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Partial electronic conductivity of Sr and Mg doped LaGaO3
Solid State Ionics 154 – 155 (2002) 481 – 486 www.elsevier.com/locate/ssi
Partial electronic conductivity of Sr and Mg doped LaGaO3 Jin Ho Jang, Gyeong Man Choi * Department of Materials Science and Engineering, Pohang University of Science and Technology, San 31, Hyoja-dong, Namku, Pohang 790-784, South Korea Accepted 14 March 2002
Abstract The partial electronic conductivities (rel) of La0.9Sr0.1Ga0.9Mg0.1O2.90 (LSGM9191), La0.9Sr0.1Ga0.8Mg0.2O2.85 (LSGM9182) and La0.8Sr0.2Ga0.8Mg0.2O2.80 (LSGM8282) were measured by Hebb – Wagner ion-blocking method between 700 and 900 jC. As the Sr and Mg content increases, both the hole and the electron conductivity decrease together with the increasing activation energy of conduction. The electronic transference numbers of the three compositions were approximately 10 2 f 10 3, much larger than that of zirconia. From the Hebb – Wagner curves, the variation of rel was obtained as a function of oxygen partial pressure ( PO2). The thermal band-gap energy (Eg) value was estimated from the conductivity minima. The possible sources of error in estimating Eg were discussed. Eg value was much smaller than that of yttria-stabilized zirconia (YSZ). D 2002 Elsevier Science B.V. All rights reserved. Keywords: Ion-blocking; Hebb – Wagener method; LaGaO3; Electronic conductivity
1. Introduction The application of solid oxide electrolytes includes solid oxide fuel cell (SOFC), oxygen probes or sensors, gas-separating membranes, etc. [1]. A typical solid oxide electrolyte is a stabilized zirconia with cubic fluorite structure to which doped CeO2 and ThO2 also belong. Ever since the introduction of a new perovskite-structured solid oxide electrolyte, the Sr and Mg doped LaGaO3 (LSGM) has attracted great interest of researchers who are in search of the solid
*
Corresponding author. Tel.: +82-54-279-2146; fax: +82-54279-2399. E-mail address: [email protected] (G.M. Choi).
electrolytes for the intermediate temperature SOFC [2]. In spite of the promising aspects of LSGM, this material has several drawbacks, such as the high cost of gallium oxide, relatively weak mechanical strength [3,4] and the chemical stability problem under highly reducing conditions at high temperatures [5,6]. Another possible problem is a nonnegligible partial electronic conductivity. Although other authors also have reported the electronic conductivities of LSGM [6 –8], the basic information such as the activation energy, thermal band-gap energy and the effects of composition on the electronic conduction properties is still lacking. The main object of this study is to examine the effect of the acceptor concentration on the partial electronic
0167-2738/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 2 7 3 8 ( 0 2 ) 0 0 4 8 6 - 1
482
J.H. Jang, G.M. Choi / Solid State Ionics 154 – 155 (2002) 481–486
conductivity of LSGM. The ion-blocking Hebb –Wagner polarization method was employed.
