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Nearly constant dielectric loss of glasses containing different mobile alkali ions
Journal of Non-Crystalline Solids 330 (2003) 122–127 www.elsevier.com/locate/jnoncrysol
Nearly constant dielectric loss of glasses containing different mobile alkali ions S. Murugavel, B. Roling
*
Institut f€ ur Physikalische Chemie and Sonderforschungsbereich 458, Westf€alische Wilhelms-Universit€at M€unster, Schlossplatz 4/7, 48149 M€unster, Germany Received 4 January 2003; received in revised form 30 April 2003
Abstract Recently, Rivera et al. [Phys. Rev. Lett. 88 (2002) 125902] found that the magnitude of the nearly constant dielectric loss (NCL) in alkali triborate glasses decreases as m1=3 with increasing alkali ion mass m. We have carried out conductivity measurements on aluminosilicate and aluminogermanate glasses containing different mobile alkali ions, and we show that the magnitude of the NCL does not follow a m1=3 relation. Instead, we find a strong correlation between the magnitude of the NCL, the dc conductivity, and the dielectric relaxation strength which is valid for various ionic glasses at temperatures above 173 K. 2003 Elsevier B.V. All rights reserved.
1. Introduction The term nearly constant loss (NCL) describes the experimental finding that the low-temperature dielectric spectra of many disordered materials are characterized by a more or less frequency-independent dielectric loss, e00 . This corresponds to an almost linear increase of the real part of the conductivity, r0 ðmÞ, with frequency. A NCL has, for instance, been found in the spectra of supercooled dipolar liquids and polymers [1–6]. The magnitude of the NCL in these materials is often relatively low, i.e., generally one finds that e00 < 102 [2,4–6].
*
Corresponding author. Tel.: +49-251 832 3430; fax: +49251 832 9138. E-mail address: [email protected] (B. Roling).
The NCL is most likely caused by relaxational movements of dipolar units. Disordered materials containing mobile ions exhibit a NCL as well. However, the magnitude of the NCL is often higher than for materials without mobile ions. [7,8]. A NCL has, for instance, been found in the spectra of ion conducting crystals and glasses [3,8–15]. In crystalline ionic conductors, a prerequisite for the occurrence of a NCL seems to be a high number density of mobile ions [16], while in amorphous materials, a NCL has also been found at low number densities of mobile ions [11]. A review paper about the NCL of ionic crystals, glasses, and melts and its dependence on various physical and chemical parameters has recently been published by Ngai [17]. The fact that the magnitude of the NCL of ionic conductors is generally higher than for materials
0022-3093/$ - see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0022-3093(03)00532-5
S. Murugavel, B. Roling / Journal of Non-Crystalline Solids 330 (2003) 122–127
without mobile ions suggests that either movements of the mobile ions contribute significantly to the NCL or that structural changes caused by the introduction of the mobile ions are responsible for the enhancement of the NCL. For instance, in silicate glasses, the addition of alkali oxide leads to a depolymerization of the silicate network and to the formation of negatively charged non-bridging oxygens. It is plausible that these structural changes cause additional reorientional movements of dipolar Si–O groups and thus an increase of the magnitude of the NCL. Since dielectric spectroscopy does not yield direct information about the types of charge carriers or dipolar units causing the dielectric loss, the physical origin of the NCL in disordered ionic conductors has not yet been clarified. There has been much discussion in the literature about different dynamic processes causing the NCL. In particular, three different viewpoints have been put forward. Viewpoint A: The NCL is caused by jellyfish-type movements of groups of atomic species in asymmetric double-well potential (ADWP) configurations [10–14,18–20]. Jellyfish-type means that several atomic species, including network atoms and mobile ions, perform highly cooperative relaxational movements with low amplitudes. Viewpoint B: The NCL is caused by hopping movements of mobile ions between neighboring sites. Theoretically, it has been shown that such localized hopping movements can lead to a NCL [21– 27]. Viewpoint C: The possibility that the NCL is caused by vibrational movements of the mobile ions in strongly anharmonic potentials was suggested by Rivera et al. [28,29]. However, this idea was abandoned by the authors in favor of the idea that the NCL originates from ion hopping in a slowly varying cage potential caused by other mobile ions [30]. Recent measurements on glasses with variable alkali oxide content have provided strong evidence that there is more than one dynamic process contributing to the NCL. Roling et al. [31] found that in a temperature range from 173 to 573 K, the composition dependence of the Jonscher behavior is closely related to the composition dependence of the NCL. The term Jonscher behavior refers to the frequency and temperature dependence of the
