4 π‘π‘Ž4.5𝐴𝑙0.5𝑆𝑖0.5𝑆4 π‘π‘Ž3𝑉𝑆4 π‘π‘Ž3𝑆𝑏𝑆4and for and with and ; for , , 216 Ξ© = π‘π‘Ž4𝑆𝑖𝑆4 π‘π‘Ž4𝑆𝑛𝑆4 𝑣(𝑀) = 3 𝑣(𝑀') = 5 136 Ξ© = π‘π‘Ž5𝐴𝑙𝑆4 π‘π‘Ž5𝐼𝑛𝑆4, , , and and 204 for with .π‘π‘Ž4.5𝐴𝑙0.5𝑆𝑖0.5𝑆4 π‘π‘Ž4𝑆𝑛𝑆4 π‘π‘Ž3𝑉𝑆4 π‘π‘Ž3𝑆𝑏𝑆4 π‘π‘Ž4𝑆𝑖𝑆4 π‘π‘Ž3.5𝑆𝑖0.5π‘‡π‘Ž0.5𝑆4 For each with and (or with ), a substantial number of Ξ© 𝑣(𝑀) = 3 𝑣(𝑀') = 5 π‘π‘Ž3.5𝑆𝑖0.5π‘‡π‘Ž0.5𝑆4random site arrangements was generated, ranging from to (from to 18,200 623,551,500 33,124,000 ) and giving a total dataset size of . From these site arrangements, 2,460,781,960 π‘›π‘‘π‘Žπ‘‘π‘Ž = 5,290,074,920we selected less than site arrangements with lowest Ewald Coulombic energies for each 6 πΈπΈπ‘€π‘Žπ‘™π‘‘case of or ( ).16-18 In the subsequent step of DFT geometry π‘π‘Ž4𝑀0.5𝑀'0.5𝑆4 π‘π‘Ž3.5𝑆𝑖0.5π‘‡π‘Ž0.5𝑆4 π‘›π‘‘π‘Žπ‘‘π‘Ž = 469optimizations, we fully relaxed the site positions and lattice parameters for the selected site arrangements. The cell structure with the lowest DFT energy or, equivalently, the lowest 𝐸𝐷𝐹𝑇, was chosen as the representative sample for each case of or for πΈβ„Žπ‘’π‘™π‘™ π‘π‘Ž4𝑀0.5𝑀'0.5𝑆4 π‘π‘Ž3.5𝑆𝑖0.5π‘‡π‘Ž0.5𝑆4the succeeding DFT-MD sampling ( ). π‘›π‘‘π‘Žπ‘‘π‘Ž = 16S2Geometry optimization with DFT. This step was performed by using the Vienna Ab Initio Simulation Package (VASP). We employed the generalized gradient approximation (GGA) and the projector augmented wave (PAW) method basis set.19-23 The geometry optimizations included both site positions and lattice constants. Monkhorst-Pack -grids were set at ,24 π‘˜ 2 Γ— 2 Γ— 2and the kinetic energy cutoff of eV was used. Convergence criteria of eVοƒ—Γ…-1 for forces 520 < 0.01and eVοƒ—atom-1 for energy were applied. Some pseudopotentials included semicore < 10 β€’ 5electrons as valence states for specific elements: Ca, Sc, and Zr (semicore s electrons); Na, V, Nb, and Ta ( ); and Ga, In, and Sn ( ). For the other elements, standard pseudopotential forms were 𝑝 𝑑employed. Then, the lowest-energy structure sample for each investigated composition was selected for subsequent DFT-MD calculations, wherein we calculated for all the samples by πΈβ„Žπ‘’π‘™π‘™using the Computational Phase Diagram App provided by MaterialsProject.org25, 26 to verify their thermodynamic (meta)stability. Bandgap energies were also examined for some of the samples 𝐸𝑔by using Heyd-Scuseria-Ernzerhof hybrid functionals (HSE06) provided under VASP.27DFT-MD for the single-temperature β€œlong-time” diagnosis. The single-temperature β€œlong-time” diagnosis was carried out at K given the geometry-optimized cell structures 𝑇 = 300described above. First, a total of DFT-MD steps ( ps) were performed to ensure thermal 10,000 10equilibrations by using the NosΓ©-Hoover thermostat ( ensemble) implemented in VASP.28, 29 𝑁𝑉𝑇Subsequently, DFT-MD production runs were executed for trajectory sampling over ps (𝜏 = 250). Throughout the DFT-MD calculations, fs, a -grid (that is, only), and a 𝑁𝑉𝑇 βˆ†πœ = 1 1 Γ— 1 