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Crystallization process and dielectric property of amorphous (Li1−xNax)2B4O7
Materials Science and Engineering A 449–451 (2007) 306–309
Crystallization process and dielectric property of amorphous (Li1−xNax)2B4O7 M. Kim, H.W. Choi, H.W. Park, Y.S. Yang ∗ School of Nano Science and Technology, RCDAMP, Department of Physics, Pusan National University, Busan 609-735, South Korea Received 21 August 2005; received in revised form 27 November 2005; accepted 15 February 2006
Abstract We prepared amorphous (Li1−x Nax )2 B4 O7 and measured thermal and dielectric properties to investigate the mixed alkali effects. Differential scanning calorimetry in the temperature range from 303 to 873 K and impedance/gain-phase analysis in the frequency range from 100 Hz to 15 MHz was used for the measurements of structural and dielectric changes. We have observed a mixed alkali effect from the anomalous change of the glass transition and crystallization temperatures. Dielectric properties in frequency and temperature domains have been analyzed by using the power law. We have found that there is a strong non-linearity of the electrical conduction with the Na concentration. The Na concentration dependence of the activation energy of the dc conductivity also shows a mixed alkali effect and the effect is understood with the structural random ion distribution model. © 2006 Elsevier B.V. All rights reserved. Keywords: Mixed alkali effect; Crystallization; dc Conductivity; Glass; Activation energy
1. Introduction The mixed alkali effect (MAE) in glasses has been an unsolved problem in glass science for several decades, and a complete understanding of the phenomenon is still lacking. A mixed alkali effect is the phenomenon where an addition of a second type of alkali ions into a single alkali glass changes a variety of properties in a non-linear way [1–6]. Mixed alkali effects have been found in ionic diffusivities and dc conductivities, in conductivity spectra, in mechanical loss spectra, and also in structural quantities like the glass transition temperature [7]. As ionic transport plays an important role in modern high technology applications of glassy electrolytes in new electrochemical devices such as solid state batteries, fuel cells, chemical sensors and smart windows, the study of the mixed alkali effect related to the ionic transport is very important for the aim of applications and understanding the diffusion mechanism of alkali ions [3]. The strength of the mixed alkali effect is strongly dependent on the annealing temperature and alkali element. The effect becomes stronger with decreasing temperature and increasing mismatch of element size [8]. In the present paper, we report the study of the composition dependence of the thermal and conductivity properties of ∗
Corresponding author. Tel.: +82 51 510 2958; fax: +82 51 516 5682. E-mail address: [email protected] (Y.S. Yang).
0921-5093/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2006.02.249
(Li1−x Nax )2 B4 O7 glasses for the investigation of a mixed alkali effect. 2. Experimental Mixed alkali glasses of compositions (Li1−x Nax )2 B4 O7 , where x = 0.2, 0.3, 0.5, 0.7, 0.9, were prepared by the meltquenching method. Li2 B4 O7 and Na2 B4 O7 powders were well mixed for an hour. The powder sample was melted in a Pt crucible in an electric furnace for 15 min at 1273 K. The melt was quenched onto a copper plate. Obtained samples were transparent, with 1 mm thickness. The glasses were identified by X-ray diffraction (Rigaku, Japan) and differential scanning calorimetry (DSC; DSC3100, Mac Science, Japan) measurements. Dielectric properties of LNBO glasses were measured by using the impedance/gain-phase analyzer. Gold electrodes with radius 1.5 mm were deposited on both of the surfaces for the polished samples by vacuum evaporation, and gold leads were attached to them with silver paste. The frequency range was from 100 Hz to 15 MHz, with a heating rate of 2 K/min. 3. Results Fig. 1 shows the DSC curves of (Li1−x Nax )2 B4 O7 (x = 0, 0.2, 0.3, 0.5, 0.7, 0.9, 1) glasses with a heating rate of 2 K/min. The glass transition temperature (Tg ), the onset of crystallization
M. Kim et al. / Materials Science and Engineering A 449–451 (2007) 306–309
Fig. 1. DSC curves of (Li1−x Nax )2 B4 O7 glasses with a heating rate of 2 K/min.
