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Nonlinear impedance in oxide glasses containing single and mixed alkali ions
Solid State Ionics 225 (2012) 359–362
Contents lists available at SciVerse ScienceDirect
Solid State Ionics journal homepage: www.elsevier.com/locate/ssi
Nonlinear impedance in oxide glasses containing single and mixed alkali ions Ryszard Jan Barczyński ⁎, Leon Murawski University of Technology, Faculty of Applied Mathematics and Technical Physics, 80-233 Gdańsk, Poland
a r t i c l e
i n f o
Article history: Received 9 September 2011 Received in revised form 26 February 2012 Accepted 29 March 2012 Available online 30 April 2012 Keywords: Nonlinear impedance Mixed alkali effect Oxide glass
a b s t r a c t The aim of the present study was to find more clues on the nonlinearities in impedance of oxide glasses. The measurements were conducted in three families of glasses in the frequency range of 1 mHz to 10 MHz and the temperature range of − 120 °C to 150 °C. The first family of glasses has a composition of FeO–P2O5–Na2O. Oxide glasses containing iron and alkali are well known for a very low alkali ion mobility and may be considered purely polaron conducting. These glasses show no detectable nonlinearities in the impedance spectra. The second was a family of ionic conducting SiO2–Na2O–Al2O3 glasses. The contents of the third harmonics at certain cases reach high values of about 10% at higher temperatures and extremely low frequency region. This may be caused by blocking properties of electrodes. It has been pointed out that such a nonlinearity may imply errors in interpretation of conventional linear impedance measurements. The third family of glasses contained mixed alkali, no detectable nonlinearities in the impedance spectra was found. © 2012 Published by Elsevier B.V.
field E(t) = E0 ∙ sin(ωt) leads to the following expression for the current density being in phase with the electric field, j′:
1. Introduction 1.1. Nonlinear impedance
0
In terms of the response signal linearity impedance measurements may be classified in two sorts: linear and nonlinear methods. Usually the impedance is only defined for linear system and only linear measurements are performed. It is a small amplitude excitation what is employed to guarantee linearity. A large excitation may cause nonlinearities. It is good assumption for conventional systems where there are no intrinsic nonlinearities and nonstationary processes. For more complicated situations nonlinear (and nonstationary) impedances may contain more complete information than conventional impedance [1]. Unfortunately, due to a lack of established methods of analysis and appropriate software such measurements are very uncommon. Nonlinear current density may be expressed in terms of electric field as [2]: 3
5
jðEÞ ¼ σ 1 E þ σ 3 E þ σ 5 E þ … where σ1 denotes linear conductivity while σ3, σ5 etc. are higher order conductivity coefficients. An application of a sinusoidal electric
⁎ Corresponding author. Tel.: + 48 58 347 1832; fax: + 48 58 347 2821. E-mail address: [email protected] (R.J. Barczyński). 0167-2738/$ – see front matter © 2012 Published by Elsevier B.V. doi:10.1016/j.ssi.2012.03.049
0
0
3
3
0
5
5
j ðEÞ ¼ σ 1 E0 sinðωt Þ þ σ 3 E0 sin ðωt Þ þ σ 5 E0 sin ðωt Þ þ … 3 0 3 ¼ σ 01 ðωÞE0 sinðωt Þ þ σ 3 ðωÞE0 sinðωt Þ 4 1 0 10 0 3 5 σ ðωÞE0 sinðωt Þ − σ 3 ð3ωÞE0 sinð3ωt Þ þ 4 16 5 5 0 1 0 3 5 σ ð5ωÞE0 sinð5ωt Þ þ … − σ 5 ð3ωÞE0 sinð3ωt Þ þ 16 16 5
j
Thus, the higher harmonic currents can be used to determinate values for the higher order conductivity coefficients σ3, σ5 etc. Note, that high order coefficients influence not only high order harmonics, but also give share in conductivity of the current of basic frequency. Conductivity coefficients represent the total sum of all conductivity mechanisms and interface effects, in our case it should not be treated as a value describing a single property of the bulk material. 1.2. Oxide glasses containing alkali and transition metal oxide ions Electrical properties of oxide glasses which contain a large amount of transition metal oxide are determined by the presence of transition metal ions in two different valence states. Electronic conductivity mechanism is small polaron hopping between such ions [3]. Our previously reported data obtained in one example of such a glass, copper aluminosilicate Cu2O–Al2O3–SiO2, show large nonlinearities which depend on frequency and temperature at very moderate electric field of an order of 1 V/mm. The contents of the third harmonics reach about 10%. We interpreted this behaviour as a result
360
R.J. Barczyński, L. Murawski / Solid State Ionics 225 (2012) 359–362
