REVISTA MEXICANA DE FíSICA 44 SUI'I.EMENTO 3. 202-207 DICIEMBRE 1998

Thermopower and lattice parameters oCYBa2Cu307_Ó thin films as a Cunction oCoxygen content

J. GiraldoDepartamemo de Física. Uni\'ersidad Nacional de Colombia. Apartado Aéreo 6790.J. Sa1ltajé de Bogotá, Colombia

A. Pulzara', P. Prielo, and M. ChacónDepartamento de F(sica. Universidad del Valle. Apartado Aéreo 25360. Cali, Colombia

Recibido el 25 de enero de 1998; aceptado el 7 de julio de 1998

The stoichiometry and structure of Y 123 compounds strongly determine Iheir physical propcrties. A theoretical and experimental study inoxygen-dcficient YBa2Cu307_Ó thin films is presellted in this reporto \Ve have mcasured resistivity and thermopower in a set of high qua litycpitaxial samples with O < o < 0.5. The e-axis lauice constant has hecn detcrmined by X-ray spcctroscopy. AH latticc lengths have beenevaluated numerically in (he same range of composition using the microscopic effective mcdium theory. The calculated results compare wellwith those reported experimcntally. A correlation has been undertaken among Ihe above and other physical quantíties. in particular bondlengths, Te. and the isotope effect. and some conclusions have been extracted. The main conclusion from the present wurk is that. althoughIhe electron-phonon interaction alone is not enough to explain the pcculiarities of YI23 based compounds and its high Te. phonons yieldimportant contrihutions to their thermal transport properties.

Ke)'words: High tempcrature superconductors: Y 123 superconducting thin film!'>;thermal and structural propcrties

La estequiometría y la estructura de los compuestos Y 123 determinan de manera radical sus propiedades físicas. En cste reporte se pre-senta un c.studio teórico y experimental de películas delgadas de YBa2Cu301_Ó deficientes en oxígcno. Hemos medido la resistividad y latcrmopotcncia de un conjunto de muestras epitaxialcs de alta calidad con O < J" < 0.5. La constante de red del eje e se ha ueler!llinadopor espectroscopía de rayos X. Todas las constantes de red se han evaluado numrricamente en el mismo rango de composición usando lateoría microscópica de medio efectivo. Los resultados calculados son comparahles a los que se reportan experimentalmente. Se ha hechouna correlación entre las anteriores cantidades y otras cantidades físicas, cn particular. las longitudes de enlace. la Te y el efecto isotópico. yse han extraído algunas conclusiones. La principal conclusión derivada del presente trabajo es que, aunque la interacción clectón-fonón porsí sola no es suficiente para explicar las peculiaridades de los compuestos basados en Y 123 Y su alta Te. los fonones contribuycn en formaimportante a sus propiedades de transporte.

Descriptores: Superconductores de alta temperatura crítica; películas delgadas superconductoras Y 123; propiedades térmicas y estructurales

PAes, 74.72.Bk; 74.76.-w; 74.25.Fy

1. Introduction

After 1I years ofhigh-T, superconductivily (HTS), YI23 inits different stoichiometries and varied compositions contin-uous being Ihe mosl studied copper oxide [1-30]. Alihoughthe number of thcories to explain the high Te is rather big,une basic column to aH bUI a few models is lhe believc lhatsuperconduclivity (Se) originates in the cuprale planes. De-fects cornmonly found in the 123 struclure. particularly in lhechains, playa dominanl role in controlling superconductingproperties. A structural question of major inlercst has heenthe variation of individual alom positions with oxygen slO-ichiomelry [2-18]. Early research on Ihis aspeel gave risetu the charge-transfcr hYPOlhcsis [1 J. Although the chainsare assumed to be insulators in Ihe original models. they arenow known to conduct and 10 exhibil SC [2.3,5,61. Funherisomorphic substitutions rcveal that CuQ.,! planes and Cu-Oehains alltogether are basic ingredients for SC [í-lOJ. Re-placemenl of Y by, e.g., Ho, Mo and other rare earths (Pr isan exception [11-14]; bUIthere are reeent repons thal clearly