(Tc ) and the exothermic peak position (Tp ) are shown. Our main aspect of this study is the mixed alkali effect occurring in the dielectric response, but we briefly mention the thermal properties for the crystallization of glass as a function of the sodium concentration x. Fig. 2 shows the variation of Tg , Tc , Tp and T (=Tc −Tg , glass forming ability [9]) as a function of Na concentration, obtained from the DSC curves in Fig. 1. As can be seen in the figure, the variation of each temperature Tg , Tc , Tp and T in DSC, which is very sensitive to the structural relaxation and transition, does not show additivity or linearity. Previous studies have shown that the glass transition temperature exhibits a negative deviation when one alkali ion is replaced by another in homogeneous glass due to a mixed alkali effect. It should be noted that there is no unique mixed alkali effect on thermodynamic or structural relaxation properties and the effect has to be related to ionic transport. Fig. 3 shows the real ( ) and imaginary ( ) parts of the dielectric constant of x = 0.7 as a function of temperature for given frequencies obtained with a heating rate of 2 K/min. Atoms actively start to migrate near Tg (712 K) with structural relaxation and the dielectric constant increases with thermal activation. The large values of and in the temperature range between 700 and 800 K is concerned with the fast movement of the alkali ions, because the light alkali atoms are easily ionized in the glass network and respond to an external electric field with increasing temperature. At higher temperatures, atoms are relatively localized as the crystal volume fraction increases and the effect appears as a decrease in the dielectric constant. It is useful to notice that the onset of decrease in dielectric constant during crystallization of glass normally occurs between Tc and Tp . These temperatures are 785 and 807 K, respectively, in Fig. 1.
307
Fig. 2. Variation of Tg , Tc , Tp and T (=Tc −Tg ) as a function of Na concentration, obtained from the DSC curves in Fig. 1. Points are the data and the lines are to the eyes.
Fig. 4 shows the frequency dependent electrical conductivity at several temperatures. At low frequency, the conductivity is almost frequency independent, approaching the dc conductivity. At high frequency, the conductivity has a dispersion that shifts
Fig. 3. Temperature dependence of the dielectric constant for (a) the real and (b) imaginary parts. The firstly marked temperature corresponds to Tg , and secondly marked temperature locates between Tc and Tp in Fig. 1.
308
M. Kim et al. / Materials Science and Engineering A 449–451 (2007) 306–309
Fig. 4. Frequency dependence of the conductivity at different temperatures. Points are the data and the lines are fits using the Jonscher’s power law.
to higher frequencies with increasing temperature. The solid lines are obtained from the fit of Jonscher’s power law of ac conductivity in glass, σ(ω) = σ dc [1 + (ω/ωh )n ], where σ dc is the dc conductivity, ωh the hopping frequency of the charge carriers, and n is the frequency exponent parameter in the range of 0–1 characterizing the deviation from Debye behavior and a measure the inter ionic coupling strength. For (Li1−x Nax )2 B4 O7 glass, the exponent n of Joncher’s power law is 0.4–0.6, indicating that the system is in the state far away from the Debye state. Jonscher’s power law is mainly adopted in this study to obtain the dc conductivity that is sensitive for examining the mixed alkali effect. We also used the complex impedance Cole–Cole plot to calculate the dc conductivity and the result was similar to the one obtained from the Jonscher’s power law. In Fig. 5, the dc conductivity as a function of Na concentration at different temperatures is shown. A very clear mixed alkali effect can be seen with the exhibition of a negative deviation. The drop in conductivity is 1–1.5 orders of magnitude and the mixed alkali effect decreases as temperature increases. Previous studies have shown that the conductivity drop is much more pronounced, 4–6 orders of magnitude, when the size difference between mixed alkali ions is large, and the mixed alkali effect diminishes with increasing temperature.
