- Email: [email protected]
Heat transfer and ion migration in the system Li2SO4–Na2SO4
Solid State Ionics 136–137 (2000) 325–330 www.elsevier.com / locate / ssi
Heat transfer and ion migration in the system Li 2 SO 4 –Na 2 SO 4 ´ *, Ernest Karawacki Bashir M. Suleiman 1 , Arnold Lunden ¨ Department of Physics, Chalmers University of Technology, S-412 96 Goteborg , Sweden
Abstract The transient plane source technique has been used for simultaneous measurements of thermal conductivity and diffusivity in the lithium–sodium sulphate system starting near 300 K. Samples with 100, 77.5, or 50% Li 2 SO 4 behave differently from pure Na 2 SO 4 . In the first case both the thermal conductivity and the diffusivity start to increase rapidly at about 640 K, while the crystal structure remains monoclinic for Li 2 SO 4 and trigonal for LiNaSO 4 . Concerning pure Li 2 SO 4 , there is an additional discontinuous increase of the two thermal parameters at the structural transition from monoclinic to cubic (fcc) at 850 K, while the temperature gradients become significantly smaller in the cubic phase than in the monoclinic one. In contrast, both the thermal conductivity and the diffusivity of Na 2 SO 4 decrease over the whole studied temperature range, which includes the phase transitions at 474 K and 520 K. Furthermore, a corresponding study was performed for silver iodide over the range 295–640 K, i.e. on both sides of the phase transition at 420 K. There is an indication of a small decrease of the thermal conductivity and the diffusivity at the phase transition. The high temperature phases fcc Li 2 SO 4 , bcc LiNaSO 4 and bcc AgI are solid electrolytes, but it is characteristic for the two sulphate phases that a coupled rotation-like motion of the sulphate ions enhances the cation migration. Obviously, such motion is also of importance for heat transport. 2000 Elsevier Science B.V. All rights reserved. Keywords: Alkali sulphates; Heat transport; Thermal conductivity; Thermal diffusivity; Heat capacitivity; Paddle-wheel mechanism; Cation migration Materials: Li 2 SO 4 ; Na 2 SO 4 ; LiNaSO 4
1. Introduction It is characteristic for a solid electrolyte that one ionic species has a much larger mobility than the other ions present, while many kinds of ions are mobile in a molten electrolyte. The ionic radius is thus a much more critical parameter in a solid phase than in a melt. There is, however, a small group of *Corresponding author. Fax: 146-31-772-3251. ´ E-mail address: [email protected] (A. Lunden). 1 Present address: University of Sharjah, College of Arts and Sciences, P.O. Box 27272, Sharjah, United Arab Emirates.
high temperature phases where a large number of uni- and divalent cations are very mobile [1]. The four phases that have been studied so far are fcc Li 2 SO 4 , bcc LiNaSO 4 , bcc LiAgSO 4 and non-cubic Li 4 Zn(SO 4 ) 3 . The first two of them belong to the Li 2 SO 4 –Na 2 SO 4 system [2], see Fig. 1, where the high-temperature phase on the Na 2 SO 4 -rich side is hexagonal. Førland and Krogh-Moe pointed out that there was a large excess of cation sites in the two cubic phases, and that strong rotational orientations must be expected for the sulphate ions [3,4]. The electrical conductivity of Li 2 SO 4 was found to be of the order of 0.9 S / cm at 823 K [5], while diffusion
0167-2738 / 00 / $ – see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S0167-2738( 00 )00467-7
326
B.M. Suleiman et al. / Solid State Ionics 136 – 137 (2000) 325 – 330
ductivity, etc. also have some influence on heat transfer. Data for the system Li 2 SO 4 –Na 2 SO 4 are also of practical interest for some applications, e.g. for high-temperature batteries, fuel cells or heat storage devices; for references see Refs. [18,19].
2. Experimental
Fig. 1. Phase diagram of the system Li 2 SO 4 –Na 2 SO 4 .
