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Na+ ion conducting glasses in the NaCl-Ga2S3-GeS2 system: A critical percolation regime
SOSI-14108; No of Pages 6 Solid State Ionics xxx (2016) xxx–xxx
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Na+ ion conducting glasses in the NaCl-Ga2S3-GeS2 system: A critical percolation regime A. Paraskiva, M. Bokova ⁎, E. Bychkov Univ Lille Nord de France, F-59000 Lille, France ULCO, LPCA, EAC CNRS 4493, F-59140 Dunkerque, France
a r t i c l e
i n f o
Article history: Received 14 June 2016 Received in revised form 28 October 2016 Accepted 4 November 2016 Available online xxxx Keywords: Na+ ion conducting glasses Ion transport mechanism Chalcogenide glasses
a b s t r a c t Sodium chalcogenide and chalcohalide glasses exhibit high ionic conductivity and can be used in all-solid-state batteries, chemical sensors and other devices. However, the available information on NaCl-containing chalcogenide glass systems is relatively poor. In this work we will present conductivity results for (NaCl)x(Ga2S3)0.2– −4 and 0.3, i.e., 3.5 orders of 0.2x(GeS2)0.8–0.8x glasses over a wide composition range, changing between x = 10 magnitude. Dc conductivity and ac impedance measurements have been used to study the electric properties of this glassy system. The room temperature conductivity increases by 11 orders of magnitude with increasing sodium concentration, ranging between 10−17 S cm−1 (x = 0) and 10−6 S cm−1 (x = 0.3, y = 10.1 at.% Na). The activation energy decreases from 0.99 to 0.35 eV, respectively. The composition dependence of the ionic conductivity shows two drastically different transport regimes at low (x ≤ 0.1, y ≤ 3.1 at.% Na) and high (x N 0.1) sodium concentrations. A characteristic feature of the conductivity isotherm for diluted glasses is a power law dependence of the ionic conductivity σi(y) ∝yT0/T, where T0 is the critical temperature related to connectivity of the host glass. The rapid increase of conductivity in a rather limited concentration range and the power law dependence of σi(y) are thus caused by a percolation-controlled mechanism. Deviations from the critical percolation regime are observed at higher sodium content and presumably related to the change in the ion transport mechanism. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Alkali-doped chalcogenide and chalcohalide glasses are promising materials for a number of applications as solid state electrolytes [1,2] or chemical sensors [3]. Lithium batteries provide the highest energy density which makes them ideal candidates for future generations of portable electronics (laptops, cellular, tablets, etc.) and hybrid electric vehicles for the time being. However, the increasing demand for lithium batteries will be limited by the fact that lithium is not an abundant material and its cost is expected to increase considerably in the coming years. In contrast, sodium resources are unlimited (fourth most abundant element in Earth's crust) and from economic point of view, sodium batteries appear as good alternative to lithium devices, particularly for large-scale stationary applications. Gallium germanium sulfides are excellent glass formers and give a variety of glasses containing alkali sulfides and chlorides. The glasses with Na2S additions are very hygroscopic and not suitable for electrochemical applications in aqueous solutions. On the other hand, NaCl-containing gallium-germanium ⁎ Corresponding author at: LPCA, EAC CNRS 4493, 189A avenue M. Schumann, 59140 Dunkerque, France. E-mail address: [email protected] (M. Bokova).
sulfides are more chemically stable in water and could be used as Na+-sensitive membranes for the ion-selective electrodes. Sodium containing Ge-Ga-S glasses have already been studied in several laboratories [4–7]. These glasses exhibit rather high ionic conductivity up to 10−5 S cm−1 for high cation concentrations. Nevertheless, very little is known about ion transport features in sodium chalcohalide systems except for a few papers [6,8]. Earlier, the detailed analysis of different conductivity mechanisms has been published for silver, copper and thallium doped glasses ([9] and references therein, [10]). Contrasting ion transport regimes were observed over a wide composition range: (i) below the percolation threshold at yc ≈ 30 ppm Ag, (ii) within the critical percolation region yc b y b 1– 3 at.% of mobile cation M+, and (iii) over the modifier-controlled domain at yN 10 at.% M+. The aim of our work is to study different transport regimes as a function of sodium concentration in the (NaCl)x(Ga2S3)0.2–0.2x(GeS2)0.8–0.8x glass system. For these purpose, we have synthesized glasses starting from the very diluted compositions (x = 10−4, y = 29 Na ppm) up to the limit of the glass forming range (x = 0.3, y = 10.1 at.% Na). Ac and dc conductivity data were used for the analysis of transport properties as well as the density and DSC results for macroscopic characterization of the samples.
http://dx.doi.org/10.1016/j.ssi.2016.11.003 0167-2738/© 2016 Elsevier B.V. All rights reserved.
Please cite this article as: A. Paraskiva, et al., Na+ ion conducting glasses in the NaCl-Ga2S3-GeS2 system: A critical percolation regime, Solid State Ionics (2016), http://dx.doi.org/10.1016/j.ssi.2016.11.003
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2. Experimental details 2.1. Glass preparation Glass sample compositions, (NaCl)x(Ga2S3)0.2–0.2x(GeS2)0.8–0.8x with 0 ≤ x ≤ 0.3, were prepared by mixing appropriate quantities of germanium (Neyco, 99.999%), sulfur (Acros Organics, 99.999%), gallium (Neyco, 99.999%) and sodium chloride (Acros Organics, 99,85%). Sample composition (typically 3 g of the total mass) was sealed under vacuum (10−6 mbar) in a cleaned silica tube with OD of 10 mm and wall thickness of 1 mm, heated slowly to 950 °C at 1 K min−1 heating rate and maintained at this temperature for a few days with repeated stirring of the melt. The melt was quenched in water at room temperature or in ice/water mixture depending on glass-forming ability. All the glasses were transparent yellow samples.