show SC in Prl23 [15]) or of Ba hy Sr and Ca does nol in-troduce scrious changcs in the normal and superconduclingslale propcrtics 116). However, in previous experimental andthcoretical work il has been cstablished lhat the subSlilutionof Cu(2) hy Fe (we follow Ihe nomenclalUre of Ref. 18) orofCu( 1) by Ga, Al or Co affeets severely 7~ [í-D. 1íl.Slrik-ingll' in Ihe latlcr case YBa2Cu3_.rCOzO¡_6. our and oth-crs results on lhe lattice paramelcr lengths a anu b followlhe same trends than on oxygen [moslly 0(1)1 deficicnt sam-pies in Iheir approach lo Ihe orthorhombic-to-Ietragonal (O-t T) transformation, while e decrcases slightly. Inslcad, oneknows f1'ol11 previous work lIS). ano is one ofthe conclusionsfrom our sludy. thal on rCll10ving O( 1) e ¡ncrcases slowly butmonotonously. Earlier reports elaim that thcrc is a notoriousplateau in lhe dccrcasing Te [2J. These earlicr results havcheco criticized lIS, 19]. Thc Raman.active modes vary COf-

respon<!ingly, being the apical [0(4)J mode Ihe mosl sensi-I;ve one ID, ID, 201, hOlh with Co doping [D-17J and oxy-gen dcfkicncy (20]. It is intercsting to note that the changeof the so called 500 mode (of frequency around 500 cm-1)on incrcasing Icmperaturc is qualitalively lhe same in both

THERMOPOWER AND LATTICE PARAMETERS OF YBa,CU,07_' THIN F1LMS AS A FUNCTION OF OXYGEN CONTENT 203

FIGURE l. Calculatcd la[(icc paramelers and unit cel! volume fordifferent O contents.

I

•

03,..

•

" ."'.•

0.2 0.3

O~yoen OefIC"ncy (51"

.02.--~-_~ ~ ,b .~I.•. 01

'00•••••••3.97r-~_~ -1

11,66

11,&4

11.&2

11,60

11.511r 11.seL_- -

1'''.'1185.&

1852

1&<1.8

1M,.

'&<1,0

strueturallransition from O -+ T symmetry [2, 18J. The evo-lution to a tetragonal struclUre is slower than in the case ofCuSubSlitulion hy Co, whieh was lhe eoneern in Refs. 10 and.I?There the results on lauice contants and phonon modes com-pare well with those oblained by Kakihana el al. [8,9J. Thebchavior Oflhc e axis lenglh evolves differently lo the Co sub-stituted case, incrcasing markedly with dccreasing oxygencontent; il dccreascs more slightly in the Co case. Jt should benOliccd thallhc SS in the lalter case remains after the O -t Ttransition takcs place, \Vhich is ill contrast lO the vanishing ofse close to the structural transformation in the case of oxy-gen deficiency. This result has to be taken ioto accounl whenrclating the structural transformation to Ihe intrinsic proper-ties 01'the SS.

Going baek lo Fig. 1, we want lo eomment lhal lhe faelthat e behaves the other way around for oxygen dcficient sam-pies lhan for Cu suhslituled by Co has an easy explanalionwithin lhe EMT seheme. Figure I in [lO) presenls the eohe-sive energy of a system in lhe EMT approaeh, the dominantlerm in Eq. (1) there. NOliee that il is higher for O and Cothan for Cu, which rneans lhal the removal of O in the chainshas the opposite effeello lhal 01'replaeing Co by Cu. In par-ticular, since the compression of the structure in the Cu sub-stitutcd case is explained in Ref. lO, on energy argumcnts,Ihe ¡ncrcasing of e has a similar origino The unit-cell vol-umc in our ca!culalions cvolves in the samc way as in the ex-perimental rep0rl. From our ealeulation of bond leng!hs [IOJand lhe experimenlal mesuremenls [18], one coneludes thatlhe dislanees between Cu planes and belween !he latlers andBa planes inerease in bOlh cases (Co SUbSlilution and O de-ficieney), where one alters the ehains. Our ealculations andrneasurcments (ef below) do nol support suddcn jumps inbond lenglhs. We menlion on passing lhal those early elaimshave been eritieized reeently [5J. Remark that lhe Cu(l )-0(4)length decreases in the case of Co SubSlitution whilc it in-