of interaction between two mechanisms of conductivity — ionic and polaronic [4]. Electronic conduction occurs by small polaron hopping between Cu + and Cu 2+ ions. On the other hand, Cu + ions themselves are mobile, and their movement is responsible for ionic conductivity — this glass is very unusual in this respect. Thus a situation may cause nonlinearities: the movements of ions change the distribution of hopping centres while the polaron hopping process influences the concentration of mobile Cu + ions. As was pointed out by Rolling [5] at low frequencies, in the case of measurements carried out with blocking electrodes the conductivity drops with decreasing frequency due to the formation of double layers at the interfaces (electrode polarization). In this frequency range, a major part of the applied voltage may drop in the double layers. Since their thickness may be in the range of nm and below, and the resulting electric fields may be very high. Such high fields result in nonlinear effects due to the double layer formation. Opposite situation can be observed in glasses in which the role of transition metal oxide plays FeO. Iron ions are not mobile, moreover in glasses containing a significant amount of ferric oxide, mobility of alkaline ions is also low. Glasses belonging to this family, even with a large amount of alkaline oxide, exhibit mainly electronic conduction [6]. This was the reason for selecting glasses from this family for comparison of their nonlinear electrical properties. The third kind of glasses we used was pure ionic conductor — alumina silicate glass doped with a large amount of sodium. The aim of the present study was to find more information on the possible nonlinearities in impedance of oxide glasses. It is known and understood that such nonlinearities may be caused by a large value of applied electric field. However, in some materials nonlinearities can be also observed while the applied electric field is very low. We intended to check several groups of materials if they exhibit such a property and eventually find any dissimilarities in the nonlinear impedance spectra due to a possible different mechanism of nonlinear conduction.
2. Experimental Three groups of samples of oxide glasses were prepared by melting substrates in alumina crucible at a temperature of 1550 °C (the first group) and 1100 °C (the second and third groups). No detectable erosion of alumina crucible was observed, however it is possible that a small amount Al2O3 contamination was introduced. We believe that it has no significant influence neither on glass structure nor on its electrical properties. The compositions were as follows (in mol %): 62:4%SiO2 þ 27:6%Na2 O þ 10%Al2 O3 ; 62:4%SiO2 þ 20:6%Na2 O þ 17%Al2 O3 ;
50%FeO þ 50%P2 O5 ; 10%Na2 O þ 40%FeO þ 50%P2 O5 ; 20%Na2 O þ 30%FeO þ 50%P2 O5 ;
50%SiO2 þ 20%PbO þ 15%K2 O þ 15%Li2 O; 50%SiO2 þ 20%PbO þ 15%Na2 O þ 15%Li2 O; 50%SiO2 þ 20%PbO þ 15%Na2 O þ 15%K2 O:
Group I
Fig. 1. Linear conductivity versus frequency measured at different temperature for 62.4SiO2–27.6Na2O–10Al2O3 glass.
measurements of high resistivity materials) which yields electric field amplitude of an order of 1 V/mm.
3. Results Figs. 1 and 2 show a first (linear) term of conductivity measured at various temperatures plotted versus frequency for the representative samples of groups I and II of mentioned above. All the Group II samples show very typical conductivity behaviour versus frequency (shown at Fig. 2): a plateau at low frequency region (dc conductivity) and a constant slope (known as universal dielectric response [7], usually described by the relation σac = Aω s) at high frequency region. Identical picture is observed in all samples containing two alkali oxides from Group III. The picture of conductivity in the Group I samples is different (Fig. 1): at low temperature region conductivity drops very significantly, probably due to the blocking of ions at the gold electrodes. Sometimes an intermediate plateau is visible. Figs. 3 and 4 present the first and third terms of conductivity measured at two different temperatures. Fig. 3 shows behaviour typical for ion conducting samples from Group I, and Fig. 4 picture typical for glasses containing iron oxide (Group II) and two alkaline ions (Group III). In both groups II and III samples the third harmonics is very low (at least three orders of magnitude lower than the linear term) at all temperatures and the whole frequency region and can be attributed to the background caused by the apparatus. Although the manufacturer of dielectric spectrometer does not provide detailed information about the level of harmonic distortion of the apparatus, we observed that in our
Group II
Group III
The samples were cut from the bulky glass with a wire saw. For ac measurements a thin circular pellet (about 1 mm thick and 15 mm in diameter) was cut and gold electrodes were evaporated at both sides of the preheated sample in a high vacuum. The low frequency linear and nonlinear impedance measurements were carried out with Concept 40 broadband dielectric spectrometer in a temperature range from −120 °C to 340 °C and in a frequency range from 2 mHz to 1 MHz. The impedance signal was observed at a voltage of 1 V (typical value for impedance
Fig. 2. Linear conductivity versus frequency measured at different temperatures for 50FeO–50P2O5 glass.
