Understanding the Origin of Enhanced Li-Ion Transport in Nanocrystalline Argyrodite-Type Li6PS5I

Argyrodite-type Li6PS5X (X = Cl, Br) compounds are considered to act as powerful ionic conductors in next-generation all-solid-state lithium batteries. In contrast to Li6PS5Br and Li6PS5Cl compounds showing ionic conductivities on the order of several mS cm–1, the iodine compound Li6PS5I turned out to be a poor ionic conductor. This difference has been explained by anion site disorder in Li6PS5Br and Li6PS5Cl leading to facile through-going, that is, long-range ion transport. In the structurally ordered compound, Li6PS5I, long-range ion transport is, however, interrupted because the important intercage Li jump-diffusion pathway, enabling the ions to diffuse over long distances, is characterized by higher activation energy than that in the sibling compounds. Here, we introduced structural disorder in the iodide by soft mechanical treatment and took advantage of a high-energy planetary mill to prepare nanocrystalline Li6PS5I. A milling time of only 120 min turned out to be sufficient to boost ionic conductivity by 2 orders of magnitude, reaching σtotal = 0.5 × 10–3 S cm–1. We followed this noticeable increase in ionic conductivity by broad-band conductivity spectroscopy and 7Li nuclear magnetic relaxation. X-ray powder diffraction and high-resolution 6Li, 31P MAS NMR helped characterize structural changes and the extent of disorder introduced. Changes in attempt frequency, activation entropy, and charge carrier concentration seem to be responsible for this increase.


INTRODUCTION
Reducing human greenhouse gas emissions to lessen the increase of global temperature is one of the biggest challenges that industrial societies are facing. The development of highly efficient, but at the same time sustainable, electrochemical devices to store electricity generated from renewable "sources" is, thus, of primary importance in materials science and engineering. 1,2 This goal is expected to be achieved with the design of lithium all-solid-state batteries 3−5 with metallic Li as the anode material. 6−8 However, many hurdles, particularly related to interfaces 9−11 and (electro-)chemical stabilities, 12−16 have to be overcome to present market-ready solutions.
A key component in such systems is the solid electrolyte. 7,17−22 Suitable electrolytes should show ionic conductivities 23,24 comparable to those of aprotic liquid blends ordinarily used in lithium-ion batteries. Over the last decade, various oxides, 17 hydrides, 25 phosphates, 18,26 and thiophosphates, 23,27,28 including especially Li 3 PS 4 , 29 Li 7 P 3 S 11 as glass ceramics, 30−34 and argyrodite-type Li 6 PS 5 X (X = Cl, Br), 35−46 were extensively studied with regard to their applicability as ceramic electrolytes. Li 6 PS 5 I was first introduced by Deiseroth and co-workers; 47,48 the authors studied the structural details, ionic conductivity, and diffusion pathways in a sample prepared by a solid-state synthesis route. Later, mechanosynthesis was used to prepare Li 6 PS 5 I with a high ionic conductivity by Tarascon and co-workers 45 as well as by Rao and Adams. 49 It is also well known that ionic conductivities in glassy Li 2 S-P 2 S 5 , Li 2 S-P 2 S 5 -LiI glasses and glass ceramics show very high ionic conductivities. 50−54 As an example, also high conductivities in Li 7 P 2 S 8 I-type compounds were reported. 55,56 Focusing, however, on highly crystalline argyrodite-type Li 6 PS 5 X, it turned out that under ambient conditions only Li 6 PS 5 Br and Li 6 PS 5 Cl, 35,57 and some variants, 41 including also compounds with higher contents of X, 58−61 are able to deliver ionic conductivities in the desired range of a few mS cm −1 . 46,62 Thus, also battery applications and electrochemical testing mainly concentrate on these compounds, 63 including glassy Li 2 S-P 2 S 5 -LiI and glass ceramics, as mentioned above. 51 Importantly, S 2− /X anion site disorder, also introduced via substitution 41,64−66 or kinetic freezing, 43 ensures that the Li + ions can quickly jump from site to site within the complex crystal structure (see Figure 1). In Li 6 PS 5 X (X = Cl, Br), Li + is subjected to facile exchange processes within and between the Li cages formed by the Li positions 48h and 24g. Such a cage is built by six 24g−48h−24g triplets, which are arranged such that intercage hopping processes can also occur. 67 Indeed, as shown by broad-band conductivity spectroscopy, the cages are connected by fast diffusion pathways in the case of X = Cl and X = Br. 46 For these two compounds, anion site disorder is seen, i.e., S 2− and X − share positions 4d and 4a ( Figure 1). 42 For Li 6 PS 5 I, on the other hand, this anion site disorder is, however, absent. 42,46 The iodine anions solely occupy the 4a positions ( Figure 1). 42 The sites 4d inside the cages are exclusively populated by the sulfur anions that also occupy the 16e sites forming the PS 4 3− tetrahedra (see also Figure 1). In contrast to anion-disordered Li 6 PS 5 X (X = Cl, Br), for the ordered counterpart with X = I, the important intercage diffusion step, being necessary to enable long-range ion transport rather than only local jump processes, is characterized by noticeably higher activation energy (see below). 46,67 Hence, despite its larger lattice constant and the presence of easily polarizable iodide anions, for the structurally ordered and unsubstituted iodine compound Li 6 PS 5 I, through-going Li + transport is rather poor. 46 The absence of a percolating network of fast diffusion pathways for Li 6 PS 5 I results in roomtemperature ion conductivities σ with values as low as 1 × 10 −6 S cm −1 associated with an activation energy E a as high as 0.47 eV. 46 For comparison, for Li 6 PS 5 Cl, a value of σ = 3.8 × 10 −3 S cm −1 has been reported. 46 In line with this increase in σ, the corresponding activation energies for X = Cl, Br are considerably lower and range from 0.25 to 0.4 eV, depending on the method applied to study ion dynamics. 46 If structural disorder plays a major role in boosting the ionic conductivity of this class of thiophosphates, the successful conversion of structurally ordered Li 6 PS 5 I into a nanocrystalline, structurally disordered counterpart should result in a significant increase of σ. Here, we synthesized highly crystalline, i.e., well-ordered, Li 6 PS 5 I by a solid-state reaction with a sufficiently long sintering period. Afterward, we gently treated the material under an inert (Ar) gas atmosphere in a high-energy ball mill. Broad-band conductivity spectroscopy 68 revealed, indeed, an increase of ionic conductivity by a factor of 100. X-ray powder diffraction, 7 Li NMR relaxometry, 69 and high-resolution (magic angle spinning, MAS) 6 Li and 31 P NMR helped us to further characterize the microstructure of the nanocrystalline sample. Our investigation represents another application-oriented example where high-energy ballmilling was successfully applied to boost ion dynamics of an originally poor ionic conductor without changing its overall chemical composition. While for previous oxide examples 70 −73 the final conductivities showed values in the μS range, mechanical treatment of Li 6 PS 5 I ensured that conductivities with values almost touching the mS regime were reached.

