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Electrical properties of molten AgCl–AgI mixtures
Journal of Non-Crystalline Solids 250±252 (1999) 488±491
www.elsevier.com/locate/jnoncrysol
Electrical properties of molten AgCl±AgI mixtures K. Ishida a, S. Ohno a b
a,*
, T. Okada
b
Niigata College of Pharmacy, 5-13-2 Kamishin'eicho, Niigata 950-2081, Japan Niigata College of Technology, 5-13-7 Kamishin'eicho, Niigata 950-2076, Japan
Abstract The composition dependence of electrical conductivity, r, for molten AgCl±AgI mixtures decreases monotonously on addition of AgI to molten AgCl. The activation energy, E1 , estimated from a plot of ln rT versus 1/T is about 0.11 eV for their mixtures. The thermoelectric power, S, of their mixtures increases with increasing temperature. The slope of line in a plot of S versus 1/T changes at temperatures between 380°C and 450°C. The heat of transport, Q*, lies in the range from 0.07 to 0.18 eV at higher temperatures. The relatively large Q* of about 0.4 eV is found in the eutectic region at the lower temperatures. Ó 1999 Elsevier Science B.V. All rights reserved.
1. Introduction
2. Experimental procedure
Recently Takeda et al. [1,2] have carried out sound absorption and structural measurements on molten AgCl±AgI mixtures. Particularly the temperature dependence of sound absorption for the mixtures has a maximum in the range between 600°C and 650°C. Their structural study indicates that the chemical short range order increases with decreasing temperature. The temperature dependence of electrical conductivity and thermoelectric power may be due to the change in chemical short range order. Several authors [3,4] have suggested that molten silver halides are similar to super ionic conductors. In this paper, therefore, we attempt to investigate the temperature dependence of r and S by using the theoretical model of super ionic conductors [5].
The electrical conductivity measurements were made by four probe method using a quartz cell [6]. Four silver electrodes were inserted into small tapered holes in quartz cell and fastened by molybdenum bands. Molybdenum lead wires were attached to the molybdenum bands. The cell constant was determined by using liquid mercury at room temperature. The measurements were carried out in an argon atmosphere to prevent oxidation and vaporization of the sample. Any bubbles that formed in the sample during the course of the experiment were removed by agitating it with a silica rod. The temperature was measured using chromel±alumel thermocouples immediately above the electrodes. The thermoelectric power measurements were made by a DT method [6]. The temperature difference between two electrodes was provided by a two zone heater. The voltage, DE, between two electrodes was measured by a digital voltmeter with the accuracy of 10ÿ8 V. DE/DT gives the thermoelectric power formed by the sample and
* Corresponding author. Tel.: +81 25 269 3170; fax: +81 25 268 1230; e-mail: [email protected]
0022-3093/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 9 9 ) 0 0 2 7 9 - 3
K. Ishida et al. / Journal of Non-Crystalline Solids 250±252 (1999) 488±491
489
molybdenum lead wires [6]. The absolute thermoelectric power was determined using the known thermoelectric power of molybdenum quoted by Cusack and Kendall [7]. For the molten mixtures, the voltage was obtained by using silver electrodes to avoid erroneous thermoelectric power measurements due to the contact potentials between the liquid and electrode. AgCl and AgI were purchased (Wako Pure Chemical). 3. Experimental results Fig. 1 shows the electrical conductivity as a function of temperature for molten AgCl±AgI mixtures. The r for molten AgCl obtained in the present work is in good agreement (rRef =rExp 0:994) with that reported by Bell and Flengas [8]. The molten mixtures have a positive temperature coecient of conductivity. The composition dependence of r decreases monotonously on addition of AgI to molten AgCl. The conductivity of AgI decreases with decreasing temperature and increases at the melting point. Fig. 2(a) and (b) show the thermoelectric power as a function of temperature for molten AgCl±AgI mixtures. The Ss at the melting point are ÿ490 and ÿ475 lV/K for AgCl and AgI, respectively. The voltage at the hotter end of the sample is negative
Fig. 2. (a) Thermoelectric power of molten AgCl1ÿc AgIc mixtures with c 6 0:4 as a function of temperature. Random error is about 11 lV/K. (b) Thermoelectric power of molten AgCl1ÿc AgIc mixtures with c P 0.6 as a function of temperature. Random error is about 11 lV/K.
with respect to that at the colder end. All mixtures have a negative S which decreases with decreasing temperature. 4. Discussion
Fig. 1. Electrical conductivity of molten AgCl1ÿc AgIc mixtures as a function of temperature. Random error is about 0.15 ohmÿ1 cmÿ1 .
