Anion Distribution in Superionic Ag - American Chemical Society

Oct 31, 2013 - ABSTRACT: The structure of roller-quenched fast ion conductive glasses (FICs). (Ag3PO4)x(AgI)1−x (0.15 ≤ x ≤ 0.50) is investigate...
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Anion Distribution in Superionic Ag3PO4−AgI Glasses Revealed by Dipolar Solid-State NMR Jinjun Ren† and Hellmut Eckert*,†,‡ †

Institut für Physikalische Chemie, Westfälische Wilhelms-Universität Münster, Corrensstr. 30, D-48149 Münster, Germany Instituto da Física São Carlos, Universidade de São Paulo, São Carlos, SP 13590, Brazil



S Supporting Information *

ABSTRACT: The structure of roller-quenched fast ion conductive glasses (FICs) (Ag3PO4)x(AgI)1−x (0.15 ≤ x ≤ 0.50) is investigated by 109Ag and 31P solid-state NMR spectroscopies. Monotonic linear dependences of 109Ag and 31P chemical shifts on x are consistent with a statistical distribution of the phosphate and iodide anions. This conclusion is quantitatively confirmed by a new 31P homonuclear magnetic dipolar recoupling method, termed double-quantum-based dipolar recoupling effects nuclear alignment reduction (DQ-DRENAR), which numerically proves a random spatial distribution of the phosphate anions. Altogether these results give the final answer to a long-standing debate on the structure of silver in AgI-based (FIC) glasses, proving the absence of previously postulated silver iodide cluster domains.



INTRODUCTION Silver iodide-based glasses belong to the ion-conducting materials with among the highest ionic conductivities. They typically consist of a silver borate, phosphate, or molybdate component which is alloyed with AgI. 1−4 Their ionic conductivity increases with increasing AgI content; however, this composition dependence is highly nonlinear, presenting a threshold behavior near 30 mol % AgI.5 On the basis of this observation, Johari et al. postulated the formation of highly conductive AgI cluster domains, which form a percolation path at this particular composition (termed cluster tissue model).5 This concept has been highly influential for the interpretation of transport data in these glasses,6−9 even though results from various structural studies have been interpreted both in support of10,11 and in opposition to it.12−14 For the AgI−AgPO3 glass system a comprehensive interpretation of such structural data, including results from extended absorption X-ray fine structure (EXAFS), vibrational spectroscopy, and solid-state NMR spectroscopy, has resulted in a modified view of the structure of these glasses (termed mixed electrolyte tissue to amorphous AgI aggregate model).15−17 While this model concedes the presence of mixed Ag(On,Im) local environments, it still seems to maintain in some way the idea of an aggregation of amorphous AgI domains, where the most mobile silver ions are encountered. In contrast to these ideas, 109Ag chemical shift trends extracted from solid-state NMR data are generally much more consistent with a more or less statistical anion arrangement, resulting in a wide distribution of mixed Ag(On,Im) local environments, without any clustering or aggregation.18−20 The distribution of local environments also implies a distribution of ionic mobilities, as suggested by a correlation of ionic mobility with the isotropic chemical shifts in some systems.21,22 Supported by these results, a fractal approach based on the percolation of domains with conductive © 2013 American Chemical Society