Γ— 1 π‘˜ Ξ“kinetic energy cutoff of eV were employed. The pseudopotentials were used in their standard 400forms except for Nb (with semicore electrons), and the calculations were performed using the 𝑝GGA and the PAW method basis set.19-23S3From the sampled trajectories, the Na-ion self-diffusion coefficients at π·π‘π‘Ž,𝑇 = 𝑀𝑠 (2𝑑) 𝑇were estimated by conducting regression analyses on the mean squared displacement (MSD) curves against sampled time intervals ; was obtained as the slope of the MSD- βˆ†πœπ‘€π‘†π· π·π‘π‘Ž,𝑇 𝑀𝑠 βˆ†πœπ‘€π‘†π·regression line at , considering the three-dimensional nature of Na-ion diffusion ( ). Then, 𝑇 𝑑 = 3the Na-ion ionic conductivity at is estimated by using the Nernst-Einstein equation πœŽπ‘π‘Ž,𝑇 𝑇, (S1)πœŽπ‘π‘Ž,𝑇 =(π‘§π‘π‘ŽπΉ)2πœŒπ‘π‘Žπ‘…π‘‡π·π‘π‘Ž,𝑇where ( ) is the valence for a Na-ion, is the Na-ion density, and and denote the π‘§π‘π‘Ž =+ 1 πœŒπ‘π‘Ž 𝐹 𝑅Faraday constant and the gas constant, respectively.DFT-MD for multi-temperature calculations. The multi-temperature DFT-MD calculations were conducted at , , , , and K for , 𝑇 = 500 600 700 800 900 π‘π‘Ž4𝑆𝑖𝑆4, , , , π‘π‘Ž4πΊπ‘Ž0.125𝑆𝑖0.75𝑃0.125𝑆4 π‘π‘Ž4πΊπ‘Ž0.25𝑆𝑖0.5𝑃0.25𝑆4 π‘π‘Ž4πΊπ‘Ž0.375𝑆𝑖0.25𝑃0.375𝑆4 π‘π‘Ž4πΊπ‘Ž0.5𝑃0.5𝑆4, , , , π‘π‘Ž3.75πΊπ‘Ž0.375𝑃0.625𝑆4 π‘π‘Ž4.25πΊπ‘Ž0.625𝑃0.375𝑆4 π‘π‘Ž3.875𝑆𝑖0.875π‘‡π‘Ž0.125𝑆4 π‘π‘Ž3.75𝑆𝑖0.75π‘‡π‘Ž0.25𝑆4, and with . First, a total of DFT-MD steps (π‘π‘Ž3.625𝑆𝑖0.625π‘‡π‘Ž0.375𝑆4 π‘π‘Ž3.5𝑆𝑖0.5π‘‡π‘Ž0.5𝑆4 Ξ© = π‘π‘Ž4𝑆𝑖𝑆4 40,000 ps) were performed to achieve thermal and volume equilibrations by using the Langevin 40thermostat with the Parinello-Rahman algorithm ( ensemble) implemented in VASP.30, 31 𝑁𝑝𝑇During this process, the averaged lattice constants were calculated over the last DFT-MD 10,000steps ( - ps) to account cell volumes expanded thermally. Subsequently, with the averaged 30 40lattice constants, thermal equilibration runs were repeated for DFT-MD steps ( ps) under 10,000 10the NosΓ©-Hoover thermostat ( ). Finally, product runs were conducted afterwards for trajectory 𝑁𝑉𝑇sampling over ps ( ). Meanwhile, the choices of , the -grid, the kinetic energy cutoff, 𝜏 = 100 𝑁𝑉𝑇 βˆ†πœ π‘˜S4and the pseudopotentials and the post-process for and were common to those of the π·π‘π‘Ž,𝑇 πœŽπ‘π‘Ž,𝑇DFT-MD for the single-temperature β€œlong-time” diagnosisS5Table S1 Lattice constants , , , , , and , unit cell volumes , and convex hull decomposition π‘Ž 𝑏 𝑐 𝛼 𝛽 𝛾 𝑉energies per atom for compositions and whose structures were πΈβ„Žπ‘’π‘™π‘™ π‘π‘Ž4𝑀0.5𝑀'0.5𝑆4 π‘π‘Ž3.5𝑆𝑖0.5π‘‡π‘Ž0.5𝑆4relaxed by using DFT across various parent structures Ξ©Composition Compositionper unit cell Ξ© π‘Ž(Γ…)𝑏(Γ…)𝑐(Γ…)𝛼(Β°)𝛽(Β°)𝛾(Β°)𝑉(Γ…3)πΈβ„Žπ‘’π‘™π‘™(meVοƒ—atom-1)Na4Al0.5P0.5S4 Na64Al8P8S64 Na5AlS4 11.563 14.190 21.618 91.693 89.528 90.045 3545.4 37.9Na4Al0.5P0.5S4 Na64Al8P8S64 Na5InS4 13.887 17.765 14.446 89.422 86.947 89.851 3558.6 26.4Na4Al0.5P0.5S4 Na64Al8P8S64 Na4.5Al0.5Si0.5S4 17.585 13.997 14.374 89.792 92.950 