studies showed that all mono- and divalent cations are very mobile in the cubic phases [6]. These phases can actually be considered as both solid electrolytes and plastic crystals [7,8]. The cation mobility is enhanced by a strong coupling to the rotation of the otherwise translationally immobile sulphate ions [1,6]. Actually, all possible kinds of transport mechanisms are enhanced. This phenomenon is depicted as the ‘paddle-wheel’ or ‘cogwheel’ model, which was first presented in 1972 [6,9,10]. The model is consistent with three neutron scattering studies viz. powder diffraction [11], single crystal diffraction [12] and total scattering evaluated by the reverse Monte Carlo technique [13], and furthermore with molecular dynamics simulations [14]. A study is in progress by means of coherent quasielastic neutron scattering [15]. Elastic constants have been determined by means of Brillouin scattering [16], and Raman spectra give evidence for sulphate ion reorientations in the high-temperature cubic phases, but not in hexagonal Na 2 SO 4 [17]. It is of interest to see whether the phase transitions that cause dramatic changes of the electrical con-
Single crystals have been used in some earlier studies of heat transport in sulphates, for references see Ref. [20]. However, nobody has yet succeeded in maintaining single crystals of lithium sulphate through the phase transition at 850 K, and we must choose a technique where we can scan wide temperature ranges. The thermal conductivity ( l) and the thermal diffusivity (k ) were measured simultaneously by means of the transient plane source (TPS) technique [21,22]. The plane heat source served at the same time as the temperature sensor. It was clamped between two discs of salt which were 12 mm thick and had a diameter of 38 mm. The TPS element and the two discs were placed in an oven. The measurements were started slightly above room temperature, and the heating rate was 0.75 K / min. Two scans with increasing temperatures were performed for Li 2 SO 4 . The agreement between them was good in the ranges where the temperature gradients were small, but large deviations occurred in the range 640–850 K, where the parameters depended on the temperature. We made only one scan for the other salts [20]. A more detailed description of the experimental procedure and the evaluation is given elsewhere [22]. The accuracy of the measurements can be checked by calculating the heat capacitivity per volume unit l /k 5 r c p where r is the density, and c p is the heat capacitivity. According to this criterion, our results for the pure salts Li 2 SO 4 and Na 2 SO 4 are more reliable than those for the equimolar compound LiNaSO 4 and the eutectoid mixture Li 1.55 Na 0.45 SO 4 . Already a view with the naked eye shows that the conductivity data are more accurate than the diffusivity data for the latter two compositions, and we have given more attention to the conductivities than to the diffusivities when discussing the four sulphates [20].
B.M. Suleiman et al. / Solid State Ionics 136 – 137 (2000) 325 – 330
327
3. Results and discussion Since the mechanisms for transfer of ions and for heat transfer are very different, one does not per se expect any correlation between, e.g. ion conductivity and heat conductivity. It is reasonable to start with the simplest case, i.e. salts where both ions are monatomic. Silver iodide has a phase transition at 420 K where the ionic conductivity increases by several orders of magnitude. We have measured the thermal conductivity ( l) and the diffusivity (k ) in the range from 295 K to 640 K at three temperatures on each side of the transition. Both parameters are nearly constant over the whole range. We obtained a thermal conductivity of 0.53 W/ mK below the transition and 0.52 W/ mK for the high-temperature phase a-AgI. The corresponding thermal diffusivities are close to 0.83 mm 2 / s. It holds for l as well as for k that the individual values can be divided in two groups where all three ‘high’ data were obtained below the phase transition and vice versa. Our conclusion is that there is a slight, but significant, decrease at least for the thermal conductivity at the phase transition and that temperature gradients are extremely small in both phases. (We have not investigated whether stable b-AgI or metastable gAgI dominates in the lower temperature range.) What happens if the anions are polyatomic, which allows some additional rotational or librational degrees of freedom? We have studied four compositions in the (Li,Na) 2 SO 4 system. It might be mentioned in passing that the thermal conductivities of all of them were somewhat higher than for AgI. We started with pure sodium sulphate and measured both the thermal conductivity and the diffusivity, see Figs. 2 and 3, respectively. The general trend is that both parameters decrease over the whole range. The phase transitions at 470 K and 520 K cause dips in the recorded conductivity and diffusivity, and their transition enthalpies give sharp peaks in the plot of the heat capacitivity (per volume unit, l /k ), see Fig. 4. There are pronounced similarities between the three compositions Li 2 SO 4 , LiNaSO 4 and Li 1.55 Na 0.45 SO 4 concerning the general features. Figs. 5–7 show the thermal conductivity, the thermal diffusivity and l /k, respectively, for Li 2 SO 4 . Only the thermal conductivities are shown for LiNaSO 4 (Fig. 8) and Li 1.55 Na 0.45 SO 4 , (Fig. 9). All three
Fig. 2. The temperature dependence of the thermal conductivity of Na 2 SO 4 .
Fig. 3. The temperature dependence of the thermal diffusivity of Na 2 SO 4 .
Fig. 4. The temperature dependence of the heat capacitivity of Na 2 SO 4 .
328
B.M. Suleiman et al. / Solid State Ionics 136 – 137 (2000) 325 – 330
Fig. 5. The temperature dependence of the thermal conductivity of Li 2 SO 4 . Fig. 8. The temperature dependence of the thermal conductivity of LiNaSO 4 .
Fig. 6. The temperature dependence of the thermal diffusivity of Li 2 SO 4 .
Fig. 9. The temperature dependence of the thermal conductivity of Li 1.55 Na 0.45 SO 4 .
