Local Tetragonal Structure of the Cubic Superionic Conductor

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Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

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Local Tetragonal Structure of the Cubic Superionic Conductor Na3PS4 Thorben Krauskopf,†,‡ Sean P. Culver,†,‡ and Wolfgang G. Zeier*,†,‡ †

Institute of Physical Chemistry and ‡Center for Materials Research (LaMa), Justus-Liebig-University Giessen, D-35392 Giessen, Germany S Supporting Information *

ABSTRACT: The sodium superionic conductor Na3PS4 is known to crystallize in one of two different structural polymorphs at room temperature (i.e., cubic or tetragonal, depending on the synthetic conditions). Experimentally, the cubic structure is known to exhibit a higher ionic conductivity than the tetragonal structure, despite theoretical investigations suggesting that there should be no difference at all. Employing a combination of Rietveld and pair distribution function (PDF) analyses, as well as electrochemical impedance spectroscopy, we investigate the open question of how the crystal structure influences the ionic transport in Na3PS4. Despite the average structures of Na3PS4 prepared via ball-milling and high-temperature routes being cubic and tetragonal, respectively, the structural analysis by PDF indicates that both compounds are best described by the structural motifs of the tetragonal polymorph on the local scale. Ultimately, the high ionic conductivity of Na3PS4 prepared by the ball-milling approach is confirmed to be independent of the crystal structure. This work demonstrates that even in ionic conductors differences can be observed between the average and local crystal structures, and it reasserts that the high ionic conductivity in Na3PS4 is not related to the crystal structure but rather differences in the defect concentration. possibly through altered Na−S interactions.21,22 A series of (100-x)Na3PS4·xNa4SiS4 glass-ceramics were also prepared with a ball-milling approach, achieving an exceptional ionic conductivity of 7.4 × 10−4 S cm−1 for the x = 6 composition.23 Alternative investigations have even led to the observance of another superionic β-Na3PS4 polymorph at elevated temperatures.24,25 Notably, the highest conductivity in the Na3PS4 system was achieved through Cl-doping, where tetragonal Na2.9375PS3.9375Cl0.0625 was found to exhibit an ionic conductivity of 1.14 × 10−3 S cm−1.18 All of the aforementioned studies have contributed to an interesting discussion regarding the origin of the outstanding ionic conductivity found in certain Na3PS4 compounds and further, if the transport behavior arises from structural differences, microstructural variations, or perhaps disparities in the defect concentration. In this work, we explore this open question using Na3PS4 prepared by two different synthetic routes (i.e., ball-milling (BM) and high temperature (HT)) using Rietveld and pair distribution function (PDF) analyses to probe the average and local structures, respectively, while also digging deeper into the reason behind the observed differences in the ionic transport using electrochemical impedance spectroscopy. While Rietveld analysis indeed points to differences in the average structures of the two different Na3PS4 materials (i.e., cubic and tetragonal), the PDF analyses show that both Na3PS4 compounds exhibit the same tetragonal structural motif on the local scale.

1. INTRODUCTION Several families of Li+ and Na+ ion conducting thiophosphates have prompted a renewed interest in solid ion conductors for use in solid-state batteries due to their intrinsic soft mechanical nature and fast ionic conduction.1,2 Recently, a multitude of structural classes exhibiting high ionic conductivities have been found (e.g., Li10MP2S12, Li6PS5X, Li3PS4, Na3PS4, and Na11Sn2PS12).3−12 In particular, Na3PS4 has drawn considerable focus due to the variety of ionic conductivities and structural polymorphs observed. For example, the tetragonal modification of Na3PS4 was initially prepared by Jansen and co-workers via solid-state synthesis;13 however in 2012, Hayashi et al. reported the stabilization of a cubic Na3PS4 phase at room temperature using a ball-milling approach.14 The achievement of an ionic conductivity of up to 4.6 × 10−4 S cm−1 for the cubic phase at room temperature has resulted in a resurgence of interest,15 given that the ionic conductivity of the tetragonal phase is generally an order of magnitude lower. Nevertheless, despite the experimental differences in the ionic conductivity between the tetragonal and cubic polymorphs, theoretical work suggests that both structures should exhibit similar ionic conductivities.9,16−18 More recently, stable solid solutions of Na3PS4−xSex (0 < x < 4) were synthesized in order to broaden the diffusion pathways, increase the lattice polarizability and thus affect the ionic conductivity.4,19,20 Here, it was shown that altering the lattice polarizability through Se substitution affects not only the activation barrier but also the Arrhenius prefactor.4 In addition, substitutions of P5+ with As5+ have been found to increase the conductivity through a widening of diffusion pathways and © XXXX American Chemical Society