2. Experimental procedure Conventional solid-state reaction method was used to synthesize Sr and Mg doped LaGaO3 (La1 xSrx Ga1 yMgyO3) where Sr2 + and Mg2 + content varying from 10 to 20 mol% (x = 0.1 – 0.2 and y = 0.1 –0.2). Three compositions were prepared, i.e., La 0.9 Sr0.1Ga0.9Mg0.1O 2.90(LSGM9191), La0.9Sr 0.1Ga0.8 Mg 0 . 2 O 2 . 8 5 (LSGM9182) and La 0 . 8 Sr 0 . 2 Ga 0 . 8 Mg0.2O2.80 (LSGM8282). The starting materials were La 2 O 3 (99.99%, GFS Chemicals, USA), SrCO 3 (99.9%, High purity Chemicals, Japan), Ga 2 O 3 (99.9%, High purity Chemicals) and MgO (99.9%, High purity Chemicals) powders. After La2O3 and MgO were fired at 1000 jC for 3 h to remove possible hydroxides and carbonates, required amounts of each powders were mixed by ball-milling with zirconia balls in ethanol for 12 h. Mixed slurry was dried, ground and calcined at 1200 jC for 6 h in air. The calcined powders were pulverized and die-pressed into pellets, followed by cold isostatic pressing at 200 MPa. Pressed pellets were sintered at 1450 jC for 6 h in air. X-ray diffraction experiment was carried out for phase characterization (XRD, MAC Science, M18XCE, Japan). The microstructure of sintered LSGM samples were observed using SEM (HITACHI, Japan). Hebb – Wagner polarization method was employed to measure the partial electronic conductivity (rel): hole conductivity (rh) and electron conductivity (re) [9]. The cell can be represented by the following configuration. ðþÞPtðreversibleÞ; airALSGM discAPtðblockingÞðÞ ð1Þ Sintered pellets of LSGM were sliced into discs with the diameter of 18 mm and the thickness varying from 0.5 to 1 mm. Pt paste (Engelhard model #6926, USA) was painted on the reversible side of the specimen followed by heat treatment at 1000 jC for 1 h. Pt-mesh (diameter of 7 mm) was attached on top of the painted Pt paste as a current collector. As a
blocking electrode, Pt paste (Engelhard model #6082, USA) and Pt foil were used. Pyrex glass crushed and mixed with water was used for sealing. Constant voltage was applied from 0.1 to 1.5 V with the step of 0.1 V (HP 4140B, Japan). The steady-state current (Iel) versus the applied voltage (Eappl) was recorded as a function of temperature (700 – 920 jC) in air.
3. Results and discussion XRD results showed trace amount of LaSrGaO4 and LaSrGa3O7 peaks in LSGM8282, whereas only LaSrGa3O7 peaks in LSGM9191. There was an extra peak in both LSGM9182 and LSGM9191 due to their slightly distorted cubic structure. The SEM microstructures of the three LSGM samples showed that the grain size of LSGM8282 is the largest (10.4 Am), while that of LSGM9191 is the smallest (1.4 Am). The grain size of LSGM9182 was 2.7 Am. The relative sintered densities of all samples were greater than 99%. The typical shape of Hebb –Wagner curve was shown for LSGM9191 as a function of temperature in Fig. 1. The partial electronic conductivity was obtained by nonlinear curve fitting of the Iel versus Eappl data with the following Hebb –Wagner equation: FEappl Iel LF o ¼ rh 1 exp ART RL FEappl o þ re exp 1 RL
ð2Þ
where rjh and rj, e respectively, are the hole and the electron conductivity at the reversible electrode. A is the area of the electrode and L, the thickness of the specimen. R, T and F have their usual meanings. The y-axis was modified to compensate the different sample dimensions for three samples. When the Hebb – Wagner curves were measured at or above 900 jC for LSGM9182 and LSGM8282, irreproducible curves were obtained possibly due to sample decomposition. LSGM9191 was the most stable among three samples. Another interesting feature is that the plateaus of LSGM9191 curves are narrower than those of LSGM9182 and LSGM8282. This
J.H. Jang, G.M. Choi / Solid State Ionics 154 – 155 (2002) 481–486
483
When the hole conductivity is divided by the ionic conductivity which varies small among three samples, the electronic (mostly by holes) transference numbers (tel) are obtained. The tel values for all three samples vary between 10 2 and 10 3 at 700 –900 jC, much larger than that ( f 10 4 at 800 jC) of yttria-stabilized zirconia (YSZ) [11]. Fig. 3 shows the oxygen partial pressure dependence of the partial electronic conductivity (rel = rh + re) for LSGM9191. Under complete ion-blocking condition, the steady state current (Iel) and applied voltage (E) satisfy the relation: rblock ¼ el
Fig. 1. Hebb – Wagner curves of LSGM9191 sample varying with temperatures between 700 and 900 jC. Air was used as the reference PO2. The y-axis was modified to accommodate the difference in the sample dimension.
