Investigation of inter- and intragrain critical currents in high Tc ceramic superconductors

Investigation of inter- and intragrain critical currents in high Tc ceramic superconductors* H. Kupfer, I. Apfelstedt, R. FliJkiger, C. Keller, R. Meier-Hirmer, B. Runtsch, A. Turowski, U. Wiech and T. W o l f Karlsruhe Nuclear Research Centre, Instttute of Techmcal Physics, and Umvermtat Karlsruhe, Postfach 3640, D-7500 Karlsruhe 1, FRG

Polycrystalhne smtered bulk samples of REBa2Cu307 with RE = Y, Gd were studted by a c suscepttbdtty and an mductwe measurement techmque wh0ch allows the separation of mtergrmn (transport) from mtragram critical current density Field and temperature dependence of the mtergram current are compared wtth theoretical predlcttons for a weakly coupled gram structure Up to fields 0 3 T the weak hnk character of the mtergram current predominates At higher fields tt changes and points to a percolatton current v)a superconducting gram boundaries A quantttatwe correlation between mtragram current and twin spacing is hidden, probably by oxygen defimency m the gram )ntenor No variation of the mtragrmn cnttcal current density wtth temperature ts observed up to 85 K m a textured specimen

Keywords h,gh Tc superconduct,v,ty, superconductors, cr,t0cal currents

Since the discovery of high temperature superconductivity in Y - B a - C u - O a and the recent progress in B1-Ca-SrC u - O 2 and T1 C a - B a - C u 0 3, new prospects for applications stimulate the cryogenic research community However, powder metallurgical processing or other preparation techniques used up to now are disappointingly far from providing any practical solution for a high current application Wire preparation requires tremendous efforts to achieve a comparable state of the art to that of conventional superconductors 4 Thin film preparation - to some extent in a better position - is restricted to special applications Within the scope of exciting possibilities presently under discussion some applications become less promising with regard to the economic point of v i e w 5 In this Paper we focus on the superconducting characterization of powder-metallurgically prepared ceramics Besides the transition temperature, To, well above the temperature of liquid nitrogen, the upper critical field, B~2, and the critical current density, j~, especially at 77 K, are a matter of an increasing number of investigations There are two main obstacles rendering high current applications of polycrystalhne oxide superconductors particularly difficult the large B~2 anisotropy and the weakly coupled grains The first problem results from an upper critical field between 5 and 10T at 7 7 K for the majority of the randomly oriented grains, which is too small for technical use This problem is an intrinsic property of the layered * Paper presented at Crttlcal Currents m High T¢ Superconductors Birmingham, UK, 16 May 1988 0011-2275/88/100650 11 $03 OO ~(~ 1988 Butterworth & Co (Pubhshers) Ltd 650 Cryogemcs 1988 Vol 28 October

structure in these materials which may be solved by epltaxlal growth in thin films or by special metallurgical processing resulting in aligned grains for bulk material This point ts somewhat less Important in the T 1 - C a - B a - C u - O system with a Tc of more than 30 K higher than in Y - B a - C u - O but a similar slope, dBc2/dT, and anlsotropy The second obstacle is the weakly coupled grains resulting in disappointingly small transport currents, about three orders of magnitude lower than in epltaxlally grown thin films 6 7 or single crystals 8 The weak coupling may be caused by the small coherence length, by the mismatch between nelghbourlng grains with different orientation, by a disturbance of the structure at the surface of the grains or simply by impurity phases between the grain boundaries 9 - l l This problem, which Is also present in the T 1 - C a - B a - C u 012-14, may probably be solved by an aligned grain structure 15 The elimination of the weak links if possible at all requires a thorough characterization, in correlation with varying preparation conditions Further Interest is related to the properties within the grains, 1 e, the intragraln critical current density which reflects the current carrying capability once the weak coupling between the grains is overcome The measurements and discussions are essentially based on two YBa2Cu307 and one GdBazCu307 specimen The paper is organized as follows • the preparation, X-ray characterization and transmission electron microscopy are summarized (for a more detailed description of the metallurgy we refer to Fluklger et al 4 and Wolf et a116),

Invest~gatton of inter- and/ntragra/n cnttca/ currents H Kupfer et al • the temperature and field dependent a c susceptlbIhty measurements and the d~scrlmlnatmn between Interand mtragraln effects are discussed, • our flux profile measurement, which enables both the lntergraln and the lntragraln critical current contributions to be known from one measurement, IS explained, • based on the results of the above method, the field and temperature dependence of the mtergram or transport current density is discussed and the connection with a Josephson current is investigated in more detail, and • the lntragraln critical current density, its temperature scahng behavlour and the influence of the twin structure are also discussed

could not be observed even in dark field, whereas residues of the Cu Ba-O melt with a volume fraction of < 0 5% were observed at some grain boundaries The gram sizes of the samples were found to be in the range of 2040/~m (see TaMe 1) A phase analysis was accomplished by X-ray diffraction of the powdered samples using CuK, radiation No second phase could be detected Figure 2 compares the (013) and the (110),(103) reflexes of sample 2 to the reflexes of another specimen prepared by the indirect slnterlng method with

In the following, physical properties related to both the grains and the lntergraln material will be distinguished by the suffixes G and J, respectively, for example,j¢ G,J~J For simplicity T~G was taken as T~

