204Tl tracer diffusion and conductivity in thallium thiogermanate glasses

Solid State Ionics 253 (2013) 101–109

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204

Tl tracer diffusion and conductivity in thallium thiogermanate glasses

M. Bokova a,b,⁎, I. Alekseev c,d, D. Kalyagin c, V. Tsegelnik c, Yu. Ermolenko c, E. Bychkov a,b a

Univ Lille Nord de France, F-59000 Lille, France ULCO, LPCA, EAC CNRS 4493, F-59140 Dunkerque, France c St. Petersburg University, 199034 St. Petersburg, Russia d V. G. Khlopin Radium Institute, 194021 St. Petersburg, Russia b

a r t i c l e

i n f o

Article history: Received 13 March 2013 Received in revised form 2 July 2013 Accepted 2 August 2013 Available online 28 September 2013 Keywords: Ionic conductivity and tracer diffusion Thallium thiogermanate glasses Haven ratio Thallium ion transport number

a b s t r a c t Conductivity and 204Tl tracer diffusion measurements have been carried out in the (Tl2S)x(GeS)60(GeS2)40−x glassy system, where the Tl2S concentration changes between 0 ≤ x ≤ 25. The room temperature dc conductivity increases by 7 orders of magnitude with increasing thallium concentration, ranging between 10−18 S cm−1 for the 60GeS-40GeS2 matrix and 10−11 S cm−1 for Tl2S-rich glasses. The activation energy decreases from 1.22 to 0.79 eV, respectively. The conductivity and thallium diffusion results reveal that the ionic transport becomes to be predominant at high thallium concentrations (≈15 at.% Tl). The thallium ion transport number t Tlþ increases from 10−3 for low cation concentrations to t Tlþ ≅1 for the x = 20 sample. The Haven ratio, HR ≈ 1, indicates uncorrelated ion motion even at rather high thallium concentrations. The obtained results are discussed in comparison with similar (Ag2S)x(GeS)60(GeS2)40−x glassy system. © 2013 Elsevier B.V. All rights reserved.

1. Introduction Chalcogenide glasses containing Ag+, Li+, Na+ or Cu+ exhibit high ionic conductivity, up to 10−2 S cm−1 at room temperature [1–9], which makes them suitable for many applications, i.e., all-solid-state batteries, phase-change memory devices, chemical sensors, etc. [10–13]. In addition, these glasses are suitable model materials to verify theories of the ion transport in disordered materials and the existence of contrasting ion transport regimes. In particular, ionic conductivity and 110mAg tracer diffusion measurements in homogeneous silver sulphide glasses over an extremely wide composition range, starting from 4 ppm to 33.3 at.% Ag, have shown three distinctly different ion transport regimes [4,14,15], which were also confirmed using a number of structural and spectroscopic techniques [16–18]. (i) Below the percolation threshold at ≈ 30 ppm Ag, the glasses are essentially electronic insulators with low silver ion transport number, 0:1≤t Agþ ≤0:2. The silver tracer diffusion coefficients and diffusion activation energy do not depend on Ag concentration and are very similar to those in pure host matrix. (ii) In the critical percolation region (between 30 ppm and ≈ 3 at.%), the ionic conductivity and diffusion depend on the silver content and connectivity of the host matrix, reflected by the average host coordination number. The mobile cation distribution is random and no preferential conduction pathways are still formed. (iii) In the modifier-controlled domain at high silver concentrations (above 10 at.%), the connectivity of

⁎ Corresponding author at: LPCA, EAC CNRS 4493, 189A avenue M. Shumann, 59140 Dunkerque, France. Tel.: +33 2 28 65 82 70; fax: +33 3 28 65 82 44. E-mail address: [email protected] (M. Bokova). 0167-2738/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ssi.2013.08.001

cation-related structural units appears to be predominant. The ionic transport is no longer caused by percolation, i.e., it becomes related to the connectivity of the cation subnetwork, forming preferential conduction pathways, with a strongly correlated motion of the Ag+ ions. Similar results were reported for Na+ and Cu+ ion-conducting glasses over extended mobile ion composition range [19,20,6]. The ionic radii for these cations, r Mþ , are however rather small, 0.77 Å ≤ rMþ ≤ 1.0 Å. The question arises whether different transport regimes can be observed for larger mobile ions. While the structure and conductivity of silver and light alkali containing chalcogenide glasses are widely studied, little is known about the ion transport of heavy alkali cations and Tl+ except for a few communications [21–25]. It is generally accepted, that the ionic conductivity of glasses increases with increasing alkali content and decreasing the alkali size [23–25]. As a result, the conductivity of heavy alkali thiogermanate glasses was found to be less than 10−12 S cm−1 caused by a large cation radius and a limited concentration of potassium, rubidium, or caesium in the glass. In contrast, Tl-rich glasses can easily be synthesised in chalcogenide systems [26]. The thallium chalcogenide glasses are not hygroscopic, and a suitable 204Tl tracer can be used for diffusion measurements [27]. To investigate the transport properties of thallium thiogermanate glasses and to compare them with similar Ag-containing vitreous alloys, we have chosen the Tl2S-GeS-GeS2 system. The (M2S)x(GeS)60(GeS2)40−x composition lines lie within the glass-forming range in the two ternary Tl-Ge-S and Ag-Ge-S systems (Fig. 1) [28–30]. The ionic conductivity and 110mAg tracer diffusion in silver thiogermanate glasses were reported previously [4].