Fig. 5. dc Conductivity as a function of Na concentration at given temperatures. Points are obtained from the power law and the lines are to the eyes.
Fig. 6. (a) Arrhenius plots and (b) the dc activation energy for different compositions. The straight lines in (a) are fits to the data and the curved line in (b) is to the eyes.
Fig. 6 shows the dc activation energy as a function of Na concentration (Fig. 6(b)). The dc conductivity, more precisely the product of the dc conductivity and temperature, often follows an Arrhenius formula in the glassy state (Fig. 6(a)), σ dc T = σ o exp(−Edc /kB T), where σ o is a prefactor, Edc a dc activation energy, kB is the Boltzmann factor. The activation energy locates its maximum near x = 0.5 and the concentration dependent activation energy clearly represents the mixed alkali effect. 4. Discussion In Fig. 2, Tg and T show a non-linear behavior with a slightly negative deviation, but the negative deviation is strong for Tc , Tp . The appearance of the non-linearity for the change in the DSC exothermic peak temperatures with the addition of Na content indicates that, not only Tg but also Tc , T, or Tp , get effected by a mixed alkali effect, in addition to the ionic transport property. Concerning the mixed alkali behavior in Figs. 5 and 6, the decrease of dc conductivity results from an increase in activation energy. Although, it is hard to choose a definite model to connect a measured macroscopic parameter such as σ(ω) and the microscopic process, the non-linear behavior of conductivity and activation energy in Figs. 5 and 6 can be partially explained from the structural random ion distribution model [1]. The model considers that the mixed alkali effect is a natural consequence of the structural changes; a large energy mismatch for ionic jumps to dissimilar alkali sites resulting in blocking of lowdimensional migration pathways. For the Na and Li mixed alkali system in this study, a Na ion cannot easily enter a site where a Li ion resides and vice versa, i.e., ions attempting to jump have
M. Kim et al. / Materials Science and Engineering A 449–451 (2007) 306–309
309
difficulties finding suitable sites and the rate of a successful jump is reduced as ions have to climb higher energy barriers.
by the Ministry of Commerce, Industry and Energy of the Korean Government.
5. Conclusion
References
Thermal and dielectric properties of (Li1−x Nax )2 B4 O7 glasses have been investigated. The glass transition temperature, crystallization temperature in the DSC curves and the dc conductivity, the activation energy of dc conductivity in the dielectric spectroscopy showed a mixed alkali effect. The weight of negative deviation on the concentration dependent dc conductivity continuously decreased with increasing temperature (order of magnitude was 1.5 at 533 K and 1.0 at 673 K). The mixed alkali effect was qualitatively understood in the framework of the structural random ion distribution model.
[1] C. Karlsson, A. Mandanici, A. Matic, J. Swenson, L. Borjesson, Phys. Rev. B 68 (2003) 064202 1–064202 9. [2] D.E. Day, J. Non-Cryst. Solids 21 (1976) 343–372. [3] Y. Gao, C. Cramer, Solid State Ionics 176 (2005) 921–927. [4] S. Ghosh, A. Ghosh, J. Chem. Phys. 119 (2003) 9106–9110. [5] H. Jain, H.L. Downing, N.L. Peterson, J. Non-Cryst. Solids 64 (1984) 335–349. [6] S.J. Kim, H.W. Choi, J.E. Kim, M. Kim, Y.S. Yang, J. Korean Phys. Soc. 46 (2005) 155–158. [7] C. Cramer, S. Brunklaus, E. Ratai, Y. Gao, Phys. Rev. Lett. 91 (2003) 266601 1–266601 4. [8] H. Jain, X. Lu, J. Non-Cryst. Solids 196 (1996) 285–290. [9] D.S. Sung, O.J. Kwon, E. Fleury, K.B. Kim, Y.C. Kim, Met. Mater. Int. 10 (2004) 575–579.