Sample preparation and characterization To obtain very dense and single phase specimens we prepared the YBa2Cu3OT-x and GdBa2Cu30 v_x samples by the direct slnterlng method 16 Powders of Y203 (99 99%) or G d 2 0 3 (99 9%), BaCO 3 (99%) and CuO (99%) were mixed very homogeneously and ground in a low energy ball mill for about 24 h The mixtures were then cold pressed at a uniaxlal pressure of 200 MPa, calcined at 850-920°C, sintered at 930-980°C and loaded with oxygen at 350-500°C without any further grinding Sample 1 was annealed in air at the following temperatures/times 850°C/66 h, 900°C/23 5 h, 930°C/2 h, 980°C/3 h, 910°C/2h, 500°C/37h, 400°C/6h and 350°C/16h Sample 1 was further annealed In air at 850°C/2 h, 900°C/18 h, 930°C/2 h, 950°C/1 h, 980°C/3 h, 940°C/17 h, 910°C/7 h, 900°C/17 h and after slow cooling at 300°C for 65 h Samples 2 and 3 were annealed at 900°C/22 5 h, 920°C/69 h and 930°C/23 h in air and then under flowing Oz at 950°C/21 5 h, cooled down to 400°C within 52 h and further annealed at 400°C/64 5 h and 350°C/3 h From sample 3 a cylinder of 2 mm in diameter was cut and addmonally heat treated at 500°C/69 h and 400~C/9 h in O z before measuring the specimen The densities of the samples were determined either by hydrostatic weighing in air and In decahn or by measunng the size of the pellets The results are listed in Table 1 The Investlgatmn of the microstructure was performed with a light microscope after polishing the specimens with 1 pm diamond paste using absolute ethanol In F~gure 1 It can be seen that the samples were very dense after sinterlng and that pores are mainly present within the grains The green phases of Y2BaCuOs and Gd2BaCuO5 Table 1

Figure 1 Dark field image of a pohshed Y-Ba-Cu-O surface The stnped regions show the dtfferent directions of twinning Circular white spots are pores within the grams I

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11 685(20) 11 6828(8)

Cryogemcs 1988 Vol 28 October

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Investtgatlon of Inter- and/ntragra/n critical currents H Kupfer et a l intermediate grlndmgs It can be seen that specimen 2 exhibits substantially sharper lines, thus reflecting a good homogenetty The difference in the peak maxima is due to different oxygen contents of the samples A review of published lattice parameters of well characterized samples has s h o wn 4'16 that the oxygen content, y = 7 - x , of YBaECU3OT-x is related to the c axis by a hnear relation y = 7-x -- 76 40 - 5 95c/~ Values of the lattice parameters a, b, c and y = 7 - x are listed in Table 1 Spectmens for T E M were prepared by mechanical grlndmg or cutting to slices of 3 m m diameter and about 100 #m thickness and subsequent Ar ton mdhng at grazing incidence These slices were investigated with a 200 keV Hitachi T E M Areas of some #m 2 at different positions of the discs were transparent for the electron beam Ftgure 3 shows the observed twin structure of specimens 2 and 3 at the same scale About 50 pictures of several slices of each sample were investigated to obtain representative results Average values for the twin spacing, g, given in Table 1 and the grain diameter were determined for both YBa2Cu30 7 and G d B a 2 C u 3 0 7 samples Within the same specimen smaller grains were usually found to show a narrower twin spacing

R e s i s t i v e a n d a c. s u s c e p t i b i l i t y measurements Resistivity, p, is an important parameter for characterizing the specimen Ftgure 4 shows p versus T for the three specimens measured by a common four probe technique with a current of 5 mA These values are representative for specimens obtained from one pellet For instance the p values at 100 K of all 12 specimens cut from pellet 2 vary between 147 and 209 # ~ c m In contrast to the striking linear p(T) behavlour, the slope dp/dT is not constant as expected from Matthlessens' rule for a metal but increases with increasing resistivity This correlation is attributed to lntragraln percolation as discussed in Reference 17

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The resistive transition width IS typically 1 K without any step In between There are two quite different possibilities for a current path resulting in zero voltage Wtth decreasing temperature the first continuous path may lead via superconducting grain boundaries The measured transition temperature then corresponds to the lntragraln transition Tc The second posslblhty offers a superconducting current path via the weak links if no percolatlve path through superconducting grain boundaries is achieved In this case the measured temperature should correspond to the phase locking temperature, Tcj Due to the broad distribution of the current carrying capability of the weak links both cases cannot be separated, but the resistive onset is much closer to T¢ than to T¢j < 90 K, which is determined by the a c

Figure 3 Charactenstm TEM images showing the difference between the average twin spacing, g, of (a) sample 2, (b) sample 3

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Cryogen)cs 1988 Vol 28 October

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Investtgatton of mter- and mtragram cnttcal currents H Kupfer et al susceptibility measurements discussed below This is a first hint for a percolation current vm superconducting grain boundaries Besides th~s, the resistive transmon in zero field does not show features pointing to enher inter- or lntragraln o n g m Only for specimens showing semiconductang behavlour above T~ and a very sensitive dependence of the transition temperature on the measuring current the second possibility may dominate This IS in agreement with a rough correlation between resistivity and transport critical current density which is not found in low resistive specimens TM The resistive transition in an applied field shows a pronounced tall at lower temperatures which is more sample dependent than the other part of the transition curve This tall probably reflects an Influence of the weak hnks which depends crucially on preparation conditions The a c susceptibility is a much more powerful measurement for characterizing the specimen and for discriminating between Inter- and lntragraln properties The d c and a c fields, B(t) = Bd~ + boSlnmt, are apphed parallel to the axis of the cylindrically shaped specimens which are in their central part surrounded by a pick-up coil From this signal of the pick-up cod one subtracts that one from a compensating coil without specimen The m-phase and out-of-phase component of this difference detected by a lock-in-amplifier, corresponds to the real and ~maglnary part of the a c susceptlblhty, l ' and l", respectively The compensation is made at 4 K, and at the remanent field < 5 m T of the superconducting solenoid with an a c amplitude of 10 - 4 T The ,4' signal of the pick-up coil was calibrated against a V 3 S1 specimen The R E B a z C u 3 0 7 specimens show f signals which coincide within 5% with those expected from complete shielding From the frequency dependence of 7' and 1:" measured up to 1 kHz, both skin effect losses in the normal state and flux flow losses in the superconducting state can be excluded as being relevant at the frequency of 1 l Hz used for the measurements discussed below The a c susceptibility shown for the three specimens in Flgmes 5a, b and ~ at Bd~ ~ 0 T reflects, therefore, the screening capabilities, l e the critical current densmes and the corresponding loss behawour of the lntragraln and lntergraln material In the following we make some comparisons between results from the a c susceptlblhty and theoretical predictions Concerning the theory we refer to the recent paper of Clem ~9 and the references therein The specimens discussed in this paper have a gram size, 2R~, much larger than the London penetration depth, 2, which becomes about 1 /~m at a reduced temperature of 0995 using t(0 K ) ~ . 0 12#m 2° The lntergranular currents do not suppress the order parameter because the Josephson coupling energy, E~=(h/2e)lo, is much smaller than the condensation energy of a gram, E(, = (HZ/8=)(4rcR3/31 With decreasing the temperature the grains become superconducting at T~ but the weak links are still resistive due to thermal fluctuations if the Josephson coupling energy, Ej, is smaller than /,T Therefore, the a c field induced screening currents flow inside the grains probing mtragraln propernes for To, the upper critical field, or ~ts temperature slope The intragraln current increases with decreasing temperature, leading to a better screening, 1 e smaller / and larger )(' because the a c amplitude still reaches the centre of the grains The imaginary p a r t , / " , which is proportional to the a c hysteresis losses has a

