Weak links in Pb-doped BiSrCaCuO ceramic superconductors

PhysicaC 167 (1990) North-Holland

188-197

WEAK LINKS P. SVOBODA

IN Pb-DOPED

BiSrCaCuO CERAMIC

SUPERCONDUCTORS

and P. VASEK

Institute of Physics, Czechoslovak Academy of Sciences, 180 40 Prague 8, Na Slovance 2. Czechoslovakia

0. SMRCKOVA

and D. SYKOROVA

Institute of Chemical Technology, 166 28 Prague 6, Suchbbtarova 5, Czechoslovakia Received 10 November 1989 Revised manuscript received 3 January

1990

The dependence of the resistive transition curve R ( T) on measuring current and magnetic field along with AC and DC magnetic susceptibility x(T) has been measured on ceramic superconductors of the nominal composition BiO.,Pb,,sSrCaCul.sOX to elucidate the nature of weak intergranular links in the samples. These weak links are shown to be responsible for pronounced currentdependent resistive tails analogous to those reported for YBaCuO [ 1: 2: 31 ceramics. The A ( T) curves can be interpreted in terms of percolative conduction in a multiphase system with superconducting regions coupled via nonsuperconducting barriers. External magnetic fields below 0.1 mT are shown to be sufficient for partial decoupling of the superconducting grains. A possible role of the Pb atoms in the formation of weak links resulting in a suppression of the transport critical current density J, is discussed.

1. Introduction One of the main obstacles for practical applications of the sintered bulk high temperature superconductors is their generally low transport critical current density J,. It is clear from magnetization experiments and from the measurement on thin crystalline films that this property is not intrinsic to the superconductor itself, but is due to the granularity of the ceramics. It has been accepted to describe such materials as a set of superconducting grains coupled via a network of some weak links. The nature and microscopic structure of such weak links apparently depend on the type and composition of the material studied and on the conditions of its preparation. In the one-phase Y,Ba2Cu307_-6 [YBCO] ceramics, prevailing evidence supports the idea of a dominant role of the intergrain weak links [l-3]. Nevertheless, the existence of intragrain weak links, represented e.g. by twinning boundaries, could also be detected [ 4,5]. The intergrain weak links are often identified with thin nonsuperconducting layers of altered composition on the surface of superconducting grains [ 6,7]. It can be e.g. oxygen deficient surface 0921-4534/90/$03.50 (North-Holland )

0 Elsevier Science Publishers

B.V.

layers, as suggested by the dependence of the character of weak links on annealing conditions reported by Yu and Sayer [ 8 1. Even “pure” large-angle grain boundaries can, however, act as weak links due to severe anisotropy in conductivity [ 9 1. Breaking of the weak links in ceramic YBCO samples and the resulting grain decoupling are widely thought to be responsible for the sensitivity of the transport critical current density J,(T) to very low magnetic fields and for the nonlinear current current-voltage characteristics observed at temperatures below T, [lo- 12 1. It has been shown [ 13 ] that either the spin-glass model (assuming intragrain Josephson weak links) or the flux-creep model (that takes only pinning forces into account and ignores any weak links) does not properly explain the low field magnetic properties of YBCO ceramics. A description of the properties of Bi-Sr-Ca-Cu0 high-temperature superconductors is complicated by the fact that more superconducting phases often coexist within one sample. At least three of them have been identified with stoichiometries given by the formula BiZSrZCan_ ,CunOX, where n = 1,2 and 3 and T,=20 K, 80 Kand 110 K, respectively [ 14,151. To