difference in the width of the plateaus predicts the higher electronic contribution to the conduction of LSGM9191 than other two compositions as will be discussed later. Fig. 2 compares the hole and electron conductivities of the three compositions in air, obtained by fitting the Hebb – Wagner curves by Eq. (2). As seen in the figure, the hole conductivity difference among three samples is small, whereas the lowest activation energy and thus the highest electron conductivity is shown for LSGM9191 at all temperatures. LSGM8282 marked the lowest electron conductivity below 850 jC. The trend is that adding more dopants increases the activation energy for electron conduction. The hole conductivity data measured by Schmidt et al. [6] and Kim and Yoo [10] through Hebb – Wagner experiment is also plotted in Fig. 2. The comparison reveals that our activation energy and hole conductivity of LSGM9182 are lower than Schmidt et al.’s values. However, the magnitude of electron hole conductivity is in good agreement with Kim and Yoo’s result [10]. For the electron conductivity, both the activation energy and the magnitude show a large discrepancy between our data and Kim and Yoo’s result.
L BIel A BE E
ð3Þ
where relblock is the partial electronic conductivity (rh + re) at the blocking electrode under a constant voltage [12]. The oxygen partial pressure at the
Fig. 2. The hole (rh) and electron (re) conductivities of the three LSGM compositions in air. Sample compositions and their activation energies are shown. Open circles represent the LSGM9191, squares for LSGM9182 and closed circles for LSGM8282. The data obtained in other study (up triangles for Ref. [6], down triangles for Ref. [10]) for LSGM9182 are also shown for the comparison.
484
J.H. Jang, G.M. Choi / Solid State Ionics 154 – 155 (2002) 481–486
Fig. 3. The PO2 dependence of the partial electronic conductivities of LSGM9191 composition calculated by using the fitted Hebb – Wagner curves. The partial electronic conductivity of YSZ [11] is also shown for the comparison.
Fig. 4. log r versus log PO2 for the three LSGM compositions (8282, 9182 and 9191) at 750 jC.
J.H. Jang, G.M. Choi / Solid State Ionics 154 – 155 (2002) 481–486
blocking electrode can be calculated from the applied voltage and Nernst equation: E¼
POrev2 RT ln block 4F PO2 POrev2
POblock 2
ð4Þ
and are the oxygen partial pressures where at the reversible electrode and the blocking electrode, respectively. From the partial electronic conductivities obtained by Eq. (3) and the oxygen pressures corresponding to the applied voltages, the PO2 dependence of the partial electronic conductivity can be estimated. In this work, the partial electronic conductivities were calculated from the derivatives of the fitted results for Hebb – Wagner data shown in Fig. 1. To get clear view of the PO2 dependence, many data points of the fitted results were plotted. The partial electronic conductivities at PO2 = 0.21 atm are the experimental values obtained by fitting the Hebb –Wagner curve using Eq. (3). For the comparison, the published data of YSZ [11] is also plotted which has the slope of 1/4 at high oxygen pressure region and 1/4 at low oxygen pressure region. Both the hole and electron conductivities are one to two orders of magnitude higher than those of zirconia. The conductivity minima for LSGM9191 sample also shift toward high PO2 side with increasing temperature, however, with much lower rate than that for YSZ. Although the oxygen ion conductivities of three LSGM samples are higher than that of zirconia, the increase in the electronic conductivity is more than that in the ionic conductivity. Thus, the higher electronic transference numbers in LSGM samples than that in zirconia were resulted. When the oxygen partial pressure dependence of the electronic conductivities are compared among three samples, it is noted that the curves shift to the left and downward as more Sr2 + and Mg2 + are added. The shift is quite apparent at 750 jC, as shown in Fig. 4. This leftward shift may indicate that LSGM supports the defect model that the increasing amount of acceptors moves the log rel versus log PO2 curve to the low PO2 side, as shown, e.g. for BaTiO3 [13]. From the downward movement of the curves, it can be anticipated that the decreased hole conductivity was caused by the increased thermal band-gap energy. The rmin in Fig. 4 is defined as the conductivity where the hole and electron conductivities are equal.