123
conductivity in the crossover regime from the dc conductivity to the dispersive conductivity. Since it is generally accepted that the Jonscher behavior is caused by hopping movements of the mobile ions, the experimental results suggest that the NCL in this temperature range arises from ionic hopping movements as well. Subsequently, Sidebottom and Murray-Krezan [32] studied the conductivity of sodium germanate glasses and of a pure GeO2 glass down to temperatures of about 85 K. Their results suggest that at low number densities of mobile ions and at low temperatures, dynamic processes present in the germanate network contribute significantly to the NCL of the sodium germanate glasses. Most likely, these are low-amplitude relaxational movements of partially charged network atoms. On the other hand, at higher number densities of mobile ions and at temperatures above 200 K, the NCL seems to be determined by hopping motions of the mobile ions, in agreement with [31]. In this context, it is important to understand the implications of recent results by Rivera et al. for the NCL in alkali triborate glasses containing different types of alkali oxides [29]. The authors found that the magnitude of the NCL decreases as m1=3 with increasing mass of the mobile alkali ions, m. On the other hand, Rivera et al. state that the magnitude of the NCL is also related to the magnitude of the dc conductivity of their glasses. The dc conductivity decreases with increasing mass of the alkali ions as well. Thus, the mass dependence of the NCL may simply reflect the apparent mass dependence of the dc conductivity. In this paper, we therefore address the following questions. (i) Is the NCL of glasses containing different types of mobile ions generally related to the mass of the ions? (ii) Is the NCL of these glasses generally related to the frequency dependence of the conductivity in the Jonscher regime? In order to answer these questions, it is important to choose a glass system where the apparent mass dependence of the dc conductivity is clearly distinct from the triborate glasses studied by Rivera and coworkers. Here, aluminosilicate and aluminogermanate glasses are suitable, since in these glasses, sodium ions are more mobile than lithium and potassium ions.
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2. Experimental Glasses of composition A2 O Æ Al2 O3 Æ 4SiO2 with A ¼ Li, Na; Li2 O Æ Al2 O3 Æ 2SiO2 ; and A2 O Æ Al2 O3 Æ 4GeO2 with A ¼ Li, Na, K were prepared by heating dry mixtures of Al2 O3 , SiO2 or GeO2 and the respective alkali carbonates in a platinum crucible under an atmosphere of air. After decomposition of the carbonates at 1000 C, the melts were homogenized at 1500–1650 C for 3–5 h. Then, the melts were cast into a preheated stainless steel mold, and the cast glass blocks were transferred to another furnace. Here, the glasses were annealed 30 K below their respective glass transition temperatures for 3 h and then cooled down to room temperature with a rate of 1 K/min. Cylindrical samples (diameter 25 mm, thickness 1 mm) were drilled from the glass blocks, and the sample surfaces were polished. Then, metal electrodes consisting of one silver and one platinum layer were sputtered onto each surface. The frequency-dependent conductivities were measured in a frequency range from 102 to 106 Hz and in a conductivity range from 1015 to 106 S/cm using the Novocontrol a-S High Resolution Dielectric Analyzer. The temperature range of the measurements extended from 173 to 573 K.
Table 1 Activation energies and preexponential factors of the dc conductivity of aluminosilicate and aluminogermanate glasses with different mobile alkali ions Glass
EAdc =eV
logðA X cm=KÞ
Li2 O Æ Al2 O3 Æ 4SiO2 Na2 O Æ Al2 O3 Æ 4SiO2 Li2 O Æ Al2 O3 Æ 2SiO2 Li2 O Æ Al2 O3 Æ 4GeO2 Na2 O Æ Al2 O3 Æ 4GeO2 K2 O Æ Al2 O3 Æ 4GeO2
0.73 ± 0.01 0.66 ± 0.01 0.71 ± 0.01 0.81 ± 0.01 0.72 ± 0.01 0.79 ± 0.01
5.5 ± 0.2 4.6 ± 0.2 5.5 ± 0.2 5.4 ± 0.2 4.6 ± 0.2 4.1 ± 0.2
Fig. 1. Conductivity spectra of A2 O Æ Al2 O3 Æ 4SiO2 glasses at T ¼ 173 K. The dashed lines denote fits using Eq. (1).