P. Svoboda et al. / Weak links in P&doped BiSrCaCuO ceramic superconductors

promote the growth of the “2223” high-T, phase, partial substitution of Pb for Bi proved to be succesful [ 16,171. Transport and magnetic properties of Bi-Sr-CaCu-0 ceramics are qualitatively similar to those observed in YBCO, indicating the presence of some weak links as well. They were detected by AC susceptibility measurement of Emmen et al. [ 18 ] and they are probably responsible for the current dependence of the resistivity transition curves reported by Togano et al. [ 161. The nature of these weak links does not seem to be firmly established yet. Microstructural investigations of undoped Bi-Sr-Ca-Cu0 ceramics [ 191 have shown a tendency to form a layer of a low-T, “22 12” phase on the surface of the grains composed of the high-Tc one. At temperatures above T,, (critical temperature of the low-T, phase), such layers would play the same role as the oxygendeficient surface layers in YBCO ceramics. In the Pbdoped samples, grains composed purely from the high-T, phase have been found, but thin amorphous Pb-rich surface layers have been frequently observed [ 193. Moreover, extreme anisotropy of the critical current observed in single crystals of the “22 12” phase [ 201 can cause a weak link behaviour even at pure grain boundaries in a polycrystalline sample with randomly oriented grains. Thus, it is probable that intergrain weak links in Bi-based ceramics are actually analogous to those observed in YBCO. We report in this paper experiments on the current and magnetic field dependence of the resistive transition curve in two Pb-doped Bi-Sr-Ca-Cu-0 ceramics with different conditions of preparation, supplemented by AC and DC susceptibility measurements on the same samples. The results are discussed in terms of the influence of the weak links on the electron transport in these granular superconductors.

2. Experimental The samples were prepared by mixing together powders of B&OS, Pbs04, SrCO, and CaCOJ and CuO in the molar ratio of Bi:Pb:Sr:Ca:Cu=1.4:0.6:2:2:3.6,

189

calcining, pressing into pellets and sintering. The conditions of preparation and some relevant parameters of the two samples discussed here have been summarized in table I. Prism-shaped samples for resistivity measurements were cut from the pellets, with dimensions as given also in table I. Having taken all the resistivity data, the middle part of the sample has been used for susceptibility measurements in order to suppress the possible influence of an inhomogeneity of the pellets. The resistivity has been measured by the four-point method, both AC and DC. In the AC method, the off-balance signal of an AC resistive bridge operating with excitation current Z,,Z 0.1 mA and frequency f= 72 Hz has been monitored. DC resistivity has been measured with currents I= I-200 mA (i.e. with current densities J= 0.05- 10 A/cm2) and a voltage resolution of lo-’ V. In both cases, the data was acquired and handled by computer controlled equipment. Electrical contacts to samples were prepared by a two-step procedure, involving short annealing ( 10 min at 600°C in air) of the samples with four contact areas, about 1 mm’ each, made by a silver paste. Subsequently, copper wires were soldered to these areas using standard PbSn solder. Contact resistance of such contacts was found to be about 0.1 R. For the resistivity measurement in steady magnetic fields, the samples were mounted into the device described in [ 2 I] and inserted into the bore of a superconducting solenoid, generating fields up to 4 T. The zero field experiments were performed with the help of a simple sample holder, where the temperature could be controlled by changing the position of the holder above the liquid He level in a transport dewar and measured by a calibrated Si diode. The AC and DC susceptibilities have been measured on small samples (total volume l-2 mm3) using a simple magnetometer with a SQUID [ 221. The DC susceptibility data has been taken in magnetic fields from zero to about 0.3 mT, generated by a coil placed inside of the superconducting shield of the susceptometer. The same coil served as a primary coil for AC susceptibility measurements. In this case, an AC field with an amplitude of about 1 uT and frequency of 160 Hz was employed.

p. Svoboda et al. / Weak links in Pb-doped BiSrCaCuO ceramic superconductors

190

Table I Parameters of the Pb-doped BiSrCaCu ceramic samples studied Sample

A B

Calcination ‘)

Sintering a)

T

t

T

t

(“C)

(h)

(“Cl

(h)

800 800

20 20

865 875

116 191

Cooling down

Cross-section (mm2)

T b’

quench. LNz furnace

1.2x 1.9 1.1x1.6

106 103

ck

a) in air. ‘) middle of the resistive transition at lowest measuring currents.

