Solid State Ionics 136–137 (2000) 1025–1029 www.elsevier.com / locate / ssi
Ion dynamics in superionic chalcogenide glasses: Complete conductivity spectra R. Belin*, G. Taillades, A. Pradel, M. Ribes ` Condensee ´ . UMR 5617, Universite´ Montpellier II. CC003 34095 Montpellier Cedex 05, Laboratoire de Physico-chimie de la Matiere France
Abstract The complete conductivity spectra of the glass 0.5Ag 2 S–0.5GeS 2 were obtained in very broad temperature and frequency ranges. The experimental data were analysed in two different ways. First, the classical and well known power law procedure was used. For this glass, the conductivity is described by the superposition of four terms. The first two terms are thermally activated, whereas the last two terms are almost temperature independent. The second data analysis is based upon the master curve procedure: the experimental data could be described only by the superposition of the master curve and the vibrational contribution. This procedure seems to be less arbitrary than the first one because the master curve can be generated without any fitted parameter and certainly displays the common origin of the microscopic processes involved. 2000 Elsevier Science B.V. All rights reserved. Keywords: Fast ion conductor; Chalcogenide glasses; Conductivity spectra; Master curve
1. Introduction The low frequency spectra of conductivity for fast ion conductors are well known. As a matter of fact, the impedance techniques required for such measurements are easily accessible. But low frequency conductivity only gives information about the long time ion dynamics. It would be interesting to observe the short time ion dynamics because it would give useful information about the microscopic mechanisms of ionic motion and consequently, about the ion environment and eventually the different types of sites present in the material. To date, complete frequency dependent conductivity spectra from the
dc conductivity to the far infrared region are still scarce because they require the use of different spectroscopic techniques (impedance, radio, microwave, FTIR) which are quite difficult to find in a single laboratory. As examples, complete conductivity spectra were obtained for alkali borate glasses such as 0.45LiBr– 0.56Li 2 O–B 2 O 3 [1], silver borate glasses 0.75AgI– 0.5Ag 2 O–B 2 O 3 [2] or silver selenate glasses such as 0.48(AgI) 2 –0.52Ag 2 SeO 4 [3]. In this work, the complete conductivity spectra for the silver chalcogenide glass 0.5Ag 2 S–0.5GeS 2 will be presented. 2. Experimental
*Corresponding author. Fax: 133-467-14-4290. E-mail address:
[email protected] (R. Belin).
The starting materials for preparation of the glass
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0.5Ag 2 S–0.5GeS 2 were silver and germanium sulphides. They were produced according to a procedure previously described [4]. The two compounds were then intimately mixed in stoichiometric quantities and sealed under vacuum. The glass was obtained after ten days of appropriate treatment: slow heating to 6008C, stage at 6008C for 24 h then rapid heating up to 10008C. Air-quenching was sufficient to obtain a glassy material. Conductivity spectra were obtained over a temperature range from 123 K to 473 K and a very broad frequency range from 10 Hz up to FIR frequencies (6 THz) was covered. Depending upon the frequency range, various spectroscopic techniques were used. The measurements by impedance spectroscopy were performed in Montpellier with a HP4192A impedance analyser in the 10 Hz–13 MHz frequency range. Beyond 13 MHz, the measurements were performed at the Institute for Physical Chemistry in Munster. Radio, microwaves and FTIR spectroscopies were utilised. Except for the samples used for FTIR measurements which needed to be very thin and were synthesised by twin roller quenching, all the samples were pressed powders.
3. Results In the following, the complete conductivity spectra of the glass 0.5Ag 2 S–0.5GeS 2 [5] will be discussed. Let us first consider the dc analysis [6]. Fig. 1 shows an Arrhenius plot of the data. The dc conductivities were measured between 123 K and 473 K. Dc conductivity is thermally activated with an activation energy of Edc 5 0.31 eV in agreement with [6]. Fig. 2 is a log–log representation of the conductivity versus frequency. It was shown for the first time by Jonscher [7] that when frequency was low enough (typically , 100 kHz), the so called ‘universal dynamic response’ (UDR) of ionic conductivity could be approximated by the following equation:
s (v ) ¯ sdc 1 Av s 1 . To fit the experimental data led to an s 1 value of 0.5. The A parameter was found to be thermally
Fig. 1. Arrhenius representation of sdc of 0.5Ag 2 S–0.5GeS 2 .
activated with an activation energy EA 50.14 eV. Within experimental error, it is in accordance with the value calculate via: EA 5 (1 2 s 1 )Edc , predicted by Funke’s jump relaxation model [8] and Ngai’s coupling model [9]. s (v ) keeps increasing with frequency. As commonly admitted [3], the crossover frequency from dc to dispersive conductivities, vc , can be defined as:
s (vc ) 5 2sdc . vc is thermally activated with the same activation energy as for sdc . The line obtained from the crossover frequencies as shown in Fig. 2 has a slope of one [10]. The different isotherm spectra can be shifted along this line. It is the procedure recently proposed by Roling to obtain the master curve [11] (see below). At higher frequencies, the power law from Jonscher was not adequate anymore to depict the spectra. It was necessary to add a second power law: s (v )5Bv s 2 . The fit of experimental data led to a value of s 2 51 (in agreement with Novick results [12]). The B term was very slightly temperature dependent. There was no need of an exponent greater than one to account for the data. This observation contrasts previous results for silver conducting oxide glasses [13] such as silver iodide / silver selenate glasses [3] or for alkali borate glasses [14]. At far infrared frequencies, the conductivity
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Fig. 2. Frequency dependent conductivity spectra of 0.5Ag 2 S–0.5GeS 2 at various temperatures (the straight line joins the crossover frequencies).