maximum if the a c field has just penetrated into the centre of the grains Below this temperature 7" decreases because the a c field no longer penetrates the whole grain and the volume m which hysteresis losses occur shrinks At the maximum of )(' the relative value l " / ) ~ z K lS expected to be 0 212 for a cylindrically bulk specimen The lntragram peaks of Flgme 5 are considerably smaller than this value because I 2 3

the grams cover only a part of the sample volume, the demagnetization of the decoupled grains is not considered, and mainly because the magnetic penetration depth, ,t, results in a suppression of the magnetic Vlslblhty, l e, of the volume in which the hysteresis losses occur 2~

For large grains as in the present investigation this magnetic suppression becomes important only very close to T c where )(73 diverges The lntragraln peak in X" may, therefore, be completely suppressed for decoupled grains with s~zes smaller than about 1 kLm The intragraln critical current density,/~6, at the temperature of the X~, peak can be estimated fromjc 6 = bo/Rc, It is about 400 A c m -2 for specimen 1 (T ~ 9 1 5 K , B ~ 0 T ) The weak links are able to carry a supercurrent if the temperature is below the phase locking temperature Tcj at which Ej becomes equal to kT This temperature corresponds to the shoulder of )( or the valley between both peaks m / ' , as indicated in F~gute 5 Below this temperature macroscopic shielding currents through grains and weak links are induced The a c losses of the junctions increase below Tcj and cause the lntergram maximum )"1' at which as for the lntragraln peak 7~ the a c field just penetrates into the centre of the specimen In the temperature region below T~j the lntergraln s~gnal dominates compared to the mtragraln one due to the much smaller lntragraln penetration depth, i e the much larger /c~J For this reason the a c susceptibility is representative for lntergraln properties at T < Tcj The height, position and width of the lntergraln maximum reflect the lntergraln volume, the lntergraln critical current density JcJ, and the distribution of the couphng energy or junction current For example, measurements on a low quality specimen show a broad maximum of 50 K width centred at 60 K in contrast to a width between 2 and 5 K centred between 85 and 90 K for the samples shown in Flgme 5 The difference between T~ and T~ is about 1 K in specimen 1 and 3, and 3 K m specimen 2 Assuming that this temperature difference ~s sufficient to neglect the residual lntragraln signal at the position of the mtergraln peak, the ratio ,~' .... /7~ m a x decreases with decreasing lntergraln volume and better homogeneity This correlation is demonstrated in Ftgure 2 by a comparison between the X-ray diffraction lines from specimen 2 and those of a specimen with the same grain size and same Lo but showing the lntergraln peak only The sharper X-ray lines of specimen 2 are in quahtatlve agreement with a five times smaller mtergraln maximum The mtergraln maximum and the temperature T~j can be used for estimating the Intergram crmcal current density, LJ At T = 86 5 K where the maximum appears one gets l~J = bo/R = 8 A c m 2 for specimen 2 This estimation does not account for the residual influence of the grams The equation kTCj = Ej = (h/2e)1o = (h/2e)jcj (2Re,.... )z results in jcj ~ 1 A cm 2 at the phase locking it

Cryogenics 1988 Vol 28 October

653

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T [K] Fngure 5 Real and imaginary part of the a c susceptabdlty Z' and Z", versus T measured with a frequency of 11 Hz and an a c field amphtude of 10 4 T )n zero field The a c loss component )s normahzed by d=v)dmg by the value of Z' at 4 2 K Tcj Js mdmated by an arrow, J and G correspond to the posmon of the )ntergram and mtragram max)ma )n X" (a) Sample 1 n , z', [], Z"/Z'42K, (b) sample 2 O , / , ©, ,~"/Z'42K, (c) sample 3 V , X', V , Z"/Z'42K

temperature Tej ~ 90 K The inductively measured value is I 6 A c m - 2 at 88 K These estimations are in fatr agreement and demonstrate that the quantitative model of weakly coupled grains proposed by Clem ~9 describes the granular YBa2CuaO7 specimens quite satisfactorily The lntergrain contribution of the a c susceptibility is severely influenced by a magnetic field, for instance by the a c amplitude as shown in Ftgure 6 This is explained by the field dependence of the Josephson coupling energy which decreases proportionally to l/B, as will be shown later in Equation (2) The temperature T < Tej for w h i c h / = - 0 9 is obtained decreases much faster with increasing amplitude as T > Tej for g ' = - 0 1 which