EXPERIMENTAL SECTION
The preparation of Li 6 PS 5 I is described elsewhere. 46 For the present study, we used the powder of the same synthesis batch, which was recently investigated 46 also by impedance measurements and NMR spectroscopy. To prepare nanocrystalline Li 6 PS 5 I, 0.5 g of the microcrystalline powder was filled in ZrO 2 milling vials (45 mL) inside an Ar-filled glovebox (H 2 O < 1 ppm, O 2 < 1 ppm). The milling jars were filled with 60 milling balls (5 mm in diameter, ZrO 2 ). To prepare nanocrystalline Li 6 PS 5 I, we used a Premium line 7 planetary mill (Fritsch), which was operated at a rotation speed of 400 rpm. The milling time was set to 120 min. Compared to other ball-milling strategies, 74 these conditions represent a rather soft approach. Afterward, the powder was transferred back to the glovebox and pressed uniaxially (0.5 tons) into pellets with a diameter of 5 mm and thicknesses of 0.93 mm (micro-Li 6 PS 5 I) and 1.17 mm (nano-Li 6 PS 5 I), respectively. For NMR measurements, see below, the powder was sealed in Duran ampoules.
X-ray powder diffraction was carried out with a Bruker D8 Advance diffractometer (Bragg Brentano geometry, Cu Kα radiation). Patterns were recorded with a step size of 0.02°(measuring time 2 s) in the 2θ-range 10−100°. The acquisition of one-pulse 6 Li and 31 P MAS NMR spectra (25 kHz spinning speed, 2.5-mm rotors) with a Bruker 500-MHz NMR spectrometer is identical to the procedure described elsewhere. 46 The same holds for the measurement of variabletemperature 7 Li NMR spin-lattice relaxation rates in both the laboratory (1/T 1 ) and rotating frames of reference (1/T 1ρ ), which was carried out with a Bruker 300-MHz NMR spectrometer. We refer to a recently published study that describes the spectrometer settings in detail. 46 To measure the impedance responses of the pellets, we coated the pellets of nanocrystalline Li 6 PS 5 I with a thin Au layer (100 nm) using a Leica EM SCD 050 sputter coater. Impedance spectra were recorded with a Novocontrol Concept 80 broad-band dielectric spectrometer; we varied the frequency from ν = 10 mHz to 10 MHz and measured complex conductivities over a relatively large temperature range, viz. from T = 173 to 433 K in steps of 20 K. The temperature in the sample holder was controlled with a Quatro Cryosystem (Novocontrol) that uses freshly evaporated nitrogen and a heater to adjust the temperature with an accuracy of ±0.5 K. The measurements were carried out in a dry nitrogen atmosphere to avoid any contaminations with water and oxygen. In addition, for some measurement runs, we used an airtight, home-built sample holder, which was placed in the ZGS active cell of the Novocontrol spectrometer. The pellet was inserted into the sample holder in an Arfilled glovebox to further eliminate any possible contact with the surrounding air. Iodine anions occupy the 4a sites. Sulfur anions reside on the 4d and 16e sites. Together with P 3+ on 4b, the latter form PS 4 3− tetrahedra. Li ions are arranged such that they build cages consisting of six 48h− 24g−48h' triplets. In general, the Li sites are only partially occupied; strong repulsive Coulomb interactions are expected for Li ions on neighboring sites 24g and 48h. Intracage jumps include hopping processes between 48h sites of two different triplets. The pathway 48h−24g−48h' allows the Li ions to perform spatially highly restricted translational movements, which are expected to leave a characteristic fingerprint in conductivity isotherms. Long-range ion dynamics is possible either directly when jumping from cage to cage (48h 1 -48h 2 ) or using the interstitial sites connecting the Li cages, as suggested by Deiseroth and co-workers (see below). 47

RESULTS AND DISCUSSION
Pure Li 6 PS 5 I was prepared in a polycrystalline form with the help of a solid-state reaction. 46 In the inset of Figure 2, the background-corrected X-ray powder diffraction is shown together with the results from Rietveld refinement; data were taken from an earlier investigation published by some of us. 46 High-energy ball-milling of polycrystalline Li 6 PS 5 I under the conditions described above results in a drastic broadening of the reflections; see Figure 2. Most importantly, no further reflections of any decomposition products emerge. Li 6 PS 5 I remains stable under the milling conditions chosen; we do not observe any chemical degradation when milling the compound under an inert gas atmosphere. This view is supported by 6 Li MAS and 31 P MAS NMR; see below. In addition, the amount of abraded material also seems to be negligible; no reflections of abraded nano-ZrO 2 appear. Chemical analysis does not even reveal traces of Zr. For comparison, the noncorrected X-ray powder diffraction pattern of the coarse-grained starting material is also shown in Figure 2.