silver ions within mixed I/O coordinations has been proposed.22 While none of the previous NMR studies give any evidence of the presence of clusters, domains, or amorphous aggregates that are composed of silver iodide, they also cannot rule out the presence of more subtle structural inhomogeneities on the nanoscale. In the present contribution we will explore this issue in glasses in the system (Ag3PO4)x(AgI)(1−x). These glasses can only be prepared by extremely rapid cooling procedures such as the roller-quenching method. The preparation and macroscopic and functional characterization of these glasses has been reported numerous times years ago.4,23 Their electrical conductivities increase with increasing AgI content, despite decreasing number densities, and the corresponding opposite trend is observed for the activation energies.4,23,24 Very little is known, however, about the structural characteristics of these glasses and their relation to ionic conductivity. Here, we present a comprehensive structural characterization by 31P and 109 Ag solid-state NMR. To explore the spatial anion distribution we apply a recently developed new dipolar recoupling technique, termed double-quantum-based dipolar recoupling effects nuclear alignment reduction (DQ-DRENAR), which is able to measure the strength of homonuclear 31P−31P magnetic dipole−dipole interactions under MAS NMR conditions.25,26 As the strength of magnetic dipole−dipole interactions is directly calculable from internuclear distances,27 this observable is a useful tool for assessing distinct structural scenarios in an unambiguous fashion, contributing to a conclusive description of the structural organization of (Ag3PO4)x(AgI)(1−x) glasses. Received: September 17, 2013 Revised: October 31, 2013 Published: October 31, 2013 24746

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Table 1. Glass Transition Temperature Tg, Crystallization Temperature Tc, Activation Energy of Ag+ Ionic Motion, Ea (From NMR, via Equation 1), Isotropic Chemical Shifts δiso of 109Ag and 31P, the 31P−31P Homonuclear Dipolar Interaction Parameter ∑kb2jk, and Density of (Ag3PO4)x(AgI)(1−x) Glasses and Crystalline Ag3PO4

a

x

Tg/°C

Tc/°C

(Tg − Tc) /K

0.15 0.2 0.3 0.4 0.5 1

n.m.a 54.0 68.5 82.2 94.6

n.m. 77.1 98.6 103.2 113.7

n.m. 23.1 30.1 21.0 19.1

Ea/eV (±0.02 eV)

δiso(109Ag) /ppm (±1 ppm)

δiso(31P) /ppm (±0.5 ppm)

∑kb2jk/105 Hz2 (±10%)

ρ/g/cm3 (±3%)

n.m. 0.23 0.27 0.31 n.m. n.m.

657 650 626 596 567 347

20.3 21.1 22.5 23.5 24.4 28.5

0.35 0.45 0.76 1.04 1.22 2.39

6.06 6.23 6.28 6.33 6.45 6.37

Not measured.

Figure 1. Solid-state MAS NMR spectra of (a) 109Ag and (b) 31P in (Ag3PO4)x(AgI)1−x glasses and crystalline model compounds. (c) Compositional dependence of 109Ag (red) and 31P (black) isotropic chemical shifts.



EXPERIMENTAL SECTION

heating rate of 10 K/min. Sample densities were measured with an AccuPycII 1340 gas pycnometer from Micromeritics. Both the 109Ag MAS and temperature-dependent static NMR measurements were carried out on a Bruker Avance DSX 500 spectrometer equipped with a 7 mm probe, using Hahn spin echos. For the static measurements, the time between the 90° and 180° pulses was 100 μs, while the MAS NMR spectra were acquired with rotor synchronization (spinning frequency of 5.0 kHz). The 90° and 180° pulse lengths were 12 and 24 μs, respectively. Chemical shifts are reported against an external reference of 9 M aqueous AgNO3 solution containing 0.24 M Fe(NO3)3. The relaxation delays used ranged from values between 2 and 1000 s, depending on sample and temperature. Variable-temperature static 109Ag NMR measurements were taken over the temperature range 124−335 K. The temperature was calibrated on the basis of static 207Pb NMR measurements of crystalline Pb(NO3)2. 31P MAS NMR experiments were

Batches (0.01 mol) of (Ag3PO4)x(AgI)1−x glasses with the compositions 0.15 ≤ x ≤ 0.5 were prepared by heating crystalline AgI and Ag3PO4 (ABCR, 99%) in the appropriate proportions at 900 °C for 15 min in a quartz crucible. The melt was rapidly poured into the 1 mm gap between a homemade roller-quenching machine (roller diameter 70 mm), operated at the spinning rate of 4000 turns/min. The prepared thin glass flakes were stored in dark containers within an Ar-filled glovebox for protection from light, water, and oxygen. The amorphous state of the glass samples was confirmed by XRD (see Figure S1, Supporting Information). Samples with compositions from x = 0.15 to 0.4 were found to be completely amorphous, and the material with composition x = 0.5 showed very weak reflection peaks of Ag3PO4. Differential scanning calorimetry was done with a Netzsch DSC-204 apparatus, at a 24747