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Fig. 1. Glass-forming regions (a) in the Ag2S-GeS-GeS2 system: ① according to Kawamoto et al. [28], ② according to Feltz and Thieme [29], and (b) in the Tl2S-GeS-GeS2 system according to Linke et al. [30]. The (M2S)x(GeS)60(GeS2)40−x composition lines, where M = Ag or Tl, are also shown.

2. Experimental details

to the intersection of two linear portions adjoining the transition elbow of the DSC trace.

2.1. Glass preparation Thallium thiogermanate glasses were prepared by mixing appropriate quantities of germanium (Aldrich, 99.999 %), sulphur (Aldrich, 99.999 %) and thallium (Fluka, 99.99 %). The mixtures were sealed under vacuum (10–6 mbar) in a cleaned silica tube (with an inner diameter of 8 mm and a wall thickness of 1 mm), heated slowly to 900 °C at 1 K min−1 heating rate and maintained at this temperature for a few days with repeated stirring of the melt. Once homogeneous, the glasses were cooled down to 800 °C and quenched in water at room temperature. To avoid the high vapour pressure of sulphur during initial steps of the synthesis, prolonged heating at 300, 500 and 800 °C was necessary. Glasses with low and very low thallium content (from 0.0083 to 0.83 at.% Tl) were prepared by dilution of a concentrated glass sample by the Tl-free glassy matrix. Typical sample mass was 3 g. The quenched samples were annealed at 20–30 °C below the glass transition temperature, Tg, for 24 h. Twelve compositions of the (Tl2S)x(GeS)60(GeS2)40−x glasses were synthesised, where x = 0, 0.01, 0.03, 0.1, 0.3, 1, 3, 5, 10, 15, 20, 25 mol.%. All the samples were dark coloured and had a shiny appearance. The amorphous nature of the samples was verified at room temperature by high energy x-ray diffraction using the 11-ID-C instrument at the Advanced Photon Source (Argonne National Laboratory, Chicago, USA) and by neutron diffraction using the GEM diffractometer at the ISIS spallation neutron source (Rutherford-Appleton Laboratory, Didcot, UK).

2.2. Density and DSC measurements 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 sample mass in air varied between 0.4 and 1 g. Differential scanning calorimetry, DSC, experiments were carried out using a Seiko SSC 5200 instrument at a heating rate of 10 K min−1 in the temperature range from 20 to 600 °C. Samples of 10 to 15 mg, encapsulated in a standard aluminium pan, were used for DSC measurements. An empty aluminium pan was 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

2.3. Conductivity measurements The dc conductivity of the samples was measured using a Hewlett Packard 4339B high resistance meter with the applied voltage of 100 V. The temperature range of the electrical measurements was usually from 20 to 200 °C or less depending on Tg and glass resistivity. The samples, prepared as rectangular plates, were polished using SiC powder (9.3 μ grain size). The sample sides were ground parallel and gold was deposited on opposite sides to form electrodes for a conductivity experiment, i.e., the electrochemical cell for conductivity measurements was Au|glass|Au. Typical thickness and area of the samples were in the range of 0.7–1.5 mm and 6–8 mm2, respectively. The temperature dependence of conductivity was studied in several cycles, each consisting of a heating and a cooling step, in order to investigate a possible hysteresis. 2.4. 204Tl tracer preparation The 204Tl tracer (the half-life t1/2 = 3.783 y) was produced by the Tl(n,γ)204Tl nuclear reaction. The TlNO3 target (144 mg, 99.9% chemical purity) was irradiated in a research reactor of St. Petersburg Nuclear Physics Institute using thermal neutrons with an average flux of 8.0(2) × 1013 n cm− 2 s− 1. After irradiation, the final (end of bombardment) specific 204Tl gamma activity was 0.3 mCi mg− 1, the radiochemical purity was 99.9%. The irradiated target was then dissolved in 5 mL of 2 M HNO3. The 204TlNO3 solution for tracer measurements was further prepared by dilution of the primary solution using 0.04 M HNO3. Typical thallium content in the last solution was below 300 μg mL− 1. 203

2.5. Tracer diffusion measurements The samples of different compositions, prepared as rectangular plates, were used for tracer diffusion measurements. Typical thickness of the samples was 800–1800 μm, the thickness uncertainty was ± 5 μm. A drop of radioactive 204TlNO3 solution was deposited onto one face of the sample, kept there for 80 min, wiped with a filter paper, washed with distilled water and ethyl alcohol, and then dried.