As shown in Fig. 1, the conductivities of the mixtures lie in the range from 2.4 to 4.8 ohmÿ1 cmÿ1 . Several authors have suggested that the molten mixtures with relatively higher conductivities may be super ionic conductors [3,4]. We attempt to analyze the data of r and S by using the theoretical model proposed by Rice and Roth [5]. According to their model, the ionic conductivity can be written by [5]
490
K. Ishida et al. / Journal of Non-Crystalline Solids 250±252 (1999) 488±491
Fig. 3. Plot of ln rT versus 1/T for molten AgCl1ÿc AgIc mixtures. Lines are drawn as guides for the eye.
r f Ze2 =3kB T gnv0 l0 exp ÿE1 =kB T ;
1
where l0 and v0 denote the mean free path and velocity of the free-ion like state excited at the gap energy, E1 . Ze and n are the charge carried by an ion and the number of ions per unit volume. We assume that v0 and l0 are constant for temperature in the molten mixtures. A plot of log rT versus 1/T can be ®tted to a linear function as shown in Fig. 3. The E1 s estimated from the slope of line are comparable to an activation energy of 0.1 eV for the mobile ions in the super ionic conductors [5]. As seen in Table 1, the E1 estimated is larger than that obtained from the simple form r A exp ÿE2 =kB T . E2 is an activation energy of ionic migration in molten salts [9]. The E2 estimated for molten AgCl is in good agreement (E2;Ref /E2;Exp 1.17) with that obtained by Harrap and Heymann [9]. It is known that there are many defects and interstitial sites in molten silver halide [3,10]. We suggest that the activation energy is indicative of a number of free-silver ions excited in molten silver halides.
Fig. 4. Plot of S versus 1/T for molten AgCl1ÿc AgIc mixture. Lines are drawn as guides for the eye.
The thermoelectric power of molten salts and super ionic conductors may be given by [5,11] S ÿQ =jejT ÿ a;
2
where Q* is the heat of transport and activation energy of silver ion. The constant a depends on the change in the entropy of silver ions and defects. As shown in Fig. 4, a plot of S versus 1/T deviates from a linear relation in the range between 380°C and 450°C. The ratio of Q* estimated at higher temperatures to E1 lies in the range 0.64±1.64. The Q*s estimated at lower temperatures are in the range from 0.32 to 0.4 eV and those of AgCl and AgBr obtained at a temperature less than the melting point are about 0.55 and 0.26 eV, respectively [10,12]. The crystal structure of AgCl is the rock salt type up to the melting point. The ionic order in the AgCl±AgI mixtures is formed in the eutectic region [1,2]. The relatively larger Q* obtained may be attributed to the ionic order expected in the eutectic region at temperatures less than the melting point of AgCl (see Table 2).
Table 1 Activation energy E1 and E2 for molten AgCl1ÿc AgIc mixtures E1 (eV) E2 (eV)
Agcl
c 0.2
c 0.4
c 0.6
c 0.8
AgI
0.120 0.041
0.113 0.037
0.115 0.043
0.108 0.037
0.114 0.040
0.104 0.020
K. Ishida et al. / Journal of Non-Crystalline Solids 250±252 (1999) 488±491
491
Table 2 Heat of transport Q* (eV) and constant a (lV/K) for molten AgCl1ÿc AgIc mixtures at lower and higher temperature Q* (H.T.) a (H.T.) Q* (L.T.) a (L.T.)
