作為固態氧化物燃料電池電解質的要求來看，離子導電性是決定工作溫度主要因素，因此本文主要探討共摻雜氧化鈰對導電性提升的機制。
針對氧化鈰基材料研究，添加不同價數的二價陽離子(Ca2+, Sr2+, Mg2+)與三價陽離子(Gd3+)共摻雜於氧化鈰基電解質當中。在計算二價陽離子與母相離子半徑差異，得出Mg2+/Ce4+ (-8.2%) 、Ca2+/Ce4+ (15%) 、Sr2+/Ce4+ (28.8%)，因為Mg離子半徑差異是負值，所產生的晶格應變機制不同於它兩個系統，且Mg溶解反應能又遠大於Ca與Sr，因此以下將分別探討三者電性表現。
Gadolinia doped ceria (GDC)添加Sr與Ca元素之系統電性比較，發現Ce0.78Gd0.2Sr0.02O1.88 較Ce0.78Gd0.2Ca0.02O1.88好，這與氧空缺半徑計算的結果相符合，於計算中 =1.0079 Å的確比 =1.0078 Å大，再加上Sr之lattice binding energy比Ca小的因素，因此結果是可預期的。在GDC摻雜Mg系統，雖然 =1.501 Å比其它兩系統大，但是因為Mg的lattice binding energy是三者中最大的，並且有晶界偏析的效應，這些因素均造成Mg 系統電性有下降情況，所以三者電性才會有Ce0.78Gd0.2Sr0.02O1.88 > Ce0.78Gd0.2Mg0.02O1.88> Ce0.78Gd0.2Ca0.02O1.88情形。由此可知共摻雜二價元素的lattice binding energy影響的效應比離子半徑來得大。
共摻雜氧化鈰的最佳電性結果(GDC摻雜Sr)，導電率在650℃時約0.019 (Scm-1) ，而Tosoh-8YSZ在800℃時導電率約0.014 (Scm-1) ，由此可知所以GDC共摻雜可使SOFC工作溫度從800℃降為600℃附近，這符合我們降低SOFC工作溫度的目標。
在顯微組織方面，GDC摻雜Sr和Ca系統中發現隨二價元素增加晶粒有成長趨勢，這可能是因為氧空缺量增多所以作為元素擴散的媒介也變多，為了進一步證明此一結果，將Sr系統的氧空缺固定在一定範圍內，結果發現隨著二價元素增加，晶粒成長趨勢的確有抑制，也說明氧空缺多寡是影響晶粒成長因素之一。而Ca系統與Sr同屬鹼金族，化性、物性相似，可預期也有相同情況，而Mg系統因本身固溶就低，所以晶粒不會有成長情況。
另外，針對氧化鈰基電解質在高溫低氧分壓情況下易還原的情形，在GDC基材上面披覆多層x wt % GDC+(100-x) wt % 8YSZ, x= 80 , 60, 40, 20 , 0的電解質層，用來解決還原問題。經由X-ray判定，GDC與8YSZ會相互固溶。另外從SEM Cross-section及X-ray mapping中發現，在斷面上已分不出有任何的層與層間的界面，X-ray mapping中也看出ZrO2有擴散到GDC基材情況。而在多層複合電解質的電性表現方面比300~600℃時較GDC差，但到溫度700℃以上卻比GDC佳，這主要是因為複合電解質晶界效應隨溫度增加而消失。在複合電解質活化能計算中，發現電性隨著x的量增多而有降低現象，而晶格常數也隨x增加會越來越大，表示晶格膨脹所造成的晶格扭曲會影響氧離子在晶格中的傳遞。

Ionic conductivity is a main characteristic for deciding the working temperature of SOFCs; for this reason, the theories of enhancing the electrical properties of ceria electrolyte was discussed in this paper.
The microstructural feature and ionic conductivity of divalent (Mg2+, Ca2+, Sr2+) and trivalent (Gd3+) cations co-doped ceria-based electrolyte were investigated and determined using scanning electron microscopy (SEM) and AC impedance spectroscopy. After calculating the ionic radius difference between Ce4+ and doped divalent cation (Mg2+, Ca2+, Sr2+), the ratio of Mg2+/Ce4+ (-8.2%) is a negative value and Ca2+/Ce4+ (15%) or Sr2+/Ce4+ (28.8%) are positive value; therefore, lattice deformation (lattice stress and lattice strain) of doped MgO in GDC is different from that of doped CaO or SrO in GDC. Besides, the solid solution reaction energy of MgO is higher than that of CaO and SrO, it is proved from the solid solution ratio of divalent oxide-ceria phase diagram. Summarize above two reasons, MgO doped GDC is a different topic from CaO doped GDC and SrO doped GDC.