M. Bokova et al. / Solid State Ionics 253 (2013) 101–109

The samples were annealed in a furnace at 200 to 300 °C (the temperature stability was ± 2 °C) for a period of 5 days to 17 months. A high-purity Ge detector (GX1018, Canberra Ind., USA) was used to measure the initial and residual activity of the sample before and after sectioning. The spectrometer calibration in the energy range from 20 keV to 1600 keV was carried out using 109Cd, 152Eu, and 241Am sources with different activities. The radioactivity of the samples was determined using characteristic 204Hg photopeaks in the energy range 60–80 keV, whose quantum efficiency was 0.095–0.789%. The samples were placed in a polyethylene cell (the radioactive face to the bottom) in a well-defined fixed geometry. The activity measurements were carried out for 1000 s. A Genie 2000 program (Canberra Ind., USA) was used for data analysis. Typical Hg Kα,β X-ray fluorescence spectrum of the sample is shown in Fig. 2. Other details concerning tracer diffusion measurements were published elsewhere [31]. 3. Experimental results

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Fig. 3. (a) X-ray SX(Q) and (b) neutron SN(Q) Faber-Ziman structure factors for 25Tl2S60GeS-15GeS2 glasses synthesised using a total mass of (a) 0.3 g and (b) 3 g, respectively. (*) The Bragg peaks in the larger sample, measured using pulsed neutrons at the ISIS Facility (Rutherford-Appleton Laboratory, UK), correspond to crystalline germanium.

3.1. Glass-forming ability, density and thermal properties of Tl-Ge-S glasses The X-ray SX(Q) and neutron SN(Q) Faber-Ziman structure factors for 25Tl2S-60GeS-15GeS2 glasses synthesised using a total mass of 0.3 g and 3 g are presented in Fig. 3. The diffraction pattern of the small sample, measured using hard X-rays, exhibit only broad features characteristic of glassy and amorphous materials. The Bragg peaks in the larger sample, measured using pulsed neutrons, correspond to crystalline germanium. For the other samples with Tl2S content below 20 mol.%, 0 ≤ x ≤ 20, the Bragg peaks were not observed. Therefore, we estimate the limit of glass formation in the (Tl2S)x(GeS)60(GeS2)40−x system to be at x ≈ 25 mol.% Tl2S in our conditions of glass synthesis and quenching. These results are in accordance with the reported glass forming range presented in Fig. 1(b) [30]. The results of high-energy X-ray scattering and pulsed neutron diffraction experiments will be discussed elsewhere. The measured densities d of the thallium thiogermanate glasses are listed in Table 1 and their composition dependence is shown in Fig. 4(a). The obtained density values are compared with those in the silver thiogermanate glasses (Ag2S)x(GeS)60(GeS2)40−x [4]. The density increases monotonically with increasing cation concentration, y, in the both glassy systems. This trend was expected since the density of the binary glass (GeS)60(GeS2)40 (3.15 g cm−3) is lower than the density of crystalline c-Tl2S (8.45 g cm−3 [32]) and c-Ag2S (7.22 g cm−3 [33]). The density values were used to calculate the mean atomic volume, Va (Table 1, Fig. 4(b)). The Va decreases with increasing Ag content from 15.54 to 13.23 cm3 mol− 1 but remains essentially invariant for Tl-containing glasses (15.29 ≤ Va ≤ 15.54 cm3 mol− 1). Similar trends were reported for alkali thiogermanate glasses [34–36]: the

Va decreases for small cations, changes slightly or even increases for heavy alkalis, i.e., caesium (rCsþ = 1.74 Å). The average interatomic distances between Tl+ ions in the glass, rTl − Tl (Table 1), were calculated assuming a random distribution of cation sites and a spherical approximation:
r Tl−Tl ¼ 2

3V a 4πN A C Tl

1 3

;

ð1Þ

where NA is the number of Avogadro and CTl is the thallium fraction. The glass transition temperatures Tg are also summarised in Table 1 and shown in Fig. 5. A single glass transition was observed for all the samples indicating a homogeneous nature of the synthesised glasses. The Tg decreases from 350 °C (x = 0) to 200 °C (x = 25) for Tl-doped glasses, indicating a strong depolymerisation of germanium-sulphur network. The obtained results are consistent with increasing modifier content that reduces the number of bridging sulphur atoms, thus creating a fragmented network structure. The decreasing Tg was also observed in the (Ag2S)x(GeS)60(GeS2)40−x glasses (Fig. 5). The Tg(y) changes are very similar for the two systems at y ≤ 5 at.% but at higher mobile ion content the Tg(y) diverges. The thallium thiogermanate glasses reveal a nearly linear decrease with an average slope of –530 K atom−1. Their silver counterparts show a nearly constant Tg ≈ 250 °C above y = 15 at.% Ag. The observed differences at high y could have a structural basis and will be analysed using diffraction data elsewhere.

Table 1 Composition and physical properties of the (Tl2S)x(GeS)60(GeS2)40−x glasses. Cation concentration

Fig. 2. Typical Hg Kα,β X-ray fluorescence spectrum of a 204Tl-containing sample.

x (mol.% Tl2S)

y (at.% Tl)

0 0.01 0.03 0.1 0.3 1 3 5 10 15 20 25

0 0.0083 0.025 0.083 0.25 0.83 2.50 4.17 8.33 12.50 16.67 20.83

d (g cm−3)

Va (cm3 mol−1)

rT1–T1 (Å)

Tg (°C)

3.15 (2) 3.15 (1) 3.15 (1) 3.16 (1) 3.17 (1) 3.22 (1) 3.43 (1) 3.61 (1) 4.03 (2) 4.44 (2) 4.81 (2) 5.22 (3)

15.54 (10) 15.54 (5) 15.55 (5) 15.53 (5) 15.56 (5) 15.59 (5) 15.38 (4) 15.31 (4) 15.29 (8) 15.30 (7) 15.44 (6) 15.45 (9)

– 83.9 58.2 39.0 27.0 18.1 12.5 10.5 8.4 7.3 6.6 6.2

350 (2) 347 (2) 354 (2) 352 (2) 346 (2) 337 (2) 310 (2) 289 (2) 268 (2) 245 (2) 221 (2) 200 (2)

Uncertainties in the last digit(s) of the parameter are given in parentheses.

