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(1)maixgmkncnjeFkeif 21: 203-226. (l995). me M IIIIIIIHIIIillHII[lili[lililllll. iI:i.iii,i,. iSitpmastsft4ttzwt)kil. ie ite M di tufgtiE, fi¥ ffQ pt. Solid Electrolytes for IV{edium - Temperature. Solid Oxide Fuel Cells e. Hideaki INABA' and Hiroaki TAGAwA" *PH'% ;EIE!Jl '･ EEIJII. iiEIIiliSi**. Abstract Fluorite oxide solid elec￡rolytes with emphasis of doped ceria are reviewed in terms. ofelectricalconductivity,diffusivityandtransferencenumber, Theeiectricalconductivity and diffusion consiant ofvarious fluoyite compounds are compared and those of. ceria"basedoxidesarealmostthehighestamongthesefluoriteoxides. Thee}ectrica] conductivity of doped ceria is much dependent of the kind and the concentration of dopants, The reason for this behavior is qualitatively given as due to the defects asso-. ciate between dopantcations and oxygen vacancies and the comparison between the theory and the experiment is presented. In order to decrease the activation energy in. theelectrica}conductivityofdopedceria,itissuggestedthatthedopantcat2onwiththe critical radius, which is about O. Ill and O. 104 nm for di - valent and tri - valent cations, respectively, is desirable to choose, The effect ofsample preparation on the. electricalconductivityisdescribedintermsofthecharacterofrawmaterials,irnpurities and the sintering condition. The factors to determine the transference nurnber and. the methods to increase the transference number at low oxygen pressures are also described.. 1. Introduction. Solid electro}ytes have received increasing attention in recent years due to their excellent. The enviromental problems such as the. suitability as ionically conductive materials in. increase in carbon dioxide in the atmosphere,. high temperature systems, such as solid oxide. acid rain and the destrttction of forests and the. fuel cells or oxygen sensors, Solid e}ectrolytes. contamination of seas and rivers are resulted. with the fluorite structure have been extensively. from the Iarge amount of energy consumption,. investigated and reviewed by Steele (1), Kilner. In order to solve the enviromental problems, it. and Steele (2), Sasaki (3) and De}1 and Hooper. is neeessary to maintain or decrease the total. (4). Among them, yttria-stabilized zirconia. energy consumption. To develop the efficient. with the cubic fluorite structure has been the. systems of electric power generatlon is the. most extensively investigated and practically. urgent problem in order to save energy con-. used.. sumption. Solidoxidefuelcellisoneoftheimportant candidate of them.. The operating temperature for the solid oxide. fuel cells using yttria - stabilized zircoRia. uezagvrteewanj*op#aszzla 7v -rcagtutw# (ueiji*,vs-*i*) ewzzs * }{Eideaki Inaba, Technical Research Laboratories, Kawasaki Steel Corporation, Guest Professor of the present IBstitute. * *Hiroaki Tagawa, Department of Environmental Energy Science, Institute of Environmental Science and Technology,. Yokohama National University, Yokohama, 240. (1994ff10n30-Xth).

(2) 204. usually taken as 1273K. It has been thought. considered. CI"hee}ectricalcoRductivity includ-. that 1273K is too hlgh as the operating tempera-. ing these oxides are shown in Fig. 1 accordlng to. ture of solid oxide fuel cells, because many in-. Steele (1). It ls seen from the figure that Bi203. terface reactions such as electrode/solid electrolyte, electrode /interconnector and. and yttria- stabilized Bi203 are most electri-. interconnector/solid electrolyte would cause. easily reduced and evaporated under reductive. the deerease ofthe efficiency and the stab"ity of. atmospheres and they are not suitable for the. cally conductive. However, these oxides are. the cells. The alternative so}id electrolyte for. e}ectro}ytesfortheso}idoxidefuelce}ls. Thus. yttrla - stab21ized zirconia has been awaited,. ￠eria - based electrolytes have collected rnuch. which has the higher electric conductivity than. attention for the alternative of the yttyia - stabil. that of yttria - stabi}ized zirconia with high. ized zirconia as the electrolyte ofthe solid oxide. ionic transference nttmber and enables us to use. fuelcell, As seeninFig.1,electricalconduc-. at medium temperatures such a$ 1073K.. tivity of gad12Ria - stabilized ceria is about one. As the candidate for the alterRative electro-. order of rnagnitude larger than that of yttria -. Iyte, Bi203 and ceria - based electrolytes may be. stabi}ized zirconia and it ls about O. 1 Scm-' at. e.. T/ ℃ 1200 1100 1000 900. 800. 700. 600. 500. 0N&,q. o. te3 9(bjs lill,`.k,o,, ke(8?C.)'t`xX'll,,. fe"O. -1 T. E. .o.. is -2. (gl} {li, 9k'3.....(2;(iJn k..afo9?gyo.. oo J. r(9h. o. qqs. ig9. -3. k. -4 O.6. O.7 O.8 0.9 1.0 1.1 1.2 KK/T Fig.1 Electrical conductivity offluorite oxides (1). 1.3.

(3) 205 1073K, It is noted, however, that ceria-based. p}otted as shown in Fig.2, where the contribu-. oxides are a}so reduced to give electron!c con-. tions due to the bulk, grain boundaries and elec-. duceion under reductive atmospheres. The. trodes are separated.. magnitude ofelectrical conductivity and the sta-. 2.2 Measurement of Ionic Transference. Number. bility under reductive atrnospheres for ceria -. based oxides are greatly dependent on the the. The oxygen concentration cell, such as,. kind and amount of doping elements, which. P02, Pt E}ectrodef(Solid Electrolyte)/Pt. E}ectrode, P'02 (1). have been critica}ly reviewed here.. ls usuaily used to obtain the ionic transference. e. number ofsolid electrolytes as functions of tem-. 2. Experimental Aspeets. perature and oxygen partia! pressure. The. 2.I MeasurementofElectriealConduetivity. theoretical e.m.f. ofthe cell is given by. Eth,.,=(RT/4F)In(P'02/P02), (2). Historical}y measurements of the electrical conductivity have been made using dc four- pro-. where R is gas constant, T the absolute tempera-. ve method on sintered ceramic samples. This. ture and F Faraday's constant. [Iihe ionic. can lead to errors because of effects due to the. transference number ti is given by. ti nErneas/Etheer. (3). grain boundaries and electrodes, which may. maskthetruebehaviorofthebulk. Thisuncertaintycanberemovedbythe'useofthecomplex. where Em.., is the observed open circuit e.m.f.. plane impedance analysis (1, 2). In this method,. side of oxygen pressuye (say P O2) is fixed as air. the complex impedance Z of a specimen ls. and the e,m.f. is obtained as a function of P'02.. forthecell. Inthepracticalexperiment,theone. Re. Rgb. Rgi '. '. Cgi. f A E -= o vN. C gb. Ce. fe. frequency. f9i. fgb. :. l`"""'"-"-'--' Rgi -"---"ptF"'---' Rgb-""-pt-"'-'---"-""--' Re -. Z'(ohm) --Fig.. 2Idealizedequivalentcircuit(a)andcompleximpedancediagram for a two phase cerami￠ electrolyte (b), Rgi, Rgb and R. denote. theelectricalresistivityduetothebulk,grainboundaryandelectrode, respectively (1, 2)..