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Figure 2. (a) Static variable-temperature 109Ag NMR spectra of a sample with x = 0.2. (b) Dependence of full width of the half-maximum (fwhm) on temperature. Onset temperatures To are indicated.

As the temperature increases, motional narrowing effects are observed, reflecting rapid silver ion exchange between individual silver ionic sites, eventually resulting in an average isotropic chemical shift on the NMR time scale. While this transition occurs over a rather narrow temperature range, indicating a relatively homogeneous distribution of silver ionic mobilities in a given sample, some indications of dynamic heterogeneity are observed in the transition region. For example, for the sample with x = 0.20, Figure 3 reveals that

carried out at 121.49 MHz on a Bruker Avance III 300 MHz spectrometer equipped with a 2.5 mm probe. Chemical shifts are reported against an external reference of 85% H3PO4 solution. For the single pulse MAS NMR experiments, the spinning rate was 8.0 kHz, and the 90° pulse length was 4.5 μs. DQ-DRENAR experiments were also measured at the spinning frequency of 8.0 kHz for glass and at 7.0 and 8.0 kHz for crystalline Ag3PO4. In these experiments the 31P nutation frequency is 7 times the spinning rate, and each POST-C7 block spans two rotor periods.



RESULTS AND DISCUSSION Homogeneous flakes were obtained, which were shown to be free from crystalline impurities within the composition range 0.15 ≤ x < 0.5 by X-ray powder diffraction; weak Ag3PO4 reflection peaks were observed for the latter sample (see Figure S1, Supporting Information). The sample color changes from dark yellow to orange with increasing x value. Glass transition temperatures increase linearly with increasing x (see Figure S2, Supporting Information), similar to previous results observed for the AgI−Ag2O−MxOy (MxOy = P2O5, V2O5, As2O5, CrO3, SO3, and SeO3) glass systems.4 The measured densities imply an increase of molar volume from 43.3 to 50.7 cm3 and also an increase of silver ion densities between 0.030 and 0.039 mol/ cm3 in going from x = 0.15 to x = 0.5. Table 1 summarizes all the glass compositions and the characterization and NMR spectroscopic results obtained within the present study. Figure 1(a) and 1(b) shows the 109Ag and 31P MAS NMR spectra of the (Ag3PO4)x(AgI)(1−x) glasses and the crystalline end members. Single-peak spectra are observed, consistent with homogeneous glass structures and the absence of Ag3PO4 or AgI microdomains. Both the 31P and the 109Ag chemical shifts depend linearly on x, indicating a monotonic evolution of their local environments. Figure 2 shows the results from static temperature-dependent 109Ag NMR studies. At sufficiently low temperatures, in the absence of motional effects, broad Gaussian-shaped signals with linewidths near 11 kHz are observed, reflecting an inhomogeneous distribution characterized by a spread of isotropic and anisotropic chemical shifts. This line shape character was already previously established by hole-burning experiments on related glasses.28 The broad envelope observed at these low temperatures is most reasonably interpreted as a superposition of the responses of different Ag(On,Im) local environments, whose chemical shifts increase with increasing m/n ratio.

