- Email: [email protected]
The ionic conductivity and dielectric properties of Ba1−xSnxF2 solid solutions prepared by mechanochemical milling
ARTICLE IN PRESS
G Model MSB 13370 1–6
Materials Science and Engineering B xxx (2013) xxx–xxx
Contents lists available at SciVerse ScienceDirect
Materials Science and Engineering B journal homepage: www.elsevier.com/locate/mseb
Short Communication
1
The ionic conductivity and dielectric properties of Ba1−x Snx F2 solid solutions prepared by mechanochemical milling
2
3
4
Q1
Mohamad M. Ahmad a,b,∗ , Yohei Yamane c , Koji Yamada c a
5
b
6
c
7
Department of Physics, College of Science, King Faisal University, Al-Ahsaa 31982, Saudi Arabia Department of Science and Mathematics, Faculty of Education in The New Valley, Assiut University, El-Kharga 72511, Egypt Department of Applied Molecular Chemistry, College of Industrial Technology, Nihon University, Narashino, Chiba 275-8575, Japan
8
a r t i c l e
9
i n f o
a b s t r a c t
10
Article history: Received 8 November 2012 Received in revised form 14 May 2013 Accepted 17 May 2013 Available online xxx
11 12 13 14
15
20
Keywords: Mechanochemical milling Ionic conductivity Impedance spectroscopy Dielectric properties
21
1. Introduction
16 17 18 19
Solid solutions of Ba1−x Snx F2 fluoride ion conductors, with x = 0.1–0.4, have been synthesized by the mechanochemical milling technique for the first time. All of the prepared materials crystallize in the cubic fluorite-type structure, which indicates that the solid solution can be synthesized in the studied composition range by the mechanochemical milling technique at ambient temperature and pressure. The ionic conduction of the investigated materials has been studied by impedance spectroscopy. The ionic conductivity increased considerably, by up to six orders of magnitude compared to pure un-milled BaF2 , with increasing SnF2 content. From the analysis of the conductivity spectra of the investigated materials it is found that the concentration of mobile fluoride ions is independent of temperature with almost the same values for the investigated materials. The present results suggest that the enhanced mobility of mobile ions is the origin of the higher ionic conductivity. The dielectric properties and the associated relaxation phenomena of the current materials are also described. © 2013 Published by Elsevier B.V.
Ionic conductors are technologically important materials that are used in many applications in electrochemical devices, such as lithium ion batteries, solid oxide fuel cells, gas sensors and supercapacitors. [1–5]. Therefore, extensive research is devoted to either discover new materials with superior ionic conduction properties or optimize/enhance the properties of the current materials. Among this class, crystalline fluoride compounds with fluorite crystal structure, such as CaF2 and -PbF2 , are interesting materials with high temperature superionic properties, characterized by a rapid and continuous increase in the ionic conductivity on heating [6,7]. It has been observed that increasing the Sn2+ content in the Pb1−x Snx F2 solid solutions leads to increasing both the unit cell volume and the ionic conductivity within the fluorite solid solutions limit of 0 < x ≤ 0.25 [8,9]. The effects of Sn2+ addition have been attributed to the greater stereoactivity of the 5s2 lone pairs of the Sn2+ ions, which have been suggested to play an important role in stabilizing the structure of PbSnF4 material [10,11].
22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38
Q2
∗ Corresponding author at: Department of Physics, College of Science, King Faisal University, Al-Ahsaa 31982, Saudi Arabia Tel.: +966 562 399692; fax: +966 35886437. E-mail addresses: [email protected], [email protected] (M.M. Ahmad).
Previously, PbSnF4 was prepared through different routes, such as the precipitation from aqueous solution and solid state reaction [12]. On the other hand, BaSnF4 and Pb1−x Snx F2 solid solutions were obtained only through multiple-steps solid-state reaction technique at high temperature [9,12–15]. For these fluoride materials, the solid state reactions are performed inside inactive expensive metal containers in inert gas conditions due to the corrosive nature of SnF2 . Therefore, it is important to search for a new synthesis technique to prepare SnF2 -containing fluoride materials. Recently, intensive research is devoted to mechanochemical milling as a synthesis tool for a variety of systems, such as alloys, glasses and oxide inorganic materials [16–20]. The mechanical milling is considered a complete general method of producing almost all forms of materials. The mechanical milling skips intermediate temperature calcination steps that are usually performed in solid state reaction technique, and it takes place at room temperature in well-sealed containers, thus effectively alleviating the loss of the volatile components. These characteristics make it a suitable tool to synthesis SnF2 -based fluoride materials. In this regards, we have successfully synthesized a series of Pb1−x Snx F2 solid solutions [21] and BaSnF4 compound through mechanochemical milling [22]. Until now, however, there are no reports on the synthesis, structural and physical properties of Ba1−x Snx F2 solid solutions. Therefore, we synthesized Ba1−x Snx F2 solid solutions with x = 0.1–0.4 through the mechanochemical milling technique, and studied their crystal structure and ionic conduction.
0921-5107/$ – see front matter © 2013 Published by Elsevier B.V. http://dx.doi.org/10.1016/j.mseb.2013.05.011
Please cite this article in press as: M.M. Ahmad, et al., Mater. Sci. Eng. B (2013), http://dx.doi.org/10.1016/j.mseb.2013.05.011
39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63
ARTICLE IN PRESS
G Model MSB 13370 1–6
M.M. Ahmad et al. / Materials Science and Engineering B xxx (2013) xxx–xxx
Ba0.9 Sn0.1 F2 , for example, shows the compound synthesized using the source composition of BaF2 :SnF2 = 0.9:0.1 here, and the actual composition of the resultant compound is not confirmed. Rietveld analyses have been performed for the XRD data of the investigated materials. The lattice parameter of these solid solutions, with cubic ˚ The XRD peaks in structure, ranges between 6.1814 and 6.1937 A. the present samples are found to be broadened. Similar broadening of XRD pattern was observed for CaF2 synthesized by mechanical milling [24]. The observed broadening of the XRD peaks of Ba1−x Snx F2 solid solutions may be due to the decrease of the crystallite size of the samples prepared by mechanochemical milling technique. The crystallite size can be estimated from the full width at half maximum (FWHM) of the XRD lines using Scherrer formula:
311
422
331 420
400
x = 0.1 222
200
220
111
2
x = 0.2
98 99 100 101 102 103 104 105 106 107 108 109 110 111
dXRD = x = 0.3 x = 0.4
20
30
40
50
60
70
80
2θ / ° Fig. 1. Rietveld refinement of XRD data at room temperature for Ba1−x Snx F2 solid solutions.
64
2. Experimental
89
Polycrystalline materials of Ba1−x Snx F2 solid solutions (x = 0.1–0.4) were synthesized by the mechanochemical milling technique at ambient conditions. Stoichiometeric amounts of the starting materials BaF2 (Soekawa 99.9%) and SnF2 (Rare metallic 99.9%) were mixed and milled in a commercial planetary mill “Pulverisette 6” (Fritsch, Germany) using stainless steel balls (five balls with a diameter of 10 cm) and bowl. The rotation speed and time for the milling process were fixed at 550 rpm and 8 h, respectively, and the balls to powder mass ratio was 10:1. The structural characterization of the product materials was performed using precise diffraction data obtained on a Bruker D8 Advance X-ray powder diffractometer (CuK␣ -radiation in the 20◦ ≤ 2 ≤ 80◦ range with scan step of 0.02◦ ) for the as-milled and annealed (200 ◦ C for 8 h) samples. The crystal structures of the annealed materials were determined by the Rietveld method using RIETAN-2000 program [23]. Complex impedance measurements were performed for the annealed samples using a compressed pellet of ∼13 mm diameter and 1 mm thickness. The pellets were obtained by applying a pressure of 370 MPa. Carbon paint was evenly applied on both sides of the pellet for better electrical contact, and the sample was then held between two spring-loaded electrodes. The impedance |Z*| and phase angle were measured in the 50 Hz–1 MHz frequency range using a HIOKI 3532 LCR meter with a heating rate of 0.5 K/min in the 220–470 K temperature range.
