Tracer diffusion studies of ion-conducting chalcogenide glasses

Solid State Ionics 136–137 (2000) 1111–1118 www.elsevier.com / locate / ssi

Tracer diffusion studies of ion-conducting chalcogenide glasses E. Bychkov* Universite´ du Littoral, 59140 Dunkerque, France

Abstract Tracer diffusion measurements allow independent and complementary information on long-range ion transport in glasses to be obtained. These experiments are rather rare for ion-conducting chalcogenide glasses although the existing diffusion data exhibit a lot of interesting examples of the combined (conductivity s and diffusion D) studies and even the phenomena which could not be observed by using the electrical measurements alone. Some selected topics of the tracer diffusion experiments in chalcogenide glasses are given and discussed in the present paper.  2000 Elsevier Science B.V. All rights reserved. Keywords: Ion conducting glasses; Long range ion-transport; Chalcogenide glasses

1. Introduction Tracer diffusion experiments were extensively used in the past to study the ion transport processes in oxide glasses [1–6]. Some important issues and phenomena were discovered during that time: markedly higher diffusion coefficients for alkali cations compared to those for alkali-earth, glass-forming (Si 41 , Al 31 , etc.) or oxygen ions; diffusivity crossover for mixed alkali glasses; universal changes in the Haven ratio HR with increasing mobile ion content from uncorrelated (HR 5 1) to strongly correlated (HR 5 0.2–0.4) ion motion. On the contrary, the diffusion measurements were rather rare for chalcogenide glasses [7–9]. Nevertheless, recent diffusion results exhibit a lot of interesting examples of the combined (electrical conductivity s and tracer diffusion D) studies and even the phenomena which *Tel.: 133-328-658-250; fax:133-328-658-244. E-mail address: [email protected] (E. Bychkov).

could not be observed by using the electrical measurements alone. Due to strict space limit, our attention will be focused on the critical percolation behaviour in Ag 1 ion conducting glasses at low silver content. Two other phenomena (degenerated mixed cation effect and non-Arrhenius ion transport at high temperature) will only be mentioned. 2. Percolation transition in Ag 1 ion conducting glasses 110

Ag tracer diffusion experiments and electrical measurements carried out for a number of homogeneous chalcogenide glasses over an extremely large composition range, covering in some cases nearly five orders of magnitude in the silver concentration, clearly show at least three distinctly different transport regimes: (i) below, (ii) just above, and (iii) far above the percolation threshold at x c ¯ 30 ppm Ag [10–12]. Characteristic features of the ion transport

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in the critical percolation region (x c , x , 1–3 at.% Ag) can be summarised as follows. The ionic conductivity si becomes predominant even for highly diluted glasses in case of the sulphide systems (Ag 2 S–GeS–GeS 2 , Ag 2 S–As 2 S 3 ). The silver ion transport number exhibits a step-like increase from 0.1–0.2 (x , x c ) to 0.7–0.8 (x 5 80– 120 ppm Ag) and increases rapidly to 1 with further silver doping (Fig. 1). The selenide glassy systems (Ag–Ge–Sb–Se, AgI–As 2 Se 3 ) reveal an enhanced residual electronic conductivity but even in this case tAg1 tends to 1 at x $ 0.3 at.% Ag. A power-law composition dependence of si (x) and DAg (x) over 2.5 orders of magnitude in the Ag concentration is observed (Fig. 2)

with temperature-dependent power-law exponent t(T ) [10]

tivity and diffusion coefficient of a hypothetical percolation-controlled phase at x51, t 0 is small and could be neglected in Eq. (3), T 0 is the critical fictive temperature which will be discussed later. Accordingly, the conductivity Ea and diffusion Ed activation energies are very similar and decrease linearly with increasing log x (Fig. 3). Three different models give nearly identical equations to describe the observed phenomena: modified classical percolation [10], the dynamic structure model [13] and a statistical (occupation) approach taking into account percolation effects on ionic conduction in glasses [14]. The modified classical percolation model predicts the effect of glass network dimensionality and seems to be more adapted to explain the obtained conductivity and diffusion results [10–12]. Classical geometrical percolation [15–17] dealing with temperature-invariant conductances in a random resistor network gives a simple relation for the conductance G( p) as a function of site or bond fraction p just above the percolation threshold pc

t(T ) 5 t 0 1 T 0 /T(T 0 /T

G( p) ~ ( p 2 pc )t

si (x,T ) 5 si (1,T )x t(T )

(1)

DAg (x,T ) 5 DAg (1,T )x t(T )21

(2)

(3)

where si (1,T ) and DAg (1,T ) are the ionic conduc-

(4)

for site, bond or correlated bond percolation models.