AgCl
c 0.2
c 0.4
c 0.6
c 0.8
AgI
0.07 404 ÿ ÿ
0.11 339 ÿ ÿ
0.17 256 0.38 ÿ31
0.17 257 0.32 28
0.17 268 0.40 ÿ49
0.18 272 ÿ ÿ
5. Conclusion
References
The temperature dependence of r and S can be explained by the theory of super ionic conductors. The activation energy, E1 , estimated from the plot of ln rT versus 1/T is about 0.11 eV for molten AgCl±AgI mixtures. The E1 s are comparable to the activation energies obtained in the super ionic conductors [5]. The slope of the linear function ®tted to a plot of S versus 1/T changes in the temperature range 380±450°C. The relatively larger Q* estimated at the lower temperatures may be closely related to the cluster formation between silver and halogen ions observed in the eutectic region below the melting point of AgCl [1,2].
[1] M. Inui, A. Hiramatsu, Y. Kawakita, S. Takeda, J. NonCryst. Solids 205±207 (1996) 159. [2] S. Takeda, A. Hiramatsu, Y. Kawakita, I. Hiraishi, Molten Salt Chem. Technol. 5 (1998) 163. [3] S. Ushioda, M.J. Delaney, Solid State Commun. 32 (1979) 67. [4] M. Aniya, M. Kobayashi, H. Okazaki, J. Phys. Soc. Jpn. 59 (1990) 4029. [5] M.J. Rice, W.L. Roth, J. Solid State Chem. 4 (1972) 294. [6] S. Ohno, A.C. Barnes, J.E. Enderby, J. Phys.: Condens. Matter 8 (1996) 3785. [7] N.E. Cusack, P.W. Kendall, Proc. Phys. Soc. 72 (1958) 898. [8] M.C. Bell, N.S. Flengas, J. Electrochem. Soc. 111 (1964) 575. [9] B.S. Harrap, E. Heymann, Trans. Faraday Soc. 51 (1955) 259. [10] R.W. Christy, J. Chem. Phys. 34 (1961) 1148. [11] T. Takahashi, O. Yamamoto, E. Nomura, Denki Kagaku 38 (1970) 360. [12] E. Haga, J. Phys. Soc. Jpn. 13 (1958) 1090.
Acknowledgements We would like to thank Professor Takeda for sending us his papers and giving valuable advice.
www.elsevier.com/locate/jnoncrysol
Electrical properties of molten AgCl±AgI mixtures K. Ishida a, S. Ohno a b
a,*
, T. Okada
b
Niigata College of Pharmacy, 5-13-2 Kamishin'eicho, Niigata 950-2081, Japan Niigata College of Technology, 5-13-7 Kamishin'eicho, Niigata 950-2076, Japan
Abstract The composition dependence of electrical conductivity, r, for molten AgCl±AgI mixtures decreases monotonously on addition of AgI to molten AgCl. The activation energy, E1 , estimated from a plot of ln rT versus 1/T is about 0.11 eV for their mixtures. The thermoelectric power, S, of their mixtures increases with increasing temperature. The slope of line in a plot of S versus 1/T changes at temperatures between 380°C and 450°C. The heat of transport, Q*, lies in the range from 0.07 to 0.18 eV at higher temperatures. The relatively large Q* of about 0.4 eV is found in the eutectic region at the lower temperatures. Ó 1999 Elsevier Science B.V. All rights reserved.
1. Introduction
2. Experimental procedure
Recently Takeda et al. [1,2] have carried out sound absorption and structural measurements on molten AgCl±AgI mixtures. Particularly the temperature dependence of sound absorption for the mixtures has a maximum in the range between 600°C and 650°C. Their structural study indicates that the chemical short range order increases with decreasing temperature. The temperature dependence of electrical conductivity and thermoelectric power may be due to the change in chemical short range order. Several authors [3,4] have suggested that molten silver halides are similar to super ionic conductors. In this paper, therefore, we attempt to investigate the temperature dependence of r and S by using the theoretical model of super ionic conductors [5].