Acknowledgement This work was supported by the program for the Training of Graduate Students in Regional Innovation which was conducted
Crystallization process and dielectric property of amorphous (Li1−xNax)2B4O7 M. Kim, H.W. Choi, H.W. Park, Y.S. Yang ∗ School of Nano Science and Technology, RCDAMP, Department of Physics, Pusan National University, Busan 609-735, South Korea Received 21 August 2005; received in revised form 27 November 2005; accepted 15 February 2006
Abstract We prepared amorphous (Li1−x Nax )2 B4 O7 and measured thermal and dielectric properties to investigate the mixed alkali effects. Differential scanning calorimetry in the temperature range from 303 to 873 K and impedance/gain-phase analysis in the frequency range from 100 Hz to 15 MHz was used for the measurements of structural and dielectric changes. We have observed a mixed alkali effect from the anomalous change of the glass transition and crystallization temperatures. Dielectric properties in frequency and temperature domains have been analyzed by using the power law. We have found that there is a strong non-linearity of the electrical conduction with the Na concentration. The Na concentration dependence of the activation energy of the dc conductivity also shows a mixed alkali effect and the effect is understood with the structural random ion distribution model. © 2006 Elsevier B.V. All rights reserved. Keywords: Mixed alkali effect; Crystallization; dc Conductivity; Glass; Activation energy
1. Introduction The mixed alkali effect (MAE) in glasses has been an unsolved problem in glass science for several decades, and a complete understanding of the phenomenon is still lacking. A mixed alkali effect is the phenomenon where an addition of a second type of alkali ions into a single alkali glass changes a variety of properties in a non-linear way [1–6]. Mixed alkali effects have been found in ionic diffusivities and dc conductivities, in conductivity spectra, in mechanical loss spectra, and also in structural quantities like the glass transition temperature [7]. As ionic transport plays an important role in modern high technology applications of glassy electrolytes in new electrochemical devices such as solid state batteries, fuel cells, chemical sensors and smart windows, the study of the mixed alkali effect related to the ionic transport is very important for the aim of applications and understanding the diffusion mechanism of alkali ions [3]. The strength of the mixed alkali effect is strongly dependent on the annealing temperature and alkali element. The effect becomes stronger with decreasing temperature and increasing mismatch of element size [8]. In the present paper, we report the study of the composition dependence of the thermal and conductivity properties of ∗
Corresponding author. Tel.: +82 51 510 2958; fax: +82 51 516 5682. E-mail address: [email protected] (Y.S. Yang).
0921-5093/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2006.02.249
(Li1−x Nax )2 B4 O7 glasses for the investigation of a mixed alkali effect. 2. Experimental Mixed alkali glasses of compositions (Li1−x Nax )2 B4 O7 , where x = 0.2, 0.3, 0.5, 0.7, 0.9, were prepared by the meltquenching method. Li2 B4 O7 and Na2 B4 O7 powders were well mixed for an hour. The powder sample was melted in a Pt crucible in an electric furnace for 15 min at 1273 K. The melt was quenched onto a copper plate. Obtained samples were transparent, with 1 mm thickness. The glasses were identified by X-ray diffraction (Rigaku, Japan) and differential scanning calorimetry (DSC; DSC3100, Mac Science, Japan) measurements. Dielectric properties of LNBO glasses were measured by using the impedance/gain-phase analyzer. Gold electrodes with radius 1.5 mm were deposited on both of the surfaces for the polished samples by vacuum evaporation, and gold leads were attached to them with silver paste. The frequency range was from 100 Hz to 15 MHz, with a heating rate of 2 K/min. 3. Results Fig. 1 shows the DSC curves of (Li1−x Nax )2 B4 O7 (x = 0, 0.2, 0.3, 0.5, 0.7, 0.9, 1) glasses with a heating rate of 2 K/min. The glass transition temperature (Tg ), the onset of crystallization
M. Kim et al. / Materials Science and Engineering A 449–451 (2007) 306–309
Fig. 1. DSC curves of (Li1−x Nax )2 B4 O7 glasses with a heating rate of 2 K/min.