Table 1 Composition and physical properties of the (NaCl)x(Ga2S3)0.2–0.2x(GeS2)0.8–0.8x glasses. Sodium concentration x
y (at.% Na)
0 0.0001 0.0003 0.001 0.003 0.01 0.03 0.10 0.15 0.20 0.25 0.30
0 0.0029 0.0088 0.0294 0.0883 0.295 0.893 3.067 4.702 6.41 8.197 10.067
d (g cm−3)
Va (cm3 mol−1)
Tg (1) (°C)
Tg (2) (°C)
2.92 (1) 2.90 (1) 2.94 (1) 2.93 (1) 2.90 (1) 2.91 (1) 2.88 (1) 2.87 (2) 2.83 (1) 2.81 (1) 2.78 (2) 2.73 (1)
15.73 (8) 15.85 (1) 15.66 (8) 15.73 (4) 15.84 (4) 15.80 (5) 15.85 (3) 15.66 (9) 15.67 (5) 15.58 (4) 15.55 (14) 15.62 (8)
426 (5) 441 (8) 420 (7) 430 (5) 441 (5) 434 (5) 432 (5) 382 (5) 320 (9) 284 (13) 299 (14) 283 (5)
358 (5)
2.2. Density and DSC measurements
Uncertainties in the last digit(s) of the parameter are given in parentheses.
The density, d, of the samples was measured by a hydrostatic method using toluene as an immersion fluid and a germanium standard (5.323 g cm− 3). A Sartorius YDK 01-0D density kit was used for the measurements. The average density value was calculated from the measurements of several glass pieces. Differential scanning calorimetry, DSC, experiments were carried out using a TA Q200 instrument at a heating rate of 10 °C min− 1 in the temperature range from 20 to 550 °C. Samples of 5 to 15 mg, encapsulated in a standard aluminium pan, were used for DSC measurements. An empty aluminium pan served as a reference, and high purity nitrogen N2 as the purge gas. DSC traces were used to obtain the glass transition temperature Tg, as the temperature corresponding to the intersection of two linear portions adjoining the transition elbow of the DSC trace. Several measurements on the samples with the same glass composition were carried out to find the average glass transition temperature Tg.
were used to calculate the mean atomic volume, Va (Table 1). The Va remains essentially invariant (15.55 ≤ Va ≤ 15.85 cm3 mol− 1) for this glassy system, Fig. 1(b). The glass transition temperatures Tg are also summarized in Table 1 and shown in Fig. 2. The Tg decreases from 426 °C (x = 0) to 283 °C (x = 0.30). According to Raman spectroscopy results [5], the Tg decrease is related to a fragmentation of the Ga-Ge-S host network and formation of [Ga(Ge)S3/2Cl]− units. The x = 0.30 glass is phase-separated and has two glass transition temperatures, Tg(1) = 283 °C and Tg(2) = 358 °C. This composition is at the limit of the glass forming region where the glassy sample can be easily crystallized. The heating of the glass during the DSC measurement could favor its crystallization and the precipitation of NaCl is possible. Consequently, the composition of the sample may be changed locally with the formation of the sodium poor NaClGa2S3-GeS2 glassy phase. Thus, the second glass transition temperature of x = 0.30 glass could be attributed to the new glass with x = 0.10–0.15 formed during the DSC analysis. It should also be noted that the elbow corresponding to the glass transition on DSC traces of synthesized glasses is usually rather large and hence difficult to analyze. This may be the reason of the moderately different Tg values reported in literature for the same glass compositions. For example, the x = 0.10 glass is characterized by Tg = 382 °C (this work), 396 °C [7] and 342 °C [4]. A high viscosity of the gallium germanium sulfide host melt can explain this thermal behavior.
2.3. Conductivity measurements Bulk glass samples, prepared as rectangular plates with parallel sides and polished using SiC powder (9.3 μm grain size) were used for conductivity measurements. Gold electrodes were sputtered on the both sides, meaning that the electrochemical cell was Au|glass|Au. The typical sample thickness was 0.7–1.5 mm with a typical area of 6–8 mm2. The dc conductivity of the samples with high resistance was measured using a Hewlett Packard 4339B high resistance meter with voltage of 100 V. For the sodium rich samples having resistance R ≤ 10 MΩ, the ac conductivity was measured using a Hewlett Packard 4194A impedance meter. The impedance modulus Z and the phase angle θ were obtained in the frequency range from 100 Hz to 15 MHz. The temperature range of the electrical measurements was usually from 20 to 200 °C. The temperature dependence of conductivity was studied in several cycles, each consisting of a heating and a cooling step. Individual conductivity measurements were made every 10 °C and were not started until the sample temperature was stable within a deviation b 0.1 °C during 30 min. 3. Experimental results 3.1. Density and thermal properties The measured densities d of the (NaCl)x(Ga2S3)0.2–0.2x(GeS2)0.8–0.8x glasses are listed in Table 1 and their composition dependence is shown in Fig. 1(a). The density decreases quasi-linearly with increasing sodium concentration y over the entire glass-forming range. Similar decrease was observed previously [4,7] and can be easily predicted since the density of sodium chloride (2.165 g/cm3) is lower than the density of the host glass 0.2Ga2S3–0.8GeS2 (2.92 g/cm3). The density values
3.2. Electric conductivity The total electrical conductivity was determined either by the complex impedance method (σ N 10−7 S cm− 1) or from dc conductivity measurements (σ b 10−7 S cm− 1). Typical complex impedance diagrams for sodium-rich (NaCl)x(Ga2S3)0.2–0.2x(GeS2)0.8–0.8x glasses at 95 °C are presented in Fig. 3. The observed distorted semicircles are typical for ion-conducting glasses. The sample resistance decreases with sodium concentration. A distinct polarization is observed on the Cole-Cole impedance plots in the low-frequency region. All these features are indicative of ionic-type conductivity. The sample resistance was determined as interception of low-frequency polarization with the │Z│cosθ axis. The total electrical conductivity σ was obtained by the normalization of the reciprocal resistance to a geometrical factor L / A, where L is the sample thickness and A the sample area. Typical temperature dependences of the measured glass conductivity σ for selected (NaCl)x(Ga2S3)0.2–0.2x(GeS2)0.8–0.8x samples are presented in Fig. 4. The conductivity obeys the Arrhenius equation σ¼
σ0 Eσ exp − ; T kT
ð1Þ
where σ0 is the pre-exponential factor, Eσ the activation energy, k the
Please cite this article as: A. Paraskiva, et al., Na+ ion conducting glasses in the NaCl-Ga2S3-GeS2 system: A critical percolation regime, Solid State Ionics (2016), http://dx.doi.org/10.1016/j.ssi.2016.11.003
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Fig. 1. (a) Density and (b) atomic volume of (NaCl)x(Ga2S3)0.2–0.2x(GeS2)0.8–0.8x glasses plotted as a function of the sodium content y.