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Fngure 6 Influence of the a c field amphtude on the temperatures at whnch X' takes the values, [ ] - 0 1 and, I , - 0 9, respectively, and where, O, the mtergram maximum, X"J, occurs The measurements were performed on a specimen with slmdar charactenzatuon to sample 1

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Cryogemcs 1988 Vol 28 October

corresponds to lntragraln material* This quite different field dependence of inter- and lntragraln A becomes more pronounced if a d c field is applied Ftgure 7a shows for specimen 2 that the lntergram peak broadens and shifts to 75 K at 0 5 T, whereas the intragraln peak is lowered by 3 K only This demonstrates increasing lntergraln losses due toAi oc 1/B and probably a broader distribution of the current carrying capability of the junctions in an applied field than in zero field With further lncreasmg field from 0 5 to 5 T the width of the distribution increases, buries the lntragraln peak and smooths the corresponding shoulder in X' The temperature at which the maximum of Z" occurs decreases rapidly between 0 and 0 5 T but much less above this field The decrease in low fields is in agreement with Ej(B, T)ocAj(B), but not the almost field independent behavlour at higher fields This is a second hint that above 0 5 T the interpretation of Aj as ajunctlon current becomes questionable The observation is in full agreement with the behavlour of B(T) at X' = - 0 9 shown in Ftgure 8, which will be discussed in detail later in this Paper The lntergraln weak links determine the lower part of the z'(B, T) transition, i e, the pronounced curvature up to 0 5 T At fields exceeding 3 T, B(T) shows a linear behawour which depends much less on the preparation than below The slope in this higher field region is intragraln specific for Z' = - 0 9, it IS close to the slope of the upper critical field, Be2 T The value of 1 T K - i is within the range observed for single crystals A further complication results from the volume fraction of the material with lower oxygen content in the interior of the grains which becomes magnetically vtsible at larger fields 22 This may result in a tail in Z' at low temperatures in an applied field This tall as well as the influence of both lntergraln porosity and BeE anlsotropy and the *The values Tc and Tcj from a c susceptlbfl0ty measurement should, m principle, be taken from the extrapolation of b o to zero amphtude Differences between thin extrapolataon and values taken from a measurement at a fixed amphtude increase for larger amphtude, and for lower ]cJ

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T [K] Figure 7 Real and =magmary part of the a c susceptlbd~ty, Z' and Z", versus Tfor spemmen 2 measured at 11 Hz and 10 4 T m a magnetic field of (a) 0 5 T and (b) 5 T, respectwely • , / , O , / ' / / 4 2 K II*

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Inducttve measurement of the inter- and ,ntragrain critical current densities The inductive flux profile measurement of the radial distribution of the critical current density in a cylindrical

H K u p f e r et al

bulk specimen was described by Rollins et al 24 The same experimental arrangement as for the a c susceptibility measurement is used After the compensation procedure an induced voltage, U,(t), results from a periodic change of the radial profile of the magnetic induction, b(x(t)/R), at the distance x(t) from the surface of the specimen, where R is the radius of the specimen The induced voltage is given byU, = ~bo~ocos~ot[l-(1 -x(t)/R)2], with the constant c being taken from the measurement in the normal conducting state UN,C=cbo~oCOStOt From the time dependent measurement of U,(t) with a fast digital voltmeter the normalized maximum penetration depth ~:(t)/R at the corresponding time is obtained The local induction at this position x(t)/R is calculated from b(x(t)) = (bo-b(t))/2 This equation m which b(t) is the induction at the surface holds if Ul(t) IS the same for increasing and decreasing a c field which is checked by measuring U,(t) in both half periods A plot of b(x(t)) versus ~c(t)/R with t as parameter reproduces the radial distribution of the magnetic flux profile from the surface up to the maximum penetration depth From the slope of this induction the radial distribution of Jc can be calculated Amplitude and frequency have to be suitably chosen to obtain a quasistatlonary flux profile which is m the critical state, and a skin penetration depth in the normal state sufficiently larger than R r o understand the result of this method m a polycrystalhne material with weak link character at the grain boundaries we model the weak links by a superconducting matrix with separated second phase particles, for example, the grains The critical current density of the matrix lSj~j, the sample radius, R, and the corresponding values of the grains are JoG and RG, respectively A non-superconductmg second phase or a superconducting one with J~G < J o lS not detectable but results in a flux profile with a constant slope up to the centre of the specimen if a homogeneous distribution of the second phase particles is assumed The critical current density taken from the constant slope is smaller than j~j because the measured U 1 results from the matrix and the grains U, = U,j + U,o If L o >%J the slope of the flux profile remains constant with a measured current density larger than /o This holds up to the condition j~(, = L j ( R / R o ) f If L6 becomes larger than Lj(R/R(,) the a c field can penetrate up to the centre of the specimen before the centre of the grains is reached This is the case for weakly coupled grains with a large lntragram critical current density, 1~(, The flux profiles in Ftgure 9, as an example, show a pronounced kink at this field h* which just penetrates the centre of the specimen For h < h* the reduced signal from the weak links dominates due to their much smaller shielding capability, 1e L(, >>LJ The lntergram critical current density can be estimated from the slope of h(x/R) neglecting U,o To compare with theoretical models and with transport current measurements the current density has to be related to the whole sample area The ratio between intergraln and sample area is obtained from the position ~*/R of the flux profile Aj A = (-,*/R)(2 - \*/R) With this value the lntergraln current density is given by l~j = (db/d(x/R)) (1 R)(x* R ) ( 2 - x* R) *Moreprectsely ~ t t s n o t t h e s a m p l e r a d l u s R w h i c h d e t e r m m e s t h t s condition but Rj obtained from the intergram area A j by Rj ~ (Aj/~z) 1 2 much smaller than R m our dense specimen

Cryogemcs 1988 Vol 28 October

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Investtgatton of rater- and mtragram crtttcal currents H Kupfer et al