Strong broadening of the reflections shows that the mean crystallite size d m was reduced from the μm range down to the nm regime. 75 Indeed, via the equation introduced by Scherrer, 76 we estimated that after the milling step d m is given by approximately 15 nm. We anticipate that clusterassembled agglomerates of smaller and larger crystallites exist, possibly embedded in an amorphous matrix. Indeed, an estimation yields that the X-ray powder diffractogram points to 10−15% of amorphous material. According to previous studies on nanocrystalline LiNbO 3 and LiTaO 3 , 70,73 a high-energy ball is in general expected to generate amorphous material. 77 In the case of fluorides, 78−80 such as BaF 2 or BaLiF 3 , this amount does, however, not dominate the overall morphology of the material. On the other hand, a powder consisting of nm-sized crystallites has a large volume fraction of interfacial regions, 77,81−86 which, in many cases, are assumed to be in a structurally disordered state, leading to a core−shell structure. 85 Ions residing in these surface-related areas are expected to have access to faster diffusion pathways than the ions located in the ordered bulk regions. This observation, which resembles that of a core−shell structure with distinct ion dynamics of the two regions, has been verified for several classes of nanocrystalline ceramics, such as single-phase (Li 2 O, 87 Li 2 O 2 , 88 and LiBH 4 86 ) and two-phase systems (LiF:Al 2 O 3 , 89 Li 2 O:X 2 O 3 (X = B, Al)). 84,87,90,91 Apart from such surface-related effects, also space-charge zones might be responsible for fast ion transport in nanostructured solids. 92−96 The most prominent examples are epitaxially grown alternating layers of BaF 2 and CaF 2 . 97 Facile fluorine conduction was not only observed along the interfaces between the two fluorides but also across as spacecharge zones overlap if the individual thickness of the fluoride layers reaches the nm regime. 97 Despite such nontrivial size effects, nanocrystalline materials produced by high-energy ballmilling will also have a large number of defects introduced in the bulk regions. 73,77 For Li 6 PS 5 I, we expect that, besides the effect of interfacial regions, defect-rich bulk regions of the nmsized crystallites will also substantially contribute to long-range ionic conduction. The latter effect has been observed for LiTaO 3 , 73,98 whose ionic conductivity can be increased by 6 orders of magnitude if mechanically treated for several hours in planetary mills.
To shed light on the kind of disorder or distortions produced and to further characterize the degree of structural disorder of the ball-milled material, we carried out highresolution 31 P MAS and 6 Li MAS NMR spectroscopy. While the 6 Li NMR signals of the two samples, the microcrystalline starting material and the nanocrystalline product, are identical, 31 P MAS NMR reveals a drastic change in line shape (see Figure 3). The 31 P MAS spectrum of coarse-grained and, thus, Figure 2. X-ray powder diffraction pattern of nanocrystalline Li 6 PS 5 I that was milled for 2 h in a planetary high-energy ball mill (400 rpm). Broad humps arise from the mercapto foil used to protect the material from moisture during the measurements. Partly, these humps overlap with those originating from some amorphous material produced by milling. In addition, significant broadening of the reflections points to a heavily disordered, nanocrystalline material. For comparison, the powder pattern of the starting material, named microcrystalline Li 6 PS 5 I, is shown at the bottom. The inset presents a background-correct version of the same pattern that has been analyzed with the method introduced by Rietveld. The latter was taken from a recently published study on ion dynamics in microcrystalline Li 6 PS 5 I. 46 It shows a phase-pure material with negligible amounts of impurities, e.g., LiI. See ref 46 for the abbreviations used.