Received: February 20, 2018

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DOI: 10.1021/acs.inorgchem.8b00458 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

diffraction data using the PDFgetX2 software.29 The collected data were first corrected for background, sample absorption, and Compton scattering. Then, normalized structure functions [S(Q)] were obtained. Finally, S(Q) was Fourier-transformed to yield G(r). A maximum scattering vector (Qmax) of 22 Å−1 was employed in the Fourier transform. Structural refinements were carried out using the PDFgui software.30 The local crystal structure of the t-Na3PS4 crystallites were refined in the P4̅21c space group, while the local structure of the “c”-Na3PS4 crystallites were refined with both the tetragonal and the cubic (I43̅ m) models. When modeling the experimental PDF over the whole r range of 1.5−20 Å, the data were not well described below 4 Å. Therefore, the range from 1.5−4 Å was fitted independently from the 4−20 Å interatomic distance range, using the same structural approach as Jensen et al.31 and Vidal Laveda et al.32 for materials containing additional amorphous or low coherence length phases. For both ranges the following parameters were refined: (1) scale factor, (2) lattice parameters, (3) correlated motion factor, (4) fractional atomic coordinates of the sulfur atoms (and sodium atoms in the tetragonal model), and (5) atomic isotropic displacement parameters. The local correlated motion factor (delta 2) was fixed at a value of 4 Å. Notably, when refining the Na thermal displacement parameters in the high-r region using the cubic structural model, unphysically large values (i.e., Biso > 10 Å2) were obtained. Thus, the atomic isotropic displacement parameters for all Na atoms were fixed to Biso = 3.9 Å2 (Uiso = 0.05 Å2). The Rw indicator was employed to assess the quality of the refined structural models.33 2.5. Electrochemical Impedance Spectroscopy. The ionic conductivity of the compounds was measured in a temperature range from 253−333 K by ac impedance spectroscopy using a SP300 impedance analyzer in the frequency range from 7 MHz to 100 mHz with an amplitude of 10 mV. The powder samples were placed between two stainless-steel rods with 10 mm diameter and coldpressed uniaxially (≈380 MPa) for 5 min using a custom-built setup under inert atmosphere.4 Fitting of the impedance spectra was performed with the Relaxis 3 software package (rhd instruments GmbH & Co. KG).

Therefore, it is unlikely that the differences in the ionic transport stem from the crystal structure itself but rather from the defects induced by the harsh ball-milling conditions. This work highlights the importance of investigating the local structure and the influence of synthetic procedures on material properties.

