Local Structural Modifications versus Transport Properties in AgI

Article pubs.acs.org/JPCC

Local Structural Modifications versus Transport Properties in AgIDoped Silver−Borate Glasses: A Detailed X‑ray Absorption Investigation Andrea Sanson,*,† Cristina Armellini,‡ Rolly Grisenti,§ and Paolo Fornasini§ †

Dipartimento di Fisica e Astronomia, Università di Padova, I-35131 Padova, Italy CNR-IFN, Istituto di Fotonica e Nanotecnologie, Unità “FBK-Fotonica”, I-38123 Povo (Trento), Italy § Dipartimento di Fisica, Università di Trento, I-38123 Povo (Trento), Italy ‡

ABSTRACT: The short-range order around iodine in AgIdoped silver−borate glasses (AgI)x(Ag2O·nB2O3)1−x has been studied as a function of both AgI content and temperature by means of extended X-ray absorption fine structure (EXAFS) spectroscopy in order to investigate the relationship between local structure and conductivity. An interpretation of the EXAFS cumulants specifically tailored for ion conducting glasses has been employed. The reduction of the number of Ag ions coordinated to I and the modifications of the I−Ag distance distribution probed by EXAFS when ionic conductivity increases, by temperature or AgI content, are strictly correlated with the progressive growth of silver ions undergoing diffusion. The results are discussed in the framework of the bond valence model and mixed iodine/oxygen coordination of silver ions. in FIC glasses.9−21 Because of the absence of long-range order and the presence of many atomic species, only partial information can be obtained from single experimental techniques, and a satisfactory explanation of the conduction mechanism is expected from the critical comparison of different experiments, accompanied by suitable theoretical supports. For AgI-doped silver borate glasses AgI−Ag2O−B2O3, it is well established that the addition of Ag2O to the glass former B2O3 modifies its structure in such a way that the number of tetrahedral BO4− units increases, while the number of triangular BO3 units decreases.22 Raman, nuclear magnetic resonance (NMR), neutron, and X-ray diffraction investigations23−25 have shown that the further addition of the AgI dopant does not affect the short-range order of the Ag2O−B2O3 host network. Swenson et al. suggested that the main role of AgI is to expand the host network and to create free volume for the ion transport, together with the increase of the number of charge carriers and the decrease of the activation energy for cation motion.25,26 More recently, by including the constraints of the bond valence model into their reverse Monte Carlo (RMC) structural investigations, Swenson et al. have shown that the conductivity in AgI-based FIC glasses can be related to the formation of a percolating pathways cluster; the corresponding pathway volume is a fraction of the free volume, where the valence mismatch for the mobile ion remains below a threshold

1. INTRODUCTION Since many years, fast ion conducting (FIC) glasses are considered interesting materials for their potential use in solid state electrochemical devices.1 The conduction properties of FIC glasses depend on their composition as well as on the relative concentration of the different components. AgI-doped glasses are the best conducting oxide glasses, their room temperature conductivity being, for some compositions, of the order of 1 S cm−1, comparable to that of crystalline AgI in the α phase, say above 147 °C.2−4 The most widely explored AgIdoped FIC glasses are borate (AgI−Ag2O−B2O3), phosphate (AgI−Ag2O−P2O5), and molybdate (AgI−Ag2MoO4) glasses. A deep understanding of the transport properties of FIC glasses, besides facilitating the design of systems tailored for specific applications, represents a challenge for the basic research activity on the connection between atomic structure and transport properties in noncrystalline materials and can contribute to the issue of the relationship between short-time dynamics (local atomic vibrations) and long-time dynamics (relaxation times) in systems affected by non-negligible ionic or atomic mobility, not only ionic conductors but also glasses near the glass transition temperature5 or even fluids in the superctitical region.6 On more general grounds, the relevance of glassy materials for nonlinear optics7 and as hosts for luminescent sources8 demands an increasing knowledge of their structural and dynamical properties by refined investigation techniques. Although many approaches have been proposed, there is not yet any widely accepted model to explain the ionic conduction © 2013 American Chemical Society

Received: January 22, 2013 Revised: February 26, 2013 Published: February 28, 2013 6081