The electrical conductivity measurements were made by four probe method using a quartz cell [6]. Four silver electrodes were inserted into small tapered holes in quartz cell and fastened by molybdenum bands. Molybdenum lead wires were attached to the molybdenum bands. The cell constant was determined by using liquid mercury at room temperature. The measurements were carried out in an argon atmosphere to prevent oxidation and vaporization of the sample. Any bubbles that formed in the sample during the course of the experiment were removed by agitating it with a silica rod. The temperature was measured using chromel±alumel thermocouples immediately above the electrodes. The thermoelectric power measurements were made by a DT method [6]. The temperature difference between two electrodes was provided by a two zone heater. The voltage, DE, between two electrodes was measured by a digital voltmeter with the accuracy of 10ÿ8 V. DE/DT gives the thermoelectric power formed by the sample and
* Corresponding author. Tel.: +81 25 269 3170; fax: +81 25 268 1230; e-mail: [email protected]
0022-3093/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 9 9 ) 0 0 2 7 9 - 3
K. Ishida et al. / Journal of Non-Crystalline Solids 250±252 (1999) 488±491
489
molybdenum lead wires [6]. The absolute thermoelectric power was determined using the known thermoelectric power of molybdenum quoted by Cusack and Kendall [7]. For the molten mixtures, the voltage was obtained by using silver electrodes to avoid erroneous thermoelectric power measurements due to the contact potentials between the liquid and electrode. AgCl and AgI were purchased (Wako Pure Chemical). 3. Experimental results Fig. 1 shows the electrical conductivity as a function of temperature for molten AgCl±AgI mixtures. The r for molten AgCl obtained in the present work is in good agreement (rRef =rExp 0:994) with that reported by Bell and Flengas [8]. The molten mixtures have a positive temperature coecient of conductivity. The composition dependence of r decreases monotonously on addition of AgI to molten AgCl. The conductivity of AgI decreases with decreasing temperature and increases at the melting point. Fig. 2(a) and (b) show the thermoelectric power as a function of temperature for molten AgCl±AgI mixtures. The Ss at the melting point are ÿ490 and ÿ475 lV/K for AgCl and AgI, respectively. The voltage at the hotter end of the sample is negative
Fig. 2. (a) Thermoelectric power of molten AgCl1ÿc AgIc mixtures with c 6 0:4 as a function of temperature. Random error is about 11 lV/K. (b) Thermoelectric power of molten AgCl1ÿc AgIc mixtures with c P 0.6 as a function of temperature. Random error is about 11 lV/K.
with respect to that at the colder end. All mixtures have a negative S which decreases with decreasing temperature. 4. Discussion
Fig. 1. Electrical conductivity of molten AgCl1ÿc AgIc mixtures as a function of temperature. Random error is about 0.15 ohmÿ1 cmÿ1 .
As shown in Fig. 1, the conductivities of the mixtures lie in the range from 2.4 to 4.8 ohmÿ1 cmÿ1 . Several authors have suggested that the molten mixtures with relatively higher conductivities may be super ionic conductors [3,4]. We attempt to analyze the data of r and S by using the theoretical model proposed by Rice and Roth [5]. According to their model, the ionic conductivity can be written by [5]
490
K. Ishida et al. / Journal of Non-Crystalline Solids 250±252 (1999) 488±491
Fig. 3. Plot of ln rT versus 1/T for molten AgCl1ÿc AgIc mixtures. Lines are drawn as guides for the eye.
r f Ze2 =3kB T gnv0 l0 exp ÿE1 =kB T ;
1
where l0 and v0 denote the mean free path and velocity of the free-ion like state excited at the gap energy, E1 . Ze and n are the charge carried by an ion and the number of ions per unit volume. We assume that v0 and l0 are constant for temperature in the molten mixtures. A plot of log rT versus 1/T can be ®tted to a linear function as shown in Fig. 3. The E1 s estimated from the slope of line are comparable to an activation energy of 0.1 eV for the mobile ions in the super ionic conductors [5]. As seen in Table 1, the E1 estimated is larger than that obtained from the simple form r A exp ÿE2 =kB T . E2 is an activation energy of ionic migration in molten salts [9]. The E2 estimated for molten AgCl is in good agreement (E2;Ref /E2;Exp 1.17) with that obtained by Harrap and Heymann [9]. It is known that there are many defects and interstitial sites in molten silver halide [3,10]. We suggest that the activation energy is indicative of a number of free-silver ions excited in molten silver halides.
