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[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)

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[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)

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Computational discovery of stable Na-ion sulfide solid electrolytes with high conductivity at room temperatureJournal ofMaterials Chemistry ACOMMUNICATIONOpen Access Article. Published on 05 August 2024. Downloaded on 10/9/2024 6:27:18 AM.  This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.View Article OnlineView Journal  | View IssueComputational daInstitute for Materials Research, Tohoku Un980-8577, Japan. E-mail: jang.seonghoon.b4bResearch Center for Energy and Environmenfor Materials Science (NIMS), 1-1 Namiki, TcLaboratory for Chemistry and Life SciencNagatsuta, Midori-ku, Yokohama, 226-8501† Electronic supplementary informationprotocol, comprehensive dataset for lattconvex hull decomposition energies forresults of the multi-temperahttps://doi.org/10.1039/d4ta02522aCite this: J. Mater. Chem. A, 2024, 12,20879Received 12th April 2024Accepted 15th July 2024DOI: 10.1039/d4ta02522arsc.li/materials-aThis journal is © The Royal Society oiscovery of stable Na-ion sulfidesolid electrolytes with high conductivity at roomtemperature†Seong-Hoon Jang, *ab Randy Jalem b and Yoshitaka Tateyama bcThe search for inorganic solid electrolytes suitable for the realizationof solid-state batteries with structural stability and high ion conduc-tivity at room temperature remains a significant challenge. In thisstudy, we employed a multi-stage density functional theory moleculardynamics (DFT-MD) sampling workflow, focusing on Na-ion sulfidesNanMmM0m0S4 with trivalent (M) and pentavalent (M0) metal ions and anexpanded selection of parent structures (U). This led to the identifi-cation of two promising sampling spaces (M,M0,U) = (Ga,P,Na4SiS4)and (Si,Ta,Na4SiS4). The predictions were validated through multi-temperature DFT-MD calculations, wherein sNa,300K T 10−3 S cm−1are attained within a thermodynamic phase stability range of 9 < Ehull <25 meV per atom (Ehull is convex hull decomposition energy): Na4-Ga0.5P0.5S4, Na3.75Ga0.375P0.625S4, Na4.25Ga0.625P0.375S4, Na3.75Si0.75-Ta0.25S4, Na3.625Si0.625Ta0.375S4, and Na3.5Si0.5Ta0.5S4. Thesecompounds are highly suggested for experimental synthesis andinvestigation. Moreover, our brute-force and highly generalizedsampling technique is expected to be applicable in uncovering othersolid electrolyte classes, thus potentially contributing to theadvancement of solid-state battery technology.The quest to identify inorganic solid electrolytes (SEs) suited forsolid-state batteries, characterized by structural stability,including experimental synthesizability and high ion conduc-tivity at room temperature, remains a longstanding challenge.Among the various classes of solid electrolytes under investi-gation, Na-ion suldes have recently gained signicant atten-tion. This increased interest can be attributed to the abundantiversity, 2-1-1 Katahira, Aoba-ku, Sendai,@tohoku.ac.jptal Materials (GREEN), National Institutesukuba, Ibaraki 305-0044, Japane, Tokyo Institute of Technology, 4259, Japan(ESI) available: Details of samplingice constants, unit cell volumes, and(M,M0,U) at m = m0 = 0.5, and theture diagnosis. See DOI:f Chemistry 2024presence of Na in the earth's crust and excellent mechanicalperformance while interfacing with active