(4) 206. dependence of the electrical conductivity a of. 3. Theoretical aspects. doped fluorite oxides has been empirically. 3.l Temperature dependenee of electrical. written as the fol}owing equationi. ffT ==A exp (- Ea/kT), (4). conductivity Oxides with high ionic conductivity have open. where A is a pre - exponential factor and E. is. structure,such as fluorite and pyyochlore. The. ' the activation eneygy of e}ectrical conduction.. ideal {'luorit.e st.ructure is shown in Fig. 3 (2).. The ionic conductivity is given by the sttm of the. products of the concentration ni and the mobi}ity pt,of charge carriers with charge qi,. t. a"2niqi #, (5) i. In the case of oxygen - ionic conductors, the. 1. 11. conduction occurs via anion vacancies, so that. cili$). 1. 11 N. Uv := Cv qv "v, (6) where the subscript v means anion vacancy and. Cv is the number of anion vacancies per unit volume (cm3). According to the Nernst- Einst,.. 1. e. ein relation, the mobUity is described w2th the. Xr. u=" qB == qD/kT, (7). t. where B is absolute mobility. The diffusivity D. t. corresponding diffusivity,. ls written as. D " a2vo exp (ASm/k) exp (' AHm/kT),. O o2-toN. e Hosr cArtoNr4.). (8) where a isjump distance ofa vacancy, vo is an. appropriate lattice vibration frequency and. OvacANcr gDOFZ,lilg.,C,A,TiON. ASrnandAH.aretheactivationentropyandactivation enthalpy of diffusion, respectively,. Fig.3 A ha}f unit cell ofthe fluorite structure. sho"Jing the position of dopant cation ' oxygen vacancy associate (2),. Since Cv is represented as:. Cv=:[Vo]{1'[Vo]}Ne, (9) where No is the number of oxygen sites per unit volume, the following equations can be obtained. This structure is relative}y open and lt shows. }arge to}erance for high levels of atornic disorder, which may be introduced either by. doping,reductionoroxidation. Ofthebinary. using Eqs. (6), (7) and (8).. aT==A'[Vo]{1-[Vo]}exp(-AH./kT), (10). A'==(4e2/k)a2voN.exp(ASm/k). (ll). oxides, Th02, Ce02, Pr02, U02 and Pu02. For smal} values of [Vo], Eq, (10) can be ap-. possess this structure in the pure state. Zr02. proximatedas '. and Hf02 are stabilized to the fluorite structure. b.v- doping with divalent or trivalentoxide, The. aT=A'[Vo]exp(-ALHm/kT). (12). The temperature dependence of the electrical. addition ofsuch dopants to these fluorlte oxides. conductivity of doped fluorite oxides, however,. gix,'es rise to the creation of oxygen vacancies,. cannot be expressed by a single exponeRtial. whichareresponsiblefortheionicconductionin. function shown in Eqs. (4), (10) or (12). The. these oxides.. actual temperature dependence of the electrical. The theory of elect.rical conduction has been. conductivity in general is schematically shown. described by Kilner and Steel (2) and Sasaki (3). tn Flg.4 according to Ki}ner and Walters (5) ,. and it is summarized here. The temperatgre. where three regions can be seen. In region I,.

(5) 207. (Cax;`Vo'')X=Cat;-Vo''. (13) App}yingthela"Jofmassactiontothisequation gives ge]aSl][Vo '']/ [(Cak` Vfi '' ]X] :=: KAL, (7i).. (14). F. 9. Substituting the eleetricaliy neutral conclition in. g. J. the }attice: [ Vo "] = [Ca`M], Eq. (14) is. th. [v,'']2=l(CatsVo'']X]KA2(T). (l5). Reciptocdtempevatvre tfT. Fig.4 A schematlc representation of the conductivity behavior of an oxide ionic con" ductor (2),. For fuH assoeSation ol' defects, [( Calf` V," )Xi>> [ v, ''],. [( cat;, v, '' )X]=c,,, (16). which is appeared at high temperatures, the. where CM is the total dopant concentration ex-. electrica}conductionisdeteyminedbytheintrin-. pressed as a site fraction of the cation sit.e,. sic defects (Schottky or Frenkel) in the crystal.. This means that "･'hen no diss()ciation occurs all. In region ll, electrical conduction ls con-. the dopantcations are bouRd to ox.vgen vacan-. tyolled by the population of charge carrying. cies. rl"he equilibrium constant KA2 can be. defects determined by an aliovalent dopant or. expanded as. impttrity. In region M, the popu}ation of. KA2 : (1/VXJ) exp (ASA2/lc) exp (- A I'Lx2/kT),. (17). charge carrying defects is determined by the. thermodynamic equilibrium between the free. where XitJ' is the number of orientations ofthe as-. defects and the associated pairs, Since doped. sociate and A SA2 and tx I'IA2 are theentropy and. fJuoriSe oxides have a large number of oxygen. ent,halpy of association, respectix･'eJy.. vacancies, they only have the regions E andM.. Substitution Eqs. (16) and (17) in }i)q. (15) we. 3.2 Theeffectofdefeetassociation It would be reasonable to asttme that the va-. obtain [Vo"] =: ( [l aSl]/2W)]"2 exp (ASA2/21<). ￠ancies induced by doping of a}iovalent cations are not free bttt are bound to dopant cations to. exp(-AHA2/21<rl'). (18). formdefectassociates. This binding enthalpy. Substitution of Eq, (l8) into Eq. (l2) giNJ･es. is mainly dtte to the coulombic attractioR okhe. a[}" :A' (CxG/2"f')i/2 exp [' -(AI'IT"-f'1/2 AiIA2). defects caused by their effeetive charges in the }attice; however it also contains terms due to re-. The second case is that the dopant cation. laxation ofthe lattice arottnd the defect, whieh. cation with the valencG of3 i:nakes an associate. depend on the effective charge, the size of the. withoxygenvacanc)i;likeY:i"in Ce02. Inthat. dopant and the cation polarizabillty. On the. case, the major defectis the associate of' dopant. defect association, a detailed review xar･as made. and oxygen vacancy with one positive charge as. by KiiRer and Steele (2). They divided the. (Y.'V,'']==Y,,'+V,,''. (20). situation of the defect associate into three possible cases. The first case is th at the dopant cation with the. valence of 2 makes an associate with oxygen vacaney. Taking an example of Ca2' in Ce02, only one simple defect associate is possible;. rThenweobtainthefollowingequationsimilarl>,' as the first case as. aT :": (A'/W) exp (ASAi/k) exp [-(AI-I.+ A. H,,) /k[l]]. (21). r}"he third case is that a}1 the oxygen x･'acancies.