2. EXPERIMENTAL METHODS 2.1. Synthesis. (BM)-“c”-Na3PS4 was synthesized using a mechanochemical or ball-milling (BM) technique first reported by Hayashi et al.,14 whereas (HT)-t-Na3PS4 was obtained using a classical high temperature (HT) solid-state synthetic route. To obtain (HT)-tNa3PS4, the starting materials Na2S (Sigma-Aldrich) and P2S5 (99%, Sigma-Aldrich) were hand-ground in a stoichiometric ratio. The resulting mixture was pressed into pellets, which were then filled into quartz ampules (10 mm inner diameter). The ampules were then sealed under vacuum and heated in a tube furnace (Nabertherm) to 772 K (50 K·h−1), annealed for 20 h and cooled down to room temperature. To prepare (BM)-“c”-Na3PS4, the starting materials Na2S (Sigma-Aldrich) and P2S5 (99%, Sigma-Aldrich) were ball-milled (Fritsch Pulverisette 7 Premium Line) for 48 h at 500 rpm using a ZrO2 milling set (80 mL bowl and 60 g of balls with a diameter of 3 mm). To prevent excessive heating of the precursor, intermediate cooling times (every 5 min for 15 min) were applied. The already cubic precursor was gently heated to 533 K (50 K·h−1) and annealed for 12 h for further crystallization. Additionally, a tetragonal phase was also prepared using a mechanochemical technique, coupled with rapid annealing (i.e., (BM)-t-Na3PS4). Therefore, “c”-Na3PS4 was rapidly annealed (20 min at 773 K), which resulted in a cubic to tetragonal phase transition.4 All preparations and sample treatments were carried out under inert argon atmosphere. 2.2. X-ray Diffraction. The X-ray diffraction measurements were carried out using a PANalytical Empyrean powder diffractometer in Bragg−Brentano θ−θ geometry with Cu Kα radiation [λ1 = 1.5405980 Å; λ2 = 1.5444260 Å; I(λ2)/I(λ1)·0.5] and a PIXcel3D area detector with 255 measuring channels. Measurements were carried out in the 2θ range of 10−90° with a step size of 0.026°. All powder samples were therefore sealed in an airtight sample holder and covered with Kapton polyimide film.4 2.3. Rietveld Analysis. Rietveld refinements were carried out using the Fullprof software.26 Pseudo-Voigt functions were used to fit the profiles and the background was described using a linear interpolation between manually set points. For “c”-Na3PS4, the structure of c-Na3PSe4 from Zhang et al. with the space group I4̅3m was used, while the structural data of t-Na3PS4 from Jansen with the space group P4̅21c was used as the starting model for the tetragonal modification.13,20 It should be noted that for “c”-Na3PS4, the defective cubic model from Tanibata et al.27 did not result in any Na occupancy on the 12d Wyckoff position and was thus excluded. The range from 10−22° was excluded from the refinement because of the high background of the polyimide film. The following parameters were initially refined: (1) peak shape, background coefficients, and lattice constants using the Le Bail method, and afterward in a Rietveld refinement, (2) scale factor, (3) fractional atomic coordinates, and (4) isotropic atomic displacement parameters. The indicators of Rwp, Rexp, and goodness of fit S were used to a assess the quality of the refinements.28 2.4. Synchrotron X-ray Structure Analysis. Capillaries made of borosilicate glass with an outer diameter of 1.5 mm were filled in an argon glovebox and were flame-sealed. X-ray scattering data suitable for pair distribution function and diffraction analysis were collected at room temperature using the I15−1 instrument at the Diamond Light Source (UK) beamline. High-energy X-rays (λ = 0.161669 Å, 76.6 keV, bent Laue monochromator) were used in combination with a PerkinElmer 1611 CP3 area detector. The crystallographic data, obtained from the refinements of the Bragg data, were used as starting values for the analysis of all PDF data. Pair distribution function G(r) data were extracted from the raw

3. RESULTS 3.1. Average Crystal Structure of “Cubic” and Tetragonal Na3PS4. Figure 1 shows the average cubic and tetragonal Na3PS4 crystal structures in their respective space groups, I4̅3m and P4̅21c, along the b-axis. The cubic structure crystallizes in such a way that all PS43− polyhedra are arranged in a body centered cubic lattice with one crystallographic Na+ position (Wyckoff 6b) on the octahedral site. An additional

Figure 1. Crystal structure of (a) cubic and (b) tetragonal Na3PS4 projected in the (010) plane. The perfectly cubic phase (i.e., no occupancy of the 12d positions) shows PS43− tetrahedra in a body centered lattice. In the tetragonal modification, a minor rotation of the tetrahedra leads to a splitting of the Na positions and an elongation of the c-lattice parameter. B