3. Results and discussion The temperature dependence of the resistance of the sample A for different values of the measuring current I is shown in fig. 1 (a). Apart from a small increase of the normal state resistance, that will be discussed below, the only change observed is the appearance of more and more pronounced resistive tails. For a single crystal of the “2212” phase, van den Berg et al. [ 23 ] estimated the critical current density in magnetic field B= 15 mT as J,( T) z 2 x 10’ ( 1- T/Tc)3'2 A/cm* (T,=86 K for their sample). Measurements on polycrystalline thin films of Bi-SrCa-Cu-0 with T,(R=O) > 100 K, i.e. with a substantial volume fraction of the “2223” phase, gave J,(T) > 100 A/cm* for T-c0.99T, [ 241. We can thus assume that the measuring current densities used (up to 8.8 A/cm2 for curve e in fig. 1 (a)) lie well below its intrinsic critical value for both the low-T, and the high-T, phases, i.e. that the current-dependent tails in zero magnetic field resistivity do not reflect changes in properties of the superconducting grains themselves. It is further supported by the fact, that the steep part of the resistive transition just below its onset does not depend on the measuring current, which holds not only for the high-T, phase (figs. 1 (a) and 3(a)), but also for the low-T, one (fig. 4(a)). It has been experimentally shown [ 25 1, that for currents exceeding the intrinsic (or intragrain) critical value, the steep main part of the resistive transition shifts to lower temperatures. The appearance of the tails on the R (T) curves in fig. 1 (a) is thus due to progressive decoupling of superconducting grains of the high-T= phase in the sample taking place at higher currents I. In terms of

the percolation conductivity model, even more and more of the weak links in the path transversed by the current become switched-over to their resistive state and progressively lower temperature is necessary to form the first continuous superconducting path connecting the two potential contacts on the sample. Figure 1 (b) shows magnetic susceptibility (both AC and DC) measured on sample A. In spite of the one-step resistive transition at low measuring currents, the sample clearly contains a volume fraction of the low-T, phase as well. The presence of weak links manifest itself in peaks in x” ( T) (curve c), whose position corresponds to temperatures, where the decoupling of superconducting regions takes place leading to a change of the effective volume that has to be screened by diamagnetic shielding currents [ 281. In sample A, the volume fraction of the highT,phase is apparently sufficient to form continuous network of the grains with most weak links interconnecting the islands of this phase only. The second step on the real part of the AC susceptibility X’ ( T) with the onset at about 100 K (curve b) then reflects the progressive locking of the network upon decreasing the temperature. There is, however, a measurable contribution of the weak links among regions of the low-T, phase as well, as indicated by small second peak at lower temperature. It is well-known that peaks in the imaginary part x” ( T) of the AC susceptibility can be observed (under suitable conditions) in normal bulk superconductors like Nb, Pb etc. [ 261. There are many reasons, however, for attributing these peaks in high-Tc superconductors to the presence of weak links, both intra- and intergranular [ 27,281. In this case, the position of the peak is expected to depend very sensitively on external magnetic field even in the range

191

P. Svoboda et al. / Weak links in Pb-doped BiSrCaCuO ceramic superconductors

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well below the lower critical field of the bulk material. We present in fig. 2 the small magnetic field dependence of the peak in x”(T) for sample A. It is seen that even the field B x 1 uT can appreciably shift its position, which can be taken as an experimental evidence for the weak links being responsible for the peak.

The role of the weak links is still more significant in sample B. In this case even the AC resistance measurement with lowest excitation current produces marked resistive tails (fig. 3 (a) ). Even here, however, the resistive curves measured at the lowest currents I do not reveal the presence of the low-T, phase, that is clearly shown on the susceptibility curves in fig. 3 (b). At the highest currents (I> 100 mA, corresponding to J,> 6 A/cm2) virtually all weak links connecting the superconducting grains are at T> 80 K in their resistive state and the resistivity saturates, at least at temperatures just below the “knee” on the R ( T) curve, where it ceases to be current dependent (see curves e and f in fig. 3(a)). At lower temperatures one sees then a second step that reveals the presence of the low-T, phase. Such a behaviour gives some information on the character of the coexistence of the two superconducting phases present in our samples. Two types of superconducting grains, one formed by the high-T, phase and the second by the low-T, one, apparently coexist in the sample [ 15,191. Upon lowering the temperature, the current “chooses” at first paths transversing the grains of the high-Tc phase coupled together via some weak links and completely by passes the islands of the lowT, phase. Once the volume fraction of the high-T,

P. Svoboda et al. / Weak links in Pb-doped BiSrCaCuO ceramic superconductors

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Fig. 3. (a) Temperature dependence R ( T) of the resistance for sample B. Curve a) AC method, Iarz 0.1 mA. b) - f ) DC method: b)I=1mA,c)1=10mA,d)1=50mA,e)1=100mAandf) I= 150 mA. (b) Temperature dependence of the susceptibility for sample B. Curve a) DC susceptibility in the FC regime (Meissner effect), Ba 30 PT. b) and c) AC susceptibility, B,ez 1 pT: b) real part x’ ( T), c) imaginary part x” ( T).