Fig. 7. The temperature dependence of the heat capacitivity of Li 2 SO 4 .
lithium-containing sulphates show a remarkable thermal feature near 640 K, i.e. at about the same temperature independent of whether we have a monoclinic phase (Li 2 SO 4 ), a trigonal one (LiNaSO 4 ) or a two-phase region (the eutectoid). Below this temperature the gradient dl / dT is negative for Li 2 SO 4 , while l is independent of the temperature for LiNaSO 4 . A rough estimate indicates that the average value over a range of about 300 K is of the order of dl / dT5 2 0.005 W/ mK 2 for Li 2 SO 4 . Regarding the eutectoid, there is a pro-
B.M. Suleiman et al. / Solid State Ionics 136 – 137 (2000) 325 – 330
nounced decrease below 380 K (dl / dT5 2 0.01 W/ mK 2 ), while l is independent of the temperature between 400 K and 640 K (dl / dT5 2 0.0005 W/ mK 2 ). Concerning the range above the event near 640 K, the conductivity graphs can be described as convex upwards in all three cases. Thus, the initial temperature gradient is dl / dT50.09 W/ mK 2 for Li 2 SO 4 , while dl / dT50.04 W/ mK 2 fits better for LiNaSO 4 as well as for the eutectoid. All three graphs flatten off, and dl / dT50.01 W/ mK 2 is a good approximation when the phase transition is approached, i.e. below 850 K for Li 2 SO 4 and 791 K for LiNaSO 4 The measurements were continued through and beyond the phase transition for Li 2 SO 4 as well as for LiNaSO 4 . The conditions for measuring were better in the fcc phase than in the bcc one. We went up to 878 K for Li 2 SO 4 . An average for four measurements in the range 858–878 K is 9.3560.08 W/ mK. This is to be compared with 6.5 W/ mK for the monoclinic phase just below the phase transition. There is thus full evidence for an increase of the thermal conductivity of Li 2 SO 4 with about 45% at the phase transition. The situation is different for LiNaSO 4 above 791 K, since it was more difficult to perform measurements in the bcc phase. We obtained data for one temperature only, according to which l is about 4.5 W/ mK at 795 K, while the average of three measurements at 777–780 K is 4.67 W/ mK. This indicates that the thermal conductivity of LiNaSO 4 does not change significantly at the trigonal–bcc transition. Let us now consider the thermal diffusivity k and the heat capacitivity c p for Li 2 SO 4 . As described above, c p is proportional to the ratio l /k. As seen from Fig. 3, the general pattern for the temperature dependence is the same for k as it is for l, i.e. the temperature gradient is negative below a thermal event near 640 K, where it changes sign. Concerning the region below 640 K, there is a tendency that the diffusivity k decreases somewhat faster than the conductivity does. This means that the heat capacitivity increases in this region. When we now go on to the region between the thermal event and the phase transition at 850 K, the question arises: how serious it is that the diffusivity data (k ) spread much more here than they did in the lower region. We can actually get important information in spite of
329
this. Thus, it is obvious that l increases faster than k does in this region. Thus it means that c p is larger here than below 640 K. Furthermore, the two highest readings among our data are close to k 51.5 mm 2 / s. Let us take this as an estimate of k for the monoclinic phase just below the transition at 850 K. It can be compared with k 53.060.1 mm 2 / K. This is the average of our above-mentioned four measurements for the fcc phase in the range 858–878 K. Thus, the thermal diffusivity k increased by 100% at the phase transition, while the above-mentioned increase of the conductivity l was about 45%. It might seem surprising that the jump at the phase transition is twice as large for the diffusivity as for the conductivity. However, this is in agreement with the information we can gain by calculating the ratio l /k. The ratio is close to 3 MJ / m 3 K at 330 K. One can consider three groups. Thus, for 36 measurements in the range 324–665 K we find that the ratio l /k lies between 2.8 and 3.9 MJ / m 3 K, while 13 measurements in the range 705–833 K give ratios between 4.1 and 9.0 MJ / m 3 K, and four measurements at 858–878 K, i.e. in the fcc phase, give 2.9 to 3.4 MJ / m 3 K. Thus, the heat capacitivity is about the same in the fcc phase as it is in the lower part of the monoclinic phase, i.e. below the thermal event that occurs near 640 K. On the other hand, both the thermal conductivity l and the thermal diffusivity k are much larger in the fcc phase than in the lower part of the monoclinic phase. In between, there is a region of about 200 degrees (ca. 640 K to 850 K) where both the conductivity l and the diffusivity k increase rapidly, while the heat capacitivity is significantly larger than outside this region. We know of no other property of monoclinic Li 2 SO 4 or trigonal LiNaSO 4 which changes drastically near 640 K. The closest should be the bandwidth broadening of a Raman frequency mode which has been studied by Frech and coworkers [23,24]. They concluded that the observed broadening was due to anharmonic contributions up to 720 K, while oriental disorder dominated above this temperature. We have referred to their results in a previous discussion [22]. Our sulphates which have plastic crystal properties have been compared with some other pure salts and binary systems which have polyatomic anions
330
B.M. Suleiman et al. / Solid State Ionics 136 – 137 (2000) 325 – 330
[10,20,25]. Studies of heat transfer in some of these systems might be of interest.