Fig. 2. Composition dependence of the glass transition temperature Tg for (NaCl)x(Ga2S3)0.2–0.2x(GeS2)0.8–0.8x glasses. The solid line is drawn as a guide for the eye.
Fig. 4. Typical temperature dependence of the total electrical conductivity σ for selected (NaCl)x(Ga2S3)0.2–0.2x(GeS2)0.8–0.8x glasses. The solid lines represent a least-square fit of the data to Eq. (1).
Table 2 Conductivity parameters for the (NaCl)x(Ga2S3)0.2–0.2x(GeS2)0.8–0.8x glasses: the roomtemperature conductivity σ298, the activation energy Eσ and the pre-exponential factor σ0. Sodium concentration
Fig. 3. Typical Cole-Cole impedance plots at 95 °C for sodium-rich (NaCl)x(Ga2S3)0.2– glasses, measured in an Au|glass|Au electrochemical cell. Arrow shows the increasing measurement frequency ω.
0.2x(GeS2)0.8–0.8x
x
y (at.% Na)
0 0.0001 0.0003 0.001 0.003 0.01 0.03 0.10 0.15 0.20 0.25 0.30
0 0.0029 0.0088 0.0294 0.0883 0.295 0.893 3.067 4.702 6.41 8.197 10.067
log σ298 (S cm−1)
Eσ (eV)
log σ0 (S cm−1 K)
−16.17 (10) −14.15 (2) −12.95 (3) −12.16 (2) −11,04 (3) −9.80 (5) −8.55 (2) −6.99 (1) −6.13 (1) −5.72 (1) −5.46 (4) −5.46 (2)
0.99 (2) 0.89 (1) 0.78 (1) 0.76 (1) 0.70 (1) 0.61 (1) 0.59 (1) 0.53 (1) 0.49 (1) 0.47 (1) 0.42 (1) 0.35 (1)
3.13 (25) 3.46 (8) 2.69 (12) 3.08 (7) 3.31 (12) 2.96 (15) 3.96 (9) 4.44 (1) 4.56 (3) 4.70 (4) 4.08 (11) 2.97 (7)
Uncertainties in the last digit(s) of the parameter are given in parentheses.
Please cite this article as: A. Paraskiva, et al., Na+ ion conducting glasses in the NaCl-Ga2S3-GeS2 system: A critical percolation regime, Solid State Ionics (2016), http://dx.doi.org/10.1016/j.ssi.2016.11.003
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Fig. 5. (a) Conductivity isotherm at 298 K, σ298, and (b) conductivity activation energy Eσ for (NaCl)x(Ga2S3)0.2–0.2x(GeS2)0.8–0.8x glasses plotted as a function of the sodium concentration y. The solid lines are drawn as a guide for the eye.
Boltzmann constant and T the temperature. The values of room-temperature conductivity σ298, Eσ, and σ0 were calculated from a least-square fit of the data to Eq. (1). The results are listed in Table 2 and shown in Fig. 5. The conductivity parameters obtained in this work for concentrated glass samples, x N 0.05, are in accordance with those reported previously for similar glassy systems [4,6,7,11]. The room-temperature conductivity, Fig. 5(a), increases by 11 orders of magnitude with increasing sodium content from 10−17 S cm−1 for the 0.2Ga2S3–0.8GeS2 matrix to 10− 6 S cm−1 for NaCl-rich glasses. A drastic conductivity increase at low y b 1–3 at.% Na is followed by a distinct saturation at high sodium concentrations. The increase in the conductivity is accompanied by a decrease in the activation energy, Fig. 5(b), from 0.99 eV to 0.35 eV. The values of the preexponential factor (Table 2) do not change significantly over the entire composition range.
4. Discussion Two concentration regions with distinctly different variations in conductivity parameters, Fig. 5, appear to be similar to those observed previously in silver chalcogenide glasses [9,12]. The only difference is related to the apparent saturation of conductivity at high sodium content y N 6 at.% Na. We will focus our attention on the low-sodium domain where extremely diluted glasses exhibit the strongest increase in conductivity with increasing y. The conductivity isotherms at room temperature and 373 K are plotted on a log-log scale in Fig. 6(a) and the conductivity activation energy is plotted on a semi-logarithmic scale in Fig. 6(b). At y ≤ 1–3 at.% Na, one observes a nearly perfect linear fit over 3 orders of magnitude in sodium concentration and 6 orders of magnitude in room-temperature conductivity. The same trend is repeated at 373 K with a lower slope t(T) and other temperatures not shown in Fig. 6. The linearity observed indicates that the conductivity
Fig. 6. (a) Conductivity isotherms at 298 K and 373 K plotted on a log-log scale and (b) conductivity activation energy Eσ plotted on a semi-logarithmic scale for (NaCl)x(Ga2S3)0.2– glasses. The origin of the solid lines is given in the text.