Fig. 1. Silver ion transport number as a function of the silver content for Ag 2 S–As 2 S 3 glasses: (i) in the electronic insulator domain below the percolation threshold at x c ¯30 ppm Ag, (ii) in the critical percolation region (x c ,x,1–3 at.% Ag), and (iii) in the modifier-controlled domain (x.10–15 at.% Ag) [12].

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Fig. 2. (a) Ionic conductivity si (x) and (b) diffusion coefficient DAg (x) isotherms at 298 K and 373 K for Ag 2 S–GeS–GeS 2 glasses plotted on a log–log scale [10]. The critical diffusion exponent t D (T ) is less than the conductivity one, t D (T )5t(T )–1, due to the Nernst–Einstein relation.

The model parameters pc and t depend primarily on the resistor network dimensionality and are mutually consistent for these three geometrical models (Table 1). One should note the pc values of 0.1–0.7 for 3D and 2D network, distinctly smaller values of the critical exponent t for 2D models, and the absence of percolation in 1D case. An allowed volume approach [10] enables to understand the observed enormous difference of four orders of magnitude between pc 50.1–0.7 and x c ¯ 3310 25 . In contrast to macroscopic classical ˚3 models, an average microscopic cage of 18–20 A occupied by the Ag 1 ion itself could not represent a site of the ‘infinite’ percolation cluster due to a certain probability to find this ion outside its residence place. An allowed volume of the glass limited by local mean-square displacements of the mobile ˚ 3 (Fig. 4). The ion is hence larger than 18–20 A allowed volume namely plays a role of the percolation cluster site. In a spherical approximation taking into account the theoretical values of pc , the atomic

volume of the Ag 1 ion and x c , the radius of the ˚ at the allowed volume sphere appears to be 16–25 A percolation threshold. This rather rough estimation is in good agreement with an average Ag–Ag distance in the extremely diluted glasses at x c assuming homogeneous distribution of the Ag 1 ions. Additionally, recent a.c. conductivity measurements carried out for Na 2 O–GeO 2 glasses [18] showed that a characteristic transport distance, deduced from the local mean-square displacements kr˜ 2 (`)l, depends on the mobile ion content approaching the values of ˚ in the limit of low sodium concentrations 20–22 A (60–70 ppm Na). Temperature dependence of the critical exponent t (Eq. (3)) can easily be understood taking into account thermally-activated si (T ) and DAg (T ). Having assumed that the pre-exponential factor s0 does not depend on x and the transport parameters si (1,T ) and DAg (1,T ) are also thermally activated, which is a good approximation for the investigated silver chalcogenide glasses [10–12], Eqs. (1–3) can be re-

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Fig. 3. Composition dependencies of the conductivity activation energy Ea for Ag 2 S–GeS–GeS 2 [10] and Ag 2 S–As 2 S 3 [11] glasses in the percolation and modifier-controlled domains. Table 1 Percolation threshold pc and critical exponent t for site, bond and correlated bond geometrical percolation models of different dimensionality [15–17] Network

pc

t

3D 2D 1D

0.12–0.43 0.35–0.70 1.00

1.6–1.7 1.0–1.2 0

written giving for the ionic conductivity, for example, the following relations:

F x E(x) 5 E 2 kT lnS]D x

E(x) si (x,T ) 5 s0 T 21 exp 2 ]] kT 0

0

G

(5) (6)

c

where E0 is the activation energy at the percolation threshold x c . The critical fictive temperature T 0 , which could be extracted either from the t(T ) values or from the Ea (x) and Ed (x) systematics, appears to