electrodes, such asformability, processability, and low elastic moduli.1–4 Moreover,the discovery of the high room-temperature Na-ion conductivitysNa,300K = 3.2 × 10−2 S cm−1 in Na2.88Sb0.88W0.12S4 underscoresthe potential for further advancements in the material search inthis class,5 with other notable series.3,6–10While numerous high-throughput sampling techniques havebeen rigorously developed for the material search of SEs,11–14 webuilt our own multi-stage density functional theory moleculardynamics (DFT-MD) sampling workow in a bid to efficientlynd stable Na-ion suldes with high sNa,300K as demonstratedin our previous study.15 Encompassing various NanMmM0m0S4ions [M and M0 denote two distinct metal ions characterized byvarying valence states, denoted as n(M) and n(M0), respectively,and n, m, and m0 are the contents of Na-, M-, and M0-ions,respectively] while maintaining parent structures U (given byNanUMmS4; nU is the content of Na ions in the structure), ouranalysis yielded that a signicant proportion of several prom-ising candidates with sNa,300K > 10−3 S cm−1 features n(M) = 3and n(M0) = 5, M = Si with n(M) = 4, and M = Ta with n(M0) = 5.In this study, leveraging the methodology and knowledgefrom our previous study,15 we aim to expand the scope ofcandidate parent structures U considering the promisingcombinations of (M,M0), freeing U from a direct associationwith M (U = NanUMUS4; MU is the host metal ion for U, notnecessarily being M). This new approach will broaden theexploration scope for material space, thereby enhancing theefficiency of identifying uncharted but synthesizable materialspossessing superior target properties such as sNa,300K. Ourobjective was to investigate whether (M,M0) may exhibitincreased stability in different polymorphs. Initially, we thor-oughly explored the material space (M,M0,U) while maintaininga xed value of m = m0 = 0.5 for NanMmM0m0 S4: 112 cases of(M,M0,U) in total. This selection, driven by the maximization ofmixing entropy, resulted in the attainment of the highest valueof sNa,300K as reported in the preceding study.15 Within thisframework, we identied two stable sampling spacesJ. Mater. Chem. A, 2024, 12, 20879–20886 | 20879http://crossmark.crossref.org/dialog/?doi=10.1039/d4ta02522a&domain=pdf&date_stamp=2024-08-10http://orcid.org/0000-0001-6026-636Xhttp://orcid.org/0000-0001-9505-771Xhttp://orcid.org/0000-0002-5532-6134https://doi.org/10.1039/d4ta02522ahttp://creativecommons.org/licenses/by-nc/3.0/http://creativecommons.org/licenses/by-nc/3.0/https://doi.org/10.1039/d4ta02522ahttps://pubs.rsc.org/en/journals/journal/TAhttps://pubs.rsc.org/en/journals/journal/TA?issueid=TA012032Journal of Materials Chemistry A CommunicationOpen Access Article. Published on 05 August 2024. Downloaded on 10/9/2024 6:27:18 AM.  This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.View Article Online(Si,Ta,Na4SiS4) and (Ga,P,Na4SiS4), both showing high promisefor sNa,300K. Subsequently, we extended our exploration byvarying the values of m and m0 within (Si,Ta,Na4SiS4) and(Ga,P,Na4SiS4). This expanded approach resulted in thediscovery of crystal structures with not only promising sNa,300Kbut also signicantly decreased convex hull decompositionenergy per atom Ehull, thereby greatly improving our ability topredict stable crystal frameworks U capable ofaccommodating M and M0.Sampling protocolWe established a sampling protocol, illustrated in Fig. 1, andbriey outlined here, with further details provided in Discus-sion S1.