485
Since the hole and the electron conductivities are expressed as rh = pelh and re = nele, respectively, rmin can be related to the thermal band-gap energy (Eg) as the following equations [14]: np ¼ r2min =ð4e2 le lh Þ ¼ NC NV exp½Eg =kT
ð5Þ
rmin ¼ 2eðle lh NC NV Þ1=2 exp½Eg =2kT
ð6Þ
where n and p are the electron and the hole concentrations, le and lh are the electron and the hole mobilities and NC and NV are the effective density of states in conduction and valence band, respectively. On the assumption that the pre-exponential term in Eq. (6) is independent of temperature, the thermal band-gap energy (Eg) can be obtained from the slope of the fitting curve in log rmin versus 1/T plot (Fig. 5) [14]. The temperature dependence of the pre-exponential term can be neglected if the band gap is large. For the acoustic phonon scattering, the mobility term and the effective density of states term also cancels each other [14]. The calculated thermal band-gap
Fig. 5. log rmin values were plotted against 1/T. The calculated thermal band-gap energies (Eg) were shown. The possible sources of error in estimating Eg values were discussed in the text. The value for YSZ [11] is also shown for comparison.
486
J.H. Jang, G.M. Choi / Solid State Ionics 154 – 155 (2002) 481–486
energies are indicated in Fig. 5 with that of YSZ for the comparison. The result shows a large variation in Eg, i.e., 2.35 –4.28 eV. YSZ has the higher band-gap energy than any LSGM compositions, explaining its low electronic conductivity. The observed variation in Eg is too large for the material with the change in acceptor concentration only. There are two possible explanations for the variation or error. When we look at the data points more carefully, LSGM9191 has more data points and less scattering than those for other two compositions, leading to more accurate Eg value. The larger Eg values obtained from the scattered data points for two other compositions may be due to the inherent inaccuracy in obtaining Eg values from the small number of Hebb – Wagner curves. The extra source of error or discrepancy may come from the inadequate assumption of temperature-independent pre-exponential factor in Eq. (6). For example, small polaron conduction is highly thermally activated and thus adds to the error in estimating Eg. In summary, although Eg value for LSGM samples was estimated as f 3 eV (approximate average of three Eg values) from the fitting of Hebb –Wagner curves, more study is necessary to reduce error in estimation.
4. Conclusion The partial electronic conductivity of LSGM9191, LSGM8282 and LSGM9182 were investigated by ion-blocking measurement. As the Sr and Mg content increases, both the hole and the electron conductivity decrease together with the increased activation energy of conduction. The electronic transference numbers of the three compositions were approximately 10 2 – 10 3, much larger than that of zirconia. In addition, the curves in log rel versus log PO2 plot shift to the low PO2 side, supporting the defect model containing
the oxygen vacancies generated by acceptor doping. As far as the partial electronic conductivities are concerned, LSGM8282 is the most suitable as the solid electrolyte for SOFC. However, the partial electronic conductivities of all LSGM samples are still much higher than that of YSZ.
Acknowledgements This paper is supported by POSCO, Korea.