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the other side, the EXAFS measurement as a function of temperature for a fixed composition gives information on the connection between atomic thermal movements and conductivity. According to the EXAFS results here presented, the increase of ionic conductivity, due to the increase of AgI content or of temperature, is always accompanied by a reduction of the number of Ag ions directly coordinated to I, the width and asymmetry of the distribution of I−Ag distances being largely unaffected. The increase of conductivity caused by temperature or by AgI content is instead accompanied by a reduction or an augmentation of the average I−Ag distance, respectively. The article is organized as follows: short accounts of the experimental procedure and of the data analysis are given in sections 2 and 3, respectively. The results, say the cumulants of the I−Ag distribution of distances as a function of both temperature and AgI content, are presented in section 4. Section 5 is dedicated to the discussion of results, and conclusions are drawn in section 6.

value; it has been found that the majority of Ag ions involved in the conduction mechanism have a mixed iodine/oxygen coordination.27−30 From NMR and conductivity data, Mustarelli et al. modeled the ionic conductivity in AgI-based glasses in terms of a percolation between a low-conductivity phase (Ag only coordinated to O) and a high-conductivity one (Ag coordinated to both I and O).31 The evaluation and the possible refinements of these recent models could greatly benefit from the independent measurement of additional structural parameters. For that reason, the aim of the present work is to give direct insights on the modifications of the short-range order of the AgI doping salt and their connection to ionic conductivity, by investigating the local structure around iodine in AgI-doped silver−borate glasses AgI−Ag2O−B2O3 by means of extended X-ray absorption fine structure (EXAFS) spectroscopy. In principle, EXAFS is one of the most powerful experimental techniques for studying the local structure and dynamics around selected atoms in multicomponent noncrystalline materials. The first pioneering studies of the local structure of AgI−Ag2O−B2O3 glasses by EXAFS32,33 had been limited by the inadequacy of the standard procedure of data analysis, based on the harmonic approximation. The success obtained in the analysis of EXAFS of crystalline AgI by the cumulant expansion method34,35 led to the tentative extension of the cumulant approach to temperature-dependent EXAFS studies of AgI-doped silver−borate glasses. However, the puzzling temperature dependencies of the cumulants of the distribution of I−Ag distances obtained for the glasses, and in particular the reduction of distance with increasing temperature,36 could not be adequately explained. Actually, the effectiveness of the cumulant method is highly questionable for very disordered systems, such as liquids and, to a lesser extent, glasses.37 To take advantage of the heuristic power of the cumulant method in spite of the expected large extent of disorder, a new approach was devised to study the environment of iodine in AgI-doped silver−molybdate glasses.38 There, the experimental cumulants were considered to parametrize a short-range narrow component of the whole distribution of I−Ag distances, corresponding to the Ag ions more tightly bound to the I ions. The soundness of this interpretation was tested by Monte Carlo simulations and confirmed by the self-consistency of the final results. A further independent confirmation of the effectiveness of EXAFS for determining the environment of iodine was obtained from the study of a large number of FIC glasses with different compositions, where a neat correlation was found between the I−Ag distance measured by EXAFS and the activation energy for ionic conduction.39 In this article, an EXAFS study of the environment of iodine as a function of temperature and of AgI content in a wide number of AgI-doped silver−borate glasses is presented. The interpretation of the cumulant analysis of EXAFS follows the guidelines introduced in the previous work on molybdate glasses, where however only the temperature dependence had been thoroughly investigated.38 Both the increase of AgI content and the increase of temperature in silver borate glasses induce an increase of the ionic conductivity; the mechanisms involved are however different, and significantly different is the information obtained from EXAFS. EXAFS measurements as a function of the AgI content at a fixed temperature give information on the connection between local structure and activation energy. On

2. EXPERIMENTAL SECTION We investigated a set of glasses belonging to the family (AgI)x(Ag2O·nB2O3)1−x, where n=

[B2O3] [Ag 2O]

x=

[AgI] [AgI] + [Ag 2O]