Figure 3. Static 109Ag NMR line shape of x = 0.2 glass at 154.5 K and fit to two distinct line shape components: a narrow line (Δ = 2530 Hz) at a chemical shift δ near 677 ppm, reflecting more mobile silver ions in more iodide-rich coordination environments and a broader line (Δ = 9900 Hz) at a chemical shift δ near 645 ppm, reflecting less mobile silver ions in environments with higher oxygen contents.

the high-frequency part of the resonance is affected by motional narrowing at somewhat lower temperatures than the lowfrequency part. This correlation of ionic mobility with chemical shift suggests that the Ag+ ions in the iodide-richer regions (higher chemical shifts) may be slightly more mobile than those in iodide-poorer regions. Similar results have been previously observed for some AgI−AgPO3.5 glasses.21 From the temperature To, which describes the onset of the motional narrowing effect, the activation energy Ea of the ionic hopping process can be estimated29 Ea (eV) ≈ 1.6 × 10−3To (K)

(1)

The values determined in this fashion (0.2−0.3 eV, see Table 1) are similar to those reported in the literature on related AgIdoped silver phosphate glasses. Previous studies have found that an extrapolation of the composition-dependent activation 24748

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energies determined from ac impedance measurements for the systems (AgI) x (AgPO 3 ) 1−x , (AgI) x (Ag 2 PO 3.5 ) 1−x , and (AgI)x(Ag3PO4)1−x to x = 1 results in a value of 0.27 eV, which closely matches the value measured for α-AgI.1,2,4 While comparable values have been obtained for the present Ag3PO4−AgI materials, these data are inconclusive regarding the issue of the structural organization of the mixed glasses, as such a convergence of activation energies could occur for either the AgI cluster model or a random mixing model. All of the NMR results discussed above are basically consistent with those obtained on other silver iodide/silver phosphate glass systems, suggesting intimate mixing of the two anionic species rather than the formation of AgI clusters.18−20 The 31P chemical shift trend indicates that the bonding state of the phosphate ions is sensitive to the proximity of iodide ions in their vicinity, and the 109Ag NMR data indicate a continuous variation of the average local Ag(On,Im) environments, with the average n/m ratio increasing monotonically with increasing x. While the latter ratio is obviously predictable from the glass composition, the nature and width of the distribution of these individual environments cannot be inferred from these experiments, as the low-temperature 109Ag NMR spectra do not resolve corresponding individual line shape contributions. It is therefore not clear whether this distribution should be considered compositionally focused (ordered) or random (following binomial statistics) or if it possesses a larger degree of heterogeneity, as would be expected from a clustering scenario representingin its extreme limita mixture of AgI and Ag3PO4 aggregates. To explore this issue further, more sophisticated experiments sensitive to the spatial distribution of the glass constituents are needed. For example, homonuclear 31P−31P magnetic dipole− dipole interactions are directly calculable from internuclear distance distributions and hence can provide quantitative information about the above distribution scenarios for the phosphate ions. We have recently developed a selective NMR method, termed DQ-DRENAR, which is able to measure the 31 P−31P dipolar coupling strength in multispin systems quantitatively under conditions of magic-angle spinning NMR.25,26 In DQ-DRENAR, double-quantum coherences are stimulated during 2n rotor periods Tr, using the POST-C7 excitation scheme.30 This causes a decrease of the longitudinal 31 P magnetization, which is then probed under systematic incrementation of this stimulation time. The pulse sequence scheme is shown in Figure 4. As in rotational echo double resonance (REDOR)31 it consists of two separate parts, resulting in the signal functions S0 and S′. The signal function S′ is measured by applying the POST-C7 pulse block over 4n rotor periods Tr. In contrast, in the S0 part the phases of all the pulses in the second half of the block are shifted by 90° with respect to those of the first half, leading to complete cancellation of the double-quantum Hamiltonian after 4nTr. The signal measured by this sequence part is then taken as the reference signal. The strength of the homonuclear multispin dipole−dipole coupling, specified by the quantity ∑kb2jk, can then be extracted by fitting the initial range up to 0.3−0.5 of the data curve (S0 − S′)/S0 vs NTr, to the expression25,26 S0 − S′ 0.86π 2 = ( (∑ bjk2 ) NTr)2 S0 (t = NT ) 15 k r

