Mixed Alkaline-Earth Effect in the Metastable Anion Conductor Ba1

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Mixed Alkaline-Earth Effect in the Metastable Anion Conductor Ba1
xCaxF2 (0 e x e 1): Correlating Long-Range Ion Transport with Local Structures Revealed by Ultrafast 19F MAS NMR A. D€uvel,*,† B. Ruprecht,† P. Heitjans,† and M. Wilkening*,†,‡ †

Institute of Physical Chemistry and Electrochemistry, Gottfried Wilhelm Leibniz University Hannover, Callinstrasse 3a, D-30167 Hannover, Germany ‡ Institute for Chemistry and Technology of Materials, Graz University of Technology, Stremayrgasse 9, A-8010 Graz, Austria

bS Supporting Information ABSTRACT: Fast ion conductors are urgently needed in many research areas of materials science. Advanced preparation strategies take advantage of an interplay of structural disorder, nanosize effects, and metastability. Getting access to detailed insights into the microstructure of such solids is crucial to identify the origins of fast ion conduction. High-resolution and high-sensitive spectroscopic techniques are well-suited to meet this challenge. Here, ion transport properties of a highly conducting, metastable fluoride with two isovalent cations were interrelated with the microscopic, atomic-scale structure probed by ultrafast 19F magic angle spinning (MAS) nuclear magnetic resonance (NMR). Nanocrystalline samples of Ba1
xCaxF2 (0 e x e 1) were prepared according to a mechanochemical route from BaF2 and CaF2. The resulting DC ion conductivity, when plotted as a function of x, passes through a well-developed maximum, which is located at xm = 0.5, while the associated activation energy Ea shows a minimum at xm. As revealed by 19F MAS NMR, five magnetically inequivalent F sites are present in the cation-mixed fluorides. These sites are characterized by a distinct number of Ba and Ca cations in the first coordination shell: [Ba]n[Ca]4
n (0 e n e 4). The mixed sites with n = 1,2,3 dominate the NMR spectra at intermediate values of x. Presumably, the mixed cation sublattice, causing the metastability of the compounds, influences both the formation energy of, for example, F interstitials, as well as the migration energy leading to the fast ion conduction observed.

I. INTRODUCTION During the past years, single- and multiphase solid fluorine ion conductors in quite different structural forms, such as glasses and glass ceramics,1
13 single crystals,14
32 as well as micro- and nanocrystalline33
55 materials, have been the topic of numerous impedance spectroscopic studies. The aim of such studies is to understand ionic conduction mechanisms by exploring the features of electrical relaxation dynamics in solids. This ongoing activity is stimulated by the increasing effort to make fast F
conductors available for a number of technical applications. In particular, highly conducting fluorides are needed for a range of different types of electrochemical devices such as energy storage systems or (gas) sensors.17,56
59 In many cases, the ionic conductivity of a given binary or ternary fluoride can be influenced by involving two or more substitutional iso- or aliovalent cations.17 As a result, the DC-conductivity σDC, when plotted as a function of composition, may pass through a maximum or minimum, which is usually associated with a contrary behavior of the activation energy Ea.3,4,17
19 Despite the profound interpretation of the diverse impedance data presented in the literature so far, often an atomic-scale structural description of such mixed fluorides is, however, missing. The latter is essential r 2011 American Chemical Society

for the comprehensive description of the structure
property relationships governing anion transport. Regarding ternary fluorides, Sarma et al.19 as well as Sorokin et al.18 have observed that in single crystals of Ca1
ySryF2 (0 e y e 1) the F
DC-conductivity σDC(x) shows a maximum at x = 0.5; see also ref 19. Cubic CaF2 (space group Fm3m) and isostructural SrF2 easily form a solid solution, which is probably due to the similarity of the ionic radii of the two cations.19,60 In contrast, under conventional solid-state synthesis conditions using high temperatures, mixing of CaF2 with cubic BaF2 (Fm3m) usually leads to phase segregation resulting in Ba- and Ca-rich regions.60,61 However, the formation of a homogeneous mixed phase over the whole composition range can be forced by the application of high-energy ball milling. Doing so, the binary source materials have been mechanochemically converted into highly metastable Ba1
xCaxF2 at ambient temperature. σDC of the resulting nanocrystalline powders passes through a distinct maximum at intermediate compositions. Around x = 0.5, the Received: September 2, 2011 Revised: October 20, 2011 Published: October 20, 2011 23784