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Ftgures lOa and b show the ]ntergram critical current density of specimen 1 There are two peculiarities regarding the field dependence o f Jc J The first striking observation is the rapid decrease by approximately two orders of magmtude from B = 0 T to about 50 m T (Figure lOa), whereas the second one is the field independent JcJ beyond this drop (Ftgure lOb) The rapid decrease and the l o w J c J w e r e taken as indications for an lntergranular junction current caused by a three dimensional array of weakly coupled grains 28-3° The field dependence can be related to the magnetic field pattern of Josephson weak links with a random orientation of the junctions in an applied field The junction current through an insulating

x/R F,gure 9 Flux profile of the magnetic mduction b(x/R) at T = 40 K and B = I T R is the sample radius, x/R is the normahzed dmtance from the sample surface, b = 0 corresponds to the apphed d c field of I T The value b* and x*/R corresponds to the condition at which the a c field penetrates u p to the centre of the speclmen The apparent spatml separat=on m the flux profile between mter- and mtragram shielding at b*(x*/R) does not correspond to the actual flux dlstnbutton but reflects the temporal order of the two mduced cnt~cal current systems I, Sample I, 2, sample 2, 3, sample 3

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E For b>b* the induced voltage U,j from the lntergranular material becomes much less irreversible than U,6 because fields larger than b* are no longer screened by the weak links To get the lntragram flux profile from the measured U,, U,j has to be subtracted This signal is approximately slnusoldal in comparison to U,G and can be estimated U,j ~ c(AjIA)bocOCOS~Ot After subtracting this voltage one obtains the profile within the grains and from the slope the critical lntragraln current density J~G = db/d(x/R)(1/RG) This estimation of both current densities assumes a cylinder geometry of the grains, l e it neglects demagnetization effects, possible magnetic suppression due to the London penetration depth and the effect of grain size or j~ distribution being not considered It is based on a sufficiently large difference between JeJ and JoG and does not work for very small grains A comparison of Jcj and J,G with transport current measurement and lntragram values obtained from magnetization measurements 23, respectively, shows a satisfying agreement If the condition JoG >>j,j(R/RG) is not fulfilled, due to a small J,G or small R G, both currents cannot be separated and the measurement technique has to be modified First, the induced voltage U, = U,j + U,G is measured on the bulk specimen Then the specimen is powdered down to an average particle size which corresponds to the average grain size or at least to a particle size R which allows us to obtain Jco >>JcJ(R/RG) In order to avoid weak hnks due to contact between the powder particles, they should be embedded in epoxy z5 before J¢G is measured 26 The difference between the induced signal U,G and U, from the bulk specimen results in jCj An inherent difficulty arises from the reversible penetration depth 2' of a pinned flux line lattice 27 if the grain size becomes comparable

656

Cryogenics 1988 Vol 28 October

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Investtgatton of rater- and mtragra/n cnttcal currents H Kupfer et al Th mtergram crlt=cal current dens~t=es B 1 corresponds to the linear T a b l e 2 Companson between measured IcJ, and theoretical, IcJ, extrapolat=on of/cJ to zero The values /c]lc are obtained by using the measured value =n zero field, B~ and the theoret=cal 1/B dependence

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barrier 31 was used by Kampwlrth and G r a y 32 to obtain an equation for the critical weak link current density of identical juncUons Th J~s (T, B = 0 T) = (nA(T))/(2epj2R6)tanh[A(T)/2kT]

(1)

where A(T) is the superconducting gap parameter of the grains and pj is the normal state res~stlv~ty of the junctions It is shown m Table 2 that the calculated values using this equation are considerably larger than the experimental ones Reasons for this discrepancy are a geometry different from a granular structure due to the high density of the specimens, a resistivity p(100K) used for the calculation which is probably considerably smaller than the lntergraln value pj and a broad dlstnbuuon of the current carrying capablhty of the weak links The temperature dependence is less affected by these differences between the assumpUons of the model and the mlcrostructure of the specimen and shows a much better agreement 33 Close to T~ the temperature dependence of jCj can be obtained from the amphtude dependence of the mtergram ZJ' peak in Figure 6 This plot demonstrates that the temperature at which the maximum of Z;' appears decreases hnearly with increasing amphtude F r o m the relation j,j = bo/R which holds at the peak of Z;', JCJ becomes proportional to (1 - T / T J which is precisely the temperature dependence predicted by Equation (1) close to T, This result is in agreement with an insulating barner at the gram boundaries We will now compare the field dependence of j~j and the Josephson pattern of a juncUon with field perpendicular to jCj The latter is described by Xh( T , )B ' =j~j XhzT. S~j [ , 0)(sln(g~b/q~o))/(gq~/q~o)

77 K between the experimental value and jcj caJc(77 K, B) =j~j(77 K, 0 T)C~o/(n22dB) With decreasing temperature the devaatlon begins at higher fields, at about 0 3 T at 4 K The discrepancy betweenjCj andj¢~ajc is about one order of magnitude at 4 K and 10 T The corresponding values of specimen 2, also given in Table 2, show the same general features but the discrepancies are even larger and become already evident at lower fields in spite of larger B1 values A comparison between sample 1 and 2 demonstrates that the mtergram current densities at low fields or m zero field are not at all correlated with the high field values This holds also for a variety of other specimens Th~s investigation shows that the mtergram current has weak hnk character m the very low field region only, m agreement w~th the a c susceptibility behavlour At fields above 0 3 T j¢~ becomes nearly field independent, very similar to the lntragraln current density discussed later This s~mllanty and the variation ofjc J of more than one order of magmtude in this field region points to a percolation current via superconducting gram boundaries Invesugat~ons of fast neutron lrradlaUon of specimen 2 are m excellent agreement with this explanation 3s Based on other observations Larbalestler et all1 proposed the same mechamsm A theoretical model similar in some aspects was recently pubhshed by Matsushlta et al 36 Percolation and the large variation of jcj In zero field strongly suggest preparation dependent origins for weak hnks instead of intrinsic