90.627 3533.2 23.7Na4Al0.5P0.5S4 Na96Al12P12S96 Na4SiS4 41.870 8.917 13.857 89.953 89.529 90.035 5173.6 14.6Na4Al0.5P0.5S4 Na96Al12P12S96 Na4SnS4 15.585 15.585 13.635 90.000 90.000 90.000 3311.6 24.6Na4Al0.5P0.5S4 Na64Al8P8S64 Na3VS4 14.169 14.611 16.480 89.235 87.477 89.334 3407.6 65.1Na4Al0.5P0.5S4 Na64Al8P8S64 Na3SbS4 19.832 13.103 20.902 88.821 89.960 89.890 5430.5 43.5Na4Al0.5V0.5S4 Na64Al8V8S64 Na5AlS4 11.681 14.390 21.401 90.865 89.541 89.608 3596.9 39.7Na4Al0.5V0.5S4 Na64Al8V8S64 Na5InS4 13.926 17.642 14.553 88.839 87.345 89.680 3570.6 33.5Na4Al0.5V0.5S4 Na64Al8V8S64 Na4.5Al0.5Si0.5S4 17.772 13.744 14.381 89.556 93.448 89.816 3506.0 24.1Na4Al0.5V0.5S4 Na96Al12V12S96 Na4SiS4 41.903 8.7802 14.081 89.999 90.011 90.023 5180.7 16.8Na4Al0.5V0.5S4 Na96Al12V12S96 Na4SnS4 15.586 15.586 13.735 90.000 90.000 90.000 3336.8 30.2Na4Al0.5V0.5S4 Na64Al8V8S64 Na3VS4 14.909 14.213 16.334 88.085 90.759 89.052 3458.4 55.6Na4Al0.5V0.5S4 Na64Al8V8S64 Na3SbS4 19.673 12.940 21.359 89.371 89.724 90.815 5436.3 46.4Na4Al0.5Nb0.5S4 Na64Al8Nb8S64 Na5AlS4 11.987 14.491 21.556 90.262 89.535 89.453 3744.1 36.2Na4Al0.5Nb0.5S4 Na64Al8Nb8S64 Na5InS4 13.728 17.710 15.066 88.779 87.839 89.545 3659.5 25.2Na4Al0.5Nb0.5S4 Na64Al8Nb8S64 Na4.5Al0.5Si0.5S4 17.908 13.925 14.502 89.564 93.126 89.544 3610.7 17.8Na4Al0.5Nb0.5S4 Na96Al12Nb12S96 Na4SiS4 42.197 8.951 14.154 90.032 90.194 90.051 5346.0 17.2Na4Al0.5Nb0.5S4 Na96Al12Nb12S96 Na4SnS4 15.659 15.659 13.864 90.000 90.000 90.000 3399.4 20.1Na4Al0.5Nb0.5S4 Na64Al8Nb8S64 Na3VS4 14.697 14.940 16.468 89.435 88.221 90.044 3613.9 40.1Na4Al0.5Nb0.5S4 Na64Al8Nb8S64 Na3SbS4 20.157 13.358 20.970 89.887 89.863 89.381 5646.0 52.9Na4Al0.5Sb0.5S4 Na64Al8Sb8S64 Na5AlS4 11.928 14.315 21.773 90.646 89.682 89.780 3717.4 39.7Na4Al0.5Sb0.5S4 Na64Al8Sb8S64 Na5InS4 13.783 17.861 15.167 87.904 87.622 88.588 3727.1 31.4Na4Al0.5Sb0.5S4 Na96Al12Sb12S96 Na4.5Al0.5Si0.5S4 17.853 14.046 14.748 89.831 92.665 89.872 3694.3 24.0Na4Al0.5Sb0.5S4 Na96Al12Sb12S96 Na4SiS4 42.002 9.1901 14.060 90.044 90.035 90.017 5427.3 26.9Na4Al0.5Sb0.5S4 Na64Al8Sb8S64 Na4SnS4 15.738 15.738 13.862 90.000 90.000 90.000 3433.5 13.9Na4Al0.5Sb0.5S4 Na64Al8Sb8S64 Na3VS4 15.221 15.015 15.946 87.826 88.415 91.302 3639.5 50.6Na4Al0.5Sb0.5S4 Na64Al8Sb8S64 Na3SbS4 20.680 13.613 20.337 89.405 89.142 89.863 5724.2 54.9Na4Al0.5Ta0.5S4 Na64Al8Ta8S64 Na5AlS4 12.098 14.542 21.711 90.707 87.790 89.364 3816.4 43.7Na4Al0.5Ta0.5S4 Na64Al8Ta8S64 Na5InS4 13.759 17.727 15.062 88.815 87.823 89.575 3670.4 27.9Na4Al0.5Ta0.5S4 Na96Al12Ta12S96 Na4.5Al0.5Si0.5S4 17.917 13.926 14.501 89.558 93.144 89.582 3612.5 20.0Na4Al0.5Ta0.5S4 Na96Al12Ta12S96 Na4SiS4 42.228 8.9538 14.139 90.029 90.229 90.064 5346.1 19.4Na4Al0.5Ta0.5S4 Na64Al8Ta8S64 Na4SnS4 15.672 15.671 13.849 89.997 89.999 89.998 3401.4 22.6Na4Al0.5Ta0.5S4 Na64Al8Ta8S64 Na3VS4 14.692 14.960 16.489 89.559 88.297 90.319 3622.4 41.1Na4Al0.5Ta0.5S4 Na64Al8Ta8S64 Na3SbS4 19.895 13.225 21.368 88.790 89.093 91.101 5619.2 