3. Results At temperatures between 273 and 573 K, the conductivity spectra of all glasses are characterized by low-frequency dc plateaux, and the dc conductivities obey an Arrhenius law, rdc T ¼ A expðEAdc =kT Þ. The values for the activation energy EAdc and for the preexponential factor A obtained from a fit of the dc conductivity data are listed in Table 1. In Fig. 1 we present the frequency-dependent real part of the conductivity, r0 ðmÞ, for a lithium and a sodium aluminosilicate glass at T ¼ 173 K. For both glasses, r0 ðmÞ increases strongly with frequency, and the slope in the log–log plot is 0.95 ± 0.02, i.e., we observe a NCL. The dashed lines denote fits of the data using the power law: r0 ðmÞ X cm ¼ ðm=mNCL Þ0:95 :
ð1Þ
Here, the frequency mNCL characterizes the magnitude of the NCL. Clearly, the magnitude is higher for the sodium ion conducting glass as compared to the lithium ion conducting glass. This observation is clearly in contrast to the findings of Rivera et al. for alkali triborate glasses. In the case of the aluminosilicate glasses, the magnitude of the NCL cannot be described by a m1=3 relation. In the legend of Fig. 1, the values of the dc conductivity of these glasses at T ¼ 298 K are given. The dc conductivity of the sodium ion conducting glass is approximately twice as high as the dc conductivity of the lithium ion conducting glass. Thus, there is evidence that the magnitude of the dc conductivity is related to the magnitude of the NCL. In Fig. 2 we plot in comparison the frequency dependence of r0 for a lithium, a sodium and a
S. Murugavel, B. Roling / Journal of Non-Crystalline Solids 330 (2003) 122–127
Fig. 2. Conductivity spectra of A2 O Æ Al2 O3 Æ 4GeO2 glasses at T ¼ 173 K. The dashed lines denote fits using Eq. (1).
potassium aluminogermanate glass at T ¼ 173 K. Again, we find a NCL with a slope of 0.95 ± 0.02 in the log–log plot, and consequently we have fitted the data using Eq. (1). In the legend of Fig. 2, the dc conductivities of the glasses at T ¼ 298 K are given. Clearly, the dc conductivity decreases in the order Na fi Li fi K. Remarkably, the magnitude of the NCL decreases in the same order. Thus, we observe again a correlation between the magnitude of the NCL and the magnitude of the dc conductivity, but again the magnitude of the NCL cannot be described by a m1=3 relation.
4. Discussion Our results show that the m1=3 dependence of the magnitude of the NCL that has been found for alkali triborate glasses is not a general feature of alkali ion conducting glasses. However, for borate, aluminosilicate and aluminogermanate glasses, there seems to be a correlation between the magnitude of the NCL and the magnitude of the dc conductivity. In order to analyze this type of correlation more quantitatively, we plot in Fig. 3 the frequencies mNCL (173 K) versus the dc conductivities at room temperature, rdc (298 K). This figure does not only contain the data of the aluminosilicate and the aluminogermanate glasses, but also the data of
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Fig. 3. Correlation between the magnitude of the nearly constant loss at T ¼ 173 K, characterized by the frequency mNCL (173 K), and the dc conductivity at room temperature, rdc (298 K).
three sodium germanate glasses of compositions 0.0051Na2 O Æ 0.9949GeO2 , 0.051Na2 O Æ 0.949GeO2 , and 0.213Na2 O Æ 0.787GeO2 and of a lithium borate glass of composition 0.373Li2 O Æ 0.627B2 O3 . The latter four glasses were chosen, since frequency-dependent conductivities at 173 K and at 298 K had been measured in our laboratory [31]. As seen from Fig. 3, there is a general trend that mNCL (173 K) increases with decreasing dc conductivity, i.e., the magnitude of the NCL decreases with decreasing dc conductivity. However, it is obvious that the correlation between mNCL (173 K) and rdc (298 K) is not very strong. For instance, the two sodium germanate glasses with 0.51 and 5.1 mol% sodium oxide exhibit similar dc conductivities, but the magnitude of the NCL differs by about one order of magnitude. We will show now that in order to obtain a better correlation, it is important to take into account the onset frequency of the conductivity dispersion, m , which we define by r0 ðm Þ ¼ 2 rdc . It is well known that for most ion conducting glasses, m is thermally activated with the same activation energy as rdc T . This implies that for a given glass, the ratio rdc T =m is a temperatureindependent quantity. This is, indeed, the case for all glasses we have studied here. Furthermore, it has been shown by Sidebottom and coworkers that
