Comparative Study of the Effects of La-Substituted Ca in (Bi, Pb):2212 and (Bi, Pb):2223 Superconductors

We report here a comparative study of the effects of La-substituted Ca on (Bi, Pb):2212 and (Bi, Pb):2223 superconductors with various La content (0.00 ≤ x ≤ 0.30). Regardless of the effects of La, it is evident that the superconducting volume fraction, excess of oxygen, critical concentration for quenching superconductivity, Vickers hardness, anisotropy, interlayer coupling, critical magnetic fields, and critical current were higher for the 2212 series than the 2223 series. In contrast, orthorhombic distortion, c-parameter, crystallite diameter, doping distance, distance between two Cu atoms, hole carrier/Cu ion ratio, melting temperature Tm, critical temperature Tc, onset of diamagnetic TcM, surface energy, elastic component, resistance pressure, and c-axis coherence length were higher for the 2223 series than the 2212 series. An inverse linear relationship between Tm and Tc was estimated for both series, and for room-temperature (RT) bismuth–strontium–calcium–copper–oxide (BSCCO) superconductors, the required Tm values should be 1048.03°C for the 2223 series and 784.48°C for the 2212 series. Surprisingly, the difference in temperature between zero resistivity and diamagnetic onset |TcM − TcR| for La = 0.30 samples is 30 K. In the critical field region (CFR), the exponents of order parameters (OPD) are two-dimensional (2D), but their values were higher for the 2212 series than the 2223 series. Further, they became three-dimensional (3D) as La increased to 0.30 due to the reduced effective length in highly substituted samples. Our results were discussed with the help of the differences in the physical parameters between the considered series. These findings revealed that the 2212 series is more suitable for applications that need higher hardness and critical fields and currents. In contrast, the 2223 series is more suitable for research for higher Tc and altering plastic deformation. To our knowledge, the present systematic investigation has not been reported elsewhere, which highlights the present work.


Experimental Details
The Bi 2 O 3 , PbO, SrO, La 2 O 3 , CaCO3, and CuO oxides and carbonates of 4N purity were thoroughly mixed in the required proportions and calcined at 825°C in air for 24 h. This exercise was repeated three times, with intermediate grinding at each stage. The resulting powder was reground, mixed, and pressed into pellets at a force of up to 10 tons. The pellets of (Bi, Pb):2212 were sintered in air at 840°C for 36 h and left in the furnace for slow cooling to room temperature at a rate of 5°/min. (Bi, Pb):2223 pellets were also sintered in air at 850°C, but for 150 h and then left in the furnace for slow cooling at the same rate of 5°/min. The phase purity of the samples was examined using an X-ray diffraction pattern (XRD) using a Philips PW-1700 with Cu-Kα radiation of wavelength λ = 1.5418 Ẳ at 40 KV and 30 mA settings and a diffraction angle range of 20°-70° with a step of 0.06°. Differential thermal analysis (DTA) and thermogravimetric analysis (TGA) of the samples in powder form were performed in the temperature range of 30-1000°C with a heating rate of 10°C/min. The electrical resistivity of the samples was obtained using the standard four-probe technique in a closed-cycle cryogenic refrigerator within the range of 18-300 K (Displex) employing helium gas. Direct-current (DC) magnetization was carried out by means of a SQUID magnetometer (Quantum Design) in both field cooling (FC) and zerofield cooling (ZFC) at a field of 20 Oe in the temperature range of 10-150 K. More precisely, the samples were first cooled to 20 K in the absence of the applied field, then the field was switched on and the data was acquired for increasing temperature (ZFC) up to 150 K. After that, the samples were cooled again and FC magnetization was acquired in the presence of the field. Finally, the Vickers microhardness of the samples at room temperature was determined using the manual microhardness tester model IN-412A with an applied load of 0.49-10 N for 10 s.