45.6Na4Ga0.5P0.5S4 Na64Ga8P8S64 Na5AlS4 11.960 14.307 21.436 90.925 89.009 89.485 3666.7 52.6Na4Ga0.5P0.5S4 Na64Ga8P8S64 Na5InS4 13.735 17.843 14.684 88.868 86.897 89.170 3592.3 31.0Na4Ga0.5P0.5S4 Na64Ga8P8S64 Na4.5Al0.5Si0.5S4 17.801 13.710 14.375 89.591 93.334 89.737 3502.3 25.1Na4Ga0.5P0.5S4 Na96Ga12P12S96 Na4SiS4 41.764 8.977 13.873 89.966 89.739 89.986 5201.4 15.8Na4Ga0.5P0.5S4 Na96Ga12P12S96 Na4SnS4 15.582 15.582 13.659 90.000 90.000 90.000 3316.3 23.8Na4Ga0.5P0.5S4 Na64Ga8P8S64 Na3VS4 14.571 14.546 16.057 88.841 89.370 89.650 3402.3 63.4Na4Ga0.5P0.5S4 Na64Ga8P8S64 Na3SbS4 20.571 13.426 20.179 89.362 89.607 88.852 5571.5 66.7Na4Ga0.5V0.5S4 Na64Ga8V8S64 Na5AlS4 11.769 14.428 21.410 90.638 89.471 89.463 3634.9 43.2Na4Ga0.5V0.5S4 Na64Ga8V8S64 Na5InS4 13.843 17.635 14.740 89.100 88.044 89.838 3595.9 41.7Na4Ga0.5V0.5S4 Na64Ga8V8S64 Na4.5Al0.5Si0.5S4 17.809 13.752 14.420 89.586 93.435 89.762 3525.1 26.2Na4Ga0.5V0.5S4 Na96Ga12V12S96 Na4SiS4 42.019 8.8071 14.050 89.991 90.034 90.029 5199.5 17.3Na4Ga0.5V0.5S4 Na96Ga12V12S96 Na4SnS4 15.589 15.589 13.770 90.000 90.000 90.000 3346.4 28.6Na4Ga0.5V0.5S4 Na64Ga8V8S64 Na3VS4 14.478 14.124 16.616 88.897 90.434 89.331 3396.5 70.4Na4Ga0.5V0.5S4 Na64Ga8V8S64 Na3SbS4 19.964 13.071 21.228 90.423 90.478 89.628 5538.9 57.7Na4Ga0.5Nb0.5S4 Na64Ga8Nb8S64 Na5AlS4 12.035 14.469 21.566 90.413 89.531 89.427 3754.9 37.3Na4Ga0.5Nb0.5S4 Na64Ga8Nb8S64 Na5InS4 14.050 17.925 14.700 88.476 86.152 89.465 3692.2 20.5Na4Ga0.5Nb0.5S4 Na64Ga8Nb8S64 Na4.5Al0.5Si0.5S4 17.893 13.969 14.593 90.061 93.354 90.129 3641.1 23.1Na4Ga0.5Nb0.5S4 Na96Ga12Nb12S96 Na4SiS4 42.238 8.9891 14.132 90.023 90.161 90.052 5365.7 17.7Na4Ga0.5Nb0.5S4 Na96Ga12Nb12S96 Na4SnS4 15.684 15.684 13.873 90.000 90.000 90.000 3412.5 18.2Na4Ga0.5Nb0.5S4 Na64Ga8Nb8S64 Na3VS4 14.938 14.408 16.596 89.045 90.590 88.645 3570.4 50.0Na4Ga0.5Nb0.5S4 Na64Ga8Nb8S64 Na3SbS4 20.081 13.156 21.388 90.195 89.683 91.129 5649.0 44.8Na4Ga0.5Sb0.5S4 Na64Ga8Sb8S64 Na5AlS4 12.239 14.404 21.927 90.946 87.669 89.082 3861.2 53.8Na4Ga0.5Sb0.5S4 Na64Ga8Sb8S64 Na5InS4 13.728 17.960 15.165 89.420 88.291 89.607 3736.8 36.1Na4Ga0.5Sb0.5S4 Na96Ga12Sb12S96 Na4.5Al0.5Si0.5S4 17.917 14.080 14.795 89.799 92.441 89.890 3728.8 29.7Na4Ga0.5Sb0.5S4 Na96Ga12Sb12S96 Na4SiS4 42.082 9.1991 14.022 90.019 89.389 90.017 5427.8 31.2Na4Ga0.5Sb0.5S4 Na64Ga8Sb8S64 Na4SnS4 15.755 15.755 13.895 90.000 90.000 90.000 3449.2 15.5Na4Ga0.5Sb0.5S4 Na64Ga8Sb8S64 Na3VS4 14.988 14.720 16.401 89.586 86.820 89.398 3612.6 61.0S6Na4Ga0.5Sb0.5S4 Na64Ga8Sb8S64 Na3SbS4 20.325 13.580 20.759 90.656 89.115 90.377 5728.5 44.2Na4Ga0.5Ta0.5S4 Na64Ga8Ta8S64 Na5AlS4 12.176 14.211 21.575 91.189 89.572 89.006 3731.9 35.9Na4Ga0.5Ta0.5S4 Na64Ga8Ta8S64 Na5InS4 13.968 17.881 14.766 88.324 87.413 89.145 3682.3 27.7Na4Ga0.5Ta0.5S4 Na96Ga12Ta12S96 Na4.5Al0.5Si0.5S4 17.942 13.951 14.539 89.594 93.122 89.533 3633.7 22.1Na4Ga0.5Ta0.5S4 Na96Ga12Ta12S96 Na4SiS4 42.303 8.9968 14.106 90.028 90.293 90.068 5368.5 