The square brackets indicate the molar concentration of the chemical species.23 Our set of samples included glasses with n = 1 and x = 0.60−0.75, n = 2 and x = 0.10−0.60, n = 3 and x = 0.20−0.40, n = 4 and x = 0.10−0.55. The molar content of AgI varied from 2.2% (glass n = 4, x = 0.10) to 60.0% (glass n = 1, x = 0.75). The glasses had been prepared by the melt quenching technique, heating at 1100−1200 K weighted amounts of silver iodide, silver oxide, and boron oxide, and pouring the melts in stainless steel molds kept at room temperature.40 No evidence of crystalline structures was found by X-ray diffraction tests. To obtain homogeneous samples of uniform thickness, as required by EXAFS measurements, the glasses were powdered and then dispersed in alcohol and slowly deposited on polytetrafluoroethylene membranes. EXAFS measurements were done at the K edge of iodine (33.169 keV) at liquid nitrogen (LN) temperature, in order to explore the dependence of the local environment of iodine on both the AgI content (x) and the [B2O3]/[Ag2O] ratio (n). To investigate the effects of temperature, the glass (AgI)0.55(Ag2O·4B2O3)0.45 was measured in the temperature range between 39 and 298 K, the glass (AgI)0.30(Ag2O·4B2O3)0.70 at LN and room temperature. Measurements were made at LN also on crystalline β-AgI, which was used as a reference for EXAFS data analysis. EXAFS measurements were performed in transmission mode at the BM29 beamline of the European Synchrotron Radiation Facility, ESRF, in two different runs. A channel cut Si(311) monochromator was used, and the detectors were ionization chambers filled with krypton gas. The samples were mounted on the coldfinger of a helium flux cryostat equipped with an electrical heater, which allowed us to vary the temperature from 39 to 300 K. At least two spectra were collected for each glass composition and temperature, in order to allow an evaluation of the experimental uncertainty. 6082

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3. EXAFS DATA ANALYSIS The pre-edge signal was preliminarily subtracted from all the spectra by a straight line best fitting. The values of the photoelectron wave vector k were calculated with respect to an energy origin set at the maximum of the first derivative of each spectrum and successively all the edges were aligned to within 0.1 eV, in order to guarantee a resolution better than 0.001 Å in the evaluation of relative distances. The EXAFS function was determined as χ(k) = [μ(k) − μ1(k)]/μ0(k), where μ(k) is the experimental absorption coefficient, μ1(k) a spline polynomial best fitting the average behavior of μ(k), and μ0(k) a smooth Victoreen-like function with absolute values normalized to the absorption jump of each spectrum. The experimental EXAFS signals of selected spectra are shown in Figure 1.

Figure 2. Fourier transform of the EXAFS signals of silver−borate glasses at LN temperature, with different content of AgI: 2.2% (panel a, glass n = 4, x = 0.10), 19.6% (panel b, glass n = 4, x = 0.55), and 60.0% (panel c, glass n = 1, x = 0.75). For comparison, panel d shows the FT of crystalline β-AgI at 300 K. Dashed and solid lines are the imaginary part and the modulus, respectively.

values ΔC*n = C*n s − C*n r, as well as the ratio of coordination numbers Ns/Nr. Actually, only a limited number of polynomial coefficients C̃ n can be reasonably obtained from the finite EXAFS signal, which in the ratio method corresponds to a limited number of relative values ΔC̃ *n = C̃ *n s − C̃ *n r. The relationship between exact cumulants and polynomial coefficients has been thoroughly studied in ref 34. There, it has been shown that the polynomial coefficients, although not corresponding to the exact cumulants for highly disordered systems, allow anyway an effective parametrization of the relevant properties of the distribution (average value, width, and asymmetry). In the following, the term cumulant refers to the polynomial coefficients obtained from the data analysis. The physical interpretation of the distributions of I−Ag distances determined by EXAFS cumulants in FIC glasses has been discussed for AgI-doped silver−molybdate glasses.38 The same approach is followed here for borate glasses.

Figure 1. Top panel: EXAFS signal of glass n = 4, x = 0.10 (solid line) and n = 1, x = 0.75 (dashed line) at LN temperature. The two glasses contain 2.2% and 60.0% of AgI, respectively. Bottom panel: EXAFS signal of glass n = 4, x = 0.55 at 39 K and room temperature (solid and dashed line, respectively).