Fig. 4. Plot of S versus 1/T for molten AgCl1ÿc AgIc mixture. Lines are drawn as guides for the eye.
The thermoelectric power of molten salts and super ionic conductors may be given by [5,11] S ÿQ =jejT ÿ a;
2
where Q* is the heat of transport and activation energy of silver ion. The constant a depends on the change in the entropy of silver ions and defects. As shown in Fig. 4, a plot of S versus 1/T deviates from a linear relation in the range between 380°C and 450°C. The ratio of Q* estimated at higher temperatures to E1 lies in the range 0.64±1.64. The Q*s estimated at lower temperatures are in the range from 0.32 to 0.4 eV and those of AgCl and AgBr obtained at a temperature less than the melting point are about 0.55 and 0.26 eV, respectively [10,12]. The crystal structure of AgCl is the rock salt type up to the melting point. The ionic order in the AgCl±AgI mixtures is formed in the eutectic region [1,2]. The relatively larger Q* obtained may be attributed to the ionic order expected in the eutectic region at temperatures less than the melting point of AgCl (see Table 2).
Table 1 Activation energy E1 and E2 for molten AgCl1ÿc AgIc mixtures E1 (eV) E2 (eV)
Agcl
c 0.2
c 0.4
c 0.6
c 0.8
AgI
0.120 0.041
0.113 0.037
0.115 0.043
0.108 0.037
0.114 0.040
0.104 0.020
K. Ishida et al. / Journal of Non-Crystalline Solids 250±252 (1999) 488±491
491
Table 2 Heat of transport Q* (eV) and constant a (lV/K) for molten AgCl1ÿc AgIc mixtures at lower and higher temperature Q* (H.T.) a (H.T.) Q* (L.T.) a (L.T.)
AgCl
c 0.2
c 0.4
c 0.6
c 0.8
AgI
0.07 404 ÿ ÿ
0.11 339 ÿ ÿ
0.17 256 0.38 ÿ31
0.17 257 0.32 28
0.17 268 0.40 ÿ49
0.18 272 ÿ ÿ
5. Conclusion
References
The temperature dependence of r and S can be explained by the theory of super ionic conductors. The activation energy, E1 , estimated from the plot of ln rT versus 1/T is about 0.11 eV for molten AgCl±AgI mixtures. The E1 s are comparable to the activation energies obtained in the super ionic conductors [5]. The slope of the linear function ®tted to a plot of S versus 1/T changes in the temperature range 380±450°C. The relatively larger Q* estimated at the lower temperatures may be closely related to the cluster formation between silver and halogen ions observed in the eutectic region below the melting point of AgCl [1,2].
[1] M. Inui, A. Hiramatsu, Y. Kawakita, S. Takeda, J. NonCryst. Solids 205±207 (1996) 159. [2] S. Takeda, A. Hiramatsu, Y. Kawakita, I. Hiraishi, Molten Salt Chem. Technol. 5 (1998) 163. [3] S. Ushioda, M.J. Delaney, Solid State Commun. 32 (1979) 67. [4] M. Aniya, M. Kobayashi, H. Okazaki, J. Phys. Soc. Jpn. 59 (1990) 4029. [5] M.J. Rice, W.L. Roth, J. Solid State Chem. 4 (1972) 294. [6] S. Ohno, A.C. Barnes, J.E. Enderby, J. Phys.: Condens. Matter 8 (1996) 3785. [7] N.E. Cusack, P.W. Kendall, Proc. Phys. Soc. 72 (1958) 898. [8] M.C. Bell, N.S. Flengas, J. Electrochem. Soc. 111 (1964) 575. [9] B.S. Harrap, E. Heymann, Trans. Faraday Soc. 51 (1955) 259. [10] R.W. Christy, J. Chem. Phys. 34 (1961) 1148. [11] T. Takahashi, O. Yamamoto, E. Nomura, Denki Kagaku 38 (1970) 360. [12] E. Haga, J. Phys. Soc. Jpn. 13 (1958) 1090.
Acknowledgements We would like to thank Professor Takeda for sending us his papers and giving valuable advice.