19.7Na4Ga0.5Ta0.5S4 Na64Ga8Ta8S64 Na4SnS4 15.698 15.698 13.896 90.000 90.000 90.000 3424.6 20.6Na4Ga0.5Ta0.5S4 Na64Ga8Ta8S64 Na3VS4 14.759 14.822 16.418 89.175 87.358 89.305 3587.1 56.3Na4Ga0.5Ta0.5S4 Na64Ga8Ta8S64 Na3SbS4 19.927 13.099 21.395 91.280 90.020 90.630 5582.6 44.5Na4In0.5P0.5S4 Na64In8P8S64 Na5AlS4 11.758 14.352 21.597 92.324 90.350 89.461 3641.1 51.8Na4In0.5P0.5S4 Na64In8P8S64 Na5InS4 13.861 18.128 14.778 89.377 86.092 89.224 3704.0 33.7Na4In0.5P0.5S4 Na64In8P8S64 Na4.5Al0.5Si0.5S4 17.824 14.209 14.613 90.834 94.312 90.583 3689.9 42.7Na4In0.5P0.5S4 Na96In12P12S96 Na4SiS4 42.123 9.1717 13.892 89.908 90.168 90.030 5366.9 31.1Na4In0.5P0.5S4 Na96In12P12S96 Na4SnS4 15.933 15.933 13.645 90.000 90.000 90.000 3463.9 30.8Na4In0.5P0.5S4 Na64In8P8S64 Na3VS4 14.500 15.823 15.860 88.948 92.706 88.796 3633.4 55.1Na4In0.5P0.5S4 Na64In8P8S64 Na3SbS4 20.314 13.460 20.538 90.131 90.212 89.445 5615.3 59.8Na4In0.5V0.5S4 Na64In8V8S64 Na5AlS4 11.772 14.432 21.640 91.785 89.711 89.663 3674.7 55.4Na4In0.5V0.5S4 Na64In8V8S64 Na5InS4 13.691 17.872 15.051 89.244 87.699 89.753 3679.4 44.4Na4In0.5V0.5S4 Na64In8V8S64 Na4.5Al0.5Si0.5S4 17.978 13.904 14.606 89.676 93.832 89.813 3642.7 44.8Na4In0.5V0.5S4 Na96In12V12S96 Na4SiS4 42.274 9.0120 14.086 89.936 90.260 90.002 5366.3 37.1Na4In0.5V0.5S4 Na96In12V12S96 Na4SnS4 15.830 15.830 13.822 90.000 90.000 90.000 3463.7 35.9Na4In0.5V0.5S4 Na64In8V8S64 Na3VS4 15.310 14.424 16.386 87.890 90.168 87.426 3612.3 68.6Na4In0.5V0.5S4 Na64In8V8S64 Na3SbS4 20.277 13.405 21.038 90.621 89.971 89.915 5718.0 70.3Na4In0.5Nb0.5S4 Na64In8Nb8S64 Na5AlS4 12.341 14.497 21.644 91.067 89.627 89.418 3871.3 53.8Na4In0.5Nb0.5S4 Na64In8Nb8S64 Na5InS4 13.734 17.925 15.315 89.199 88.186 89.796 3767.8 34.8Na4In0.5Nb0.5S4 Na64In8Nb8S64 Na4.5Al0.5Si0.5S4 18.133 14.160 14.717 89.714 93.364 89.577 3772.0 37.3Na4In0.5Nb0.5S4 Na96In12Nb12S96 Na4SnS4 15.836 15.836 13.969 90.000 90.000 90.000 3503.3 23.5Na4In0.5Nb0.5S4 Na64In8Nb8S64 Na3VS4 14.799 14.470 17.068 89.110 88.201 88.816 3651.8 64.4Na4In0.5Nb0.5S4 Na64In8Nb8S64 Na3SbS4 20.598 13.690 20.627 89.555 90.625 90.787 5815.5 58.1Na4In0.5Sb0.5S4 Na64In8Sb8S64 Na5AlS4 12.390 14.411 21.110 90.680 89.885 89.314 3768.8 48.7Na4In0.5Sb0.5S4 Na64In8Sb8S64 Na5InS4 13.744 18.116 15.357 89.189 87.797 89.721 3820.6 37.5Na4In0.5Sb0.5S4 Na96In12Sb12S96 Na4.5Al0.5Si0.5S4 18.257 14.280 14.711 89.514 92.722 89.247 3830.7 44.1Na4In0.5Sb0.5S4 Na96In12Sb12S96 Na4SiS4 42.153 9.4950 14.132 89.886 90.249 90.065 5656.0 36.6Na4In0.5Sb0.5S4 Na64In8Sb8S64 Na4SnS4 15.916 15.916 13.957 90.000 90.000 90.000 3535.6 17.4Na4In0.5Sb0.5S4 Na64In8Sb8S64 Na3VS4 14.857 15.198 16.623 89.589 87.892 89.608 3750.7 56.7Na4In0.5Sb0.5S4 Na64In8Sb8S64 Na3SbS4 20.936 13.919 20.249 90.720 88.452 89.507 5897.6 60.0Na4In0.5Ta0.5S4 Na64In8Ta8S64 Na5AlS4 12.350 14.500 21.647 91.009 89.503 89.417 3875.4 56.3Na4In0.5Ta0.5S4 Na64In8Ta8S64 Na5InS4 13.765 17.962 15.279 89.131 87.971 89.767 3775.0 36.8Na4In0.5Ta0.5S4 