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rdc T =m is proportional to the product De T [32,33]. Here, De ¼ e0 ð0Þ e0 ð1Þ denotes the dielectric relaxation strength due to hopping motions of the mobile ions. e0 ð1Þ is the high-frequency permittivity due to vibrational and electronic polarization. Since in a real experiment, electrode polarization effects complicate the determination of the dielectric relaxation strength, we now calculate an estimate for De T by using the equation [32] ðDe T Þest ¼
rdc T : m e 0
ð2Þ
Here, e0 denotes the permittivity of free space. Now we use ðDe T Þest to normalize the mNCL axis in Fig. 3. Thus, in Fig. 4 we plot mNCL ð173 KÞ Æ ðDe T Þest versus the dc conductivity at room temperature, rdc (298 K). Obviously, the additional consideration of ðDe T Þest improves the correlation enormously. Since there is general agreement that the dc conductivity and the dielectric relaxation strength are determined by hopping movements of the mobile ions, the strong correlation observed in Fig. 4 provides strong evidence that the NCL in our temperature window is also caused by ionic hopping movements. Thus, we can state that the present results on glasses containing different types of mobile alkali ions
agree with recent results on glasses with different number densities of mobile ions [31,32]. Finally, we would like to note that from our results, no conclusions can be drawn on the origin of the NCL at cryogenic temperatures. Jain and coworkers [11,12,15] and Sidebottom and MurrayKrezan [32] found strong experimental evidence that at temperatures below 100 K, localized relaxational motions of partially charged glass network atoms (jellyfish-type motions) contribute significantly to the NCL or even determine the magnitude of the NCL. In this context, it would certainly be interesting to reanalyse the low-temperature conductivity data of germanate glasses with very low alkali oxide contents and of heavy metal fluoride glasses which were published by Jain and coworkers [11,12,15].
5. Conclusions The frequency- and temperature-dependent conductivity spectra of aluminosilicate and aluminogermate glasses containing different types of mobile alkali ions were analyzed and discussed. It was shown that there is no correlation between the magnitude of the nearly constant loss and the mass of the alkali ions. However, in the temperature range of our study, the magnitude of the NCL is closely related to the dc conductivity and the dielectric relaxation strength of the glasses. This provides strong evidence that the NCL is caused by hopping motions of the mobile alkali ions. On the other hand, our results do not exclude the possibility that at temperatures below 173 K, localized relaxational motions of partially charged glass network atoms (jellyfish-type motions) contribute significantly to the NCL.
Acknowledgements
Fig. 4. Correlation between the product mNCL ð173 KÞ ðDe T Þest and the dc conductivity at room temperature, rdc (298 K). The dashed line is drawn to guide the eye.
We are indebted to S. Pas for critically reading the manuscript. Furthermore, we would like to thank the Deutsche Forschungsgemeinschaft for financial support via the SFB 458 and the Alexander von Humboldt foundation for providing a research fellowship for S.M.
S. Murugavel, B. Roling / Journal of Non-Crystalline Solids 330 (2003) 122–127
References [1] A. Hofmann, F. Kremer, E.W. Fischer, A. Sch€ onhals, Disorder Effects on Relaxational Processes, Springer, Berlin, 1994. [2] P. Hedvig, Dielectric Spectroscopy of Polymers, Adam Hilger, Budapest, 1977. [3] D.L. Sidebottom, P.F. Green, R.K. Brow, J. Non-Cryst. Solids 203 (1996) 300. [4] A. Kudlik, S. Benkhof, T. Blochowicz, C. Tschirwitz, E. R€ ossler, J. Molec. Struct. 479 (1999) 201. [5] J. Wiedersich, T. Blochowicz, S. Benkhof, A. Kudlik, N.V. Surovtsev, C. Tschirwitz, V.N. Novikov, E. R€ ossler, J. Phys.: Condens. Matter 11 (1999) A147. [6] K.L. Ngai, J. Non-Cryst. Solids 274 (2000) 155. [7] K.L. Ngai, U. Strom, O. Kanert, Phys. Chem. Glasses 33 (1992) 109. [8] A.S. Nowick, B.S. Lim, J. Non-Cryst. Solids 172–174 (1994) 1389. [9] W.-K. Lee, J.F. Liu, A.S. Nowick, Phys. Rev. Lett. 67 (1991) 1559. [10] A.S. Nowick, B.S. Lim, A.V. Vaysleyb, J. Non-Cryst. Solids 172–174 (1994) 1243. [11] X. Lu, H. Jain, J. Phys. Chem. Solids 55 (1994) 1433. [12] X. Lu, H. Jain, O. Kanert, J. Non-Cryst. Solids 172–174 (1994) 1436. [13] D.L. Sidebottom, P.F. Green, R.K. Brow, Phys. Rev. Lett. 74 (1995) 5068.