The kχ(k) functions, multiplied by a 10% Gaussian window, were Fourier transformed in the interval k = 2.5−14 Å−1. Figure 2 shows the Fourier transforms (FT) of selected spectra corresponding to different contents of AgI. All glasses display a striking similarity in their Fourier transforms. The comparison with both magnitude and imaginary part of the Fourier transform of crystalline β-AgI (panel d of Figure 2) strongly suggests that the structure between about 1.5 and 3 Å is only due to the contribution of nearest-neighbors Ag ions (although not all Ag ions necessarily contribute to it). Owing to the effect of disorder, the contributions from farther neighbors are negligible. The structure between about 1.5 and 3 Å was Fourier backtransformed and the filtered EXAFS signal analyzed by the cumulant approach and the ratio method.41−43 The first (C1*) and second (C*2 ) cumulants measure the average value and the variance of the distribution of nearest-neighbor distances, respectively. The higher order cumulants characterize the deviation from the Gaussian shape; in particular, the third cumulant (C*3 ) measures the asymmetry of the distribution. The ratio method separately compares phases and amplitudes of the EXAFS signals of a sample (s) with respect to a reference (r). In principle, the ratio method should give the relative

4. RESULTS The presentation of results is divided in two parts. The first part is dedicated to the dependence of the EXAFS cumulants on the AgI content for all considered glasses at LN temperature. The second is dedicated to the dependence of the EXAFS cumulants on temperature for the glass n = 4, x = 0.55. 4.1. Dependence on AgI Content. The analysis of the EXAFS spectra of the glasses as a function of the AgI content was performed using the LN spectrum of crystalline β-AgI as reference. The four panels of Figure 3 show the parameters obtained from the EXAFS analysis plotted against the percent of AgI content, calculated as 100x/[1 + n(1 − x)]. The difference of the average I−Ag distance in glasses with respect to crystalline β-AgI (Figure 3a) progressively increases from about −0.03 Å for glasses with low AgI content to about +0.04 Å for glasses with high AgI content. A clear correlation exists between AgI content and I−Ag distance: glasses with higher content of AgI display longer I−Ag distances, 6083

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Figure 4. Temperature dependence of the average distance (panel a), coordination number (panel b), variance (panel c), and skewness parameter (panel d) of the short-range I−Ag distance distribution in (AgI)0.55:(Ag2O:4B2O3)0.45 glass (solid circles) and crystalline β-AgI (open circles). In panel a, the distance variations are reported with respect to the glass measured at 39 K.

Figure 3. Average I−Ag distance variation (panel a, with respect to crystalline β-AgI), coordination number (panel b), variance (panel c), and skewness parameter (panel d) of the short-range I−Ag distance distribution in (AgI)x(Ag2O·nB2O3)1−x glasses at LN temperature, plotted against the AgI content. Symbols refer to the glasses with n = 1 (open squares), n = 2 (full squares), n = 3 (open circles), and n = 4 (full circles).

and x = 0.55, which contains about 19.6 molar percent of AgI. For comparison, also the parameter values for crystalline β-AgI have been reported.38 In the glass, the average I−Ag distance shrinks by about 0.02 Å between 39 and 298 K (panel a); on the contrary, in crystalline β-AgI, the distance expands. Also, the coordination number (panel b) is reduced when the temperature increases, from about 3.6 to 3.1, while the variance C*2 and the skewness parameter C3*/(C2*)1.5 (panel c and d, respectively) are nearly independent of the temperature: C2* increases from about 0.013 to 0.015 Å2; C*3 /(C*2 )1.5 is nearly constant around the value 0.45. These variations are much weaker than those of crystalline β-AgI, where in the same temperature range C2* increases from about 0.003 to 0.014 Å2, C3*/(C2*)1.5 from about 0 to 0.45. In a previous EXAFS study at the I L3 edge of the same glass, n = 4 and x = 0.55, the dependence on temperature of the second cumulant, there denoted as σ2, was found much stronger that in the present work and similar to that of β-AgI.44 Actually, the analysis of EXAFS at the I L3 edge had been performed by imposing a constant value of the coordination number, N = 4, to reduce the number of fitting parameters in view of the shortness of the available signal. In agreement with

independently of the chemical composition of the host glassy matrix, say of the ratio [B2O3]/[Ag2O]. Figure 3b displays the behavior of the I−Ag coordination number. The absolute value has been determined through the direct comparison with the coordination number of crystalline β-AgI, which is 4 at LN temperature. The I−Ag coordination number decreases with increasing the AgI content, quite independently of the chemical composition of the host glassy matrix. Figure 3c,d shows the variance C*2 and the skewness parameter C3*/(C2*)1.5 of the I−Ag distribution; the absolute values of the second and third cumulant were obtained from the difference with respect to crystalline β-AgI, where the absolute values at LN temperature are C*2 ≃ 0.0043 Å2 and C*3 ≃ 0.5 × 10−4, respectively.38 All glasses exhibit similar values of variance and skewness parameter, independently of their chemical composition (and ionic conductivity). 4.2. Dependence on Temperature. Figure 4 shows the temperature dependence of the parameters describing the short-range I−Ag distance distribution of the glass with n = 4 6084