0.2x(GeS2)0.8–0.8x
Please cite this article as: A. Paraskiva, et al., Na+ ion conducting glasses in the NaCl-Ga2S3-GeS2 system: A critical percolation regime, Solid State Ionics (2016), http://dx.doi.org/10.1016/j.ssi.2016.11.003
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The critical temperature T0 can be determined either from the conductivity isotherms on a log-log scale, Figs. 6(a) and 7, or from the E(y) composition dependence on a semi-logarithmic scale, Fig. 6(b). The conductivity isotherm analysis yields T0 = 660 ± 24 K, while the critical temperature T0 = 599 ± 60 K was obtained from the activation energy data. Thus, the two methods give consistent results. It should also be noted that the critical temperature T0 is comparable with the glass transition temperature for the glassy host, 699 ± 5 K (Table 1). Similar results were reported previously for silver and copper chalcogenide glasses [14]). It was also found that the critical temperature is related to the average local coordination number of the host matrix hn0 i ¼ ∑ yi Ni , where yi and Ni are the atomic fraction and the local coi
ordination number of atomic species i in the host glass, i.e., to the host network connectivity [9]: Fig. 7. Temperature dependence of the critical exponent t(T) for (NaCl)x(Ga2S3)0.2– glasses.
T 0 ∝hn0 i−2:
at low y corresponds to the critical percolation regime and obeys power-law composition dependence [12,13]:
In other words, the critical percolation regime does not predict a percolation behavior for chain structures, 〈n0〉 = 2, in accordance with classical models (no percolation in a 1D network) [15]. Plotting the critical temperature T0, obtained in this work, with the results for silver chalcogenide glasses, one observes that the critical percolation regime and derived percolation parameters are very similar for the studied (NaCl)x(Ga2S3)0.2–0.2x(GeS2)0.8–0.8x glasses and their Ag+ ion-conducting counterparts (Fig. 8). The mobile cation distribution in the critical percolation regime is random and no preferential conduction pathways are yet formed. The transport mechanism at higher sodium content (y N 1 at.% Na) could be called as modifier-controlled regime [9]. In the modifier-controlled domain, the connectivity of the cation-related structural units is predominant and serves as preferential conduction pathways, ensure high mobility of the sodium ions. Further 22Na tracer diffusion measurements are necessary to verify Na+ ion transport at low sodium content, 30 ppm Na ≤ y ≤ 1 at.% Na and understand saturation effects at high y N 6 at.% Na. The observed two drastically different ion transport regimes in (NaCl)x(Ga2S3)0.2–0.2x(GeS2)0.8–0.8x glasses could be universal characteristics of the ionic conductivity in glasses. Raman spectroscopy, pulsed neutron and high-energy diffraction studies are in progress to provide structural information for these exciting ion-conducting glasses.
0.2x(GeS2)0.8–0.8x
σ i ðy; T Þ ¼ σ i ð1; T Þyt ðT Þ ;
ð2Þ
where σi(1, T) is the ionic conductivity of a hypothetical percolationcontrolled phase at y = 1, and t(T) is the temperature-dependent power-law exponent. The observed temperature dependence of the critical exponent can be written as t ðT Þ≅t 0 þ T 0 =T;
ð3Þ
where t0 is the critical exponent at T = ∞ and T0 is the critical temperature. The t0 parameter is small and could be neglected in Eq. (3). The conductivity activation energy E(y) also depends on T0: EðyÞ ¼ E0 −kT 0 ln
y ; yc
ð4Þ
where E0 is the activation energy at the percolation threshold yc. The linear decrease of E(y) plotted on a semi-logarithmic scale, Fig. 6(b), is consistent with Eq. (4). The critical exponent t(T) was calculated using the conductivity isotherms taken in the temperature range from 25 to 200 °C; the results are plotted vs. reciprocal temperature T−1 in Fig. 7. As expected, the critical exponent obeys Eq. (3) and decreases linearly with increasing temperature.
Fig. 8. Critical temperature T0 for (□) Ag2S-As2S5 [9], (○) Ag2S-As2S3 [9], (Δ) AgI-As2Se3 [16], (♦) Na2S-B2S3 [8] (◊) Ag-Ge-Sb-Se [12], (∇) Ag2S-GeS-GeS2 [12], (■) NaCl-Ga2S3GeS2 (this work) plotted as a function of the average local coordination number bn0 N of the host matrix.
ð5Þ
5. Conclusions Dc conductivity and ac impedance measurements have been used to study the electric properties of (NaCl)x(Ga2S3)0.2–0.2x(GeS2)0.8–0.8x glasses, where sodium concentration changes from y = 29 ppm Na (x = 10−4) to y = 10.1 at.% Na (x = 0.3), i.e., 3.5 orders of magnitude in sodium content. The room temperature conductivity increases by 11 orders of magnitude with increasing x or y, ranging between 10−17 S cm−1 (x = 0) and 10−6 S cm−1 (x = 0.3). The activation energy decreases from 0.99 to 0.35 eV, respectively. The composition dependence of ionic conductivity shows two drastically different transport regimes at low (x ≤ 0.1) and high (x N 0.1) NaCl content. Diluted sodium chloride glasses exhibit all characteristic features typical for the critical percolation regime observed previously for silver and copper fast ionconducting chalcogenide glasses, including power-law dependence of ionic conductivity σi(y) ∝ yT0/T, where T0 is the critical temperature related to connectivity of the host glass. Deviations from the critical percolation regime are observed at higher sodium content and presumably related to the change in the ion transport mechanism. References [1] K. Takada, T. Inada, A. Kajiyama, M. Kouguchi, H. Sasaki, S. Kondo, Y. Michiue, S. Nakano, M. Tabuchi, M. Watanabe, Solid State Ionics 172 (2004) 25–30. [2] A. Hayashi, K. Noi, A. Sakuda, M. Tatsumisago, Nat. Commun. 3 (2012) 856.
