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Ionic conductivities in crystalline, glassy, and liquid AgAsS2
Solid State Ionics 269 (2015) 106–109
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Solid State Ionics journal homepage: www.elsevier.com/locate/ssi
Ionic conductivities in crystalline, glassy, and liquid AgAsS2 K. Tanaka ⁎, Y. Miyamoto Department of Applied Physics, Graduate School of Engineering, Hokkaido University, Sapporo 060-8628, Japan
a r t i c l e
i n f o
Article history: Received 2 August 2014 Received in revised form 20 November 2014 Accepted 26 November 2014 Available online 10 December 2014
a b s t r a c t Ionic conductivity in AgAsS2 has been measured at 20–600 °C for crystalline, glassy, supercooled, and liquid states. The liquids possess substantially smaller activation energies (~0.2 eV) and conductivity prefactors (~3 S/cm) than those in the solids. Other electrical characteristics are discussed, taking calorimetric and dilatometric results into account. © 2014 Elsevier B.V. All rights reserved.
Keywords: Chalcogenide glass Chalcogenide liquid Ionic conductivity Temperature dependence Thermal analyses
1. Introduction The ionic conduction in condensed matters has been a subject of continuous studies stemming from fundamental interests in iontransport mechanisms and wide applications to batteries, photographic films, ion sensors, and so forth. Mobile ions are H+, Li+, Ag+, etc., and matrices may be oxides, chalcogenides, and halides of crystalline, glassy, powdered, and ceramic forms, in which an ion-conducting glass remains to be a focus, due to its good conductivity and compositional variability [1]. However, the conduction mechanisms remain vague, with a primary reason that the atomic structure in non-crystalline materials, which may be heterogeneous, cannot be explicitly identified. Among the ion-conducting glasses, the Ag-chalcogenide system attracts substantial interest since it is relatively stable [2–4] and a heavy atom Ag is, in comparison with Li etc., easily detected by x-rays. In addition, the material behaves as an “ion-conducting amorphous semiconductor” [5], which exhibits promising photo-electro-ionic phenomena [6]. Accordingly, a lot of electrical studies have been performed so far, most of which concern with compositional [2,7–11] and/ or spectral [12–16] variations. We may refer also to recent computeraided structural analyses [17,18]. However, temperature dependence is less explored, or varied temperature ranges have been limited to solid phases [7,13,15,16,19], and the ionic conductivity in (supercooled) liquid states has hardly been studied [12]. Extending previous studies [5,20–22], we here investigate the ionic conductivity in AgAsS2 of crystalline, glassy, and liquid forms using a special sampling technique. Thermal properties have also been inspected, and these results are discussed in a unified way for obtaining ⁎ Corresponding author. Tel.: +81 11706400. E-mail address: [email protected] (K. Tanaka).
http://dx.doi.org/10.1016/j.ssi.2014.11.025 0167-2738/© 2014 Elsevier B.V. All rights reserved.
insights into the ionic conduction in condensed matters. Specifically, we will consider the ionic conductivity in a supercooled phase in light of the free-volume model. 2. Experiments AgAsS2 glass (g-AgAsS2) was prepared through the conventional melt-quenching method, the detail being described previously [21]. The glass was crushed into powders, and those of about 5 mg were inserted into quartz-glass pipes with a length of ~ 2 cm and an inner diameter of 1 mm and then packed in to the central part using two Au rods with a diameter of 1 mm and a length of ~2 mm, which were compressed with Cu rods with the same diameter, which were connected to Cu wires. As exemplified in Fig. 1, the powder became to ~ 2 mm in length upon compression. (We tried also Ag rods instead of Au, but the conductivity of AgAsS2 could not be evaluated owing to a resistance drop at temperatures above ~200 °C, which was probably caused by formation of conducting crystalline Ag2S paths.) This encapsulated Cu:Au: AgAsS2:Au:Cu sample was set in an Ar-flowing small furnace and heated. Sample temperature was monitored, with an accuracy of about ±10 °C, using a thermocouple in a quartz-glass pipe, which was bundled with the sample pipe. Such a sample assembly having small thermal capacity is required for obtaining rapid quenching rates. Ac conductivity of the sample was evaluated from currents, which were measured using a lock-in amplifier (NF, 5610B) under applied voltages of 1 − 100 mV, at sample temperatures of 20–600 °C. However, upon temperature variations, the packed AgAsS2 could not retain the columnar shape, due to material leakage during melting and thermal volume changes. Accordingly, the accuracy of the conductivity value may be ± 50%, or the absolute value may be twice of the calculated ones, owing to the leakage. In addition, subsidiary thermal analyses
K. Tanaka, Y. Miyamoto / Solid State Ionics 269 (2015) 106–109
107
Fig. 1. A photograph of an encapsulated Cu:Au:AgAsS2:Au:Cu sample.