90
3. Results and discussion
65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88
91 92 93 94 95 96 97
Room temperature XRD patterns of the Ba1−x Snx F2 samples (with x = 0.1–0.4) prepared by ball milling are shown in Fig. 1. The XRD patterns for these samples exhibit the same reflections as that of the cubic BaF2 , where no peaks of secondary phases, such as SnF2 or BaSnF4 , are detected. This means that the mechanochemical milling technique successfully produces Ba1−x Snx F2 solid solutions up to x = 0.4. However, in the current work the expression of
ˇ cos
(1)
where dXRD is the crystallite size, ˇ is the line’s FWHM, is the Bragg angle and (0.154 nm) is wavelength of the X-ray radiation. Using this formula for the XRD reflections at about 26◦ , the crystallite size of the samples is found to range between 22 nm and 26 nm for the investigated materials. The above results indicate that mechanochemical milling technique can probably produce fluoride materials in the nano-size scale at room temperature. Representative complex impedance diagrams of the Ba0.7 Sn0.3 F2 of nominal composition x = 0.3 are shown in Fig. 2a at selected temperatures. Similar complex plane diagrams of the impedance are observed for the materials with other compositions, and representative complex impedance plots of all compositions at room temperature are shown in Fig. 2b. For each sample, one nonideal semicircular arc is observed at the high frequency side. With increasing temperature, interfacial polarization effects at the electrodes appear at the low frequency region. The non-ideal behavior of the arcs may be ascribed to the distribution of relaxation times, as usually observed in disordered ionic conducting materials. Since there are no pronounced grain boundary contributions in the complex impedance diagrams of Fig. 2, the determined conductivity can be assigned to the bulk effect. Assuming zero electronic transport, the ionic conductivity of the investigated materials is determined from the interception of the semicircles with the real axis of the impedance. The variation of the ionic conductivity with temperature for the Ba1−x Snx F2 solid solutions is shown in Fig. 3. The mechanical milling of pure BaF2 has already increased considerably the ionic conductivity compared to un-milled sample by about three orders of magnitude (see Fig. 3). Moreover, recent work by Patro and Hariharan showed that mechanical milling of SnF2 induced an increased conductivity by 1–2 orders of magnitude [25]. In the current work the substitution of Sn instead of Ba in the mechanosynthesized solid solutions leads to further enhancement of the ionic conductivity compared with the milled BaF2 and SnF2 . It is noticed from this Fig. 3 that considerable enhancement of the ionic conductivity is observed when increasing the SnF2 content. For example the ionic conductivity value for Ba0.9 Sn0.1 F2 of nominal composition x = 0.1 at ∼455 K is 1.81 × 10−5 S/cm, which is about one order of magnitude larger than that of pure milled BaF2 (2.09 × 10−6 S/cm), whereas the conductivity value of 2.63 × 10−3 nm S/cm for Ba0.6 Sn0.4 F2 of nominal composition x = 0.4 is about three orders of magnitude larger than pure milled BaF2 at the same temperature. The conductivity (Fig. 3) is clearly thermally activated and follows the Arrhenius type relation: T = 0 exp
−E , kT
(2)
where 0 is the pre-exponential factor, E is the activation energy for ionic conduction and k is Boltzmann constant. The values of
Please cite this article in press as: M.M. Ahmad, et al., Mater. Sci. Eng. B (2013), http://dx.doi.org/10.1016/j.mseb.2013.05.011
112
113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156
157
158 159
ARTICLE IN PRESS
G Model MSB 13370 1–6
M.M. Ahmad et al. / Materials Science and Engineering B xxx (2013) xxx–xxx
20
2.0
(a)
241 K 251 K 260 K
3
(b)
x = 0.1 x = 0.2 x = 0.3 x = 0.4
1.5
ρ" (Ω cm) x10
ρ" (Ω cm) x10
6
6
15
10
1.0
0.5
5
0
0.0 0
10
5
15
20
0.0
0.5
6
1.0
1.5
2.0
6
ρ' (Ω cm) x10
ρ' (Ω cm) x10
Fig. 2. (a) Complex impedance diagrams for Ba0.7 Sn0.3 F2 of nominal composition x = 0.3 at representative temperatures. (b) Representative complex impedance diagrams for all compositions at room temperature. The lines through the data points are guidance to the eyes.
-2
log σ (S / cm)
equivalently ωH ) are the parameters that control the conductivity. Since Sn2+ is isovalent substitution for Ba2+ , it is expected that the concentration of mobile ions will remain the same for the different compositions. Therefore, studying the temperature dependence of nc and ωH is expected to explain the overall conductivity behavior. The transport properties of ionic conductors depend largely upon the relaxation dynamics of mobile ions. The relaxation dynamics are usually studied by the electrical relaxation measurements, and the obtained experimental data are often presented and analyzed in terms of the complex conductivity [26]. Therefore, we have analyzed the frequency dependent conductivity data at different temperatures. The conductivity spectra, the frequency dependent real part of the complex conductivity, of different ionic materials are usually analyzed by a power-law model [27],
x = 0.1 x = 0.2 x = 0.3 x = 0.4 un-milled-BaF2 milled-BaF2
-4
-6
-8
2.0
2.5
3.0
(ω) = dc 1 +
3.5
-1
1000 / T (K ) Fig. 3. Temperature dependence of the ionic conductivity of the Ba1−x Snx F2 solid solutions together with that of pure BaF2 [Ref. [18]].