The mieroseopie effeelive medium theory (EMT) is an ex-cellent tool to evaluate fram first principies the clectronicproperties of metal s [451. It avoids the heavy computa-lions that are usual in Ihcse kind of calculations. In a re-cenl work il was sueeessfully applied hy lhe firsl limelo lhe high-Te eompounds lo sludy Ihe lalliee proper-lies of YBa,Cu3-xCOx07_ó [10, 17J. Using an improvedEMT (17), we have ealculaled now lhe struelural parame-lers a, b and e and Ihe volume V = abe of Ihe unil eellof YBa2Cu,07_ó for different oxygen eontent 7 - J, whereO < J < 0.5. Our approaeh is Iikcly nol reliable for J > 0.5.The resullS are presented in Fig. l. They compare ralher wellwith the experimenlal rcsults of Jorgensen el al. [18J, al-though ours adjusI to an almost linear behavior. Similar toour previous case study, [lOJ we notice that a increases whileb decreases with d up to d = 0.5, where one is c10se lo a

2. Calculation of laltice parameters

cases, O-defieienl and Co-dopcd samples. Though il is iso-tope shifled to a lesser degree Ihan lhe CuO, plane modes, itis signifieantly broadened [9,21, 22).

Regarding YBa,Cu,07_', lheir physieal properties arevery sensitive to oxygen content and preparation (18). Themetallie phase, with high Te '" 90 K for J '" O, firstlylransforms into the scmiconducting phasc al Ó ::::::0.6 andlhen lo lhe antifcrromagnetic compound. The cxacl way inwhieh Te evolves Wilh J is delermined primarily by the typeof samplc preparation. Disordering in lhe CuO chaios SCCIllS

lo be lhe main reason for this feature [22,23J. Olher prop-crties that have beco lhoroughly studied for dilTcrcnt COITl-

posilions are lhe isolope cffeet eoeffieienl [33), Raman andinfrared modes [21,22), and many Iransport properties. Ii isvcry valuablc to study lhe correlation bctwccn lhe many pos-sible microscopic arrangcments and lhe physical propcrticsin lhe normal (NS) and in the supereondueting slale (SS).Mostly sincc theTe are scrious doubts 1hal lhe se cffcel re-sides exelusively in the planes [6,191 and sinee il has heenestablished that even earefully prepared erystals exhibit localrnicroscopic disorder [25]. HeTe, we concentrate on structuralparamelers and thermopower. There is a large body 01'previ-QUSrescarch 011lhe las( suhject and we rcfer lhe rcaders 10 lheeurrenl literalure [26-44]. In Ihis work we presenl and dis-cuss lhe result of measurcmeots pcrformed in a rather shorttemperalure range around eD (80 K < T < 300 K; te)/) isthe Debye temperalUrc); wc confirm that Ihere is a universaltrend of the Seebeck coefficient S to be understood. namclya huge peak above Te followed by a deereasing of S al higherT and a correlarion betwecn resistivity and thermopowcr thatwas pointed oul by the firsl lime in ReL 35. As in our pre-vious work on doped-Bi eompounds [35J, we \ViII follow aralher conventional approach lO cxplain the rcsults 00 ther-mopower in YI23 oxygen-defieient thin films 135-381. T-hisis the second part of our reporto Firstly, the slructural prop-erlies evaluated using Ihe local densily approximation (LDA)as a basis, are presenled and discussed.

Rev. Mex. Fís. 44 S3 (1998) 202-207

20~ J. GIRALDO, A. PULZARA, P PRIETO, AND M. CHACÓN

.6=0.4906=0.46• 6=0.43

1.2

>.~ 1.0<:"£ 0.8o",~ 0.6

"E50.4Z

0.2

0.038.0

'" <D .., '" <D ~.. .. .. .., N Nci ci ci ci ci ci

" " " " " """ "" "" "" "" ""

38.4 38.829 (Degreesl

(005)

39.2

0.40

0.35

0.30

_ 0,25N

":> 0.20.:,t: 0.15CIl

0.10

0.05

0.00

•

•

•

50 100 150 200 250T (K)

300

FIGURl:. 2. Normalizcd imcnsity of ¡he X-ray diffr~ction peak(0.0.5) of ¡he films for differcnt O conlcnts. Thc Rocking curvewidth indicates Ihat the 1I1ms are complctcly oricnted.

FIGURE 3. Plots of S/T ~'S.T for differenl oxygen contcnt á. Notethe parabolic shape in i.he rcgion aboye Te.