(Tc ) and the exothermic peak position (Tp ) are shown. Our main aspect of this study is the mixed alkali effect occurring in the dielectric response, but we briefly mention the thermal properties for the crystallization of glass as a function of the sodium concentration x. Fig. 2 shows the variation of Tg , Tc , Tp and T (=Tc −Tg , glass forming ability [9]) as a function of Na concentration, obtained from the DSC curves in Fig. 1. As can be seen in the figure, the variation of each temperature Tg , Tc , Tp and T in DSC, which is very sensitive to the structural relaxation and transition, does not show additivity or linearity. Previous studies have shown that the glass transition temperature exhibits a negative deviation when one alkali ion is replaced by another in homogeneous glass due to a mixed alkali effect. It should be noted that there is no unique mixed alkali effect on thermodynamic or structural relaxation properties and the effect has to be related to ionic transport. Fig. 3 shows the real ( ) and imaginary ( ) parts of the dielectric constant of x = 0.7 as a function of temperature for given frequencies obtained with a heating rate of 2 K/min. Atoms actively start to migrate near Tg (712 K) with structural relaxation and the dielectric constant increases with thermal activation. The large values of and in the temperature range between 700 and 800 K is concerned with the fast movement of the alkali ions, because the light alkali atoms are easily ionized in the glass network and respond to an external electric field with increasing temperature. At higher temperatures, atoms are relatively localized as the crystal volume fraction increases and the effect appears as a decrease in the dielectric constant. It is useful to notice that the onset of decrease in dielectric constant during crystallization of glass normally occurs between Tc and Tp . These temperatures are 785 and 807 K, respectively, in Fig. 1.
307
Fig. 2. Variation of Tg , Tc , Tp and T (=Tc −Tg ) as a function of Na concentration, obtained from the DSC curves in Fig. 1. Points are the data and the lines are to the eyes.
Fig. 4 shows the frequency dependent electrical conductivity at several temperatures. At low frequency, the conductivity is almost frequency independent, approaching the dc conductivity. At high frequency, the conductivity has a dispersion that shifts
Fig. 3. Temperature dependence of the dielectric constant for (a) the real and (b) imaginary parts. The firstly marked temperature corresponds to Tg , and secondly marked temperature locates between Tc and Tp in Fig. 1.
308
M. Kim et al. / Materials Science and Engineering A 449–451 (2007) 306–309
Fig. 4. Frequency dependence of the conductivity at different temperatures. Points are the data and the lines are fits using the Jonscher’s power law.
to higher frequencies with increasing temperature. The solid lines are obtained from the fit of Jonscher’s power law of ac conductivity in glass, σ(ω) = σ dc [1 + (ω/ωh )n ], where σ dc is the dc conductivity, ωh the hopping frequency of the charge carriers, and n is the frequency exponent parameter in the range of 0–1 characterizing the deviation from Debye behavior and a measure the inter ionic coupling strength. For (Li1−x Nax )2 B4 O7 glass, the exponent n of Joncher’s power law is 0.4–0.6, indicating that the system is in the state far away from the Debye state. Jonscher’s power law is mainly adopted in this study to obtain the dc conductivity that is sensitive for examining the mixed alkali effect. We also used the complex impedance Cole–Cole plot to calculate the dc conductivity and the result was similar to the one obtained from the Jonscher’s power law. In Fig. 5, the dc conductivity as a function of Na concentration at different temperatures is shown. A very clear mixed alkali effect can be seen with the exhibition of a negative deviation. The drop in conductivity is 1–1.5 orders of magnitude and the mixed alkali effect decreases as temperature increases. Previous studies have shown that the conductivity drop is much more pronounced, 4–6 orders of magnitude, when the size difference between mixed alkali ions is large, and the mixed alkali effect diminishes with increasing temperature.