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Contents lists available at ScienceDirect
Solid State Ionics journal homepage: www.elsevier.com/locate/ssi
Na+ ion conducting glasses in the NaCl-Ga2S3-GeS2 system: A critical percolation regime A. Paraskiva, M. Bokova ⁎, E. Bychkov Univ Lille Nord de France, F-59000 Lille, France ULCO, LPCA, EAC CNRS 4493, F-59140 Dunkerque, France
a r t i c l e
i n f o
Article history: Received 14 June 2016 Received in revised form 28 October 2016 Accepted 4 November 2016 Available online xxxx Keywords: Na+ ion conducting glasses Ion transport mechanism Chalcogenide glasses
a b s t r a c t Sodium chalcogenide and chalcohalide glasses exhibit high ionic conductivity and can be used in all-solid-state batteries, chemical sensors and other devices. However, the available information on NaCl-containing chalcogenide glass systems is relatively poor. In this work we will present conductivity results for (NaCl)x(Ga2S3)0.2– −4 and 0.3, i.e., 3.5 orders of 0.2x(GeS2)0.8–0.8x glasses over a wide composition range, changing between x = 10 magnitude. Dc conductivity and ac impedance measurements have been used to study the electric properties of this glassy system. The room temperature conductivity increases by 11 orders of magnitude with increasing sodium concentration, ranging between 10−17 S cm−1 (x = 0) and 10−6 S cm−1 (x = 0.3, y = 10.1 at.% Na). The activation energy decreases from 0.99 to 0.35 eV, respectively. The composition dependence of the ionic conductivity shows two drastically different transport regimes at low (x ≤ 0.1, y ≤ 3.1 at.% Na) and high (x N 0.1) sodium concentrations. A characteristic feature of the conductivity isotherm for diluted glasses is a power law dependence of the ionic conductivity σi(y) ∝yT0/T, where T0 is the critical temperature related to connectivity of the host glass. The rapid increase of conductivity in a rather limited concentration range and the power law dependence of σi(y) are thus caused by a percolation-controlled mechanism. Deviations from the critical percolation regime are observed at higher sodium content and presumably related to the change in the ion transport mechanism. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Alkali-doped chalcogenide and chalcohalide glasses are promising materials for a number of applications as solid state electrolytes [1,2] or chemical sensors [3]. Lithium batteries provide the highest energy density which makes them ideal candidates for future generations of portable electronics (laptops, cellular, tablets, etc.) and hybrid electric vehicles for the time being. However, the increasing demand for lithium batteries will be limited by the fact that lithium is not an abundant material and its cost is expected to increase considerably in the coming years. In contrast, sodium resources are unlimited (fourth most abundant element in Earth's crust) and from economic point of view, sodium batteries appear as good alternative to lithium devices, particularly for large-scale stationary applications. Gallium germanium sulfides are excellent glass formers and give a variety of glasses containing alkali sulfides and chlorides. The glasses with Na2S additions are very hygroscopic and not suitable for electrochemical applications in aqueous solutions. On the other hand, NaCl-containing gallium-germanium ⁎ Corresponding author at: LPCA, EAC CNRS 4493, 189A avenue M. Schumann, 59140 Dunkerque, France. E-mail address: [email protected] (M. Bokova).
sulfides are more chemically stable in water and could be used as Na+-sensitive membranes for the ion-selective electrodes. Sodium containing Ge-Ga-S glasses have already been studied in several laboratories [4–7]. These glasses exhibit rather high ionic conductivity up to 10−5 S cm−1 for high cation concentrations. Nevertheless, very little is known about ion transport features in sodium chalcohalide systems except for a few papers [6,8]. Earlier, the detailed analysis of different conductivity mechanisms has been published for silver, copper and thallium doped glasses ([9] and references therein, [10]). Contrasting ion transport regimes were observed over a wide composition range: (i) below the percolation threshold at yc ≈ 30 ppm Ag, (ii) within the critical percolation region yc b y b 1– 3 at.% of mobile cation M+, and (iii) over the modifier-controlled domain at yN 10 at.% M+. The aim of our work is to study different transport regimes as a function of sodium concentration in the (NaCl)x(Ga2S3)0.2–0.2x(GeS2)0.8–0.8x glass system. For these purpose, we have synthesized glasses starting from the very diluted compositions (x = 10−4, y = 29 Na ppm) up to the limit of the glass forming range (x = 0.3, y = 10.1 at.% Na). Ac and dc conductivity data were used for the analysis of transport properties as well as the density and DSC results for macroscopic characterization of the samples.
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Please cite this article as: A. Paraskiva, et al., Na+ ion conducting glasses in the NaCl-Ga2S3-GeS2 system: A critical percolation regime, Solid State Ionics (2016), http://dx.doi.org/10.1016/j.ssi.2016.11.003
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2. Experimental details 2.1. Glass preparation Glass sample compositions, (NaCl)x(Ga2S3)0.2–0.2x(GeS2)0.8–0.8x with 0 ≤ x ≤ 0.3, were prepared by mixing appropriate quantities of germanium (Neyco, 99.999%), sulfur (Acros Organics, 99.999%), gallium (Neyco, 99.999%) and sodium chloride (Acros Organics, 99,85%). Sample composition (typically 3 g of the total mass) was sealed under vacuum (10−6 mbar) in a cleaned silica tube with OD of 10 mm and wall thickness of 1 mm, heated slowly to 950 °C at 1 K min−1 heating rate and maintained at this temperature for a few days with repeated stirring of the melt. The melt was quenched in water at room temperature or in ice/water mixture depending on glass-forming ability. All the glasses were transparent yellow samples.
