NMR Investigations of Crystalline and Glassy Solid Electrolytes for Lithium Batteries: a Brief Review

International Journal of Molecular Sciences

Review NMR Investigations of Crystalline and Glassy Solid Electrolytes for Lithium Batteries: A Brief Review

Daniel J. Morales 1,2 and Steven Greenbaum 1,*

1 Department of Physics and Astronomy, Hunter College of the City University of New York, New York, NY 10065, USA; [email protected] 2 Ph.D. Program in Physics, CUNY Graduate Center, New York, NY 10036, USA * Correspondence: [email protected]

Received: 9 April 2020; Accepted: 28 April 2020; Published: 11 May 2020

Abstract: The widespread use of energy storage for commercial products and services have led to great advancements in the ﬁeld of lithium-based battery research. In particular, solid state lithium batteries show great promise for future commercial use, as solid electrolytes safely allow for the use of lithium-metal anodes, which can signiﬁcantly increase the total energy density. Of the solid electrolytes, inorganic glass-ceramics and Li-based garnet electrolytes have received much attention in the past few years due to the high ionic conductivity achieved compared to polymer-based electrolytes. This review covers recent work on novel glassy and crystalline electrolyte materials, with a particular focus on the use of solid-state nuclear magnetic resonance spectroscopy for structural characterization and transport measurements.

Keywords: NMR; inorganic electrolytes; glassy electrolytes; ceramic electrolytes

1. Introduction As lithium ion batteries continue to permeate the commercial market, the search continues to produce an all solid-state equivalent with the same or superior performance. While liquid organic electrolytes continue to exhibit high performance and long cyclability, the risk of thermal runaway and inability to utilize Li metal anodes without the risk of dendrite formation are ongoing issues. The use of solid electrolytes would allow for the use of lithium metal anodes, which would nearly double the current energy density seen in Li-ion batteries. This attractive prospect has fueled considerable research into a variety of solid electrolytes—in particular, inorganic solid electrolytes. Inorganics comprise many diﬀerent families of materials, including glasses, glass-ceramics, garnets, and others, with a wide range of structural and electrochemical properties, as sampled in the table below. Depending on the 7 2 material, one can achieve ionic conductivities on the order of 10− to 10− S/cm at room temperature, as seen in Figure1, the high end of which is comparable to liquid electrolytes [1] It is often useful, and indeed important, to study the Li-ion dynamics in these systems and relate it back to the structure, as it may lead to insights into the nature of the ionic conductivity and oﬀer solutions in terms of improving the electrolyte performance.

Int. J. Mol. Sci. 2020, 21, 3402; doi:10.3390/ijms21093402 www.mdpi.com/journal/ijms Int. J. Mol. Sci. 2017, 18, x FOR PEER REVIEW 2 of 26 Int. J. Mol. Sci. 2020, 21, 3402 2 of 24 Figure 1. Various types of solid electrolytes and reported conductivities. Courtesy of Cao et al. [2].

Figure 1. Various types of solid electrolytes and reported conductivities. Courtesy of Cao et al. [2]. It is often useful, and indeed important, to study the Li-ion dynamics in these systems and relate 2.it Techniquesback to the structure, in Nuclear as Magnetic it may lead Resonance to insights into the nature of the ionic conductivity and offer solutions in terms of improving the electrolyte performance. Of the many analytical techniques available to probe these materials, NMR Spectroscopy is uniquely capable of studying electrolyte structure and ion dynamics, with a variety of pulse sequences 2. Techniques in Nuclear Magnetic Resonance and experiments to determine both long- and short-range dynamics. Nuclear spins precess about a staticOf magnetic the many ﬁeld analyticalB0 at a characteristic techniques Larmor available frequency to probeω these[3], materials, NMR Spectroscopy is uniquely capable of studying electrolyte structure and ion dynamics, with a variety of pulse sequences and experiments to determine bothω long-= γ andB short-range dynamics. Nuclear spins precess − 0 about a static magnetic field at a characteristic Larmor frequency [3], where γ is the gyromagnetic ratio of the nucleus.= These − spins form a net magnetization in the direction ofwhereB0 and can is the be manipulatedgyromagnetic by ratio application of the nucleus. of a smaller These resonant spins form rf pulse. a net The magnetization net magnetization in the relaxesdirection back of to equilibriumand can be according manipulated to longitudinal by application and of transverse a smaller relaxation resonant rftimes pulse. T1 and The Tnet2. Inversionmagnetization and saturation relaxes back recovery to equilibrium experiments according can determine to longitudinal these andcharacteristic transverse relaxation relaxation times, times whichT1 and are T mediated2. Inversion bylocal and nuclear, saturation and in recovery some cases experiments quadrupolar can spin determine interactions. these These characteristic relaxation timesrelaxation are functions times, of which both temperature are mediated and by frequency local nuclear, and have and historically in some been cases well quadrupolar described by spin the Bloembergen,interactions. ThesePurcell, relaxation and Pound times (BPP) are relaxation functions theory, of both which temperature relates relaxation and frequency times to rotational and have correlationhistorically times beenτ wellc [4], described by the Bloembergen, Purcell, and Pound (BPP) relaxation theory, 4 2 1 3γ } which relates relaxation times to rotational= correlation[J(ω) + times4J(2ω )] [4], (1) 6 T1 10r 0 = () () ( ) (1) where J ω , the spectral density function, is the probability of ﬁnding a molecule rotating at a given frequency ω, where (), the spectral density function, is the probabilityτ of finding a molecule rotating at a given J(ω) = c frequency , 1 + ω2τ2 c () = Correlation times exhibit Arrhenius behavior and can be expressed as 1

Correlation times exhibit Arrhenius behavior andE cana be expressed as τ (T) = τ e kT (2) c 0 () = (2) allowing one to extract activation energies Ea from variable temperature (VT) relaxation measurements. allowing one to extract activation energies from variable temperature (VT) relaxation One simple example of a relaxation experiment is the inversion-recovery pulse sequence, where a π measurements. One simple example of a relaxation experiment is the inversion-recovery pulse pulse rotates the equilibrium magnetization into the negative z-axis and relaxes for a time t before a π sequence, where a pulse rotates the equilibrium magnetization into the negative z-axis and relaxes2 pulse is applied and the resulting signal intensity is measured. The intensity is dependent on both t for a time t before a pulse is applied and the resulting signal intensity is measured. The intensity and T1 [3], t is dependent on both t and [3], T S(t) = S0 1 2e− 1 (3) − ( ) One caveat of this experiment is the fact = that the − relaxation can only be found at one frequency,(3) which is dependent on the ﬁeld strength of the superconducting magnet used. In ﬁeld cycling (FC) Int. J. Mol. Sci. 2020, 21, 3402 3 of 24

NMR, the magnetic field is varied over a wide range (10 kHz–1 MHz), allowing for measurements of T1 as a function of larmor frequency [5,6]. Pulsed Field Gradient (PFG) NMR is another technique which is well-suited for studying ion transport in a system. As the Larmor frequency of individual spins depends on the local magnetic field, the application of a magnetic field gradient can encode the spatial position of the nuclear spins. By encoding the spins position, allowing time for diffusion, and decoding the spins through a reverse gradient, it is possible to determine the self-diffusion coefficient D of the probe nucleus [7] through the Stejskal-Tanner equation: D(γδg)2(∆ δ ) S(g) = S0e− − 3 (4) where g is the gradient strength, δ is the gradient pulse length, γ is the nucleus-dependent gyromagnetic ratio, and ∆ is the diffusion time. Self-diffusion as a quantity is tied to various transport properties useful in the field of energy storage, such as cation transference numbers and ionic conductivities of materials through the Nernst–Einstein Equation:

F2 X σ = c D (5) NMR RT i i i where F is Faraday’s constant, R is the ideal Gas constant, T is the temperature in Kelvin, and ciDi is the product of molar concentration and self-diffusion coefficient of each charge carrier in a material. Aside from ion dynamics, NMR is well known for its ability to perform structural characterization, usually through the use of magic angle spinning (MAS) NMR. The NMR Hamiltonian contains many terms (homo and heteronuclear dipolar interaction, first order quadrupolar interaction, chemical shift anisotropy, etc.) that contain a second order Legendre polynomial term 3 cos2 θ 1. By rotating a − sample at a specific angle to the magnetic field, such that this term cancels out (θ 54.7), one can ≈ average out most anisotropic interactions, leaving only isotropic shifts, and significantly increasing spectral resolution [8]. This technique can also be paired with cross-polarization (CP) NMR [9], where magnetization is transferred from nearby abundant nuclei—usually protons—to less sensitive or abundant nuclei. This review will focus on recent publications on glassy and crystalline electrolytes studied through the lens of NMR spectroscopy. Although these selected works do not comprise the entirety of NMR research on solid electrolytes, they do represent most of the major techniques and approaches currently used in the field.

3. Glassy Electrolytes Glass-ceramic solid electrolytes have garnered much attention over the past few decades, due to their notable advantages over their crystalline counterparts. They are relatively easier to make into thin ﬁlms, and their amorphous nature from the lack of a grain boundary allows for more uniform ion conduction and higher ionic conductivity, making it an attractive electrolyte candidate. Most glasses take the form of a mixture of Li2S, GeS2, SiS2, and P2S5 in various compositions. Depending on the 7 composition and concentration of lithium, one can achieve ionic conductivities ranging from 10− to 2 10− S/cm [2,10]. Many glassy electrolytes are usually prepared by ball-milling rather than through a melt, which leads to diﬃculties in scaling up. Glasses that come from a melt tend to lack crystalline conduction pathways or interfaces, which are desirable in discouraging Li dendrite formation. Kaup et al. recently reported on the synthesis of a quaternary glass system containing aLi2S-γB2S3-xSiO2-zLiI (LIBOSS), which exhibited high room temperature conductivity (~1 mS/cm) [11]. In addition, LIBOSS glasses were prepared solely through a melt, which allows for a high yield and relative scalability compared to ball-milling. Using MAS NMR, the authors studied the relationship between the silica content x with the changes in ionic conductivity. Int. J. Mol. Sci. 2020, 21, 3402 4 of 24

Int. J. Mol. Sci. 2017, 18, x FOR PEER REVIEW 4 of 26 Figure2 shows both the activation energy and ionic conductivity of the glass as a function of SiO 2 content.Figure Initially, 2 shows the xboth= 0 glassthe activation revealed aenergy signiﬁcant and amountionic conductivity of crystalline of LiIthe (~28 glass wt%), as a whichfunction may of accountSiO2 content. for the Initially, lower conductivity. the x = 0 glass However, revealed small a significant amounts amount of silica of (0 crystallinex 0.25) LiI drastically (~28 wt%), improve which ≤ ≤ themay solvation account offor LiI, the andlower between conductivity. 0.25 However,x 0.75, allsmall of the amounts LiI is dissolvedof silica (0 into≤ ≤ the0.25) glass drastically matrix. ≤ ≤ ≤ ≤ Pastimprove x = 0.75, the however,solvation theof LiI, solubility and between limit of 0.25 LiI and SiO0.75,2 is all reached of the LiI and is it dissolved begins to into recrystallize. the glass Additionally,matrix. Past the x = ionic 0.75, conductivity however, the of LIBOSS solubility peaks limit at a of silica LiI content and SiO of2 0.25is reached (2 mS/cm), and but it decreases begins to andrecrystallize. remains steady Additionally, at higher the x, ionic until conductivity dropping at xof= LIBOSS0.75, when peaks the at LiI a silica crystallizes. content of 0.25 (2 mS/cm), but decreases and remains steady at higher x, until dropping at x = 0.75, when the LiI crystallizes.