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The Journal of Physical Chemistry C exceptionally high value of approximately 1.4 mS cm
1 (T = 554 K) is reached; see also refs 62 and 63. The nanometer-sized crystallites (ca. 20
50 nm in diameter) are anticipated to be characterized by a high defect density, which is introduced during the milling procedure.62,63 As compared to single-phase nanocrystalline BaF2, the increase of σDC turns out to be about 2 orders of magnitude.62 It might be the direct consequence of the combination of both (i) the metastability of the cation-mixed crystal structure and (ii) the associated (localized) substitutional disorder. Presumably, this leads to a highly conducting phase with frozen-in defects and low migration (or activation) barriers being responsible for the fast, long-range ion transport observed. To a certain degree, (macroscopic) space charge effects64
67 at the contact area of individual crystallites might also contribute to σDC. These have been shown to considerably govern the ion conductivity in structurally well-defined BaF2:CaF2 heterolayers prepared by molecular beam epitaxy.33,68 Similar to glassy materials, the disorder introduced during mechanical treatment makes it difficult to gain information on structural properties from an atomic-scale point of view by XRPD, for example. Even the use of 19F (spin-1/2) magic angle spinning (MAS) NMR spectroscopy requires high magnetic fields and large spinning speeds (up to 60 kHz, see below) to achieve a sufficient resolution in some cases. Here, we have applied 19F ultrafast MAS NMR carried out at magnetic fields of 11.7 T and 14.1 T, respectively, to uncover the various magnetically inequivalent F sites in structurally disordered, nanocrystalline (Ba, Ca)F2. NMR has been used as a diagnostic tool to gather information on the alkaline earth ions in the direct neighborhood of the F anions; see also refs 62, 63, 69
72. To achieve a sufficiently high spectral resolution, here, the NMR spectra have been recorded at an ultrafast spinning speed of 60 kHz.

II. EXPERIMENT Nanocrystalline samples of Ba1
xCaxF2 (0 e x e 1) were prepared at ambient temperature by high-energy ball milling of BaF2 (99.99%, Sigma Aldrich) together with CaF2 (99.99%, Alfa Aesar) in a Fritsch Pulverisette 7 (premium line) planetary mill. The total mass of the mixture was about 2 g. A grinding beaker made of stabilized ZrO2 with a volume of 45 mL was employed. The mixture was mechanically treated between 6 and 99 h using 140 milling balls (ZrO2, 5 mm in diameter) at 600 rpm. For comparison, the ternary fluorides Ba0.5Sr0.5F2 and Ca0.5Sr0.5F2 have also been prepared using the same milling conditions. Sample characterization of the powders was carried out at room temperature using X-ray powder diffraction (XRPD) with a Bruker D8 Advance operating with Cu Kα radiation at 40 kV. For the impedance measurements, an HP 4192 A analyzer as well as a Novocontrol Concept 80 broadband dielectric spectrometer were employed. Details of the two setups have been described in ref 71 recently. Prior to the measurements, the powder samples were uniaxially cold-pressed at 1 GPa to cylindrical pellets (8 mm in diameter and approximately 1 mm in thickness). Electrodes were applied by Au evaporation using an Edwards 306. If not stated otherwise, 19F MAS NMR spectra were recorded with a Bruker Avance III spectrometer operating at 471 MHz. The NMR spectra were acquired using a single excitation pulse whose length was approximately 2 μs. The spinning speed was νrot = 60 kHz (1.3 mm rotor) with room-temperature bearing gas. The ppm-scale of the NMR spectra was referenced to C6F6.

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Figure 1. XRPD patterns of mechanosynthesized Ba1
xCaxF2 (0 e x e 1) using a planetary mill (600 rpm) and a ZrO2 vial set. For example, the continuous shift of the peak at 41.2
(nanocrystalline cubic BaF2) toward 47.0
reveals the formation of a solid solution (see also the peak at approximately 25
). “1” indicate the peaks of abraded ZrO2 by which two samples are contaminated. Under the present milling conditions, orthorhombic BaF2, being one of the high-pressure modifications of BaF2, shows up at small values of x. However, these additional phases do not show any significant effect on the DC-conductivity, which seems to be predominantly governed by the alkaline-earth effect.