[14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29]
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C.H. Hsieh, H. Jain, J. Non-Cryst. Solids 203 (1996) 293. H. Jain, X. Lu, J. Non-Cryst. Solids 196 (1996) 285. A.S. Nowick, Solid State Ionics 136&137 (2000) 1307. K.L. Ngai, J. Chem. Phys. 100 (1999) 10576. O. Kanert, R. K€ uchler, J. Dieckh€ ofer, X. Lu, H. Jain, K.L. Ngai, J. Non-Cryst. Solids 172–174 (1994) 1277. H. Jain, X. Lu, J. Am. Ceram. Soc. 80 (1997) 517. H. Jain, S. Krishnaswami, O. Kanert, J. Non-Cryst. Solids 307 (2002) 1017. M. Pollak, G.E. Pike, Phys. Rev. Lett. 28 (1972) 1449. S.R. Elliott, Adv. Phys. 36 (1987) 135. A. Hunt, Solid State Commun. 80 (1991) 151. K. Funke, D. Wilmer, Solid State Ionics 136&137 (2000) 1329. J.C. Dyre, T.B. Schroder, Rev. Mod. Phys. 72 (2000) 873. T.B. Schroder, J.C. Dyre, Phys. Rev. Lett. 84 (2000) 310. B. Roling, PCCP 3 (2001) 5093. C. Leon, A. Rivera, A. Varez, J. Sanz, J. Santamaria, K.L. Ngai, Phys. Rev. Lett. 86 (2001) 1279. A. Rivera, C. Leon, C.P.E. Varsamis, G.D. Chryssikos, K.L. Ngai, C.M. Roland, L.J. Buckley, Phys. Rev. Lett. 88 (2002) 125902. K.L. Ngai, C. Leon, Phys. Rev. B 66 (2002) 064308. B. Roling, C. Martiny, S. Murugavel, Phys. Rev. Lett. 87 (2001) 085901. D.L. Sidebottom, C.M. Marray-Krezan, Phys. Rev. Lett. 89 (2002) 195901. D.L. Sidebottom, Phys. Rev. Lett. 82 (1999) 3653.
Nearly constant dielectric loss of glasses containing different mobile alkali ions S. Murugavel, B. Roling
*
Institut f€ ur Physikalische Chemie and Sonderforschungsbereich 458, Westf€alische Wilhelms-Universit€at M€unster, Schlossplatz 4/7, 48149 M€unster, Germany Received 4 January 2003; received in revised form 30 April 2003
Abstract Recently, Rivera et al. [Phys. Rev. Lett. 88 (2002) 125902] found that the magnitude of the nearly constant dielectric loss (NCL) in alkali triborate glasses decreases as m1=3 with increasing alkali ion mass m. We have carried out conductivity measurements on aluminosilicate and aluminogermanate glasses containing different mobile alkali ions, and we show that the magnitude of the NCL does not follow a m1=3 relation. Instead, we find a strong correlation between the magnitude of the NCL, the dc conductivity, and the dielectric relaxation strength which is valid for various ionic glasses at temperatures above 173 K. 2003 Elsevier B.V. All rights reserved.
1. Introduction The term nearly constant loss (NCL) describes the experimental finding that the low-temperature dielectric spectra of many disordered materials are characterized by a more or less frequency-independent dielectric loss, e00 . This corresponds to an almost linear increase of the real part of the conductivity, r0 ðmÞ, with frequency. A NCL has, for instance, been found in the spectra of supercooled dipolar liquids and polymers [1–6]. The magnitude of the NCL in these materials is often relatively low, i.e., generally one finds that e00 < 102 [2,4–6].
*
Corresponding author. Tel.: +49-251 832 3430; fax: +49251 832 9138. E-mail address: [email protected] (B. Roling).