Figure 2. (Top) Activation energy and (bottom) room temperature ionic conductivity of Figure 2. (Top) Activation energy and (bottom) room temperature ionic conductivity of aLi2S-B2S3- aLi2S-γB2S3-xSiO2-zLiI (LIBOSS) with varying silica content [11]. xSiO2-zLiI (LIBOSS) with varying silica content [11]. 11B and 29Si MAS NMR, as seen in Figure3, were utilized to elucidate this trend. The 11B spectra 11B and 29Si MAS NMR, as seen in figure 3, were utilized to elucidate this trend. The 11B spectra of the x = 0 sample revealed the presence of multiple boron-containing tetrahedral units, such as BO3, of the x = 0 sample revealed the presence of multiple boron-containing tetrahedral units, such as BO3, BO2S, BS3, and BS4 [12,13]. In particular, the peaks are 2.9 ppm and 0.5 ppm correspond to BS4 BO2S, BS3, and BS4[12,13]. In particular, the peaks are –2.9− ppm and –0.5− ppm correspond to BS4 with with 2–4 bridging sulfur atoms and BS4 with 0–1 bridging sulfurs, respectively. As the silica content 2–4 bridging sulfur atoms and BS4 with 0–1 bridging sulfurs, respectively. As the silica content increases, the intensities of these two peaks swap, confirming the increased presence of isolated boron increases, the intensities of these two peaks swap, confirming the increased presence of isolated boron tetrahedra, and suggesting that BS4 plays less of a bridging role compared to SiO2. The increase in tetrahedra, and suggesting that BS4 plays less of a bridging role compared to SiO2. The increase in non-bridging sulfur units forms smaller inorganic units, which increases the solubility of LiI in the non-bridging sulfur units +forms smaller inorganic units, which increases the solubility of LiI in the glass, and increases the Li ion density. In addition, a preference for BO3 arises with increasing Si glass, and increases the Li+ ion density. In addition, a preference for BO3 arises with increasing Si content, as boron has a stronger affinity for oxygen over sulfur, leading the sulfur to bond with silicon. content, as boron has a stronger affinity for oxygen over sulfur, leading the sulfur to bond with silicon. This is seen in the 29Si spectra, with the presence of two peaks at 7 ppm and 4.5 ppm, corresponding This is seen in the 29Si spectra, with the presence of two peaks at 7 ppm and −– 4.5 ppm, corresponding to SiS4 and SiOS3 units, respectively. to SiS4 and SiOS3 units, respectively. The lithium environment can also give insight into the nature of the Li+ ion mobility. At x = 0, the 7Li spectra shows a sharp peak at 4.5 ppm, corresponding to LiI, with a broad peak near 0 − ppm corresponds to a distribution of Li in proximity to nonbridging sulfur (in x = 0) or a mixture of sulfur/oxygen (x = 0.25, 0.5). The solubility of LiI greatly increases with increasing Si content, leading to a significantly reduced, albeit nonzero signal intensity in the corresponding peak. The inability of XRD to detect this small amount of LiI suggests the existence of nanoaggregates, which would still hinder the ionic conductivity.

Int.Int. J. J. Mol. Mol. Sci. Sci. 20172020, ,1821, ,x 3402 FOR PEER REVIEW 55 of of 26 24

Figure 3. (A) 11B, (B) 29Si, and (C) 7Li magic angle spinning (MAS) spectra of LIBOSS for x = 0 (blue), Figure 3. (A) 11B, (B) 29Si, and (C) 7Li magic angle spinning (MAS) spectra of LIBOSS for x = 0 (blue), x x = 0.25 (orange), and x = 0.5 (green) [11]. = 0.25 (orange), and x = 0.5 (green) [11].

As the SiO2 content increases, the 0 ppm peak exhibits great motional narrowing, suggesting + increasedThe lithium Li ion mobility. environment In addition, can also the give peak insight shifts tointo lower the frequencynature of atthe higher Li ion Si content,mobility. suggesting At x = 0, 7 thea more Li spectra ionic interaction shows a sharp between peak Li at and - 4.5 the ppm, glass. corresponding to LiI, with a broad peak near 0 ppm corresponds to a distribution of Li in proximity to nonbridging sulfur (in x = 0) or a mixture of In general, the addition of SiO2 has the effect of increasing the fraction of non-bridging sulfur/oxygensulfur/oxygen containing(x = 0.25, 0.5). units, The which solubility results of LiI in small greatly inorganic increases units, with allowing increasing for Si a greatercontent, degree leading of tofreedom a significantly in the glass reduced, network albeit and nonzero more terminal signal intensity chalcogenide in the ions, corresponding leading to greater peak. LiThe+ ion inability mobility. of XRD to detect this small amount of LiI suggests the existence of nanoaggregates, which would still However, at higher SiO2 content, the ionic character of these inorganic groups dominates, and lead to hindera greater the electrostatic ionic conductivity. interaction with Li+ ions near the nonbridging chalcogen, which in turn reduces the ionicAs the conductivity. SiO2 content increases, the 0 ppm peak exhibits great motional narrowing, suggesting increasedWhile Li MAS ion is mobility. extremely In useful addition, at determining the peak shifts the local to lower structure frequency of glassy at materials, higher Si alternate content, suggestingmethods such a more as relaxometry ionic interaction can probe between the Li ionand dynamicsthe glass. at various timescales [14]. Marple et al. In general, the addition of SiO2 has the effect of increasing the fraction of non-bridging studied the Li-ion dynamics of Chalcogenide Glasses, composed of Li2S, Ga2Se3, and GeSe2 (LGGS) in sulfur/oxygenmixed compositions, containing ranging units, from which 7.5% results to 50% in Li small [15,16 inorganic]. They performed units, allowing electrochemical for a greater impedance degree + ofspectroscopy freedom in (EIS)the glass to find network ionic conductivities and more terminal as a function chalcogenide of both ions, composition leading to and greater temperature, Li ion mobility.and extracted However, Li ion at activation higher SiO energies2 content, from the the ionic subsequent character Arrhenius of these plots.inorganic In particular, groups dominates, the highest and lead to a greater electrostatic interaction with Li+ ions near the nonbridging chalcogen, which in room temperature DC conductivity was found in the 50–10–40 Li2S–Ga2Se3–GeSe2 glass, approximately turn4 reduces the ionic conductivity. 10− S/cm. While7 MAS is extremely useful at determining the local structure of glassy materials, alternate Li NMR lineshape analysis was performed on three phases of the LGGS glasses, 40–60 Li2S–GeSe2, methods such as relaxometry can probe the Li ion dynamics at various timescales[14]. Marple et al. 15–25–60 Li2S–Ga2Se3–GeSe2, and 50–10–40 Li2S–Ga2Se3–GeSe2, in order to highlight the differing Li studiedion dynamics the Li-ion with dynamics composition of Chalcogenide and temperature. Glasses, Static composed NMR spectra of Li2S, were Ga2Se obtained3, and GeSe using2 (LGGS) a solid in mixed compositions, π ranging π from 7.5% to 50% Li [15,16].They performed electrochemical echo pulse sequence of 2 2 pulses, in order to clearly study the quadrupolar effects that are impedance spectroscopy (EIS)x − to yfind ionic conductivities as a function of both composition and commonly seen in 7Li. temperature, and extracted Li ion activation energies from the subsequent Arrhenius plots. In From the Variable Temperature (VT) Spectra in Figure4, a broad Gaussian central transition peak particular, the highest room temperature DC conductivity was found in the 50–10-40 Li2S–Ga2Se3– and broader satellite peaks are present; the broad central transition is due to homonuclear dipolar GeSe2 glass, approximately 10-4 S/cm.

Int. J. Mol. Sci. 2017, 18, x FOR PEER REVIEW 6 of 26

7 7Li NMR lineshape analysis was performed on three phases of the LGGS glasses, 40–60 Li2S– Li NMR lineshape analysis was performed on three phases of the LGGS glasses, 40–60 Li2S– GeSe2, 15–25–60 Li2S–Ga2Se3–GeSe2, and 50–10–40 Li2S–Ga2Se3–GeSe2, in order to highlight the GeSe2, 15–25–60 Li2S–Ga2Se3–GeSe2, and 50–10–40 Li2S–Ga2Se3–GeSe2, in order to highlight the differing Li ion dynamics with composition and temperature. Static NMR spectra were obtained using a solid echo pulse sequence of − pulses, in order to clearly study the quadrupolar using a solid echo pulse sequence of − pulses, in order to clearly study the quadrupolar Int. J. Mol. Sci. 2020, 21, 3402 7 6 of 24 effects that are commonly seen in 7Li. From the Variable Temperature (VT) Spectra in figure 4, a broad Gaussian central transition peak and broader satellite peaks are present; the broad central transition is due to homonuclear dipolar interactionsand broader between satellite primarily peaks are7 Lipresent; ions. This the isbroad corroborated central transition by the fact is that due the to central homonuclear transition dipolar peak 7 interactions between primarily 7Li ions. This is corroborated by the fact that the central transition linewidthinteractions increases between with primarily increasing Li Liions. content. This is As corroborated the temperature by the increases, fact that both the central central and transition satellite peak linewidth increases with increasing Li content. As the temperature increases, both central and transitionspeak linewidth narrow increases monotonically, with increasing which isLi indicative content. As of the averaged temperature motion increases, of the Li ionsboth overcomingcentral and satellite transitions narrow monotonically, which is indicative of averaged motion of the Li ions thesatellite strong transitions dipolar interaction narrow monotonically, and suggests a which random is distribution indicative of of averaged Li ions in motion the glass. of the Li ions overcoming the strong dipolar interaction and suggests a random distribution of Li ions in the glass.

7 Figure 4. (Left) Static 77Li NMR spectra with temperature in the 40–60 Li2S–GeSe2 glass. (Right) Figure 4. 4. (Left) Static Li NMR spectra with with temperature temperature in in the the 40–60 40–60 Li Li2S–GeSe2S–GeSe22 glass.glass. (Right) Motional narrowingnarrowing of of both both the the central central transition transition (CT) (CT) peak peak is clearly is clearly seen seen at elevated at elevated temperatures temperatures [16]. [16]. Plotting the 7Li NMR lineshapes for each glass reveals a characteristic sigmoid shape. The inflection 7 pointPlotting of these thelineshape 7Li NMR functions lineshapes can give for insight each glass into how reveals fast aLi characteristic ions jump in the sigmoid material, shape. through The calculationinflection point of the of correlationthese lineshape time, functionsτc. At the can inflection give insight point, into the how Li-ion fast jumpLi ions rate jump can in be the estimated material, through calculation of the correlation time, . At the inflection point, the Li-ion jump rate can be asthrough1/2πν calculationin f lection, where of theνin correlation f lection is the time, inflection . At point the inflection linewidth point, [17]. the Additionally, Li-ion jump one rate can can also be estimated as 1/2, where is the inflection point linewidth[17]. Additionally, one approximateestimated as 1/2 the activation, energywhere for the Liis ion the jumps inflection by finding point linewidth[17]. the temperature Additionally, at whichthis one inflectioncan also approximate occurs [17]. Marplethe activation et al. calculated energy for hopping the Li ion frequencies jumps by and finding their the corresponding temperature activation at which energiesthis inflection using this occurs[17]. method, Marple which are et al.highlighted calculated in hoppingFigure5. These frequencies results and were their in close corresponding agreement withactivation EIS derived energies hopping using this frequencies method, which and activation are highlighted energies. in Figure From 5. this These agreement, results were the authorsin close arguedagreement that with the hopping EIS derived frequency hopping corresponds frequencies to and Li ion activation jumps between energies. an From average this Li–Li agreement, separation the distanceauthors argued and were that able the to hopping estimate frequency the DC conductivity corresponds using to Li the ion Nernst–Einstein jumps between relation. an average Li–Li separation distance and were able to estimate the DC conductivity using the Nernst–Einstein relation.