III. RESULTS AND DISCUSSION In the stacked line plot of Figure 1, the X-ray powder diffraction patterns of Ba1
xCaxF2 (0 e x e 1) recorded at room temperature are shown. Starting from nanocrystalline pure BaF2, the XRPD peaks shift toward larger diffraction angles the more Ca ions are introduced during milling. As expected, this clearly reflects lattice contraction. Finally, at x = 0.9, the peaks have almost reached those positions being characteristic of pure nanocrystalline CaF2. These are identical to the peak positions of a micrometer-sized CaF2 sample serving as internal reference. The successful incorporation of all of the Ca ions depends on both x and milling time td. At intermediate values of x, the milling time, that is, the duration of the mechanochemical reaction, has to be increased to td = 99 h to obtain XRPD patterns from which it can be concluded that a large amount of separate Ba- or Ca-rich phases is absent. Below x = 0.3 and above x = 0.65, milling times shorter than 99 h are sufficient to prepare solid solutions; increasing td does not lead to any further changes of the XRPD patterns of the formed (Ba,Ca)F2 phase (not shown here for the sake of brevity). The same is valid for the pure end members; a short td of 6 h is sufficient to reach the final XRPD pattern, which 23785

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Figure 2. Variation of the DC-conductivity σDC (determined at T = 554 K) as well as the activation energy Ea with Ca-content x in nanocrystalline Ba1
xCaxF2. Note that the observed trends turn out to be independent of milling time td when varied between 6 and 99 h. At intermediate compositions, the F environments [Ba]n[Ca]4
n with n = 1,2,3 dominate the 19F MAS NMR spectra (see below). For comparison, the values of σDCT and Ea of M1
ySryF2 with M = Ba, Ca are also included (see the dashed lines). The DC-conductivity of nanocrystalline SrF2, which lies between those of BaF2 and CaF2 at 554 K, is indicated by a horizontally drawn dashed line.

differs from that of the respective coarse-grained (micrometersized) counterpart only in peak widths. It is worth mentioning that in the present case there are no indications of significant amounts of amorphous material formed by ball-milling the binary fluorides. This has been studied in detail in a preceding study on samples of (Ba,Ca)F2 prepared in a very similar way; see ref 63. At milling times that ensure full incorporation of Ca, the corresponding (mean) lattice constant a follows Vegard’s law. This is the expected behavior of a solid solution. Using the formalism introduced by Williamson and Hall,73 from XRPD peak broadening of pure BaF2 (as well as CaF2), a mean crystallite size Ædæ of 25 nm can roughly be estimated. The additional broadening observed for 0.1 < x < 0.9 might be ascribed to an even smaller value of Ædæ, which could be the result of grinding two ceramics differing in hardness. Alternatively, this broadening might be due to internal strain (the parameter ε ranges from 0.004 to 0.006) and/or a distribution of lattice constants as a result of cation mixing, that is, substitutional disorder. The latter is suggested by the 19F MAS NMR spectra presented below. Interestingly, the difference in peak width is not reflected in the σDC values shown in Figure 2. The same is valid regarding the circumstances that (i) at x < 0.3 a small amount of orthorhombic BaF2 is formed and (ii) two samples (those at x = 0.6 and x = 0.65) are slightly contaminated by abraded ZrO2. The DC-conductivity values of Figure 2 (which were plotted as log(σDCT) versus x) also show that the same trend is already observed for td = 6 h. Hence, even if the formation of a solid solution is not completely finished, a network of fast, long-range diffusion pathways has already been formed leading to the observed maximum