† The sampling space (M,M0,U) encompasses combi-nations of trivalent M (Al, Ga, and In), pentavalent metal ions M0(P, V, Nb, Sb, and Ta), as well as (M,M0) = (Si,Ta), and sevendifferent U, namely Na5AlS4,10,16 with which Na5GaS4 is iso-structural,17 Na5InS4,18 Na4.5Al0.5Si0.5S4,10 Na4SiS4,6,10,19,20Na4SnS4,7,9,21 Na3VS4,8,22,23 and Na3SbS4.5,24–26 Initially, wegenerated a substantial number of random site arrangementsfor NanM0:5M00:5S4 supercells to represent (M,M0,U), resulting ina total dataset size of ndata = 5, 290, 074, 920. From thesearrangements, we selected fewer than six with the lowest Ewaldcoulombic energies EEwald for each (M,M0,U): ndata = 469.27–29 Inthe subsequent step of DFT geometry optimizations, we fullyrelaxed the site positions and lattice parameters for the selectedarrangements. The cell structure with the lowest DFT energyEDFT, or equivalently, the lowest Ehull, was identied toFig. 1 Sampling protocol to identify stable Na-ion sulfide solid electrolytetwo parts: sampling for NanM0:5M00:5S4 and further sampling within twdenotations, please refer to the main text. Details are provide in Discuss20880 | J. Mater. Chem. A, 2024, 12, 20879–20886determine the most suitable U for (M,M0): ndata = 16. Then, weconducted a DFT-MD sampling, named the single-temperature“long-time” diagnosis, for the selected (M,M0,U), estimatings*Na;300K (represented as sNa,300K values in this step). This wasachieved by performing DFT-MD calculations with a time stepof s = 1 fs over a simulation time of s = 250 ps at a constanttemperature of T= 300 K. Two criteria were applied for selectingpromising samples: Ehull < 25 meV per atom, which is compa-rable to the case of Li10GeP2S12 (Ehull = 19 meV per atom),30 ands*Na;300K . 10�2 S cm�1. Based on these criteria, we selected twosampling spaces, namely (M,M0,U) = (Ga,P,Na4SiS4) and(Si,Ta,Na4SiS4), for further analysis in the multi-temperaturediagnosis.Next, we employed 11 compositions with varying m (andcorrespondingly, m0) for (M,M0,U) = (Ga,P,Na4SiS4) and(Si,Ta,Na4SiS4) by adding 9 compositions (Na4SiS4, Na4Ga0.125-Si0.75P0.125S4, Na4Ga0.25Si0.5P0.25S4, Na4Ga0.375Si0.125P0.375S4,Na3.75Ga0.375P0.625S4, Na4.25Ga0.625P0.375S4, Na3.875Si0.875Ta0.125-S4, Na3.75Si0.75Ta0.25S4, and Na3.625Si0.625Ta0.375S4) to the exist-ing 2 compositions (Na4Ga0.5P0.5S4 and Na3.5Si0.5Ta0.5S4). Thesame procedure for the structure search was executed again. Wegenerated a substantial number of random site arrangementsfor these supercells by adding a dataset size of ndata = 10, 842,306, 118 for the 9 compositions. From these arrangements, weselected the lowest EEwald case for each composition by addingndata = 9.27–29 In the subsequent step of DFT geometry optimi-zations, we fully relaxed the site positions and lattice parame-ters for the selected arrangements. Then, we estimated sNa,300Kand Na-ion activation energies Ea by performing DFT-MDs with high conductivity at room temperature. The protocol compriseso material space (M,M0,U) = (Ga,P,Na4SiS4) and (Si,Ta,Na4SiS4) (Forion S1.†).This journal is © The Royal Society of Chemistry 2024http://creativecommons.org/licenses/by-nc/3.0/http://creativecommons.org/licenses/by-nc/3.0/https://doi.org/10.1039/d4ta02522aCommunication Journal of Materials Chemistry AOpen Access Article. Published on 05 August 2024. Downloaded on 10/9/2024 6:27:18 AM.  