Chemistry of Materials pubs.acs.org/cm Article highly crystalline Li 6 PS 5 I is composed of a sharp signal located at 96.3 ppm (an aqueous solution of 85% H 3 PO 4 served as the primary reference). The line represents the P ions located at the Wyckoff position 4b. The ordered and regular arrangement of the tetrahedra gives rise to a single line; all PS 4 3− units are magnetically equivalent. This situation greatly changes after the material has been milled for 120 min. A broad Gaussianshaped signal appears whose center shifts toward smaller ppm values. The broad signal resembles that of a glassy material with a wide distribution of magnetically inequivalent P sites; a range of different 31 P environments has also been observed for Li 6−x PS 5−x Br 1+x quite recently by Wang et al. 61 We assume that defects, polyhedra distortions, and variations in P−S bond lengths are responsible for this drastic change, which is also seen for mechanosynthesized oxides 99 and fluorides. 100,101 The spectrum of nanocrystalline Li 6 PS 5 I also reveals a residual sharp line at the original position of micro-Li 6 PS 5 I. This line represents a tiny amount of highly crystalline Li 6 PS 5 I that survived the milling step as the ZrO 2 balls cannot reach all areas in the milling jars. The area fraction under the line shows that the milled sample consists of 2% of crystalline Li Li 6 PS 5 I. In conclusion, 31 P MAS NMR shows that all P sites experience the effect of ball-milling and not only those near the surface regions. Hence, from an atomic-scale point of view, mechanical treatment converts the entire material into a structurally distorted form. As mentioned above, local defects and severe  (a) Arrhenius representation of the temperature behavior of ionic DC conductivities plotted as log 10 (σ DC T) against the inverse temperature expressed as 1000/T; T denotes the absolute temperature in K. When going from microcrystalline to nanocrystalline Li 6 PS 5 I, the ionic conductivity near room temperature (see the vertical bar) increases by 2 orders of magnitude. For comparison, data for Li 6 PS 5 Br are also shown. In agreement with this increase in ionic conductivity, the activation energy reduces from 0.47 to 0.36 eV for T > 293 K. (b) So-called conductivity isotherms of nanocrystalline Li 6 PS 5 I. The isotherms show the dependence of the real part, σ', of the complex conductivity as a function of frequency ν; altogether, we covered a frequency window spanning a range of almost eight decades. Distinct DC plateaus are visible from which σ DC can directly be read off, as indicated for the isotherm referring to ϑ = 20°C. Dashed lines are used to analyze the frequency dependence in the dispersive regimes according to σ' ∝ ν p . p → 1 indicates the NCL behavior of the electric permittivity. See the text for further explanation. polyhedral distortions are responsible for the 31 P response. Such distortions would greatly affect the 31 P NMR line but would still produce broadened and clearly visible reflections in X-ray diffraction; see above. The latter fact points to a nanocrystalline material with lattice distortions.
The same structural effect should also be observed using 6 Li MAS NMR. As Li + is, however, highly mobile on a local scale also in Li 6 PS 5 I, the 6 Li MAS NMR line at room temperature already represents a so-called motionally narrowed signal at the temperature at which the spectrum was recorded. In addition, the chemical shift range of 6 Li is much smaller than that of phosphorus. Only low-temperature 6 Li MAS NMR may be able to resolve the magnetically inequivalent Li sites. It has to be noted that our recent 7 Li relaxometry NMR study 46 revealed fast intracage Li ion-exchange processes. These hopping processes, which are spatially confined, are sufficient to cause a coalesced NMR signal under ambient conditions. As mentioned above, the important intercage jump process is much less frequent in Li 6 PS 5 I as compared to Li 6 PS 5 X with X = Br, Cl. 67 Now, we have to ask the question as to whether this important intercage process is switched on in structurally disordered Li 6 PS 5 I. Indeed, as seen from broad-band conductivity spectroscopy, and in line with similar approaches in the literature, 45 we observe an increase of the roomtemperature direct current (DC) ionic conductivity by 2 orders of magnitude as compared to the starting material; see the Arrhenius plot of ionic conductivities shown in Figure 4.
In Figure 4b, the so-called conductivity isotherms of nanocrystalline Li 6 PS 5 I are shown that were constructed by plotting the real part, σ′, of the complex conductivity, σ, as a function of frequency ν. The isotherms reveal a universal shape and indicate a homogeneous matrix with no possibilities to differentiate between amorphous regions and structurally distorted crystalline cores. Dispersive regimes, however, point to intrinsic heterogeneous ion dynamics. At low frequencies, the decrease of σ′ for each isotherm reflects the piling up of the Li + ions in front of the blocking electrodes applied to the pellets. 68,102 At sufficiently high frequencies, σ′ passes into the so-called frequency-independent plateau, which is determined by σ DC . Further increase in ν causes σ′ to enter the dispersive regime. While the DC regime reflects successful Li + displacements that lead to long-range ion transport, 103 the dispersive regimes give evidence for correlated (forward−backward) jump processes proceeding on a much shorter length scale. 68,103 The dispersive regime is best seen at low temperatures. By comparing the isotherms recorded at −60°C and at −100°C, we recognize that this regime is composed of two contributions. We analyzed the frequency dependence with the help of Jonscher's power law ansatz: 104 σ′ ∝ ν p . The dispersive regime that is directly connected to the DC transport process is given by σ′ ∝ ν 0.61 ; p ≈ 0.6 is expected for a 3D, correlated jump process. 