Figure 5. EIS and NMR-derived ion jump frequencies and activation energies for three LGGS glasses [16]. Figure 5. EIS and NMR-derived ion jump frequencies and activation energies for three LGGS glasses.[16] Theglasses. calculated[16] conductivities were well in agreement with EIS calculated conductivities, which further suggest that the model of intersite Li ion jumps is correct. The calculated conductivities were well in agreement with EIS calculated conductivities, which ItThe is calculated known that conductivities combinations were of glass well formersin agreement can lead with to EIS anomalously calculated conductivities, ionic conductivities, which further suggest that the model of intersite Li ion jumps is correct. hereafterfurther suggest referred that to the as themodel “mixed of intersite glass former Li ion jumps effect” is (MGFE) correct. [ 12,14,18–20]. This effect can either It is known that combinations of glass formers can lead to anomalously ionic conductivities, drasticallyIt is known increase that or decrease combinations ionic conductivity, of glass formers known can as the lead positive to anomalously and negative ionic MGFE, conductivities, depending hereafter referred to as the “mixed glass former effect” (MGFE) [12,14,18–20]. This effect can either onhereafter the compositions referred to and as the concentrations “mixed glass of former the glasses effect” mixed. (MGFE) NMR [12,14,18–20]. lineshape and This relaxation effect can studies either drastically increase or decrease ionic conductivity, known as the positive and negative MGFE, havedrastically been used increase to study or decrease this eff ect. ionic Storek conductivity, et al. looked known at as a series the positive of glasses and containing negative MGFE, mixed concentrations sodium borosilicate and sodium borophosphate glasses, known to produce a negative and positive MGFE, respectively [21]. Using 23Na NMR spectra, they attempted to correlate short-range structural information with microscopic origins of the MGFE. From the 23Na lineshapes, there was clear motional narrowing observed for all glasses with increased temperature, with clear differences in the inflection point linewidth depending on the Int. J. Mol. Sci. 2017, 18, x FOR PEER REVIEW 7 of 26 depending on the compositions and concentrations of the glasses mixed. NMR lineshape and relaxation studies have been used to study this effect. Storek et al. looked at a series of glasses containing mixed concentrations sodium borosilicate and sodium borophosphate glasses, known to produce a negative and positive MGFE, respectively [21]. Using 23Na NMR spectra, they attempted toInt. correlate J. Mol. Sci. short-range2020, 21, 3402 structural information with microscopic origins of the MGFE. 7 of 24 From the 23Na lineshapes, there was clear motional narrowing observed for all glasses with increased temperature, with clear differences in the inflection point linewidth depending on the composition of of the the glass. glass. This This eff ect effect was evenwas evenmore pronounced more pronounced when looking when at looking spin-lattice at spin-lattice relaxation measurements, as shown in Figure6. The borosilicate glasses 0.33Na O + 0.67[xB O + (1 x)2SiO ] relaxation measurements, as shown in figure 6. The borosilicate glasses2 0.33Na2O2 + 30.67[xB−2O3 + (1 2− experienced slower relaxation rates than the borophosphate glasses and decreased with increasing x)2SiO2] experienced slower relaxation rates than the borophosphate glasses and decreased with B O content, experiencing a relaxation minimum around x = 0.6; this suggests a negative MGFE. increasing2 3 B2O3 content, experiencing a relaxation minimum around x = 0.6; this suggests a negative Conversely, the borophosphate glass 0.35Na O + 0.65[xB O + (1 x)P O ] experienced an increase MGFE. Conversely, the borophosphate glass2 0.35Na2O 2 +0.65[xB3 2−O3 + 2 (1 5 − x)P2O5] experienced an increasein relaxation in relaxation rates with rates increasing with increasing Boron content,Boron content, eventually eventually reaching reaching a maximum a maximum when when x = 0.4,x = 0.4,indicating indicating a positive a positive MGFE. MGFE.

23 Figure 6. 23NaNa Relaxation Relaxation data data as asa function a function of Boron of Boron concentration concentration in (a) in borosilicate (a) borosilicate glasses glasses and (b,c) and (b,c) various borophosphate glasses [21]. various borophosphate glasses [21]. To explain this behavior, the authors attempted to model the relaxation data using only one To explain this behavior, the authors attempted to model the relaxation data using only one tunable parameter, the mean activation energy Ea. In glasses, it is generally agreed that there is a tunablebroad range parameter, of energies, the mean so a gaussianactivation distribution energy Ea. ofIn energiesglasses, wasit is assumed.generally Usingagreedexpressions that there is for a broadthe relaxation range of ratesenergies, and linewidthsso a gaussian dependent distribution on thisof energies model, was the authorsassumed. were Using able expressions to accurately for the relaxation rates and linewidths dependent on this model, the authors were able to accurately and and simultaneously ﬁt the data [22,23] and extracted mean activation energies on the order of simultaneously fit the data [22,23] and extracted mean activation energies on the order of 0.1–1 eV, 0.1–1 eV, depending on the B2O3 content. Comparing these activation energies with those found from depending on the B2O3 content. Comparing these activation energies with those found from conductivity measurements shows that conductivity-measured energies are consistently lower than conductivitytheir NMR-derived measurements counterparts. shows The that authors conductivity-measured proposed that conductivity energies are measurements consistently were lower unable than their NMR-derived counterparts. The authors proposed that conductivity measurements were to detect below a certain threshold activation energy. Proposing an NMR-based model using the unablegaussian to energydetect below distribution, a certain they threshold calculated activation the threshold energy. activation Proposing energy an NMR-based to be in agreement model using with conductivity measurements, underscoring the utility of the model. In addition, 11B MAS NMR, detailed in Figure7, was used to determine the fraction of network (3) (4) (2) (3) (4) forming units (NFUs) for Si , Si ,B ,B , and B in the borosilicate glasses, depending on B2O3 content, and compared to the Yun and Bray model [24,25], which was in good agreement. From the model, it was thought that the Na ions preferred to cluster around Si atoms, and the addition of boron Int. J. Mol. Sci. 2017, 18, x FOR PEER REVIEW 8 of 26 the gaussian energy distribution, they calculated the threshold activation energy to be in agreement with conductivity measurements, underscoring the utility of the model. In addition, 11B MAS NMR, detailed in figure 7, was used to determine the fraction of network Int. J. Mol. Sci. 2020, 21, 3402 8 of 24 forming units (NFUs) for Si(3), Si(4), B(2), B(3), and B(4) in the borosilicate glasses, depending on B2O3 content, and compared to the Yun and Bray model [24,25], which was in good agreement. From the model,reduces it thiswas clusteringthought that leading the Na to ions slower preferred Na ion to dynamicscluster around and lowerSi atoms, conductivity, and the addition i.e., a of negative boron reducesMGFE. Thisthis clustering eﬀect was leading also seen toin slower other Na mixed ion glassdynamics systems, and suchlower as conductivity, sodium germanophosphate i.e., a negative MGFE.glasses This (NGP) effect [26], was further also lending seen in credibilityother mixed to theglass model. systems, such as sodium germanophosphate glasses (NGP) [26], further lending credibility to the model.

FigureFigure 7. 7. NetworkNetwork forming forming unit unit (NFU) (NFU) fractions fractions of of sodium sodium borosilicate borosilicate glasses glasses as as determined determined (a) (a) by by 1111BB NMR, NMR, and and (b) (b )by by the the Yun Yun and and Bray Bray model model [21] [21].. 4. Glass Ceramic Electrolytes 4. Glass Ceramic electrolytes Aside from pure-glass electrolytes, much work has been done studying glass-ceramics, Aside from pure-glass electrolytes, much work has been done studying glass-ceramics, which which simultaneously exhibit both amorphous and crystalline phases [27]. Typical glass-ceramics simultaneously exhibit both amorphous and crystalline phases[27]. Typical glass-ceramics exhibit exhibit comparable ionic conductivities to glasses—up to 10 2 S/cm at room temperature [28,29]—which comparable ionic conductivities to glasses—up to 10-2 S/cm− at room temperature [28,29]—which is is possibly due to the reduction of grain boundary resistance during the crystallization process. possibly due to the reduction of grain boundary resistance during the crystallization process. Gobet et al. studied one such glass-ceramic, Li3PS4, which is known to exhibit a high ionic Gobet et al. studied3 one such glass-ceramic, Li3PS4, which is known to exhibit a high ionic conductivity of ~10− S/cm [30,31] and is chemically stable versus metallic lithium [32]. Li3PS4 conductivity of ~10-3 S/cm [30,31] and is chemically stable versus metallic lithium [32]. Li3PS4 can can exhibit different phases and under conventional ball-milling techniques presents as a γ phase, exhibit different phases and under conventional ball-milling techniques presents as a phase, which which exhibits a low ionic conductivity [33]. However, a new synthesis technique, discovered by exhibits a low ionic conductivity [33]. However, a new synthesis technique, discovered by Liang et Liang et al., revealed that Li3PS4 can be formed through the desolvation of THF in a mixture of Li2S and al., revealed that Li3PS4 can be formed through the desolvation of THF in a mixture of LiS and PS, P S , leaving behind a nanoporous structure. This structure was shown to exhibit an ionic conductivity leaving2 5 behind a nanoporous structure. This structure was shown to exhibit an ionic conductivity three orders of magnitude higher than γ-Li3PS4 and is referred to as β-Li3PS4. As this novel synthesis three orders of magnitude higher than -Li3PS4 and is referred to as -Li3PS4. As this novel synthesis approach appeared to change the phase of the glass-ceramic, solid state NMR measurements were approach appeared to change the phase of the glass-ceramic, solid state NMR measurements were performed to understand the structural evolution of β-Li3PS4. performed to understand the structural evolution of -Li3PS4. 1H, 31P, and 6Li and 7Li MAS NMR experiments were performed to understand and characterize 1H, 31P, and 6Li and 7Li MAS NMR experiments were performed to understand and characterize the synthesis process. Samples of Li2S–P2S5 precursors in THF were treated at various temperatures the synthesis process. Samples of Li2S–P2S5 precursors in THF were treated at various temperatures to drive off the THF solvent and observe the formation steps of the final product. Spectra were compared to those of pure γ-Li3PS4 and β-Li3PS4 (prepared with THF). Single-pulse measurements were performed at a range of spinning speeds, from 4 kHz to 17 kHz; 1H–31P and 1H–7Li cross polarization (CP) experiments were also performed at 4 kHz to study potential interactions between Int. J. Mol. Sci. 2017, 18, x FOR PEER REVIEW 9 of 26 to drive off the THF solvent and observe the formation steps of the final product. Spectra were comparedInt. J. Mol. to those Sci. 2020 of, 21 pure, 3402 -Li3PS4 and β-Li3PS4 (prepared with THF). Single-pulse measurements9 of 24 were performed at a range of spinning speeds, from 4 kHz to 17 kHz; 1H–31P and 1H–7Li cross polarization (CP) experiments were also performed at 4 kHz to study potential interactions between 7 the solvent and probe nuclei. PFG experiments were also performed at 100 ◦C to determine the Li the solvent and probe nuclei. PFG experiments were also performed at 100°C to determine the 7Li diffusion coefficients. diffusion coefficients. From the 1H spectra in Figure8, the presence of a peak at ~3 ppm confirms the presence of From the 1H spectra in figure 8, the presence of a peak at ~3 ppm confirms the presence of THF THF in the sample, when compared to liquid spectra of pure THF. At higher treatment temperatures, in the sample, when compared to liquid spectra of pure THF. At higher treatment temperatures, the the intensity of this peak is significantly diminished, suggesting the removal of THF, as expected. intensity of this peak is significantly diminished, suggesting the removal of THF, as expected.