R.J. Barczyński, L. Murawski / Solid State Ionics 225 (2012) 359–362
Fig. 3. First (H1) and third (H3) order conductivity coefficients measured at two temperatures 153 K and 423 K for 62.4SiO2 27.6Na2O 10Al2O3 glass. At the temperature of 153 K and at temperature of 423 K above frequency of approx. 1 kHz the level of the third harmonic is of an order of magnitude of 0.1% of the first one, and it may be attributed to the apparatus background.
ranges of measurement parameters it is of an order of 0.1%. This value may change if the measurements are performed with different frequency range, conductivity of the sample and excitation voltage. A different situation is observed in the case of ion conducting samples of the first family. At low frequency region when temperature is sufficiently high one can see an increase in the third harmonics, even up to 10% of linear conductivity. This phenomenon is observed at frequencies corresponding to the decrease of conductivity due to the electrode blocking. 4. Discussion Fig. 5 presents third order coefficient relative to linear conductivity versus frequency measured at different temperatures for 62.4SiO2– 27.6Na2O–10Al2O3 glass belonging to Group I. Table 1 shows third to first harmonic ratio maximum frequency, position and onset of electrode blocking effect. All glasses of this family exhibit pronounced electrode blocking, and according to Rolling [5] this may cause nonlinear effects due to high electric field in the double layers developed at the blocking electrodes. As can be seen from Table 1 nonlinear conductivity arouses at frequency much lower than onset of electrode blocking, when the double layer is already well developed. The behaviour of nonlinearity versus temperature change presented at
361
Fig. 5. Third order coefficient relative to linear conductivity versus frequency measured at different temperatures for 63.4SiO2–27.6Na2O–10Al2O3 glass.
Fig. 5 is different than previously observed in copper alumina-silicate glasses [4]. With the increase in temperature position of the maximum level of nonlinearities shifts towards higher frequency and its height at first increases and then decreases. In copper alumina-silicate glass the maximum increases monotonically with the temperature and at higher temperatures remains at almost fixed frequency. This difference in behaviour is quite pronounced, but its significance remains unclear. It may be an indicator of different mechanisms of nonlinearity generation in these two families of glasses, but data available so far are very incomplete. Glasses from Group III contain alkali oxides, but due to the mixed alkali effect conductivity is low and no blocking at electrodes is observed under our measurement conditions. Mixed alkali effect itself does not cause any measurable nonlinearities as well. Glasses from Group II, despite a large alkali contents, are polaronic conductors and also do not show any nonlinear behaviour. The absence of electrode polarization prevents from double layer formation and the applied electric field is not sufficient for the observation of nonlinear impedance in bulk of these materials. It should be noted, that a large amount of higher-order conductivity term present in the impedance spectra of some glasses may cause problems when interpreting results of linear impedance measurements. They influence linear part of the response of the material, as it can be written as: 3 0 0 0 3 j ðEÞ ¼ σ 1 ðωÞE0 sinðωt Þ þ … þ σ 3 ðωÞE0 sinðωt Þ þ … 4 10 0 5 σ ðωÞE0 sinðωt Þ þ 16 5
The error introduced by nonharmonic behaviour may easily reach almost 10% of the measured linear impedance. The error correction procedure should be adopted for the increase in the precision and reliability of impedance measurements. Some proposals have been given by Kiel et al. in [8].
Table 1 Third to first harmonic ratio maximum frequency and position and onset of electrode blocking effect for 62.4SiO2–27.6Na2O–10Al2O3 glass.