105 The isotherm recorded at −100°C reveals a change in exponent p for the high-frequency regime. p = 0.95 is a strong indication for a so-called nearly constant loss (NCL) behavior 106−109 meaning that the imaginary part, ε″, of the complex permittivity, ε, is independent of frequency. p = 1 is frequently found for materials that provide spatially restricted cation or anion movements. In Li 6 PS 5 I, we attribute this finding to the localized Li jump processes within the 24g−48h−24g triplet structure of the Li-rich cages. Such cagelike motions were found in materials with pocketlike structures such as RbAg 4 I 5 being prone to show NCL behavior. 110,111 The distinct DC plateaus shown in Figure 4b allowed us to easily determine σ DC values with high precision. The associated capacitance values C of the DC conductivity plateau, with its dispersive regime, are in the pF range, i.e., unquestionably referring to a bulk process that is probed by σ DC . 112 As an example, for the room-temperature isotherm, C turned out to  Figure 5a. At −100°C, the permittivities ε′(0) and ε′(∞) take values of 38 and 13.8, respectively; see Figure 5b, which displays the ε′-isotherms of nano-Li 6 PS 5 I. Hence, there is no evidence for a strong influence of any ion-blocking grain boundary regions, although the volume fraction of such regions is certainly larger in nano-Li 6 PS 5 I than in its microcrystalline counterpart. This observation is also in agreement with the shape of the conductivity isotherms. At ϑ = 20°C, σ DC is given by 0.2 mS cm −1 , which is higher than the corresponding value of unmilled Li 6 PS 5 I by 2 orders of magnitude. In fact, the introduction of structural disorder greatly helped to enhance the dynamics. The change of σ DC with temperature, as shown in Figure 4a, was analyzed in terms of an Arrhenius ansatz: σ DC T = σ 0 exp (−E a /(k B T)), where T denotes the absolute temperature, σ 0 is the pre-exponential factor, and k B is Boltzmann's constant. As a result of high-energy ball-milling, the activation energy for ionic hopping reduces from 0.47 to 0.36 eV. For comparison, in Figure 4a, we included not only the behavior of σ DC for microcrystalline Li 6 PS 5 I but also that of Li 6 PS 5 Br, showing an even higher ionic conductivity. 46 As σ DC T also depends on σ 0 , we also looked at the associated prefactors. 102 Interestingly, for temperatures above ambient (regime I), σ 0 does not change much when going from microcrystalline to nanocrystalline Li 6 PS 5 I; it increases only slightly from log 10 (σ 0 /(S cm −1 K)) = 4.61 (micro-Li 6 PS 5 I) to 5.05 (nano-Li 6 PS 5 I). Generally, σ 0 contains a range of parameters, such as the mean jump distance, the migration (and/or formation) entropy for ionic hopping ΔS m(f) , and the attempt frequency ω a , which are expected to change upon mechanical treatment. Surprisingly, although the degree of structural disorder has largely been increased, the change in σ 0 turned out to be moderate. This finding is, however, only valid for temperatures above ambient. Below ϑ = −20°C, we see that σ DC T of both samples follows Arrhenius lines with the same slope (ca. 0.35 eV; see regime II). The Arrhenius line in the low-T regime of microcrystalline Li 6 PS 5 I is, however, characterized by a much lower prefactor of only log 10 (σ 0 /(S cm −1 K)) = 2.25. Hence, ion dynamics in this temperature range is governed by a significant enhancement of σ 0 , which turned out to be on the order of almost 3 orders of magnitude; see regime II.
In general, σ DC itself does not only depend on the mobility μ of the charge carriers but also on the charge carrier density N −1 , σ DC ∝ μN −1 . To study any change of N −1 , also whether it is a function of temperature, we took advantage of the electric modulus representation to analyze ion dynamics in nanocrystalline Li 6 PS 5 I. The complex modulus M is given by the inverse of the complex permittivity 1/ε. 78,113 In Figure 6, its imaginary part, M″, is plotted vs frequency ν. The peak frequency, ν max = 1/τ M , can be interpreted as a characteristic relaxation frequency that is proportional to the (mean) hopping rate of the Li + ions 1/τ. Each peak corresponds to the σ DC plateau in Figure 4b.
First, we see that for each temperature a single M″(ν) peak appears; even in the half-logarithmic plot used to analyze the data, no shoulders or minor peaks with reduced amplitude appear. Again, electrical relaxation in nano-Li 6 PS 5 I appears homogeneously, with no distinct differences between amorphous and (distorted) crystalline regions. In general, as M max ∝ 1/C, peaks with reduced amplitude would be diagnostic for any relaxation processes that are being characterized by large capacitance values, e.g., expected for electrical relaxation processes influenced by thin grain boundary regions. Here, we do not find any hints that amorphous regions block ion dynamics; on the contrary, structural distortions enhance ionic transport. Other materials might behave differently; as an example, amorphous regions in Li 7 SiPS 8 , as shown by Lotsch and co-workers, limit intergrain ionic conductivity and have a detrimental effect on through-going ion transport. 114 Second, we notice that the M″(ν) peaks for nanocrystalline Li 6 PS 5 I are shifted toward higher frequencies. Since Li + ion dynamics is fast in nanocrystalline Li 6 PS 5 I, the M″(ν) analysis covers only the low-temperature regime. The shift of the peak maxima by 2 orders of magnitude is similar to but not exactly Chemistry of Materials pubs.acs.org/cm Article the same as that seen for σ DC T in this low-T regime (vide supra), as σ 0 increases by more than a factor of 100 below ambient temperature. This agreement in comparison tells us that the increase in σ DC can be mainly attributed to an enhancement of μ but also to an enhancement of N −1 . As E a remains almost unchanged, we suppose that the boost in the mobility of the Li + ions below ambient temperature has to be attributed to a change of either the attempt frequency ω a or the activation entropy ΔS, assuming that the influence of other factors governing σ 0 cannot produce such a large increase.