XRD and DTA Analysis
The XRD patterns of the samples shown in Fig. 1a and b show that the 2212 H (hkl) and 2223 H (hkl) superconducting phases were responsible for the majority of the obtained peaks, which correspond to T c = 89 K and 110 K, respectively. In contrast, the minority peaks of very low intensity indicated by L (hkl) belong to the minority superconducting phases of Bi (Pb):2201 and Bi (Pb):2212, with T c of 23 and 89, respectively, which are normally formed 1 3 during the synthesis of Bi (Pb):2212 and Bi (Pb):2223, respectively. In addition, they are formed with very lower intensities in BSCCO systems and therefore cannot be considered as impurity phases, consistent with the results reported elsewhere. 14,19,22,29,30 The superconducting volume fractions of the 2212 (V 2212 ) and 2223 (V 2223 ) series were determined by 7,33,34 and respectively.
It is also clear from Fig. 2a that V 2212 is higher than V 2223 . This is because the 2201 minority phase formed in the 2212 series at 750°C, whereas the minority 2212 phase formed at 825-850°C in the 2223 series. As the temperature increased to the sintering point (850°C), the majority of the 2201 phases were transferred to 2212, and therefore V 2212 was increased. In the case of the 2223 series, the amount of the 2212 minority phase was not completely transferred to the 2223 phase, which in turn decreased the 2223 majority phase. The porosity of the samples was calculated as PS = [1 − (ρ exp /ρ th )] and shown in Fig. 2b. It is seen that PS was decreased by La for both series, but it was higher for the 2223 series than the 2212 series. This behavior may be related to the ratio of dislocation density and oxygen vacancies between them, which may be higher for the 2223 series than for the 2212 series.
The c-parameter and orthorhombic distortion OD = [(b − a)/a] against La are shown in Fig. 3a and b for both series. It was found that the OD for pure 2212 was generally higher than that for 2223, while the opposite was true for the Lasubstituted samples. However, this was related to the amount of excess oxygen and the length of the Cu-O bond in the Cu-O 2 planes in both series, as reported elsewhere. [36][37][38][39] Consequently, the length of the in-plane Cu-O bond was decreased, which is helpful for more effectively reducing the a-parameter of pure 2212 as compared to pure 2223. Otherwise, the change in the b-parameter is related to the  change in the hole carrier concentration per Cu ion, which is induced by La doping within these planes. [40][41][42][43] Thus, the rate of decrease or increase in the (a/b) ratio for La-substituted samples is responsible for the further increase of OD in the 2223 series than that of the 2212 series. On the other hand, the c-parameter of the 2223 series was higher than that of the 2212 series. This was due to increasing the number of CuO 2 planes in 2223 (three planes) as compared to 2212 (two planes). The average crystallite diameter, D hkl , evaluated by Scherer's equation, and also the dislocation density, β = 1/D hkl 2 , against La content are shown in Fig. 4a and b. D hkl values are higher for pure 2212 and La = 0.05 samples than for similar samples of the 2223 aeries, while the opposite is true for La-substituted samples. This may be related to the behavior of V 2212 and V 2223 against La for both series. β values were decreased by La, and they were slightly higher for the 2223 series than the 2212 series. This behavior indicated that La samples have very few lattice defects and good crystalline quality. 44,45 Further, the increase in the 2223 series may be related to increasing both the c-parameter, OD, and D hkl . Figure 5a and b shows the DTA patterns of the samples. It is worth noting that when T was raised to around 800°C, the crystallization tendencies for 2201 in the 2212 series and 2212 in the 2223 series almost vanished. Figure 6a and b shows the heat loss and melting temperature T m at the peak against the La content for both series. The heat loss of pure 2212 was higher than that of pure 2223 and decreased by La for both series, but it was higher for the 2223 series than the 2212 series. This result indicated that the amount of 2201 minority phase formed in the 2212 series was melted below 800°C and after that it decomposed into the 2212 majority phase. 46 In contrast, the 2212 minority phase formed in the 2223 series was melted above 800°C, and after that, it decomposed into the 2223 majority phase. 47 The T m was increased by La for both series, but it was higher for the 2223 series than the 2212 series even for pure samples. This may be attributed to increasing the optimum temperature required for melting the mixture due to La, which facilitated the growth of majority phases. 47,48 Such an observed increase in T m emphasizes the role of La addition in the internal structure of the examined samples.   Figure 7a shows the oxygen content y against the La content for both series, and it is seen that for pure samples, there is an excess of oxygen above the stoichiometric values of 8 and 10 for both systems (y = 8.1 for 2212 and 10.07 for 2223). Furthermore, values of y were gradually increased by La for the two series, but it is higher for the 2223 series than the 2212 series, which indicates that La helps with more excess oxygen for the two series. For more clarity, the excess oxygen is 0.10, 0.17, 0.47, and 0.58 for 2212, which is higher than 0.07, 0.12, 0.37, and 0.53 determined for 2223, as well as the OD behavior obtained from XRD. However, according to the mechanism of excess oxygen in a pure BSCCO system, the electrons were transferred from Cu to the BiO layer, leading to the formation of holes on Cu and electrons on Bi according to Bi 3+ +Cu 2+ → Bi 3−x +Cu 2+x . These changes in the valence state of Bi are due to excess oxygen and are reflected as the changes of hole carriers in the Cu-O 2 planes. Since the superconductivity of copper-oxide systems is localized in the Cu-O 2 planes where the majority of holes are supposed to reside, it is believed or expected that the majority of excess of oxygen will be in the Cu-O 2 planes.