References [1] S. Geller, Solid Electrolytes, Springer-Verlag, Heidelberg, Germany, 1977, pp. 143 – 168, 207 – 210. [2] T. Ishihara, H. Matsuda, Y. Takita, J. Am. Chem. Soc. 116 (1994) 3801. [3] J. Drennan, V. Zelizko, D. Hay, F.T. Ciacchi, S. Rajendran, S.P.S. Badwal, J. Mater. Chem. 7 (1997) 79. [4] N.M. Sammes, F.M. Keppeler, H. Na¨fe, F. Aldinger, J. Am. Ceram. Soc. 81 (1998) 3104. [5] K. Yamaji, T. Horita, M. Ishikawa, N. Sakai, H. Yokokawa, Solid State Ionics 121 (1999) 217. [6] S. Schmidt, F. Berckemeyer, W. Weppner, Ionics 6 (2000) 139. [7] T. Ishihara, H. Matsuda, Y. Takita, Solid State Ionics 79 (1995) 147. [8] J.W. Stevenson, T.R. Armstrong, L.R. Pederson, J. Li, C.A. Lewinsohn, S. Baskaran, Solid State Ionics 113 – 115 (1998) 571. [9] M.H. Hebb, J. Chem. Phys. 20 (1952) 185. [10] J.H. Kim, H.I. Yoo, Solid State Ionics 140 (2001) 105. [11] J.H. Park, R.N. Blumenthal, J. Electrochem. Soc. 136 (1989) 2867. [12] O.T. Sørensen, Nonstoichiometric Oxides, Academic Press, New York, 1981, p. 312. [13] N.H. Chan, R.K. Sharma, D.M. Smyth, J. Am. Ceram. Soc. 64 (1981) 556. [14] G.M. Choi, H.L. Tuller, D. Goldschmidt, Phys. Rev. B 34 (1989) 6972.
Partial electronic conductivity of Sr and Mg doped LaGaO3 Jin Ho Jang, Gyeong Man Choi * Department of Materials Science and Engineering, Pohang University of Science and Technology, San 31, Hyoja-dong, Namku, Pohang 790-784, South Korea Accepted 14 March 2002
Abstract The partial electronic conductivities (rel) of La0.9Sr0.1Ga0.9Mg0.1O2.90 (LSGM9191), La0.9Sr0.1Ga0.8Mg0.2O2.85 (LSGM9182) and La0.8Sr0.2Ga0.8Mg0.2O2.80 (LSGM8282) were measured by Hebb – Wagner ion-blocking method between 700 and 900 jC. As the Sr and Mg content increases, both the hole and the electron conductivity decrease together with the increasing activation energy of conduction. The electronic transference numbers of the three compositions were approximately 10 2 f 10 3, much larger than that of zirconia. From the Hebb – Wagner curves, the variation of rel was obtained as a function of oxygen partial pressure ( PO2). The thermal band-gap energy (Eg) value was estimated from the conductivity minima. The possible sources of error in estimating Eg were discussed. Eg value was much smaller than that of yttria-stabilized zirconia (YSZ). D 2002 Elsevier Science B.V. All rights reserved. Keywords: Ion-blocking; Hebb – Wagener method; LaGaO3; Electronic conductivity
1. Introduction The application of solid oxide electrolytes includes solid oxide fuel cell (SOFC), oxygen probes or sensors, gas-separating membranes, etc. [1]. A typical solid oxide electrolyte is a stabilized zirconia with cubic fluorite structure to which doped CeO2 and ThO2 also belong. Ever since the introduction of a new perovskite-structured solid oxide electrolyte, the Sr and Mg doped LaGaO3 (LSGM) has attracted great interest of researchers who are in search of the solid
*
Corresponding author. Tel.: +82-54-279-2146; fax: +82-54279-2399. E-mail address: [email protected] (G.M. Choi).
electrolytes for the intermediate temperature SOFC [2]. In spite of the promising aspects of LSGM, this material has several drawbacks, such as the high cost of gallium oxide, relatively weak mechanical strength [3,4] and the chemical stability problem under highly reducing conditions at high temperatures [5,6]. Another possible problem is a nonnegligible partial electronic conductivity. Although other authors also have reported the electronic conductivities of LSGM [6 –8], the basic information such as the activation energy, thermal band-gap energy and the effects of composition on the electronic conduction properties is still lacking. The main object of this study is to examine the effect of the acceptor concentration on the partial electronic
0167-2738/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 2 7 3 8 ( 0 2 ) 0 0 4 8 6 - 1
482
J.H. Jang, G.M. Choi / Solid State Ionics 154 – 155 (2002) 481–486
conductivity of LSGM. The ion-blocking Hebb –Wagner polarization method was employed.