31 31 FigureFigure 8. (Left) 8. (Left) Proton Proton MAS MASspectra spectra of the of Li the3PS Li4 glasses3PS4 glasses treated treated at various at various temperatures. temperatures. (Right) (Right) P P MAS MASspectra spectra of the of same the sameLi3PS4 Li glasses.3PS4 glasses. The asterisks The asterisks indicate indicate spinning spinning sidebands sidebands [30]. [30].

31 The 31TheP spectraP spectra in figure in Figure 8 paints8 paints a more a more interesting interesting picture. picture. Li3PS Li4 3withPS4 withTHF THFexhibits exhibits three three 3 separateseparate peaks, peaks, suggesting suggesting several several chemical chemical environments environments surrounding surrounding the PS the43- PS tetrahedra.4 − tetrahedra. As the As the samplesample is heat-treated, is heat-treated, these these peaks peaks give way give in way favor in favor of a broad of a broad amorphous amorphous component component near near85 ppm 85 ppm and atand 100 at °C, 100 only◦C, onlythe broad the broad component component remains. remains. This Thisagrees agrees with withthe proton the proton spectra spectra at the at same the same 3 temperature,temperature, suggesting suggesting that thatthere there is no is longer no longer any anyTHF THF to interact to interact with with the PS the43- PS tetrahedra.4 − tetrahedra. At even At even 3 higherhigher temperatures, temperatures, a separate a separate peak peakemerges emerges which which suggests suggests the presence the presence of isolated of isolated PS43 tetrahedra PS4 tetrahedra associatedassociated with with the the -Liβ-Li3PS3PS4 4 phase,phase, which could could not not be be determined determined by long-range by long-range analytical analytical techniques techniquessuch as such XRD. as In XRD. the 7InLi the spectra, 7Li spectra, the presence the presence of spinning of spinning sidebands sidebands suggested suggested a greater a quadrupolargreater quadrupolarinteraction interaction due to the due presence to the of electric presence ﬁeld of gradients electric fieldthat are gradients not eﬀectively that are averaged not effectively by rapid ionic averagedmotion. by rapid These ionic sidebands motion. greatly These decreased sidebands in intensitygreatly decreased when the in samples intensity were when heat-treated, the samples which is wereindicative heat-treated, of increased which is indicative ion mobility. of increased ion mobility. ThroughThrough CP-MAS CP-MAS experiments, experiments, the the authors authors were were able able to to probe probe the the extent extent of the of THF’s the THF’s interaction interactionand proximity and proximity to other toprobe other nuclei,probe nuclei, as CP isas mediated CP is mediated through through the nuclear the nuclear dipole-dipole dipole-dipole interaction. 31 7 interaction.In the unheated In the unheated Li PS 3THF Li3PS mixture,4•3THF mixture,CP experiments CP experiments for P and forLi 31 wereP and nearly 7Li were identical nearly to their 3 4• identicalsingle to pulsetheir single counterparts, pulse counterparts, suggesting that suggesting both nuclei that were both surrounded nuclei were by surrounded nearby proton-containing by nearby 31 proton-containingTHF molecules. THF For molecules. the sample For treated the sample at 70 ◦ C,treated comparison at 70 °C, of comparisonP CP and singleof 31P CP pulse and experiments, single pulseas experiments, seen in Figure as9 seen, revealed in figure the 9, presence revealed of the a broad presence peak of that a broad does peak not couple that does to the not THF couple molecules to 3 the THFnear molecules 84 ppm. near This 84 peak ppm. is knownThis peak to belongis known to to a combinationbelong to a combination of PS4 − and of PS PS3O43-− andpeaks PS3O [34- ,35], which suggests that THF molecules decomposed during the heating process, leading to an O–S exchange.

Int. J. Mol. Sci. 2017, 18, x FOR PEER REVIEW 10 of 26

peaks [34,35], which suggests that THF molecules decomposed during the heating process, leading to an O–S exchange. 7Li PFG experiments revealed the self-diffusion coefficient to be on the order of 10-13 m2/s. Comparison with the EIS and NE derived diffusion reveals a D on the order 10-12 m2/s, which is a clear discrepancy. This could be due to multiple factors, including structural evolution of the sample Int.during J. Mol. the Sci. course2020, 21 ,of 3402 the experiments, or underestimation of the NMR diffusion coefficients due10 of to 24 the long diffusion time needed for the experiment (~500 ms).

31 Figure 9. 31PP cross-polarization cross-polarization (CP) (CP) and and single-pulse single-pulse spectra spectra for for the the Li3PS Li34PS glass4 glass treated treated at 70 at °C. 70 The◦C. Thebroad broad peak peak around around 84 ppm84 ppm does does not not interact interact with with the the THF THF and and thus thus does does not not appear appear in in the CP CP spectrum [[30]30]..

7Li PFG experiments revealed the self-diffusion coefficient to be on the order of 10 13 m2/s. Another recent work on glass-ceramics by Murakami et al. looked at Li7P3S11, known to− exhibit Comparison with the EIS and NE derived diffusion reveals a D on the order 10 12 m2/s, which is a a room temperature conductivity of 10-3 S/cm[36]. Li7P3S11 is a metastable material,− formed by clear discrepancy. This could be due to multiple factors, including structural evolution of the sample annealing (Li2S)70(P2S5)30 at temperatures over 500K. From XRD analysis, it is known that Li ions in duringthe material the course are situated of the experiments, between PS4or tetrahedra underestimation and P2S of7 ditetrahedra. the NMR diff Inusion addition, coeffi cientsthey are due known to the longto conduct diffusion through time neededtwo pathways—a for the experiment Li stable (~500 and a ms). Li metastable region [37]. As an electrolyte, the Li7P3AnotherS11 system recent has been work studied on glass-ceramics previously from by Murakami the NMRet perspective al. looked [38]. at Li 7InP 3orderS11, known to further to exhibit study 3 athe room origins temperature of the high conductivity ionic conductivity, of 10− theS/cm authors [36]. employed Li7P3S11 is solid a metastable state 6/7Li material,and 31P NMR. formed by annealingThe authors (Li2S)70 prepared(P2S5)30 at three temperatures samples for over NMR 500 measurements: K. From XRD analysis,(Li2S)70(P it2S is5)30 known glass-ceramic that Li ions(70gc), in the material are situated between PS tetrahedra and P S ditetrahedra. In addition, they are known (Li2S)75(P2S5)25 glass-ceramic (75gc), and4 (Li2S)70(P2S5)30 glass2 7 (70g). MAS single pulse spectra, as well toas conductT1 saturation through recovery two pathways—ameasurements, Li were stable performed and a Li as metastable a function region of temperature, [37]. As an ranging electrolyte, from the250 LiK 7toP3 nearlyS11 system 400 K. has been studied previously from the NMR perspective [38]. In order to further 6/7 31 studyFrom the origins the 7Li oflineshapes, the high ionic it is conductivity,apparent that the motional authors narrowing employed of solid the statespectraLi takes and placeP NMR. with increasedTheauthors temperature, prepared as the three Li–Li samples dipolar for couplings NMR measurements: and Li quadrupolar (Li2S) interaction70(P2S5)30 glass-ceramic are averaged (70out. gc), This (Li motional2S)75(P2 Snarrowing5)25 glass-ceramic gives rise (75 to gc),the presence and (Li2S) of70 multiple(P2S5)30 glassconvoluted (70 g). peaks. MAS Further single pulsepeak spectra,analysis asperformed well as T 1onsaturation the 70 gc recoverysample, highlighted measurements, in figure were 10, performed revealed as the a functionpresence ofof temperature,three peaks, rangingtwo narrow from and 250 Kone to nearlybroad. 400The K. narrow peaks were attributed to mobile Li ions in a crystalline 7 structure,From while the Li the lineshapes, smaller broad it is apparentpeak corresponded that motional to more narrowing less mobile of the Li spectra ions in takesthe structure. place with increased temperature, as the Li–Li dipolar couplings and Li quadrupolar interaction are averaged out. This motional narrowing gives rise to the presence of multiple convoluted peaks. Further peak analysis performed on the 70 gc sample, highlighted in Figure 10, revealed the presence of three peaks, two narrow and one broad. The narrow peaks were attributed to mobile Li ions in a crystalline structure, while the smaller broad peak corresponded to more less mobile Li ions in the structure. 6/7 31 Li and PT1 measurements, as seen in Figure 11, allowed the authors to calculate the associated activation energies for 70 gc, 18 kJ/mol. In addition, the authors found that the phosphorus nuclei bore the same temperature dependence as lithium nuclei at lower temperatures, but diverged after 300 K, suggesting independent motion. To understand the role of this motion and its contribution to the ionic conductivity, the authors studied the 31P MAS spectra of 70 g and 75 gc as a function of temperature. They noticed that the lineshapes of the 31P spectra did not significantly narrow with increased temperature, which seems to suggest that the rotational motion of the PxSy groups is responsible for the anomalous relaxation at higher temperatures, rather than translational motion. In 70 gc, there are 31 4 4 3 three distinct P sites, corresponding to P2S6 −,P2S7 −, and PS4 −. The lineshapes for all three peaks remained temperature independent until 300 K, after which motional narrowing was observed for all 31 31 but the P2S6 peak. Additionally, P– P radio-frequency-driven recoupling (RFDR) experiments were Int. J. Mol. Sci. 2020, 21, 3402 11 of 24

performed to examine the line widths further. Off-diagonal peaks in the 2D spectrum merged into 4 the P2S7 − peak at higher temperatures, and the authors argued that the peak could not be attributed 4 to a particular asymmetric ditetrahedra structure of P2S7 −. This suggested a distribution of local 4 structures associated with P2S7 − and that the dynamical motions of the ditetrahedra allowed for a pathway for Li ions to conduct at a lower energy barrier, leading to higher conductivity. The Li10GePsS12 (LGPS) family of lithium superionic conductors (LISICONs) have been extensively studied since it’s 2011 discovery by Kanno et al. [39] due to their high room-temperature conductivities 2 + (~10− S/cm for LGPS) resulting from the formation of a 1D conduction pathway for Li ions. In general, the family can be classified as Li11 xM2 xP1+xS12, where M can be Si, Ge, or Sn. Though sporting − − high conductivity, these materials exhibit poor stability at the interface against metallic Li due to the formation of interphases containing Li3P, Li2S, and Li–Ge alloys, which promotes reduction of the electrolyte and can lead to a short-circuit [40]. To counteract this, Harm et al. synthesized a new LGPS-like glass ceramic, Li7SiPS8 (LSiPS), and characterized its structure and Li-ion mobility through 29Si and 31P MAS, and 7Li PFG NMR [41]. The authors synthesized LSiPS through mixing stoichiometric amounts of Li2S, Si, red P, and sublimed S and annealing the mixtures at differing Int.temperatures J. Mol. Sci. 2017,for 18, x five FOR days, PEER yieldingREVIEW both tetragonal and orthorhombic phases. 11 of 26