(6) 208 at high temperatures but easily reduced at low. to be i'ree, In that case, we obtain. oT=:A'CNfexp(-AH./kT), (22). oxygen partial pressures (4). The pure Ce02Tx. where the electrical conductivity increases pro-. (more than 4N purity) is a mixed conductor. portionally as the dopant concentration jn-. with almost the same partial conductivities of. creases.. oxygen ion, electron and hole according to. Panhans and Blurnenthal (6). The partlal 4. Experimental data on the electrieal coR--. ductivity. ￠onductivities of 3NCe02-x at 1 atm oxygen pressure are shown in Fig.5 (6), where the ionic. conduetivity is significantly increased by the. 4.l Generaltrends. impurity atoms such as Na2 O, CaO and SrO.. The electrical conductivity ofvarious types of. The additive effect of alkaline earth oxides as. f]uorite oxides are shown in Fig.l (1). The. dopants in ceria such as CaO, SrO, MgO and. electrical conductivity is in the order of. BaO was studied by Arai et al. (7, 8) and the. 6 -Bi203> Ce02> Zr02> Th02> Hf02-related. electrical conductivity of these doped oxides is. system. Among these, 6-Bi203 has an. shown in Fig.6, As seen in Fig.6, the addition. oxygeB deficient fluorite structure where 1/4 of. of CaO and SrO enhances electrical conductivity,. the normal fluorite anion sltes are vacant and shows the highest oxygen 2on conductivity so far. TeTnperature. .. reported for the solid oxide electrolytes.. (qc}. geo 7oo. However, this oxide has little chemical stabil-. i. b. l. t. 500 l. 1. ity; it is monoclinic structure at ]ow tempera-. tures and becomes cubic with ionic conduction. -2. TOOO'C. 1. seo. o -o o e o eo o. T. AEv -4 s 't -g-. bti -5. g. x. 600. Legend. eo. -3. 10 2. o ionic. 9 ioi. o n-lype. T. A P-- tYPe o. o. RN)eb Ea=O'8O ev. xox. x. K xoO. o o. st. g. s. g. o. N. i>,,. 6H. o. e. Odb O. -aD a o aab oR o. lo-l. Xk. "N. x,ts×ts. b. s s. m. o. -6. o. ep. -7. 789 10 11 12 io4/T (eK"i). Fig. 5 Partial conductivities of ionic, n - type. and p- type at l atm oxygen pressure from fit for 3N Ce02-x (6),. O.8 LO 7--1 1.2 i.4 l.6 "o3 K-l} Fig. 6 Arrhenius p}ots of ionic conductivity of. ceria based oxides doped with alkalineearth oxides according to Yashiro et al, (7). A: (CeO2)o.g (CaO)o.t, A: (CeO2)o.7 (CaO)o.3, O: (Ce02)o.g (SyO)D.], e:(Ce 02)o.7 (SrO)e,3, [I]: (CeO2)o,g (BaO)D,i, O: (Ce02)e.g (MgO)e,i, zflx: (Zr02)o,ss (CaO)e.is, @: Ce02.

(7) 209. 3. ofceria and makes the activation energy }ower.. The addition of BaO and MgO, however, does not increase the ekectrical conductivlty very. T fi. additive effect of various rare earth oxides as. o. has been studied by many investigators (9 - i6).. Electrica] conductivity ofceria doped with 10. m. 1. ae. o. D. wooo -. + X=Sm e X=Gd. -1. -2 -3. o. +. AeA o"a e. G･. Ceo.sXo.201.g. F--･". mol% Sm203, Gd203, Pr203, Y203, r{'b203 and Er203 reported by Yashir6 et al. (9) and Balags. ･+. b`. much as compared with CaO and SrO. The dopants in ceria on the elect.rical conductivity. +++ :･ ixiii. 2 ""'. .. A X:Pr. + e. +. A. e. ･. e. ". t. D m. o. . X=[lb. m X=Er. t /. and Glass (IO) are shown in Fig.7 and 8, respec-. O.7 O.8 O.9 1 1.1 1.2 l.3 1,4. ￡ively, where Ceo,s Smo.2 Oi.g is seen to be the highest electrical conductivity among ceria - ba. Fig .8 Ionic conductlvity ofceria doped with 10. sed oxides, Electrica] conductivities of ceria doped with 10. i. 1.5. 1ooO/T (K-i). mol% Sm203, Gd203, Pr203, Tb20n or E b203 ac￠ordlng to Ba}azs and Glass (IO).. mol% rare earth (M203) and alkaline earth (MO) oxides at 1073K obtained from t･he data by. Yashiro et al. (9) aRd Eguchi et al,(11) are. plottedagainsttheradiusofdopantioninFig.9.. Ternperature lec. 3. 900800700 6oo 500. The doping of Sm3' ion among rare earth oxides and Ca2'ion among alkaline earth oxides with an ionlc radius of about O. 11 nm. %igSs o.. givesthemaximumelectricaiconductivity. The maximum electrical conductivity at this radius. 2. of dopant, ion is the similar ionic radius as the. host ion resulting in the minimum association. 2. enthalpy between dopant ion and oxygen. T'. gi. Q :t. @. m. @. o. eD. @. vacancy, which will be discussed in the next section, The e}ectrical conductivities doped. o []. 9. o tw. @. N. wit/h MgO and BaO are exceptiona}ly. Iow as seen in Fig.9 (7), which may be ascribed to the insufficient solttbility of these oxides in ceria , as the. lattice parameter of ceria - alka3ine earth oxides is shown in Fig.IO (7).. t The lattice parameter of ceria doped with rare earth oxides as a function of dopant concentra-. -1. Q7 Q8 O,9 1.0 1.1 1.2 1,3 1.4 lo3･T-1 !K-1. tion was measured by Bevan and Summerville (17) and it is shown in Fig.ll, where higher solubi}ity ofrare earth oxides can be seen. It is. Fig.7 Arrhenius plots of ionic conductivity of. eeria based oxides doped with rare-eart h oxides according to Yashiro et al. (9).. a}so seen in Fig,11 that the }attice parameter of. these doped ceria is much dependent on the kind. O: (Ce02)e.s (SmOi,s)e,2, A: (Ce02)o.e. ofdopants. Thelinearrelationshipbetweenthe. (GdOi.s)e,2, Kl7: (Ce02)e,s (YOi,s)D,2, n:. lattice parameter and the radius oi' dopaRt. (Ce02)e,s (CaO)o.2, ge: Ce02, @: (Zr. cations has been observed by Yashiro et al. (9),. 02)O.85(YOi.5)O.i5. which is shown 2n Fig.12..

(8) 210. 9 t 8 > t9. 8 =. O.546. G8+ sg+ D;' Y3+. 2.0. E Q545. ys+ OHg+ Ns+. 1.8. E. /9Lg'ee ,s. .,eig'. E O.544. 1.6. g. / xx X/" fe(M2'))N. 1.4. o. U $ Q542. !ca"fe(M3")/ igBa!". -O,2. :im[P---[H-O. 8 O,543. O.09 e,10 O.11 e.12 O.13 O.14. -･--. as. a Q541. Radjus of dopant cation/mm. Q540. Fig .9 Ionic conductivity ofdoped ceria atI073K against the radius of dopant cation. rc. shown in the horizontal axis ls the critical radius of the di - valent or tri u. -iCXm-ibr"-"mm'rO,'m'-'mtCYN]v-. O O,1 O.2 O.3 O,4 O.5 O.6 X. Fig .10 Latticeconstants ofceria based oxides, : (Ce02)i-x (MOy)x, as a function ot. dopant concentration, x, where y=1. valent cation (7, 9, 11, 21),. except for y == 1. 5 in M == Sm according to. Yashiro et al, (7). M: e; Sm, A; Mg, O; Ca, []; Sr, A; Ba. O.546 La?Ol. 5.SO. g im. x o.544. E ..r-rl. Nd20] 5･Se. lt. K. SM20]. 8 .a. s tg. w:. Gd201. SKO. g ]. G(l. 2 O.542. Dy. 8 o. ,9 Q540. = g. O.538. Q09. O.10 O.11. Radius of ciopant cation. L. ZZz7az 5-]O. O.12. /nm. Fig .12 Lattice constant of doped ceria Ceo.s Dy2O]. ¥20]. Ro.2 02-y agains￡ the ionic rad ius of dopaRt cation (9).. 4.2 The dependence of dopant concentration on the eleetrieal conductivity Yb201. s?o. o MOLE X ROI.s. Fig. ll. so lce. The electrical conductivities of ceria doped with. alkaline -earth oxides, Sm203 and Y203 were. The variation of 3attice parameter with. measured by Yashiro et al. (7, 14) and Wang et. dopant concentration for the fluorite. al. (l5) and is shown as a function of dopant. oxides Cei-x R. 02-y (l7).. concentration in Fig.13, 14 and 15, respectively,.