Fig. 4. First (H1) and third (H3) order conductivity coefficients measured at two temperatures 153 K and 423 K for 50FeO50P2O5 glass. At both temperatures and full frequency range the level of the third harmonic is less than 0.1% of the first one, and it may be attributed to the apparatus background.
Temperature [K]
H3/H1 maximum frequency [Hz]
H3/H1 ratio maximum value
Onset of electrode blocking effect [Hz]
333 363 393 423
0.012 0.017 0.13 0.97
4.8% 6.3% 7.3% 5.5%
2.6 39 1.1 · 103 4.3 · 103
362
R.J. Barczyński, L. Murawski / Solid State Ionics 225 (2012) 359–362
5. Conclusion Glasses of FeO–P2O5–Na2O composition containing mixed alkali oxides do not show detectable nonlinearities in ac conductivity. Oxide glasses containing iron and alkali are well known for very low alkali ion mobility and may be considered purely polaron conducting. The family of ionic conducting SiO2–Na2O–Al2O3 glasses shows the contents of the third harmonics at certain cases reaching high values of about 10%. This may be caused by blocking properties of electrodes. Nonlinearities result in errors in the impedance measurements carried out in materials under such conditions. The analysis of higher harmonics should be performed to get evidence for the reliability of the results.
The change of nonlinear conductivity versus temperature and frequency is different to that observed previously in copper alumina– silica glass. References [1] [2] [3] [4] [5] [6] [7] [8]
Q. Huang, R. Hui, B. Wang, J. Zhang, Electrochim. Acta 52 (2007) 8144. S. Murugavel, B. Roling, J. Non-Cryst. Solids 351 (2005) 2819. L. Murawski, C.H. Chung, J.D. Mackenzie, J. Non-Cryst. Solids 32 (1979) 91–104. R.J. Barczyński, J. Non-Cryst. Solids 356 (2010) 1962. B. Roling, J. Non-Cryst. Solids 357 (2011) 1831. L. Murawski, R.J. Barczynski, D. Samatowicz, Solid State Ionics 157 (2003) 293–298. A.K. Jonscher, Dielectric Relaxation in Solids, Chelsea Dielectrics, London, 1983. M. Kiel, O. Bohlen, D.U. Sauer, Electrochim. Acta 53 (2008) 7367.
Contents lists available at SciVerse ScienceDirect
Solid State Ionics journal homepage: www.elsevier.com/locate/ssi
Nonlinear impedance in oxide glasses containing single and mixed alkali ions Ryszard Jan Barczyński ⁎, Leon Murawski University of Technology, Faculty of Applied Mathematics and Technical Physics, 80-233 Gdańsk, Poland
a r t i c l e
i n f o
Article history: Received 9 September 2011 Received in revised form 26 February 2012 Accepted 29 March 2012 Available online 30 April 2012 Keywords: Nonlinear impedance Mixed alkali effect Oxide glass
a b s t r a c t The aim of the present study was to find more clues on the nonlinearities in impedance of oxide glasses. The measurements were conducted in three families of glasses in the frequency range of 1 mHz to 10 MHz and the temperature range of − 120 °C to 150 °C. The first family of glasses has a composition of FeO–P2O5–Na2O. Oxide glasses containing iron and alkali are well known for a very low alkali ion mobility and may be considered purely polaron conducting. These glasses show no detectable nonlinearities in the impedance spectra. The second was a family of ionic conducting SiO2–Na2O–Al2O3 glasses. The contents of the third harmonics at certain cases reach high values of about 10% at higher temperatures and extremely low frequency region. This may be caused by blocking properties of electrodes. It has been pointed out that such a nonlinearity may imply errors in interpretation of conventional linear impedance measurements. The third family of glasses contained mixed alkali, no detectable nonlinearities in the impedance spectra was found. © 2012 Published by Elsevier B.V.