4. DisclIssion of thcrmopowcr resllll~

In Fig. -l \••..e plOl ST \'S, T'l. in a rcstrictcd Icrnpcralurc range(lóO < T < 300). As in a previous work [35.3G]. in lberangc under consideration the rcsults adjusl weH to the fol-lowing cxprcssion (",,'c use lhe samc nomenclalurc than inRe!'. 35):

wherc {/ takcs inlo :.u.:count additional conlrihutions \29J.'\' (1') provides Ihe Icmpcrature depcndence 01' cffccts duc(o Ihe ('-p intcraclion. 1I is inlcresting to note thal Ihe ex.Irapolalion of each curve in Ihe linear region lo their inlcr-seclion at T = O increases with ó. This feiJture is disclIssedbclow. \Vhat we want lo undcrline from Fig. 1 is Ihe parabolicshapc al' Ihe set of curves. This suggesls that. in addition toIhe usual (almost linear) diffusion tcrm due to clcclrons, thcrcis an important contri hUIion proporlionallo T-l• Prohahly iris a manifestation of lhe ('-1' inlcraction. as il will he argucdbelo\\'.

(I)

(2)(JS=nT+'j"

elsewhclc 1441. The trends 01" Ihc results on resistivityand thcrmopowcr rcscmblc Ihose previously found in Cu-suhstituled bismulh compounds 135,36], We follow a sim-ilar approach to the cooventional one discussed in Ref. 35ror Ihe interpreralion 01' Ihe lhermopower Illcao;uremcols 00

oxygcn-deficienl Y 123 lhin Iilms. Figure 3 conlains Ihe rc-sults of plotting SIT against T. This allows one lo discusslhe elTecl of lhe elcclron-phon()n (f'-p) mass enhancemenl asinvestigated by Kaiser [291. He cxpresscs the ditTusion lher-mopower in lerms 01' Ihe renormalization parametcr..\. and Ihebare lhermopowcr parameler .\ b = Sb /T (Sb bcing Ihe harethcnllopower. which for non-magnelic syslems is expcctcd lohe approximately linear in T) as

~ = '\b[1 + a.\.\, S(T)].

\Ve lum now tu (he experimental techniqucs and mcasurc-Illcnts of e-axis Icngth. transition tcmpcraturc. resistivily andthcrmopower of thin films, Most of these propcrtics are cx-pecled lo be lhe same as in hulk samples HGI. In particular,thcflllopowcr is almosl thc SUIllC for hulk samples and in nottoo lhin filOls. which is our case (441.

The films were prepared ;11 .f;tIl by spultcring al highoxygen pressure (3.8 mhar) on SrTiO, (0.0.1) Illonocrystals,lhc oxygenation and dcoxygenalion was made hy varyinglhe oxygen parlial prcssure during the cooling proccss ahout8[IO°C until room tempcrature. lhc Rocking curvc width01' Ihe (0.0.5) peak shows values 01' Jw helow 0,5°, X-raydiffraction indicates that lhe films (grown on SrTi03) arecomplctely oricnlcd wilh their e-axis perpendicular to thesuhstralc. lhe filllls h,',ve a very high degrce 01' cryslallinily,Figure 2 is a plot 01' the nonnalizcd intcnsily ol' Ihe X-raydiffraclion peak (0,0.5) 01' our superconducling Ihin films. X-ray technique allows us lo determine the e-axis Icngth in ourfilms; Ihey agrce very wcll wilh lhe results reponed in Ref. IRamJ with lhe above nUlllcrical rcsults. In the latter case. the O-t T transilion scellls to he below Ihe lIsunlly reponed ex-perimental value. This could be due lo Ihe exclusion 01' thehyhridil.ation ter!TI in our calculalions,

As in Ref. 35. Ihe experimental procedure (O measure re-sistivilY and thermopower were lhe four-prohe lcchnique andth~ differcntial method, respectively. The delails are reported

3. Measurements of thermopower and e-axislength

cr~ascs in the case 01' oxygcn removal. Thc final resull inYBa:,?Cu3_.tCO.rOi_ó is a dccrcase of e undcr doping withen. whilc il increascs in Yha1Cu30¡_J with oxygcn rcmoval.In bOlh cases a dctailcd rcdislrihution 01' charge takes placewithin (he cnvironrncnt uf t.he chains, in contrasl to the origi-nal charge lransfcr hypothcsis.