(9) 211. 10 o. The maximum conductivity is obtained at 10. mol% for alkaline-earth oxides (MO) and Sm203and4%forY203. Theactivationenergy for various rare eayth oxides as a function of. dopant concentration was studied by Faber et al, (l6) and it is shown in Fig.l6, It shows a. minimum value at a certain concentration de-. pendingonthedopantcations, Thebehaviors shown in Fig.13- 16 suggest that there are some. loH2. H '. N o. . ca. x b. 10 -4. interactionsbetweendopa" ntionsandoxygenva-. canciesandtheconcentrationofoxygenvacancy shown in Eq. (l.9) is a complex function of dopant concentration depending on the dopant.. 10 -6. It is also noted here that ehe maximum of the. O O.1 O.2 O.3 O.4 O.5 O.6. electricalconductivity and the minimum of the. activation energy aye not always associated. Fig. 14. Concentration dependence of conductivities for (Ce02)i-x (SmOi.s). (14). O;. with the the same dopant concentration as seen. gooec, Ai soooc, rr: 7oooc, e: 6oooc, Ai. in Fig.15, because the pre - exponential factor is. 5000C, - - -: (Zr02)i-x (CaO)x at 8000C.. also a function of the dopant concentration and. the dopant concentration corresponding to the. maximum of the conductivity depends on temperature,. z/ 't'" io-1. x. l.4. 1o'6. tn.O .)-T ,'. 'N. lo-2. t". HIE. IN IN. l. o m. {l. lo+7. l.2 s. He (ev). N N. N '. v. lt. -3 o 10. s N. .. l,O. N tt. lo-8. N l. x<. 1o-'4. O 10 20 30 40 50. Content of adidiitive (rnol gXb). Fig .13 Conductivities of ceria - alkallne earth oxides systems at 1073K as a function of. dopant (7), A･(Ce02)i-x (SrO)i, O (Ce. , He O.8. IO-ug. O.6. 1o-1o. .05 .1 .2 .5 12 5 IO 20 40 % Y203. Fig .I5 Variationofthelowtemperatureactivation enthalpy, Ho' with concentration,. 02)i-x (CaO)x, [] (Ce02)i-x (BaO).,. the latter plotted on a }ogarithmic scale,. (Ce02)i-. (MgO)x, - - - (Zr02)i-N (CaO)x.. as a function of ￠oncentration (15).. Also shown is the conductivity at 182℃.

(10) 212. as O. 5 eV according to Faber et al, (16) or O. 61 12 Ea[eV]. eV according to Wang et al, (15) and then A HA is ca}culated from the experimental value of A. `. I. 1. Ea.. The theoretica} calculation of the association. /. Yb. enthalpy on eeria doped with some rare earth. oxides was conducted by Butler et a}. (18) assuming the fully ionic model, Born - Mayer. l.O. f/. potential for short range interionic forces and. theshellmodelfortheionicpolarization. The results are shown in Fig.l7 together with the ex-. perimental resu}ts by Gerhardt- Anderson and. Nowick(12). Figure17showsthatthetheoretP cal calcu]ation predicts quantitatively the asso-. Gd. ciation enthalpies ofthe associate. Kilner (19) has pointed out referring the similar relation ip. Nd. doped MgO system that the dependence of asso-. O.7. O.}X ]tt. 10'1. tn(MOIn). ciation entha}py oR dopant size is much smaller. o. Fig.I6 Activation energy against dopant･ concentration for various doped cerias (l6).. for ions lager than the host than for those. smal2erthanthehostcationsize, Thesimilar relation between activation energy and dopant radius on rare earth - doped zirconia was giveR. by Ki}ne}" and Brook (20) and it is shown in. Fig.l8. It would be necessary, however, to 5. Interpretation of the electrical eondue-. tivity. 5.1 The relation between association entha}py of defeet associate and ionie radius of dopants As has been shown ln the previous section, the. maximum electrical conductivity "r･as obtained at the radius of dopant ion similar to the ionic. radius ofthe host ion, This fact shows that there is an optimum ionic radius of the dopant. ion, which gives the minimum association. enthalpy between dopant ion and oxygen vacancy. Kilner and Steele (2) emphasized the importance of the defect pairs between oxygen. vacanciesandaliovalentcationsasshowninEsq, (20). Thetotalactivat,ion energy is thus given by the following expression:. AEa =: AHm+AHA, (23) where AHA is the association enthalpy of the. complexdefectsuchas(YM'Vo'') :lrhe enthalpy for migration A Hm can be estimated. makeasma]}butimportantmodif2cationabout this theoretical analysis as pointed out by Kim. (21), Mederivedtheempiricalequationsforthe lattice parameters of fluorite - related oxides. doped with various valent cations considering. thechargeeffectaswellasthedifferenceofionic. radiusbetweenthehostanddopaRtions, For the radius of ￠at2ons the 8 - coordinated values. compiled by ShannoR and Prewik (22) were chosen. Heproposedthecriticairadius,re,in order to better understaRd the relation betNNreen. association eRthalpy and dopant radlus, which corresponds to the ionic radius of the dopant whose substitut!on for the host cation causes neither expansion nor contractlon in the fluorite. lattice. Theeriticalradii,r,,ford2-valentand. tri-valentcationsasdopantsinceriaare￠aiculated as O.1106 and O.1038 nm, respective!y, which are much closer to the radii of dopants. corresponding to the maximum eJectrical conductivity as shown in Fig.9 as compared with the radius of host ion. In Fig,19, the critica}.

(11) 213 O.l3. radius for severa} different va}encies is plotted. asafunctionofhostcationradius. Healsocalculated the deviation of the lattice parameter. E. O.12. =. co-. from the hypothetica} pure zirconia in the. -]-. systemofZr02-Th02-Y203(21), Theactiva-. as L.. tion energy of the electrical conduction can thus. v. O.11. .9. =. .9. O,10. becorrelatedwiththedeviationofthelatticepa-. E. rameter from the hypothetical pure zirconia as. ao v. shown in Fig,20.. tu. di .9 .L. ". depan! vateticy O.09. + U O A. e.os. o. +1 +2 +3 +4. O.07. O.07 O.08 O.09 O.10 O.11 O.12 O.13 s[]+ T. e･7. >-. e･6. eq. e. it in. e･s. Y]' gd]'I. SI. lonic radius of host cation, nm. LaY ,. Criticaldopantradius,rc,inthefluorite 3attice as a function of host catioR. Fig. 19. e Experimefita[. radius for dopants of several dii'ferent. o [a[cu[ated. valencies (21).. t=. M. g. o･q. ib.. .E. co. O･3. I. xxL"'. O･2. e･1. o. O-6 O･9 1･O 1･1 1･2 lonic Radius {A}. Fig .17 Calculated and observed association. enthalpyofthedefectassociateofdoped ceria against ionic radius of dopant. 120. A. -o. o E. E pt -M. o c o = .9. 100. o o. di .>-. cation (18).. ilO. ). 5. 90. <. o 80. o.oe2 o,oo4 o.oo6 o.oos o.ole Deviation in lattice parameter, nm. Fig. 20 Activation energy for conduction in the. ;. e. system Zr02 - Th02 - Y203 against the. 1･1. it. 10. B =. 1. O･9. c. O･8. N .l v <. O-7. deviation in the lattice parameter from the hypothetical pure Zr02 (21). Sm3.. e. .9. Steele(1)furtherproposedthatbecausetheasO･6. sociation enthalpy is dependent on the relative. O･8Ionice･9 radlus1･O of dopant1･1 A. Fig.18 Activation energy for conduction in doped zirconia as a function of ionlc radius of dopaRt cation (20).. radii of host and dopant, plots of latti￠e pa-. rameter versus concentration should yield re}ex;ant qualitative information about the expected strain component, and derived values for Th02, BiOi.s, Ce02 and Zr02 host lattices.