By comparing E a of microcrystalline Li 6 PS 5 I from both the σ DC T analysis and from M″(ν), we recognize that the two corresponding activation energies (0.47 eV, see Figure 4a; 0.37 eV, see Figure 6b) differ by approximately 0.1 eV. Provided both techniques sense the same electrical relaxation process, and only in this case, the steeper increase in σ DC can be explained by a temperature-dependent charge carrier concentration N −1 = f(1/T), which itself follows an Arrhenius-like behavior with an activation energy of ca. 0.1 eV. In such a case, σ DC T would increase faster with 1/T than 1/τ M . This behavior contrasts with that seen for nanocrystalline Li 6 PS 5 I. For nano-Li 6 PS 5 I, we notice that the two activation energies (0.36 eV (σ DC T); (0.38 eV (M″)) are very similar. In fact, the increase of 1/τ M is even slightly more pronounced than that seen for σ DC T. Roughly speaking, for structurally disordered nano-Li 6 PS 5 I, having a large number of defect sites and locally distorted regions, we find evidence for a charge carrier concentration N −1 that is almost temperature independent but larger than that in the microcrystalline sample. This finding is in line with the general understanding of ion dynamics in the solid state: disorder, distortions, and a higher number fraction of (point) defects ensure a high, in many cases temperature independent, number density of charge carriers.
To conclude, at low T, the increase in σ DC for the ball-milled sample is due to an enhanced Arrhenius prefactor and, to a lesser degree, also an enhanced number fraction of mobile charge carriers. At temperatures higher than ambient, the lower conductivity of the microcrystalline sample increases stronger than expected, as N −1 increases for this sample with temperature. Interpreting the higher activation energy (0.47 eV) of microcrystalline Li 6 PS 5 I in terms of N −1 = f(1/T), we have to conclude that the activation energy for the intercage jump is comparable to that in compounds with X = Cl or Br; it is, however, governed by a much lower prefactor τ 0 (k B T)). This conclusion is in line with the soft lattice concept developed earlier for this class of materials. 42,65 Finally, we used resistivity measurements, M″/ω, 115 to extract activation energies over a larger dynamic range; see Figure 6b. The above-mentioned analysis of modulus peaks was restricted to temperatures where the peaks M″(ν) appear at frequencies that correspond to the crossover from σ′ = σ DC to σ′ ∝ ν p . Analyzing M″/ω at frequencies of 1.2 and 10 MHz allows, however, for the detection of both long-range ion dynamics and short-range ion-hopping processes, as it is also possible via 7 Li NMR relaxometry 116 (see Figure 7). For nanocrystalline Li 6 PS 5 I, a plot of log 10 (M″/ω) vs 1000/T reveals asymmetric peaks whose flanks characterize lengthscale-dependent ion dynamics (Figure 6b). While E a referring to the high-T flank is somehow comparable to E a from M″(ν), particularly for microcrystalline Li 6 PS 5 I, we clearly see that for nano-Li 6 PS 5 I, an asymmetric peak appears, pointing to a large distribution of jump processes as a consequence of a highly  T 1(ρ) ). The lines show linear fits to extract the activation energies, E a , indicated. Arrows point to the peak maxima. A reversible phase transition occurs at ca. 165 K. (b) The same figure as in (a) but with the inclusion of 7 Li NMR rates of microcrystalline Li 6 PS 5 I; the rates of nano-Li 6 PS 5 I are indicated by crosses (+). Whereas the 1/T 1 peaks reflect fast intracage ion dynamics with almost the same jump rates in the two samples, 1/T 1(ρ) shows that upon ball-milling, the shallow peak seen at 360 K (0.26 eV) for micro-Li 6 PS 5 I gains in intensity and shifts by 100 K toward lower T; see the two asterisks (*). See the text for further explanation. irregular energy landscape. The stronger this asymmetry, the more heterogeneous the Li + ion dynamics.
The activation energy of the low-T flank of the M″/ω peaks is given by 0.15 eV. Such a low value should also be detectable by 7 Li NMR spin-lattice relaxation measurements (see Figure  7). 69,88,116 Indeed, the diffusion-induced 7 Li NMR spin-lattice relaxation rates 1/T 1 and 1/T 1ρ , measured either in the laboratory frame or in the rotating frame of reference, yield lower E a values than that seen by σ DC , which is solely sensitive to successful ion jump processes. Localized processes, forward−backward jumps, and within-site movements are, on the other hand, detectable by nuclear spin relaxation in addition. 88 The rates presented in Figure 7 were determined from diffusion-induced magnetization transients M 1(ρ) (t (lock) ) that were analyzed with stretched exponential functions. The stretching exponents γ 1(ρ) are shown in the upper graphs of Figure 7. While 1/T 1 relaxation follows almost monoexponential time behavior (γ 1 ≈ 1), the exponents characterizing the transients corresponding to spin-lock relaxation (1/ T 1ρ ) strongly depend on temperature and can only be parametrized by stretched functions: M 1ρ (t lock ) ∝ exp(−(t/ T 1(ρ) ) γ ). 117 Note that 1/T 1 senses ion dynamics on the MHz time scale (ω 0 /2π = 116 MHz), while 1/T 1ρ probes magnetic fluctuations in the kHz regime; we used a spin-lock frequency of ω 1 /2π = 20 kHz to record the 1/T 1ρ rates. We see that the 1/T 1 (1/T) peak is asymmetric in shape, with the low-T side being characterized by 0.138 eV. This value is highly comparable to those deduced from the asymmetric M″/ω peaks (see Figure 6b) and represents short-range ion dynamics in the nanocrystalline sample. In general, a 1/T 1 (1/T) NMR rate peak occurs when the mean Li + jump rate τ −1 , which is within a factor of two identical to the underlying motional correlation rate τ c −1 , 118,119 reaches the order of the Larmor (ω 0 ) or locking (ω 1 ) frequency. Thus, at the peak maximum, we have τ c −1 ω 0(1) ≈ 1. 69 The lower the ω 0(1) , the more the peak shifts toward lower temperatures.