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Fig. 4. (a) Density and (b) mean atomic volume of (●) (Tl2S)x(GeS)60(GeS2)40−x (this work) and (○) (Ag2S)x(GeS)60(GeS2)40−x [4] glasses plotted as a function of the cation content. The solid lines are drawn as a guide for the eye.

3.2. Electric conductivity Typical temperature dependences of the total electrical conductivity σ for selected (Tl2S)x(GeS)60(GeS2)40−x glasses are presented in Fig. 6. The conductivity follows the Arrhenius law: σ¼


 σ0 E exp − σ ; T kT

ð2Þ

where σ0 is the pre-exponential factor, Eσ the activation energy, k the Boltzman constant and T the temperature. The room-temperature conductivity σ298, Eσ, and σ0 were calculated from a least-square fit of the data to Eq. (2). The results are listed in Table 2 and shown in Fig. 7. The room-temperature conductivity increases by 7 orders of magnitude with increasing thallium concentration from 10−18 S cm−1 for the 60GeS-40GeS2 matrix to 10−11 S cm−1 for Tl2S-rich glasses. The increase in conductivity is accompanied by a decrease in the activation energy from 1.22 to 0.79 eV. In contrast, the values of the preexponential factor (Table 2) do not change significantly within the experimental uncertainty. Similar trend was reported previously for the (Ag2S)x(GeS)60(GeS2)40 − x glasses [4] but the σ298 in the Ag-glasses increases considerably faster, Fig. 7(a). The conductivity ratio of the glasses with the same cation concentration changes within 104 ≤ σ298(Ag)/σ298(Tl) ≤ 106. Correspondingly, the conductivity activation energy Eσ in the silver thiogermanate glasses also decreases faster yielding a difference of 0.4 to 0.6 eV compared to their thallium relatives, Fig. 7(b).

Fig. 5. Composition dependence of the glass transition temperature Tg for (●) (Tl2S)x (GeS)60(GeS2)40−x (this work) and (○) (Ag2S)x(GeS)60(GeS2)40−x [16] glasses. The solid lines are drawn as a guide for the eye.

We should note a significant difference in conductivity (≈ 3 orders of magnitude at room temperature) for pure glassy matrix (GeS)60(GeS2)40 observed between our results and those reported earlier [4]. Di Salvo et al. [37] have shown that a common problem for extremely diluted chalcogenide glasses synthesised using insufficiently pure silica tubes, except for ultra-pure SiO2 (b0.2 ppm Fe), is an impurity iron diffusion from the tube into glass-forming melt at high temperature. The silica tubes used previously [4] could contaminate the glass at the ppm level (≤ 10 ppm Fe) reported for similar systems using magnetic susceptibility measurements over 4.2–300 K temperature range [38]. The transition metal impurities increase the electronic conductivity of chalcogenide glasses via small-polaron hopping between the transition metal ions in different oxidation states [39,40]. Thus, a possible reason of the observed discrepancy is an enhanced electronic conductivity caused by iron impurities. The suggested small-polaron hopping does not affect the ionic conductivity of the most diluted Ag-Ge-S glass (83 ppm Ag) studied previously [4]. The reported conductivity parameters for this glass are nearly identical to our

Fig. 6. Typical temperature dependence of the total electrical conductivity σ for selected (Tl2S)x(GeS)60(GeS2) 40−x glasses. The solid lines represent a least-square fit of the data to Eq. (2).

M. Bokova et al. / Solid State Ionics 253 (2013) 101–109 Table 2 Conductivity parameters for the (Tl2S)x(GeS)60(GeS2)40−x glasses: the room-temperature conductivity σ298, the activation energy Eσ, and the pre-exponential factor σ0. Thallium concentration x (mol.% Tl2S)

y (at.% Tl)

0 0.01 0.03 0.1 0.3 1 3 5 10 15 20 25

0 0.0083 0.025 0.083 0.25 0.83 2.50 4.17 8.33 12.50 16.67 20.83

log σ298 (S cm−1)

Eσ (eV)

log σ0 (S cm−1 K)

−17.78(37) −17.40(72) −17.18(53) −16.89(12) −16.67(26) −15.98(18) −15.65(11) −15.47(10) −14.90(10) −13.88(10) −12.57(12) −10.54(21)

1.22 (6) 1.25 (9) 1.21(10) 1.18 (2) 1.19 (4) 1.13 (4) 1.17 (2) 1.15 (2) 1.10 (2) 1.01 (2) 0.84 (2) 0.79 (4)

5.2 (6) 6.1(10) 5.7(13) 5.4 (3) 5.9 (4) 5.5 (5) 6.5 (3) 6.4 (3) 6.0 (3) 5.6 (3) 4.0 (3) 5.3 (5)