This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.View Article Onlinesimulations with s = 1 fs and s = 100 ps at different tempera-tures T = 500, 600, 700, 800, and 900 K.Fig. 2 Average widest Na–3S solid angles max(UNaSx) for polyhedraNaSx and average Na–S bond lengths dNa–S for 16 compositionsNa4M0:5M00:5S4 and Na3.5Si0.5Ta0.5S4 whose structures were relaxed byusing DFT with parent structures U that stabilized most (giving thelowest Ehull for each composition). Each composition is denoted by Mand M0, and 9 (7) compositions in the high (low) region of dNa–S have U= Na4SiS4 (Na4SnS4). The red dots represent the cases of Na4Ga0.5-P0.5S4 and Na3.5Si0.5Ta0.5S4 with high values of both max(UNaSx) anddNa–S.Promising material spacesThe results of the geometry optimizations for NanM0:5M00:5S4 andNa3.5Si0.5Ta0.5S4 are presented in Table 1. Among the variouscombinations ofM andM0, it was observed thatM= Al or Ga,U=Na4SiS4 tends to be the most stable, except for M0 = Sb, in whichU = Na4SnS4 appeared to be more stable. Notably, with M = In,stability was exclusively observed in U = Na4SnS4. In terms of thecalculated Ehull values, the majority of the optimized cell struc-tures exhibited Ehull < 25 meV per atom, with a few exceptions,such as Na4In0.5P0.5S4 (Ehull = 30.8 meV per atom), Na4In0.5V0.5S4(Ehull= 35.9meV per atom), and Na4In0.5Ta0.5S4 (Ehull= 26.0 meVper atom). Additional cases of U are provided in Table S1.†Furthermore, the results from the single-temperature “long-time”diagnosis indicated that Na4Ga0.5P0.5S4 and Na3.5Si0.5Ta0.5S4 meetEhull < 25 meV per atom and s*Na;300K . 10�2 S cm�1.As illustrated in our previous study, s*Na;300K is limited by theshort timescale for site-to-site jumps at low T, however, it servesas a computationally efficient metric for identifying promisingcandidates with high sNa,300K.15 Besides, in our previous study,given the xed v(M) and v(M0), we identied two key descriptorsfor achieving high sNa,300K: the average widest Na–3S solid anglemax(UNaSx) for NaSx polyhedra and the average Na–S bondlength dNa–S.15 These descriptors with high values would facili-tate the release of self-diffusing Na-ions from the cages of NaSx.Notably, Na4Ga0.5P0.5S4 and Na3.5Si0.5Ta0.5S4 exhibit high valuesfor not only s*Na;300K but also max(UNaSx) and dNa–S (see Fig. 2),indicating their potential for excellent sNa,300K. Based on theseobservations, our focus shied towards investigating (M,M0,U)= (Ga,P,Na4SiS4) and (Si,Ta,Na4SiS4) with varying m.Table 1 Lattice constants a, b, and c, unit cell volumes V, and convNa4M0:5M00:5S4 and Na3.5Si0.5Ta0.5S4 whose structures were relaxed by usEhull for each composition). The two compositions satisfying Ehull < 25Na3.5Si0.5Ta0.5S4. Lattice constants a, b, and g were close to 90°. In the fithe last row, the room-temperature Na-ion conductivities s*Na;300K are pr“long-time” diagnosis with s = 1 fs, s = 250 ps, and T = 300 K, and “—”Composition U a (Å) b (Å)Na4Al0.5P0.5S4 (Na96Al12P12S96) Na4SiS4 41.87 8.917Na4Al0.5V0.5S4 (Na96Al12V12S96) Na4SiS4 41.90 8.780Na4Al0.5Nb0.5S4 (Na96Al12Nb12S96) Na4SiS4 42.20 8.951Na4Al0.5Sb0.5S4 (Na96Al12Sb12S96) Na4SnS4 15.74 15.74Na4Al0.5Ta0.5S4 (Na96Al12Ta12S96) Na4SiS4 42.23 8.954Na4Ga0.5P0.5S4 (Na96Ga12P12S96) Na4SiS4 41.76 8.977Na4Ga0.5V0.5S4 (Na96Ga12V12S96) Na4SiS4 42.02 8.807Na4Ga0.5Nb0.5S4 (Na96Ga12Nb12S96) Na4SiS4 42.24 8.989Na4Ga0.5Sb0.5S4 (Na96Ga12Sb12S96) Na4SnS4 15.76 15.76Na4Ga0.5Ta0.5S4 (Na96Ga12Ta12S96) Na4SiS4 42.30 8.997Na4In0.5P0.5S4(Na96In12P12S96) Na4SnS4 15.93 15.93Na4In0.5V0.5S4 (Na96In12V12S96) Na4SnS4 15.83 15.83Na4In0.5Nb0.5S4 (Na96In12Nb12S96) Na4SnS4 15.84 15.84Na4In0.5Sb0.5S4 (Na96In12Sb12S96) Na4SnS4 15.92 15.92Na4In0.5Ta0.5S4 (Na96In12Ta12S96) Na4SnS4 15.85 15.85Na3.5Si0.5Ta0.5S4 (Na84Si12Ta12S96) Na4SiS4 41.65 8.937This journal is © The Royal Society of Chemistry 2024The outcomes of the geometric optimizations conducted forthe 11 compositions across (M,M0,U) = (Ga,P,Na4SiS4) and(Si,Ta,Na4SiS4) are presented in Table 2 as well. It is noteworthythat a decrease in the Si content (that is, the deviation from U)results in an increase in the value of Ehull. For all the investi-gated compositions, Ehull remains below 25 meV per atom,signifying their structural (meta)stability and the feasibility ofex hull decomposition energies per atom Ehull for 16 compositionsing DFT with parent structures U that stabilized most (giving the lowestmeV per atom and s*Na;300K . 10�2 are boldened: Na4Ga0.5Ta0.5S4 andrst row, the compositions per unit cell are presented in parentheses. Inesented, which were estimated by performing the single-temperaturedenotes the absence of observed Na-ion migrations)c (Å) V (Å3) Ehull (meV per atom) s*Na;300KðS cm�1Þ13.86 5174 14.6 4.10 × 10−314.08 5181 16.8 3.25 × 10−314.15 5346 17.2 —13.86 3434 13.9 1.52 × 10−314.14 5346 19.4 —13.87 5201 15.8 1.03 × 10−214.05 5200 17.3 3.04 × 10−314.13 5366 17.7 1.10 × 10−313.90 3449 15.5 3.73 × 10−414.11 5369 19.7 2.35 × 10−413.65 3464 30.8 1.66 × 10−313.82 3464 35.9 5.16 × 10−513.97 3503 23.5 8.41 × 10−313.96 3536 17.4 —13.97 3507 26.0 2.44 × 10−514.08 5241 24.1 3.34 × 10−2J. Mater. Chem. A, 2024, 12, 20879–20886 | 20881http://creativecommons.org/licenses/by-nc/3.0/http://creativecommons.org/licenses/by-nc/3.0/https://doi.org/10.1039/d4ta02522aTable 2 Lattice constants a, b, and c, unit cell volumes V, convex hull decomposition energies per atom Ehull, and bandgap energies Eg for the 11compositions adopted in the multi-temperature diagnosis. Lattice constants a, b, and g were close to 90°. The parent structures p were set toNa4SiS4 for all the cases. In the first row, the compositions per unit cell are presented in parenthesesComposition a (Å) b (Å) c (Å) V (Å3) Ehull (meV per atom) Eg (eV)Na4SiS4 (Na96Si24S96) 41.61 8.791 13.88 5077 0 4.03Na4Ga0.125Si0.75P0.125S4(Na96Ga3Si18P3S96)41.71 8.820 13.88 5106 4.26 2.98Na4Ga0.25Si0.5P0.25S4 (Na96Ga6Si12P6S96) 41.86 8.843 13.87 5136 8.27 3.12Na4Ga0.375Si0.25P0.375S4 (Na96Ga9Si6P9S96) 41.60 8.912 13.88 5145 8.88 3.12Na4Ga0.5P0.5S4 (Na96Ga12P12S96) 41.76 8.977 13.87 5201 15.8 2.44Na3.75Ga0.375P0.625S4 (Na90Ga9P15S96) 40.81 8.953 13.93 5091 19.7 3.00Na4.25Ga0.625P0.375S4 (Na102Ga15P9S96) 42.21 8.996 13.98 5308 20.7 2.92Na3.875Si0.875Ta0.125S4 (Na93Si21Ta3S96) 41.66 8.782 13.95 5102 5.20 3.03Na3.75Si0.75Ta0.25S4 (Na90Si18Ta6S96) 41.75 8.782 14.00 5134 9.26 3.02Na3.625Si0.625Ta0.375S4 (Na87Si15Ta9S96) 41.77 8.767 14.10 5134 14.7 2.70Na3.5Si0.5Ta0.5S4 (Na84Al12Ta12S96) 41.65 8.937 14.08 5241 24.1 2.85Journal of Materials Chemistry A CommunicationOpen Access Article. Published on 05 August 2024. Downloaded on 10/9/2024 6:27:18 AM.  