7 6 FigureFigure 10. 10. 7Li MASLi MAS NMR NMR spectra spectra of 70gc of 70 at gc (a at) 360K (a) 360 and( Kb and() 270K.b) 270 (c) 6 K.Li (MASc) Li NMR MAS spectrum NMR spectrum of 70gc of 70 gc at room temperature [36]. at room temperature.[36]

6/7Li and 31P T1 measurements, as seen in figure 11, allowed the authors to calculate the associated activation energies for 70 gc, 18 kJ/mol. In addition, the authors found that the phosphorus nuclei bore the same temperature dependence as lithium nuclei at lower temperatures, but diverged after 300 K, suggesting independent motion. To understand the role of this motion and its contribution to the ionic conductivity, the authors studied the 31P MAS spectra of 70 g and 75 gc as a function of temperature.

Int. J. Mol. Sci. 2017, 18, x FOR PEER REVIEW 11 of 26

Int. J. Mol. Sci. 2017, 18, x FOR PEER REVIEW 12 of 26 Figure 10. 7Li MAS NMR spectra of 70gc at (a) 360K and(b) 270K. (c) 6Li MAS NMR spectrum of 70gc Figureat room 11. temperature. Plots of 6Li[36] (triangle), 7Li (circle), and 31P (square) T1’s for 70gc (red), 75gc (blue), and 70g (black). The solid line through 7Li T1 data points for 70gc is the least-squares fit one to a straight line. [36]6/7Li and 31P T1 measurements, as seen in figure 11, allowed the authors to calculate the associated activation energies for 70 gc, 18 kJ/mol. In addition, the authors found that the phosphorus nuclei bore Theythe same noticed temperature that the lineshapes dependence of asthe lithium 31P spectra nuclei did at notlower significantly temperatures, narrow but withdiverged increased after temperature,300 K, suggesting which independent seems to suggest motion. that To the understand rotational the motion role ofof thisthe motionPS groups and its is responsiblecontribution for to theInt. J.anomalousionic Mol. Sci.conductivity,2020 relaxation, 21, 3402 the at authors higher temperatures, studied the 31 ratherP MAS than spectra translational of 70 g and motion. 75 gc In as 70 a gc, function there12 ofare of 24 threetemperature. distinct 31P sites, corresponding to P2S64−, P2S74−, and PS43−. The lineshapes for all three peaks remained temperature independent until 300 K, after which motional narrowing was observed for all but the P2S6 peak. Additionally, 31P–31P radio-frequency-driven recoupling (RFDR) experiments were performed to examine the line widths further. Off-diagonal peaks in the 2D spectrum merged into the P2S74- peak at higher temperatures, and the authors argued that the peak could not be attributed to a particular asymmetric ditetrahedra structure of P2S74-. This suggested a distribution of local structures associated with P2S74- and that the dynamical motions of the ditetrahedra allowed for a pathway for Li ions to conduct at a lower energy barrier, leading to higher conductivity.

The LiGePS (LGPS) family of lithium superionic conductors (LISICONs) have been extensively studied since it’s 2011 discovery by Kanno et al. [39] due to their high room-temperature conductivities (~10-2 S/cm for LGPS) resulting from the formation of a 1D conduction pathway for Li+ ions. In general, the family can be classified as Li11-xM2-xP1+xS12, where M can be Si, Ge, or Sn. Though sporting high conductivity, these materials exhibit poor stability at the interface against metallic Li due to the formation of interphases containing Li3P, Li2S, and Li–Ge alloys, which promotes reduction of the electrolyte and can lead to a short-circuit [40]. To counteract this, Harm et al. synthesized a new Figure 11. Plots of 6Li (triangle), 7Li (circle), and 31P (square) T ’s for 70 gc (red), 75 gc (blue), and 70 g LGPS-like glass ceramic, Li7SiPS8 (LSiPS), and characterized its1 structure and Li-ion mobility through 7 29Si and(black). 31P The MAS, solid and line through7Li PFGLi NMR[41]. T1 data points The for authors 70 gc is the synthesized least-squares LSiPS fit one through to a straight mixing line [36]. stoichiometric amounts of Li2S, Si, red P, and sublimed S and annealing the mixtures at differing temperaturesThe authors for five first days, attempted yielding to characterizeboth tetragonal the and structure orthorhombic of LSiPS phases. through 31P MAS, the results 31 of whichThe authors are shown first inattempted Figure 12 to. characterize In tetra-LSiPS, the theystructure found of two LSiPS peaks through at ~73 P ppm MAS, and the 95 results ppm, ofcorresponding which are shown to phosphorus in figure 12. nuclei In tetra-LSiPS, inhabiting thethey 2b found and 4d two sites, peaks respectively, at ~73 ppm while and one95 ppm, main correspondingpeak at ~88 ppm to phosphorus was detected nuclei for inhabiting ortho-LSiPS, the 2b corresponding and 4d sites, respectively, to the 4c position. while one In main addition, peak atthe ~88 authors ppm was identified detected an amorphousfor ortho-LSiPS, side phasecorresponding in the tetra-LSiPS to the 4c sample, position. constituting In addition, almost the authors 20% of identifiedthe signal an intensity. amorphous side phase in the tetra-LSiPS sample, constituting almost 20% of the signal intensity.

FigureFigure 12. (Left)(Left) 3131PP NMR NMR spectra spectra of of tetrahedral tetrahedral (top) (top) and orthorhombic (bottom) LSiPS. (Right) 2929SiSi NMRNMR spectra spectra of tetrahedral LSiPS [41] [41]..

FurtherFurther evidence evidence of of an an amorphous phase phase appears appears in in the the 2929SiSi spectra spectra of of the the tetra-LSiPS tetra-LSiPS sample. sample. The main peak near 10 ppm corresponds to an expected substitution of of Si Si into the phosphorus 4d 4d sites,sites, but but a a small peak (~3% signal signal intensity) intensity) near near 0 0 ppm ppm further further lends lends credit credit to to the the presence presence of of the amorphousamorphous phase. phase. As As this this peak peak could could not not be be detected detected in in XRD XRD measurements, measurements, it it was was concluded concluded that that tetra-LSiPStetra-LSiPS crystals crystals were were embedded embedded in in a a glassy matrix, indicative of a glass-ceramic. By By comparing thethe relative relative NMR NMR signal intensities to XRD-derived weight weight percentages, percentages, the the authors authors proposed proposed the the amorphousamorphous phase to be LiLi3.23.2Si0.20.2PP0.80.8S4S. 4In. In addition, addition, this this phase phase only only appears appears at at samples samples prepared prepared at at intermediate temperatures, which suggests that the glassy phase plays a role in the transition from ortho-LSiPS to tetra-LSiPS. As this proposed structure does not share the same stoichiometry with the crystalline phase, it is thought that this amorphous phase is the result of a peritectic phase separation of the tetragonal phase and thus may be less stable than tetragonal LGPS. To understand the nature of Li-ion diffusion in this novel material, the authors employed variable temperature 7Li PFG NMR at two different diffusion times (10 ms and 100 ms) and calculated the respective activation energies, the results of which are plotted in Figure 13. Using diffusion coefficients Int. J. Mol. Sci. 2017, 18, x FOR PEER REVIEW 13 of 26 intermediate temperatures, which suggests that the glassy phase plays a role in the transition from ortho-LSiPS to tetra-LSiPS. As this proposed structure does not share the same stoichiometry with the crystalline phase, it is thought that this amorphous phase is the result of a peritectic phase separation of the tetragonal phase and thus may be less stable than tetragonal LGPS. Int. J.To Mol. understand Sci. 2020, 21, 3402 the nature of Li-ion diffusion in this novel material, the authors employed13 of 24 variable temperature 7Li PFG NMR at two different diffusion times (10 ms and 100 ms) and calculated the respective activation energies, the results of which are plotted in figure 13. Using diffusion coefficientsat room temperature, at room thetemperature, authors calculated the authors the di calculatedffusion length the at diffusion both time length scales throughat both atime first-order scales approximation, rrms = √2DNMR∆NMR, and found that the distances were both on the order of 200 nm, through a first-order approximation, = 2Δ, and found that the distances were which suggests a fast diffusion process over a small range. Assuming that the crystalline phase both on the order of 200 nm, which suggests a fast diffusion process over a small range. Assuming primarily contributed to conductivity, the authors assumed the diffusion radius to be the mean size of that the crystalline phase primarily contributed to conductivity, the authors assumed the diffusion the crystallites. radius to be the mean size of the crystallites.

Figure 13. Arrhenius plots of variable temperature diffusion in tetra-LSiPS, at both 10 ms and 100 ms Figure 13. Arrhenius plots of variable temperature diffusion in tetra-LSiPS, at both 10 ms and 100 ms diffusion time [41]. diffusion time [41]. In addition, the authors deduced that diffusion at shorter timescales was higher and exhibited a lowerIn addition, activation the energy,authors deduced suggesting that at diffusion an overall at shorter mixed timescales intergrain was and higher intragrain and exhibited diffusion a lowerprocess, activation in agreement energy, with suggesting the assumption at an overall of crystallites mixed intergrain embedded and in intragrain an amorphous diffusion matrix. process, Both inNMR-calculated agreement with and the EIS assumption conductivities of crystallites were on the embedded order of 1in mS an/ cm,amorphous lower than matrix. tetragonal Both NMR- LGPS, calculatedwhich suggests and EIS that conductivities the inclusion ofwere the on glassy the order phase of comes 1 mS/cm, at the lower cost ofthan increased tetragonal impedance. LGPS, which suggests that the inclusion of the glassy phase comes at the cost of increased impedance. 5. Argyrodite Electrolytes