Note added in proof We have recently performed some additional experiments of heat transfer in the system Li 2 SO 4 – Na 2 SO 4 . Thanks to improved experimental conditions, we have been able to go to higher temperatures than before. Thus, while our first study of Na 2 SO 4 was terminated at 590 K, our new study went up to 780 K. Both the thermal conductivity and the thermal diffusivity decreased slighly up to about 640 K, where we obtained the same feature as found previously for Li 2 SO 4 , Li 1.55 Na 0.45 SO 4 and LiNaSO 4 , namely that the temperature gradients become positive, as shown in Figs. 5, 6, 8 and 9. We have now also studied the composition Li 0.5 Na 1.5 SO 4 , where we have a binary mixture of LiNaSO 4 and Na 2 SO 4 at room temperature and a solid solution of Li in hexagonal Na 2 SO 4 at high temperatures. The sharp change of the temperature gradient near 640 K occurred also in this case. Thus, we have found for the thermal properties of the system Li 2 SO 4 –NA 2 SO 4 that both the conductivity and the diffusivity increase rapidly at high temperatures. The onset temperature is independent of the crystal structure as well as of the cation concentrations. However, both the conductivity and the diffusivity are larger for lithium sulphate than for sodium sulphate, while the mixtures fall in between. This holds over the whole temperature range. Work is in progress on the evaluation of the new series of experiments.
Acknowledgements We thank Dr. Silas Gustafsson and Dr. Bengt-Erik Mellander for their assistance. This investigation has ¨ Smaltverk. ¨ been supported by Stiftelsen Vargons
References ´ J. Thomas, in: T. Takahashi (Ed.), High Con[1] A. Lunden, ductivity Solid Ionic Conductors, World Scientific, Singapore, 1989, p. 45.
[2] K. Schroeder, H. Ljungmark, A. Kvist, Z. Naturforsch. 27a (1972) 1252. [3] T. Førland, J. Krogh-Moe, Acta Chem. Scand. 11 (1957) 565. [4] T. Førland, J. Krogh-Moe, Acta Crystallogr. 11 (1958) 224. ´ Z. Naturforsch. 20a (1965) 235. [5] A. Kvist, A. Lunden, ¨ ´ Solid State Ionics 90 (1996) 209. [6] R. Tarneberg, A. Lunden, ¨ [7] B. Janson, C.-A. Sjoblom, Rheol. Acta 16 (1977) 628. ¨ [8] B. Janson, C.-A. Sjoblom, Rheol. Acta 20 (1981) 360. ´ in: B. Scrosati, A. Magistris, C.M. Mari, G. [9] A. Lunden, Mariotto (Eds.), Fast Ion Transport in Solids, NATO ASI Series E:250, Kluwer, Dordrecht, 1993, p. 181. ´ Z. Naturforsch. 50a (1995) 1067. [10] A. Lunden, [11] L. Nilsson, J.O. Thomas, B.C. Tofield, J. Phys. C, Solid State Phys. 13 (1980) 6441. ´ J.O. [12] R. Kaber, L. Nilsson, N.H. Andersen, A. Lunden, Thomas, J. Phys., Condens. Mat. 4 (1992) 1925. [13] L. Karlsson, R.L. McGreevy, Solid State Ionics 76 (1995) 301. [14] M. Ferrario, M.L. Klein, I.R. McDonald, Mol. Phys. 86 (1995) 923. [15] K. Funke, D. Wilmer, H. Feldmann, R.E. Lechner, in: Y. Kirschbaum, R. Michaelsen (Eds.), BENSC Experimental Reports 1998, Berlin Neutron Scattering Center, HMI, Berlin, 1999, p. 152. [16] R. Aronsson, L.M. Torell, Phys. Rev. B 36 (1987) 4926. ¨ [17] L. Borjesson, L.M. Torell, Proc. Electrochem. Soc. 86–1 (1986) 21. ´ in: B.V.R. Chowdari (Ed.), Materials for Solid [18] A. Lunden, State Batteries, World Scientific, Singapore, 1986, p. 149. ´ in: M. Sørlie, T. Østvold, R. Huglen (Eds.), [19] A. Lunden, International Harald A. Øye Symposium, Trondheim, Norway, Feb. 2–3, 1995, Inst. Inorg. Chem., Norwegian Inst. Technology, Trondheim, Norway, 1995, p. 95. ´ B.M. Suleiman, E. Karawacki, in: H.A. Øye, A. [20] A. Lunden, Wærnes (Eds.), International Terje Østvold Symposium, Røros, Norway, Nov. 2–3 1998, Inst. Inorg. Chem., Norwegian Inst. Technology, Trondheim, Norway, 1998, p. 65. [21] S.E. Gustafsson, Rev. Sci. Instrum. 62 (1991) 797. ´ J. [22] B.M. Suleiman, M. Gustavsson, E. Karawacki, A. Lunden, Phys. D, Appl. Phys. 30 (1997) 2553. [23] R. Frech, E. Cazzanelli, Solid State Ionics 9–10 (1983) 95. [24] D. Teeters, R. Frech, Phys. Rev. B 26 (1982) 5897. ´ in: B.V.R. Chowdari, M.A.K.L. Dissanayake, [25] A. Lunden, M.A. Careem (Eds.), Solid State Ionics: New Developments, World Scientific, Singapore, 1996, p. 23.