were performed using a conventional calorimeter (DTA) and a dilatometer. (The actual composition in these thermal measurements was found to be Ag30As20S50 by x-ray microprobe analyses, while its thermal property could be regarded to be nearly the same to that in AgAsS2). 3. Results Fig. 2 exemplifies frequency dependence of ac currents at room and high temperatures. We see in both cases that the currents are nearly constant at a frequency range of 102–104 Hz, which suggests that the value is governed by bulk dc ionic components without electrode and capacitance effects [16]. Accordingly, we select 1.2 kHz for investigating temperature variations. Fig. 3(a) shows a DTA curve of g-AgAsS2 obtained under a heating process at a rate of 10 °C/min. We see a glass-transition step at ~150 °C, in consistent with previous results [2,23,24]. Then two exothermic peaks appear at around 250 °C, which can be ascribed to crystallization to proustite (Ag3AsS3 crystal with a crystallization temperature of ~210 °C) and smithite (AgAsS2 crystal, ~260 °C) [23]. At ~430 °C, we see a prominent endothermic dip, a signature of the melting of smithite [2,23]. The melting of proustite at 490 °C [2] is located out of the measurement range (≤ 450 °C), and it cannot be seen. We have examined also a dilatometric characteristic (not shown) using a polished glass rod with a diameter of ~ 5 mm and a length of ~15 mm. Around room temperature, the sample expanded with a linear coefficient α of 1.7 × 10−5/K, in consistent with a previous datum [24], and then it increased to 2.4 × 10−5/K above ~145 °C (≈ Tg). At ~160 °C, the sample became fluid, which hindered further measurements. Trials
Fig. 3. Heat flow (a) and electrical conductivity (b), upon rapid (○), and slow (Δ) coolings, in AgAsS2 as a function of temperature T. Electrical conductivities of single-crystalline AgAsS2 [19] and Ag3AsS3 [27] are also plotted by dashed lines for comparison. Upper and lower-directing arrows in (b) indicate phase transition points in AgAsS2 [19] and Ag3AsS3 [28,29], and the red solid line delineates a VFT curve (see, the text).
measuring thermal expansion coefficients in the liquid state were unsuccessful due to material bubbling. Fig. 3(b) shows a series of results of the electrical conductivity σ upon temperature changes. At the outset, the sample was heated to a liquid phase, ~580 °C, compacted there, and cooled down. In the liquid phase, σ ≈ 10−1 S/cm, the value being at a superionic level. In addition, it seems that the liquid undergoes an Arrhenius-type temperature variation, σ ≈ σ0 exp(−Ea/kBT), in consistent with results reported for Ag-S(Se) [25,26]. (However, the limited measurable range of ~100 °C in the liquid phase makes this assertion tentative.) The parameters σ0 and Ea are listed in Table 1. Behaviors after solidification depended upon cooling rates.
Table 1 Summary of the activation parameters obtained in the present study, in comparison with those previously reported. The parameters are calculated at room temperature, except for the values in the liquid and supercooled phases and the parenthesized ones, which are averaged over the crystalline phases from room temperature to 420 °C. Note that σ0 is evaluated through extrapolation so that the accuracy is worse. Material
σ0 [S/cm]
Ea [eV]
Reference
Liquid Supercooled Glassy
4 2 50 ± 20 50 30 7 100 0.02 (~20) 100 3 20 0.1
0.25 0.17 0.45 ± 0.05 0.45 0.38 0.37 0.48 0.32 (~0.5) 0.62 0.42 0.17 0.39
Present Present Present 7 19 16 15 Present 19 27 28 29
Crystalline Smithite Proustite Fig. 2. Frequency spectra of current densities in an Au:AgAsS2:Au sample in glassy (a) and liquid (b) states under the applied voltages (V0) specified.