160 161 162 163 164 165 166
167
168 169 170 171
the activation energy for ionic conduction are determined from the straight-line fits of the conductivity data in Fig. 3 for the different compositions. It is found that E decreases with increasing SnF2 content as shown in Table 1. It is important to understand the origin of the considerably higher conductivity in the studied solid solutions. The ionic conductivity can be given by the Nernst–Einstein relation: = enc =
nc
e2 2 kT
(3)
ωH ,
where nc is the concentration of mobile charge carriers, is their mobility, e is the electron charge, is a geometrical factor for ion hopping, is the hopping distance, and ωH is the hopping rate of mobile ions. It is clear from Eq. (3) that nc and/or (or
ω n ωc
,
(4)
where dc is the dc conductivity, ω is the angular frequency, n is the power-law exponent, and ωc is the crossover radial frequency from dc to the dispersive conductivity region. It is widely accepted in the literature that ωc of Eq. (4) represents a good estimate of the true hopping rates of mobile ions [28–31]. Therefore, we have analyzed the conductivity spectra of the investigated materials using Eq. (4) in order to determine the values of dc and ωc , and consequently calculate the values of nc at different temperatures. The conductivity spectra at different temperatures of Ba0.9 Sn0.1 F2 of nominal composition x = 0.1 and Ba0.7 Sn0.3 F2 of nominal composition x = 0.3 are shown in Fig. 4a and b, respectively. The conductivity spectra in Fig. 4 exhibit common features usually found in ionic conductors. At low and intermediate frequencies, a quasistatic plateau region is observed, representing the dc conductivity. The frequency dispersion of starts at a higher frequency as the temperature is increased. The frequency dispersion associated with a power-law exponent n indicates a subdiffusive motion of mobile ions with repeated forward-backward
Table 1 The ionic conductivity at room temperature, the activation energy E for the ionic conduction, the average values of the concentration of mobile ions, nc and the mobility of mobile ions at room temperature for Ba1−x Snx F2 solid solutions. x
(S/cm) (at 300 K)
E (eV)
nc (cm−3 )
(cm2 V−1 s−1 )
0.1 0.2 0.3 0.4
7.87 × 10−9 4.74 × 10−7 3.54 × 10−6 9.90 × 10−6
0.59 0.50 0.45 0.41
8.57 × 1020 8.55 × 1020 6.80 × 1020 5.20 × 1020
6.63 × 10−11 4.43 × 10−9 3.41 × 10−8 1.09 × 10−7
Please cite this article in press as: M.M. Ahmad, et al., Mater. Sci. Eng. B (2013), http://dx.doi.org/10.1016/j.mseb.2013.05.011
172 173 174 175 176 177 178 179 180 181 182 183 184 185
186
187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204
ARTICLE IN PRESS
G Model MSB 13370 1–6
M.M. Ahmad et al. / Materials Science and Engineering B xxx (2013) xxx–xxx
4
-5.0 (b)
(a)
-5.5
-6.5
-7.0 300 K 310 K 320 K 330 K 340 K 350 K 360 K
-7.5
-8.0 3
4
5
6
log σ' (S / cm)
log σ' (S / cm)
-6.0
-6.0
-6.5 241 K 251 K 260 K 271 K 281 K 290 K 301 K
-7.0
-7.5 3
7
4
log ω (rad / s)
5
6
7
log ω (rad / s)
Fig. 4. Analysis of the conductivity spectra at different temperatures by the power-law model [Eq. (3)] for the (a) Ba0.9 Sn0.1 F2 of nominal composition x = 0.1 and (b) Ba0.7 Sn0.3 F2 of nominal composition x = 0.3. The solid curves are the best fits to Eq. (3).
207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248
hops before performing a successful displacement. At high temperatures, the effect of interfacial polarization is observed at low frequencies, leading to a decrease of with decreasing frequency. The fitting results of the conductivity data are shown as solid curves in Fig. 4. It is found that the exponent n has average values of 0.6–0.62 for x = 0.1 composition and 0.54–0.56 for x = 0.3 composition. The temperature dependencies of dc and ωc , extracted from the fitting process, are shown in Fig. 5a and b, respectively for all compositions. For each specific composition, both dc and ωc are thermally activated with almost the same activation energy, see Fig. 5. These results indicate that the concentration of mobile ions is independent of temperature in the studied temperature range. The values of nc are calculated by Eq. (3) using the extracted values of dc and ωc . In Eq. (3), is taken as 1/6 and the hopping distance is supposed to be equal to 2.8 × 10−8 cm [29–31]. nc is found to be independent of temperature, as shown in Fig. 6, and its average values are listed in Table 1 for all compositions. Here we can notice that the concentration of mobile ions is very close for the all compositions, and consequently it cannot be the reason for the observed large enhancement in the conductivity. On the contrary, the hopping rates of the Ba0.7 Sn0.3 F2 of nominal composition x = 0.3 are roughly three orders of magnitude higher than that of the Ba0.9 Sn0.1 F2 of nominal composition x = 0.1. This means that the mobility of fluoride ions is considerably enhanced with increasing SnF2 content, leading to the observed enhancement of the ionic conductivity in the investigated solid solutions. The values of the mobility of mobile ions as calculated from Eq. (3) are listed in Table 1 for the different compositions. The enhanced mobility may be a result of the greater stereoactivity of the 5s2 lone pairs of the Sn2+ ions. Moreover, grain-boundary regions in the current materials may represent diffusion pathways with low activation energy for the fluoride ion transport, leading to the increased mobility of the ions and increased ionic conductivity. The conductivity spectra at different temperatures of the x = 0.1 and x = 0.3 compositions have been scaled according to the procedure described previously, where dc and ωc are used as the scaling parameters for the and ω axes, respectively [32]. The scaling results are shown in Fig. 7, which shows that the conductivity spectra at different temperatures for each composition are found to scale properly into a single master curve, indicating that the relaxation dynamics of mobile fluoride ions are independent of temperature. The frequency dependence of the real part of the dielectric permittivity, ε , for Ba0.7 Sn0.3 F2 of nominal composition x = 0.3 at
-5
log σdc (S / cm)
206
(a) x = 0.1 x = 0.2 x = 0.3 x = 0.4
0.43 eV
0.51 eV
-6
-7 0.45 eV
0.58 eV
-8
2.8
3.2
3.6
4.0
-1
1000 / T (K ) 8
(b) x = 0.1 x = 0.2 x = 0.3 x = 0.4
0.43 eV
7
log ωc (rad / s)
205
0.47 eV
6
5
0.45 eV 0.58 eV
4 2.6
2.8
3.0
3.2
3.4
3.6
3.8
4.0
4.2
-1
1000 / T (K ) Fig. 5. Reciprocal temperature dependence of (a) the dc conductivity and (b) the crossover radial frequency for the Ba1−x Snx F2 solid solutions. The solid lines are the straight-line fits and the corresponding activation energies are shown in the graphs.
Please cite this article in press as: M.M. Ahmad, et al., Mater. Sci. Eng. B (2013), http://dx.doi.org/10.1016/j.mseb.2013.05.011
ARTICLE IN PRESS
G Model MSB 13370 1–6
M.M. Ahmad et al. / Materials Science and Engineering B xxx (2013) xxx–xxx
6
x = 0.1 x = 0.2 x = 0.3 x = 0.4
222 K 241 K 260 K 281 K 301 K 320 K
5
-3
log n c (cm )
22
5
4
log ε'
21
3
2
20 240
280
320
360
Temperature (K)
1 3
4
5
253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272
271 K 281 K 290 K 301 K 311 K 320 K 331 K 341 K 350 K
15
10
tan δ
252
7
Fig. 8. Frequency dependence of ε at selected temperatures for Ba0.7 Sn0.3 F2 of nominal composition x = 0.3.
5
0 3
4
5
6
7
log ω (rad / s) Fig. 9. Frequency dependence of tan ı for Ba0.7 Sn0.3 F2 of nominal composition x = 0.3 at selected temperatures.