Na96In12Ta12S96 Na4.5Al0.5Si0.5S4 18.136 14.143 14.729 89.680 93.319 89.586 3771.5 39.9Na4In0.5Ta0.5S4 Na96In12Ta12S96 Na4SiS4 42.515 9.2180 14.184 89.963 90.513 90.026 5558.5 38.8Na4In0.5Ta0.5S4 Na64In8Ta8S64 Na4SnS4 15.845 15.845 13.970 90.000 90.000 90.000 3507.2 26.0Na4In0.5Ta0.5S4 Na64In8Ta8S64 Na3VS4 14.899 14.593 16.949 89.268 88.186 88.355 3681.4 62.3Na4In0.5Ta0.5S4 Na64In8Ta8S64 Na3SbS4 21.081 13.973 20.244 89.628 87.973 89.403 5959.4 75.4Na3.5Si0.5Ta0.5S4 Na56Si8Ta8S64 Na5AlS4 11.602 14.197 22.060 90.395 91.871 90.771 3631.3 44.7Na3.5Si0.5Ta0.5S4 Na56Si8Ta8S64 Na5InS4 13.625 18.213 14.391 90.715 86.832 91.114 3565.0 30.6Na3.5Si0.5Ta0.5S4 Na56Si8Ta8S64 Na4.5Al0.5Si0.5S4 17.824 13.896 14.345 91.525 93.518 90.139 3545.0 31.7Na3.5Si0.5Ta0.5S4 Na84Si12Ta12S96 Na4SiS4 41.654 8.9369 14.080 90.072 89.220 90.088 5241.0 24.1Na3.5Si0.5Ta0.5S4 Na56Si8Ta8S64 Na4SnS4 15.802 15.445 13.845 90.360 90.620 89.424 3378.6 24.3Na3.5Si0.5Ta0.5S4 Na56Si8Ta8S64 Na3VS4 14.192 13.926 16.324 89.917 89.817 89.664 3226.1 42.6S7Table S2 Na-ion conductivity (in Sοƒ—cm-1) and Na-ion self-diffusion coefficient (in cm2οƒ—s-πœŽπ‘π‘Ž,𝑇 π·π‘π‘Ž,𝑇1) for the compositions adopted in the multi-temperature diagnosis with fs, ps, 11 βˆ†πœ = 1 𝜏 = 100and , , , , and K (β€œ ” denotes the absence of observed Na-ion migrations). 𝑇 = 500 600 700 800 800 β€’By extrapolating the values in the Arrhenius plots [see Figures 1(i) and 2(h)], Na-ion activation energies and were estimated as well. In , the standard errors are presented. In the first πΈπ‘Ž πœŽπ‘π‘Ž,300𝐾 πΈπ‘Žrow, the compositions per unit cell are presented in parentheses.CompositionπœŽπ‘π‘Ž,300𝐾( )π·π‘π‘Ž,300πΎπœŽπ‘π‘Ž,500𝐾( )π·π‘π‘Ž,500πΎπœŽπ‘π‘Ž,600𝐾( )π·π‘π‘Ž,600πΎπœŽπ‘π‘Ž,700𝐾( )π·π‘π‘Ž,700πΎπœŽπ‘π‘Ž,800𝐾( )π·π‘π‘Ž,800πΎπœŽπ‘π‘Ž,900𝐾( )π·π‘π‘Ž,900πΎπΈπ‘Ž(meV)π‘π‘Ž4𝑆𝑖𝑆4( )π‘π‘Ž96𝑆𝑖24𝑆962.57 Γ— 10 β€’ 15(2.00 Γ— 10 β€’ 20)β€’7.01 Γ— 10 β€’ 5(1.26 Γ— 10 β€’ 9)3.48 Γ— 10 β€’ 4(7.43 Γ— 10 β€’ 9)1.38 Γ— 10 β€’ 2(3.40 Γ— 10 β€’ 7)1.16 Γ— 10 β€’ 1(3.27 Γ— 10 β€’ 6)1250Β± 145π‘π‘Ž4πΊπ‘Ž0.125𝑆𝑖0.75𝑃0.125𝑆4( )π‘π‘Ž96πΊπ‘Ž3𝑆𝑖18𝑃3𝑆962.26 Γ— 10 β€’ 11(1.84 Γ— 10 β€’ 16)4.47 Γ— 10 β€’ 5(6.69 Γ— 10 β€’ 10)β€’1.14 Γ— 10 β€’ 2(2.45 Γ— 10 β€’ 7)1.98 Γ— 10 β€’ 1(4.99 Γ— 10 β€’ 6)4.11 Γ— 10 β€’ 1(1.18 Γ— 10 β€’ 5)965Β± 43.1π‘π‘Ž4πΊπ‘Ž0.25𝑆𝑖0.5𝑃0.25𝑆4( )π‘π‘Ž96πΊπ‘Ž6𝑆𝑖12𝑃6𝑆969.48 Γ— 10 β€’ 9(7.89 Γ— 10 β€’ 14)5.11 Γ— 10 β€’ 4( )7.73 Γ— 10 β€’ 97.39 Γ— 10 β€’ 3(1.35 Γ— 10 β€’ 7)1.66 Γ— 10 β€’ 1(3.63 Γ— 10 β€’ 6)1.25 Γ— 10 β€’ 1(3.15 Γ— 10 β€’ 6)7.13 Γ— 10 β€’ 1(2.05 Γ— 10 β€’ 5)747Β± 88.1π‘π‘Ž4πΊπ‘Ž0.375𝑆𝑖0.25𝑃0.375𝑆4( )π‘π‘Ž96πΊπ‘Ž9𝑆𝑖6𝑃9𝑆966.03 Γ— 10 β€’ 11(4.89 Γ— 10 β€’ 16)4.52 Γ— 10 β€’ 5(6.83 Γ— 10 β€’ 10)1.04 Γ— 10 β€’ 2(1.92 Γ— 10 β€’ 7)1.88 Γ— 10 β€’ 2(4.07 Γ— 10 β€’ 7)2.12 Γ— 10 β€’ 1(5.39 Γ— 10 β€’ 6)7.08 Γ— 10 β€’ 1(2.07 Γ— 10 β€’ 5)948Β± 111π‘π‘Ž4πΊπ‘Ž0.5𝑃0.5𝑆4( )π‘π‘Ž96πΊπ‘Ž12𝑃12𝑆969.71 Γ— 10 β€’ 4( )7.92 Γ— 10 β€’ 97.00 Γ— 10 β€’ 2( )1.07 Γ— 10 β€’ 61.51 Γ— 10 β€’ 1(2.78 Γ— 10 β€’ 6)1.48 Γ— 