Figure 4. DQ-DRENAR pulse sequence, based on dipolar recoupling using the double-quantum (DQ) Hamiltonian created by POST-C7 blocks. The pulse unit of C′ in S0 is the same as that of C, but the overall phase of the C′ block is kept 90° shifted relative to that of the C block. In the S′ block, both the C blocks are identical.

bjk =

μ0 ℏγ 2 4π 2πr jk3

(3)

specifies the dipolar coupling constant between the observed species j and another nucleus k of the same kind, separated by the distance rjk. In multispin systems, effective summed squares of dipole−dipole coupling constants can be accurately estimated by this technique. Using DQ-DRENAR, internuclear distances in two-spin systems, as well as connectivities and spatial distributions in multispin systems, can be investigated in a quantitative fashion. Figure 5(a) shows the experimental results obtained for the present glasses and the crystalline model compound Ag3PO4. The curvatures of data curves gradually increase with Ag3PO4 content reflecting a corresponding increase of the 31P−31P homonuclear dipolar coupling strength. The quantities ∑kb2jk, determined from eq 2 by fitting the data range ΔS/S0 ≤ 0.4, are summarized in Table 1. The value measured for crystalline Ag3PO4 (2.39 × 105 Hz2) is in excellent agreement with the value predicted from the crystal structure (2.38 × 105 Hz2). Figure 5(b) shows these values as a function of average molar phosphate concentration in the glasses and crystalline Ag3PO4. These concentrations are calculated from the compositions and experimental densities of samples listed in Table 1. ∑kb2jk shows a linear dependence on phosphate concentration for the glass samples, including the origin at x = 0. This linearity is exactly expected for, and hence proves, the existence of a spatial distribution of the phosphate ions that is strictly random. The slightly higher dipolar effect measured for crystalline Ag3PO4 might arise from the structural difference between this compound and the glassy materials. Thus, as Ag3PO4 is added into AgI, the closest 31P−31P distances increase. Figure 5(b) proves that there are no Ag3PO4 or AgI aggregates in these glasses and that there is also no hint at any more subtle type of nanoscale inhomogeneity. To summarize, the 31P dipolar solid-state NMR results obtained within the present study indicate that roller-quenched superionic glasses with composition (Ag3PO4)x(AgI)1−x have a spatial anion distribution that is strictly random. On the basis of this finding, we propose that the local Ag coordinations are characterized by binomial distributions of Ag(InOm) environments without any element of heterogeneity, let alone AgI clustering. The establishment of these mixed Ag coordinations is the main factor governing the increase in ionic mobility, and the increase in mobility (and hence the ionic conductivity) with

(2)