DOI: 10.1021/acs.inorgchem.8b00458 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry interstitial site for Na+ (Wyckoff 12d), proposed to arise from a high number of jumps from 6b to 6b,17 has been suggested by Tanibata et al.27 but has not yet been further corroborated experimentally.4 In the tetragonal modification, a minor rotation of the PS43− polyhedra is observed around the [111] axis leading to two crystallographically independent Na+ positions (namely Wyckoff 4d and 2a). Due to the polyhedral rotation and Na+ displacement, the lattice parameter ratio c/a increases away from unity, inducing tetragonality. In this work, the tetragonal and the apparent cubic phase were synthesized using a high temperature and a ball-milling approach, respectively. Rietveld refinements of the obtained Bragg diffraction data are shown in Figure 2. As expected, the

moderately different crystal structures. However, the nature of the Na+ positions, and with it the local structure, remains unclear. 3.2. Local Structure of “Cubic” and Tetragonal Na3PS4. In order to gain a better understanding of the local structural differences between the cubic and the tetragonal Na3PS4, synchrotron pair distribution function (PDF) analyses were performed. Figure 3 shows the obtained atomic pair distances

Figure 3. Experimentally obtained G(r) data for (a) HT-t-Na3PS4 and (b) BM-“c”-Na3PS4 showing that there is no significant difference in the local structure. BM-“c”-Na3PS4 was fitted using a (c) tetragonal model, shaded in green and a (d) cubic model shaded in red. Experimental data are shown as black points. The red line denotes the calculated pattern, and the difference profile is shown in blue. A fit to the low-r range (1.5−4 Å) was independently performed and leads to larger scale factors, thereby indicating an additional fraction of amorphous content or phase with a low coherence length.

Figure 2. Rietveld refinements of X-ray diffraction data for (BM)-“c”Na3PS4 and HT-t-Na3PS4. In “c”-Na3PS4, a low intensity reflection can be found at approximately 38.5° 2θ, which may correspond to the (212) reflection of the tetragonal polymorph, and is highlighted with a star. Experimental data are shown as points; the red line denotes the calculated pattern. The difference profile is shown in blue. Calculated positions of the Bragg reflections are shown as green vertical tick marks. A small fraction of Na4P2S6 impurity phase (i.e., 1.8(1) mol %) can be found in (HT)-t-Na3PS4, which may result from sulfur loss during the thermal treatment.34

for (a) (BM)-“c”-Na3PS4 and (b) (HT)-t-Na3PS4. Upon visual inspection of the experimental G(r), the considerable qualitative similarities suggest that both structures are nearly analogous on the local scale. In an attempt to elucidate the local structures, the G(r) were fitted with a least-squares refinement using the average structures, obtained from the Rietveld refinements, as starting models. A plot showing the modeled G(r) for the tetragonal phase can be found in the Supporting Information, along with all extracted structural parameters from the PDF analyses (Figures S3 and Tables S4−S8). First, it should be mentioned that fitting the data in the range of 1.5− 20 Å leads to deviations in the low-r region (i.e., 1.5 Å ≤ r ≤ 4 Å). In this region, the P−S and S−S distances of 2.03(2) and 3.2(1) Å, respectively, are not well described. Similar behavior has been observed by Jensen et al.31 in LiFePO4 containing a certain fraction of amorphous side phases and by Vidal Laveda et al.32 in nanostructured cathode materials possessing reduced coherence lengths, and other superionic thiophosphates.35,36 Given the chemical similarities between the aforementioned materials and the herein studied Na3PS4, the G(r) for both Na3PS4 polymorphs were independently fitted in the two r ranges of 1.5 Å ≤ r ≤ 4 and 4 Å ≤ r ≤ 20 Å. Interestingly, a slightly larger scale factor was noted in the low-r region (see Table S8), which indeed indicates the presence of a certain fraction of amorphous content or a phase with a low coherence length.31,32 Of particular importance, however, are the PDF analyses conducted on (BM)-“c”-Na3PS4. Figure 3c,d show the