field E(t) = E0 ∙ sin(ωt) leads to the following expression for the current density being in phase with the electric field, j′:
1. Introduction 1.1. Nonlinear impedance
0
In terms of the response signal linearity impedance measurements may be classified in two sorts: linear and nonlinear methods. Usually the impedance is only defined for linear system and only linear measurements are performed. It is a small amplitude excitation what is employed to guarantee linearity. A large excitation may cause nonlinearities. It is good assumption for conventional systems where there are no intrinsic nonlinearities and nonstationary processes. For more complicated situations nonlinear (and nonstationary) impedances may contain more complete information than conventional impedance [1]. Unfortunately, due to a lack of established methods of analysis and appropriate software such measurements are very uncommon. Nonlinear current density may be expressed in terms of electric field as [2]: 3
5
jðEÞ ¼ σ 1 E þ σ 3 E þ σ 5 E þ … where σ1 denotes linear conductivity while σ3, σ5 etc. are higher order conductivity coefficients. An application of a sinusoidal electric
⁎ Corresponding author. Tel.: + 48 58 347 1832; fax: + 48 58 347 2821. E-mail address: [email protected] (R.J. Barczyński). 0167-2738/$ – see front matter © 2012 Published by Elsevier B.V. doi:10.1016/j.ssi.2012.03.049
0
0
3
3
0
5
5
j ðEÞ ¼ σ 1 E0 sinðωt Þ þ σ 3 E0 sin ðωt Þ þ σ 5 E0 sin ðωt Þ þ … 3 0 3 ¼ σ 01 ðωÞE0 sinðωt Þ þ σ 3 ðωÞE0 sinðωt Þ 4 1 0 10 0 3 5 σ ðωÞE0 sinðωt Þ − σ 3 ð3ωÞE0 sinð3ωt Þ þ 4 16 5 5 0 1 0 3 5 σ ð5ωÞE0 sinð5ωt Þ þ … − σ 5 ð3ωÞE0 sinð3ωt Þ þ 16 16 5
j
Thus, the higher harmonic currents can be used to determinate values for the higher order conductivity coefficients σ3, σ5 etc. Note, that high order coefficients influence not only high order harmonics, but also give share in conductivity of the current of basic frequency. Conductivity coefficients represent the total sum of all conductivity mechanisms and interface effects, in our case it should not be treated as a value describing a single property of the bulk material. 1.2. Oxide glasses containing alkali and transition metal oxide ions Electrical properties of oxide glasses which contain a large amount of transition metal oxide are determined by the presence of transition metal ions in two different valence states. Electronic conductivity mechanism is small polaron hopping between such ions [3]. Our previously reported data obtained in one example of such a glass, copper aluminosilicate Cu2O–Al2O3–SiO2, show large nonlinearities which depend on frequency and temperature at very moderate electric field of an order of 1 V/mm. The contents of the third harmonics reach about 10%. We interpreted this behaviour as a result
360
R.J. Barczyński, L. Murawski / Solid State Ionics 225 (2012) 359–362
of interaction between two mechanisms of conductivity — ionic and polaronic [4]. Electronic conduction occurs by small polaron hopping between Cu + and Cu 2+ ions. On the other hand, Cu + ions themselves are mobile, and their movement is responsible for ionic conductivity — this glass is very unusual in this respect. Thus a situation may cause nonlinearities: the movements of ions change the distribution of hopping centres while the polaron hopping process influences the concentration of mobile Cu + ions. As was pointed out by Rolling [5] at low frequencies, in the case of measurements carried out with blocking electrodes the conductivity drops with decreasing frequency due to the formation of double layers at the interfaces (electrode polarization). In this frequency range, a major part of the applied voltage may drop in the double layers. Since their thickness may be in the range of nm and below, and the resulting electric fields may be very high. Such high fields result in nonlinear effects due to the double layer formation. Opposite situation can be observed in glasses in which the role of transition metal oxide plays FeO. Iron ions are not mobile, moreover in glasses containing a significant amount of ferric oxide, mobility of alkaline ions is also low. Glasses belonging to this family, even with a large amount of alkaline oxide, exhibit mainly electronic conduction [6]. This was the reason for selecting glasses from this family for comparison of their nonlinear electrical properties. The third kind of glasses we used was pure ionic conductor — alumina silicate glass doped with a large amount of sodium. The aim of the present study was to find more information on the possible nonlinearities in impedance of oxide glasses. It is known and understood that such nonlinearities may be caused by a large value of applied electric field. However, in some materials nonlinearities can be also observed while the applied electric field is very low. We intended to check several groups of materials if they exhibit such a property and eventually find any dissimilarities in the nonlinear impedance spectra due to a possible different mechanism of nonlinear conduction.