Uncertainties in the last digit(s) of the parameter are given in parentheses.

results for a 85 ppm Ag glass synthesised in our laboratory. The consistency of the conductivity data seems to be not surprising since Di Salvo et al. [37] have observed that doping the chalcogenide glasses with small amounts of Cu, Ag, or Au significantly reduces the Curie tail in magnetic susceptibility caused by iron impurities, i.e., decreases the impurity Fe content in the glass. The obtained results for the 85 ppm glass and a much lower conductivity of the presumably low-Fe glassy matrix open up a possibility to study the percolation threshold in Ag-Ge-S glasses in details. Our preliminary conductivity results show that the Ag-Ge-S glasses with even lower Ag content (up to 8.5 ppm) exhibit intermediate conductivity values between the 85 ppm glass and pure Ge-S matrix (Fig. 7). Further work is in progress and will be published elsewhere. 3.3. 204Tl tracer diffusion results Penetration profiles for 204Tl tracer diffusion in the (Tl2S)x (GeS)60(GeS2)40 − x glasses obey the usual solution of Fick's law for

105

an infinitesimally thin deposit of radioactive isotope on a semi infinite specimen [41] 1−

Aða; t Þ ¼ erf ðqÞ; A0

ð3Þ

where a q ¼ pffiffiffiffiffiffiffiffiffi ; 2 DTl t

ð4Þ

A(a,t) is the residual activity of the sample after a thickness a was removed, t is the diffusion anneal time, A0 is the initial residual activity, DTl is the tracer diffusion coefficient, and erf(q) is the Gauss error function. Experimentally determined values of A(a,t) and A0 yield q values which, when plotted vs. a, produce a straight line passing through the origin (Fig. 8). The thallium tracer diffusion coefficients DTl, determined from the slope of the penetration profiles at 220 °C, are shown in Fig. 9, plotted as DTl vs. y on a log–log scale. The 204Tl tracer diffusion coefficient increases by three orders of magnitude with increasing thallium concentration from 6.9 × 10−15 cm2 s−1 (y = 0.83 at.%) to 5.1 × 10−12 cm2 s−1 (y = 16.67 at.%) at 220 °C. It should be noted that the measured diffusion coefficients for Tl-poor glasses are at the limit of the sectioning method and need a very long diffusion anneal time of several months or more. Consequently, we were limited to rather high Tl concentrations in the glass, y ≥ 0.8 at.% Tl, in contrast to silver diffusion measurements, where ymin was 4 ppm Ag [14]. In addition, the x = 25 sample (20.83 at.% Tl), a limiting composition of the glass forming region, was too small for diffusion measurements. The silver thiogermanate glasses exhibit much higher DAg (5 orders of magnitude at y b 5 at. %) compared to the thallium glasses (Fig. 9). Nevertheless, this difference reduces to three orders of magnitude at high y. The critical percolation regime is clearly seen for the silver glasses below 5 at.% Ag, a power-law composition dependence of DAg over 2.5 orders of magnitude in y, which will be discussed in the next

Fig. 7. (a) Room-temperature conductivity σ298 and (b) conductivity activation energy Eσ for (●) (Tl2S)x(GeS)60(GeS2)40−x (this work) and (○) (Ag2S)x(GeS)60(GeS2)40−x [4] glasses plotted as a function of the cation concentration y. Conductivity data for (□) extremely diluted (Ag2S)x(GeS)60(GeS2)40−x glasses (8.5 ≤ y ≤ 85 ppm Ag) synthesised in this work are also shown (see text for details). The solid lines are drawn as a guide for the eye.

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20Tl2S-60GeS-20GeS2 220°C

HR ¼ 1.0

ð6Þ

In our dc experiments, we have measured the total conductivity σ of the glasses, representing the sum of ionic and electronic contributions:

0.5

σ ¼ σ i þ σ e; 0.0 0.000

0.005

0.010

0.015

0.020

0.025

Fig. 8. Typical 204Tl tracer diffusion profile for a (Tl2S)20(GeS)60(GeS2)20 glass annealed at 220 °C for 140 d. The solid circles correspond to penetration depth calculated using weight changes; the open symbols represent direct thickness measurements. The solid h line shows i −1 Þ 1− AðAa;t : a least-square fit of the experimental data points to Eq. (4), where q ¼ erf 0

section. The thallium thiogermanate glasses seem to show a similar trend at low y, however, complementary 204Tl tracer diffusion measurements at 0.1 ≤ y ≤ 1 at.% are necessary to endorse or disapprove this assumption. 4. Discussion 4.1. Composition dependence of the thallium ion transport number in glasses The diffusion coefficient Dσ can be calculated from the ionic conductivity σi using the Nernst–Einstein relation kTσ i ; NðzeÞ2

ð5Þ

where N is the concentration of the mobile species, ze is the electric charge of the carrier ion, and k and T have their usual meaning. The

Ag or Tl tracer diffusion coefficient DM

(cm2

s-1)

xM2S 60GeS (40-x)GeS2 10-8 10-9

M = Ag

10-10

σ i ¼ t Tlþ σ:

ð8Þ

Consequently, the measured total conductivity gives the apparent Haven ratio t Tlþ H R : t Tlþ HR ¼