Heat transfer and ion migration in the system Li 2 SO 4 –Na 2 SO 4 ´ *, Ernest Karawacki Bashir M. Suleiman 1 , Arnold Lunden ¨ Department of Physics, Chalmers University of Technology, S-412 96 Goteborg , Sweden
Abstract The transient plane source technique has been used for simultaneous measurements of thermal conductivity and diffusivity in the lithium–sodium sulphate system starting near 300 K. Samples with 100, 77.5, or 50% Li 2 SO 4 behave differently from pure Na 2 SO 4 . In the first case both the thermal conductivity and the diffusivity start to increase rapidly at about 640 K, while the crystal structure remains monoclinic for Li 2 SO 4 and trigonal for LiNaSO 4 . Concerning pure Li 2 SO 4 , there is an additional discontinuous increase of the two thermal parameters at the structural transition from monoclinic to cubic (fcc) at 850 K, while the temperature gradients become significantly smaller in the cubic phase than in the monoclinic one. In contrast, both the thermal conductivity and the diffusivity of Na 2 SO 4 decrease over the whole studied temperature range, which includes the phase transitions at 474 K and 520 K. Furthermore, a corresponding study was performed for silver iodide over the range 295–640 K, i.e. on both sides of the phase transition at 420 K. There is an indication of a small decrease of the thermal conductivity and the diffusivity at the phase transition. The high temperature phases fcc Li 2 SO 4 , bcc LiNaSO 4 and bcc AgI are solid electrolytes, but it is characteristic for the two sulphate phases that a coupled rotation-like motion of the sulphate ions enhances the cation migration. Obviously, such motion is also of importance for heat transport. 2000 Elsevier Science B.V. All rights reserved. Keywords: Alkali sulphates; Heat transport; Thermal conductivity; Thermal diffusivity; Heat capacitivity; Paddle-wheel mechanism; Cation migration Materials: Li 2 SO 4 ; Na 2 SO 4 ; LiNaSO 4
1. Introduction It is characteristic for a solid electrolyte that one ionic species has a much larger mobility than the other ions present, while many kinds of ions are mobile in a molten electrolyte. The ionic radius is thus a much more critical parameter in a solid phase than in a melt. There is, however, a small group of *Corresponding author. Fax: 146-31-772-3251. ´ E-mail address: [email protected] (A. Lunden). 1 Present address: University of Sharjah, College of Arts and Sciences, P.O. Box 27272, Sharjah, United Arab Emirates.
high temperature phases where a large number of uni- and divalent cations are very mobile [1]. The four phases that have been studied so far are fcc Li 2 SO 4 , bcc LiNaSO 4 , bcc LiAgSO 4 and non-cubic Li 4 Zn(SO 4 ) 3 . The first two of them belong to the Li 2 SO 4 –Na 2 SO 4 system [2], see Fig. 1, where the high-temperature phase on the Na 2 SO 4 -rich side is hexagonal. Førland and Krogh-Moe pointed out that there was a large excess of cation sites in the two cubic phases, and that strong rotational orientations must be expected for the sulphate ions [3,4]. The electrical conductivity of Li 2 SO 4 was found to be of the order of 0.9 S / cm at 823 K [5], while diffusion
0167-2738 / 00 / $ – see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S0167-2738( 00 )00467-7
326
B.M. Suleiman et al. / Solid State Ionics 136 – 137 (2000) 325 – 330
ductivity, etc. also have some influence on heat transfer. Data for the system Li 2 SO 4 –Na 2 SO 4 are also of practical interest for some applications, e.g. for high-temperature batteries, fuel cells or heat storage devices; for references see Refs. [18,19].
2. Experimental
Fig. 1. Phase diagram of the system Li 2 SO 4 –Na 2 SO 4 .
