The Correlation of Miller Indices with the Conductivity Mechanism of Cu-Based High-Tc Superconductor

The high temperature superconductor of CuBa2Ca2Cu3O8+δ(Cu-1223) was synthesized experimentally by solid-state reaction. There were many parameters affecting the preparation technique such as oxygen flow, sintering temperature, sintering time, and compacted pressure. The XRD-pattern exhibited a tetragonal phase for both Cu-1223, and Cu-1212. The resistivity measurement was considered the important experiment to show the predominant phase of superconductor if it was a high phase or low phase. The critical temperature (Tc) was about (128 K) for the high phase of Cu-1223, whereas the low phase of (Cu-1212) appeared at (Tc = 64 K). The correlation between the Miller indices and resistivity measurements was a good tool to predicate the expected mechanism of conductivity within the unit cell. It was clear that the arrangement of these planes was aligned in the a-c direction. That should make the motion of the charge to be simpler by a stepping plane toward c-axis.


Introduction
The high-T c superconductor cuprate like HgBa 2 Ca n-1 Cu n O 2n+2+δ , with different values of (n = 1, 2, 3) was recorded a critical temperature of about (T c = 138 K) at (n = 3) [1].This compound was classified as Hg-family, and the most interesting focused upon the third member (n = 3) by the series (Hg-1223) due to its high critical temperature.Many attempts were made to develop Hg-family high-T c superconductor; part of them were applied the preparation methods, physical or chemical methods [2] [3].The other attempts concentrated on the preparation condition of the applied method [4].The last group depends on the partial substation of isovalent atoms [5] [6], and the change the parameter (n > 3) [7] [8] [9].It was difficult to obtain the single phase of Hg-family ceramic compound because it contains both high phase Hg-1223 and low phase (Hg-1212).The most important thing in production of Hg-family high-T c superconductor was how to control the oxygen pressure and mercury pressure; for this reason there were no specific values for oxygen and mercury pressures [10].
The normal solid-state reaction was not used in preparation of Hg-family superconductor because of high evaporation of Hg-element in the mixture; to avoid this problem, the technique of a sealed quartz tube applied thermally in solid-state reaction [11].The solving of this problem was the replacing of a metal ion instead of Hg-ion such as Cu-ion, and producing a new family like Hg-1223 family [12] [13].That was the aim of the research, and studying the electrical and structural properties of Cu-1223 was the main purpose to specify this superconductor type like Hg-1223.The correlation between them should be important to understand the conductivity mechanism, as shown in Figure 1.The previous studies appeared the multi-phase in (Hg-1223) compound, and then the multiphase is acceptable in Cu-1223.

Experimental Work
The Cu-1223 compound synthesized by solid-state reaction using the principle materials like CuO, BaO, CaO, with an appropriate weight in proportion to their molecular weights according to this reaction.into a pellet form with a diameter (1.5 cm) and thickness (3 cm).The pelletized sample sintered at a temperature (900˚C for 24 h) in oxygen flow by a rate of about (0.5 L/m) under a heating rate (45˚C/hr) and cooling rate (40˚C/hr).Later, there were many samples examined by XRD analysis and resistivity measurement in order to make a correlation between them.This correlation would help us to understand the conductivity mechanism in Cu-1223 high temperature superconductor.