Experimental results exhibit that the ionic conductivity of Ce0.78Gd0.2Sr0.02O1.88 is higher than that of Ce0.78Gd0.2Ca0.02O1.88, the ionic conductivity increases with an increase of oxygen vacancy radius ( =1.0079 Å> =1.0078 Å); not only that, the lattice binding energy of SrO lower than that of CaO is another proof to support this phenomenon. Although oxygen vacancy radius of Ce0.8-xGd0.2MgxO1.9-x ( =1.501 Å)is higher than that of Ce0.8-xGd0.2SrxO1.9-x and Ce0.8-xGd0.2CaxO1.9-x, but the lattice bonding energy is the highest and MgO segregated at grain boundaries was found, because the solid solution of MgO-CeO2 does not form easily. According to above statement we get two conclusions. First, the electrical properties of SrO doped GDC is the highest, MgO doped GDC is medium and CaO doped GDC is the worst. Second, the effect of lattice binding energy of divalent ions is more significant than that of ionic radius of divalent oxides for enhancing the ionic conductivity of ceria co-doping system.
From experiments, we find out SrO is the best divalent element doping into GDC. It’s ionic conductivity is 0.019 (Scm-1) when x=0.02 at 650℃, this is higher than that of Tosoh-8YSZ(0.014 Scm-1) at 800℃, so we could say ceria based co doped system make SOFC working temperature decrease near 600℃.
Grain growth was observed in Ce0.8-xGd0.2SrxO1.9-x and Ce0.8-xGd0.2CaxO1.9-x, and grain size increases with an increase of divalent cation content. This is possible the amount of defect diffusion path increases following the amount of oxygen vacancy increasing. For proving this mechanism, the amount of oxygen vacancy controlled around 11-15 mol% by fixing co-doped dopants content at 20 mol% in ceria and the result displays grain growth was restrained.
In order to overcome the reduction problem of ceria based electrolyte and resolve TEC problem, multi-layer of x wt% GDC+(100-x) wt% 8YSZ, wherein x=80,60, 40, 20, 0 on GDC bulk between 8YSZ and GDC was coated using screen printing. 8YSZ and GDC diffuse into each other in multi-layer was observed using x-ray mapping method. Notwithstanding, the ionic conductivity of multi-layer composite electrolyte is lower than that of GDC bulk at 300℃ to 600℃; the electrical property of multilayer composite electrolyte is higher than that of GDC above 700℃. It is explained that effect of grain boundary disappears with an increase of measured temperature. The ionic conductivity of x wt% GDC+(100-x) wt% 8YSZ, wherein x=80, 60, 40, 20, 0 was measured respectively and the activation energy was estimated. The result presents the ionic conductivity of x wt% GDC+(100-x) wt% 8YSZ is independent of the amount of GDC .

1.黃鎮江, ”燃料電池”, 全華科技圖書,中華民國九十二年十一月
2.M. sossina, Haile, “Fuel cell materials and components,” Acta materialia.,51, p5981-6000(2003).
3.Dufour A U., “Fuel cells-a new contributor to stationary power,” Journal of Power Sources, 71, p19-25(1998).
4.Fleig J., “Electrochemical reaction at electrode: mechanisms and modeling,”.
5.韓敏芬、彭蘇萍, ”固態氧化物燃料電池材料及製備,” 科學出版
(北京).
6.Stephen J. Skinner and John A. Kilner, “Oxygen ion conductors, ” Materials Today, Volume 6, Issue 3, p30-37(March 2003).
7.Hideaki Inaba, Hiroaki Tagawa, “Ceria-based solid electrolytes,” Solid State Ionics 83, p1-16 (1996).
8.J. Kaspar, P. Fornasiero, and M. Graziani, Catal. Today, 50, p285-298 (1999).
9.N. Izu, T. Omata and S. Otsuka-Yao-Matsuo, J. Alloys. Compds., 270, p107-114 (1998).
10.T. Omata, H. Kishimoto, S. Otsuka-Yao-Matsuo, N. Ohtori, and N. Umesaki, J. Solid State Chem., 147, p673-583 (1999).
11.D. J. M. Bevan and J. Kordis, J. Inorg. Nucl. Chem., 26, p1509-1523 (1964).