-2
x = 0.1 x = 0.2 x = 0.3 x = 0.4
2.0 -3
2.0 1.5 1.5 1.0 1.0 0.5 0.1
0.5
log τtanδ (s)
251
log σ ' / σ dc
250
selected temperatures is shown in Fig. 8. It is observed in this figure that ε approaches a limiting constant value at high frequencies, ε∞ . This value is unrelated to the hopping dynamics of the mobile ions and instead it is the result of much more rapid polarization processes occurring in the material. Moreover, the dielectric constant is found to increase rapidly at low frequencies. Similar dielectric behavior is observed for other compositions, and it is found that ε∞ has values of 8–25 for the investigated materials. The dielectric relaxation properties of the investigated materials are studied through the frequency dependence of the dissipation factor, tan ı = ε /ε , where ε is the imaginary part of the dielectric permittivity. Fig. 9 shows the frequency dependence of tan ı at different temperatures for x = 0.3. The large values of tan ı observed in Fig. 9 reflect the large contribution of the high ionic conductivity to the dielectric permittivity in the current materials. Well-defined peaks in the tan ı vs log ω plots are observed in Fig. 9, corresponding to dielectric relaxation phenomena. The position of the peaks shifts to high frequencies with increasing temperature, indicating a thermally activated process. We obtain the relaxation time, tan ı , of this process as a function of temperature from the condition that ωmax tan ı = 1 at the peak. The temperature dependence of tan ı is shown in Fig. 10 for the different investigated compositions. The values of the activation energy, Etan ı , of the dielectric relaxation process are 0.61, 0.50, 0.47 and 0.43 eV for x = 0.1, 0.2, 0.3 and 0.4
log σ ' / σ dc
249
6
log ω (rad / s)
Fig. 6. Temperature dependence of the concentration of mobile ions for different compositions of the Ba1−x Snx F2 solid solutions.
-4
-5
0.0 -6
0.
0.0
-0.5 -7
-4
-2
0
2
log ω / ω c Fig. 7. Scaling of the conductivity spectra at different temperatures of the Ba0.9 Sn0.1 F2 of nominal composition x = 0.1 and Ba0.7 Sn0.3 F2 of nominal composition x = 0.3.
2.0
2.5
3.0
3.5
4.0
-1
1000 / T (K ) Fig. 10. Reciprocal temperature dependence of the relaxation time for the Ba1−x Snx F2 solid solutions.
Please cite this article in press as: M.M. Ahmad, et al., Mater. Sci. Eng. B (2013), http://dx.doi.org/10.1016/j.mseb.2013.05.011
G Model MSB 13370 1–6
ARTICLE IN PRESS M.M. Ahmad et al. / Materials Science and Engineering B xxx (2013) xxx–xxx
6
275
compositions, respectively. It can be noticed that the values of Etan ı agree well with E , indicating that they have originated from the ionic hopping process.
276
4. Conclusions
273 274
289
Mechanochemical milling technique is successfully used to synthesize Ba1−x Snx F2 solid solutions for the first time at ambient conditions for the composition range x = 0.1–0.4. These fluoride solid solutions crystallize in the fluorite-type structure similar to pure BaF2 , with no secondary phases. The ionic conductivity, determined from the impedance data, increases considerably with increasing SnF2 content. The ionic conductivity of these solid solutions is up to six orders of magnitude higher than that of pure un-milled BaF2 . The concentration of mobile fluoride ions is found to be almost independent of SnF2 content, whereas the mobility is enhanced considerably with increasing SnF2 content. The enhanced mobility may be a result of the greater stereoactivity of the 5s2 lone pairs of the Sn2+ ions.
290
Acknowledgment
277 278 279 280 281 282 283 284 285 286 287 288
293
M.M.A. acknowledges the financial support from the Deanship of Scientific Research, King Faisal University under grant No. DSR110019.
294
References
291 292
295 296 297
[1] [2] [3] [4]
J.-M. Tarascon, M. Armand, Nature 414 (2001) 359. M. Armand, J.-M. Tarascon, Nature 451 (2008) 652. M. Whittingham, Chemical Reviews 104 (2004) 4271. G.A. Niklasson, C.G. Granqvist, Journal of Materials Chemistry 17 (2007) 127.
[5] F.C. Grozema, L.D.A. Siebbeles, International Reviews in Physical Chemistry 27 (2008) 87. [6] S. Hull, Reports on Progress in Physics 67 (2004) 1233. [7] M. Castiglione, P.A. Madden, P. Berastegui, S. Hull, Journal of Physics: Condensed Matter 17 (2005) 845. [8] P. Lagassie, J. Grannec, J.M. Reau, Solid State Ionics 21 (1986) 343. [9] Y. Ito, T. Mukoyama, K. Ashio, K. Yamamoto, Y. Suga, S. Yoshikado, C. Julian, T. Tanaka, Solid State Ionics 106 (1998) 291. [10] S. Vilminot, G. Perez, W. Granier, L. Cot, Solid State Ionics 2 (1981) 87. [11] S. Vilminot, G. Perez, W. Granier, L. Cot, Solid State Ionics 2 (1981) 91. [12] A. Collin, G. Denes, D. Le Roux, M.C. Madamba, J.M. Parris, A. Salaun, International Journal of Inorganic Materials 1 (1999) 289. [13] G. Denes, T. Birchall, M. Sayer, M.F. Bell, Solid State Ionics 13 (1984) 213. [14] G. Denes, Y.H. Yu, T. Tyliszczak, A.P. Hitchcock, Journal of Solid State Chemistry 91 (1991) 1. [15] S. Yoshikado, Y. Ito, J.M. Reau, Solid State Ionics 154/155 (2002) 503. [16] C. Suryanarayana, Progress in Materials Science 46 (2001) 1. [17] E. Gaffet, F. Bernard, J.C. Niepce, F. Charlot, C. Gras, G. Le Caer, J.L. Guichard, P. Delcroix, A. Mocellin, O. Tillement, Journal of Materials Chemistry 9 (1999) 305. [18] B. Ruprecht, M. Wilkening, A. Feldhoff, S. Steuernagelc, P. Heitjans, Physical Chemistry Chemical Physics 11 (2009) 3071. [19] M.R. Diaz-Guillen, K.J. Moreno, J.A. Diaz-Guillen, A.F. Fuentes, K.L. Ngai, J. GarciaBarriocanal, J. Santamaria, C. Leon, Physical Review B 78 (2008) 104304. [20] L.B. Kong, T.S. Zhang, J. Ma, F. Boey, Progress in Materials Science 53 (2008) 207. [21] M.M. Ahmad, Y. Yamane, K. Yamada, S. Tanaka, Journal of Physics D: Applied Physics 40 (2007) 6020. [22] M.M. Ahmad, Y. Yamane, K. Yamada, Journal of Applied Physics 106 (2009) 074106. [23] F. Izumi, T. Ikeda, Materials Science Forum 321–324 (2000) 198. [24] G. Scholz, I. Dorfel, D. Heidemann, M. Feist, R. Stosser, Journal of Solid State Chemistry 179 (2006) 1119. [25] L.N. Patro, K. Hariharan, Materials Letters 80 (2012) 26. [26] J.C. Dyre, Journal of Applied Physics 64 (1988) 2456. [27] D.P. Almond, G.K. Ducan, A.R. West, Solid State Ionics 8 (1983) 159. [28] S. Bhattacharya, A. Ghosh, Physical Review B 74 (2006) 184308. [29] M.M. Ahmad, K. Yamada, T. Okuda, Solid State Ionics 167 (2004) 285. [30] J.R. Macdonald, M.M. Ahmad, Journal of Physics: Condensed Matter 19 (2007) 046215. [31] M.M. Ahmad, K. Yamada, Journal of Chemical Physics 127 (2007) 124507. [32] A. Ghosh, A. Pan, Physical Review Letters 84 (2000) 2188.