phase within the sample is sufficient to make this possible, we will observe a one-step resistive transition even in the sample that contains a rather large amount of the low-T, phase. Increasing the current I at a fixed temperature T (T,, c T-c Tc2, with T,, and Tc2 denoting the transition temperatures of the lowT, and the high-Tc phases, respectively) simply in-

creases the proportion of the weak links converted into their resistive state, which then determine the effective resistance of the sample at T. Lowering further the temperature below Tel, it can become advantageous for the current to “look for” other paths, transversing the regions of the low-T, phase with their own network of weak links. This is the situation, where we can detect the presence of the low-T, phase from the R(T) curves. Comparing figs. l(b) and 3(b), we can see a marked difference between the temperature dependencies of both the real part x’ (T) (curves B) and the imaginary part 1” (T) (curves c) of the AC susceptibility. Only one peak in x” ( T) centered at about 60 K appears in sample B. It is hard to distinguish whether the weak links responsible for the peak interconnect the grains of the low-T, phase in the sample, where the volume fraction of the high-Tc phase lies well below percolation threshold, or whether they are the same as in sample A but with such a low coupling energy that they lock at much lower temperatures. Localization of the peak seems to prefer the former possibility. In any case, the disproportion in the relative heights of the two steps seen both on DC and AC susceptibilities (curves a and b in fig. 3 (b ), respectively) indicate that the lower step on curve b represents a superposition of the superconducting transition of the low-T, phase and a contribution due to the locking of weak links. For comparison, we present in fig. 4 the data taken on an undoped Bi-Sr-Ca-Cu-0 sample. Properties of this sample, provided to us kindly by M. Neviiva, are more thoroughly discussed separately [ 291. Two current independent steps in R(T) are seen in fig. 4 (a) with relative small resistive tails. In this sample there is clearly no conducting path available that would bypass the regions of the low-T, phase. The volume fraction of the high-T, phase is in this sample very low, as indicated by susceptibility data in fig. 4(b). We have already mentioned that for the undoped Bi-Sr-Ca-Cu-0 sample, HREM observations indicate possible coexistence of both superconducting phases within one grain in such a way that the low-T, phase forms on the surface of the high-T, one [ 15,191. In this case a sufficiently thin layer of the low-T, phase could play the role of the weak link that would lock at Tr Tc2. Although a contribution of such weak links cannot be excluded, two distinct

P. Svoboda et al. / Weak links in Pbdoped BiSrCaCuO ceramic superconductors

50

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Fig. 4. (a) Temperature dependence R(T) of the resistance for the unleaded BiSrCaCuO sample [ 29 1.DC method: a) I= 1mA, b)I=lOmAandc)1=100mA. (b) Temperature dependence of the susceptibility for the unleaded BiSrCaCuO sample [ 291. a) DC susceptibility in the FC regime (Meissner effect), Bz 30 FT. b) and c) AC susceptibility, BcRz 1 uT: b) real part x’ (T) and c) imaginary part x” (T).

steps at TX 80 K on curve b in fig. 4(b) along with the position of the peak in X” (T) seems to support the idea that weak links formed by nonsuperconducting layers on the contact among adjacent regions of the low-T, phase play an important role in the undoped sample. The quality of the weak links plays a crucial role even in the effect of aging, that causes irreversible

193

changes of R ( T) curves [ 29 1. The chemical changes on the surface of the grains in porous sintered samples due to reaction with the environment are probably responsible for the slight change of the normal state resistance seen in fig. 1 (a), where the upper two curves have been measured two days later than the other ones. The effects of aging are more pronounced in samples with extremely weak links as in our sample B. After 10 days of storing the sample in air at room temperature, the resistive tail extends to much lower temperatures, as can be seen by inspecting the curves b in fig. 3 (a) and a in fig. 5 (b) taken under identical conditions 10 days apart. It means a suppression of J, due to aging of the sample. This spurious effect has been observed in all our samples of high temperature ceramic observed in all our samples of high temperature ceramic superconductors [ 29 1. It is similar to that observed by Goldschmidt [ 121 in YBCO ceramics and it gives another argument in favour of the identification of weak links with compositionally altered layers on surfaces of adjacent superconducting grains. Additional information on the character of the weak links in our samples comes from the study of the changes of the R ( T) dependence due to reaction with water reported in [ 301. The dramatic changes of the R(T) curve for a sample cut from the same pellet as sample A discussed here (see fig. 4 in [ 301) are consistent with a new semiconducting phase arising on the surface of superconducting grains due to a chemical reaction. Layers of these phase are eventually capable to destroy completely any superconducting path across the sample. In this sense, the current dependence of the resistive tails in fig. 1 (a) can be interpreted as a manifestation of a network of intergrain junctions of the S-N-S or S-N-I-N-S type with a rather wide distribution of critical currents, which reflects varying thickness of compositionally altered nonsuperconducting surface layers and adjacent grains and/or varying area of the contact among them. Up to now, we have discussed the data taken in zero magnetic field (resistivity ) or in very small fields well below the lower critical field H,, [ 3 11. In fig. 5, we present the magnetic field dependence of R(T) curves. In both samples, the application of a small magnetic field (Bc0.015 T) produces virtually the same change of the R(T) curves as an increase of