Rt'l'. Me.\". Fr'i. 44 S3 (199H) 202-207

TfIERMOPOWER AND LATTICE PARAMETERS OF YB.,Cu,O,_, THIN FILMS AS A FUNCTlON OF OXYGEN CONTENT 205

:::::......" ...•. ." .

•

TABLE 1. Resistance just aboye Te (Ron$ed. and at 200 K (!l200);. .interccpr {3in Fig. 4 and bare thermopower parameter.\b [Eq, (1»)for diffcrent oxygen contents .

J Ron~t"t (11) R200 (n) f3(IN) .\b (,IV K-')

0.21 02.31 05.44 0128.91 0.00380.26 12.40 22.16 1240.10 0.00740.35 31.61 40.13 1840.10 0.00850.43 33.18 36.20 1986.04 0.02290.46 37.39 39.80 2948.14 0.03820.49 40.21 47.07 3678.95 0.0468

.', •

FIGURE 4. PlolS of ST t's. T2 for diffcrent oxygcn contcnt o.• Ó ; O.4n; • J ; 0.46; • Ó ; 0.43; o Ó ; 0.35; • Ó ; 0.26;O Ó ; 0.21.

JS'S; ; bTp. (4)

~'hcre 65 can be seen as a correerion lerm 10 MOll formula.The most exacl form 01' cach lerm is vcry eumbcrsome. evenin SM [39-421. 11has been sho\Vn Ibal in SM (Fermi liqui~FL-Iike model) Ihe sum of scveral correction Icrms arisingfrom Ihe e-p inlemelion (\Ve eall il 65') is negligible 1381.Al 10\Vlemperalures (T < EJD) an~ assuming Ihal S. is lin-ear in T. il ¡ncreases cuadralically. For T > 0D il decreascsas r-I• Herc we sumrnarizc the argumenl thal leads us tobelieve Ihal Ihis contribution is significant in Ihe cuprates.

In convenlional me!als an~ allo\V T. (65' /S.) is propor-Iionallo Ihe resislivily p 135. 381;

\Ve bclicvc that within lhe rangc 01' T undcr discussionlhe two tcrms aboye are lhe main contrihutions lO ther-rnopowcr in oolh cases (bismuth-dopcd compounds andoxygen-~efieienl Y 123 Ihin films). The firsllerm can he inler-prctcd as lhe usual linear diffusion tcrm in Motl formula (lhedominant (crm); following Rcf. 34, wc wrilc il as Sb ::: oT,Le.. .\b = o. The second Icrm has been rcfcrrcd lo as aphonon drago We bclicvc that this intcrprctation ariscs froma misundcrstanding found in current lilcraturc, whcrc oothcffccts are lrcatcd on an cqual footing [39]. 'fhe phonon-induccd mass cnhancclllcnt resulls in an increase in the clce-lronie ~ensily of slales (DOS) 1381. The peak of Ihe normalphonon drag is cxpccted lo happen at \'ery low lempcrnlurcs(T « (-1/). As in previous \Vorks 134-411. \Ve prefer lO in-Icrprel lhe eleclron mass cnhanccmcnl as a rcsuh of ti moregeneral ('-p intcraction lo all orders. 11docs not requirc Ihepresencc of a phonon flux. bUI it should include the phollYphonon-drag in a more gencral model.

Recenl calculalions include Ihe full elcclron-phonon in-leraelion in simple melals (SM) 138]. UlJimalely Ihe Seebeekcocfficicnl can be wriltcn as

\Vhere b '" ]o' /(n cm K). The euprales can be ~eseribe~ ashad Illelals H71. Ir we mainlain Ihat the linear dcpenJcncc inp holds above Te in lhe melallie slale of Ihe copper oxides.and since p in Ihe cupralcs is three or more ordcrs of llIagni-lu~e grealer Ihan in SM. one can expeellhal (6S/SbJ '" 1 ina ccrlain rangc of T. For T > 0D Ihe leading lcrm in 65'deereases as I/T2;

while it is linear in T at low T. l.e .• there musl be a maxi-IllUIll in (65/5.) belo\V EJD. Ii should be nOle~ Ihal (-)D inIhe euprales is higher Ihan in SM, \Vhieh enhanees Ihe rela-lionship above. Ii is likely Ihal Ihe peak above T, comes oulfrom Ihe e-p conlribulion. although ils exacI form on Ihco.retical grounds is nOl known YCl. Adding up Ihis contributionto olher correelion lerms. one has a significant 65 thal com-peles wilh Sb and gives rise lo the universal trend of 5 in thecuprales. wilhout rcsorting 10 exotic models.