Please cite this article in press as: M.M. Ahmad, et al., Mater. Sci. Eng. B (2013), http://dx.doi.org/10.1016/j.mseb.2013.05.011
298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337
G Model MSB 13370 1–6
Materials Science and Engineering B xxx (2013) xxx–xxx
Contents lists available at SciVerse ScienceDirect
Materials Science and Engineering B journal homepage: www.elsevier.com/locate/mseb
Short Communication
1
The ionic conductivity and dielectric properties of Ba1−x Snx F2 solid solutions prepared by mechanochemical milling
2
3
4
Q1
Mohamad M. Ahmad a,b,∗ , Yohei Yamane c , Koji Yamada c a
5
b
6
c
7
Department of Physics, College of Science, King Faisal University, Al-Ahsaa 31982, Saudi Arabia Department of Science and Mathematics, Faculty of Education in The New Valley, Assiut University, El-Kharga 72511, Egypt Department of Applied Molecular Chemistry, College of Industrial Technology, Nihon University, Narashino, Chiba 275-8575, Japan
8
a r t i c l e
9
i n f o
a b s t r a c t
10
Article history: Received 8 November 2012 Received in revised form 14 May 2013 Accepted 17 May 2013 Available online xxx
11 12 13 14
15
20
Keywords: Mechanochemical milling Ionic conductivity Impedance spectroscopy Dielectric properties
21
1. Introduction
16 17 18 19
Solid solutions of Ba1−x Snx F2 fluoride ion conductors, with x = 0.1–0.4, have been synthesized by the mechanochemical milling technique for the first time. All of the prepared materials crystallize in the cubic fluorite-type structure, which indicates that the solid solution can be synthesized in the studied composition range by the mechanochemical milling technique at ambient temperature and pressure. The ionic conduction of the investigated materials has been studied by impedance spectroscopy. The ionic conductivity increased considerably, by up to six orders of magnitude compared to pure un-milled BaF2 , with increasing SnF2 content. From the analysis of the conductivity spectra of the investigated materials it is found that the concentration of mobile fluoride ions is independent of temperature with almost the same values for the investigated materials. The present results suggest that the enhanced mobility of mobile ions is the origin of the higher ionic conductivity. The dielectric properties and the associated relaxation phenomena of the current materials are also described. © 2013 Published by Elsevier B.V.
Ionic conductors are technologically important materials that are used in many applications in electrochemical devices, such as lithium ion batteries, solid oxide fuel cells, gas sensors and supercapacitors. [1–5]. Therefore, extensive research is devoted to either discover new materials with superior ionic conduction properties or optimize/enhance the properties of the current materials. Among this class, crystalline fluoride compounds with fluorite crystal structure, such as CaF2 and -PbF2 , are interesting materials with high temperature superionic properties, characterized by a rapid and continuous increase in the ionic conductivity on heating [6,7]. It has been observed that increasing the Sn2+ content in the Pb1−x Snx F2 solid solutions leads to increasing both the unit cell volume and the ionic conductivity within the fluorite solid solutions limit of 0 < x ≤ 0.25 [8,9]. The effects of Sn2+ addition have been attributed to the greater stereoactivity of the 5s2 lone pairs of the Sn2+ ions, which have been suggested to play an important role in stabilizing the structure of PbSnF4 material [10,11].
22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38
Q2
∗ Corresponding author at: Department of Physics, College of Science, King Faisal University, Al-Ahsaa 31982, Saudi Arabia Tel.: +966 562 399692; fax: +966 35886437. E-mail addresses: [email protected], [email protected] (M.M. Ahmad).
Previously, PbSnF4 was prepared through different routes, such as the precipitation from aqueous solution and solid state reaction [12]. On the other hand, BaSnF4 and Pb1−x Snx F2 solid solutions were obtained only through multiple-steps solid-state reaction technique at high temperature [9,12–15]. For these fluoride materials, the solid state reactions are performed inside inactive expensive metal containers in inert gas conditions due to the corrosive nature of SnF2 . Therefore, it is important to search for a new synthesis technique to prepare SnF2 -containing fluoride materials. Recently, intensive research is devoted to mechanochemical milling as a synthesis tool for a variety of systems, such as alloys, glasses and oxide inorganic materials [16–20]. The mechanical milling is considered a complete general method of producing almost all forms of materials. The mechanical milling skips intermediate temperature calcination steps that are usually performed in solid state reaction technique, and it takes place at room temperature in well-sealed containers, thus effectively alleviating the loss of the volatile components. These characteristics make it a suitable tool to synthesis SnF2 -based fluoride materials. In this regards, we have successfully synthesized a series of Pb1−x Snx F2 solid solutions [21] and BaSnF4 compound through mechanochemical milling [22]. Until now, however, there are no reports on the synthesis, structural and physical properties of Ba1−x Snx F2 solid solutions. Therefore, we synthesized Ba1−x Snx F2 solid solutions with x = 0.1–0.4 through the mechanochemical milling technique, and studied their crystal structure and ionic conduction.
0921-5107/$ – see front matter © 2013 Published by Elsevier B.V. http://dx.doi.org/10.1016/j.mseb.2013.05.011
Please cite this article in press as: M.M. Ahmad, et al., Mater. Sci. Eng. B (2013), http://dx.doi.org/10.1016/j.mseb.2013.05.011
39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63
ARTICLE IN PRESS
G Model MSB 13370 1–6
M.M. Ahmad et al. / Materials Science and Engineering B xxx (2013) xxx–xxx
Ba0.9 Sn0.1 F2 , for example, shows the compound synthesized using the source composition of BaF2 :SnF2 = 0.9:0.1 here, and the actual composition of the resultant compound is not confirmed. Rietveld analyses have been performed for the XRD data of the investigated materials. The lattice parameter of these solid solutions, with cubic ˚ The XRD peaks in structure, ranges between 6.1814 and 6.1937 A. the present samples are found to be broadened. Similar broadening of XRD pattern was observed for CaF2 synthesized by mechanical milling [24]. The observed broadening of the XRD peaks of Ba1−x Snx F2 solid solutions may be due to the decrease of the crystallite size of the samples prepared by mechanochemical milling technique. The crystallite size can be estimated from the full width at half maximum (FWHM) of the XRD lines using Scherrer formula:
311
422
331 420
400
x = 0.1 222
200
220
111
2
x = 0.2
98 99 100 101 102 103 104 105 106 107 108 109 110 111
dXRD = x = 0.3 x = 0.4
20
30
40
50
60
70
80
2θ / ° Fig. 1. Rietveld refinement of XRD data at room temperature for Ba1−x Snx F2 solid solutions.
64
2. Experimental
89
Polycrystalline materials of Ba1−x Snx F2 solid solutions (x = 0.1–0.4) were synthesized by the mechanochemical milling technique at ambient conditions. Stoichiometeric amounts of the starting materials BaF2 (Soekawa 99.9%) and SnF2 (Rare metallic 99.9%) were mixed and milled in a commercial planetary mill “Pulverisette 6” (Fritsch, Germany) using stainless steel balls (five balls with a diameter of 10 cm) and bowl. The rotation speed and time for the milling process were fixed at 550 rpm and 8 h, respectively, and the balls to powder mass ratio was 10:1. The structural characterization of the product materials was performed using precise diffraction data obtained on a Bruker D8 Advance X-ray powder diffractometer (CuK␣ -radiation in the 20◦ ≤ 2 ≤ 80◦ range with scan step of 0.02◦ ) for the as-milled and annealed (200 ◦ C for 8 h) samples. The crystal structures of the annealed materials were determined by the Rietveld method using RIETAN-2000 program [23]. Complex impedance measurements were performed for the annealed samples using a compressed pellet of ∼13 mm diameter and 1 mm thickness. The pellets were obtained by applying a pressure of 370 MPa. Carbon paint was evenly applied on both sides of the pellet for better electrical contact, and the sample was then held between two spring-loaded electrodes. The impedance |Z*| and phase angle were measured in the 50 Hz–1 MHz frequency range using a HIOKI 3532 LCR meter with a heating rate of 0.5 K/min in the 220–470 K temperature range.