DTl ; Dσ ðtotalÞ

xTl2S 60GeS (40-x)GeS2

10-12

M = Tl

10-13 -14

10-15

ð9Þ

where the conductivity coefficient Dσ(total) was calculated replacing the ionic conductivity in Eq. (5) by σ ¼ σ i =t Tlþ . The derived mean values of the t Tlþ H R are shown in Fig. 10. All the glasses except for the x = 20 sample (16.7 at.% Tl) exhibit very low values of the apparent Haven ratio starting at t Tlþ H R ≈ 10−3 and increasing with y. The Tl-rich sample yields t Tlþ H R = 0.93 ± 0.10 and appears to be ionic conductor, i.e., t Tlþ ≅ 1 and σi ≫ σe. The Haven ratio HR in oxide and chalcogenide glasses shows a universal trend: HR ≅ 1 at low mobile cation concentrations and decreases with increasing y [42–45,16]. The decreasingt Tlþ H R with decreasing y in the thallium thiogermanate glasses is therefore related to the decreasing t Tlþ while HR ≅ 1. In addition, the Haven ratio in glasses changes between 0.2 ≤ HR ≤ 1 [42–45,16] and thus t Tlþ H R ≈ 10−3 can only be related to t Tlþ ≈ 10−3. The calculated thallium ion transport numbers t Tlþ are shown in Fig. 11 plotted together with t Agþ for different silver sulphide and silver selenide glasses [46,4,47,14,17]. The silver diffusion coefficients are similar in sulphide and selenide glassy systems but the residual electronic conductivity is significantly higher in the silver selenide vitreous alloys compared to their sulphide counterparts; 10−10 S cm−1 ≤ σe (Se-glasses) ≤ 10− 7 S cm− 1 vs. 10− 14 S cm− 1 ≤ σe (S-glasses) ≤ 10− 10 S cm− 1 [48,49,40,4,9]. Consequently, the limiting value t Agþ ≅ 1 for the silver selenide systems is shifted to y ≈ 2 at.% Ag

10-11

10

ð7Þ

where σi is essentially the Tl+ cation conductivity, and σe the electronic conductivity. The ionic conductivity σi is related to the measured total conductivity σ via the thallium ion transport number t Tlþ :

Depth a (cm)

Dσ ¼

DTl : Dσ

220°C 0.01

0.1

1

10

Cation Concentration y (at.%) Fig. 9. Thallium and silver tracer diffusion coefficients at 220 °C for (●) (Tl2S)x (GeS)60(GeS2)40 −x (this work) and (○) (Ag2S)x(GeS)60(GeS2)40−x [4] glasses. The solid line at y ≤ 5 at.% Ag in the silver thiogermanate glasses and the dotted lines correspond to the critical percolation model discussed in the text. The other solid lines at y N 5 are drawn as a guide for the eye.

Apparent Haven Ratio tTl+HR

q = erf -1(1-A(a,t)/A0)

1.5

calculated values of Dσ and the experimentally-determined thallium tracer diffusion coefficients DTl can be compared using the Haven ratio, HR,

100

10-1

10-2

10-3 1

10

Thallium Concentration y (at.%) Fig. 10. Composition dependence of the apparent Haven ratio t Tlþ H R in the (Tl2S)x (GeS)60(GeS2)40−x glasses. The line is drawn as a guide for the eye.

M. Bokova et al. / Solid State Ionics 253 (2013) 101–109

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verify a possible decrease of HR at higher y. It is interesting to note the reported difference in HR for sodium germanate and sodium borosilicate glasses [43–45]. The low conducting Na2O-B2O3-SiO2 glasses (the difference in σi of 4 orders of magnitude compared to Na2O-GeO2) reveal the HR ≅ 1 up to 2.6 mol.% Na2O (y ≈ 1.2 at.% Na) while the sodium germanate vitreous alloys exhibit rapidly decreasing Haven ratio even at lower sodium content and HR ≈ 0.6 for y = 1.33 at.% Na. 4.2. Composition dependence of the ionic conductivity and tracer diffusion coefficient

Fig. 11. Composition dependences of the ion transport number t Mþ in (●) (Tl2S)x (GeS)60(GeS2)40−x (this work), (○) (Ag2S)x(GeS)60(GeS2)40−x [4], (□) (Ag2S)x(As2S3)100−x [46,14], (◊) Ag-Ge-Sb-Se [4], and (Δ) AgI-As2Se3 [47,17] glasses. The lines are drawn as a guide for the eye.

compared to y ≈ 0.1 at.% for the silver sulphide vitreous alloys. The thallium diffusion coefficients (and Tl+ ion mobility) are by a factor of 105 lower compared to DAg in the silver thiogermanate glasses (Fig. 9). As a result, the ionic conductivity becomes predominant, i.e., σi/σe ≫ 1 and t Tlþ ≅ 1, at even higher y ≥ 15 at.% Tl. The observed value of the Haven ratio, HR ≈ 1, for the x = 20 sample clearly shows that the Tl+ ion motion is uncorrelated at this rather high mobile ion concentration y = 16.67 at.%. In contrast, the uncorrelated motion of the Ag+ ions was only observed in Ag-diluted glasses at y ≤ 0.1 at.% [4]. The question arises why interionic Ag+– Ag+ interactions appear to be strong and leading to a correlated motion and a distinct HR decrease at large Ag-Ag separation distance rAg − Ag ≤ 30 Å while a similar phenomenon can only be observed at rTl − Tl ≤ 7 Å (Table 1). The low mobility of the Tl+ ions (5 orders of magnitude compared to the Ag+ ionic species) could be a possible reason of weaker electrodynamic interactions implying a relative insensitivity of HR within the investigated y-range. Further studies of new Tl-Ge-S glasses with higher Tl concentrations are needed to