(12) 214 together with t,he rare earth elements are shown. enthalp.v and association enthalpy. The. in Fig.21, It. can be dravLrn from Fig. 21 that. mobility enthalpy of doped ceria was taken as. Th';+is,ingeneral,too]argeahostcation;most. O.5 eN," by Faber et al. (16) considering the. dopants are smaller and high strain components. results of NMR study (23) and O. 61 eV by Wang. are predicted and Zr`' is, in generai, too small a. et aj. (l5) taking into account the activation. host cation as most dopant cations have ]arger. energyofpureceriaanddopedceria. Sincethe. radius.. mobi}ity enthalpy is considered to be independ-. ent of dopant, the variation of the activation. energy with dopants can be acribed to the asociationenthalpy･. The activation energy of. S60. La. Th 02. calcia - doped ceria is obtained as O. 83 - O. 89 eV. over the concentration range up to 80% CaO ac-. BiO ts. Pr. cording to Arai et a]. (8); almost no compositional dependence is obtained as expected from. A v. o((. Nd. sso. L or cu. Sm. .4---. a. ----. ca. q. x. The concentration dependence of association enthalpy in a low concentration range of Y203. Gd. ce 02. 5.40. or w --.L.F･ re. J U "= U vovoD. defects are expected.. Eu. E. ro L rc. Eq. (13), where the defect associate has no effec-. tive cltarge and no further interactions between ... was analyzed by VkJang et al, (15), [l]he unique feature of rare earth - doped ceria is that the. Tb. Ho S.30. Y. defect assoclation lnvoives incomplete compen-. gy. sation; i,e, the ( YM ' VoH ] pair retains a residual eharge, as do the remaining isolated YM' defect･s. They derived the following equa-. Er. tions assuming the energetically fovorable elec-. Tm. trostatic interaction between the defects and the. Yb. S.20. surrounding charges:. Lu. HA =KAOuAEint, (24) AEint=:O.42co"/'3/B, (25). .Y. D =U. o re. whereHAOistheassoeiat.ionenthalpyatinfinite. zro2. dilution, AE,.i is the mean interaction energy. S.10. with the surrounding charges involved in the. ?. ?. proeess of association, ce is the dopant concen-. tration and B is a dimensionjess parameter for aveyaging the electric field. fChe fitting of the. sc. theoretical equatlon to the experimental results is shovLfn in Fig. 22, where MA decreases and the. 4.9O. eleck"ical conductivity increases with the 113 Fig. 21. Lattice. parameter rnaps. of the varl.ous. fluorite oxides (1).. power of the yttria concentration over the dilute. range as shown in Eq, (25).. Adler and Smit.h (24) demonstrated the impor-. 5.2 Aetivation energy and pre - exponential. term As has been described in the previous section , the activation energy is the sum of the mobility. tance of long-range forces on the oxygeR trans-. port iR yttria-doped ceria using the Monte Car]o simulation based on the point defect model with a Debye - HUckel modification..

(13) 215 The simulated ionic conduct.ix･'it-x,J･ of vyttria - dop. (l6) and are shown in Figs. 24 and 25, respec-. ed ceria is shown in I?ig. 23, where "extent pa-. tiveltt, where the numbers marked in t.he figures. rameter" R : the range of Coulombic forces is. denote the order of the concentration. As the. given as infinite, otherwise it does not explain. concentration of the dopants increases, the. the experimental resuits. These theoret,ical. 2･ oL. -5.5 e. .4e HA. loga. !. !-. -. /. f. -. p. L. ti. l. N I. "2t. -6.0. L. s s. A. st s. r. s. co. ,35. "¥. 1. b. -6.5 g9. =(. '. ''. x. 7o. s s. i' x. a xPr -4. s. rc. R. s. 9o. .50. -6 -7.0. k. xei .. Xe. r E. .25. 103 K/T -･. .20. Fig. 23 Simulated ionic conductivity of yttria-. doped ceria for the case of Coulombic. o. Fig. 22. 7.5. 113 (10-Ce) Variation of activation energy and }og a (at 182 OC) with 1/3 power ofthe yttria. concentration over the yttria concentration over t.he dilute range (15).. forces between particles (the ext.ent pa-. rameter is taken as infinity), The dashed lines are the predictions of an ideal point- defect rnodel. The solid. }ines are the predictions based on a point defect model which iRcludes a. Debye-KUckel correction. Dopant concentrations are quoted in moi% Y2 03 in Ce02 (24).. analyses can only be applied to a dilute range of. activation energy decreases significaRtly while. dopantconcentration;they collapse around the. the pre-exponential term keeps almost. concentration of the maximurn electrica! ￠on-. constant. Thepre-exponentialtermbeginsto. ductivity.. inerease significantly after the activation energy. As aiready described, the maximum of the. becomes minimum. The maximum electrical. electrical conductivity and the minimum of ￡he activation energy are not necessarily associated. conductivity is obtained at a higher concentra-. with the same dopant concentration, because the. tioR than that at the minimum activation energy. Itisnotedthattheconcentrationwhich. pre-exponentialfactorisalsoafunctionofcon-. gives the maximum electrical conductivity is. ceRtration. The electricalconductivity and the. quite different between yttria - aRd gad}inia-. pre - exponential term of yttria - and gad!inia. dopedceria;4%foryttria'andIO%forgadlinia -doped cerla, The pre -exponential term. m doped ceria are plotted as a function of the ac-. tivation energy using the data by Faber et al.. begins to decrease at higher concent･rat.ions,.