90
3. Results and discussion
65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88
91 92 93 94 95 96 97
Room temperature XRD patterns of the Ba1−x Snx F2 samples (with x = 0.1–0.4) prepared by ball milling are shown in Fig. 1. The XRD patterns for these samples exhibit the same reflections as that of the cubic BaF2 , where no peaks of secondary phases, such as SnF2 or BaSnF4 , are detected. This means that the mechanochemical milling technique successfully produces Ba1−x Snx F2 solid solutions up to x = 0.4. However, in the current work the expression of
ˇ cos
(1)
where dXRD is the crystallite size, ˇ is the line’s FWHM, is the Bragg angle and (0.154 nm) is wavelength of the X-ray radiation. Using this formula for the XRD reflections at about 26◦ , the crystallite size of the samples is found to range between 22 nm and 26 nm for the investigated materials. The above results indicate that mechanochemical milling technique can probably produce fluoride materials in the nano-size scale at room temperature. Representative complex impedance diagrams of the Ba0.7 Sn0.3 F2 of nominal composition x = 0.3 are shown in Fig. 2a at selected temperatures. Similar complex plane diagrams of the impedance are observed for the materials with other compositions, and representative complex impedance plots of all compositions at room temperature are shown in Fig. 2b. For each sample, one nonideal semicircular arc is observed at the high frequency side. With increasing temperature, interfacial polarization effects at the electrodes appear at the low frequency region. The non-ideal behavior of the arcs may be ascribed to the distribution of relaxation times, as usually observed in disordered ionic conducting materials. Since there are no pronounced grain boundary contributions in the complex impedance diagrams of Fig. 2, the determined conductivity can be assigned to the bulk effect. Assuming zero electronic transport, the ionic conductivity of the investigated materials is determined from the interception of the semicircles with the real axis of the impedance. The variation of the ionic conductivity with temperature for the Ba1−x Snx F2 solid solutions is shown in Fig. 3. The mechanical milling of pure BaF2 has already increased considerably the ionic conductivity compared to un-milled sample by about three orders of magnitude (see Fig. 3). Moreover, recent work by Patro and Hariharan showed that mechanical milling of SnF2 induced an increased conductivity by 1–2 orders of magnitude [25]. In the current work the substitution of Sn instead of Ba in the mechanosynthesized solid solutions leads to further enhancement of the ionic conductivity compared with the milled BaF2 and SnF2 . It is noticed from this Fig. 3 that considerable enhancement of the ionic conductivity is observed when increasing the SnF2 content. For example the ionic conductivity value for Ba0.9 Sn0.1 F2 of nominal composition x = 0.1 at ∼455 K is 1.81 × 10−5 S/cm, which is about one order of magnitude larger than that of pure milled BaF2 (2.09 × 10−6 S/cm), whereas the conductivity value of 2.63 × 10−3 nm S/cm for Ba0.6 Sn0.4 F2 of nominal composition x = 0.4 is about three orders of magnitude larger than pure milled BaF2 at the same temperature. The conductivity (Fig. 3) is clearly thermally activated and follows the Arrhenius type relation: T = 0 exp
−E , kT
(2)
where 0 is the pre-exponential factor, E is the activation energy for ionic conduction and k is Boltzmann constant. The values of
Please cite this article in press as: M.M. Ahmad, et al., Mater. Sci. Eng. B (2013), http://dx.doi.org/10.1016/j.mseb.2013.05.011
112
113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156
157
158 159
ARTICLE IN PRESS
G Model MSB 13370 1–6
M.M. Ahmad et al. / Materials Science and Engineering B xxx (2013) xxx–xxx
20
2.0
(a)
241 K 251 K 260 K
3
(b)
x = 0.1 x = 0.2 x = 0.3 x = 0.4
1.5
ρ" (Ω cm) x10
ρ" (Ω cm) x10
6
6
15
10
1.0
0.5
5
0
0.0 0
10
5
15
20
0.0
0.5
6
1.0
1.5
2.0
6
ρ' (Ω cm) x10
ρ' (Ω cm) x10
Fig. 2. (a) Complex impedance diagrams for Ba0.7 Sn0.3 F2 of nominal composition x = 0.3 at representative temperatures. (b) Representative complex impedance diagrams for all compositions at room temperature. The lines through the data points are guidance to the eyes.
-2
log σ (S / cm)
equivalently ωH ) are the parameters that control the conductivity. Since Sn2+ is isovalent substitution for Ba2+ , it is expected that the concentration of mobile ions will remain the same for the different compositions. Therefore, studying the temperature dependence of nc and ωH is expected to explain the overall conductivity behavior. The transport properties of ionic conductors depend largely upon the relaxation dynamics of mobile ions. The relaxation dynamics are usually studied by the electrical relaxation measurements, and the obtained experimental data are often presented and analyzed in terms of the complex conductivity [26]. Therefore, we have analyzed the frequency dependent conductivity data at different temperatures. The conductivity spectra, the frequency dependent real part of the complex conductivity, of different ionic materials are usually analyzed by a power-law model [27],
x = 0.1 x = 0.2 x = 0.3 x = 0.4 un-milled-BaF2 milled-BaF2
-4
-6
-8
2.0
2.5
3.0
(ω) = dc 1 +
3.5
-1
1000 / T (K ) Fig. 3. Temperature dependence of the ionic conductivity of the Ba1−x Snx F2 solid solutions together with that of pure BaF2 [Ref. [18]].