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Upon slow cooling of ~ 1 °C/min (triangles), the conductivity undergoes an inflection at 490 °C and a discontinuous drop at 430 °C. These temperatures seem to correspond to the melting temperatures of proustite Ag3AsS3 and smithite AgAsS2 [2,23]. Actually, x-ray diffraction patterns, which were taken at room temperature after electrical measurements, manifested that the slowly cooled materials are mixtures of these crystals. In consistent with the observations, we see in Fig. 3(b) that the conductivity curve is located in between those of single-crystalline proustite [27] and smithite [19]. (For proustite, however, reported conductivity results [27–29] are appreciably scattered.) In the crystalline state, the conductivity decreases with Arrhenius-type behaviors, with the parameters of σ0 ≈ 20 S/cm and Ea ≈ 0.5 eV when averaged over temperatures. Small discontinuities, arrowed in Fig. 3(b), probably reflect phase transitions in the crystals; those at ~ 70 and ~ 140 °C arising from smithite [19] and ~ 30 and ~ 230 °C from proustite [27,28]. Re-heating the sample from room temperature at a rate of 10 °C/min has traced nearly the same line (not shown). On the other hand, when the liquid is cooled rapidly with ~100 °C/min (circles), the conductivity hardly changes at the melting points, decreasing more-or-less smoothly to room temperature. However, a closer inspection can divide the conductivity curve into two parts at ~ 150 °C (≈ Tg). Above this temperature, the material resides in a supercooled liquid state. The conductivity curve is convex upwards, which can be fitted with the Vogel–Fulcher–Tammann (VFT) formula [30,31]; σ ðT Þ ¼ σ 0 expf−B=ðT − T 0 Þg;
ð1Þ
where a least-square fitting procedure gives σ0 = 2 S/cm, B = 2000 K (kBB = 0.17 eV), and T0 = 220 ± 40 K, the result being delineated in Fig. 3(b) by a red solid curve. Here, T0 is the so-called ideal glasstransition (Vogel) temperature, which is known to be lower than the actual glass-transition temperature [30,31]. The present σ0 and kBB values are comparable with those (~ 5 S/cm, 0.1–0.3 eV) reported for supercooled states of oxides and iodines [30]. On the other hand, the conductivity below ~150 °C is ascribed to ion motions in a glassy state. The curve can be approximated with the Arrhenius-type equation with the parameters listed in Table 1, which are consistent with those reported for g-AgAsS2 [7,16,19,21]. Re-heating the sample with a rate of 10 °C/min gave a similar trace (not shown) up to ~200 °C, above which the conductivity abruptly dropped a few times, which are ascribable to the crystallization. 4. Discussion We have obtained unified conductivity data for crystalline, glassy, supercooled, and liquid states of AgAsS2. Among the results, three observations attract special interests. First, we see in Fig. 3(b) that the glass possesses higher conductivity than that of the crystal. Such a trend seems to be general in the ionic conduction. The reason may be ascribed to a smaller material density of the glass by ~5% [7], which provides open space for ions, while quantitative analyses remain. In more detail, as compared in Table 1, the difference of the electrical conductivity in the glass and the crystal lies mainly in σ0, with Ea being roughly the same. More advanced analyses may be feasible if σ can be resolved to the carrier density n and the mobility μ as σ = qnμ, where q is the charge of Ag ions. Temperature variation can then be written as qn0exp(− Ena /kBT)μ0exp(− E μa/kBT), and accordingly, Ea = Ena + Eμa. A previous [20] and successive (reported elsewhere) studies using electrical time-of-flight experiments have demonstrated Ea ≈ Ena for Ag-As-S glasses, i.e., the conductivity activation is governed by the increase in mobile-ion density. The similar Ea in the crystal may suggest the same situation. However, we should note that the present crystalline samples are composed with mixtures of poly-crystalline AgAsS2 and Ag3AsS3
with unknown grain sizes, which are probably defective and connected through interfacial regions, so that it is difficult to know which component governs the crystalline conductivity. Second is the VFT-type conductivity variation in the supercooled state. The free-volume model assumes that an effective atomic volume v at T (N T0) can be written down as vðT Þ ¼ v0 þ v0 βðT − T 0 Þ;
ð2Þ
where the first term represents a fixed volume, which may be regarded as the atomic volume (~(2.8 A)3 [2,24]), and the second is a free volume, where β is the volumetric expansion coefficient. The model presumes that the ionic conductivity σ(T) can be represented as [30] σ ðT Þ expf−v =v0 βðT − T 0 Þg;