The NCL is most likely caused by relaxational movements of dipolar units. Disordered materials containing mobile ions exhibit a NCL as well. However, the magnitude of the NCL is often higher than for materials without mobile ions. [7,8]. A NCL has, for instance, been found in the spectra of ion conducting crystals and glasses [3,8–15]. In crystalline ionic conductors, a prerequisite for the occurrence of a NCL seems to be a high number density of mobile ions [16], while in amorphous materials, a NCL has also been found at low number densities of mobile ions [11]. A review paper about the NCL of ionic crystals, glasses, and melts and its dependence on various physical and chemical parameters has recently been published by Ngai [17]. The fact that the magnitude of the NCL of ionic conductors is generally higher than for materials
0022-3093/$ - see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0022-3093(03)00532-5
S. Murugavel, B. Roling / Journal of Non-Crystalline Solids 330 (2003) 122–127
without mobile ions suggests that either movements of the mobile ions contribute significantly to the NCL or that structural changes caused by the introduction of the mobile ions are responsible for the enhancement of the NCL. For instance, in silicate glasses, the addition of alkali oxide leads to a depolymerization of the silicate network and to the formation of negatively charged non-bridging oxygens. It is plausible that these structural changes cause additional reorientional movements of dipolar Si–O groups and thus an increase of the magnitude of the NCL. Since dielectric spectroscopy does not yield direct information about the types of charge carriers or dipolar units causing the dielectric loss, the physical origin of the NCL in disordered ionic conductors has not yet been clarified. There has been much discussion in the literature about different dynamic processes causing the NCL. In particular, three different viewpoints have been put forward. Viewpoint A: The NCL is caused by jellyfish-type movements of groups of atomic species in asymmetric double-well potential (ADWP) configurations [10–14,18–20]. Jellyfish-type means that several atomic species, including network atoms and mobile ions, perform highly cooperative relaxational movements with low amplitudes. Viewpoint B: The NCL is caused by hopping movements of mobile ions between neighboring sites. Theoretically, it has been shown that such localized hopping movements can lead to a NCL [21– 27]. Viewpoint C: The possibility that the NCL is caused by vibrational movements of the mobile ions in strongly anharmonic potentials was suggested by Rivera et al. [28,29]. However, this idea was abandoned by the authors in favor of the idea that the NCL originates from ion hopping in a slowly varying cage potential caused by other mobile ions [30]. Recent measurements on glasses with variable alkali oxide content have provided strong evidence that there is more than one dynamic process contributing to the NCL. Roling et al. [31] found that in a temperature range from 173 to 573 K, the composition dependence of the Jonscher behavior is closely related to the composition dependence of the NCL. The term Jonscher behavior refers to the frequency and temperature dependence of the
123
conductivity in the crossover regime from the dc conductivity to the dispersive conductivity. Since it is generally accepted that the Jonscher behavior is caused by hopping movements of the mobile ions, the experimental results suggest that the NCL in this temperature range arises from ionic hopping movements as well. Subsequently, Sidebottom and Murray-Krezan [32] studied the conductivity of sodium germanate glasses and of a pure GeO2 glass down to temperatures of about 85 K. Their results suggest that at low number densities of mobile ions and at low temperatures, dynamic processes present in the germanate network contribute significantly to the NCL of the sodium germanate glasses. Most likely, these are low-amplitude relaxational movements of partially charged network atoms. On the other hand, at higher number densities of mobile ions and at temperatures above 200 K, the NCL seems to be determined by hopping motions of the mobile ions, in agreement with [31]. In this context, it is important to understand the implications of recent results by Rivera et al. for the NCL in alkali triborate glasses containing different types of alkali oxides [29]. The authors found that the magnitude of the NCL decreases as m1=3 with increasing mass of the mobile alkali ions, m. On the other hand, Rivera et al. state that the magnitude of the NCL is also related to the magnitude of the dc conductivity of their glasses. The dc conductivity decreases with increasing mass of the alkali ions as well. Thus, the mass dependence of the NCL may simply reflect the apparent mass dependence of the dc conductivity. In this paper, we therefore address the following questions. (i) Is the NCL of glasses containing different types of mobile ions generally related to the mass of the ions? (ii) Is the NCL of these glasses generally related to the frequency dependence of the conductivity in the Jonscher regime? In order to answer these questions, it is important to choose a glass system where the apparent mass dependence of the dc conductivity is clearly distinct from the triborate glasses studied by Rivera and coworkers. Here, aluminosilicate and aluminogermanate glasses are suitable, since in these glasses, sodium ions are more mobile than lithium and potassium ions.
124
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2. Experimental Glasses of composition A2 O Æ Al2 O3 Æ 4SiO2 with A ¼ Li, Na; Li2 O Æ Al2 O3 Æ 2SiO2 ; and A2 O Æ Al2 O3 Æ 4GeO2 with A ¼ Li, Na, K were prepared by heating dry mixtures of Al2 O3 , SiO2 or GeO2 and the respective alkali carbonates in a platinum crucible under an atmosphere of air. After decomposition of the carbonates at 1000 C, the melts were homogenized at 1500–1650 C for 3–5 h. Then, the melts were cast into a preheated stainless steel mold, and the cast glass blocks were transferred to another furnace. Here, the glasses were annealed 30 K below their respective glass transition temperatures for 3 h and then cooled down to room temperature with a rate of 1 K/min. Cylindrical samples (diameter 25 mm, thickness 1 mm) were drilled from the glass blocks, and the sample surfaces were polished. Then, metal electrodes consisting of one silver and one platinum layer were sputtered onto each surface. The frequency-dependent conductivities were measured in a frequency range from 102 to 106 Hz and in a conductivity range from 1015 to 106 S/cm using the Novocontrol a-S High Resolution Dielectric Analyzer. The temperature range of the measurements extended from 173 to 573 K.