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of σDC with its corresponding minimum of Ea (Figure 2). The same holds for the pure end members; increasing td does not lead to any further increase of ionic conductivity. Let us note that the σDC values have been read out from well-developed DC plateaus of the conductivity isotherms σ0 (ν) (see Figure S1, Supporting Information). σDCT strictly follows Arrhenius behavior within the temperature range investigated (425
625 K, see also Figure S2, Supporting Information). Annealing the samples for many hours at temperatures higher than 700 K causes decomposition of the samples, which can be easily proved by XRPD; the diagnostic peaks of BaF2 and CaF2 show up in the corresponding XRPD patterns (Figure S3). At x ≈ 0.5, the DC-conductivity turns out to be about 1.4 mS cm
1 (554 K), and the activation energy amounts to 0.62 eV. These values are in very good agreement with those estimated from our previous measurements of σDC on a CaF2-rich, mixed (Ba,Ca)F2 sample (∼1.8 mS cm
1, 0.57 eV).62,63 Note that the latter was obtained using a different milling equipment (vial set of tungsten carbide) and under different milling conditions (Pulverisette 6 mill, tmill = 3 h). Under these conditions, the overall formation of a solid solution has not been completed yet.62,63 Hence, the previously investigated samples are very similar to those that have been studied here but milled just for 6 h (see above and Figure 2). As compared to the preceding studies,62,63 slight differences in activation energies and DC-conductivities of single phase, nanocrystalline BaF2 (as well as CaF2) can also be explained by variations of the milling conditions such as the vial set and type of mill used as well as the milling times chosen. The microscopic reasons for the observed maximum shown in Figure 2 might be recognized by regarding the 19F MAS NMR spectra of the cation-mixed fluorides Ba1
xCaxF2 shown in Figure 3. In accordance with a recent study,63 the 19F MAS NMR spectra of pure BaF2 and CaF2, even when mechanically treated for many hours in a planetary mill, are composed of a single NMR line located at 152 and 58 ppm, respectively.62,63,74 As compared to the coarse-grained starting material, the line width slightly increases by approximately 1
2 ppm, which is due to structural disorder introduced.63 In the case of the pure fluorides, new NMR lines do not emerge with increasing milling time.75 This is in contrast to the mixed samples with 0 < x < 1 revealing, even after a very short milling period of just a few hours, distinct NMR lines greatly varying in chemical shift δiso. The corresponding values, which have been referenced to C6F6, are indicated in Figure 3; they range from 55 to 182 ppm. δiso varies with composition and scales linearly with x, that is, with the lattice constant a. Thus, the behavior of δiso(x) is the NMR analogue of Vegard’s law. This observation is very similar to that found for (Ba,Sr)LiF3, which has been investigated quite recently.71 Taking into account the composition x and the number of generatable mixed sites [Ba]n[Ca]4
n with n = 1,2,3, the assignment presented in Figure 3 can be readily understood (each F anion is tetrahedrally coordinated by a combination of four alkaline earth ions). Recently, the 19F MAS NMR spectra of Ca1
ySryF2,72 Ba1
ySryF2, and Ba1
ySryLiF3, see ref 71, have been interpreted in the same way. For comparison, the corresponding 19 F MAS NMR spectra of mechanosynthesized M1
ySryF2 (y = 0.5) with M = Ba,Ca are also shown in Figure 4. In the case of Ca0.5Sr0.5F2, the five distinct 19F NMR lines, altogether covering a chemical shift range from 53 to 89 ppm, are equally spaced by Δ ≈ 10 ppm. Δ increases by a factor of 2.5 when Ba is substituted for Ca. Presumably, the δiso values of 19F are affected by a transfer of positive electron spin density from the Ba centers. This observation 23786

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Figure 4. 19F MAS NMR spectra of Ba0.5Ca0.5F2 (471 MHz) and M0.5Sr0.5F2 with M = Ba, Ca. Note that the spectra of the Sr-containing fluorides have been recorded at a magnetic field of 14.1 T, which corresponds to a nominal resonance frequency of 565 MHz. The 19F NMR isotropic chemical shift of pure SrF2 is 78 ppm. The Ba0.5Sr0.5F2 sample reveals a small contamination with CaF2. NMR spinning sidebands are marked with asterisks.

Figure 3. 19F MAS NMR spectra of Ba1
xCaxF2, which have been recorded at ambient bearing gas temperature and a spinning speed of 60 kHz. The nominal resonance frequency was 471 MHz. For comparison with the δiso values indicated for the various [Ba]n[Ca]4
n (0 e n e 4) environments, the NMR signals of pure, nanocrystalline BaF2 and CaF2, which have been prepared in the same way as the mixed samples, show up at 152 and 58 ppm. NMR spinning sidebands are marked with asterisks.

is associated with an increase of the NMR line widths. Additionally, the structural disorder introduced by mixing two isovalent cations largely differing in ionic radii (rCaF2 = 106 pm, rSrF2 = 127 pm, and rBaF2 = 143 pm) is expected to influence the NMR spectra. Although recorded at a lower magnetic field as compared to that applied for the acquisition of the NMR spectra of M1
ySryF2, the NMR lines of metastable Ba1
xCaxF2 turn out to be extremely broad. As an example, as compared to pure, ball-milled CaF2, see ref 63, the width (full width at half-maximum) of the NMR line showing up at δiso = 55 ppm (x = 0.80, 24 h, see Figure 4) and referring to the [Ca]4-unit is increased from 2.5 to 6 ppm. This increase is much more pronounced for the mixed sites; the corresponding NMR line widths range from 30 to 40 ppm when