Table 1 Composition and physical properties of the (NaCl)x(Ga2S3)0.2–0.2x(GeS2)0.8–0.8x glasses. Sodium concentration x
y (at.% Na)
0 0.0001 0.0003 0.001 0.003 0.01 0.03 0.10 0.15 0.20 0.25 0.30
0 0.0029 0.0088 0.0294 0.0883 0.295 0.893 3.067 4.702 6.41 8.197 10.067
d (g cm−3)
Va (cm3 mol−1)
Tg (1) (°C)
Tg (2) (°C)
2.92 (1) 2.90 (1) 2.94 (1) 2.93 (1) 2.90 (1) 2.91 (1) 2.88 (1) 2.87 (2) 2.83 (1) 2.81 (1) 2.78 (2) 2.73 (1)
15.73 (8) 15.85 (1) 15.66 (8) 15.73 (4) 15.84 (4) 15.80 (5) 15.85 (3) 15.66 (9) 15.67 (5) 15.58 (4) 15.55 (14) 15.62 (8)
426 (5) 441 (8) 420 (7) 430 (5) 441 (5) 434 (5) 432 (5) 382 (5) 320 (9) 284 (13) 299 (14) 283 (5)
358 (5)
2.2. Density and DSC measurements
Uncertainties in the last digit(s) of the parameter are given in parentheses.
The density, d, of the samples was measured by a hydrostatic method using toluene as an immersion fluid and a germanium standard (5.323 g cm− 3). A Sartorius YDK 01-0D density kit was used for the measurements. The average density value was calculated from the measurements of several glass pieces. Differential scanning calorimetry, DSC, experiments were carried out using a TA Q200 instrument at a heating rate of 10 °C min− 1 in the temperature range from 20 to 550 °C. Samples of 5 to 15 mg, encapsulated in a standard aluminium pan, were used for DSC measurements. An empty aluminium pan served as a reference, and high purity nitrogen N2 as the purge gas. DSC traces were used to obtain the glass transition temperature Tg, as the temperature corresponding to the intersection of two linear portions adjoining the transition elbow of the DSC trace. Several measurements on the samples with the same glass composition were carried out to find the average glass transition temperature Tg.
were used to calculate the mean atomic volume, Va (Table 1). The Va remains essentially invariant (15.55 ≤ Va ≤ 15.85 cm3 mol− 1) for this glassy system, Fig. 1(b). The glass transition temperatures Tg are also summarized in Table 1 and shown in Fig. 2. The Tg decreases from 426 °C (x = 0) to 283 °C (x = 0.30). According to Raman spectroscopy results [5], the Tg decrease is related to a fragmentation of the Ga-Ge-S host network and formation of [Ga(Ge)S3/2Cl]− units. The x = 0.30 glass is phase-separated and has two glass transition temperatures, Tg(1) = 283 °C and Tg(2) = 358 °C. This composition is at the limit of the glass forming region where the glassy sample can be easily crystallized. The heating of the glass during the DSC measurement could favor its crystallization and the precipitation of NaCl is possible. Consequently, the composition of the sample may be changed locally with the formation of the sodium poor NaClGa2S3-GeS2 glassy phase. Thus, the second glass transition temperature of x = 0.30 glass could be attributed to the new glass with x = 0.10–0.15 formed during the DSC analysis. It should also be noted that the elbow corresponding to the glass transition on DSC traces of synthesized glasses is usually rather large and hence difficult to analyze. This may be the reason of the moderately different Tg values reported in literature for the same glass compositions. For example, the x = 0.10 glass is characterized by Tg = 382 °C (this work), 396 °C [7] and 342 °C [4]. A high viscosity of the gallium germanium sulfide host melt can explain this thermal behavior.
2.3. Conductivity measurements Bulk glass samples, prepared as rectangular plates with parallel sides and polished using SiC powder (9.3 μm grain size) were used for conductivity measurements. Gold electrodes were sputtered on the both sides, meaning that the electrochemical cell was Au|glass|Au. The typical sample thickness was 0.7–1.5 mm with a typical area of 6–8 mm2. The dc conductivity of the samples with high resistance was measured using a Hewlett Packard 4339B high resistance meter with voltage of 100 V. For the sodium rich samples having resistance R ≤ 10 MΩ, the ac conductivity was measured using a Hewlett Packard 4194A impedance meter. The impedance modulus Z and the phase angle θ were obtained in the frequency range from 100 Hz to 15 MHz. The temperature range of the electrical measurements was usually from 20 to 200 °C. The temperature dependence of conductivity was studied in several cycles, each consisting of a heating and a cooling step. Individual conductivity measurements were made every 10 °C and were not started until the sample temperature was stable within a deviation b 0.1 °C during 30 min. 3. Experimental results 3.1. Density and thermal properties The measured densities d of the (NaCl)x(Ga2S3)0.2–0.2x(GeS2)0.8–0.8x glasses are listed in Table 1 and their composition dependence is shown in Fig. 1(a). The density decreases quasi-linearly with increasing sodium concentration y over the entire glass-forming range. Similar decrease was observed previously [4,7] and can be easily predicted since the density of sodium chloride (2.165 g/cm3) is lower than the density of the host glass 0.2Ga2S3–0.8GeS2 (2.92 g/cm3). The density values
3.2. Electric conductivity The total electrical conductivity was determined either by the complex impedance method (σ N 10−7 S cm− 1) or from dc conductivity measurements (σ b 10−7 S cm− 1). Typical complex impedance diagrams for sodium-rich (NaCl)x(Ga2S3)0.2–0.2x(GeS2)0.8–0.8x glasses at 95 °C are presented in Fig. 3. The observed distorted semicircles are typical for ion-conducting glasses. The sample resistance decreases with sodium concentration. A distinct polarization is observed on the Cole-Cole impedance plots in the low-frequency region. All these features are indicative of ionic-type conductivity. The sample resistance was determined as interception of low-frequency polarization with the │Z│cosθ axis. The total electrical conductivity σ was obtained by the normalization of the reciprocal resistance to a geometrical factor L / A, where L is the sample thickness and A the sample area. Typical temperature dependences of the measured glass conductivity σ for selected (NaCl)x(Ga2S3)0.2–0.2x(GeS2)0.8–0.8x samples are presented in Fig. 4. The conductivity obeys the Arrhenius equation σ¼
σ0 Eσ exp − ; T kT
ð1Þ
where σ0 is the pre-exponential factor, Eσ the activation energy, k the
Please cite this article as: A. Paraskiva, et al., Na+ ion conducting glasses in the NaCl-Ga2S3-GeS2 system: A critical percolation regime, Solid State Ionics (2016), http://dx.doi.org/10.1016/j.ssi.2016.11.003
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Fig. 1. (a) Density and (b) atomic volume of (NaCl)x(Ga2S3)0.2–0.2x(GeS2)0.8–0.8x glasses plotted as a function of the sodium content y.