10 β€’ 1(3.28 Γ— 10 β€’ 6)6.39 Γ— 10 β€’ 1(1.65 Γ— 10 β€’ 5)8.24 Γ— 10 β€’ 1(2.41 Γ— 10 β€’ 5)297Β± 56.3π‘π‘Ž3.75πΊπ‘Ž0.375𝑃0.625𝑆4( )π‘π‘Ž90πΊπ‘Ž9𝑃15𝑆962.07 Γ— 10 β€’ 3( )1.77 Γ— 10 β€’ 81.19 Γ— 10 β€’ 1( )1.91 Γ— 10 β€’ 62.77 Γ— 10 β€’ 1(5.41 Γ— 10 β€’ 6)4.35 Γ— 10 β€’ 1(1.02 Γ— 10 β€’ 5)9.44 Γ— 10 β€’ 1(2.55 Γ— 10 β€’ 5)1.30 Γ— 100(4.07 Γ— 10 β€’ 5)290Β± 18.0π‘π‘Ž4.25πΊπ‘Ž0.625𝑃0.375𝑆4( )π‘π‘Ž102πΊπ‘Ž15𝑃9𝑆966.57 Γ— 10 β€’ 4( )5.26 Γ— 10 β€’ 94.96 Γ— 10 β€’ 2( )7.23 Γ— 10 β€’ 71.83 Γ— 10 β€’ 1(3.27 Γ— 10 β€’ 6)2.61 Γ— 10 β€’ 1(5.47 Γ— 10 β€’ 6)4.52 Γ— 10 β€’ 1(1.10 Γ— 10 β€’ 5)8.61 Γ— 10 β€’ 1(2.41 Γ— 10 β€’ 5)316Β± 22.6π‘π‘Ž3.875𝑆𝑖0.875π‘‡π‘Ž0.125𝑆4( )π‘π‘Ž93𝑆𝑖21π‘‡π‘Ž3𝑆964.93 Γ— 10 β€’ 5(4.22 Γ— 10 β€’ 10)2.06 Γ— 10 β€’ 2( )3.19 Γ— 10 β€’ 76.53 Γ— 10 β€’ 2(1.24 Γ— 10 β€’ 6)1.47 Γ— 10 β€’ 1(3.30 Γ— 10 β€’ 6)4.06 Γ— 10 β€’ 1(1.05 Γ— 10 β€’ 5)8.40 Γ— 10 β€’ 1(2.48 Γ— 10 β€’ 5)413Β± 27.4π‘π‘Ž3.75𝑆𝑖0.75π‘‡π‘Ž0.25𝑆4( )π‘π‘Ž90𝑆𝑖18π‘‡π‘Ž6𝑆962.36 Γ— 10 β€’ 3( )2.10 Γ— 10 β€’ 88.62 Γ— 10 β€’ 2( )1.39 Γ— 10 β€’ 61.38 Γ— 10 β€’ 1(2.72 Γ— 10 β€’ 6)9.09 Γ— 10 β€’ 2(2.11 Γ— 10 β€’ 6)4.26 Γ— 10 β€’ 1(1.14 Γ— 10 β€’ 5)6.83 Γ— 10 β€’ 1(2.09 Γ— 10 β€’ 5)246Β± 77.5π‘π‘Ž3.625𝑆𝑖0.625π‘‡π‘Ž0.375𝑆4( )π‘π‘Ž87𝑆𝑖15π‘‡π‘Ž9𝑆964.53 Γ— 10 β€’ 3( )4.25 Γ— 10 β€’ 81.12 Γ— 10 β€’ 1( )1.91 Γ— 10 β€’ 64.70 Γ— 10 β€’ 1(9.75 Γ— 10 β€’ 6)3.78 Γ— 10 β€’ 1(9.23 Γ— 10 β€’ 6)7.64 Γ— 10 β€’ 1(2.14 Γ— 10 β€’ 5)1.02 Γ— 100(3.32 Γ— 10 β€’ 5)252Β± 40.8π‘π‘Ž3.5𝑆𝑖0.5π‘‡π‘Ž0.5𝑆4( )π‘π‘Ž84𝐴𝑙12π‘‡π‘Ž12𝑆961.35 Γ— 10 β€’ 2( )1.27 Γ— 10 β€’ 72.53 Γ— 10 β€’ 1( )4.47 Γ— 10 β€’ 63.90 Γ— 10 β€’ 1(8.39 Γ— 10 β€’ 6)5.34 Γ— 10 β€’ 1(1.35 Γ— 10 β€’ 5)1.03 Γ— 100(3.07 Γ— 10 β€’ 5)1.23 Γ— 100(4.22 Γ— 10 β€’ 5)215Β± 21.7S8Figure S1 Mean squared displacement (MSD) curves against sampled time intervals given βˆ†πœπ‘€π‘†π·by the multi-temperature diagnosis (with fs and ps at , , , , and βˆ†πœ = 1 𝜏 = 100 𝑇 = 500 600 700 800 K) for the seven samples within : (a) , (b) 900 (𝑀, 𝑀',Ξ©) = (πΊπ‘Ž, 𝑃,π‘π‘Ž4𝑆𝑖𝑆4) π‘π‘Ž4𝑆𝑖𝑆4, (c) , (d) , (e) , (f) π‘π‘Ž4πΊπ‘Ž0.125𝑆𝑖0.75𝑃0.125𝑆4 π‘π‘Ž4πΊπ‘Ž0.25𝑆𝑖0.5𝑃0.25𝑆4 π‘π‘Ž4πΊπ‘Ž0.375𝑆𝑖0.25𝑃0.375𝑆4 π‘π‘Ž4πΊπ‘Ž0.5𝑃0.5𝑆4, and (g) . The dashed lines with slopes represent regression π‘π‘Ž3.75πΊπ‘Ž0.375𝑃0.625𝑆4 π‘π‘Ž4.25πΊπ‘Ž0.625𝑃0.375𝑆4analyses, and the insets present the trajectory density plot at 500 K represented by yellow 𝑇 =isosurfaces. S9Figure S2 Mean squared displacement (MSD) curves against sampled time intervals given βˆ†πœπ‘€π‘†π·by the multi-temperature diagnosis (with fs and ps at , , , , and βˆ†πœ = 1 𝜏 = 100 𝑇 = 500 600 700 800 K) for the four samples within : , 900 (𝑀, 𝑀',Ξ©) = (𝑆𝑖, π‘‡π‘Ž,π‘π‘Ž4𝑆𝑖𝑆4) π‘π‘Ž3.875𝑆𝑖0.875π‘‡π‘Ž0.125𝑆4, , and . For the MSD curves of , π‘π‘Ž3.75𝑆𝑖0.75π‘‡π‘Ž0.25𝑆4 π‘π‘Ž3.625𝑆𝑖0.625π‘‡π‘Ž0.375𝑆4 π‘π‘Ž3.5𝑆𝑖0.5π‘‡π‘Ž0.5𝑆4 π‘π‘Ž4𝑆𝑖𝑆4Figure S1a is referred to. The dashed lines with slopes represent regression analyses, and the insets present the trajectory density plot at 500 K represented by yellow isosurfaces. 