ð3Þ
where v* is the smallest free volume necessary for ion migration. Here, a comparison of the Eqs. (1) and (3) gives v*/v0 = Bβ, and putting the present observations B = 2000 K and β = 3α = 3 × 2.4 × 10−5/K, we obtain v*/v0 = 0.14. It seems that ~ 1/10 excess volume per atom, which may be distributed in heterogeneous and percolated ways [11], is needed for free migration of Ag ions in a supercooled AgAsS2 structure. Finally, Table 1 shows that the activation energies in the (supercooled) liquid states are about a half of those in the solid (glassy and crystalline) states: ~0.2 and ~0.4 eV. We may envisage that all of Ag atoms are mobile at the melting temperature, and further activation is accomplished by a mobility enhancement with Eμa ≈ 0.2 eV, to which macroscopic material flows in the liquid states may contribute. Nevertheless, theoretical studies of ionic transport in liquids appear to be very limited [32–35], and further analyses will be valuable to elucidate the ion dynamics in condensed matters. 5. Conclusions The ionic conductivity in all the condensed states of AgAsS2 has been evaluated as a function of temperature. Glassy and crystalline states possess roughly the same activation energy ~0.4 eV with a marked difference of the prefactor. By contrast, the liquid and supercooled phases exhibit appreciable smaller activation energies than those in the solid states. It is tempting to envisage that the conductivity activation in the solid and liquid states are governed by the changes in mobile-ion density and mobility, respectively. Acknowledgment The authors would like to thank Professor H. Hosono for calorimetric and dilatometric measurements. References [1] A. Bunde, K. Funke, M.D. Ingram, Solid State Ionics 105 (1998) 1. [2] Z.U. Borisova, Glassy Semiconductors, Plenum, New York, 1981. (Chap. 6). [3] I. Kaban, P. Jóvári, T. Wágner, M. Bartoš, M. Frumar, B. Beuneu, W. Hoyer, N. Mattern, J. Eckert, J. Non-Cryst. Solids 357 (2011) 3430. [4] K.S. Andrikopoulos, J. Arvanitidis, V. Dracopoulos, D. Christofilos, T. Wagner, S.N. Yannopoulos, Appl. Phys. Lett. 99 (2011) 171911. [5] K. Tanaka, J. Non-Cryst. Solids 164-166 (1993) 1179. [6] M. Frumar, T. Wagner, Curr. Opinion Solid State Mater. Sci. 7 (2003) 117. [7] Y. Kawamoto, M. Nishida, J. Non-Cryst. Solids 20 (1976) 393. [8] M. Kawasaki, J. Kawamoto, Y. Nakamura, M. Aniya, Solid State Ionics 123 (1999) 259. [9] M.A. Urenã, A.A. Piarristeguy, M. Fontana, B. Arcondo, Solid State Ionics 176 (2005) 505. [10] C. Holbrook, P. Chen, D.I. Novita, P. Boolchand, IEEE Trans. Nanotechnol. 6 (2007) 530. [11] E. Bychkov, Solid State Ionics 180 (2009) 510. [12] C. Cramer, M. Buscher, Solid State Ionics 105 (1998) 109. [13] A. Pradel, G. Tailladesa, C. Cramerb, M. Ribesa, Solid State Ionics 105 (1998) 139. [14] K. Shimakawa, T. Wagner, J. Appl. Phys. 113 (2013) 143701. [15] I.P. Studenyak, Yu.Yu. Meimet, M. Kranjčec, A.M. Solomon, A.F. Orliukas, A. Kežionis, E. Kazakevičius, T. Šalkus, J. Appl. Phys. 115 (2014) 033702. [16] D.S. Patil, K. Shimakawa, V. Zima, T. Wagner, J. Appl. Phys. 115 (2014) 143707. [17] De N. Tafen, D.A. Draold, M. Mitkova, Phys. Rev. B 72 (2005) 054206.
K. Tanaka, Y. Miyamoto / Solid State Ionics 269 (2015) 106–109 [18] J. Akola, P. Jóvári, I. Kaban, I. Voleská, J. Kolář, T. Wágner, R.O. Jones, Phys. Rev. B 89 (2014) 064202. [19] S.V. Karpachev, G.M. Zlokazova, L.Ya. Kolelev, V.B. Zlokazov, Sov. Phys. Dokl 33 (1988) 833. [20] Y. Miyamoto, M. Itoh, K. Tanaka, Solid State Commun. 92 (1994) 895. [21] M. Ohto, M. Itoh, K. Tanaka, J. Appl. Phys. 77 (1995) 1034. [22] K. Tanaka, Y. Miyamoto, M. Itoh, E. Bychkov, Phys. Status Solidi A 173 (1999) 317. [23] S. Maruno, M. Noda, T. Yamada, Yogyo-Kyokai-Shi 81 (1973) 445. [24] Y. Kawamoto, M. Agata, S. Tsuchihashi, Yogyo-Kyokai-Shi 82 (1974) 46 [in Japanese]. [25] H. Endo, M. Yao, K. Ishida, J. Phys. Soc. Jpn. 48 (1980) 235. [26] T. Usuki, K. Abe, O. Uemura, Y. Kameda, J. Phys. Soc. Jpn. 70 (2001) 2061.
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[27] O. Madelung, M. Schulz, H. Weiss, in: K.-H. Hellwege (Ed.), Springer, Berlin1982 (Vol. III/17 h). [28] S.R. Yang, K.N.R. Taylor, J. Appl. Phys. 69 (1991) 420. [29] A. Gągor, A. Pawłowski, A. Pietraszko, J. Solid State Chem. 182 (2009) 451. [30] J.L. Souquet, M. Duclot, M. Levy, Solid State Ionics 105 (1998) 237. [31] M. Ikeda, M. Aniya, J. Non-Cryst. Solids 371–372 (2013) 53. [32] K. Funke, B. Roling, M. Lange, Solid State Ionics 105 (1998) 195. [33] I. Chaudhuri, F. Inam, D.A. Drabold, Phys. Rev. B 79 (2009) 100201. [34] M. Aniya, J. Therm. Anal. Calorim. 99 (2010) 109. [35] B. Prasai, D.A. Drabold, Phys. Rev. B 83 (2011) 094202.