To reinforee Ihe argulllenl we have buih up Table 1 far~ifferenl oxygen con len! of our films. The seeon~ and Ihir~column conlain Ihe value of Ihe resislance for cach samplejusI al Ihe onsel of supereonduelivily and al 200 K. Al alow conccntration level il increases more al' less Iinearly asa funelion of [l. in aeeor~anee \Vilh Eq. (4). One fin~s oulthal Ihe universally observed inerease of S wilh p is lo becxpected. Thc founh column contains Ihe valuc of Ihe inler-eepl in Fig. 4. The slope is presenle~ in Ihe fiflh eolumll. Theevolution of Ihese \'alues with 6 is very rneaningful: lhe bareparameler Xb = o increases by an order 01' magnilude inlhe 6-range under consideration. which means that dilfusionthcrmopower increases considcrably. This is reasonable duelo disorder. Thc intercept 13 increases even more, in the samepropon ion than p as secn from Ronseto in strike accordancewilh Eq. (4¡).

(5)65' ')S; (X (EJ/)/T)-.

(3 )S; S. + 65.

Rev. Mex. Fís. 44 S3 (1998) 202-207

206 J GIRALDO. A. PULZARA. P PRIETO. AND M. CHACÓN

l/l oe • •'" oe 0,2 Qoc. •x • a oW 0.1 cu •'"c.O • Oxygen defíciency

O 0.0l/l

Transition Temperature (K)

4

-¡,,"

2

,.••• .55

0.4

0.3

o

40

• •o •

50

•

60 70 80

0.5

0.4

0.3

¡¡0.2

oo

• 0.1

0.090 100

FIGURE 5. Plot of the naturallogarithm ol"Ihe Secbeck cocfticiental 100 K (In 5100) \'S. the oxygen conten! 6.

5. Oxygen deficiency, e-axis length and ther-mopower

Por many reasans, it is important lo cstablish corrclations bc-{wccn ditTcrcnt propcrtics as a funClion 01'composition. Fromthe forcgoing seclion. one concludes thal thefe is a corrcla-tion bctwccn p aod ó and. thercforc, bctwccn S and J. Thclaucr follow5 directly from Fig. 5, whcrc we plot lhe naturallogarilhm 01' 5 al 100 K \'.1'. Ihe oxygen deficiency o. We lind,approximately:

In 5100 = 1.0+ 5.20. (6)

FIGURE 6. Isotopc exponem Q and oxygen eontent b as as a fune-(ion ofthe transition tcmperature Te for YBa2CU3_rCOzOj_ó, TheOCll values are taken from Ref. 33. For eomparison. the oxygenisotopc cocfficients 00 in YBa2_rLa.rCu3Üy from Ref. 50 are in-duded.

Por comparison, the oxygen-isotope exponent inYUa:¿_xLaxCuJOy is incluJeo [50]. Thesc results are inagrecment with those very-well known in La214 com-pounds [51,52J. In lhe la"t work we have established a rela-tiollship bctween the van Hove singularity shift and the Fermilevel as a function of doping, thcrefore betwecn x and Te, inLa2_xBaxCu04. Thc same trend íL'i in Fig. 6 is found in thiscase belween D and J' wilh Te (for delails see Ref. 52). AHlhe correlations above are of worth to unravel the intricatepairing mechanism in the cuprates.

Similar cxpressions are valid relating thcrmopowcr aod lal-(ice constant c. The laSI one has been looked for sincc veryearly [48]. A more qualitative relalionship has been ohtainedby Cornejo el al. [49], who elaim thal il is linear. Qur ex-perimental rcsults providc us with the following approxi-mate linear relation between e and l5for the oxygen-deficientfilms: e = 11.48 + 0.256, while Ihe ealculations hased onEMT (Fig. 1) yield the following one for volume samples:e = 11.57 + 0.186. The latler is c10ser lo Ihe experimenlalresults for volume samples in Ref. 18. The struetural proper-ties of thin films are more Iikely sensitive to surface effcets.What is more striking is the faet that our results do not sup-port a linear relation betwcen S and c. On the eontrary, one istempted to propose an almost linear behavior bctwecn p and6 (ef Tahle 1).