Results and Discussion
The prepared sample of CuBa 2 Ca 2 Cu 3 O 8+δ compound studied by the X-ray diffraction to find the structural nature and the presence of single or multiphase within the structure.The XRD diffraction pattern for Cu-1223 had appeared as in Figure 2.
The obtained results showed the peaks related to high superconductor phase Cu-1223, which were more than the low phase of Cu-1212.The ratio of high phase was about 74% of the whole structure.This result agreed with the data sheet concluded from database information for low phase Cu-1212 and high phase Cu-1223.The appearance of two phases accepted due to a polycrystalline structure.The XRD analysis was applied in the Refine program in order to find the lattice parameter a = b = 4.171 Å and c = 16.743Å.It found that Cu-1223 had a tetragonal phase, and the lattice constants were larger than the lattice parameter for Hg-1223 especially in the basal plane [8].That was might be attributed to high oxidation of Cu-ion rather than Hg-ion in the basal plane, which made more absorption of extra oxygenin comparison with Hg-1223.The database of (ICDD) with pdf file (98-004-1652) was used to analysis the pattern of Cu-1223 system.The small change in lattice constant might be related to the variation of (2θ) position.The observed change in lattice parameters was agreed with the strain happened in Cu-1223 compound that was about (0.885 ± 0.149).The planes of low phase had peaks (013), (005), ( 014), ( 015), ( 006), (022), and (025) with different intensity at (2θ = 31.951,35.349, 36.356,42.758, 43.053, 49.761, and 60.417) respectively.They were compared with the international center for diffraction data (ICDD) with pdf file (98-007-4104), it was found that the planes (006), (007), (008), ( 0010 These planes acted as a correlation factor between the planes along the c-axis. Increasing the concentration of these planes tend to increase the factors affected the mechanism of conductivity and then improve the T c -value.Then the enhancement of superconductivity mechanism was happening during the presence of Cu-ion in the basal plane and forming the active bond (Cu 2 O) linking the basal plane.The common thing was the appearance of Cu-1223 phase like Hg-1223 with some variation in the lattice constant.This result might be a positive effect on the resistivity measurement in order to determine the superconducting phase as mentioned before [11].The small difference in the crystal structure related to the appearance of low phase Cu-1212, which formed by the ratio 26% of the whole structure.The improvement of the physical properties of Cu-1223 compound done by removing the low phase Cu-1212.The pre-sintering of the sample under study examined by the XRD pattern as shown in Figure 3.
It was found that the high phase Cu-1223 formalizes 45% of the whole structure and the low phase Cu-1212 formalize 55% of the whole structure, so the low phase Cu-1212 was the predominate phase.The common peaks between the two last figures had the planes (005), (022).The first plane had a small shifting in (011), ( 024) and (017) were represented the stepping layers to satisfy the conductivity mechanism during the motion of charge carriers along the a-c direction through principle planes (005), ( 003), ( 004) and (009) as mentioned a conducting layers along c-axis.It observed that the appearance of those planes in Cu-1212 by the pre-sintering made less than in the first one.The plane (020) had played the same role in the high phase.It linked the basal plane and investigated the structural symmetry.There was a new plane (118) occurred in the low phase.The applying of Refine program tend to conclude the lattice constant a = b = 3.55 Å and c = 12.37 Å as a tetragonal phase.
The electrical resistivity was the most important factor to show the superconductivity, and it considered a good tool to show the correlation of miller indices with interlayer coupling of the charge carriers.The last was the reason for understanding the conductivity mechanism.The resistivity measurement done by using a closed cycle cryogenic system worked by liquid helium, as shown by  007), ( 008) and (0010) as mentioned before.These planes are responsible on the conductivity mechanism because they considered correlated planes within the unit cell.
They considered linking planes for charge transfer.The presence of two phases, low and high phase, is confirmed by Ginzburg-Landau theory [15].They stated the presence of two phases during different temperature range and they said there was a vortex state including the low and high phase superconductor.That was defined a type-II high temperature superconductor.
The pre-sintering had been done to explain the more oxygen excess that was the reason to conform the low phase as shown in Figure 5.That related the  complete occupation of the vacant site in the basal planes, which was the reason to restrict the motion of charge carriers through the stepping planes in order to link the basal planes.The resistivity measurement showed the single low phase of Cu-1212, it supported by XRD where the low phase predominated within the crystal structure.The critical temperature was about 64 K, then it was interested to note that sample after the pre-sintering the normal resistivity had 0.01 Ω•mm, half the normal resistivity of the sample before the pre-sintering.That related to the presence of a single phase rather than the multiphase for the sample prepared after the first sintering.On the other hand, the pre-sintering means the long sintering time and the absorption of extra oxygen was more increased, which had a direct effect on the concentration of charge carriers producing a high conductivity.Then the pore size distribution decreased and the sample became dense, that was the reason why the conductivity increased after pre-sintering.It observed was noticed, the T c -value had half the T c -value of the sample before pre-sintering that was related to diminish the most peaks causing the high phase Cu-1223.

Conclusion
The producing of new high T c superconductor compound like Hg-1223 phase is possible by the replacement of Cu-ion by Hg-ion in the basal plane.A high phase of Cu-1223 created a tetragonal structure through XRD spectrum, which was different from the phase Hg-1223.There were more Miller planes in Cu-1223 those were the reason to enhance the conductivity mechanism.The motion of charge carriers was investigated during the a-c direction, toward the c-axis.On the other hand, there were both phases created, high phase Cu-1223 and low phase Cu1212 but the predominant one was Cu-1223.The pre-sintering done to show the single phase was present, but the conductivity mechanism was continuing through a-c direction forward to c-direction.These results considered a good tool to understand the conductivity mechanism.It considered a base on the future work related.The applying of these results was theoretically the main future topic to give a complete view on the conductivity mechanism in high temperature superconductor like Cu-1223 phase.
) at (2θ = 34.153,40.062, 58.178, and 59.704) had high intensity in Cu-1223 rather than Cu-1212.The full Cu-substitution appeared by the replacing Cu-ion instead of Hg-ion in the basal plane as mentioned in Figure 1.It found the plane (006) had the same value of 2θ in Hg-1223.Whereas the plane (007) had a small shifting in 2θ.On the other hand, the plane (0010) created in Cu-1223.These planes considered a conducting plane because they related to charges connection through the c-axis.The planes (110), (130) and (220) in Cu-1223 had the same effect of the plane (110) in Hg-1223 compound.They linked the basal planes of both the bottom and the top of unit cell.On the other hand, the plane (020) was making the correlation between both basal planes in the unit cell.It was indicated the presence of extra oxygen in the basal planes of Cu-1223 unit cell.As well known, the conductivity mechanism depended on the motion of the charge carriers through the principle planes along the a-c direction.That means the planes (022), (026), (027), (014), (016), (017), (0110), and (025) considered the stepping layers for the charge motion toward c-axis during the chain.There were two common peaks (115) and (111) of Cu-1223 and Hg-1223 but at different intensity and a small shifting in 2θ.The appearance of new planes (112), (117), (121), (123), (119), and (126) at (2θ = 34.855,52.646, 54.045, 65.889, 64.453 and 65.47) in Cu-1223 compound.

Figure 4 for
Figure 4 for Cu-1223 under the first sintering.It was clear that there were two regions in the resistivity curve one of them belong to high phase of Cu-1223 and the other belongs the low phase of Cu-1212.A predominate of high phase Cu-1223 was exhibited a normal resistivity of about 0.0215 Ω•mm, and critical temperature was about 128 Κ.The low phase of Cu-1212 showed normal resistivity of about 0.0115 Ω•mm, and a critical temperature of about 66 Κ.The appearance of the two phases and the predominated high phase of Cu-1223 was supported the result of XRD during the high concentration of the planes including in Cu-1223.There were many peaks related to Cu-1223 such as (006), (007), (008)