showed a frequency dependence in v 2 and a very weak temperature dependence. It corresponds to the low frequency flank of the lowest lying vibrational mode. It was easy to extrapolate such a contribution to lower frequencies and to subtract it from the complete spectra. The obtained spectra could then be solely interpreted in terms of a hopping motion of the ions. But no high frequency plateau could be observed even after subtracting the vibrational contribution. So, the whole spectra could be perfectly fitted by the relation:
s (v ) 5 sdc 1 Av 0.5 1 Bv 1 1 Cv 2 The temperature–frequency diagram displayed in Fig. 3 allows the visualisation of the four conductivity regimes. Obviously, there is a narrowing of regime III (exponent 1) to the benefit of regimes II and IV (exponents 0.5 and 2 respectively) when the temperature is increased. In the next part of this section, the spectra will be
Fig. 3. Temperature–frequency diagram of 0.5Ag 2 S–0.5GeS 2 .
analysed using the master curve procedure. Constructing a master curve consists of shifting the conductivity spectra along the straight line of slope
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Fig. 4. Master curve of the conductivity data of 0.5Ag 2 S–0.5GeS 2 .
one defined previously. If the curves log(s /sdc ) versus log(n /sdc T ) are plotted, all spectra fall onto one master curve. The resulting scaling plot is shown in Fig. 4. For clarity, four of the isotherm spectra from which the vibrational contribution was subtracted are shown. One can notice that the spectra nicely superimpose. The master curve tends towards a straight line of slope one. There are no point steeper than the master curve. It is in agreement with the fact that there is no super-linear frequency dependence. So, the conductivity spectra can be accounted for by the superposition of both the master curve and a vibrational term.
4. Conclusion This fitting procedure involving power law exponents has been used during many years. For our material, it needs the superposition of four terms. The dc conductivity and the A-term are thermally
activated in an Arrhenius fashion, whereas the B and C-terms are only slightly temperature dependent. There is no term with a super-linear frequency dependence. The drawback of this procedure is that the Jonscher-type contribution and the Novick-type contribution appear to be different phenomena. If the master curve scaling procedure is considered, the distinction between these two terms is no longer advisable, for the underlying microscopic processes are the same. In this glass, it was possible to account for the conductivity spectra with two terms: the master curve and the vibrational contribution. This behaviour has been observed in polaron conducting glasses, but it is the first time that it can be observed in an ion conducting glass. The power law fitting procedure is still right, but the master curve fitting procedure is more advisable because it can be generated without the need of any fitted parameters [15]. The second procedure is less arbitrary and its use displays the common origin of the underlying processes.
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Acknowledgements Financial support from the french–german PROCOPE is gratefully acknowledged. The authors wish to thank Dr. Cornelia Cramer for her help in high frequency measurements and for fruitful discussions and Professor K. Funke for receiving one of us (R.B.) in his institute.
References [1] C. Cramer, K. Funke, T. Saatkanp, D. Wilmer, M.D. Ingram, Z. Naturforsch. 50a (1995) 613. [2] C. Cramer, K. Funke, K. El-Egili, et al., unpublished data on glassy 0.5AgI–0.5AgPO 3 and 0.7SAgI–0.5Ag 2 O–B 2 O 3 . [3] C. Cramer, M. Buscher, Solid State Ionics 105 (1998) 109.
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[4] E. Rolbinel, B. Carette, M. Ribes, J. Non-Cryst. Solids 57 (1983) 49. [5] A. Pradel, G. Taillades, C. Cramer, M. Ribes, Solid State Ionics 105 (1998) 139. [6] M. Ribes, G. Taillades, A. Pradel, Solid State Ionics 105 (1998) 159. [7] A.K. Jonscher, Nature 267 (1977) 673. [8] K. Funke, Progr. Solid State Chem. 22 (1993) 111. [9] K.L. Ngai, Comm. Solid State Phys. 9 (1980) 141. [10] B. Roling, K. Funke, A. Happe, M.D. Ingram, Phys. Rev. Lett. 78 (1997) 2160. [11] B. Roling, Solid State Ionics 105 (1998) 185. [12] A.S. Novick, A.V. Vaysleyb, W. Lu, Solid State Ionics 105 (1998) 121. [13] C. Cramer, K. Funke, T. Saatkamp et al., Solid State Ionics 86–88 (1996) 481. [14] C. Cramer, Ber. Bunsenges. Phys. Chem. 100 (1996) 1497. [15] K. Funke, B. Roling, M. Lange, Solid State Ionics 105 (1998) 195.