Finally, it is interesting to establish a eorrelation betweenlhe isolOpe effeel coeffieienl D, Ihe oxygen deficieney o andthe critical temperature Te. This is summarized in Fig. 6,where the isotope eoefficient was taken from the experimen-tal resulls 01' Zhao el al. [33]. They used high purily cop-per oxides with different copper isolopes (6'CU and .'Cu).

6. Conclusions

In summary, using the microscopic EMT we have calculatedlhe ialticc paramctcrs for the unit cel! of YBa2Cu307_ó asa function of l5 and compared them with the experimentalresuhs bOlh in high-quality oxygen-defieient YBa2Cu3Q7_,Ihin films and in hulks samples. The ealculated and experi-mental results compare rathcr wel!. We have mcasured resis-tivity and thermopower in a set of epitaxially grown samplesin lhe range O < 6 < 0.5 and discussed lhe resuhs in lermsof conventional models that resort to the e-p interaction. Fi-nally, sorne correlations between different structural, com-positional and transport properties, have been presented anddiscussed. Adding up these rcsults to those prcviously foundin YBa2Cu3_xCOz07_ó (vibrational and structural proper-lies) and in doped Ili compounds (thermopower), we con-c1ude lhal phonons play an imporlanl role in lhe NS and IheSS of the cuprates. In particular. we provide an cxplanation ofthermopower in lerms 01' FL models Ihal include high-ordercorrection contributions in the e-p interaction.

Re\'. Me.\. Fú. 44 S3 (1998) 202-207

THERMDPOWERAND LATTICEPARAMETERSDF YB.,CU3D,_, THIN FILMS AS A FUNCTIDN DF DXYGENCDNTENT 207

Acknowledgments

We acknowledgc valuablc comments from Prof. A. Kaiser,This work has been parlially supported by Instilulo Colom-biano para el Desarrollo de la Ciencia y la Teenologfa, COL-

Prescnt address: Departamento de Ciencias. Universidad Na-cional de Colombia, A.A. 127, Manizales, Colombia.

1. P.H. Hor el al., Phys. Rev. Lett. 58 (1987) 1891.

2. M.-H. Whangbo et al .. loorg. ehem. 27 (1988) 467.

3. Y. SUluki el 01., Phys. Re" Lett. 73 (1994) 328.

4. D.N. Basov el al. Phys. ReI'. Lett. 74 (1995) 598.

5. H.A. Rlaekstead and JO. Dow.1. Supercond. 9 ( 1996) 205.

6. A.M. Cueolo el al., Phys. Re\'. B 53 (1996) 6764.

7. P.E Mieeli el al.. Phys. Re\'. ¡¡37 (1988) 5932.

8. M. Kakihana<'l al., Phys. Re\'. B 40 (1989) 6787.

9. M. Kakihana el al .. Phys. Rel'. B 47 (1993) 5659.

lO. U. Yxklinten anu J. Giraldo. Physica e 234 (1994) 291.11. L. Soderholm et al., Nature 3211(1987) 604.

12. W Guan el al., Phys. Rel'. ¡¡49 (1994) 15993.

13. N.B. Radousky. J. Mat. Res. 7 (1992) 1917.

14. A.Das el al., Physica e 273 (1997) 301.15. H.A. Blackstcad el al .• Phys. Ret'. B 54 (1996) 6122; Z. Zou el

al .. Phys. Re" Lett. 80 (1998) 1074.

16. B. Raveau el al., "Crystal Chemistry of High-TcSuperconducting Copper Oxides'", Springer SerieJ in MaterialsScience 15 (Springer- Verlag, Berlin, 1992).

17. J. Giraldo and U. Yxklimen. J. SlIpercoad. 8 (1995) 635.

18. JO. Jorgensen el al., Phys. Rel'. ¡¡41 (1990) 1863.

19. J. Dow and H.A. Blackstead, Bull. Am. Phys. Soco 43 (1998)S77.

20. e Thomscn el a/., So/id. Slme Commufl. 65 (1988) 55.