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It is reasonable to assume that the silver ions more distant from iodine ions, say less tightly bound, are more easily involved in the ionic conduction, so that the short-range distribution is progressively spoiled on the high-distance side when temperature increases, giving rise to the reduction of the average I−Ag distance measured by EXAFS. Correspondingly, also the static contribution to the width and asymmetry of the distribution is reduced, to a good extent counterbalancing the increase of width and asymmetry induced by thermal motion. In crystalline solids unaffected by ionic or atomic mobility, the width of the nearest-neighbor distribution, measured by the second cumulant, corresponds to the mean square relative displacement (MSRD) of the atomic pair induced by thermal vibrations, whose temperature dependence is well reproduced by Einstein-like theoretical models. The correlation of nearestneighbors motion is strong in tetrahedrally coordinated systems, such as Ge or β-AgI. In amorphous systems, again unaffected by ionic or atomic mobility, the width of the distribution is determined by the sum of a MSRD contribution, generally similar to that of the crystalline counterpart and the temperature-independent contribution of static disorder.53 The situation is quite different in systems affected by nonnegligible ionic or atomic mobility. Here, the temperature dependence of the width of the distribution of nearest-neighbor distances is determined not only by the relative local vibrations but also by the modifications induced by atom mobility; one can also expect that the modification of the local disordered structure induces a temperature dependence of the effect of correlation of atomic motion. The relationship between short-time dynamics (local atomic vibrations) and long-time dynamics (relaxation times) is a fundamental issue for ionic conductors and for glasses near the glass transition temperature. To our knowledge, up to now, no way of directly disentangling the two effects by EXAFS has been devised. The interpretation of EXAFS cumulants presented here can be considered as a first step in this direction. The soundness of this interpretation is supported by the results of an EXAFS study of the β → α transition in AgI made by Yoshiasa and Maeda;55 particularly significant is that those authors found a weaker dependence on temperature of the second cumulant in the superconducting α phase than in the normal β phase. 5.2. Dependence on AgI Content. Since the ionic conductivity increases when the AgI content increases, it is convenient to plot for each glass the I−Ag distance and the coordination number directly against the dc ionic conductivity measured at room temperature40 (Figure 5). Width and asymmetry of the distributions are weakly affected by the AgI content (Figure 3c,d). They are anyway much larger than in β-AgI, indicating a high degree of local structural disorder. The variation of distance and coordination number further indicate that the local structure changes with the amount of AgI. These results are consistent with previous XANES measurements at the I L3 edge of iodine in the glasses with n = 4 and x = 0.1−0.5. Not only are the XANES of glasses clearly different from those of β-AgI, they also show a progressive variation when the AgI content is varied.56 The reduction of the coordination number when the AgI content increases can be qualitatively explained, as for the temperature dependence, as due to a progressive increase of Ag ions in the conduction pathway. The increase of the I−Ag distance can be, again qualitatively, connected to the increase of the free volume, which is in turn responsible for the increase of

the analytical expressions derived in ref 45, the discrepancy of those old results with respect to the present ones can be quantitatively accounted for by the neglect of the variability of the coordination number. The behavior observed in this work for silver−borate glasses is similar to the behavior found in AgI-doped silver−molybdate glasses (with AgI content up to 60%), where both I−Ag distance and coordination number similarly decrease when the temperature increases.38 A similar behavior is also observed in the glass with n = 4 and x = 0.30 (7.9% of AgI content), where, in going from LN to room temperature, the I−Ag distance decreases by about 0.01 Å and the coordination number decreases from about 3.8 to 3.3.