high-temperature route leads to the tetragonal modification with refined lattice parameters of a = 6.9528(2) Å and c = 7.0973(2) Å. Meanwhile, the synthetic conditions associated with the ball-milling procedure lead to Na3PS4 with a cubic diffraction pattern and a refined lattice parameter of a = 6.9893(2) Å. All other refined structural parameters can be found in the Tables S1 and S2. In addition to the main cubic phase, a low intensity reflection at approximately 38.5° 2θ can also be seen in (BM)-“c”-Na3PS4. This additional reflection may correspond to the (212) reflection of the tetragonal phase, suggesting a minor tetragonal phase content, or could be indicative of an ordered supercell with a defective cubic structural as described by Yu et al.21 Upon comparing the Rietveld refinements of the two different materials, it becomes clear that the thermal displacement parameters for Na+ are significantly higher (and possibly unphysical; Biso ∼ 10 Å2) for the cubic phase compared to Biso ∼ 5−6 Å2 in the tetragonal phase. While these large thermal displacement parameters may be due to the fast-ionic conductive nature of the materials, it could also suggest a discrepancy in the original cubic structural solution. These data show that on average the different synthetic conditions lead to two different materials with C

DOI: 10.1021/acs.inorgchem.8b00458 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry calculated fits and the associated profile differences for the two relevant structural models (i.e., tetragonal and cubic) applied to the data of (BM)-“c”-Na3PS4. Notably, when refining the thermal displacement parameters for the Na atoms in the high-r region using the cubic structural model, unphysically large values (i.e., Biso > 10 Å2) were obtained. Therefore, in order to obtain a fair comparison between the cubic and tetragonal models, the Biso values for all Na atoms were constrained to 3.9 Å2 (Uiso = 0.05 Å2; see Tables S4 and S5), which is the value obtained from the tetragonal model. Upon comparing the cubic and tetragonal fits against the G(r) data for (BM)-“c”-Na3PS4, the tetragonal model was found to achieve a much lower residual value (i.e., Rw = 12.5% for the tetragonal model vs Rw = 33.1% for the cubic model), thereby providing a better description of the local crystal structure. Thus, modeling of the G(r) data and the resultant profile residuals show that the tetragonal model provides a better fit to the Na3PS4 local structure, independent of the synthetic route (i.e., Rw = 11.2% for (HT)-t-Na3PS4 and Rw = 12.5% for (BM)-“c”-Na3PS4). In addition to the cubic and tetragonal models, the local structure of (BM)-“c”-Na3PS4 was also fitted using a defective cubic model. Here, the previously mentioned 12d position was allowed to be occupied during the refinement, where an occupancy of 12 ± 2% Na was obtained, corresponding well with the value reported by Tanibata et al., as determined from Rietveld refinements of powder X-ray diffraction data.27 Nevertheless, this model does not provide a reasonable description of the local structure, given that the resultant Rw value of 27% is still much higher than for the tetragonal model. Further evidence of the tetragonal local structure can be found in Figure S4, where a visual comparison of the experimental G(r) for (BM)-“c”-Na3PS4, (HT)-t-Na3PS4, and the known cubic structure of Na3PSe4 can be found. Here, the distinct differences between (BM)-“c”-Na3PS4 and cubic Na3PSe4 highlight that the local structure of (BM)-“c”-Na3PS4 cannot be described by the cubic model, despite appearing cubic on the average scale. However, it should be noted that, while the local structure is best described by the structural motif of the tetragonal phase, the obtained lattice parameters are nearly cubic (a = 6.91(2) Å and c = 6.93(3) Å), with just a minor deviation from unity in the c/a ratio. Two main conclusions can be drawn from the analyses of the pair distribution function analyses: (1) Similar to other thiophosphates,35,36 an underlying amorphous phase or a phase with a low coherence length is present. (2) There are no significant differences in the experimental PDFs of the herein studied Na3PS4 materials prepared under different synthetic conditions, thereby suggesting that the local structure of (BM)“c”-Na3PS4, while appearing cubic by Bragg diffraction, is indeed tetragonal on the local scale, albeit with a lattice that is close to cubic. Nevertheless, these data suggest that the “cubic phase” has not yet relaxed into the tetragonal structure, with the corresponding Na+ positions. While it is often observed that the average structure does not agree with the local structure in a variety of materials,37−39 these data raise the question as to why the “cubic” phase of Na3PS4 leads to a higher observed ionic conductivity at all if the structure is not so different from the tetragonal phase. 3.3. Ionic Transport. In order to gain insight into the transport properties of the different Na3PS4 phases, the BM-“c”Na3PS4 was rapidly annealed in order to obtain the tetragonal structure. A comparison of the Bragg diffraction patterns for the (BM)-t-Na3PS4, (HT)-t-Na3PS4, and (BM)-“c”-Na3PS4 can be