P. Svoboda et al. / Weak linb in Pb-doped BiSrCaCuO ceramic superconductors

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measuring current I (compare curve b in fig. 5(a) with e in fig. l(a), and b in fig. 5(b) with fin fig. 3 (a) ). Such a field did not measurably influence the main steep part of the resistive transition. The magnetic field dependence of the resistive transition of Bi-Sr-Ca-Cu-0 superconductors has been studied in single-crystals [ 321, thin films [ 331 and ceramic samples [34,35]. The resistive tails arising in high field up to 12 T [ 321 have been discussed in terms of flux-creep, i.e. as being intrinsic

to the superconducting phase itself. The exponentially lower part of the tails has been found to follow closely the formula P=Poexp( - U,/T) with a temperature independent activation energy of the flux line motion U. [ 32,341. The prefactor p. was found to be field independent in single-crystals of the “22 12” phase [ 32 1, but it was strongly field dependent in ceramics with a high fraction of the “2223” phase [ 341. Even if the detailed interpretation in terms of simplified flux creep models is rather disputable [ 33 1, the concept seems to be useful for the description of the behaviour of the Bi-Sr-Ca-Cu-0 superconductors in fields exceeding H,, and it is probably applicable to our results in higher fields. The single-crystal data of Palstra et al. [ 321 are independent of measuring current even in the lowest magnetic fields. It should correspond to the absence of any detectable intragrain weak links or at least to their large critical currents. It is interesting to note the hump seen on the curves taken in the highest fields perpendicular to the &plane [ 321 (ignored in their discussion), that would perhaps indicate a presence of weak links with very large critical currents. Current dependence of the resistive tails has been reported for ceramic samples [ 35 1. This dependence could be suppressed by external magnetic field and it nearly disappeared in the field B= 1 T. The authors interpret the current-independent resistivity tail as a result of the broadened resistive transition of the low-T, phase. This broadening can, however, influence only the part of the R(T) curve below T,, x 80 K. Moreover, it would imply a very low value of the upper critical field H,, of the lowT, phase. We would suggest that the disappearance of the current dependence in a field Bo, which is equivalent to the appearance of a linear currentvoltage characteristics, can be connected with the existence of an upper critical field for a set of all the weak links present in the sample. The field B. is sufficient to break all the intergrain weak links in the sample and the tail then corresponds to the total ohmic resistivity of the network of the broken weak links superimposed on resistive transition of the lowT, phase below T,,. In this interpretation, the measurement of the current-voltage characteristics at T-c T,, as a function of the applied magnetic field would provide an information on the coupling