2. Experimental procedure Conventional solid-state reaction method was used to synthesize Sr and Mg doped LaGaO3 (La1 xSrx Ga1 yMgyO3) where Sr2 + and Mg2 + content varying from 10 to 20 mol% (x = 0.1 – 0.2 and y = 0.1 –0.2). Three compositions were prepared, i.e., La 0.9 Sr0.1Ga0.9Mg0.1O 2.90(LSGM9191), La0.9Sr 0.1Ga0.8 Mg 0 . 2 O 2 . 8 5 (LSGM9182) and La 0 . 8 Sr 0 . 2 Ga 0 . 8 Mg0.2O2.80 (LSGM8282). The starting materials were La 2 O 3 (99.99%, GFS Chemicals, USA), SrCO 3 (99.9%, High purity Chemicals, Japan), Ga 2 O 3 (99.9%, High purity Chemicals) and MgO (99.9%, High purity Chemicals) powders. After La2O3 and MgO were fired at 1000 jC for 3 h to remove possible hydroxides and carbonates, required amounts of each powders were mixed by ball-milling with zirconia balls in ethanol for 12 h. Mixed slurry was dried, ground and calcined at 1200 jC for 6 h in air. The calcined powders were pulverized and die-pressed into pellets, followed by cold isostatic pressing at 200 MPa. Pressed pellets were sintered at 1450 jC for 6 h in air. X-ray diffraction experiment was carried out for phase characterization (XRD, MAC Science, M18XCE, Japan). The microstructure of sintered LSGM samples were observed using SEM (HITACHI, Japan). Hebb – Wagner polarization method was employed to measure the partial electronic conductivity (rel): hole conductivity (rh) and electron conductivity (re) [9]. The cell can be represented by the following configuration. ðþÞPtðreversibleÞ; airALSGM discAPtðblockingÞðÞ ð1Þ Sintered pellets of LSGM were sliced into discs with the diameter of 18 mm and the thickness varying from 0.5 to 1 mm. Pt paste (Engelhard model #6926, USA) was painted on the reversible side of the specimen followed by heat treatment at 1000 jC for 1 h. Pt-mesh (diameter of 7 mm) was attached on top of the painted Pt paste as a current collector. As a
blocking electrode, Pt paste (Engelhard model #6082, USA) and Pt foil were used. Pyrex glass crushed and mixed with water was used for sealing. Constant voltage was applied from 0.1 to 1.5 V with the step of 0.1 V (HP 4140B, Japan). The steady-state current (Iel) versus the applied voltage (Eappl) was recorded as a function of temperature (700 – 920 jC) in air.
3. Results and discussion XRD results showed trace amount of LaSrGaO4 and LaSrGa3O7 peaks in LSGM8282, whereas only LaSrGa3O7 peaks in LSGM9191. There was an extra peak in both LSGM9182 and LSGM9191 due to their slightly distorted cubic structure. The SEM microstructures of the three LSGM samples showed that the grain size of LSGM8282 is the largest (10.4 Am), while that of LSGM9191 is the smallest (1.4 Am). The grain size of LSGM9182 was 2.7 Am. The relative sintered densities of all samples were greater than 99%. The typical shape of Hebb –Wagner curve was shown for LSGM9191 as a function of temperature in Fig. 1. The partial electronic conductivity was obtained by nonlinear curve fitting of the Iel versus Eappl data with the following Hebb –Wagner equation: FEappl Iel LF o ¼ rh 1 exp ART RL FEappl o þ re exp 1 RL
ð2Þ
where rjh and rj, e respectively, are the hole and the electron conductivity at the reversible electrode. A is the area of the electrode and L, the thickness of the specimen. R, T and F have their usual meanings. The y-axis was modified to compensate the different sample dimensions for three samples. When the Hebb – Wagner curves were measured at or above 900 jC for LSGM9182 and LSGM8282, irreproducible curves were obtained possibly due to sample decomposition. LSGM9191 was the most stable among three samples. Another interesting feature is that the plateaus of LSGM9191 curves are narrower than those of LSGM9182 and LSGM8282. This
J.H. Jang, G.M. Choi / Solid State Ionics 154 – 155 (2002) 481–486
483
When the hole conductivity is divided by the ionic conductivity which varies small among three samples, the electronic (mostly by holes) transference numbers (tel) are obtained. The tel values for all three samples vary between 10 2 and 10 3 at 700 –900 jC, much larger than that ( f 10 4 at 800 jC) of yttria-stabilized zirconia (YSZ) [11]. Fig. 3 shows the oxygen partial pressure dependence of the partial electronic conductivity (rel = rh + re) for LSGM9191. Under complete ion-blocking condition, the steady state current (Iel) and applied voltage (E) satisfy the relation: rblock ¼ el
Fig. 1. Hebb – Wagner curves of LSGM9191 sample varying with temperatures between 700 and 900 jC. Air was used as the reference PO2. The y-axis was modified to accommodate the difference in the sample dimension.