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Figure 5. 31P−31P homonuclear dipole−dipole coupling strength measured via DQ-DRENAR in (Ag3PO4)x(AgI)1−x glasses. (a) Homonuclear dipolar dephasing curves and (b) effective summed squares of dipole−dipole coupling constants, extracted from these curves via eq 2, vs the average number of 31P per 103 cm3. Open square shows the data point for crystalline Ag3PO4 (15.2 mol 31P/103 cm3). The solid line shows a linear fit to the data obtained for the glasses. Extrapolation of the AgI Composition Dependence in AgI−Ag2O− P2O5 Glasses. J. Phys.: Condens. Matter 2003, 15, 3867−3873. (5) Mangion, M. B. M.; Johari, G. P. The Dielectric Behavior and Conduction of AgI-AgPO3 Glass of Various Compositions. Phys. Chem. Glasses 1988, 29, 225−234. (6) Vaidhyanathan, B.; Asokan, S.; Rao, K. J. High Pressure Studies on AgI-Ag2O-MoO3 Glasses. Pramana 1994, 43, 189−192. (7) Mercier, R.; Tachez, M.; Malugani, J. P.; Rousselot, C. Microstructure of Silver Superionic Glasses. Mater. Chem. Phys. 1989, 23, 13−27. (8) Rocca, F.; Dalba, G.; Fornasini, P.; Tomasi, A. Structural Study of AgI-Ag2O-B2O3 Glasses by X-ray Absorption Spectroscopy. Solid State Ionics 1992, 53−56, 1253−1259. (9) Tachez, M.; Malugani, J. P.; Mercier, R.; Chieux, P. Quasielastic and Inelastic Neutron Scattering from AgPO3-AgI Glass. Solid State Ionics 1986, 18/19, 372−373. (10) Gunawan, M.; Kartini, E.; Putra, E.G. R. Small Angle Neutron Scattering Experiments on Solid Electrolyte (AgI)x (AgPO3)1−x. J. Solid State Electrochem. 2008, 12, 903−907. (11) Dianoux, A. J.; Tachez, M.; Mercier, R.; Malugani, J. P. Neutron Scattering by Superionic Conductor Glasses. J. Non-Cryst. Solids 1991, 131−133, 973−980. (12) Martin, S. W.; Schiraldi, A. Glass Formation and High Conductivity in the Ternary System Silver Iodide + Silver Arsenate (Ag3AsO4) + Silver Metaphosphate (AgPO3): Host to Glassy AlphaSilver Iodide? J. Phys. Chem. 1985, 89, 2070−2076. (13) Lee, J. H.; Elliott, S. R. Isotopic-substitution Neutron-diffraction Studies of (AgI)0.5(AgPO3)0.5 Glass. Phys. Rev. B 1996, 54, 12109− 12114. (14) Wicks, J. D.; Börjesson, L.; Bushnell-Wye, G.; Howells, W. S.; Mc Greevy, R. L. Structure and Ionic Conduction in (AgI)x(AgPO3)1‑x Glasses. Phys. Rev. Lett. 1995, 74, 726−729. (15) Cramery, C.; Price, D. L.; Saboungi, M. Structure of Silver Iodide/Silver Selenate Fast-ion-conducting Glasses: Neutron Diffraction Experiments. J. Phys.: Condens. Matter 1998, 10, 6229−6241. (16) Hanaya, M.; Nakayama, M.; Hatate, A.; Ogumi, M. Effect of Variation in the Glass-former Network Structure on the Relaxation Properties of Conductive Ag+ Ions in AgI-based Fast Ion Conducting Glasses. Phys. Rev. B 1995, 52, 3234−3240. (17) (a) Baskaran, N.; Voindaraj, G.; Narayanasamy, A. A.c. Conductivity and Relaxation Processes in Silver Selenochromate Glass. Solid State Ionics 1997, 98, 217−227. (b) Baskaran, N. Conductivity Relaxation and Ion Transport Processes in Glassy Electrolytes. J. Appl. Phys. 2002, 92, 825−833. (18) Olsen, K. K.; Zwanziger, J. W. Multi-nuclear and Multidimensional Nuclear Magnetic Resonance Investigation of Silver Iodide-silver Phosphate Fast Ion Conducting Glasses. Solid State Nucl. Magn. Reson. 1995, 5, 123−132.

decreasing x reflects the continuous increase in the fractional contribution of iodide anions in the first coordination sphere of the silver ions, consistent with the fractal modeling approach described in ref 22. Finally, the results of the present study illustrate that the quantitative measurement of homonuclear dipole−dipole interactions by suitable 2D techniques can substantially increase the informational content of solid-state NMR spectroscopy for structural studies of glasses.



ASSOCIATED CONTENT

S Supporting Information *

S1: X-ray powder diffraction pattern of glass and crystalline samples. S2: Differential scanning thermograms of glass samples are included. This material is available free of charge via the Internet at http://pubs.acs.org.



AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.