studies showed that all mono- and divalent cations are very mobile in the cubic phases [6]. These phases can actually be considered as both solid electrolytes and plastic crystals [7,8]. The cation mobility is enhanced by a strong coupling to the rotation of the otherwise translationally immobile sulphate ions [1,6]. Actually, all possible kinds of transport mechanisms are enhanced. This phenomenon is depicted as the ‘paddle-wheel’ or ‘cogwheel’ model, which was first presented in 1972 [6,9,10]. The model is consistent with three neutron scattering studies viz. powder diffraction [11], single crystal diffraction [12] and total scattering evaluated by the reverse Monte Carlo technique [13], and furthermore with molecular dynamics simulations [14]. A study is in progress by means of coherent quasielastic neutron scattering [15]. Elastic constants have been determined by means of Brillouin scattering [16], and Raman spectra give evidence for sulphate ion reorientations in the high-temperature cubic phases, but not in hexagonal Na 2 SO 4 [17]. It is of interest to see whether the phase transitions that cause dramatic changes of the electrical con-
Single crystals have been used in some earlier studies of heat transport in sulphates, for references see Ref. [20]. However, nobody has yet succeeded in maintaining single crystals of lithium sulphate through the phase transition at 850 K, and we must choose a technique where we can scan wide temperature ranges. The thermal conductivity ( l) and the thermal diffusivity (k ) were measured simultaneously by means of the transient plane source (TPS) technique [21,22]. The plane heat source served at the same time as the temperature sensor. It was clamped between two discs of salt which were 12 mm thick and had a diameter of 38 mm. The TPS element and the two discs were placed in an oven. The measurements were started slightly above room temperature, and the heating rate was 0.75 K / min. Two scans with increasing temperatures were performed for Li 2 SO 4 . The agreement between them was good in the ranges where the temperature gradients were small, but large deviations occurred in the range 640–850 K, where the parameters depended on the temperature. We made only one scan for the other salts [20]. A more detailed description of the experimental procedure and the evaluation is given elsewhere [22]. The accuracy of the measurements can be checked by calculating the heat capacitivity per volume unit l /k 5 r c p where r is the density, and c p is the heat capacitivity. According to this criterion, our results for the pure salts Li 2 SO 4 and Na 2 SO 4 are more reliable than those for the equimolar compound LiNaSO 4 and the eutectoid mixture Li 1.55 Na 0.45 SO 4 . Already a view with the naked eye shows that the conductivity data are more accurate than the diffusivity data for the latter two compositions, and we have given more attention to the conductivities than to the diffusivities when discussing the four sulphates [20].
B.M. Suleiman et al. / Solid State Ionics 136 – 137 (2000) 325 – 330
327
3. Results and discussion Since the mechanisms for transfer of ions and for heat transfer are very different, one does not per se expect any correlation between, e.g. ion conductivity and heat conductivity. It is reasonable to start with the simplest case, i.e. salts where both ions are monatomic. Silver iodide has a phase transition at 420 K where the ionic conductivity increases by several orders of magnitude. We have measured the thermal conductivity ( l) and the diffusivity (k ) in the range from 295 K to 640 K at three temperatures on each side of the transition. Both parameters are nearly constant over the whole range. We obtained a thermal conductivity of 0.53 W/ mK below the transition and 0.52 W/ mK for the high-temperature phase a-AgI. The corresponding thermal diffusivities are close to 0.83 mm 2 / s. It holds for l as well as for k that the individual values can be divided in two groups where all three ‘high’ data were obtained below the phase transition and vice versa. Our conclusion is that there is a slight, but significant, decrease at least for the thermal conductivity at the phase transition and that temperature gradients are extremely small in both phases. (We have not investigated whether stable b-AgI or metastable gAgI dominates in the lower temperature range.) What happens if the anions are polyatomic, which allows some additional rotational or librational degrees of freedom? We have studied four compositions in the (Li,Na) 2 SO 4 system. It might be mentioned in passing that the thermal conductivities of all of them were somewhat higher than for AgI. We started with pure sodium sulphate and measured both the thermal conductivity and the diffusivity, see Figs. 2 and 3, respectively. The general trend is that both parameters decrease over the whole range. The phase transitions at 470 K and 520 K cause dips in the recorded conductivity and diffusivity, and their transition enthalpies give sharp peaks in the plot of the heat capacitivity (per volume unit, l /k ), see Fig. 4. There are pronounced similarities between the three compositions Li 2 SO 4 , LiNaSO 4 and Li 1.55 Na 0.45 SO 4 concerning the general features. Figs. 5–7 show the thermal conductivity, the thermal diffusivity and l /k, respectively, for Li 2 SO 4 . Only the thermal conductivities are shown for LiNaSO 4 (Fig. 8) and Li 1.55 Na 0.45 SO 4 , (Fig. 9). All three
Fig. 2. The temperature dependence of the thermal conductivity of Na 2 SO 4 .
Fig. 3. The temperature dependence of the thermal diffusivity of Na 2 SO 4 .
Fig. 4. The temperature dependence of the heat capacitivity of Na 2 SO 4 .
328
B.M. Suleiman et al. / Solid State Ionics 136 – 137 (2000) 325 – 330
Fig. 5. The temperature dependence of the thermal conductivity of Li 2 SO 4 . Fig. 8. The temperature dependence of the thermal conductivity of LiNaSO 4 .
Fig. 6. The temperature dependence of the thermal diffusivity of Li 2 SO 4 .
Fig. 9. The temperature dependence of the thermal conductivity of Li 1.55 Na 0.45 SO 4 .