5. DISCUSSION Both the increase of AgI content and the increase of temperature induce an increase of ionic conductivity. In the first case, one deals with a structural effect, and in the second case with a dynamical effect. According to EXAFS, the number of Ag ions coordinated to iodine decreases when the AgI content or the temperature increases (Figures 3 and 4, panel b). A striking difference concerns instead the nearest-neighbor distance I−Ag: it increases when the AgI content increases, while it decreases when the temperature increases (Figures 3 and 4, panel a). Width and asymmetry of the distribution of I−Ag distances undergo no significant variations. 5.1. Dependence on Temperature. The dependence of EXAFS cumulants on temperature is apparently inconsistent with the behavior commonly encountered in other systems. The interpretation of the first cumulant behavior in terms of a bond contraction of purely thermal origin is incompatible with the positive macroscopic expansion measured by dilatometric techniques46−49 as well as with the experimental evidence that the nearest-neighbor distance increases with temperature also in materials with negative macroscopic thermal expansion.50−52 Besides, the very weak increase of the second cumulant and of the skewness parameter with respect to β-AgI contrasts with the behavior found in other cases, where the thermal effects on EXAFS is very similar in amorphous systems and in their crystalline counterparts.54 The reduction of the coordination number with increasing temperature is the clue for a global interpretation of cumulants, which was introduced and tested in the previous work on AgIdoped silver−molybdate glasses,38 which are affected by static disorder and by conduction properties comparable to those of silver−borate glasses. The EXAFS cumulants are considered to parametrize a short-range narrow component of the whole distribution of I−Ag distances, corresponding to the Ag ions more tightly bound to the I ions; the remaining long-range tail of the distribution, which escapes EXAFS detection (more precisely, which gives a negligible total I−Ag EXAFS signal), contains Ag ions directly involved in conduction. Consistently with this interpretation, the decrease of the coordination number is correlated with the increase of the ionic conductivity and is attributed to the progressive depletion of the short-range I−Ag distribution due to the migration of more and more Ag ions within the conduction pathways. Conduction Ag ions contribute to the long-range component of the whole I−Ag distribution that does not contribute to EXAFS. According to Monte Carlo simulations on molybdate glasses,38 the distribution tail should extend at least in the range 3.4 to 4 Å. 6085

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been investigated by EXAFS as a function of both AgI content and temperature. The experimental EXAFS cumulants have been interpreted as referring not to the whole distribution of I− Ag distances but only to its short-range component. The remaining highly disordered long-range component, which escapes EXAFS detection, is connected to Ag ions moving along the conduction pathways. It has been found that glasses with higher content of AgI (i.e., higher ionic conductivity) display longer I−Ag distances and lower coordination number, independently of the chemical composition of the host-glassy-matrix. Moreover, both the average I−Ag distance and the coordination number decrease with the temperature increasing. These local modifications of the I−Ag distance probed by EXAFS have been interpreted as monitoring the growth of ionic diffusion, more precisely, as monitoring the progressive transition of Ag ions from the short-range to the highly disordered long-range component of the whole I−Ag distribution. These experimental results, besides being consistent with some recent models of conduction, according to which the pathways for ionic diffusion are characterized by mixed iodine and oxygen environments, are an excellent testbench for more detailed theoretical models.

Figure 5. I−Ag distance variation (top panel) and coordination number (bottom panel) potted against the dc ionic conductivity at room temperature. Symbols refer to the same glasses as those in Figure 3.

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the pathway volume for ionic conduction, characterized by mixed iodine and oxygen environments.28−31 The expansion of the I−Ag distance can be attributed to the progressive growth of the number of Ag ions with mixed coordination with both oxygen and iodine: the attraction of Ag ions by the oxygen ions causes an increase of the mean I−Ag distance. An alternative, less qualitative interpretation can be based on the bond valence model. The valence of iodine is expressed as

Vi =

Corresponding Author

*(A.S.) E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge the European Synchrotron Radiation Facility (ESRF) for financial support (projects HS-1666 and HD-114) and O. Mathon and the staff of BM29 (now BM23) at ESRF for technical assistance. We are grateful to F. Rocca and G. Dalba for experimental help and for stimulating discussions.