At first glance, the 1/T 1 (1/T) peak observed for nanocrystalline Li 6 PS 5 I is almost identical to that measured for its microcrystalline counterpart; see Figure 7b. It is worth noting that both peaks are produced by extremely fast localized ionexchange processes restricted to the Li cages in Li 6 PS 5 I (0.138 eV (nanocrystalline Li 6 PS 5 I), 0.20 eV (microcrystalline Li 6 PS 5 I); see Figure 7a,b). As has been discussed recently for microcrystalline Li 6 PS 5 X (X = Br, Cl, I), 46 these processes are sufficiently fast to generate a full relaxation rate peak, which is comparable to those seen for Li 6 PS 5 Br and Li 6 PS 5 Cl. Regardless of whether the intercage exchange process is fast or slow, this relaxation peak showing facile intracage ion dynamics is a universal feature 46 for all types of Li-bearing argyrodites with the structural motifs shown in Figure 1. It is also in line with the coalesced (motionally averaged) 6 Li MAS NMR signal seen at ambient bearing gas pressure (see Figure  3a).
Importantly, for microcrystalline Li 6 PS 5 I, a symmetric peak 1/T 1 (1/T) is seen. Obviously, Li 6 PS 5 I seems to be a good model system to study the influence of structural disorder on the nuclear spin relaxation. 120 Our observation supports the general idea that structural disorder and Coulomb interactions produce this asymmetry in materials with strongly heterogeneous ion dynamics. 121−123 We realize that the boost in σ DC affecting long-range ion dynamics is hardly seen in 1/T 1 relaxation. On the contrary, careful inspection reveals that the 1/T 1 (1/T) peak of nano-Li 6 PS 5 I is even shifted by 50 K toward higher T; see below. Hence, the introduction of polyhedral distortions slows down Chemistry of Materials pubs.acs.org/cm Article local, intracage ion dynamics (vide infra). Simultaneously, long-range diffusion is, however, switched on for nano-Li 6 PS 5 I. The latter change in conduction properties clearly leaves its marks in spin-lock 1/T 1ρ NMR relaxation, being sensitive to ion dynamics on a longer length scale. Starting with 1/T 1ρ (1/T) of micro-Li 6 PS 5 I, the peak corresponding to 1/T 1 is expected to appear at temperatures near or below the temperature T tr at which Li 6 PS 5 I reversibly transforms into a low-T modification; see Figure 7b. Above T tr , we probe a high-T flank whose slope seems to be governed by the intracage jump processes. Near 360 K, a shallow 1/T 1ρ (1/ T) peak is seen whose origin was unclear so far. Its high-T side is characterized by an activation energy of 0.26 eV. Most interestingly, 1/T 1ρ (1/T) of the nanocrystalline material helps identify this relaxation process. Again, the 1/T 1ρ (1/T) peaks associated with that seen in T 1 are expected at very low temperatures. Indeed, the rates pass through such a shallow peak at ca. 190 K. Surprisingly, another peak is seen at a higher temperature of 265 K (see Figure 7a). We anticipate that this peak corresponds to the one also seen for the microcrystalline sample but at much higher temperatures. Obviously, as this turned out to be the main difference in nuclear spin relaxation of the two samples, the peak might reflect additional diffusion processes taking place in nanocrystalline Li 6 PS 5 I. These additional processes might take advantage of interstitial Li positions connecting the Li cages; see Figure 1. Most likely, these sites become partly occupied by the Li + ions as a consequence of ball-milling. Such sites have been suggested on the basis of molecular dynamics simulations (500 K) by Pecher et al., 47 who called them type 2, type 3, and type 4. The free enthalpies, when referenced to the site energies of the regularly occupied Li + sites (see Figure 1), turned out to be 0.27, 0.39, and 0.14 eV. These values agree with those probed by NMR and electrical spectroscopy; see Figures 4,6,and 7. Going back to spin-lattice relaxation NMR, we recognize that the additional spin-lock nuclear relaxation process cannot serve as the only explanation for the enhancement seen in σ DC , as one would expect the corresponding 1/T 1ρ (1/T) to be shifted to even lower temperatures to explain values of 0.2 mS cm −1 at 20°C. We assume that ball-milling also affects the direct intercage Li + hopping process as this is the process needed to enable the ions to move over long distances. Possibly, this process is also influenced by interstitial sites located between the Li cages. As mentioned above, we suppose that these are easily reachable for the Li ions in structurally distorted Li 6 PS 5 I. These intercage jump processes are, however, "switched off" for microcrystalline Li 6 PS 5 I as can be clearly probed by variable-temperature 7 Li NMR line-shape measurements (see Figure 8a). 46 Whereas for Li 6 PS 5 X, the static NMR line width reaches its limiting value well below room temperature, Li 6 PS 5 I shows a so-called two-step decay behavior.
With increasing temperature, the fast intracage hopping processes are able to considerably average dipole−dipole interactions mainly determining the broad NMR line in the socalled rigid lattice at low temperatures. This averaging remains, however, incomplete until 300 K as, up to this temperature, the intercage jump rate is lower than the spectral width of the NMR line. Above 300 K, the exchange rate reaches values finally affecting the line width, which results in full narrowing. For nanocrystalline Li 6 PS 5 I, averaging via intercage hopping is much more effective as shown in Figure 8b: at 300 K, the line width has almost reached its final value. Note that the nanocrystalline sample still resembles the behavior of the nonmilled sample as a shallow two-step behavior is still detectable. The regime of extreme narrowing is reached at a temperature above 400 K.