80

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where 22 is the junction thickness and ~ its area For a more detailed discussion we refer to Peterson and Ekm 34 Values for B 1 at d~fferent temperatures were taken as shown for 77 K m Ftgure lOa and plotted versus temperature In Ftgure 11 From Equation (3) and 2(T) = 2(0)/(1 - T/T~)~ we get a mean value of about 0 2 #m for dwhlch results m a junction area 10~ times smaller than the gram area The solid hne in Ftgure 11 shows the agreement with Equation (3) using the mean value of d This agreement becomes worse investigating jc~ at higher fields Equation (2) predicts a maximum current ver~u~ field proportional to 1/B From Figure lOb it is obvious that th~s correlaUon becomes increasingly wrong at larger fields where j~ stays constant As shown in Table 2 the deviation is more than 100% at 1T and

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C r y o g e n i c s 1 9 8 8 Vol 28 O c t o b e r

657

Investigation of Inter- and mtragram critical currents H Kupfer et al reasons, for example, mlsahgnment of grams The recogmtion - j u n c t i o n currents occur via weak links at low fields while percolation currents occur via superconducting grain boundaries at higher fields - suggests optimizing the current at higher fields by improved preparation cond~tmns in order to ehmlnate the weak link problem

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Intragram critical current density In the following we discuss the lntragraln critical current denstty, Yco Measurements of the transport current on epltaxlally grown films 6'7 and on single crystals a showyc values about 103 times larger In zero field and 106 times larger at higher fields than in sintered ceramics Reasons for these large differences are weak links and percolation in polycrystalhne material as discussed above This was proven investigating ceramic materml by magnetization37 38 or flux profile measurements 26 Before and after powdering, the critical current value was about the same and comparable to the hlghj¢ values in epltaxlally grown films and smgle crystals Flux profile measurements demonstrate that the current in the grains is a bulk current without surface contribution 22'26 It was argued that twin and gram boundaries 2s'39 are probably the responsible pinning centres for the large JoG Decoration techniques of the flux lattice 4°-42 support this and show that pores in the grains, as seen in Figure 1, are effective pinning centres in addition Grain boundary pruning due to electron scattering or amsotropy of the upper critical field, B¢2, can be excluded as the dominant pinning mechanism because of the large gram size and because high J¢G IS observed also in single crystals Twin boundaries formed at the phase transition from the tetragonal to the orthorhomblc phase remain the most probable elementary pruning centres acting by means of electron scattering at the twm planes In order to calculate the volume pinning force, Fp =J¢GB, these elementary forces have to be summed up wlth respect to elastic and plastic Interactions of the flux line lattice In spite of the still unsolved summation problem a common feature of the variety of pruning models is an increasing Fp with increasing pin density, l e smaller twin spacing We exclude the saturation phenomenon which is accompanied by quite a different field dependence than the measured one The correlation between )~G and twin spacing should also be observed in polycrystalhne material with B¢2 anlsotropy of randomly oriented grains But a quantltatwe comparison can only be obtained from measurement on oriented single crystals as discussed by

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specimens The field dependence Is similar for all specimens After a very pronounced decrease at low fields AG exhibits a minimum below B = 3T and a subsequent maximum which is beyond 12 T at lower temperatures The minimum of Fp or JeG at low fields occurs for T > 40 K, roughly at the same B, i e it does not show a temperature scaling behavlour This leads to the assumption that the rapid decrease of jc G results from another mechanism than pinning at twin planes One poss~bihty as that the lntragraln pores become effecUve pmnlng centres at very low fields, as shown for large voids in V 3 Si 44 However, in contrast to th~s investigation the

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BIT] Figure 12 Crmcal mtragram current densities as a function of the applied field, measured at various temperatures (a) Sample 1, (b) s a m p l e 2 (c) sample 3 4 K, , 10 K, [ ] 20 K , \ , 40 K, 0 60 K, ~ , 77 K

Investtgatton of mter- and mtragram crtttcal currents H Kupfer et al decrease of 1~, in Ftgure 12 clearly rejects a temperature scahng The field dependence xn low fields, similar to that of a junction current, wdl be discussed in detail in Reference 22 The maxima ofje G show a pronounced shift to higher fields with decreasing temperature and point to a scahng law 45 of Fp~c(B~2(T))"f(B/Bc2) where f(B/B~2 ) and (Bc2(T))" describes the field and the temperature dependence, respectwely With the maxima of Fp and the corresponding fields we get an exponent n of about 3 for specimen 3 where the maxima are most clearly developed This value is within the range commonly observed m conventional superconductors Due to the particular angular dependence of B~2 obtained from single crystals 46, most of the randomly oriented grams have an upper crmcal field close to B~21 at which the direction of the field is perpendicular to the basal plane Considering only th~s majority of the grains the reduced field at which the current maxima occur is about 0 3 using a B~2 derived from a constant slope dBcz±/dT=O5TK-~ (see Reference 47) This results m B c 2 ± = 8 T at 77 K, which ~s not in contradiction w~th the measurement of specimen 3 as indicated by the dashed line in Figure 12c We should point out that JCG corresponds excluswely to the superconductmg grains, induced stgnals from grams dnven normal by a field being already subtracted This explains the constant or even slightly increasing JoG for B > Be2± Measurements on a highly textured specimen with B perpendicular to the basal plane indicate Bc21(77 K) of about (7 _+ 2) T as shown m Figure 13 This specimen was additionally measured at a constant reduced field of 0 3 up to 85 K, assuming a hnear B,2~ versus T dependence Figure 14 shows log Fp versus log B~2± which gives the same exponent 3 as from Ftgure 12c From these observations we conclude that m this specimen JoG shows a constant temperature dependence up to 85 K, ~e it does not drop faster m the temperature region above 60 K The elementary force arising from electron scattering at twin boundaries was estimated by Matsush~ta et a148 f~ = 2 5 x 1 0 - S N m -~ (1-B/B~2) at 7 7 K With direct summation of f~ one obtains