P. Svoboda et al. / Weak links in Pbdoped BiSrCaCuO ceramic superconductors

strength of the “strongest” weak links within the sample. To study the decoupling of the superconducting grains in very small magnetic fields, the DC susceptibility has been measured both in the zero-fieldcooling (ZFC ) and the field-cooling (FC ) regime. In the ZFC regime, diamagnetic shielding takes place and we obtain for the DC susceptibility a similar temperature dependence as for the real part of the AC susceptibility. The signal observed is not proportional to the volume of the superconducting phase present in the sample at a given temperature, but rather to the total volume enclosed within the superconducting “envelopes” formed by coupled superconducting grains. This difference can be very important in ceramic superconductors, where pores and nonsuperconducting phases can occupy a substantial part of the volume of the sample. Once these “envelopes” are not broken, it is not possible to distinguish, whether they are “empty” or “full”. On the contrary, in the FC regime we deal with the Meissner effect and the signal observed is directly proportional to the volume occupied by superconducting phase only. We have measured the temperature dependence of the DC susceptibility in both regimes for several magnetic fields up to 0.3 mT. From these curves, the magnetic field dependence drawn in fig. 6 has been determined. While in the FC regime we get a signal nearly independent of the external magnetic field, the marked reduction of the ZFC signal is observed already in the smallest fields above about 30 pT. This is the field, at which the decoupling of superconducting grains starts. As a result, the field can then penetrate into the nonsuperconducting interior of the still superconducting, but already partially decoupled “envelope”. This leads to a reduction of the effective volume that contributes to the ZFC signal. The decoupling is, however, far from being complete in the fields used in our measurement, because the ZFC signal remains substantially higher than the FC. The onset of the reduction of the ZFC signal should therefore correspond to critical fields of the “weakest” links present in the sample. We can thus estimate from R ( T) and x( T) experiments both upper and lower limits of the distribution of critical fields, characterizing coupling strengths of the weak links acting a in a sample.

0

100

195

,200 B,xth~T]

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Fig. 6. Magnetic field dependence of the DC diamagnetic shift Ax at fixed temperature T=45 K for the sample B. a) ZFC regime and b) FC regime.

It should be emphasized, that the critical parameters of the weak links deduced from these DC susceptibility studies need not generally be the same as those obtained from the resistivity studies in very small external magnetic fields, i.e. from the magnetic field dependence of the transport critical current density J,. It is due to the fact that only the weak links in at least the two-dimensional network of coupled superconducting grains that encloses a finite volume of the sample can influence the ZFC signal. The weak links, say, in linear superconducting chains crossing the sample, which can dominate in R ( T) curves, play no role in DC susceptibility measurements. Partial substitution of Pb for Bi, which is known to promote the growth of the high-T, “2223” phase, can influence the nature of the weak links. Pb-rich surface layers observed by Ramesh et al. [ 191 would certainly suppress the value of the transport critical current density in the sample and enhance the effects related to the presence of weak links. Both the relatively high concentration of Pb in our samples (well above the solubility limit found by Green et al. [ 15 ] ) and rather high sintering temperatures used can be beneficial for the existence of weak links of this type. These factors are probably responsible for the rather low quality of our samples as characterized by trans-

196

P. Svoboda et al. / Weak links in Pbdoped BiSrCaCuO ceramic superconductors

port critical current densities reaching J,( 77 K) 2 2 A/cm2 in the better one from our two Pb-doped samples. On the other hand, this low quality of the samples has enabled us to observe the effects of weak links by relatively low measuring currents and/or magnetic fields, and to separate them from the effects connected with intrinsic properties of Bi-SrCa-Cu-0 superconductors. Some compromise in the conditions of sample preparation has to be apparently found to improve the value of J, without losing the high volume fraction of the high-T, phase, typical for Pb-doped samples.

4. Conclusions Weak links present in our ceramic samples have been shown to influence substantially the form of the R(T) at higher currents, to suppress the transport critical current density J, and to manifest themselves both in AC and DC susceptibilities of the samples. These weak links start to break already by very small measuring currents (below 0.1 mA in sample B) or in magnetic fields of about 30 PT. The behaviour of these weak links is characteristic for junctions of the S-N-S or S-N-I-N-S type. They are sensitive to environmental effects and are thus probably caused by compositionally altered nonsuperconducting layers arising on the surfaces of individual grains. Current dependence of the resistive tails in zero magnetic field has been interpreted as a progressive decoupling of superconducting grains. The broken weak links then bring a finite contribution to the sample resistivity, once the last continuous path for the supercurrent was disconnected. On multi-step R (T) curves, frequently observed in Bi-Sr-Ca-Cu0 ceramic samples of a lower quality, this current dependence at current densities well below the intrinsic ones can help to distinguish whether a particular step belongs to another superconducting phase or whether it should be attributed to weak links. It is suggested, that measurement of the magnetic field dependence of current-voltage characteristics can give the value of the critical field of “strongest” weak intergrain links in a sample. On the contrary, the critical field of the “weakest” weak links can be found from the measurements of the DC magnetic susceptibility of the sample in both the ZFC and FC

modes. These quantities are sample-dependent and they can serve for a characterization of its quality.

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