Fig. 7. The temperature dependence of the heat capacitivity of Li 2 SO 4 .
lithium-containing sulphates show a remarkable thermal feature near 640 K, i.e. at about the same temperature independent of whether we have a monoclinic phase (Li 2 SO 4 ), a trigonal one (LiNaSO 4 ) or a two-phase region (the eutectoid). Below this temperature the gradient dl / dT is negative for Li 2 SO 4 , while l is independent of the temperature for LiNaSO 4 . A rough estimate indicates that the average value over a range of about 300 K is of the order of dl / dT5 2 0.005 W/ mK 2 for Li 2 SO 4 . Regarding the eutectoid, there is a pro-
B.M. Suleiman et al. / Solid State Ionics 136 – 137 (2000) 325 – 330
nounced decrease below 380 K (dl / dT5 2 0.01 W/ mK 2 ), while l is independent of the temperature between 400 K and 640 K (dl / dT5 2 0.0005 W/ mK 2 ). Concerning the range above the event near 640 K, the conductivity graphs can be described as convex upwards in all three cases. Thus, the initial temperature gradient is dl / dT50.09 W/ mK 2 for Li 2 SO 4 , while dl / dT50.04 W/ mK 2 fits better for LiNaSO 4 as well as for the eutectoid. All three graphs flatten off, and dl / dT50.01 W/ mK 2 is a good approximation when the phase transition is approached, i.e. below 850 K for Li 2 SO 4 and 791 K for LiNaSO 4 The measurements were continued through and beyond the phase transition for Li 2 SO 4 as well as for LiNaSO 4 . The conditions for measuring were better in the fcc phase than in the bcc one. We went up to 878 K for Li 2 SO 4 . An average for four measurements in the range 858–878 K is 9.3560.08 W/ mK. This is to be compared with 6.5 W/ mK for the monoclinic phase just below the phase transition. There is thus full evidence for an increase of the thermal conductivity of Li 2 SO 4 with about 45% at the phase transition. The situation is different for LiNaSO 4 above 791 K, since it was more difficult to perform measurements in the bcc phase. We obtained data for one temperature only, according to which l is about 4.5 W/ mK at 795 K, while the average of three measurements at 777–780 K is 4.67 W/ mK. This indicates that the thermal conductivity of LiNaSO 4 does not change significantly at the trigonal–bcc transition. Let us now consider the thermal diffusivity k and the heat capacitivity c p for Li 2 SO 4 . As described above, c p is proportional to the ratio l /k. As seen from Fig. 3, the general pattern for the temperature dependence is the same for k as it is for l, i.e. the temperature gradient is negative below a thermal event near 640 K, where it changes sign. Concerning the region below 640 K, there is a tendency that the diffusivity k decreases somewhat faster than the conductivity does. This means that the heat capacitivity increases in this region. When we now go on to the region between the thermal event and the phase transition at 850 K, the question arises: how serious it is that the diffusivity data (k ) spread much more here than they did in the lower region. We can actually get important information in spite of
329
this. Thus, it is obvious that l increases faster than k does in this region. Thus it means that c p is larger here than below 640 K. Furthermore, the two highest readings among our data are close to k 51.5 mm 2 / s. Let us take this as an estimate of k for the monoclinic phase just below the transition at 850 K. It can be compared with k 53.060.1 mm 2 / K. This is the average of our above-mentioned four measurements for the fcc phase in the range 858–878 K. Thus, the thermal diffusivity k increased by 100% at the phase transition, while the above-mentioned increase of the conductivity l was about 45%. It might seem surprising that the jump at the phase transition is twice as large for the diffusivity as for the conductivity. However, this is in agreement with the information we can gain by calculating the ratio l /k. The ratio is close to 3 MJ / m 3 K at 330 K. One can consider three groups. Thus, for 36 measurements in the range 324–665 K we find that the ratio l /k lies between 2.8 and 3.9 MJ / m 3 K, while 13 measurements in the range 705–833 K give ratios between 4.1 and 9.0 MJ / m 3 K, and four measurements at 858–878 K, i.e. in the fcc phase, give 2.9 to 3.4 MJ / m 3 K. Thus, the heat capacitivity is about the same in the fcc phase as it is in the lower part of the monoclinic phase, i.e. below the thermal event that occurs near 640 K. On the other hand, both the thermal conductivity l and the thermal diffusivity k are much larger in the fcc phase than in the lower part of the monoclinic phase. In between, there is a region of about 200 degrees (ca. 640 K to 850 K) where both the conductivity l and the diffusivity k increase rapidly, while the heat capacitivity is significantly larger than outside this region. We know of no other property of monoclinic Li 2 SO 4 or trigonal LiNaSO 4 which changes drastically near 640 K. The closest should be the bandwidth broadening of a Raman frequency mode which has been studied by Frech and coworkers [23,24]. They concluded that the observed broadening was due to anharmonic contributions up to 720 K, while oriental disorder dominated above this temperature. We have referred to their results in a previous discussion [22]. Our sulphates which have plastic crystal properties have been compared with some other pure salts and binary systems which have polyatomic anions
330
B.M. Suleiman et al. / Solid State Ionics 136 – 137 (2000) 325 – 330
[10,20,25]. Studies of heat transfer in some of these systems might be of interest.