(14) 216. te.7 s. 6 .." - S'Xx xXN-N )gJ. . .gb-''. 8.5. 7 SX's.e. ,E 8. -O.5. -ffJfi. <an 9. 43. -l.5. 7. x. x. 6.5. 1. bi. Ea/eV rl"hepre-exponentialfactor(logA)and. -O.5. s -1 -b bD -o. 6x bN2 x. 5. x. -l.5 x x. 2 x. -2. 6.5. 1. bl. -2. O.65 O.7 O,7S O.S O.85 O.9. O.65 O.7 O.75 O.8 O.85 O,9. Fig. 24. xxxxSx. Nx x. 43. x. 2. .e.7 s /x 7 Xx.e. Xb3. 7.5. xx. x. 6 "t. e .e" )9,-. 8 -i F.". 6N b2 5%. o. 4i. xx x. 7,S. 7. 8.5. s. Xe3. <7g. u. 9. o. 9. Fig. 25. Ea1eV Thepre-exponentialfactor(logA)and the electrical conductivity (}og a T at. the electrical conductiLJ･it>r (Iog a T at. 1073K) of yttria - doped ceria as a. 1073K) of gadlinia -doped ceria as a. function of the activation energy (16).. function of the activation energy (16),. s,. The numbers marked in the figure show. The numbers marked in the figure show. the concentration of yttria as follows;. theconcentration ofgadlinia as follows;. 1:O, 05%, 2iO. 15%, 3iO.5%, 4i1%,. 1:O.1%,2iO.5%,3i1%,4:2%,5:3%, 6i5% 7i10% 8i15%.. 5i2%,6i4%,7i6%,8:10%,9:15%.. Tl. rl'he concentration dependence of pre ' exponen-. anion sublattice (O, F, or Cl) are shown, The. tial factor in doped fluorite oxides has not been. diffusion constants in the anion sublattice are. well unclerstood yet, but this depeRdence may come from the ASAi term in Eq. (21), because. sever41 orders of magnitude lager than those of. other terms are considered to be independent on. et a}, (26, 27), It is noted that the activation. the concentration, The decrease in the pre - ex. energi'. ponent,ial term at the higher dopant concent.ra-. U02, Th02, Pu02, CaF2 SrC12, and BaF2 are. tions ma-y be due to the partial ordering of the. much higher than those of nonstoichiornetric. defects, Thepartia}1.v ordered structures were detected by ,tXIipress and Rossel} (25) by means. compounds and doped solid solutions. This phenomenon may be undeystood using the fol-. of' electron diffraction using anRealed samples. lowing equation:. ofcalcia - stabiHzed zirconia and hafnia, which. cation sublattice, which were compiled by Oislti. es of stoichiometric compounds such as. Ea =:AHrn +AHf, (26). showecl lower electrical conductivity as. where AHf is the enthalpy of vacancy forma-. compared x･i,'it,1i the sample of no annealing,. tion, Inthecaseofstoichiometriccompounds, A Hf has a large value because a]most all the. 6. Diffusivity The diffusion constants of fluorite - re}ated. anions in the sublattice are occupied; while in. the case of nonstoichiometric compottnds or doped solid solutions, anion vacancies are. compounds obtained from the various. already present in some forms and there is no. literatures (26-39) are compiled and shown in. needtocreateanionvacancies, Thetermrepre-. I?ig, 26, where the diffusion constants in the. sented by AHf (AHA in this case) may be.

(15) 217. 10咽4. 1『。. 亀. 欝亀・q魂6鈍. 1『6. 10−7. も魔 10−8 髪. 踏（句. 奄. ミ1『9. Q 10−1。. 冷. 1Q一11. 10噌12. 10−13. i. O，5. O．6 0．7 0．8 0．9. 1．○. 1．1. 1．2 1．3. KK／T Fig．26 Diffusion constanもs of anion sublatもice in various fluorite cornpOu慧ds． ⑦Zr。．85Ca。、、，O、．，、（26），⑧CaF、（28），⑨BaF、（29），⑩SrCl、（29），⑪Ce。、6 Y。、、O、，8（30），⑫Ce。．、Y。．，○、．、（30），⑬Ce。．g Y。．、01、，，（30），⑭CeO、（30），. ⑮Zr、．85Ca、、 L 501、85（3！），⑯UO，（32），⑰PuO，（33），⑱UO、（34），⑲ThO，（35），. ⑳ThO、（36），⑳UO，．。（x−0．01）（37），⑳PuO，．．（x−0． Ol）（38），⑳UO、＋．（x諜. 0。01）（39），⑳CeO1、8（30），⑳CeOLg2（30）．.

(16) 218. assigned as some interaction term between defects, whieh is much smaller than that of. In Fig. 28, the diffusion constant is represented as:. Eu/Tm. D==Doexp(- ). stoichiometriccompollnds.. kT/Tni, (28). In order to compare these diffusion constants. with those of doped fluorite oxides shown in Fig. 1, the electrica} conductivity is converted. into the diffusion constant using the NernstEinstein relation as the follo"Ting equat!on: D == okrl" ti/ (4Cve2) == okT tiao3/ (166e2),. (27) where ao and 6 is the lattiee parameter and the. molar vacant concentrat,ion in the form of M02-e, respectiveJy, the quadratic term on oxygen vacancy in Eq. (9) is neglected and the correlat2on factor ofthe diffusion is assumed to. be unity. The lattice parameters of various doped fluorite oxides are obtained from the em-. piricalequations given by Kim (21), The converted diffusion ￠onstants from the electrica] conductivities are shown in I?ig. 27, wheye the. diffusion constants of various fluorite com-. pounds shown in Fig, 26 are also shown for comparison. It is seen from Fig. 27 that 6 Bi203, gadlinia - doped ceria and yttria - doped. zirconia give the highest diffusion constants. among these fluorite compounds, which are known as solid electrolytes. The activation energies of the diffusion for these solid electro-. where Do is frequen￠y factor and Tm is the. meltingpoint. ItwasshownbyOish!etal.(26, 27) that the diffusion constant against the nor-. malized temperature plot of cation sublatiice was tend to be converged in a single line, but that for anion sublattice was rather scattered as belng characteristic as the liquid - like behavior. even at low temperatures. it should a!so be noted that the diffusion constant of anion. sub}attice is very sensitive to the nonstoichiometry and impurities of sample such as a large difference in that between U02 and U02-x (x ==O. Ol) as seen in Fig, 27 and these nt. effects also contribute to the scatter in Fig. 28.. Neverthe}ess, the diffusion constants at the melting point (T/T.i=1) tend to be around the value 10-'i cm2sTi in Fig. 28, which shows the diffusion constant of a iiquid. It is noted that 6 - Bi203 (O in Fig, 28) lies just ￠!ose to the. melting point, which is in quite different position in Fig. 27.. 7. Transfereneenumber The total e!ectrical conductivity at of solid is. lytes Iie somewhere between those of. the sum of the coRtributions dtte to ion electron. stoichiometric compounds and nonstoichio-. and hole as follows;. ,. metric compounds, since the behavioys of the. crt= oion mlT ae+ah, (29). activatlon energy of doped fluorite oxides. where ion, e and h mean ion, electron and hole,. are malnly determined by those of the. respectively. These partial conductivities are. defect associates as described in the previous. expressed according to Patterson(41) by. sectlon.. The plot of the diffusion constants of various. fluoritecompottndsagainsttheRorrnalizedtem-. Oien=aOionexp("Qion/kT) (30) ah ==crOhP.2ii"exp(-QhlkT) (31) a. =:: aOeP.2'i'"exp(-QelkT), (32). perature: the temperature divided by the melting. where X2 is gas (in the case of oxides, 02), P is. point, was first conducted by Matzke (40) and. the partial pressure ofgas, aO and Q are pre-. then Oishi et ai. (26, 27). The diffusion con-. exponential factor and activation eneygy, re-. stants of various fluorite compouRds shown in. spectively, and n is the factor determined by the. Fig. 27 are plotted against the normalized tem-. predominantdefectstructure. Theconduction. perature as shown in Fig. 28, where the unknown melting points such as gadlinia-. domains are determined by using Eqs. (30 - 32). doped ceria and yttria-doped ceria are assumed. The electro}yte domain is determlned by. to be the same as the pure oxides such as ceria.. measuring the transference number o"on, ti,. aRd they are schematically shown in Fig, 29,.