This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.View Article Onlinetheir synthesis. We represent several examples of the visualizedcrystal structures in Fig. 3a and 4a. In addition, their bandgapenergies Eg, a metric for electron-insulating properties, exhibi-ted high values: around 3 eV for most cases.In Table S2,†we provide the values for sNa,T andDNa,T obtainedthrough multi-temperature DFT-MD calculations for (M,M0,U) =(Ga,P,Na4SiS4). Furthermore, in Fig. S1a–g,† we present meansquared displacement (MSD) curves, most of which exhibit linearresponses against the sampled time intervals sMSD. As indicatedin their insets, the trajectories at T = 500 K showed limitedinterconnectivity until the Si-ion content becomes zero. Theinterconnected trajectories, indicative of site-to-site jumps, arenoticeable in Na4Ga0.5P0.5S4, Na3.75Ga0.375P0.625S4, and Na4.25-Ga0.625P0.375S4. This observed trend is also reected in theArrhenius plot, where we estimated the interpolated Ea and theextrapolated sNa,300K (see Fig. 3b). For these three samples, Ea wassuppressed to less than 350meV, while sNa,300K either exceeded orremained around 10−3 S cm−1. We note that a possible explana-tion of an order of magnitude discrepancy betweens*Na;300K z 10�2 S cm�1 and sNa,300K z 10−3 S cm−1 for Na4Ga0.5-P0.5S4 is the insufficient timescale for site-to-site jumps consid-ered in s*Na;300K. It is noteworthy that a decrease in the Na-ioncontent, as seen in Na3.75Ga0.375P0.625S4, resulted in a suppres-sion of Ea and an enhancement of sNa,300K, likely due to thecreation of the additional free space for Na-ion self-diffusions. Asillustrated in Fig. 3c, achieving sNa,300K T 10−3 S cm−1 for(M,M0,U) = (Ga,P,Na4SiS4) would be realized at the expense ofdecreased phase stability (15 < Ehull < 21 meV per atom, which arerelative to zero decomposition energy of the pristine structure U):Na4Ga0.5P0.5S4, Na3.75Ga0.375P0.625S4, and Na4.25Ga0.625P0.375S4.In Table S2,† we also provide the values for sNa,T and DNa,Tobtained through multi-temperature DFT-MD calculations for(M,M0,U) = (Si,Ta,Na4SiS4). Additionally, in Fig. S2a–d,† wepresent linear MSD curves against sMSD. As indicated in theirinsets, even at T= 500 K, trajectories exhibited interconnectivity,even for the relatively low doping levels of the Ta-ion. Notably,the interconnected features were predominantly observedaround Ta-ions, wherein Na vacancies exist. This trend is re-ected in the Arrhenius plot (see Fig. 4b). For instance, in the20882 | J. Mater. Chem. A, 2024, 12, 20879–20886case of Na3.875Si0.875Ta0.125S4, Ea= 413meV and sNa,300K= 4.93×10−5 S cm−1 were estimated. Furthermore, with an increase inthe Ta-ion doping level (or a decrease in the Na-ion content), Eawas further suppressed, accompanied by an enhancement ofsNa,300K. In the case of Na3.5Si0.5Ta0.5S4, Ea = 215 meV andsNa,300K = 1.35 × 10−2 S cm−1 were estimated. As illustrated inFig. 4c, achieving sNa,300K T 10−3 S cm−1 for (M,M0,U) =(Si,Ta,Na4SiS4) would be realized at the expense of decreasedphase stability (9 < Ehull < 25 meV per atom): Na3.75Si0.75Ta0.25S4,Na3.625Si0.625Ta0.375S4, and Na3.5Si0.5Ta0.5S4. The high values ofsNa,300K T 10−3 S cm−1 for Na4Ga0.5P0.5S4 and Na3.5Si0.5Ta0.5S4partly justify the use of m = m0 = 0.5 in the initial step of thesampling protocol. We also discuss the electrochemical stabilitywindows for the 11 compositions in the Discussion S2.