12.S. P. Ray, A. S. Nowick and D. E. Cox, J. Solid State Chem, 15, p344-351 (1975).
13. R. D. Shannon and C. T. Prewitt, Acta Cryst., B25, 925-1048 (1969).
14. Hidernori Yahiro, Tatsuya Ohuchi, Koichi Eguchi, Hiromichi Arai,
J. Mater. Sci., 23, p1036(1988).
15.Mogensen, M.; Lindegaard, T.; Hansen, U. R.; Mogensen, G., J. Electrochem. Soc., 141, 2112(1994).
16. H. Yahiro, K. Eguchi and H. Arai, Solid State lonics 36, p71(1989).
17.K. Eguchi, T. Setoguchi, T. Inoue and H. Arai, “Electrical properties of ceria-based oxides and their application to solid oxide fuel cells,” Solid State Ionics 52, p165-172 (1992).
18.H. Yahiro, T. Ohuchi, K. Eguchi and H. Arai, “Electrical Properties and microstructure in the System Ceria-alkaline Earth Oxide,” J. Mater. Sci., 23, p1036 (1988)
19.Zhang Tianshu, Peter Hing, Haitao Huang, J. Kilner, “Ionic conductivity in the CeO2–Gd2O3 system (0.05 Gd/Ce 0.4) prepared by oxalate coprecipitation”, Solid State Ionics 148, p567-573(2002).
20.D. J. Kim, “Lattice parameters, ionic conductivities, and solubility limits in fluorite-structure MO2 oxide (M = Hf4+, Zr4+, Ce4+, Th4+, U4+) solid solutions,”J. Am. Ceram. Soc. 72, p1415 (1989).
21.V. Butler, C. R. A. Catlow, B. E. F. Fender and J. H. Harding,” Dopant ion radius and ionic conductivity in cerium dioxide,” Solid State Ionics, 8, p109-113 (1983).
22.J. V. Herle, D. Seneviratne, A.J. McEvoy, ” Lanthanide co-doping of solid electrolytes: AC conductivity behaviour ,” J. Eur. Ceram. Soc. 19, p837-841 (1999).
23.G J K Acres,J C Frost,G A Hards,R J Potter,T R Ralph,D Thompsett,G T Burstein,G J Hutchings,“Electrocatalysts for fuel cells,” Catalysis Today, p383-400（1997）.
24.H. Yoshida, T. Inagaki, K. Miura, M. Inaba, Z. Ogumi, “Density functional theory calculation on the effect of local structure of doped ceria on ionic conductivity ,”Solid State Ionics 160, p109-116 (2003).
25.H. Yoshida, H. Deguchi, K. Miura, M. Horiuchi, “Investigation of the relationship between the ionic conductivity and the local structures of singlyand doubly doped ceria compounds using EXAFS measurement ,” Solid State Ionics 140, p191-199 (2001).
26.H. Yamamura, E. Katoh, M. Ichikawa, K. Kakinuma, T. Mori, H.
Haneda, “Multiple doping effect on the electrical conductivity in the
(Ce1-x-yLaxMy)O2-d (M = Ca, Sr) system,” Electrochemistry 68, 455
(2000).
27.F. Y. Wang, S. Chen and S. Cheng, “Gd3+ and Sm3+ co-doped ceria
based electrolytes for intermediate temperature solid oxide fuel cells”, Electrochemistry Communications, 6, p743–746 (2004).
28.S. Lubke, H.-D. Wiemhofer, “Electronic conductivity of Gd-doped
ceria with additional Pr-doping” Solid State Ionics 117, p229-243(1999).
29.N. Kim., B.-H. Kim, D. Lee, “Effect of co-dopant addition on
properties of gadolinia-doped ceria electrolyte” Journal of Power
Source 90, p139-143(2000).
30.F. Y. Wang, S. Chen, Q. Wang, S. Yu, S. Cheng, “Study on Gd and Mg co-doped ceria electrolyte for intermediate temperature solid oxide fuel cells” Catalysis Today 97,p189-194 (2004).
31.H. Yahiro, K. Eguchi and H. Arai, ” Electrical properties and reducibilities of ceria-rare earth oxide systems and their application to solid oxide fuel cell ,” Solid State Ionics 36 (1989).
32.H. Yahiro, K. Eguchi and H. Arai, ”Ionic conduction and microstructure of the ceria-strontia system,” Solid State Ionics 21 (1986).