Fig. 4. Allowed volume approach: the atomic volume of the Ag 1 ˚ 3 ) is much less than the allowed volume of the glass, ion (18–20 A which is restricted by local mean-square displacements of the mobile cation. The allowed volumes play a role of sites in an ‘infinite’ percolation cluster, and hence their volume fraction should be of the order of pc for the onset of percolation.

be a primordial parameter to describe the percolation phenomena in the glass. The percolative ion transport depends on the number of ‘infinite’ percolation clusters, on the one hand, and on their interconnectivity, on the other. The second term in Eq. (6) represents hence a configuration entropy term, where ln(x /x c ) reflects the number and T 0 the interconnectivity of conduction pathways frozen below T g . The interconnectivity of clusters embedded in a host matrix should depend on the host network connectivity if the dopant does not change considerably the microstructural organisation of the network. Plotting the critical fictive temperature T 0 versus the average local coordination number of the host matrix knl, one obtains a nearly linear decrease of T 0 with decreasing knl (Fig. 5). The most important conclusion, which could be drawn from this dependence, is a suggested absence of the percolative transport (T 0 ¯ 0) for chain structures (knl52). This prediction is identical to the absence of percolation for 1D network in classical models (Table 1). Silver diffusion measurements on amorphous Se and Se–Ag

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Fig. 5. Critical fictive temperature T 0 , characterising interconnectivity of percolation clusters, versus the average local coordination number of the host glass matrix.

vitreous alloys could clarify this point. Neutron diffraction experiments [19] also show that in the percolation-controlled domain of Ag 2 S–As 2 S 3 glasses neither the short- nor the intermediate-range order exhibits any significant transformation, justifying the choice of the host network average coordination number knl in Fig. 5.

The Haven ratio HR decreases with increasing Ag content in the percolation domain [10,12]. More specifically, an empirical relation is found between HR and inverse Ag–Ag interatomic distance (Fig. 6): a HR 5 1 2 ]] rAg – Ag

Fig. 6. Haven ratio HR for Ag 2 S–GeS–GeS 2 glasses [10] plotted as a function of the inverse Ag–Ag interatomic distance.

(7)

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where a is a constant, reflecting interaction forces between the Ag 1 ions assumed to be homogeneously distributed in the glass network. In contrast, these interactions remain very similar and strong in the modifier-controlled domain (HR 50.2–0.4) leading to correlated motion of the mobile cations. Direct contacts of AgS 3 trigonal pyramids, evidenced by ˚ [19], relatively short Ag–Ag correlations at ¯3 A are responsible for this particular HR (x) behaviour and, in general, for drastic changes in the ion transport mechanism. 3. Degenerated mixed cation effect in (Cu 1 , Ag 1 ) ion conducting glasses In contrast to usual behaviour of mixed cation glasses (large deviations from additivity with a pronounced minimum at the conductivity isotherms and a diffusivity crossover when guest cations reduce the mobility of ions coming from the host matrix), the CuI–AgI–As 2 Se 3 [20] and Cu–Ag–As–Se [21] glassy systems exhibit exciting differences in the transport properties. First, the ionic conductivity increases monotonically by four orders of magnitude when AgI gradually replaces CuI, without any minimum at intermediate concentrations (Fig. 7). Secondly, no diffusivity crossover was observed in the two systems, which were studied using both 64 Cu and 110 Ag tracers (Fig. 8). Moreover, the 64 Cu tracer diffusion coefficient increases by a factor of 20–50 when copper is substituted by silver. The observed degenerated mixed cation effect seems to be closely related to a strongly reduced mobility of the Cu 1 ions in chalcogenide glassy systems [22,23]. The copper diffusion coefficient DCu in single copper chalcogenide or chalcohalide glasses is usually about four orders of magnitude lower than the silver diffusion coefficient DAg in single silver glasses of similar composition. There is no obvious structural reason of this effect. Both EXAFS [24,25] and neutron diffraction [26] showed that the short-range order in silver and copper chalcogenide glasses is rather similar. Larger activation energy of the Cu 1 ion motion might be caused by an enhanced electrostatic interaction between a Cu 1 ion and its nearest neighbours (chalcogen or iodine atoms) simply because of smaller ionic radius

Fig. 7. Conductivity isotherm at 298 K for CuI–AgI–As 2 Se 3 glasses [20]: (s) the total conductivity st was obtained from the a.c. impedance measurements; (d) the ionic conductivity si was calculated using the Cu 1 ion transport number for a 0.5CuI? 0.5As 2 Se 3 glass [23]; st ¯ si at AgI /(AgI1CuI).0.2.