†Descriptors for convex hulldecomposition energyWe established a multivariate linear regression model todiscern descriptors inuencing Ehull, leveraging a dataset ofNanM0:5M00:5S4 given in the structure search step, encompassingvarious U = NanUMUS4; the data are presented in Table S1†(ndata = 110). The proposed model comprises three descriptors:Ehull ¼ 7:80 meV per atomðn� nUÞþ 25:5 meV per atom����12�vðMÞ þ v�M0��� vðMUÞ����þ 23:3 meV per atom per Å�12�rðMÞ þ r�M0��� rðMUÞ�þ 22:0 meV per atom: (1)Themodel exhibits a substantial R2-value (R2= 0.711) and anF-value of 87.0 with a signicantly low p-value (p < 0.001), whileall t-tests for the constant term and the three coefficientsrevealed p < 0.001. The variance ination factors (VIF) weresufficiently small, indicating an absence of multicollinearityissues: VIF= 1.02, 1.06, and, 1.08 for the rst, second, and thirdThis journal is © The Royal Society of Chemistry 2024http://creativecommons.org/licenses/by-nc/3.0/http://creativecommons.org/licenses/by-nc/3.0/https://doi.org/10.1039/d4ta02522aFig. 3 (a) Crystal structures of Na4Ga0.5P0.5S4, Na3.75Ga0.375P0.625S4,and Na4.25Ga0.625P0.375S4, (b) Arrhenius plots in the sNa,TT–T domain,and (c) sNa,300K values extrapolated in (b) for the seven samples within(M,M0,U) = (Ga,P,Na4SiS4): Na4SiS4, Na4Ga0.125Si0.75P0.125S4, Na4-Ga0.25Si0.5P0.25S4, Na4Ga0.375Si0.25P0.375S4, Na4Ga0.5P0.5S4, Na3.75-Ga0.375P0.625S4, and Na4.25Ga0.625P0.375S4. In (c), convex hulldecomposition energies per atom Ehull in meV per atom are alsorepresented in parentheses.Fig. 4 (a) Crystal structures for Na3.75Si0.75Ta0.25S4, Na3.625Si0.625-Ta0.375S4, and Na3.5Si0.5Ta0.5S4, (b) Arrhenius plots in the sNa,TT–Tdomain, and (c) sNa,300K values extrapolated in (b) for the five sampleswithin (M,M0,U) = (Si,Ta,Na4SiS4): Na4SiS4, Na3.875Si0.875Ta0.125S4,Na3.75Si0.75Ta0.25S4, Na3.625Si0.625Ta0.375S4, and Na3.5Si0.5Ta0.5S4. In (c),convex hull decomposition energies per atom Ehull in meV per atomare also represented in parentheses.Communication Journal of Materials Chemistry AOpen Access Article. Published on 05 August 2024. Downloaded on 10/9/2024 6:27:18 AM.  This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.View Article Onlinecoefficients, respectively. Here, r(M) denotes the Shannon ionicradius for a metal ion M.31,32 The data plot for this model ispresented in Fig. 5.This journal is © The Royal Society of Chemistry 2024The rst term n − nU suggests that Ehull would increase if theNa-ion sites are added (rather than omitted) during structuralmodications from the pristine U. The second termJ. Mater. Chem. A, 2024, 12, 20879–20886 | 20883http://creativecommons.org/licenses/by-nc/3.0/http://creativecommons.org/licenses/by-nc/3.0/https://doi.org/10.1039/d4ta02522aFig. 5 Data plot for the multivariate regression model against Ehullcalculated by using DFT (presented in Table S1†) with a substantial R2-value (R2 = 0.711). For the model, eqn (1) was adopted with ndata = 110.Journal of Materials Chemistry A CommunicationOpen Access Article. Published on 05 August 2024. Downloaded on 10/9/2024 6:27:18 AM.  This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.View Article Online����12 fvðMÞ þ vðM0 Þg � vðMUÞ���� suggests that Ehull would increasewhen the average valence for M andM0 deviates from that of MU.The third term12frðMÞ þ rðM0Þg � rðMUÞ suggests that Ehullwould increase with a larger average ionic radius for M and M0compared to that of MU. In light of these ndings, two samplingspaces, namely (M,M0,U) = (Ga,P,Na4SiS4) and (Si,Ta,Na4SiS4),with high sNa,300K, are deemed appealing for experimentalrealizations. For Na4Ga0.5P0.5S4 with Ehull = 15.8 meV per atom,it is given that n − nU = 0,����12 fvðMÞ þ vðM0 Þg � vðMUÞ���� ¼ 0, and12frðMÞ þ rðM0 Þg � rðMUÞ ¼ 0:138 Å. Similarly, for Na3.5Si0.5-Ta0.5S4 Ehull = 24.1 meV per atom, it is given that n − nU =−0.5,����12 fvðMÞ þ vðM0Þg � vðMUÞ���� ¼ 0, and12frðMÞ þ rðM0Þg � rðMUÞ ¼ 0:145 Å. The numerical analyseselucidate