ACKNOWLEDGMENTS Support by the Deutsche Forschungsgemeinschaft, project SFB 858, and by FAPESP (Sao Paulo Research Foundation), grant number 2013/07793-6 (CERTEV − Center for Research, Technology and Education in Vitreous Materials), is most gratefully acknowledged. We thank Wilma Pröbsting for the DSC characterization and Prof. Dr. Leo van Wüllen (University of Augsburg) for providing access to his roller quenching facilities.



REFERENCES

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(19) Mustarelli, P.; Tomasi, G.; Magistris, G.; Linati, L. Carrier Density and Mobility in AgI-AgPO3 Glasses: A NMR Study. Phys. Rev. B 2001, 63, 144203−144208. (20) Tomasi, C.; Mustarelli, P.; Garcia, M. P.I.; Magistris, A.; Mandacini, A. Low-temperature Ionic Conductivity in AgI: AgPO3 Glasses. Philos. Mag. 2002, 82, 475−483. (21) Vogel, M.; Brinkmann, C.; Eckert, H.; Heuer, A. TwoDimensional 109Ag NMR and Random-Walk Simulation Studies of Silver Dynamics in Glassy Silver Ion Conductors. A. Solid State Nucl. Magn. Reson. 2002, 22, 344−362. (22) Mustarelli, P.; Tomasi, C.; Magistris, A. Fractal Nanochannels as the Basis of the Ionic Transport in AgI-Based Glasses. J. Phys. Chem. B 2005, 109, 17417−17421. (23) Machida, N.; Kawachi, M.; Ueda, A.; Shigematsu, T.; Nakanishi, N.; Takahashi, N.; Minami, T. Mixed Anion Effect of Silver Ion Conducting Glasses in the Systems AgI-Ag2MoO4-Ag3PO4 and AgIAg2MoO4-Ag2PO3.5 and Structural Study by 31P MAS-NMR. Solid State Ionics 1995, 79, 273−278. (24) Hanaya, M.; Echigo, K.; Ogumi, M. Anomalous AgI Composition Dependence of the Thermal and Dielectric Properties of AgI-Ag2O-P2O5 Glasses: Evidence for the Formation of Amorphous AgI Aggregate Regions as Dominating the fast Ag+ Ion Conduction. J. Phys.: Condens. Matter 2005, 17, 2281−2292. (25) Ren, J.; Eckert, H. DQ-DRENAR: a New NMR Technique to Measure Site-Resolved Magnetic Dipole-Dipole Interactions in Multispin-1/2 Systems. Theory and Applications to Phosphate Materials. J. Chem. Phys. 2013, 138, 164201−164216. (26) Ren, J.; Eckert, H. A Homonuclear Rotational Echo Double Resonance (REDOR) Method for Measuring Site-resolved Distance Distributions in I = 1/2 Spin Pairs, Clusters, and Multi-spin Systems. Angew. Chem., Int. Ed. 2012, 51, 12888−12891. (27) van Vleck, J. H. The Dipolar Broadening of Magnetic Resonance Lines in Crystals. Phys. Rev. 1948, 74, 1168−1183. (28) Kawamura, J.; Kuwata, N.; Nakamura, Y.; Erata, T.; Hatori, T. Evidence of Multisite Exchange in AgI−AgPO3 Glasses: 109Ag NMR Hole-Burning Spectra. Solid State Ionics 2002, 154−155, 183−188. (29) Waugh, J. S.; Fedin, E. Determination of Hindered-rotation Barriers in Solids. Sov. Phys.-Solid State 1963, 4, 1633−1636. (30) Hohwy, M.; Jakobsen, H. J.; Edén, M.; Levitt, M. H.; Nielsen, N. C. Broadband Dipolar Recoupling in the Nuclear Magnetic Resonance of Rotating Solids: A Compensated C7 Pulse Sequence. J. Chem. Phys. 1998, 108, 2686−2694. (31) Gullion, T.; Schaefer, J. Rotational-echo Double-resonance NMR. J. Magn. Reson. 1989, 81, 196−200.

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