Creep and diffusion in high Tc superconductors

J. Phys. III F anc-e 4 (1994) 253-260 FEBRUARY 1994, PAGE 253 Classi ica ion Physic-s Abs ac s 74. 90 C eep and di usion in high l~ supe conduc o s A. Dominguez-Rod iguez (I), M. Jimdnez-Melendo (I), Nan Chen (~), K.C. Go e a (~), S. J. Ro hman (~) and J. L. Rou bo (~) (lj Depa amen o Fisica Ma e ia Condensada, Uni e sidad de Se illa, Spain (2) A gonne Na ional Labo a o y, A gonne, 1L60439, U-S-A- (Recei ed 18 Decembe J992, e ised J5 Oc obe J993, accep ed 22 Oc obe J993) Abs ac , Da a om s eady-s a e c eep and ace di usion es s a e p esen ed o he high- T~ supe conduc o s YBa~CU~O~ and Bi~s j ~CaCU~O~. Bo h compounds exhibi ~xygen nons oichio- me y and possess o ho hombic, laye ed pe o ski e c ys al s uc u es in which Cu occupies he B si es and he o he ca ions occupy he A si es. Fo each, he A-si e ca ions di use mos slowly. Fo e e y species ha has been measu ed, di usion is much as e in he ah-plane han in he c- di ec ion. A low s esses, bo h supe conduc o s de o m by di usional c eep wi h he a e- con olling species being aA-si e ca ion in YBa~CU~O~. In oduc ion. C eep is among he ew expe imen s able o yield in o ma ion abou he di usion p ocesses o he mino i y poin de ec s. When ama e ial is comp essed a high empe a u e, he pu e anspo o ma e , I-e- g ain bounda y sliding accommoda ed by anspo o ma e (GBS) and he nonconse a i e mo ion o disloca ions a e among he di e en mechanisms con olling i s plas ic de o ma ion. Isola ed o clus e ed poin de ec s can ac as elemen a y s eps o di usion. These di usion p ocesses a e esponsible o disloca ion climb ( eco e y c eep) o o anspo o ma e (Naba o, Coble, o GBS c eep). The di e en models desc ibing high- empe a u e plas ic beha iou lead o agene alized c eep ela ion be ween he s ain a e (@) and an e ec i e di usion coe icien (D~~~) =A ~)~ l I~D~~~ (I) d kT p whe e A is adimensionless cons an , b he Bu ge s ec o , d he g ain size, p he shea modulus and « he applied s ess. The o he pa ame e s ha e hei usual meaning. In his c eep equa ion A, h, and na e model-dependen pa ame e s. The e ec i e di usion coe icien equi es some explana ion. I he ma e ial is apu e elemen , only one species pa icipa es in he di usion. On he o he hand, i he ma e ial is a 254 JOURNAL DE PHYSIQUE III N° 2 compound all species mus pa icipa e in di usion. A he same ime, each species can ha e di e en di usion pa hs. An equa ion o he e ec i e di usion coe icien o each species, x, in he compound, can be w i en : D[~~ =D[ +10 "D$ +~D ~ (2) P ~ d whe e he supe sc ip s indica e he pa h o he di usion (I =bulk, p=disloca ion co es and GB =g ain bounda ies) and is he g ain bounda y wid h. In acompound, he poin de ec s a e o en associa ed wi h ade ia ion om s oichiome y. The he modynamic equilib ium is ixed by he apou p essu e o he di e en componen s o he compound. In oxides, whe e he oxygen p essu e (Po~) is la ge, he wo he modynamic condi ions T and Po~ can be easily con olled, so a high empe a u e whe e kine ics a e as , he modynamic equilib ium is easy o achie e. Plas ic de o ma ion unde hese condi ions occu s wi hou decomposi ion o he ma e ial. The e o e, he luxes o he componen s mus be in he same a io as in he compound. Fo A~ Bp O~, ~~~ ~~~~ ~~~~ These equa ions can be ew i en in wo di e en o ms, depending on whe he we assume ha he o e all composi ion is cons an o is cons an along each pa h. De ails may be ound in Iii- I i is assumed ha he o e all composi ion is