(Ba,Ca)F2 is regarded. Similar trends can be observed for M1
ySryF2. In the case of the Sr-containing fluorides, the line widths of the mixed sites amount to approximately 20 ppm (M = Ba) and 7 ppm (M = Ca), respectively. For further comparison with the reference samples M1
ySryF2, the spacing parameter Δ of Ba1
xCaxF2 has only slightly increased from Δ ≈ 25 (M = Ba) to range from 30 to 40 ppm. Obviously, the large substitutional disorder in the cation sublattice leads to a broad distribution of isotropic NMR chemical shifts centered around the indicated mean values (Figure 4). Note that in the series shown in Figure 4, the ternary fluoride Ba1
xCaxF2 is characterized by the largest difference in cation radii (approximately 37 to 16 (21) pm in the case of the Srcontaining counterparts). The NMR lines attributed to the mixed sites [Ba]n[Ca]4
n show up also in the corresponding spectra of the samples milled for 6 h only. The resulting 19F MAS NMR spectra (see Figure S4, Supporting Information) are highly comparable with those of the above-mentioned samples previously prepared under different milling conditions.62,63 Obviously, the number fraction of mixed sites generated after 6 h of mechanical treatment seems to be already sufficient to cause the same maximum of σDC(x) as that obtained for Ba1
xCaxF2 when td g 24 h. It is worth mentioning that the solid solutions of Ca1
ySryF2 and Ba1
ySryF2 turned out to be not metastable.19,60,76 They can be easily prepared by using conventional high-temperature synthesis routes.18,60 As mentioned above, σDC of single-crystalline 23787

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The Journal of Physical Chemistry C Ca1
ySryF2 shows a maximum when plotted as a function of x.19 However, this maximum is difficult to detect when nanocrystalline samples prepared by high-energy ball-milling have to be investigated. This is simply due to two reasons: (i) from the outset, the DC-conductivity of the pure end members of ballmilled M1
ySryF2 is characterized by a much larger conductivity as compared to their single-crystalline forms and (ii) the change of σDC with composition y turned out to be much weaker than in the case of Ba1
xCaxF2. For comparison with Ba0.5Ca0.5F2, the ionic conductivities σDC of the corresponding Sr-containing fluorides are by 2
3 orders of magnitude lower. While σDC of Ca1
ySryF2 with y = 0.5 is 0.001 mS cm
1 (T = 554 K), the cation-mixed analogue Ba1
ySryF2 is characterized by 0.02 mS cm
1 (T = 554 K). These values are also indicated in Figure 2 by dashed lines. The corresponding activation energies of the samples amount to approximately 0.95 and 0.80 eV, respectively. Most likely, ionic conductivity in the Sr-containing samples is mainly influenced by the overall structural disorder introduced during ball milling rather than by the additional substitutional disorder generated. The first is known to be also responsible for an enhancement of ion conductivity of singlephase nanocrystalline ion conductors.77
79 However, this is in contrast to Ba1
xCaxF2 for which the contribution due to substitutional disorder clearly surpasses the ionic conductivity of pure nanocrystalline BaF2 (as well as CaF2) prepared by mechanical treatment. Its metastability, probably being a direct consequence of mixing two cations largely differing in size, might be an additional cause for fast through-going diffusion pathways with low energy barriers the ions have to overcome. For the sake of completeness, we have analyzed the conductivity isotherms in more detail. When the samples were heated up for the first time beyond 600 K, thermally induced structural relaxation took place, which is found to be similar to that observed for mechanosynthesized BaLiF3;80 see also ref 81 for a similar analysis of an oxygen ion conductor. However, the DC-conductivity is only slightly influenced by this process. Subsequent measurements resulted in highly reproducible conductivity isotherms irrespective of the chronology of their acquisition. Fitting the obtained isotherms σ0 (ν) according to σ0 (ν) = σDC[1 + (ν/νc)q], ref 82, reveals that the exponent q turns out to be temperature independent. This shows that the time
temperature superposition principle is fulfilled, indicating that there is no change of the transport mechanism in the temperature range covered. Moreover, the characteristic frequency νc, when plotted in an Arrhenius diagram, yields the same activation energies as obtained from the corresponding σDC versus (1/T) plots. The agreement shows that the number of charge carriers N does not greatly change with rising temperature. Furthermore, N does not significantly vary with composition x. Because σ is solely controlled by N and the mobility μ, which is equivalent to νc, the increase in DC-conductivity is therefore mainly caused by a pronounced decrease of the (mean) activation energy in Ba1
xCaxF2.