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Solid State Ionics journal homepage: www.elsevier.com/locate/ssi
Ionic conductivities in crystalline, glassy, and liquid AgAsS2 K. Tanaka ⁎, Y. Miyamoto Department of Applied Physics, Graduate School of Engineering, Hokkaido University, Sapporo 060-8628, Japan
a r t i c l e
i n f o
Article history: Received 2 August 2014 Received in revised form 20 November 2014 Accepted 26 November 2014 Available online 10 December 2014
a b s t r a c t Ionic conductivity in AgAsS2 has been measured at 20–600 °C for crystalline, glassy, supercooled, and liquid states. The liquids possess substantially smaller activation energies (~0.2 eV) and conductivity prefactors (~3 S/cm) than those in the solids. Other electrical characteristics are discussed, taking calorimetric and dilatometric results into account. © 2014 Elsevier B.V. All rights reserved.
Keywords: Chalcogenide glass Chalcogenide liquid Ionic conductivity Temperature dependence Thermal analyses
1. Introduction The ionic conduction in condensed matters has been a subject of continuous studies stemming from fundamental interests in iontransport mechanisms and wide applications to batteries, photographic films, ion sensors, and so forth. Mobile ions are H+, Li+, Ag+, etc., and matrices may be oxides, chalcogenides, and halides of crystalline, glassy, powdered, and ceramic forms, in which an ion-conducting glass remains to be a focus, due to its good conductivity and compositional variability [1]. However, the conduction mechanisms remain vague, with a primary reason that the atomic structure in non-crystalline materials, which may be heterogeneous, cannot be explicitly identified. Among the ion-conducting glasses, the Ag-chalcogenide system attracts substantial interest since it is relatively stable [2–4] and a heavy atom Ag is, in comparison with Li etc., easily detected by x-rays. In addition, the material behaves as an “ion-conducting amorphous semiconductor” [5], which exhibits promising photo-electro-ionic phenomena [6]. Accordingly, a lot of electrical studies have been performed so far, most of which concern with compositional [2,7–11] and/ or spectral [12–16] variations. We may refer also to recent computeraided structural analyses [17,18]. However, temperature dependence is less explored, or varied temperature ranges have been limited to solid phases [7,13,15,16,19], and the ionic conductivity in (supercooled) liquid states has hardly been studied [12]. Extending previous studies [5,20–22], we here investigate the ionic conductivity in AgAsS2 of crystalline, glassy, and liquid forms using a special sampling technique. Thermal properties have also been inspected, and these results are discussed in a unified way for obtaining ⁎ Corresponding author. Tel.: +81 11706400. E-mail address: [email protected] (K. Tanaka).
http://dx.doi.org/10.1016/j.ssi.2014.11.025 0167-2738/© 2014 Elsevier B.V. All rights reserved.
insights into the ionic conduction in condensed matters. Specifically, we will consider the ionic conductivity in a supercooled phase in light of the free-volume model. 2. Experiments AgAsS2 glass (g-AgAsS2) was prepared through the conventional melt-quenching method, the detail being described previously [21]. The glass was crushed into powders, and those of about 5 mg were inserted into quartz-glass pipes with a length of ~ 2 cm and an inner diameter of 1 mm and then packed in to the central part using two Au rods with a diameter of 1 mm and a length of ~2 mm, which were compressed with Cu rods with the same diameter, which were connected to Cu wires. As exemplified in Fig. 1, the powder became to ~ 2 mm in length upon compression. (We tried also Ag rods instead of Au, but the conductivity of AgAsS2 could not be evaluated owing to a resistance drop at temperatures above ~200 °C, which was probably caused by formation of conducting crystalline Ag2S paths.) This encapsulated Cu:Au: AgAsS2:Au:Cu sample was set in an Ar-flowing small furnace and heated. Sample temperature was monitored, with an accuracy of about ±10 °C, using a thermocouple in a quartz-glass pipe, which was bundled with the sample pipe. Such a sample assembly having small thermal capacity is required for obtaining rapid quenching rates. Ac conductivity of the sample was evaluated from currents, which were measured using a lock-in amplifier (NF, 5610B) under applied voltages of 1 − 100 mV, at sample temperatures of 20–600 °C. However, upon temperature variations, the packed AgAsS2 could not retain the columnar shape, due to material leakage during melting and thermal volume changes. Accordingly, the accuracy of the conductivity value may be ± 50%, or the absolute value may be twice of the calculated ones, owing to the leakage. In addition, subsidiary thermal analyses
K. Tanaka, Y. Miyamoto / Solid State Ionics 269 (2015) 106–109
107
Fig. 1. A photograph of an encapsulated Cu:Au:AgAsS2:Au:Cu sample.