21. B. Friedel. C. Thomsen, and M. Cardona. So/id Slale Commufl.78 (1991) 291.

22. E. A1lhendorf el al., Phys. Rel'. ¡¡43 (1991) 2771.

23 \Y. Veal el a/., Phys. Re\'. B ..•2 (1990) 6305; Rcncvier el aJ.•Phvsica e 220 (1994) 143.

24. lF. Annen in Physica/ Propenies of High Temperalure Super.COflduclors, edilcd by Ginsberg (\Yorld Sci. Pub., 1(96), Vol. V.p.375.

25. SB. Qauri el al., App. Phys. Lell. 68 (1996) 2729: VM. Brown-ing et al., Phys. Rel'. B 56 (1997) 2860.

26. A.B. Kaiser a!lu G. Muuntjoy. Phys. Rev. R 43 (1991) 6266.

27. e.R. Varoy. f!.J. Trodahl, R.G. Buckley, and A.B. Kaiser. Phys.Rel'. ¡¡46 (1992) 463.

CIENCIAS, Colombia. JO aeknowledges a visillO lhe Super-eondueting Thin Films Oroup al lhe Departmenl 01' PhysiesofUniversidad del Valle (Cali, Colombia). where most 01' lhiswork was performed.

28. J. Mosqueira el al., Physica e 253 (1995) 1.

29. A.B. Kaiscr and C. Uher. in Sludies oflfigh TemperaLUreSuper-conducLOrs, ediled by A.V. Narlikar, (Nova, New York, 1991),Vol. 7, p. 353.

30. J.-S. Zhou and JB. Godcnough. Phys. Rev. B 51 (1995) 3104:54 (1996) 488.

31. 5.0. Obenelli, J.R. Coopero and J.L. Tallon. Phys. Rev. B 46(1992) 14928.

32. G.e. Mclntosh anu A.B. Kaiser, Phys. Re" B 54 (1996) 12569.

33. G-M. Zhao el al., Phys. Rev. R 54 (1996) 14956.

34. A.B. Kaiser. AlIst. J. Phys. 39 (1986) 909.

35. 1. Giraldo. lE. Rodriguez. and A. ~1atiño, Phys. Rev. 8 56(1997) 23R3.

36. lE. Rodríguez, A. t\1ariño. and J. Giraldo, Physica e 285(1997) 1305.

37. A.B. Kaiser, Physica e 2K5 (1997) 1297.

38. M. Jonson ;¡nd G.D. Mahan, Phys. Rel'. n 42 (1990) 9350.39. EJ. Blatt, P.A. Schrooer. and eL. Foiles, ThermoeJeclric Pm"'eI"

of Meta/s, (Plenum Press, New York, 1976). Sce especially p.238.

40. P.E. Nielseo and P.L. Taylor. Phys. Rel: R 10 (1974) 4061.

41. A. Vilenkin and P.L. Taylor. Phys. Rel'. B 18 5280 (1978): Phys.Rev. Lett. 42 (1979) 597.

42. W.llanseh and G.D. Maha!l. Phys. Re" B 28 (1983) IS86.

-13. HJ. Trodahl, Phys. Re\'. ¡¡ 51 (1995) 6175: E.e. Jones el al.,Phys. Rev. B 52 (1995) 743.

44. A. Pulzara, PhD. Thcsis, Univcrsidad del Valle (Cali, Colom.bia. 1997) (unpuhlished).

45. K.W. Jac!lbsen el al .. Phys. Rel'. ¡¡ 35(19S7) 7423: J.M.Norskov. 1. ehem. Phys. 90 (19S9) 7461.

46. J. Ye and K. Naknmura, Phys. Rev. B 48 (1993) 7544.

-17. V.J. Emery and S.A. Kivelson. Phys. Rel'. Lell. 74 (1995) 3253.

.18. M. Slaski et a/., Tmns[J. Prop. Supercond. 25 (1990) 502; M.Buchgeisler el a/ .. ibid p. 511.

49. lA Cornejo el "l ..1. Mata Re.'.8 (1993) 255.

50. H.J. Bornemann and D.E. Mortis. Phys. Re\~ 844 (1991) 5322.

51. J.P. Franck el al., Phys. Rev. Lell. 71 (1993) 283.

52. J. Giraldo and R. Baquero. Physica C 257 (1996) 160: R. Ba-qucroelaf., Physica C271 (1996) 122.

Re" Mex. Frs. 44 S3 (1998) 202-207