cons an , he e ec i e, combined di usion coe icien can be w i en e a#y~~ ~com~ i+~+j (4~) ~A ~B ~~ o i i is assumed ha he composi ion along each pa h is cons an , D[)$ =l~ +~, +~+10 "~~j +~~ +~~ + D~ D~ Do PD~ D~ Do ~~jB ~~B ~jB ~~'~~ A B 0 I is easy o see ha he o ms o D[($ a e qui e di e en and a e only equal i he di usion coe icien o one species is much smalle han he o he s, o any pa h. I we assume ha A and Bha e di usion coe icien s smalle han he coe icien 0, D[(~~ becomes (Eq. (4aj) e " ~ ~~~~ ~ ~~~~~ ~~ ~~~~~j ~)~~ ~~ ~~~~i~j B+lo ~~j ~w& ~~ (5,a) o (Eq. (4.b)) : aD' +pD' -1 ~aDP +pDP -' D($~ = ~ ~ +10 ~l' ~ ~ + D[ xD~ PD~ xD( ~~~/~jB ~p/~jB -1 ~d/~GB ~/~GB ~~'~~ A B N° 2CREEP AND DIFFUSION IN HIGH T~ SUPERCONDUCTORS 255 I he di usion h ough one pa h is much as e han h ough he o he wo, he wo e ec i e combined di usion coe icien s become equal. I , o example, g ain bounda y is he as es /~e "8D(~ x iGB~ cam " B daD(~ +p/~GB A (6) I is always possible o w i e he e ec i e di usion coe icien as D~~~ =D° l~( exp (- ~(7) Po~ ~ kT whe e, D° is he p eexponen ial e m, Po~ is he pa ial p essu e o oxygen, P$~ is he e e ence pa ial p essu e o oxygen and AH is he ac i a ion ene gy o he di usion p ocess. See [2] o mo e de ails. I one species has he smalle di usion coe icien , mand AH a e cha ac e is ic o he poin de ec s esponsible o sel -di usion. Howe e , in he mo e gene al case ha DA =D~, and assuming ha di usion p oceeds ia he same a omic de ec , mis s ill cha ac e is ic o he poin de ec s, bu AH ep esen s an a e age ac i a ion ene gy o he A and Bspecies. When he concen a ion o poin de ec s is small, he equa ions o de ec c ea ion o annihila ion and he law o mass ac ion a e applicable o each species, and he alues o mand AH ob ained o c eep co ela e wi h he one ob ained o di usion. Howe e , i he concen a ion o poin de ec s is la ge (no mally ~l§b), he co ela ion be ween mand AH and he poin de ec s is mo e complica ed because o de ec -de ec in e ac ions. High-T~ supe conduc o s p esen se e al p oblems. One is ha a leas wo species ha e e y simila di usion coe icien s. Ano he is ha he concen a ion o anion poin de ec s is la ge. In addi ion, oxygen ions ha e mul iple si es, each wi h adi e en ca ion en i onmen . The esul s o c eep and di usion s udies in he YBa~CU~O~ (YBCO) and Bi~S ~CaCU~O~, (BSCCO) high-T~ supe conduc o s will now be discussed. Di usion. YBa~CU~O~. Oxygen ion acancies a e he majo i y species in YBCO. T ace di usion o oxygen has been measu ed in bo h polyc ys alline and single-c ys al YBCO using ~~O as he ace [3-5]. Concen a ion p o iles we e de e mined by seconda y ion mass spec ome y. The di usion coe icien in he c-di ec ion is 106 lowe han he di usion in he a-di ec ion a 300 °C. Di usion in polyc ys als is gi en by D=1.4 x10~ ~exp (- 93.5 kJ mole ~/RT) cm~/s and is, wi hin a ac o o wo unce ain y, independen o Po~. Di usion in he c- di ec ion is go e ned by an ac i a ion ene gy o abou 174 kJ/mole. The esul s sugges ed ha di usion in he ab-plane may ake place ia amodi ied in e s i ial mechanism which esul s when an oxygen ion a he end o a ow o O(I si es jumps in o an O(5 si e, mo es along O(5 )si es un il i comes o ano he ow end, and a aches i sel he e. The ac i a ion ene gy o di usion is hen made up mos ly o he ene gy o mo e om an O(I si e a he end o a ow o aneighbo ing O(5) si e. Ca ion acancies a e mino i y species in YBCO. T ace di usion o Cu [6], and Ba and Y [7, 8] has been in es iga ed in YBCO. The