2. Experimental Three groups of samples of oxide glasses were prepared by melting substrates in alumina crucible at a temperature of 1550 °C (the first group) and 1100 °C (the second and third groups). No detectable erosion of alumina crucible was observed, however it is possible that a small amount Al2O3 contamination was introduced. We believe that it has no significant influence neither on glass structure nor on its electrical properties. The compositions were as follows (in mol %): 62:4%SiO2 þ 27:6%Na2 O þ 10%Al2 O3 ; 62:4%SiO2 þ 20:6%Na2 O þ 17%Al2 O3 ;
50%FeO þ 50%P2 O5 ; 10%Na2 O þ 40%FeO þ 50%P2 O5 ; 20%Na2 O þ 30%FeO þ 50%P2 O5 ;
50%SiO2 þ 20%PbO þ 15%K2 O þ 15%Li2 O; 50%SiO2 þ 20%PbO þ 15%Na2 O þ 15%Li2 O; 50%SiO2 þ 20%PbO þ 15%Na2 O þ 15%K2 O:
Group I
Fig. 1. Linear conductivity versus frequency measured at different temperature for 62.4SiO2–27.6Na2O–10Al2O3 glass.
measurements of high resistivity materials) which yields electric field amplitude of an order of 1 V/mm.
3. Results Figs. 1 and 2 show a first (linear) term of conductivity measured at various temperatures plotted versus frequency for the representative samples of groups I and II of mentioned above. All the Group II samples show very typical conductivity behaviour versus frequency (shown at Fig. 2): a plateau at low frequency region (dc conductivity) and a constant slope (known as universal dielectric response [7], usually described by the relation σac = Aω s) at high frequency region. Identical picture is observed in all samples containing two alkali oxides from Group III. The picture of conductivity in the Group I samples is different (Fig. 1): at low temperature region conductivity drops very significantly, probably due to the blocking of ions at the gold electrodes. Sometimes an intermediate plateau is visible. Figs. 3 and 4 present the first and third terms of conductivity measured at two different temperatures. Fig. 3 shows behaviour typical for ion conducting samples from Group I, and Fig. 4 picture typical for glasses containing iron oxide (Group II) and two alkaline ions (Group III). In both groups II and III samples the third harmonics is very low (at least three orders of magnitude lower than the linear term) at all temperatures and the whole frequency region and can be attributed to the background caused by the apparatus. Although the manufacturer of dielectric spectrometer does not provide detailed information about the level of harmonic distortion of the apparatus, we observed that in our
Group II
Group III
The samples were cut from the bulky glass with a wire saw. For ac measurements a thin circular pellet (about 1 mm thick and 15 mm in diameter) was cut and gold electrodes were evaporated at both sides of the preheated sample in a high vacuum. The low frequency linear and nonlinear impedance measurements were carried out with Concept 40 broadband dielectric spectrometer in a temperature range from −120 °C to 340 °C and in a frequency range from 2 mHz to 1 MHz. The impedance signal was observed at a voltage of 1 V (typical value for impedance
Fig. 2. Linear conductivity versus frequency measured at different temperatures for 50FeO–50P2O5 glass.
R.J. Barczyński, L. Murawski / Solid State Ionics 225 (2012) 359–362
Fig. 3. First (H1) and third (H3) order conductivity coefficients measured at two temperatures 153 K and 423 K for 62.4SiO2 27.6Na2O 10Al2O3 glass. At the temperature of 153 K and at temperature of 423 K above frequency of approx. 1 kHz the level of the third harmonic is of an order of magnitude of 0.1% of the first one, and it may be attributed to the apparatus background.
ranges of measurement parameters it is of an order of 0.1%. This value may change if the measurements are performed with different frequency range, conductivity of the sample and excitation voltage. A different situation is observed in the case of ion conducting samples of the first family. At low frequency region when temperature is sufficiently high one can see an increase in the third harmonics, even up to 10% of linear conductivity. This phenomenon is observed at frequencies corresponding to the decrease of conductivity due to the electrode blocking. 4. Discussion Fig. 5 presents third order coefficient relative to linear conductivity versus frequency measured at different temperatures for 62.4SiO2– 27.6Na2O–10Al2O3 glass belonging to Group I. Table 1 shows third to first harmonic ratio maximum frequency, position and onset of electrode blocking effect. All glasses of this family exhibit pronounced electrode blocking, and according to Rolling [5] this may cause nonlinear effects due to high electric field in the double layers developed at the blocking electrodes. As can be seen from Table 1 nonlinear conductivity arouses at frequency much lower than onset of electrode blocking, when the double layer is already well developed. The behaviour of nonlinearity versus temperature change presented at
361
Fig. 5. Third order coefficient relative to linear conductivity versus frequency measured at different temperatures for 63.4SiO2–27.6Na2O–10Al2O3 glass.