were performed using a conventional calorimeter (DTA) and a dilatometer. (The actual composition in these thermal measurements was found to be Ag30As20S50 by x-ray microprobe analyses, while its thermal property could be regarded to be nearly the same to that in AgAsS2). 3. Results Fig. 2 exemplifies frequency dependence of ac currents at room and high temperatures. We see in both cases that the currents are nearly constant at a frequency range of 102–104 Hz, which suggests that the value is governed by bulk dc ionic components without electrode and capacitance effects [16]. Accordingly, we select 1.2 kHz for investigating temperature variations. Fig. 3(a) shows a DTA curve of g-AgAsS2 obtained under a heating process at a rate of 10 °C/min. We see a glass-transition step at ~150 °C, in consistent with previous results [2,23,24]. Then two exothermic peaks appear at around 250 °C, which can be ascribed to crystallization to proustite (Ag3AsS3 crystal with a crystallization temperature of ~210 °C) and smithite (AgAsS2 crystal, ~260 °C) [23]. At ~430 °C, we see a prominent endothermic dip, a signature of the melting of smithite [2,23]. The melting of proustite at 490 °C [2] is located out of the measurement range (≤ 450 °C), and it cannot be seen. We have examined also a dilatometric characteristic (not shown) using a polished glass rod with a diameter of ~ 5 mm and a length of ~15 mm. Around room temperature, the sample expanded with a linear coefficient α of 1.7 × 10−5/K, in consistent with a previous datum [24], and then it increased to 2.4 × 10−5/K above ~145 °C (≈ Tg). At ~160 °C, the sample became fluid, which hindered further measurements. Trials
Fig. 3. Heat flow (a) and electrical conductivity (b), upon rapid (○), and slow (Δ) coolings, in AgAsS2 as a function of temperature T. Electrical conductivities of single-crystalline AgAsS2 [19] and Ag3AsS3 [27] are also plotted by dashed lines for comparison. Upper and lower-directing arrows in (b) indicate phase transition points in AgAsS2 [19] and Ag3AsS3 [28,29], and the red solid line delineates a VFT curve (see, the text).
measuring thermal expansion coefficients in the liquid state were unsuccessful due to material bubbling. Fig. 3(b) shows a series of results of the electrical conductivity σ upon temperature changes. At the outset, the sample was heated to a liquid phase, ~580 °C, compacted there, and cooled down. In the liquid phase, σ ≈ 10−1 S/cm, the value being at a superionic level. In addition, it seems that the liquid undergoes an Arrhenius-type temperature variation, σ ≈ σ0 exp(−Ea/kBT), in consistent with results reported for Ag-S(Se) [25,26]. (However, the limited measurable range of ~100 °C in the liquid phase makes this assertion tentative.) The parameters σ0 and Ea are listed in Table 1. Behaviors after solidification depended upon cooling rates.
Table 1 Summary of the activation parameters obtained in the present study, in comparison with those previously reported. The parameters are calculated at room temperature, except for the values in the liquid and supercooled phases and the parenthesized ones, which are averaged over the crystalline phases from room temperature to 420 °C. Note that σ0 is evaluated through extrapolation so that the accuracy is worse. Material
σ0 [S/cm]
Ea [eV]
Reference
Liquid Supercooled Glassy
4 2 50 ± 20 50 30 7 100 0.02 (~20) 100 3 20 0.1
0.25 0.17 0.45 ± 0.05 0.45 0.38 0.37 0.48 0.32 (~0.5) 0.62 0.42 0.17 0.39
Present Present Present 7 19 16 15 Present 19 27 28 29
Crystalline Smithite Proustite Fig. 2. Frequency spectra of current densities in an Au:AgAsS2:Au sample in glassy (a) and liquid (b) states under the applied voltages (V0) specified.