5. Argyrodite Electrolytes + The cubic mineral argyrodite, with the composition Ag8GeS6, is known to conduct Ag ions veryThe easily. cubic Replacing mineral Agargyrodite, with another with the cation, composition in this case Ag Li8GeS+, will6, is stillknown preserve to conduct the cubic Ag+ ions structure. very easily.As a result, Replacing much Ag research with another has been cation, done in into this argyrodite-typecase Li+, will still electrolytes preserve the for cubic Li batteries structure. [42 As–44 a], result,with Li much7PS6 emergingresearch has as abeen possible done candidateinto argyrodite-type [28]. However, electrolytes it loses for its Li cubic batteries structure [42–44], at roomwith Litemperature7PS6 emerging and as above; a possible partial candidate substitution [28]. However, of S for a halogenit loses its has cubic been structure shown toat room preserve temperature the cubic andstructure above; and partial ionic substitution conductivity of S [ 43for,45 a ].halogen Typical has Argyrodite been shown electrolytes to preserve are the of cubic the formstructure Li6PS and5X, ionicwhere conductivity[43,45]. X is typically Br, Cl,Typical or I. Argyrodite Hanghofer electrolytes et al. studied are of these the form halogen-containing Li6PS5X, where X argyrodites, is typically Br,in orderCl, or toI. Hanghofer understand et the al. naturestudied of these Li ion halogen-containing conductivity and argyrodites, its dependence in order on the to choiceunderstand of halide the 7 natureion [46 of]. TheLi ion authors conductivity studied and Li 6itsPS dependence5I, Li6PS5Br, on and the Li choice6PS5Cl, of and halide performed ion[46]. The static authorsLi relaxation studied Liexperiments6PS5I, Li6PS to5Br, determine and Li6PS activation5Cl, and energies performed and static jump 7Li rates, relaxation as well asexperiments31P MAS to to understand determine activationstructural energies characteristics and jump of each rates, material. as well as 31P MAS to understand structural characteristics of each material.Figure 14 displays the 31P and 7Li MAS spectra of all three materials. From the 31P MAS spectra, 31 7 31 it wasFigure clear that14 displays the halide the ion P plays and aLi large MAS role spectra in the structureof all three of thematerials. material. From Li6PS the5I exhibitedP MAS spectra, a single itnarrow was clear peak, that suggesting the halide an ion ordered plays a crystalline large role environment in the structure around of the the material. phosphorus Li6PS nuclei5I exhibited [47,48 a], singlewhile Linarrow6PS5Cl peak, revealed suggesting barely resolvable an ordered peaks, crystalline suggesting environment a considerable around amount the phosphorus of anion disorder; nuclei Li6PS5Br presented multiple disordered peaks as well.

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[47,48], while Li6PS5Cl revealed barely resolvable peaks, suggesting a considerable amount of anion disorder;[47,48],Int. J. Mol. while Li Sci.6PS2020 5LiBr,6 PS21presented,5 3402Cl revealed multiple barely disordered resolvable peaks peaks, as well.suggesting a considerable amount of 14anion of 24 disorder; Li6PS5Br presented multiple disordered peaks as well.

Figure 14. (Left) 31P and (Right) 6Li MAS spectra for all three argyrodites [46]. Figure 14. (a) 31P and (b) 6Li MAS spectra for all three argyrodites [46]. Figure 14. (Left) 31P and (Right) 6Li MAS spectra for all three argyrodites [46]. InIn addition, addition, 7Li7Li relaxation relaxation measurements, measurements, as asseen seen in infigure Figure 15, 15 show, show that that the the degree degree of cation of cation disorderdisorderIn addition,is is also also dependent dependent 7Li relaxation on on the the choicemeasurements, choice of ofhalide. halide. asUsing Usingseen modified in modified figure BPP 15, BPP models, show models, that the the authorsthe authors degree calculated calculatedof cation thedisorderthe activation activation is also energies energies dependent of of each each on material,the material, choice both of both halide. at atlow low Using temperature temperature modified and andBPP high highmodels, temperatures. temperatures. the authors It was It calculated was clear clear that Li6PS5Br exhibited the lowest activation energies on both temperature flanks of the relaxation thethat activation Li6PS5Br exhibitedenergies of the each lowest material, activation both energies at low temperature on both temperature and high flanks temperatures. of the relaxation It was clear peak, peak, followed by Li6PS5Cl, with Li6PS5I exhibiting the highest energy barriers; this was further thatfollowed Li6PS by5Br Li exhibited6PS5Cl, with the Lilowest6PS5I exhibitingactivation theenergies highest on energy both barriers;temperature this wasflanks further of the confirmed relaxation by confirmed by EIS measurements, pinning Li6PS5I as having the lowest room temperature peak,EIS measurements, followed by pinningLi6PS5Cl, Li with6PS5 I Li as6PS having5I exhibiting the lowest the room highest temperature energy barriers; conductivity this was of the further series. conductivity of the series. From this data, one could not ignore the relationship between anion confirmedFrom this data, by oneEIS could measurements, not ignore the pinning relationship Li6PS5I between as having anion the disorder lowest and room cation temperature mobility. disorder and cation mobility. conductivity of the series. From this data, one could not ignore the relationship between anion disorder and cation mobility.

Figure 15. Arrhenius relaxation plots of Li6PS5X in the (a) lab frame of reference, (b) rotating frame of Figure 15. Arrhenius relaxation plots of Li6PS5X in the (a) lab frame of reference, (b) rotating frame of reference of 20 kHz, and (c) combined relaxation plots of Li6PS5I[46]. reference of 20 kHz, and (c) combined relaxation plots of Li6PS5I [46]. Figure 15. Arrhenius relaxation plots of Li6PS5X in the (a) lab frame of reference, (b) rotating frame of To try and explain this phenomenon, the authors employed lineshape analysis of 7Li spectra to Toreference try and of explain 20 kHz, this and phenomenon,(c) combined relaxation the authors plots employed of Li6PS5I [46]lineshape. analysis of 7Li spectra to observe the onset of motional narrowing, which is expected to arise due to increased intercage jumps observe the onset of motional narrowing, which is expected to arise due to increased intercage jumps between Li sites in the lattice. While this lineshape averaging was seen at low temperatures (~250 K) betweenTo Litry sites and inexplain the lattice. this phenomenon,While this lineshape the authors averaging employed was seen lineshape at low temperaturesanalysis of 7Li (~250 spectra K) to for Li6PS5Br and Li6PS5Cl, the Li6PS5I spectra exhibited considerably less narrowing, achieving the forobserve Li6PS 5theBr andonset Li of6PS motional5Cl, the Linarrowing,6PS5I spectra which exhibited is expected considerably to arise dueless tonarrowing, increased achievingintercage jumpsthe same narrow lineshapes nearly 100 ◦C higher than other two materials. This suggests that Li6PS5I samebetween narrow Li sites lineshapes in the lattice. nearly While 100 °C this higher lineshape than otheraveraging two materials.was seen atThis low suggests temperatures that Li (~2506PS5I K) exhibits much higher activation energy barriers to account for the slower jump process, which could exhibitsfor Li6PS much5Br and higher Li6 PSactivation5Cl, the Lienergy6PS5I barriersspectra exhibitedto account considerablyfor the slower less jump narrowing, process, which achieving could the be due to the rigid anion structure seen via the 31P spectrum. besame due narrowto the rigid lineshapes anion structure nearly 100 seen °C via higher the 31 Pthan spectrum. other two materials. This suggests that Li6PS5I exhibits6. Garnet much Electrolytes higher activation energy barriers to account for the slower jump process, which could 31 be due to the rigid anion structure seen via the P spectrum. Garnet-type oxide electrolytes have received much attention over the past few years, ever since the discovery of Li7La3Zr2O12 (LLZO) by Murugan et al. [28,49]. These garnets are cubic in structure, Int. J. Mol. Sci. 2017, 18, x FOR PEER REVIEW 15 of 26

6.Int. Garnet J. Mol. Sci. Electrolytes2020, 21, 3402 15 of 24 Garnet-type oxide electrolytes have received much attention over the past few years, ever since themaintain discovery high of working Li7La3Zr voltages2O12 (LLZO) against by Li Murugan [50], and et exhibit al. [28,49]. high ionic These room garnets temperature are cubic conductivities, in structure, 4 maintainon the order high of 10 working− S/cm in voltages LLZO. Many against recent Li works [50], in and the exhibit field of garnet high ionic electrolytes room have temperature involved conductivities,doping the Li oron Zrthe sites order in of LLZO, 10-4 S/cm in order in LLZO. to improve Many recent the ionic works conductivity in the field of [51 garnet–56], and electrolytes NMR is havewell suitedinvolved at studyingdoping the the Li subsequent or Zr sites structuralin LLZO, changesin order andto improve defect chemistriesthe ionic conductivity [55,57] as well [51–56], as Li andion dynamics.NMR is well suited at studying the subsequent structural changes and defect chemistries [55,57] as wellOne as group,Li ion dynamics. Larraz et al. sought to elucidate the distribution of Li ions in LLZO, as the 7Li isotropicOne chemicalgroup, Larraz shifts et tend al. tosought fall in to a elucidate narrow window the distribution in these materials, of Li ions making in LLZO, it di asffi thecult 7Li to isotropicresolve separate chemical peaks shifts [ 58tend]. Thisto fall di ffiinculty a narrow is further window compounded in these materials, by the presence making ofit 7difficultLi dipolar to resolvebroadening, separate which peaks[58]. is still present This when difficulty performing is further MAS. compounded In addition, by the the exposure presence of these of 7Li crystals dipolar to broadening,air allows for which proton-lithium is still present exchange when and performing for new secondaryMAS. In addition, phases and the impuritiesexposure of to these form, crystals such as toLiOH air allows and Li for2CO proton-lithium3 which further exchange compound and for the new problem secondary [59,60 phases]. To work and impurities around this, to form, the group such assynthesized LiOH and LLZO Li2CO using3 which enriched further6Li, compound to allow forthe much problem[59,60]. more resolvable To work spectra. around These this, crystals the group were synthesizedthen purposefully LLZO exposedusing enriched to air by 6Li, annealing to allow for to allow much for more proton-Li resolvable exchange spectra. in These order tocrystals vary thewere Li thencontent purposefully in the octahedral exposed and to air tetragonal by annealing sites of to the allow crystal. for proton-Li exchange in order to vary the Li contentFigure in the 16 octahedral shows the and7Li tetragonal and 6Li spectra sites of ofthe tetrahedral crystal. LLZO (t-LLZO) before and after 6Li enrichment.Figure 16 It isshows immediately the 7Li and apparent 6Li spectra from the of MAStetrahedral spectra LLZO that there (t-LLZO) was a before significant and after increase 6Li enrichment.in the resolution It is immediately of 6Li spectra apparent when prepared from the with MAS enriched spectra that6Li, asthere is evident was a significant by the now-detected increase in 6 6 thepresence resolution of a small of Li peak spectra near when 0.1 ppm prepared attributed with to enriched Li2CO3 from Li, theas is synthesis evident process.by the now-detected presence of a small peak near 0.1 ppm attributed to Li2CO3 from the synthesis process.