esul s a e p esen ed in A henius equa ion o m and compa ed o ~~O di usion in igu e I. Di usion o some a e ea h elemen s, Dy, Ho, and Gd a e also shown. Cu di uses mo e slowly han oxygen, bu as e han Ba, Yo he a e ea hs. The ac i a ion ene gies and he dependencies o di usion on Po~ a e gi en in able I. The slowes mo ing species is Y. These esul s a e in acco d wi h ecen a omis ic simula ions 256 JOURNAL DE PHYSIQUE III N° 2 io*8 18~ ,~.10 4~ (m ~ '10"'~ cu ~Ba ,~.14 iii Y* iB ,~ a io° 0.7 0.8 0.9 1.0 1,I .2 loco/T ST~) Fig, I.-A henius plo s o di usion o O, Cu, Ba, Y, and a e ea hs in YBCO a Po~= Ix10~ Pa ( illed diamonds ep esen Y, squa es wi h cen al do s ep esen Dy, squa es wi h single diagonal lines ep esen Ho, and he squa e wi h he c oss ep esen s Gd) om e e ence [7]. Table I. -Ac i a ion ene gies and o.<ygen pa ial p essu e dependencies o di usion o componen s in bulk polyc ys alline YBCO. T ace QPo, Re e ence (kJ/mole) Dependence O93. 5±2.9 no e ec 3-5 Cu 256 ±4nega i e 6 Ba 890 ±125 no e ec 7,8 Y10~ ±200 unknown 7,8 o poin de ec s in YBCO, which indica e ha he o ma ion ene gies o Ba and Y de ec s a e ex emely high [9]. Calcula ions using he same po en ial yield alues o 820 and 1350 kJ/mole o he ac i a ion ene gy o he di usion'o Ba and Y, espec i ely [10]. I should be men ioned ha he di usion o Ba is aniso opic, wi h di usion along he c-axis being mo e han h ee o de s o magni ude slowe han di usion in andomly o ien ed polyc ys als [8]. Bi-S -Ca-Cu-O. Oxygen (whose acancies a e he majo i y species in BSCCO) ace di usion has been measu ed in single- and poly-c ys alline Bi~S ~CaCU~O~ (2212) and in single c ys als o Bi~S ~CUO= (2201) [11, 12]. The di usion coe icien s in polyc ys alline 2212 a e gi en by D=1.7 x10~~exp(-89.7kJ mole~~/RT) cm~/s, while he di usion coe icien s pa allel o he c-axis a e D=0.6 exp(212.3 kJ mole~ ~/RT) cm2/s. Coe icien s o di usion in he ab-plane o 2201 single c ys als a e iden ical o hose measu ed o N° 2 CREEP AND DIFFUSION IN HIGH T~ SUPERCONDUCTORS 257 polyc ys alline 2212, while hose measu ed o di usion in he c-di ec ion o 2201 a e close o. bu sligh ly smalle han, hose ob ained o he 2212. The esul s sugges ha di usion in he ab-plane occu s ia an in e s i ial mechanism and ha di usion in he c-di ec ion occu s ia a acancy mechanism. The dependence o he oxygen di usi i y on Po~ has no been in es iga ed. Li le is known abou he di usion o ca ions in 2212. To da e, he only ca ion in es iga ed has been Ag [13]. The di usion coe icien o Ag in polyc ys alline BSCCO is gi en by D=8.9 exp (181.4 kJ mole~ ~/RT) cm~/s and is no asensi i e unc ion o Po~ 11 3]. The Ag esul s a e compa ed o hose o oxygen in igu e 2. lO~ ~ lO~ ~~~~~ ~E ° ,~ alo ~~O di usion 10 ~~iz O.9 1-O I,I 1,2 1.3 1.4 1.5xlO~ /T (1 /K) Fig. 2.-A henius plo o he di usion o Ag and oxygen in polyc ys alline 2212 a Po~" Ix10~ Pa (a e Re . [13]). C eep. YBa~CU~O~. The samples used in he de o ma ion expe imen s a e he same as hose used in di usion. The sample p epa a ion is desc ibed in [14]. The samples, wi h a e age g ain sizes anges om 7 o 76 ~Lm, we e de o med in comp ession unde con olled a mosphe e a a cons an c osshead eloci y o a cons an load unde con olled a mosphe e [151. Tempe a u es anged be ween 850 and 980 °C and he Po~ be ween 10~ and 105 Pa. In all cases as eady s a e was eached a e abou 2§6 de o ma ion and he pa ame e s o he c eep equa ion we e de e mined by s ain a e, load, o empe a u e changes. S ains o 20§6 we e ou inely achie ed wi hou c acking. Fo mo e de ails, see [14, 15]. The s ess exponen (n =I and g ain size exponen (h =2. 