IV. CONCLUSIONS AND OUTLOOK A fast fluorine ion conductor can be prepared by mixing the binary fluorides BaF2 and CaF2 in a high-energy planetary mill. The resulting metastable solid solution reveals an ion conductivity, which is by about 2 orders of magnitude larger (x = 0.5) than that of mechanically treated BaF2. The substitutional disorder has been probed on an atomic scale by high-resolution 19F NMR

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spectroscopy revealing the distinct crystallographic environments of the F anions. The relatively broad 19F MAS NMR lines observed indicate a highly distorted crystal lattice leading to a large distribution of isotropic chemical shifts. The combination of structural disorder and metastability, which is caused by mixing two isovalent cations differing greatly in ionic radii, is regarded to be the main reason for the observed maximum in σDC and the associated minimum in activation energy. Substitutional disorder being present in a metastable phase is anticipated to cause a large impact on its defect density, that is, on the number of fluorine vacancies and interstitials as well as on the corresponding formation energies. This directly affects the activation energy of long-range ion transport in the cation-mixed phase. Provided a sufficiently large defect concentration is present, the low activation energy of 0.6 eV found for ball-milled (Ba,Ca)F2 might be dominated by the overall migration energy of anion transport.

’ ASSOCIATED CONTENT

bS

Supporting Information. Additional figures. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected] (A.D.); [email protected], [email protected] (M.W.).

’ ACKNOWLEDGMENT We thank E. Merzlyakova, K. Partovi, and D. Kliem for their help in sample preparation as well as with various NMR and dcconductivity measurements. We gratefully acknowledge financial support by the Deutsche Forschungsgemeinschaft (DFG) within the priority program 1415, Kristalline Nichtgleichgewichtsphasen. ’ REFERENCES (1) Lanfredi, S.; Saia, P.; Lebullenger, R.; Hernandes, A. Solid State Ionics 2002, 146, 329. (2) Bobe, J. M.; Reau, J. M.; Senegas, J.; Poulain, M. Solid State Ionics 1995, 82, 39. (3) Ghosh, S.; Ghosh, A. J. Chem. Phys. 2003, 119, 9106. (4) Kulkarni, A. R.; Sundar, H. G. K.; Angell, C. A. Solid State Ionics 1987, 253, 122. (5) Bobe, J. M.; Reau, J. M.; Senegas, J.; Poulain, M. J. Non-Cryst. Solids 1997, 209, 122. (6) Reau, J.; Jun, X.; Senegas, J.; LeDeit, C.; Poulain, M. Solid State Ionics 1997, 95, 191. (7) Kavun, V. Y.; Merkulov, E. B.; Sinebryukhov, S. L.; Gnedenkov, S. V.; Goncharuk, V. K. Inorg. Mater. 2009, 45, 315. (8) Kavun, V.; Sorokin, N.; Merkulov, E.; Goncharuk, V. Inorg. Mater. 2001, 37, 515. (9) Kavun, V. Y.; Slobodyuk, A. B.; Voit, E. I.; Sinebryukhov, S. L.; Merkulov, E. B.; Goncharuk, V. K. J. Struct. Chem. 2010, 51, 862. (10) Reau, J.; Poulian, M. Mater. Chem. Phys. 1989, 23, 189. (11) Chowdari, B. V. R.; Mok, K. F.; Xie, J. M.; Gopalakrishnan, R. Solid State Ionics 1995, 76, 189. (12) Chowdari, B. V. R.; Rong, Z. Solid State Ionics 1995, 78, 133. (13) Bueno, L.; Donoso, J.; Magon, C.; Kosacki, I.; Filho, F.; Tambelli, C.; Messaddeq, Y.; Ribeiro, S. J. Non-Cryst. Solids 2005, 351, 766. (14) Hoff, C.; Wiemh€ofer, H.; Glumov, O.; Murin, I. Solid State Ionics 1997, 101, 445. (15) Sorokin, N. I.; Breiter, M. W. Solid State Ionics 1997, 99, 241. 23788

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