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B [rl Figure 13 Intragraln critical current density versus B at 77 K measured on a textured spemmen YBa2Cu307 with B field direction, O, perpendicular and O parallel to the basal plane Bc2 is about (7_+2) T a t 7 7 K

150#flcm (100 K) were investigated with particular attention to distinguish between Inter- and lntragranular effects In a d d m o n to a c susceptibility we used for this purpose an inductive flux profile measurement technique which allows us to discriminate between both current systems in one and the same measurement on a bulk specimen From the a c susceptlbdity we obtain the phase locking temperature, Toj, while the lntergraln volume and the mtergram (or transport) critical current density, JcJ, are deduced from height and position of the maximum of the imaginary part These results, as well as jcj(B, T) from the mduetwe measurement are at low fields B < 0 5 T in satisfying agreement with a Josephson current in a three

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where ~bo is the flux quantum and g ~s the twin spacing given m Table 1 The corresponding equation for the critical current density at 77 K, B = 2 T and B~2~ = 7 T results m 3~G=25 x 104Acre -z for specimen 1 and 2 and 3 ~ = 3 9 x 104 A cm -2 for specimen 3, neglecting d~fferences m the superconducting properties between YBazCu3Ov and G d B a z C u 3 0 v Compared to the calculated values, the experimental values for specimen 1 and 2 are lower while those for specimen 3 are higher Th~s does not confirm the hnear dependence of j ~ on the reverse twin spacing m analogy to the gram size dependence ofj¢ in Nb~Sn For specimen 3 J,G is about one order of magmtude larger for 40% reduction of the twin spacing Thts discrepancy becomes smaller considermg the different superconducting grains probably due to different oxygen content in these specimens 22 Conclusions Polycrystalhne REBa2Cu3OT_ x ( R E = Y , Gd) with densmes above 90% and low res~stWltles of about

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Cryogemcs 1988 Vol 28 October

659

Invest/gatton of mter- and/ntragra/n crttmal currents H Kupfer dimensional array of weak hnks The temperature dependence of jej, especially its hnearity near T¢ is consistent w~th an msulatmg layer between the gram boundaries Above 0 5 T, the a c susceptibihty shows a different behavlour from that expected for a pure junctton current This difference above 0 5 T is clearly demonstrated by a field independent jcj, contrary to the AJ oc I/B expected from a weak hnk current Based on the large varlatton of Aj for different samples m this high field region - not correlated with the value of the junctton current - we assume a percolation current at those superconducting boundartes not showing weak link character This means that the weak hnk problem is not of intrmsic nature and that a solution does not consist in optimizing the transport current in zero field but at field larger than 0 5 T The mtragrain critical current density, A6, shows a temperature dependence proportional to (B¢2(T)) 2 measured at about the same reduced field in GdBa2Cu307 between 40 and 77 K and m a textured YBazCu307 up to 85 K An estimation of the volume pinning force assummg direct summation results in values within the same order of magnitude as the experimental ones With decreasmg twin spacing from 110 to 70 nm, A~ increases by about a factor of l0 reaching 5 x 106A cm -2 at 4 K and 12 T A quantitative correlation between twin spacing and AG ts hidden by the fact that interior parts of the grains may have degraded superconducting properties due to oxygen deficiency

References 1 Wu, M K, Ashburn,J R, Torng, C.J, Hor, P H, Meng, R L, Gao, L, Huang, Z J , Wang, Y Q and Chu, C W Phts Rev Lett (1987)58 908-910 2 Maeda,H, Tanaka, Y, Fukutoml, M and Asauo, T Jpn J ApplPhys Lett (1988) (in press) 3 Sbeng,Z Z and ltermauu, A M Nature (1988) 332 138 139 4 Fluklger,R, Muller, T, Wolf,T, Apfelsteflt,I, Selbt, E, Kupfer,H and Sehaoer, W International Conference on Materials and Mechanisms of Superconducttvttv Interlaken, Switzerland (1988) 5 SchauerF, Jungst, K P, Komarek, P and Maurer, W Report KfK 4308 Nuclear Research Centre Karlsruhe. FRG (1987) 6 Chandhary, P, Koch, R H. Lalbomtz, R B, McGmre, T R and Gamblno, R J Phvs Rev Lett (1987) 58 2684-2686 7 Enomoto,Y, Murakamt, T, Suzuki, M and Morlwakl, K Jpn J Appl Phvs (1987) 26 LI248-L1250 8 Dinger,T R, Worthington, T K, Gallagher, W J and Sandstrom, R L Phvs Rev Lett (1987) 58 2687-2690 9 Deutscber, G and Muller, K A Phw Rev Lett (1987) 59 1745-1747 I0 Ekln, J E Adv Ceram Mater (1987) 2 586-592 11 Larbalesoer, D C , Babcock, SE, Cal, X, Daeumhng, M, Hampshire. D P , Kelly, T F . Lavanier, LA. Lee, P J and Seunqens,J Internatwnal Conference on Materzals and Mechamsms of Superconductzwt) Interlaken. Switzerland (1988) 12 Sheng,Z Z, Klehl, W, Bennett, J, El Ah, A, Marsh, D, Mooney, G B0 Arammash, F, Smith, J, Vtar, D and Hermann, A M (in preparation) 13 Zhao, Z X, Chen,L Q, Mal, Z H, Huang, Y Z, Xlao, Z L, Chu, X, Zheng, D N, Jla, S L, Wang, J H, Chen, G H, NI, Y M, BI, J Q, Yang, Q S, Shen, D H and Wang, L Z Mod Ph vs Lett B (1988) (m press) 14 Kupfer, H, Green, S M, Jlang, C, Met, Yu, Luo, H L, MeierHtrmer, R and Polms, C Z Phys B (1988) (in press) 15 Jm. S, Tmfel.T, Sherwood. R and van Dover, B Paper presented at