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Upon slow cooling of ~ 1 °C/min (triangles), the conductivity undergoes an inflection at 490 °C and a discontinuous drop at 430 °C. These temperatures seem to correspond to the melting temperatures of proustite Ag3AsS3 and smithite AgAsS2 [2,23]. Actually, x-ray diffraction patterns, which were taken at room temperature after electrical measurements, manifested that the slowly cooled materials are mixtures of these crystals. In consistent with the observations, we see in Fig. 3(b) that the conductivity curve is located in between those of single-crystalline proustite [27] and smithite [19]. (For proustite, however, reported conductivity results [27–29] are appreciably scattered.) In the crystalline state, the conductivity decreases with Arrhenius-type behaviors, with the parameters of σ0 ≈ 20 S/cm and Ea ≈ 0.5 eV when averaged over temperatures. Small discontinuities, arrowed in Fig. 3(b), probably reflect phase transitions in the crystals; those at ~ 70 and ~ 140 °C arising from smithite [19] and ~ 30 and ~ 230 °C from proustite [27,28]. Re-heating the sample from room temperature at a rate of 10 °C/min has traced nearly the same line (not shown). On the other hand, when the liquid is cooled rapidly with ~100 °C/min (circles), the conductivity hardly changes at the melting points, decreasing more-or-less smoothly to room temperature. However, a closer inspection can divide the conductivity curve into two parts at ~ 150 °C (≈ Tg). Above this temperature, the material resides in a supercooled liquid state. The conductivity curve is convex upwards, which can be fitted with the Vogel–Fulcher–Tammann (VFT) formula [30,31]; σ ðT Þ ¼ σ 0 expf−B=ðT − T 0 Þg;
ð1Þ
where a least-square fitting procedure gives σ0 = 2 S/cm, B = 2000 K (kBB = 0.17 eV), and T0 = 220 ± 40 K, the result being delineated in Fig. 3(b) by a red solid curve. Here, T0 is the so-called ideal glasstransition (Vogel) temperature, which is known to be lower than the actual glass-transition temperature [30,31]. The present σ0 and kBB values are comparable with those (~ 5 S/cm, 0.1–0.3 eV) reported for supercooled states of oxides and iodines [30]. On the other hand, the conductivity below ~150 °C is ascribed to ion motions in a glassy state. The curve can be approximated with the Arrhenius-type equation with the parameters listed in Table 1, which are consistent with those reported for g-AgAsS2 [7,16,19,21]. Re-heating the sample with a rate of 10 °C/min gave a similar trace (not shown) up to ~200 °C, above which the conductivity abruptly dropped a few times, which are ascribable to the crystallization. 4. Discussion We have obtained unified conductivity data for crystalline, glassy, supercooled, and liquid states of AgAsS2. Among the results, three observations attract special interests. First, we see in Fig. 3(b) that the glass possesses higher conductivity than that of the crystal. Such a trend seems to be general in the ionic conduction. The reason may be ascribed to a smaller material density of the glass by ~5% [7], which provides open space for ions, while quantitative analyses remain. In more detail, as compared in Table 1, the difference of the electrical conductivity in the glass and the crystal lies mainly in σ0, with Ea being roughly the same. More advanced analyses may be feasible if σ can be resolved to the carrier density n and the mobility μ as σ = qnμ, where q is the charge of Ag ions. Temperature variation can then be written as qn0exp(− Ena /kBT)μ0exp(− E μa/kBT), and accordingly, Ea = Ena + Eμa. A previous [20] and successive (reported elsewhere) studies using electrical time-of-flight experiments have demonstrated Ea ≈ Ena for Ag-As-S glasses, i.e., the conductivity activation is governed by the increase in mobile-ion density. The similar Ea in the crystal may suggest the same situation. However, we should note that the present crystalline samples are composed with mixtures of poly-crystalline AgAsS2 and Ag3AsS3
with unknown grain sizes, which are probably defective and connected through interfacial regions, so that it is difficult to know which component governs the crystalline conductivity. Second is the VFT-type conductivity variation in the supercooled state. The free-volume model assumes that an effective atomic volume v at T (N T0) can be written down as vðT Þ ¼ v0 þ v0 βðT − T 0 Þ;
ð2Þ
where the first term represents a fixed volume, which may be regarded as the atomic volume (~(2.8 A)3 [2,24]), and the second is a free volume, where β is the volumetric expansion coefficient. The model presumes that the ionic conductivity σ(T) can be represented as [30] σ ðT Þ expf−v =v0 βðT − T 0 Þg;