The room temperature ionic conductivity σi for the Tl-Ge-S glasses was calculated from the measured total conductivity σ298 and thallium ion transport number t Tlþ using Eq. (8). The results are plotted on a loglog scale in Fig. 12(a) together with σi for the Ag-Ge-S glasses. The conductivity activation energy Eσ for the two thiogermanate glassy systems is plotted on a semi-logarithmic scale in Fig. 12(b). Two different ion transport regimes are clearly seen for the (Ag2S)x (GeS)60(GeS2)40−x glasses in Figs. 7, 9 and 12: the critical percolation above the percolation threshold at yc ≈ 30 ppm [14] and below y ≈ 3 at.% Ag, and the modifier-controlled regime at y ≥ 10 at.% Ag. In the critical percolation domain at yc ≤ y ≤ 1000 yc, the ionic conductivity σi(y,T) and tracer diffusion coefficient DM(y,T) follow a power-law dependence as a function of the mobile ion content y and temperature T [4,14]: t ðT Þ

σ i ðy; T Þ ¼ σ i ðl; T Þy

t ðT Þ−1

DM ðy; T Þ ¼ DM ðl; T Þy

ð10Þ ð11Þ

with temperature-dependent power-law exponent t(T) t ðT Þ ¼ t 0 þ T 0 =T≅T 0 =T;

ð12Þ

where σi(l,T) and DM(l,T) are the ionic conductivity and tracer diffusion coefficient of a hypothetical percolation-controlled phase at the mole

Fig. 12. (a) Room-temperature ionic conductivity σ i ¼ t Mþ σ 298 and (b) conductivity activation energy for (●) (Tl2S)x(GeS)60(GeS2)40−x (this work) and (○) (Ag2S)x(GeS)60(GeS2)40−x [4] glasses plotted on a log-log scale. The origin of the solid lines is given in the text.

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fraction y = 1, respectively; t0 is the critical exponent at T = ∞, and T0 is the critical fictive temperature. The values of t0 are negligibly small for chalcogenide glasses and could be neglected in Eq. (12). The conductivity or diffusion activation energy E(y) also depends on T0: EðyÞ ¼ E0 −kT 0 ln


 y ; yc

ð13Þ

where E0 is the activation energy at the percolation threshold yc. Thus, the percolation properties in chalcogenide systems are essentially dependent on a single parameter: the critical temperature T0. The T0 can be determined either from the conductivity and/or diffusion isotherms on a log–log scale (the solid lines in Figs. 12(a) and 9), or from the composition dependence of the activation energy on a semilogarithmic scale (the solid line in Fig. 12(b)). The two methods give consistent results, T0 = 549 ± 5 K for the (Ag2S)x(GeS)60(GeS2)40−x glasses [4]. It was also found that the critical temperature is related to the average local coordination number of the host matrix 〈n0〉 = ∑ iyiNi (where yi and Ni are the atomic fraction and the local coordination number of atomic species i in the host glass), i.e., to the matrix connectivity [15,18]: T 0 ∝hn0 i−2

ð14Þ

The ionic conductivity analysis in the (Tl2S)x(GeS)60(GeS2)40−x glassy system at y ≤ 4.2 at.% Tl yields the critical exponent t298 = 1.4 ± 0.3 and the critical temperature T0 = 420 ± 90 K in reasonable agreement with those for the silver thiogermanate glasses, especially taking into account a very limited number of the available experimental data points. A simple relocation of the critical percolation isotherms for the Ag-glasses into the Tl+ ion conductivity or 204Tl diffusion domains, shown in Figs. 12(b) and 9 by solid and dotted lines shifted by 8.5 and 5.3 orders of magnitude, respectively, suggest that the thallium thiogermanate glasses also exhibit a critical percolation regime at low y with a similar critical temperature T0 since the host glass in the two glassy systems is identical, (GeS)60(GeS2)40. The conductivity activation energy of the Tl-glasses plotted vs. log y, Fig. 12(b), does not show the