difference in the width of the plateaus predicts the higher electronic contribution to the conduction of LSGM9191 than other two compositions as will be discussed later. Fig. 2 compares the hole and electron conductivities of the three compositions in air, obtained by fitting the Hebb – Wagner curves by Eq. (2). As seen in the figure, the hole conductivity difference among three samples is small, whereas the lowest activation energy and thus the highest electron conductivity is shown for LSGM9191 at all temperatures. LSGM8282 marked the lowest electron conductivity below 850 jC. The trend is that adding more dopants increases the activation energy for electron conduction. The hole conductivity data measured by Schmidt et al. [6] and Kim and Yoo [10] through Hebb – Wagner experiment is also plotted in Fig. 2. The comparison reveals that our activation energy and hole conductivity of LSGM9182 are lower than Schmidt et al.’s values. However, the magnitude of electron hole conductivity is in good agreement with Kim and Yoo’s result [10]. For the electron conductivity, both the activation energy and the magnitude show a large discrepancy between our data and Kim and Yoo’s result.
L BIel A BE E
ð3Þ
where relblock is the partial electronic conductivity (rh + re) at the blocking electrode under a constant voltage [12]. The oxygen partial pressure at the
Fig. 2. The hole (rh) and electron (re) conductivities of the three LSGM compositions in air. Sample compositions and their activation energies are shown. Open circles represent the LSGM9191, squares for LSGM9182 and closed circles for LSGM8282. The data obtained in other study (up triangles for Ref. [6], down triangles for Ref. [10]) for LSGM9182 are also shown for the comparison.
484
J.H. Jang, G.M. Choi / Solid State Ionics 154 – 155 (2002) 481–486
Fig. 3. The PO2 dependence of the partial electronic conductivities of LSGM9191 composition calculated by using the fitted Hebb – Wagner curves. The partial electronic conductivity of YSZ [11] is also shown for the comparison.
Fig. 4. log r versus log PO2 for the three LSGM compositions (8282, 9182 and 9191) at 750 jC.
J.H. Jang, G.M. Choi / Solid State Ionics 154 – 155 (2002) 481–486
blocking electrode can be calculated from the applied voltage and Nernst equation: E¼
POrev2 RT ln block 4F PO2 POrev2
POblock 2
ð4Þ
and are the oxygen partial pressures where at the reversible electrode and the blocking electrode, respectively. From the partial electronic conductivities obtained by Eq. (3) and the oxygen pressures corresponding to the applied voltages, the PO2 dependence of the partial electronic conductivity can be estimated. In this work, the partial electronic conductivities were calculated from the derivatives of the fitted results for Hebb – Wagner data shown in Fig. 1. To get clear view of the PO2 dependence, many data points of the fitted results were plotted. The partial electronic conductivities at PO2 = 0.21 atm are the experimental values obtained by fitting the Hebb –Wagner curve using Eq. (3). For the comparison, the published data of YSZ [11] is also plotted which has the slope of 1/4 at high oxygen pressure region and 1/4 at low oxygen pressure region. Both the hole and electron conductivities are one to two orders of magnitude higher than those of zirconia. The conductivity minima for LSGM9191 sample also shift toward high PO2 side with increasing temperature, however, with much lower rate than that for YSZ. Although the oxygen ion conductivities of three LSGM samples are higher than that of zirconia, the increase in the electronic conductivity is more than that in the ionic conductivity. Thus, the higher electronic transference numbers in LSGM samples than that in zirconia were resulted. When the oxygen partial pressure dependence of the electronic conductivities are compared among three samples, it is noted that the curves shift to the left and downward as more Sr2 + and Mg2 + are added. The shift is quite apparent at 750 jC, as shown in Fig. 4. This leftward shift may indicate that LSGM supports the defect model that the increasing amount of acceptors moves the log rel versus log PO2 curve to the low PO2 side, as shown, e.g. for BaTiO3 [13]. From the downward movement of the curves, it can be anticipated that the decreased hole conductivity was caused by the increased thermal band-gap energy. The rmin in Fig. 4 is defined as the conductivity where the hole and electron conductivities are equal.