Figure 16. 7Li (solid) and 6Li (dotted) MAS spectra of t-LLZO prepared using natural abundance Li CO . The same 6Li spectra (dashed) is also presented when prepared with enriched 6Li [58]. Figure2 3 16. 7Li (solid) and 6Li (dotted) MAS spectra of t-LLZO prepared using natural abundance 6 6 LiFigure2CO3. The17 shows same Li the spectra6Li spectra (dashed) of is LLZO also presented after being when exposed prepared to with air, enriched which allowed Li [58]. protons to 6 enter the sample. After protonation, the authors determined from the Li spectra of Li3.8H3.2La3Zr2O12 Figure 17 shows the 6Li spectra of LLZO after being exposed to air, which allowed protons to the presence of three distinct Li peaks belonging to three diﬀerent sites in the crystal located at 1.6, 1.2, enter the sample. After protonation, the authors determined from the 6Li spectra of Li3.8H3.2La3Zr2O12 and 0.6 ppm, which they extrapolated back to sites in the original LLZO lattice. By comparing the the presence of three distinct Li peaks belonging to three different sites in the crystal located at 1.6, intensities of peaks before and after protonation, the authors were able to deduce that the 1.2 ppm 1.2, and 0.6 ppm, which they extrapolated back to sites in the original LLZO lattice. By comparing band belonged to Li ions in distorted octahedral sites, on account of previous models suggesting lower the intensities of peaks before and after protonation, the authors were able to deduce that the 1.2 ppm activation energies required for Li-proton exchange [61]. Though not as straightforward, the authors band belonged to Li ions in distorted octahedral sites, on account of previous models suggesting also attributed the 0.6 ppm band to the tetragonal site and the 1.6 ppm band to another, less distorted lower activation energies required for Li-proton exchange [61]. Though not as straightforward, the octahedral site [52]. authors also attributed the 0.6 ppm band to the tetragonal site and the 1.6 ppm band to another, less distorted octahedral site [52].

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Figure 17. 6Li MAS spectra of (a) enriched LLZO prepared as is (b) protonated LLZO before and (c) after Figure 17. 6Li MAS spectra of (a) enriched LLZO prepared as is (b) protonated LLZO before and (c) washing of impurities, and (d) with proton decoupling. The dotted lines represent the deconvolution after washing of impurities, and (d) with proton decoupling. The dotted lines represent the ﬁt [58]. deconvolution fit [58].

To study the dynamics of Li ions in these sites, the group also performed T1 inversion recovery experiments,To study and the founddynamics that of the Li octahedral ions in these sites sites, exhibited the group a greater also performed mobility than T1 inversion the tetragonal recovery site, whichexperiments, was expected, and found further that strengthening the octahedral their sites assignments. exhibited a greater Finally, mobility6Li-1H CP than MAS the spectra tetragonal revealed site, which was expected, further strengthening their assignments. Finally, 6Li-1H CP MAS spectra motional narrowing occurring around 70 ◦C and deduced that the Li ions exchange between octahedral andrevealed tetragonal motional sites. narrowing occurring around 70 °C and deduced that the Li ions exchange between octahedralNMR relaxationand tetragonal studies sites. are also extremely useful for studying Li ion dynamics and probing self-diNMRffusion, relaxation especially studies when are PFG also measurements extremely useful cannot for studying be performed, Li ion dynamics as is often and the probing case in solid self- electrolytes.diffusion, especially Bottke et al.when previously PFG measurements studied 7Li relaxation cannot be in Al-dopedperformed, LLZO as is and often observed the case anomalous in solid 7 relaxationelectrolytes. behavior; Bottke depending et al. previously on whether studied the measurementsLi relaxation were in Al-doped performed LLZO in the lab and frame observed or in theanomalous spin-locked relaxation rotating behavior; frame, theydepending noticed on vastly whether different the measurements activation energies were performed ranging from in the 0.1 lab eV upframe to 0.4or in eV the [62 spin-locked]. Wondering rotating if this frame, was unique they noticed to this vastly system, different the authors activation performed energies relaxation ranging from 0.1 eV up to 0.4eV [62]. Wondering if this was unique to this system, the authors performed measurements again, this time on Li6.5La3Zr1.75Mo0.25O12 (LLZMO) crystals [63]. relaxationFigure measurements 18 highlights again, the lineshapes this time ofon the Li6.57LaLi3 spectraZr1.75Mo as0.25O a12 function (LLZMO) of crystals temperature. [63]. From the 7 lineshapes,Figure the18 authorshighlights discovered the lineshapes a near homogeneousof the Li spectra motional as a function narrowing, of temperature. compared to Al-dopedFrom the LLZO.lineshapes, From the the authors intensities discovered of the a quadrupolar near homogeneous interactions motional (~300 narrowing, kHz) in the compared lineshapes, to Al-doped and the subsequentLLZO. From vanishing the intensities at higher of temperatures,the quadrupolar the authorsinteractions also deduced(~300 kHz) that in the the Li lineshapes, ions were extremely and the subsequent vanishing at higher temperatures,6 1 the authors also deduced that the Li ions were mobile, with mean jump rates of at least 10 s− . By performing SLR measurements in the lab and 6 -1 rotatingextremely frame mobile, of reference, with mean they jump found rates the of same at least mean 10 activations . By performing energy of ~0.29 SLR measurements eV, lower than thatin the of tetragonallab and rotating LLZO frame [62,64 of], suggestingreference, they high found Li ion the diff sameusion. mean From activation these plots, energy they of were ~0.29 also eV, able lower to estimatethan that the of Litetragonal self-diffusion LLZO[62,64], coefficient suggesting using the Einstein–Smoluchowski high Li ion diffusion. From (ES) relation these plots, [65] to they be aboutwere also15 able2 to estimate the Li self-diffusion coefficient using the Einstein–Smoluchowski (ES) relation 10− m /s. -15 2 [65] toAdditionally, be about 10 the m authors/s. employed spin alignment echo (SAE) spectroscopy to further validate the measured activation energy [64,66], the results of which are plotted in Figure 19. By using a preparation time of 10 µs and arraying the mixing time between 10 µs and 10 s, the authors were able to probe different Li ion dynamics by observing the corresponding echo amplitude, including slow jump processes between sites with different electric field gradients (EFGs), spin diffusion, or ordinary spin lattice relaxation. The authors expected that the jump process operated on a slower time scale than diffusion or relaxation, leading to a two-step amplitude decay, and this was indeed seen in experiment. The activation energies deduced from these amplitudes were also in agreement with the previously calculated activation energy of 0.3 eV.

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Int. J. Mol. Sci. 2020, 21, 3402 17 of 24 Int. J. Mol. Sci. 2017, 18, x FOR PEER REVIEW 17 of 26

Figure 18. (Left) Single Pulse 7Li spectra of Li6.5La3Zr1.75Mo0.25O12 (LLZMO) with temperature. (Right) The same temperature dependent spectra zoomed in to see the averaging of quadrupolar effects [63].

time scale than diffusion or relaxation,7 leading to a two-step amplitude decay, and this was indeed Figure 18. (a) Single Pulse Li7 spectra of Li La Zr Mo O (LLZMO) with temperature. seen inFigure experiment. 18. (Left) TheSingle activation Pulse Li spectraenergies of Lideduced6.5La6.53Zr1.753 fromMo1.750.25 theseO12 0.25(LLZMO) amplitudes12 with weretemperature. also in (Right)agreement (b) The same temperature dependent spectra zoomed in to see the averaging of quadrupolar eﬀects [63]. with theThe previouslysame temperature calculated dependent activation spectra energy zoomed of in 0.3eV. to see the averaging of quadrupolar effects [63].

Additionally, the authors employed spin alignment echo (SAE) spectroscopy to further validate the measured activation energy [64,66], the results of which are plotted in figure 19. By using a preparation time of 10 and arraying the mixing time between 10 μs and 10 s, the authors were able to probe different Li ion dynamics by observing the corresponding echo amplitude, including slow jump processes between sites with different electric field gradients (EFGs), spin diffusion, or ordinary spin lattice relaxation. The authors expected that the jump process operated on a slower time scale than diffusion or relaxation, leading to a two-step amplitude decay, and this was indeed seen in experiment. The activation energies deduced from these amplitudes were also in agreement with the previously calculated activation energy of 0.3eV.

FigureFigure 19. 19.Two-time Two-time correlationcorrelation functions functions measured measured from fromSAE experiments, SAE experiments, showing showingtwo-step decay two-step decay[63] [63. ].

In particular,In particular, at low at low temperatures temperatures and and high high preparationpreparation times, times, the the spin spin echo echo amplitude amplitude decayed decayed to a plateau,to a plateau, which which the the authors authors attributed attributed to to aa LiLi ionion jump jump process process between between 96 96h sites h sites of the of LLZMO the LLZMO lattice,lattice, through through a secondary a secondary jump jump to to the the 24 24 d d site site [[67,68].67,68]. OtherOther groups groups have have attempted attempted to to rectify rectify discrepantdiscrepant measurements measurements of ofLi Liion iondynamics dynamics in the in the garnets. As has been explained in this work, T1 relaxation, lineshape analysis, PFG NMR ,and other garnets. As has been explained in this work, T1 relaxation, lineshape analysis, PFG NMR, and other experiments can be used to independently deduce Li ion self-diffusion coefficients [65,69–73]. Many experiments can be used to independently deduce Li ion self-diffusion coefficients [65,69–73]. Many of these experimentsFigure 19. Two-time were performed correlation on functions polycrystalline measured from samples, SAE experiments, due to the showing relative two-step ease of decay synthesizing the large samples[63]. necessary for NMR. However, the measured diffusion coefficients have varied greatly, 13 2 18 2 in a manner not seen in liquid or homogeneous electrolytes, ranging from 10− m /s to 10− m /s at room temperature.In particular, To at try low and temperatures rectify this and discrepancy, high preparation Dorai times, et al. the employed spin echo PFG amplitude NMR experimentsdecayed to a plateau, which the authors attributed to a Li ion jump process between 96 h sites of the LLZMO on single crystalline and powder Li6.5La3Zr1.5Ta0.5O12 (LLZTO) [74]. The standard stimulated echo lattice, through a secondary jump to the 24 d site [67,68]. pulse sequence, as shown in Figure 20, was used, comprising three π pulses and two intermediate Other groups have attempted to rectify discrepant measurements2 of Li ion dynamics in the gradient pulses. In an attempt to minimize any magnetic field inhomogeneity effects, which could garnets. As has been explained in this work, T1 relaxation, lineshape analysis, PFG NMR ,and other also interfereexperiments with can di ffbeusion used coeto independentlyfficient calculation, deduce the Li ion aforementioned self-diffusion coefficients gradient pulses [65,69–73]. were Many not pure square pulses but rather a composite of a Quarter-sine pulse, followed by a standard square pulse, ending with a linear ramp down to minimize eddy current effects from fast ramping. Int. J. Mol. Sci. 2017, 18, x FOR PEER REVIEW 18 of 26 of these experiments were performed on polycrystalline samples, due to the relative ease of synthesizing the large samples necessary for NMR. However, the measured diffusion coefficients have varied greatly, in a manner not seen in liquid or homogeneous electrolytes, ranging from 10-13 m2/s to 10-18 m2/s at room temperature. To try and rectify this discrepancy, Dorai et al. employed PFG NMR experiments on single crystalline and powder Li6.5La3Zr1.5Ta0.5O12 (LLZTO) [74]. The standard stimulated echo pulse sequence, as shown in figure 20, was used, comprising three pulses and two intermediate gradient pulses. In an attempt to minimize any magnetic field inhomogeneity effects, which could also interfere with diffusion coefficient calculation, the aforementioned gradient pulses Int. J. Mol. Sci. 2020, 21, 3402 18 of 24 were not pure square pulses but rather a composite of a Quarter-sine pulse, followed by a standard square pulse, ending with a linear ramp down to minimize eddy current effects from fast ramping.