160 161 162 163 164 165 166
167
168 169 170 171
the activation energy for ionic conduction are determined from the straight-line fits of the conductivity data in Fig. 3 for the different compositions. It is found that E decreases with increasing SnF2 content as shown in Table 1. It is important to understand the origin of the considerably higher conductivity in the studied solid solutions. The ionic conductivity can be given by the Nernst–Einstein relation: = enc =
nc
e2 2 kT
(3)
ωH ,
where nc is the concentration of mobile charge carriers, is their mobility, e is the electron charge, is a geometrical factor for ion hopping, is the hopping distance, and ωH is the hopping rate of mobile ions. It is clear from Eq. (3) that nc and/or (or
ω n ωc
,
(4)
where dc is the dc conductivity, ω is the angular frequency, n is the power-law exponent, and ωc is the crossover radial frequency from dc to the dispersive conductivity region. It is widely accepted in the literature that ωc of Eq. (4) represents a good estimate of the true hopping rates of mobile ions [28–31]. Therefore, we have analyzed the conductivity spectra of the investigated materials using Eq. (4) in order to determine the values of dc and ωc , and consequently calculate the values of nc at different temperatures. The conductivity spectra at different temperatures of Ba0.9 Sn0.1 F2 of nominal composition x = 0.1 and Ba0.7 Sn0.3 F2 of nominal composition x = 0.3 are shown in Fig. 4a and b, respectively. The conductivity spectra in Fig. 4 exhibit common features usually found in ionic conductors. At low and intermediate frequencies, a quasistatic plateau region is observed, representing the dc conductivity. The frequency dispersion of starts at a higher frequency as the temperature is increased. The frequency dispersion associated with a power-law exponent n indicates a subdiffusive motion of mobile ions with repeated forward-backward
Table 1 The ionic conductivity at room temperature, the activation energy E for the ionic conduction, the average values of the concentration of mobile ions, nc and the mobility of mobile ions at room temperature for Ba1−x Snx F2 solid solutions. x
(S/cm) (at 300 K)
E (eV)
nc (cm−3 )
(cm2 V−1 s−1 )
0.1 0.2 0.3 0.4
7.87 × 10−9 4.74 × 10−7 3.54 × 10−6 9.90 × 10−6
0.59 0.50 0.45 0.41
8.57 × 1020 8.55 × 1020 6.80 × 1020 5.20 × 1020
6.63 × 10−11 4.43 × 10−9 3.41 × 10−8 1.09 × 10−7
Please cite this article in press as: M.M. Ahmad, et al., Mater. Sci. Eng. B (2013), http://dx.doi.org/10.1016/j.mseb.2013.05.011
172 173 174 175 176 177 178 179 180 181 182 183 184 185
186
187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204
ARTICLE IN PRESS
G Model MSB 13370 1–6
M.M. Ahmad et al. / Materials Science and Engineering B xxx (2013) xxx–xxx
4
-5.0 (b)
(a)
-5.5
-6.5
-7.0 300 K 310 K 320 K 330 K 340 K 350 K 360 K
-7.5
-8.0 3
4
5
6
log σ' (S / cm)
log σ' (S / cm)
-6.0
-6.0
-6.5 241 K 251 K 260 K 271 K 281 K 290 K 301 K
-7.0
-7.5 3
7
4
log ω (rad / s)
5
6
7
log ω (rad / s)
Fig. 4. Analysis of the conductivity spectra at different temperatures by the power-law model [Eq. (3)] for the (a) Ba0.9 Sn0.1 F2 of nominal composition x = 0.1 and (b) Ba0.7 Sn0.3 F2 of nominal composition x = 0.3. The solid curves are the best fits to Eq. (3).
207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248
hops before performing a successful displacement. At high temperatures, the effect of interfacial polarization is observed at low frequencies, leading to a decrease of with decreasing frequency. The fitting results of the conductivity data are shown as solid curves in Fig. 4. It is found that the exponent n has average values of 0.6–0.62 for x = 0.1 composition and 0.54–0.56 for x = 0.3 composition. The temperature dependencies of dc and ωc , extracted from the fitting process, are shown in Fig. 5a and b, respectively for all compositions. For each specific composition, both dc and ωc are thermally activated with almost the same activation energy, see Fig. 5. These results indicate that the concentration of mobile ions is independent of temperature in the studied temperature range. The values of nc are calculated by Eq. (3) using the extracted values of dc and ωc . In Eq. (3), is taken as 1/6 and the hopping distance is supposed to be equal to 2.8 × 10−8 cm [29–31]. nc is found to be independent of temperature, as shown in Fig. 6, and its average values are listed in Table 1 for all compositions. Here we can notice that the concentration of mobile ions is very close for the all compositions, and consequently it cannot be the reason for the observed large enhancement in the conductivity. On the contrary, the hopping rates of the Ba0.7 Sn0.3 F2 of nominal composition x = 0.3 are roughly three orders of magnitude higher than that of the Ba0.9 Sn0.1 F2 of nominal composition x = 0.1. This means that the mobility of fluoride ions is considerably enhanced with increasing SnF2 content, leading to the observed enhancement of the ionic conductivity in the investigated solid solutions. The values of the mobility of mobile ions as calculated from Eq. (3) are listed in Table 1 for the different compositions. The enhanced mobility may be a result of the greater stereoactivity of the 5s2 lone pairs of the Sn2+ ions. Moreover, grain-boundary regions in the current materials may represent diffusion pathways with low activation energy for the fluoride ion transport, leading to the increased mobility of the ions and increased ionic conductivity. The conductivity spectra at different temperatures of the x = 0.1 and x = 0.3 compositions have been scaled according to the procedure described previously, where dc and ωc are used as the scaling parameters for the and ω axes, respectively [32]. The scaling results are shown in Fig. 7, which shows that the conductivity spectra at different temperatures for each composition are found to scale properly into a single master curve, indicating that the relaxation dynamics of mobile fluoride ions are independent of temperature. The frequency dependence of the real part of the dielectric permittivity, ε , for Ba0.7 Sn0.3 F2 of nominal composition x = 0.3 at
-5
log σdc (S / cm)
206
(a) x = 0.1 x = 0.2 x = 0.3 x = 0.4
0.43 eV
0.51 eV
-6
-7 0.45 eV
0.58 eV
-8
2.8
3.2
3.6
4.0
-1
1000 / T (K ) 8
(b) x = 0.1 x = 0.2 x = 0.3 x = 0.4
0.43 eV
7
log ωc (rad / s)
205
0.47 eV
6
5
0.45 eV 0.58 eV
4 2.6
2.8
3.0
3.2
3.4
3.6
3.8
4.0
4.2
-1
1000 / T (K ) Fig. 5. Reciprocal temperature dependence of (a) the dc conductivity and (b) the crossover radial frequency for the Ba1−x Snx F2 solid solutions. The solid lines are the straight-line fits and the corresponding activation energies are shown in the graphs.
Please cite this article in press as: M.M. Ahmad, et al., Mater. Sci. Eng. B (2013), http://dx.doi.org/10.1016/j.mseb.2013.05.011
ARTICLE IN PRESS
G Model MSB 13370 1–6
M.M. Ahmad et al. / Materials Science and Engineering B xxx (2013) xxx–xxx
6
x = 0.1 x = 0.2 x = 0.3 x = 0.4
222 K 241 K 260 K 281 K 301 K 320 K
5
-3
log n c (cm )
22
5
4
log ε'
21
3
2
20 240
280
320
360
Temperature (K)
1 3
4
5
253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272
271 K 281 K 290 K 301 K 311 K 320 K 331 K 341 K 350 K
15
10
tan δ
252
7
Fig. 8. Frequency dependence of ε at selected temperatures for Ba0.7 Sn0.3 F2 of nominal composition x = 0.3.
5
0 3
4
5
6
7
log ω (rad / s) Fig. 9. Frequency dependence of tan ı for Ba0.7 Sn0.3 F2 of nominal composition x = 0.3 at selected temperatures.