Oxygen Content Analysis
The effective Cu eff valance was obtained by Figure 7b shows the Cu eff against La for the two series. It was found that the values of Cu eff are higher for the 2223 series than the 2212 series. This can be explained in terms of increasing the number of holes which may be introduced by La as a result of such substitution. Thus it is illogical to replace Ca 2+ by La 3+ , and therefore, Cu eff , should be decreased, but this is discussed in the next paragraph. (2) ; for 2212; and  The excess oxygen in the form of excess doping density Σ −1 is converted into a doping distance d as follows 23,49 : where a is lattice parameter, and Σ given by It is evident from Fig. 8 that Σ −1 is higher for the 2212 series than the 2223 series, while d is higher for the 2223 series than the 2212 series; see Fig. 8a and b. This, of course, is clear evidence of changing the hole carrier concentrations between the series as a result of such substitution. Increasing d for the 2223 series rather than the 2212 series is related to the difference in the c-axis between them. The distance z between the two nearest Cu atoms was calculated by 23,50,51 ; for 2212; and ; for 2223 Moreover, the crystal geometry factor (CGF) of the area of superconducting planes can be obtained from where n is the number of CuO 2 planes, and m eff is the effective mass of the hole (m eff = 2m e = 18.210 −31 kg).
It is evident from Fig. 9a and b that z is higher for the 2223 series than the 2212 series. The CGF factor is higher for pure 2223 than for pure 2212, and the difference in CGF between them is gradually decreased by La until it becomes zero for La = 0.15 and 0.30 samples. This behavior can be considered good evidence for hole carrier behavior between the series, as presented in the next paragraph. Figure 10a and b depicts the electrical resistivity versus temperature for the two series. Figure 11a depicts the critical T c , onset temperature T on , and transition width ΔT c for the samples. It was found that T c and T on were higher  for the 2223 series than the 2212 series. This was due to the difference in T c for pure samples (94 K for 2212 and 119 K for 2223). The reduced T c [T c (x)/T c (0)] against La is also shown in Fig. 11b. It was found that the critical concentration x c of La for quenching superconductivity can be extended above 0.30 for both series, which is higher than that reported (0.25). [8][9][10][11][12][13][14][15][16][18][19][20][21][22]26,52,53 It was also clear that La slightly had a higher solubility in the 2212 series, and it was less detrimental to the superconductivity as compared to the 2223 series; that is [T c (x)/T c (0)] α (1/T c ) for BSCCO systems.

Resistivity Analysis
An inverse linear relation could be obtained between T m obtained from DTA and T c as shown in Fig. 12b. The linear relations are given by T c (K) = −3.406 T m + 2963.3 for 2212 and T c (K) = −2.5413 T m + 2963.3 for 2223, which is consistent with reported values for high-T c systems. 54,55 This finding suggests that to achieve a higher T c , an eutectic compound with a lower melting point should be looked into. Based on the above data, a composition of T m = 784.48°C for 2212 and 1048.03°C for 2223 is required for RT superconductivity with T c = 300 K.