Note added in proof We have recently performed some additional experiments of heat transfer in the system Li 2 SO 4 – Na 2 SO 4 . Thanks to improved experimental conditions, we have been able to go to higher temperatures than before. Thus, while our first study of Na 2 SO 4 was terminated at 590 K, our new study went up to 780 K. Both the thermal conductivity and the thermal diffusivity decreased slighly up to about 640 K, where we obtained the same feature as found previously for Li 2 SO 4 , Li 1.55 Na 0.45 SO 4 and LiNaSO 4 , namely that the temperature gradients become positive, as shown in Figs. 5, 6, 8 and 9. We have now also studied the composition Li 0.5 Na 1.5 SO 4 , where we have a binary mixture of LiNaSO 4 and Na 2 SO 4 at room temperature and a solid solution of Li in hexagonal Na 2 SO 4 at high temperatures. The sharp change of the temperature gradient near 640 K occurred also in this case. Thus, we have found for the thermal properties of the system Li 2 SO 4 –NA 2 SO 4 that both the conductivity and the diffusivity increase rapidly at high temperatures. The onset temperature is independent of the crystal structure as well as of the cation concentrations. However, both the conductivity and the diffusivity are larger for lithium sulphate than for sodium sulphate, while the mixtures fall in between. This holds over the whole temperature range. Work is in progress on the evaluation of the new series of experiments.
Acknowledgements We thank Dr. Silas Gustafsson and Dr. Bengt-Erik Mellander for their assistance. This investigation has ¨ Smaltverk. ¨ been supported by Stiftelsen Vargons
References ´ J. Thomas, in: T. Takahashi (Ed.), High Con[1] A. Lunden, ductivity Solid Ionic Conductors, World Scientific, Singapore, 1989, p. 45.
[2] K. Schroeder, H. Ljungmark, A. Kvist, Z. Naturforsch. 27a (1972) 1252. [3] T. Førland, J. Krogh-Moe, Acta Chem. Scand. 11 (1957) 565. [4] T. Førland, J. Krogh-Moe, Acta Crystallogr. 11 (1958) 224. ´ Z. Naturforsch. 20a (1965) 235. [5] A. Kvist, A. Lunden, ¨ ´ Solid State Ionics 90 (1996) 209. [6] R. Tarneberg, A. Lunden, ¨ [7] B. Janson, C.-A. Sjoblom, Rheol. Acta 16 (1977) 628. ¨ [8] B. Janson, C.-A. Sjoblom, Rheol. Acta 20 (1981) 360. ´ in: B. Scrosati, A. Magistris, C.M. Mari, G. [9] A. Lunden, Mariotto (Eds.), Fast Ion Transport in Solids, NATO ASI Series E:250, Kluwer, Dordrecht, 1993, p. 181. ´ Z. Naturforsch. 50a (1995) 1067. [10] A. Lunden, [11] L. Nilsson, J.O. Thomas, B.C. Tofield, J. Phys. C, Solid State Phys. 13 (1980) 6441. ´ J.O. [12] R. Kaber, L. Nilsson, N.H. Andersen, A. Lunden, Thomas, J. Phys., Condens. Mat. 4 (1992) 1925. [13] L. Karlsson, R.L. McGreevy, Solid State Ionics 76 (1995) 301. [14] M. Ferrario, M.L. Klein, I.R. McDonald, Mol. Phys. 86 (1995) 923. [15] K. Funke, D. Wilmer, H. Feldmann, R.E. Lechner, in: Y. Kirschbaum, R. Michaelsen (Eds.), BENSC Experimental Reports 1998, Berlin Neutron Scattering Center, HMI, Berlin, 1999, p. 152. [16] R. Aronsson, L.M. Torell, Phys. Rev. B 36 (1987) 4926. ¨ [17] L. Borjesson, L.M. Torell, Proc. Electrochem. Soc. 86–1 (1986) 21. ´ in: B.V.R. Chowdari (Ed.), Materials for Solid [18] A. Lunden, State Batteries, World Scientific, Singapore, 1986, p. 149. ´ in: M. Sørlie, T. Østvold, R. Huglen (Eds.), [19] A. Lunden, International Harald A. Øye Symposium, Trondheim, Norway, Feb. 2–3, 1995, Inst. Inorg. Chem., Norwegian Inst. Technology, Trondheim, Norway, 1995, p. 95. ´ B.M. Suleiman, E. Karawacki, in: H.A. Øye, A. [20] A. Lunden, Wærnes (Eds.), International Terje Østvold Symposium, Røros, Norway, Nov. 2–3 1998, Inst. Inorg. Chem., Norwegian Inst. Technology, Trondheim, Norway, 1998, p. 65. [21] S.E. Gustafsson, Rev. Sci. Instrum. 62 (1991) 797. ´ J. [22] B.M. Suleiman, M. Gustavsson, E. Karawacki, A. Lunden, Phys. D, Appl. Phys. 30 (1997) 2553. [23] R. Frech, E. Cazzanelli, Solid State Ionics 9–10 (1983) 95. [24] D. Teeters, R. Frech, Phys. Rev. B 26 (1982) 5897. ´ in: B.V.R. Chowdari, M.A.K.L. Dissanayake, [25] A. Lunden, M.A. Careem (Eds.), Solid State Ionics: New Developments, World Scientific, Singapore, 1996, p. 23.