(17) 219. 1o-g. N. ...<2). 1O-:. ×9x x9 N N.... 'ss`.Q l})tul x.-. XNs..s .h. N. s.s. X. pm. @<(i!)g. a. @. XtN XtNxxXXxXx xx. 132 ts. @. 1o-s. N Xx XNN NNs. s.. NN... x (fiS'N CY XN. 1o-6. 1o-7. ". @. @. ge. xxxx 9Xx xx x N x x. ×Xx lo. r,. c.`x,. 8. Eili. o ×. a. 1o-g. @. x. 7. 1o-io. 1O-". 16. 1o-i2. 1o-i3. [. t. 1. l. i. l. O.5 O.6 O.7 O.8 O.9 1.0 1.1 1.2 1.3 KK/T Fig. 27 Diffusion constants of anion sublattice in xiarious fluorite cornpounds (1).. O 6 - Bi203, @ CeLs Gdo.2 Oi,g, @ (Zr02)o.g <Y203)e.i, @ (CaO){" :i' (ZrO2)o.s7, @ (ThO2)o.g3 (Y2 O3)e.oT, (6) (CaO)o.i2 (i}IfO2)e.ss.. The data marked 7- 25 are the same as those in the caption of Fig, 26..

(18) 220. 1o-4. .O. 1o-s. xx. xx. @ @. 1o-6. @. 1o-7. xx. xx. × @ × xrst..-..... × (21)Nx. xx x N. xx x N x(S)X"-x.... Nx. 13. pa. × ×× xx Xxx@ Xx. @x@ XXxxxx XXxx x@. 1o-s. di. rr ..`,X). E o. ee. @. 1o-g. ×. a. ×x xx ×. 14. g). @. 1o-ie. ge. @. @ @. 1o-g. to 1o-i2. o. 1o-i3. 1o-i4. l. 1. 3. 2. 4. Tm /T Fig. 28. The diffuslon constants of anion sublattice in various fluorlte compounds as. a function ofnormalized temperature. The compounds marked 1- 25 are the same as those in the caption of Fig. 27,.

(19) 221. LoG ph --n({;k'Znv,,Q,h). +n LoG 6oi'gOO" 7. 6h Domain CL"o6. 6"0. -. 6N￡. Electrolytic. domain. cu. a o o J. ×. Oe Domain. ass q. Qs. LoG o.s/oon Hliii)>>,. LoG pe :-n({l.igB",,Qi). +n l/T-. Fig .29 Relationship between the electrolyte domain. and eiectronic. domains in the iog Px2 veysus 1/T piane (41).. according to Eq, (3) and taking ti =O. 5 as func-. (41-45) and are shown in Fig. 31, where the. tionsoftemperatureaRdpressure, Theresults. inner zones of shaded marks show eiectrolyte. ofionic transference nttmbey mea$urements for. domain. As shown, thoria-and zirconia-. yttria-doped ceria measured by Tulier and. based oxides show a wide range of electroiyte. Nowick (42) aye shown in Fig. 30 as an example.. domain even at low oxygen pressures, Doped. The lonic transference number decreases when. Bi2 03 and ceyia are less stable at low oxygen. the temperature iR￠reases aBd oxygen par￡iai pressure decreases, because doped ceria shows a. pressures, The effect of dopants among ceria. n m type conduction at low oxygen partial pres-. POI, at ti = O.5 and 1073K was studied by. sures and high temperatuyes as:. Oer1/202+VoH+2e, (33). - based oxides on the critical oxygen pressure, Yashiro et al. (9) and the results are shown in Fig. 32, where POE is plotted against the radius. and thenumber n in Eq. (32) becomes 4 in this. of dopant ion. P02' becomes minimum. case. The electrolyte domains for various. around O.11nm of the dopant radius. This figure is analogous to Fig. 9, where the. f!uorite oxides are compiled from the references.

(20) 222. electrical conduetlvitx･' shows maximum around. v. O.1lnmofthedopantradius. rl"hisrelationship. T/℃. 2eeo16oo 12ooleoo soo7oo 6oo. suggeststhattomaximizetheeleetricalconduc-. l. l. 1. tA,･ity is also effectix･'e to maxiinize the region of 10. electrolyte ciomain. Since PO; is a measure of. l .il. reducibllity of oxides, the reduction experiment. wasalsocoRductedbvYashiroeta}.(9). The v. weightlossofsampleexpressedasthedeviation from stoichiometry, 6,in (Ce02-o-1 o.s. shown in Fig, 33. iXs seen in Fig. 33, Sir)doped ceriaismost stable against reduction.. t. fl!fl!/ !1. !7fl lfll. lt ll ... E. e. II. ts. x o Ao. o",. <LnOi.s)o,2where Ln == Sm, Gd, Nd and ¥b is. ii. (2). '. Z. -10. Z !1!1 f(4>. -. "/- (3). -f. -20. (6). -3e. (2). O.4 e.6 O.8 ,Il 1,e l.2 l.4. al. (46) by doubly doping Pr in gadlinia ' doped. F. ceria. AsshowRinl'"'ig.34,thecrlticaloxygen. l. i. 1. '. KK/T s･. partial pressure POi decrease by about two. orders of magnitude by doping 3% Pr in. (5}. (1). The attempt to increase the electrolyte domain was conducted on Ceo,s Gdo,2 02-y by "tiaricle et. seo. il(1) ltil (s). Fig. 31. The electroJyte domains (ti"vl) for various fluorite oxides. (l) CSZ (42), (2). gadlinia - doped ceria.. YDT (42), (3) (Y203)e,os (Ce02)o,gs (41), (4) (CaO)e,is (La2 03)o.ss (43) (5) (Y203)o.27 (Bi2 03)e,73 (44), (6) Ceo.s Gdo,2 Oi,g (45).. lo. l F i. '. ] 1. 6]sec. oB t. i. L. O5P. s i 9. ! e` E. H 9 z 9. seo. [. 2 E. L. i 1] l. L.. o2 t. o. o. j. SCoec. lo-15. Sm. looo c li50. le-14 o. l ' -20.0 -22,5 -2.5 -S.Q -7S -IO.O -i2.5 -15.0 -IZ5 Iog Pbtfotm}. Fig. 3e rl'heionic transference number of yttria. - doped ceria as a function of P02 for various temperatures (42).. 10-13. E" O 10-12 x * eu o nt. Gct. DY O Ybo o/Y. 10-l!. O[u. Nd. o. Ld. 10-10. O.09 O.10 O.11 O.12 Ractius of Dopdnt CatjoB 1 nm. Fig. 32. Correlation between the critical oxygeR partial pressure (at ti":O.5) and the radius of dopant cation of ceria based oxides (9)..