Fig. 2. Composition dependence of the glass transition temperature Tg for (NaCl)x(Ga2S3)0.2–0.2x(GeS2)0.8–0.8x glasses. The solid line is drawn as a guide for the eye.
Fig. 4. Typical temperature dependence of the total electrical conductivity σ for selected (NaCl)x(Ga2S3)0.2–0.2x(GeS2)0.8–0.8x glasses. The solid lines represent a least-square fit of the data to Eq. (1).
Table 2 Conductivity parameters for the (NaCl)x(Ga2S3)0.2–0.2x(GeS2)0.8–0.8x glasses: the roomtemperature conductivity σ298, the activation energy Eσ and the pre-exponential factor σ0. Sodium concentration
Fig. 3. Typical Cole-Cole impedance plots at 95 °C for sodium-rich (NaCl)x(Ga2S3)0.2– glasses, measured in an Au|glass|Au electrochemical cell. Arrow shows the increasing measurement frequency ω.
0.2x(GeS2)0.8–0.8x
x
y (at.% Na)
0 0.0001 0.0003 0.001 0.003 0.01 0.03 0.10 0.15 0.20 0.25 0.30
0 0.0029 0.0088 0.0294 0.0883 0.295 0.893 3.067 4.702 6.41 8.197 10.067
log σ298 (S cm−1)
Eσ (eV)
log σ0 (S cm−1 K)
−16.17 (10) −14.15 (2) −12.95 (3) −12.16 (2) −11,04 (3) −9.80 (5) −8.55 (2) −6.99 (1) −6.13 (1) −5.72 (1) −5.46 (4) −5.46 (2)
0.99 (2) 0.89 (1) 0.78 (1) 0.76 (1) 0.70 (1) 0.61 (1) 0.59 (1) 0.53 (1) 0.49 (1) 0.47 (1) 0.42 (1) 0.35 (1)
3.13 (25) 3.46 (8) 2.69 (12) 3.08 (7) 3.31 (12) 2.96 (15) 3.96 (9) 4.44 (1) 4.56 (3) 4.70 (4) 4.08 (11) 2.97 (7)
Uncertainties in the last digit(s) of the parameter are given in parentheses.
Please cite this article as: A. Paraskiva, et al., Na+ ion conducting glasses in the NaCl-Ga2S3-GeS2 system: A critical percolation regime, Solid State Ionics (2016), http://dx.doi.org/10.1016/j.ssi.2016.11.003
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Fig. 5. (a) Conductivity isotherm at 298 K, σ298, and (b) conductivity activation energy Eσ for (NaCl)x(Ga2S3)0.2–0.2x(GeS2)0.8–0.8x glasses plotted as a function of the sodium concentration y. The solid lines are drawn as a guide for the eye.
Boltzmann constant and T the temperature. The values of room-temperature conductivity σ298, Eσ, and σ0 were calculated from a least-square fit of the data to Eq. (1). The results are listed in Table 2 and shown in Fig. 5. The conductivity parameters obtained in this work for concentrated glass samples, x N 0.05, are in accordance with those reported previously for similar glassy systems [4,6,7,11]. The room-temperature conductivity, Fig. 5(a), increases by 11 orders of magnitude with increasing sodium content from 10−17 S cm−1 for the 0.2Ga2S3–0.8GeS2 matrix to 10− 6 S cm−1 for NaCl-rich glasses. A drastic conductivity increase at low y b 1–3 at.% Na is followed by a distinct saturation at high sodium concentrations. The increase in the conductivity is accompanied by a decrease in the activation energy, Fig. 5(b), from 0.99 eV to 0.35 eV. The values of the preexponential factor (Table 2) do not change significantly over the entire composition range.
4. Discussion Two concentration regions with distinctly different variations in conductivity parameters, Fig. 5, appear to be similar to those observed previously in silver chalcogenide glasses [9,12]. The only difference is related to the apparent saturation of conductivity at high sodium content y N 6 at.% Na. We will focus our attention on the low-sodium domain where extremely diluted glasses exhibit the strongest increase in conductivity with increasing y. The conductivity isotherms at room temperature and 373 K are plotted on a log-log scale in Fig. 6(a) and the conductivity activation energy is plotted on a semi-logarithmic scale in Fig. 6(b). At y ≤ 1–3 at.% Na, one observes a nearly perfect linear fit over 3 orders of magnitude in sodium concentration and 6 orders of magnitude in room-temperature conductivity. The same trend is repeated at 373 K with a lower slope t(T) and other temperatures not shown in Fig. 6. The linearity observed indicates that the conductivity
Fig. 6. (a) Conductivity isotherms at 298 K and 373 K plotted on a log-log scale and (b) conductivity activation energy Eσ plotted on a semi-logarithmic scale for (NaCl)x(Ga2S3)0.2– glasses. The origin of the solid lines is given in the text.