The phase diagram of high-T c systems is well described by 56 where T c x and T c m are the critical and maximum T c , respectively, and p is the hole carrier concentration per Cu ion. It is evident from Fig. 12a that p is higher for the 2223 series than the 2212 series due to the extra positive charges transferred to the CuO 2 planes, which disagrees with the role of substitution for decreasing P due to replacing Ca 2+ by La 3+ . 57,58 To clarify this point, we suppose that La decreases the hole carrier concentration due to replacing Ca 2+ by La 3+ , but in contrast, the excess oxygen introduces some excess holes in the Cu-O 2 planes, and consequently, the effective (net) number of holes is increased, but the rate of increase is higher in 2223 than in 2212. This can also be supported by the behavior of doping distance and density of excess doping presented above.   zero at T cM for both series, the area of diamagnetic is higher than zero, indicating the presence of a superconducting state with an expected critical current, as previously reported. 59,60 As shown in Fig. 14a and b, the onset of diamagnetism T cM decreases with increasing La for both series, followed by a sharp increase to 80 K for La = 0.30 samples. T cM average values for 2223 are higher than for 2212, as well as for T cR (R = 0). Interestingly, as La increased to 0.15, the temperature difference |T cM − T cR | also increased, and it was greater for the 2223 series than for the 2212 series. However, when La was increased to 0.30, the |T cR − T cM | sharply increased up to 30 K for both series. This was because it was possible to determine the T cM of the first islands due to pure clusters that were present essentially and appeared in the superconducting sample using high-accuracy magnetic measurements. 59,61,62 This is, of course, impossible in the case of resistivity measurements, because they are measured across the sample's cross-sectional area.

Microhardness Analysis
It is evident from the curves of microhardness H v versus F shown in Fig. 15a and b that they were decreased by increasing F for the two series, and at fixed F, the H v is higher for the 2212 series than the 2223 series. The higher values of H v for 2212 are due to the decreased porosity of the 2212 series and therefore alter the point of plastic deformation. 37,63,64 The diagonal length d p is related F according to 15,65 H t is true hardness, and γ is surface energy. The plots of F/d p against d p are shown in Fig. 16a and b. Figure 17a and b shows that H t is greater for the 2212 and 2223 series, as is H v . But, the values of γ are higher for the 2223 series than the 2212 series, indicating that a more compacted surface   has higher hardness, and thus lower surface energy was obtained. Firstly, the indentation size effect assumes that the indentation contains an elastic portion of the deformation besides plastic deformation. 66,67 This is explained by adding an elastic component d e to the measured elastic component d p as follows 68,69 :     The plot of d p versus F 1/2 is shown Fig. 18a and b for the two series where the slope represents [(1854.4) 1/2 (H t ) − 1/2 ], and the vertical intercept represents d e .
Secondly, the effect of energy dissipative processes and therefore H t was obtained by subtracting dissipative part F 0 from applied load F as follows 70 : The slope of the linear plot of F against d p 2 is shown in Fig. 19a and b for the two series, in which H t /1854.4 is the slope, and the intercept is the resistance pressure F o . Also, Fig. 20a and b represents the behaviors of both d e and F o against La for both series. It is seen that they are slightly higher for the 2223 series than the 2212 series, which emphasizes the hardness suppression indicated above.