that a combination of Ga, P, and Ta would constitutean appropriate blend for the parent structure Na4SiS4.Summary and outlookIn this study, we employed the multi-stage sampling protocol11to identify promising Na-ion suldes NanMmM0m0 S4 character-ized by high sNa,300K within the constraints of limited choicesfor M and M0, but with an expanded selection of parent struc-tures U to effectively pinpoint unexplored yet synthesizablematerials with superior conductivity sNa,300K. Our approachbegan with the identication of U that stabilizes each combi-nation of (M,M0) most. Subsequently, circumventing the tedioustasks of the exhaustive access for the sampling spaces, we effi-ciently predicted that (M,M0,U) = (Ga,P,Na4SiS4) and(Si,Ta,Na4SiS4), characterized by wide max(UNaSx) and long dNa–S, have the potential to achieve high sNa,300K through the single-temperature “long-time” diagnosis.20884 | J. Mater. Chem. A, 2024, 12, 20879–20886These predictions were subsequently validated through multi-temperature DFT-MD calculations. Notably, sNa,300K T10−3 S cm−1 were attainable within a range of 9 < Ehull < 25 meVper atom: Na4Ga0.5P0.5S4, Na3.75Ga0.375P0.625S4, Na4.25Ga0.625-P0.375S4, Na3.75Si0.75Ta0.25S4, Na3.625Si0.625Ta0.375S4, and Na3.5Si0.5-Ta0.5S4. Based on our observations, we expect that the co-dopingof Ga, P, and Ta into the parent structure Na4SiS4, leading to theformation of compositions Na4+g−p−tGagSi1−g−p−tPpTatS4, wouldpresent an intriguing avenue for further investigation in futurestudies. The limitation of this study should be noted also;although sNa,300K were optimized at m = m0 = 0.5, as observed inNa4Ga0.5P0.5S4 and Na3.5Si0.5Ta0.5S4, other choices ofm (m0) in theinitial step of the sampling protocol are worth exploring. Futurestudies should assess these alternatives.We believe that these two identied sampling spaces, char-acterized by both thermodynamic stability and fast Na-ionconductivity, warrant further experimental investigations.Additionally, this brute-force sampling technique has thepotential to explore other classes of solid electrolytes, whichcould be pivotal in the ongoing advancement of solid-statebattery technology.Data availabilityData for this article, including crystal structures and moleculardynamics results for (M,M0,U) = (Ga,P,Na4SiS4) and (Si,Ta,Na4-SiS4) are available at github at https://github.com/JerryGarcia1995/NasuldesExt. The data supporting thisarticle have been included as part of the ESI† as well.Conflicts of interestThere are no conicts to declare.AcknowledgementsThis research was supported in part by MEXT as “Program forPromoting Research on the Supercomputer Fugaku” grantnumber JPMXP1020230325, Data Creation and Utilization TypeMaterial Research and Development Project grant numberJPMXP1122712807 and Materials Processing Science project(“Materealize”) grant number JPMXP0219207397, and by JSPSKAKENHI grant numbers JP21K14729 and JP24H02203, as wellas JST through ALCA-SPRING grant number JPMJAL1301, COI-NEXT grant number JPMJPF2016, and GteX Program Japangrant number JPMJGX23S4. The calculations were performedon the supercomputers at NIMS (Numerical Materials Simu-lator) and the supercomputer Fugaku at the RIKEN through theHPCI System Research Project (project IDs: hp230154 andhp230205). 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Computational discovery of stable Na-ion sulfide solid electrolytes with high conductivity at room temperatureElectronic supplementary information (ES...