485
Since the hole and the electron conductivities are expressed as rh = pelh and re = nele, respectively, rmin can be related to the thermal band-gap energy (Eg) as the following equations [14]: np ¼ r2min =ð4e2 le lh Þ ¼ NC NV exp½Eg =kT
ð5Þ
rmin ¼ 2eðle lh NC NV Þ1=2 exp½Eg =2kT
ð6Þ
where n and p are the electron and the hole concentrations, le and lh are the electron and the hole mobilities and NC and NV are the effective density of states in conduction and valence band, respectively. On the assumption that the pre-exponential term in Eq. (6) is independent of temperature, the thermal band-gap energy (Eg) can be obtained from the slope of the fitting curve in log rmin versus 1/T plot (Fig. 5) [14]. The temperature dependence of the pre-exponential term can be neglected if the band gap is large. For the acoustic phonon scattering, the mobility term and the effective density of states term also cancels each other [14]. The calculated thermal band-gap
Fig. 5. log rmin values were plotted against 1/T. The calculated thermal band-gap energies (Eg) were shown. The possible sources of error in estimating Eg values were discussed in the text. The value for YSZ [11] is also shown for comparison.
486
J.H. Jang, G.M. Choi / Solid State Ionics 154 – 155 (2002) 481–486
energies are indicated in Fig. 5 with that of YSZ for the comparison. The result shows a large variation in Eg, i.e., 2.35 –4.28 eV. YSZ has the higher band-gap energy than any LSGM compositions, explaining its low electronic conductivity. The observed variation in Eg is too large for the material with the change in acceptor concentration only. There are two possible explanations for the variation or error. When we look at the data points more carefully, LSGM9191 has more data points and less scattering than those for other two compositions, leading to more accurate Eg value. The larger Eg values obtained from the scattered data points for two other compositions may be due to the inherent inaccuracy in obtaining Eg values from the small number of Hebb – Wagner curves. The extra source of error or discrepancy may come from the inadequate assumption of temperature-independent pre-exponential factor in Eq. (6). For example, small polaron conduction is highly thermally activated and thus adds to the error in estimating Eg. In summary, although Eg value for LSGM samples was estimated as f 3 eV (approximate average of three Eg values) from the fitting of Hebb –Wagner curves, more study is necessary to reduce error in estimation.
4. Conclusion The partial electronic conductivity of LSGM9191, LSGM8282 and LSGM9182 were investigated by ion-blocking measurement. As the Sr and Mg content increases, both the hole and the electron conductivity decrease together with the increased activation energy of conduction. The electronic transference numbers of the three compositions were approximately 10 2 – 10 3, much larger than that of zirconia. In addition, the curves in log rel versus log PO2 plot shift to the low PO2 side, supporting the defect model containing
the oxygen vacancies generated by acceptor doping. As far as the partial electronic conductivities are concerned, LSGM8282 is the most suitable as the solid electrolyte for SOFC. However, the partial electronic conductivities of all LSGM samples are still much higher than that of YSZ.
Acknowledgements This paper is supported by POSCO, Korea.
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