Fig. 5. dc Conductivity as a function of Na concentration at given temperatures. Points are obtained from the power law and the lines are to the eyes.
Fig. 6. (a) Arrhenius plots and (b) the dc activation energy for different compositions. The straight lines in (a) are fits to the data and the curved line in (b) is to the eyes.
Fig. 6 shows the dc activation energy as a function of Na concentration (Fig. 6(b)). The dc conductivity, more precisely the product of the dc conductivity and temperature, often follows an Arrhenius formula in the glassy state (Fig. 6(a)), σ dc T = σ o exp(−Edc /kB T), where σ o is a prefactor, Edc a dc activation energy, kB is the Boltzmann factor. The activation energy locates its maximum near x = 0.5 and the concentration dependent activation energy clearly represents the mixed alkali effect. 4. Discussion In Fig. 2, Tg and T show a non-linear behavior with a slightly negative deviation, but the negative deviation is strong for Tc , Tp . The appearance of the non-linearity for the change in the DSC exothermic peak temperatures with the addition of Na content indicates that, not only Tg but also Tc , T, or Tp , get effected by a mixed alkali effect, in addition to the ionic transport property. Concerning the mixed alkali behavior in Figs. 5 and 6, the decrease of dc conductivity results from an increase in activation energy. Although, it is hard to choose a definite model to connect a measured macroscopic parameter such as σ(ω) and the microscopic process, the non-linear behavior of conductivity and activation energy in Figs. 5 and 6 can be partially explained from the structural random ion distribution model [1]. The model considers that the mixed alkali effect is a natural consequence of the structural changes; a large energy mismatch for ionic jumps to dissimilar alkali sites resulting in blocking of lowdimensional migration pathways. For the Na and Li mixed alkali system in this study, a Na ion cannot easily enter a site where a Li ion resides and vice versa, i.e., ions attempting to jump have
M. Kim et al. / Materials Science and Engineering A 449–451 (2007) 306–309
309
difficulties finding suitable sites and the rate of a successful jump is reduced as ions have to climb higher energy barriers.
by the Ministry of Commerce, Industry and Energy of the Korean Government.
5. Conclusion
References
Thermal and dielectric properties of (Li1−x Nax )2 B4 O7 glasses have been investigated. The glass transition temperature, crystallization temperature in the DSC curves and the dc conductivity, the activation energy of dc conductivity in the dielectric spectroscopy showed a mixed alkali effect. The weight of negative deviation on the concentration dependent dc conductivity continuously decreased with increasing temperature (order of magnitude was 1.5 at 533 K and 1.0 at 673 K). The mixed alkali effect was qualitatively understood in the framework of the structural random ion distribution model.
[1] C. Karlsson, A. Mandanici, A. Matic, J. Swenson, L. Borjesson, Phys. Rev. B 68 (2003) 064202 1–064202 9. [2] D.E. Day, J. Non-Cryst. Solids 21 (1976) 343–372. [3] Y. Gao, C. Cramer, Solid State Ionics 176 (2005) 921–927. [4] S. Ghosh, A. Ghosh, J. Chem. Phys. 119 (2003) 9106–9110. [5] H. Jain, H.L. Downing, N.L. Peterson, J. Non-Cryst. Solids 64 (1984) 335–349. [6] S.J. Kim, H.W. Choi, J.E. Kim, M. Kim, Y.S. Yang, J. Korean Phys. Soc. 46 (2005) 155–158. [7] C. Cramer, S. Brunklaus, E. Ratai, Y. Gao, Phys. Rev. Lett. 91 (2003) 266601 1–266601 4. [8] H. Jain, X. Lu, J. Non-Cryst. Solids 196 (1996) 285–290. [9] D.S. Sung, O.J. Kwon, E. Fleury, K.B. Kim, Y.C. Kim, Met. Mater. Int. 10 (2004) 575–579.
Acknowledgement This work was supported by the program for the Training of Graduate Students in Regional Innovation which was conducted