Fluctuation Analysis
The linear fit of normal resistivity ρ n versus T, shown in Fig. 21a and b, follows the formula. The mean field temperature (T c mf ) was estimated from the peak of dρ/dT against the T plot, which is shown in Fig. 22a and b. By using the values of excess conductivity ∆σ and reduced temperatures, Є, we plotted ln∆σ against lnε as shown in Fig. 23a and b. However, the linear fit of each curve in the normal field region (NFR), mean field region (MFR), and critical field region (CFR) is mentioned. In Fig. 24, the crossover temperatures, T o1 and T o2 , and T c mf against La are shown in Fig. 24a and b. It is noted that their values are higher for the 2223 series than the 2212 series, as well as T c . The interlayer coupling J and the c-axis coherence length ξ c (0) were calculated, in which d = c/2 for BSCCO systems as follows 71,72 :   This means that the OPD is 2D for both series, but it becomes 3D for La = 0.30 samples rather than 2D as reported for BSCOO systems. 71,72 This behavior is related to another generated reduced length (11) ln Δ = ln A − ln  or dimension perpendicular to the direction of current flow. 65,73 In addition, anisotropy is given by N G is the Ginzberg reduced number given by N G = and H c (0) is the thermodynamic critical field at 0 K given by; , and λ(0) is the London penetration depth at 0 K which is about 250 nm and 300 nm for 2212 and 2223 superconductors, respectively. 48 The upper critical fields at 0 K along the c-axis H c2 (c -axis) and along the a-b plane H c2 (ab -plane) , and also the critical current density at 0 K and J c (0) were calculated by using the following relations 74-76 :  As indicated in Fig. 26a, the values of anisotropy are higher for the 2212 series than the 2223, while the values of NG shown in Fig. 26b are higher for the 2223 series than the 2212. On the other hand, Fig. 27a and b shows the critical field and critical current for both series, in which they are higher for the 2212 series than the 2223 series. In light of these observations, one can say that the increase in excess oxygen and hole carrier/Cu ions introduced by La into the CuO 2 planes of the BSCOO system may also affect the path of current flow in the system and improve the critical fields and currents. This leads to electronic   or chemical inhomogeneity in the charge reservoir layer (BiO/SrO), which supplies the charge carriers to the CuO 2 planes through which the actual super-current is believed to flow. 31,76,77 However, and regardless of the effects of La discussed in detail in Refs. 29-32, it is found that x c for quenching superconductivity, Vickers hardness, critical magnetic fields, and critical current density are higher for the 2212 series than the 2223 series. In contrast, the melting temperature T m , critical temperature T c , onset of diamagnetic T cM , surface energy, elastic component, and resistance pressure are higher for the 2223 series than the 2212 series. These findings are due to the differences in superconducting volume fraction, crystallite diameter, porosity, excess oxygen, hole carrier/Cu ion ratio, doping distance, spacing between two neighboring Cu atoms, anisotropy, and interlayer coupling between the two series. For example, superconducting volume fraction, excess of oxygen, anisotropy, and interlayer coupling are higher for the 2212 series, and they are responsible for the former performance of the 2212 series, while the orthorhombic distortion, c-parameter, crystallite diameter, doping distance, distance between two neighboring Cu atoms, hole carrier/Cu ion ratio, and c-axis coherence length, which are higher for the 2223 series, are responsible for the latter performance of the 2223 series. To our knowledge, the present systematic investigation has not been reported elsewhere, which highlights the present work.

Conclusion
A comparative study between the effects of La-substituted Ca in (Bi, Pb):2212 and (Bi, Pb):2223 superconductors has been well investigated. We have shown that the critical concentration for quenching superconductivity, Vickers hardness, critical fields, and critical current J c are higher for the 2212 series than the 2223 series. In contrast, the critical temperature T c , melting temperature T m , onset of diamagnetism T cM , and resistance pressure are found to be higher for the 2223 series than the 2212 series. An inverse linear relationship between T m and T c could be obtained for both series. The 1048.03°C and 784.48°C T m values are required for RT superconductors of 2223 and 2212. Surprisingly, for both series, the temperature difference between zero resistivity and diamagnetic onset, |T cM − T cR | for La = 0.30 samples is 30 K. The order parameter exponents in the critical field region are 2D for both series, but they become 3D as La increases to 0.30 due to the expected reduced effective length in highly substituted samples. The preference of the 2212 over the 2223 for the former parameters is mainly attributed to the superconducting volume fraction, excess of oxygen, anisotropy, and interlayer coupling, which are higher for the 2212 series than the 2223 series. Meanwhile, orthorhombic distortion, c-parameter, crystallite diameter, doping distance, distance between two Cu atoms, hole carrier/Cu ion ratio, and c-axis coherence length, which are higher for the 2223 than the 2212, are responsible for the latter preference of the 2223 series. These findings reveal that the 2212 series is more suitable for applications that need higher hardness and critical fields and currents. In contrast, the 2223 series is more suitable for research for higher T c and altering plastic deformation. To our knowledge, the present systematic investigation has not been reported elsewhere, which highlights the present work.