Fig. 5 is different than previously observed in copper alumina-silicate glasses [4]. With the increase in temperature position of the maximum level of nonlinearities shifts towards higher frequency and its height at first increases and then decreases. In copper alumina-silicate glass the maximum increases monotonically with the temperature and at higher temperatures remains at almost fixed frequency. This difference in behaviour is quite pronounced, but its significance remains unclear. It may be an indicator of different mechanisms of nonlinearity generation in these two families of glasses, but data available so far are very incomplete. Glasses from Group III contain alkali oxides, but due to the mixed alkali effect conductivity is low and no blocking at electrodes is observed under our measurement conditions. Mixed alkali effect itself does not cause any measurable nonlinearities as well. Glasses from Group II, despite a large alkali contents, are polaronic conductors and also do not show any nonlinear behaviour. The absence of electrode polarization prevents from double layer formation and the applied electric field is not sufficient for the observation of nonlinear impedance in bulk of these materials. It should be noted, that a large amount of higher-order conductivity term present in the impedance spectra of some glasses may cause problems when interpreting results of linear impedance measurements. They influence linear part of the response of the material, as it can be written as: 3 0 0 0 3 j ðEÞ ¼ σ 1 ðωÞE0 sinðωt Þ þ … þ σ 3 ðωÞE0 sinðωt Þ þ … 4 10 0 5 σ ðωÞE0 sinðωt Þ þ 16 5
The error introduced by nonharmonic behaviour may easily reach almost 10% of the measured linear impedance. The error correction procedure should be adopted for the increase in the precision and reliability of impedance measurements. Some proposals have been given by Kiel et al. in [8].
Table 1 Third to first harmonic ratio maximum frequency and position and onset of electrode blocking effect for 62.4SiO2–27.6Na2O–10Al2O3 glass.
Fig. 4. First (H1) and third (H3) order conductivity coefficients measured at two temperatures 153 K and 423 K for 50FeO50P2O5 glass. At both temperatures and full frequency range the level of the third harmonic is less than 0.1% of the first one, and it may be attributed to the apparatus background.
Temperature [K]
H3/H1 maximum frequency [Hz]
H3/H1 ratio maximum value
Onset of electrode blocking effect [Hz]
333 363 393 423
0.012 0.017 0.13 0.97
4.8% 6.3% 7.3% 5.5%
2.6 39 1.1 · 103 4.3 · 103
362
R.J. Barczyński, L. Murawski / Solid State Ionics 225 (2012) 359–362
5. Conclusion Glasses of FeO–P2O5–Na2O composition containing mixed alkali oxides do not show detectable nonlinearities in ac conductivity. Oxide glasses containing iron and alkali are well known for very low alkali ion mobility and may be considered purely polaron conducting. The family of ionic conducting SiO2–Na2O–Al2O3 glasses shows the contents of the third harmonics at certain cases reaching high values of about 10%. This may be caused by blocking properties of electrodes. Nonlinearities result in errors in the impedance measurements carried out in materials under such conditions. The analysis of higher harmonics should be performed to get evidence for the reliability of the results.
The change of nonlinear conductivity versus temperature and frequency is different to that observed previously in copper alumina– silica glass. References [1] [2] [3] [4] [5] [6] [7] [8]
Q. Huang, R. Hui, B. Wang, J. Zhang, Electrochim. Acta 52 (2007) 8144. S. Murugavel, B. Roling, J. Non-Cryst. Solids 351 (2005) 2819. L. Murawski, C.H. Chung, J.D. Mackenzie, J. Non-Cryst. Solids 32 (1979) 91–104. R.J. Barczyński, J. Non-Cryst. Solids 356 (2010) 1962. B. Roling, J. Non-Cryst. Solids 357 (2011) 1831. L. Murawski, R.J. Barczynski, D. Samatowicz, Solid State Ionics 157 (2003) 293–298. A.K. Jonscher, Dielectric Relaxation in Solids, Chelsea Dielectrics, London, 1983. M. Kiel, O. Bohlen, D.U. Sauer, Electrochim. Acta 53 (2008) 7367.