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Cryogenics 1988 Vol 28 October

et a l

the Materials Research Society Fall Meeting, Boston, USA (1987) 16 Wolf, T, Apfelstedt, I, Goldaeker, W, Kupfer, H and Flukiger, R International Conference on Materials and Mechamsms Supertonducttvtty Interlaken, Switzerland (1988)

of

17 Halbrltter,J, Dietrich. M, Kupfer, H, Runtsch, B and Wahl, H Z Phvs B (1988) (in press) 18 Kupfer,H, Apfelstedt, I, Sehauer, W., Flukiger, R, MeJer-Hirmer, R, Wuhl, H and Scheurer,H Z Phys B Condensed Matter (1987) 69 167-171 19 Clem,J R Internatwnal Conference on Materzal~ and Mechanisms of Superconductivity Interlaken, Switzerland (1988) 20 Worthington,T K, Gallagher, W.J and Dmger, T R Phvs Rev Lett (1987) 59 1160-1163 21 Clem,J R and Kogan, V G Proceedmg~ L T 18 Kyoto, Japan (1987) 1161-1162 22 Kupfer,H, Apfelstedt,L, Flukiger, R, Keller,C, Meier-Hirmer,R, Runtsch, B, Turowskl, A, Wiech, U, and Wolf, T (in preparation) 23 Kupfer,H, Apfelstedt, I, Flukiger, R, Meler-Hlrmer, R, Schauer, W, Wolf, T and Wuhl, H Proceedings of the International Discussion Meeting on Hlgh-Tc Superconductom Mauterndorf, Austria (1988) 24 Rollins, RW, Kupfer, H and Gey, W J App! Phvs (1974) 45 5392-5398 25 Farrel, D E, Chandrasekhar, B S, De Gmre, M R, Fang, M M, Kogan, V G, Clem, J R and Finnemore, D K Phvs Rev B(1987) 36 4025~1~327 26 Kupfer,H, Apfelstedt, 1, Sehauer, W, Flukiger, R, Meler-Hirmer, R and Wahl, !t Z Phrs B - Condensed Matter (1987) 69 159-166 27 Campbell, A M J Phys C (1969) 2 1492-1501 28 Larbalestier, D C, Daeumhng, M, Cal, X, Seuntlens, J , McKmnell, J, Hampshire, D, Lee, P, Memgast, C, Willis, T, Muller, H, Ray, R D, Ddlenburg,R G, Hellstrom, E E and Joynt, R J Appl Phys (1987) 62 3308-3313 29 Ekln, d W, Bragmskl, A I, Panson, A J, Janocko, M A, Capone, D W, Zaluzec, N, Flandermeyer, B, de Lima, O F, Hong, M., Kwo, J and Liou, S H J Appl Phys (1987) 62 4821~,828 30 Kwak,J F, Venturlnl, E L and Glnley, D S Phystca (1987) 148B 426-428 31 Ambegaokar, V and Baratoff, A Phys Rev Left (1963) 10 486490 32 Kampwlrth, RT and Gray, KE 1EEE Trans Magn (1981) 17 565-568 33 Kupfer,H, Apfelstedt, I, Fluklger, R, Meler-Hirmer, R, Schauer, W, Wolf,T and Wuhl,H Internatwnal Conference on Materials and Mecham~ms of Superconducttwtv Interlaken. Switzerland (1988) 34 Peterson, R L and Ekln, J W (In preparation) 35 Kupfer,H, Wlech,U, Apfelstedt.I, Flukiger, R, Memr-HIrmer,R and Wolf, T (m preparation) 36 Matsushlta, T, N1, B, Sndo, Y, Iwakuma, M. Funaki. K, Takeo. M and Yamafup, K (in preparation) 37 Ghosh, A K, Suenaga, M, Asano, T, Moodenbaugh, A R and Sabaam, R L, Adv Cryog Eng (1988) 34 607-612 38 Newcomb,S B, Glowackl, B A, Campbell, A M, Evetts, J E and Stobl~, W M Br Ceram Proc (1988) (In press) 39 Campbell, A M Proceedmg~ LT18 Kyoto, Japan (1987) 40 Ourmazd,A, Rentschler,J A, Skocpol, W J and Johnson,Jr, D W Ph~s Rev B (1987) 36 8914-8917 41 Jou, CJ,Weber, ER,Washburn, J andSaffa, WA ApplPhysLett (1988) 52 326-327 42 Vmmkov,L Ya, Emelchenko, G A, Kononovleh,P A, OSslpyan, Yu A, Sehegolev,I F, Buravov,L I and Laukhln,V N lnternatwnal Conference on Materials and Mechamsms of Superconducnvtty

Interlaken, Switzerland (1988) 43 Kes,P H International Conference on Materials and Mechanism ~of Superconductivity Interlaken, Switzerland (1988) 44 Meler-Hirmer, R and Kupfer, H J Nucl Mater (1982) 108 & 109 593-601 45 Fletz, W A and Webb, W W Phvs Rev (1969) 178 657-665 46 Noel, H, Gougeon,P, Padlou, J, Lever,J C, Potel, M, Laborde, O and Moneeau, P Sohd State Commun (1987) 63 915-917 47 Crabtree, G W, Kwok, W K and Umezawa. A in Quantum Fwld Theor) as an lnterdtsclphnarv Bavts World Soenhfic Publ Co (1988) 48 Matsushlta, T, Iwakuma, M, Sndo, Y, NI, B, Kisu,T, Funakl K, Takeo, M andYamafup, K JpnJApplPhv~(1987)26L1524-L1526