˚ compared to Ag 1 (1.26 A) ˚ [27]. of Cu 1 (0.96 A) Another possible explanation involves higher quadrupolar deformability of the Ag 1 ion reducing the energy barrier associated with the ionic motion [28].

4. Non-Arrhenius vs. Arrhenius behaviour of superionic glasses at high temperatures Recently, a non-Arrhenius temperature dependence of the d.c. ionic conductivity was found for a number of superionic chalcogenide glasses [29,30]. It was interesting to prove whether a similar phenomenon could be observed in a tracer diffusion experiment. The temperature dependence of DAg for a 0.5Ag 2 S?0.5GeS 2 glass was measured using a thinlayer absorption method [31], which was found to be

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Fig. 8. 110 Ag and 64 Cu tracer diffusion isotherms at 298 K for Cu x Ag 252x As 37.5 Se 37.5 glasses plotted as a function of the copper fraction Cu /(Cu1Ag) [21].

particularly useful for highly conducting superionic solids [20,32]. This glass was chosen because of its high ionic conductivity at room temperature (¯10 23 S cm 21 ) and the high glass transition temperature T g ¯3008C. The temperature dependence of the 110 Ag tracer diffusion coefficient clearly shows a nearly perfect Arrhenius-type behaviour over the entire investigated temperature range (Fig. 9a, [33]). In contrast, the ionic conductivity si (T ) exhibits negative deviations from the expected Arrhenius dependence at high temperatures T $1808C (Fig. 9b) in accordance with previous results [30]. The observed discrepancies between si (T ) and DAg (T ) in our case seem to be caused by an enhanced interfacial resistance at the Pt / glass or Au / glass interface, which becomes comparable with the bulk resistance of the sample at high temperatures. Accordingly, we cannot measure the real ionic conductivity of the sample. Conductivity measurements on samples having 2–3 cm in thickness are planned to verify this hypothesis.

Fig. 9. Temperature dependence (a) of the silver diffusion coefficient DAg and (b) of the ionic conductivity si for 0.5Ag 2 S? 0.5GeS 2 glass [33].

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5. Conclusions Tracer diffusion measurements remain an important experimental technique to study the ion transport phenomena in solids due to their complementarity to the d.c. and a.c. conductivity measurements, NMR relaxation, quasielastic neutron scattering and other methods available to obtain information on the ionic motion on local and macroscopic scale. More specific applications of the tracer diffusion experiments, discussed in the present paper, include low conducting chalcogenide glasses to distinguish between electronic and ionic conductivity in the limit of low Ag concentrations, changes in the ion transport mechanism evidenced by the composition dependence of the Haven ratio, absence of the diffusivity crossover for mixed (Cu 1 , Ag 1 ) chalcogenide glasses, and finally verification of the conductivity anomalies observed for superionic glasses at high temperatures.

Acknowledgements The author would like to thank Dr. P. Armand, Dr. A. Bolotov, Prof. P. Boolchand, Prof. M. Duclot, Dr. Y. Grushko, Dr. A. Ibanez, Dr. J.-C. Jumas, Dr. A. Pradel, Prof. D.L. Price, Prof. M. Ribes, Dr. M.-L. Saboungi, Prof. J.-L. Souquet, Dr. G. Taillades, Prof. K. Tanaka, Dr. V. Tsegelnik, Prof. Yu. Vlasov for many stimulating discussions and comments.