(21) 223 obtained by Rgess et al, (47) and t.he fornier sample was obtained froi:n the coprecipitation method with a narrow distribution of poxx･'der sj.ze and the lat.ter from the mixing of Ce02 and. Gd203 with a wide distribution of powder size,. lo-2. e. V℃. lceogeo soo 7oc 6eo. 5oe. M=-MT,Tm=-, l･ // /i:, I. ･･ {1} i-. 10-3. le2. ･×･･･":･}･･･. (5)X<S ]. 9. lo-14 lo-16 lo-18. 'Qx l-. T'. E 9. Po2 ! atm. leT. co. Fig. 33 Isothermal plots of weight loss with the. vF. ;)>,.X'". 'x-.. I. ℃. {4) X. X"..Xx.l. deviation from nonstoichiometry, 6,. X'xxX. Xl xl Nt xl. lei. versus oxygen part2al pressure for (Ce 02-e")o,s (LnOi.s)o.2 at, 1073K (9); O Sm,. e Gd, A Nd, I:] Yb.. O,8 e.9 1.e 1.1 1.2 1,3. i i. KK/T. le -il ur:[I]Ce2t"tL,tPti.iOt."//rstt,/dv. :t 10 '". Fig. 35. t(W.I.r)C'oesGtL.IE,teoa',tlObnvnsh,. [. The variation ef electrical conductix･'itx'. ". i le "". of Ceo,s Gdo,2 Oi a. obtained from dif'fer-. z. ent authors and different met.hods. (1)[. 8. (45), (2): (47), (3)i (47), (4)i (10), (5)i. ta `iS. z. i. (H).. 8 io "". 9. y. o" io '" ff. sU. WIO-t+ -]. le -:1 r-'T'n=5115I37TT"Tt,-ff. T,1I."-'i "-6rgli rri "trll6Ii]-'Ti rrTJi,"., rT'iTttl-6,. o.. 10'/K ('K-'). Fig. 34 ri'he effect of double doping of Pr in gad. }inia -doped oxides on the critical oxygen partial pressure (46),. They regarded the difference in th'e elect,rical. coRdu￠tivity of gad}inia - doped ceria as imhomogeneity in the Gd distribution and the larger activation energy was interpreted as due. 8. The effect of sample preparation. to the formation of Gd - rich grain boundary. The effect of density and impurities was studied. The electri￠al conductixJities of Ceo.s Gdo.2 Oi,g obtalned from various authors (10, 11, 45,. by Gerhardt and Nowick (48) anckhe results are. 47) are shown in Fig, 35. This figure wou}d. of densjty is rat.her small as seen in Fig. 36, but. show that the electrical conductivity is depen-. the impurity of Si makes the electrical conduc-. shownin Fig.36 and37,respectivel.v. Theeffect. dentonsamplepreparation:poxvderofrawrna-. tivity of grain boundary }arger drastically as. terials, impurities, sintering condition and so. seen in Fig. 37, :"his effect is interpreted as due. on.. The both plots of (2) and (3) in Fig. 35 are. to the formation of high resistive g}ass.v phase in. the grain boundary..

(22) 224. CeOz:5XGd20J. x N. a 9SX DENSE O 70X DENSE. kx. tsx. loO. xk. xx. x. zE. RN. Xxeqx. y E. E. RxxNabLN. hb. lo-l. x. X. Nxk. ,vx NX ij,. K. R x. 10-2. 1.1 1.3 l.S l.7 i.9 2.i 101IT. Fig. 36 EIectrical conductivity curves of two. samples of gadlinia - doped ceria with differentdensity, Soiid lines represent the bulk behavior and the broken lines the grain - boundary behavior (48).. z" Cohrn). 700. 38se c. ce02:6%Gd20]. },10]. Qny1000pprnSi. 6< 10ppmSi. l"{ohm}. 1ttoJ. ltIOI. 3t10. Z'COhm}. 500. 5i10. A. A 3OO. A. o 1OO. AAA. oco. A. A. '`:`iiiiEsttroo ]oXt'K soo 7oo .goo ' Z'CQhm}. '. Fig .37 Complex impedance curves at 388℃ of two gadlinia - doped ￠eria prepared with different starting materials: open circles are for the conventional samples containing 1000ppm Si, whereas triangles are prepared froma "Si- free"( <IOppm) material. The inset shows the compleie second arc for the sample containing 1000ppm Si (48)..

(23) 225 9. Concludingremarl<s. electronic conduction becomes signit'icant at. low oxygen partial pressures. Jn order to. Thediffusionconstantsofceriaubasedoxides. increase the electrolvte domain, to increase in. are estimated to be almost the highest among. the ionic eonduct.ix･'it.y b>,' an.v ineans, of cour'se,. ". the f}uorite oxides by cornpar.ing the diffusion. is effective. It is suggest.ed that. the doubl.x.･'. data of' these oxides using the Nernst - EiRstein. doping of }'r is effective to increase the electro-. relationship. Thepre-exponential term and. }yte domaln without chang'ing t,he inagnitude ol'. the activation energy of the eleetrical conductlv-. ionic conductivitv.. ity of ceria doped N･x･'ith tri u x,alent cation can be. expressedas: G A == (4e2/kW)a2v- No exp (ASm!k). "-. 'I'he import.ance ofthe method for the sample. preparation is also described. 'l-he most serious problem in the sample preparation c)f'. exp (A SAi/k) (34). rare earth - doped eeria xvould be the h()n'ioge-. l]'u=Al'In} -1- A}'IA (35). neity of rare eart}i atoins in the sample, slnce. In order t.o search the oxides with higher electri-. electrical conduction is much dependent on the. calconductivity the f'ollo"J･ing points should be. concentration of rare earth element.s. The in-. considered.. clusion ofimpurit.y Si drasticaH-v increa.ses the. (1) Since AS. is considered to be constant when. grain boundar>,r resist.ixJit>,･ b>g making hig}i. the host lattice is determined, maximization of. resistivity layer including Si in the grain. vo and ASAi is necessarv in order to increase A. boundarv,. J. in Eq, (28). Thein￠rease in vo at a giv･en tem-. perature may be achieved by lowering the melting point of the oxtdes, since the plot ol' the. diffusion constant against the normalized t.emperatu}-e approaches IO"` cm2s'' at the rnelting. point. The mechanism to increase A SAi is not･ clear at present, but it wou}d be effect･ive to. doubly or trip}y dope proper ions in order to suppress the diefeets ordering.. (2)InordertoloweractivationeRergy,theasso-. v. 10. Aeknowledgement The authors wish to thank Prof. Junichiro Nilizusaki of' rl"ohoku Unixrei-sitv foi" x･'aluab]e dis-. v. cussions ancl comments. 'Ii"inancial support from N Y] I)0 for an lnternational Joint Research Grant. is also gratefull-y cackRc)wleclgecl.. Il. References. ciation enthalpy A H,xi in Eq, (35) should be. (1) B. C. I'{. Steele in "Hggh Conductix,ity Solid. minimized since A H. is considered to be constant. The theoretical predict.ion to. Seientlfic Publis}iing C()., Singapore (1989>.. miniiyiize A Hm is rather apparent. as was dis-. Ionic Conductors," T. Takahashi, ed., XN' or}cl. (2) J. A. Kilner and B. C. J. Steele. clissed in section 4. The optimum radius of. in"Nonstoichiomet.ric Oxicles," O. rr.. dopant cations shou}d be the critical radius,. Sorensen, ed,, Academic })ress, New York. which is about O. 111 and O. 104 nm for di- v･alent. and tri - valent cations in the ceria ' based. oxides, respectively. In order to obtain the latt･ice constant with no expansion nor contrac-. (1981). (3) K. Sasaki, a doctc)ral di$sertation subtniF. ted to the S"J･iss Federal Inst,it.ute of Technology, Zui-ich (1993),. tion in doub}y or triply doped ceria, the combi-. (4) R, M, {)ell and A. Hooper, p. 291 in "Solid. Bation of dopant cations so as to obtain the. 11trlectro}ytes," }'. i'Iageni/n#ller ancl X･X,". Van. same value as average as the critical radius of the one dopant system would be effective.. The increase in the region of elect.rol>rte. domain of doped ceria is also an important problem, because it is apt to be reduced aRd. Gool, ed., .iXcademic Press (1978). (5) J. A. Kilner and C, {), XK･;alters, Solicl State. Ionics, 6 (l982) 253,. (6) M. A, I)anhans and R. N. Blumenthal, Solid State Ionics, 60 (1993) 279..

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