same or similar slope ∂ Eσ/∂ log y as in the Ag-Ge-S system at y b 5 at.% Ag. The last observation is not surprising since the thallium thiogermanate glasses are essentially electronic conductors in this composition range. Assuming the critical percolation regime at low y in the thallium glasses with similar or identical T0, we should note a drastic difference in σi(l,T), DM(l,T) and E0. This difference is presumably related to a larger ionic radius of Tl+ species (1.59 Å) compared to r Agþ = 1.0 Å. Although any further direct proof of the critical percolation can only be obtained using 204Tl diffusion, indirect evidence of similar structural changes in the host matrix on Tl or Ag doping is given by the Tg(y) evolution at y ≤ 5 at.% (Fig. 5). Fragmentation of the host network and formation of infinite percolation cluster(s) are accompanied by similar macroscopic changes in the two systems. Another question remaining unaddressed concerns the percolation threshold in the (Tl2S)x(GeS)60(GeS2)40−x glasses: could the yc be expected within a range of 30 ppm≤yc ≤1000 ppm Tl? In the modifier-controlled domain at y N 10 at.%, dramatic changes in the ion transport properties were observed (Figs. 9 and 12). Silverand thallium-rich glasses are characterised by an additional significant increase of the ionic conductivity (3.5 orders of magnitude for Ag+ and 7 orders of magnitude for Tl+ conducting glasses) and by a respective increase of DAg (a factor of 15 at 220 °C) and DTl (three orders of magnitude). The observed difference in the ionic conductivity and tracer diffusion evolution between silver and thallium thiogermanate glasses could be related to a different connectivity of the cationcentred structural units in the two systems. The analysis of high-energy X-ray scattering and pulsed neutron diffraction data is in progress to obtain a detailed structural information on the short- and intermediaterange ordering in the (Tl2S)x(GeS)60(GeS2)40−x system. The cation size remains however a key factor for fast ion transport. Fig. 13(a) shows the room-temperature ionic conductivity for a number of thiogermanate glasses in the modifier-controlled domain (this work and Ref. [2,4,24]). Small cations (Li+, Na+, Ag+) reveal a much higher conductivity compared to larger ionic species (K+, Rb+, Cs+, Tl+). Nevertheless, it should be noted that hypothetical heavy ion rich glasses (y ≥ 40 at.%) could also offer a potentially high ionic conductivity. The effect of ion size is even more evident for the conductivity activation

Fig. 13. (a) Room temperature ionic conductivity in the modifier-controlled domain as a function of the mobile cation concentration y, and (b) conductivity activation energy vs. cation radius at y = 13.33 at.%. (M2S)x(GeS)60(GeS2)40−x glasses: M = Tl (this work), M = Ag [4]; (M2S)x(GeS2)100−x glasses: M = Li, Na, K, Rb, Cs [2,24]. The lines are drawn as a guide for the eye.

M. Bokova et al. / Solid State Ionics 253 (2013) 101–109

energy, Fig. 13(b). A monotonic increase of Eσ with rMþ was observed, ∂Eσ =∂r Mþ = 0.4 ± 0.1 eV Å−1 at y = 13.33 at.%, irrespectively of the cation chemical nature (alkalis, thallium or silver) within the experimental uncertainty. Similar trend was reported for M2S-Ga2S3-GeS2 glasses (M = Li, Na, K, Cs) [25] and discussed using the modified Anderson-Stuart model [50–52]. 5. Conclusions Conductivity and 204Tl tracer diffusion measurements have been carried out in the (Tl2S)x(GeS)60(GeS2)40−x glassy system, where 0 ≤ x ≤ 25. The room temperature dc conductivity increases by 7 orders of magnitude with increasing thallium concentration, ranging between 10−18 S cm−1 for the 60GeS-40GeS2 matrix and 10−11 S cm−1 for Tl-rich glasses. The conductivity activation energy decreases from 1.22 to 0.79 eV. The conductivity and thallium diffusion results reveal that the ionic transport becomes predominant at high thallium concentrations (≈15 at.% Tl). The thallium ion transport number t Tlþ increases from 10−3 for low cation concentrations to t Tlþ ≅1 for the x = 20 sample. The Haven ratio, HR ≈ 1, indicates uncorrelated ion motion even at rather high thallium concentrations. The thallium thiogermanate glasses show two different ion transport regimes: the critical percolation below ≈5 at.% Tl, and the modifier-controlled regime at higher Tl concentrations. Further thallium diffusion measurements and detailed structural analysis are needed to decode the structural basis of the Tl+ ion transport, to obtain precise percolation parameters and to observe correlation effects of the ion motion. Acknowledgments The authors are grateful to Dr. Chris J. Benmore (Argonne) and Dr. Alex C. Hannon (ISIS) for their help with high-energy X-ray scattering and neutron diffraction measurements, respectively. The work at the Université du Littoral was supported by the EC within the Interreg IVA programme (the CleanTech project). References [1] M. Ribes, B. Barrau, J.L. Souquet, J. Non-Cryst. Solids 38&39 (1980) 271–276. [2] J.L. Souquet, E. Robinel, B. Barrau, M. Ribes, Solid State Ionics 3&4 (1981) 317–321. [3] M. Menetrier, A. Hojjaji, C. Estournes, A. Levasseur, Solid State Ionics 48 (1991) 325–330. [4] E. Bychkov, V. Tsegelnik, Yu. Vlasov, A. Pradel, M. Ribes, J. Non-Cryst. Solids 208 (1996) 1–20. [5] J. Kincs, S.W. Martin, Phys. Rev. Lett. 76 (1996) 70–73. [6] E. Bychkov, A. Bolotov, V. Tsegelnik, Yu. Grushko, Yu. Vlasov, Defect Diff. Forum 194–199 (2001) 919–924. [7] T. Usuki, S. Saito, K. Nakajima, O. Uemura, Y. Kameda, T. Kamiyama, M. Sakurai, J. Non-Cryst. Solids 312–314 (2002) 570–574.

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