∑ Sij j

(1)

where the sum is over all the bonds of an I anion with Ag cations, and the bond valences are given, using the same parameters as Adams and Swenson,28−30 by ⎛ 2.08 − R ij ⎞ Sij = exp⎜ ⎟ ⎝ 0.53 ⎠

AUTHOR INFORMATION

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REFERENCES

(1) Vashista, P.; Mundy, J. N.; Shenoy, G. K. Fast Ion Transport in Solids; Elsevier: New York, 1979. (2) Minami, T. J. Non-Cryst. Solids 1985, 73, 273. (3) Ingram, M. D. Phys. Chem. Glasses 1987, 28, 215. (4) Tatsumisago, M.; Shinkuma, Y.; Minami, T. Nature 1991, 354, 217. (5) Larini, L.; Ottochian, A.; De Michele, C.; Leporini, D. Nat. Phys. 2008, 4, 42. (6) Simeoni, G. G.; Bryk, T.; Gorelli, F. A.; Krisch, M.; Ruocco, G.; Santoro, M.; Scopigno, T. Nat. Phys. 2010, 6, 503. (7) Majchrowski, A.; Ebothe, J.; Gondek, E.; Ozga, K.; Kityk, I. V.; Reshak, A. H.; Łukasiewicz, T. J. Alloys Compd. 2009, 485, 29. (8) Satyanarayana, T.; Brik, M. G.; Venkatramaiah, N.; Kityk, I. V.; Plucinski, K. J.; Ravikumar, V.; Veeraiah, N. J. Am. Ceram. Soc. 2010, 93, 2004. (9) Ravaine, D. J. Non-Cryst. Solids 1985, 73, 287. (10) Glass, A. M.; Nassau, K. J. Appl. Phys. 1980, 51, 3756. (11) Rousselot, C.; Malugani, J. P.; Mercier, R.; Tachez, M.; Chieux, P.; Pappin, A. J.; Ingram, M. D. Solid State Ionics 1995, 78, 211. (12) Tachez, M.; Mercier, R.; Malugani, J. P.; Dianoux, A. J. Solid State Ionics 1986, 20, 93. (13) Ingram, M. D. Philos. Mag. B 1989, 60, 729. (14) Funke, K. Prog. Solid State Chem. 1993, 22, 111. (15) Grande, T. Phys. Chem. Glasses 1997, 38, 327. (16) Sidebottom, D. L. Phys. Rev. Lett. 1999, 83, 983. (17) Fontana, A.; Rocca, F.; Fontana, M. P. Phys. Rev. Lett. 1987, 58, 503.

(2)

The valence saturated by the bonds measured by EXAFS progressively decreases from about 1 for the glass with 2.2% AgI content to about 0.8 for the glass with 60% AgI content. If we assume that the total valence is Vi = 1, independent of the AgI content, the bonds escaping EXAFS detection, related to Ag ions in the conduction pathways, should be able to guarantee the residual valence, which increases from 0 to 0.2 when the AgI content increases. If, according to the Monte Carlo simulations,38 one further assumes that the I−Ag distances that do not contribute to EXAFS are spread over a range from 3.4 to 4 Å, the number of these invisible Ag ions should be at least two to guarantee that the total valence is Vi = 1. By converse, if we assume that the number of Ag ions in the conduction pathway, neighbors to iodine but escaping EXAFS detection, increases when the AgI content increases, then the increase of the I−Ag distance detected by EXAFS is necessary to guarantee the correct valence of the iodine ion.

6. CONCLUSIONS In this work, the local environment around iodine in AgI-doped silver−borate glasses with different chemical compositions has 6086

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The Journal of Physical Chemistry C