found in Figure S2. The structure of the rapidly annealed (BM)-t-Na3PS4 can be adequately described by the tetragonal space group (P4̅21c) and results in similar structural parameters to (HT)-t-Na3PS4 (see Figure S1b and Table S3). This shows that a short exposure of the ball-milled sample to 773 K leads to a change in the average structure (i.e., a relaxation of the lattice parameters and Na+ positions), while retaining the microstructure and defect concentration of the ball-milled sample, as recently shown by Krauskopf et al.4 Temperature-dependent impedance spectroscopy was performed on all three Na3PS4 samples. Representative Nyquist plots from room-temperature impedance data on the three samples are shown in Figure 4a. The impedance data can be fit with an equivalent circuit consisting of a constant phase element (CPE) in parallel with a resistor, connected in series with another CPE to represent the blocking electrode behavior. The obtained conductivities of the different samples can be found in the Arrhenius plot in Figure 4b. Moreover, the

Figure 4. (a) Nyquist plots of t-Na3PS4 and “c”-Na3PS4 synthesized using the different synthetic approaches. Data points are only displayed up to 2 MHz. (b) Arrhenius plots for all compounds. (c) Activation energy and room temperature ionic conductivity for each of the Na3PS4 compounds, showing that while the activation barrier for ionic motion remains unchanged the ball-milling procedure leads to much higher conductivities irrespective of the crystal structure. D

DOI: 10.1021/acs.inorgchem.8b00458 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

routes was investigated. While Bragg diffraction suggests that (BM)-Na3PS4 and (HT)-Na3PS4 possess two different average crystal structures (i.e., cubic and tetragonal), probing of the local structure via PDF analysis suggests that both compounds exhibit the structural motifs of the tetragonal polymorph. Materials that have local dipoles, such as ferroelectrics, can exhibit structural differences on the local and average scales. However, to the best of our knowledge this has not yet been observed in superionic thiophosphates. Most importantly, this work further evidence that the reason for the difference in the ionic conductivities of Na3PS4 is not the underlying crystal structure but likely differences in the defect concentration.