8), oge he wi h amic os uc- u al obse a ions indica ing acons an g ain shape, a e consis en wi h de o ma ion by g ain bounda y sliding accommoda ed by di usion. The iden i ica ion o he a e-con olling species is complex due o he change o he ac i a ion ene gy wi h Po (964 kJ/mole Po om 10~-10~ Pa and 646 kJ/mole a 10~ Pal. JOURNAL DL pHyqiouE ii T4N. 2 FEBRUIRY 19~4 ~ 258 JOURNAL DE PHYSIQUE III N° 2 These esul s a e shown in igu e 3. The Po~ exponen (m ), he o he pa ame e ela ed o he a e-con olling di using species canno be de e mined due o he change o AH wi h Po~. Howe e , om igu e 3 i is possible o de e mine m, assuming ha he mechanism con olling he plas ic de o ma ion does no change wi h he Po~. o w o 8.2 8.4 8.6 8.8 9.0 9.2 10000/T [1/KJ Fig. 3. Dependence o s ain a e in YBCO on I/T o Po~ o 103 ( iangles) and 104 Pa (ci cles) a mI MPa. In his case, we can w i e : e, «~ (Po~)i AH~ AH~ [«~ (P~~)~ ~~~ kT and mwill be equal o 15.3 o 10~/T =8.5. Al hough mchanges wi h T (Fig. 3), he main alue o mis due o he di e ence in ac i a ion ene gy wi h Po~. This alue p obably does no ha e aphysical meaning so he assump ion made o ob ain mmay no be alid and he mechanisms o species con olling he plas ic de o ma ion may change wi h Po~. This beha iou has been ound in COO [16, 17] whe e he ac i a ion ene gy changes wi h Po~. In he COO case, he explana ion was ha he na u e o he mino i y poin de ec s con olling he mechanical beha iou changed om oxygen in e s i ials o oxygen acancies [16, 17]. I he same change om in e s i ials o acancies happens in he ca ionic subla ice in YBCO, om igu e 3, asingle m alue canno be ob ained, howe e insu icien in o ma ion conce ning he mino i y species on he ca ionic subla ice exis s o ca y his specula ion u he . Recen ace di usion esul s indica e ha Ba di uses independen ly o Po~ so we may assume ha he de o ma ion o polyc ys alline YBCO is con olled by he di usion o Y. Howe e , mo e wo k needs o be done on sel -di usion o Y as unc ion o T and p~~ in o de o e i y he esul s ob ain by c eep. The hypo hesis o achange o he na u e o he poin de ec s can explain he change o AH and he un ealis ic alue o m. N° 2CREEP AND DIFFUSION IN HIGH T~ SUPERCONDUCTORS 259 Bi~s j,~CaCU~O~. The sample p epa a ion has been desc ibed in [181. The samples we e de o med in comp ession as desc ibed o YBCO. Mos o he es s we e pe o med in ai , bu in a ew es s, amix u e o lowing I§b O~/99 §b N~ o 10 §6 10 §b O~/90 §b N~ was used. Tempe a u es anged om 785 o 835 °C. In all cases, appa en s eady s a es we e gene ally achie ed wi hin 2 §b o s ain. The pa ame e s o he c eep equa ion we e de e mined as o YBCO. Fo «<3MPa, @a«. The ac i a ion ene gy was 10.3 ±2.0 eV/kT and he oxygen pa ial p essu e dependence was equal o 0. The dependence wi h g ain size was no examined. These esul s sugges ha he plas ici y occu ed by di usional low, howe e he e ec o g ain size combined wi h amic os uc u e s udy will be necessa y o de e mine he ac ual mechanism con olling he plas ic de o ma ion. The e is alack o ca ion di usion da a o he 2212 compound so i is impossible o know which specie con ols plas ici y. As in he YBCO compound, much mo e wo k needs o be pu sued in de o ma ion as well as di usion o ha e a ue pic u e o he mechanism con olling he plas ici y. Conclusions. S eady-s a e c eep o YBa~CU~O~ and Bi~s j ~CaCU~O~ occu ed by