ð3Þ
where v* is the smallest free volume necessary for ion migration. Here, a comparison of the Eqs. (1) and (3) gives v*/v0 = Bβ, and putting the present observations B = 2000 K and β = 3α = 3 × 2.4 × 10−5/K, we obtain v*/v0 = 0.14. It seems that ~ 1/10 excess volume per atom, which may be distributed in heterogeneous and percolated ways [11], is needed for free migration of Ag ions in a supercooled AgAsS2 structure. Finally, Table 1 shows that the activation energies in the (supercooled) liquid states are about a half of those in the solid (glassy and crystalline) states: ~0.2 and ~0.4 eV. We may envisage that all of Ag atoms are mobile at the melting temperature, and further activation is accomplished by a mobility enhancement with Eμa ≈ 0.2 eV, to which macroscopic material flows in the liquid states may contribute. Nevertheless, theoretical studies of ionic transport in liquids appear to be very limited [32–35], and further analyses will be valuable to elucidate the ion dynamics in condensed matters. 5. Conclusions The ionic conductivity in all the condensed states of AgAsS2 has been evaluated as a function of temperature. Glassy and crystalline states possess roughly the same activation energy ~0.4 eV with a marked difference of the prefactor. By contrast, the liquid and supercooled phases exhibit appreciable smaller activation energies than those in the solid states. It is tempting to envisage that the conductivity activation in the solid and liquid states are governed by the changes in mobile-ion density and mobility, respectively. Acknowledgment The authors would like to thank Professor H. Hosono for calorimetric and dilatometric measurements. References [1] A. Bunde, K. Funke, M.D. Ingram, Solid State Ionics 105 (1998) 1. [2] Z.U. Borisova, Glassy Semiconductors, Plenum, New York, 1981. (Chap. 6). [3] I. Kaban, P. Jóvári, T. Wágner, M. Bartoš, M. Frumar, B. Beuneu, W. Hoyer, N. Mattern, J. Eckert, J. Non-Cryst. Solids 357 (2011) 3430. [4] K.S. Andrikopoulos, J. Arvanitidis, V. Dracopoulos, D. Christofilos, T. Wagner, S.N. Yannopoulos, Appl. Phys. Lett. 99 (2011) 171911. [5] K. Tanaka, J. Non-Cryst. Solids 164-166 (1993) 1179. [6] M. Frumar, T. Wagner, Curr. Opinion Solid State Mater. Sci. 7 (2003) 117. [7] Y. Kawamoto, M. Nishida, J. Non-Cryst. Solids 20 (1976) 393. [8] M. Kawasaki, J. Kawamoto, Y. Nakamura, M. Aniya, Solid State Ionics 123 (1999) 259. [9] M.A. Urenã, A.A. Piarristeguy, M. Fontana, B. Arcondo, Solid State Ionics 176 (2005) 505. [10] C. Holbrook, P. Chen, D.I. Novita, P. Boolchand, IEEE Trans. Nanotechnol. 6 (2007) 530. [11] E. Bychkov, Solid State Ionics 180 (2009) 510. [12] C. Cramer, M. Buscher, Solid State Ionics 105 (1998) 109. [13] A. Pradel, G. Tailladesa, C. Cramerb, M. Ribesa, Solid State Ionics 105 (1998) 139. [14] K. Shimakawa, T. Wagner, J. Appl. Phys. 113 (2013) 143701. [15] I.P. Studenyak, Yu.Yu. Meimet, M. Kranjčec, A.M. Solomon, A.F. Orliukas, A. Kežionis, E. Kazakevičius, T. Šalkus, J. Appl. Phys. 115 (2014) 033702. [16] D.S. Patil, K. Shimakawa, V. Zima, T. Wagner, J. Appl. Phys. 115 (2014) 143707. [17] De N. Tafen, D.A. Draold, M. Mitkova, Phys. Rev. B 72 (2005) 054206.
K. Tanaka, Y. Miyamoto / Solid State Ionics 269 (2015) 106–109 [18] J. Akola, P. Jóvári, I. Kaban, I. Voleská, J. Kolář, T. Wágner, R.O. Jones, Phys. Rev. B 89 (2014) 064202. [19] S.V. Karpachev, G.M. Zlokazova, L.Ya. Kolelev, V.B. Zlokazov, Sov. Phys. Dokl 33 (1988) 833. [20] Y. Miyamoto, M. Itoh, K. Tanaka, Solid State Commun. 92 (1994) 895. [21] M. Ohto, M. Itoh, K. Tanaka, J. Appl. Phys. 77 (1995) 1034. [22] K. Tanaka, Y. Miyamoto, M. Itoh, E. Bychkov, Phys. Status Solidi A 173 (1999) 317. [23] S. Maruno, M. Noda, T. Yamada, Yogyo-Kyokai-Shi 81 (1973) 445. [24] Y. Kawamoto, M. Agata, S. Tsuchihashi, Yogyo-Kyokai-Shi 82 (1974) 46 [in Japanese]. [25] H. Endo, M. Yao, K. Ishida, J. Phys. Soc. Jpn. 48 (1980) 235. [26] T. Usuki, K. Abe, O. Uemura, Y. Kameda, J. Phys. Soc. Jpn. 70 (2001) 2061.
109
[27] O. Madelung, M. Schulz, H. Weiss, in: K.-H. Hellwege (Ed.), Springer, Berlin1982 (Vol. III/17 h). [28] S.R. Yang, K.N.R. Taylor, J. Appl. Phys. 69 (1991) 420. [29] A. Gągor, A. Pawłowski, A. Pietraszko, J. Solid State Chem. 182 (2009) 451. [30] J.L. Souquet, M. Duclot, M. Levy, Solid State Ionics 105 (1998) 237. [31] M. Ikeda, M. Aniya, J. Non-Cryst. Solids 371–372 (2013) 53. [32] K. Funke, B. Roling, M. Lange, Solid State Ionics 105 (1998) 195. [33] I. Chaudhuri, F. Inam, D.A. Drabold, Phys. Rev. B 79 (2009) 100201. [34] M. Aniya, J. Therm. Anal. Calorim. 99 (2010) 109. [35] B. Prasai, D.A. Drabold, Phys. Rev. B 83 (2011) 094202.