Before summarizing our results, we go back to the 1/T 1 (1/ T) peaks seen in Figure 7b. As mentioned above, by precisely comparing the position of the two 1/T 1 (1/T) peaks, i.e., before and after mechanical treatment, we recognize that the peak for nano-Li 6 PS 5 I appears at somewhat higher T (370 K) than that for the microcrystalline counterpart (320 K). In agreement with this shift, which is indicated by the vertical two arrows in Figure 7b, also the corresponding 1/T 1(ρ) (1/T) of nano-Li 6 PS 5 I is shifted to higher T and becomes detectable for this sample at ca. 190 K (see Figure 7a). In contrast, for microcrystalline Li 6 PS 5 I, the spin-lock rates do not reach the peak maximum before T = 160 K. These consistent shifts indicate that the intracage process in disordered, nanocrystalline Li 6 PS 5 I slightly slowed down. Obviously, as concluded above, this decrease has no detrimental effect on long-range ion transport as ionic mobility is determined by the number of successful intercage jump events. The latter seems to greatly benefit from the structural distortions introduced.
To sum up, Li 6 PS 5 I served as an attractive and highly suitable model system to show how mechanical treatment, that is, the introduction of structural disorder, is able to convert poor ion conductors into highly conducting electrolytes. For the materials studied so far, e.g., LiTaO 3 , LiNbO 3 , and LiAlO 2 , this concept resulted in conductivities of 10 −6 S cm −1 . In the present case, high-energy ball-milling was successfully applied to reach DC conductivities almost approaching the mS regime. Changing the milling conditions and increasing the milling time might lead to materials showing even higher conductivities.
Preliminary experiments show that nano-Li 6 PS 5 I can completely be reconverted into its crystalline form. Reordering sets in at temperatures as high as 200°C; a fully crystalline sample is reobtained after heat treatment at 500°C already for 2 h. This sample shows the same conductivity isotherms (with regimes I and II) as that of the initial one. In addition, we saw that 7 Li NMR 1/T 1 measurements carried out at constant temperatures of 200 and 160°C for 2 h led to a continuous decrease of the rate. This decrease indicates that the original peak 1/T 1 (1/T) is reobtained. Note that the difference in 1/T 1 for nano-Li 6 PS 5 I and unmilled Li 6 PS 5 I is rather small due to the fast, localized motions governing spin-lattice relaxation in both forms. Importantly, when the sample was left inside the glovebox for 3 months (at 25°C), we also observed reordering and a significant drop in ionic conductivity. The same change has been observed quite recently for mechanosynthesized RbSn 2 F 5 . 115 The latter, also showing high F anion conductivity, is metastable if present in a nanocrystalline, distorted form. We anticipated that fast ion dynamics triggers reordering of such samples. The same could be the case for nano-Li 6 PS 5 I. Thus, the structural stability of disordered samples has to be kept in mind if we think about the implementation of distorted fast ion conductors in batteries.
A systematic study on the influence of the milling conditions and subsequent thermal treatment is currently under way in our laboratory. Such a study is, however, beyond the scope of the present investigation. The initial results indicate that increasing the milling time to 4 h does not significantly change the room temperature of Li 6 PS 5 I. Hence, we conclude that a limiting value for σ DC is already reached after 2 h. Also, for Chemistry of Materials pubs.acs.org/cm Article some oxides, a very similar dependence on milling time is seen: the main structural changes occur during the early steps of milling. 73,98 We assume that Li 6 PS 5 I might be converted into a fully amorphous phase if one doubles the number of milling balls. A total of 60 balls, as used here, is rather low for mechanochemical synthesis under dry conditions.

CONCLUSIONS
Li 6 PS 5 I, with its ordered anion sublattice, shows fast Li + jump processes on a local scale, most likely restricted to translational intracage ion dynamics. Unfortunately, the important intercage hopping processes occur less frequently, resulting in poor ionic DC conductivities with a value on the order of 1 μS cm −1 under ambient conditions. High-energy ball-milling was used to introduce structural disorder, such as point defects, polyhedra distortions, and strain, to boost ion dynamics up to DC conductivities of 0.2 mS cm −1 at 20°C. X-ray diffraction and 31 P NMR helped us to characterize the extent of structural disorder. Broad-band conductivity spectroscopy and the analysis of electric modulus spectra show that both a change in charge carrier mobility, through enhanced Arrhenius prefactors, and an increase in charge carrier concentration seem to be responsible for this increase. Variable-temperature spin-lock 7 Li nuclear spin relaxation revealed that in nanocrystalline Li 6 PS 5 I one of the diffusion processes seen is clearly enhanced as compared to the unmilled starting material. We assume that structural distortions enhance the intercage jump rate, leading to through-going Li + diffusion. Most likely, interstitial sites assist in Li + diffusivity as they might be easily reachable for the Li ions in structurally distorted Li 6 PS 5 I. Thus, the iodide represents an attractive application-oriented model system to study the effect of structural disorder on the elementary steps of ion hopping. We showed that soft mechanical treatment is able to convert poor ionic conductors into highly conducting electrolytes, with DC conductivities almost reaching values in the mS cm −1 regime.