di usional low in he anges o empe a u e and s ess ha we e s udied. The ac i a ion ene gy o each ma e ial was 9-10 eV. Fo YB~CU~O~, his alue ag ess wi h he ac i a ion ene gy measu ed o Ydi usion. Di usion o he A-si e ca ions has no been measu ed o Bi~s j~cacu~o~. YBa~CU~O~ exhibi s awide ange o oxygen nons oichiome y and i was ound ha c eep a es inc eased as oxygen pa ial p essu e dec eased. Bi~s i ~CaCU~O,, exhibi s amuch smalle ange o nons oichiome y and no dependence o c eep on oxygen pa ial p essu e was obse ed. Acknowledgmen s. This wo k was suppo ed by he U-S- Depa men o Ene gy (DOE), Basic Ene gy Sciences and by Conse a ion and Renewable Ene gy, as pa o aDOE p og am o de elop elec ic powe echnology, unde con ac W-31-109-ENG-38. Wo k a Se illa was suppo ed by CICYT, MATBB-O181-C02 (Minis e io de Euducac16n yCiencia). Re e ences [ii Jimdnez M., Dominguez-Rod iguez A., Cas aing J. and Mi quezR., Di usion and c eep applica ion o de o ma ion maps on NiO, Sc ip a Me all. 20 (1986) 839. [2] B e heau T., Cas aing J., Rabie J. and eyssib e P., Mou emen des disloca ions e plas ici d h hau e empd a u e des oxydes binai es e emai es, Ad. Phys. 28 (1979) 835. [31Sab as J., Mon y C., Pe eaudeau G. and Be joan R., Oxygen di usion, oxygen acancy concen a ions and chemical di usion in Yj _~Ba~_ cu~_~07-6, J. Less-Common. Me . 239 (1990) 164-165. [4]Ro hman S. J.. Rou bo J. L, and Bake J-E-, T ace di usion o oxygen in YBa~CUIO~_~, Phys. Re '. B 40 (1989) 8852. [51 Ro hman S. J., Rou bo J. L., Welp U. and Bake J. E., Aniso opy o oxygen ace di usion in single c ys als YBa~CU~O~_ ~, Phys. Re . B 44 (1991) 2326. [61 Rou bo J. L., Ro hman S. J., Chen N., Mundy J. N. and Bake J. E., Si e selec i i y and ca ion di usion in YBa~CUIO~_ ~Phys. Re . B 43 (1991) 5489. [7] Nan Chen, Ca ion Di usion in polyc ys alline YBa2CU~O~, Ph. D. Thesis, Illinois Ins i u e o Technology, Chicago, IL (1991). 260 JOURNAL DE PHYSIQUE III N° 2 [8] Nan Chen, Ro hman S. J., Rou bo J. L. and Go e a K. C., T ace di usion o Ba and Yin YBa~CU~O~, J. Ma e . Res. 7(1992) 2308. [91Bae zold R. C., Compu a ions o poin de ec ene gies in YBa~CU~O~~, Physic-a C181 (1991) 252. [10] Bae zold R. C., p i a e communica ion (1992). [ll] Runde M., Rou bo J. L., Ro hman S. J., Go e a K. C., Mundy J. N., Xu X, and Bake J. E., T ace di usion o oxygen in Bi~S ~CaCU~O~. Phys. Re . B45 (1992) 7375. [121 Runde M., Rou bo J. L., Mundy J. N., Ro hman S. J., Wiley C. L, and Xu X., Di usion o ~~O in B12S ~CuO~ single c ys als, Phys. Re . B46 (1992) 3142. [13] Fang Y., Danyluk S., Go e a K. C., Nan Chen, Runde M., Ro hman S. J, and Rou bo J. L., T ace di usion o I'°Ag in Bi~S ~CaCU~O~, Appl. Phys. Le . 60 (199? 2?91. Ii 4] on S umbe g A. W., Nan Chen, Go e a K. C, and Rou bo J. L., High empe a u e de o ma ion o YBa~CU~O~_~, J, Appl. Phys. 66 (1989) 2079. lis Go e a K. C., Rou bo J. L., Biondo A. C., Gao Y., de A ellano-L6pez A. R, and Dominguez- Roddguez A., Comp essi e c eep o YBa~CU~O~_~, J. Ma e . Res. 5(1990) 2766. [161Rou bo J. L., The s oichiome y dependence o he de o ma ion o Coj_~O, Ac a Me all. 30 (1982) 663. l17] Dominguez-Rod iguez A., Cab e a Cano J., M6 quez R. and Cas aing J., Poin de ec s and high- empe a u e c eep o non-s oichiome ic Nacl- ype oxide single c ys als II. COO, Philos. Mag, A46 (1982) 411. [181 Rou bo J. L., Go e a K. C., Mille D. J., Kazelas D. B., Clauss C. and Dominguez-Rod iguez A., Comp essi e c eep o dense Bi~s i 7CaCu~O~, J. Ma e . Res. 7(1992) 2360.