33.H. Yahiro, K. Eguchi and H. Arai, ”Electrical properties of calcia-doped ceria with oxygen ion conduction,” Solid State Ionics 20 (1986).
34.T. Inoue, T. Setoguchi, K.Eguchi and H. Arai, ” Study of a solid oxide fuel cell with a ceria-based solid electrolyte,” Solid State Ionics 35 (1989).
35.H. Yahiro, Y. Baba, K. Eguchi, H. Arai, ” High Temperature Fuel Cell with Ceria-Yttria Solid Electrolyte,” J. Elctrochem. Soc., p135(1988).
36.K. Eguchi, ” Ceramic materials containing rare earth oxides for solid oxide fuel cell,” Journal of Alloys and Compounds, 250, (1-2) (1997).
37.K. Eguchi, T. Setoguchi, T. Inoue and H. Arai, ”Electrical properties of ceria-based oxides and their application to solid oxide fuel cell,” Solid State Ionics 52 (1992)
38.Tompsett, G. A., Sammes, N. M., Yamamoto, O., ”Ceria-yttria-stabilized zirconia composite ceramic system for application as low-temperature electrolytes. Journal of the American Ceramic Society, 80, (12)( 1997).
39.Dokiya, M., Second Internation Meeting of Pacific Rim Ceramics Societies, Cairns, Australia (1996).
40. Lide and David, “CRC Handbook of Chemistry and Physics: Ed. 71”, Boca Raton: CRC Press, (1990).
41.Z. F. MA, G. C. LIANG, J. S. LIANG, “Crystal Defect Behaviors in CeO2-based Electrolyte Doped with Alkaline Earth Oxides,” Acta Phys. –Chim. Sin., 21(6) (2005).
42.Hidenori Yahiro, Koichi Eguchi and Hiromichi Arai, ” Ionic conduction and microstructure of the ceria-strontia system,” Solid State Ionics 21 (1986)
43.E. D. Wachsman, “Effect of oxygen sub-lattice order on conductivity in highly defective fluorite oxides,” J. Eur. Ceram. Soc., 24, p1281–1285 (2004).
44.H. Yamamura, E. Katoh, M. Ichikawa, K. Kakinuma, T. Mori, H. Haneda, “Multiple doping effect on the electrical conductivity in the (Ce1-x-yLaxMy)O2-d (M = Ca, Sr) system,” Electrochemistry 68, p455 (2000).
45.Robert S. Roth, Taki Negas, and Lawrence P. Cook, “Phase diagrams for ceramics,” The American Ceramic Society, inc, Volume IV, p220 Fig. 5418 (1981).
46.Hong, S. J. and Virkar, A. V., Lattice parameters and densities of rare-earth oxide doped ceria electrolytes. J. Am. Ceram. Soc., 78, p433–439 (1995).
47.N.Q. Minh, J. Am. Ceram. Soc. 76 (1993)
48.F. Tietz, Ionics 5, p129(1999).
49.Hideko Hayashi, Mariko Kanoh, Chang Ji Quan, Hideaki Inaba, Shaorong Wang, Masayuki Dokiya, Hiroaki Tagawa, ” Thermal expansion of Gd-doped ceria and reduced ceria,” Solid State Ionics 132 (2000).
50.F. Meschke, R.W. Steinbrech, in: M. Dokiya, S.C. Singhal (Eds.), Proc. 6th Int. Symp. Solid Oxide Fuel Cells, PV 99-19, The Electrochem. Soc., Pennington, NJ, 1999, p1047.
51.R. Vassen, R.W. Steinbrech, F. Tietz, D. Sto¨ver, in: P. Stevens (Ed.), Proc. 3rd Eur. SOFC Forum, Oberrohrdorf, Switzerland, 1998, p. 557.
52.Pol Duwez and Francis Odell, J. Am. Ceram. Soc., 33 [9] 280 (1950).
53.Tsoga, A., Gupta, A., Naoumidis, A., Skarmoutsos, D. and
Nikolopoulos, P., Ionics, 1999, 4, 234.
54.Tsoga, A., Naoumidis, A., Gupta, A. and Sto¨ver, D., Materials Science Forum 1999, 308–311, 794
55.A. Tsoga, A. Naoumidis, W. Jungen and D. StoÈ ver, “Processing and Characterisation of Fine Crystalline Ceria Gadolinia-Yttria Stabilized Zirconia Powder,” J. Eurpo. Ceram. Soc 19 , 907-912 (1999).