Table 1 Activation energies and preexponential factors of the dc conductivity of aluminosilicate and aluminogermanate glasses with different mobile alkali ions Glass
EAdc =eV
logðA X cm=KÞ
Li2 O Æ Al2 O3 Æ 4SiO2 Na2 O Æ Al2 O3 Æ 4SiO2 Li2 O Æ Al2 O3 Æ 2SiO2 Li2 O Æ Al2 O3 Æ 4GeO2 Na2 O Æ Al2 O3 Æ 4GeO2 K2 O Æ Al2 O3 Æ 4GeO2
0.73 ± 0.01 0.66 ± 0.01 0.71 ± 0.01 0.81 ± 0.01 0.72 ± 0.01 0.79 ± 0.01
5.5 ± 0.2 4.6 ± 0.2 5.5 ± 0.2 5.4 ± 0.2 4.6 ± 0.2 4.1 ± 0.2
Fig. 1. Conductivity spectra of A2 O Æ Al2 O3 Æ 4SiO2 glasses at T ¼ 173 K. The dashed lines denote fits using Eq. (1).
3. Results At temperatures between 273 and 573 K, the conductivity spectra of all glasses are characterized by low-frequency dc plateaux, and the dc conductivities obey an Arrhenius law, rdc T ¼ A expðEAdc =kT Þ. The values for the activation energy EAdc and for the preexponential factor A obtained from a fit of the dc conductivity data are listed in Table 1. In Fig. 1 we present the frequency-dependent real part of the conductivity, r0 ðmÞ, for a lithium and a sodium aluminosilicate glass at T ¼ 173 K. For both glasses, r0 ðmÞ increases strongly with frequency, and the slope in the log–log plot is 0.95 ± 0.02, i.e., we observe a NCL. The dashed lines denote fits of the data using the power law: r0 ðmÞ X cm ¼ ðm=mNCL Þ0:95 :
ð1Þ
Here, the frequency mNCL characterizes the magnitude of the NCL. Clearly, the magnitude is higher for the sodium ion conducting glass as compared to the lithium ion conducting glass. This observation is clearly in contrast to the findings of Rivera et al. for alkali triborate glasses. In the case of the aluminosilicate glasses, the magnitude of the NCL cannot be described by a m1=3 relation. In the legend of Fig. 1, the values of the dc conductivity of these glasses at T ¼ 298 K are given. The dc conductivity of the sodium ion conducting glass is approximately twice as high as the dc conductivity of the lithium ion conducting glass. Thus, there is evidence that the magnitude of the dc conductivity is related to the magnitude of the NCL. In Fig. 2 we plot in comparison the frequency dependence of r0 for a lithium, a sodium and a
S. Murugavel, B. Roling / Journal of Non-Crystalline Solids 330 (2003) 122–127
Fig. 2. Conductivity spectra of A2 O Æ Al2 O3 Æ 4GeO2 glasses at T ¼ 173 K. The dashed lines denote fits using Eq. (1).
potassium aluminogermanate glass at T ¼ 173 K. Again, we find a NCL with a slope of 0.95 ± 0.02 in the log–log plot, and consequently we have fitted the data using Eq. (1). In the legend of Fig. 2, the dc conductivities of the glasses at T ¼ 298 K are given. Clearly, the dc conductivity decreases in the order Na fi Li fi K. Remarkably, the magnitude of the NCL decreases in the same order. Thus, we observe again a correlation between the magnitude of the NCL and the magnitude of the dc conductivity, but again the magnitude of the NCL cannot be described by a m1=3 relation.