associated capacitances and the ideality factor of the CPE are summarized in Table S9. While the bulk and grain contributions to the transport could not be deconvoluted, the obtained capacitances and ideality factors correspond well with bulk transport.40 Finally, the activation barriers for ionic transport can also be extracted from the Arrhenius plots and are shown in Figure 4c. To further clarify the underlying reason behind the anomalously high ionic conductivity exhibited by (BM)-“c”Na3PS4, the (HT)-t-Na3PS4 sample was sintered at 500 °C for 10 h to remove grain boundary contributions (see Figure S5). Analysis of the sintered (HT)-t-Na3PS4 sample should help distinguish between microstructural and defect concentrationbased effects on the ionic conductivity. Upon sintering, scanning electron micrographs demonstrate that the pellet surface becomes exceptionally smooth and dense. Interestingly, sintering of (HT)-t-Na3PS4 only resulted in a slight increase in the ionic conductivity to 2.9 × 10−5 S cm−1, thereby suggesting that the high conductivity found in (BM)-“c”-Na3PS4 does not stem from grain boundary effects. These data further strengthen the idea that the defect concentration is the key factor behind the enhanced conductivity in (BM)-“c”-Na3PS4. A comparison of the different synthetic routes shows that the ionic conductivity of the mechanochemically synthesized compounds is much higher, irrespective of annealing treatments. In other words, regardless of whether the ball-milled sample possesses a cubic or a tetragonal average crystal structure (i.e., before or after rapid-annealing), both materials exhibit comparably high ionic conductivities. Therefore, the structural differences between the tetragonal and cubic crystal structures cannot explain the differences in the transport of the samples made by the different synthetic procedures, especially considering that the ball-milled sample already exhibits a more tetragonal local structure. Thus, there are two possible explanations for the higher ionic conductivities of the mechanochemically derived samples, relative to the hightemperature sample: (1) The milling procedure leads to a much smaller grain size, as recently shown by Krauskopf et al.,4 which is typical for a mechanochemical synthesis approach. Smaller grain sizes have already been suggested to provide faster ionic transport in thiophosphate electrolytes.41 (2) The harsh synthetic conditions during the ball-milling induce more defects, leading to a higher defect concentration and ultimately to a higher prefactor for ionic motion, which has already been suggested theoretically.16−19 While the first explanation seems likely, given that the microstructure of a classical hightemperature route usually exhibits larger grains, the obtained capacitances of the impedance response suggests bulk transport to be dominant and sintering of (HT)-t-Na3PS4 did not lead to a significant improvement in the ionic conductivity. In other words, the influence of grain boundaries appears to be very small in these mechanically soft materials. Thus, a minor change in the composition from the mechanochemical synthesis, leading to a slight nonstoichiometry, seems more likely as it would only affect the prefactor and not the activation barrier (see Table S9). If indeed ball-milling induces more defective structures, then the syntheses of other ionic conductors, such as Li10GeP2S12,3,7 need to be investigated further as mechanochemical routes are often used.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.8b00458. Rietveld refinement results for the Bragg XRD data as well as the PDF analysis results for the X-ray synchrotron diffraction data, a comparison of the G(r) data of Na3PS4 and Na3PSe4 can be found here, transport data from the electrochemical impedance spectroscopy measurements are also provided, transport data and scanning electron microscopy images for the (HT)-t-Na3PS4 samples before and after sintering are provided (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Wolfgang G. Zeier: 0000-0001-7749-5089 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Diamond Light Source for access to beamline I15-1 (EE17257-1) that contributed to the results presented here. The research was supported by the Deutsche Forschungsgemeinschaft (DFG) under grant number ZE 1010/4-1. S.C. gratefully acknowledges the Alexander von Humboldt Foundation for financial support through a Postdoctoral Fellowship.

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REFERENCES

(1) Janek, J.; Zeier, W. G. A solid future for battery development. Nat. Energy 2016, 1, 16141. (2) Bachman, J. C.; Muy, S.; Grimaud, A.; Chang, H.-H.; Pour, N.; Lux, S. F.; Paschos, O.; Maglia, F.; Lupart, S.; Lamp, P.; et al. Inorganic solid-state electrolytes for lithium batteries: mechanisms and properties governing ion conduction. Chem. Rev. 2016, 116, 140−162. (3) Kamaya, N.; Homma, K.; Yamakawa, Y.; Hirayama, M.; Kanno, R.; Yonemura, M.; Kamiyama, T.; Kato, Y.; Hama, S.; Kawamoto, K.; et al. A lithium superionic conductor. Nat. Mater. 2011, 10, 682−686. (4) Krauskopf, T.; Pompe, C.; Kraft, M. A.; Zeier, W. G. Influence of Lattice Dynamics on Na+ Transport in the Solid Electrolyte Na3PS4−xSex. Chem. Mater. 2017, 29, 8859−8869. (5) Kraft, M. A.; Culver, S. P.; Calderon, M.; Böcher, F.; Krauskopf, T.; Senyshyn, A.; Dietrich, C.; Zevalkink, A.; Janek, J.; Zeier, W. G. Influence of Lattice Polarizability on the Ionic Conductivity in the Lithium Superionic Argyrodites Li6PS5X (X = Cl, Br, I). J. Am. Chem. Soc. 2017, 139, 10909−10918.

5. CONCLUSION In this work, the discrepancy between the average and local crystal structures of Na3PS4 prepared by different synthetic E

DOI: 10.1021/acs.inorgchem.8b00458 Inorg. Chem. XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.inorgchem.8b00458 Inorg. Chem. XXXX, XXX, XXX−XXX