0.2x(GeS2)0.8–0.8x
Please cite this article as: A. Paraskiva, et al., Na+ ion conducting glasses in the NaCl-Ga2S3-GeS2 system: A critical percolation regime, Solid State Ionics (2016), http://dx.doi.org/10.1016/j.ssi.2016.11.003
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The critical temperature T0 can be determined either from the conductivity isotherms on a log-log scale, Figs. 6(a) and 7, or from the E(y) composition dependence on a semi-logarithmic scale, Fig. 6(b). The conductivity isotherm analysis yields T0 = 660 ± 24 K, while the critical temperature T0 = 599 ± 60 K was obtained from the activation energy data. Thus, the two methods give consistent results. It should also be noted that the critical temperature T0 is comparable with the glass transition temperature for the glassy host, 699 ± 5 K (Table 1). Similar results were reported previously for silver and copper chalcogenide glasses [14]). It was also found that the critical temperature is related to the average local coordination number of the host matrix hn0 i ¼ ∑ yi Ni , where yi and Ni are the atomic fraction and the local coi
ordination number of atomic species i in the host glass, i.e., to the host network connectivity [9]: Fig. 7. Temperature dependence of the critical exponent t(T) for (NaCl)x(Ga2S3)0.2– glasses.
T 0 ∝hn0 i−2:
at low y corresponds to the critical percolation regime and obeys power-law composition dependence [12,13]:
In other words, the critical percolation regime does not predict a percolation behavior for chain structures, 〈n0〉 = 2, in accordance with classical models (no percolation in a 1D network) [15]. Plotting the critical temperature T0, obtained in this work, with the results for silver chalcogenide glasses, one observes that the critical percolation regime and derived percolation parameters are very similar for the studied (NaCl)x(Ga2S3)0.2–0.2x(GeS2)0.8–0.8x glasses and their Ag+ ion-conducting counterparts (Fig. 8). The mobile cation distribution in the critical percolation regime is random and no preferential conduction pathways are yet formed. The transport mechanism at higher sodium content (y N 1 at.% Na) could be called as modifier-controlled regime [9]. In the modifier-controlled domain, the connectivity of the cation-related structural units is predominant and serves as preferential conduction pathways, ensure high mobility of the sodium ions. Further 22Na tracer diffusion measurements are necessary to verify Na+ ion transport at low sodium content, 30 ppm Na ≤ y ≤ 1 at.% Na and understand saturation effects at high y N 6 at.% Na. The observed two drastically different ion transport regimes in (NaCl)x(Ga2S3)0.2–0.2x(GeS2)0.8–0.8x glasses could be universal characteristics of the ionic conductivity in glasses. Raman spectroscopy, pulsed neutron and high-energy diffraction studies are in progress to provide structural information for these exciting ion-conducting glasses.
0.2x(GeS2)0.8–0.8x
σ i ðy; T Þ ¼ σ i ð1; T Þyt ðT Þ ;
ð2Þ
where σi(1, T) is the ionic conductivity of a hypothetical percolationcontrolled phase at y = 1, and t(T) is the temperature-dependent power-law exponent. The observed temperature dependence of the critical exponent can be written as t ðT Þ≅t 0 þ T 0 =T;
ð3Þ
where t0 is the critical exponent at T = ∞ and T0 is the critical temperature. The t0 parameter is small and could be neglected in Eq. (3). The conductivity activation energy E(y) also depends on T0: EðyÞ ¼ E0 −kT 0 ln
y ; yc
ð4Þ
where E0 is the activation energy at the percolation threshold yc. The linear decrease of E(y) plotted on a semi-logarithmic scale, Fig. 6(b), is consistent with Eq. (4). The critical exponent t(T) was calculated using the conductivity isotherms taken in the temperature range from 25 to 200 °C; the results are plotted vs. reciprocal temperature T−1 in Fig. 7. As expected, the critical exponent obeys Eq. (3) and decreases linearly with increasing temperature.
Fig. 8. Critical temperature T0 for (□) Ag2S-As2S5 [9], (○) Ag2S-As2S3 [9], (Δ) AgI-As2Se3 [16], (♦) Na2S-B2S3 [8] (◊) Ag-Ge-Sb-Se [12], (∇) Ag2S-GeS-GeS2 [12], (■) NaCl-Ga2S3GeS2 (this work) plotted as a function of the average local coordination number bn0 N of the host matrix.
ð5Þ
5. Conclusions Dc conductivity and ac impedance measurements have been used to study the electric properties of (NaCl)x(Ga2S3)0.2–0.2x(GeS2)0.8–0.8x glasses, where sodium concentration changes from y = 29 ppm Na (x = 10−4) to y = 10.1 at.% Na (x = 0.3), i.e., 3.5 orders of magnitude in sodium content. The room temperature conductivity increases by 11 orders of magnitude with increasing x or y, ranging between 10−17 S cm−1 (x = 0) and 10−6 S cm−1 (x = 0.3). The activation energy decreases from 0.99 to 0.35 eV, respectively. The composition dependence of ionic conductivity shows two drastically different transport regimes at low (x ≤ 0.1) and high (x N 0.1) NaCl content. Diluted sodium chloride glasses exhibit all characteristic features typical for the critical percolation regime observed previously for silver and copper fast ionconducting chalcogenide glasses, including power-law dependence of ionic conductivity σi(y) ∝ yT0/T, where T0 is the critical temperature related to connectivity of the host glass. Deviations from the critical percolation regime are observed at higher sodium content and presumably related to the change in the ion transport mechanism. References [1] K. Takada, T. Inada, A. Kajiyama, M. Kouguchi, H. Sasaki, S. Kondo, Y. Michiue, S. Nakano, M. Tabuchi, M. Watanabe, Solid State Ionics 172 (2004) 25–30. [2] A. Hayashi, K. Noi, A. Sakuda, M. Tatsumisago, Nat. Commun. 3 (2012) 856.
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Please cite this article as: A. Paraskiva, et al., Na+ ion conducting glasses in the NaCl-Ga2S3-GeS2 system: A critical percolation regime, Solid State Ionics (2016), http://dx.doi.org/10.1016/j.ssi.2016.11.003