References [1] R.H. Doremus, in: J.D. Mackenzie (Ed.), Modern Aspects of the Vitreous State, Vol. 2, Butterworths, London, 1962. [2] K.K. Evstrop’ev, Diffusion Processes in Glass, Stroiizdat, Leningrad, 1970. [3] G.H. Frischat, Ionic Diffusion in Oxide Glasses, TransTech, Aedermannsdorf, 1975. [4] R. Terai, R. Hayami, J. Non-Cryst. Solids 18 (1975) 217. [5] J.E. Kelly, M. Tomozawa, J. Non-Cryst. Solids 51 (1982) 345.

[6] M.P. Thomas, N.L. Peterson, Solid State Ionics 14 (1984) 297. [7] Y. Kawamoto, M. Nishida, Phys. Chem. Glasses 18 (1977) 19–23. [8] E.A. Kazakova, Ph.D. Thesis, Leningrad University, Leningrad, 1980. [9] M.P. Thomas, N.L. Peterson, E. Hutchinson, J. Am. Ceram. Soc. 68 (1985) 99. [10] E. Bychkov, V. Tsegelnik, Yu. Vlasov, A. Pradel, M. Ribes, J. Non-Cryst. Solids 208 (1996) 1. [11] E. Bychkov, A. Bychkov, A. Pradel, M. Ribes, Solid State Ionics 113–115 (1998) 691. [12] Yu. Drugov, V. Tsegelnik, A. Bolotov, Yu. Vlasov, E. Bychkov, Solid State Ionics 136–137 (2000) 1091. [13] A. Bunde, M.D. Ingram, P. Maass, J. Non-Cryst. Solids 172–174 (1994) 1222. [14] A. Hunt, J. Non-Cryst. Solids 175 (1994) 59. [15] S. Kirkpatrick, Rev. Mod. Phys. 45 (1973) 574. [16] S. Kirkpatrick, AIP Conf. Proc. 40 (1978) 99. [17] S. Kirkpatrick, in: R. Balian, R. Maynard, G. Toulouse (Eds.), Ill-Condensed Matter, North-Holland, Amsterdam, 1979, p. 321. [18] B. Roling, C. Martiny, K. Funke, in press. [19] E. Bychkov, D.L. Price, Solid State Ionics 136–137 (2000) 1041. [20] A. Bolotov, E. Bychkov, Yu. Gavrilov, Yu. Grushko, A. Pradel, M. Ribes, V. Tsegelnik, Yu. Vlasov, Solid State Ionics 113–115 (1998) 697. [21] V. Tsegelnik, A. Bolotov, E. Bychkov, unpublished results. [22] Yu. Vlasov, E. Bychkov, Solid State Ionics 14 (1984) 329. [23] E. Bychkov, A. Bolotov, Yu. Grushko, Yu. Vlasov, G. Wortmann, Solid State Ionics 90 (1996) 289. [24] V. Mastelaro, S. Benazeth, H. Dexpert, J. Non-Cryst. Solids 185 (1995) 274. [25] E. Bychkov, A. Bolotov, P. Armand, A. Ibanez, J. NonCryst. Solids 232–234 (1998) 314. [26] P.S. Salmon, J. Liu, J. Non-Cryst. Solids 205–207 (1996) 172. [27] K. Tanaka, Y. Miyamoto, M. Itoh, E. Bychkov, Phys. Stat. Sol. A173 (1999) 317. [28] M.A. Ratner, A. Nitzan, Solid State Ionics 28–30 (1988) 3. [29] J. Kincs, S.W. Martin, Phys. Rev. Lett. 76 (1996) 70. [30] M. Ribes, G. Taillades, A. Pradel, Solid State Ionics 105 (1998) 159. [31] S.N. Kryukov, A.A. Zhukhovitskii, Doklady Akad. Nauk SSSR 90 (1953) 379. [32] Yu. Vlasov, E. Bychkov, V. Tsegelnik, Y.M. Ben-Shaban, Radiokhimiya 37 (1995) 281. [33] A. Bolotov, V. Tsegelnik, Y. Vlasov, E. Bychkov, in: International Glass Meeting dedicated to Prof. R.L. Muller (St. Petersburg University, St. Petersburg, May, 1999).