𝑇 =S10Discussion S2 Electrochemical stability windowsWe present the electrochemical stability windows and decomposition phases for the materials systems and in Table S3. These values were (𝑀, 𝑀',Ξ©) = (πΊπ‘Ž, 𝑃,π‘π‘Ž4𝑆𝑖𝑆4) (𝑆𝑖, π‘‡π‘Ž,π‘π‘Ž4𝑆𝑖𝑆4)calculated using the Computational Phase Diagram App provided by MaterialsProject.org.25, 26 The electrochemical stability window for , , π‘π‘Ž4πΊπ‘Ž0.125𝑆𝑖0.75𝑃0.125𝑆4 π‘π‘Ž4πΊπ‘Ž0.25𝑆𝑖0.5𝑃0.25𝑆4, , , and is V π‘π‘Ž4πΊπ‘Ž0.375𝑆𝑖0.25𝑃0.375𝑆4 π‘π‘Ž4πΊπ‘Ž0.5𝑃0.5𝑆4 π‘π‘Ž3.75πΊπ‘Ž0.375𝑃0.625𝑆4 π‘π‘Ž4.25πΊπ‘Ž0.625𝑃0.375𝑆4 [1.24, 1.55]vs. Na/Na+, with multiple decomposition phases identified as , , , and . π‘π‘Ž4𝑆𝑖𝑆4 π‘π‘Ž3πΊπ‘Žπ‘†3 π‘π‘Ž3𝑃𝑆4 π‘π‘Ž2𝑆When these decomposition phases form around solid interface regions, such as at the anode and cathode, the interphase-controlled electrochemical stability windows extend to V vs. [0.77, 2.12]Na/Na+.Similarly, the electrochemical stability window for , π‘π‘Ž3.875𝑆𝑖0.875π‘‡π‘Ž0.125𝑆4, , and is V vs. Na/Na+, with π‘π‘Ž3.75𝑆𝑖0.75π‘‡π‘Ž0.25𝑆4 π‘π‘Ž3.625𝑆𝑖0.625π‘‡π‘Ž0.375𝑆4 π‘π‘Ž3.5𝑆𝑖0.5π‘‡π‘Ž0.5𝑆4 [1.00, 1.91]decomposition phases being and . The interphase-controlled electrochemical π‘π‘Ž4𝑆𝑖𝑆4 π‘π‘Ž3π‘‡π‘Žπ‘†4stability window for these materials extends to V versus Na/Na+. Given that the narrow [0.77, 2.03]electrochemical stability windows for and are not (𝑀, 𝑀',Ξ©) = (πΊπ‘Ž, 𝑃,π‘π‘Ž4𝑆𝑖𝑆4) (𝑆𝑖, π‘‡π‘Ž,π‘π‘Ž4𝑆𝑖𝑆4)significantly improved by interphase control, it is advisable to incorporate electrochemically stable interphase layers in battery design.32 This is particularly important at the interfaces between the solid electrolyte and the anode, as well as between the solid electrolyte and the cathode.S11Table S3. Electrochemical stability windows for the compositions and decomposition phases 11adopted in the multi-temperature diagnosis.Composition Electrochemical stability windows (potential in V vs. Na/Na+)πœ™(Corresponding decomposition phases if exist)π‘π‘Ž4𝑆𝑖𝑆4 [0.77, 1.91]π‘π‘Ž4πΊπ‘Ž0.125𝑆𝑖0.75𝑃0.125𝑆4[1.24, 1.55]( , )π‘π‘Ž4𝑆𝑖𝑆4 π‘π‘Ž3πΊπ‘Žπ‘†3, π‘π‘Ž3𝑃𝑆4, π‘π‘Ž2π‘†π‘π‘Ž4πΊπ‘Ž0.25𝑆𝑖0.5𝑃0.25𝑆4[1.24, 1.55]( , )π‘π‘Ž4𝑆𝑖𝑆4 π‘π‘Ž3πΊπ‘Žπ‘†3, π‘π‘Ž3𝑃𝑆4, π‘π‘Ž2π‘†π‘π‘Ž4πΊπ‘Ž0.375𝑆𝑖0.25𝑃0.375𝑆4[1.24, 1.55]( , )π‘π‘Ž4𝑆𝑖𝑆4 π‘π‘Ž3πΊπ‘Žπ‘†3, π‘π‘Ž3𝑃𝑆4, π‘π‘Ž2π‘†π‘π‘Ž4πΊπ‘Ž0.5𝑃0.5𝑆4[1.24, 1.55]( )π‘π‘Ž3πΊπ‘Žπ‘†3, π‘π‘Ž3𝑃𝑆4, π‘π‘Ž2π‘†π‘π‘Ž3.75πΊπ‘Ž0.375𝑃0.625𝑆4[1.24, 1.55]( )π‘π‘Ž3πΊπ‘Žπ‘†3, π‘π‘Ž3𝑃𝑆4, π‘π‘Ž2π‘†π‘π‘Ž4.25πΊπ‘Ž0.625𝑃0.375𝑆4[1.24, 1.55]( )π‘π‘Ž3πΊπ‘Žπ‘†3, π‘π‘Ž3𝑃𝑆4, π‘π‘Ž2π‘†π‘π‘Ž3.875𝑆𝑖0.875π‘‡π‘Ž0.125𝑆4[1.00, 1.91]( )π‘π‘Ž4𝑆𝑖𝑆4, π‘π‘Ž3π‘‡π‘Žπ‘†4π‘π‘Ž3.75𝑆𝑖0.75π‘‡π‘Ž0.25𝑆4[1.00, 1.91]( )π‘π‘Ž4𝑆𝑖𝑆4, π‘π‘Ž3π‘‡π‘Žπ‘†4π‘π‘Ž3.625𝑆𝑖0.625π‘‡π‘Ž0.375𝑆4[1.00, 1.91]( )π‘π‘Ž4𝑆𝑖𝑆4, π‘π‘Ž3π‘‡π‘Žπ‘†4π‘π‘Ž3.5𝑆𝑖0.5π‘‡π‘Ž0.5𝑆4[1.00, 1.91]( )π‘π‘Ž4𝑆𝑖𝑆4, π‘π‘Ž3π‘‡π‘Žπ‘†4π‘π‘Ž3πΊπ‘Žπ‘†3 [0.79, 1.65]π‘π‘Ž3𝑃𝑆4 [1.24, 2.12]π‘π‘Ž2𝑆 [0, 1.55]π‘π‘Ž3π‘‡π‘Žπ‘†4 [1.00, 2.03]S12References1. 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