4. Discussion Our results show that the m1=3 dependence of the magnitude of the NCL that has been found for alkali triborate glasses is not a general feature of alkali ion conducting glasses. However, for borate, aluminosilicate and aluminogermanate glasses, there seems to be a correlation between the magnitude of the NCL and the magnitude of the dc conductivity. In order to analyze this type of correlation more quantitatively, we plot in Fig. 3 the frequencies mNCL (173 K) versus the dc conductivities at room temperature, rdc (298 K). This figure does not only contain the data of the aluminosilicate and the aluminogermanate glasses, but also the data of
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Fig. 3. Correlation between the magnitude of the nearly constant loss at T ¼ 173 K, characterized by the frequency mNCL (173 K), and the dc conductivity at room temperature, rdc (298 K).
three sodium germanate glasses of compositions 0.0051Na2 O Æ 0.9949GeO2 , 0.051Na2 O Æ 0.949GeO2 , and 0.213Na2 O Æ 0.787GeO2 and of a lithium borate glass of composition 0.373Li2 O Æ 0.627B2 O3 . The latter four glasses were chosen, since frequency-dependent conductivities at 173 K and at 298 K had been measured in our laboratory [31]. As seen from Fig. 3, there is a general trend that mNCL (173 K) increases with decreasing dc conductivity, i.e., the magnitude of the NCL decreases with decreasing dc conductivity. However, it is obvious that the correlation between mNCL (173 K) and rdc (298 K) is not very strong. For instance, the two sodium germanate glasses with 0.51 and 5.1 mol% sodium oxide exhibit similar dc conductivities, but the magnitude of the NCL differs by about one order of magnitude. We will show now that in order to obtain a better correlation, it is important to take into account the onset frequency of the conductivity dispersion, m , which we define by r0 ðm Þ ¼ 2 rdc . It is well known that for most ion conducting glasses, m is thermally activated with the same activation energy as rdc T . This implies that for a given glass, the ratio rdc T =m is a temperatureindependent quantity. This is, indeed, the case for all glasses we have studied here. Furthermore, it has been shown by Sidebottom and coworkers that
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rdc T =m is proportional to the product De T [32,33]. Here, De ¼ e0 ð0Þ e0 ð1Þ denotes the dielectric relaxation strength due to hopping motions of the mobile ions. e0 ð1Þ is the high-frequency permittivity due to vibrational and electronic polarization. Since in a real experiment, electrode polarization effects complicate the determination of the dielectric relaxation strength, we now calculate an estimate for De T by using the equation [32] ðDe T Þest ¼
rdc T : m e 0
ð2Þ
Here, e0 denotes the permittivity of free space. Now we use ðDe T Þest to normalize the mNCL axis in Fig. 3. Thus, in Fig. 4 we plot mNCL ð173 KÞ Æ ðDe T Þest versus the dc conductivity at room temperature, rdc (298 K). Obviously, the additional consideration of ðDe T Þest improves the correlation enormously. Since there is general agreement that the dc conductivity and the dielectric relaxation strength are determined by hopping movements of the mobile ions, the strong correlation observed in Fig. 4 provides strong evidence that the NCL in our temperature window is also caused by ionic hopping movements. Thus, we can state that the present results on glasses containing different types of mobile alkali ions
agree with recent results on glasses with different number densities of mobile ions [31,32]. Finally, we would like to note that from our results, no conclusions can be drawn on the origin of the NCL at cryogenic temperatures. Jain and coworkers [11,12,15] and Sidebottom and MurrayKrezan [32] found strong experimental evidence that at temperatures below 100 K, localized relaxational motions of partially charged glass network atoms (jellyfish-type motions) contribute significantly to the NCL or even determine the magnitude of the NCL. In this context, it would certainly be interesting to reanalyse the low-temperature conductivity data of germanate glasses with very low alkali oxide contents and of heavy metal fluoride glasses which were published by Jain and coworkers [11,12,15].
5. Conclusions The frequency- and temperature-dependent conductivity spectra of aluminosilicate and aluminogermate glasses containing different types of mobile alkali ions were analyzed and discussed. It was shown that there is no correlation between the magnitude of the nearly constant loss and the mass of the alkali ions. However, in the temperature range of our study, the magnitude of the NCL is closely related to the dc conductivity and the dielectric relaxation strength of the glasses. This provides strong evidence that the NCL is caused by hopping motions of the mobile alkali ions. On the other hand, our results do not exclude the possibility that at temperatures below 173 K, localized relaxational motions of partially charged glass network atoms (jellyfish-type motions) contribute significantly to the NCL.
Acknowledgements
Fig. 4. Correlation between the product mNCL ð173 KÞ ðDe T Þest and the dc conductivity at room temperature, rdc (298 K). The dashed line is drawn to guide the eye.
We are indebted to S. Pas for critically reading the manuscript. Furthermore, we would like to thank the Deutsche Forschungsgemeinschaft for financial support via the SFB 458 and the Alexander von Humboldt foundation for providing a research fellowship for S.M.
S. Murugavel, B. Roling / Journal of Non-Crystalline Solids 330 (2003) 122–127
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