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(18) Maass, P.; Bunde, A.; Ingram, M. D. Phys. Rev. Lett. 1992, 68, 3064. (19) Bischoff, C.; Schuller, K.; Beckman, S. P.; Martin, S. W. Phys. Rev. Lett. 2012, 109, 075901. (20) Shaw, A.; Ghosh, A. J. Phys. Chem. C 2012, 116, 24255. (21) Larink, D.; Eckert, H.; Reichert, M.; Martin, S. W. J. Phys. Chem. C 2012, 116, 26162. (22) Feller, S. A.; Dell, W. J.; Bray, P. J. J. Non-Cryst. Solids 1982, 15, 21. (23) Chiodelli, C.; Magistris, A.; Villa, M.; Bjorksta, J. L. J. Non-Cryst. Solids 1982, 51, 143. (24) Carini, G.; Cutroni, M.; Fontana, A.; Mariotto, G.; Rocca, F. Phys. Rev. B 1984, 29, 3567. (25) Swenson, J.; Börjesson, L.; McGreevy, R. L.; Howells, W. S. Phys. Rev. B 1997, 55, 11236. (26) Swenson, J.; Börjesson, L. Phys. Rev. Lett. 1996, 77, 3569. (27) Karthikeyan, A.; Rao, K. J. J. Phys. Chem. B 1997, 101, 3105. (28) Adams, S.; Swenson, J. Phys. Rev. Lett. 2000, 84, 4144. (29) Adams, S.; Swenson, J. Phys. Rev. B 2000, 63, 054201. (30) Swenson, J.; Adams, S. Phys. Rev. B 2001, 64, 24204. (31) Mustarelli, P.; Tommasi, C.; Magistris, A. J. Phys. Chem. B 2005, 109, 17417 and references therein. (32) Dalba, G.; Fontana, A.; Fornasini, P.; Mariotto, G.; Masullo, M. R.; Rocca, F. Solid State Ionics 1983, 9&10, 597. (33) Dalba, G.; Fornasini, P.; Rocca, F. J. Non-Cryst. Solids 1990, 123, 310. (34) Dalba, G.; Fornasini, P.; Rocca, F. Phys. Rev. B 1993, 47, 8502. (35) Dalba, G.; Fornasini, P.; Gotter, R.; Rocca, F. Phys. Rev. B 1995, 52, 149. (36) Dalba, G.; Fornasini, P.; Grisenti, R.; Rocca, F. J. Non-Cryst. Solids 2004, 345&346, 7. (37) Filipponi, A. J. Phys.: Condens. Matter 2001, 13 R1. (38) Sanson, A.; Rocca, F.; Dalba, G.; Fornasini, P.; Grisenti, R. New J. Phys. 2007, 9, 88. (39) Sanson, A.; Rocca, F.; Armellini, C.; Dalba, G.; Fornasini, P.; Grisenti, R. Phys. Rev. Lett. 2008, 101, 155901. (40) Chiodelli, G.; Campari Viganǒ, G.; Flor, G.; Magistris, A. Solid State Ionics 1983, 8, 311. (41) Bunker, G. Nucl. Instrum. Methods Phys. Res. 1983, 207, 437. (42) Crozier, E. D.; Rehr, J. J.; Ingalls, R. In X-ray Absorption: Principles, Applications, Techniques of EXAFS, SEXAFS and XANES; Koningsberger, D. C., Prins, R., Eds.; John Wiley & Sons: New York, 1988. (43) Fornasini, P.; Monti, F.; Sanson, A. J. Synchrotron Radiat. 2001, 8, 1214. (44) Rocca, F.; Dalba, G.; Fornasini, P.; Tomasi, A. Solid State Ionics 1992, 53−56, 1253. (45) Sanson, A. J. Synchrotron Radiat. 2009, 16, 864. (46) Uhlmann, D. R.; Shaw, R. R. J. Non-Cryst. Solids 1969, 1, 347. (47) Shelby, J. E. J. Am. Ceram. Soc. 1983, 66, 225. (48) Boulos, E. N.; Kreidl, N. J. J. Am. Ceram. Soc. 1971, 54, 368. (49) D’Angelo, G. Private communication. (50) Sanson, A.; Rocca, F.; Dalba, G.; Fornasini, P.; Grisenti, R.; Dapiaggi, M.; Artioli, G. Phys. Rev. B 2006, 73, 214305. (51) Fornasini, P.; Ahmed, S. I.; Sanson, A.; Vaccari, M. Phys. Status Solidi B 2008, 245, 2497. (52) Ahmed, S. I.; Dalba, G.; Fornasini, P.; Vaccari, M.; Rocca, F.; Sanson, A.; Li, J.; Sleight, A. W. Phys. Rev. B 2009, 79, 104302. (53) Dalba, G.; Fornasini, P.; Diop, D.; Grazioli, M.; Rocca, F. J. NonCryst. Solids 1993, 164−166, 159. (54) Dalba, G.; Fornasini, P.; Grazioli, M.; Rocca, F. Phys. Rev. B 1995, 52, 11034. (55) Yoshiasa, A.; Maeda, H. Solid State Ionics 1999, 121, 175. (56) Dalba, G.; Fornasini, P.; Fontana, A.; Rocca, F.; Burattini, E. Solid State Ionics 1988, 28−30, 713.

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dx.doi.org/10.1021/jp400735n | J. Phys. Chem. C 2013, 117, 6081−6087