FigureFigure 20. 20. PFGPFG stimulated stimulated echo echo pulse pulse sequence, sequence, with with composite composite gradient gradient pulses [74] [74]..

13 2 The measured single crystal didiffusionffusion coecoefficientsfficients fromfrom NMRNMR werewere onon thethe orderorder ofof 10 10−-13 m2/s,/s, which agrees with earlier works on similarsimilar LLZTOLLZTO materials.materials. A clear discrepancy appeared upon comparison of NMR didiffusionffusion and EIS-calculated didiffusion.ffusion. Computing the Haven ratio, which is simply the ratio of NMR diffusion diffusion to EIS diffusion, diffusion, to be 0.4, this discrepancy is thought to be due to correlated Li ion motion in the material, rather than pure Brownian motion [[75].75]. Molecular dynamics simulations on this material have yielded the same ratio, and suggested that this correlated motion comes from from the the combined combined migration migration of of Li Li ions ions in in tetrahedral tetrahedral and and octahedral octahedral sites[76]. sites [76 In]. addition, In addition, the authorsthe authors attempted attempted to see to seewhether whether changing changing the the time time scale scale of of the the diffusion diffusion experiment experiment changed changed the value ofof thethe di diffusionffusion coe coefficient,fficient, which which would would imply imply diff eringdiffering Li ion Li dynamicsion dynamics on di ffonerent different time scales. time scales.However, However, although although the diff usionthe diffusion time was time arrayed was fromarrayed 20–600 from ms, 20–600 as shown ms, as in Figureshown 21in, figure there was 21, thereno significant was no significant change in thechange measured in the measured diffusion coe diffusionfficient. coefficient. Comparing the diffusion in the single crystal to that in the powder, it was clear that the powder exhibited slower overall Li ion diffusion. In addition, there was a more significant time dependence seen in the powders that was not seen in the single crystals, which could be due to the grain boundaries induced by the powder, which restricted Li ion mobility.

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Figure 21. Signal Attenuation plots for single crystalline Li6.5La3Zr1.5Ta0.5O12 (LLZTO) at diffusion Figure 21. Signal Attenuation plots for single crystalline Li6.5La3Zr1.5Ta0.5O12 (LLZTO) at diffusion times (a) from 20–70 ms and (b) from 100–600 ms [74]. times (a) from 20–70 ms and (b) from 100–600 ms.[74] 7. NASICON Electrolytes Comparing the diffusion in the single crystal to that in the powder, it was clear that the powder Sodium superionic conductor (NASICON)-type electrolytes are another attractive family of exhibited slower overall Li ion diffusion. In addition, there was a more significant time dependence crystalline electrolytes, with the general structure AM X O , where A is an alkali metal, M is either Ti seen in the powders that was not seen in the single2 3 crystals,12 which could be due to the grain or Ge, and X is either Si or P. Classic NASICON materials, such as LiTi (PO4) (LTP) and LiGe (PO ) boundaries induced by the powder, which restricted Li ion mobility. 2 3 2 4 3 (LGP) were potential electrolyte candidates, as LTP can exhibit room temperature conductivities up 5 7.to NASICON 10− S/cm, Electrolytes and LGP is known to be stable against Li up to 6 V [77]. Attempts to improve upon + 3+ this conductivity have shown that partial substitution of Li with Al , forming Li1.5Al0.5Ge1.5(PO4)3 (LAGP),Sodium yields superionic such a result conductor [78,79]. (NASICON)-type electrolytes are another attractive family of crystallineVyalikh electrolytes, et al. discovered with the ageneral five-fold structure increase AM of2X the3O12 ionic, where conductivity A is an alkali of LAGP metal, throughM is either the Tiaddition or Ge, of and yttrium X is oxide, either forming Si or P. LAGPY Classic [ 80 NASICON]. X-ray di ff materials,raction and such electron as LiTi microscopy2(PO4)3 (LTP) studies and on LiGe2(PO4)3 (LGP) were potential electrolyte candidates, as LTP can exhibit room temperature LAGPY suggested that the YPO4 lies at the LAGP grain boundaries, allowing for faster ion mobility -5 conductivitiesthrough said boundaries. up to 10 S/cm, Employing and LGP7Li is lineshape known to analysis, be stable relaxation against experiments,Li up to 6V[77]. and Attempts diffusometry to + 3+ improvestudies, they upon attempted this conductivity to understand have shown the nature that of partial Li-ion substitution dynamics and of howLi with it is Alaffected , forming by the Licrystal1.5Al0.5Ge geometry.1.5(PO4)3 From(LAGP), lineshape yields such analysis a result[78,79]. performed on LAGP and LAGPY, the authors calculated Vyalikh et al. discovered a five-fold increase of the ionic conductivity4 1of LAGP through the correlation times and Li ion jump rates, which were both on the order of 10− s− , as shown in Figure 22. addition of yttrium oxide, forming LAGPY [80]. X-ray diffraction and electron microscopy studies on This suggests that Li ions were not hopping from site to site faster from the addition of Y2O3. Repeating LAGPYthis measurement suggested usingthat the field YPO cycling4 lies at NMR, the LAGP the authors grain foundboundaries, no significant allowing change for faster in the ion jump mobility rates 7 throughand calculated said a boundaries. mean of 0.37 Employing eV for both materials.Li lineshape analysis, relaxation experiments, and diffusometryIt was also studies, possible they to probe attempted ionic motion to understand through thethe use nature of PFG of NMR.Li-ion VT dynamics diffusion and measurements how it is affectedon LAGPY by revealedthe crystal an geometry. activation Fromenergy lineshape of 0.32 eV, analysis which appears performed to agree on LAGP with FC and Measurements. LAGPY, the -4 -1 authorsThrough calculated the Einstein–Smoluchowski correlation times and relation Li ion jump [65], taking rates, which an average were jumpboth on length the order to be of the 10 distance s , as shown in figure 22. This suggests that Li ions were not hopping13 2 from site to site faster from the between Li1 and Li3 sites and a room temperature D ~ 10− m /s, the authors calculated a jump rate additionan order of magnitude Y2O3. Repeating higher than this foundmeasurement from relaxation using field measurements, cycling NMR, which the suggested authors that found LAGPY no significantexhibited significantchange in the dynamical jump rates heterogeneity. and calculated a mean of 0.37 eV for both materials.

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Figure 22. PlotsPlots of of Li Li jump jump rates rates with with inverse inverse temperature temperature for for ( (aa)) LAGPY LAGPY and and ( (bb)) LAGP, LAGP, recorded using a combination of linewidth analysis, spin lattice relaxation (SLR) measurements, FC NMR, PFG NMR, and EIS [80] [80]..

ItFinally, was alsothrough possible DFT calculations, to probe ionic the motionauthors deducedthrough thethat use the addition of PFG of NMR. Y2O 3 VTchanged diffusion the measurementsconcentration ofon Li LAGPY ions occupying revealed Li1an activation and Li3 sites; energy the increasedof 0.32 eV, concentration which appears of Lito agree ions in with the Li3FC Measurements.sites had the eﬀ ectThrough of pushing the Einstein–Smoluchowski ions in Li1 sites to other relation Li3 sites, [65], lowering taking thean average hopping jump energy length barrier. to beThus, the distance NMR and between DFT showed Li1 and thatLi3 sites the introductionand a room temperature of Y2O3 into D ~ LAGP 10-13 m led2/s, tothe a authors denser calculated intergrain amicrostructure jump rate an [ 81 order], while of electron magnitude microscopy higher than showed found improved from relaxation grain boundaries, measurements, leading which to the suggestedaforementioned that LAGPY increase exhibited in conductivity. significant dynamical heterogeneity. Finally, through DFT calculations, the authors deduced that the addition of Y2O3 changed the 8. Conclusions concentration of Li ions occupying Li1 and Li3 sites; the increased concentration of Li ions in the Li3 sites hadThis the review effect has of shownpushing only ions a in few Li1 of sites the ways,to other using Li3 sites, selected lowering representative the hopping examples, energy in barrier. which Thus,nuclear NMR magnetic and DFT resonance showed can that be utilizedthe introduction to probe solidof Y2O inorganic3 into LAGP electrolyte led to systemsa denser and intergrain extract microstructurecrucial structural [81], and while dynamical electron information. microscopy The showed wide applicabilityimproved grain of NMR boundaries, to most leading materials, to andthe aforementionedthe time/length scalesincrease which in conductivity. it can probe, further demonstrate the power of the technique. NMR spectroscopy as an analytical tool will surely prove invaluable in aiding the search to produce a viable 8.all Conclusion solid-state battery over the coming years.

AuthorThis Contributions: review has shownD.J.M. performedonly a few the of primarythe ways, literature using selected search and representative wrote most of examples, the manuscript. in which S.G. nucleardefined themagnetic range of resonance topics to be can covered, be utilized and provided to probe guidance solid and inorganic editing ofelectrolyte the manuscript. systems All authorsand extract have crucialread and structural agreed to theand published dynamical version information. of the manuscript. The wide applicability of NMR to most materials, and theAcknowledgments: time/length scalesThe authorswhich it acknowledge can probe, supportfurther fromdemonstrate Oak Ridge the National power Laboratory of the technique. Asst. Secretary, NMR spectroscopyEnergy Efficiency as an and analytical Renewable tool Energy will surely (EERE), prove Vehicle invaluable Technologies in aiding Office the (VTO) search through to produce the Advanced a viable Battery Materials Research (BMR) Program. D.J.M. acknowledges additional support from the National Institutes allof Healthsolid-state RISE programbattery over at Hunter the coming College years. (grant GM060665). Acknowledgments:Conflicts of Interest: TheThe authors authors acknowledge have no conflict support of interest from to Oak declare. Ridge National Laboratory Asst. Secretary, Energy Efficiency and Renewable Energy (EERE), Vehicle Technologies Office (VTO) through the Advanced BatteryReferences Materials Research (BMR) Program. D.M. acknowledges additional support from the National Institutes of Health RISE program at Hunter College (grant GM060665). 1. Seki, S.; Hayamizu, K.; Tsuzuki, S.; Takahashi, K.; Ishino, Y.; Kato, M.; Nozaki, E.; Watanabe, H.; Umebayashi, Y. AuthorDensity, Contributions: Viscosity, IonicD.M performed Conductivity, the andprimary Self-Di literatureffusion Coe searchfficient and of wrote Organic most Liquid of the Electrolytes: manuscript. Part S.G I. defined the range of topics to be covered, and provided guidance and editing of the manuscript. Propylene Carbonate + Li, Na, Mg and Ca Cation Salts. J. Electrochem. Soc. 2018, 165, A542–A546. [CrossRef] Conflicts2. Cao, of C.; Interest Li, Z.-B.;: The Wang, authors X.-L.; have Zhao, no conflicts X.; Han, of W.-Q. interest Recent to declare. Advances in Inorganic Solid Electrolytes for Lithium Batteries. Front. Energy Res. 2014, 2, 2. [CrossRef] References 1. Seki, S.; Hayamizu, K.; Tsuzuki, S.; Takahashi, K.; Ishino, Y.; Kato, M.; Nozaki, E.; Watanabe, H.; Umebayashi, Y. Density, Viscosity, Ionic Conductivity, and Self-Diffusion Coefficient of Organic Liquid

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