-2
x = 0.1 x = 0.2 x = 0.3 x = 0.4
2.0 -3
2.0 1.5 1.5 1.0 1.0 0.5 0.1
0.5
log τtanδ (s)
251
log σ ' / σ dc
250
selected temperatures is shown in Fig. 8. It is observed in this figure that ε approaches a limiting constant value at high frequencies, ε∞ . This value is unrelated to the hopping dynamics of the mobile ions and instead it is the result of much more rapid polarization processes occurring in the material. Moreover, the dielectric constant is found to increase rapidly at low frequencies. Similar dielectric behavior is observed for other compositions, and it is found that ε∞ has values of 8–25 for the investigated materials. The dielectric relaxation properties of the investigated materials are studied through the frequency dependence of the dissipation factor, tan ı = ε /ε , where ε is the imaginary part of the dielectric permittivity. Fig. 9 shows the frequency dependence of tan ı at different temperatures for x = 0.3. The large values of tan ı observed in Fig. 9 reflect the large contribution of the high ionic conductivity to the dielectric permittivity in the current materials. Well-defined peaks in the tan ı vs log ω plots are observed in Fig. 9, corresponding to dielectric relaxation phenomena. The position of the peaks shifts to high frequencies with increasing temperature, indicating a thermally activated process. We obtain the relaxation time, tan ı , of this process as a function of temperature from the condition that ωmax tan ı = 1 at the peak. The temperature dependence of tan ı is shown in Fig. 10 for the different investigated compositions. The values of the activation energy, Etan ı , of the dielectric relaxation process are 0.61, 0.50, 0.47 and 0.43 eV for x = 0.1, 0.2, 0.3 and 0.4
log σ ' / σ dc
249
6
log ω (rad / s)
Fig. 6. Temperature dependence of the concentration of mobile ions for different compositions of the Ba1−x Snx F2 solid solutions.
-4
-5
0.0 -6
0.
0.0
-0.5 -7
-4
-2
0
2
log ω / ω c Fig. 7. Scaling of the conductivity spectra at different temperatures of the Ba0.9 Sn0.1 F2 of nominal composition x = 0.1 and Ba0.7 Sn0.3 F2 of nominal composition x = 0.3.
2.0
2.5
3.0
3.5
4.0
-1
1000 / T (K ) Fig. 10. Reciprocal temperature dependence of the relaxation time for the Ba1−x Snx F2 solid solutions.
Please cite this article in press as: M.M. Ahmad, et al., Mater. Sci. Eng. B (2013), http://dx.doi.org/10.1016/j.mseb.2013.05.011
G Model MSB 13370 1–6
ARTICLE IN PRESS M.M. Ahmad et al. / Materials Science and Engineering B xxx (2013) xxx–xxx
6
275
compositions, respectively. It can be noticed that the values of Etan ı agree well with E , indicating that they have originated from the ionic hopping process.
276
4. Conclusions
273 274
289
Mechanochemical milling technique is successfully used to synthesize Ba1−x Snx F2 solid solutions for the first time at ambient conditions for the composition range x = 0.1–0.4. These fluoride solid solutions crystallize in the fluorite-type structure similar to pure BaF2 , with no secondary phases. The ionic conductivity, determined from the impedance data, increases considerably with increasing SnF2 content. The ionic conductivity of these solid solutions is up to six orders of magnitude higher than that of pure un-milled BaF2 . The concentration of mobile fluoride ions is found to be almost independent of SnF2 content, whereas the mobility is enhanced considerably with increasing SnF2 content. The enhanced mobility may be a result of the greater stereoactivity of the 5s2 lone pairs of the Sn2+ ions.
290
Acknowledgment
277 278 279 280 281 282 283 284 285 286 287 288
293
M.M.A. acknowledges the financial support from the Deanship of Scientific Research, King Faisal University under grant No. DSR110019.
294
References
291 292
295 296 297
[1] [2] [3] [4]
J.-M. Tarascon, M. Armand, Nature 414 (2001) 359. M. Armand, J.-M. Tarascon, Nature 451 (2008) 652. M. Whittingham, Chemical Reviews 104 (2004) 4271. G.A. Niklasson, C.G. Granqvist, Journal of Materials Chemistry 17 (2007) 127.
[5] F.C. Grozema, L.D.A. Siebbeles, International Reviews in Physical Chemistry 27 (2008) 87. [6] S. Hull, Reports on Progress in Physics 67 (2004) 1233. [7] M. Castiglione, P.A. Madden, P. Berastegui, S. Hull, Journal of Physics: Condensed Matter 17 (2005) 845. [8] P. Lagassie, J. Grannec, J.M. Reau, Solid State Ionics 21 (1986) 343. [9] Y. Ito, T. Mukoyama, K. Ashio, K. Yamamoto, Y. Suga, S. Yoshikado, C. Julian, T. Tanaka, Solid State Ionics 106 (1998) 291. [10] S. Vilminot, G. Perez, W. Granier, L. Cot, Solid State Ionics 2 (1981) 87. [11] S. Vilminot, G. Perez, W. Granier, L. Cot, Solid State Ionics 2 (1981) 91. [12] A. Collin, G. Denes, D. Le Roux, M.C. Madamba, J.M. Parris, A. Salaun, International Journal of Inorganic Materials 1 (1999) 289. [13] G. Denes, T. Birchall, M. Sayer, M.F. Bell, Solid State Ionics 13 (1984) 213. [14] G. Denes, Y.H. Yu, T. Tyliszczak, A.P. Hitchcock, Journal of Solid State Chemistry 91 (1991) 1. [15] S. Yoshikado, Y. Ito, J.M. Reau, Solid State Ionics 154/155 (2002) 503. [16] C. Suryanarayana, Progress in Materials Science 46 (2001) 1. [17] E. Gaffet, F. Bernard, J.C. Niepce, F. Charlot, C. Gras, G. Le Caer, J.L. Guichard, P. Delcroix, A. Mocellin, O. Tillement, Journal of Materials Chemistry 9 (1999) 305. [18] B. Ruprecht, M. Wilkening, A. Feldhoff, S. Steuernagelc, P. Heitjans, Physical Chemistry Chemical Physics 11 (2009) 3071. [19] M.R. Diaz-Guillen, K.J. Moreno, J.A. Diaz-Guillen, A.F. Fuentes, K.L. Ngai, J. GarciaBarriocanal, J. Santamaria, C. Leon, Physical Review B 78 (2008) 104304. [20] L.B. Kong, T.S. Zhang, J. Ma, F. Boey, Progress in Materials Science 53 (2008) 207. [21] M.M. Ahmad, Y. Yamane, K. Yamada, S. Tanaka, Journal of Physics D: Applied Physics 40 (2007) 6020. [22] M.M. Ahmad, Y. Yamane, K. Yamada, Journal of Applied Physics 106 (2009) 074106. [23] F. Izumi, T. Ikeda, Materials Science Forum 321–324 (2000) 198. [24] G. Scholz, I. Dorfel, D. Heidemann, M. Feist, R. Stosser, Journal of Solid State Chemistry 179 (2006) 1119. [25] L.N. Patro, K. Hariharan, Materials Letters 80 (2012) 26. [26] J.C. Dyre, Journal of Applied Physics 64 (1988) 2456. [27] D.P. Almond, G.K. Ducan, A.R. West, Solid State Ionics 8 (1983) 159. [28] S. Bhattacharya, A. Ghosh, Physical Review B 74 (2006) 184308. [29] M.M. Ahmad, K. Yamada, T. Okuda, Solid State Ionics 167 (2004) 285. [30] J.R. Macdonald, M.M. Ahmad, Journal of Physics: Condensed Matter 19 (2007) 046215. [31] M.M. Ahmad, K. Yamada, Journal of Chemical Physics 127 (2007) 124507. [32] A. Ghosh, A. Pan, Physical Review Letters 84 (2000) 2188.
Please cite this article in press as: M.M. Ahmad, et al., Mater. Sci. Eng. B (2013), http://dx.doi.org/10.1016/j.mseb.2013.05.011
298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337